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Professor  FredeLrick  Tracy 


LECTURES 


ON 


LOGIC 

BY 

SIR  WILLIAM  HAMILTON,  BART. 

PEOPE880R  09  LOGIC  AND  MKTAPHY8IC8  IN  THK  UNIVKRSITY  OJ-  EDINBCnOH 


XDITED   BY    THB 

REV.  HENRY  L.  MANSEL.  B.D.,LL.D.. 

TTATirFLBTK   PSOFESSOR  Or  MORAL   AND  UKTAPHTSICAL  rBILOSOI-IIT,  O.TPOKD, 
AND 

JOHN  VEITCH,  M.A., 

PBOrSSSOB  OF  LOGIC, EUETOBIC,  AMD  MBTAPUTSICS,  ST.  .l.N  liliKWS. 


NEW     Y  O  K  K  : 

SHELDO]^r   A:^rD    compain^y, 

8       MUKRAY        StKKET. 

1883. 


ON     EAr-TH,     THERE     IS    KOTIIINO     GUEAT    HUT     Ma:!' 
IK    MAN,    TUKRE    18    NOTUINO     ORKAT      Biri      MIND. 


s/ 


i>  B  :e]  :Er  ^  o  Ei . 


TflE  Lectures  comprised  in  the  present  Volume  form 
tile  second  And  concluding  portion  of  the  Biennial 
Gourde  on  Metaphysics  and  Logic,  which  was  com- 
menced by  Sir  William  Hamilton  on  his  election  to 
the  Professorial  Chair  in  1836,  and  repeated,  with  but 
Blight  alterations,  till  his  decease  in  1856.  The  Ap- 
f^ndix  contains  various  papers,  composed  for  the  most 
part  during  this  period,  which,  though  portions  of 
th«ir  contents  were  publicly  taught  at  least  as  early 
as  184<0,  Were  only  to  a  very  small  extent  incorporated 
into  the  text  of  the  Lectures. 

The  Lectures  on  Logic,  like  those  on  Metaphysics, 
Were  chiefly  composed  during  the  session  in  which  they 
were  first  delivered  (1837-8) ;  and  the  statements  made 
in  the  Preface  to  the  previous  volume,  as  regards  the 
circumstances  and  manner  of  their  composition,  are 
equally  applicable  to  the  present  course.  In  this,  as 
in  the  preceding  series,  the  Author  has  largely  availed 


VI  PREFACE. 

himself  of  the  labors  of  previous  writers,  many  of 
whom  are  but  little  known  in  this  country.  To  the 
works  of  the  German  logicians  of  the  present  century, 
particularly  to  those  of  Krug  and  Esser,  these  Lectures 
are  under  special  obligations. 

In  the  compilation  of  the  Appendix,  some  responsi- 
bility rests  with  the  Editors ;  and  a  few  words  of  ex- 
planation may  be  necessary  as  regards  the  manner  in 
which  they  have  attempted  to  perform  this  portion  of 
then-  task.  In  publishing  the  papers  of  a  deceased 
writer,  composed  at  various  intervals  during  a  long 
period  of  years,  and  treating  of  difficult  and  contro- 
verted questions,  there  are  two  opposite  dangers  to  be 
guarded  against.  On  the  one  hand,  there  is  the  dan- 
ger of  compromising  the  Author's  reputation  by  the 
publication  of  documents  which  his  maturer  judgment 
might  not  have  sanctioned;  and,  on  the  other  hand, 
there  is  the  danger  of  committing  an  opposite  injury 
to  him  and  to  the  public,  by  withholding  writings  of 
interest  and  value.  Had  Sir  William  Hamilton,  at  any 
period  of  his  life,  published  a  systematic  treatise  on 
Eogic,  or  had  his  projected  New  Analytic  of  Logical 
Forms  been  left  in  a  state  at  all  approaching  to  com- 
pleteness, the  Editors  might  probably  have  obtained  a 
criterion  by  which  to  distinguish  between  those  specu- 
lations which  would  have  received  the  final  imprimatur 
of  their  Author,  and  those  which  would  not.      In  the 


PREFACE.  VII 

absence  of  any  such  criterion,  they  have  thought  it 
better  to  run  the  risk  of  giving  too  much  than  too 
little  ;  —  to  publish  whatever  appeared  to  have  any 
philosophical  or  historical  interest,  without  being  in- 
fluenced by  its  coincidence  with  their  own  opinions,  or 
by  its  coherence  with  other  parts  of  the  Author's  writ- 
ings. It  is  possible  that,  among  the  papers  thus  pub- 
lished, may  be  found  some  which  are  to  be  considered 
rather  as  experimental  exercises  than  as  approved  re- 
sults ;  but  no  papers  have  been  intentionally  omitted, 
except  such  as  were  either  too  fragmentary  to  be  Intel- 
ligible,  or  manifestly  imperfect  sketches  of  what  has 
been  published  here  or  elsewhere  in  a  more  matured 
form. 

The  Notes,  in  this  as  in  the  previous  volume,  are 
divided  into  three  classes.  Those  printed  from  the 
manuscript  of  the  Lectures  appear  without  any  dis- 
tinctive mark;  those  supplied  from  the  Author's  Com- 
monplace-Book  and  other  papers  are  enclosed  within 
square  brackets  without  signature ;  and  those  added  by 
the  Editors  are  marked  by  the  signature  "Ed."  These 
last,  as  in  the  Lectures  on  Metaphysics,  are  chiefly  con- 
fined to  occasional  explanations  of  the  text  and  verifi- 
cations  of  references. 

In  conclusion,  the  Editors  desire  to  express  their  ac- 
knowledgments to  those  friends  from  whom  they  have 
received  assistance  in  tracing  the  numerous  quotations 


Vni  PREFACE. 

and  allusions  scattered  through  this  and  the  preceding 
volume.  In  particular,  their  thanks  are  due  to  Hubert 
Hamilton,  Esq.,  whose  researches  among  his  father's 
books  and  papers  have  supplied  them  with  many  val- 
uable materials ;  and  to  H.  W.  Chandler,  Esq.,  Fellow 
of  Pembroke  College,  Oxford,  who  has  aided  them  from 
the  resources  of  a  philosophical  learning  cognate  in 
many  respects  to  that  of  Sir  William  Hamilton  himself. 


COISr  TENTS 


LECTURE    I. 

INTRODUCTION. 

FAOB. 

LOGIC  — I.   ITS  DEFINITION I 


LECTURE    II. 

LOGIC  — I.. ITS  DEFINITION— HISTORICAL  NOTICES   OF  OPINIONS 

REGARDING  ITS  OBJECT  AND  DOMAIN  —  II.   ITS  UTILITY,    .       14 


LECTURE    III. 

LOGIC  —  II.  ITS  UTILITY  —  III.  ITS   DIVISIONS  —  SUBJECTIVE  AJSD 

OBJECTIVE  —  GENERAL  AND  SPECIAL, 2»; 


LECTURE    IV. 

,U)GIC  — m.  ITS  DIVISIONS  — PURE  AND  MODIFIEE|,  j       *       ,       m 

LECTURE    V. 

t 

PURE    LOGIC. 

PART    I.   STOICHEIOLOGY.  —  SECTION    I.   NOETIC.  —  ON  THE  FUN- 
DAMENTAL   LAWS   OF   THOUGHT  —  THEIR   CONTENTS    AND 

HISTORY,      .        .        .        .       .       58- 

B 


X  CONTENTS. 

LECTURE    VI. 

PAOB 

THE   FUNDAMENTAL   LAWS    OF   THOUGHT  -  "FHEIR   CLASSIFICA- 
TION AND  IMPORT, 69 


LECTURE    VII. 

SECTION  II.  OF  THE  PRODUCTS  OF  THOUGHT.  — I.  ENNOEMATIC 
—  OF  CONCEPTS  OR  NOTIONS  — A.  OF  CONCEPTS  IN  GEN- 
ERAL,     83 


LECTURE    VIII. 

ENNOEMATIC  —  A.    OF  CONCEPTS  IN    GENERAL  ;    B.    IN  SPECTAL. 

—  L  THEIR  OBJECTIVE  RELATION  —  QUANTITY,       .        .        .         .W 


LECTURE    IX. 

ENNOEMATIC.  —  B.  OF  CONCEPTS  IN  SPECIAL.  —  II.  THEIR  SUB- 
JECTIVE RELATION— QUALITY, Ill 

■;p.' 

LECTURE    X. 

ENNOEMATIC.  —  IMPERFECTION  OF  CONCEPTS, 121 

LECTURE    XI. 

ENNOEMATIC.  —  m.  RECIPROCAL  RELATIONS  OF  CONCEPTS.  —  A. 
QUANTITY  OF  EXTENSION  —  SUBORDINATION  AND  COORDI- 
NATION  132 


CONTEIfTS.  XI 

LECTURE    XII. 

PAGE 

ENNOEMATIC.  —  III.   RECIPROCAL    RELATIONS  OF    CONCEPTS. —B. 

QUANTITY   OF  COMPREHENSION, 150 


LECTURE    XIII. 

JL     APOPHANTIC,    OR    THE    DOCTRINE    OF    JUDGMENTS,  —  JUDG- 
MENTS—THEIR NATURE  AND   DIVISIONS,  ....        159 


LECTURE    XIV. 

APOPHANTIC.  —  JUDGMENTS  —  THEIR  QUALITY,  OPPOSITION,  AND 

CONVERSION, .        173 


LECTURE    XV. 

HI.  DOCTRINE  OF  REASONINGS.  —  REASONING  IN  GENERAL.  — 
SYLLOGISMS  —  THEIR  DIVISIONS  ACCORDING  TO  INTERNAL 
FORM, 189 


LECTURE    XVI. 

DOCTRINE  OF  REASONINGS.  —  SYLLOGISMS  —  THEIR  DIVISIONS 
ACCORDING  TO  INTERNAL  FORM.  —  A.  SIMPLE  —  CATEGORI- 
CAL. —  I.   DEDUCTIVE   IN   EXTENSION,  .....        206 


LECTURE    XVII. 

DOCTRINE  OF  REASONINGS.  —  SYLLOGISMS  —  THEIR  DIVISIONS 
ACCORDING  TO  INTERNAL  FORM.  —  A.  SIMPLE  —  CATEGORI- 
CAL. —  II.  DEDUCTIVE  IN  COMPREHENSION. —  IIL  INDUCTIVE 
IN  EXTENSION  AND  COMPREHENSION.  —  B.  CONDITIONAL-: 
DISJUNCTIVE, 221 


LECTURE    XVIII. 

PAQR 

DOCTRINE  OF  «EASONINGS.  —  SYLLOGISMS  —  THEIR  DIVISIONS 
ACCORDING  TO  INTERNAL  FORM.  —  B.  CONDITIONAL  —  HY- 
POTHETICAL AND  HYPOTHETICO-DISJUNCTIVE,        ...        239 


LECTURE    XIX. 

DOCTRINE  OF  REASONINGS.  —  SYLLOGISMS  —  THEIR  DIVISIONS 
ACCORDING  TO  EXTERNAL  FORM.  —  A.  COMPLEX  —  EPI- 
CHEIREMA  AND  SORITES, .2.57 


LECTURE    XX. 

fi«OGTRINE  OF  REASONINGS.  —  SYLLOGISMS  —  THEIR  DIVISIONS 
ACCORDING  TO  EXTERNAL  FORM.  -  B.  DEFECTIVE  —  EN- 
THYMEME.  —  C.  REGULAR  AND  IRREGULAR  —  FIGURE  AND 
MOOD  — FIRST  AND  SECOND  FIGURES, 275 


LECTURE    XXI. 

DOCTRINE  OF  REASONINGS.  —  SYLLOGISMS  —  THEIR  DIVISIONS 
ACCORDING  TO  EXTERNAL  FORM.  —  THIRD  AND  FOURTH 
FIGURES,  294 


LECTURE    XXII. 

DOCTRINE  OF  REASONINGS.  —  SYLLOGISMS  —  THEIR  DIVISIONS 
ACCORDING  TO  EXTERNAL  FORM.  —  C.  REGULAR  AND  IR- 
REGULAR. —  FIGURE  —  REDUCTION, 306 


LECTURE    XXIII. 

DOCTRINE    OF   REASONINGS.  —  SYLLOGISMS  —  THEIR    DIVISIONS 
.       ACCORDING  TO  VALIDITY.  —  FALLACIES,      .....       321 


LECTURE    XXAY^ 

PAOB 

PURE   LQG^e. 

PART  If.  METHODOLOGY.  —  SECTION  I.  METHOD  IN  GENERAL.— 
SECTION  II.  METHOD  IN  SPECIAL,  OR  LOGICAL  METHODOLr- 
OGY.  — I.   DOCTRINE  OF  DEFINITION,     .        .    •    .        .        .        .        335 


LECTURE    XXV. 

METHODOLOGl. 
LOGICAL  METHODOLOGY.  — 11.  DOCTRINE  OF  DIVISION,         .        .       350 


LECTURE    XXVI. 

LOGICAL  METHODOLOGY,  —  III.  DOCTRINE  OF  PROBATION,  .        .       W. 

LECTURE    XXVII. 

MODIFIED   LOGIC. 

PART    I.   MODIFIED    STOICHEIOLOGY.  —  SECTION    I.    DOCTRINE    OF 

TRUTH  AND  ERROR.  —  TRUTH  —  ITS  CHARACTER  AND  KINDS,     3W 

LECTURE    XXVIII. 

MODIFIED    STOICHEIOLOGY. 

SECTION  L  DOCTRINE  OF  TRUTH  AND  ERROR.  —  SECTION  II.  ER- 
ROR -  JTS  CAUSES  AND  REMEDIES.  -^  A.  GENERAL  CIRCUM- 
STANCES —  SOCIETY,      ,,...,.,,.       387 


LECTURE    XXIX. 

ERROR -ITS  CAUSESI  AND  REMEDIES,  —  A.  GENERAL  CIRCUM- 
STANCES —  SOCIETY.  —  B.  AS  IN  POWERS  OF  COGNITION, 
FEELING,  ANP  DESIR?.  —  L  AFFECTIONS  —  PRECIPITANCY  ^ 
SLOTH  —  POPE  AJJD  fEAJ^  —  gELF-LOVE,  .  .        ,        .       .       ,397 


XIV  CONTENTS. 

LECTURE    XXX. 

PAOB 

EKROR  — ITS  CAUSES  AND  REMEI>IES.  —  B.  AS  IN  THE  COGNI- 
TIONS, FEELINGS,  AND  DESIRES.  —  11.  WEAKNESS  AND  DI&- 
PROPORTIONED  STRENGTH  OF  THE  FACULTIES  OF  KNOWL- 
EDGE,          ........       411 


LECTURE-  XXXI. 

ERROR— ITS   CAUSES    AND  REMEDIES.  —  C.  LANGUAGE.  — D.  OB- 
JECTS OF  KNOWLEDGE, 432 


LECTURE    XXXII 


MODIFIED    METHODOLOGY. 


SECTION  I.  OF  THE  ACQUISITION  AND  PERFECTING  OF  KNOWL- 
EDGE. —  L  EXPERIENCE.  —  A.  PERSONAL:  —  OBSERVATION — 
INDUCTION  AND  ANALOGY, 44i 


LECTURE   XXXIII. 

OF  THE  ACQUISITION  AND  PERFECTING  OF  KNOWLEDGE.  —  I. 
EXPERIENCE.  —  B.  FOREIGN :  — ORAL  TESTIMONY  —  ITS  CRED- 
IBILITY,         ^77 


LECTURE   XXXIV. 

OF  THE  ACQUISITION  AND  PERFECTING  OF  KNOWLEDGE.  —  I. 
EXPERIENCE.  —  B.  FOREIGN:  RECORDED  TESTIMONY  AND 
WRITINGS  IN  GENERAL. —  II.   SPECULATION K8 


LECTURE    XXXV. 

OF  THE  ACQUISITION  AND  PERFECTING  OF  KNOWLEDGE.  —  III. 
COMMUNICATION  OF  KNOWLEDGE.  —  A.  INSTRUCTION  — 
ORAL  AND  WRITTEN. —  B.  CONFERENCE  —  DIALOGUE  AND 
DISPUTATION, 478 


CONTENTS.  XT- 

APPENDIX. 

PAOB 

I.  —  THE  CHARACTER  AND  COMPREHENSION  OF  LOGIC  —  A  FRAG- 

MENT,     495 

II.  —  GENUS  OF  LOGIC,  4a8 

HI.  —  DIVISIONS,   VARIETIES,  AND  CONTENTS  OF  LOGIC,       .        .       WI 

IV  —  LAWS  OF  THOUGHT,    .        T S06 

,V.  —  NEW    ANALYTIC    OF   LOGICAL   FORMS  —  GENERAL    RESULTS 
—FRAGMENTS. 

I.  —  EXTKACT   FROM   PBOSPECTCS  OF   "ESSAY   TOWARDS   A   NEW 

ANALYTIC   OF   LOGICAL  FORMS," 509 

,  II.  —  LOGIC,  —  ITS    POSTULATES, 512 

III.  —  QUANTIFICATION     OF     PREDICATE, —  IMMEDIATE      INFER- 

ENCE,—  CONVERSION,  —  OPPOSITION,        ....  514 

IV.  —  APPLICATION   OF   DOCTRINE    OF   QUANTIFIED    PREDICATE 

TO   PROPOSITIONS, 52^ 

V.  —  APPLICATION    OF     DOCTRINE    OF     QUANTIFIED    PREDICATE 

TO   SYLLOGISMS,    .  . 53tJ 

VI. — OBJECTIONS    TO    THE    DOCTRINE    OF    A    QUANTIFIED    PRED- 
ICATE   CONSIDERED, 53!il 

VII.  —  HISTORICAL     NOTICES      OF     DOCTRINE     OF     QUANTIFIED 

PREDICATE, 546 

VI. —  CANONS    OF    SYLLOGISM;    GENERAL    HISTORICAL    NOTICES 
AND  CRITICISM. 


A.  HISTORICAL  NOTICES. 

I.  —  FUNDAMENTAL   LAWS   OF   SYLLOGISM  —  QUOTATIONS, 
n.  —  FUNDAMENTAL   LAWS    OF    SYLLOGISM  —  REFERENCES, 

III.  —  ENUNCIATIONS    OF    THE    HIGHER   LAWS    OF   SYLLOGISM, 

IV.  —  OBJECTIONS   TO   THE   DICTUM    DE    OMNI    ET    NULLO, 

V.  —  GENERAL   LAWS   OF    SYLLOGISM    IN    VERSE, 

VI.  —  SPECIAL   LAWS   OF   SYLLOGISM   IN   VERSE, 


559 
575 
570 
578 
578 
579 


B.  CEITICISM. 

I.— CRITICISM   OF  THE   SPECIAL   LAWS   OP   SYLLOGISM,       .  .  579 

II. —  LAWS   OP   SECOND   FIGURE,         ....  .  .  582 

III.  —  author's     supreme     canons     of     CATEGORICAL     SYLLO- 

GISMS,      583 

IV.  —  ULTRA-TOTAL   QUANTIFICATION   OF   MIDDLE    TERM,  .  584 


XVf  CONTENTS. 

VII.  —  INDUCTION  AND  EXAMPLE. 

PASS 

I.  —  QUOTATIOXS    FKOM   AUTHOKS,  .  ....  .  .  589 

II.  — MATERIAL  INDUCTION, 597 

Aim.  —  HYPOTHETICAL  AND  DISJUNCTIVE  REASONING  —  IMMEDI 
ATE  INFERENCE. 

I. —author's  doctrine  —  FRAGMENTS, 598 

II.  —  HISTORICAL  notices, 612 

U..  —  SORITES, 619 

X.  -  SYLLOGISM. 

I.  —  1T8  ENOUNCEMENT  —  ANALYTIC    AND    8TNT^ETIC  —  ORDER 

OF  PREMISES. 

(a)  ENOUNCEMENT   OF    SYLLOGISM,                ....  621 

>-:.  (b)  ORDER  OF  PREMISES, 624 

II.  —  FIGURE  —  UNFIGURED  AND   FIGURED   SYLLOGISM. 

(1803)   (a)    CONTRAST    AND    COMPARISON    OF    THE    VARI- 
OUS   KINDS   OF    FORMAL  SYLLOGISM  —  DIFFERENCE    OF 
>  FIGURE  ACCIDENTAL,        .......  626 

(6)   DOUBLE    CONCLUSION     IN    SECOND    AND    THIRD   FIG- 
URES, .         .         .         .  .         .         .         .         .         627 

III- — HISTORICAL   NOTICES   REGARDING   FIGURE   OF  SYLLOGISM,        632 
.     „  IV.  —  SYLLOGISTIC   MOODS. 

I.  —  DIRECT  AND  INDIRECT   MOODS,  ....  658 

II.—  INDIRECT  MOODS   OF  SECOND  AND  THIRD  FIGURES,       663 
III-  —  NEW  MOODS  —  NOTES  UPON  TADLE  OF  SYLLOGISMS.      66.'> 

XI.  —  LOGICAL  NOTATION. 

I.  —  Lambert's  linear  notation,       ......       6ff7 

II. —  NOTATION    BY    MAASS, 669 

.  Ill-  —  author's  scheme  of  notation. 

j  no.  I.   linear, 670 

^  NO.   II.    UNFIGURED   AND  FIOURBD   SYLLOGISM,      .  .  6TJ 

NO.    III.    FIGURPD   SYLLOGISM — TABLE    OF   MOODS,        .  678 


LECTURES   ON    LOGIC. 


LECTURE    I  * 

ENTRODUCTION. 

LOGIC— I.    ITS    DEFINITION. 

Gentlemen  :  — We  are  now  about  to  enter  on  the  consideration 
of  one«of  the  most  important  branches  of  Men- 
Logic  proper,— mode      tai  Philosophy,  —  the  science  which  is  conver- 
in  which  itsconsidera-       ^^^^  ^^^^^  ^^^  j^^^^  ^^  Thought.    But,  before 

tion  ought  to  be  con-  , 

ducted.  commencing  the  discussion,  I  would  premise  a 

word  in  regard  to  the  mode  in  which  it  ought 

to  be  conducted,  with  a  view  to  your  information  and  improvemi-nt. 
The  great  end  which  every  instructor  ought  to-' 

End  of  instruction.  °       .       ,  .        .  „  .  . 

ptopose  in  the  communication  oi  a  science,  is,  to 
afford  the  student  clear  and  distinct  notions  of  its  several  parts,  of 
their  relations  to  each  other,  and  to  the  whole  of  which  they  are 
the  constituents.  For  unless  he  accomplish  this,  it  is  of  compara- 
tively little  moment  that  his  information  be  in  itself  either  new  or 
important;  for  of  what  consequence  are  all  the  qualities  of  a  doc- 
trine, if  that  doctrine  be  not  communicated?  —  and  communicated 
it  is  not,  if  it  be  not  undei-stood. 

But  in  the  communication  of  a  doctrine,  the  methods  to  be  fol 

lowed  by  an  instructor  who  writes,  and  by  an 
Methods  of  written       instructor  who  spealcs,  are  not  the  same.     They 

and    oral    instruction  .       „  .  ,,        ,.™ 

different  ^^®'  ^"  ^^^*'  ^^  ^  Certain  extent,  necessarily  dii- 

ferent :  for,  while  the  reader  of  the  one  can  al- 
ways be  referred  back  or  forward,  can  always  compare  one  part,  of  a 

*  The  first  seven  Lectares  of  the  Metaphysical  Course  (Lectures  on  Metaphysics,  pp. 
1—90)  were  delivered  hy  Sir  William  Hamilton  as  a  General  Introdaction  to  the 
Course  of  Logic  proper.  —  Ed.  ^ 

1 


2  LOGIC.  Lect.  I. 

hook  \rith  another,  and  can  always  meditate  at  leisure  on  each  step 
of  the  evolution  ;  the  heai-er  of  the  other,  on  the  contraiy,  must  at 
every  moment  be  prepared,  by  what  has  preceded,  to  comprehend 
at  once  what  is  to  ensue.  The  oral  instructor  has  thus  a  much  more 
arduous  problem  to  solve,  in  accomplishing  the  end  which  he  pro- 
poses. For  if,  on  the  one  hand,  he  avoid  obscurity  by  communicat- 
ing only  what  can  easily  be  understood  as  isolated  fragments,  he  is 
intelligible  only  because  he  communicates  nothing  worth  learning : 
and  if,  on  the  other,  he  be  unintelligible  in  proportion  as  his  doc- 
trine is  concatenated  and  systematic,  he  equally  fails  in  his  attempt ; 
for  as,  in  the  one  case,  there  is  nothing  to  teach,  so,  in  the  other, 
there  is  nothing  taught.  It  is,  therefore,  evident,  that  the  oral  in- 
structor must  accommodate  his  mode  of  teaching  to  the  circum- 
stances under  which  he  acts.  He  must  endeavor  to  make  his  audi- 
ence fully  understand  each  step  of  his  movement  before  another  is 
attempted  ;  and  he  must  prepare  them  for  details  by  a  previous  sur- 
vey of  generals.  In  short,  what  follows  should  always  be  seen  to 
evolve  itself  out  of  what  precedes.  It  is  in  consequence  of  this 
condition  of  oral  instruction,  that,  where^  the  development  of  a  sys- 
tematic doctrine  is  attempted  in  a  course  of  Lee- 
Use  of  Text-book  in       t^j-Q^^  jt  is  usual  for  the  lecturer  to  facilitate  the 

a  systematic  course  of        ,    ,  ,  .  .,  i    ,  •  -.fi  i  -i  •  • 

j^j.jjjj.^  labor  to  his  pupils  and  himself,  by  exhibiting  in 

a  Manual  or  Text-book  the  order  of  his  doctrine 
and  a  summary  of  its  contents.  As  I  have  not  been  able  to  prepare 
this  useful  subsidiary,  I  shall  endeavor,  as  far  as  possible,  to  supply 
its  want.  I  shall,  in  the  first  place,  endeavor  always  to  present  you 
with  a  general  statement  of  every  doctrine  to 

u  or  8  met  o  ^^^  explained,  before  descending  to  the  details 
of  explanation ;  and  in  order  that  you  may  be 
insured  in  distincter  and  more  comprehensive  notions,  I  shall,  where 
it  is  possible,  comprise  the  general  statements  in  Propositions  ot 
Paragraphs,  which  I  shall  slowly  dictate  to  you,  in  order  that  they 
may  be  fully  taken  down  in  writing.  This  being  done,  I  shall  pro- 
ceed to  analyze  these  propositions  or  paragraphs,  and  to  explain 
their  clauses  in  detail.  This,  I  may  observe,  is  the  method  followed 
in  those  countries  where  instruction  by  prelection  is  turned  to  the 
best  account;  —  it  is  the  one  prevalent  on  the  Continent,  more  es- 
pecially in  the  universities  of  Germany  and  Holland. 

In  pursuance  of  this  plan,  I  at  once  commence  by  giving  you, 
as  the  first  proposition  or  paragraph,  the  following.  I  may  notice, 
however,  by  parenthesis,  that,  as  we  may  have  sometimes  occasion 
to  refer  articulately  to  these  propositions,  it  would  be  proper  for 
you  to  distinguish  them  by  «ign  and  number. 


Lect.  I.  LOGIC.  "8 

The  first  paragraph,  then,  is  this  : 

^  I.  A  System  of  Logical  Instruction  consists  of  Two  Parts, 
—  1°,  Of  an   Introduction  to   the   science; 
Jrof'LogllTonsrt's;       2°,  Of  a  Body  of  Doctrine  constituting  the 
Science  itself. 

Thiese,  of  course,  are  to  be  considered  in  their  order. 

^  II.  The  Introduction  to  Logic  should  afford  answere  to  the 
following  questions:    i.  What  is  Logic?   ii. 

Par.  n    The  Intro-  ^^^^  j^  j^^  y^j^^^  ^      jj._  ^^^^  ^^.^  .^^  j)j^.j^_ 

duction  to  Iioglc. 

ions  ?  iv.  What  is  its  History  ?  and,  v. 
What  is  its  Bibliography,  that  is,  what  are  the  best  books  upon 
the  subject? 

In  regard  to  the  first  of  these  questions,  it  is  evident  that  its 
answer  is  given  in  a  definition  of  Logic.  I  therefore  dictate  to 
you  the  third  paragraph.  , 


Par.  m.    I.  Defini- 
tion of  liOgic. 


•fill.  What  is  Logic?  Answer  —  Logic 
is  the  Science  of  the  Laws  of  Thought  as 
Thought. 


This  definition,  however,  cannot  be  understood  without  an  ar- 
ticulate exposition  of  its  several  parts.     I  there- 
Explication.  ^  ... 

fore  proceed  to  this  analysis  and  explanation, 

and  shall  consider  it  under  the  three  following  heads.  In  the  first, 
I  shall  consider  the  meaning,  and  history,  and  synonyms  of  the 
word  Logic.  In  the  second,  I  shall  consider  the  Genus  of  Logic, 
that  is,  explain  why  it  is  defined  as  a  Science.  In  the  third,  I  shall 
consider  the  Object-matter  of  Logic,  that  is,  explain  to  you  what 
is  meant  by  saying,  that  it  is  conversant  about  the  Laws  of  Thought 
as  Thought. 

First,  then,  in  regard  to  the  significance  of  the  word.    Logic,  you 
are  aware,  is  a  Greek  word,  XoytK?;;  and  Xoytfo^, 

1.  The  word  I^g-ic —         i-i  r,  /  /^\  /t-i 

nice  ypafL^aTLKi),  prp-opixr],  TrovqTUcrj,  ocoAeicTiKiy,  1  neeu 

hardly  tell  you,  is  an  adjective,  one  or  other  of 
the  substantives  iTna-rrnvr},  science,  rix^^,  (^rt,  or  Trpayfiareia,  Study,  or 
rather  matter  of  study,  being  understood.  The  term  XoyiKt],  in  this 
special  signification,  and  as  distinctly  marking  out  a  particular  sci- 
ence, is  not, so  old  as  the  constitution  of  that  science  itself  Aris- 
totle did  not  designate  by  the  term  AoytKt;,  the  science  whose  doc- 


4  LOGIC.  Lect.  t 

trine  he  first  fully  developed.     He  uses,  indeed,  the  adjective  \oyucos 

in  various  combinations  with  other  substantives. 

Thus  I  find  in  his  Physics,  Xoyucq  airopw^  —  in 
his  Rhetoric,  AoyiKai  Sva^epeiai,^  —  in  his  Jifetapht/Sics,  XoyiKas  airoheCi- 
tts,^  —  in  his  Posterior  Analytics,  hia  XoytKa*  —  in  his  Topics,  Xoyi- 
Kov  -n-pofiXrjfia.^  He,  likewise,  not  unfreqiiently  makes  use  of  the 
adverb  Xoyi/cws.^  By  whom  the  term  XoyiK-rj  was  first  applied,  as  the 
word  expressive  of  the  science,  does  not  appear.  Boethius,  W'ho 
flourished  at  the  close  of  the  fifth  and  commencement  of  the  sixth 
<tentui-y,  says,  in  his  Commentary  on  the  Topics  of  Cicero^  that  the 

name  of  Logic  was  first  given  by  the  ancient 

enpa  e  ics.       Peripatetics.   In  the  works  of  Alexander  of  Aph- 

Alexander  of  Aph-       rodisias,  the  oldest  commentator  we  possess  on 

the  works  of  Aristotle  (he  flourished  towards 
the  end  of  the  second  century),  the  term  Aoyoci;,  both  absolutely 
and  in  combination  with  TrpayfiareLa,  etc.,  is  frequently  employed ; ' 
and  the  word  is  familiar  in  the  writings  of  all  the  subsequent  Aris- 
totelians.     Previously,  however,  to  Alexander,  it  is  evident  that 

XoviKM  had  become  a  common  designation  of  the 

Cicero.  .  . 

science;  for  it  is  once  and  again  thus  applied 
by  Cicero.®  So  much  for  the  history  of  the  word  JLogic,  in  so  far 
as  regards  its  introduction  and  earlier  employment.  We  have  now 
to  consider  its  derivation  and  meaning. 

It  is  derived  from  Ao'yos,  and  it  had  primarily 

(b)  Its  derivation  and       the  Same  latitude  and  variety  of  signification  as 

"^oid  meaning  of      its  original.     What  then  did  Xoyo9  signify  ?     In 

xiiyos.  Greek   this  word  had  a  twofold  meaning.     It 

denoted  both  thought  and  its  expression ;  it  was 
equivalent  both  to  the  ratio  and  to  the  oratio  of  the  Latins.     Tlie 

»  B.  iii.  c.  3.    'Exsi   5'  airopiay  \oyiirfiv.  *  E.  g.,  Anal.  Poxt.,  i.  21,  32  j  Phys.  viii.  8; 

"  Dubitationem  quae  non  e  rerum  singularium  -Me/apA.,  vi.  4, 17;  xi.  1.  — Ed. 

(pby8icarum)contemplatione,  sed  e  ratiocina-  ^  ^-i-  sub  init.  —  ^o. 

tione  sola  orta  est."    Waitz,  ad  Arist.  Org.,  ^  See,  especially,  bis  commentary  on  the 

vol.  ii.  p  354.     Logical  and  diaUctical  reason-  P^'°'"   Analytics,  f.  2  (Scholia,  ed,  Brandis,  p. 

ing  in  Aristotle  mean  the  same  thing,  — viz.,  1*1)'  where  he  divides  v  ^oyitcfi  re  koI  av\- 

reasoniug  founded  only  on  general  principles  A.<>7«errw^   itpaynartia  into  four  branches, 

of  probability,  not  on  necessary  truths  or  on  airoSfi/cTi/cVj,    8ja\€JCTtKii,    irfipaffTiK-^,    and 

special  experiences.  —  Ed.  ffOi(>UTTiK-fi.     Here  Logic  is  used   in   a  wiri<T 

5  This  expression  occurs  not  in  the  Rhetoric,  *«*«e  **>*«  **>®  adjective  and  adverb  bear  ii. 

bnt  in  the  Metaphysics,  B.  i!i.  (iv.)  c.  3,  and  B.  Aristotle,  while  the  cognate  term  dialectic  re- 

xiii.  (xiv.)c.  1.    In  ihe  Rhetoric  we  find  the  tains  its  original  signification.  —  Ed. 

expression  KoytKol  ffv?<\oyt(rfioi  B.   i    c.  1.  ^  ^®®  ^'  Finxbus,  i.  7;   Tusc.  Qaast.,  iv.  14. 

—  Ed.  Cicero  probably   borrowed   this  use  of  the 

n'f    n   rr          .    •  term  from  the  Stoics,  to  who.oe  founder,  Zcno, 

Cf.  De  Gener.  Antm.,  ,                   ..    „           .^      ..          ■  ■       r  n 
Laertius  (vii.  39)  ascribes  the  ongm  of  tlw 

division  of  Philosophy  into  'Logic,  Physloi, 
and  Ethics,  sometimes  erroneously  mttribiit«d 
to  Plato.  — Ed. 


.■»B. 

xiii. 

.  (xiv 

.)c. 

1 

ii.  8.- 

-Ed. 

4B. 

i.e. 

24  - 

-Ed. 

SB. 

y.  c. 

L  — 

Ed- 

tEOT.L  LOGIC.  6 

Greeks,  in  order  to  obviate  the  ambiguity  thus  arising  from  the 
confusion  of  two  different  things  under  one  expression,  were  com- 
pelled to  add  a  diflferential  epithet  to  the  common  term.  Aristo- 
tle, to  contradistinguish  Xoyos,  meaning  thought^ 
How  expressed  by  ^^^^  Xoyos,  meaning  speech,  calls  the  former  rov 
Aristotle.  ^  ^  ^  .t.  i*? 

£o-(j,  —  Tov  ev  TTj  i/^xW'  —  ^'^^^  Within^  —  that  %n  the 

ffiind/  and  the  latter,  t6v  tftu,  —  that  without}  The  same  distinc- 
tion came  subsequently  to  be  expressed  by  the 
Aoyos  cvSta-Jeros,  for  thought,  the  verbum  mentis  ; 
and  by  Xoyos  irpotftopiKo^,  for  language,  the  verbum  oris?  It  was  nec- 
essary to  give  you  this  account  of  the  ambiguity  qf  the  word  Xoyos, ' 
because  the  same  passed  into  its  derivative  XoyuciJ ;  and  it  also  was 
necessary  that  you  should  be  made  aware  of  the  ambiguity  in  the 
name  of  the  science,  because  this  again  exerted  an  influence  on  the 
views  adopted  in  regard  to  the  object-matter  of  the  science. 

But  what,  it  may  be  asked,  was  the  appellation  of  the  science 

before  it  had  obtained  the  name  of  Logic  f  for, 

Appellations  of  the      gg  j  jj^ye  g^j^^  ^jj^  doctriue  had  been  discrimi- 

ecience        afterwards  ,    ,  i  •    i  /«       • 

called  Logic.  nated,  and  even  carried  to  a  very  high  perfection, 

before  it  received  the  designation  by  which  it  is 
now  generally  known.  The  most  ancient  name  for  what  was  sub- 
sequently denominated  Logic^  was  Dialectic.  But  this  must  be 
understood  with  certain  limitations.  By  Plato,  the  term  dialectic  is 
frequently  employed  to  mark  out  a  particular  section  of  philosophy. 
But  this  section  is,  with  Plato,  not  coextensive  with  the  domain  of 
Logic ;  it  includes,  indeed.  Logic,  but  it  does  not  exclude  Metaphysic, 
for  it  is  conversant  not  only  about  the  form,  but  about  the  matter 
of  our  knowledge.  (The  meaning  of  these  expressions  you  are 
soon  to  learn.) 

This   word,   StoXeKn/c^    (tcj^vt/,   or   iTrurr-^fir],   or    Trpay/iaTCto,   being 

understood)    is  derived,    you   are   aware,  from 

t    (KTiHTj— I sey-      SiaXeyco'^ai,   to  hold  conversation  or  discourse 

inology.  ' 

together ;  dialectic,  therefore,  literally  signifies, 
of  a  conversation,  colloquy,  controversy,  dispute.  But  Plato,  who 
defined  thought  an  internal  discourse  of  the  soul  with  itself,^  and 
who  explained  to  StoX^yccr^ai  by  the  ambiguous  expression  tw  Xoyul 

1  jlnaZ.  Port.,  1. 10.  —  Ed.  originated   with   the   Stoics.     See  Wytten- 

2  E.  g  ,  Philo,  Be  Vita  Mosis,  p.  672,  edit,  bach's  note  on  Plutarch's  Moralia,  p.  44  A 
I'liiis.  1640;  Plutarch,  Philos.  esse  cumprincipi-  (torn.  vi.  pars  1,  p.  378,  edit.  Oxon,  1810).— 
i>i/s.  c.  2  (vol.  ii.  p.  777,  C,  ed.  Francof.,  1620);  Ed. 

Sextus  Empiricus,  Pyrrh.  Hyp.,  i.  65;  Simpli-  8  Fishaber,  p.  10.  [Lehrbuehder  LogikfEmM- 
vinf.  Ta  Categ.  Arist.,  p.  7;  DamSLScenvs,  Fiit.  tung.  See  necetetus  p.  ISQ.  Sophista,  p- 266 
•MiUoii.,  ii.  21.     The   expressions  probably     — Ed.] 


LOGIC.  Lect.  L 


Xprja-Sai,^   did  not  certainly  do  violence  either  to  the  Greek  lan- 
guage or    to  his   own    opinions,  in   giving  the 
seo  tie  term     a-       jj^mc  of  dialectic  to  the  process,  not  merely  of 

leetic  by  riato.  '^  ^        •      ■,  i 

logical  inference,  but  of  metaphysical  specula- 
tion.     In  our  own  times,  the  Platonic  signification  of  the  word 
has  been  revived,  and  Hegel  has  applied  it,  in 
^    ^^  ■  even  a  more  restricted  meaning,  to  metaphysical 

speculation   alone.^      But   if   Plato  employed   the  term  Dialectic 
to  denote  more  than  Logic,  Aristotle  employed 
Aristotle's  employ-      j^.  ^^  denote  Icss.     With  him,  Dialectic  is  n»^t 

ment  of  Dialectic.  r  -i  •  i  •  • 

a  term  for  the  pure  science,  or  the  science  in 
general,  but  for  a  particular  and  an  applied  part.  It  means 
merely  the  Logic  of  Probable  Matter,  and  is  thus  convertible 
with  what  he  otherwise  denominates  Topics  (tottoo/).'  This,  I 
may  observe,  has  been  very  generally  misunderstood,  and  it  i.s 
commonly  supposed  that  Aristotle  uses  the  term  Dialectic  in  two 
meanings,  —  in  one  meaning  for  the  science  of  Logic  in  general, 
in  another  for  the  Logic  of  Probabilities.  This  is,  however,  a 
mistake.  There  is,  in  fact,  only  a  single  passage  in  his  writings, 
on  the  ground  of  which  it  can  possibly  be  maintained  that  he  ever 
employs  Dialectic  in  the  more  extensive  meaning.  This  is  in  his 
Rhetoric  i.  1  '*  but  the  passage  is  not  stringent,  and  Dialectic  may 
there  be  plausibly  interpreted  in  the  more  limited  signification. 
But  at  any  rate  it  is  of  no  authority,  for  it  is  an  evident  interpola- 
tion, —  a  mere  gloss  which  has  crept  in  from  the  margin  into  the 
text.*  Thus  it  appears  that  Aiistotle  possessed  no  single  term  by 
which  to  designate  the  general  science  of  which  he  was  the  prin- 
cipal author  and  finisher.  Analytic^  and  Apo- 
.  ""  ^"'' ' ''"  "'^'  deictic  with  Topic  (equivalent  to  Dialectic^ 
and  including  Sophistic),  were  so  many  special 
names  by  which  he  denoted  particular  parts,  or  particular  applica 
tions  of  Logic.  I  say  nothing  of  the  vacillating  and  various  em- 
ployment of  the  terms  Logic  and  Dialectic  by  the  Stoics,  Epicu- 
reans, anfl.  other  ancient  schools  of  philosophy;  ajid  now  proceed 
to  explain  to  you  the  second  head  of  the  definition,  —  viz.,  the 
Genus,  —  class,  of  Logic,  which  I  gave  as  Science. 

It  was  a  point  long  keenly  mooted  by  the  old  logicians,  whether 

1  I.  Alcih.,  p.  129.  Sri.  Tb  Se  tiaXeyt^a^at  ■*  Ilepl  lik  cvWoyiafiov  ifiolws  Sltoitos 
Kol  TV  X6ja>  -xpriff^ai  toutoV  itov  KdKfts;  ttjs  hidKtKTiKris  iffTtv  Ihfti'  ^  outtjs  S\»ji  ^ 
AA  rioci;  76.    Cf.  Gassendi,  io?/ca,  frooem.     fxipovs  riv6s.  —  Y.Xi. 

Opera,  t.  i.  p.  32.  —  Ed.  r,  g,,^  jjaiforeus.  [R.  Balforei  Commentarius  in 

2  See  Encyklopddie,  §  81.  -  Eo.  ^  Organum  Logieum  Aristotelis,  Burdigala.  1618. 
S  Topica,  i.  1.    AtaA€/cT.Kj)s   5e  ffvWoyiff-      qu.  h.  ^  3^  p.  jj.    Muretus,  in  his  version. 

«J)s  &  i^  fySd^yu  cvWoyi(6ixtyos.  —  Ed.  omits  this  passage  as  an  interpolation.  —  Ed.J 


Lect.  I.  LOGIC.  7 

Logic  were  a  science,  or  an  ai't,  or  neither,  or  both  ;  and  if  a  science, 

•  whether  a  science  practical,  or  a  science  specu- 

2.  Logic— Its  Genus       lative,  or    at   once    speculative    and    practical. 

—  whether  Science  or  t     ,      -1-.1  •  •  -,  •  •  1 

^^  Jrlato  and  the  Jrlatonists  Viewed  it  as  a  science;' 

but  with  them  Dialectic,  as  I  have  noticed, 
was  coextensive  with  the  Logic  and  Metaphysics  of  the  Peripatetics 
taken  together.  By  Aristotle  himself  Logic  is  not  defined.  The 
Greek  Aristotelians,  and  many  philosophers  since  the  revival  of 
letters,  deny  it  to  be  either  science  or  art.^  The  Stoics,  in  general, 
viewed  it  as  a  science  ;^  and  the  same  was  done  by  the  Arabian  and 
Latin  schoolmen-*  In  more  modern  times,  however,  many  Aris- 
totelians, all  the  Ramists,  and  a  majority  of  the  Cartesians,  main- 
tained it  to  be  an  ai't;*  but  a  considerable  party  were  found  who 
defined  it  as  both  art  and  science.^  In  Germany,  since  the  time  of 
Leibnitz,  Logic  has  been  almost  universally  regarded  as  a  science. 
The  controversy  which  has  been  waged  on  this 

The  question  futile.  .         .  ,.     .,      •        1 

point  IS  perhaps  one  01  the  most  futile  in  the 
history  of  speculation.  In  so  far  as  Logic  is  concerned,  the  decis- 
ion of  the  question  is  not  of  the  very  smallest  import.  It  was  not 
in  consequence  of  any  diversity  of  opinion  in  regard  to  the  scope 
and  nature  of  this  doctrine,  that  philosophers  disputed  by  what 
name  it  should  be  called.  The  controversy  was,  in  fact,  only  about 
what  was  properly  an  art,  and  what  was  properly  a  science ;  and  as 
men  attached  one  meaning  or  another  to  these  terms,  so  did  they 
affirm  Logic  to  be  an  art,  or  a  science,  or  both,  or  neither.  I  should 
not,  in  fact,  have  thought  it  necessary  to  say  anything  on  this  head, 
were  it  not  to  guard  you  against  some  mistakes  of  the  respectable 
author,  whose  work  on  Logic  I  have  recommended  to  your  atten- 
tion,—  I   mean   Dr.  Whately.      In  the   opening   sentence   of  his 

Elements,  it  is  said  :  "  Logic,  in  the  most  exten- 

Whately  quoted.  .  1  •   ,       , 

sive  sense  which  the  name  can  with  propriety 
be  made  to  bear,  may  be  considered  as  the  Science,  and  also  the 
Art  of  Reasoning.  It  investigates  the  principles  on  which  argumen- 
tation is  conducted,  and  furnishes  rules  to  secure  the  mind  from 


1  [Camerarius,  Dwputoft'ones  PAi/o5opWc«,  p.  1.  §  1.  subs.  4,  tt  seg.,  p.  8,  ed.  1711.  —  Ed.] 
30.]  [Pars  i.  qu.  3,  ed.  Farisiis,  1630.  See  Gerard  John  Vossius,  De  Nat.  Artium,  sive  de 
also  Qu.  4,  p.  44.  —  Ed.]  I^gica^  c.  vi  ] 

2  [See  Themistius,  In  Anal.  Post.,  1.  i.  c.  24,  3  [See  Laertius,  In  Vita  Zenonis,  1.  vii.]  [J  62. 
[Opera,  p.  6,  Venice,  1554.  —  Ed.]  Ammonius     Ed.] 

Hermiae,  iii  Ca«<'g-.,  Prasf.  [p.  3,  ed.  Aid.  1503.  *  ro     *         n.  j-           .      r\      t     iii •. 

^         „.       ,.f^„^„,„  *  [Scotus,    Prcedicamenta,  Qu.   i.   Albertus 

—  Ed.]    Simplichis. /rt  Oiifg-.,  Praef.  [§  25,  p.  „              r    r,    r,    ..,■    >.•,,.          i, 

^     .,         ,,  ,        „          „  ,        .,  Magnus,  In  De  Praduabtlibus,  c.  1.] 

5,   ed.   Basilese.  1551.  —  Ed  ]     Zabarella,  Z»«  ^       '                                   '         ' 

Natura  Logicee,  [1.  i.  c.  5,  et  seg.  —  Ed.]    Smi-  ^  [Ramus,  Instit.  Dialect.,  1.  i.  c.  1.    Bur- 

glecius,  Logica,  Disp.  ii.  qu.  4,  [p.  69,  ed.  Ox-  gersdicius,  Instit.  Log.,  1.  i.  c.  1,  [§  4.  —  Ed.] 

onii,  1658.  —  Ed.]  Logica  Conimbricensis,  [Tract  6  •  See  Smiglecius,  as  abore.  —  "Ed. 


8  '  LOGIC.  Lect.  1. 

error  in  its  deductions.  Its  most  appropriate  office,  however,  is 
that  of  instituting  an  analysis  of  the  process  of  the  mind  in  rescu- 
ing; and  in  this  point  of  view  it  is,  as  has  been  stated,  strictly  a 
science;  while  mentioned  in  reference  to  the  practical  rules  above 
mentioned,  it  may  be  called  the  art  of  reasoning.  This  distinction, 
as  will  hereafter  appear,  has  been  overlooked,  or  not  clearly  pointed 
out,  by  most  writers  on  the  subject;  Logic  having  been  in  general 
regarded  as  merely  an  art,  and  its  claim  to  hold  a  place  among  the 
sciences  having  been  expressly  denied." 

All  this  is,  from  first  to  last,  erroneous.     In  the  first  place,  it  is 
erroneous  in  what  it  says  of  the  opinion  prev- 

Criticized.  ,  i  -i  i  .  n  i 

alent  among  philosophers,  in  regard  to  the  genus 
of  Logic.  Logic  was  not,  as  is  asserted,  in  general  regarded  as  an 
art,  and  its  claim  to  hold  a  place  among  the  sciences  expressly 
denied.  The  contrary  would  have  been  correct;  for  the  immense 
majority  of  logicians,  ancient  and  modem,  have  regarded  Logic  as 
a  science,  and  expressly  denied  it  to  be  an  art.  In  the  second  place, 
supposing  Dr.  Whately's  acceptation  of  the  terms  art  and  science 
to  be  correct,  there  is  not  a  previous  logician  who  would  have 
dreamt  of  denying  that,  on  such  an  acceptation,  Logic  was  both  a 
science  and  an  art.  But,  in  the  third  place,  the  discrimination 
itself  of  art  and  science  is  wrong.  Dr.  Whately  considers  science 
to  be  any  knowledge  viewed  absolutely,  and  not  in  relation  to  praC" 
tice,  —  a  signification  in  which  every  art  would,  in  its  doctrinal 
part,  be  a  science ;  and  he  defines  art  to  be  the  application  of 
knowledge  to  practice,  in  which  sense  Ethics,  Politics,  Religion, 
and  all  practical  sciences,  would  be  arts.  The  distinction  of  arts 
and  sciences  is  thus  wrong.^  But,  in  the  fourth  place,  were  the 
distinction  correct,  it  would  be  of  no  value,  for  it  would  distinguish 
nothing,  since  art  and  science  would  mark  out  no  real  difierence 
between  the  various  branches  of  knowledge,  but  only  different 
points  of  view  under  which  the  same  branch  might  be  contemplated 
by  us,  —  each  being  in  different  relations  at  once  a  science  and  an 
art.  In  fact,  Dr.  Whately  confuses  the  distinction  of  science  theo- 
retical and  science  practical  with  the  distinction  of  science  and  art. 
I  am  well  aware  that  it  would  be  no  easy  matter  to  give  a  general 
definition  of  science,  as  contradistinguished  from  art,  and  of  art,  as 
contradistinguished  from  science ;  but  if  the  words  themselves  can- 
not validly  be  discriminated,  it  would  be  absurd  to  attempt  to  dis- 
criminate anything  by  them.  When  I,  therefore,  define  Logic  by 
the  genus  science^  I  do  not  attempt  to  give  it  more  than  the  general 
denomination  of  a  branch  of  knowledge ;  for  I  reserve  the  discrimi- 

I  Compare  Lectures  on  Metaphysics,  p.  81  et  seq.  —  Ed. 


Lk.CT.  I.  LOGIC.  9 

nation  of  its  peculiar  character  to  the  differential  quality  afforded 
by  its  object-matter.  You  will  find,  when  we  have  discussed  the 
third  head  of  the  definition,  that  Logic  is  not  only  a  science,  but  a 
demonstrative  or  apodictic  science ;  but  so  to  have  defined  it,  would 
have  been  tautological ;  for  a  science  conversant  about  laws  is  con- 
versant about  necessary  mattei-,  and  a  science  conversant  about 
necessary  matter  is  demonstrative. 

I  proceed,  therefore,  to  the  third  and  last  head  of  the  defini- 
tion,—  to  explain  to  you  what  is  meant  by  the 
^^'    ^   °^  object^matter   of   Logic,  —  viz.,   the    Laws   of 

Thought  as  Thought.  The  consideration  ot 
this  head  naturally  divides  itself  into  three  questions :  1,  What  is 
Thought?  2,  What  is  Thought  as  Thought?  3,  What  are  the  Laws 
of  Thought  as  Thought  ? 

In  the  first  place,  then,  in  saying  that  Logic  is  conversant  about 
Thought,  we  mean  to  say  that  it  is  conversant 

(a)  Thought,  —  what.  ,  .  ,  .     ,  ,i     i         m. 

about   thought   strictly   so   called.      The   term 

thought  is  used  in  two  significations  of  different  extent.      In  the 

wider  meaning,  it  denotes  every  cognitive  act 

In  its  wider  and  nar.       ^^atcvcr ;   by  somc  philosophers,  as  Descartes 

rower  meaning.  -,,•-,••%        ■    • 

and  his  disciples,  it  is  even  used  for  every  mental 
modification  of  which  we  are  conscious,  and  thus  includes  the  Feel- 
ings, the  Volitions,  and  the  Desires.'  In  the  more  limited  meaning, 
it  denotes  only  the  acts  of  the  Understanding  properly  so  called, 
that  is,  of  the  Faculty  of  Comparison,  or  that  which  is  distinguished 
as  the  Elaborative  or  Discursive  Faculty.^  It  is  in  this  more  re- 
stricted signification  that  thought  is  said  to  be 
Objects  that  lie  be-       ^^xe  object-matter  of  Logic.      Thus  Logic  does 

yond    the    sphere   of  •  t  i       i  t  •   i  i  ,  , 

j^^^.j.  not  consider  the  laws  which  regulate  the  other 

powers  of  mind.  It  takes  no  immediate  account 
of  the  faculties  by  which  we  acquire  the  rude  .materials  of  knowU 
edge;  it  supposes  these  materials  in  possession,  and  considers  only 
the  manner  of  their  elaboration.  Jt  takes  no  account,  at  least  in 
the  department  of  Pure  Logic,  of  Memory  and  Imagination,  or  of 
the  blind  laws  of  Association,  but  confines  its  attention  to  connec- 
tions regulated  by  the  laws  of  intelligence.  Finally,  it  does  not 
consider  the  laws  themselves  of  Intelligence  as  given  in  the  Regu- 
lative Faculty,  —  Intelligence,  - — Common  Sense  ;  for  in  that  faculty 
these  laws  are  data,  facts,  ultimate  and,  consequently,  inconceivable ; 

1  Descartes,  Prindpia,  p.  i.  i  9.     "  Cogita-  intelligere,  velle,  imaginari,  sed  etiam  sentire. 

tionis  nomine  intelligo  ilia  omnia  quas  nobis  idem  est  hie  quod  cogitare."  —  Ed. 

conseiis  in   nobis  fiunt,  quatenus  eorum   in  2  See  Lectures  on  Mttaphysics,  lect.  xxxiv. 

nobis  conscieutia  est.    Atque  ita  non  modo  p.  463.  —  Ed. 

2 


10  LOGIC.  Lect.  L 

but  whatever  transcends  the  sphere  of  the  conceivable,  transcends 
the  sphere  of  Logic, 

Such  are  the  functions  about  which  Logic  is  not  conversant,  and 
such,  in  the  limited  signification  of  the  word,  are  the  acts  which  are 
not  denominated  Thought.  We  have  hitherto  found  what  thought 
is  not ;  we  must  now  endeavor  to  determine  generally  what  it  is. 

The  contemplation  of  the  world  presents  to  our  subsidiary  facul- 
ties a  multitude  of  objects.  These  objects  are 
oug     proper.  ^^^  ^^^^  materials  submitted  to  elaboration  by  a 

higher  and  self-active  faculty,  which  operates  upon  them  in  obedi- 
ence to  certain  laws,  and  in  conformity  to  certain  ends.  The  opera- 
tion of  this  faculty  is  Thought.  All  thought  is  a  comparison,  a 
recognition  of  similarity  or  difference ;  a  conjunction  or  disjunc- 
tion ;  —  in  other  words,  a  synthesis  or  analysis  of  its  objects.  In 
Conception,  that  is,  in  the  formation  of  concepts  (or  general  notions), 
it  compares,  disjoins,  or  conjoins  attributes;  in  an  act  of  Judgment, 
it  compares,  disjoins,  or  conjoins  concepts;- in  Reasoning,  it  com- 
pares, disjoins,  or  conjoins  judgments.  In  each  step  of  this  process 
there  is  one  essential  element ;  to  think,  to  compare,  to  conjoin,  or 
disjoin,  it  is  necessary  to  recognize  one  thing  thi-ough  or  under 
another;  and  therefore,  in  defining  Thought  proper,  we  may  either 
define  it  as  an  act  of  Comparison,  or  as  a  recognition  of  one  notion 
as  in  or  under  another.  It  is  in  performing  this  act  of  thinking  a 
thing  under  a  general  notion,  that  we  are  said  to  understand  or 
comprehend  it.  For  example :  an  object  is  presented,  say  a  book ; 
this  object  determines  an  impression,  and  I  am  even  conscious  of  the 
impression,  but  without  recognizing  to  myself  what  the  thing  is; 
in  that  case,  there  is  only  a  perception,  and  not  properly  a  thought. 
But  suppose  I  do  recognize  it  for  what  it  is,  in  other  words,  com- 
pare it  with,  and  reduce  it  under,  a  certain  concept,  class,  or  com- 
plement of  attributes,  which  I  call  book;  in  that  case,  there  is  more 
than  a  perception,  —  there  is  a  thought. 

All  this  will,  however,  be  fully,  explained  to  you  in  the  sequel ;  at 
present  I  only  attempt  to  give  you  a  rude  notion  of  what  thinking 
is,  to  the  end  that  you  may  be  able  vaguely  to  comprehend  the  lim- 
itation of  Logic  to  a  certain  department  of  our  cognitive  functions, 
and  what  is  meant  by  saying  that  Logic  is  a  science  of  thought. 

But  Thought  simply  is  still  too  undetermined;  the  proper  object 

of  Logic  is  something  still  more  definite ;  it  is 

-what"*^    *^    °"^         "^*'  t^<^"ght  in  general,  but  thought  considered 

merely  as  thought,  of  which  this  sc^icnce  takes 

cognizance.     This  expression  requires  explanation ;  we  come  there- 


Lect.  L  logic.  11 

fore  to  the   second   question,  —  What   is   meant   by  Thought  as 
Thought  ? 

To  answer  this  question,  let  us  remember  what  has  just  been  said 
of  the  act  constitutive  of  thought,  —  viz.,  that  it  is  the  recognition 
of  a  thing  as  coming  under  a  concept ;  in  other  words,  the  marking 
an  object  by  an  attribute  or  attributes  previously  known  as  common 
to  sundry  objects,  and  to  which  we  have  accordingly  given  a  general 
name.     "  In  this  process  we  are  able,  by  abstraction,  to  distinguish 

from  each  other,  —  1°,  The  object  thought  of; 
,„       .  and,  2°,   The  kind  and  manner  of  thinking  it. 

Let  us,  employing  the  old  and  established  tech^ 
nical  expressions,  call  the  first  of  these  the  matter,  the  second  the 
form,  of  tlie  thought.  For  example,  when  I  think  that  the  book 
before  me  is  a  folio,  the  matter  of  this  thought  is  book  and  folio ; 
the  form  of  it  is  a  judgment.  Now,  it  is  abundantly  evident  that 
this  analysis  of  thought  into  two  phases  or  sides  is  only  the  work 
of  a  scientific  discrimination  and  contrast ;  for  as,  on  the  one  hand, 
the  matter  of  which  we  think  is  only  cogitable  through  a  certain 
form,  so,  on  the  other,  the  form  under  which  we  think  cannot  be- 
realized  in  consciousness,  unless  in  actual  application  to  an  object."* 

Now,  when  I  said  that  Logic  was  conversant 
Logic  properly  con-       ^^^^^  thought  Considered  merely  as  thought,  I 

versaut  only  with  the  ,        ,  i  t        •      • 

Form  of  Thought  meant  simply  to  say,  that  Logic  is  conversant 

with  the  form  of  thought,  to  the  exclusion  of 
the  matter.  This  being  understood,  I  now  proceed  to  show  how 
Logic  only  proposes  —  how  Logic  only  can  propose  —  the  form  of 
thought  for  its  object  of  consideration.  It  is-  indeed  true,  that  this 
limitation  of  Logic  to  the  form  of  thought  has  not  always  been 
kept  steadily  in  view  by  logicians;  that  it  is  only  gradually  that 
proper  views  of  the  science  have  been  speculatively  adopted,  and 
still  more  gradually  that  they  have  been  carried  practically  into 
eflTect,  insomuch  that  to  the  present^ hour,  as  I  shall  hereafter  show 
you,  there  are  sundry  doctrines  still  taught  as  logical,  which,  as 
relative  to  the  matter  of  thought,  are  in  fact  foreign  to  the  science 
of  its  form. 

"But  although  it  is  impossible  to  show  by  the  history  of  the 

science,  that  Logic  is  conversant  with  the  form, 

This  shown  by  a  con-       ^o  the  cxclusiou  of  the  matter,  of  thought ;  this 

sideration  of  the  na-  ■■  ,  ,•    p     ,      •^       t  i  -i 

ture  and  conditions  of      Can,  however,  be  Satisfactorily  done  by  a  consid- 

the  thing  itself.  eration   of  the   nature   and   conditions   of  the 

thing  itself     For,  if  it  be  maintained  that  Logic 

takes  not  merely  the  form,  but  the  matter  of  thought  into  account 

1  Esser,  Logik,  i,  3,  p.  4,  2d  edit.    MUnster,  1830.  —  Ed. 


12  LOGIC.  Lect.  I 

(the  matter,  you  will  recollect,  is  a  collective  expression  for  the 
several  objects  about  which  thought  is  conversant),  in  tiiat  case, 
Logic  must  either  consider  all  those  objects  without  distinction,  or 
make  a  selection  of  some  alone.  Now  the  former  of  these  alterna- 
tives is  manifestly  impossible ;  for  if  it  were  required  that  Logic 
should  comprise  a  full  discussion  of  all  cogitable  objects,  —  in  other 
words,  if  Logic  must  draw  within  its  sphere  all  other  sciences,  and 
thus  constitute  itself  iu  lact  the  one  universal  science,  -^  every  one  at 
once  perceives  the  absurdity  of  the  requisition,  and  the  impossibility 
of  its  fulfilment.  But  is  the  second  alternative  more  reasonable? 
Can  it  be  proposed  to  Logic  to  take  cognizance  of  certain  objects 
of  thought  to  the  exclusion  of  others?  On  this  supposition,  it 
nmst  be  shown  why  Logic  should  consider  this  particular  object, 
and  not  also  that;  but  as  none  but  an  arbitrary  answer — that  is, 
no  answer  at  all  —  can  be  given  to  this  interrogation,  the  absurdity 
of  this  alternative  is  no  less  manifest  than  that  of  the  other.  The 
particular  objects,  or  the  matter  of  thought,  being  thus  excluded, 
the  form  of  human  thought  alone  remains  as  the  object-matter  of 
our  science ;  in  other  words.  Logic  has  only  to  do  with  thinking  as 
thinking,  and  has  no,  at  least  no  immediate,  concernment  with  that 
which  is  thought  about.  Logic  thus  obtains,  in  common  parlance, 
the  appellation  of  a  fonnal  science,  not  indeed  in  the  sense  as  if 
Logic  had  only  a  form  and  not  an  object,  but  simply  because  the 
form  of  human  thought  is  the  object  of  Logic;  so  that  the  title 
formal  science  is  properly  only  an  abbreviated  expression."  * 

I  proceed  now  to  the  question  under  this  head,  —  viz..  What  is 

meant  by  the  Laws  of  Thought  as  Thought  ?  in 

n^*^^  u.'^  -^u^^  u?        Other  words.  What  is  meant  by  the  Formal  Laws 

Thought  as  ThouRht.  •' 

of  Thought  ? 
We  have  already  limited  the  object  of  Logic  to  the  form  of 
thought.  But  there  is  still  required  a  last  and  final  limitation  ;  for 
this  form  contains  more  than  Logic  can  legitimately  consider.  "  Hu- 
man thought,  regarded  merely  in  its  formal  relation,  may  be  consid- 
ered in  a  twofold  point  of  view ;  for,  on  the  one  hand,  it  is  either 
known  to  us  merely  from  experience  or  observation, —we  are 
merely  aware  of  its  phenomena  historically  or  empirically,  or,  on  the 
other,  by  a  reflective  speculation,  —  by  analysis  and  abstraction,  we 
seek  out  and  discriminate  in  the  manifestations  of  thought  what  is 
contained  of  necessary  and  universal.  The  empirical  or  historical 
consideration  of  our  thinking  faculty  does  not  belong  to  Logic,  but 
to  the  PhaBuomenology  of  Mind,  —  to  Psychology.    The  empirical 

I  Esser,  Lo^k,  i  3,  pp.  5,  6.     Cf.  Krng,  DenkUhre  oder  Logik,  (  8,  p.  17  tt  seq.,  2d  edit.  1819 
—  Ed. 


Lect.  I.  LOGIC.  13 

observation  of  the  phenomena  necessarily,  indeed,  precedes  their 
speculative  analysis.  But,  notwithstanding  this.  Logic  possesses  a 
peculiar  province  of  its  own,  and  constitutes  an  independent  and 
exclusive  science.  For  where  our  empirical  consideration  of  the 
mind  terminates,  there  our  speculative  consideration  commences; 
the  necessary  elements  which  the  latter  secures  from  the  contingent 
materials  of  observation,  —  these  are  what  constitute  the  laws  of 
thought  as  thought."*  > 

1  Cf.  Eeser,  LogUc,  §  4,  pp.  6,  7.  —  Bd 


LECTURE  II. 

INTRODUCTION. 

LOGIC  — I.  Its  definition— historical  notices  of  opinions 

REGARDING  ITS  OBJECT  AND  DOMAIN  — IL    ITS  UTILITY. 

In  my  last  Lecture  I  commenced  the  consideration  of  Logic, — 
of  Losric  properly  so  denominated,  —  a  science 

Recapitulation.  „  ,  ,  .        .  /.       ,  •   ,  ^ 

for  the  cultivation  oi  which  every  European 
university  has  provided  a  special  chair,  but  which,  in  this  country,  in 
consequence  of  the  misconceptions  which  have  latterly  arisen  in  re- 
gard to  its  nature  and  its  end,  has  been  very  generally  superseded  ; 
insomuch  that,  for  a  considerable  period,  the  chairs  of  Logic  in  our 
Scottish  universities  have  in  fact  tauglit  almost  everything  except 
the  doctrine  which  they  were  established  to  teach.  After  some  pre- 
cursory observations  in  regard  to  the  mode  of  communication  which 
I  should  follow  in  my  Lectures  on  this  subject,  I  entered  on  the  treat- 
ment of  the  science  itself,  and  stated  to  you  that  a  systematic  view 
of  Logic  would  consist  of  two  parts,  the  one  being  an  Introduction 
to  the  doctrine,  the  other  a  body  of  the  Doctrine  itself.  In  the  in- 
troduction vieve  considered  certain  preparatory  points,  necessary  to 
be  understood  before  entering  on  the  discussion  of  the  science  itself; 
and  I  stated  that  these  preparatory  points  were,  in  relation  to  our 
science,  exhausted  in  five  questions  and  their  answers — 1°,  What  is 
Logic  ?  2°,  What  is  its  value  ?  3°,  How  is  it  distributed  ?  4°,  What 
is  its  history?  5°,  What  are  its  subsidiaries? 

I  then  pi'oceeded  to  the  consideration  of  the  first  of  these  ques- 
tions ;  and  as  the  answer  to  the  question,  —  what  is  Logic,  —  is  given 
in  its  definition,  I  defined  Logic  to  be  the  science  conversant  about 
the  laws  of  thought  considered  merely  as  thought ;  warning  you, 
however,  that  this  definition  could  only  be  understood  after  an  artic- 
ulate explanation  of  its  contents.  Now  this  definition,  I  showed 
you,  naturally  fell  into  three  parts,  and  each  of  these  parts  it  be- 
hooved to  consider  and  illustrate  by  itself  The  first  was  the  word 
significant  of  the  thing  defined,  —  Logic.  The  second  was  the 
genus  by  which  Logic  was  defined,  —  science.     The  third  was  the 


Lect.  II.  LOGIC.  15 

object-matter  constituting  the  differential  quality  of  Logic,  —  the 
laws  of  thought  as  thought.  Each  of  these  I  considered  iu  its  order, 
I,  first  of  all,  explained  the  original  meaning  of  the  term  Logic,  and 
gave  you  a  brief  history  of  its  application.  I  then  stated  what  was 
necessary,  in  regard  to  the  genus,  —  science ;  and,  lastly,  what  is  of 
principal  importance,  I  endeavored  to  make  you  vaguely  aware  of 
that  which  you  cannot  as  yet  be  supposed  competent  distinctly  to 
comprehend ;  I  mean  the  peculiar  character  of  the  object,  —  object- 
matter,  —  about  which  Logic  is  conversant.  The  object  of  Logic, 
as  stated  in  the  definition,  is  the  laws  of  thought  as  thought.  This 
required  an-  articulate  explanation ;  and  such  an  explanation  I  en- 
deavored to  afford  you  under  three  distinct  heads ;  expounding, 
1°,  What  was  meant  by  thought;  2°,  What  was  meant  by  thought 
as  thought ;  3°,  What  was  meant  by  the  laws  of  thought  as  thought. 
In  reference  to  the  first  head,  I  stated  that  Logic  is  conversant 
about  thought  taken  in  its  stricter  signification,  that  is,  about  thought 
considered  as  the  operation  of  the  Understanding  Proper,  or  of  that 
faculty  which  I  distinguished  as  the  Elaborative  or  Discursive,  — 
the  Faculty  of  Relations,  or  Comparison.  I  attempted  to  make  you 
vaguely  apprehend  what  is  the  essential  characteristic  of  thought, 
—  viz.,  the  comprehension  of  a  thing  under  a  general  notion  or  attri- 
bute. For  such  a  comprehension  enters  into  every  act  of  the  dis- 
cursive faculty,  in  its  different  gradations  of  Conception,  Judgment, 
and  Reasoning.  But  by  s.iying  that  Logic  is  convers.int  about 
thought  proper,  Logic  is  not  yet  discriminated  as  a  peculiar  science, 
for  there  are  many  sciences,  likewise,  inter  alia,  convei'sant  about  the 
operations  and  objects  of  the  Elaborative  Faculty.  There  is  re- 
quired a  further  determination  of  its  object-matter.  This  is  done 
by  the  limitation,  that  Logic  is  conversant  not  merely  about  thought, 
but  about  thought  as  thought.  The  explanation  of  this  constituted 
the  second  head  of  our  exposition  of  the  object-matter.  Thought,  I 
showed,  could  be  viewed,  by  an  analytic  abstraction,  on  two  sides 
or  phases.  We  could  either  consider  the  object  thought,  or  the 
manner  of  thinking  it ;  in  other  words,  we  could  scientifically  dis- 
tinguish from  each  other  the  matter  and  the  form  of  thought.  Not 
that  the  matter  and  form  have  any  separate  existence ;  no  object 
being  cogitable  except  under  some  form  of  thought,  and  no  form  of 
thought  having  any  existence  in  consciousness  except  some  object 
be  thought  under  it.  This,  however,  formed  no  impediment  to  our 
analysis  of  these  elements,  through  a  mental  abstraction.  This  is  in 
fact  only  one  of  a  thousand  similar  abstractions  we  are  in  the  habit 
of  making;  and  if  such  were  impossible,  all  human  science  would 
be  impossible.     For  example :  extension  is  only  presented  to  sense, 


16  LOGIC.  Lect.  U. 

under  some  modification  of  color,  and  even  imagination  cannot  rep- 
resent extension  except  as  colored.  We  may  view  it  in  phantasy 
as  black  or  white,  as  translucent  or  opaque  ;  but  represent  it  we  can- 
not, except  either  under  some  positive  variety  of  light,  or  under  the 
negation  of  light,  which  is  darkness.  But,  psychologically  consid- 
ered, darkness  or  blackness  is  as  much  a  color,  that  is,  a  positive 
sensation,  as  whiteness  or  redness ;  and  thus  we  cannot  image  to 
ourselves  aught  extended,  not  even  space  itself,  out  of  relation  to 
color.  But  is  this  inability  even  to  imagine  extension,  apait  from 
some  color,  any  hinderance  to  our  considering  it  scientifically  apart 
from  all  color  ?  Not  in  the  smallest ;  nor  do  Mathematics  and  the 
other  sciences  find  any  difficulty  in  treating  of  extension,  without 
even  a  single  reference  to  this  condition  of  its  actual  manifestation. 
The  case  of  Logic  is  precisely  the  same.  Logic  considere  the  form 
apart  from  the  matter  of  thought ;  and  it  is  able  to  do  this  without 
any  trouble ;  for  though  the  form  is  only  an  actual  phenomenon 
when  applied  to  some  matter,  —  object,  —  yet,  as  it  is  not  necessa- 
rily astiicted  to  any  object,  we  can  always  consider  it  abstract  from 
all  objects  ;  in  other  words,  from  all  matter.  For  as  the  mathema- 
tician, who  cannot  construct  his  diagrams,  either  to  sense  or  to  im- 
agination, apart  from  some  particular  color,  is  still  able  to  consider 
the  properties  of  extension  apart  from  all  color ;  so  the  logician, 
though  he  cannot  concretely  represent  the  forms  of  thought  except 
in  examples  of  some  particular  matter,  is  still  able  to  consider  the 
properties  of  these  forms  apart  from  all  matter.  The  possibility  be- 
ing thus  apparent  of  a  consideration  of  the  form  abstractly  from 
the  matter  of  thought,  I  showed  you  that  such  an  abstraction  was 
necessary.  The  objects  (the  matter)  of  thought  are  infinite;  no 
one  science  can  embrace  them  all,  and  therefore,  to  suppose  Logic 
conversant  about  the  matter  of  thought  in  general,  is  to  say  that 
Logic  is  another  name  for  thQ  encyclopaedia  —  the  omne  scibile  — 
of  human  knowledge.  The  absurdity  of  this  supposition  is  appar- 
ent. But  if  it  be  impossible  for  Logic  to  treat  of  all  the  objects 
of  thought,  it  cannot  be  supposed  that  it  treats  of  any ;  for  no  rea-' 
son  can  be  given  why  it  should  limit  its  consideration  to  some,  to  the 
exclusion  of  others.  As  Logic  cannot,  therefore,  possibly  include  all 
objects,  and  as  it  cannot  possibly  be  shown  why  it  should  include 
only  some,  it  follows  that  it  must  exclude  from  its  domain  the  con- 
sideration of  the  matter  of  thought  altogether ;  and  as,  apart  from 
the  matter  of  thought,  there  only  remains  the  form,  it  follows  that 
Logic,  as  a  special  science  of  thought,  must  be  viewed  as  convei-sant 
exclusively  about  the  form  of  thought. 

But  the  limitation  of  the  object-matter  of  Logic  to  the  form  of 


Lkct.  II.  LOGIC.  .37 

thought  (and  the  expression  form  of  thought  is  convertible  with 

the  expression   thought  as  thought),  is  not  yet 

(c)    The       ws  o        enousrh  to  discriminate  its  province  from  that  of 

Thought  «8  Thought.  ^,    ^     .  f      T>      ^:^  41,     T?       • 

other  sciences;    tor  Psychology,  or  the  xLmpir- 

ical  Science  of  Mind,  is  likewise,  among  the  other  mental  phaenom- 
ena,  conversant  about  the  pbsenomena  of  formal  thought.  A  still 
further  limitation  is  therefore  requisite ;  and  this  is  given  in  say- 
ing that  Logic  is  the  science  not  merely  of  Thought  as  Thought, 
but  of  the  Laws  of  Thought  as  Thought.  It  is  this  determination 
which  affords  the  proximate  and  peculiar  difference  of  Logic,  in 
contradistinction  from  all  other  sciences;  and  the  explanation  of  its 
meaning  constituted  the  third  head  of  illustration,  which  the  object- 
matter  in  the  definition  demanded. 

The  phaenomena  of  the  formal,  or  subjective  phases  of  thought, 

are  of  two  kinds.     They  are  either  such  as  are 

The  phaenomena  of      contingent,  that  is,  such  as  may  or  may  not  ap- 

formal  thought  are  of.  ,  ,  ^i     ^    • 

.     ..  _,         ^.       ^       pear ;  or  they  are  such  as  are  necessary,  that  ls, 

two  kinds— contingent         r  t  j  j '  i 

and  necessary.  such  as  cannot  but  appear.     These  two  classes- 

of  phaenomena  are,  however,  only  manifested  in 
conjunction;  they  are  not  discriminated  in  the  actual  operations  of 
thought;  and  it  requires  a  speculative  analysis  to  separate  them 
into  their  several  classes.  In  so  far  as  these  phaenomena  are  con- 
sidered merely  as  phaenomena,  that  is,  in  so  far  as  philosophy  is 
merely  observant  of  them  as  manifestations  in  general,  they  belong 
to  the  science  of  Empirical  or  Historical  Psychology.  But  when 
philosophy,  by  a  reflective  abstraction,  analyzes  the  necessary  from 
the  contingent  forms  of  thought,  there  results  a  science,  which  is 
distinguished  from  all  others  by  taking  for  its  object-matter  the 
former  of  these  classes ;  and  this  science  is  Logic.  Logic,  there- 
fore, is  at  last  fully  and  finally  defined  as  the  science  of  the  neces- 
sary forms  of  thought.  Here  terminated  our  last  Lecture.  But 
though  full  and  final,  this  definition  is  not  explicit;  and  it  still 
remains  to  evolve  it  into  a  more  precise  expression. 

Now,  when  we  say  that  Logic  is  the  science  of  the  necessaiy 
forms  of  thought,  what  does  the  quality  of  necessity  here  imply  ? 

"In  the  first  place,  it  is  evident  that  in  so  far 

Form  of  thought.  —  „  ,.      ,  ,         .  ,  •      ^ 

Four  conditions  of  its  ^^^  ^o™  ^^   thought    IS  ncccssary,  this  form 

necessity.  must  be  determined  or  necessitated  by  the  na- 

1.  Determined  by  the  .  ture  of  the    thinking   subject   itself;   for  if  it 

naureo     e    in  ing  -^^re  determined   by  anything  external  to  the 

subject  it-self.  j  j  is 

mind,  then  would  it  not  be  a  necessary,  but  a 
merely  contingent  determination.     The  first  condition,  therefore, 

3 


18  LOGIC.  Lect.  n. 

of  the  necessity  of  a  form  of  thought  is,  that  it  is  subjectively,  not 
objectively,  determined. 

"In  the  second  place,  if  a  form  of  thought  be  subjectively  neces- 
sary, it  must  be  original  and  not  acquired.     For 

2.  Original.  . .  .•"  .      n      ,  ,  , 

II  It  were  acquired,  there  must  have  been  a  time 
when  it  did  not  exist ;  but  if  it  did  ever  actually  not  exist,  we  must 
be  able  at  least  to  conceive  the  possibility  of  its  not  existing  now. 
But  if  we  are  so  able,  then  is  the  form  not  necessary;  for  the  crite- 
rion of  a  contingent  cognition  is,  that  we  can  represent  to  ourselves 
the  possibility  of  its  non-existence.  The  second  condition,  there- 
fore, of  the  necessity  of  a  form  of  thought  is,  that  it  is  original,  and 
not  acquired. 

"  In  the  third  place,  if  a  form  of  thought  be  necessary  and  origi- 
nal, it  must  be  universal ;  that  is,  it  cannot  be 

3.  Universal.  ...  •  t     i 

that  it  necessitates  on  some  occasions,  and  does 
not  necessitate  on  others.  For  if  it  did  not  necessitate  universally, 
then  would  its  necessitation  be  contingent,  and"  it  would  conse- 
quently not  be  an  original  and  necessary  principle  of  mind.  The 
third  condition,  therefore,  of  the  necessity  of  a  form  of  thought  is, 
that  it  is  universal. 

"  In  the  fourth  place,  if  a  form  of  thought  be  necessary  and  uni- 
versal, it  must  be  a  law ;  for  a  law  is  that  which 
applies  to  all  cases  without  exception,  and  from 
which  a  deviation  is  ever,  and  everywhere,  impossible,  or,  at  least, 
unallowed.     The  fourth  and  last  condition,  therefore,  of  the  neces- 
sity of  a  form  of  thought  is,  that  it  is  a  law."*     This  last  condition, 
likewise,  enables  us  to  give  the  most  explicit  enunciation  of  the 
object-matter  of  Logic,  in  saying  that  Logic  is 
The  Object-matter      ^^xe  Science  of  the  Laws  of  Thought  as  Thought, 

of    Logic    explicitly  ,  .  /»   i      -n  it  r.  mi  i 

enounced  ®^  ^"^  sciencc  oi  the  t  ormal  Laws  of  Thought,  or 

the  science  of  the  Laws  of  the  Form  of  Thought ; 
for  all  these  are  merely  various  expressions  of  the  same  thing. 

Before  proceeding  further,  it  may  be  proper 

General   historical       ^q  ^sikQ  a  very  general  retrospect  of  the  views 

re  rospec  <>  ^'^^^^  *»       ^\^c^^^  have  prevailed  in  regard  to  the  object  artd 

regard    to   the  object  _  r^         ^  ®  **      _ 

and  domain  of  Logic.       domain  of  Logic,  from  the  era  when  the  science 
received  its  first  giand  and  distinctive  develop- 
ment from  the  genius  of  Aristotle  to  the  present  time. 

I  may  say,  in  general,  that  the  view  which  I 
Merit  of  the  Author's       j^^^,^  ^^^  presented  to  you  of  the  object  and 

view  of  Logic.  ... 

domain  of  Logic,  is  the  one  which  concentrates, 
corrects,  and  completes  the  views  which  have  been  generally  held 

1  EsBer,  LogUc,  i  6,  pp.  9, 10,  with  a  few  original  interpolations.  —  Ed 


Lect.  n.  LOGIC.  19 

by  logicians  of  the  peculiar  province  of  their  science.     It  is  the  one 
to  which  they  all  gravitate. 

It  is  unfortunate,  that  by  far  the  greater  number  of  the  logical 
writings  of  Aristotle  have  perished,  and  that 

Aristotle.  .  i  .1  •  ,      ,  .        . 

those  which  reraam  to  us  exhibit  only  his  views 
of  the  science  considered  in  its  parts,  or  in  certain  special  relations. 
None  of  the  treatises  which  are  now  collected  in  the  Organon^ 
considers  the  science  from  a  central  point;  and  we  do  not  even 
possess  a  general  definition  of  Logic  by  its  illustrious  founder.'  It 
<V^ould,  therefore,  be  unjust  to  the  mighty  master,  if,  as  has  usually 
been  done,  we  estimated  his  conception  of  the  science  only  by  the 
partial  views  contained  in  the  fragmentary  or  special  treatises  which 
have  chanced  to  float  ashore  from  the  genei'al  wreck  of  his  logical 
writings.  These  by  themselves  are  certainly  enough  to  place  the 
Stagirite  high  above  comparison  with  any  subsequent  logician ;  but 
still,  if  he  has  done  so  much  in  the  half-dozen  treatises  that  still 
remain,  what  may  we  not  conceive  him  to  have  accomplished  in 
the  forty  which  are  recorded  and  seem  to  have  been  lost  ?  It  is, 
therefore,  not  to  be  attributed  to  Aristotle,  that  subsequent  logi- 
cians, mistaking  his  surviving  treatises  of  a  logical  nature  —  few  in 
number,  and  written,  in  general,  not  in  exposition  of  the  pure  sci- 
ence, but  only  of  the  science  in  cer^in  modified  applications  —  for 
a  systematic  body  of  logical  doctrine,  should  have  allowed  his  views 
of  its  partial  relations  to  influence  their  conceptions  of  the  science 
absolutely  and  as  a  whole.  By  this  influence  of  the  Aristotelic 
treatises,  we  may  explain  the  singular  circumstance,  that,  while 
many,  indeed  most,  of  the  subsequent  logicians  speculatively  held 
the  soundest  views  in  regard  to  the  proper  object  and  end  of  Logic, 
few  or  none  of  them  have  attempted  by  these  views  to  purify  the 
science  of  those  extraneous  doctrines,  to  which  the  authority  of 
Aristotle  seemed  to  have  given  a  right  of  occupancy  within  its 

domain.     I  shall  not  attempt  to  show  you,  in 

Greek  Aristotelians  ^  i_  j.    •  ^  ^i  ,  • 

^  ^  ,.   „  ^    ,  extenso,  how  correct,  in  general,  were  the  notions 

and  Latin  Schoolmen.  \  '        o  ' 

entertained  by  the  Greek  Aristotelians,  and  even 
by  the  Latin  schoolmen,  for  this  would  require  an  explanation  of 
the  signification  of  the  terms  in  which  their  opinions  were  embod- 
ied, which  would  lead  me  into  details  which  the  importance  of  the 
matter  would  hardly  warrant.  I  shall  only  say,  in  general,  that,  in 
their  multifarious  controversies  under  this  head,  the  diversity  of 
their  opinions  on  subordinate  points  is  not  more  remarkable  than 
their  unanimity  on  principal.     Logic  they  all  discriminated  as  a  sci- 

1  See  below,  p.  24.  —  Ed. 


'iQ  LOGIC.  Lect.  it 

ence  of  the  form  and  not  of  the  matter  of  thought.'  Those  of  ttie 
schoolmen  who  held  the  object  of  Logic  to  be  things  idn  general, 
held  this,  however,  under  the  qualification  that  things  in  general 
,  were  not  immediately  and  in  themselves  considered  by  the  logician, 
.  but  only  as  they  stood  under  the  general  forms  imposed  on  them 
by  the  intellect  ("  quatenus  secundis  intentionibus  substabant "),  — 
a  mode  of  speaking  which  is  only  a  periphrasis  of  our  assertion,  that 
Logic  is  conversant  about  the  forms  of  thought."  The  other  scliool- 
men,  again,  who  maintained  that  the  object  of  Logic  was  thought 
in  its  processes  of  simple  apprehension,  judgment,  and  reasoning 
(three,  two,  or  one),  carefully  explained  that  these  operations  were 
not  in  their  own  nature  proposed  to  the  logician,  for  as  such  they 
belonged  to  Animastic,  as  they  called  it,  or  Psychology,  but  only  in 
so  far  as  they  were  dirigible  or  subject  to  laws,  —  a  statement  which 
is  only  a  less  simple  expression  of  the  fact,  that  Logic  is  the  science 
.of  the  laws  of  thought.'  Finally,  those  schoolmen  who  held  that 
the  object-matter  of  Logic  was  found  in  second  notions  as  applied 
to  first,  only  meant  to  say  that  Logic  was  conversant  Avith  concep- 
tions, judgments  and  reasonings,  not  in  themselves,  but  only  as  i-eg- 
ulators  of  thought,'* — a  statement  which  merely  varies  and  per- 
plexes the  expression,  that  the  object  of  Logic  is  the  formal  laws 
of  thought. 

The  same  views,  various  in  appearance,  but,  when  analyzed,  es- 
sentially the  same,  and  essenti.illy  correct,  may 
Leibnitio-woifian       j^^  ^^.^^^^^  through  the  Leil)nitio-W<)lfian  school 

and  Kantian  Schools.  .  ^  •  i- 

into  the  Kantiaii ;  so  tliat,  while  it  must  be 
owned  that  they  were  never  adequately  carried  out  into  priicticnl 
application,  it  cannot  be  denied  that  they  were  theoretically  not 
unsound. 

The  conntiy  in  which,  perhaps,  the  nature  of 

Bacon,  —  Locke.  ^        .      ••  i  i        i  a  ii 

Logic  has  been  most  completely  and  generally 
misunderstood,    is    Great    Britain.     Bacon    wholly    misconceived 

1  "Logicus  solas  considerat  formas  inten-  ideo  qujedam  secundse  intentiones  invent* 

tionum  communes."     Albertus  Magnus,  In  sunt  ad  regulandum  discursum,  de  quibus 

De  Anima,  L.  I.  trac.  i.  c.  8.     For  various  proprie  est  Logica  "    See  also  Zabarella  and 

I   scholastic  theories  on  the  object-matter  of  Camerarius  as  above.  —  Ed. 

.  Logic,  see  Scotus,  Super  Univ.  Porphyrii,  On.         ,  ,_,  .         _.        nt-r     t>    •  i    . 

•'■     rrv      ,,      ,^    ,r  r  ,-1.    •  3  [Camefarius,  Bifp.   Phil.,  V.  i.  qu.  1,  p. 

111.:  Zabarella,  X)e  Natura  iMgicfr,  ho.  \.  cap.  „        ».,     ,     o.  l    «        r.L->        l-  an-    n      . 

,„'.,.'  „.       ..  ,     .,  3. —Ed.]    Schuler,  PAi/oioM'OjP- 30(,[L.  V  , 

19;  Smiglecius,  Z.ogico,  Disp.  u.  qu.  1 ;  Came-  ,      .      »,  .       j    ,i  /■,  „•.■     i-co 

„.  .  „f,        ,.       „         .  Z.off(ca,  Exer.  1.,  ed.  Hagae  Comitis,  1(63 — 

ranus,  Ditiputattones  Phnosophicee,  F&n.  i.  qu.  „     ,     V^, . ,         .     -r,  •      nn^    .  .■     -r  .• 

■        '       '  ,^  '.        .  ,„-  Ed.1     D'Abra  de  Raconis,  [Tratiatio   Totita 

Ku.  2,  et  seq.     Compare  DucwstoTU,  p.  138.  „, .,        ..      „     ,    ..    r  t>  .»    „  i  «  >to 

'  ff  Philosophiee,  Praeludia  Logica,  Post.,  c.  i.  p.  4.8, 

4  r/-     T    -I-     J        n     T,T  .     A  .■  T^      cd.  Parisiis,  1640.  —  Ed.] 

8  [G.   J.  Vossius,  De  Nat.  Artium  stve  De  ' 

Logica,  c.  iv]  -  Compare  Alex,  de  Ales,  In         <  See  Zabarella  and  Camerarius,  as  above. 

Metaph.  1.  iv.  t.  5.    "Dialectica  est  inventa  ad      —  Ed.    [Compare  Poncius,  Cursus  Philosophi- 

regulandum  discursum  intellectus  et  rationis;     ct«,  Disp.  i.  qu.  ult.,  p.  48,  2d  ed.  Paris,  1649  ! 


itp^  cl^ai;acter  in  certain  respects;,  but  his  errors  are  insignificant, 
wnen  compared  with  the  total  misapprehension  of  its  nature  by 
l,ocke.  Tl^e  character  of  these  mistakes  I  shall  have  occasion  to 
iliustrate  in  the  sequel;  at  present  I  need  only  say,  that,  while 
those  who,  till  lately,  attempted  to  write  on  I^iogic  in  the  English 
language  were  otherwise  wholly  incompetent  to  the  task,  they,  at 
the  same  time,  either  shared  the  misconceptions  of  its  nature  with 
Xiocke,  or  only  contributed,  by  their  own  hapless  attempts,  to  jus- 
tify the  prejudices  prevalent  against  the  science  which  they  professed 
to  cultivate  and  improve. 

It  would  be  unjust  to  confound  with  other  attempts  of  our  country- 
men in  logical  science  the  work  of  Di\  "V^bately. 

whateiy,- general       rpj^^  author,  if  not  endowed  with  any  high  tal- 

cbaracter  of  his  Ele-  n  ^  ^^  i  •      i  i      • 

j^gjjjg  «  ent  for  philosophical  speculation,  possesses  at 

least  a  sound  and  vigorous  understanding.  He 
unfortunately,  however,  wrote  his  Elements  of  Logic  in  singular 
unacquaintance  with  all  that  had  been  written  on  the  science  in 
a,ncient  and  in  modern  times,  with  the  exception,  apparently,  of  two 
works  of  two  Oxford  logicians,  —  the  Institutio  of  Wallis,  and  the 

Compendium  of  Aldrich,  —  both  written  above 
Aid  '^h  ^  century  ago,  neither  of  them  rising  above  a 

humble  mediocrity,  even  at  the  date'of  its  com- 
position ;  and  Aldrich,  whom  Whateiy  unfortunately  regards  as  a 
safe  and  learned  guide,  had  himself  written  his  book  in  ignorance 
of  Aristotle  and  of  all  the  principal  authors  on  the  science,  —  an 
ignorance  manifested  by  the  grossest  errors  in  the  most  elementary 
parts  of  the  science.  It  is  not,  therefore,  to  be  wondered  at,  that 
the  Elements  of  Whateiy,  though  the  production  of  an  able  man, 
are^so  far  behind  the  advancement  of  the  science  of  which  they 
treat ;  that  they  are  deformed  with  numerous  and  serious  errors ; 
and  that  the  only  recommendation  they  possess,  is  that  of  being  the 
best  book  on  the  subject  in  a  language  which  has  absolutely  no 
other  deserving  of  notice  I* 

i  have  now,  therefore,  to  call  your  attention  lo  Dr.  Whately's 

account   of  t^ie   object-matter   and   domain   of 
Whateiy '8  view  of      Logic.     "The  treatise  of  Dr.  Whateiy,"  says  his 

e  o  jec   ma   er  an  Vice-Princi,pal  and  epitomator  Dr.  Hinds,^  "  dis- 

ci omam  of  Logic  stat-  '        **.    .  -r        €  ' 

e4  and  criticized.  P^ys^  and  i^  is  ^he  .o^ly  oue  that  has  clearly 

done  so,  the  true  nature  and  use  of  Logic ;  so 

that  it  may  be  approached  no  longer  as  a  dark,  curious,  and  merely 

I  See  Dhextssions,  p.    ^,  second   edition,         2  Introduction  to  Logic,  Preface,  p.  vilL  Qjc- 


22  LOGIC.  Lect.  IL 

speculative  study,  such  as  one  is  apt  in  fancy  to  class  with  astrology, 
and  alchemy." 

Let  us  try  whether  this  eulogy  be  as  merited  as  it  is  unmeasured. 
Now,  Dr.  Whately  cannot  truly  be  said  clearly  to  display  the  na- 
ture of  Logic,  because  in  different  passages  he 
Whately  proposes  to      proposes  to   it  different  and  contradictory  ob- 

Losic    different    and         .,  ji  .   ■,  •j^j-i         ^x.      ^ 

^    _,.  ^.  ^       lects ;  and  he  cannot  be  said  to  display  the  true 

contradictory    object-        «*  '  ^  r     .^  ^ 

matter.  nature  of  Logic,  for  of  these  different   objects 

there  is  not  one  which  is  the  true. 
In  several  passages,^  he  says  that  "  the  process  or  operation  of 
reasoning  is  alone  the  appropriate  province  of  Logic."     Now,  this 
statement  is  incorrect  in  two  respects.     In  the  first  place,  it  is  in- 
correct, inasmuch  as  it  limits  the  object-matter  of  Logic  to  that 
part  of  the  Discursive  Faculty  which  is  especially  denominated 
Reasoning.     In  this  view  Logic  is  made  convertible  with  Syllogis- 
tic.    This  is  an  old  error,  which  has  been  fi-equently  refuted,  and 
into  which  Whately  seems  to  have  been  led  by  his  guide  Dr.  Wallia. 
In  the  second  place,  this  statement  is  incorrect,  inasmuch  as  it 
makes  the  process,  or,  as  he  also  calls  it,  the  op- 
The  operation  of  Kea-      eration,  of  reasoning  the  object-matter  of  Logic. 
Boningno      e  o  jec  -      jj^qw    a   definition   which   merely   afiirms   that 

matter   ot    Logic,  as  '  _  _  •' 

Whately  affirms.  Logic  is  the  scieucc  which  has  the  process  of 

reasoning  for  its  object,  is  not  a  definition  of 
this  science  at  all;  it  does  not  contain  the  differential  quality  by 
which  Logic  is  discriminated  from  other  sciences ;  and  it  does  not 
prevent  the  most  erroneous  opinions  (it  even  suggests  them)  from 
being  taken  up  in  regard  to  its  nature.  Other  sciences,  as  Psychol- 
ogy and  Metaphysic,  propose  for  their  object  (among  the  other  fac- 
ulties) the  operation  of  reasoning,  but  this  considered  in  its  veal 
nature :  Logic,  on  the  contrary,  has  the  same  for  its  object,  but  only 
in  its  formal  capacity;  in  fact,  it  has  in  propriety  of  speech  nothing 
to  do  with  the  process  or  operation,  but  is  conversant  only  with  its 
laws.  Dr.  Whately's  definition  is  therefore  not  only  incompetent, 
but  delusive ;  it  would  confound  Logic  and  Psychology  and  Meta- 
physic, and  tend  to  perpetuate  the  misconceptions  in  regard  to  the 
nature  of  Logic  which  have  been  so  long  prevalent  in  this  country. 
_      .  But  Dr.  Whately  is  not  only  wrong  as  meas- 

Whately  erroneous-  •'  -■    ,       • 

ly  and  contradictorily  "'6^  by  a  foreign  Standard,  he  is  wrong  as  meaa- 

makes  Language  the  ured  by  his  own ;  he   is   himself  contradictory, 

adequate   object-mat-  You   have  just    secn  that,  in  some   places,  he 

^'  ■  makes  the  operation  of  reasoning  not  only  the 

principal  but  the  adequate  object  of  Logic.      Well,  in  others  he 

1  See  pp.  1, 18, 140,  third  edition. 


Lect.  n.  LOGIC.  2o 

makes  this  total  or  adequate  object  to  be  language.  But  as  there 
cannot  be  two  adequate  objects,  and  as  language  and  the  opera- 
tion of  reasoning  are  not  the  same,  there  is,  therefore,  a  contradic- 
tion. "In  introducing,"  he  says,  "the  mention  of  language  previ- 
ously to  the  definition  of  logic,  I  have  departed  from  established 
practice,  in  order  that  it  may  be  clearly  understood  that  logic  is 
entirely  conversant  about  language ;  a  truth  which  most  writers  on 
the  subject,  if  indeed  they  were  fully  aware  of  it  themselves,  have 
certainly  not  taken  due  care  to  impress  on  their  readers."^  And 
again :  "  Logic  is  wholly  concerned  in  the  use  of  language."  ^ 

In  our  last  Lecture,  I  called  your  attention  to  the  ambiguity  of 
the  term  Xoyos,  in  Greek,  meaning  ambiguously  either  thought  or  its 
expression;  and  this  ambiguity  favored  the  rise  of  two  counter- 
opinions  in  regard  to  the  object  of  logic ;  for  while  it  was  generally 
and  correctly  held  to  be  immediately  conversant  about  the  internal 
Xoyos,  thought^  some,  however,  on  the  contrary,  maintained  that  it 
was  immediately  conversant  about  the  external  Xoyo9,  language. 
Now,  by  some  unaccountable  illusion.  Dr.  Whately,  in  different 
places,  adopts  these  opposite  opinions,  and  enunciates  them  without 
a  word  of  explanation,  or  without  even  a  suspicion  that  they  are 
contradictory  of  each  other.* 

From  what  I  have  now  said,  you  may,  in  some  degree,  be  able  to 

judge  how  far  credit  is  to  be  accorded  to  the 

The  true  nature  of       assertion,  that  Dr.  Whately  is  the  only  logician 

Logic  more  correctly       ^j^^,  ^^.^^  clearly  displayed  the  true  nature  and 

understood     by     the  /.  t        •  t       ^     ^  i?       •      .1  • 

scholastic  logicians  '^se  of  Logic.  In  fact,  SO  far  is  this  assertion 
than  by  Whately.  from  the  truth,  that  the  object-matter  and  scope 

of  Logic  was  far  more  correctly  understood 
even  by  the  scholastic  logicians  than  by  Dr.  Whately ;  and  I  may 
caution  you,  by  the  way,  that  what  you  may  find  stated  in  the  Ele- 
ments of  the  views  of  the  schoolmen  touching  the  nature  and  end 
of  Logic,  is  in  general  wrong;  in  particular,  I  may  notice  one 
most  erroneous  allegation,  that  the  schoolmen  "  attempted  to  employ 
logic  for  the  purpose  of  physical  discovery." 

But  if,  compared  only  with  the  older  logicians,  the  assertion  of 
Dr.  Hinds  is  found  untenable,  what  will  it  be  found,  if  we  compare 
Whately  with  the  logicians  of  the  Kantian  and  Leibnitian  schools, 
of  whose  writings  neither  the  Archbishop  nor  his  abbreviator  seems 
ever  to  have  heard  ?  And  here  I  may  observe,  that  Great  Britain  is, 
I  believe,  the  only  country  of  Europe  in  which  books  are  written 
by  respectable  authors  upon  sciences,  of  the  progress  of  which,  for 

1  Page  56.  2  Page  74.  3  Besides  most  vague.  —Jotting. 


24  LOGIC.  Lect.  IL 

above  a  century,  they  have  never  taken   the  trouble   to   inform 
themselves. 

The  second  question,  to  which  in  the  Introduction  to  Logic  an 
answer  is  required,  is,  —  What  is  the  Value  or 
Loo-ic  ^  ^  ^  y  °  Utility  of  this  science  ?  Before  proceeding  to 
a  special  consideration  of  this  question,  it  may 
be  proper  to  observe,  in  general,  that  the  real  utility  of  Logic  has 
been  obscured  and  disparaged  by  the  false  utilities  which  have  too 
fi-equently  been  aiTogated  to  it ;  for  when  logic  was  found  unable 
to  accomplish  what  its  unwise  encomiasts  had  promised,  the  recoil 
was  natural,  and  as  it  failed  in  performing  everything,  it  was  lightly 
infen-ed  that  it  coidd  perfonn  nothing.  Both  of  these  extremes  are 
equally  erroneous.  There  is  that  which  Logic  can,  and  there  is  that 
which  Logic  cannot,  perform ;  and,  therefore,  before  attempting  to 
show  what  it  is  that  we  ought  to  expect  from  the  study  of  this 
science,  it  will  be  proper  to  show  what  it  is  that  we  ought  not.  I 
shall  therefore,  in  the  first  place,  consider  its  false  utilities,  and,  in 
the  second,  its  true. 

The  attribution  of  every  false  utility  to  Lo^c  has  arisen  from  er- 
roneous opinions  held  in  regard  to  the  object  of 

utilities    falsely  at-         ,,  .  c^       i  •.  t      i     . 

tributedtoLo  ic  science.     ho  long  as  it  was  supposed  that 

logic  took  any  cognizance  of  the  matter  of 
thought,  —  so  long  as  it  was  not  distinctly  understood  that  the  form 
of  thought  was  the  exclusive  object  of  this  science,  and  so  long  as 
it  was  not  disencumbered  of  its  extraneous  lumber,  —  so  long  must 
erroneous  opinions  have  been  prevalent  as  to  the  nature  and  oomi- 
prehension  of  its  end. 

It  was  accordingly,  in  the  fi^rst  place,  frequently  supposed  that 
Logic  was,  in  a  certain  sort,  an  instrument  of 

As  an  instrument  of  .       ,.^        ,.  rrii        .-.i  /»    >-■> 

.    ...    ,.  scientmc  discovery.      Ihe  title  oi   Orqanoix, — 

scientific  discovery.  •'  if  ~i 

instrument^  —  bestowed  on  the  collectioh  we 
possess  of  the  logical  treatises  of  Aristotle,  contributed  to  this  ei^ 
ror.  These  treatises,  as  I  observed,  are  but  a  few  of  the  many  writ- 
ings of  the  Stagirite  on  Logic,  and  to  him  we  owe  neither  the  order 
in  which  they  stand  arranged,  nor  the  general  name  under  whicli 
they  are  now  comprehended.*  In  later  times,  these  treatises  were 
supposed  to  contain  a  complete  system  of  Logic,  and  Logic  was 
viewed  as-  the  organ  not  only  of  Pliilosophy,  but  of  the  sciences  in 
general.  Thus  it  was  that  Logic  obtained  not  only  the  name  of  in- 
strument^ or  instrumental  philosophy^  but  many  other  high-sound- 

1  See  Brandis  AristoteUs,  seine  akac/emis:hfn      140.    Trendelenburg,   EletTunta  Log.  AmtoC, 
Zeitgenossen  und  n'dchsten  Nachfalgery  P.  i.  p.      p.  38.— Ed. 


liECT.  n.  LOGIC.  25 

ing  titles.  It  was  long  generally  styled  the  Art  of  arts  and  Sci- 
ettce  of  sciences.  "  Logica,"  says  Scotus,  "  est  ars  artiuiu  et  scien- 
tia  scientiarum,  qua  aperta,  omnes  aliae  aperiuntur;  et  qua  clausa, 
omnes  aliae  clauduntur ;  cum  qua  quaelibet,  sine  qua  nulla."  ^  In 
modern  times,  we  have  systems  of  this  science  under  the  titles  of 
Via  adVeritatem^ —  Gynosura  Veritatis^ —  Caput  et  Apex  Philos- 
ophim^  —  Heuristica,  sive  Introductio  ad  Artem  Inveniendi^  etc. 
But  it  was  not  only  viewed  as  an  instrument  of  discovery,  it  was 
likewise  held  to  be  the  infallible  corrector  of  our 

As  the  corrector  of         •    j.   n      ^       i       •  ^i,       •       •  a.  c  '    a.   ^ 

.     „        ,   .  intellectual  vices,  the  invisforator  of  our  intel- 

intellectual  vices.  ... 

lectual  imbecility.  Hence  some  entitled  their 
Logics,  The  Medicine  of  the  Mind^  The  Art  of  Thinking^  The 
Lighthouse  of  the  Intellect^  The  Science  teaching  the  Right  Use 
•  of  Measo7i^  etc.,  etc.  Now,  in  all  this  there  is  a  mixture  of  truth 
and  error.  To  a  certain  extent,  and  in  certain  points  of  view.  Logic 
is  the  organ  of  philosophy,  the  criterion  of  truth,  and  the  corrector 
of  error,  and  in  others  it  is  not. 

In  reference  to  the  dispute,  whether  logic  may  with  propriety  be 

called  the  instrument^  the  organon  of  the  other 

In  what  respect  Logic      scicHces,  the  question  may  be  at  once  solved  by 

is  an  instrument  of  the  t.>..        •  r\  •  i  i    t     i 

„„.„„„„  a  distinction.     One  science  may  be  stvled  the 

instrument  of  another,  either  in  a  material  or  in 
a  formal  point  of  view.  In  the  former  point  of  view,  one  science  is 
the  organ  of  another  when  one  science  determines  for  another  its 
contents  or  objects.  Thus  Mathematics  may  be  called  the  material 
instrument  of  the  various  branches  of  physical  science  ;  Philology  — 
or  study  of  the  languages,  Latin,  Greek,  Hebrew,  Chaldee,  etc., 
with  a  knowledge  of  their  relative  history  —  constitutes  a  material 
instrument  to  Christian  Theology;  and  the  jurist,  in  like  manner, 
finds  a  material  instrument  in  a  knowledge  of  the  history  of  the 
country  whose  laws  he  expounds.^"    Thus,  also.  Physiology,  in  a 

\  MnMritii    JBxpositio     QueBstionum    Doctoris         5  Gunner,  Ars  Heuristica  Intelleclvalis,  Lip- 

Subtilis  in  quinque  Universalia  Porphyrii,  Quaest.  sise,  1756.     Traltato  di  Messer  Sebasliano  Erizzo, 

i.   {Scoti    Opera,   Lugd.   1639,  torn.  i.  p.  434.)  deW  Instrumento  et  Via  Inventrice  de  gli  antichi 

Mauritius  refers  to  St.  Augustin  as  his  author-  nelle  scientie,  Venice,  1554.  —  Ed. 
ity  for  the  above  quotation.    It  slightly  re-         6  Tschirnhausen,  Medicina  Mentis,  sive  Arlis 

sembles  a  passage  in  the  De  Ordine,  1.  ii.  c.  13.  Inveniendi    Prcecepta     Generalia,   Amst.    1687.  y 

—  Ed.  Lange,  Medicina  Mentis,  Hal%,  1703.  —  Ed. 

2  Gundliug,  Via  ail  Veritatem  Moralem,  Ha-         7  L'Art  de  Penser,  commonly  known  as  the   / 
Jje,  1713.      Daries,  Via  ad    Veritatem,  Jenae,  Port  Royal  Logic.    Several  other  works  have 
1764  (2d  edit).  —Ed.  appeared  under  the  same  title.  —  Ed. 

3  P,  Laurembergiug,  Cynosura  Bona  Mentis  ,       8  Grosserus,    P/tarus    intellecttts,  sive   Logica 
».  Logica  Rostoch,  1633.    R.  Loenus,  Cynosura  Electiva,  Lips.,  1697.  —Ed. 

Rationis,  Arnhem,  1667.  —  Ed.  ^  9  Watts,  Logic,  or  the  Right  Use  oj  Reason.  -~^ 

4  See  Krujr,  Logik,.^  9,  p.  23,  from  whom      Ed. 

several  of  the  above  definitions  were  probably         10  See  Genovesl,  p.  41,  [Elementorum  Artis 
taken.  —  Ed.  Logica  ■  Oitica  Libri  T. ,  1 .  i.  C.  iii.  —  Ed.] 

4 


26  LOGIC.  Lect.  li. 

material  point  of  view,  is  the  organon  of  medicine ;  Aristotle  has 
indeed  well  said,  that  medicine  begins  where  the  philosophy  of 
nature  leaves  oiF.^  In  the  latter  point  of  view,  one  science  is  the 
organon  of  another,  when  one  science  determines  the  'scientific 
form  of  another.  Now,  as  it  is  generally  admitted  that  Logic 
stands  in  this  relation  to  the  other  sciences,  as  it  appertains  to 
Logic  to  consider  the  general  doctrine  of  Method  and  of  sys- 
tematic construction,  in  this  respect  Logic  may  be  properly 
allowed  to  be  to  the  sciences  aii  instrument,  but  only  a  formnl 
instrument.^ 

In  regard  to  the  other  titles  of  honor.  Logic  cannot  with  pro- 
priety be   denominated   a   [Heuretic    or]    Art 

ogic  not  proper  y       ^^  Discoverv.     "  For  discoverv  or  invention  is 

an   art  of  discovery.  •'  •' 

not  to  be  taught  by  rules,  but  is  either  the 
free  act  of  an  original  genius,  or  the  consequence  of  a  lucky  acci- 
dent, which  either  conducts  the  finder  to  something  unknown,  or 
gives  him  the  impulse  to  seek  it  out.  Logic  can  at  best  only  analyt- 
ically teach  how  to  discover,  that  is,  by  the  development  and  dis- 
memberment of  what  is  already  discovered.  By  this  process  there 
is  nothing  new  evolved,  and  our  knowledge  is  not  amplified ;  all 
that  is  accomplished  is  a  cleai-er  and  disrtncter  comprehension  of 
the  old ;  our  knowledge  is  purified  and  systematized."  ^  It  is 
well  observed  by  Antonius,  in  Cicero :  "  Nullum  est  praeceptum 
in  hac  arte  quomodo  verum  inveniatur,  sed  tantum  est,  quomodo 
judicetur."^  Logic  is  thus  not  creative;  it  is  only  plastic,  only 
formative,  in  relation  to  our  knowledge. 

Again:  "Logic  cannot  with  propriety  be  styled  the  medicine  of 

the  mind,  at  least  without  some  qualifying  ad- 
in  what  sense  Logic      jectivc,  to  sliow  that   the  Only  remedy  it  can 

can  be  styled  the  med-  ,      .  c  ^  i  -i  •   i 

icine  of  the  mind.  ^PPv  ^^  *o  our  lormai  errors,  while  our  matenal 

errors  lie  beyond  its  reach.  This  is  evident. 
Logic  is  the  science  of  the  formal  laws  of  thought.  But  we  cannot, 
in  limiting  our  consideration  to  the  laws  of  formal  thinking,  investi- 
gate the  contents,  —  the  matter  of  our  thought.  Logic  can,  there- 
fore, only  propose  to  purge  the  understanding  of  those  errors  which 
lie  in  the  confusion  and  perplexities  of  an  inconsequent  thinking. 
This,  however,  it  must  be  confessed,  is  no  radical  cure,  but  merely  a 
purification  of  the  understanding.  In  this  respect,  however,  and  to 
this  extent.  Logic  may  justly  pretend  to  be  the  medicine  of  the 

1  De  Sensn  et  Sensili,  c.  i.  3  Krug,  Logik,  J  9,  p.  24.  —  Ed.    Cf.  [Rich* 

2  Krug,  Logik,  §  9,  p.  23:  Cf.  Platner,  Philo-      ter,  Logik,  p.  83  et  seq.] 
iophische  Aphorismen,  I't.  i,  p.  23,  ed.  1793.— Ed.         <  De  Oratore,  ii.  38.  —  Ed. 


Lect.  n.  LOGIC.  27 

mind,  and  may  therefore,  in  a  formal  relation,  be  styled,  as  by  some 
logicians  it  has  in  fact  been,  Catharticon  intellectus. 

"  By  these  observations  the  value  of  Logic  is  not  depreciated ; 
they  only  prepare  us  to  form  an  estimate  of  its  real  amount.  Pre- 
cisely, in  fact,  as  too  much  was  promised  and  expected  from  thi* 
study,  did  it  lose  in  credit  and  esteem."  ^ 

1  Krug,  Logik,  s  9,  pp.  24-6.  —  Ed.    Cf.  tBichter,  Logik,  p.  86.] 


LEGTUBE    III. 

INTRODUCTION. 

LOGIC —  n.  ITS    UTILITY  — III.  ITS    DIVISIONS  — SUBJECTIVE 
AND    OBJECTIVE  —  GENEKAL    AND    SPECIAL. 

The  last  Lecture  was  occupied  with  the  consideration  of  the 
latter  part  of  the  introductory  question, — What 

BecapitulatioD.  -x-r.  iii  /.i\.  n. 

IS  Logic  r  and  with  that  of  the  nrst  part  oi  the 
second,  —  What  is  its  Utility  ?  In  the  Lecture  preceding  the  last, 
I  had  given  the  definition  of  Logic,  as  the  science  of  the  laws  of 
thought  as  thought,  and,  taking  the  several  parts  of  this  definition, 
had  articulately  explained,  1°,  What  was  the  meaning  and  history 
of  the  word  Logic ;  2°,  What  Avas  the  import  of  the  term  science^ 
the  genus  of  Logic ;  and,  3°,  What  was  signified  by  laws  of  thought 
as  thought,  the  object-matter  of  Logic,  This  last  I  had  considered 
under  three  heads,  explaining,  1°,  What  is  meant  by  thought ;  2°, 
What  is  meant  by  thought  as  thought ;  and,  3°,  What  is  meant  by 
laws  of  thought  as  thought.  It  was  under  the  last  of  these  heads 
that  the  last  Lecture  commenced.  I  had,  in  the  preceding,  shown 
that  the  form  of  thought  comprises  two  kinds  of  phenomena,  given 
always  in  conjunction,  but  that  we  are  able  by  abstraction  and 
analysis  to  discriminate  them  from  each  other.  The  one  of  these 
classes  comprehends  what  is  contingent,  the  other  what  is  necessary, 
in  the  manifestations  of  thought.  The  necessary  element  is  the 
peculiar  and  exclusive  object  of  Logic;  whereas  the  phaenomena  of 
thought  and  of  mind  in  general  are  indiscriminately  proposed  to 
Psychology.  Logic,  therefore,  I  said,  is  distinguished  from  the 
other  philosophical  sciences  by  its  definition,  as  the  science  of  the 
necessary  form  of  thought.  This,  however,  though  a  full  and  final 
definition,  is  capable  of  a  still  more  explicit  enunciation;  and  I 
showed  how  we  are  entitled  to  convert  the  term  necessary  into  the 
term  laws;  and,  in  doing  so,  I  took  the  opportunity  of  explaining 
how,  the  necessity  of  a  mental  element  being  given,  there  is  also 
implicitly  given  the  four  conditions,  1°,  That  it  is  subjective;  2°, 
That  it  is  original ;  3°,  That  it  is  universal ;  and,  4°,  That  it  is  a 
law.     The  full  and  explicit  definition  of  Logic,  therefore,  is,  —  the 


Lkct.  III.       ■  LOGIC.  29 

science  of  the  Laws  of  Thought  as  Thought;  or,  the  science  of  the 
Laws  of  the  Foi-m  of  Thought ;  or,  the  science  of  the  Formal  Laws 
of  Thought; — these  being  only  three  various  expressions  of  what 
is  really  the  same. 

Logic  being  thus  defined,  I  gave  a  brief  and  general  retrospect 
of  the  history  of  opinion  in  regard  to  the  proper  object  and  domain 
of  Logic,  and  showed  how,  though  most  logicians  had  taken,  specu- 
latively and  in  general,  a  very  correct  view^  of  the  nature  of  their 
science,  they  had  not  c'arried  this  view  out  into  application,  by 
excluding  from  the  sphere  of  Pure  and  Abstract  Logic  all  not 
strictly  relative  to  the  form  of  thought,  but  had  allowed  many 
doctrines  relative  merely  to  the  matter  of  thought  to  complicate 
'arid  to  deform  the  Science. 

I  then  called  attention  to  the  opinions  of  the  author  whom  I 
recommend' to  your  attention,  and  showed  that  Dr.  Whately,  in  his 
statements  relative  to  the  object-matter  of  Logic,  is  ' vague  sin d 
obscure,  erroneous  and  self-contradictory;  and  that  so  far  from 
being  entitled  to  the  praise  of  having  been  the  only  logician  who 
has  clearly  displayed  the  true  nature  of  the  science,  on  the  contrary, 
in  the  exposition  of  this  nature,  he  is  far  inferior,  not  only  in  per- 
spicuity and  precision,  but  in  truth,  to  the  logicians  of  almost  every 
age  and  country"  except  our  own. 

And  here,  taking  a  view  of  what  we  have  already  established, 
I  would  interpolate  some  observations  which  I 

Observations  inter-       ought  in  my  last  Lecture  to  have  made,  before 

posed  relative  to  the         <         ,        .  .  i_  •  i         ^.  /.  .i        j?     ^  x- 

„,.   .     .        leavmg  the  consideration  oi  the  nrst  question, 

question,  —  n  hat      is  ^     °  _  ^ 

Logic?  — viz.,  What  is  Logic  ?     Logic,  we  have  seen,  is 

exclusively  conversant  about  thought,  —  about 
thought  considered  strictly  as  the  operation  of  Comparison,  or  the 
faculty  of  Relations  ;  and  thought,  in  this  restricted  signification,  is 
the  cognition  of  any  mental  object  by  another  in  which  it  is  consid- 
ered as  included  ;^  in  other  words,  thought  is  the  knowledge  of 
.-,  things  under  conceptions.    By  the  way,  I  would 

The  terms  Conception         t  x  i  i  a*  xi 

_,  „  here  pause  to  make  an   observation  upon  the 

and  Concept.  ^  ^ 

word  cofiception,  and  to  prepare  you  for  the  em- 
ployriient  of  a  term  which  I  mean  hereafter  to  adopt.  You  are 
aware,  from  what  I  have  already  said,  that  I  do  not  use  conception 
in  the  signification  in  which  it  is  applied  by  Mr.  Stewart.  He 
usurps  it  in  a  very  limited  meaning,  in  a  meaning  which  is  peculiar 
to  himself,  —  viz.,  for  the  simple  and  unmodified  representation  of 
an  object  presented  in  Perception.'  Reid,  again,  vacillates  in  the 
signification  he  attaches  to  this  term,  —  using  it  sometimes  as  a 

1  See  Lectures  on  Metaphysics,  lect.  xxxiii.  p.  452.  — Ed. 


so  LOGIC.  Lect.  m. 

synonym  for  Imagination,  sometimes  as  comprehencling  not  only 

Imagination,  but  Undei-standing  and  the  object  of  Understanding.^ 

It  is  in  the  latter  relation  alone  that  I  ever  em- 

Author-s employment         .       •     ^^^  ^j^j^  -^  -^^  correct  and  genuine  signi- 

of  these  terms.  i 

fication,  whether  we  regard  the  derivation  of 
the  word,  or  its  general  use  by  philosophers.  Conception,  in  English, 
is  equivalent  to  conceptio  and  concepUis  in  Latin ;  and  these  terms, 
by  the  best  philosophei-s,  and  the  most  extensive  schools,  have  been 
employed  as  synonymous  for  notion  (notio),  the  act  or  object  of  the 
Understanding  Propei*,  or  Faculty  of  Relations.  So  far,  therefore, 
you  are  sufficiently  prepared  not  to  attribute  to  the  word  conception, 
when  you  hear  it  from  me,  the  meaning  which  it  bears  in  the  philo- 
sophical writings  with  which  you  are  most  likely  to  be  familiar. 
What  is  the  precise  meaning  of  the  term  will  be  soon  fully  ex- 
plained in  its  proper  place,  wben  we  commence  the  treatment  of 
Logic  itself.  But  what  I  principally  pause  at  present  to  say  is  — 
that,  for  the  sake  of  perspicuity,  I  think  it  necessary,  in  reference  to 
this  word,  to  make  the  following  distinction.  The  term  conception, 
like  perception,  imagination,  etc.,  means  two  things,  or  rather  the 
same  thing  in  two  different  relations,  —  relations,  however,  which  it 
is  of  great  importance  to  distinguish,  and  to  mark  the  distinction 
by  the  employment  of  distinct  words.  Conception  means  both  the 
act  of  conceiving,  and  the  object  conceived;  a?,  perception,  both  the 
act  of  perceiving,  and  the  thing  perceived;  imagination,  both  the 
act  of  imagining,  and  what  is  imagined.  Now,  this  is  a  source  of 
great  vagueness  in  our  philosophical  discussions :  have  we  no  means 
of  avoiding  this  inconvenience?  I  think  we  have;  and  that,  too, 
without  committing  any  violence  upon  language.  I  would  propose 
the  following  distinction  :  For  the  act  of  conceiving,  the  tenn  con- 
ception should  be  employed,  and  that  exclusively ;  while  for  the 
object  of  conception,  or  that  which  is  conceived,  the  term  concept 
should  be  uscd.^  Concept  is  the  English  of  the  Latin  conceptum, — 
id  quod  conceptum  est,  —  and  had  it  no  vested  right  as  an  actual 
denizen  of  the  language,  it  has  good  warrant  for  its  naturalization. 
There  are  a  thousand  words  in  English  formed  on  precisely  the 
same  analogy,  as  precept,  digest,  etc.,  etc.  But  we  have  no  occasion 
to  appeal  to  analogy.  The  term  concept  was  in  common  use  among 
the  older  philosophical  writers  in  English,^  though,  like  many  other 
valuable  expressions  of  these  authors,  it  has  been  overlooked  by  our 

1  See  Leetttres  on  Metaphysics,  lect.  xxxiii.  p.  intellijjendi."  See  Occam,  In  Sent.,  1.  1.  d.  2, 
452.  —  Ed.  qu.  8;  and  Biel,  1.  i.  d.  3,  q.  5] 

2  See  Biel,  [  la  Sent.,  1.  i.  dist.  2,  qu.  8;  1.  ii.  3  See  Zacliary  Coke,  Art  of  Logiek.  London 
Uist.  2,  qu.  2  By  Occam  and  most  others,  1654,  pp.  11,  101,  et  alibi;  Gideon  Harvey, 
eonceptus  is  used  as  "  id  quod  terminat  actum  Archelogia  Phiiosophica  Nova,  or  New  PrincipUi 


LecT.  in.  LOGIC.  31 

English  lexicographers.  I  may  add,  that  nearly  the  same  fortune 
has  befallen  the  tei-m  in  French.  Concept  was  in  ordinary  use  by 
the  old  French  philosophers,  but  had  latterly  waxed  obsolete.  It 
has,  however,  I  see,  been  reinstated  in  its  rights  since  the  reawaken- 
ing of  philosophy  in  France ;  and,  in  particular,  it  is  now  employed 
in  that  language  in  translating  from  the  German  the  term  Begriff. 
I  shall,  therefore,  make  no  scruple  in  using  the  expression  concept 
for  the  object  of  conception,  and  conception  I  shall  exclusively  em- 
ploy to  designate  the  act  of  conceiving.  Whether  it  might  not,  in 
like  manner,  be  proper  to  introduce  the  term  percept  for  the  object 
of  perception,  I  shall  not  at  present  inquire. 

But  to  return  from  this  digression.  Logic,  we  have  seen,  is  ex- 
clusively conversant  about  thought  strictly  so 

Analogy  between  denominated,  and  thought  proper,  we  have  seen, 
Logic  and  Mathemat-  jg  ^hg  cognition  of  One  objcct  of  thought  by  an- 
other, in  or  -under  which  it  is  mentally  included  ; 
—  in  other  words,  thought  is  the  knowledge  of  a  thing  through  a 
concept  or  general  notion,  or  of  one  notion  through  another.  In 
thought,  all  that  we  think  about  is  considered  either  as  something 
containing,  or  as  something  contained;  —  in  other  words,  every  pro- 
cess of  thought  is  only  a  cognition  of  the  necessary  relations  of  our 
concepts.  This  being  the  case,  it  need  not  move  our  wonder  that 
Logic,  within  its  proper  sphere,  is  of  such  irrefragable  certainty, 
that,  in  the  midst  of  all  the  revolutions  of  philosophical  doctrines, 
it  has  stood  not  only  unshattered  but  unshaken.  In  this  respect. 
Logic  and  Mathematics  stand  alone  among  the  sciences,  and  their 
peculiar  certainty  flows  from  the  same  source.  Both  are  conversant 
about  the  relations  of  certain  a  priori  forms  of  intelligence:  — 
Mathematics  about  the  necessary  forms  of  Imagination;  Logic  about 
the  necessary  forms  of  Understanding ;  Mathematics  about  the  re- 
lations of  our  representations  of  objects,  as  out  of  each  other  in 
space  and  time ;  Logic  about  the  relations  of  our  concepts  of  ob- 
jects, as  in  or  under  each  other,  that  is,  as,  in  different  relations, 
respectively  containing  and  contained.  Both  are  thus  demonstra- 
tive or  absolutely  certain  sciences  only  as  each  develops  what  is 
given  —  what  is  given  as  necessary,  in  the  mind  itself.  The  laws 
of  Logic  are  grounded  on  the  mere  possibility  of  a  knowledge 
through  the  concepts  of  the  Understanding,  and  through  these  we 
know  only  by  comprehending  the  many  under  the  one.  Concern- 
ing the  nature  of  the  objects  delivered  by  the  Subsidiary  Faculties 

of  Philosophy.    Lend.  1663,  P.  i.,  b.  ii.,  c.  4,  p.      Baynes,  New  Analytic  of  Logical  Forms,  pp.  5 
22.    For  several  authorities  for  the  use  of  this     6,  note.  —  Ed. 
term  among  the  older  English  logicians,  see 


82  LOGIC.  Lect.  Ill 

to  the  Elaborative,  Logic  pronounces  nothing,  but  restricts  its  con- 
sideration to  the  laws  according  to  which  tlieir  agreement  or  disa- 
greement is  affirmed.* 

It  is  of  itself  manifest  that  every  science  must  obey  the  laws  of 

Logic.      If  it  does  not,  such  pretended  science 

Logic  is  the  negative       j^  ^^^  founded  ou  reflection,  and  is  only  an  irra- 

condition  of  tratn.  .  ah-/. 

tional  absurdity.  All  inference,  evolution,  con- 
catenation, is  conducted  on  logical  principles  —  principles  which 
are  ever  valid,  ever  imperative,  ever  the  same.  But  an  extension 
of  any  science  through  Logic  is  absolutely  impobsible ;  for  by  con- 
forming to  logical  canons  we  acquire  no  knowledge  —  receive  noth- 
ing new,  but  are  only  enabled  to  render  what  is  already  obtained 
more  intelligible,  by  analysis  and  arrangement.  Logic  is  only  the 
negative  condition  of  truth.^  To  attempt  by  a  mere  logical  knowl- 
edge to  amplify  a  science,  is  an  absurdity  as  great  as  if  we  should 
attempt  by  a  knowledge  of  the  grammatical  laws  of  a  language  to 
discover  what  was  written  in  this  language,  without  a  perusal  of  the 
several  writings  themselves.  But  though  Logic  cannot  extend, 
cannot  amplify  a  science  by  the  discovery  of  new  facts,  it  is  not  to 
be  supposed  that  it  does  not  contribute  to  the  progress  of  science. 
The  ])rogress  of  the  sciences  consists  not  merely  in  the  accumulation 
of  new  matter,  but  likewise  in  the  detection  of  the  relations  subsist- 
ing among  the  materials  accumulated ;  and  the  reflective  abstraction 
by  which  this  is  eflfected,  must  not  only  follow  the  laws  of  Logic, 
but  is  most  powerfully  cultivated  by  the  habits  of  logical  study. 
In  these  intercalary  observations  I  have,  however,  insensibly  en- 
croached upon  the  second  question, — What  is  the  Utility  of  Logic? 
On  this  question  I  now  dictate  the  following  paragraph  : 

%  IV.  As  the  rules  of  Logic  do  not  regard  the  matter  bat* 

only  the  form  of  thought,  the  Utility  of 

Pap.  IV.   utuity  of      Logic  must,  in  like  manner,  be  viewed  as 
Logic.  ,.    ®     ,  .       .    ^ 

limited  to  Its  influence  on  our  mnnror  of 

thinking,  and  not  sought  for  in  any  effect  it  can  exert  upon 

what  M'e  think  about.     It  is,  therefore,  in  the  first  place,  not  to 

be  considered  useful  as  a  Material  Instrument,  that  is,  as  a  mean 

of  extending  our  knowledge  by  the  discovery  of  new  truths ; 

but  merely  as  a  Formal  Instrument,  that  is.  as  a  mean  by  which 

knowledge,  already  acquired,  may  be  methodized  into  the  form 

accommodated  to  the  conditions  of  our  understanding.     In  the 

.•■econd  place,  it  is  not  to  be  regarded  as  a  JMedicino  of  the  minfl 

1  Cf.  Bachmann,  LoyiJc,  Einlcitung,  §  20.  2  [AnoilloD,  Esitais  Philosnp/uques,  t.  iL  p 

Edit.  1828. —Ed.  291.] 


lect.  m. 


L  0  r.  I  c .  33 


to  the  extent  of  reniedyino:  the  vnrious  errors  which  originate 
in  the  nature  of  the  objects  of  our  knowledge,  but  merely  to 
the  extent  of  purging  the  mind  of  those  errors  which  arbe 
from  inconsequence  and  confusion  in  thinking.* 

Logic,  however,  is  still  of  eminent  utility,  not  only  as  presenting 
to  us  the  most  interesting  object  of  contemplation  in  the  mechanism 
of  human  thought,  but  as  teaching  how,  in  many  relations,  to  dis- 
criminate truth  from  error,  and  how  to  methodize  our  knowledge 
into  system  ;  while,  at  the  same  time,  in  turning  the  mind  upon 
itself,  it  affords  to  our  higher  faculties  one  of  their  most  invigorating 
exercises.  Another  utility  is,  that  Logic  alone  affords  us  the  means 
requisite  to  accomplish  a  rational  criticism,  and  to  communicate  its 
results. 

What  is  now  summarily  stated  in  the  preceding  paragraph,  I 
illustrated,  in  my  last  Lecture,  in  detail,  —  in  so  far  as  it  was  requis- 
ite to  disencumber  the  real  value  of  our  science  from  those  false 
utilities  which,  in  place  of  enhancing  its  worth  in  the  opinion  of 
the  world,  have,  in  fact,  mainly  contributed  to  reduce  the  common 
estimate  of  its  importance  far  beneath  the  truth.  I  now  proceed 
to  terminate  what  I  have  to  say  under  this  head  by  a  few  words,  in 
exposition  of  what  renders  the  cultivation  of  Logic  —  of  genuine 
logic  —  one  of  the  most  important  and  profitable  of  our  studies. 

"  Admitting,  therefore,  that  this  science  teaches  nothing  new, — 

that  it  neither  extends  the  boundaries  of  knowl- 

Logic  gives  us,  to  a      ^^       j^^^  unfolds  the  mysterics  which  lie  beyond 

certain  extent,  domin-  n      i  n        •  r         i^ 

ion  over  our  thoughts.  ^^^  compass  of  the  reflective  intellect,  —  and 
that  it  only  investigates  the  immutable  laws  to^ 
which  the  mind  in  thinking  is  subjected,  still,  inasmuch  as  it  devel- 
ops the  application  of  these  laws,  it  bestows  on  us,  to  a  certain  ex- 
tent, a  dominion  over  our  thoughts  themselves.  And  is  it  nothing 
to  watch  the  secret  workshop  in  which  nature  fabricates  cognitions 
and  thoughts,  and  to  penetrate  into  the  sanctuary  of  self-conscious- 
ness, to  the  end  that,  having  learnt  to  know  ourselves,  we  may  be 
qualified  rightly  to  understand  all  else?  Is  it  nothing  to  seize  the 
helm  of  thought,  and  to  be  able  to  turn  it  at  our  will  ?  For,  through 
a  research  into  the  laws  of  thinking,  Logic  gives  us,  in  a  certain: 
sort,  a  possession  of  the  thoughts  themselves.  .  It  is  true,  indeed,, 
that  the  mind  of  man  is,  like  the  universe  of  matter,  governed  by 
eternal  laws,  and  follows,  even  without  consciousness,  the  invari- 
able canons  of  its  nature.     But  to  know  and  understand  itself  and 

1  Cf.  Krug,  Logik,  i  9.  —  Ed. 
5 


34  LOGIC.  lect.  in. 

out  of  the  boundless  chaos  of  phaenomena  presented  to  the  senses 
to  form  concepts,  through  concepts  to  reduce  that  chaos  to  harmony 
and  arrangement,  and  thus  to  establish  the  dominion  of  intelligence 
over  the  universe  of  existence,  —  it  is  this  alone  which  constitutes 
man's  grand  and  distinctive  preeminence."^  "Man,"  says  the  great 
Pascal,  "is  but  a  reed,  —  the  very  frailest  in  nature ;  but  he  is  a  reed 
that  thinks.  It  needs  not  that  the  whole  universe  should  arm  to 
crush  him.  He  dies  from  an  exhalation,  from  a  drop  of  water.  But 
should  the  universe  conspire  to  crush  him,  man  would  still  be  nobler 
than  that  by  which  he  falls ;  for  he  knows  that  he  dies;  and  of  the 
victory  which  the  universe  has  over  him,  the  universe  knows  noth- 
ing.    Thus  our  whole  dignity  consists  in  thought Let 

us  labor,  then,  to  think  aright;  this  is  the  foundation  of  morality."  ■^ 

In  the  world  of  sense,  illusive  appearances  hover  around  us  like 

evil  spirits ;    unreal  dreams  mingle  themselves 

Supplies  in  part  the       ^-^.j^  ^^^^  knowledge;  the  accustomed  assumes 

criterion  of  truth  from  /,  .  .,     ,  .      . 

^^j.^j.  the  character  oi  certainty ;  and  the  associations 

of  thought  are  mistaken  for  the  connections  of 
existence.  We  thus  require  a  criterion  to  discriminate  truth  from 
error ;  and  this  criterion  is,  in  part  at  least,  supplied  to  us  by  Logic. 
Logic  teaches  us  to  analyze  the  concrete  masses  of  our  knowledge 
into  its  elements,  and  thus  gives  us  a  clear  and  distinct  apprehension 
of  its  parts,  it  teaches  us  to  think  consistently  and  with  method,  and 
it  teaches  us  how  to  build  up  our  accumulated  knowledge  into  a  firm 
and  harmonious  edifice.^  "  The  study  of  logic'  is  as  necessary  for 
correct  thinking,  as  the  study  of  grammar  is  for  correct  speaking ; 
were  it  not  otherwise  and  in  itself  an  interesting  study  to  inves- 
tigate the  mechanism  of  the  human  intellect  in  the  marvellous 
processes  of  thought.  They,  at  least,  who  are  familiar  with  this 
mechanism,  are  less  exposed  to  the  covert  fallacies  which  so  easily 
delude  those  unaccustomed  to  an  analysis  of  these  processes."* 
But  it  is  not  only  by  aflfording  knowledge  and  skill  that  Logic  is 
thus  useful ;  it  is  perhaps  equally  conducive  to 
nv  gora  es    e    n-      ^j^^  same  end  by  bestowing  power.     The  retor- 

derstanding.  _  •'  or 

sion  of  thought  upon  itself —  the  thinking  of 
thought  —  is  a  vigorous  effort,  and,  consequently,  an  invigorating 
exercise  of  the  Undei*standing ;  and  as  the  understanding  is  the  in- 
strument of  all  scientific,  of  all  philosophical,  speculation.  Logic,  by 
preeminently  cultivating  the  understanding,  in  this  respect  likewise 

1  [Heinrich  Richter],  [  W?r   den  Gegenstand  FaugAre.)     Compare    Discusfiom,    p.   811.— 

und  den  Vmfang  der  Logik,  pp.  3,  4,  Leipsio,  Ed. 

1825.  —  Ed.  ]  3  Cf.  Richter,  Logik,  pp.  6,  6, 12.  —  El> 

V  Pensies,  P.  1.  art.  iv.  }  6,  (vol.  ii.  p.  84.  ed.  4  Krug,  Logik,  (  9,  p.  26.  —  £d. 


LrcT.  m.  LOGIC.  35 

vindicates  its  ancient  title  to  be  viewed  as  the  best  preparatory  dis- 
cipline for  Philosophy  and  the  sciences  at  large. 

There  is,  however,  one  utility  which,  though  of  a  subordinate 
kind,  I  must  not  omit,  though  I  do  not  remember  to  have  seen  it  in- 
sisted on  by  any  logical  writer.  In  reference  to  this,  I  give  you  the 
following  paragraph : 

f  V.  But  Logic  is  further  useful  as  affording  a  Nomenclature 
of  the  laws  by  which  legitimate  thinking 

Par.    V.     Utility    of  . 

Logic, -as  affording       is  govemcd,  and  of  the  violation  of  these 
a  Bcientiflc  nomenoia-       \siws,  throug^h  which  thought  bccomes  vicious 

ture.  - 

or  null. 

Illustration.  It  is  Said,  in  Hudibras,* — 

"  That  all  a  Rhetorician's  rules 
Serve  only  bat  to  name  his  tools ;  " 

and  it  may  be  safely  confessed  that  this  is  one  of  the  principal  utili- 
ties of  Rhetoric.  A  mere  knowledge  of  the  rules  of  Rhetoric  can 
no  more  enable  us  t^o  compose  well,  than  a  mere  knowledge  of  the 
rules  of  Logic  can  enable  us  to  think  well.  There  is  required  from 
nature,  in  both,  the  faculty ;  but  this  faculty  must,  in  both  depart- 
ments, be  cultivated  by  an  assiduous  and  also  a  well-directed  exer- 
cise; that  is,  in  the  one,  the  powers  of  Comparison  must  be  ex- 
ercised according  to  the  rules  of  a  sound  Rhetoric,  in  the  other, 
according  to  the  rules  of  a  sound  Logic. '  In  so  far,  therefore,  the 
utility  of  either  science  is  something  more  than  a  mere  naming  of 
their  tools.  But  the  naming  of  their  tools, 
mportance  o  a  sci-       though  in  itself  of  little  valuc,  is  valuable  as  the 

enfinc  nomenclature.  °  ^  '  _ 

condition  of  an  important  function,  which,  with- 
out this,  could  not  be  performed.  Words  do  not  give  thoughts;  but 
without  words,  thoughts  could  not  be  fixed,  limited,  and  expressed. 
They  are,  therefore,  in  general,  the  essential  condition  of  all  think- 
ing, worthy  of  the  name.  Now,  what  is  true  of  human  thought  in 
general,  is  true  of  Logic  and  Rhetoric  in  particular.  The  nomencla- 
ture in  these  sciences  is  the  nomenclature  of  certain  general  analy- 
ses and  distinctions,  which  express  to  the  initiated,  in  a  single  word, 
what  the  uninitiated  could  (supposing — what  is  not  probable  — 
that  he  could  perform  the  relative  processes)  neither  understand  nor 
express  without  a  tedious  and  vague  periphrasis ;  while,  in  his  hands, 
it  would  assume  only  the  appearance  of  a  particular  observation,  in- 
stead of  a  particular  instance  of  a  general  and  acknowledged  rule. 
To  take  a  very  simple  example  :  there  is  in  Logic  a  certain  sophism, 

IP.  Cant  i.  89  —  Ed 


S6  LOGIC.  Lect.  nii 

or  act  of  illegal  interference,  by  which  two  things  are,  perhaps  in  a 
very  concealed  and  circuitous  manner,  made  to 

Example.  i         i  -».t  i  -         •, 

prove  each  other.  rJow,  the  man  unacquainted 
with  Logic  may  perhaps  detect  and  be  convinced  of  the  fallacy ; 
but  how  will  he  expose  it  ?  He  must  enter  upon  a  long  state- 
ment and  explanation,  and  after  much  labor  to  himself  and  others, 
he  probably  does  not  make  his  objection  clear  and  demonstrative 
after  all.  But  between  those  acquainted  with  Logic,  the  whole 
matter  would  be  settled  in  two  words.  It  would  be  enough  to  say 
and  show  that  the  inference  in  question  involved  a  drculus  in  con- 
eludendo,  and  the  refutation  is  at  once  understood  and  admitted.  It 
is  in  like  manner  that  one  lawyer  will  express  to  another  the  ratio 
decidendi  of  a  case  in  a  single  technical  expression  ;  while  their 
clients  will  only  perplex  themselves  and  others  in  their  attempts  to 
set  forth  the  merits  of  their  cause.  Now,  if  Logic  did  nothing  more 
than  establish  a  certain  number  of  decided  and  decisive  rules  in 
reasoning,  and  afford  us  brief  and  precise  expressions  by  which 
to  bring  particular  cases  under  these  general  rules,  it  would  confer 
on  all  who  in  any  way  employ  their  intellect  —  that  is,  on  the  culti- 
vators of  every  human  science  —  the  most  important  obligation. 
For  it  is  only  in  the  possession  of  such  established  rules,  and  of  such 
a  technical  nomenclature,  that  we  can  accomplish,  with  facility,  and 
to  an  adequate  extent,  a  criticism  of  any  work  of  reasoning.  Logi- 
cal language  is  thus,  to  the  general  reasoner,  what  the  notation  of 
Arithmetic,  and  still  more  of  Algebra,  is  to  the  mathematician. 
Both  enable  us  to  comprehend  and  express,  in  a  few  significant  sym- 
bolsj  what  would  otherwise  overpower  us  by  their  complexity ;  and 
tfcus  it  is  that  nothing  would  contribute  moi^e  to  facilitate  and  ex- 
tend the  faculty  of  reasoning,  than  a  general  acquaintance  with  the 
rules  and  language  of  Logic,  —  an  advantage  extending  indeed  to 
every  department  of  knowledge,  but  more  especially  of  importance 
to  those  professions  which  are  occupied  in  inference,  and  conversant 
with  abstract  matter,  such  as  Theology  and  Law. 

I  now  proceed  to  the  third  of  the  preliminary  questions  —  viz., 

How  is  Logic  divided  ?    Now,  it  is  manifest  that 
.       V     M  o         ^^.^  question  may  be  viewed  in  two  relations ; 

for,  in  asking  how  is  Logic  divided,  we  eitlier 
mean  how  many  kinds  are  there  of  Logic,  or  into  how  many  con- 
stituent parts  is  it  distributed  ?^  We  may  consider  Logic  either  aa 
a  universal,  or  as  an  integi-ate,  whole. 

1  Division  of  Logic  into  Natural  and  Artificial,  inept. 

"  He  hit!  each  point  -with  native  force  of  mind. 
Whilst  puzzled  T>ogic  struggles  tar  behind." 

Cf.  Krug,  LogH,  p.  29.    Troxler   Tagik,  i.  48. 


Lect.  Ill  LOGIC.  S>T 

It  is  necessary  to  consider  the  former  question  first ;  for,  before 

proceeding  to  show  what  are  the  parts  of  which 

e    pecies  o        ^  logic  is  made  up,  it  is  i-equisite  previously  to 

detennine  what  the  logic  is  of  which  these  parts 

are  the  components.     Under  the  former  head,  I  therefore  give  you 

the  following : 

1  VI.  Logic,' considered  as  a  Genus  or  Class,  may,  in  differ- 
ent relations,  be  divided  into  different  Spe- 
pe!atioI^to  the  m  Ji      ^1^8.     And,  in  the  first  place,  considered  by 
is.objeotiveand  Sub.       relation  to  the  mind  or  thinking  subject, 
jeouve.  Logic  is  divided  into  Objective  and  Subjec- 

tive, or,  in  the  language  of  some  older  authors,  into  Logica 
systematica  and  Logica  habituaZis} 

By  Objective  or  Systematic  Logic  is  meant  that  complement  of 
doctrines  of  which  the  science  of  Logic  is  made 

.     Explication.  c,    ,  .        .  tt   i  •         it        •      • 

up;  by  Subjective  or  Habitual  Logic  is  meant 
the  speculative  knowledge  of  these  doctrines  which  any  individual, 
(as  Socrates,  Plato,  Aristotle)  may  possess,  and  the  practical  dex 
terity  with  which  he  is  able  to  apply  them. 

Now,  it  is  evident  that  both  these  Logics,  or,  rather.  Logic  con- 
sidered in  this  twofold  relation,  ought  to  be  pro 
Both  these    Logics       posed  to  himself  by  an   academical  instructor. 

ought  to  be  proposed         -^^  ...  ^  i      i.        vi  T        • 

„ ,.       ^    ,  ,    ■    ,       We  must,  theretore,  neglect  neither.    Logic  con- 
as  the  end  of  logical  '  '       »  a 

instruction.  sidcred  as  a  system  of  rules,  is  only  valuable  as 

a  mean  towards  logic  considered  as  a  habit  of 
the  mind ;  and,  therefore,  a  logical  instructor  ought  not  to  think 
that  he  fulfils  his  duty  —  that  he  accomplishes  all  that  he  is  called 
on  to  perform  —  if  he  limit  himself  to  the  mere  enouncement  of  a 
code  of  doctrine,  leaving  his  pupils  to  turn  his  instructions  to  their 
own  account  as  best  they  may.  On  the  contrary,  he  is  bound  to  rec- 
ollect that  he  should  be  something  more  than  a  book;  that  he  ought 
not  only  hitnself  to  deliver  the  one  Logic,  but  to  take  care  that  his 
pupils  acquire  the  other.  The  former,  indeed,  he  must  do  as  a  con- 
dition of  the  latter ;  but  if  he  considers  the  systematic  logic  which 
he  pronounces,  as  of  any  value,  except  in  so  far  as  his  pupils  convert 
it  into  an  habitual  logic,  he  understands  nothing  of  the  character  of 
the  function  which  he  attempts  to  perform.     It  is,  therefore,  incuni- 

,1  Sec  Tirapler,  p.  877,-  Vossius,  p.  217;  Pa-  various  divisions  of  Logic,  seeTimpler,  Ln^i- 

<;.:;f.     ILngicep.   Syslema,  cmthort  M.    CUmente  ccb  Systema,  1.  i.   c.   1,  q.   13 — 20,  p.  40 — 5fi, 

r.w//ifro,  Uano viae,  1612.    Vossius,  X><  Aatura  Gisbert   ab   Isendoom,   Effata    Philosophica, 

Anium,  1.  iv.  Sive  de  Logica,  c.  ix.  Pacius,  In  [Cent.  i.  §  51—63,  p.  95  «i  teq.,  ed.  B&ventriae 

i'o»j>Ayr»»ijafirogrm,  p.  2,  ed.  Francof,1697.  On  1643.  — Ed.] 


and  Concrete  or  Spe- 
cial. 


C8  LOGIC.  Lect.  m 

bent  on  an  academical  instructor,  to  do  what  in  him  lies  to  induce 
h\^  pupils,  by  logical  exercise,  to  digest  what  is  presented  to  them 
as  an  objective  system  into  a  subjective  habit.  Logic,  therefore,  in 
both  these  relations  belongs  to  us,  and  neither  can  be  neglected 
without  compromising  the  utility  of  a  course  like  the  present. 

If  VII.  In  the  second  place,  by  relation  to  its  application  or 

non-application  to  objects.  Logic  is  divided 

Par.  VII.  i-o^io.  by       -j^^Q  Abstract  or  General,  and  into  Concrete 

relation  to  otrjects,  is  ' 

Abstract  or  General.  or  Spccial.  The  fomicr  of  thcsc  is  called, 
by  the  Greek  Aristotelians,  SioXcktikt^  xi^P'-'^ 
irpay/iaTwv,  and,  by  the  Arabian  and  Latin 

schoolmen,  Logica  docens;   while  the  latter  is  denominated,  by 

the  Greeks,  SioAc/ctik^  Iv  ^^pi^crei.  kuI   yv/JLvaaia  vpayfidrbiv ;  by  the 

Arabians  and  Latins,  Logica  utens. 

Abstract  Logic  considers  the  laws  of  thought  as  potentially  appli- 
cable to  the  objects  of  all  arts  and  sciences,  but 
as  not  actually  applied  to  those  of  any;  Con- 
crete Logic  considers  these  laws  in  their  actual  and  immediate  appli- 
cation to  the  object-matter  of  this  or  that  particular  science.  The 
former  of  these,  is  one,  and  alone  belongs  to  philosophy,  whereas 
the  latter  is  as  multiform  as  the  arts  and  sciences  to  which  it  is 
relative.^ 

This  division  of  Logic  does  not  remount  to  Aristotle,  but  it  is 

found  in  his  most  ancient  commentator,  Alexan- 

Thi8  division  of  Logic       ^^^  ^j^^  Aphrodisian,  and,  after  him,  in  most  of 

lemonnts   to  Alexan-  /-.        i      x        •    •  *  i  i         -n 

der  the  Aphrodisian.  ^^^^  Other  Greek  Logicians.  Alexander  illus- 
trates the  opposition  of  the  logic  divorced  from 
things  (x<»>pis  TT/aa-y/xaTwv, —  rebus  avulsa),  to  the  logic  applied  to 
things  (ev  xprjcTii.  Kol  yviivaaia.  irpay/iaTtov,  —  rebus  applicato),  by  a 
simile.  "The  former,  he  says,  "may  be  resembled  to  a  geometrical 
figure,  say  a  triangle,  when  considered  abstractly  and  in  itself; 
whereas  the  latter  may  be  resembled  to  the  same  triangle,  as  con- 
cretely existing  in  this  or  that  particular  matter :  for  a  triangle  con- 
sidered in  itseiris  ever  one  and  the  same ;  but  viewed  in  relation  to 
its  matter,  it  varies  according  to  the  variety  of  that  matter ;  for  it 
is  different  as  it  is  of  silver,  gold,  lead  —  as  it  is  of  wood,  of  stone, 
etc.*     The  same  holds  good  of  Logic.     General  or  Abstract  Logic 


1  See  Krug,  p.  27  [Logik^  §  10,  Anm.  —  El).]  ganum,  p.  23.  q.  v.  \  2.    "  Alexander  Aphro- 

2  (Isendoorn,  Ilffata,  Cent.  i.  55;  Crellius,  disiensis  Logicatn  rllam  abjuuctam  sirailein 
hngoge  Logica,  p.  12.]  The  illustration  is  esse  ait  figura;  gcomefrica;,  utpote  triaugulo, 
('ally  given  by  Balforeu8,  CommtiUariiu  in  Or-  dum  iu  M  et  per  se  speotatur;  Logicam  vero 


Lect.  m.  LOGIC.  39 

is  always  one  and  the  same ;  but  as  applied  to  this  or  to  that  object 
of  consideration,  it  appears  multiform."  So  far  Alexander.  This 
appearance  of  multiformity  I  may,  however,  add,  is  not  real ;  for 
the  mind  has  truly  only  one  mode  of  thinking,  one  mode  of  reason- 
ing, one  mode  of  conducting  itself  in  the  investigation  of  truth, 
whatever  may  be  the  object  on  which  it  exercises  itself     Logic 

may  therefore  be  again  well  compared   to  the 
us  ra  e     y  com-      authority  of  an   universal  empire  —  of  an  em- 

pire  governing  the  world  by  common  laws.  In 
Kuch  a  dominion  there  are  many  provinces,  various  regions,  and  dif- 
ferent praefectui'es.  There  is  one  praefect  in  Asia,  another  in  Europe, 
51  third  in  Africa,  and  each  is  decorated  by  different  titles ;  but  each 
governs  and  is  governed  by  the  common  laws  of  the  empire  con- 
fided to  his  administration.  The  nature  of  General  Logic  may 
likewise  be  illustrated  by  another  comparison.  The  Thames,  for 
instance  in  passing  London,  is  a  single  river,  ^is  one  water, — but  is 
there  applied  to  many  and  different  uses.  It  is  employed  for  drink- 
ing, for  cooking,  for  brewing,  for  washing,  for  irrigation,  for  naviga- 
tion, etc.  In  like  manner.  Logic  in  itself  is  one :  as  a  science  or 
an  art,  it  is  single ;  but,  in  its  applications,  it  is  of  various  and  multi- 
form use  in  the  various  branches  of  knowledge,  conversant  be  it  with 
necessary,  or  be  it  with  contingent  matter.  Or  further,  to  take  the 
example  of  a  cognate  science,  if  any  one  were  to  lay  down  different 
grammars  of  a  tongue,  as  that  may  be  applied  to  the  different  pur- 
poses of  life,  he  would  be  justly  derided  by  all  grammarians,  indeed 
by  all  men ;  for  who  is  there  so  ignorant  as  not  to  know  that  there 
is  but  one  grammar  of  the  same  language  in  all  its  various  applica- 
tions ?  ^ 

Thus,  likewise,  there  is  only  one  method  of  reasoning,  which  all 
the  sciences  indifferently  employ ;  and  although  men  are  severally 
occupied  in  different  pursuits,  and  although  one  is,  therefore,  entitled 
a  Theologian,  another  a  Jurist,  a  third  a  Physician,  and  so  on,  each 

cum  rebus   conjuuctam  similem  eidem  tri-  l  See  Rami  Sch.,  p.  350,  [P.  Rami  Scholce  in 

angulo  huic  aut  illi  materiae  impresso.    Nam  Liberales  Artes,  Basileae,  1578.    "  Unus  est  Lu- 

trianguli  in  se  una  est  et  eadem  ratio;  at  pro  tetiae  Sequana,  ad  multos  tamen  usus  et  varios 

varietate  materia  varia.    Aliud  enim  est  ar-  accommodatus,  lavaiidum,  aquandum,  vehen- 

genteum,  aliud  aureum,  aliud  ligneum,  lapi-  dum,  irrigandum,  coquendum:   sic  una  est 

deum,  aut  plumbeum."    The  passage  referred  Logica,  varii  et  multiplicis  usus,  in  propoei- 

to  is  probably  one  in  the  Commentary  on  the  tione  necessaria,  probabili,  captiosa;  ars  ta- 

Prior  Analytics,  p.  2,  ed.  Aid.    The  distinction  men  una.     Si  Grammaticas  tres  aliquis  inep- 

itself,  though  not  the  illustration,  is  given  tus  nobis  instituat,  unam  civilem,  alteram 

more  exactly  in  the  language  of  the  text  by  agrestem,  tertiam  de  vitis  amborum,  merito 

some  of  the  later  commentators.    See  the  In-  rideatur  a  Grammaticis  omnibus,  qui  unam 

troductions  of  Ammonius  to  the  Categories,  Grammaticam  norunt  omnium  ejusdem  lin- 

and  of  Philoponus  to  the  Prior  Analytics.—  guae  hominum  communem."— Ed.] 
JEd.] 


40  LOGIC.  Lect.  UL 

employs  the  same  processes,  and  is  governed  by  the  same  laws,  of 

thought.     Logic  itself  is,  therefore,  widely  differ- 

Generai    Logic  is       ent   from  the  use  —  the  application  of   Logic. 

alone    one;    Special       For  Logic  is  astricted  to  no  determinate  matter. 

Logic  is  manifold,  and  .  n     i        . 

part  of  the  science  in       ^"^  ^^  extended  to  all  that  is  the  object  of  reason 
which  it  is  applied.  and  intelligence.     The  use  of  Logic,  on  the  con- 

trary, although  potentially  applicable  to  ev- 
ei-y  matter,  is  always  actually  manifested  by  special  reference  to 
some  one.  In  point  of  fact,  Logic,  in  its  particular  applications,  no 
longer  remains  logic,  but  becomes  part  and  parcel  of  the  art  or  sci- 
ence in  which  it  is  applied.  Thus  Logic,  applied  to  the  objects  of 
geometry,  is  nothing  else  than  Geometry;  Logic,  applied  to  the 
objects  of  physics,  nothing  else  than  Natural  Philosophy.  We  have, 
indeed,  certain  treatises  of  Logic  in  reference  to  different  sciences, 
which  may  be  viewed  as  something  more  than  these  sciences  them- 
selves. For  example :  we  have  treatises  on  Legal  Logic,  etc ;  but 
such  treatises  are  only  introductions  —  only  methodologies  of  the 
art  or  science  to  which  they  relate.  For  such  special  logics  only 
exhibit  the  mode  in  which  a  determinate  matter  or  object  of  sci- 
ence, the  knowledge  of  which  is  presupposed,  must  be  treated,  the 
conditions  which  regulate  the  certainty  of  inferences  in  that  mat- 
ter, and  the  methods  by  which  our  knowledge  of  it  may  be  con- 
structed into  a  scientific  whole.  Special  Logic  is  thus  not  a  sin- 
gle discipline,  not  the  science  of  the  universal  laws  of  thought,  but 
a  congeries  of  disciplines,  as  numerous  as  there  are  special  sciences 
in  which  it  may  be  applied.  Abstract  or  General  Logic,  on  the  con- 
trary, in  virtue  of  its  universal  character,  can  only  and  alone  be 
one;  and  can  exclusively  pretend  to  the  dignity  of  an  independent 
science.    This,  therefore,  likewise  exclusively  concerns  us. 


LECTURE    IV. 

INTRODUCTION. 

LOGIC— III.    ITS  DIVISIONS  — PURE  AND  MODIFIED. 

In  my  last  Lecture,  after  terminating  the  consideration  of  the  seo 
end  introductory  question,  touching  the  Utilities  of  Logic,  I  pro- 
ceeded  to   the   third  introductory  question, — 

Recapitulation. 

What  are  the  Divisions  of  Logic?  and  stated 
to  you  the  two  most  general  classifications  of  this  science.  Of 
these,  the  first  is  the  division  of  Logic  into  Objective  and  Subjec- 
tive, or  Systematic  and  Habitual ;  the  second  is  its  division  into 
General  and  Special,  or  Abstract  and  Concrete. 

To  speak  only  of  the  latter.  Abstract  or  General  Logic  is  logic 
viewed  as  treating  of  the  formal  laws  of  thought,  without  respect 
to  any  particular  matter.  Concrete  or  Special  Logic  is  logic  viewed 
as  treating  of  these  laws  in  relation  to  a  cei'tain  matter,  and  in  sub- 
ordination to  the  end  of  some  determinate  science.  The  former  of 
these  is  one,  and  belongs  alone  to  philosophy,  that  is,  to  the  science 
of  the  universal  principles  of  knowledge ;  the  latter  is  as  manifold 
as  the  sciences  to  which  it  is  subservient,  and  of  which  it,  in  fact, 
constitutes  a  part,  —  viz.,  their  Methodology.  This  division  of 
logic  is  given,  but  in  diflTerent  terms,  by  the  Greek  Aristotelians  and 
by  the  Latin  schoolmen.  The  Greek  division  does  not  remount  to 
Aristotle,  but  it  is  found  in  his  earliest  expositor,  Alexander  of 
Aphrodisias,  and  he  was  probably  not  the  first  by  whom  it  was 
enounced.  It  is  into  SiaXexTtK^  X'^P'^'*  ""pay/xaTtov,  Logica  rebus  avulsa, 
that  is,  Logic  merely  formal.  Logic  apart  from  things;  in  other 
words,  abstract  from  all  particular  matter ;  and  SuxXc/crt/d)  ev  XPW^'- 
Koi  yvfivacTui  irpayfidrtav,  Logica  rebus  applicata,  that  is.  Logic  as  used 
and  exercised  upon  things ;  in  other  words,  as  applied  to  certain 
special  objects. 

This  distinction  of  Logic  by  the  Greek  Aristotelians  seems  alto- 
gether unknown  to  modern  logicians.  The  division  of  Logic  by  the 
scholastic  Aristotelians  is  the  same  with  the  preceding,  but  the 
terms  in  which  it  is  expressed  are  less  precise  and  unambiguous. 

6 


42  LOGIC.  Lect.  it. 

This  division  is  into  the  Logica  docens  and  JLogica  utens.  The 
Logica  dopens  is  explained  as  logic  considered  as  an  abstract  the- 
ory, —  as  a  preceptiv6  system  of  rules,  —  "  que  tradit  praecepta ; "  — 
the  Logica  uteris^  as  logic  considered  as  a  concrete  practice,  —  as  an 
application  of  these  rules  to  use,  —  "  quae  utitur  praeceptis."  ^ 

This  scholastic  division  of  Logic  into  docens  and  utens  has,  I  see, 

been  noticed  by  some  of  the  more  modern  au- 

nie  division  of  Log-      thors  ;  but  it  has  been  altogether  mistaken,  whicli 

ica   ocens,  an      og-       .^  would  not  have  been,  had  these  authors  been 

ica  utens,  mistaken  by  ... 

some  modern  authors.  aware  of  the  meaning  in  which  the  terms  were 
employed,  and  had  they  not  been  ignorant  of 
the  more  explicit  expression  of  it  by  the  Greeks.  Thus  the  terms 
docens  and  utens  are  employed  by  Wolf  to  mark  a  distinction  not 
the  same  as  that  which  they  designate  in  the  scholastic  logic,  and 
as  the  Wolfian  distinction  will  not  stand  the  test  of  criticism,  the 
terms  themselves  have  been  repudiated  by  those  who  were  not 
aware  that  there  was  an  older  and  a  more  valid  division  which 
they  alone  properly  expressed.^  Wolf  makes  the  Logica  docens^ 
the  mere  knowledge  of  the  rules :  the  Logica  utens,  the  habit  or 
dexterity  of  applying  them.  This  distinction  of  General  and  Spe- 
cial logic,  Wolf  and  the  Wolfian  logicians,  likewise,  denote  by  that 
of  Theoretical  and  Practical  Logic."  These  terms  are  in  themselves 
by  no  means  a  bad  expression  of  the  distinction  ;  but  those  by  whom 
they  were  employed,  unfortunately  did  not  limit  their  Practical 
Logic  to  what  I  have  defined  as  Special,  for  under  Practical  they 
included  not  only  Special,  but  likewise  Modified  Logic,  of  which 
we  are  now  to  speak. 

Having  explained,  then,  this  primary  division  of  Logic  into  Gen- 
eral and  Special,  and  stated  that  General  Logic,  as  alone  a  branch 
of  philosophy,  is  alone  the  object  of  our  consideration ;  I  proceed 
to  give  the  division  of  General  Logic  into  two  great  species,  or 
rather  parts,  —  viz.,  into  Pure  or  Abstract,  and  Modified  or  Con- 
crete. 

%  VIII.  In  the  third  place,  considered  by 
Par.  vrn.   General       reference  to  the  circumstances  under  which 

ZiOeic,    divided     into  .  .  'it- 

Pure  and  Modified.  it  Can   comc  mto  excrcisc  by  us,  Logic  — 

Logic  General  or  Abstract  —  is  divided  into 

Pure  and  Modified ;  —  a  division,  however,  which  is  perhaps 

1  SmigUcii  Logica,  Disp.  ii.  q.  vi.  For  scho-  3  Wolf,  Philosophia  Rationaiis,  }§  8,  9,  10, 12. 
lastic  authorities,  see  Aquinas, /n /K.  Me/apA.,  — Ed.  [Cf.  Stattler,  Sauter,  and  Mako,] 
lect.  iv.  Scotus,  Suptr  Univ.  Porphyrii,  q.  i.  —  [Stattler,  Logica,  ^  18,  p.  12;  Sauter,  Positiontt 
Eiv  Logica.  P.  I.  and  II,  1778;  Instil.  Leg.,  V  1.  and 

2  [As  Krug]  [see  his  Logtk.  §  11,  p.  30.  Com-  II.  1799;  Paulus  Mako  do  Kerek-Gede,  Comr,. 
pare  Kant,  Logik,  Kinleitung,  ii.  —  Kd.J  Log.  Iru-ait.  P.  I.  and  II.,  4th  edit.,  1773.  —  Li)^ 


Lect.  IV.  LOGIC.  43 

rather  the  distribution  of  a  science  into  its  parts  than  of  a  genus 
into  its  species.  Pure  Logic  considers  the  laws  of  thought 
proper,  as  contained  a  priori  in  the  nature  of  pure  intelligence 
itself.  Modified  Logic,  again,  exhibits  these  laws  as  modified 
in  their  actual  applications  by  certain  general  circumstances 
external  and  internal,  contingent  in  themselves,  but  by  which 
human  thought  is  always  more  or  less  influenced  in  its  mani- 
festations.^ 

Pure  Logic  considers  Thought  Proper  simply  and  in  itself,  and 
apart  from  the  various  circumstances  by  which 
it  may  be  affected  in  its  actual  application.    Hu- 
man thought,  it  is  evident,  is  not  exerted  except  by  men  and  indi- 
vidual men.     By  men,  thought  is  not  exerted  out  of  connection 
with  the  other  constituents  of  their  intellectual  and  moral  charac- 
ter, and,  in  each  individual,  this  character  is  variously  modified  by 
various  contingent  conditions  of  different  original  genius,  and  of 
different  circumstances  contributing  to  develop  different  faculties 
and  habits.     Now,  there  may  be  conceived  a  sci- 

Modifled  Logic.  ...  •  t  i  i  ■> 

ence,  which  considers  thought  not  merely  as 
determined  by  its  necessaiy  and  universal  laws,  but  as  contingently 
affected  by  the  empirical  conditions  under  which  thought  is  actually 
exerted;  —  which  shows  what  these  conditions  are,  how  they  im- 
pede, and,  in  general,  modify,  the  act  of  thinking;  and  how,  in  fine, 
their  influence  may  be  counteracted.    This  science  is.  Modified  or 

Concrete  Logic.  What  I  have  called  Modified 
Nomenclature    of      -^     -^  j^  identical  with  what  Kant  and  other 

Modified  Logic.  f  i  t  •  i  .         t       • 

philosophers  have  denominated  Applied  Logic. 
(Angewandte  Logik,  Logica  applicata.y    This  expression  I  think 
improper.      For  the  term  Applied  Logic  can 
The  term  Applied       only  with  propriety  be.  used  to  denote  Special 
^**''  or  Concrete  Logic ;  and  is,  in  fact,  a  brief  and 

excellent  translation  of  the  terms  by  which  Special  Logic  was  des- 
ignated by  the  Greeks,  as  that  cv  ^(fyrja-ei  koL  yvixvaa-ia.Trpayfxa.Twv.  And 
so,  in  fact,  by  the  Latin  Logicians  was  the  Greek  expression  ren- 
dered. Let  us  consider  the  meaning  of  the  term  applied.  Logic, 
as  applied,  must  be  applied  to  something,  and  that  something  can 

1  For  distinction  of  reason  in  abstracto  and  quet,p.  236,  [Sammlung  der  Sehriftenwelcht  den 

reason  in  concreto,  grounding  the  distinction  Logischen  Calcul  Herrn  Prof.  Ploucquets  betreffrn, 

of  an  Abstract  (or  Pure),  and  a  Concrete  (or  Tubingen,  1773.  —  Ed.] 

Modified)  Logic,  see  Boyle's  IVbris,  iv.  p.  164.  2  Kant,   Logik,  Einleitung  ii.;    Hoffbauer, 

See  also  Lambert  [Neues  Organon,  Dianoiolo-  AnfangsgriXndt  der  Logik,  H  17)  406;    Krug, 

/ne,  i.— Ed],  J  444,  who  says  that  the  sciences  Logik,  Einleitung,  i  11;    Fries,   System   da 

in  general  are  only  applied  logics.   Cf.  Plouo-  Logik,  {  2. — £d. 


44  LOGIC.  Lect.  IV. 

only  be  an  object  or  matter.  Now,  Special  Logic  is  necess;jnly  an 
applied  logic;  therefore  the  term  applied^  if  given  to  what  I  would 
call  Modified  Logic,  would  not  distinguish  Modified  from  Special 
Logic.  But  further,  the  term  apjplied  as  given  to  Modified  Logic, 
considered  in  itself,  is  wrong ;  for  in  Modified  Logic  thought  is  no 
more  considered  as  actually  applied  to  any  particular  matter  than 
in  Pure  Logic.  Modified  Logic  only  considers  the  necessary  in 
conjunction  with  the  contingent  conditions  under  which  thought  is 
actually  exertible;  but  it  does  not  consider  it  as  applied  to  one 
class  of  objects  more  than  to  another;  that  is,  it  does  not  consider 
it  as  actually  applied  to  any,  but  as  potentially  applicable  to  all. 
In  every  point  of  view,  therefore,  the  term  applied^  as  given  to 
Modified  Logic,  is  improper ;  whereas,  if  used  at 

How  properly  em-      ^11,  it  ought  to  be  used  as  a  synonym  for  special; 
^'^^^  '  which  I  would  positively  have  done,  were  it  not 

that,  having  been  unfortunately  bestowed  by  high  authority  on  what 
I  have  called  Modified  Logic,  the  employment  of  it  to  designate 
a  totally  different  distinction  might  generate  confusion.  I  have 
therefore  refrained  from  making  wie  of  the  term.  I  find,  indeed, 
that  all  logicians  who,  before  Kant,  ever  employed  the  expression 
Applied  Logic,  employed  it  as  convertible  with  Special  or  Concrete 
Logic'  In  fine,  it  is  to  be  observed  that  the  terms  pure  and  ap- 
plied,*as  usually  employed  in  opposition  in  the  Kantian  philosophy, 
and  in  that  of  Germany  in  general,  are  not  properly  relative  and 
correlative  to  each  othrr.  For  jt>i^re  has  its  proper  correlative  in 
modified  or  mixed /  applied  its  proper  relative  in  unapplied^  that 
is,  divorced  from,  things,  that  is,  abstract. 

But  passing  from  words  to  things,  I  may  observe  that  it  can  be 
questioned  whether  Modified  or  Concrete  Logic 

Modified  Logic  not       ^^  entitled  to  the  dignity  of  an  essential  part  of 

properly   an  essential         -^        .      .  %  f  t  • 

part  of  Logic.  Logic  ixx  general,  far  less  of  a  coordmate  species 

as  opposed  to  Pure  or  Abstract  Logic.  You  are 
aware,  from  what  I  have  previously  stated  under  the  firet  introduc- 
tory question,  that  Logic,  as  convereant  about  a  certain  class  of 
mental  phaenomena,  is  only  a  part  of  the  general  philosophy  of 
mind  ;  but  that,  as  exclusively  conversant  about  what  is  necessary 
in  the  phsenoraena  of  thought,  that  is,  the  laws  of  thinking,  it  is 
contradistinguished  from  Empirical  Psychology,  or  that  philosophy 
of  mind  which  is  merely  observant  and  inductive  of  the  mental 
phaenomena  as  facts.     But  if  Modified  or  Concrete  Logic  be  consid- 

1  See  B»)foreu8,  [R.  Baiforei  CommentGriva     separatam ;  aliam  rebua  applioatam  et  cam  iif 
in    Orgatium,  q.   v.  4  2,   p.   22.     '' Grxci      .  .       coujunctam."  —  Ed.J 
aliam  dicuut  Logicuin  abjuuctam  et  &  rebiu 


LncT.  IV.  LOGIC.  45 

ered  either  as  a  part  or  as  a  species  of  General  Logic,  this  discrim- 
ination of  Logic,  as  the  Nomology  of  thought,  from  Psychology,  as 
the  Phaenomenology  of  mind,  will  not  hold.  For  Modified  Logic, 
presupposing  a  knowledge  of  the  general  and  the  contingent  phae- 
nomena  of  mind,  will  thus  either  comprise  Psychology  within  its 
sphere,  or  be  itself  compiised  within  the  sphere  of  Psychology. 
But  whichever  alternative  may  be  preferred,  the  two  sciences  are 
no  longer  distinct.  It  is  on  this  ground  that  I  hold,  that,  in  reality, 
Modified  Logic  is  neither  an  essential  part  nor  an  independent  spe- 
cies of  General  Logic,  but  that  it  is  a  mere  mixture  of  Logic  and 
Psychology,  and  may,  therefore,  be  called  either  Logical  Psychol- 
ogy or  Psychological  Logic.^  There  is  thus  in  truth  only  one 
Logic,  that  is.  Pure  or  Abstract  Logic,  liut  while  this,  I  think, 
must  be  admitted  in  speculative  rigor,  still,  as  all  sciences  are  only 
organized  for  human  ends,  and  as  a  general  consideration  of  the 
modifying  circumstances  which  affect  the  abstract  laws  of  thought 
in  their  actual  manifestations,  is  of  great  practical  utility,  I  trust 
that  I  shall  not  be  regarded  as  deforming  the  simplicity  of  the  sci- 
ence, if  I  follow  the  example  of  most  modern  logicians,  and  add  (be 
it  under  protest)  to  Pure  or  Abstract  Logic  a  part,  or  an  appendix, 
under  the  name  of  Modified  Logic.  In  distributing  the  science, 
therefore,  into  these  two  principal  heads,  you  will  always,  I  re- 
quest, keep  steadily  in  mind,  that,  in  strict  jn-opriety.  Pure  Logic 
is  the  only  science  of  Logic  —  Modified  Logic  being  only  a  scien- 
tific accident,  ambiguously  belonging  either  to  Logic  or  to  Psy- 
chology. 

This  being  understood,  I  now  proceed  to  state  to  you  the  dis- 
tribution of  the  general  science  into  its  parts ; 

onspectus  o    t  e       ^^^  ^^  j^  -^  ^^  high  importance  that  you  now 

Course  of  Logic  ,  .  .  . 

obtain  a  comprehensive  view  of  the  relation  of 
these  parts  to  each  other  and  to  the  whole  which  they  constitute, 
in  order  that  you  may  clearly  understand  the  point  towai'ds  which 
we  travel,  and  every  stage  in  our  progress,  —  I  shall  comprise  this 
whole  statement  in  the  following  paragraph,  which  I  shall  endeavor 
to  make  sufficiently  intelligible  without  much  subsequent  illustra- 
tion. That  illustration,  however,  I  will  give  in  my  next  Lecture. 
As  this  paragraph  is  intended  to  afford  you  a  conspectus  of  the 
ensuing  Course,  in  so  far  as  it  will  be  occupied  with  Logic,  I  need 
hardly  say  that  yon  will  find  it  somewhat  long.  It  is,  however,  I 
believe,  the  only  paragraph  of  any  extent  which  I  shall  hereafter 
be  obliged  to  dictate. 

1  [8ee  Rkihter,  p  e7,[Oberdim  Cfegetutand und den  XTmfang dtr  Logik,  S  17,  Leip8ic,18ffi.— Ed.J 


46  LOGIC.  Lect.  J\. 

%  IX.  Gkxei:ai,  or  Adstract  Logic,  we 
par.  IX    Distribu-       havG  seeii,  IS  divided  into  two  paits,  —  into 

tjon  of  Logic  into  its  t»  a     •     m.        nt  /-vp^t 

Pure   and   into   Modified.      Of  these   m 

parts. 

their  order. 

I.  —  Pure  Logic  may,  I  think,  best  be  distributed  upon  the  follow- 
ing principles.  We  may  think ;  and  we  may  think  well.  On 
the  one  hand,  the  conditions  of  thinking  do  not  involve  the 
conditions  of  thinking  well ;  but  the  conditions  of  thinking 
well  involve  the  conditions  of  thinking.  Logic,  therefore,  as 
the  science  of  thought,  must  necessarily  consider  the  conditions 
of  the  possibility  of  thought.  On  the  other  hand,  the  end  of 
thought  is  not  merely  to  think,  but  to  think  well ;  therefore,  as 
the  end  of  a  science  must  be  conformed  to  the  end  of  its  ob- 
ject-matter. Logic,  as  the  science  of  thought,  must  display  not 
only  the  laws  of  possible,  but  the  laws  of  perfect,  thinking. 
Logic,  therefore,  naturally  falls  into  two  parts,  the  one  of  which 
investigates  the  formal  conditions  of  mere  thinking ;  the  other, 
the  formal  conditions  of  thinking  well. 

i.  —  In  regard  to  the  former: — The  conditions  of  mere 
thinking  are  given  in  certain  elementary  requisites;  and  that 
part  of  Logic  which  analyzes  and  considers  these,  may  be  called 
its  Stoicheiology,  or  Doctrine  of  Elements.  These  elements 
are  either  Laws  or  Products. 

ii.  — In  regard  to  the  latter,  as  perfect  thinking  is  an  end,  and 
as,  the  elementary  means  being  supposed,  the  conditions  of  an 
end  are  the  ways  or  methods  by  which  it  maybe  accomplished, 
that  part  of  Logic  which  analyzes  and  considere  the  methods 
of  perfect  thinking,  may  bo  called  its  Methodology,  or  Doctrine 
of  Method. 

Thus  Pure  Logic  is  divided  into  two  parts,  —  into  Stoichei- 
ology, or  the  Doctrine  of  Elements,  and  Methodology,  or  the 
Doctrine  of  Method.     Of  these  in  their  order. 

Logical  Stoicheiology,  or  the  doctrine  conversant  about  the 
elementary  requisites  of  mere  thought,  I  shall  divide  into  two 
parts.  The  first  of  these  treats  of  the  Fundamental  Laws  of 
thinking;  in  other  words,  of  the  universal  conditions  of  the 
thinkable  —  Noetic — Nomology.  The  second  treats  of  the 
laws  of  thinking,  as  governing  the  special  functions,  faculties, 
or  products  of  thought,  in  its  three  gradations  of  Conception  ; 
or,  as  it  is  otherwise  called.  Simple  Apprehension, — Judg- 
ment, and  Reasoning,  —  Diaonetic  —  Dynamic. 

This  second  part  of  Stoicheiology  will,  therefore,  fall    into 


i 


Lic'JT.  IV.  LOGIC.  4 1 

three  subordinate  divisions  corresponding  to  these  several  de- 
■  grees  of  Conception,  Judgment,  and  Reasoning.     So  much  for 
the  Doctrine  of  Elements. 

Logical  Methodology,  or  the  doctrine  conversant  about  the 
regulated  ways  or  methods  in  which  the  means  of  thinking 
are  conducted  to  their  end  of  thinking  well,  is  divided  into  as 
many  parts  as  there  are  methods,  and  there  are  as  many  meth- 
ods as  there  are  different  qualities  in  the  end  to  be  differently 
accomplished.  Now;  the  perfection  of  thought  consists  of  three 
virtues,  —  Clear  Thinking,  Distinct  Thinking,  and  Connected 
Thinking ;  each  of  these  virtues  is  accomplished  by  a  distinct 
method  ;  and  the  three  methods  will  consequently  afford  the 
division  of  Logical  Methodology  into  three  parts. 

The  first  part  comprises  the  method  of  Clear  Thinking,  or 
the  doctrine  of  Illustration  or  Definition. 

The  second  part  comprises  the  Method  of  Distinct  Thinking, 
or  the  doctrine  of  Division. 

The  third  part  comprises  the  Method  of  Concatenated  or 
Connected  Thinking,  or  the  Doctrine  of  Proof. 

These  parts  are  only,  however,  three  particular  applications 
of  Method;  they,  therefore,  constitute  each  only  a  Special 
Methodology.  But  such  methodology,  or  union  of  methodolo- 
gies, supposes  a  previous  consideration  of  method  in  general,  in 
its  notion,  its  species,  and  its  conditions.  Logical  Methodology 
will  therefore  consist  of  two  parts,  of  a  General  and  of  a  Spe- 
cial, —  the  Special  being  subdivided,  as  above  stated.  So  much 
for  the  distribution  of  Pure  Logic. 
11.  —  Modified  Logic  falls  naturally  into  Three  Parts. 

The  First  Part  treats  of  the  nature  of  Truth  and  Error,  and 
of  the  highest  laws  for  their  discrimination,  —  Alethiology. 

The  Second  treats  of  the  Impediments  to  thinking,  with  the 
Means  of  their  Removal.  These  impediments  arise,  1°,  from 
the  Mind ;  2°,  From  the  Body  ;  or,  3°,  From  External  Circum- 
stances. In  relation  to  the  Mind,  these  impediments  originate 
in  the  Senses,  in  Self-Consciousness,  in  Memory,  in  Associa- 
tion, in  Imagination,  in  Reason,  in  the  faculty  of  Language,  in 
the  Feelings,  in  the  Desires,  in  the  Will.  In  relation  to  the 
Body,  they  originate  in  Temperament,  or  in  the  state  of  Health. 
In  relation  to  External  Circumstances,  they  originate  in  the  di- 
versities of  Education,  of  Rank,  of  Age,  of  Climate,  of  Social 
Intercoui'se,  etc. 

The  Third  Part  treats  of  the  Aids  or  Subsidiaries  of  think- 


48  LOGIC.         /  Lect.  IV. 

ing;  and  thinking  is  aided  either,  1°,  Through  the  Acquisition, 
or,  2",  Through  the  Communication,  of  Knowledge. 

The  former  of  these  subsidiaries  (the  acquisition  of  knowl- 
edge) consists,  1°,  Of  Experience  (and  that  either  by  ourselves 
or  by  others)  ;  2®,  Of  Generalization  (and  this-  through  Induc- 
tion and  Analogy)  ;  and,  3°,  Of  Testimony  (and  this  either  Oral 
or  "Written).  Under  this  last  head  falls  to  be  considered  the 
Credibility  of  Witnesses,  the  Authenticity  and  Integrity  of 
Writings,  the  Rules  of  Criticism  and  of  Interpretation. 

The  latter  of  these  subsidiaries,  the  Communication  of  Knowl- 
edge, is  either  One-sided  or  Reciprocal.  The  former  consists 
of  Instruction,  either  Oral  or  Written  ;  the  latter  of  Conversa- 
tion, Conference,  Disputation. 

So  much  for  the  distribution  of  Modified  Logic. 

Tabular  view  of  the  On  the  Opposite  page  is  a  general  tabular  view 

nivisions  of  Logic.  of  the  Divisions  of  Logic  now  given. 

The  fourth  and  fifth  questions  of  the  Introduction  would  now 

fall  to  be  considered,  —  viz..  What  is  the  History 

IV.  The  History  of      and  what  is  the  Bibliography,  of  Logic  ?     Were 

''"""'■  I  writing  a  book,  and  not  ffivinf]r  a  coui-se  of  Lec- 

This  question  post-  °  .  °         . 

j.y^gjj  tures  upon  Logic,  I  would  certainly  consider  these 

questions  in  the  introduction  to  the  science ;  but 
I  would  do  this  with  the  admonition  that  beginners  should  pass 
these  over,  and  make  themselves  first  of  all  familiar  with  the  doc- 
trines of  which  the  science  is  itself  the  complement.  For  why  ? 
The  history  of  u  science  is  a  narrative  of  the  order  in  which  its 
several  parts  have  been  developed,  and  of  the  contributions  which 
have  been  made  to  it  by  difierent  cultivators ;  but  such  a  narrative 
necessarily  supposes  a  previous  knowledge  of  the  contents  of  the 
science,  —  a  knowledge  which  is  identical  with  a  knowledge  of  the 
science  itself.  It  is,  therefore,  evident,  that  a  history  of  Logic  can 
only  be  proposed  with  advantage  to  those  who  are  already  in  some 
degree  familiar  with  Logic  itself;  and  as,  in  a  coui-se  like  the  present, 
I  am  bound  to  presume  that  you  are  not  as  yet  conversant  with  the 
science,  it  follows  that  such  a  history  cannot  with  any  propriety  be 
attempted  in  the  commencement,  but  only  towards  the  conclusion, 
of  the  Lectures.  • 

In  regard  to  the  fifth  question,  —  What  is  the  Bibliography  or 
Literature  of  Logic  ?  —  the  same  is  true,  in  so 
p^'j^  j^  far  as  a  knowledge  of  the  books  written  upon  a 

science  is  correlative  to  a  knowledge  of  its  his- 
tory.    At  the  same  time,  nothing  could  be  more  unprofitable  than 


Lect.  IV. 


LOGIC. 


49 


A    TABULAR    VIEW 


DIVISIONS     OF     LOaiC. 


'1.  Noetic,— 
Nomology. 


i.  Stoicheiology. 


1 2.  Diaonetic 
Dynamic. 


'  a.Conception, 
'  b.  Judgment. 
c.  Reasoning. 


Pure. 


ii.  Methodology. 


General 

OR 

Abstract " 
Logic. 


<n.  Modified. 


Gear  Thinking.—  Definition 
or  Illustration. 

'Distinct  Thinking.  — 2.  Di- 
vision. 

Connected   Thinking.  —  3. 
Probation  or  Proving. 


1.  The  Mind. 

i.  Truth  and  Error  —  Cer- 
tainty and  Illusion. 

u.  Impediments  to  Think-\  2-  The  Body. 
ing,  with  Remedies. 
These    Impediments/ 
arise  from    .    .    .    y3.  Exteraal  Circumstances. 

1.  The  Acquisition  of  Knowl- 
edge 

iii.  Aids  or  Subsidiaries  to , 
Thinking — through 

2.  The  Communication  of 
Knowledge,  etc. 


50  LOGIC.  Lect.  rv- 

for  me  to  recite  to  you  a  long  series  of  works  to  which  you  have  not 
access,  by  authors  of  whom  you  probably  never  heard,  often  in  lan- 
guages which  few  of  you  understand.  In  the  present  stage  of  your 
studies,  it  is  not  requisite  that  you  should  know  of  many  books,  but 
that  you  should  read  attentively  a  few  ;  —  non  inulta  sed  miiltura. — 
I  shall  therefore  adjourn,  at  least,  the  consideration  of  the  question, 
What  in  general  are  the  principal  books  on  the  science  of  Logic? — 
simply  recommending  to  you  a  few,  not  absolutely  the  best,  but  such 
as  you  can  most  easily  procure;  such  as  are  in  languages  which  most 
of  you  can  read,  and  which  are  of  such  a  character  as  maybe  studied 
with  most  general  advantage. 

Of  works  in  our  own  language,  as  those  most  accessible  and  most 
intelligible  to  all,  there  are  unfortunately  hardly 

General    notice    of  ■!_•   -l  t  i  ^  ^  •^  •^• 

^    .  any  which  1  can  recommend  to  you  as  exhibiting 

•works  on  Logic.  •'  _         _  •'  ® 

the  doctrines  of  Logic,  either  in  purity  or  com- 
pleteness. The  Logic  of  Watts,  of  Duncan,  and  others,  ai'e  worth 
reading,  as  books,  but  not  as  books  upon  Logic.  The  Elements  of 
Logic  by  Dr.  Whately  is,  upon  the  whole,  the  one  best  entitled  to 
your  attention,  though  it  is  erroneous  in  various  respects,  and  imper- 
fect in  more.  The  abridgment  of  this  work  by  Hinds  contains  what 
of  the  original  is  most  worthy  of  study,  in  the  commencement  of  a 
logical  education.  In  French,  there  are  sundry  works  deserving  of 
your  attention  (Dnmiron,^  Delariviere) ;-  but  the  only  one  which  I 
would  at  present  earnestly  recommend  to  your  study,  is  the  cele- 
brated Port  Royal  Art  of  Thinking, — L^ Art  de  Penser^ — an  anony- 
mous work,  but  the  authors  of  which  were  the  two  distinguished 
Jansenists,  Arnauld  and  Nicole.  It  has  been  frequently  reprinted  ; 
and  there  is  recently  a  stereotyped  edition,  by  Hacht  tte,  of  Paris, 
which  can  easily  be  procured.  There  are  more  than  one  trans- 
lation of  the  work  into  Latin,  and  at  least  two  English  vei-sions,  both 
bad.'' 

In  Latin  there  is  a  very  elegant  compend  of  Logic  by  the  late 
illustrious  Daniel  Wyttenbach,  of  Leyden.  Besides  the  Dutch  edi- 
tions, which  are  handsome,  there  is  a  cheap  reprint  published  by 
Professor  Maas,  of  Halle,  who  hns,  however,  ventured  on  the  unwar- 
rantable liberty  of  silently  altering  the  text,  besides  omitting  what 
he  did  not  consider  as  ;ibsoliitely  indispensable  for  a  text-book.  Tliis 
work  can  be  easily  ])rocured.     There  is  also  in  Latin  a  system  of 

1  Cows  de  PhUosophie,  t.  iv.;  Logique,  Paris,  burgh,  1850;  2d  edition,  1851.    In  the  Iiitro- 
1837. —  Ed.  duction  to  this  version  will    be    found   on 

2  Logique  Clnnsiqur,  Paris,  1829.  — Ed.  account  of  the  various  editions  and  transla- 

3  A  third  and  far  superior  translation  ha.s  tions  of  the  work.  —  Ed. 
•ubsequently  appeared  by  Mr.  Baynes,  E^in- 


Lect.  IV.  LOGIC.  61 

Logic  by  Genovesi,  under  the  title,  Genxiensis  Ars  Logico-critica. 
This  work  is,  however,  extremely  rare  even  in  Italy,  and  it  was 
many  years  before  I  was  able  to  procure  a  copy.  There  was  an  edition 
of  this  work  published  in  Germany  in  1760,  at  Augsburg,  but  the 
impression  seems  to  have  been  small,  for  it  also  is  out  of  print.  The 
Italian  Logic  of  Genovesi  has,  however,  been  repeatedly  reprinted, 
and  this,  with  the  valuable  addition  of  Romagnosi,  is  easily  obtained. 
Of  the  older  writers  on  Logic  in  Latin,  the  one  I  would  principally 
recommend  to  you  is  Burgersdyk  —  Burgersdicius.  His  Institu- 
tiones  Logicce  is  not  a  rare  work,  though,  as  there  are  no  recent 
editions,  it  is  not  always  without  trouble  to  be  obtaloed. 


LECTURE  V. 

PURE    LOGIC. 

PART   I.  -  STOICHEIOLOay. 

SECTION    I.    NOETIC  — ON  THE  FUNDAMENTAL  LAWS  OP 
THOUGHT  — THEIR  CONTENTS  AND  HISTORY. 

Having  terminated  our  consideration  of  the  various  questions  of 
which  the  Introduction  to  Loeic  is  composed, 

Stoicheiology.  ,  ,        ,  .  ,  .   ,  ,       *        , 

we  proceed  to  the  doctrines  which  make  up  the 
science  itself  and  commence  the  First  Great  Division  of  Pure  Logic 

—  that  which  treats  of  its  elementary  or  constituent  processes,  — 
Stoicheiology.     But  Stoicheiology  was  again  divided  into  two  parts, 

—  into  apart  which  considered  the  Fundamental  Laws  of  Thought 
in  general,  and  into  a  part  which  considered  these  laws  as  applied 
to  and  regulating  the  special  function  of  Thought  in  its  various 
gradations  of  Conception,  Judgment,  and  Reasoning.  The  title, 
therefore,  of  the  part  of  Logic  on  which  we  are  about  to  enter  is, — 
Pure  Logic^  Part  I.  Stoicheiology  —  Section  I.  N^oetic.  On  the 
Fundainental  Laws  of  Thought. 

Before,  however,  descending  to  the  consideration  of  these  laws,  it 

is  necessary  to  make   one  or  two   preliminary 

_,      .  ^  .  ,  statements  touching  the  character  of  that  thought 

Thought  in  general.  _  *  _  _  ® 

of  which  they  are  the  necessary  conditions;  and, 
on  this  point,  I  give,  in  the  first  place,  the  following  paragraph  : 

^  X.     Logic   considers   Thought,  not  as  the  operation   of 
thinking,  but  as  its   product ;   it  does   not 
treat  of  Conception,  Judgment,  and   Rea- 
soning, but  of  Concepts,  Judgments,  and  Reasonings. 

I  have  already  endeavored  to  give  you  a  general  knowledge  of 
what  is  meant  by  thought.     You  are  aware  that 
loug     as     e  o  -       ^i^j^  term  is,  in  relation  to  Lotjio,  employed  in 
ject  of  Logic.  .  .  '  ..... 

its  strictest   and  most  limited    signification,  — 

viz.,  as  the  act  or  product  of  the  Discursive  Faculty,  or  Faculty  of 


Lect.  V.  LOGIC.  53 

Relations;  but  it  is  now  proper  to  consider,  somewhat  more  closely, 
the  determinate  nature  of  this  process,  and  the  special  point  of 
view  in  which  it  is  regarded  by  the  logician. 

In  an  act  of  thinking,  there  are  thi-ee  things  which  we  can  dis- 
criminate in   consciousness,  —  1°,  There  is  the 
The  subject,  form,      tiji^king    subject,   that    is,   the    mind    or   ego, 

and  matter  of  thought.  &  J        '  '  &   » 

which  exerts  or  manifests  the  thought;  2°, 
There  is  the  object  about  which  we  think,  which  is  called  the  matter 
of  thought;  and,  3°,  There  is  a  relation  between  subject  and  ob- 
ject of  which  we  are  conscious,  —  a  relation  always  manifested  in 
some  determinate  mode  or  manner;  —  this  is  the/brm  of  thought. 

Now,  of  these  three.  Logic  does  not  consider 
Thought  as  the  ob-       either  the  first  or  the  second.     It  takes  no  ac- 

ject     respectively    of  ^        ^    i        .  t  />,i  i 

Psychology  and  of  couut,  at  Icast  no  du'cct  account,  of  the  real 
Logic.  subject,  or  of  the  real  object,  of  thought,  but  is 

limited  exclusively  to  the  form  of  thought.  This 
has  been  already  stated.  But,  again,  this  form  of  thought  is  con- 
sidered by  Logic  only  in  a  certain  aspect.  The  form  of  thought 
may  be  viewed  on  two  sides  or  in  two  relations.  It  holds,  as  has 
been  said,  a  relation  both  to  its  subject  and  to  its  object,  and  it  may 
accordingly  be  viewed  either  in  the  one  of  these  relations  or  in  the 
other.  In  so  far  as  the  form  of  thought  is  considered  in  reference 
to  the  thinking  mind,  —  to  the  mind  by  which  it  is  exerted, —  it  is 
considered  as  an  act,  or  operation,  or  energy ;  and  in  this  relation  it 
belongs  to  Phaenomenal  Psychology.  Whereas,  in  so  far  as  this 
form  is  considered  in  reference  to  what  thought  is  about,  it  is  con- 
sidered as  the  product  of  such  an  act,  and,  in  this  relation,  it  be- 
longs to  Logic.  Thus  Phaenomenal  Psychology  treats  of  thought 
proper  as  conception,  judgment,  reasoning;  Logic,  or  the  Nomology 
of  the  understanding,  treats  of  thought  proper  as  a  concept,  as  a 
judgment,  as  a  reasoning.  Whately,  I  have  already  shown  you, 
among  other  errors  in  his  determination  of  the  object-matter  of 
Logic,  confounds  or  reverses  this;  for  he  proposes  to  Logic,  not 
thought  considered  as  a  product,  but  reasoning  alone ;  and  that,  too, 
considered  as  a  producing  operation.  He  thus  confounds  Logic 
with  Phaenomenal  Psychology. 

•Be  it,  therefore,  observed,  that  Logic,  in  treating  of  the  formal 
laws  of  thought,  treats  of  these  in  reference  to  thought  considered 
as  a  product ;  that  is,  as  a  concept,  a  judgment,  a  reasoning  ;*whereas 
Psychology,  as  the  Phaenomenology  of  mind,  considei-s  thought  as 
the  producing  act,  that  is,  as  conception,  judgment,  reasoning. 
(You  here  see,  by  the  way,  the  utility  of  distinguishing  concept  and 
conception.     It  is  unfortunate  that  we  cannot  also  distinguish  more 


^4  LOGIC.  Lect.  V. 

precisely  judgment  and  reasoning  as  producing  acts,  from  a  judg- 
ment and  a  reasoning  as  products.) 

Par.  XI.  Thought  a  ^  ^^'     Thouglit,  as  the  knowledge  of 

mediate  and  complex       one  thing  in  relation  to  another,  is  a  medi- 
ate and  complex  cognition. 


cognition. 


The  distinctive  peculiarity  of  thinking  in  general  is,  that  it  in- 
volves the  cognition  of  one  thing  by  the  cognition  of  another.  All 
thinking  is,  therefore,  a  mediate  cognition ;  and 
is  thus  distinguished  from  our  knowledge  in  per- 
ception, extern.al  and  internal,  and  in  imagination  ;  in  both  of  which 
acts  we  are  immediately  cognitive  of  the  object,  external  or  internal, 
presented  in  the  one,  and  of  the  object,  external  or  internal  re- 
presented in  the  other.  In  the  Presentative  and  Representative 
Faculties,  our  knowledge  is  of  something  considered  directly  and  in 
itself;  in  thought,  on  the  contrary,  we  know  one  object  only  through 
the  knowledge  of  another.  Thus  in  perception,  of  either  kind,  and 
in  imagination,  the  object  known  is  always  a  single  determinate  ob- 
ject; whereas  in  thought,  —  in  thought  pi'oper,  —  as  one  object  is 
only  known  through  another,  there  must  always  be  a  plurality  of 
objects  in  every  single  thought.  Let  us  take  an  example  of  this, 
in  regard  to  the  simplest  act  of  thought.  When  I  see  an  individ- 
ual,—  say  Bucephalus  or  Highflyer, — or  when  I  represent  him  in 
imagination,  I  have  a  direct  and  immediate  apprehension  of  a  cer- 
tain object  in  and  through  itself,  without  reference  to  aught  else. 
But  when  I  pronounce  the  term  ITorse,  I  am  unable  either  to  per- 
ceive in  nature,  or  to  represent  in  imagination,  any  one  detei-rainate 
object  corresponding  to  the  word.  I  obtain  the  notion  con*espond- 
ing  to  this  word,  only  as  the  result  of  a  comparison  of  many  per- 
ceptions or  imaginations  of  Bucephalus,  Highflyer,  Dobbin,  and 
other  individual  hoi^es ;  it,  therefore,  contains  many  representations 
under  it,  has  reference  to  many  objects,  out  of  relation  to  which  it 
cannot  possibly  be  realized  in  thought ;  and  it  is  in  consequence  of 
this  necessity  of  representing  (potentially  at  least)  a  plurality  of 
individual  objects  under  the  notion  horse,  that  it  obtains  the  denom- 
ination concept,  that  is,  something  taken  up  or  apprehended  in  con- 
nection with  something  else.  This,  however,  requires  a  further  ex- 
plicatiorf.  When  we  perform  an  act  of  thought,  of  positive  thought, 
this  is  done  by  thinking  something,  and  we  can  think  anything  only 
by  thinking  it  as  existing;  while,  again,  we  cannot  think  a  thing  to 
exist  except  in  certain  determinate  modes  of  existence.  On  the 
other  hand,  when  we  perform  an  act  of  negative  thought,  this  is 


Lect.  V.  LOGIC.  55 

done  by  thinking  something  as  not  existing  in  this  or  that  determi- 
nate mode,  and  when  we  think  it  as  existing  in  no  determinate 
mode,  we  cense  to  think  it  at  all ;  it  becomes  a  notliing,  a  logical 
nonentity  {non-ens  Logicum). 

It  being  thus  understood  that  thought  can  only  be  realized  by 
thinking  something;  it  being  further  understood  that  this  some- 
thing, as  it  is  thought,  must  be  thought  as  existing ;  and  it  being 
still  further  understood  that  we  can  think  a  thing  as  existing  only 
by  thinking  it  as  existing  in  this,  that,  and  the  other  determinate 
maimer  of  existence,  and  that  whenever  we  cease  to  think  some- 
thing, something  existing,  something  existing  in  a  determinate  man- 
ner of  existence,  we  cease  to  think  at  all ; — this,  I  say,  being  under- 
stood, it  is  here  proper  to  make  you,  once  for  all,  acquainted  with 
the  various  terms  by  which  logicians  designate  the  modes  or  man- 
ners of  cogitable  existence.  I  shall  therefore  comprise  these  in 
the  following  paragraph : 

1  XII,     When  we  think  a  thing,  this  is  done  by  conceiving 

it  as  possessed  of  certain  modes  of  being, 

Par.  XII.  The  vari-       or  qualitics,  and  the  sum  of  these  qualities 

OU8  terms   by  which         cOUStitUtCS    itS  COHCept   OV   UOtion    (votjua,  ev- 

the    modes    of    cogi-  ^ 

table     existence    are         VOVOL,    CTTlVOta,     COHCeptum,     COnCCptUS^     notio). 

designated.  ^g  thcsc  qualities  or  modes  (irow-np-e';,  qual- 

itates,  modi)  are  only  identified  with  the 
thing  by  a  mental  attribution,  they  are  called  attributes  {Ka-rf- 
yopovfjiO'CL,  attributa)  ;  as  it  is  only  in  or  through  them  that  we 
say  or  enounce  aught  of  a  thing,  the)''  are  called  predicates^ 
predicables,  and  predicaments^  or  categories^  these  words  being 
hei"e  used  in  their  more  extensive  signification  (Ac-yo/ieva  x«pA 
KaTrjyoplai,  KarqyoprjfiaTa  KaTrjfyopoviJieva,  prcedicata^  prcedicahilia^ 
prmdicainenta)  ;  as  it  is  only  in  and  through  them  Ihat  we  lec- 
ognize  a  thing  for  what  it  is,  they  are  called  notes,  signs,  marks, 
characters  {notee,  signa,  characteres,  discrimina) ;  finally,  as  it 
is  only  in  and  through  them  that  we  become  aware  that  a  thing 
is  possessed  of  a  peculiar  and  determinate  existence,  they  are 
called  2>f'operties,  differences,  detertninations  (^proprietates,  de- 
term,inationes).  As  consequent  on,  or  resulting  fi-om,  the  exist- 
ence of  a  thing,  they  have  likewise  obtained  the  name  of  con- 
sequents (ETro/ttcva,  cotisequentia,  etc.).  What  in  reality  has  no 
qualities,  has  no  existence  in  thought,  —  it  is  a  logical  nonen- 
tity; hence,  e  converso,  the  scholastic  aphorism,  —  non-entis 
nulla  sunt  prmdicaZa.    What,  again,  has  no  qualities  attributed 


50  LOGIC.  Lect.  V. 

to  it,  though  attributable,  is  said  to  be  indetermined  (dlSiopioroi', 
indeterminatum) ;  it  is  only  a  possible  object  of  thought.^ 

This  paragraph,  which  I  have  dictated  that  you  might  be  made 

once  for  all  acquainted  with  the  relative  terms  in 

ExpiicaUon.    What       ^gg  among  logicians,  requires  but  little  explaua- 

is  involved  in  think-  .  _  ,  i  ,  •     i         , 

j     ^^  ^^.^^  tion.    1  may  state,  however,  that  the  mind  only 

thinks  an  object  by  separating  it  from  others ; 
that  is,  by  marking  it  out  or  characterizing  it ;  and  in  so  far  as  it 
does  this,  it  encloses  it  within  certain  fixed  limits,  tliat  is,  determines 
it.  But  if  this  discriminative  act  be  expressed  in  words,  I  predicate 
the  marks,  notes,  characters,  or  determinations  of  the  thing ;  and  if, 
again,  these  be  comprehended  in  one  total  thought,  they  constitute 
its  concept  or  notion.  I£,  for  example,  I  think  of  Socrates  as  son  of 
SqphroniscuSy  as  Athenian^  as  philosopher,  as  pug-nosed,  these  are 
only  so  many  charactei's,  limitations,  or  determinations,  which  I  pre- 
dicate of  Socrates,  which  distinguish  him  from  all  other  men,  and 
together  make  up  ray  notion  or  concept  of  him. 

But  as  thought,  in  all  its  gradations  of  conception,  judgment,  and 

reasoning,  is  only  realized  by  the  attribution  of 

The  attribution  in-       certain  qualities  or  characters  to  the  objects  of, 

Tolred  in  thought  is  i  .    ,  i  .  .,       .         . 

recuiated  by  laws.  ^^'  ^bout  which  we  thmk ;  SO  this  attribution  is 

regulated  by  laws,  which  render  a  great  part  of 

this  process  absolutely  necessary.     But  wlien  I  speak  of  laws  and  of 

their  absolute  necessity  in  relation  to  thouglit. 

What  is  meant  by  a  ^  ^^^^  ^^^  gupp^ge  t^^t  ^hegg  j^^s  and  that 

law  as   applicable   to         "  j.-,  •      .1  u      ^       •    j 

free  intelligence.  necessity  are  the  same  in  the  world  01  mind  as 

in  the  world  of  matter.  For  free  intelligences, 
a  law  is  an  ideal  necessity  given  in  the  form  of  a  precept,  which  we 
ought  to  follow,  but  which  we  may  also  violate  if  we  please ; 
whereas,  for^the  existences  which  constitute  the  universe  of  nature, 
a  law  is  only  another  name  for  those  causes  whicli  operate  blindly 
and  universally  in  producing  certain  inevitable  results.  By  law  of 
thought,  or  by  logical  necessity,  we  do  not,  therefore,  mean  a  physi- 
cal law,  such  as  the  law  of  gravitation,  but  a  general  precept  which 
we  are  able  certainly  to  violate,  but  which  if  we  do  not  obey,  our 
whole  process  of  thinking  is  suicidal,  or  absolutely  null.  These  laws 
are,  consequently,  the  primary  conditions  of  the  possibility  of  valid 
thought,  and  as  the  whole  of  Pure  Logic  is  only  an  articulate 
development  of  the  various  modes  in  which  they  are  applied,  their 
consideration  in  general  constitutes  the  first  chapter  in  an  orderly 

1  [Schulze,  Logik,  1,   13.      RiSsling,  p.  63.]      [DU  Lehrtn  der  reinen  Logik,  Ulin,  1826.    CC 
Krug,  Logik,  S  16.  —  Ed.] 


Lect.  V.  LOGIC.  57 

system  of   the  science.     Now,  in  explaining  to  you  this  subject, 

the  method  I  shall  pursue  is  the  following :     I 

Order  of  considera-      ^^xaW,  first  of  all,  State  in  general  the  number  and 

tion  of  the  fundamen-  .       .-,  /.  ^i       i  i  •       -, 

tai  laws  of  thought.  Significance  of  the  laws  as  commonly  received  ; 

I  shall  then  more  particularly  consider  each  of 
these  by  itself  and  in  relation  to  the  others ;  then  detail  to  you  their 
history;  and,  finally,  state  to  you  my  own  views  in  regard  to  their 
deduction,  number,  and  arrangement. 

%  XIII.   The  Fundamental  Laws  of  Thought,  or  the  condi- 
tions of  the  thinkable,  as  commonly  received, 
Par.  XIII.    Pun-         arcfour:  — 1.  The  Law  of  Identity;  2.  The 

damental    Ijaws    of  ,      , 

Thought.  Law  of  Contradiction  ;  3.  The  Law  of  Ex- 

clusion or  of  Excluded  Middle  ;  and,  4.  The 
Law  of  Reason  and  Consequent,  or  of  Sufiicient  Reason. 

Of  these  in  their  order. 

%  XIV.    The  principle  of  Identity  (principium  Identitatis) 

expresses  the  relation  of  total  sameness  in 

Par.  XIV.  Law  of        which  a  coucept  stands  to  all,  and  the  rela- 

Identity.  ^    ^  .  ' 

tion  of  partial  sameness  in  which  it  stands 
to  each,  of  its  constituent  characters.  In  other  words,  it  de- 
clares the  impossibility  of  thinking  the  concept  and  its  charac- 
ters as  reciprocally  unlike.  It  is  expressed  in  the  formula  A  is 
Ay  or  Az=A;  and  by  A  is  denoted  every  logical  thing,  every 
product  of  our  thinking  faculty,  —  concept,  judgment,  reason- 
ing, etc.^ 

The  principle  of  Identity  is  an  application  of  the  principle  of  the 
absolute  equivalence  of  a  whole  and  of  all  its 
parts  taken  together,  to  the  thinking  of  a  thing 
by  the  attribution  of  constituent  qualities  or  characters.  The  concept 
of  the  thing  is  a  whole,  the  characters  are  the  parts  of  that  whole.^ 
This  law  may,  therefore,  be  also  thus  enounced,  —  Everything  is 
equal  to  itself,  —  for  in  a  logical  relation  the  thing  and  its  concept 
coincide ;  as,  in  Logic,  we  abstract  altogether  from  the  reality  of  the 
thing  which  the  concept  represents.  It  is,  therefore,  the  same 
whether  we  say  that  the  concept  is  equal  to  all  its  characters,  or 
that  the  thing  is  equal  to  itself.^ 

The  law  has,  likewise,  been  expressed  by  the  formula  —  In  the 

1  [Schulze,  Logik,  §  17.    Gerlach,  Logik,  i         2  See  Schulze,  iogiA,  p.  32-3.  —  Ed. 
37.]    Cf.  Krug-,  Logik,  §  17.  —  Ed.  3  See  Krug,  Lo^k,  p.  40.  —  Ed. 

8 


58  LOGIC.  Lect.  V. 

predicate,  the  whole  is  contained  explicitly,  which  in  the  subject  is 
contained  implicitly.  It  is  also  involved  in  the  axiom  —  Nota  notcn 
est  nota  rei  ipsius} 

The  logical  importance  of  the  law  of  identity  lies  in  this  —  that 
Its  logical  importance  '^^  ^^  ^he  principle  of  all  logical  affirmation  and 
—The  principle  of  all       definition.     An  example  or  two  may  be  given  to 

logical  affirmation  and         illustrate  this. 

'^''^""'•'"•-  1.    In  a  concept,  which  we  may  call  Z,  the 

characters  a,  5,  and  c,  are  thought  as  its  constituents;  consequently, 

the  concept,  as  a  unity,  is  equal  to  the  characters 

This  illustrated.  ,  ^  I  „         ,  j         ^-r-.,^ 

taken  together  —  Z  =  (a  +  o  +  c).  If  the  former 
be  affirmed,  so  also  is  the  latter  ;  therefore,  Z  being  {a-^h  +  c)  is  a, 
is  J,  is  c.  To  take  a  concrete  example :  The  concept  man  is  a 
complement  made  up  of  the  characters,  1°,  substance,  2°,  material, 
S°,  organized^  4",  animated^  5°,  rational^  6°,  of  this  earth  ;  in  other 
words  man  is  substance,  is  material,  is  organized,  is  animated,  is  ra- 
tional. JSeitig,  as  entering  into  every  attribution,  may  be  discharged 
as  affording  no  distinction. 

2.  Again,  suppose  that,  in  the  example  given,  the  character  a  is 
made  up  of  the  characters  I,  m,  n,  it  follows,  by  the  same  law  of 
Identity,  that  Z  =  a  =  (^  m,  n)  is  I,  is  m,  is  n.  The  concept  man 
contains  in  it  the  character  animal,  and  the  character  animal  con- 
tains in  it  the  characters  corporeal,  organized,  limn{f,  etc. 

The  second  law  is  the  principle  of  Contradiction  or  Non-contra- 
diction, in  relation  to  which  I  shall  dictate  the  following  paragraph  : 

%  XV.   When  an  object  is  determined  by  the  affirmation  of 
a  certain  character,  this  object  cannot  be 
Contradiction.  thought  to  be  the  samc  when  such  charactei" 

is  denied  of  it.  The  impossibility  of  this  is 
enounced  in  what  is  called  the  principle  of  Contradiction 
(principiuTn  Contradictionis  seu  HepiignatiticB).  Assertions 
concerning  a  thing  are  mutually  contradictory,  when  the  one 
asserts  that  the  thing  possesses  the  character  which  the  other 
asserts  that  it  does  not.  This  law  is  logically  expressed  in  the 
fonnula — What  is  contradictory  is  unthinkable.  A  =  not 
A=zO,  or  A~A=0. 

Now,  in  the  first  place,  in  regard  to  the  name 
Its propername.  n    ^  •     ■,  •  \  ^  i     i 

ot  this  law.  It  may  be  observed  that,  as  it  en- 
joins the  absence  of  contradiction  as  the  indispensable  condition  of 

1  See  Kant,  Logik,  p.  40.  —  £o. 


Li:CT.  V.  LOGIC.  59 

thought,  it  ought  to  be  called,  not  the  Law  of  Contradiction,  but 
the  Law  of  Non-contradiction,  or  of  non-repugnantia} 

This  law  has  frequently  been  enounced  in  the  formula  —  It  is 
impossible  that  the  same  thing  can  at  once  be  and 
not  be ;  but  this  is  exposed  to  sundry  objections. 
It  is  vague,  and  therefore  useless.  It  does  not  indicate  whether  a 
real  or  a  notional  existence  is  meant ;  and  if  it  mean  the  former, 
then  is  it  not  a  logical  but  a  metaphysical  axiom.  But  even  as  a 
metaphysical  axiom  it  is  imperfect ;  for  to  the  expression  at  once 
{simul)  must  be  added,  in  the  same  place,  in  the  same  respect,  etc? 

This  law  has  likewise  been  expressed  by  the  formula  —  Contra- 
dictory attributes  cannot  be  united  in  one  act  of  consciousness.  But 
this  is  also  obnoxious  to  objection.  For  a  judgment  expresses  as 
good  a  unity  of  consciousness  as  a  concept.  But  when  I  judge,  that 
round  and  square  are  contradictory  attributes,  there  'are  found  in 
this  judgment  contradictory  attributes,  but  yet  a  unity  of  con- 
sciousness. The  formula  is,  therefore,  vaguely  and  inaccurately 
expressed. 

The  logical  import  of  this  law  lies  in  its  being  the  principle  of  all 
logical  negation  and  distinction. 

The  principle  of  all  r^^^  j.^^^  ^f  Identity  and  the  law  of  Contra- 

logical    negation    and  -,.      .  i-  -,  •  n  i      • 

distinction.  diction  are  coordinate  and  reciprocally  relative, 

'"~~ancnTertTier  can  be  educed  as  second  from  the 


other  as  first ;  for  in  every  such  attempt  at  derivation,  the  supposeoT 
secondary  law  is,  in  fact,  always  necessarily  presuppose<L^^rhese 
are,  in  iact,  one  and  the  same  law,  di^ring  only  by  a  positive  and 
negative  expression. 

In  relation  to  the  third  law,  take  the  following  paragraph  : 

t  XVI.  The  principle  of  Excluded  Third  or  Middle  —  viz., 
between  two  contradictories  (p'inciphan 
Excluded  Middir  "  JBxclusi  MedH  vel  Tertii),  enounces  that 
condition  of  thought  which  compels  us,  of 
two  repugnant  notions,  which  cannot  both  coexist,  to  think 
either  the  one  or  the  other  as  existing.  Hence  arises  the  gen- 
eral axiom  —  Of  contradictory  attributions,  we  can  only  affirm 
one  of  a  thing ;  and  if  one  be  explicitly  affirmed,  the  other  is  im- 
plicitly denied.     A  either  is  or  is  not.     A  either  is  or  is  not  B.^ 

By  the  laws  of  Identity  and  Contradiction,  I  am  warranted  to 

1  Compare  Krug,  Logik,  §  18.  —  Ed.  3  This  is  shown  more  in  detail  by  Hoffbauer 

2  Compare  the  criticism  of  Kant,  Kritik  d.r.      ^nfaas^grHnde  der  Logik,  §  23.  --  Ed. 
v.,  p.  134,  ed.  Kosenkranz.  —  Ed.  4  See  Schulze,  Xog^i,  §  19;  —  Ed. 


60  LOGIC.  Lect.  V. 

conclude  from  the  truth  of  one  contradictory  proposition  to  the 

falsehood  of  the  other,  and  by  the  law  of  Ex- 

Logicai  significance       ^j^^^^  Middle,  I  am  warranted  to  conclude  from 

of  this  law. 

the  falsehood  of  one  contradictory  proposition  to 
the  truth  of  the  other.  And  in  this  lies  the  peculiar  force  and  import 
of  this  last  principle.  For  the  logical  significance  of  the  law  of  Ex- 
cluded Middle  consists  in  this,  that  it  limits  or  shuts  in  the  sphere 
of  the  thinkable  in  relation  to  affirmation  ;  for  it  determines,  that, 
of  the  two  forms  given  in  the  laws  of  Identity  and  Contradiction, 
and  by  these  laws  affirmed  as  those  exclusively  possible,  the  one  or 
the  other  must  be  affirmed  as  necessary. 

The  law  of  Excluded  Middle  is  the  principle  of  Disjunctive  Judg- 
ments, that  is,  of  judgments  iu  which  a  plurality 
The  principle  of  Dis-      of  judgments  are  contained,  and  which  stand  in 

janctive  Judgments.  ,  .  i       i      •  i  i  /v.  • 

\  such  a  reciprocal  relation  that  the  affirmation  of 

one  is  the  denial  of  the  other. 
I  now  go  on  to  the  fourth  law. 

%  XVII.     The  thinking  of  an  object,  as  actually  character- 
ized by  positive  or  by  negative  attributes,  is 
Par.  xvn.  Law  of      not  left  to  the  caprice  of  Understanding  — 
Sufficient  Beason.  or       ^^^  faculty  of  thought ;    but  that   faculty 

of  Beason  and  Conse-  "^  . 

quent.  must  be  necessitated  to  this  or  that  deter- 

minate act  of  thinking  by  a  knowledge  of 
something  different  from,  and  independent  o^  the  process  of 
thinking  itself.  This  condition  of  our  understanding  is  ex- 
pressed by  the  law,  as  it  is  called,  of  Sufficient  Reason  {princi- 
pium  Rationis  Siifficientis)  ;  but  it  is  more  properly  denomi- 
nated the  law  of  Reason  and  Consequent  {principiurn  Mationis 
et  Consecutionis).  That  knowledge  by  which  the  mind  is 
necessitated  to  affirm  or  posit  something  else,  is  called  the  logi- 
cal reason,  ground,  or  antecedent;  that  something  else  which 
the  mind  is  necessitated  to  affirm  or  posit,  is  called  the  logical 
consequent;  and  the  relation  between  the  reason  and  conse- 
quent, is  called  the  logical  connection  or  consequence.  This 
law  is  expressed  in  the  formula  —  Infer  nothing  without  a 
ground  or  reason.* 

Relations  between  The    relations   between   Reason   and   Conse- 

Beason  and  Conse-  quent,  when  comprehended  in  a  pure  thought, 
**"*"*■  are  the  following : 

1.  When  a  reason  is  explicitly  or  implicitly  given,  then  there  must 

1  See  Scliulzc,  Losik,  §  19,  and  Krug,  Logik,  §  20.  —  Ei>. 


Lect.  V.  LOGIC.  01 

exist  a  consequent;  and,  vice  versa,  when  a  consequent  is  given, 
there  must  also  exist  a  reason. 

2.  Where  there  is  no  reason  there  can  be  no  consequent ;  and, 
vice  versa,  where  there  is  no  consequent  (either  implicitly  or  explic- 
itly) thei-e  can  be  no  reason.     That  is,  the  concepts  of  reason  and  of 
consequent,  as  reciprocally  relative,  involve  and  suppose  each  other. 
The  logical  significance  of  the  law  of  Reason  and  Consequent  lies 
in  this, — That  in  vii'tue  of  it,  thought  is  consti- 
^IIJjcBi^significance      ^^^^^^  -^^^^  ^  g^^.j^^  ^f  ^^^^  ^^j  indissolubly  Con- 
nected ;    each  necessarily    inferring   the   other. 
Thus  it  is  that  the  distinction  and  opposition  of  possible,  actual  and 
necessary  mattei*,  which  has  been  introduced  into  Logic,  is  a  doc- 
trine wholly  extraneous  to  this  science. 

I  may  observe  that  "Reason  is  something  different  from  Cause, 

and  Consequent  something  different  from  Effect; 

Reason  and  Conse-       ^hough  cause  and  effect,  iu  SO  far  as  they  are 

quent,  and  Cause  and  .        ^  .  .        , 

Effect.  conceived  m  thought,  stand  to  each  other  m  the 

relation  of  reason  and  consequent.  Cause  is 
thus  thought  of  as  a  real  object,  which  affords  the  reason  of  the 
existence  of  another  real  object,  the  effect ;  and  effect  is  thought  of 
as  a  real  object,  which  is  the  consequent  of  another  real  object,  the 
cause.  Accordingly,  every  cause  is  recognized  in  thought  as  a  rea- 
son, and  every  effect  is  recognized  in  thought  as  a  consequent ;  but 
the  converse  is  not  true,  that  every  reason  is  really  considered  a 
cause,  and  every  consequent  really  considered  an  effect.  We  must, 
therefore,  carefully  distinguish  mere  reason  and  mere  consequent, 
that  is,  ideal  or  logical  reason  and  consequent,  from  the  reason 
which  is  a  cause  and  the  consequent  which  is  an  effect,  that  is,  real 
or  metaphysical  reason  and  consequent. 

"  The  expression  logical  reason  and  consequent  refers  to  the  mere 

synthesis  of  thoughts;  whereas  the  expression 

Logical  and  Meta-       metaphysical  reason  and  consequent  denotes  the 

physical   Reason  and  ,  .  ^       .  tt  i  • 

r,  .  real  connection  ot  existences.     Hence  the  axiom 

Consequent. 

of  Causality,  as  a  metaphysical  principle,  is  es- 
sentially different  from  the  axiom  of  Reason  and  Consequent,  as  a 
logical  principle.  Both,  however,  are  frequently  confounded  with 
each  other;  and  the  law  of  Reason  and  Consequent,  indeed,  for- 
merly found  its  place  in  the  systems  of  Metaphysic,  while  it  was 

not,  at  least  explicitly,  considered  in  those  of 
Generality  of  the       Logic.    The  two  terms  condition  and  conditioned 

terms  Condition  and         i      "^    -i  ,  ,^  ^    ^-  \,    j.x.       e 

„     ...      ,  happily  express  at  once  the  relations   both   oi 

reason  and  consequent,  and  of  cause  and  effect. 

A  condition  is  a  thing  which  determines  (negatively  at  least)  the 


62  LOGIC.  Lect.  V. 

existence  of  another;  the  conditioned  is  a  thing  whose  existence  is 
determined  in  and  by  another.  If  used  in  an  ideal  or  logical  signifi- 
cation, condition  and  conditioned  import  only  the  reason  in  conjunc- 
tion with  its  consequent ;  if  used  in  a  real  or  metaphysical  sense, 
they  express  the  cause  in  connection  with  its  effect." ' 

I  have  now,  in  the  prosecution  of  our  inquiry  into  the  fundamen- 
tal laws  of  logical  thinking,  to  say  a  few  words 
History  of  the  de-       in  regard  to  their  History,  — their  history  being 
veiopment  of  the  fun-       ^^^  narration  of  the  order  in  which,  and  of  the 

damental     Laws     of  .      i        i 

Thought.  philosophers  by  whom,  they  were  articulately 

developed. 

Of  the  first  three  laws,  which,  from  their  intimate  cognition,  may 

not  unreasonably  be  regarded  as  only  the  three 

The  law  of  Identity      gj^jgg  ^^  phascs  of  a  single  law,  the  law  of  Iden- 

last  developed  in  the  .  i      r>  •        i  i  n 

order  of  time  *^*y»  which  Stands  farst  in  the  order  of  nature, 

was  indeed  that  last  developed  in  the  order  of 
time ;  the  axioms  of  Contradiction  and  of  Excluded  Middle  having 
been  long  enounced,  ere  that  of  Identity  had  been  discriminated 
and  raised  to  the  rank  of  a  coordinate  principle.     I  shall  not,  there- 
fore, now  follow  the  order  in  which  I  detailed  to  you  these  laws, 
but  the  order  in  which  they  were  chronologically  generalized. 
The  principles  of  Contradiction  and  of  Excluded  Middle  can  both 
be  traced  back  to  Plato,  by  whom   they  were 
The  principles    of       euounccd  and  frequently  applied ;  though  it  was 
,*"! "?  «.!T,  ""     ^        not  till  long  after,  that  either  of  them  obtained 

eluded  Middle  can  be  ... 

traced  back  to  Plato.        ^  distinctive  appellation.     To  take  the  principle 

of  Contradiction  first.   This  law  Plato  frequently 

employs,  but  the  most  remarkable  passages  are  found  in  the  Phcedo^ 

in  the  Sophista^  and  in  the  fourth  and  seventh  books  of  the  Reiyublic? 

This  law  was,  however,  more  distinctively  and 

Law  of  Contradic-       emphatically   enounced   by  Aristotle.     In  one 

tion         emphatically  ,         «  ,  x     •  •/• 

enoanced  by  Aristotle.      V^^^^^  "^  says :  « It  IS  manifest  that  no  one  can 

conceive  to  himself  that  the  same  thing  can  at 

once  be  and  not  be,  for  thus  he  would  hold  repugnant  opinions, 

1  Kmg,  Lo^iA,  pp.  62,  63.    This  exposition  For,  in  as  much  as  this  principle  is  not  mate- 

of  the  law  of  Reason  and  Consequent  does  rial,  it  is  only  a  derivation  of  the  three  for 

not  represent  the  Author's  latest  view.    In  a  mal  laws;  and  in  as  much  as  it  is  material,  it 

note  to  the  Discussions,  p.  160  (where  a  similar  coincides  with  the  principle  of  Causality,  and 

doctrine  had  been  maintained  in  the  article  is  extra-logical."      The  Laws  of   Thought, 

as  originally  published),  he  says:  "The  logi-  properly  so  called,  are  thus  reduced  to  three, 

cal  relation  of  Reason  and  Consequent,  as  more  —those  of    Identity,    Contradiction,    rad  Ex- 

than  a  mere  corollary  of  the  law  of  Noneon-  eluded  Middle.  — Ed. 

fra(fJf/ion  in  its  three  phases,  is,  I  am  confident  „„      „,              ,„„     „    ,.           ^_    _ 

of  proving,  erroneous."    And  again,  in  the  />  See  PA^rfo,  p.  103;  5i>pA»«a,  p.  252;  Repub- 

same  work,  p.  603 :  "  The  principle  of  S.ffi-     '"'  *''•  P'  *^'  "*'•  P"  ^-  "  ^- 
cient  Reason  should  be  excluded  from  Logic.         3  Metaph.,  I.  iii.  (iv.)  c.  8. 


Lect.  V.  LOGIC.  63 

and  subvert  the  reality  of  truth.  Wlierefore,  all  who  attempt  to 
demonstrate,  reduce  everything  to  this  as  the  ultimate  doctrine ;  for 
this  is  by  nature  the  principle  of  all  other  axioms."  And  in  several 
passages  of  his  Metaphysics^^  in  his  Prior  Analytics^-  and  in  his 
Posterior  Analytics,^  he  observes  that  "some  had  attempted  to 
demonstrate  this  pririciple,  —  an  attempt  which  betrayed  an  igno- 
rance of  those  things  whereof  we  ought  to  i-equire  a  demonstration, 
and  of  those  things  whereof  we  ought  not :  for  it  is  impossible  to 
demonstrate  everything;  as  in  tliis  case,  Ave  must  regress  and  re- 
gress to  infinity,'  and  all  demonstration  would,  on  that  supposition, 
be  impossible." 

Following  Aristotle,  the  Peripatetics  established  this  law  as  the 

highest  principle   of   knowledge.       From    the 

•    J    u- !    !"^^  ^•"      Greek  Aristotelians   it   obtained  the  name   by 

ics  the  highest  priuci-  _  ^  •' 

pie  of  knowledge.  Ob-  which  it  has  Subsequently  been  denominated, 
tained  its  name  from  the  principle,  ov  law,  OY  axiom,  of  contradiction^ 
the  Greek    Aristote-       (--^^'^^a  T^5  (lvTi<^(io-£a>s).     This  name,  at  least,  is 

found  in  the  Commentaries  of  Ammonius  and 
Philoponus,  where  it  is  said  to  be  "  the  criterion  which  divides  truth 

from  falsehood  throughout  the  universe  of  exist- 
g     g  '  ence."*    The  schoolmen,  in  general,  taught  the 

same  doctrine;  and  Suarez  even  says,  that  the 
law  of  contradiction  holds  the  same  supremacy  among  the  princi- 
ples of  existence.^ 

After  the  decline  of  the  Aristotelian  philosophy,  many  controver- 
sies arose  touching  the  truth,  and  still  more  touching  the  primitive 

or  Axiomatic  character,  of  this  law.     Some  main- 
Controversies      re-       tained  that  it  was  indemonstrable  ;  others  that  it 

specting  the  truth  and  ,,,  •-,  -         ....  ,, 

character  of  this  law.        ^ould  be  proved,  but  provcd  only  andn-ectly  by  a 

reductio  ad  absurdum;  while  others,  again,  held 

that  this  could  be  directly  done,  and  that,  consequently,  the  law  of 

Contradiction  was  not  entitled  to  the  dignity  of  a  first  principle.* 

L.  iii.  c.  4.  T^f  ovToiv  koL  fxyj  ovtwv  StatptT  rh  iptvSos  kcH 

2  L.  ii.  c.  2.  T^y  aXri^elav.     In  Anal.  Post.,  1,  i.  c.  xi.  f  30 

"  ^-  '•  *'•  2-  b.  — Ed.    [Cf.  Augustinus  Niphus  Suessanus, 

4  For  the  name,  see  Ammonins,  In  De  Inter-  /„  ^„ai.  Post.,  p.  88,  ed.  Paris,  1540.] 
pnt.,  Comment.,  p.  153  b.  ed.  Aid.  Venet.  1546. 

Philoponus,  In  Anal.  Pr.,  p.    13  b,  38  b,  ed.  ^  ^^^  [Alstedius,  4rt,«m  Liberallum  Syslema 

Vcnet.  1535.     In  Anal.  Post.,  p.  30  b,  ed.  AM.  <^^'°''  P"  l'*'     "  Cognitio  a  priori  est  principi- 

Venet.  1534.    The  language  quoted  in  the  text  "'■"™ '  '''^"  *!"'*  *«"''"  '^"*'"  ^"""^  ^mposs,b,U 

is  nearly  a  translation  of  Ammonius /n  Cat.g..  "'  i'lnn  esse  et  non  esse.  .  .  .  Consule  Metaph., 

,,„         ■„      \       V             /                 1    ,     ,    '  Suarezii : — 'Hoc,   inquam,  tenet    primatum 

p.  140  a.      H  fiev  yap  Kara^acrts  kcu  airdd)-  .   ,          ...                        j-     •„  »  r»„.,„  ,-„*„, 

..      ,         ,  inter  pnncipia  cognoscendi,  sicut  Deus  inter 

affis  ad  iirl  ttuutwu  rwv  ovriav  Koi  m/J  ovtwv  principia  esseudi.'  "] 

S.oipe?  Tb  d-yija^s  Ka\  rh  vj/eDSos.    Ammon-  6  Cf.  Suarez.2>«>pwta«(on«  JMe/apAysir«,  Disp. 

ius  is  followed  by  Philoponus,  who  says,—  iii.^3._ED.    [Alstedius,  Encyc?o/j«rfio.  1.  iii., 

Ti  8i  rrts  avricpd(rea>s  a^i<i>/xa  eirl  iravTuv  ftkv  Archelogia,  c.  vii.  p.  80] 


64  LOGIC.       ,  Lbct.  V. 

In  like  manner,  its  employment  was  made  a  further  matter  of 
controversy.  Finally,  it  was  disputed  whether  it  were  an  imme- 
^ii^tCj^ jiatiA'e,_or  «  ^tor/^^timi  of  intelligence;  or  whether  it 
were  an  a  posteriori  and  adventitious  generalization  from  experi- 
ence. The  latter  alternative,  that  it  was  only  an  induction,  was 
maintained  by  Locke.^  This  opinion  was,  how- 
^*"^^"  ever,  validly  refuted  bv  Leibnitz,  who  showed 

Leibnitz.  ,         .     .        \     .        , 

that  it  IS  admitted  the  moment  the  terms  of  its 
enunciation  are  understood,  and  that  we  implicitly,  follow  it  even 
when  we  are  not  explicitly  conscious  of  its  dictate.^  Leibnitz,  in 
some  parts  of  his  works,  seems  to  identify  the  principles  of  Iden- 
tity and  Contradiction  ;  in  others,  he  distinguishes  them,  but  educes 
the  law  of  Identity  out  of  the  law  of  Contradiction.^  It  is  needless 
to  pursue  the  subsequent  history  of  this  principle,  which  in  latter 
times  has  found  none  to  gainsay  the  necessity 
Its  truth  denied  by       ^^^  universality  of  its  truth,  except  among  those 

modern  absolutists.  .1  ,  1        •     /-i 

philosophers  who,  m  Germany,  have  dreamt  that 
man  is  competent  to  a  cognition  of  the  absolute  :  and  as  a  cognition 
of  the  absolute  can  only  be  established  through  positions  repug- 
nant, and,  therefore.  On  logical  principles,  mutually  exclusive,  they 
have  found  it  necessary  to  start  with  a  denial  of  the  fundamental 
laws  of  thought;  and  so,  in  their  effort  to  soar  to  a  philosophy 
above  logic  and  intelligence,  they  have  subverted  the  conditions  of 
human  philosophy  altogether.  Thus  Schelling  and  Hegel  prudently 
repudiated  the  principles  of  Contradiction  and  Excluded  Middle  as 
having  any  application  to  the  absolute ;  *  while  again  those  philoso- 
phers (as  Cousin)  who  attempt  a  cognition  of  the  absolute  without 
a  preliminary  repudiation  of  the  laws  of  Logic,  at  once  involve 
themselves  in  contradictions,  the  cogency  of  which  they  do  not  deny, 
and  from  which  they  are  wholly  unable  to  extricate  themselves.* 
• 

1  'EsM.y^  B  i.  ch.  ii.  §  4. —Ed.  pointed  out  by  the  latter  in  his  GeicAiehie  der 

2  Noiiveaiix  K'isnis,  li.  i.  ch.  i   §4.  — Ed.  Philosophic,   {Werke,    xv.    p.   598.)  — Ed.     [On 

3  Compare  Tlicodicie,  (  44,  Monadologie,^  31,  rejection  of  the  Logical  Laws,  by  Schelling, 
with  Nouvtaux  Essais,  1.  i.  ch.  i.  §  10;  1.  iv.  IIegeI,etc.,see  Baclimann,  Uber  die  Philosophie, 
ch.  ii.  §  1.  —  Ed.  tneiner  Zeic,  p.  218,  ed.  Jena,  1816.    Bolzano, 

4  See  Schelling,  Voin  Ich  als  Princip  drr  Phi-  WssenschaftsUhre,  iv.,  Logik,  §  718.  Sigwart, 
loxophif,  §  10;  Hegel,  Logik,  b.  ii.  c.  2;  Encyk-  Logilc,  5  58,  p.  42,  ed.  1835.  Herbart,  De  Priu- 
lopdrJie,  §  115,  119.  Schelling  endeavors  to  cipio  Logieo  Exclusi  Medii  inter  ContrtuJictoria 
abrogate  the  principle  of  Contradiction  in  nan  negligendo,  Gofting,  1833.  Hartenstein, 
relation  to  the  higher  philosophy,  by  assnm-  Df  Meihodn  Phitosophia  Logica  Lfgihux  adxtrin- 
ing  that  of  Identity;  the  empirical  antago-  g'ti'lti,  Jinibiis  non  terminanda,  Lipsix,  1836. 
nism  between  ego  and  non-ego  being  merged  Ou  the  logical  and  metaphysical  significance 
in  the  identity  of  the  absolute  ego.  Hegel  of  the  principle  of  Contradiction,  see  Plat- 
regardsbofh  principles  alike  as  valid  only  for  ner,  P/til.  Aph..  I.  ^  673,  and  Kant,  Kritik  d. 
the  finite  Understanding,  and  as  innpplicnble  rtinen  IWnunft.  p.  191.  ed.  1790.] 

to  the  higher  processes  of  the  Reason.    This         «  See  the  Author's  criticism  of  Cousin,  Dir 
difference  between  the  two  philosophers  is     cussions,  p.  I  tt  seq. — Ed. 


Lect.  V.  LOGIC.  65 

But  this  by  the  way,  and  on  a  subject  which  at  present  you  cannot 
all  be  supposed  to  understand. 

The  law  of  Excluded  Middle  between  two  contradictories  re- 
mounts, as  I  have  said,  also  to  Plato,  though  the 
Law  of  Excluded       ^econd  AlciUades,  the  dialogue  in  which  it  is 

Middle.  '  ° 

most  clearly  expressed,  must  be  admitted  to  be 

spurious.^     It  is  also  in  the  fragments  of  Pseudo-Archytas,  to  be 

'    found  in  Stobaeus.^     It  is  explicitly  and  emphat- 

Expiicitiy  enounced       .^j^jj     enounced  by  Aristotle  in  many  passages 

by  Aristotle.  ''  *^  ^    i  o 

both  of  his  Metaphysics  (1.  iii.  (iv.)  c.  7.)  and 
of  his  Aoialytics,  both  Prior  (1.  i.  c.  2)  and  Posterior  (1.  i.  c.  4).    In 
the  first  of  these,  he  says :  "  It  is  impossible  that  there  should  exist 
any  medium  between  contradictory  opposites,  but  it  is  necessary 
either  to  afiimi  or  to  deny  everything  of  everything."     And  his  ex- 
pressions are  similar  in  the  other  books.     Cicero  says  "that  the 
foundation    of   Dialectic   is,   that   whatever    is; 
enounced  is  either  true  or  false."     This  is  from 
his  Academics  (1.  ii.  c.  xxix.),  and  there  are  parallel  passages  in  his 
Topics  (c.  xiv.)  and  his  De  Oratore  (1.  ii.  c.  xxx.).     This  law,  though  i 
universally  recognized  as  a  principle  in  the  Greek  Peripatetic  school, , 
and  in  the  schools  of  the  middle  ages,  only  received  the  distinctive  • 
appellation  by  which  it  is  now  known  at  a  comparatively  modern ; 
date.^     I  do  not  recollect  having  met  with  the  term  principium  eX'- 
clusi  medii  in  any  author  older  than  the  Leib— 
nitzian  Baumgarten,*  though  Wolf*  speaks  of 
the  exclusio  medii  inter  contradictoria. 

The  law  of  Identity,  I  stated,  was  not  explicated  as  a  coordinate- 
principle  till  a  comparatively  recent  period.    The. 
Law  of  Identity.  earliest  author  in  whom  I  have  found  this  done, 

Antonius  Andreas. 

is  Antonius  Andreas,  a  scholar  of  Scotus,  who-^ 
flourished  at  the  end  of  the  thirteenth  and  beginning  of  the  four- 
teenth century.  The  schoolman,  in  the  fourth  book  of  his  Com- 
mentary of  Aristotle's  Metaphysics^^  —  a  commentary  which  is  fullC 
of  the  most  ingenioiis  and  original  views, —  not  only  asserts  to  the- 
law  of  Identity  a  coordinate  dignity  with  the  law  of  Contradiction,. 

1  Second  Alcibiadef,  p.   139.      See   also    So-  nseus  Elementa  Loglea,  1.  ii.  c.  14,  [p.  172,  ed. 
phista,  p.  250.  —  Ed.  1603.   "  Contradicentium  usus  explicatur  uno  • 

2  Ecloga.  1.  ii.  c.  2,  p.  158,  ed.  Antwerp,  1575;  axiomate :  —  Contradicentia  non  possunt  de  • 
Part  ii,  torn.  1,  p.  22,  ed.  Heeren.  Cf.  Simpli-  eodem  simul  esse  vera;  et  necessarium  est. 
cius,  In  Arist.  Categ.,  pp.  97,  103,  ed.  Basil,  contradicentium  alterum  cuilibet  rei  conven- 
1551.  —  Ed.                              •  ire,  alterum  non  convenire."  —  Ed.] 

3  Lex  contradictoriamm,  principium  cotUradi-  ^  j^taphysica,  §  10.  -  Ed. 
eentium  (sc.  propositionum),    as    used  in  the 

schools,  included  the  law  of  Contradiction         *  On/oiog-io,  H  62,  53. 

and  the  law  of  Excluded  Middle.    See  Moli-        6  Quaestio  v.  p.  21  a,  ed.  Venet.,  1513.  —  Ed» 


66  LOGIC.  Lect.  V. 

but,  against  Aristotle,  he  maintains  that  the  principle  of  Identity, 
and  not  the  principle  of  Contradiction,  is  the  one  absolutely  firat. 
The  formula  in  which  Andreas  expressed  it  was  Ens  est  ens.     Sub- 
sequently to  this  author,  the  question  concerning  the  relative  prior- 
ity of  the  two  laws  of  Identity  and  of  Contradiction  became  one 
much  agitated  in  the  schools ;  though  there  were  also  found  some 
who  asserted  to  the  law  of  Excluded  Middle  this  supreme  rank.* 
Leibnitz,  as  I  have  said,  did  not  always  distin- 
guish the  principles  of  Identity  and  of  Contra- 
diction.    By  Wolf  the  former  was  styled  the  principle  of  Certainty, 
{principium   Certiticdinis) -^^  but  he,  no   more 
than  Leibnitz  himself,  sufficiently  discriminated 
between  it  and  the  law  of  Contradiction.     Tiiis  was,  however,  done 
by  Baumgarten,  another  distinguished  follower 

Baumgarten.  ^t-i-^         in  ^  •       •  •       i     ^ 

01  Leibnitz,'^  and  irom  him  it  received  the  name 
of  the  principle  of  Position,  that  is,  of  Affirmation   or  Identity, 
{princiinum  Positionis  sive  Identitqtis),  —  the  name  by  which  it  is 
now  universally  known.     This  principle  has  found  greater  favor,  in 
the  eyes  of  the  absolutist  philosophers,  than  those  of  Contradiction 
and  Excluded  Middle.    By  Fichte  and  Schelling 
Fichte  and  Schei-       -^  j^jjg  ^jggQ  placed  as  the  primary  principle  of  all 
jj*    ,  philosophy.*    Hegel  alone  subjects  it,  along  witl> 

the  other  laws  of  thought,  to  a  rigid  but  fall.i- 
cious  criticism  ;  and  rejects  it  along  with  them,  as  belonging  to  that 
lower  sphere  of  knowledge,  which  is  conversant  only  with  the  rela- 
tive and  finite.* 

The  fourth  law,  that  of  Reason  and  Conso- 
Law  of  Reason  and  quent,  which  Stands  apart  by  itself  from  the  othc:- 
n  equen  .  three,  was,  like  the  laws  of  Contradiction  and 

Secognized  by  Plato  ' 

and  Aristotle.  Excluded  Middle,  recognized  by  Plato.®    He  lays 

it  down  as  a  postulate  of  reason,  to  admit  noth- 
ing without  a   cause ;    and    the    same   is  frequently  done    by  his 
.    „       ,  scholar  Aristotle.^     Both,  however,  in  reference 

,.,».,  to  this  principle,  employ  the   ambis^uous  term 

cause  (alria  aiTiov).  Aristotle,  indeed,  distin- 
guishes the  law  of  Reason,  as  the  ide.'il  principle  of  knowledge  (apxrj 

I  [Alex,  de  Ales,  Tn  Arist.  Metapk.,  iv.  t.  9.]         »  Metaphysica.  i  11.  — Ed. 
Compare  Suarez,  Disp.  Mftaph.,  Disp.  iii.  §  3.  *  See  Fichte,  Cruiuilage  der  gtsammten  Ww- 

Alexander  professes  to  agree  with  Aristotle  stnxckq/UUhre,  }  I.  Schelling,  Vom  IcA,  §  7.  - 

in  Riving  the  first  place  to  the  principle  of  Ed. 

Contradiction,  but,  in  fact,  he  identifies  it        5  See  above,  p.  64,  note  4.  —  Ed. 
with  that  of  Excluded  Middle,  de  ptovis  affix-         6  PMUbus,  p.  26.  —  Ed. 
•natio  vel  nrgatio.  —  ElD.  7  E.  g.  Atuil.  Post.,  ii.  16;  Phys  ,  ii.  3;  Metapk^ 

3  Ontologia, }  65,  288.  —Ed.  i.  1.  3;  Rktt.,  Ii.  23.  —  Ed. 


Lect.  V.  LOGIC.  67 

T^s  yvoKTeo)?,  principium   cognoscendi),  from  the  real  principle  cf 

Production,  (a/3X7  ""^  ycveo-coj?,  principium  Jiendi,  — prificipium  c,^ 

sendi)}     By  Cicero,  the  axiom  of  reason    and 

J!^°^1"\.    ,  consequent  was,  in  like  manner,  comprehended 

The  Schoolmen.  ^  »  if 

under  the  formula,  nihil  sine  causa," — a  formuL; 
adopted  by  the  schoolmen ;  although  they,  after  Aristotle,  distin- 
gnished  under  it  the  ratio  essendi,  and  the  ratio  cognoscendi.' 

In  modern  times,  the  attention  of  philosophers  was  called  to  this 
law  of  Leibnitz,  who,  on  the  two  principles  of 
Leibnitz  called  at-      Rcason  and  ^of^oiitrgdtction"; Tounded  the  whole" 

tention  to  Law  of  Suf-  -t*.^  n   i  '         i  m — i""    ■»        tt     i"   "      i        "; — 

ficient  Reason.  edigce  of  his  philosophy.^ IJnder  the   latter 

law,  as  I  have  mentioned,  he  comprehended, 
however,  the  principle  of  Identity ;  and  in  the  former  he  did  not 
sufficiently  discriminate,  in  terms,  the  law  of  Causality,  as  a  real 
principle,  from  the  law  of  Reason,  properly  so  called,  as  a  formal  or 
ideal  principle.  To  this  axiom  he  gave  various  denominations,  — 
now  calling  it  the  principle  of  Determining  Reason,  now  the  princi- 
ple of  Sufficient  Reason,  and  now  the  principle  of  Convenience  or 
Agreement  {convenientia) ;  making  it,  in  its  real  relation,  the  ground 
oF  all  existence ;  in  its  TcleaT7  tEe  ground  of  all  positive  knowledge. 
Orrtfaissubject  there  was  a  celebratelTcohtroversy  between  Leibnitz 
and^Dr.  Samuel  Clarke,  —  a  controversy  on  this,  as  on  other  points, 
eminerftly  worthy  ot  your  stu'dy.  Tlie  documents  in  which  this  con- 
troytfrsy  is  containetl,  w/'61'e  published  in  the  English  edition  under 
the  title,  ^1  collection  of  Papers  which  passed  between  the  late  learned 
Mr.  Leihnitz  and  Dr.  Clarke,  in  the  years  1715  and  1716,  relating 
to  the  Principles  of  Natural  Philosophy  and  Religion,  London, 
1717.* 

Wolf,  the  most  distinguished  follower  of  Leibnitz,  employs  the 

formula  —  "Nothing  is  without  a  sufficient  rea- 
Wolf.  ,      .    .  .         ,  ,      •     •  ,        . 

son  why  it  is,  rather  than  why  it  is  not ;  that  is, 

if  anything  is  supposed  to  be  {ponitur  esse),  something  also  must 
be  supposed,  whence  it  may  be  understood  why  the  same  is  rather 
than  is  not."^  He  blames  the  schoolmen  for  confusing  reason 
{ratio)  with  cause  (causa) :  but  his  censure  equally  applies  to  his 
master  Leibnitz,  as  to  them  and  Aristotle ;  for  all  of  these  philoso- 
phers, though  they  did  not  confound  the  two  principles,  employed 
ambiguous  terms  to  denote  them. 

1  Metaph.,iv.{v.)l. — Ed.  or  Identity  is  assumed  as  the  foundation  ol 

2  De  Divinatione,  ii.  c.  28.  —  Ed.  all  mathematics  and  that  of  Sufficient  Ilea- 

3  See  Tkcodicce,  §  44.    Monadologie,  §§  81,32.  son  as  the  foundation  of  natural  philosopliy 
--Ed.  —Ed. 

*  See  especially,  Leibnitz's  Second  Letter,         5  See  Fischer's  Logik,  [§  59,  p-  38,  ed.  1888 
D.  20,  in  which  the  principle  of  Contradiction      Compare  Wolf,  Ontologia,  §§  70,  71.  — Ed.] 


68  LOGIC.  Lect.  r. 

The   Leibnitian   doctrine  of  the  universality  of  the  law  of  Suffi- 
cient Reason,  both  as  a  principle  of  existence 
Discussion  regard-       ^^^  ^f  thought,  cxcitcd  much  discussion  among 

ing    the    Leibnitzian  ,         ,.,  ,  ^'      ^     -i        p  /^ 

doctrine  of  the  law  of  the  philosophers,  more  particularly  of  Germany. 
Sufficient  Reason.  In  the  earlier  half  of  the  last  century,  some  con- 

troverted the  validity  of  the  principle,  others 
attempted  to  restrict  it.^  Among  other  arguments,  it  is  alleged,  by 
the  advocates  of  the  former  opinion,  if  the  principle  be  admitted, 
that  everything  must  have  a  sufficient  reason  why  it  is,  rather  than 
why  it  is  not,  —  on  this  hypothesis,  error  itself  will  have  such  a  rea- 
son, and,  therefore,  must  cease  forthwith  to  be  error.^ 

Many  philosophers,  as  Wolf  and  Baumgarten,  endeavored  to 
demonstrate  this  principle  by  the  principle  of  Contradiction  ;  while 
others,  with  better  success,  showed  that  all  such  demonstrations 
were  illogical.^ 

In  the  more  recent  systems  of  philosophy,  the  universality  and 
necessity  of  the  axiom  of  Reason  has,  with  other  logical  laws,  been 
controverted  and  rejected  by  speculators  on  the  absolute.* 

1  As  Feuerlin  and  Daries.    See  Bachmann,  S  [Kiesewetter,  AUgemeine  Logik,  P.  i.  p.  67] ; 

Logik,  p.  66,  Leipsig,  1828 ;  Cf.  Degerando,  compare  Lectures  on  Metaphysics,  ii.  pp.  396, 

Hist.  Comp.  des  Syst.  de  PhU.,  t.  ii.  p.  146,  ed.  397,  notes.  —Ed. 

1804.  —  Ed.  *  [On    principle   of   Double   Negation  as 

S  See  Bachmann,  Logik,  p.  66.    With  the  another  law  of  Thought,  see  Fries,  Logik,  i 

foregoing  history  of  the  laws  of  Thought,  41,  p.  190;  Calker,  Denldehre  oder  Logik  und 

oompare  the  samb  author,  Logik,  §  18-31.—  Dialtktik,  §  166,  p.  463;  Beneke,  Lehrbuchder 

Ed.  Logik, }  64,  p.  41.] 


LECTURE    VI. 

STOICHEIOLOOY. 
SECTION    L  — NOETIC. 

THE  FUNDAMENTAL  LAWS   OF  THOUGHT  —  THEIR  CLASSIFI- 
CATION AND  IMPORT. 

Having  concluded  the  Introductory  Questions,  we  entered,  in 
our  last  Lecture,  upon  our  science  itself.     The 
api  u  a  1    .  g^^^  ^^^  ^^  Pure  Logic  is  the  Doctrine  of  Ele- 

ments, or  that  which  considers  the  conditions  of  mere  or  possible 
thinking.  These  elements  are  of  two  kinds,  —  they  are  either  the 
fundamental  laws  of  thought  as  regulating  its  necessary  products,  or 
they  are  the  products  themselves  as  regulated  by  those  laws.  The 
fundamental  laws  are  four  in  number,  —  the  law  of  Identity,  the  law 
of  Contradiction,  the  law  of  Excluded  Middle,  the  law  of  Reason 
and  Consequent.^  The  products  of  thought  are  three,  —  1°,  Con- 
cepts or  Notions ;  2°,  Judgments ;  and,  3°,  Reasonings.  In  our  last 
Lecture,  we  considered  the  first  of  these  two  parts  of  the  doctrine 
of  elements,  and  I  went  through  the  general  explanation  of  the  con- 
tents and  import  of  the  four  laws,  and  their  history.  Without  re- 
capitulating what  was  then  stated,  I  shall  now  proceed  to  certain 
general  observations,  which  may  be  suggested  in  relation  to  the  four 
laws. 

And,  first  of  all,  I  may  remark,  that  they  naturally  fall  into  two 
classes.     The  first  of  these  classes  consists  of 

General  observations  .      ,  t  •         ^ 

in  relation  to  the  four  the  three  principles  of  Identity,  Contradiction, 
ftindamentai  laws  of  and  Excluded  Middle ;  the  second  comprehends 
fhought.    These  fall       ^he  principle  of  Reason  and  Consequent  alone. 

into  two  classes.  mi  •       i        •/»        •         •     /.         t    -i    i  i       j-/i« 

Ihis  classification  is  founded  both  on  the  aitter- 
ent  reciprocal  connection  of  the  laws,  and  on  the  difierent  nature  of 
their  results. 

In  the  first  place,  in  regard  to  the  difiference  of  connection  be- 
tween the  laws  themselves,  it  is  at  once  evident  that  the  first  three 

1  See,  however,  p.  62,  note  1.—  Ed. 


70  LOGIC.  Lect.  VL 

st:uicl  in  a  far  more   proximate  relation  to  each  other  than  to  the 

fourth.      The  first   three   are,  indeed,   so   inti- 

This  classification       mately  Connected,  that  though  it  has  not  even 

founded,  1°,  On  the       ^^^^  attempted  to  carry  them  up  into  a  higher 

difference  of  connec-  ...  ,  ,  . 

tion  between  the  laws      pnnciple,  and  though  the  various  and  contradic- 

themseives.  tory  endeavofs  that  hav^  been  made  to  elevate 

one  or  other  into  an  antecedent,  and  to  degrade 

others  into  consequents,  have  only  shown,  by  their  failure,  the  im- 

})ossibility  of  reducing  the  three  to  one;  still  so  intimate  is  their 

connection,  that  each  in  fact  supposes  the  othei-s.     They  are  like  the 

three  sides  of  a  triangle  ;  not  the  same,  not  reducible  to  unity,  eacli 

pretending  with  equal  right  to  a  prior  consideration,  and  each,  if 

considered  first,  giving  in  its  own  existence  the  existence  of  the 

other  two.     This  intimacy  of  relation  does  not  subsist  between  the 

principle  of  Reason  and  Consequent  and  the  three  other   laws; 

they  do  not,  in  the  same  necessary  manner,  suggest  each  other  in 

thought.     The  explanation  of  this  is  found  in  the  diflTerent  nature 

of  their  results;  and  this  is  the  second  subject  of  our  consideration.^ 

In  the  second  place,  then,  the  distinction  of  the  four  laws  into 

two  classes  is  not  only  warranted  by  the  differ- 

2°,  On  the  diiiference      ^nce  of  their  mutual  dependence  in  thought,  but, 

of  the  end  wliich  the        ,.,         .        i       .,        t«.  «  .,  -,       i  •    i    ^i 

likewise,  b^-  the  dinerenco  oi  the  end  winch  the 

two   classea   severally  '     •' 

accomplish.  two  classes  severally  accomplish.     For  the  first 

three  laws  not  only  stand  apart  by  themselves 
(forming,  as  it  were,  a  single  principle  viewed  in  three  diffeient 
aspects),  but  they  necessitate  a  result  very  different,  both  in  kind 
and  in  degree,  from  that  determined  by  the  law  of  Reason  and  Con- 
sequent. The  difference  in  their  result  consists  in  this,  —  whatever 
violates  the  laws,  whether  of  Identity,  of  Contradiction,  or  of  Ex- 
cluded Middle,  we  feel  to  be  absolutely  impossible,  not  only  in 
thought  but  in  existence.  Thus  we  cannot  attribute  even  to  Om- 
nipotence the  i)Ower  of  making  a  thing  different  from  itseU^  of  mak- 
ing a  thing  at  once  to  be  and  not  to  be,  of  making  a  thing  neither 
to  be  nor  not  to  be.  These  three  laws  thus  detennine  to  us  the 
sphere  of  possibility  and  of  impossibility;  and  this  not  merely  in 
thought  but  in  reality,  not  only  logically  but  metaphysically.  Very 
different  is  the  result  of  the  law  of  Reason  and  Consequent.  This 
principle  merely  excludes  from  the  sphere  of  positive  thought  what 
we  cannot  comprehend ;  for  whatever  we  comprehend,  that  through 
which  we  comprehend  it  is  its  reason.    What,  therefore,  violates  the 

1  For  a  later  development  of  the  Author's  philoeophjr  as  regards  the  diatinetion  bere  indfr 
cated,  see  JHset$ssiom,  p.  602  ttstq.—' £d. 


Lrct.  VI.  LOGIC.  71 

law  of  Reason  and  Consequent  merely,  in  virtue  of  this  law  becomes 
:i  logical  zero;  that  is,  we  are  compelled  to  think  it  as  unthinkable, 
but  not  to  think  it,  though  actually  non-existent  subjectively  or  in 
thought,  as  therefore  actually  non-existent  objectively  or  in  reality. 
And  why,  it  may  be  asked,  does  the  law  of  Reason  and  Consequent 
not  equally  determine  the  sphere  of  general  possibility,  as  the  laws 
of  Identity,  Contradiction,  and  Excluded  Middle  ?  Why  are  we  to 
view  the  unthinkable  in  the  one  case  not  to  be  equally  impossible  in 
reality,  as  the  unthinkable  in  the  other?  Some  philosophers  have, 
on  the  one  hand,  asserted  to  the  Deity  the  power  of  reconciling  con- 
tradictions ;  ^  while,  on  the  other,  a  greater  number  have  made  the 
conceivable  in  human  thought  the  gauge  of  the 
Two  counter  opin-  possible  in  existence.  What  warrants  us,  it  may 
ions    regar  ing      e      y^^  asked,  to  Condemn  these  opposite    proced- 

hmits     of     objective  '  rr  r 

possibility.  ures  as  equally  unphilosophical  ?     In  answer  to 

this,  though  the  matter  belongs  more  properly 
to  Metaphysic  than  to  Logic,  I  may  say  a  few  words,  which,  how- 
ever, I  am  aware,  cannot,  by  many  of  you,  be  as  yet  adequately 
understood. 

To  deny  the  universal  application  of  the  first  three  laws,  is,  in 
fact,  to  subvert  the  reality  of  thought ;  and  as  this  subversion  is 
itself  an  act  of  thought,  it  in  fact  annihilates  itself 

When,  for  example,  I  say  that  A  is,  and  then  say  that  A  is  not, 

by  the  second  assertion  I  sublate  or  take  away 

The      respective      what,  by  the  first  assertion,  I  posited  or  laid 

spheres  of  the   two      down ;    thought,  in  the  one  case,  undoing  by 

classes  or"  the  laws  of  .  ■,  •        ^  i  •      i      i    i  /«• 

thought  defined  and  negation  what,  m  the  other,  it  had  by  afhrma- 

iiiustrated.  tion   done.      But  when  it  is  asserted,  that  A 

To  deny  the  univer-  existing  and  A  non-existing  are  at  once  true, 

sal  application  of  the  ^j^^^  ^^^^  ^j^j^  ..    ^    j^  implies  that  negation 

first  three  laws,  is  to  in*-  -i 

subvert  the  reality  of      ^^d  affirmation  correspond  to  nothing  out  of  the 
thought.  mind  —  that    there   is   no   agreement,  no  disa- 

greement between  thought  and  its  objects ;  and 
this  is  tantamount  to  saying  that  truth  and  falsehood  are  merely 
empty  sounds.  For  if  we  only  think  by  affirmation  and  negation, 
and  if  these  are  only  as  they  are  exclusive  of  each  other,  it  follows, 
that  unless  existence  and  non-existence  be  opposed  objectively  in 
the  same  manner  as  affirmation  and  negation  are  opposed  subjec- 
tively, all  our  thought  is  a  mere  illusion.  Thus  it  is,  that  those  who 
would  assert  the  possibility  of  contradictions  being  at  once  true, 
in  fact  annihilate  the  possibility  of  truth  itself,  and  the  whole  signifi* 
cance  of  thought. 

1  Compare  Le  Clerc,  Logiea,  p.  ii.  c.  3.~-£i>. 


7^  LOGIC.  Lect.  Tl; 

But  this  is  not  the  case  when  we  deny  the  universal,  the  absolute 

application  of  the   law  of  Reason  and  Conse- 

But  this  is  not  in-       quent.     When  I  say  that  a  thing  may  be,  of 

voived  in  the  denial  of      ^hich  I  cannot  conceivc  the  possibility  (that  is, 

the  universal  applica-         ,  •    •  -^  ^i  ^      /> 

tionoftheiaw  fRe  ^  conceiving  it  as  the  consequent  or  a  certain 

son  and  Consequent.        reason),  I  Only  Say  that  thought  is  limited ;  but, 
within  its  limits,  I  do  not  deny,  I  do  not  sub- 
Aert,  its  truth.     But  how,  it  may  be  asked,  is  it  shown  that  thought 
is  thus  limited?     How  is  it  shown  that  the  inconceivable  is  not  an 
index  of  the  impossible,  and  that  those  philosophers  who  have  era- 
ployed  it  as  the  criterion  of  the  absurd,  are  themselves  guilty  of 
iibsurdity  ?     This  is  a  matter  which  will  come  under  our  considera- 
tion at  another  time  and  in  its  proper  place ;  at 
This  law  shown  in       present  it  will  be  sufficient  to  state  in  general 
general  not  to  be  the       ^^^^  ^^^  hypothesis  which  makes  the  thinkable 

measure    of  objective  /»    i  m  i      i    •  i     ■ 

possibility.  ^^^  measure  of  the  possible,  brings  the  principle 

of  Reason  and  Consequent  at  once  into  collision 
with  the  three  higher  laws,  and  this  hypothesis  itself  is  thus  reduced 
at  once  to  contradiction  and  absurdity.  For  if  we  take  a  compre- 
hensive view  of  the  phaBnomena  of  thought,  we  shall  find  that  all 
that  we  can  positively  think,  that  is,  all  that  is  within  the  jurisdic- 
tion of  the  law  of  Reason  and  Consequent,  lies  between  two  oppo- 
site poles  of  thought,  which,  as  exclusive  of  each  other,  cannot,  on 
the  principles  of  Identity  and  Contradiction,  both  be  true,  but  of 
which,  on  the  principle  of  Excluded  Middle,  the  one  or  the  other 
mast.  Let  us  take,  for  example,  any  of  the  general  objects  of  our 
knowledge.  Let  us  take  body,  or  rather,  since  body  as  extended  is 
included  under  extension,  let  us  take  extension  itself,  or  space. 
Now,  extension  alone  will  exhibit  to  us  two  pairs  of  contradictory 
inconceivables,  that  is,  in  all,  four  incomprehensibles,  but  of  which, 
though  all  are  equally  unthinkable,  and,  on  the  liypothesis  in  ques- 
tion, all,  therefore,  equally  impossible,  we  are  compelled,  by  the  law 
of  Excluded  Middle,  to  admit  some  two  as  true  and  necessary. 

Extension,  then,  may  be  viewed  either  as  a  whole  or  as  a  part ; 

and,  in  each  aspect,  it  affords  us  two  incogitable  contradictories. 

1°,  Taking  it  as  a  whole :  —  space,  it  is  evident. 

By  reference  to  Ex-       j^jjjg^  gitiigj.  fee  limited,  that  is,  have  an  end,  a 

^Ij^j^'      '  circumference;    or  unlimited,  that  is,  have  no 

end,  no  circumference.  These  are  contradictory 
suppositions ;  both,  therefore,  cannot,  but  one  must,  be  true.  Now 
let  us  try  positively  to  comprehend,  positively  to  conceive,  the  pos- 
sibility of  either  of  these  two  mutually  exclusive  alternatives.  Can 
we  represent  or  realize  in  thought  extension  as  absolutely  limited  ? 


Lect.  vl  logic.  73 

in  other  words,  can  we  mentally  hedge  round  the  whole  of  space, 

conceive  it  absolutely  bounded,  that  is,  so  that  beyond  its  boundary 

there    is  no   outlying,  no   surrounding,  space? 

Space  or  extension       rp^-^  jg  impossible.     Whatever  compass  of  space 

as  absolutely  bounded,  .  ,.      .        .  t   . 

unthinkable.  '^^  ^'^Y  inclose  by  any  limitation  oi  thought,  we 

shall  find  that  we  have  no  difficulty  in  transcend- 
ing these  limits.     Nay,  we  shall  find  that  we  cannot  but  transcend 
thera ;  for  we  are  unable  to  think  any  extent  of  space  except  as 
within  a  still  ulterior  space,  of  which,  let  us  think  till  the  powers  of 
thinking  fail,   we   can  never  reach  the  circumference.     It  is  thus 
impossible  for  us  to  think  space  as  a  totality,  that  is,  as  absolutely 
bounded,  but  all-containing.     We  may,  therefore,  lay  down  this  first 
extreme  as  inconceivable.     We  cannot  think  space  as  limited. 
Let  us  now  consider  its  contradictory ;  can  we  comprehend  the 
possibility  of  infinite  or  unlimited  space?     To 
Space  unlimited  in-       suppose  this  is  a  direct  contradiction  in  terms ; 

conceivable,    as    con-         .     ;  . 

tradictory.  ^^  ^^  ^^  Comprehend  the  incomprehensible.     We 

think,  we  conceive,  we  comprehend,  a  thing,  only 
as  we  think  it  as  within  or  under  something  else;  but  to  do  this  of 
the  infinite  is  to  think  the  infinite  as  finite,  which  is  contradictory 
and  absurd. 

Now,  here  it  may  be  asked,  how  have  we  then  the  word  infinite  f 
How  have  we  the  notion  which  this  word  ex- 
Objection  from  the       presses?      The  answer  to  this  question  is  con- 
name   and    notion  of  .,.,,...  „         ..  - 

the  intinite  obviated.  ^^ined  in  the  distinction  of  positive  and  negative 
thought.      We   have   a  positive    concept   of  a 

thing,  when  we  think  it  by  the  qualities  of  which  it  is  the  comple- 
ment.    But  as  the  attribution  of  qualities  is  an 

Distinction  of  posi-      affirmation,  as  affirmation  and  negation  are  rela- 
tive     and      negative        ,.  ,  ,     .  ,  i      •  t 
,  ^     ^     ,.              tives,  and  as  relatives  are  known  only  in  and 

thought  and  notion.  '  •' 

through  each  other,  we  cannot,  therefore,  have  a 
consciousness  of  the  affirmation  of  any  quality,  without  having  at 
the  same  time  the  correlative  consciousness  of  its  negation.  Now, 
the  one  consciousness  is  a  positive,  the  otlier  consciousness  is  a  neg- 
ative notion.  But,  in  point  of  fact,  a  negative  notion  is  only  the 
negation  of  a  notion ;  we  think  only  by  the  attribution  of  certain 
qualities,  and  the  negation  of  these  qualities  and  of  this  attribution, 
is  simply,  in  so  far,  a  denial  of  our  thinking  at  all.  As  affirmation 
always  suggests  negation,  every  positwe  notion  must  likewise  sug- 
gest a  negative  notion  ;  and  as  languag^e  Js  the  reflex  of  thought, 
the  positive  and  negative  notions  are  expres^sed  by  positive  and 
negative  names.  Thus  it  is  with  the  infinite.  The  finite  is  the  only 
object,  of  real  or  positive  though\, ;  it  is  thai  alone  which  we  think 

10 


74  LOGIC.  Lect.  VL 

by  the  attribution  of  determinate  characters ;  the  infinite,  on  the 

contrary,  is  conceived  only  by  the  thinking  away  of  every  character 

by  which  the  finite  was  conceived;    in  other 

The    Infinite   ex-       words,  wc  conccivc  it   Only   as   inconceivable. 

presse      y  negative      rj^j^.^   relation   of  the   infinite   to   the   finite   is 

terms. 

shown,  indeed,  in  the  terras  by  which  it  is  ex- 
pressed in  every  language.     Thus  in  Latin,  infinitum ;  in  Greek, 
ttTTcipov ;  in  German,  unendlich  ;  in  all  of  which  original  tongues  the 
word  expressive  of  the  infinite  is  only  a  negative  expression  of  tlie 
finite  or  limited.     Thus  the  very  objection  from  the  existence  of  a 
name  and  notion  of  the  infinite,  when  analyzed,  only  proves  more 
clearly  that  the  infinite  is  no  object  of  thought;  that  we  conceive 
it,  not  in  itself,  but  only  in  congelation  and  contrast  to  the  finite. 
The  indefinite  is,  however,  sometimes  confounded  w4th  the  infin- 
ite ;  though  there  are  hardly  two  notions  which, 
The  Indefinite  and      ^ithout  being  Contradictory,  differ  more  widely. 

Infinite,  — how  distin-         mi        •     i    /»    •        i  i  •        •  i        •    /»    • 

jgjjg^  ihe  indefinite  has  a  subjective,  the  infinite  an 

objective  relation.     The  one  is  merely  the  nega- 
tion of  the  actual  apprehension  of  limits,  the  other  the  negation  of 
the  possible  existence  of  limits. 
But  to  return  whence  we  have  been  carried,  it  is  manifest  that 
we  can  no  more  realize  the  thought  or  concep- 
Space  as  bounded       tjon  of  infinite,  unbounded,  or  unlimited  space, 
»nd  space  as  unbound-       i\^^^  ^r^  ^an  realize  the  conception  of  a  finite  or 

>d  being  two  incon-  '■ 

^eivabie  contradicto-  absolutely  bouuded  spacc.  But  these  two  incon- 
ries,  the  law  of  Reason  ceivables  are  reciprocal  contradictories,  and  if 
>nd  Consequent  can-       ^,g  ^^^  unable  to  Comprehend  the  possibility  of 

*ot,    therefore,    form  .^  i  -i       i  xi  •      •    \         c  -tk 

'he  criterion  of  objec-  ^^^hcr,  while,  howcvcr,  ou  the  principle  of  Ex. 
Jive  possibility.  cluded  Middle  one  or  other  must  be  admitted, 

the  hypothesis  is  manifestly  false,  that  proposes 
the  subjective  or  formal  law  of  Reason  and  consequent  as  the  crite- 
rion of  real  or  objective  possibility. 
It  is  needless  to  show  that  the  same  result  is  given  by  the  exper- 
iment made  on  extension  considered  as  a  part, 
This  further  shown       ^^  divisible.      Here,  if  we  attempt  to  divide  ex- 

by  reference  to  Exten-  ...  ,  ■,     ■,^         ■  ■,  i 

^on  2°  As  a  Part.  tcusiou  lu  thought,  wc  shall  neither,  on  the  one 
hand,  succeed  in  conceiving  the  possibility  of  an 
absolute  minimum  of  space,  that  is,  a  minimum  ex  hi/pothesi  ex- 
tended, but  which  cannot  be  conceived  as  divisible  into  parts,  nor, 
on  the  other,  of  cari-ying  on  this  division  to  infinity.  But  as  these 
are  contradictory  opposites,  they  again  afford  a  similar  refutation  of 
the  hypothesis  in  question. 
But  the  same  conclusion  is  reached  by  simply  considering  the 


Lect.  vl  logic.  75 

law  of  Reason  and  Consequent  in  itself.     This  law  enjoins  —  Think 

nothing  without  a  reason  why  we  must  think  it; 

3^  By  reference  to      ^j^^t  is,  think  nothing  except  as  contained  in, 

the  law  of  Reason  and  ,       , 

Consequent  itself.  ^^   cvolved   out  of,   Something   else   which   we 

already  know.  Now,  this  reason,  —  this  some- 
thing else,  —  in  obedience  to  this  very  law,  must,  as  itself  known, 
be  itself  a  consequent  of  some  other  antecedent ;  and  this  antece- 
dent be  again  the  consequent  of  some  anterior  or  higher  reason ; 
and  so  on,  ad  infinitum.  But  the  human  mind  is  not  possessed  of 
infinite  powers,  or  of  an  infinite  series  of  reasons  and  consequents ; 
on  the  contrary,  its  faculties  are  very  limited,  and  its  stock  of  knowl- 
edge is  very  small.  To  erect  this  law,  therefore,  into  a  standard  of 
existence,  is,  in  fact,  to  bring  down  the  infinitude  of  the  universe  to 
the  finitude  of  man,  —  a  pi'oceeding  than  which  nothing  can  be  im- 
agined more  absurd.  The  fact  is,  that  the  law 
The  laws  of  Reason       ^f  Reason  and  Consequent  can,  with  the  law  of 

!l°d^udbreTT higher       ^'^"^^  ^"^  ^^^^t'  the  law  of   Substaucc   and 
principle.  Phsenomenon,  etc.,  be,  if  I  am  not  mistaken,  all 

reduced  to  one  higher  principle,  —  a  principle 
which  explains  from  the  very  limitation  of  the  human  mind,  from 
the  very  imbecility  of  its  powers,  a  great  variety  of  phaenomena, 
which,  from  the  liberality  of  philosophers,  have  obtained  for  their 
solution  a  number  of  positive  and  special  principles.  This,  how- 
ever, is  a  discussion  which  would  here  be  out  of  place.^  What,  how- 
ever, has  been  said  may  sufiice  to  show  that, 
Summary  statement      ^yi^^g  ^^e  first  three  laws  of  thought  are  of  an 

of  the  spheres  of  the  ,       ,  _         .  ,  t       n         i    •  t 

laws  of  thought.  absolute  and  universal  cogency,  the  fourth  is  only 

of  a  cogency  relative  and  particular ;  that,  while 
the  former  determine  the  possibility,  not  only  of  all  thought,  but  of 
all  real  knowledge,  the  latter  only  regulates  the  validity  of  mediate 
or  reflective  thought.    The  laws  of  Identity,  Contradiction  and  Ex- 
cluded Middle  are,  therefore,  not  only  logical  but  metaphysical  prin- 
ciples, the  law  of  Reason  and  Consequent  a  logical  principle  alone ;  a 
doctrine  which  is,  however,  the  converse  of  what  is  generally  taught. 
I  proceed,  now,  to  say  a  few  words  on  the  general  influence  which 
these  laws  exert  upon  the  operations  of  think- 
The   general  iufln-       ing.      These  Operations,  however  various   and 
ence  which  the  forego-       multiform  they  may  seem,  are  so  governed  in  all 

ing  laws  exert  on  the  .  .„.,         ,  ,.  , 

operations  of  think-       ^hcir  manifestations  by  the  preceding  laws,  that 

ing.  no  thought  can   pretend  to  validity  and  truth 

which  is  not  in  consonance  with,  which  is  not 

governed  by,  them.     For  man  can  recognize  that  alone  as  real  and 

1  Se«  DUeussions,  p.  609.  —  Eo. 


76  LOGIC.  Lect.  VI 

assured,  which  the  laws  of  his  understanding  sanction ;  and  he  can. 
not  but  regard  that  as  false  and  unreal,  which  these  laws  condemn. 
From  this,  however,  it  by  no  means  follows  that  what  is  thought  in 
conformity  to  these  laws,  is  therefore  true;  for  the  sphere  of  thought 
is  far  wider  than  the  sphere  of  reality,  and  no  inference  is  valid 
fi-om  the  correctest  thinking  of  an  object  to  its  actual  existence. 
While  these  laws,  therefore,  are  the  highest  criterion  of  the  non- 
reality  of  an  object,  they  are  no  criterion  at  all  of  its  reality ;  and 
they  thus  stand  to  existence  in  a  negative  and  not  in  a  positive  rela- 
tion. And  what  I  now  say  of  the  fundamental  principles  of  thought 
in  general,  holds  equally  of  all  their  proximate  and  special  applica- 
tions, that  is,  of  the  whole  of  Logic.  Logic,  as  I  have  already  ex- 
plained, considering  the  form  alone  of  thought  to  the  exclusion  of 
its  matter,  can  draw  no  conclusion  from  the  con-ectness  of  the  man- 
ner of  thinking  an  object  to  the  reality  of  the  object  itself.  Yet 
among  modern,  nay  recent,  philosophers,  two 

The  true  relations  of  -^       j       ^   •  i  ^  i  •    i 

-     .  ,    ,  ^  .        opposite  doctrines  have  sprung  up,  which,  on 

Logic    overlooKed    m  ^^       _  ^  r-         o       r'  j 

two  ways:— 1.  Logic  Opposite  sides,  have  overlooked  the  true  rela- 
erroneousiy  held  to  tions  of  Logic.  "One  party  of  philosophers 
be  the  positive  stand-       defining  truth  in  general,  — the  absolute   har- 

ard  of  truth.  ®  .  . 

mony  of  our  thoughts  and  cognitions,  —  divide 

truth  into  a  formal  or  logical,  and  into  a  material  or  metaphysical, 

according  as  that  harmony  is  in  consonance  witli 

The  division  of  truth       ^^le  laws  of  formal  thought,  or,  over  and  above, 

into  logical  and  meta-  •  i      i       i  c  ^  ^  i     t        i      mi 

physical,- criticized.  ^ith  the  laws  of  real  knowledge.^  The  criterion 
of  formal  truth  they  place  in  the  principles  of 
Contradiction  and  of  Sufficient  Reason,  enouncing  that  what  is  non- 
contradictory  and  consequent  is  formally  true.  This  criterion,  which 
is  positive  and  immediate  of  formal  truth  (inasmuch  as  what  is 
non-contradictory  and  consequent  can  always  be  thought  as  possi- 
ble), they  style  a  negative  and  mediate  criterion  of  material  truth : 
as  what  is  self-contradiotory  and  logically  inconsequent  is  in  reality 
impossible ;  at  the  same  time,  what  is  not  self-contradictory  and  not 
logically  inconsequent,  is  not,  however,  to  be  regarded  as  having  an 
actual  existence.  But  here  the  foundation  is  treacherous ;  the  no- 
tion of  truth  is  false.  When  we  speak  of  truth,  we  are  not  satisfied 
with  knowing  that  a  thought  harmonizes  with  a  certain  system  of 
thoughts  and  cognitions ;   but,  over  and  above,  we  require   to  be 

,    assured  that  what  we  think  is  real,  and  is  as  we 
Truth,  — what.  ,.,.  .  •  j^    -, 

think  it  to  be.     Are  we  satisfied  on  this  point, 

we  then  regard  our  thoughts  as  true ;  whereas  if  we  are  not  satis- 
fied of  this,  we  deem  them  false,  how  well  soever  they  may  quad- 

1  See  Kant,  Logik,  Einleitung,  vii. ;  Krug,  Logik,  $  22;  Fries,  Logik,  {  42.  —  Ed. 


Lkct.  vl  logic.  77 

rate  with  any  theoiy  or  system.  It  is  not,  therefore,  in  any  absolute 
harmony  of  mere  thought  that  truth  consists,  but  solely  in  the  cor- 
respondence of  our  thoughts  with  their  objects.  The  distinction  of 
formal  and  material  truth  is  thus  not  only  unsound  in  itself,  but 
opposed  to  the  notion  of  truth  universally  held,  and  embodied  in  all 
languages.  But  if  this  distinction  be  inept,  the  title  of  Logic,  as  a 
positive  standard  of  truth,  must  be  denied  ;  it  can  only  be  a  nega- 
tive criterion,  being  conversant  with  thoughts  and  not  with  things, 
with  the  possibility  and  not  with  the  actuality  of  existence."^ 

The  preceding  inaccuracy  is,  however,  of  little  moment  compared 
with  the  heresy  of  another  class  of  philosophers, 
2.   The  Absolutists       to  whose  observations  on  this  point  I  can,  how- 
proceed  on  a  subver-      ^         ^^j     allude.     Some  of  you  may,  perhaps, 

sion    of   the    logical         „       '      _.r.      ,.,,..  •;  •"  ^  /    ' 

i^^g  iind  a  dimculty  in  beheving  the  statement,  that 

there  is  a  considerable  party  of  philosophers, 
illustrious  for  the  highest  speculative  talent,  and  whose  systems,  if 
not  at  present,  were,  a  few  years  ago,  the  most  celebrated,  if  not  the 
most  universally  accredited  in  Europe,  who  establish  their  meta- 
physical theories  on  the  subversion  of  all  logical  Iruth.^  I  refer  to 
those  philosophers  who  hold  that  man  is  capable  of  more  than  a 
relative  notion  of  existence,  —  that  he  is  competent  to  a  knowledge 
of  absolute  or  infinite  being  (for  these  terms  they  use  convertibly), 
in  an  identity  of  knowledge  and  existence,  of  himself  and  the 
Divinity.  This  doctrine,  which  I  shall  not  now  attempt  to  make 
you  understand,  is  developed  in  very  various  schemes ;  that  is,  the 
different  philosophers  attempt,  by  very  diiferent  and  contradictory 
methods,  to  arrive  at  the  same  end  ;  all  these  systems,  however, 
agree  in  this,  —  they  are  all  at  variance  with  the  four  logical  laws. 
Some,  indeed,  are  established  on  the  express  denial  of  the  validity 
of  these  laws;  and  othei-s,  without  daring  overtly  to  reject  their  au- 
thority, are  still  built  in  violation  of  their  precept.  In  fact,  if  con- 
tradiction remain  a  criterion  of  falsehood,  if  Logic  and  the  lawG  of 
thought  be  not  viewed  as  an  illusion,  the  philosophy  of  the  absolute, 
in  all  its  forms,  admits  of  the  most  direct  and  easy  refutation.  But 
on  this  matter  I  only  now  touch,  in  order  that  you  may  not  be 
ignorant  that  there  are  philosophers,  and  philosophers  of  the  high- 
est name,  who,  in  pursuit  of  the  phantom  of  absolute  knowledge, 
are  content  to  repudiate  relative  knowledge,  logic,  and  the  laws  of 
thought.  This  hallucination  is,  however,  upon  the  wane,  and  as 
each  of  these  theorists  contradicts  his  brother,  Logic  and  Common 
Sense  will  at  length  refute  them  all. 

Before  leaving  the  consideration  of  this  subject,  it  is  necessary  to 

1  Eeser,  Lo^k,  p.  6&-6.  —  Ed.  2  See  above,  p.  64,  note  4.  —  Ed. 


78  LOGIC.  Lect.  VI. 

notice  a  mistake  of  Dr.  Reid,  which   it  is   not  more  remarkable 

that  he  should  have  committed,  than  that  others 

Mistake  of  Reid  in       j^^^^^  ^^^^  ^^^^^^^  ^^  f^,j^^,  ^^^^  applaud  it,  as  the 

regard  to  Conception.  '  ' 

correction  of  a  general  error.  In  the  fourth 
^ssay  on  the  Intellectual  Powers.,  and  in  the  third  chapter,  entitled 
Mistakes  concerning  Conceptions^  there  is  the  following  passage, 
which  at  once  exhibits  not  only  his  own  opinion,  but  the  universality 
of  the  doctrine  to  which  it  is  opposed : 

"  There  remains,"  he  says,  "  anotlier  mistake  concerning  concep- 
tion, which  deserves  to  be  noticed.     It  is,  that 

Reid  quoted.  ,  /.    .  •  •  ».    i     • 

our  conception  oi  thmgs  is  a  test  oi  their  pos- 
sibility, so  that,  what  we  can  distinctly  conceive,  we  may  conclude 
to  be  possible  ;  and  of  what  is  impossible,  we  can  have  no  con- 
ception. 

"  This  opinion  has  been  held  by  philosophere  for  more  than  a  hun- 
dred years,  without  contradiction  or  dissent,  as  far  as  I  know ;  and, 
if  it  be  an  error,  it  may  be  of  some  use  to  inquire  into  its  origin,  and 
the  causes  that  it  has  been  so  generally  received  as  a  maxim  whose 
truth  could  not  be  brought  into  doubt." 

I  may  here  observe  that  this  limitation  of  the  prevalence  of  the 
opinion  in  question  to  a  very  modern  period  is  altogether  incorrect ; 
it  was  equally  prevalent  in  ancient  times,  and  as  many  passages  could 
easily  be  quoted  from  the  Greek  logicians  alone  as  Dr.  Reid  has 
quoted  from  the  philosophers  of  the  century  prior  to  himself.  Dr. 
Reid  goes  on : 

"  One  of  the  fruitless  questions  agitated  among  the  scholastic 
philosophers  in  the  dark  ages  was.  What  is  the  criterion  of  truth? 
As  if  men  could  have  any  other  way  to  distinguish  truth  from  error, 
but  by  the  right  use  of  that  power  of  judgment  which  God  has 
given  them. 

"Descartes  endeavored  to  put  an  end  to  this  controveray,  by 
making  it  a  fundamental  principle  in  his  system,  that  whatever  we 
clearly  and  distinctly  perceive,  is  true. 

"  To  understand  this  principle  of  Descartes,  it  must  be  observed 
that  he  gave  the  name  of  perception  to  every  power  of  the  human 
understanding;  and  in  explaining  this  very  maxim,  he  tells  us 
that  sense,  imagination,  and  pure  intellection,  are  only  different 
modes  of  perceiving,  and  so  the  maxim  was  understood  by  all  his 
followers. 

"The  learned  Dr.  Cudworth  seems  also  to  have  adopted  this  prin- 
ciple. 'The  criterion  of  true  knowledge,'  he  says,  'is  only  to  be 
looked  for  in  our  knowledge  and  conceptions  themselves:  for  the 

1  Collected  Works,  p.  376-8.  —Ed. 


Lect.  VI.  LOGIC.  79 

entity  of  all  theoretfcal  truth  is  nothing  else  but  clear  intelligibility, 
and  whatever  is  clearly  conceived  is  an  entity  and  a  truth ;  but  that 
which  is  false,  Divine  power  itself  cannot  make  it  to  be  clearly  and 
distinctly  understood.  A  falsehood  can  never  be  clearly  conceived 
or  apprehended  to  be  true.'  —  {Eternal  and  immutable  Morality,  p. 
172,  etc.) 

"  This  Cartesian  maxim  seems  to  me  to  have  led  the  way  to  that 
now  under  consideration,  which  seems  to  have  been  adopted  as  the 
proper  correction  of  the  former.  When  the  authority  of  Descartes 
declined,  men  began  to  see  that  we  may  clearly  and  distinctly  con- 
ceive what  is  not  true,  but  thought  that  our  conception,  though  not 
in  all  cases  a  test  of  truth,  might  be  a  test  of  possibility. 

"  This  indeed  seems  to  be  a  necessary  consequence  of  the  received 
doctrine  of  ideas  ;  it  being  evident  that  there  can  be  no  distinct  im- 
age, either  in  the  mind  or  anywhere  else,  of  that  which  is  impos- 
sible. The  ambiguity  of  the  word  conceive,  which  we  observed. 
Essay  i.  chap,  i.,  and  the  common  phraseology  of  saying,  we  cannot 
conceive  such  a  thing,  when  we  would  signify  that  we  think  it  im- 
possible, might  likewise  contribute  to  the  reception  of  this  doctrine. 

"  But  whatever  was  the  origin  of  this  opinion,  it  seems  to  prevail 
universally,  and  to  be  received  as  a  maxim. 

" '  The  bare  having  an  idea  of  the  proposition  proves  the  thing  not 
to  be  impossible ;  for  of  an  impossible  proposition  there  can  be  no 
idea.'  —  Dr.  Samuel  Clarke. 

"'Of  that  which  neither  does  nor  can  exist  we  can  have  no  idea.' 
—  Lord  Bolingbroke. 

"'The  measure  of  impossibility  to  us  is  inconceivableness,  thatof 
which  we  have  no  idea,  but  that  reflecting  upon  it,  it  appears  to  be 
nothing,  we  pronounce  to  be  impossible.'  —  Abernethy. 

"'In  every  idea  is  implied  the  possibility  of  the  existence  of  its 
object,  nothing  being  clearer  than  that  there  can  be  no  idea  of  an 
impossibility,  or  conception  of  what  cannot  exist.'  —  Dr.  Price. 

" '  Impossibile  est  cujus  nullam  notionem  formare  possumus;  pos 
sibile  e  contra,  cui  aliqua  respondet  notio.'  —  Wolfii  Ontolog. 

" '  It  is  an  established  maxim  in  metaphysics,  that  whatever  the 
mind  conceives,  includes  the  idea  of  possible  existence,  or  in  other 
woi-ds,  that  nothing  we  imagine  is  absolutely  impossible.'  —  D. 
Hume. 

"  It  were  easy  to  muster  up  many  other  respectable  authorities  for 
this  maxim,  and  I  have  never  found  one  that  called  it  in  question. 

"If  the  maxim  be  true  in  the  extent  which  the  famous  Wolfius 
has  given  it  in  the  passage  above  quoted,  we  shall  have  a  short  road 
to  the  determination  of  every  question  about  the  possibility  or  im- 


80  LOGIC.  Lect.  VL 

possibility  of  things.  We  need  only  look  into  our  own  breast,  and 
that,  like  the  Urim  and  Thuramim,  will  give  an  infallible  answer.  If 
we  can  conceive  the  thing,  it  is  possible  ;  if  not,  it  is  impossible. 
And  surely  every  man  may  know  whether  he  can  conceive  what  is 
affirmed,  or  not. 

"Other  philosophers  have  been  satisfied  with  one  half  of  the 
maxim  of  Wolfius.  They  say,  that  whatever  we  can  conceive  is 
possible  ;  but  they  do  not  say,  that  whatever  we  cannot  conceive  is 
impossible." 

On  this  I  may  remai'k,  that  Dr.  Reid's  criticism  of  Wolf  must  be 
admitted  in  so  far  as  that  philosopher  maintains  our  inability  to  con- 
ceive a  thing  as  possible,  to  be  the  rule  on  which  we  are  entitled  to 
pronounce  it  impossible.  But  Dr.  Reid  now  advances  a  doctrine 
which  I  cannot  but  regard  as  radically  erroneous. 

"I  cannot  help  thinking  even  this  to  be  a  mistake  which  philoso- 
phers have  been  unwarily  led  into,  from  the  causes  before  mentioned. 
My  reasons  are  these  : 

"  1,  Whatever  is  said  to  be  possible  or  impossible  is  expressed  by 
a  proposition.  Now,  what  is  it  to  conceive  a  proposition  ?  I  think 
it  is  no  more  than  to  understand  distinctly  its  meaning.  I  know  no 
more  that  can  be  meant  by  simple  apprehension,  or  conception, 
when  applied  to  a  proposition.  The  axiom,  therefore,  amounts  to 
this :  —  Every  proposition,  of  which  you  understand  the  meaning 
distinctly,  is  possible.  I  am  persuaded  that  I  understand  as  distinctly 
the  meaning  of  this  proposition,  Any  two  sides  of  a  triangle  are  to- 
gether equal  to  the  third,  as  of  this.  Any  two  sides  of  a  triangle  are 
together  greater  than  the  third;  yet  the  first  of  these  is  impossible." 

Now  this  is  a  singular  misunderstanding  of  the  sense  in  which  it 

has  been  always  held  by  philosophei-s,  that  what 
Criticized. 

is  contradictory  is  conceived  as  inconceivable  and 

impossible.^  No  philosopher,  I  make  bold  to  say,  ever  dreamt  of 
denying  that  we  can  distinctly  understand  the  meaning  of  the  propo- 
sition, the  terms  of  which  we  recognize  to  be  contradictory,  and,  as 
contradictory,  to  annihilate  each  other.  When  we  enourtce  the  pro- 
position, A  is  not  A,  we  clearly  comprehend  the  separate  meaning 
of  the  terms  A  and  not  A,  and  also  the  import  of  the  assertion  of 
their  identity.  But  this  very  understanding  consists  in  the  con- 
sciousness that  the  two  terms  are  contradictories,  and  that  as  such 
it  is  impossible  to  unite  them  in  a  mental  judgment,  though  they 
stand  united  in  a  verbal  proposition.  If  we  attempt  this,  the  two 
mutually  exclusive  terms  not  only  cannot  be  thought  as  one,  but  in 
fad  annihilate  each  other ;  and  thus  the  result,  in  place  of  a  positive 

1  See  the  Author's  notes,  Rtid^s  Worka^  p.  877.  —  Ed. 


Lkct.  VI  LOGIC.  81 

judgraent,  is  a  negation  of  thouglit.  So  fai*  Dr.  Reid  is  wrong.  But 
lie  is  not  guilty  of  the  absurdity  attributed  to  him  by  Dr.  Gleig;  he 
does  not  say,  as  by  that  writer  he  is  made  to  say,  that  "  any  two 
sides  of  a  triangle  may  be  conceived  to  be  equal  to  the  third,  as  dis- 
tinctly as  any  two  sides  of  a  triangle  may  be  conceived  to  be  greater 
tlian  the  third."  ^  These  are  not  Dr.  Reid's  words,  and  nothing  he 
says  warrants  the  attribution  of  such  expressions  to  him,  in  the  sense 
in  which  they  are  attributed.  He  is  made  to  hold,  not  merely  that 
we  can  understand  two  terms  as  contradictory,  but  that  we  are  able 
to  combine  them  in  the  unity  of  thought.  After  the  passage  ah'eady 
quoted,  Reid  goes  on  to  illustrate,  in  various  points  of  view,  the 
supposed  error  of  the  philosophers ;  but  as  all  he  says  on  this 
head  originates  in  the  misconception  already  shown  of  the  opin- 
ion he  controverts,  it  is  needless  to  take  <^ny  further  notice  of  his 
arguments. 

We  have  thus  considered  the  conditions  of  Logic,  in  so  far  as  cer- 
tain laM's  or  principles  are  prescribed  ;  we  have 

Postulates  of  Logic.  ,  .,         .  -,.^.  .  „ 

now  to  consider  its  conditions,  m  so  tar  as  cer- 
tain postulates  are  demanded.  Of  these  there  are  more  than  one  : 
but  one  alone  it  is  here  requisite  to  signalize  ;  for  although  it  be  ne- 
cessarily supposed  in  the  science,  strange  to  say,  it  has,  by  logical 
writers,  not  only  been  always  .passed  over  in  silence,  but  frequently 
and  inconsistently  violated.  This  postulate  I  comprise  in  the  follow- 
ing paragraph  : 

%  XVIII.  The  only  postulate  of  Logic  which  requires  an  ar- 
ticulate enouncement  is  the  demand,  that 
Par.  x^i-  The  logi-       jjefore  dealing  with  a  ludgment  or  reasoning 

oal  postulate.  o  j       o  o 

expressed  in  language,  the  import  of  its 
terms  should  be  fully  understood  ;  in  other  words.  Logic  postu- 
lates to  be  allowed  to  state  explicitly  in  language  all  that  is 
implicitly  contained  in  the  thought. 

This  postulate  cannot  be  refused.    In  point  of  fact,  as  I  have  said,. 
Logic  has  always  proceeded  on  it,  in  overtly  ex— 

This  postulate  can-  •  n    iu         x  £•  ^i,  ^   i 

^    ^     ^  pressing  all  the  steps  ot  the  mental  process  m- 

not  be  refused.  .  .   .  . 

reasoning,  —  all  the  propositions  of  a  syllogism;: 
whereas,  in  common  parlance,  one  at  least  of  these  steps  or  proposi- 
tions is  usually  left  unexpressed.  This  postulate,  as  we  shall  have 
occasion  to  observe  in  the  sequel,  though  a  fundamental  condition 
of  Logic,  has  not  been  consistently  acted  op  by  logicians  in  their 
development  of  the  science  ;  and  from  this  omission  have  arisen 

1  Art.  "Metaphysics,"  Sncyclopadi/z  Eritannica,  Ttbedit.,  p.  620. — Ed 

11 


82  LOGIC.  Lect.  VI. 

much  confusion  and  deficiency  and  error  in  our  present  system  of 
Logic.  The  illustration  of  this  postulate  will  appropriately  find  its 
place  on  occasion  of  its  applications.  I  now  articulately  state  it, 
because  it  immediately  follows  in  order  the  general  axioms  of  the 
science  ;  and,  at  present,  I  only  beg  that  you  will  bear  it  in  mind.  I 
may,  however,  before  leaving  the  subject,  observe 
This  postulate  im-  (what  has  already,  I  believe,  been  mentioned), 
plied  in  the  doctrine       ^j^^^  Aristotlc  States  of  syllogistic— and,  of  course, 

of  Syllogism,  accord-  ,.  t        •     • 

ing  to  Aristotle.  "^^  Statement  applies  to  Logic  m  general  — that 

the  doctrine  of  syllogism  deals,  not  with  the  ex- 
teraal  expression  of  reasoning,  in  ordinary  language,  but  with  the 
internal  reasoning  of  the  mind  itself.^  But  of  this  again,  and  more 
fully,  in  the  proper  places. 

In  like  manner,  we  might  here,  as  is  done  in  Mathematics,  pre- 
mise certain  definitions ;  but  these  it  will  be  more  convenient  to 
state  as  they  occur  in  the  progress  of  our  development.  I  there- 
fore pass  on  to  the  Second  Section  of  the  Doctrine  of  Elements, 
which  is  occupied  with  the  Products  of  Thought ;  in  other  words, 
with  the  processes  regulated  by  the  previous  conditions. 

1  AnaL  PNt.,  i.  10.  — IEd.  t 


LECTURE    VII. 

STOICHEIQLOGY. 

SECTION    II.— OF  THE  PRODUCTS   OF  THOUGHT. 

I.    ENNOEMATIC  — OF  CONCEPTS  OR  NOTIONS. 

A.    OF  CONCEPTS  IN  GENERAL. 

I  CONCLUDED,  in  my  last  lecture,  all  that  I  think  it  necessary  to 
say  in  regard  to  the  Fundamental  Laws  of  Thought,  or  the  neces- 
sary conditions  of  the  thinkable.  The  discussion,  I  am  aware,  must 
have  been  found  somewhat  dry,  and  even  abstruse ;  not  that  there 
is  the  smallest  difficulty  in  regard  to  the  apprehension  of  the  laws 
themselves,  for  these  are  all  self-evident  propositions,  but  because, 
though  it  is  necessary  in  a  systematic  view  of  Logic  to  commence 
with  the  elementary  principles  of  thought,  it  is  impossible,  in  speak- 
ing of  these  and  their  application,  not  to  employ  expressions  of  the 
most  abstract  generality,  and  even  not  to  suppose  a  certain  acquaint- 
ance with  words  and  things,  which,  however,  only  find  their  expla- 
nation in  the  subsequent  development  of  the  science. 

Having  considered,  therefore,  the  four  Laws  of  Thought,  with  the 
one  Postulate  of  Logic,  which  constituted    the 

The  products  of  First  Section  of  the  Doctrine  of  Logical  Ele- 
Thought,     Concepts,       j^^^j^^     j    j^^^^.    proceed  to  the    Second  — that 

Judgments  and    Rea-  ,  .   ,     .  x        •      i    t-»       t 

sonings.  which  18    conversant   about   Logical  Froducts. 

These  products,  though  identical  in  kind,  are  of 
three  different  degrees ;  for  while  Concepts,  Judgments,  and  Rea- 
sonings, are  all  equally  the  products  of  the  same  Faculty  of  Compar- 
ison, they  still  fall  into  three  classes,  as  the  act. 
These  are  all  pro-       and,  consequently,  the  result  of  the  act,  is  of  a 
ducts  of  Comparison,  ^atcr  or  a  less  simplicity.    These  three  degrees 

and  all  modifications         °  .  i  .^  •  r     i, 

of  judgment.  ^^^  ^^^  i"  fi'ct,  strictly,  only  modifications  of  the 

second,  as  both  concepts  and  reasonings  may  hv 
reduced  to  judgments;  for  the  act  of  judging,  that  is,  the  act  of 
affirming  or  denying  one  thing  of  another  in  thought,  is  that  in 
which  the  Understanding  or  Faculty  of  Comparison  is  essentially 


84  LOGIC.  Lect.  VH, 

expressed.  By  anticipation  : — A  concept  is  a  judgment;  for,  on 
the  one  hand,  it  is  nothing  but  the  result  of  a  foregone  judgment,  or 
series  of  judgments,  fixed  and  recorded  in  a  word  —  a  sign  ;  and  it 
is  only  amplified  by  the  annexation  of  a  new  attribute,  through  a 
continuance  of  the  same  process.  On  the  other  hand,  as  a  concept 
is  thus  the  synthesis  or  complexion,  and  the  record,  I  may  add,  of 
one  or  more  prior  acts  of  judgment,  it  can,  it  is  evident,  be  analyzed 
into  these  again ;  every  concept  is,  in  fact,  a  judgment  or  a  fascicu- 
lus of  judgments  —  these  judgments  only  not  explicitly  developed 
in  thought,  and  not  formally  expressed  in  terms. 

Again,  a  reasoning  is  a  judgment ;  for  a  reason  is  only  the  affirma- 
tion of  the  connection  of  two  things  with  a  third,  and,  through  that 
third,  with  each  other.  It  is  thus  only  the  same  function  of  thought, 
which  is  at  work  in  Conception,  Judgment,  and  Reasoning ;  arid 
these  express  no  real,  no  essential,  distinction  of  operation,  but 
denote  only  the  different  relations  in  which  we  may  regard  the  indi- 
visible act  of  thought.  Thus,  the  consideration  of  concepts  cannot 
be  effected  out  of  all  relation  to,  and  without  even  some  anticipation 
of,  the  doctrine  of  judgments.  This  being  premised,  I  now  proceed 
to  the  consideration  of  the  Products  of  Thought,  viewed  in  the 
three  relations  of  the  three  degi-ees,  of  Concepts,  Judgments,  and 
Reasonings.^ 

Under  the  Second  Section  of  Stoicheiology,  Concepts  or  Notions 
form  the  first  chapter. 

Now,  in  treating  of  Concepts,  the  order  I  shall  follow  is  this  :  — I 
shall,  in  the  first  place,  treat  of  them  in  general ; 

I.  Of  Concepte  or      j^  ^^^  second,  treat  of  them  in  special.     Under 

Notions, —  order    of  ,       ^  i    i        i        mi    i  -j         j 

discussion.  ^"^  former,  or  general  head,  will  be  considered, 

1°,  What  they  are ;  2°,  How  they  are  produced. 

Under  the  latter,  or  special  head,  they  will  be  considered  under 

their  various  relations.      And   here,  I  may  obser^'e,  that  as  you 

obtain  no  information  from  Dr.  Whately  in  re- 

Whateiy*  omission         ^^^  ^^  ^j^^,  primary  laws  of  thought,  —  these 

ofthedoctrineof  Con-         »  .         . 

ggptg  laws  being  in  fact  apparently  unknown  to  every 

British  logician,  old  or  new,  —  so  you  will  find 
but  little  or  no  aid  from  his  Elements  towards  an  understanding  of 
the  doctrine  of  concepts.  His  omission,  in  this  respect,  cannot  be  ex- 
cused by  his  error  in  regard  to  the  object-matter  of  Logic ;  that  object, 
you  will  recollect,  being  on  his  view,  or  rather  one  of  his  views,  not 
thought  in  general,  or  the  products  of  the  comparative  faculty  in 

1  [Hume,  Treatise  of  Human  Nature,  Bk.  i.  prehension  is  impossible  without  judgment 
part  iii.  {  7-  Jac.  Thomasius,  Physica,  p.  295]  Compare  also  Kmg,  LogUc,  f  23,  Anm.  ii.  p.  TO 
[c.  zljx.  ( 112,  where  be  holds  that  simple  ap-     —  Ed.] 


ILect.  VIL  LOGIC.  ^5 

their  three  degrees,  but  reasoning  or  argumentation  alone  ;  for  even 
on  the  hypothesis  that  Logic  is  thus  limited,  still,  as  the  doctrine  of 
reasoning  can  only  be  scientifically  evolved  out  of  the  doctrine  of 
concepts,  the  consideration  of  the  latter  forms  the  indispensable 
condition  of  a  satisfactory  treatment  of  the  former.  But  not  only  is 
Whately's  doctrine  of  concepts,  or,  in  his  language,  of  "  the  process 
of  simple  apprehension,"  meagre  and  imperfect,  it  is  even  necessary 
to  forewarn  you  that  it  leads  to  confusion  and  error.  There  is  a 
iundamental  distinction  of  what  is  called  the  Extension  and  the 
Comprehension  of  notions  —  a  distinction  which, 
Whateiy  abusively       in  fact,  as  you  will  find,  forms  the  very  cardinal 

employs  the  terms  Ex-  -^^  ^^  ^j^-^j^  ^^^  ^j^^j^  ^y^  ^^  ^-^  ^^^.^^ 

tension  and  Compre-         i.^  ,.,.,..         .  ..... 

hensioii  as  convertible.         ^^^  "^^t  Only  IS  thlS  distmction  not  explained.  It  IS 

not  even  articulately  stated ;  nay,  the  very  words 
which  logicians  have  employed  for  the  expression  of  this  contrast, 
are  absolutely  used  as  synonymous  and  convertible.  Instead,  there- 
fore, of  referring  you  for  information  in  regard  to  our  present  object 
of  consideration,  to  Dr.  Whateiy,  I  am  sorry  to  be  compelled  to 
caution  you  against  putting  confidence  in  his  guidance.  But  to  re- 
turn. The  following  I  dictate  as  the  title  of  the  first  head  to  be 
considered  : 

A.  Of  Concepts  or  ^    Qf  Concepts  or  Notions  in  General :  What 

Notions    in     general.  i         o  '  » 

What  they  are.  ^rC  they  ? 

In  answering  this  question,  let  us,  first,  consider  the  meaning  of 
the  expressions ;  and,  secondly,  the  nature  of  the  thing  expressed, 

^  XIX.      Concept  or   notion    (^evvoia,    iwoiQixxi,   vorjfia,    cTrtvoia,' 

conceptio,  notio),  are  terms   employed    as 

Far.  XIX.  Concepts.       Convertible,  but,  while  they  denote  the  same 

term^*^*^"^*  ^       ^       thi"g»  they  denote  it  in  a  diflferent  point  of 

view.     Conception,  the  act  of  which  concept 

is  the  result,  expresses  the  act  of  comprehending  or  grasping  up 

1  In  Greek,  the  terms  ?»'j'oia    {fvvor)TiK6s),  Uus,  Lexicon  Pkilosophicum,  v. 'N6Tifia,  p.  890, 
iwoviJia  (4vvorifmTiK6s),  inivoia  [iirivoririK-  and  p.  80,  [i-.  Alad^fiara.    Cf.  p.  310,  v.  Con- 
is),  viy,^,  to  say  nothing  of  iniV07t,u>.  {iir^-  ''Ptus;  p.  633,  t,.  Intentio.-E.T>^    Onvo^f^ara. 
/  V             „                     ......  see  Aristotle,  De /n<erpr..c  1.  and  Waitz,  Coni- 

v<n)u.a,rtKOS),  are  all  more  or  less  objection-  „„_     ,      •    ■  ^  i..       I^     t    ■ 

^'           ,    '               ,             ,  .           ,           J  -  mejUanus,  p.   327.     In  Aristotle,   De  Anirna. 

able,  as  all  more  or  less  ambiguously  used  for  ,   ...         „    ,,,  ^    ,.,  „  ,_,      .         „/.  _,_ 

^.     ',.    ,            ^     .    4..K        i,»  •             .    /•  1- lii.  CO.  6,    7    7,    8    8,  9,  etc.,  vo^^aTa  are 

the  object  or  product  of  thought,  in  an  act  of  ,       ,           .     ,   \                    . 

.,.        .                  ,,        „   .  clearly  equivalent  to  concept.'in  our  meaning. 

Conception,  or,  as  it  has  been  usually  called  ,      .»             >«        /            i 

l.v  the  logicians,  Simple  Apprehension.     See  ^^    "'         '^                              '^    ^        ,      „      > 

!•  immidas.  Epitome  Logica[c.  V.  UtpVEvLv-  roirois,  irepj  &  ovk  tan  rh  iptvSos  iv  ols  Sf 

<'a^.  p  31.  ed.  1605. —  Ed  ];  Eugenics,  Logica  %ai.  rh  ^fvios  koH  rh  iX-r^fS,  aivbevis  -ti 

lAivi/c)),  c.  ii.  p.  170,  Leipsic,  1766.  — Ed  ]  ^5,j  votiiiATtcv  &<nr(p  %v  6vtcdv.  k.  t.  ^. — 

Slephanus,  Thesaurus,  v.  tiovs;  Hiicker,  CZavis  Ed j 

P/iii.  Arist.,  V.  No^j/taro,  p.  227  et  seq. ;  Micrae- 


t'5  LOGIC.  lect.  vn. 

into  unity  the  various  qualities  by  which  an  object  is  character- 
ized; notion  {notio)^  again,  signifies  either  the  act  of  appre- 
hending, signalizing,  that  is,  the  remarking  or  taking  note  of, 
the  various  notes,  marks,  or  characters  of  an  object,  which  its 
qualities  afford ;  or  the  result  of  that  act. 

In  Latin,  the  word  cancipere^  in  its  many  various  applications, 

always  expresses,  as  the  etymology  would  indi- 

iiinstfated,  —  em-       cate,  the  process  of  embracing  or  comprehending 

*^  /  ^       the  many  into  the  one,  as  could  be  shown  by  an 

«« mente  conctpere,  and  .  . 

animi  conceptiu.  articulatc   analysis  of  the  phrases  in  which  the 

term  occurs.  It  was,  accordingly,  under  this 
general  signification,  that  this  word  and  its  derivatives  were  ana- 
logically applied  to  the  ojjeration  of  mind.  Animo  vel  mente  con- 
cipere,  as  used  by  Cicero,  Pliny,  Seneca,  and  other  Roman  writers, 
means  to  comprehend  or  understand,  that  is,  to  embrace  a  multitude 
of  different  objects  by  their  common  qualities  into  one  act  of 
thought ;  and  animi  conceptus  was,  in  like  manner,  applied  by  the 
ancient  writers  to  denote  this  operation,  or  its  result.  The  employ- 
ment of  concipere,  conceptus,  and  conceptio,  as 
Oi  c<mcip.re,  concep.       ^e^jj^j^j^^i    ^crms.  In   the  Philosophy  of  Mind, 

Iks,  and  conceptio,  with-  ^  _  •*     "^ 

out  adjunct.  without    the  explanatory  adjunct,  was  of  a  later 

introduction  —  was,  indeed,  only  possible  after 
they  had  been  long  familiarly  used  in  a  psychological  relation.  But 
when  so  introduced,  they  continued  to  be  employed  by  philosophere 
in  general  in  their  proper  signification  as  convertible  with  thought  or 
comprehension,  and  as  opposed  to  the  mere  apprehension  of  Sense 
or  Imagination.  Not,  indeed,  that  examples  enough  may  not  be 
adduced  of  their  abusive  application  to  our  immediate  cognitions  of 
individual  objects,  long  before  Mr.  Stewart  formally  applied  the 
term  conception  to  a  certain  accidental  form  of  representation  —  to 
the  simple  reproduction  or  repetition  of  :'.n  act  of  perception  in 
imagination.'  In  using  the  temis  conception  and  concept  in  the 
sense  which  I  have  explained,  I  therefore  employ  them  not  only  in 
strict  conformity  to  their  grammatical  meaning,  but  to  the  meaning 
which  they  have  generally  obtained  among  philosophers. 

The  term  notion,  like  conception,  expresses  both  an  act  and  its 

product.     I   shall,  however,  as   has   commonly 

The  term  notion,-       -^^^^   AowQ,  usc  it  Only  in  this  latter  relation. 

Iiow  employed  by  the        _,,  .  i    i  ti  .1 

^^jjjjjj.  Ihis  word  has,  like  conception,  been  sometimes 

abusively  applied  to  denote  not  only  our  knowl- 
edge of  things  by  their  common  characters,  but,  likewise,  to  include 

1  See  Lectuns  on  Melaphysica,  p.  462  uq.  —  Ed. 


I 


Lect.  Vn.  LOGIC.  87 

the  mere  presentations  of  Sense  and  representations  of  Phantasy. 
This  abusive  employment  has,  however,  not  been  so  frequent  in 
reference  to  this  terra  as  to  the  term  conception ;  but  it  must  be 
acknowledged,  that  nothing  can  be  imagined  more  vague  and  vacil- 
lating than  the  meaning  attached  to  notion  in  the  writings  of  all 
British  philosophere,  without  exception.  So  much  for  the  expres- 
sions concept  and  notion.     I  now  go  on  to  that  which  they  express. 

^  XX.^  —  In  our  Consciousness  —  apprehension — of  an  indi- 
vidual  object,  there  may  be  distinguished 
Par.  XX.  Concepts.       ^hc   two   following   coguitious :  —  1°,    The 

—  (b)  Nature    of    the  ,  o  o 

tiling.  immediate  and  irrespective  knowledge  we 

have  of  the  individual  object,  as  a  comple- 
ment of  certain  qualities  or  characters,  considered  simply  as 
belonging  to  itself.  2°,  The  mediate  and  relative  knowledge 
we  have  of  this  object,  as  comprising  qualities  or  characters 
common  to  it  with  other  objects. 

The  former  of  these  cognitions  is  that  contained  in  the  Pre- 
sentations of  Sense,  external  and  internal,  and  Representations 
of  Imagination.  They  are  only  of  the  individual  or  singular. 
The  latter  is  that  contained  in  the  Concepts  of  the  Under- 
standing, and  is  a  knowledge  of  the  common,  general,  or  uni- 
versal. 

The  conceiving  an  object  is,  therefore,  its  recognition  medi- 
ately through  a  concept;  and  a  Concept  is  the  cognition  or 
idea  of  thq  general  character  or  characters,  point  or  points,  in 
which  a  plurality  of  objects  coincide. 

This  requires  some  illustration,  and  it  will  be  best  afforded  by 

considering  the  history  of  our  knowledge.     Our 

Concepts,— their  na.       mental  activity  is  not  first  exerted  in  an  appre- 

ture  illustrated  by  ref-        ,  .  /.    ,  i  .  „ 

erence  to  the  history  heusiou  of  the  general,  common  properties  of 
of  our  knowledge.  things.     On  the  Contrary,  objccts  are  originally 

Objects  are  originally       presented  to  US  in  coufused  and  imperfect  percep- 

presented  in  confused         ,  •  mi_  t  ^-i^        "iti        o 

,  .       ^  ^  tions.     Ihe  rude  materials  lurnished  by  bense, 

and  imperfect  percep-  ^  .    . 

tions.  retained   in   Memory,  reproduced   by  Reminis- 

cence, and  represented  in  Imagination,  the  Un- 
derstanding elaborates  into  a  higher  knowledge,  simply  by  means 
of  Comparison  and  Abstraction.  The  primary  act  of  Comparison 
is  exerted  upon  the  individual  objects  of  Perception  and  Imagination 

1  On  this  and  three  following  paragraphs     tt  seq.  —  [Meditationes  de   Cognitione    Teritatst 
apply  Leibnitz's  distinction  of  Intuitive  and      et  Ideis.  —  Ed.] 
Symbolical  Knowledge,  see  Opera  II.  i.  p.  14 


88  LOGIC.  Lect.  VIL 

alone.     In  the  multitude  and  complexity  of  these   objects,  certain 

attributes  are  found  to  produce  similar,  others 

Offices  of  Compan-       ^^  produce  dissimilar,  impressions.     The  obser- 

8on    and    Abstraction  .  ^    ,  ,      r-  i  •  a      .• 

or  attention  vation  of  this  lact  determmes  a  reflective  con- 

sideration of  their  properties.  Objects  are  in- 
tentionally compared  together  for  the  purpose  of  discovering  their 
similarities  and  differences.  When  things  are  found  to  agree  or  to 
disagree  in  certain  respects,  the  consciousness  is,  by  an  act  of  voli- 
tion, concentrated  upon  the  objects  which  thus  partially  agree,  and, 
in  them,  upon  those  qualities  in  or  through  which  they  agree ;  and 
by  tliis  concentration  —  whicl*  constitutes  the  act  called  Attention 
—  Avhat  is  eflfected  ?  On  the  objects  and  qualities,  thus  attentively 
considered,  a  strong  light  is  shed;  but  precisely  in  proportion  as 
these  are  illuminated  in  consciousness,  the  others,  to  which  we  do 
not  attend,  are  thrown  into  obscurity. 

The  result  of  Attention,  by  concentrating  the  mind  upon  certain 

qualities,  is  thus  to  withdraw  or  abstract  it  from 

Prescision,  Attention,       j^ll  elsc.     In  technical  language,  we  are  said  to 

and    Abstraction   are  •     y  ^^  t  l  •   i  i      •      i 

,  ^.  -         prescind  the  phaenomena  whicli  we  exclusively 

correlative  names  for  . 

the  same  process.  Consider.    To  prescind^  to  attend^  and  to  abstract, 

are  merely  different  but  correlative  names  for 
the  same  process ;  and  the  first  two  are  nearly  convertible.  When 
we  are  said  to  prescind  a  quality,  we  are  merely  supposed  to  attend 
to  that  quality  exclusively ;  and  when  we  abstract,  we  are  properly 
said  to  abstract  from,  that  is,  to  throw  otlier  attributes  out  of  ac- 
count. I  may  observe  that  the  term  abstraction  is  very  often  abu- 
sively employed.  By  Abstraction  we  are  frequently  said  to  attend 
exclusively  to  certain  phaenomena,  —  those,  to  wit,  which  we  ab- 
stract; whereas,  the  term  abstraction  is  properly  applied  to  the 
qualities  which  we  abstract  from ;  and  by  abstracting  from  some,  we 
are  enabled  to  consider  others  more  attentively.  Attention  and 
Abstraction  arc  only  the  same  process  viewed  in  diffeient  relations. 
They  are,  as  it  were,  the  positive  and  negative  poles  of  the  same 
act.' 

By  Comparison,  the  points  of  resemblance  among  things  being 
thus  discovered,  and  by  Attention  constituted  into  exclusive  ob- 
jects ;  by  the  same  act  they  are  also  reduced  in  consciousness  from 
multitude  to  unity.  What  is  meant  by  this  will  be  apparent  from 
the  following  considerations. 


1  See   Lecturts   on    Metapkysies,  p.  474  ,  and      Logik,  i&;Krixf(,  LogiJc,i  i9. —E,T>.    [Schulze 
Baobmann,    Logilc,   i    44      Compare  Kant,     Logile,  i  28;  Drobisch,  LogHe,i  li,  p.  11  ette<ii 


Lect.  VII.  LOGIC.  89 

We  are  conscious  to  ourselves  that  we  can  repeat  our  acts  of  con« 
sciousness  — that  we  can  think  the  same  thought 

Thereduction  of  Ob-         ^^^^  ^^^    ^^^^       rpj^j^  ^^.   ^j^-^  thought,  is  al- 

jects   from   multitude  o      ^ 

to  unity,  — explained       ways  in  reaUty  the  same,  though  manifested  at 

and  illustrated.  different  times :  for  no  one  can  imagine  that  in 

Thought  is  one  and       ^he  repetition  of  one  and  the  same  thought,  he 

the    fame,    while    its         ,  i         v^        ^  ^i,  i_i        j?       i        • 

contents  are  identical.       ^^^  a  plurahty  of  thoughts  ;  for  he  IS  conscious 
that  it  is  one  and   the  same  thought  which  is 
repeated,  so  long  as  its  contents  remain  identical. 

Now,  this  relation  of  absolute  similarity  which  subsists  between 

the  repetitions  of  the  same  thought,  is  found  to 

Objects  are  to  us  the      hold  between  our  representations  of  the  resem- 

same  when  we  are  un-         •,,.  ,.,.  /«     i-      -        m  t.-      x    i 

,,     ,      .. ,.      .^       bung  qualities  01  obiects,    Iwo  obiects  have  sim- 

able     to     distmguish         ...  . 

their  cognitions.  i^^r   qualities  only  as   these   qualities   afford   a 

similar  presentation  in  sense  or  a  similar  repre- 
sentation in  imagination,  and  qualities  are  to  us  completely  similar, 
when  we  are  unable  to  distinguish  their  cognitions.  But  what  we 
cannot  distinguish,  is,  to  us,  the  same ;  therefore,  objects  which  de- 
termine undistinguishable  impressions  upon  us,  are  perceived  and 
represented  in  the  same  mental  modification,  and  are  subjectively 
to  us  precisely  as  if  they  were  objectively  identical. 

But  the  consciousness  of  identity  is  not  merely  the  result  of  the 

indiscernible   similarity   of  total   objects,  it  is 

The  consciousness       equally  the  result  of  the  similarity  of  any  of 

of  identity  is  equally       their    parts  —  partial    characters.      For   by  ab- 

the  result  of  the  simi-  j.        i.'  -u  i*  x*  xi,  tx-  •    i 

,    .       „  ,   ,         stracting  observation  from  the  quahties,  points, 

lanty   of  any  cf  the         ,  ,    °  _  ,  .... 

partial  characters  of      i^  which  objects  differ,  and  limiting  it  to  those 
objects.  in  which  they  agree,  we  are  able  to  consider 

them  as  identical  in  certain  respects,  however 
diverse  they  may  appear  to  be  in  othei-s,  which,  for  the  moment, 
we  throw  out  of  view.  For  example :  let  B,  G,  and  T>  represent  a 
series  of  individual  objects,  which  all  agree  in  possessing  the  resem- 
bling attributes  of  y  y  y,  and  severally  differ  in  ench  respectively 
possessing  the  non-resembling  attributes  i,  o,  u.  Now,  in  so  far  as 
we  exclusively  attend  to  the  resembling  qualities,  we,  in  the  first 
place,  obscure  or  remove  out  of  view  their  non-resembling  charac- 
ters i,  o,  u,  while  we  remain  exclusively  conscious  of  their  resem- 
bling qualities  y  y  y.  But,  in  the  second  place,  the  qualities 
expressed  \yj  yy  y  determine  in  us  cognitive  energies  which  we  are 
unable  to  distinguish,  and  which  we,  therefore,  consider  as  the 
same.  We  therefore  view  the  three  similar  qualities  in  the  three 
different  objects  as  also  identical ;  we  consider  the  y  in  this,  the  y 
in  that,  and  the  y  in  the  third  object,  as  one ;  and  in  so  far  as  the 

12 


90  LOGIC.  Lect.  VIL 

three  objects  participate  in  this  oneness  or  identity,  we  regard  them 
as  also  the  same.  In  other  words,  we  classify  B,  C,  and  D,  under  y  ; 
y  is  the  genus  ;  B,  C,  and  D  are  its  individuals  or  species,  severally 
distinguished  from  each  other  by  the  non-resembling  properties,  t, 
o,  u.  Now,  it  is  the  points  of  similarity  thus  discovered  and  iden- 
tified in  the  unity  of  consciousness,  which  constitute  Concepts  or 
Notions. 

It  is  evident  that  the  same  process  of  Comparison  and  Abstrac- 
tion may  be  again  performed  on  the  concepts  thus  fonned.     They 
are,  in   like    manner,   compared   togethei-,   and 

Generalization.  .  .  '  r  &  » 

their  points  of  resemblance  noted,  exclusively 
considered,  and  reduced  to  one  in  the  synthesis  of  thought.  This 
process  is  called  Generalization;  that  is,  the  process  of  evolving  the 

general  or  one,  out  of  the  individual  and  mani- 

concepts  or  notions      fold.     Notions  and  concepts  are  also  sometimes 

super  uousy    sy  designated  by  the   style  of  general  notions  — 

general  conceptions.  This  is  supei-fluous  ;  for,  in 
propriety  of  speech,  notions  and  concepts  are,  in  their  very  nature, 
general ;  while  the  other  cognitive  modifications  to  which  they  are 
opposed,  —  perceptions  and  imaginations,  —  have,  in  like  manner, 
their  essence  in  their  individuality. 

By  the   way,  you  may  have  noticed  that  I  never  use  the  term 

idea.     The  reason  of  my  non-employment  of 

jrffa,— reason  why      that  word  i§  this:  There  is  no  possible  diversity 

not  regularly  employ-       ^f  meaning  in  which  that  term  has  not  been 

ed,  and  sense  in  which  ^  .  it        i  /»  -r 

it  is  occasionally  used,  usurped ;  and  It  would  only  confuse  you,  were  I 
by  the  Author.  to  attempt  to  enumerate  and  explain  them.     I 

may,  however,  occasionally  not  eschew  the 
word  ;  but  if  you  ever  hear  it  from  me,  I  beg  you  to  observe,  that  I 
apply  it,  in  a  loose  and  general  signification,  to  comprehend  the 
presentations  of  Sense,  the  representations  of  Phantasy,  and  the 
concepts  or  notions  of  the  Understanding.  We  are  in  want  of  a 
generic  term  to  express  these ;  and  the  word  representation  {repre- 
sentatio),  which,  since  the  time  of  Leibnitz,  has  been  commonly 
used  by  the  philosophers  of  the  Continent,  I  have  restricted  to 
denote,  what  it  only  can  in  propriety  express,  the  immediate  object 
or  product  of  Imagination.  We  are,  likewise,  in  want  of  a  general 
term  to  express  what  is  common  to  the  presentations  of  Perception, 
and  the  representations  of  Phantasy,  that  is,  their  individuality  and 
immediacy.  The  Germans  express  this  by  the  term  Anschauungy 
which  can  only  be  translated  by  intuition  (as  it  is  in  Latin  by  Ger- 
mans), which  literally  means  a  looking  at.  Tliis  expression  has, 
however,  been  preoccupied  in  English  to  denote  the  apprehension 


Lect.  Vn.  LOGIC.  91 

we  have  of  self-evident  truths,  and  its  application  in  a  different  sig- 
nification, vrould  therefore  be,  to  a  certain  extent,  liable  to  am- 
biguity. I  shall,  therefore,  continue,  for  the  present  at  least,  to 
struggle  on  without  such  a  common  term,  though  the  necessity  thus 
imposed  of  always  opposing  presentation  and  representation  to  con- 
cept is  both  tedious  and  perplexing. 

^  XXI.    A  concept  or  notion  thus  involves  —  1°.  The  repre- 
sentation of  a  part  only  of  the  various  attri- 
Generai  Characters       ^^^^^  ^^  characters  of  which  an  individual 

of  Concepts. 

Par.  XXI.  (a)  A  Con-  objcct  is  the  sum  ;  and,  consequently,  affords 
only  a  one-sided  and  inadequate  knowledge 
of  the  things  which  are  thought  under  it. 


cept  affords  only  in- 
adequate Icnowledge, 


This  is  too  simple  to  require  any  commentary.     It  is  evident  that 
when  we  think  Socrates  by  any  of  the  concepts. 

Explication.  .,.  ^ttt  y  ■       ^  . 

—  At/ienian,  Cireefc,  Jburopean,  man,  oipea,  ani- 
mal, being, —  we  throw  out  of  view  the  far  greater  number  of 
characters  of  which  Socrates  is  the  complement,  and  those,  like- 
wise, which  more  proximately  determine  or  constitute  his  individu- 
ality. It  is,  likewise,  evident,  that  in  proportion  as  we  think  him 
by  a  more  general  concept,  we  shall  represent  him  by  a  smaller 
bundle  of  attributes,  and,  consequently,  represent  him  in  a  more 
partial  and  one-sided  manner.  Thus,  if  we  think  him  as  Athe- 
nian, we  shall  think  him  by  a  greater  number  of  qualities  than  if  we 
think  him  by  Greek ;  and,  in  like  manner,  our  representation  will 
be  less  and  less  adequate,  as  we  think  him  by  every  higher  concept 
in  the  series,  —  European,  man,  biped,  animal,  being. 

^  XXII.     2°,  A  concept  or  notion,  as  the  result  of  a  compari- 
son, necessarily  expresses  a  relation.     It  is. 

Par.  XXII.  (b)  A  Con.  ,  „  "^  .      ii     •       •         i^       i  •       • 

cept  affords  no  abso-  therefore,  not  cognizable  m  itself;  that  is,  it 
lute  object  of  knowi-  affords  uo  absolute  or  irrespective  object  of 
knowledge,  but  can  only  be  realized  in  con- 
sciousness by  applying  it,  as  a  term  of  relation,  to  one  or  more 
of  the  objects,  which  agree  in  the  point  or  points  of  resem- 
blance which  it  expresses. 

In  this  paragraph  (if  I  may  allude  to  what  you  may  not  all  be 
aware  of)  is  contained  a  key  to  the  whole  mystery  of  Generalization 
and  General  Terms ;  for  the  whole  disputes  between  the  Concep- 
tualists  and  Nominalists  (to  say  nothing  of  the  Realists)  have  only 
arisen  from  concepts  having  been  regarded  as  affording  an  irre- 


92  LOGIC.  '  Lect.  VII. 

spective    and  independent  object  of  thought.*      This  illusion  ha.s 

arisen  from  a  very  simple  circumstance.     ObjeelB 

Tiiis  paragraph  con-       compared  together  are  found  to  possess  certain 

tains  a  key  to    the       attributes,    which,   as    producing    indisceraible 

mystery  of  General!-  Tn      ^-  •  \  i       i    ^   i        •      -i 

zation    and  General      modincations  m  US,  are  to  us  absolutely  similai*. 
Ternis.  They  are,  therefore,  considered  the  same.     The 

relation  of  similarity  is  thus  converted  into 
identity,  and  the  real  plurality  of  resembling  qualities  in  nature  is 
factitiously  reduced  to  a  unity  of  thought ;  and  this  unity  obtains  a 
name  in  which  its  relativity,  not  being  expressed,  is  still  further 
removed  from  observation. 

But  the  moment  we  attempt  to  represent  to  ourselves  any  of 

these  concepts,  any  of  these  abstract  generalities, 

Wherein    consists       j^g  absolute  objects,  by  thcmselves,  and  out  of 

^  °      '  ^  relation  to  any  concrete  or  individual  realities, 

their  relative  nature  at  once  reappears ;  for  we 
find  it  altogether  impossible  to  represent  any  of  the  qualities  ex- 
pressed by  a  concept,  except  as  attached  to  some  individual  and 
determinate  object ;  and  their  whole  generality  consists  in  this,  — 
that  though  we  must  realize  them  in  thought  under  some  singular 
of  the  class,  we  may  do  it  under  any.  Thus,  for  example,  we  can- 
not actually  represent  the  bundle  of  attributes  contained  in  the 
concept  man,  as  an  absolute  object,  by  itself^  and  apart  from  all  that 
reduces  it  from  a  general  cognition  to  an  individual  representation. 
We  cannot  figure  in  imagination  any  object  adequate  to  the  general 
notion  or  term  man;  for  the  man  to  be  here  imagined  must  be 
neither  tall  nor  short,  neither  fat  nor  lean,  neither  black  nor  whit**, 
neither  man  nor  woman,  neither  young  nor  old,  but  all  and  yet 
none  of  these  at  once.  The  relativity  of  our  concepts  is  thus  shown 
in  the  contradiction  and  absurdity  of  the  opposite  hypothesis. 

1  For  a  ftill  accooot  of  this  dispute,  see  Leeturea  on  Mttapkysies,  p.  477  «( to. — Bd. 


LECTURE   VIII. 

STOICHEIOLOGY. 

SECTION    II.— OF    THE    PRODUCTS   OF    THOUGHT 

L— ENNOEMATIC. 

A.    OF   CONCEPTS   IN  GENERAL;   B.    IN  SPECIAL— I.    THEIR 
OBJECTIVE   RELATION  — QUANTITY. 

In  our  last  Lecture,  we  began  the  Second  Section  of  Stoicheiol- 

ogy,  —  the  consideration  of  the  Products  of  Thought.    The  product 

of  thought  may  be  considered  as  Concepts,  as 

Recapitulation,  with      Judgments,  and  as  Reasonings ;  these,  however, 

further      explanation  ,  .  ,  ,^  ,  „-,.^ 

andiiiustration.  ^'"^  "°^  ^^  "®  Viewed  as  the  results  of  different 

faculties,  far  less  as  processes  independent  of 
each  other,  for  they  are  all  only  the  product  of  the  same  energy  in 
different  degrees,  or  rather  in  simpler  or  more  complex  applications 
to  its  objects. 

In  treating  of  Concepts?,  which  form  the  subject  of  the  First 
Chapter  of  this  Second  Section,  I  stated  that  I  should  first  consider 
them  in  general,  and  then  consider  them  in  special ;  and,  in  my  Inst 
Lecture,  I  had  nearly  concluded  all  that  I  deem  it  requisite  under 
the  former  head  to  state,  in  regard  to  their  peculiar  character,  their 
origin,  and  their  general  accidents.  I,  first  of  all,  explained  the 
meaning  of  the  two  terms,  concept  and  notion,  —  words  convertible 
with  each  other,  but  still  severally  denoting  a  different  aspect  of 
the  simple  operation,  which  they  equally  express.  Notion  being 
relative  to  and  expressing  the  apprehension,  —  the  remarking, — 
the  taking  note  of,  the  resembling  attributes  in  objects;  concept, 
the  grasping  up  or  synthesis  of  these  in  the  unity  of  thought. 

Having  shown  what  was  properly  expressed  by  the  terms  notion 
and  concept,  or  conception,  I  went  on  to  a  more  articulate  explana- 
tion of  that  which  they  were  employed  to  denote.  And  here  I 
•Tgain  stated  what  a  Concept  or  Notion  is  in  itself,  and  in  contrnst 
to  a  Presentation  of  Perception,  or  Representation  of  Phantasy. 
Our  knowledge  through  either  of  the  latter,  is  a  direct,  immediate. 


94  LOGIC.  Lect.  Vm 

irrespective,  determinate,  individual,  and  adequate  cognition ;  that 
is,  a  singular  or  individual  object  is  known  in  itself,  by  itself,  through 
all  its  attributes,  and  without  reference  to  aught  but  itself.  A  con- 
cept, on  the  contrary,  is  an  indirect,  mediate,  relative,  indeterminate, 
and  partial  cognition  of  any  one  of  a  number  of  objects,  but  not  an 
actual  representation  either  of  them  all,  or  of  the  whole  attributes 
of  any  one  object. 

Though  it  be  not  strictly  within  the  province  of  Logic  to  explain 
the  origin  and  formation  of  our  notions,  the  logician  assuming,  as 
data,  the  laws  and  products  of  thought,  jxs  the  mathematician  as- 
sumes, as  data,  extension  and  number  and  the  axioms  by  which 
their  relation  is  determined,  both  leaving  to  the  metaphysician 
the  inquiry  into  their  grounds ;  —  this  notwithstanding,  I  deemed 
it  not  improper  to  give  you  a  very  brief  statement  of  the  mode  and 
circumstances  in  which  our  concepts  are  elaborated  out  of  the  pre- 
sentations and  representations  of  the  subsidiary  faculties.  Different 
objects  are  complements  partly  of  similar,  partly  of  different,  attri- 
butes. Similar  qualities  are  those  which  stand  in  similar  relation 
to  our  organs  and  faculties,  and  where  the  similarity  is  complete, 
the  effects  which  they  determine  in  us  are,  by  us,  indiscernible.  To 
us  they  are,  therefore,  virtually  the  same,  and  the  same  we,  accord- 
ingly, consider  them  to  be,  though  in  different  objects ;  precisely  as 
we  consider  the  thought  of  the  same  object  to  be  itself  the  same, 
when  repeated  at  intervals  —  at  different  times  —  in  consciousness. 
This,  by  way  of  preface,  being  understood,  I  showed  that,  in  the 
formation  of  a  concept  or  notion,  the  process  may  be  analyzed  into 
four  momenta.  In  the  first  place,  we  must  have  a  plurality  of  ob- 
jects presented  or  represented  by  the  subsidiary  faculties.  These 
faculties  must  furnish  the  rude  material  for  elaboration.  In  the  sec- 
ond place,  thg  objects  thus  supplied  are,  by  an  act  of  the  Under- 
standing, compared  together,  and  their  several  qualities  judged  to 
be  similar  or  dissimilar.  In  the  third  place,  an  act  of  volition, 
called  Attention,  concentrates  consciousness  on  the  qualities  thus 
recognized  as  similar;  and  that  concentration,  by  attention  on  them, 
involves  an  abstraction  of  consciousness  from  those  which  have 
been  recognized  and  thrown  aside  as  dissimilar ;  for  the  power  of 
consciousness  is  limited,  and  it  is  clear  or  vivid  precisely  in  propor- 
tion to  the  simplicity  or  oneness  of  its  object.  Attention  and  Ab- 
straction are  the  two  poles  of  the  same  act  of  thought ;  they  are 
like  the  opposite  scales  in  a  balance  —  the  one  must  go  up  aa  the 
other  goes  down.  In  the  fourth  place,  the  qualities,  which  by  com- 
parison are  judged  similar,  and  by  attention  are  constituted  into  an 
exclusive  object  of  thought,  —  these  are  already,  by  this  process, 


Lect.  viii.  logic.  95 

idcntifieil  in  consciousness;  for  tliey  are  only  judged  similar,  inas- 
much as  they  produce  in  us  indiscernible  effects.  Their  synthesis  in 
consciousness  may,  however,  for  precision's  sake,  he  stated  as  a 
fourth  step  in  the  jirocess  ;  Ijut  it  must  be  remembered,  tliat  at  least 
the  three  latter  steps  arc  not,  in  reality,  distinct  and  independent 
acts,  but  are  oldy  so  distinguished  and  stated,  in  order  to  enable 
us  to  com])rehend  and  speak  about  the  indivisible  0])eration,  in  the 
different  aspects  in  which  we  may  consider  it.  In  the  same  way, 
you  ai-e  not  to  su])pose  that  tlie  mental  sentence  which  must  be  ana- 
lyzed in  order  to  be  expressed  in  laugua^e,  lias  as  manv  parts  in 
consciousness,  as  it  has  words,  or  clauses,  in  s]>eech  ;  for  it  f  )rms,  in 
reality,  one  organic  and  indivisible  whole.  To  rc])eat  an  illustra- 
tion 1  have  already  given,  —  the  ]»arts  of  an  act  of  thought  stand  in 
the  same  relation  to  each  other  as  the  parts  of  a  triangle,  —  a  figure 
Avhicli  we  cannot  resolve  into  any  simpler  figure,  but  whose  sides 
and  angles  we  may  consi<ler  apart,  and,  therefore,  as  parts;  though 
these  are,  in  reality,  inseparable,  being  tlie  necessary  conditions  of 
each  other.     lUit  this  by  the  way. 

The  qualities  of  ditlcrcnt  individual  things,  thus  identified  in 
tliought,  and  constituting  concepts,  under  which,  as  classes,  these 
individual  things  themselves  are  ranged;  —  these  primary  concepts 
may  themselves  be  subjected  to  the  same  process,  by  which  they 
were  elaborated  from  the  concrete  realities  given  in  Perception  and 
Imagination.  We  may,  again,  compare  different  concepts  together, 
again  find  in  the  jilurality  of  attributes  which  they  comprehend, 
some  like,  some  unlike;  we  may  again  attend  only  to  the  similar, 
and  again  identify  these  in  the  synthesis  of  consciousness;  and  this 
process  of  evolving  concepts  out  of  concepts  we  may  go  on  per- 
forming, until  the  generalization  is  arrested  in  that  ultimate  or  pri- 
mary concejjt,  the  basis  itself  of  all  attributes,  —  the  conce])t  of 
Being  or  Existence. 

Having  thus  endeavored  to  give  you  a  general  view  of  what  con- 
cepts are,  and  by  what  process  they  are  formed,  I  stated,  by  way  of 
corollary,  some  of  their  general  characteristics.  The  first  of  these  I 
mentioned  is  their  partiality  or  inadequacy;  that  is,  they  compre- 
hend only  a  larger  or  smaller  portion  of  the  whole  attributes  belong- 
ing to  the  things  classified  or  contained  under  them. 

The  second  is  their  relativity.     Formed  by  comparison,  they  ex- 
press only  a  relation.     They  cannot,  therefore, 

e  a  ui  y  o     .on-       ^^^  held  up  as  an  absolute  object  to  consciousness, 

cepts.  ^  •' 

—  they  cannot  be  represented,  as  universals,  in 
imagination.  They  can  only  be  thought  of  in  relation  to  some  one 
of  the  individual  objects  they  classify,  and  when  viewed  in  relation 


96  LOGIC.  Lect.  Vm 

to  it,  they  can  be  represented  in  imagination ;  but  then,  as  so  actu- 
ally represented,  they  no  longer  constitute  general  attributions,  they 
fall  back  into  more  special  determinations  of  the  individual  object  in 
which  they  are  represented.  Thus  it  is,  that  the  generality  or  uni- 
versality of  concepts  is  potential,  not  actual.  They  are  only  gener- 
als, inasmuch  as  they  may  be  applied  to  any  of  the  various  objects 
they  contain ;  but  while  they  cannot  be  actually  elicited  into  con- 
sciousness, except  in  application  to  some  one  or  other  of  these,  so, 
they  cannot  be  so  applied  without  losing,  joro  tanto,  their  universal- 
ity. Take,  for  example,  the  concept  horse.  In  so  far  as  by  horse 
we  merely  think  of  the  word,  that  is,  of  the  combination  formed  by 
the  letters  A,  o,  r,  s,  e,  —  this  is  not  a  concept  at  all,  as  it  is  a  mere 
representation  of  certain  individual  objects.  This  I  only  state  and 
eliminate,  in  order  that  no  possible  ambiguity  should  be  allowed  to 
lurk.  By  horse,  then,  meaning  not  merely  a  representation  of  the 
word,  but  a  concept  relative  to  certain  objects  classed  under  it;  — 
the  concept  horse,  I  say,  cannot,  if  it  remain  a  concept,  that  is,  a 
universal  attribution,  be  represented  in  imagination ;  but,  except  it 
be  represented  in  imagination,  it  cannot  be  applied  to  any  object; 
and,  except  it  be  so  applied,  it  cannot  be  real- 
Concepts  have  a  po-       j^ed  in  thought  at  all.     You  may  try  to  escape 

tential,  not  an  actual,  ,       ,  />    i        ti  t  17- 

univereaiitv.  ^'^^  horns  oi  the  dilemma,  but  you  cannot.    You 

cannot  realize  in  thought  an  absolute  or  irrespec- 
tive concept,  corresponding  in  univei-sality  to  the  application  of  the 
word ;  for  the  supposition  of  this  involves  numerous  contradictions. 
An  existent  horse  is  not  a  relation,  but  an  extended  object  possessed 
of  a  determinate  figure,  color,  size,  etc.;  horse,  in  general,  cannot, 
therefore,  be  represented,  except  by  an  image  of  something  extended, 
and  of  a  determinate  figure,  color,  size,  etc.  Here  now  emerges  the 
contradiction.  If,  on  the  one  hand,  you  do  not  represent  something 
extended  and  of  a  determinate  figure,  color,  and  size,  you  have  no 
representation  of  any  horee.  There  is,  therefore,  on  this  alternative, 
nothing  which  can  be  called  the  actual  concept  or  image  of  a  hoi-se 
at  all.  If,  on  the  other  hand,  you  do  represent  something  extended 
and  of  a  determinate  figure,  color,  and  size,  then  you  have,  indeed, 
the  image  of  an  individual  liorse,  but  not  a  universal  concept  coad- 
equate  with  horse  in  general.  For  how  is  it  possible  to  have  an  act- 
ual representation  of  a  figure,  which  is  not  a  determinate  figure  ? 
but  if  of  a  determinate  figure,  it  must  be  that  of  some  one  of  the 
many  different  figures  under  which  horses  appear ;  but  then,  if  it  be 
only  of  one  of  these,  it  cannot  be  the  general  concept  of  the  othei*s, 
which  it  does  not  represent.  In  like  manner,  how  is  it  possible  to 
have  the  actual  representation  of  a  thing  colored,  which  is  not  the 


Lect.  yiii.  logic.  9.7 

representation  of  a  determinate  color,  that  i.s,  either  white,  or  black, 
or  gray,  or  brown,  etc.  ?  but  if  it  be  any  one  of  these,  it  can  only 
represent  a  horse  of  this  or  that  particular  color,  and  cannot  be  the 
o-eneral  concept  of  horses  of  every  color.  The  same  result  is  given 
by  the  other  attributes ;  and  what  I  originally  stated  is  thus  mani- 
fest, —  that  concepts  have  only  a  potential,  not  an  actual,  universal- 
ity;  that  is,  they  are  only  universal,  inasmuch  as  they  may  be  applied 
to  any  of  a  certain  class  of  objects,  but  as  actually  applied,  they  are 
no  longer  general  attributions,  but  only  special  attributes. 

But  it  does  not  from  this  follow  that  concepts  are  mere  words, 
and  that  there  is  nothing  general  in  thought  it- 

But  concepts  are  not,         ^^jf.      rpj^j^  j^  ^^^  j^^^^^  j^^j^  j^  ^^^-^^        , 
therefore,  mere  words.  .  j       j         j 

philosopher ;  for  no  philosopher  has  ever  denied 
that  we  are  capable  of  apprehending  relations,  and  in  particular 
the  relation  of  similarity  and  difference ;  so  that  the  whole  contro- 
versy between  the  conceptualist  and  nominalist  originates  in  the 
ambiguous  employment  of  the  same  terms  to  express  the  represen- 
tations of  Imagination  and  the  notions  or  concepts  of  the  under- 
standing.   This  is  significantly  shown  by  the  absolute  non-existence 
of  the  dispute  among  the  philosophers  of  the  most  metaphysical, 
country  in  Europe.     In  Germany,  the  question  of  nominalism  and' 
conceptualism  has  not  been  agitated,  and  why?     Simply  because 
the  German  language  supplies  terms  by  which  concepts  (or  notions 
of  thought  proper)  have  been  contradistinguished  from  the  presen- 
tations and  representations  of  the  subsidiary  faculties.'      But  this 
is  not  a  subject  on  which  I  ought  at  present  to  have  touched,  as  it 
is,  in  truth,  foreign  to  the  domain  of  Logic;  and  I  have  only  been 
led  now  to  recur  to  it  at  all,  in  consequence  of  some  difficulties  ex- 
pressed to  me  by  members  of  the  class.     All  that  I  wish  you  now 
to  understand  is  —  that  concepts,  as  the  result  of  comparison,  that 
is,  of  the  apprehension  and  affirmation  of  a  relation,  are  necessarily, , 
in  their  nature  relative,  and,  consequently,  not  capable  of  represen- 
tation as  absolute  attiibutes.     I  shall  terminate  the  consideration  ^ 
of  concepts  in  general  by  the  following  paragraph,  in  which  is- 
stated,  besides  their  inadequacy  and  i-elativity,  their  dependence  on . 
language : 

%  XXIII.     The  concept  thus  formed  by  an  abstraction  of 
the  resembling  from  the   non-resembling  qualities  of  objects,, 
would  again  fall  back  into  the   confusion  and  infinitude  from.' 


1  See  the  Author's  note,  Reicfs  Works,  p.  412;  and  Lectures  on  Metaphysics,  p.  477   et  seq. 
—  Ed. 

13 


98  LOGIC.  Lect.  vin. 

which  it  has  been  called  out,  were  it  not  rendered  permanent 

for  consciousness,  by  being  fixed  and  ratified 

Par.  xxirr.     Con-       in  a   verbal  sign.      Considered  in  general, 

cepts,-(o)  xheir  de-       thought  and  language  are  reciprocally  de- 

pendenoe      on      Lan-  ^  o       o  i  j 

guage.  pendent;  each  bears  all  the  imperfections 

and  perfections  of  the  other;   but  without 

language  there  could  be  no  knowledge  realized  of  the  essential 

properties  of  things,  and  of  the  connection  of  their  accidental 

states. 

This  also  is  not  a  subject  of  which  the  consideration  properly 

belongs  to  Logic,  but  a  few  words  may  not  be 

The  relation  of  Lan-       inexpedient  to  make  you  aware,  in  general,  of  the 

guage  to  Thought,  and       intimate  connections  of  thought  and  its  expres- 

the  influence  which  it  ,  -,       ^  .-,  r  t    •    n  t-ii 

exerts  on  our  mental  ^^^n,  and  of  the  powerful  influence  which  Ian- 
operations.  guag6  exerts  upon  our  mental  operations.  Man, 
in  fact,  only  obtains  the  use  of  his  faculties  in 
obtaining  the  use  of  speech  ;  for  language  is  the  indispensable  mean 
of  the  development  of  his  natural  powere,  whether  intellectual  or 
moral. 

For  Perception,  indeed,  for  the  mere  consciousness  of  the  similar- 
ities and  dissimilarities  in  the  objects  perceived, 
Language  unneces-       f^^.  ^Y\e  apprehension  of  the  causal  connection 
Orations  ^^  Certain  things,  and  for  the  application  of  this 

knowledge  to  the  attainment  of  certain  ends, 
no  language  is  necessary ;  and  it  is  only  the  exaggeration  of  a  truth 
into  an  error,  when  philosophers  maintain  that  language  is  the  indis- 
pensable condition  of  even  the  simpler  energies  of  knowledge. 
Language  is  the  attribution  of  signs  to  our  cognitions  of  things. 
But  as  a  cognition  must  have  been  already  there,  before  it  could 
receive  a  sign ;  consequently,  that  knowledge  which  is  denoted  by 
the  formation  and  application  of  a  word,  must  have  preceded  the 
symbol  which  denotes  it.  Speech  is  thus  not  the  mother,  but  the 
godmother,  of  knowledge.  But  though,  in  general,  we  must  hold 
that  language,  as  the  product  and  correlative  of  thought,  must  be 
viewed  as  posterior  to  the  act  of  thinking  itself;  on  the  other  hand, 
it  must  be  admitted,  that  we  could  never  have  risen  above  the  very 
lowest  degrees  in  the  scale  of  thought,  without  the  aid  of  signs. 
A  sign  is- necessary,  to  give  stability  to  our  intellectual  progress, — 
to  establish  each  step  in  our  advance  as  a  new  starting-point  for 
our  advance  to  another  beyond. 

A  country  may  be  overrun  by  an  armed  host,  but  it  is  only 
conquered    by   the   establishment  of   fortresses.     Words   are   th«» 


i:ect.  VIIL  logic.  99 

fortresses  of  thought.     They  enable  us  to  realize  our  dominion  over 

what  we  have  already  overrun  in  thought;  to 

•  Mental  operations  to       make    every  intellectual  conquest  the  basis  of 

w  ic    anguage  is  in-       operations  for  others  still  beyond.     Or  another 

dispensable,    and    its         ^  ^  ^  •' 

relation  to  these  illustration  :     You  have  all  heard  of  the  process 

of  tunnelling,  of  tunnelling  through  a  sand-bank. 
In  this  operation  it  is  impossible  to  succeed,  unless  every  foot,  nay 
almost  every  inch  in  our  progress,  be  secured  by  an  arch  of  masonry, 
before  we  attempt  the  excavation  of  another.  Now,  language  is  to 
the  mind  precisely  what  the  arch  is  to  the  tunnel.  The  power  of 
thinking  and  the  power  of  excavation  are  not  dependent  on  the 
word  in  the  one  case,  on  the  mason-work  in  the  other ;  but  without 
these  subsidiaries,  neither  process  could  be  cairied  on  beyond  its  rud- 
imentary commencement.  Though,  therefore,  we  allow  that  every 
movement  forward  in  language  must  be  determined  by  an  antece- 
dent movement  forward  in  thought ;  still,  unless  thought  be  accom- 
panied at  each  point  of  its  evolution,  by  a  corresponding  evolution 
of  language,  its  further  development  is  arrested.  Thus  it  is,  that 
the  higher  exertions  of  the  higher  faculty  of  Understanding,  —  the 
classification  of  the  objects  presented  and  represented  by  the  subsi- 
diary powers  in  the  formation  of  a  hierarchy  of  notions,  the  connec- 
tion of  these  notions  into  judgments,  the  inference  of  one  judgment 
from  anothqjTi  and,  in  general,  all  our  consciousness  of  the  relations 
of  the  universal  to  the  particular,  consequently  all  science  strictly 
so  denominated,  and  every  inductive  knowledge  of  the  past  and 
future  from  the  laws  of  nature :  —  not  only  these,  but  all  ascent 
from  the  sphere  of  sense  to  the  sphere  of  moral  and  religious  intelli- 
gence, are,  as  experience  proves,  if  not  altogether  impossible  without 
a  language,  at  least  possible  to  a  very  low  degree. 

Admitting  even  that  the  mind  is  capable  of  certain  elementary 
concepts  without  the  fixation  and  signature  of  language,  still  these 
are  but  sparks  which  would  twinkle  only  to  expire;  and  it  I'equires 
words  to  give  them  prominence,  and,  by  enabling  us  to  collect  and 
elaborate  them  into  new  concepts,  to  raise  out  of  what  would  oth- 
erwise be  only  scattered  and  transitory  scintillations  a  vivid  and 
enduring  light. 

I  here  terminate  the  General  and  proceed  to  the  Special  consid- 
eration of  Concepts  —  that  is,  to  view  them  in 
B  Of  Concepts  or      ^j^^j^.  gg^g^^j  Relations.     Now,  in  a  logical  point 

notions  in  special.  ,  .  i        i 

of  view,  there  are,  it  seems  to  me,  only  three 
possible  relations  in  which  concepts  can  be  considered  ;  for  the  only 
relations  they  hold  are  to  their  objects,  to  their  subject,  or  to  each 


LOGIC.  Lect.  vm, 

other.  In  relation  to  their  objects,-^ they  are  considered  as  inclu- 
sive of  a  greater  or  smaller  number  of  attributes,  that  is,  as  applica- 
ble to  a  greater  or  smaller  number  of  objects;  this  is  technically 
styled  their  Quantity.  In  relation  to  their  subject,  that  is,  to  the 
mind  itself,  they  are  considered  as  standing  in  a  higher  or  a  lower 
degree  of  consciousness,  —  they  are  more  or  less  clear,  more  or  less 
distinct ;  this,  in  like  manner,  is  called  their  Quality.  In  relation' 
to  each  other,  they  are  considered  as  the  same  or  different,  coordi- 
nated or  subordinated  to  each  other ;  this  is  their  Relation,  strictly 
so  called.*  Under  these  three  heads  I  now,  therefore,  proceed  to 
treat  them ;  and,  first,  of  their  Quantity. 

^  XXIV.    As  a  concept,  or  notion^  is  a  thought  in  which  an 
indefinite  plurality  of  characters  is  bound 

Par.     XXrV.  Quan.  .  .  „  .  ,  ,. 

tity  of  coneeptB  of      up  luto  a  uuity  oi  consciousucss,  and  appli- 
two  kinds.  Intensive       cable  to  an  indefinite  plurality  of  objects,  a 

and  Extensive.  •         i  i>  •  i 

concept  IS,  thereiore,  necessarily  a  quantity, 
and  a  quantity  varying  in  amount  according  to  the  greater 
or  smaller  numbers  of  characters  of  which  it  is  the  complement, 
and  the  greater  or  smaller  number  of  things  of  which  it  may 
be  said.  This  quantity  is  thus  of  two  kinds  ;  as  it  is  either  an 
Intensive  or  an  Extensive.  The  Internal  or  Intensive  Quantity 
of  a  concept  is  determined  by  the  greater  or  smoker  number 
of  constituent  character  contained  in  it.  The  External  or  Ex- 
tensive Quantity  of  a  concept  is  determined  by  the  greater  or 
smaller  number  of  classified  concepts  or  realities  contained  un- 
der it.  The  former  (the  Intensive  Quantity)  is  called  by  some 
latter  Greek  logicians  the  depth  ()8a5os),  by  the  Latin  logical 
writers  the  comprehension  {comprehension  quantitas  eompre- 
hensionis,  complexits,  or  quantitas  comjilexus).  The  latter  (the 
Extensive  Quantity)  is  called  by  the  same  latter  Greek  Logi- 
cians, the  breadth  (irXaTo?) ;  by  Aristotle,  -q  irepto)^  to  TrcpUxfty, 
TO  ir€p«;^€o--Sai ;  -  by  the  logical  writers  of  the  western  or  Latin 
world,  the  extension  or  circuit  \exte7isio,  quantitas  extensionis^ 
hi. 

*  On  their  relation  to  their  origin  as  direct  9P,  By  relation  to  each  other  they  hare  m- 

or  indirect,  see  Esser,  [System  der  Lo^k,  (  49,  lation  strictly  so  called, 

p.  96. —  Ed.]  40.  By  relation  to  their  subject  they  have 

Mem.  —  N.  B.  Notions  may  be  thus  better  clearness  and  distinctness. 

divided  {?):  (This  last  had  bettor  be  relef^ated  to  Method- 

10    ».         1    ••        A     AX.  ,         At.       X.         AX.         olojrv.) — Memoranda. 

l".  By  relation  to  themselves  thev  have  the         „  „      .  .,       1     .  <.. 

^   ^,.       -  .        .  iSec  Lectures  on  Metnphystes,  p.  4t  An.     Arii«- 

qtMntity  of  comprehension.  .  ,.     ^  .  i.  .         ., 

totle  does  not  use  -rtptoxv  as  a  substantive, 

2^,  By  relation  to  their  objects  they  have     though  the  verb,  both  active  and  passive,  ia 

the  quantity  of  extension.    These  two  thus     employed  in  this  siffnification, «./;.  .4ihi/.  IV<^ 

quantity  in  general.  i.  27;  Rlut.  iii.  6.  —  Ed.  ( 


t*OT.  vm.  tOGie.  101 

ambitus,   quantitus  ambitus) ;    and    likewise  the   cfo/iuxi;.   or 
sphere  of  a  notion  {regie,  sphcBra)} 

The  Internal  Quantity  of  a  notion,  its  Intension  or  Comprehen- 
sion, is  made  up  of  those  different  attributes  of 
<ieneral  Explication.  ,  .   .      ,  •       ,  .       ,  , 

which  the  concept  is  the  conceived  sum ;  that 

is,  the  various  characters  connected  by  the  concept  itself  into  a 
single  whole  in  thought.  The  External  Quantity  of  a  notion  or  its 
extension  is,  on  the  other  hand,  made  up  of  the  number  of  objects 
which  are  thought  mediately  through  a  concept.  For  example,  the 
attributes  ratiotial,  sensible,  moral,  etc.,  go  to  constitute  the  inten- 
sion or  internal  quantity  of  the  concept  m,a7i;  whereas  the  attributes 
European,  American,  philosopher,  tailor,  etc.,  go  to  make  up  a  con- 
cept of  this  or  that  individual  man.  These  two  quantities  are  not 
convertible.  On  the  contrary,  they  are  in  the  inverse  ratio  of  each 
other;  the  greater  the  depth  or  comprehension  of  a  notion  the  less 
its  breadth  or  extension,  and  vice  versa.  You  will  observe,  like- 
wise, a  distinction  which  has  been  taken  by  the  best  logicians. 
Both  quantities  are  said  to  contain,'  but  the  quantity  of  extension 
is  said  to  contain  under  it;  the  quantity  of  comprehension  is  said  to 
contain  in  it. 

By  the  intension,  comprehension,  or  depth  of  a  notion,  we  think 
the  most  qualities  of  the  fewest  objects ;  whereas  by  the  extension 
or  breadth  of  a  concept,  we  think  the  fewest  qualities  of  the  most 
objects.  In  other  words,  by  the  former,  we  say  the  most  of  the 
least ;  by  the  latter,  the  least  of  the  most. 

Again ;  you  will  observe  the  two  following  distinctions :  the  first, 
—  the  exposition  of  the  comprehension  of  a  notion  is  called  its 
Definition  (a  simple  notion  cannot,  therefore,  be  defined) ;  the 
second,  * —  the  exposition  of  the  Extension  of  a  notion  is  called  its 
Division  (;m  individual  notion  cannot  be  divided). 

1  (Cf.  Porpltyrii,  Isagoge,  cc.  i.  ii.  viii. ;  Caje-  hic  extensive.    Porphyrius  autem  loquebatur 

tan.  In  Porphyrii  Praidicabilia,  CC.  i.  ii.  [p.  37  ett  hic  de  extensiva  collectioue,  ideo  dixit,  genu* 

1579 ;  prefixed  to  his  Commentary  on  the  Cat-  esse  magis  collectivum."    Quoted  by  Stahl, 

fgories.  first   published    in    1496.     "  Ad  hoc  Regulce  Pliilosophicct,  tit.  xii.,  reg.  5,  p.  381. 

breviter  dicitur,  quod  esse  magis  collectivum  Cf.  reg.  6,  ed.  London,  1658.  —  Ed.]    [Port- 

multorum   potest    intelligi    dupliciter:    uno  Royal  Logic,  P.  i.  c.  6,  p.  74,  ed.  1718.    Boe- 

modo  intensive,  et  sic  species  magis  est  collec-  thius,  Introductio  ad  Syllogismos,  Opera,  p.  562: 

tiva,  quia  magis  unit  adunata;  alio  modo  ex-  Tn  Topica  Cieeronis  Cornmentarii,  lib.  i.,  Opern, 

tensive,  et  sic  genus  est   magis  collectivum,  p.  765,  ed.  Basilar,  1570.     Reuschius,   Systema 

nuia  multo  plura  sub  sua  adunatione  cadunt,  Logicum,  pp.  11,  92;    Baumgarten,   Acmo^'-i 

<ni»m  sub  speciei  ambitu.    Unde  species  et  Lo?»>a,  §§  56.  57,  ed.  Hala  Magdeburgse.  177$ 

pcnus  Fo  habent  sicut  duo  duces,  quorum  alter  Rrug,  Losik,  §  26;  Schulze,  Logil:  §  30;  Esther, 

laVctcxercitumparvumsedvaldeunanimem,  Logik,  ?  34  et  seg. ;   Eugenics,  p.  194  et  .<■«/. 

•.liter    cxercitum    magnum,    sed    diversarum  [Ao7(k:^,    c.  iv.,   Hepl  'Ewoiwi'   Bct&OJ/y    t« 

Eactionum.    1  lie  enim  magis  colligit  intensive,  KolUxiiTovs Ed.] 


102  LOGIC.  Lect.  vm 

What  follows  is  in  further  illustration  of  the  paragraph.     Notions 

or  concepts  stand  in  a  necessary  relation  to  cer- 

Speciai  iiinstration       ^^-^  objects,  thought  through  them ;  for  without 

of     Paragraph.  —  A  /.  '  f  ,.       f  i  -i 

concept  is  a  quantity.        Something   to  thmk   of,   there   could   exist   no 
thought,  no  notion,  no  concept.     But  in  so  far 
as  we  think  an  object  through  a  concept,  we  think  it  as  part  of,  or 
as  contained  under,  that  concept :  and  in  so  far  as  we  think  a  con- 
cept of  its  object  or  objects,  we  think  it  as  a  unity  containing, 
actually  or  potentially,  in  it  a  plurality  of  attributions.     Out  of  the 
relation  of  a  concept  to  its  object  it  necessarily  results,  that  a  con- 
cept is  a  quantum  or  quantity ;  for  that  which  contains  one  or  more 
units  by  which  it  may  be  measured,  is  a  quantity. 
But  the  quantity  of  a  concept  is  of  two,  and  two  opposite,  kinds. 
Considered  internally,  that  is,  as  a  unity  whicl^ 
This  quantity  of  two  ^^^  generally  does,  contain  in  it  a  plurality 

Jcinds:  —  !.  Intensive.  „  .,  ' 

of  parts  or  component  attributes,  a  concept  has 
a  certain  quantity,  which  may  be  called  its  internal  or  intensive 
quantity.  This  is  generally  called  its  comprehensiony  sometimes  its 
depths  PaJ^o^y  and  its  quantitas  complexus.  Here,  the  parts,  that  is, 
the  several  attributes  or  characters,  which  go  to  constitute  the  total 
concept,  are  said  to  be  contained  in  it.  For  example,  the  concept 
man  is  composed  of  two  constituent  parts  or  attributes,  that  is,  of 
two  partial  concepts,  —  rational  and  animal;  for  the  characters 
rational  and  animal  are  only  an  analytical  expression  of  the  syn- 
thetic unity  of  the  concept  man.  But  each  of  these  partial  con- 
cepts, which  together  make  up  the  comprehension  of  the  total 
concept  mariy  are  themselves  wholes,  made  up  in  like  manner  of 
parts.  To  take  only  the  concept  animal ;  —  this  comprehends  in 
it,  as  parts,  living  and  sensitive  and  organized^  for  a  living  and  sen- 
tient organism  may  be  considered  as  an  analytical  development  of 
the  constituents  of  the  synthetic  unity  animal.  But  each  of  these, 
ag.iin,  is  a  concept,,  comprehending  and  made  up  of  parts;  and  these 
parts,  again,  are  relative  wholes,  divisible  into  other  constituent 
concepts;  nor  need  we  stop  in  our.  analysis  till  we  reach  attributes 
which,  as  simple,  stand  as  a  primary  or  ultimate  element,  into  which 
the  series  can  be  resolved.  Now,  you  will  observe,  that  as  the 
parts  of  the  parts  are  parts  of  the  whole,  the  concept  man^  as  imme- 
diately comprehending  the  concepts  rational  and  animal,  medi- 
ately comprehends  their  parts,  and  the  parts  of  their  parts,  to  tho 
end  of  the  evolution.  Thus,  we  can  s.ny,  not  only  that  man  is  an 
animal,  but  that  he  is  a  living  being,  a  sentient  being,  etc.  The' 
logical  axiom,  Nota  notes  est  nota  ret  ipaittSy  or,  as  otherwise  ex- 


I 


Lect.  Vm.  LOGIC.  103 

pressed,  Prcedicatum  prcedicati  est  prcedicatum  suhjecti,^  —  is  only 
a  special  enunciation  of  the  general  principle,  that  the  part  of  a  part 
is  a  part  of  the  whole.  You  will,  hereafter,  see  that  the  Compre- 
hension of  notions  affords  one  of  the  two  great  branches  of  reason- 
ing, which,  though  marvellously  overlooked  by  logicians,  is  at  least 
of  equal  importance  with  that  which  they  have  exclusively  devel- 
oped, and  which  is  founded  on  the  other  kind  of  quantity  exhibited 
by  concepts,  and  to  which  I  now  proceed. 

But  a  concept  may  also  be  considered  externally,  that  is,  as  a  unity 

which  contains  under  it  a  plurality  of  classifyins: 
2    Extensive.  .  . 

attributes  or  subordinate  concepts,  and,  in  this 

respect,  it  has  another  quantity  which  may  be  called  its  external  or  ea- 
tensive  quantity.  This  is  commonly  called  its  extension-  sometimes 
its  sphere  or  domain,  sphcera,  regio,  quantitas  ambitus/  and,  by  the 
Greek  logicians,  its  breadth  or  latitude,  ttAcitos.^  Here  the  parts  which 
the  total  concept  contains,  are  said  to  be  contained  under  it,  because, 
holding  the  relation  to  it  of  the  particular  to  the  general,  they  are  sub- 
ordinated or  ranged  under  it.  For  example,  the  concepts  man,  horse, 
dog,  etc.,  are  contained  under  the  more  general  concept  animal, — 
the  concepts  triangle,  square,  circle,  rhombus,  rhomboid,  etc.,  are  con- 
tained under  the  more  general  cowce^t  figure;  inasmuch  as  the  sub- 
ordinate concepts  can  each  or  any  be  thought  through  the  higher  or 
more  general.  But  as  each  of  these  subordinate  concepts  is  itself  a 
whole  or  general,  which  contains  under  it  parts  or  more  particular 
concepts,  it  follows,  again,  on  the  axiom  or  self-evident  truth  that  a 
part  of  a  part  is  a  part  of  the  whole,  —  an  axiom  which,  you  will  here- 
after see,  constitutes  the  one  principle  of  all  Deductive  reasoning,  — 
it  follows,  on  this  axiom,  that  whatever  is  contained  under  the  par- 
tial or  more  particular  concept,  is  contained  under  the  total  or  more 
general  concept.  Thus,  for  example,  triangle  is  contained  under 
figure;  all,  therefore,  that  is  contained  under  triangle,  as  rectangled 
triangle,  equilateral  triangle,  etc.,  will,  likewise,  be  contained  under 
figure,  by  which  we  may,  accordingly,  think  and  describe  them. 

Such,  in  general,  is  what  is  meant  by  the  two  quantities  of  con- 
cepts—  their  Comprehension  and  Extension. 

But  these  quantities  are  not  only  different,  they 

Intensive  and  Ex-      Qxe  opposed,  and  SO  opposed,  that  though  each 

tensive  quantities  are  .■■  .,  ^,  ,. ,.  „  ., 

opposed  toeach other.       supposes  the  Other  as  the  condition  of  Its  own 
existence,  still,  however,  within  the  limits  of  con- 
junct, of  correlative  existence,  they  stand  in  an  inverse  ratio  to  each 

1  A  traiiRlotion  of  Aristotle's  first  nntipre-      xarriyopov/xevov  Keyerat  irdvra  Kal  Karh  rod 
dicameiital  rule,  Ca/eg-.,  iii.  l."Off«  (cara  toC      vTroKeiixivo'j    f>ri^-fi(reTai.  —  Ed. 
'■i  Seu  above,  p  100,  r.ote  2,  p.  101,  no'o  1.—  V.v. 


Wi  LOGIC.  Lkct.  vnL 

other,  — the  maximum  of  the  one  being  the  minimum  of  the  other. 
On  this  I  give  you  the  following  paragraph  : 

%  XXV.  A  notion  is  intensively  great  in  proportion  to  the 

greater   number,  and  intensively  small   in 

Par.  XXV.  Law  reg-       proportiou  to  the  Smaller  number,  of  deter- 

nlating  the  mutual  re-  ..  ^^-i,  •!.•.         t 

lationB  of  Extension  mmatious  OF  attributes  contained  m  it.  Is 
and  Comprehension  the  Comprehension  of  a  concept  a  mini- 
mum, that  is,  is  the  concept  one  in  which  a 
plurality  of  attributes  can  no  longer  be  distinguished,  it  is 
called  simi^le  ;  whereas,  inasmuch  as  its  attributes  still  admit  of 
discrimination,  it  is  called  complex  or  compound} 

A  notion  is  extensively  great  in  proportion  to  the  greater  num- 
ber, and  extensively  small  in  proportiou  to  the  smaller  number, 
of  determinations  or  attributes  it  contains  under  it.  When 
the  Extension  of  a  concept  becomes  a  minimum,  that  is,  when  it 
contains  no  other  notions  under  it,  it  is  called  an  individual.^ 

These  two  quantities  stand  always  in  an  inverse  ratio  to  each 
other :  For  the  greater  the  Comprehension  of  a  concept,  the  less 
is  its  Extension ;  and  the  greater  its  Extension,  the  less  its  Com- 
prehension.^ 

To  illustrate  this :    When  I  take  out  of  a  concept,  that  is,  ab- 
stract from  one  or  more  of  its  attributes,  I  dimin- 

lUustration.  •  i    •  i  •  m,  ,         />  i 

ish  Its  comprehension.  1  hus,  when  from  the  con- 
cept man,  equivalent  to  rational  animal,  I  abstract  from  the  attribute 
or  determination  rational,  I  lessen  its  internal  quantity.  But  by  this 
diminution  of  its  comprehension  I  give  it  a  wider  extension ;  for  what 
remains  is  the  concept  animal,  and  the  concept  animal  embraces 
under  it  a  far  greater  number  of  objects  than  the  concept  man. 

Before,  however,  proceeding  further  in  illustrating  the  foregoing 
paragraph,  it  may  be  proper  to  give  you  also  the  following : 

%  XXVI.     Of   the  logical  processes  by 
Par.  XXVI.  prooess-       which  thcsc  countcr  quantities  of  concepts 

«B  by  which  the  Com-  ,  ^  ,  ' 

prehension  and  Ex.       are  amplified,  —  the  one  which  amplifies  the 
tension   of   Notions       Comprehension     is    called    Detertnination, 

sre      amplified      and  *  .  n     t    >-. 

resolved.  and  somctimes  called  Concretion,  the  other 

which  amplifies  the  Extension  is  called  Ab- 
straction or  Generalization.   Dejinitian  and  Division  are  sever- 

1  Knig,  Logik^  \  28.  —Ed.  o&rck  ciSw*'  irtpioxf)  Tck  8J  cWr/  rHv  ytt-mr 

a  Krug,  iWd  ,  §  29.  -  Ed.  xXwi/efC"  raTj  o.Vei'aj  5ia*opa?j.     "f-ri  oCr, 

3  Krug,  Loffiyt,  f  27.  — Ed.;  [Schulze,  Loff'*,  ,,./,-                -                 *         v 

♦  88.    Cf.  Porphyry,  Isagog,,  c.  viii.  H  9, 10.]  ^^  '^"^  T*'^"'    '^  y*y^'->r<TOV'  offrc  t* 


Lect.  Vm.  LOGIC.  105 

ally  the  resolntion  of  the  Compi*ehension  and  of  the  Extension 
of  notions,  into  their  parts.  A  Simple  notion  cannot  be  defined ; 
an  Individual  notion  cannot  be  divided.^ 

The  reason  of  this  opposition  of  the  two  quantities  is  manifest  in 

a  moment,  from  the  consideration  of  their  sev- 

iiiustration  o    t  e       ^^^  natures.   The  comprehension  of  a  concept  is 

two    foregoing    para-  .  '■  ^ 

rapijg.  nothmg  more  than  a  sum  or  complement  of  the 

distinguishing   characters,   attributes,  of  which 
the  concept  is  made  np ;  and  the  extension  of  a  concept  is  nothing 
more  than  the  sum  or  complement  of  the  objects 
Comprehension  and       themselves,  whose   resembling  characters  were 
Extension    are    op-       abstracted  to  Constitute  the  concept.     Now,  it 
ratio  to  each  other.  ^®  evident,  that  the  more  distinctive  characters 

the  concept  contains,  the  more  minutely  it  will 
distinguish  and  determine,  and  that  if  it  contain  a  plenum  of  dis- 
tinctive characters,  it  must  contain  the  distinctive  —  the  deter- 
mining—  characters  of  some  individual  object.  How  do  the  two 
quantities  now  stand  ?  In  regard  to  the  comprehension  or  depth,  it 
is  evident,  that  it  is  here  at  its  maximum,  the  concept  being  a  com- 
plement of  the  whole  attributes  of  an  individual  object,  which,  by 
these  attributes,  it  thinks  and  discriminates  from  every  other.  On 
the  contrary,  the  extension  or  breadth  of  the  concept  is  here  at  its 
minimum ;  for,  as  the  extension  is  great  in  proportion  to  the  num- 
ber of  objects  to  which  the  concept  can  be  applied,  and  as  the  object 
is  here  only  an  individual  one,  it  is  evident  that  it  could  not  be  less, 
without  ceasing  to  be  at  all.  Again,  to  reverse  the  process :  throw- 
ing out  of  the  comprehension  of  the  concept,  that  is,  abstracting 
from  those  attributes,  which  belonging  exclusively  to,  exclusively  dis- 
tinguish, the  individual, —  we  at  once  diminish  the  comprehension, 
by  reducing  the  sum  of  its  attributes,  and  amplify  the  extension  of 
the  concept,  by  bringing  within  its  sphere  all  the  objects,  which  the 
characteristics,  now  thrown  out  of  the  comprehension,  had  pre- 
viously excluded  from  the  extension.  Continuing  the  process,  by 
abstraction  we  throw  out  of  the  sum  of  qualities  constituting  the 
comprehension,  other  discriminating  attributes,  and  forthAvith  the 
extension  is  pi'oportionally  amplified,  by  the  entrance  into  its  sphere 
of  all  those  objects  which  had  previously  been  debarred  by  the 
determining  characteristics  last  discarded.  Thus  proceeding,  and 
at   each  step    ejecting  from   the  comprehension  those   characters 

1  ISynonyms  of  Abstraction:  — 1,  Analysis  — 1,  Analysis  (of  Extension);  2, Synthesis;  3, 

(of  Comprehension);  2,  Syntliesis;  3,  Gener-  Specification;   4,  Kestrictionj   5,  Individua- 

ification;  4,  Induction;  5,  Ampliflcation.  tion.] 

Synonyms  of  Determination  or  Concretion : 

u 


106  LOGIC.  Lkct.  vni. 

which  are  found  the  proximate  impediments  to  the  amplification  of 
the  extension  of  the  concept,  we  at  each  step  diminish  the  former 
quantity  precisely  as  we  increase  the  latter;  till,  at  last,  we  arrive 
at  that  concept  which  is  the  necessary  constituent  of  every  other,  — 
at  that  concept  which  all  comprehension  and  all  extension  must 
equally  contain,  but  in  which  comprehension  is  at  its  minimum, 
extension  at  its  maximum,  —  I  mean  the  concept  of  Being  or  Exist- 
ence} 

We  have  thus  seen,  that  the  maximum  of  comprehension  and 
the  minimum  of  extension  are  found  in  the  con- 
Definition  and  Di-      ^g^  Qf  ^^  individual,  —  that  the  maximum  of 

vision,  —  are  the  pro-  '■         ,  t      ,  •    •  «  i  • 

cesses  by  which  Com-  extension  and  the  minimum  of  comprehension 
prehension  and  Ex-       are  fouud  in  the  concept  of  the  absolutely  sim- 

tension  of  Concepts  p]g^  ^^^  Jg^  J^  ^j^g  COllCept  of  existence.  NoW, 
are  resolved.  ,  .  ,         ^         .  ... 

comprehension  and  extension,  as  quantities,  are 
wholes ;  for  wholes  are  only  the  complement  of  all  their  parts,  and 
as  wholes  are  only  by  us  clearly  comprehended  as  we  distinctly 
comprehend  their  parts,  it  follows :  —  1°,  That  comprehension  and 
extension  may  each  be  analyzed  into  its  parts ;  and,  2",  That  this 
analysis  will  afford  the  mean  by  which  each  of  these  quantities  can 
be  clearly  and  distinctly  understood.  But  as  the  two  quantities  are 
of  an  opposite  nature,  it  is  manifest,  that  the  two  processes  of  analy- 
sis will,  likewise,  be  opposed.  The  analysis  of  the  intensive  or 
comprehensive  quantity  of  concepts,  that  is,  their  depth,  is  accom- 
plished by  Definition  ;  that  of  their  extensive  quantity,  or  breadth, 
by  division.  On  Definition  and  Division  I  at  present  touch,  not  to 
consider  them  in  themselves  or  on  their  own  account,  that  is,  as  the 
methods  of  clear  and  of  distinct  thinking,  for  this  will  form  the  mat- 
ter of  a  special  discussion  in  the  Second  Part  of  Logic  or  Method- 
ology, but  simply  in  so  far  as  it  is  requisite  to  speak  of  them  in 
illustration  of  the  general  nature  of  our  concepts. 

The  expository  or -explanatory  analysis  of  a  concept,  considered 

as  an  intensive  whole  or  quantum,  if  properly 
Definition  Illustrated.  „  ,.,  ,.  ,.         .  rrj 

eftected,  is  done  by  its  resolution  into  two  con- 
cepts of  which  it  is  proximately  compounded,  that  is,  into  the  higher 
concept  under  which  it  immediately  stands,  and  into  the  concept 
which  affords  the  character  by  which  it  is  distinguished  from 
the  other  coordinate  concepts  under  that  higher  concept.  This  is 
its  definition  ;  that  is,  in  logical  language,  its  exposition  by  an 
analysis  into  its  Genus  and  Differential  Quality;  —  the  genus  b6ing 
the  higher  concept,  under  which  it  stands ;  the  differential  qujility 

I  ThI.*,  like  other  logical  relations,  may  be  typified  by  a  sensible  figure.    (See  below,  p.  IW. 
—  Ed.] 


Lect.  VUL  LOGIC.  107 

the  lower  concept,  by  which  it  is  distinguished  from  the  other  con- 
cepts subordinate  to  the  genus,  and  on  a  level  or  coordinate  with 
itself,  and  which,  in  logical  language,  are  called  /Species.  For  ex- 
ample :  if  we  attempt  an  expository  or  explanatory  analysis  of  the 
concept  man^  considered  an  an  intensive  quantity  or  complexus  of 
attributes,  we  analyze  it  into  animal^  this  being  the  higher  concept 
or  genus,  under  which  it  stands ;  and  into  rational,  the  attribute  of 
reason  being  the  characteristic  or  differential  quality  by  which  man 
is  distinguished  from  the  other  concepts  or  species  which  stand 
coordinated  with  itself  under  the  genus  animal,  —  that  is,  irrational 
animal  or  brute. 

Here  you  will  observe,  that  though  the  analysis  be  of  the  compre- 
hension, yet  it  is  regulated  by  the  extension  ;  the  extension  regulat- 
ing the  order  in  which  the  comprehension  is  resolved  into  its  parts. 

The  expository  analysis  of  a  concept,  an  extensive  whole  or 
quantum,  is  directly  opposed  to  the  preceding, 
to  which  it  is  correlative.  It  takes  the  higher 
concept,  and,  if  conducted  aright,  resolves  it  into  its  proximately 
lower  concepts,  by  adding  attributes  which  afford  their  distinguish- 
ing characters  or  differences.  This  is  division :  —  Thus,  for  exam- 
ple, taking  the  highest  concept,  that  of  ens  or  existence,  by  adding 
to  it  the  differential  concepts  per  se  or  substantial,  and  no7i  per  se 
or  accidental,  we  have  substantial  existence  or  existence  per  se, 
equivalent  to  substance,  and  accidental  existence  or  existence  nan  per 
se,  equivalent  to  accident.  We  may  then  divide  substance  by  sim- 
ple and  not-simple,  equivalent  to  compound,  and  again  simple  by 
material  and  non-material,  equivalent  to  immaterial,  equivalent  to 
spiritual;  —  and  matter  or  material  substance  by  organized  and  not- 
organized,  equivalent  to  brute  matter.  Organized  matter  we  may 
divide  by  sentient  or  animal,  and  non-sentient  or  vegetable.  Ani- 
mal  we  may  divide  by  rational  and  irrational,  and  soon,  till  we 
reach  a  concept  which,  as  that  of  an  individual  object,  is,  in  fact, 
not  a  general  concept,  but  only  in  propriety  a  singular  representa- 
tion. 

Thus,  it  is  manifest,  that,  as  Definition  is  the  analysis  of  a  complex 
concept  into  its  component  parts  or  attributes, 

The  Indefinable  and         •/.  ^  v        •        i       x-l    ^  •      -^  '^  a.   •      •      -^ 

J  ..  . ...  II  a  concept  be  simple,  that  is,  if  it  contain  m  it 

only  a  single  attribute,  it  must  be  indefinable ; 
and  again,  that  as  Division  is  the  analyses  of  a  higher  or  more  gen- 
eral concept  into  others  lower  and  less  general,  if  a  concept.be  an 
individual,  that  is,  only  a  bundle  of  individual  qualities,  it  is  indi- 
visible, is,  in  fact,  not  a  proper  or  abstract  concept  at  all,  but  only  a 
concrete  representation  of  Imagination. 


108 


LaGIC. 


Lbot.  YSL 


Diagram  represent- 
ing Extension  and 
Comprehension  of 
Concepts. 


B. 

D. 

'vi. 

1. 

V. 

2. 

iv. 

3. 

iii. 

4. 

iL 

5. 

i. 

6. 

The  following  Diagram^  represents  Breadth 
and  Depth,  with  the  relations  of  Affirmation  and 
legation  to  these  quantities. 


Schemes  of  the  Two  QuAifTiTiES. 
Line  of  BreadtTu 


Aff.  Neg. 


A 

A 

A 

A 

A 

A    \A 

< 

E 

E 

E 

E 

E 

\E 

I' 

I 

I 

I 

I 

\I 

^ 

V 

O 

O 

O 

|0: 

U 

U 

1^^ 

s 

Y 

1^ 

1  '    " 
zlz   z 

... 

k 


Ground  of  Reality. 


Explanation. 


In  the  preceding  Table  there  are  represented :  —  by  A,  A,  etc., 
the  highest  genus  or  widest  attribute ;  by  Y,  the 
lowest  species  or  narrowest  attribute;  whilst 
the  other  four  horizontal  series  of  vowels  typify  the  subaltern  gen- 
era and  species,  or  the  intermediate  attributes.  The  vowels  are 
reserved  exclusively  for  classes,  or  common  qualities;  whereas  the 
consonants  z,  /,  z"  (and  which,  to  render  the  contrast  more  obtru- 
sive, are  not  capitals)  represent  individuals,  or  singulars.  Every 
higher  class  or  more  common  attribute  is  supposed  (in  conformity 
with  logical  precision)  to  be  dichotomized,  —  to  be  divided  into  two 
by  a  lower  class  or  attribute,  and  its  contradictory  or  negative. 
This  contradictory,  of  which  only  the  commencement  appears,  is 
marked  by  an  italic  vowel,  preceded  by  a  perpendicular  line  (  |  ) 
signifying  not  or  now,  and  analogous  to  the  minus  ( — )  of  the  math- 
ematicians. This  being  understood,  the  table  at  once  exhibits  the 
reed  identity  and  rational  differences  of  Breadth  and  Depth,  which, 
though  denominated  quantities,  are,  in  reality,  one  and  the  same 
quantity,  viewed  in  counter  relations  and  from  opposite  ends.  Noth- 
ing is  the  one,  which  is  not  pro  tanto,  the  other. 

In  Sreadtk :  the  supreme  genus  (A,  A,  etc.)  is,  as  it  appears,  abso- 


1  The  Diagram  and  relative  text  to  end  of  Leotore  ire  extracted  by  the  Editors  ttom  the 
Author's  Ditcussionaf  p.  699—701.  —  Ed. 


Lect.  Vm.  LOGIC«  109 

lately  the  greatest  whole ;  an  individual  (z)  absolutely  the  smallest 
part ;  whereas  the  intermediate  classes  are  each  of  them  a  relative 
part  or  species,  by  reference  to  the  class  and  classes  above  it;  a 
relative  whole  or  genus,  by  reference  to  the  class  or  classes  below 
it.  In  Depth :  the  individual  is  absolutely  the  greatest  whole,  the 
highest  genus  is  absolutely  the  smallest  part;  whilst  every  relatively 
lower  class  or  species,  is  relatively  a  greater  whole  than  the  class, 
classes,  or  genera,  above  it.  The  two  quantities  are  thus,  as  the 
diagram  represents,  precisely  the  inverse  of  each  other.  The  greater 
the  Breadth,  the  less  the  Depth  ;  the  greater  the  Depth,  the  less  the 
Breadth ;  and  each,  within  itself,  affording  the  correlative  differences 
of  whole  and  part,  each,  therefore,  in  opposite  respects,  contains  and 
is  contained.  But,  for  distinction's  sake,  it  is  here  convenient  to 
employ  a  difference,  not  altogether  arbitrary,  of  expression.  We 
should  say:  —  "containing  and  contained  under^  for  Breadth;  — 
"containing  and  contained  iVi,"  for  Depth.  This  distinction,  which 
has  been  taken  by  some  modern  logicians,  though  unknown  to  many 
of  them,  was  not  observed  by  Aristotle.  We  find  him  (to  say  noth- 
ing of  other  ancient  logicians)  using  the  expression  Iv  oAw  dvai  or 
vwdpxeiv,  for  either  whole.  Though  different  in  the  order  of  thought, 
{ratione),  the  two  quantities  are  identical  in  the  nature  of  things, 
{re).  Each  supposes  the  other ;  and  Breadth  is  not  more  to  be  dis- 
tinguished from  Depth,  than  the  relations  of  the  sides,  from  the  rela- 
tions of  the  angles,  of  a  triangle.  In  effect  it  is  precisely  the  same 
reasoning,  whether  we  argue  in  Depth,  —  "z'  is  {i.e.  as  subject, 
contains  in  it  the  inherent  attribute)  some  Y ;  all  Y  is  some  U ;  all 
U  is  some  O ;  all  O  is  some  I ;  all  I  is  some  E ;  all  E  is  some  A ;  — 
therefore,  z'  is  some  A : "  or  whether  we  argue  in  Breadth,  —  "  Some 
A  is  {i.  e.  as  class,  contains  under  it  the  subject  part)  all  E ;  some 
E  is  all  I ;  some  I  is  all  O ;  some  O  is  all  U  ;  some  U  is  all  Y ;  some 
Y  is  z' ;  therefore,  some  A  is  z'."  The  two  reasonings,  internally 
identical,  are  externally  the  converse  of  each  other;  the  premise 
and  term,  which  in  Breadth  is  major,  in  Depth  is  minor.  In  syllo- 
gisms also,  where  the  contrast  of  the  two  quantities  is  abolished, 
there,  with  difference  of  figure,  the  differences  of  major  and  minor 
premise  and  term  fall  likewise.  In  truth,  however,  common  lan- 
guage in  its  enouncement  of  propositions,  is  hei-e  perhaps  more  cor- 
rect and  philosophical  than  the  technical  language  of  logic  itself. 
For  as  it  is  only  an  equation  —  only  an  affirmation  of  identity  or 
its  negation^  which  is,  in  either  quantity,  proposed  ;  therefore  the 
substantive  verb  {is,  is  not),  used  in  both  cases,  speaks  more  accu- 
rately, than  the  expression,  contained  (or  not  contained),  in  of  the 
one,  contained  (or  not  contained)^  under  of  the  other.     In  fact,  the 


no  LOGIC.  Lkct.  VIIL 

two  qtcantities  and  the  two  quantifications  have  by  logicians  been 
neglected  together. 

This  Table  (the  principle  of  which  becomes  more  palpably  dem- 
onstrative when  the  parts  of  the  table  are  turaed  into  the  parts  of  a 
circular  machine  ^ )  exhibits  all  the  mutual  relations  of  the  counter 
quantities.  —  1°,  It  represents  the  classes,  as  a  series  of  resemblances 
thought  as  one  (by  a  repetition  of  the  same  letter  in  the  same 
series),  but  as  really  distinct  (by  separating  lines).  Thus,  A  is  only 
A,  not  A,  A,  A,  etc ;  some  Animal  is  not  some  Animal ;  one  class 
of  Animals  is  not  all,  every,  or  any  other;  this  Animal  is  not  that; 
Socrates  is  not  Plato  ;  z  is  not  z'.  On  the  other  hand,  E  is  E  A; 
and  YisYUOIEA;  every  lower  and  higher  letter  in  the  series 
coalescing  uninterruptedly  into  a  series  of  reciprocal  subjects  and 
predicates,  as  shown  by  the  absence  of  all  discriminating  lines. 
Thus  Socrates  (z')  is  Athenian  (Y),  Greek  (U),  European  (O),  Man 
(I),  Mammal  (E),  Animal  (A).  Of  course  the  series  must  be  in 
grammatical  and  logical  harmony.  We  must  not  collate  notions 
abstract  and  notions  concrete.  —  2°,  The  Table  shows  the  inverse 
correlation  of  the  two  quantities  in  respect  of  amount.  For  exam- 
ple :  A  (t,  e.  A,  A,  etc.),  the  highest  genus  represented  as  having  six 
times  the  Breadth  of  Y ;  whilst  Y  (t.  e.  Y — A),  the  lowest  species, 
has  six  times  the  Depth  of  A. —  3",  The  table  manifests  all  the 
classes,  as  in  themselves  unreal,  subjective,  ideal ;  for  these  are 
merely  fictions  or  artifices  of  the  mind,  for  the  convenience  of  think- 
ing. Univereals  only  exist  in  nature,  as  they  cease  to  be  universal 
in  thought;  that  is,  they  are  reduced  from  general  and  abstract 
attributes  to  individual  and  concrete  qualities.  A — ^Y  are  only  truly 
objective  as  distributed  through  z,  z',  z",  etc. ;  and  in  that  case  they 
are  not  universals.  As  Boethius  expresses  it :  "  Omne  quod  est,  eo 
quod  est,  singulare  est."  —  4°,  The  opposition  of  class  to  class, 
through  contradictory  attributes,  is  distinguished  by  lines  different 
from  those  marking  the  separation  of  one  part  of  the  same  class 
from  another.  Thus,  Animal,  or  Sentiently-organized  (A),  is  con- 
trasted with  Not-animal,  or  Not-sentiently-organized  (  |  A)^  by  lines 
thicker  than  those  which  merely  discriminate  one  animal  (A)  from 
another  (A).' 

1  A  machine  of  this  kind  vras  constrncted         t  See  Airther  in  Diuusnoiu,  p.  701  «t  »tq.— 
by  the  Author,  and  used  in  the  clasR-room  to     £i>. 
illustrate  the  doctrine  of  the  text.  — Ed. 


LECTUKE    IX. 

STOIOHEIOLOOY. 

SECTION  II.  — OF  THE    PRODUCTS    OF    THOUGHT. 

I.— ENNOEMATIC. 

B.    OF  CONCEPTS    IN    SPECIAL.  — II.   THEIR    SUBJECTIVE  RELA- 
TION—QUALITY. 

Having  concluded  the  consideration  of  the  relation  of  concepts 

.     to  their  objects,  —  the  relation  in  which  their 

Relation  of  Concepts       Quantity  is  given,  —  I  now  proceed  to  consider 

to  their  subject.  ;    •  i      •  \     •  •    •  i  •  , 

their  relation  to  their  conceiving  subject  —  the 
relation  in  which  is  given  their  Quality.  This  consideration  of  the 
quality  of  concepts  does  not,  in  my  opinion,  belong  to  the  Doctrine 
of  Elements,  and  ought,  in  scientific  rigor,  to  be  adjourned  alto- 
gether to  the  Methodology,  as  a  virtue  or  perfection  of  thought. 
As  logicians,  however,  have  generally  treated  of  it  likewise  undei 
the  former  doctrine,  I  shall  do  so  too,  and  commence  with  the  fol- 
lowing paragraph. 

IT  XXVII.     A  concept  or  notion  is  the  unity  in  conscious- 
ness of  a  certain  plurality  of  attributes,  and 

Par.    XXVU.     The  ..  .i  .i  /> 

Quality  Of  Concept,  1*,  conscqucutly,  supposcs  the  powcr  of 
consists  in  its  logical  thinking  thcsc,  both  separately  and  to- 
perfeotion  or  imper-       gethcr.     But  as  there  are  many  gradations 

feotion.  o  ,  .  -^   o 

in  the  consciousness  with  which  the  charac- 
ters of  a  concept  can  be  thought  severally  and  in  conjunction, 
there  will  consequently  be  many  gradations  in  the  actual  Per- 
fection or  Imperfection  of  a  notion.  It  is  this  perfection  or 
imperfection  which  constitutes  the  logical  Quality  of  a  con- 
cept.^ 

It  is  thus  the  greater  or  smaller  degree  of  consciousness  which 
accompanies  the  concept  and  its  object,  that  determines  its  quality, 

1  Krug,  Logik,  i  30.    C£.  Esser,  Logik.  j  46  «t  seq,  —  Ed.  ^ 


112  LOGIC.  Lect.IX. 

and  according  to  which  it  is  called  logically  perfect  or  logically 
imperfect.  Now,  there  may  be  distinguished  two  degrees  of  this 
logical  perfection,  the  nature  of  which  is  summarily  expressed  in  the 
following  paragraph. 

IF  XXVIII.     There  are  two  degrees  of 

Par.  XXVIII.    The       tJje  logical  perfection   of  concepts,  —  viz., 

ioL°oai  Perfection  and      their  Cleamess  Qxxdi  thciY  Distinctness,  imdi^ 

Imperfection  of  Con-       conscqucntly,  two  oppositc  dcgrccs  of  their 

oepts,  —  their     Clear-  , .  .  o      .•  •  .  i      • 

ness    and   Distinct-       correspondmg    impcrfection,  —  viz.,   their 
neas,  and  their  Ob-        Obscurity  and  their  Indistinctness.     These 

Bcurity      and      India-  /.  ,.,.  ,•,  n      .•  j    • 

tinotness  ^^'^^  qualities  express  the  peiiection  and  im- 

perfection of  concepts  in  extremes.  But 
between  these  extremes  there  lie  an  indefinite  number  of  inter- 
mediate degrees. 

A  concept  is  said  to  be  clear  (clara),  when  the  degree  of 
consciousness  is  such  as  enables  us  to  distinguish  it  as  a  whole 
from  others ;  and  obscure  {obscura),  when  the  degree  of  con- 
sciousness is  insufficient  to  accomplish  this.  A  concept  is  said 
to  be  distinct  {distincta,  perspicua),  when  the  degree  of  con- 
sciousness is  such  as  enables  us  to  discriminate  from  each  other 
the  several  characters,  or  constituent  parts  of  which  the  con- 
cept is  the  sum ;  and  indistinct  or  confused  (indistincta,  con- 
fusa,  imperspicita),  when  the  amount  of  consciousness  requisite 
for  this  is  wanting.  Confused  (confusa),  may  be  employed  as 
the  genus  including  obscure  and  indistinct} 

The  expressions  clearness   and   obscurity,  and  distinctness  and 

indistinctness,  as  applied  to  concepts,  originally 

Original  application       denote    certain   modifications   of  vision ;    from 

of    the    expressions       ^.j^j^^^  ^|^_  ^^.^^^  analogically  extended  to  the 

clfarness,  obscurity,  etc.  ...  t      /?        ii 

iiiusfrated  by  refer-       Other    scnscs,   to    imagination,   and    finally    to 
encc  to  vision.  thought.    It  may,  therefore,  enable  us  the  better 

to  comprehend  their  secondary  application,  to 
consider  their  primitive.  To  Leibnitz"  we  owe  the  precise  distinc- 
tion of  concepts  into  clear  and  distinct,  and  from  him  I  borrow  the 
following  illustration.  In  darkness  —  the  complete  obscurity  of 
night  —  we  see  nothing, — there  is  no  perception,  —  no  discrimina- 


1  Compare  Kriig,  Logik,  31  (t  seq.—  ED.  Essais,!.  ii.  ch.  xxix.  The  illustration,  how- 
[niiflici',  Logique,  i  345  et  seq.  Kant,  Kr.  rf.  r.  ever,  does  not  occur  in  either  of  these  p»8- 
Vernini/i,  l\.  ii.Trans  Dial.,  art.  i.,  p.  414,3d  sages.    It  was  probably  borrowed  from  K  rug, 

ed.  1790.)  Logik,  i  81,  and  attributed  to  Leibnita  by  an 

2  Sol-  his  Mulilationex  dr.  Cognitione,  Vetilate  oversight. — Ed. 
tt  Litis  (  Ofxra,  ed.  Erdmann,  p.  79),  Nouveaux 


lkct.  IX.  LOGIC.  iia 

tion  of  objects.  As  the  light  dawns,  the  obscurity  diminishes,  the 
deep  and  uniform  sensation  of  darkness  is  modified,  —  we  are  con- 
scious of  a  change,  —  we  see  something,  but  are  still  unable  to 
distinguish  its  features,  —  we  know  not  what  it  is.  As  the  light 
increases,  the  outlines  of  wholes  begin  to  appear,  but  still  not  with 
a  distinctness  sufficient  to  allow  us  to  perceive  them  completely ; 
but  when  this  is  rendered  possible,  by  the  rising  intensity  of  the 
light,  we  are  then  said  to  see  clearly.  We  then  recognize  moun- 
tains, plains,  houses,  trees,  animals,  etc.,  that  is,  we  discriminate 
these  objects  as  wholes,  as  unities,  from  each  other.  But  their 
parts,  —  the  manifold  of  which  these  unities  are  the  sum,  —  their 
parts  still  lose  themselves  in  each  other,  they  are  still  but  indis- 
tinctly visible.  At  length,  when  the  daylight  has  fully  sprung,  we 
are  enabled  likewise  to  discriminate  their  parts ;  we  now  see  dis- 
tinctly what  lies  around  us.  But  still  we  see  as  yet  only  the  wholes 
which  lie  proximately  around  us,  and  of  these  only  the  parts  which 
possess  a  certain  size.  The  more  distant  wholes,  and  the  smaller 
parts  of  nearer  wholes,  are  still  seen  by  us  only  in  their  conjoint 
result,  only  as  they  concur  in  making  up  that  whole  which  is  for  us 
a  visible  minimum.  Thus  it  is,  that  in  the  distant  forest,  or  on  the 
distant  hill,  we  perceive  a  green  surface ;  but  we  see  not  the  several 
leaves,  which  in  the  one,  nor  the  several  blades  of  grass,  which  in 
the  other,  each  contributes  its  effect  to  produce  that  amount  of 
impression  which  our  consciousness  requires.  Thus  it  is,  that  all 
which  we  do  perceive  is  made  up  of  parts  which  we  do  not  perceive,, 
and  consciousness  is  itself  a  complement  of  impressions,  which  lie 
beyond  its  apprehension,^  Clearness  and  distinctness  are  thus  only 
relative.  For  between  the  extreme  of  obscurity  and  the  extreme 
of  distinctness,  there  are  in  vision  an  infinity  of  intermediate  de- 
grees. Now,  the  same  thing  occurs  in  thought.  For  we  may  either 
be  conscious  only  of  the  concept  in  general,  or  we  may  also  be  con- 
scious of  its  various  constituent  attributes,  or  both  the  concept  and 
its  parts  may  be  lost  in  themselves  to  consciousness,  and  only  recog- 
nized to  exist  by  effects  which  indirectly  evidence  their  existence. 
The  perfection  of  a  notion,  as  I  said,  is  contained  in  two  degrees 
or  in  two  virtues,  —  viz.,  in  its  clearness  and  in  its 
earness  an    o         distinctness !  and,  of  course,  the  opposite  vices  • 

tcnnty  as  in  concepts.  .     '  '  '  ^^ 

of  obscurity  and  indistinctness  afford  two  de- 
grees or  two   vices,  constituting  its  imperfection.     "A  concept  is 
said  to  be  clear^  when  the  degree  of  consciousness  by  which  it  is- 
accompanied  is  sufficient   to  discriminate    what  we   think  in  and 
through   it,  from  what  we  think  in  and  through  other  notions;. 

1  See  Lectures  on  Metaphysics,  p.  241  tt  uq.  —  Ed. 

15 


114  LOGIC.  Lect.  IX. 

whereas  if  the  degree  of  consciousness  be  so  remiss  that  this  Mid 
other  concepts  run  into  each  other,  in  that  case  the  notion  is  said  to 
be  obscure.  It  is  evident  that  clearness  and  obscurity  admit  of 
various  degrees ;  each  being  capable  of  almost  infinite  gradations, 
according  as  the  object  of  the  notion  is  discriminated  with  greater 
or  less  vivacity  or  precision  froni  the  objects  of  other  notions.  A 
concept  is  aJbsolutdy  clear,  when  its  object  is 
The  absolutely  clear      distinguished  from  all  Other  objccts ;  a  concept 

and     absolutely     ob-         •  i       .        7  i  1  .  ,  .  , 

pjjjij^  IS  <wsohitely  obscure,   when    its  object  can   be 

di.stinguished  from  no  other  object.  But  it  is 
only  the  absolutely  clear  and  the  absolutely  obscure  which  stand 
opposed  as  contradictory  extremes;  for  the  same  notion  can  at 
once  be  relatively  or  comparatively  clear,  and  relatively  or  com- 
paratively obscure.  Absolutely  obscure  notions,  that  is,  concepts 
whose  objects  can  be  distinguished  from  nothing  else,  exist  only  in 
theory  ;  —  an  absolutely  obscure  notion  being,  in  fact,  no  notion  at 
all.  For  it  is  of  the  very  essence  of  a  concept,  that  its  object 
should,  to  a  certain  degree  at  least,  be  comprehended  in  its  peculiar, 
consequently,  in  its  distinguishing,  characteristics.  But,  on  the 
oUier  haild,  of  notions  absolutely  clear,  that  is,  notions  whose 
objects  cannot  possibly  be  confounded  with  aught  else,  whether 
known  or  unknown,  —  of  such. notions  a  limited  intelligence  is  pos- 
sessed of  very  few,  and,  consequently,  om*  human  concepts  are, 
properly,  only  a  mixture  of  the  opposite  qualities ;  —  dear  or  obscure 
as  applied  to  them,  meaning  only  that  the  one  quality  or  the  other 
is  the  preponderant.  In  a  logical  relation,  the  illustration  of  notions 
consists  in  the  raising  them  from  a  preponderant  obscurity  to  a  pre- 
ponderant clearness  —  or  from,  a  lower  degree  to  a  higher."^  So 
much  for  the  quality  of  clearaess  or  obscurity  considered  in  itself 
me  Di«tinctressand  ^^^  ^  ^^^^^  concept  may  be  either  Distinct  or 

indutinctnessofCon-       Indistinct;   the  distinctness  and   indistinctness 
"***  of  concepts  are  therefore  to  be  considered  apart 

from' their  clearness  and  obscurity. 

But  before  entering  upon  the  nature  of  the  distinction  itselij  I 

may  observe  that  we  owe  the  disciiraination  of 

Historical  notice  of      Distinct  and  Indistinct  from  Clear  and  Obscure 

this  distinction.  .  t     -i     • 

Due  to  Leibnitz.  notions  to  the  acutcncss  of  the  great  Leibnitz. 

By  the  Cartesians  the  distinction  had  not  been 

taken  ;  though  the  authors  of  the  Port  lioyal  Logic  come  so  near, 

that  we  may  well  marvel  how  they  failed  explicitly  to  enounce  it.* 

1  Eeser,  pp.  91, 92,  [Log-i'i,  S  46.  —  Ed.]  Descartes  and  Leibnitz,  see  the  Appeudix  to 

2  Tart  I.  ch.  i.v. — For  a  comparison  of  this      Mr.   Baynes's  translation  of  the   Tort  Roytd 
(tatcment  of  the  distinction  with  those  of     Lo^'it,  p.  423  (second  edition). —Ed. 


Lect.  IX.  LOGIC.  116 

Though  Locke  published  his  Essay  Concerning  Human  Under- 
standing  some  five  years  subsequfent  to  the  paper 
in  which  Leibnitz  —  then  a  very  young  man  — 
had,  among  other  valuable  observations,  promulgated  this  distinc- 
tion, Locke  did  not  advance  beyond  the  limit  already  reached  by 
the  Cartesians;  indeed,  the  praises  that  are -so  frequently  lavished 
on  this  philosopher  for  his  doctrine  concerning  the  distinctions  of 
Ideas,  —  the  conditions  of  Definition,  etc.,  —  only  prove  that  his 
encomiasts  are  ignorant  of  what  had  been  done,  and,  in  many  re- 
spects, far  better  done,  by  Descartes  and  his  school ;  —  in  fact,  with 
regard  to  the  Cartesian  Philosophy  in  general,  it  must  be  confessed, 
that  Locke  has  many  en-ors  to  expiate,  arising  partly  from  oversight, 
and  partly  from  the  most  unaccountable  misapprehension  of  its  doc- 
trines. It  is  almost  needless  to  say,  that  those  who,  in  this  country, 
have  written  ourthis  subject,  posterior  to  Locke,  have  not  advanced 
a  step  beyond  him  ;  for  though  Leibnitz  be  often  mentioned,  and 
even  occasionally  quoted,  by  our  British  philosophers,  I  am  aware 
of  none  who  possessed  a  systematic  acquaintance  with  his  philoso- 
phy, and,  I  might  almost  say,  who  were  even  superficially  versed 
either  in  his  own  writings  or  in  those  of  any  of  the  illustrious  think- 
ers of  his  school.  ,  {xj , 
But  to  consider  the  distinction  in  itself  We  have  seen  that, a 
concept  is  clear,  wheft  we  are  able  to  recognize 

distinction    in 
itself. 


IS  inc  ion    n       it  as  different  froni  Other  concepts.    But  we  may 


discriminate  a  whole  from  other  wholes,  we  may 
discriminate  a  concept  from  other  concepts,  though  we  have  only  a 
confused  knowledge  of  the  parts  of  which  that  whole,  or  of  the 
characters  of  which  that  concept,  is  made  up.     This  may  be  illus- 
trated by  the  analogy  of  our  Perceptive  and 
Illustrated   by  the       Representative  Faculties.   We  are  all  acquainted 

analogy  of  Perception  .,  ,  -.,..,,  ,. 

and  Representation.  ^ith  many,,  say  a  thousand,  individuals ;  that  is, 
we  recognize  such  and  such  a  countenance  as 
the  countenance  of  John,  and  as  not  the  countenance  of  James, 
Thomas,  Richard,  or  any  of  the  other  999.  This  we  do  with  a  clear 
and  certain  knowledge.  But  the  countenances,  which  we  thus  dis- 
tinguish from  each  other,  are,  each  of  them,  a  complement  made  up 
of  a  great  number  of  separate  traits  of  featui-es ;  and  it  might,  at 
first  view,  be  supposed  that,  as  a  whole  is. only  the  sum  of  its  parts, 
a  clear  cognition  of  a  whole  countenance  can  only  be  realized 
through  a  distinct  knowledge  of  each  of  its  constituent  features. 
But  the  slightest  consideration  will  prove  that  this  is  not  the  case. 
For  how  few  of  us  are  able  to  say  of  any,  the  most  familiar  face, 
what  are  the  particulai-  traits  which  go  to  form  the  general  result ; 


116  LOGIC.  Lect.  IX. 

and  yet,  on  that  account,  we  hesitate  neither  in  regard  to  our  own 
knowledge  of  an  individual,  nor  in  regard  to  the  knowledge  pos- 
sessed by  others.    Suppose  a  witness  be  adduced 

The  judicial    deter-         .  ^     i?  •      a.-       ^  xi       •  i        • 

mination  betweeniife  .^^  »  ^^^^^  of  justice  to  prove  the  identity  Or  non- 
and  death  supposes  identity  of  a  certain  individual  with  the  perpe- 
the  difference  between       trator   of  a   certain    Crime,  the  commission  of 

a   clear   and    distinct  i_'t.'u-lji_  3  ^  ii.i 

which  he  had  chanced  to  see,  —  would  the  coun- 

knowledge.  ' 

sel  be  allowed  to  invalidate  the  credibility  of  the 
witness  by,  first  of  all,  requiring  him  to  specify  the  various  elements 
of  which  the  total  likeness  of  the  accused  was  compounded,  and 
then  by  showing  that,  as  the  witness  either  could  not  specify  the 
several  traits,  or  specified  what  did  not  agree  with  the  features  of 
the  accused,  he  was,  therefore,  incompetent  to  prove  the  identity  or 
non-identity  required  ?  This  would  not  be  allowed.  For  the  court 
would  hold  that  a  man  might  have  a  clear  perception  and  a  clear 
representation  of  a  face  and  figure,  of  which,  however,  he  had  not 
separately  considered,  and  could  not  separately  image  to  himself^ 
the  constituent  elements.  Thus,  even  the  judicial  determination  of 
life  and  death  supposes,  as  real,  the  difference  between  a  clear  and 
a  distinct  knowledge :  for  a  distinct  knowledge  lies  in  the  knowl- 
edge of  the  constituent  parts ;  while  a  clear  knowledge  is  only  of 
the  constituted  whole. 

Continuing  our  illustra'tions  from  the   human  countenance :  we 
all  have  a  clear  knowledge  of  any  face  which  we 

Further  illustration        j^^^g   ggg„^  ^^^^   f^^   ^f  ^^   ]^^^q   distinct   knowl- 
from  the  human  coun-  .  „    .  *  1        1  •   1  n       •^• 

j^jj^j^^g  edge  even  of  those  with  which  we  are  lamiliar ; 

but  the  painter,  who,  having  looked  upon  a 
countenance,  can  retire  and  reproduce  its  likeness  in  detail,  has 
necessarily  both  a  clear  and  a  distinct  knowledge  of  it.  Now,  what 
is  thus  the  case  with  perceptions  and  representations,  is  equally  the 
case  with  notions.  We  may  be  able  clearly  to  discriminate  one 
concept  from  another,  although  the  degree  of  consciousness  does 
not  enable  us  distinctly  to  discriminate  the  various  component  char- 
acters of  either  concept  from  each  other.  The  Clearness  and  the 
Distinctness  of  a  notion  are  thus  not  the  same ;  the  former  involves 
merely  the  power  of  distinguishing  the  total  objects  of  our  notions 
from  each  other;  the  latter  involves  the  power  of  distinguishing  the 
several  characters,  the  several  attributes,  of  which  that  object  is 
the  sum.  In  the  former  the  unity,  in  the  latter  the  multiplicity, 
of  the  notion  is  called  into  relief. 

The  distinctness  of  a  concept  supposes,  however,  the  Clearness ; 
and  may,  therefore,  be  regarded  as  a  higher  degree  of  the  same 
quality  or  perfection.     "To  the  distinctness  of  a  notion,  over  and 


LeCT.  IX.  LOGIC.  IIV 

above  its  general  clearness,  there  are  required  three  conditions,  — 

1°,  The  clear  apprehension  of  its  several  char- 

Speciaiconditionflof      acters  or  Component  parts;    2°,  The  clear  con- 

the  Distinctness  of  a      ^^^^  ^^  discrimination  of  these:  and,  3°,  The 

Concept,  and    of   its  .   .  , 

^  ,^^  clear  recognition  oi    the   nexus   by  which  the 

several  parts  are  bound  up  into  a  unity  or  whole. 

"  As  the  clearness,  so  the  distinctness,  of  a  notion  is  susceptible 
of  many  degrees.  A  concept  may  be  called  distinct^  when  it  in- 
volves the  amount  of  consciousness  i-equired  to  discriminate  fi'om 
each  other  its  principal  characters ;  but  it  is  so  much  the  more  dis- 
tinct, 1°,  In  proportion  to  the  greater  number  of  the  characters 
apprehended ;  2°,  In  proportion  to  the  greater  clearness  of  their 
discrimination ;  and,  3°,  In  proportion  to  the  precision  with  which 
the  mode  of  their  connection  is  recognized.  But  the  greater  dis- 
tinctness is  not  exclusively  or  even  principally  determined  by  the 
greater  number  of  the  clearly  apprehended  characters ;  it  depends 
still  raoi-e  on  their  superior  importance.  In  particular,  it  is  of  mo- 
ment whether  the  characters  be  positive  or  negative,  internal  or 
external,  permanent  or  transitory,  peculiar  or  common,  essential  or 
accidental,  original  or  derived.  From  the  mere  consideration  of  the 
differences  subsisting  between  attributes,  there  emerge  three  rules 
to  be  attended  to  in  bestowing  on  a  concept  its  requisite  distinct- 
ness. In  the  first  place,  we  should  endeavor  to  discover  the  posi- 
tive characters  of  the  object  conceived;  as  it  is  our  purpose  to 
know  what  the  object  is,  and  not  what  it  is  not.  When,  however, 
as  is  not  unfrequently  the  case,  it  is  not  at  once  easy  to  discover 
what  the  positive  attributes  are,  our  endeavor  should  be  first  di- 
rected to  the  detection  of  the  negative  ;  and  this  not  only  because 
it  is  always  an  advance  in  knowledge,  when  we  ascertain  what  an 
object  is  not,  but,  likewise,  because  the  discovery  of  the  negative 
characters  conducts  us  frequently  to  a  discovery  of  the  positive. 

^  In  the  second  place,  among  the  positive  qualities  we  should  seek 
out  the  intrinsic  and  permanent  before  the  extrinsic  and  transitory ; 
for  the  former  give  us  a  purer  and  more  determinate  knowledge  of 
an  object,  though  this  object  may  likewise,  at  the  same  time,  pre- 
sent many  external  relations  and  mutable  modifications.  Among 
the  permanent  attributes,  the  proper  or  peculiar  always  merit  a 
preference,  if  for  no  other  reason,  because  through  them,  and  not 
through  the  common  qualities,  can  the  proper  or  peculiar  nature  of 
ihc  object  become  known  to  us. 

"In  the  third  place,  among  the  permanent  characters  we  ought 
first  to  hunt  out  the  necessary  or  essential,  and  then  to  descend 
from  them  to  the  contingent  or  accidental;  and  this  is  not  only 


1-3  LOGIC.  Lect.  IX 

because  we  thus  give  order  and  connection  to  our  notions,  but, 
likewise,  because  the  contingent  characters  are  frequently  only  to 
be  comprehended  through  the  necessary."^ 

But  before  leaving  this  part  of  our  subject,  it  may  be  proper  to 
illustrate  the  distinction  of  Clear  and  Distinct 

The  distinction  of      notions  by  one  or  two  concrete  examples.     Of 

Clear  and  Distinct  no-  ,•■•  ■■  ,  i.^.^-.-^- 

ti  ns  illustrated  b  i"any  things  We  havo  clear  but  not  distinct  no- 
eoacrete  examples.  tions.     Thus,  we  have  a  dear,  but  not  a  distinct,' 

notion  of  colors,  sounds,  tastes,  smells,  etc.  For 
we  are  fully  able  to  distinguish  red  from  white,  to  distinguish  an 
acute  from  a  grave  note,  the  voice  of  a  friend  from  that  of  a  stran- 
ger, the  scent  of  roses  from  that  of  onions,  the  flavor  of  sugar  from 
that  of  vinegar;  but  by  what  plurality  of  separate  and  enunciable 
characters  is  this  discrimination  made?  It  is  because  we  are  unable- 
to  do  this,  that  we  cannot  describe  such  perceptions  and  represen- 
tations to  others. 

*'If  you  ask  of  me,"  says  St.  Augustine,  "what  is  Time,  I  knoW^ 
not;  if  you  do  not  ask  me,  I  know."^  What  does  this  mean? 
Simply  that  he  had  a  clear,  but  not  a  distinct,  notion  of  Time. 

Of  a  triangle  we  have  a  clear  notion,  when  we  distinguish  a  tri- 
angle from  other  figures,  without  specially  considering  the  charao^ 
ters  which  constitute  it  what  it  is.  But  when  we  think  it  as  a  por- 
tion of  space  bounded  by  three  lines,  as  a  figure  whose  three  angleR 
are  equal  to  two  right  angles,  etc.,  then  we  obtain  of  it  a  distinct 
concept. 

We  now  come  to  the  consideration  of  the  question,  —  How  doea 
the  Distinctness  of  a  concept  stand  aflfected  by 

How  the  Distinctness         .1,  ^•,.  /.  ^  n  i    •  f 

',■  -^        ,.    ».  ,  J       the  two  quantities  of  a  concept .''  —  and  in  ret- 

of  a  Concept  18  affected  ^  '■ 

by  the  two  quantities  erence  to  this  point  I  would,  in  the  first  place, 
of  a  Concept.  dictate  to  you  the  following  paragraph : 

%  XXIX.  As  a  concept  is  a  plurality  of  characters  bound  up 

into  unity,  and  as  that  plurality  is  contained 

Pap.  XXIX. Distinct.       partly  in  its  Intensive,  partly  under  its  Ex- 

ness.  Internal  and  £x-  ^  .       ■  ..^        .^      -rx*    .*       ^  •       •      1-1 

^^j^^i  tensive,  quantity,  its  Distinctness  is,  m  lik*' 

manner,  in  relation  to'  these  quantitie^^ 
partly  an  Internal  or  Intensive,  partly  an  external  or  Extensive' 
Distinctness.' 

In  explanation  of  this,  it  is  to  be  observed,  that,  as  the  distinct- 
ness of  a  concept  is  contained  in   the  clear   apprehension  of  the 

I  Kwer,  Loglk,  f  47,  p  93-95.  —  Ed.  »  Kmg,  Logik,  f  S(;  EsBer,  Logik,  J  «.  - 

»  Cdn/i««<»M,'xi.  c;  14.--El>.  Bb. 


Lbct.  IX  LOGIC.  119 

various  attributes  of  which  it  is  the  sum,  as  it  is  the  sum  of  these 
attributes  in   two   opposite  relations,  which  con- 

£xplicatioii.  .  .      „  . 

stitute,  m  lact,  two  opposite  quantities  or  wholes, 
and  as  these  wholes  are  severally  capable  of  illustration  by  analysis, 
it  follows,  that  each  of  these  analyses  will  contribute  its  peculiar 
share  to  the  general  distinctness  of  the  concept.  Thus,  if  the  dis- 
tinctness of  a  notion  bears  reference  to  that  plurality  which  consti- 
tutes its  comprehension,  in  other  words,  to  that  which  is  contained 
in  the  concept,  the  distinctness  is  denominated  an  internal  or  in- 
tensive distinctness,  or  distinctness  of  comprehensio7i.  On  the  other 
hand,  if  the  distinctness  refers  to  that  plurality  which  constitutes 
the  extension  of  the  notion,  in  other  words,  to  what  is  contained 
under  it,  in  that  case,  the  distinctness  is  called  an  external  or  exten- 
sive distinctness,  a  distinctness  of  extension.  It  is  only  when  a 
notion  combines  in  it  both  of  these  species  of  distinctness,  it  is  only 
when  its  parts  have  been  analyzed  in  reference  to  the  two  quan- 
tities, that  it  reaches  the  highest  degree  of  distinctness  and  of  per- 
fection. 

The  Internal  Distinctness  of  a  notion  is  accomplished  by  Exposi- 
tion or  Definition,  that  is,  by  the  enumeration 
Definition  and  Divi-       ^^  ^^^q  characters  or  partial  notions  contained  in 

sion  . 

it ;  the  External  Distinctness,  again,  of  a  notion 
is  accomplished  through  Division,  that  is,  through  the  enumer- 
ation of  the  objects  which  are  contained  under  it.  Thus  the  con- 
cept man  is  rendered  intensively  more  distinct,  when  we  declare 
that  man  is  2i  rational  animal ;  it  is  rendered  extensively  more  dis- 
tinct, when  we  declare  that  man  is  partly  m.ale^  partly /emafe  man} 
In  the  former  case,  we  resolve  the  concept  man  into  its  several 
characters,  —  into  its  partial  or  constituent  attributes  ;  in  the  latter, 
we  resolve  it  into  its  subordinate  concepts,  or  inferior  genera.     In 

simple  notions,  there  is  thus  possible  ah  exten- 

Simpie  notions  ad-      sive,  but  not  an  intensive,  distinctness ;  in  indi- 

mit  of  an  extensive,       yi^ual  notions,  there  is   possible  an   intensive, 

individual  notions  of  .  ,.     .  „       r^^^  ^ 

an  intensive,  distinct-      t)ut  not  an  extensive,  distinctness.2     Thus  the 
ness.  concepts  existence,  green,  sweet,  etc.,  though,  as 

absolutely  or  relatively  simple,  their  compre- 
hension cannot  be  analyzed  into  any  constituent  attributes,  and  they 
do  not,  therefore,  admit  of  definition ;  still  it  cannot  be  said  that 
they  are  incapable  of  being  rendered  more  distinct.  For  do  we  not 
analyze  the  pluralities  of  which  these  concepts  are  the  sum,  when 
we  say,  that  existence  is  either  ideal  or  real,  that  green  is  a  yellowish 

1  King,  p.  95,  iLogik, }  31.  —  Ed.]  3  Easer,  Logik,  §  48.  —  Ed. 


120'  LOGIC.  Lbct.  IX. 

or  a  bluish  green,  that  sweet  is  a  pungent  or  a  mawkish  sweet  ?  — 

and  do  we  not,  by  this  analysis,  attain  a  greater  degree  of  logical 

perfection,  than  when  we  think  them  only  clearly  and  as  wholes  ? ' 

"A  concept,  has,  therefore,  attained  its  highest 

The  highest  point  of      point  of  distinctness,  when  there  is  such  a  con- 

Distiuctness  of  a  Con-  .  r-  -^       t  .         .1     ^    •  !••>. 

sciousness  01  its  characters  that,  m  rendenng  its 
comprehension  distinct,  we  touch  on  notions 
which,  as  simple,  admit  of  no  definition,  and,  in  rendering  its  exten- 
sion distinct,  we  touch  on  notions  which,  as  individual,  admit  of  no 
ulterior  division.  It  is  true,  indeed,  that  a  distinctness  of  this 
degree  is  one  which  is  only  ideal ;  that  is,  one  to  which  we  are 
always  approximating,  but  which  we  never  are  able  actually  to 
reach.  In  order  to  approach  as  near  as  possible  to  this  ideal,  we 
must  always  inquire,  what  is  contained  in,  and  what  under,  a  notion, 
and  endeavor  to  obtain  a  distinct  consciousness  of  it  in  both  rela- 
tions. What,  in  this  research,  first  presents  itself  we  must  again 
analyze  anew,  with  reference  always  both  to  comprehension  and 
to  extension ;  and  descending  from  the  higher  to  the  lower,  from 
the  greater  to  the  less,  we  ought  to  stop  only  when  our  process  is 
arrested  in  the  individual  or  in  the  simple.''  * 

1  Emg,  Logik,  f  Si,  Anmerk.,  i.  pp.  95,  96.  —  Ed.  "  Ha^er,  Logik,  i  48,  p.  96.  -^1» 


LECTURE    X. 

STOICHEIOLOGY. 

SECTION  II.  — OF  THE  PRODUCTS  OF  THOUGHT. 

I.  — EKNOEMATIC. 

IMPERFECTION  OF  CONCEPTS. 

It  is  now  necessary  to  notice  an  Imperfection  to  which  concepts 
are  peculiarly  liable,  and   in  the  exposition  of 

Imperfection  of  Con-  i  •   i     x   ^     j    •>.  ,  i 

^^  which  1  nnd  it  necessary  to  employ  an  expres- 

sion, which,  though  it  has  the  highest  philosoph- 
ical authority  for  its  use,  I  would  still,  in  consequence  of  its  ambiguity 
in  English,  have  avoided,  if  this  could  have  been  done  without 
compromising  the  knowledge  of  what  it  is  intended  to  express. 
The  expression  I  mean,  is  intuitive,  in  the  particular  signification  in 
which  it  is  used  by  Leibnitz,^  and  the  continental  philosophers  in 
general,  —  to  denote  what  is  common  to  our  direct  and  ostensive 
cognition  of  individual  objects,  in  Sense  or  Imagination  (Presen- 
tation or  Representation),  and  in  opposition  to  our  indirect  and 
symbolical  cognition  of  general  objects,  through  the  use  of  signs  or 
language,  in  the  Understanding.  But,  on  this  head,  I  would,  first 
of  all,  dictate  to  you  the  following  paragraph. 

%  XXX.    As  a  notion  or  concept  is  the  factitious  whole  or 
unity  made  up  of  a  plurality  of  attributes, 

fe!«on.''o1coacTpt""  "  ^  .^^^^^     ^^^^    ^^^^     ""^    ^    ^^''^    COmplcx 

multiplicity ;  and  as  this  piultiplicity  is  only 
mentally  held  together,  inasmuch  as  the  concept  is  fixed  and 
ratified  in  a  sign  or  word;  it  frequently  happens,  that,  in  its 
employment,  the  word  does  not. suggest  the  whole  amount  of 
thought  for  which  it  is  the  adequate  expression,  but,  on  the 
contrary,  we  frequently  give  and  take  the  sign,  either  with  an 

1  Meditationes  de  Cognitione,  Veritate  ct  Tdeis,  Opera,  ed.  Erdmann,  p.  80.  —  Ed. 

16 


122  LOGIC.  Lect.  X. 

obscure  or  indistinct  consciousness  of  its  meaning,  or  even 
without  an  actual  consciousness  of  its  signification  at  alL 

This  liability  to  the  vices  of  Obscurity  and  Indistinctness  arises, 
1°,  From  the  very  nature  of  a  concept,  which  is 
^  ****'  the  binding  up  of  a  multiplicity  in  unity ;  and 

2°,  From  its  dependence  upon  language,  as  the  necessary  condition 
of  its  existence  and  stability.  In  consequence  of  this,  when  a 
notion  is  of  a  very  complex  and  heterogeneous  composition,  we  are 
frequently  wont  to  use  the  term  by  which  it  is  denoted,  without  a 
clear  or  distinct  consciousness  of  the  various  characters  of  which 
the  notion  is  the  sum ;  and  thus  it  is,  that  we  both  give  and  take 
words  without  any,  or,  at  least,  without  the  adequate  complement 
of  thought.  I  may  exemplify  this :  You  are  aware,  that  in  coun- 
tries where  bank-notes  have  not  superseded  the  use  of  the  precious 
metals,  large  payments  are  made  in  bags  of  money,  purporting  to 
contain  a  certain  number  of  a  certain  denomination  of  coin,  or,  at 
least,  a  certain  amount  in  value.  Now,  these  bags  are  often  sealed 
up  and  passed  from  one  person  to  another,  without  the  tedious  pro- 
cess, at  each  transference,  of  counting  out  their  contents,  and  this 
upon  the  faith,  that,  if  examined,  they  will  be  found  actually  to 
contain  the  number  of  pieces  for  which  they  are  marked,  and  for 
which  they  pass  current.  In  this  state  of  mattei-s,  it  is,  however, 
evident,  that  many  errors  or  frauds  may  be  committed,  and  that  a 
bag  may  be  given  and  taken  in  payment  for  one  sum,  which  con- 
tains another,  or  which,  in  fact,  may  not  even  contain  any  money  at 
all.  Now  the  case  is  similar  in  regard  to  notions.  As  the  sealed 
bag  or  rouleau  testifies  to  the  enumerated  sum,  and  gives  unity  to 
what  would  otherwise  be  an  unconnected  multitude  of  pieces,  each 
only  representing  its  separate  value ;  so  the  sign  or  word  proves  and 
ratifies  the  existence  of  a  concept,  that  is,  it  vouches  the  tying  up  of 
a  certain  number  of  attributes  or  characters  in  a  single  concept, — 
attributes  which  would  otherwise  exist  to  us  only  as  a  multitude  of 
separate  and  unconnected  representations  of  value.  So  far  the 
analogy  is  manifest;  but  it  is  only  general.  The  bag,  the  guaran- 
teed sum,  and  the  constituent  coins,  represent  in  a  still  more  proxi- 
mate manner  the  term,  the  concept,  and  the  constituent  characters. 
For  in  regard  to  each,  we  may  do  one  of  two  things.  On  the  one 
hand,  we  may  test  the  bag,  that  is,  open  it,  and  ascertain  the  accu- 
racy of  its  stated  value,  by  counting  out  the  pieces  which  it  pur. 
ports  to  contain ;  or  we  may  accept  and  pass  the  bag,  without  such 
a  critical  enumeration.  In  the  other  case,  we  may  test  the  general 
term,  prove  that  it  i&  valid  for  the  amount  and  quality  of  thought  of 


Lect.  X  LOGIC.  123 

which  it  is  the  sign,  by  spreading  out  in  consciousness  the  various 
characters  of  which  the  concept  professes  to  be  the  complement ;  or 
we  may  take  and  give  the  term  without  such  an  evolution.^ 

It  is  evident  from  this,  that  notions  or  concepts  are  peculiarly 
liable  to  great  vagueness  and  ambiguity,  and  that  their  symbols  are 
liable  to  be  passed  about  without  the  proper  kind,  or  the  adequate 
amount,  of  thought. 

This  interesting  subject  has  not  escaped  the  observation  of  the 

philosophers  of  this  country,  and  by  them  it 

The  liability  to  am-      lias,  in  fact,  with   great   ingenuity  been  illus- 

biguity  and  vagueness       ^^.^^^^      ^^^   ^^   ^^        ^^^    apparently   ignorant 

of  concepts  noticed  by  /.  .»       o 

British  piiiiosophers.  that  the  matter  had,  before  them,  engaged  the 
attention  of  sundry  foreign  philosophei-s,  by 
whom  it  has  been  even  more  ably  canvassed  and  expounded,  I 
shall,  in  the  exposition  of  this  point,  also  do  justice  to  the  illustrious 
thinkers  to  whom  is  due  the  honor  of  having  originally  and  most 
satisfactorily  discussed  it. 

The  following  passage  from  Mr.  Stewart  will  afford  the  best  foun- 
dation  for  ray  subsequent  remarks :     "  In  the 
Stewart  quoted  on       j^^^  section  I  mentioned  Dr.  Campbell  as  an  in- 

this  subject.  ^ 

genious  defender  of  the  system  of  the  Nomin- 
alists, and  I  alluded  to  a  particular  application  which  he  has  made 
of  their  doctrine.  The  reasonings  which  I  had  then  in  view,  are  to 
be  found  in  the  seventh  chapter  of  the  second  book  of  his  Philoso- 
phy of  Rhetoric^  in  which  chapter  he  proposes  to  explain  how  it 
happens,  '  that  nonsense  so  often  escapes  being  detected  both  by  the 
writer  and  the  reader.'  The  title  is  somewhat  ludicrous  in  a  grave 
philosophical  work,  but  the  disquisition  to  which  it  is  prefixed,  con- 
tains many  acute  and  profound  remarks  on  the  nature  and  power 
of  signs,  both  as  a  medium  of  communication,  and  as  an  instrument 
of  thought. 

"  Dr.  Campbell's  speculations  with  respect  to  language  as  an  in- 
strument of  thought,  seem  to  have  been  sug- 

Kefers  to  Hume.  _    ,         ,        ,.  „        '  •      ,r      tt  , 

gested  by  the  loUowmg  passage  in  Mr.  Hume  s 
Treatise  of  Human  Nature  .'^  'I  believe  every  one  who  examines 
the  situation  of  his  mind  in  reasoning,  will  agree  with  me,  that  we 
do  not  annex  distinct  and  complete  ideas  to  every  term  we  make 
use  of;  and  that  in  talking  of  Government,  Church,  Negotiation, 
Conquest,  we  seldom  spread  out  in  our  minds  all  the  simple  ideas 
of  which  these  complex  ones  are  composed.  It  is,  however,  observ- 
able, that  notwithstanding  this  imperfection,  we  may  avoid  talking 

1  A  hint  of  this  illustration  is  to  be,  found  in  Degerando,  Dea  Signes,  vol.  i.  chap.  viii.  p. 
200.-ED.  SParti.  J7.  — Ed. 


124  LOGIC.  Lect.  X. 

nonsense  on  these  subjects,  and  may  perceive  any  repugnance 
among  the  ideas,  as  well  as  if  we  had  a  fall  comprehension  of  them. 
Thus  if,  instead  of  saying,  that  in  war  the  weaker  have  always  re- 
C/Ourse  to  negotiation,  we  should  say,  that  they  have  always  recourse 
to  conquest ;  the  custom  which  we  have  acquired,  of  attributing 
certain  relations  to  ideas,  still  follows  the  words,  and  makes  us 
immediately  perceive  the  absurdity  of  that  proposition.' 

*'  In  the  remarks  which  Dr.  Campbell  has  made  on  this  passage, 
he  has  endeavored  to  explain  in  what  manner  our  habits  of  thinking 
and  speaking  gradually  establish  in  the  mind  such  relations  among 
the  words  we  employ,  as  enable  us  to  carry  on  processes  of  reason- 
ing by  means  of  them,  without  attending  in  every  instance  to  their 
particular  signification.  With  most  of  his  remarks  on  this  subject 
I  perfectly  agree;  but  the  illustrations  he  gives  of  them  are  of  too 
great  extent  to  be  introduced  here,  and  I  would  not  wish  to  run 
the  risk  of  impairing  their  perspicuity  by  attempting  to  abridge 
them.  I  must,  therefore,  refer  such  of  my  readers  as  wish  to  pros- 
ecute the  speculation,  to  his  very  ingenious  and  philosophical 
treatise. 

" '  In  consequence  of  these  circumstances,'  says  Dr.  Campbell,  '  it 
happens  that,  in   matters   which  are   perfectly 

And  Campbell.  ^       .,.  ,  ,  , 

familiar  to  us,  w^e  are  able  to  reason  by  means 
of  words,  without  examining,  in  every  instance,  their  signification. 
Almost  all  the  possible  applications  of  the  terms  (in  other  words, 
all  the  acquired  relations  of  the  signs)  have  become  customary  to 
us.  The  consequence  is,  that  an  unusual  application  of  any  term 
is  instantly  detected ;  this  detection  breeds  doubt,  and  this  doubt 
occasions  an  immediate  recourse  to  ideas.  The  recourse  of  the 
mind,  when  in  any  degree  puzzled  with  the  signs,  to  the  knowledge 
it  has  of  the  things  signified,  is  natural,  and  on  such  subjects  per- 
fectly easy.  And  of  this  recourse  the  discovery  of  the  meaning, 
or  of  the  unmeaningness  of  what  is  said,  is  the  immediate  effect. 
But  in  matters  that  are  by  no  means  familiar,  or  are  treated  in  an 
uncommon  manner,  and  in  such  as  are  of  an  abstruse  and  intricate 
nature,  the  case  is  widely  different.'  The  instances  in  which  we 
are  chiefly  liable  to  be  imposed  on  by  words  without  meaning,  are 
(according  to  Dr.  Campbell)  the  three  following: 

"•First,  When  there  is  an  exuberance  of  metaphor. 

^Secondly,  When  the  terms  most  frequently  occurring  denote 
things  which  are  of  a  complicated  nature,  and  to  which  the  mind 
is  not  sufficiently  familiarized.  Such  are  the  words  —  Government, 
Church,  State,  Constitution,  Polity,  Power,  Commerce,  Legislature, 
Jurisdiction,  Pioportion,  Symmetry,  Elegance. 


Lect.  X.  LOGIC.  125 

'-'■  Thirdly,  "When  the  terms  employed  are  very  abstract,  and  con 
sequently  of  very  extensive  signification. 

"'The  more  general  any  word  is  in  its  signification,  it  is  the  more 
liable  to  be  abused  by  an  improper  or  unmeaning  application.  A 
very  general  term  is  applicable  alike  to  a  multitude  of  diflferent 
individuals,  a  particular  term  is  applicable  but  to  a  few.  When  the 
rightful  applications  of  a  word  are  extremely  numerous,  they  can- 
not all  be  so  strongly  fixed  by  habit,  but  that,  for  greater  security, 
we  must  perpetually  recur  in  our  minds  from  the  sign  to  the  notion 
we  have  of  the  thing  signified  ;  and  for  the  reason  aforementioned, 
it  is  in  such  instances  diflUcult  precisely  to  ascertain  this  notion. 
Thus  the  latitude  of  a  word,  though  different  from  its  ambiguity, 
hath  often  a  similar  effect.'"^ 

Now,  on  this  I  would,  in  the  first  place,  observe,  that  the  credit 
;tj     z.T         attributed  to  Hume  by  Dr.  Campbell  and  Mr. 

Locke  anticipated  Stewart,  as  having  been  the  first  by  whom  the 
Hume  in   remarking       observation  had  been  made,  is,  even  in  relation 

the    employment      of  -n   •   •   i        i  m  i  tt  i 

terms  without  distinct       to  British  philosophers,  not  Correct.     Hume  has 
meaning.  Stated  nothing  which  had  not,  with  equal  em- 

phasis and  an  equal  development,  been  previ- 
ously stated  by  Locke,  in  four  difierent  places  of  his  Essay. '^ 

Thus,  to  take  only  one  out  of  at  least  four  passages  directly  to  the 
same  efiect,  and  out  of  many  in  which  the  same  is  evidently  main- 
tained, he  says,  in  the  chapter  entitled —  Of  the  Abuse  of  Words: 
"Others  there  be,  who  extend  this  abuse  still 

Locke  quoted.  /.       ,  ,  ,  ,.     ,  ,         ,  , 

larther,  who  take  so  little  care  to  lay  by  words, 
which  in  their  primary  notation  have  scarce  any  clear  and  distinct 
ideas  which  they  are  annexed  to,  that  by  an  unpardonable  negli- 
gence they  familiarly  use  words,  which  the  propriety  of  language 
has  fixed  to  very  important  ideas,  without  any  distinct  meaning  at 
all.  Wisdom,  glory,  grace,  etc.,  are  words  frequent  enough  in 
every  man's  mouth  •  but  if  a  great  many  of  those  who  use  them 
should  be  asked  what  they  mean  by  them,  they  would  be  at  a  stand, 
and  not  know  what  to  answer:  a  plain  proof,  that  though  they  have 
learned  those  sounds,  and  have  them  ready  at  their  tongue's  end, 
yet  there  are  no  determined  ideas  laid  up  in  their  minds,  which  are 
to  be  expressed  to  others  by  them.  Men  having  been  accustomed 
fi^om  their  cradles  to  learn  words,  which  are  easily  got  and  retained, 
before  they  knew,  or  had  framed  the  complex  ideas  to  which  they 
were  annexed,  or  which  were  to  be  found  in  the  things  they  were 

1  Elements,  voL  I.,  TTorfcs,  vol.  ii.  chap.  iv.  5  2  Compare  Essay,  B.  ii.,  ch.  xxii ,  §  7;  ii., 
4,  pp  193,165.  jcxix.  9;  ii.  xxxi.  8;  iii-  ix.  6;  iii.,x.2.  — En 


126  LOGIC.  Lect.  X. 

thought  to  stand  for,  they  usually  continue  to  do  so  all  their  lives ; 
and  without  taking  the  pains  necessary  to  settle  in  their  minds  de- 
termined ideas,  they  use  their  words  for  such  unsteady  and  confused 
notions  as  they  have,  contenting  themselves  w  ith  the  same  words 
other  people  use :  as  if  their  very  sound  necessarily  cai-ried  with  it 
constantly  the  same  meaning.  This,  though  men  make  a  shift  with, 
in  the  ordinary  occurrences  of  life,  where  they  find  it  necessary  to  be 
understood,  and  therefore  they  make  signs  till  they  are  so ;  yet  this 
insignificancy  in  their  words,  when  they  come  to  reason  concerning 
either  their  tenets  or  interest,  manifestly  fills  their  discourse  with 
abundance  of  empty,  unintelligible  noise  and  jargon,  especially  in 
moral  matters,  where  the  words,  for  the  most  part,  standing  for 
arbitrary  and  numerous  collections  of  ideas,  not  regularly  and  per- 
manently united  in  nature,  their  bare  sounds  are  often  only  thought 
on,  or  at  least  very  obscure  and  uncertain  notions  annexed  to 
them.  Men  take  the  words  they  find  in  use  among  their  neighbors, 
and  that  they  may  not  seem  ignorant  what  they  stand  for,  use  them 
confidently,  without  much  troubling  their  heads  about,  a  .certain 
fixed  meaning :  whereby,  besides  the  ease  of  it,  they  obtain  this 
advantage,  that  as  in  such  discourses  they  are  seldom  in  the  right, 
80  they  are  as  seldom  to  be  convinced  that  they  are  in  the  wrong ;  it 
being  all  one  to  go  about  to  draw  those  men  out  of  their  mis- 
takes, who  have  no  settled  notions,  as  to  dispossess  a  vagrant  of 
his  habitation  who  has  no  settled  abode.  This  I  guess  to.be  so; 
and  eveiy  one  may  observe  in  himself  and  others,  whether  it  be  or 
no."> 

From  a  comparison  of  this  passage  with  those  I  have  given  you 
from  Stewart,  Campbell,  and  Hume,  it  is  manifest  that,  among  Brit- 
ish philosophers,  Locke  is  entitled  to  the  whole  honor  of  the  obser- 
vation: for  it  could  easily  be  shown,  even  from  the  identity  of 
expression,  that  Hume  must  have  borrowed  it  from  Locke;  and 
of  Hume's  doctrine  the  two  other  philosophers  profess  only  to  be 
expositors. 

This  curious  and  important  observation  was  not,  however,  firet 
made  by  any  British  philosopher ;  for  Leibnitz 

The  distinction  of  \^r^^  jjot  Only  anticipated  Locke,  in  a  publication 
Vk'^^wLd  ^"fi*  t  prior  to  the  Essay,  but  afforded  the  most  pre- 
taken  by  Leibnitz.  <5ise  and  universal  explanation  of  the  phaenome- 

non,  which  has  yet  been  given. 

To  him  we  owe  the  memorable  distinction  of  our  knowledge  into 
Intuitive  and  Symbolical,  in  which  distinction  is  involved  the  expla- 

I  Enay  conctming  Humcui  Understanding,  vol.  ii.  p.  228;  [B.  III.,  ch.  x.  f|  3, 4  — ED.] 


Lect.  X.  LOGIC.  127 

nation  of  the  phaenomenon  in  question.     It  is  the  establishment  of 
this  distinction,  likewise,  which  has   superseded 
This  distinction  lias      in  Germany  the  whole  controversy  of  Nominal- 
superseded  the  contro-       jgj^  jjjjjj  Conceptualism,  —  which,  in  consequence 
^^T^,        X    .•      .         of  the  non-establishment  of  this  distinction,  and 

and  Conceptualism  in  ' 

Germany.  the   relative  imperfection   of  our   philosophical 

language,  has  idly  agitated  the  Psychology  of 
this  country  and  of  France. 

That  the  doctrines  of  Leibnitz,  on  this  and  other  cardinal  points 

of  psychology,  should  have  remained  apparently 

Unacqnaintance  of      unknown  to  every  philosopher  of  this  country, 

the    philosophers  of      j^  ^  ^^^^^^.  ^^^  f^^^  ^^  wonder  than  of  regret, 

this  country  with  the  " 

doctrines  of  Leibnitz.       and  is  Only  to  be  excused  by  the  manner  in 
which  Leibnitz  gave  his  writings  to  the  world. 
His  most  valuable  thoughts  on  the  most  important  subjects  were 
generally  thrown  out  in  short  treatises  or  letters,  and  these,  for  a 
long  time,  were  to  be  found  only  in  partial  col- 
Manner  in  which  he       lections,  and  sometimes  to  be  laboriously  sought 

«ive  his   writings  to  .     ■,.  t         ^i  •      >.i_ 

-;  out,  dispersed  as  they  were,  in  the  various  scien- 

tific Journals  and  Transactions  of  every  country 
of  Europe;  and  even  when  his  works  were  at  length  collected,  the 
attempt  of  his  editor  to  arrange  his  papers  according  to  their  sub- 
jects (and  what  subject  did  Leibnitz  not  discuss?)  was  baffled  by 
the  multifarious  nature  of  their  contents.  The  most  important 
of  his  philosophical  writings  —  his  Assays  in  refutation  of  Locke 

—  were  not  merely  a  ])ostliumous  publication,  but  only  published 
after  the  collected  edition  of  his  Works  by  Dntens ;  and  this  trea- 
tise, even  after  its  publication,  was  so  little  known  in  Britain,  that 
it  remained  absolutely  unknown  to  Mr.  Stewart  —  (the  only  British 
philosopher,  by  the  way,  who  seems  to  have  had  any  acquaintance 
Avith  the  works  of  Leibnitz)  — until  a  very  recent  period  of  his  life. 
The  matter,  however,  vrith  which  we  are  at-  present  engaged,  was 
discussed  by  Leibnitz  in  one  of  his  very  earliest  writings ;  and  in  a 

paper  entitled  JDe  Cognitione,  Veritate,  et  Ideis, 
#His  paper,    e    og-      published  in  the  Acta  EnuUtorum  of  1684,  we 

nttione,Ventate,ft  Jaeis  ■*  _ 

have,  in  the  compass  of  two  quarto  pages,  all 
that  has  been  advanced  of  principal  importance  in  regard  to  the 
peculiarity  of  our  cognitions  by  concept,  and  in  regard  to  the  depen- 
dence of  our  concepts  upon  language.  In  this  paper,  besides  estab- 
lishing the  difference  of  Clear  and  Distinct  knowledge,  he  enounces 
the  memorable  distinction  of  Intuitive  and  Symbolical  knowledge, 

—  a  distinction  not  certainly  unknown  to  the  later  philosophers  of 
this  country,  but  which,  from  their  not  possessing  terms  in  which  pre- 


128  LOGIC.  Lect.  X. 

cisely  to  embody  it,  has  always  remained  vague  and  inapplicable  to 

common  use.     Speaking  of  the  analysis  of  complex  notions,  he  says : 

"For  the  most  part,  however,  especially  in  an 

Leibnitz  quoted  on       analysis  of  any  length,  we  do  not  view  at  once 

Intuitive  and  Symbol-  ,  •        i    •    >  \     >  ■,     ^         i 

ic  1  kno  1  d  e  (non   smiul  intuemur)  the  whole  characters  or 

attributes  of  the  thing,  but  in  place  of  these  we 
employ  signs,  the  explication  of  which  into  what  they  signify,  we  are 
wont,  at  the  moment  of  actual  thought,  for  the  sake  of  brevity,  to 
omit,  knowing  or  believing  that  we  have  this  explication  always  in 
our  power.  Thus,  when  I  think  a  chiliogon  (or  polygon  of  a  thou- 
sand equal  sides),  I  do  not  always  consider  the  various  attributes, 
of  the  side,  of  the  equality,  and  of  the  number  a  thousand,  but  use 
these  words  (whose  meaning  is  obscurely  and  imperfectly  presented 
to  the  mind)  in  lieu  of  notions  which  I  have  of  them,  because  I 
remember,  that  I  possess  the  signification  of  these  words,  though 
their  application  and  explication  I  do  not  at  present  deem  to  be 
necessary: — this  kind  of  thinking  I  am  used  to  call  blind  or  sym- 
bolical: we  employ  it  in  Algebra  and  in  Arithmetic,  but  in  fact 
universally.  And  certainly,  when  the  notion  is  very  complex,  we 
cannot  think  at  once  all  the  ingredient  notions :  but  where  this  is 
possible  —  at  least,  inasmuch  as  it  is  possible  —  I  call  the  cognition 
intuitive.  Of  the  primary  elements  of  our  notions,  there  is  given 
no  other  knowledge  than  the  intuitive :  as  of  our  composite  notions, 
there  is,  for  the  most  part,  possible  only  a  symbolical.  From  these 
considerations  it  is  also  evident,  that  of  the  things  which  we  dis- 
tinctly know  we  are  not  conscious  of  the  ideas,  except  in  so  far 
as  we  employ  an  intuitive  cognition.  And,  indeed,  it  happens 
that  we  often  falsely  believe  that  we  have  in  our  mind  the  ideas 
of  things ;  erroneously  supposing,  that  certain  terms  which  we  em- 
ploy, had  been  applied  and  explicated ;  and  it  is  not  true,  at  least 
it  is  ambiguously  expressed,  what  some  assert,  —  that  we  cannot 
speak  concerning  anything,  understanding  what  we  say,  without 
having  an  idea  of  it  actually  present.  For  we  frequently  npply  .any 
kind  of  meaning  to  the  several  words,  or  we  merely  recollect  us, 
that  we  have  formerly  understood  them,  but  because  we  are  content 
with  this  blind  thinking,  and  do  not  follow  out  the  resolution  of 
the  notions,  it  happens,  that  contradictions  are  allowed  to  lie  hid, 
which  perchance  the  composite  notion  involves."  ..."  Thus,  at 
.first  sight,  it  must  seem,  that  we  could  form  an  idea  of  a  maximum 
velocity  (motus  c«lerrimi),  for  in  using  the  terms  we  understand 
what  we  say ;  we  shall  find,  however,  that  it  is  impossible,  for  the 
notion  of  a  quickest  motion  is  shown  to  be  contradictory,  and, 
therefore,  inconceivable.     Let  us  suppose,  that  a  wheel  is  turned 


I 


Lect.  X.  LOGIC.  129 

with  a  velocity  absolutely  at  its  maximum ;  every  one  perceives 
that  if  one  of  its  spokes  be  produced,  its  outer  end  will  be  moved 
more  rapidly  than  the  nails  in  the  circumference  of  the  wheel ;  the 
motion,  therefore,  of  these  is  not  a  maximum,  which  is  contrary  to 
the  hypothesis,  and,  therefore,  involves  a  contradiction.." 

This  quotation  will  suffice  to  show  you  how  correctly  Leibnitz  ap- 
prehended the  nature  of  concepts,  as  opposed  to 
Effect  of  this  distinc-       the  presentations  and  representations  of  the  sub- 
tion  by  Leibnitz  on       gidiary  facilities ;  and  the  introduction  of  the  term 

the  philosophy  of  Ger-  „        77.      ti  it         .       t      •  .1       n 

^  Symoohcal  knowledge,  to  designate  the  former, 

and  the  term  Intuitive  knowledge  to  comprehend 
the  two  latter,  —  terms  which  have  ever  since  become  classical  in  his 
own  country,  —  has  bestowed  on  the  German  language  of  philosophy,, 
in  thisj-espect,  a  powerand  precision  to  which  that  of  no  other  nationi 
can  lay  claim.     In  consequence  of  this,  while  the  philosophers  of 
this  country  have  been  all  along  painfully  expounding  the  phienom- 
enon  as  one  of  the  most  recondite  arcana  of  psychology,  in  Germany 
it  has,  for  a  century  and  a  half,  subsided  into  one  of  the  elementary 
doctrines  of  the  science  of  mind.     It  was  in  consequence  of  the 
establishment  of  this  distinction  by  Leibnitz,  that  a  peculiar  expres- 
sion {Begriff,  conceptus)  was  appropriated  to  the  symbolical  notions 
of  the  Understanding,  in  contrast  to  the  intuitive  presentations  of 
Sense  and  representations  of  Imagination,  which  last  also  were  fur-- 
nished  with  the  distinctive  appellations  of  intuitio7is  (Anschauun-  . 
gen,  intuitus).    Thus  it  is,  that,  by  a  more  copious  and  well-ap- 
pointed language,  philosophy  has,  in  Germany,  been  raised  above 
various  controversies,  which,  merely  in  consequence  of  the  poverty 
and  vagueness  of  its  English  nomenclature,  have  idly  occupied  out 
speculations.     But,  to  return  to  the^mere  logical  question. 

The  doctrine  of  Leibnitz  in  regard  to  this  natural  imperfection  of 

our  concepts  was  not  overlooked  by  his  disciples, . 
The  distinction  ap-       ^^^  j  shall  read  you  a  passage  from  the  Lesser 
pies  of  Leibnitz.  Logic  of  Wolf,  —  a  work  abovc  a  century  old,  and " 

which  was  respectably  translated  from  <jermaii' 
into  Engl'gb  '"  *^f^  y^"''  ^  '^'^'\j  This  translation  is  now  rarely  to  be  met 
with,  which  may  account  for  its  being  apparently  totally  unknown  tO' 
our  British  philosophers;  and  yet,  upon  the  whole,  with  all  its  faults- 
and  imperfections,  it  is  perhnps  the  most  valuable  work  on  Logic  (to- 
say  nothing  of  the  Port  Royal  Logic)  in  the  English  language. 

"By  Words,    we    usually   make    known   our 
o   quoec.     or  »       thoughts  to  Others:  and  thus  they  are  nothing 

or  terms.  —  what.  °  _  _  •'       •  ° 

but  uttered  articulate  signs  of  our  thoughts  for 
the  information  of  others:  for  exnmple,  if  one  asks  me  what  I  am, 

17 


130  LOGIC.  Lect.  X. 

thinking  of,  and  I  answer,  the  sun ;  by  this  word  I  acquaint  him 
what  object  my  thoughts  are  then  employed  about. 

"  If  two  persons,  therefore,  are  talking  together,  it  is  requisite,  in 
order  to  be  understood,  first,  that  he  who  speaks,  shall  join  some 
notion  or  meaning  to  each  word  ;  secondly,  that  he  who  hears,  shall 
join  the  very  same  notion  that  the  speaker  does. 

"  Consequently,  a  certain  notton  or  meaning  must  be  connected 
with,  and  therefore  something  be  signified  by,  each  word. 

"  Now,  in  order  to  know  whether  we  understand  what  we  speak, 
or  that  our  words  are  not  mere  empty  sound,  we  ought,  at  every 
word  we  utter,  to  ask  ourselves  what  notion  or  meaning  we  join 
therewith. 

"  For  it  is  carefully  to  be  observed,  that  we  have  not  always  the 

notion  of  the  thing  present  to  us,  or  in  view, 

infpeakingorthink-       when  we  spcak  or  think  of  it;  but  are  satisfied 

ing,    le  meaning  o        when    wc   imagine  we    suflSciently  understand 

words      not     always  °  •' 

attended  to.  what  we  speak,  if  we  think  we  recollect  that 

we  have  had  at  another  time  the  notion  which 
is  to  be  joined  to  this  or*the  other  word  ;  and  thus  we  represent  to 
ourselves,  as  at  a  distance  only,  or  obscurely,  the  thing  denoted 
by  the  term  (§  9,  c.  i.). 

"  Hence  it  usually  happens,  that  when  we  combine  words  to- 
gether, to  each  of  which   apart  a  meaning  or 
How  words  without       notion  answcrs,  we  imagine  we  understand  what 
r^^t'od  ™*'^  ^^®  utter,  though  that  which  is  denoted  by  such 

combined  words  be  impossible,  and,  consequently, 
can  have  no  meaning;  for  that  which  is  impossible  is  nothing  at  all ; 
and  of  nothing  there  can  be  no  idea.  For  instance,  we  have  a 
notion  of  gold,  as  also  of  iron  :  but  it  is  impossible  that  iron  can,  at 
any  time,  be  gold;  consequently  neither  can  we  have  any  notion 
of  iron-gold ;  and  yet  we  understand  what  people  mean  when  they 
mention  iron-gold. 

"  In  the  instance  alleged,  it  certainly  strikes  every  one  at  first 

that  the  expression  iron-gold  \&  an  empty  sound: 
Further  proved.        ,  ,^  ,  ^    ^  ,  .         .  .  .    . 

but  yet  there  are  a  thousand  instances  m  which  it 

does  not  so  easily  strike :  For  example,  when  I  say  a  rectilineal  two- 
line  figure,  contained  under  two  right-lines,  I  am  equally  well  under- 
stood as  when  I  say  a  right-lined  tiiangle,  a  figure  contained  under 
three  right-lines:  and  it  should  seem  we  had  a  distinct  notion  of 
both  figures  (§  13,  c.  i.).  However,  as  we  show  in  geometry  that 
two  right-lines  can  never  contain  a  space,  it  is  also  impossible  to 
form  a  notron  of  a  rectilineal  two-lined  figure ;  and,  consequently, 
that  expression  is  an  empty  sound.    Just  so  it  holds  with  the  vege- 


Lect.  X.  LOGIC.  131 

table  soul  of  plants,  supposed  to  be  a  spiritual  being,  whereby 
plants  are  enabled  to  vegetate  and  grow:  for  though  those  words 
taken  apart  are  intelligible,  yet  in  their  combination  they  have  no 
manner  of  meaning.  Just  so  if  I  say  that  the  Attractive  Spirit,  or 
Attractive  Cord,  as  Linus  calls  it,  or  the  Attractive  Force,  as  some 
philosophers  at  this  day,  is  an  immaterial  principle  superadded  to 
matter,  whereby  the  attractions  in  nature  are  performed ;  no  notion 
or  meaning  can  possibly  be  joined  with  these  words.  To  this  head 
also  belong  the  Natural  Sympathy  and  Antipathy  of  Plants ;  the 
Band  of  Right  or  law  {vinculum  juris),  used  in  the  definition  of 
Obligation,  by  Civilians ;  the  principle  of  Evil  of  the  Manicheans," 
etc' 

1  Logic,  or  Rational  Thoughts  on  the  Powers  of     the  German  of  Baron  Wolfius,  C.  il.,  p.  54 — 67; 
the  Human   UntiersUuuiing.      Transiated  from     London,  1770.— £d. 


LECTUEE    XI. 

STOICHEIOLOOY. 

SECTION   I.— OF    THE    PRODUCTS    OF    THOUGHT. 

I.    ENNOEMATIC. 

ni.    RECIPROCAL  RELATIONS   OF   CONCEPTS. 


QUANTITY  OF  EXTENSION  — SUBORDINATION  AND  CO- 
ORDINATION. 


I  NOW  proceed  to  the  third  and  last  Relation  of  Concepts,  —  that 
of  concepts  to  each  other.  The  two  former  relations  of  notions  — 
to  their  objects  and  to  their  subject — gave  their  Quantity  and  Qual- 
ity. This,  the  relation  of  notions  to  each  other,  gives  what  is 
emphatically  and  strictly  denominated  their  Relation.  In  this  rig- 
orous signification,  the  Relation  of  Concepts  may  be  thus  defined. 

^  XXXI.     The  Relation  proper  of  notions  consists  in  those 

determinations  or  attributes  which  belong 

Par.  XXXI.  Beeip-      ^q  them,  not  vicwcd  as  apart  and  in  them- 

rocal     Belations     of  .  i        /-^ 

Concepts.  '  sclvcs,  but  US  rcciprocally  compared.     Con- 

cepts can  only  be  compared  together  with 
reference,  either,  1°,  To  their  Extension ;  or,  2°,  To  their  Com- 
prehension. All  their  relations  are,  therefore,  dependent  on  the 
one  or  on  the  other  of  these  quantities.* 

^  XXXII.     As  dependent  upon  Extension,  concepts  stand 

to  each  other  in  the  five  mutual  relations, 

i^lnif^'  """""^       1°.  Of  Exclusion ;  2°,  Of  Coextension ;  3°, 

Of  Subordination ;  4°,  Of  Coordination ;  and 

5°,  Of  Intersection. 

1.  One  concept  excludes  another,  when  no  part  of  the  one 
coincides  with  any  part  of  the  other.     2.  One  concept  is  coex- 

1  Cf.  Krug,  Logik, )  36.  —  Ed.  S  See  diagram,  p.  133. 


Lect.  XI. 


LOGIC. 


133 


CONCEPTS,  THEIR  RELATIONS  PROPER 


1  Exelosionl 


2.  CoSxtension 


8.  Sabordinatioa 


4.  Coiirdination 


6.  Intersection,  or 
Partial  Coinclu- 
sion  and  CoSx- 
elusion. 


lOWlT  OF 


I I I. 


I I 


© 


1  The  notation  by  straight  lines  was  first  employed  by  the  author  in  184S. — Ed. 


134  LOGIC.  Lkct.  X£ 

tensive  with  another,  when  each  has  the  same  number  of  sub- 
ordinate concepts  under  it.  3.  One  concept  is  subordinate  to 
another  (which  may  be  called  the  Superordiiiate)  when  the 
former  is  included  within,  or  makes  a  part  of,  the  sphere  or 
extension  of  the  latter.  4.  Two  or  more  concepts  are  coordi- 
nated, when  each  excludes  the  other  from  its  sphere,  but  when 
both  go  immediately  to  make  up  the  extension  of  a  third  con- 
cept, to  which  they  are  cosubordinate.  5.  Concepts  intersect 
each  other,  when  the  sphere  of  the  one  is  partially  contained 
in  the  sphere  of  the  other.' 

Of  Exclusion,  horse,  syllogism,  are  examples :  there  is  no  abso- 
lute exclusion. 
Examples  of  the  five  ^^  examples  of  Coextension,— the  concepts 

mutual    relations   of  .  ,    .  .      t     »    . 

Concepts.  livinff,   detnff,   and    orf/amzed    beings,   may   be 

given.  For,  using  the  term  life  as  applicable  to 
plants  as  well  as  animals,  there  is  nothing  living  which  is  not  organ- 
ized, and  nothing  organized  which  is  not  living.  This  reciprocal 
relation  will  be  represented  by  two  circles  covering  each  other,  or 
by  two  lines  of  equal  length  and  in  positive  relation. 

As  examples  of  Subordination  and  Coordination,  —  man,  dog, 
horse,  stand,  as  correlatives,  in  subordination  to  the  concept  animal, 
and,  as  reciprocal  correlatives,  in  coordination  with  each  other. 

What  I  would  call  the  reciprocal  relation  of  Intersection,  takes 
place  between  concepts  when  their  spheres  cross  or  cut  each  other, 
that  is,  fall  partly  within,  partly  without,  each  other.  Thus,  the 
concept  black  and  the  concept  heavy  mutually  intersect  each  other, 
for  of  these  some  black  things  are  heavy,  some  not,  and  some  heavy 
things  are  black,  some  not. 

Of  these  relations,  those  of  Subordination  and 
Subordination   and       Coordination  are  of  principal  importance,  as  on 

Coordination  of  priii-  ,  i  -i     i  /^       i        ... 

oipai  importance.  ^^^^m    reposes   the  whole    system    of  clas.sitica- 

tion;  and  to  them  alone  it  is,  therefore,  neces- 
sary to  accord  a  more  particular  consideration. 

Under  the  Subordination  of  notions,  there  are  various  terms  to 

express   the   different    modes   of  this  relation ; 

Terms  expressive  of       these  it  is  necessary  that  you  should  now  learn 

the  different  modes  of  ji  a.        \  •  •     :i     e        ^t  r- 

_-  .  and  hereafter  bear  m  mind,  for  they  lorm  an 

the  relation  of  Subor-  ^  <     '  •'  _ 

dination.  essential  part  of  the  language  of  Logic,  and  Mill 

come  frequently,  in  the  sequel,  to  be  employed 
in  considering  the  analysis  of  Reasonings. 

1  Cf.  Krng;  Lagik,  f  41.  —Ed. 


Li;ci.  XL  LOGIC.  135 

%  XXXIII.     Of  notions  which  stand  to  each  other  in  the 
relations  of  Subordination,  —  the  one  is  the 

Par.  XXXin.  Supe-  rr-    i  a  •        /       ^-  i. 

rior    and    Inferior,       Higher  Or  l^upenor  {notio,  conceptus,  supe- 

Broader  and  Narrow-  riOV),     the      Other      the     LoweV     OX     InfeviOT 

(notio,  conceptus,  iiiferior).  The  superior 
notion  is  likewise  called  the  Wider  or  broader  (latior),  the 
inferior  is  likewise  called  the  Narrower  {angustior)} 

The  meaning  of  these  expressions   is  sufficiently  manifest.     A 
notion  is  called  the  higher  or  superior,  inasmuch 

Explication.  .      .        .  ,  ,.  i         •        » 

as  it  IS  viewed  as  standing  over  another  in  the 
relation  of  subordination,  —  as  including  it  within  its  domain  or 
sphere ;  and  a  correlative  notion  is  called  the  lower  or  inferior,  as 
thus  standing  under  a  superior.  Again,  the  higher  notion  is  called 
the  wider  or  broader,  as  containing  under  it  a  greater  number  of 
things ;  the  lower  is  called  the  narrower,  as  containing  under  it 
a  smaller  number. 

^  XXXIV.     The  higher  or  wider  concept  is  also  called,  in 

contrast  to  the  lower  or  narrower,  a  JJni- 

Par.  XXXIV.    Tini-      i^ersal  or   General   Notion  (vo-naa   koSoXov, 

versal  and  Particular  ^ 

notions.  uotio,  conceptus,  Universalis,  generuUs) ;  the 

lower  or  narrower  concept,  in  contrast  to 
the  higher  or  wider,  a  Particular  Notion,  vo-qjxa  fx-epiKov,  notio, 
conceptus  particularis? 

The  meaning  of  these  expressions,  likewise,  requires  no  illustra- 
tion. A  notion  is  called  universal,  inasmuch  as 
it  is  considered  as  binding  up  a  multitude  of 
parts  or  inferior  concepts  into  the  unity  of  a  whole ;  for  universus 
means  in  unum  versus  or  ad  unum  versus,  that  is,  many  turned 
into  one,  or  many  regarded  as  one,  and  universal  is  employed  to 
denote  the  attribution  of  this  relation  to  objects.  A  notion  is  called 
particular,  inasmuch  as  it  is  considered  as  one  of  the  parts  of  a 
higher  concept  or  whole. 

^  XXXV.  A  superior  concept,  inasmuch  as  it  constitutes  a 
common  attribute  or  character  for  a  number  of  inferior  con- 
cepts, is  called  a  General  Notion  (vvq/xa  koSoXov,  notio  conceptus 
generalis),  or,  in  a  single  word,  a    Genus  (yeyos,  genus).    A 

1  Cf.  Krug,  Logi'lc,  §  42.  — Ed.  lati,  Rudimenta  Lo^ca,  p.  39]    [Logica,  torn. 

2  rSee  Ammonius,  In  De  Interpret.,  f  72  b.,      i.,  P.  I.,  c.  iv.  §  8,  4th  edit ,  Venice,  1772.    C£ 
(Brandis,  Scholia  in  Ari^cot.,  p.  113);  Faccio-     Krug,  Logik,  §  42.  —  Ed.] 


136  LOGIC.  Lect.  XL 

notion,  inasmuch  as  it  is  considered  as  at  once  affording  a  com- 
mon  attribution  for  a  certain  complement 

Par.  ZXXV.    Oenus  /••x'-  ^  •T-iii-^ 

and  Species  *^^   interior  couccpts  or  individual  objects, 

and  as  itself  an  inferior  concejit,  contained 
under  a  higher,  is  called  a  Special  Notion  (vorjfxa  ctScKoV,  notio, 
conceptus,  specialis),  or,  in  a  single  word,  a  /Species  (ttSos,  spe- 
cies). The  abstraction  which  carries  up  species  into  genera,  is 
called,  in  that  respect,  Generijication,  or,  more  loosely,  Gener- 
alization. The  determination  which  divides  a  genus  into  its 
species  is  called,  in  that  respect.  Specification.  Genera  and 
Species  are  both  called  Classes ;  and  the  arrangement  of  things 
under  them  is,  therefore.  Classification.^ 

It  is  manifest  that  the  distinction  into  Genera  and  Species  is  a 

merely  relative  distinction ;  as  the  same  notion 

Explication.     The      ig^  Jq  one  rcspect,  a  genus,  in  another  respect,  a 

distinction  of  Genus  igg.      For   except  a  notion   has  no  higher 

and    Species    merely  ...  o        - 

relative.  notion,  that  is,  except  it  be  itself  the  widest  or 

most  universal  notion,  it  may  always  be  regarded 
as  subordinated  to  another ;  and,  in  so  far  as  it  is  actually  thus  re- 
garded, it  is  a  species.  Again,  every  notion  except  that  which  has 
under  it  only  individuals,  is,  in  so  far  as  it  is  thus  viewed,  a  genus. 
For  example,  the  notion  triangle,  if  viewed  in  relation  to  the  notion 
of  rectilineal  figure,  is  a  species,  as  is  likewise  rectilineal  figure 
itself,  as  viewed  in  relation  to  figure  simply.  Again,  the  concept 
triangle  is  a  genus,  when  viewed  in  reference  to  the  concepts, — 
right-angled  triangle,  acute-angled  triangle,  etc.  A  right-angled 
triangle  is,  however,  only  a  species,  and  not  possibly  a  genus,  if 
under  it  be  necessarily  included  individuals  alone.  But,  in  point  of 
fact,  it  is  impossible  to  reach  in  theory  any  lowest  species ;  for  we 
can  always  conceive  some  difference  by  which  any  concept  may  be 
divided  ad  infinitum.  This,  however,  as  it  is  only  a  speculative 
curiosity,  like  the  infinitesimal  divisibility  of  matter,  may  be  thrown 
out  of  view  in  relation  to  practice;  and,  therefore,  the  definition,  by 
Porphyry  and  logicians  in  general,  of  the  lowest  species  (of  which 
I  am  immediately  to  speak),  is  practically  correct,  even  though  it 
cannot  be  vindicated  against  theoretical  objections.  On  the  other 
hand,  we  soon  and  eiisily  renoh  the  highest  genus,  which  is  given  in 
TO  6v,  ens  aliquid,  being,  thing,  something,  etc.,  which  are  only  vari- 
ous  expressions   of  the  same  absolute  universality.     Out  of  these 

1  Krug.  hoe:ik,  S  43.  —  Ed. 


I 


Lect.  XI.  LOGIC.  137 

conditions  there  arise  certain  denominations  of  conccitts,  which  it 
is,  likewise,  necessary  that  you  be  made  aware  of. 

In  regard  to  the  tei-nis  Generification  and  Specification^  these  are 
limited  expressions  for  the  processes  of  Abstrac- 

Generiflcation  and       ^j^^  ^^^^  Determination,  considered  in  a  particu- 

iSpecitication, —  what.  .  i    -r>v  •         • 

lar  relation.  Abstraction  and  Determination, 
you  will  recollect,  we  have  already  spoken  of  in  general;^  it  will, 
therefore,  be  only  necessary  to  say  a  very  few  words  in  reference  to 
them,  as  the  several  operations  by  which  out  of  species  we  evolve 
genera,  and  out  of  genera  we  evolve  species.     And  first,  in  regard 

to   Abstraction    and    Generification.      In    every 

Generification.  .  t      .  .  • 

complex  notion,  we  can  limit  our  attention  to  its 
constituent  characters,  to  the  exclusion  of  some  one.  We  thus 
think  away  from  this  one,  —  we  abstract  from  it.  Now,  the  concept 
which  remains,  that  is,  the  fasciculus  of  thought  minus  the  one  char- 
acter which  we  have  thrown  out,  is,  in  relation  to  the  original,  —  the 
entire  concept,  the  next  higher,  —  t^ie  proximately  superior  notion. 
But  a  concept  and  a  next  higher  concept  are  to  each  other  as  species 
and  genus.  The  process  of  Abstraction,  therefore,  by  which  out  of 
a  proximately  lower  we  evolve  a  proximately  higher  concept,  is, 
when  we  speak  with  logical  precision,  called  the  process  of  Generi- 
fication. 

Take,  for  example,  the  concept  man.  This  concept  is  proxi- 
mately composed  of  the  two  concepts  or  constituent  characters,  — 
animal  and  rational  being.  If  we  think  either  of  these  characters 
away  from  the  other,  we  shall  have  in  that  other  a  proximately 
higher  concept,  to  which  the  concept  man  stands  in  the  relation  of 
a  sj)ecies  to  its  genus.  If  we  abstract  from  animal,  then  man  will 
stand  as  a  species  in  subordination  to  the  genus  rational  being,  and 
the  concept  animal  will  then  afford  only  a  difference  to  distinguish 
man  as  a  coordinate  species  from  immaterial  intelligences.  If,  on 
the  other  hand,  we  abstract  from  rational  being,  then  man  will 
stand  as  a  species  in  subordination  to  the  genus  animal,  having  for 
a  coordinate  species  irrational  animal.  Such  is  the  process  of 
Generification.     ISTow  for  the  converse  process  of  Specification. 

Every  series  of  concepts  which  has  been  obtained  by  abstraction, 
may  be  reproduced  in  an  inverted  order,  when. 

Specification.  i  -■•         r  .,        v..    .  •  i 

descending  irom  the  highest  notion,  we,  step  by 
step,  add  on  the  several  characters  from  which  we  had  abstracted  in 
our  ascent.  This  process,  as  you  remember,  is  called  Determina- 
tion; —  a  very  appropriate  expression,  inasmuch  as  by  each  charac- 

1  See  above,  p.  87  et  stq.  —  Ed. 

18 


138  LOGIC.  Lect.  XL 

ter  or  attribute  which  we  add  on,  we  limit  or  determine,  more  and 
more,  the  abstract  vagueness  or  extension  of  the  notion ;  until,  at 
last,  if  every  attribute  be  annexed,  the  sum  of  attributes  contained 
in  the  notion  becomes  convertible  with  the  sum  of  attributes  of 
which  some  concrete  individual  or  reality  is  the  complement.  Now, 
when  we  determine  any  notion  by  adding  on  a  suboi'dinate  concept, 
we  divide  it ;  for  the  extension  of  the  higher  concepts  is  precisely 
equal  to  the  extension  of  the  added  concept  plus  its  negation.  Thus, 
if  to  the  concept  animal  we  add  on  the  next  lower  concept  ratiom  I, 
we  divide  its  extension  into* two  halves,  —  the  one  equal  to  rational 
animal — the  other  equal  to  its  negation,  that  is,  to  irrational  ani- 
7nal.  Thus  an  added  concept  and  its  negation  always  constitute  the 
immediately  lower  notion,  into  which  a  higher  notion  is  divided. 
But  as  a  notion  stands  to  the  notions  proximately  subordinate  to  it, 
in  the  immediate  relation  of  a  genus  to  its  species,  the  process  of 
Determination,  by  which  a  concept  is  thus  divided,  is,  in  logical 
language,  appropriately  denominated  Specification. 

So  much  in  general  for  the  Subordination  of  notions,  considered 
as  Genera  and  Species.  There  are,  however,  various  gradations  of 
this  relation,  and  certain  terms  by  which  these  are  denoted,  which 
it  is  requisite  that  you  should  learn  and  lay  up  in  memory.  The 
most  important  of  these  are  comprehended  in  the  following  para-> 
gi-aph : 

%  XXXVI.     A  Genus  is  of  two  degrees,  —  a  highest  and  a 
lowei".     In  its  highest  degree,  it  is  called 

Par  XXXVI.  Orada-  ,,  fv  i^  ^  t^ 

tions  of  Genera  and  the  Supreme  or  Most  (jrcneral  Genus  {ytvot 
Species,  and  their  des.  ycviKWTaTov,  ffe?ius  »umm,um,  OY  generalissi- 
mum),  and  is  defined,  "that  which  being  a 
genus  cannot  become  a  si)ecies."  In  its  lower  degree,  it  is 
called  a  Subaltern  or  Intermediate  (ycvos  vTraXkqKov^  genus  sub- 
altevnum  or  m,edium)y  and  is  defined,  "  that  which  being  a 
genus  can  also  becoine  a  species."  A  Species  also  is  of  two 
degrees,  —  a  lowest  and  a  higher.  In  its  lowest  degree,  it  is 
called  a  lowest  or  Jlost  Special  Species  (JSo?  tiSiKwraToi',  species 
infima,  ultima^  or  specialissima),^  and  is  defined,  "  that  which 
being  a  species  cannot  become  a  genus."  In  its  higher  degree, 
it  is  called  a  Subaltern  or  Intermediate  Species  (eiSos  trTroXXi^Xov, 
species  subalterna  media),  and  is  defined,  "  that  which  being  a 
.species  may  also  become  a  genus."  Thus  a  Subaltern  Genus 
and  a  Subaltern  Species  are  convertible. 

I  vide  Timpler,  p.  ?68  [TogiV*  Ft/stftra,  L  ii  c.  J.q.  16— Ed.] 


Lect.  XI.  LOGIC  139 

The  distinctions  and  definitions  in  this  paragraph  are  taken  from 
the  celebrated  Introduction  ^  of  Porphyry  to  the 
Categories  of  Aristotle,  and  they  have  been  gen- 
erally adopted  by  logicians.  It  is  evident,  that  the  only  absolute 
distinction  here  established,  is  that  between  the  Highest  or  Supreme 
Genus  and  the  Lowest  Species ;  for  the  other  classes  —  to  wit,  the 
Subaltern  or  Intermediate  —  are,  all  and  each,  either  genera  or 
species,  according  as  we  regard  them  in  an  ascending  or  a  descend- 
ing order, — the  same  concept  being  a  genus,  if  considered  as  a 
whole  containing  under  it  inferior  concepts  as  parts,  and  a  species, 
if  considered  as  itself  the  part  of  a  higher  concept  or  whole.  The 
distinction  of  concepts  into  Genus  and  Species,  into  Supreme  and 
Intermediate  Genus,  into  Lowest  and  Intermediate  Species,  is  all 
that  Logic  takes  into  account ;  because  these  are  all  the  distinctions 
of  degree  that  are  given  necessarily  in  the  form  of  thought,  and  as 
abstracted  from  all  determinate  matter. 

It  is,  however,  proper  here  to  say  a  word  in  regard  to  the  Cat- 
egories or  Predicaments  of  Aristotle.   These  are 
Categories  of  Aris-       ^^^  ^^^^^^^  ^^^^  ^^^^^  Existence  is  divided,— 

totle. 

viz.,  1,  Substance;  2,  Quantity;  3,  Quality;  4, 
Relation  ;  5,  Action ;  6,  Passion ;  7,  Where ;  8,  When ;  9,  Posture ; 
and  10,  Habit.  (By  this  last  is  meant  the  relation  of  a  containing 
to  a  contained.)  They  are  comprehended  in  the  two  following 
verses : 

Arbor,  sex  servos,  fervore,  refrigerat  ustos, 
Ruri  eras  stabo,  nee  tunicatus  ero.2 

In  regard  to  the  meaning  of  the  word  category,  it  is  a  term  bor- 
rowed from  the  courts  of  law,  in  which  it  lit- 
Originai   meaning       erally  signifies  an  accnsatioji.    In  a  philosophical 
and  employment   of      application,  it  has  two  meanings,  or  rather  it  is 

the  term  category.  *  ^       ^  ,  *^. 

used  in  a  general  and  m  a  restricted  sense.  In 
its  general  sense,  it  means,  in  closer  conformity  to  its  original  ap- 
plication, simply  a  predication  or  attribution,'  in  its  restricted 
sense,  it  has  been  deflected  to  denote  predications  or  attributions 
of  a  very  lofty  generality,  in  other  words,  certain  classes  of  a  very 
wide  extension.  I  may  here  notice,  that,  in  modern  philosophy,  it 
has  been  very  arbitrarily,  in  fact  very  abusively,  perverted  from 
both  its  primary  and  its  secondary  signification  among  the  ancients. 
Aristotle  first  employed  the  term  (for  the  supposition  that  he  bor- 

1  C  ii.,  §§  23,  28,  29.  Facciolati,  LogUa,  [t.  i.,  Rudimenta  iMgica,  V. 

2  Murmellii  Isagoge,  c.  i.     Vide  Micralius      I.  c.  iii.  p.  32.  —  Ed.] 
{Lex.   Phil.   V.    Prtedkamenta-      Eo.]  p.    1086. 


140 


LOGIC. 


Lkct.  XL 


rowed  his  categories,  name  and  thing,  from  the  Pythagorean  Archy- 
las  is  now  exploded  —  the  treatise  under  the  name  of  this  philos- 
opher being  proved  to  be  a  comparatively  recent  forgery'),  —  I 
say,  Aristotle  first  employed  the  term  to  denote  a  certain  classifica- 
tion, a  posteriori,  of  the  modes  of  objective  or  real  existence;^  and 
the  word  was  afterwards  employed  and  applied  in  the  same  manner 
by  Plotinus,'  and  other  of  the  older  philosophers. 
By  Kant*  again,  and,  in  conformity  to  his  ex- 
ample, by  many  other  recent  philosophers,  the 
word  has  been  usurped  to  denote  the  a  priori  cognitions,  or  fun- 
damental forms  of  thought.  Nor  did  Kant  stop  here ;  and  I  may 
explain  to  you  the  genealogy  of  another  of  his 
/expressions,  of  which  I  see  many  of  his  German 
disciples  are  unaware.  By  the  Schoolmen, 
whatever,  as  more  general  than  the  ten  cate- 
gories, could  not  be  contained  under  them,  was 
said  to  rise  beyond  them  —  to  transcend  them ;  and,  accordingly, 
such  terras  as  being,  one,  ichole,  good,'  etc.,  were  called  transcendent 
or  transcendental  {transcendentia  or  transcendentalia')?  Kant,  as 
he  had  twisted  the  term  category,  twisted  also  these  correlative 
expressions  from  their  original  meaning.  He  did  not  even  employ 
the  two  terms  transcendent  and  transcendental  jxs  correlative.     The 


Kant's  employment 
of  the  term. 


Transcendent  and 
Transcen/ientai,  —  their 
original  employment 
and  use  by  Kant. 


1  See  Discussions,  p.  140.  —  Ed. 

2  See  especially  Metaph.,  iv.  7.  In  the  trea- 
tise specially  devoted  to  them,  the  Cetepories 
are  viewed  rather  in  a  grammatical  than  iu  a 
metaphysical  aspect.  —  Ed. 

3  Enn.  VI.,  1.  i.,  c.  i.  — Ed. 

■4  Kritik.d.  r.  V.,  p.  78  (ed.  Rosenkranz),  Pro- 
eegoinena,  §  39.  —  Ed, 

fi  [Sec  Facciolati,  Rud.,  p.  39;  and  Inst.,  p. 
26.]  [Lo^ca,  t.  i.,  Rudimenta  Logica,  P.  I.,  c. 
iv.,  (  7.  "  Aliud  est  categoricum,  quod  significat 
ccrtam  quamdam  rem  catcgoria  comprchen- 
8nm:  aliud  vagum,  quod  nulla  categoria  con- 
tinetur,  sed  per  omucs  vagatur,  cujusmodi 
sunt  essentia,  bonitas,  ordo,  et  similia  multa." 
Ldgica,  t.  ii.,  Institutiones  Logicm,  P.  I.,  c.  ii. 
"  Sunt  qusedam  vocabula,  quae  vaga  et  (ran- 
jc^n(/en<iadicuntur:  quod  genus  quodlibetex- 
supcrent  in  omni  categoria.  Uujusmodi  sunt 
tns,  aliquid,  res,  wnum,  vertim,  bonum."  Cf. 
Reid^s  Works,  p.  687  note  §.  — Ed.] 

Excluded  from  the  Aristotelic  Categories, 
all  except  the  following: 

Ex  parte  vocis  —  "  Vox  una  et  simplex,  re- 
bus concinna  locandis." 

K.v  ]-arto  rci  —  "  Entia  per  scsc,  finita,  ri-alia, 
tota." 

See   others   in   HurincUius,   Isagoge,  c.    i.  J 


Sanderson,  p.  20,  [Murmellius  gives  as  his 
own  the  verses  — 

Complexum,  Consignlficans,  Fictum,  Poly- 
semum. 
Vox  logicse,  Deus,  Ezcedens,  Priratio,  Pars- 

.que, 
Haec,  studiose,  categoriis  non  accipiuntur. 
And  Sanderson  [Logica,  L.  i.  c.  viii.),  after 
citing  the  mnemonic  of  the  Categories  them- 
selves, adds,  "In  aliqua  istarum  classium 
quicquid  uspiam  rerum  est  collocatur;  mode 
sit  unum  quid,  reale,  completum,  limitatepgue  ac 
Jinita,  natitrct.  Exttlant  ergo  his  sedibus  In- 
ttntiones  Seeundae,  Privationes,  et  Ficta,  quia 
non  sunt  realia;  Concreta,  Er/uivoca,  et  Com- 
plexa,  quia  non  sunt  una;  Pars,  quia  non  est 
completum  quid;  Deus,  quia  non  est  finite; 
Tranacendens,  quia  non  est  limitatae  natune. 
Hinc  versiculi : 

Complexum,  Consign iflcans,  Privatio,  Fic- 
tum, 

Pars,    Deus,    iE/quivocum,    Transcendeos, 
Ens  rationis: 

Sunt  exclusa  decern  classibus  Ista  novem."' 
—  Ed.] 
[That  the  Categories  of  Aristotle  are  not  ap- 
plicable to  God,  see  (Pseudo)  Augustin,  D* 
Cognition*  Vera  Vila,  c.  iii.] 


Lkct.  XL  L-OGIC.  141 

latter  he  applied  as  a  synonym  for  a  priori,  to  denote  those  elements 
of  thought  which  were  native  and  necessary  to  the  mind  itself,  and 
which,  though  not  manifested  out  of  experience,  were  still  not  con- 
tingently derived  from  it  by  an  a  posteriori  process  of  generaliza- 
tion. The  term  transcendeiit,  on  the  contrary,  he  applied  to  all 
pretended  knowledge  that  transcended  experience,  and  was  not 
given  in  an  original  principle  of  the  mind.  Transcendental  he  thus 
applied  in  a  fovorable,  transcendeiit  in  a  condemnatory  accepta- 
tion.^    But  to  return  from  this  digression. 

The  Categories  of  Aristotle  do  not  properly  constitute  a  logical^ 

but  a  metaphysical,  ti'eatise  ;  and  they  are,  ac- 

categories  of  Aris-       pordingly,   not    Overlooked    in    the   Aristotelic 

totle  Sletaphysical.  °  •' 

books  on  the  First  Philosophy,  which  have  ob- 
tained the  name  of  Metaphysics  {to.  pxra  ra  (fiva-iKa).  Their  insertion 
in  the  series  of  the  surviving  treatises  of  Aristotle  on  a  logical 
argument,  is,  therefore,  an  error.^ 

But,  looking  at  these  classes  as  the  highest  genera  into  which 
simple  being  is  divided,  they  are,  I  think,  obnoxious  to  various  ob- 
jections.  Without  pausing  to  show  that  in  other 
Categories  criticized       j-gspects  they  are  imperfect,  it  is  manifest  that 

as  a  classification   of  ,  t-,  . 

Bgi^  the    supreme  genus   or   category  Being  is  not 

immediately  divided  into  these  ten  classes,  and 
that  they  neither  constitute  coordinate  nor  distinct  species.  For 
Being  (to  ov,  ens^  is  primarily  divided  into  Being  by  itself  (ens  per 
se),  and  Being  by  accideti.t  (ens  per  accidens).  Being  by  itself  corre- 
sponds to  the  first  Category  of  Aristotle,  equivalent  to  substance; 
Being  by  accident  comprehends  the  other  nine,  but  is,  I  think,  more 
properly  divided  in  the  following  manner  :  —  Beitig  by  accident  is 
viewed  either  as  absolute  or  as  relative.  As  absolute,  it  flows  either 
from  the  matter,  or  from  the  form  of  things.  If  from  the  matter, 
it  is  Quantity,  Aristotle's  second  category ;  if  from  the  form,  it  is 
Quality,  Aristotle's  third  category.  As  relative,  it  corresponds  to 
Aristotle's  fourth  category.  Relation  ;  and  to  Relation  all  the  other 
six  may  be  reduced.  For  the  category  Where  is  the  relation  of  a 
thing  to  other  things  in  space;  the  category  When  is  the  relation  of 
a  thing  to  other  things  in  time.  Action  and  Passion  constitute  a 
single  relation,  —  the  relation  of  the  agent  and  the  patient.  Posture 
is  the  relation  of  the  parts  of  the  body  to  each  other;  finally,  Habit 

1  Kriiih  d.  r.  V.,  p.  240,   edit.  Rosenkranz.         3  With  this  classification  of  the  Categories, 
Ed.  compare  Aquina.'s,    In   Arist.    MetapJi.,  h.   v. 

2  That  the  Categories  of  Aristotle  are  not     lect.    9.     Suarez,   Dispuiationes    Metaphysiae. 
logical  but  metaphysical,  see   C.   Carleton;      Disp.  39,  §§  12, 15.  —  Ed. 

rrhomas  Compton  Carleton,  Philosophia,  Uni- 
versa,  Disp.  Met.  d.  vi.  §  1.  —  Ed.] 


142 


LOGIC. 


Lect.  Xl 


is  the  relation  of  a  thing  containing  and  a  thing  contained.  The 
little  I  have  now  said  in  regard  to  the  categories  of  Aristotle  is 
more,  perhaps,  than  I  was  strictly  warranted  to  say,  considering, 
them,  as  I  do,  as  wholly  extralogical,  and  I  have  merely  referred  to 
them  as  exhibiting  an  example  of  the  application  of  the  doctrine 
of  classification.^ 

I  may,  likewise,  notice,  by  the  way,  that  in  the  physical  sciences  of 
arrangement^  the  best  instances  of  which  are  seen 
in  the  different  departments  of  Natural  History, 
it  is  found  necessary,  in  order  to  mark  the  relative 
place  of  each  step  in  the  ascending  and  descend- 
ing series  of  classes,  to  bestow  on  it  a  particular 
designation.  Thus  kingdom^  class,  order,  tribe^ 
family,  genus,  subgenus,  species,  subspecies,  variety,  and  the  like,  are 
terms  that  serve  conveniently  to  mark  out  the  various  degrees  of 
generalization,  in  its  application  to  the  descriptive  sciences  of  na- 
ture. With  such  special  applications  and  contingent  differences, 
Logic  has,  however,  no  concei-n.  I  therefore  proceed  to  the  last 
relative  denomination  of  concepts  under  the  head  of  Subordination 
in  Extension.    It  is  expressed  in  the  following  paragraph : 


Names  for  the  differ- 
ent steps  in  the  series 
of  classes  in  the  physi- 
cal sciences  of  ar- 
rangement. 


%  XXXVII.  A  genus  as  containing  under  it  species,  or  a 
species  as  containing  under  it  individuals,  is 
called  a  Logical,  or  Universal,  or  Sub)ect, 
or  Subjective,  or  Potential  Whole ;  while 
species  as  contained  under  a  genus,  and  in- 
dividuals as  contained  under  a  species,  are  called  Logical,  or 
Universal,  or  Subject,  or  Subjective,  or  Potential  Parts.    E  con- 


Par.  XZZVn.  Loari- 
oal  and  Metaphysical 
Wholes  and  Farts. 


1  There  is  nothing  in  regard  to  which  a 
greater  diversity  of  opinion  lias  prevailed, 
even  among  Logicians,  th.-iu  the  number  of 
Categories.  For  some  alio w  only  two  —  Sub- 
stance and  Mode;  others  three  —  Substance, 
Mode,  and  Relation ;  others  four  —  Mind, 
Space,  Matter,  and  Motion;  others  seven 
which  are  comprehended  in  the  following 
distich : 
"  JW«n,t,  yirmway  Quits,  Motus,  Positura,  Fig- 

ura, 
Crassaque  Materies,  dederunt  exordia  rebus." 
Second  line  better  — 

"  Sunt  cum  Materia,  cunctarum  exordia  re- 
rum." 

AristotWs  Logic,  c.  ii.  H  1)2;  Reiifs  Account 
of,  Works,  p.  6S5  ft  sfq.  See  Facciolati,  Logica, 
t.  i.  Rudimenla  Logica,  V.  I.,  c.  iii.  p.  32. 
Purohot,  Imtit.  Philos.,  t.  i.    Logica,  p.  82,  ed. 


1716.  Cbauvin,  Lexicon  Philosopkieum,  v.  Cate- 
gorema.  [For  various  attempts  at  reduction 
and  classification  of  the  categories,  see  IMoti- 
nus,  Ennend ,  VI.  L.  ii.,  c.  8  et  seq.  (Tenne- 
mann,  Gesch.  der  Phil.,  vi.,  p.  175  et  ug.)  Da- 
vid  the  Armenian,  in  Brandis,  Scholia  ad 
Arisiot.,  p.  49.  Ramus,  Animad.  Aristot.  [L. 
iv.,  p.  80  et  seq.,  ed.  1560,  Ed.]  Jo.  Picua  Mi- 
randulanus.  Conclusions,  Opera,  p.  90,  ed. 
Basil,  1572;  Laurentius  Valla,  [Wa/uctiVo!  Dis- 
putationes,  cc.  i.  ii. —  Ed.]  Eugenics,  Aoyuci) 
p.  125  et  seq.  On  categoric  tables  of  various 
authors,  see  Denzinger,  Jnst.  Log  ,  ii.  ^  606,  p. 
55.  On  history  of  categories  in  antiquity,  sec 
Petersen,  Chrysippem  Phil.  Fundamenta,  p.  1 
et  ftq.  For  the  doctrines  of  the  Platonists 
and  Stoics  on  the  subject  of  the  Categories, 
see  Facciolati,  Inst.  Log.,  [Logira  t.  ii.,  p.  il  , 
p.  84  et  seq.  Cf  Trendelenburgh,  OtsekichU 
der  KatfgoritnXehre,  pp.  251,  267.—  Ed.] 


I 


Lect.  XI.  LOGIC.  143 

verso,  —  an  individual  as  containing  in  it  species,  or  a  species  as 
containing  in  it  genera,  is  called  a  Metaphysical  or  Formal  or 
Actual  Whole  ;  while  species  as  contained  in  an  individual,  and 
genera  as  contained  in  species,  are  called  Metaphysical,  or  For- 
mal, or  Actual  Parts}  This  nomenclature,  however,  in  so  far  as 
metaphysical  is  opposed  to  logical,  is  inept ;  for  we  shall  see 
that  both  those  wholes  and  parts  are  equally  logical,  and  that 
logicians  have  been  at  fault  in  considering  one  of  them,  in  their 
doctrine  of  reasoning,  to  the  exclusion  of  the  other. 

A  whole  is  that  which  contain^  parts ;  a  part  is  that  which  is 
contained  in  a  whole.     But  as  the  relation  of  a 

EbcpHcation.  i     ,  t  •  i      •  i  t 

whole  and  parts  is  a  relation  dependent  on  the 
point  of  view  from  which  the  mind  contemplates  the  objects  of  its 
knowledge,  and  as  there  are  different  points  of  view  in  which  these 
may  be  considered,  it  follows  that  there  may  also  be  different  wholes 
and  parts.  Philosophers  have,  accordingly,  made  various  enumera- 
tions of  wholes  ;  and,  without  perplexing  you  with  any  minute  dis- 
cussion of  their  various  divisions,  it  may  be  proper,  in  order  to 
make  you  better  aware  of  the  two  wholes  with  which  Logic  is  con- 
versant, —  (and  that  there  are  two  logical  wholeg,  and  consequently, 
two  grand  forms  of  reasoning,  and  not  one  alone,  as  all  logicians 

have  hitherto  taught,  I  shall  hereafter  endeavor 
General   view  of       ^^^  convince  you),  —  to  this  end,  I  say,  it  may  be 

the    various    possible  ,.  .  ■,       •  ^    ■, 

Yf\io\ee,  expedient  to   give  you  a  general  view  oi  the 

various  wholes  into  which  the  human  mind  may 
group  up  the  objects  of  its  speculation. 

Wholes  may  first  be  divided  into  two    genera,  —  into  a  Whole 

by  itself  {totum  per  se),  and  a  Whole  by  acci- 
Whoie  eracciutn^^        dent  {totuni  per  accidens).     A  Whole  per  se  is 

that  which  the  parts  of  their  proper  nature 
necessarily  constitute ;  thus  body  and  soul  constitute  the  man.  A 
Whole  per  accidens  is  that'which  the  parts  make  up  contingently ; 
as  when  man  is  considered  as  made  up  of  the  poor  and  the  rich. 
A  Whole  per  se  may,  again,  be  subdivided  into  five  kinds,  into  a 

Logical,  a  Metaphysical,  a  Physical,  a   Mathe- 
whoie per^e divided       niatical,  and  a  Collective.     1°,  A  Logical,  styled 

into,  1°,  Logical;    2°,  ,  '      .  ,  ^    ,  .  o    ,  •        •  V. 

Metaphysical.  ^^^^  ^  Universal,  a  subject  or  Subjective,  a  Po- 

tential Whole ;  and,  2°,  A  Metaphysical,  styled 
also  a  Formal  or  an  Actual  Whole,  —  these  I  have  defined  in  the  j)ara- 

1  See  Timpler,  iog-ica,  [p.  232  er  seq.\  Fac-  ica  Restituta,  P.  III.,  c.  ii.,  §  2,  ed.  Generse, 
siolati,  [Logica,  t.  i.,  Rudimenta  Logica,  P.  II.,  16G8.  —  Ed.]  Burgersdyk,  [Institutionei  Log- 
c.  vi.,  p.  51,  52.  —  Ed.]    Derodon,  p.  447  [Log-     icm,  p.  51  —  Ed.] 


144  LOGIC.  Lect.  XI. 

graph.  It  is  manifest  that  the  logical  and  metaphysical  wholes  are 
the  converse  of  each  otiier.  For  as  the  logical  whole  is  the  genus, 
the  logical  parts  the  species  and  individual ;  in  the  metaphysical, 
e  contra^  an  individual  is  the  whole  of  which  the  species,  a  species  the 
whole  of  which  the  genera,  are  the  parts.  A  metaphysical  whole  is 
thus  manifestly  the  whole  determined  by  the  comprehension  of  a 
concept,  as  a  logical  Avhole  is  that  M'hole  determined  by  its  exten- 
sion ;  and  if  it  can  be  shown  that  the  whole  of  comprehension 
affords  the  conditions  of  a  process  of  reasoning  equally  valid, 
equally  useful,  equally  easy,  and,  to  say  the  least  of  it,  equally  natu- 
ral, as  that  afforded  by  the  w4iole  of  the  extension,  it  must  be 
allowed  that  it  is  equally  well  entitled  to  the  name  of  a  logicnl 
whole,  as  the  whole  which  has  hitherto  exclusively  obtained  that 

denomination.     3°,  A  Physical,  or,  as  it  is  like- 
so,  Physical.  .  „     ,  ^  '         .    ,  *'__,     ,       .       ,  ,  .   , 

Wise  called,  an  Essential  Whole,  is  that  which 

consists  of  matter  and  of  form,  in  other  words,  of  substance  and  of 

.„  „   ^      ,.    ,  accident,  as  its   essential  parts.     4°,  A  Mathe- 

4°,  Mathematical.  '  .  .  *^  ' 

matical,  called  likewise  a  Quantitative,  an  In- 
tegral, more  properly  an  Integrate,  Whole  {totum  integratutn),  is 
that  which  is  composed  of  integral,  or,  more  properly,  of  integrant 
parts  (partes  integrantes).  In  tliis  whole  every«part  lies  out  of  every 
other  part,  whereas,  in  a  physical  whole,  the  matter  and  form,  the 
substance  and  accident,  permeate  and  modify  each  other.  Thus,  in 
the  integrate  whole  of  a  human  body,  the  head,  body,  and  limbs,  its 

integrant  parts,  are  not  contained  in,  but  each  lies 
6°,  Collective.  °.        \        ,  r„    .   ^   „        .  ,    ,     , 

out  01,  each  other,    o  ,  A  Collective,  styled  also  a 

Whole  of  Aggregation,  is  that  which  has  its  material  parts  separate 
and  accidentally  thrown  together,  as  an  army,  a  heap  of  stones,  a 
]ule  o.f  wheat,  etc' 

But  to  proceed  now  to  an  explanation  of  the  terras  in  the  para- 
graph last  dictated.  Of  these,  none  seem  to  require  any  exposition, 
save  the  words  subjective  and  potential^  as  synonyms  applied  to  a 
Logical  or  Universal  whole  or  parts. 

The  former  of  these,  —  the  term  subjective^  or  more  properly  sub- 
ject, as  applied  to  the  species  as  parts  subjacent 
The  terms  .ii/ft/^rt  and       ^^^  q,.  lying  under,  a  geiius,  — to  the  individuals, 

subjective  as  applied  to  ^  i  •  ^    ^  i    •  j 

.  .  ,       as  parts  subjacent  to,  or  lying  under,  a  species, 

p„,t8.  is  a  clear  and  appro]^riate  expression.     But,  as 

applied  to  genus  or  species,  considered  as 
wholes,  the  term  subject  is  manifestly  improper,  and  the  term  sub- 
jective hardly  defensible.     In  like  manner,  the  term  universal,  as 

1  See  above,  p.  143,  note.  — Ed. 


^^v^r.  XI.  LOGIC.  145 

applied  to  genus  or  species,  considered  as  logical  wholes,  is  correct ; 
but  as  applied  to  individuals,  considered  as  logical  parts,  it  is  used 
in  opposition  to  its  proper  meaning.  The  desire,  however,  to  obtain 
epithets  common  both  to  the  parts  and  to  the  whole,  and  thus  to 
indicate  at  once  the  relation  in  general,  has  caused  logicians  to  vio- 
late the  proprieties  both  of  language  and  of  thought.  But  as  tljo 
terms  have  been  long  established,  I  think  it  sufficient  to  put  you  on 
your  guard  by  this  observation. 

In  regard  to  the  term  jyotential,  —  I  shall,  before  saying  anything, 

read  to  you  a  passage  from  the  Antient  Meta- 

The  term  poifnuai.      physics  of  the  learned  Lord  Monboddo.^     "  In 

J^rd  Monboddo  quo-         ^,        />      ^      i  •.    •      •  -ui       i.      ^t,  x  c 

the  nrst  place,  it  is  impossible,  by  the  nature  of 
things,  that  the  genus  should  contain  the  species 
as  a  part  of  it,  and  the  species  should  likewise  contain  the  genus,  in 
the  same  respect.     But,  in  different  respects,  it  is  possible  that  each 
of  them  may  contain  the  other,  and  be  contained  by  it.     We  mnst,. 
therefore,  try  to  distinguish  the  different  manners  of  containing,  and 
being  contained.     And  there  is  a  distinction  that  runs  throusrh  the 
whole   of    ancient   philosophy,  solving   many   difficulties   that   are 
otherwise  unsurmountable,  and  which,  I  hope,  Avill  likewise  solve 
tliis  difficulty.     The  distinction  I  mean  is  the  distinction  betwixt - 
what  exists  8waju,ei,  or  potentially  only,  and  that  which  exists  ti'cpyeio,. 
or  actually.     In  the  first  sense,  everything  exists  in  its  causes;  and,, 
in   the  other  sense,  nothing  exists  but  what  is  actually  produced.. 
Now,  in  this  first  sense,  the  whole  species  exists  in  the  genus ;  for 
the  genus  virtually  contains  the  whole  species,  not  only  what  actu- 
ally exists  of  it,  but  what  may  exist  of  it  in  any  future  time.     In 
the  same  manner,  the  lowest  species,  below  which  there  is  nothing- 
but  individuals,  contains  virtually  all  those  individuals,  present  and 
future.     Thus,  the  species  man  comprehends  all  the  individuals  now 
existing,  or  that  shall  hereafter  exist;  Avhich,  therefore,  are  said  to* 
be  parts  of  the  species  man.     On  the  other  hand,  the  genus  is  actu- 
ally contained  in  the  species ;  and  the  species,  likewise,  in  each  of 
the  individuals  under  it.     Thus,  the  genus  animal  is  actually  con- 
tained in  the  species  m,an.,  without  which  it  could  not  be  conceived 
to  exist.     And,  for  the  same  reason,  the  species  man  is  actually  con-- 
tained  in  each  individual.     It  is  a  piece  of  justice  which  I  think  I 
owe  to  an  author,  hardly  known   at   all  in  the  western  parts  of 
Europe,  to  acknowledge  that  I  got  the  hint  of  the  solution  of  this; 
difficulty  from  him.     The  author  I  mean  is  a  living  Greek  author, 
Eugenius  Diaconus,  at  present  Professor,  as  I  am  informed,  in  the 

1  Vol.  i.  p.  479. 

19 


14G  LOGIC.  Lect.  XL 

Patriarch's    University   at    Constantinople,   who    has    written    :in 
excellent  system  of  logic  in  very  good  Attic  Greek." 

This,  or  rather  a  similar  passage  at  p.  73  of  the  fourth  volume  of 

the  Antient  Metaphysics,  affords  Mr^  Stewart  an 

Stewart's  strictures       opportunity  of  making  sundry  unfavorable  stric- 

.  ijp^gjj  tures  on   the   technical   language   of  Logic,  in 

legard  to  which  he  asserts,  "  the  adepts  are  not, 
to  this  day,  unanimously  agreed ; "  and  adds,  that  "  it  is  an  extraor- 
dinary circumstance,  that  a  discovery  on  which,  in  Lord  Monbod- 
do's  opinion,  the  whole  truth  of  the  syllogism  depends,  should  be  of 
so  very  recent  a  date."^  Now  this  is  another  example  which  may 
.serve  to  put  you  on  your  guard  against  any  confidence  in  the  asser- 
tions and  arguments  even  of  learned  men.  You  may  be  surprised 
to  hear,  that  so  far  is  Eugenius  from  being  the  author  of  this  ob- 
servation, and  of  the  term  potential  as  applied  to  a  logical  whole, 
that  both  are  to  be  found,  with  few  exceptions,  in  all  the  older  sys- 
tems of  Logic.  To  quote  only  one,  but  one  of  the  best  and  best 
known,  that  of  Burgei"sdyck,  —  he  says,  speaking  of  the  logical 
whole :  "  Et  quia  universale  subjectas  species  et  individua  non  actii 
continet  sed  potentia ;  factum  est,  ut  hoc  totum  dictum  sit  totum  po- 
tentiale,  cum  ceterie  species  totius  dicantur  totum  acttiale,  quia  partes 
suas  actu  continent."^  Aristotle  notices  this  difference  of  the  two 
wholes.' 

Having  thus  terminated  the  consideration  of  concepts  as  recipro- 
cally related  in  the  perpendicular  line  of  Subordination,  and  in  the 
quantity  of  Extension,  in  so  far  as  they  are  viewed  as  containing 
classes,  —  I  must,  before  proceeding  to  consider  them  under  thiH 
quantity  in  the  horizontal  line  of  Coordination,  state  to  you  two 
terms  by  which  characters  or  concepts  are  denominated,  in  so  far  as 
they  are  viewed  as  differences  by  which  a  concept  is  divided  into 
two  subordinate  parts. 

%  XXXVIIL  The  character,  or  complement  of  characters,  by 

which   a  lower  genus  or  species  is  distin- 

par.xxxviu.  Gen-       jruishcd,  both  from  the  genus  to  which  it  is 

erio,  Speeiflo.  and  In-         °  .  ° 

dividual  Difference.  Subordinate,  and  from  the  other  genera  or 
species  with  which  it  is  coordinated,  is 
called  the  Generic  or  the  Specific  Difference  (8ta<^po  yevurfi, 
and  8ia<f>opa  (iBiKrj,  differentia  generica,  and  differentia  specijica). 
The  sum  of  characters,  again,  by  which  a  singular  or  individual 

1  EUmenti,  vol.  ii.,  c.  iii.,  S  1;   ITor*,*,  vol.  »  Vide  Timp'cr.  LngUa,  [L  II.  c.  I.  Dt  1>ut 
Mi ,  p  199  and  p.  200,  note.                                     ft  Parte.  —  Ei>.] 

2  Lib.  I.,  c.  xiv.,  p.  48,  ed.  16G0.  —  Kd. 


Lkct.  XI.  LOGIC.  147 

thing  is  discriminated  from  the  species  under  which  it  stands 
and  from  other  individual  things  along  with  which  it  stands, 
is  called  the  Individual  or  Singular  or  Numerical  Difference 
{differentia  individualis  vel  singiUaris  vel  numerica)} 

Two  things  are  thus  said  to  be  generically  different,  inasmuch  as 

they  lie  apart  in  two  different  genera;  specifi- 

p  ica  ion.  cally  different,  inasmuch  as  they  lie  apart  in  two 

different  species ;  individually  or  numerically  different,  inasmuch  as 

they  do  not  constitute  one  and  the  same  I'eality.     Thlis  animal  and 

stone  may  be  said  to  be  generically  different ;  horse  and  ox  to  be 

specifically  different ;  Highflyer  and  Eclipse  to 

Generic  and  Specific         ,  •      n  •     t    'j       n        j'/v.  ^        t^    • 

Difference  "®  numencally  or  mdividually  ditterent.     It  is 

evident,  however,  that  as  all  genera  and  species, 
except  the  highest  of  the  one  and  the  lowest  of  the  other  may  be 
styled  indifferently  either  genera  or  species,  generic  difference  and 
specific  difference  are  in  general  only  various  expressions  of  the  same 
thing;  and,  accordingly,  the  terms  heterogeneous  and  homogeneous^ 
which  apply  properly  only  to  the  correlation  of  genera,  are  usually 
applied  equally  to  the  correlation  of  species. 
"  Individual  existences  can  only  be  perfectly  discriminated  in  Per- 
ception, external  or  internal,  and  their  numerical 
Individual  or  Sin-       differences  are  endless  ;  for  of  all  possible  contra- 

Ijular  Difference.  '■ 

dictory  attributes  the  one  or  the  other  must,  on 
the  principles  of  Contradiction  and  Excluded  Middle,  be  considered 
as  belonging  to  each  individual  thing.  On  the  other  hand,  species 
and  genera  may  be  perfectly  discriminated  by  one  or  few  charac- 
ters. For  example,  m.an^  is  distinguished  from  eveiy  genus  or 
species  of  animal  by  the  one  character  of  rationality;  triangle^  from 
every  other  class  of  mathematical  figures,  by  the  single  character  of 
trilalerality.  It  is,  therefore,  far  easier  adequately  to  describe  a 
genus  or  species  than  an  individual,  existence  ;  as  in  the  latter  case, 
we  must  select,  out  of  the  infinite  multitude  of  characters  which  an 
individual  comprises,  a  few  of  the  most  prominent,  or  those  by 
which  the  thing  may  most  easily  be  recognized."^  But  as  those 
which  we  thus  select  are  only  a  few,  and  are  only  selected  with 
reference  to  our  faculty  of  apprehension  and  our  capacity  of  mem- 
ory, they  always  constitute  only  a  petty,  and  often  not  the  most 
essential  part  of  the  numerical  differences  by  which  the  individuality 
of  the  object  is  determined. 

Having  now  terminated  the  consideration  of  the  Subordination  of 

1  Krng,  Logfk,  i  46.  —  Ed.  a  Krug,  Log*, »  46,  p.  184-6.  —  Ed. 


LOGIC.  Lect.  XI. 

concepts  under  Extension,  it  is  only  necessary  to  observe  that  their 
Coordination  under  that  quantity  affords  nothing  which  requires 
explanation,  except  what  is  contained  in  the  following  paragraph  : 

%  XXXIX.  Notions,  in  so  far  as  they  are  considered  the 
coordinate  species  of  the  same  genus  may 
dS^tio^^^f  concSu."  ^6  ca"^  Conspecies  ;  and  in  so  far  ns  Con- 
species  are  considered  to  be  different  but 
not  contradictory,  they  aie  properly  called  Discrete  or  Dis- 
junct Nbtions  (notionea  discretes  vel  disjunctce).  The  term 
Disparate  {notiones  disparatce)  is  frequently  applied  to  this 
opposition  of  notions,  but  less  properly ;  for  this  ought  to  be 
reserved  to  denote  the  corresponding  opposition  of  notions  in 
the  quantity  of  Comprehension- 

I  conclude  the  consideration  of  concepts,  as  dependent  on  Exten- 
«on,  by  a  statement  of  the  two  general  laws,  by  which  both  Sub- 
ordination and  Coordination  of  notions,  under  tliis  quantity,  are 
regulated. 

^  XL.     The  whole  classification  of  things  by  Genera  and 

Species  is  governed  by  two  laws.     The  one 

p»r.  XL.       e  two       ^^  thcsc,  the  law  of  Honxoqaieitu  (prluci- 

general  laws  by  which  '  u  j     \x^ 

Subordination  and  Co-      piuTH  IIomogeneitatis\  is,  —  That  how  dif- 
ordination.nnder  Ex-      fgrent  socvcr   may   be   any  two   concepts, 

tension,  are   regtilat-  J  J  J       ' 

ed,-viE.,  of  Homoge-  they  both  Still  Stand  subordinated  under 
nS  '°'*  °'*"°*^"  some  higher  concept;  in  other  words,  things 
the  most  dissimilar  must,  in  certain  respects, 
be  similar.  The  other,  the  law  of  Heterogeneity  (pn'/tcipivm 
Ileterogeneitatis)^  is,  —  That  every  concept  contains  other  con- 
cepts under  it ;  and,  therefore,  when  divided  proximately,  we 
descend  always  to  other  concepts,  but  never  to  individuals;  in 
other  words,  things  the  most  homogeneous  —  similar — must, 
in  certain  respects,  be  heterogeneous  —  dissimilar. 

Of  these  two  laws,  the  former,  as  the  principle  which  enables, 

and  in  fact  compels,  us  to  rise  from  species  to 

Explication.  genus,  is  that  which  determines  the  process  of 

Geiieriflcation     and  .„.  ■,-,■,  i... 

speciflcation.  Gcnerification ;  and  the  latter,  as  the  pnnciple 

which  enables,  and  in  fact  compels,  us  to  find 
always  species  under  a  genus,  is  that  which  regulates  the  process  of 
Specification.  The  second  of  these  laws,  it  is  evident,  is  only  true 
ideally,  only  true  in  theory.     The  infinite  divisibility  of  concepts, 


Lect.  XL  LOGIC.  149 

like  the  infinite  divisibility  of  space  and  time,  exists  only  in  specula- 
tion.   And  that  it  is  theoretically  valid,  will  be 
Law  of    Ueteroge-       manifest,  if  we  take  two  similar  concepts,  that 
nei  y  rue  on  y  in  .^^  ^^^  concepts  witli  a  Small  difference :  let  us 

then  clearly  represent  to  ourselves  this  difference, 
and  we  shall  find  that  how  small  soever  it  may  be,  we  can  always 
conceive  it  still  less,  without  being  nothing,  that  is,  we  can  divide  it 
ad  infinitum;  but  as  each  of  these  infinitesimally  diverging  differ- 
ences affords  always  the  condition  of  new  species,  it  is  evident  that 
we  can  never  end,  that  is,  reach  the  individual,  except  per  saltum} 
There  is  another  law,  which  Kant  promulgates  in  the   Critique 
of  Pure  Meason'  and   which  may  be  called   the  law  of  Logical 
Affinity,  or  the  law  of  Logical  Continuity.     It 
aw  o     ogic       -       ig  tiiig^  —  That  no  two  coordinate  species  touch 
'^'  so  closely  on  each  other,  but  that  we  can  con- 

ceive other  or  others  intermediate.  Thus  man  and  orang-outang^ 
elephant  and  rhinoceros^  are  proximate  species,  but  still  how  great 
is  the  difference  between  them,  and  how  many  species  can  we  not 
imagine  to  ourselves  as  possibly  inteijacent? 

This  law  I  have,  however,  thrown  out  of  account,  as  not  univer- 
sally true.     For  it  breaks  down  when  we  apply 
Grounds  on  which       -^  j.^,  mathematical  classifications.     Thus  all  an- 

this  law  muBt  be  re-  ,  .  ,  ,  ...  ,  _> 

.   .  ,  gles  are  either  acute  or  right  or   obtuse,     hot 

j€cted.  '^  _  *  _ 

between  these  three  coordinate  species  or  genera 
no  others  can  possibly  be  interjected,  though  we  may  always  subdi' 
vide  each  of  these,  in  various  manners,  into  a  multitude  of  lower 
sjjecies.  This  law  is  also  not  true  when  the  coordinate  species  are 
distinguished  by  contradictory  attributes.  There  can  in  these  be 
no  interjacent  species,  on  the  principle  of  Excluded  Middle.  For 
example: — in  the  Cuvierian  classification  the  genus  animal  is 
divided  into  the  two  species  of  vertebrata  and  invertebrata,  that  is, 
into  animals  with  a  backbone  —  with  a  spinal  marrow ;  and  animals 
without  a  backbone  —  without  a  spinal  marrow.  Is  it  possible  to 
conceive  the  possibility  of  any  intermediate  class  ? ' 

I  Cf.  Krug,  Logik,  }  45  p.  135,  and  pp.  136,  3  Bachmann,  [Logik,  i  61,  pp.  102,  103.— 

137.  —  Ed.  Ed.]    [Compare  Fries,  Logik,  §  21.  —  Ed.] 

i  P.  510.  ed.  Boeenkranz,  C£  Kmg,  Logik, 
p.  138.— Ed. 


LECTURE    XII. 

STOICHEIOLOGY. 

SECTION   II.  — OF    THE    PRODUCTS  OF  THOUGHT. 

L  — ENNOEMATIC. 

m.  RECIPROCAL  RELATIONS  OF  CONCEPTS. 

B.   QUANTITY  OF   COMPREHENSION. 

Having  now  concluded  the  consideration  of  the  Reciprocal  Re- 
lation of  Concepts  as  determined  by  the  quantity 
Reciprocal  Relation       ^f  Extension,  I  proceed  to  treat  of  that  rela- 

of  notions  in  Compre-        ^.  i    ^    j    i        ^i.  ^  ^-^         i» 

tion  as  regulated  by  the  counter  quantity  of 


beusion. 

paragraph :  — 


Compreheiisiou.      On   this  take   the  following 


^  XLI.    When  two  or  more  concepts  are  compared  together 

according    to    their    Comprehension,   they 

Par.    xLi.   identi-       either  coincidc  or  they  do  not ;  that  is,  they 

cal  and  Different  no-  •  i  -i 

tions.  either  do  or  do  not  comprise  the  same  char- 

acters. Notions  are  thus  divided  into  Iden- 
tical and  Different  {conceptus  identici  et  diversi).  The  Iden- 
tical are  either  absolutely  or  relatively  the  same.  Of  notions 
Absolutely  Identical  there  are  actually  none ;  notions  Relatively 
Identical  are  called,  likewise,  Similar  or  Cognate  {notiones 
similes,  afflnes,  coynatw) ;  and  if  the  common  attributes,  by 
which  they  are  allied,  be  proximate  and  necessaiy,  they  are 
called  Reciprocating  or  Convertible  {notiones  reciprocce,  con- 
vertibiles)} 

In  explanation  of  this  paragraph,  it  is  only  necessary  to  say  a 
word  in   regard  to  notions  absolutely  Identical.     That   such  are 

1  [Esser,  Logik,  S  86.] 


Lect.  Xn.  LOGIC.  161 

impossible,  is  manifest.     "  For,  it  being   assumed  that  such   exist, 

as  absolutely  identical,  they  necessarily  have  no 

Explication.  differences  by  which  they  can  be  distinguished : 

Absolutely  Identical         v     ,       i     .  •     -i-  mi  i.     i  -iL 

...  but  what  are  indiscernible  can  be  known,  neither 

notions  impossible.  ' 

as  two  concepts,  nor  as  two  identical  concepts ; 
because  we  are,  ex  hypothesis  unable  to  discriminate  the  one  from 
the  other.  They  are,  therefore,  to  us  as  one.  Notions  absolutely 
identical  can  only  be  admitted,  if,  abstracting  our  view  altogether 
from  the  concepts,  we  denominate  those  notions  identical,  which 
have  reference  to  one  and  the  same  object,  and  which  are  conceived 
either  by  different  minds,  or  by  the  same  mind,  but  at  different 
times.  Their  difference  is,  therefore,  one  not  intrinsic  and  neces- 
sary, but  only  extrinsic  and  contingent.  Taken  in  this  sense,  Abso- 
lutely Identical  notions  will  be  only  a  less  correct  expression  for 
Heciprocating  or  Convertible  notions."  * 

\  XLII.  Considered  under  their  Comprehension,  concepts, 
again,  in  relation  to  each  other,  are  said  to 
.itiouo?cLep°r°"  ^e  either  Congruent  or  Agreeing,  inasmuch 
as  they  may  be  connected  in  thought ;  or 
Conflictive,  inasmuch  as  they  cannot.  >  The  confliction  consti- 
tutes the  Opposition  of  notions  (jo  avriKelcrSaL,  oppositio).  This 
is  twofold ;  —  1°,  Immediate  or  Contradictory  Opposition,  called 
likewise  Repugnance  (to  dvTi<^aTtKois  avriKv-d^ai,  dvTi</)ao-is,  opposi- 
tio immediata  sive  contradictoria,  repugnantia) ;  and,  2°,  Me- 
diate or  Contrary  Opposition  (to  ei/aKTiws  dvTUfcicr^ai,  cvavnoTiys, 
oppositio  mediata  A^el  contraria).  The  former  emerges  when 
one  concept  abolishes  (tollit),  directly  or  by  simple  negation, 
what  another  establishes  (jponit) ;  the  latter,  when  one  concept 
does  this  not  directly  or  by  simple  negation,  but  through  the 
aflSrmation  of  something  else.^ 

"  Identity  is  not  to  be  confounded  with  Agreement  or  Congru- 
ence, nor  Diversity  with  Confliction.     All  iden- 
Expiication.  tical  Concepts  are,  indeed,  congruent;   but  all 

dentrty  and  Agree-       congruent  notions  are  not  identical.   Thus  leam- 

ment,    Diversity    and  , 

Confliction.  ^'^9  ^'^•^  Virtue,  beauty  and  riches,  magnanimity 

and  stature,  are  congruent  notions,  inasmuch  as, 

in  thinking  a  thing,  they  can  easily  be  combined  in  the  notion  we 

form  of  it,  although  in  themselves  very  different  from  each  other. 

1  [Esser,  Logih,  \  36,  p.  79.]   Cf.  Kmg,  Logik,        2  Cf.  Drobisch,  Logik,  p.  17,  §  25  aeq. 
i  37,  and  Anm.  i.  — Ed. 


152  LOGIC.  Lect.  XII 

In  like  manner,  all  conflictive  notions  are  diverse  or  different  notions, 
for  unless  different,  they  could  not  be  mutually  conflictive ;  but  on 
the  other  hand,  all  different  concepts  are  not  conflictive  ;  but  those 
only  whose  difference  is  so  great  that  each  involves  the  negation  of 
the  other ;  as,  for  example,  virtue  and  vice,  beauty  and  deformity, 
wealth  and  poverty.  Thus  these  notions  are  by  preeminence, —  kut 
iio)(r]v,  —  said  to  be  opposed,  although  it  is  true  that,  in  thinking,  we 
can  opposcj  or  place  in  antithesis,  not  only  different,  but  even  iden- 
tical, concepts." 

"  To  speak  now  of  the  distinction  of  Contradictory  and  Contrary 
Opposition,  or  of  Contradiction  and  Contrariety ; 

Coutradictory     and  ^    ^i  ^i  /•  /-i       ^       j-    ^• 

„    ^       r,       :■  —  01    these    the    former  —  Contradiction  —  is? 

Contrary  Oppositiou. 

exemplified  in  the  opposites,  —  yellow,  not  yeL 
low,  walking,  not  walking.  Here  each  notion  is  directly,  inimedis 
ately,  and  absolutely,  repugnant  to  the  other,  —  they  are  reciprocal 
negatives.  This  opposition  is,  therefore,  properly  called  that  of 
Contradiction  or  of  Repugnance  /  and  the  opposing  notions  them- 
selves are  contradictory  or  repugnant  notions,  in  a  single  word,  con- 
tradictories. The  latter,  or  Contrary  Opposition,  is  exemplified  in 
the  opposites,  yellow,  blue,  red,  etc.,  walking,  standing,  lying,  etc." 

"In  the  case  of  Contradictory  Opposition,  there  are  only  two 
conflictive  attributes  conceivable ;  and  of  these  one  or  other  must 
be  predicated  of  the  object  thought.  In  the  case  of  Contrary  Oppo- 
sition, on  the  other  hand,  more  than  two  conflictive  characters  are 
possible,  and  it  is  not,  therefore,  necessary,  that  if  one  of  these  be 
not  predicated  of  an  object,  any  one  other  must.  Thus,  though  I 
cannot  at  once  sit  and  stand,  and  .consequently  sitting  and  standing 
are  attributes  each  severally  incompatible  with  the  other ;  yet  I  may 
exist  neither  sitting  nor  standing,  —  I  may  lie ;  but  I  must  either  sit 
or  not  sit,  I  must  either  stand  or  not  stand,  etc.  Such,  in  general, 
are  the  oppositions  of  Contradiction  and  Contrariety." 

"It  is  now  necessary  to  say  a  word  in  regard  to  their  logical  sig- 
nificance. Immediate  or  Contr;idictory  Oppo- 
Logicai  significance       g-^j^j^  constitutes,  in  Logic,  afiirmativc  and  neg- 

of  Contradictory  and  .  .  t\  i         r-  i  •  • 

Contriiry  Opposition.  ^^^e  notions.  By  the  former  somethmg  is 
posited  or  affinned  (ponitur,  affirmatur) ;  by 
the  latter,  something  is  sublated  or  denied  {tollitur,  negatur).  This, 
however,  is  only  done  potentially,  in  so  far  as  concepts  are  viewed 
apart  from  judgments,  for  actual  aftirmation  and  actual  negation 
suppose  an  act  of  judgment ;  but,  at  the  same  time,  in  so  far  as  two 
concepts  afford  the  elements,  and,  if  brought  into  relation,  necessi- 
tate the  formation  of  an  aflirmative  or  negative  proposition,  they 
may  be  considered  as  in  themselves  negative  and  aflirmative." 


Lect.  Xn.  LOGIC.  153 

"  Further,  it  is  evident  that  a  notion  can  only  be  logically  denied 
by  a  contradiction.  For  when  we  abstract  from  the  matter  of  a 
notion,  as  Logic  does,  it  is  impossible  to  know  that  one  concept 
excludes  another,  unless  the  one  be  supposed  the  negation  of  the 
other.  Logically  considered,  all  positive  or  affirmative  notions  are 
congruent,  that  is,  they  can,  as  far  as  their  form  is  concerned,  be  all 
conceived  or  thought  together;  but  whether  in  reality  they  can 
coexist  —  that  cannot  be  decided  by  logical  rules.  If,  therefore, 
we  would,  with  logical  precision  and  certainty,  oppose  things,  we 
must  oppose  them  not  as  contraries  {A  S  0),  but  as  contradicto- 
ries (A  —  not  A  JB  —  not  B  O — not  C).  Hence  it  also  follows, 
that  there  is  no  negation  conceivable  without  the  concomitant  con- 
ception of  an  affirmation ;  for  we  cannot  deny  a  thing  to  exist,  with- 
out having  a  notion  of  the  existence  which  is  denied."  ^ 

There  are  also  certain  other  relations  subsisting  between  notions, 
compared  together  in  reference  to  their  Comprehension. 

%  XLIII.    Notions,  as  compared  with  each  other  in  respect 
of  their  Comprehension,  are  further  distin- 
Bion'otioDB  '  '       guished  into  Intrinsic  and  Extrinsic.     The 

former  are  made  up  of  those  attributes 
which  are  essential,  and,  consequently,  necessary  to  the  object 
of  the  notion :  these  attributes,  severally  considered,  are  called 
Essentials^  or  Internal  Denominations  (oiauLSr],  essentialia,  de- 
nominationes  internee,  intrinsicce),  and,  conjunctly,  the  Essence 
(ova-Lo,  essentia).  The  latter,  on  the  contrary,  consist  of  those 
attributes  which  belong  to  the  object  of  the  notion  only  in  a 
contingent  manner,  or  by  possibility ;  and  which  are,  therefore, 
styled  Accidetits,  or  Extrinsic  Denominations  (a-vfiPe^rjKOTOy 
accidentia,  denomi?iationes  externce  or  extrinsicce).^ 

So  much  for  the  mutual  relations  of  notions  in  reference  to  their 
Comprehension,  when  considered  not  in  the  relations  of  Involution 
and  Coordination. 

Having  thus  given  you  the  distinctions  of  no- 

invoiution  and  Co-       tions,  as  founded  on  their  more  general  relations 

ordination  of  Concepts       ^^der  the   quantity  of  Comprehension,  I  now 

under        Comprehen-  -  •  i  i  t  i  • 

sion,— these    wholly       proceed  to  Consider  them  under  this  quantity 
neglected  by  logicians.       in  their  proximate  relations;  that  is,  in  the  rela- 
tion of  Involution  and  the  relation  of  Coordi- 
nation.    These  relations  have  been,  I  may  say,  altogether  neglected 

1  Krug,  Log^,  p.  118—120.  —Ed.  S  Krug,  Logik,  J  39.— Ed. 

20 


164  LOGIC.  Lect.  xn 

by  logicians;  and,  in  consequence  of  this,  they  have  necessarily 

overlooked  one  of  the  two  great  divisions  of  all 

Hence  reasoniDg  in      reasoning ;  for  all  our  reasoning  is  either  from 

comprehension    over-  i  i     i  i  i   /.  »  i 

looked  by  logicians.  ^^^  ^hole  to  the  parts  and  from  the  parts  to  the 
whole,  in  the  quantity  of  extension,  or  from  the 
whole  to  the  parts  and  from  the  parts  to  the  whole,  in  the  quantity 
of  comprehension.  In  each  quantity  there  is  a  deductive,  and  in 
each  quantity  there  is  an  inductive,  inference ;  and  if  the  reasoning 
under  either  of  these  two  quantities  were  to  be  omitted,  it  ought, 
perhaps,  to  have  been  the  one  which  the  logicians  have  exchisively 
cultivated.  For  the  quantity  of  extension  is  a  creation  of  the  mind 
itself^  and  only  created  through,  as  abstracted  from,  the  quantity  of 
comprehension ;  whereas  the  quantity  of  comprehension  is  at  once 
given  in  the  very  nature  of  things.  The  former  quantity  is  thus 
secondary  and  factitious,  the  latter  primary  and  natural. 

That  logicians  should  have  neglected  the  process  of  reasoning 
which  is  competent  betM'een  the  parts  and  whole 
But  probably  con-       ^f  ^j^g  quantity  of  Comprehension,  is  the  more 
.  remarkable,  as,  after  Aristotle,  they  have  in  gen- 

eral articulately  distinguished  the  two  quantities 
from  each  other,  and,  after  Aristotle,  many  of  them  have  explicitly 
enounced  the  special  law  on  which  the  logic  of  comprehension  pro- 
ceeds. This  principle  established,  but  not  applied,  is  expressed  in 
the  axiom  —  The  character  of  the  character  is  the  character  of  the 
thing;  or,  The  predicate  of  the  predicate  is  the  predicate  of  the 
subject  {Nbta  notce  est  nota  rei  ipsius  ;  PrcBclicatuni  prcedicati  est 
pr(Bdicatum  sulgecti).  This  axiom  is  enounced  by  Aristotle ;  *  and 
its  application,  I  have  little  doubt,  was  fully  understood  by  him.  In 
fact,  I  think  it  even  possible  to  show  in  detail  that  his  whole  analy- 
sis of  the  syllogism  has  reference  to  both  quantities,  and  that  the 
great  abstruseness  of  his  Prior  Analytics,  the  treatise  in  which  he 
develops  the  general  forms  of  reasoning,  arises  from  this,  —  that  he 
has  endeavored  to  rise  to  formulee  sufficiently  general  to  express  at 
once  what  was  common  to  both  kinds  ; —  an  attempt  so  far  beyond 
the  intelligence  of  subsequent  logicians,  that  they  have  wholly  mis- 
understood and  perverted  his  doctrine.  They  understand  this  doc- 
trine, only  as  applied  to  the  reasoning  in  extensive  quantity;  and  in 
relation  to  this  kind  of  reasoning,  they  have  certainly  made  palpa- 
ble and  easy  what  in  Aristotle  is  abstract  and  difficult.  But  then 
they  did  not  observe  that  Aristotle's  doctrine  applies  to  two  species, 
of  which  they  only  consider  one.    It  was  certainly  proper  to  briivg 

1  aiter.,0.  iii.— £d. 


Lkct,  Xn.  LOGIC.  155 

down  the  Aristotelic  logic  from  its  high  abstraction,  and  to  deliver 
its  rules  in  proximate  application  to  each  of  the  two  several  species 
of  reasoning.  This  would  have  been  to  fill  up  the  picture  of  which 
the  Stagirite  had  given  the  sketch.  But  by  viewing  the  analytic  as 
exclusively  relative  to  the  reasoning  in  extension,  though  they  sim- 
plified the  one-half  of  syllogistic,  they  altogether  abolished  the 
other.  This  mistake  —  this  partial  conception  of  the  science  —  is 
common  to  all  logicians,  ancient  and  modern ;  for  in  so  far  as  I  am 
aware,  no  one  has  observed,  that  of  the  quantities  of  comprehension 
and  extension,  each  affords  a  reasoning  proper  to  itself;  and  no  one 
has  noticed  that  the  doctrine  of  Aristotle  has  reference  indifferently 
to  both ;  although  some,  I  know,  having  perceived  in  general  that 
we  do  reason  under  the  quantity  of  comprehension,  have  on  that 
founded  an  objection  to  all  reasoning  under  the  quantity  of  exten- 
sion, that  is,  to  the  whole  science  of  Logic  as  at  present  constituted. 
I  have,  in  some  degree,  at  present  spoken  of  matters  which  properly 
find  their  development  in  the  sequel ;  and  I  have  made  this  antici- 
pation, in  order  that  you  should  attend  particularly  to  the  relation 
of  concepts,  under  the  quantity  of  comprehension,  as  containing 
and  contained,  inasmuch  as  this  affords  the  foundation  of  one,  and 
that  not  the  least  important,  of  the  two  great  branches,  into  which 
all  reasoning  is  divided. 

1  XLIV.    We  have  seen  that  of  the  two  quantities  of  no- 
tions   each   affords   a    logical  Whole   and 
Par.   XLIV.  invo-      Parts  1  and  that,  by  opposite  errors,  the  one 

lution  and  Coordlna-  n     ■,  i  i  .       ,       . 

tion.  o*  these  has,  through  over  inclusion,  been 

called  the  logical;  whilst  the  other  has, 
through  over  exclusion,  been  called  the  metaphysical.  Thus, 
in  respect  of  their  Comprehension,  no  less  than  of  their  Exten- 
sion, notions  stand  to  each  other  in  a  relation  of  Containing 
and  Contained ;  and  this  relation,  which,  in  the  one  quantity 
(extension)  is  styled  that  of  /Subordination^  may  in  the  other 
(comprehension),  for  distinction's  sake,  be  styled  that  of  Invo- 
lution. Coordination  is  a  term  which  may  be  applied  in  either 
quantity.^ 

In  the  quantity  of  comprehension,  one  notion  is  involved  in 
another,  when  it  forms  a  part  of  the  sum  total  of  characters, 
which  together  constitute  the  comprehension  of  that  other; 
and  two  notions  are  in  this  quantity  coordinated,  when,  whilst 
neither  comprehends  the  other,  both  are  immediately  compre- 
hended in  the  same  lower  concept. 

1  [Cf.  Drobiscb,  Logik,  n  22, 23.    Fischer,  Logii,  f  49.] 


166  LOGIC.  Lbct.  XIL 

From  what  has  been  formerly  stated,  you  are  aware  that  the 
quantity  of  comprehension,  belonginar  to  a  no- 

Explication.  ^  .   "^  ,  \  '  *     ^        ,  .   ,     . 

tion,  IS  the  complement  oi  characters  which  it 
contains  in  it ;  and  that  this  quantify  is  at  its  maximum  in  an  indi- 
vidual. Thus  the  notion  of  the  individual  Socrates,  contains  in  it, 
besides  a  multitude  of  others,  the  characters  of  /Son  of  Sophronis- 
cus,  Athenian,  Greek,  European,  man,  animal,  organized  being,  etc. 
But  these  notions,  these  characters,  are  not  all  equally  proximate 
and  immediate ;  some  are  only  given  in  and  through  othei*s.  Thus 
the  character  Atfienian  is  applicable  to  Socrates  only  in  and  through 
that  of  Son  of  Sophroniscus,  —  the  character  of  Greek,  only  in 
and  through  that  of  Athenian,  —  the  character  of  JEuropean,  only 
in  and  through  that  of  Greek,  —  and  so  forth ;  in  other  words,  Soc- 
rates is  an  Athenian  only  as  the  son  of  Sophroniscus,  only  a  Greek 
as  an  Athenian,  only  a  European  as  a  Greek,  only  a  man  as  a  Euro- 
pean, only  an  animal  as  a  man,  only  an  organized  being  as  an  ani- 
mal. Those  characters,  therefore,  that  are  given  in  and  through 
othei-s,  stand  to  these  others  in  the  relation  of  parts  to  wholes ;  and 
it  is  only  on  the  principle  —  Part  of  the  part  is  a  part  of  the  whole, 
that  the  remoter  parts  are  the  parts  of  the  primary  whole.  Thus, 
if  we  know  that  the  individual  Socrates  comprehends  the  character 
son  of  Sophroniscus,  and  that  the  character  son  of  Sophroniscus 
comprehends  the  character  Athenian/  we  are  then  warranted  in 
saying  that  Socrates  comprehends  Athe7iian,  in  other  words,  that 
Socrates  is  an  Athenian.  The  example  here  taken  is  too  simple  to 
show  in  what  manner  our  notions  are  originally  evolved  out  of  the 
more  complex  into  the  more  simple,  and  that  the  progress  of  science 
is  nothing  more  than  a  progressive  unfolding  into  distinct  conscious- 
ness of  the  various  elements  comprehended  in  the  characters,  origi- 
nally known  to  us  in  their  vague  or  confused  totality. 

It   is   a  famous   question   among  philosophers,  —  Whether  our 

knowledge  commences  with  the  general  or  with 

Controversy  regard-      ^^^  individual,  —  whether  children  first  employ 

ing  the  Pnmum  Cogni-  .  ,  -r        ,  . 

^^^  common,  or  nrst  employ  proper,  names.    In  this 

controversy,  the  reasoners  have  severally  proved 
the  opposite  opinion  to  be  untenable ;  but  the  question  is  at  once 
solved  by  showing  that  a  third  opinion  is  the  true,  —  viz.,  that  our 
knowledge  commences  with  the  confused  and  complex,  which,  as 
regarded  in  one  point  of  view  or  in  another,  may  easily  be  mistaken 
either  for  the  individual,  or  for  the  general.  The  discussion  of  this 
problem  belongs,  however,  to  Psychology,  not  to  Logic'  It  is  suffi- 
cient to  say  in  general,  that  all  objects  are  presented  to  «s  in 

1  Sae  Lutura  tm  MMtapkt/tit*,  1.  zzzrL,  p.  498  mq.  — El>. 


Lect.  Xn.  LOGIC.  157 

complexity;  that  we  are  at  first  more  struck  with  the  points  of 
resemblance  than  with  the  points  of  contrast ;  that  the  earliest  no- 
tions, and,  consequently,  the  earliest  terms,  are  those  that  corre- 
spond to  this  synthesis,  while  the  notions  and  the  terms  arising 
from  an  analysis  of  this  synthesis  into  its  parts,  are  of  a  subsequent 
formation.  But  though  it  be  foreign  to  the  province  of  Logic  to 
develop  the  history  of  this  procedure;  yet,  as  this  procedure  is 
natural  to  the  human  mind.  Logic  must  contain  the  form  by  which 
it  is  regulated.  It  must  not  only  enable  us  to  reason  from  the  sim- 
ple and  general  to  the  complex  and  individual ;  it  must,  likewise, 
enable  us  to  reverse  the  process,  and  to  reason  from  the  complex 
and  individual  to  the  simple  and  the  general.  And  this  it  does  by 
that  relation  of  notions  as  containing  and  contained,  given  in  the 
quantity  of  comprehension.  The  nature  of  this  reasoning  can 
.  indeed  only  be  shown,  when  we  come  to  treat 
In  Comprehension,  of  syllogism ;  at  present,  I  only  request  that 
the  involving  notion       y^^  ^jn  t,ejjr  in  mind  the  relations  of  Involu- 

18  the  more  complex  ;  .  ~i    /-~i    ..    -i-         •  •  t  •    ^  •  i 

the  involved,  the  more       t^^"  ^^^  Coordmation,  m  which  notions  stand 
simple.  to  each  other  in  the  whole  or  quantity  of  com- 

prehension. In  this  quantity  the  involving  no- 
tion or  whole  is  the  more  complex  notion ;  the  involved  notion  or 
part  is  the  more  simple.  Thus  pigeon  as  comprehending  bird, 
bird  as  comprehending  Jeathered,  feathered  as  comprehending  t^jarw- 
blooded,  warm-blooded  as  comprehending  heart  with  four  cavities^ 
heart  with  four  cavities  as  comprehending  breathinff  with  lungs,  are 
severally  to  each  other  as  notions  involving  and  involved.  Again, 
notions,  in  the  whole  of  comprehension,  are  coordinated  when  they 
stand  together  as  constituting  parts  of  the  no- 

CoHrdination  in  Com-         .•         •  i-   r    >.t.  u    ii.    •  t   ^   i 

^     .  tion  in  which  they  are  both  immediately  com- 

prehension. •'  •' 

prehended.  Thus  the  characters  oviparous  and 
warm-blooded,  heart  with  four  cavities,  and  breathing  by  lungs,  as 
all  immediately  contributing  to  make  up  the  comprehension  of  the 
notion  bird,  are,  in  this  respect,  severally  considered  as  its  coordi- 
nate parts.  These  characters  are  not  relative  and  correlative  —  not 
containing  and  contained.  For  we  have  oviparous  animals  which 
are  not  warm-blooded,  and  warm-blooded  animals  which  are  not 
oviparous.  Again,  it  is  true,  I  believe,  that  all  warm-blooded  ani- 
mals have  hearts  with  four  cavities  (two  auricles  and  two  ventricles), 
and  that  all  animals  with  such  hearts  breathe  by  lungs  and  not  by 
gills.  But  then,  in  this  case,  we  have  no  right  to  suppose  that  the 
first  of  these  characters  comprehends  the  second,  and  that  the  sec- 
ond comprehends  the  third.  For  we  should  be  equally  entitled  to 
assert,  that  all  animals  breathing  by  lungs  possessed  hearts  of  four 


168  LOGIC.  Lkct.  xn. 

cavities,  and  that  all  animals  with  such  hearts  are  warm-blooded. 
They  are  thus  thought  as  mutually  the  conditions  of  each  other ; 
and  whilst  we  may  not  know  their  reciprocal  dependence,  they  aae, 
however,  conceived  by  us,  as  on  an  equal  footing  of  coordination. 
(This  at  least  is  true  of  the  two  attributes  heart  with  four  cavities 
and  breathing  by  lungs;  for  these  must  be  viewed  as  coordinate ; 
but,  taken  together,  they  may  be  viewed  as  jointly  necessitating 
the  attribute  of  warm-blooded^  and,  therefore,  may  be  viewed  as 
comprehending  it.)     On  this  I  give  you  the  following  paragraph. 

^  XLV.    Notions  coordinated  in  the  whole  of  comprehen- 
sion, are,  in   respect  of  the  discriminating 
Par.  XLV.  coordi-      charactei*s,  different  without  any  similarity. 

nation  of  notious  In  ,  , 

Comprehension.  They  are  thus,  pro  tanta,  absolutely  differ- 

ent ;  and,  accordingly,  in  propriety  are  called 
Disparate  Notions  (notiones  disparatoi).  On  the  other  hand, 
notions  coordinated  in  the  quantity  or  whole  of  extension,  are, 
in  reference  to  the  objects  by  them  discriminated,  different  (or 
diverse) ;  but,  as  we  have  seen,  they  have  always  a  common 
attribute  or  attributes  in  which  they  are  alike.  Thus  they  are 
only  relatively  different  (or  diverse) ;  and,  in  logical  language, 
are  properly  called  Disjunct  or  Discrete  Notions  {notiones^  dis- 
junctcB^  discretes)} 

I  [Drobisoh,  Logik,  H  28, 2L    Cf.  Fiaeher,  Logik,  f  49  tt  Mf.] 


LECTURE    XIII. 

STOICHEIOLOGY. 

SECTION    II.— OF  THE    PRODUCTS   OF  THOUGHT. 

II.  —  APOPHANTIC,  OR   THE     DOCTRINE   OF   JUDGMENTS. 

JUDGMENTS.  — THEIR  NATURE  AND  DIVISIONS. 

Having  terminated  the  Doctrine  of  Concepts,  we  now  proceed 
to  the  Doctrine  of  Judgments.      Concepts  and  Judgments,  as  I 

originally  stated,  are  not  to  be  viewed  as  the 
octrine  o      u  g-       results  of  different  operations,  for  every  concept, 

as  the  product  of  some  preceding  act  of  Com- 
parison, is  in  fact  a  judgment  fixed  and  ratified  in  a  sign.  But  in 
consequence  of  this  acquired  permanence,  concepts  afford  the  great 
means  for  all  subsequent  comparisons  and  judgments,  and  as  this 
now  forms  their  principal  relation,  it  behoved,  for  convenience, 
throwing  out  of  view  their  original  genealogy,  to  consider  Notions 
as  the  first  product  of  the  Understanding,  and  as  the  conditions  or 
elements  of  the  second.  A  concept  may  be  viewed  as  an  implicit 
or  undeveloped  judgment;  a  judgment  as  an  explicit  or  developed 
concept.     But  we  must  now  descend  to  articulate  statements. 

*ir  XL VI.     To  Judge  (xpivctv,^  judicare)  is  to  recognize  the 
relation  of  congruence  or  of  confliction,  in 
ment.-wiiat.  which  two  couccpts,  two  individual  things, 

or  a  concept  and  an  individual,  compared 
together,  stand  to  each  other.  This  recognition,  considered  as 
an  internal  consciousness,  is  called  a  Judgment  (Xoyos  aTro<f>avTi- 
K6<i,  Judicium) ;  considered  as  expressed  in  language,  it  is  called 
a  Proposition  or   Predication  (d7ro'<^ai/Tis,  irporaa-i^,^  Staomy/Ao, 

1  The  verb  Kpiveiv,  to  judge,  and  still  more  2  [Aristotle  uses  the  term  irpSraffis  merely 

the  substantive,  Kplffn,  judgment,  are  rarely  for  the  premise  of  a  syllogism,  especially  the 

used  by  the  Greeks  —  (never  by  Aristotle) —  major  (he  has  no  other  word  for  premise); 

as  technical  terms  of  Logic  or  Psychology.  whereas  aird^ou^is  he  employs  always  for  aa 


160  LOGIC.  Lect.  xm. 

propositio,  prcedicatio,  pronunciatum,  enunciation  effatum,  pro- 
faturn^  axioTnd)} 

As  a  judgment  supposes  a  relation,  it  necessarily  implies  a  plural- 
ity of  thoughts,  but  conversely  a  plurality  of 
Explication,— what  thoughts  does  not  necessarily  imply  a  judgment, 
men"^  '*  *"  "  ^  The  thoughts  whose  succession  is  determined 
by  the  mere  laws  of  Association,  are,  though 
manifested  in  plurality,  in  relation,  and,  consequently,  in  connection, 
not,  however,  so  related  and  so  connected  as  to  constitute  a  judg- 
ment. The  thoughts  water,  iron,  and  rusting,  may  follow  each 
other  in  the  mental  train ;  they  may  even  be  viewed  together  in  a 
sinmltaneous  act  of  consciousness,  and  this  without  our  considering 
them  in  an  act  of  Comparison,  and  without,  therefore,  conjoining 
or  disjoining  them  in  an  act  of  judgment.  But  when  two  or  more 
thoughts  are  given  in  consciousness,  there  is  in  general  an  endeavor 
on  our  part  to  discover  in  them,  and  to  develop  a  relation  of  con- 
gruence or  of  confliction  ;  that  is,  we  endeavor  to  find  out  whethei* 
these  thoughts  will  or  will  not  coincide  —  may  or  may  not  be 
blended  into  one.  If  they  coincide,  we  judge,  we  enounce,  their 
congiuence  or  compatibility;  if  they  do  not  coincide,  we  judge,  we 
enounce,  their  confliction  or  incompatibility.  Thus,  if  we  compare 
tlie  thoughts  —  wafer,  iron,  and  rusting,  —  find  them  congru,ent, 
.•md  connect  them  into  a  single  thought,  thus — water  rusts  iron, — 
in  that  case  we  form  a  Judgment.^ 

But  if  two  notions  be  judged  congruent,  in  other  words,  be  con- 
ceived as  one,  this  their  unity  can  only  be  real- 

CondiUon     under       j^ed  in  consciousncss,  inasmuch  as  one  of  these 

wliicli  notions  arc  con-  .  .        .  ,  ^^   -i     ^  j    ^  • 

, .  _.  ^  notions  IS  viewed  as  an  attribute  or  aetermma- 

fiiaered  congruent. 

tion  of  the  other.  For,  on  the  one  haad,  it  is 
impossible  for  us  to  think  as  one  two  attributes,  that  is,  two  things 
viewed  as  determining,  and  yet  neither  determining  or  qualifying 
the  other ;  nor,  on  the  other  hand,  two  subjects,  that  is,  two  things 
thought  as  determined,  and  yet  neither  of  them  determined  or  qual- 
ified by  the  other.  For  example,  we  cannot  think  the  two  attri- 
butes electrical  and  polar  as  a  single  notion,  unless  we  convert  the 
one  of  these  attributes  into  a  subject  to  be  determined  or  qualified  by 
the  other :  but  if  we  do,  —  if  we  say,  what  is  electrical  is  polar,  we 
at  once  reduce  the  duality  to  unity,  —  we  judge  XhdX  polar  is  one  of 

enunciation  considered  not  as  merely  syllo-  I.  p.  868.    Organon  Aict't,  i^.  92, 127,  240  «  se^^ 

gistic.    See  Ammonium,  In  De  Interpret.,  f.  4  a.  416,  417.] 

Ur.  p.  4.  Lat.  Facc\o\a.i\^Rudimenta  Logica,  F.  1  By  Stoics  and  Ramists. 

il.  c.  i.  p.  59.    Waitz,  Commentariua  in  Organon,  2  Cf.  Kmg,  Logik,  {  61.   Anm.  i.  p.  149, 160. 


lect.  xm.  LOGIC.  161 

the  constituent  characters  of  the  notion  electrical^  or  that  what  is 
electrical  is  contained  under  the  class  of  things  marked  out  by  the 
common  character  of  polarity.  In  like  manner,  we  cannot  think 
the  two  subjects  iron  and  mineral  as  a  single  notion,  unless  we  con- 
vert the  one  of  the  subjects  into  an  attribute  by  which  the  other  is 
determined  or  qualified  ;  but  if  we  do,  —  if  we  say,  iron  is  a  min- 
eral, we  again  reduce  the  duality  to  unity ;  we  judge  that  one  of  the 
attributes  of  the  subject  iron  is,  that  it  is  a  mineral,  or  that  iron  is 
contained  under  the  class  of  things  marked  out  by  the  common 
character  of  mineral. 

From  what  has  now  been  said,  it  is  evident  that  a  judgment 

must  contain  and  express  three  notions,  which, 

'    J"  ^™^"     ™"*       however,  as  mutually  relative,  constitute  an  indi- 

contain  three  notions.  '  •'  ' 

visible  act  of  thought.  It  must  contain,  1°,  The 
notion  of  something  to  be  c^etermined;  2°,  The  notion  of  some- 
thing by  which  another  is  determined;  and,  3°,  A  notion  of  the 
relation  of  determination  between  the  two.  This  will  prepare  you 
to  understand  the  following  paragraph. 

\  XL VII.     That  which,  in  the  act  of  Judging,  we  think  as 
the  determined  or  qualified  notion,  is  tech- 
par.   xLvn.    Sub-      nically  called  the  Subject  (vTrofcci/xevov,  sv^- 
cop'uia.  '  jectum)  ;  that  which  we  think  as  the  deter-  - 

mining  or  qualifying  notion,  the  Predicate 
(Karriyopovfifvov,  prcBdicatum) ;  and  the  relation  of  determina- 
tion, recognized  as  subsisting  between  the  subject  and  the  pred- 
icate, is  called  the  Copula.  By  Aristotle,  the  predicate  includes 
the  copula ;  ^  and,  from  a  hint  by  him,  the  latter  has,  by  subse- 
quent Greek  logicians,  been  styled  the  Appredicate  (Trpoa-KaTr]- 
yopovixevov,  apprcedicatum).^  The  Subject  and  Predicate  of  a 
proposition  are,  after  Aristotle,  together  called  its  Terms  or 
JEkctr ernes  ^  (opot  a.Kpa  irepara,  termini) ;  as  a  proposition  is  by 
him  sometimes  called  an  Interval  (SLdaTrjfjia)*  being,  as  it  were, 
a  line  stretched  out  between  the  extremes  or  terms.  We  may, 
therefore,  articulately  define  a  judgment  or  proposition  to  be 
the  product  of  that  act  in  which  we  pronounce,  that,  of  twO' 


1  See  De  Interp.,  c.  3,  where  the  pvfia,  or  to  denote  the  predicate  of  a  proposition,  see 
verb,  includes  the  predicate  and  copula  Ammonius,  on  De  Interp.,  p.  110,  b.  ed.  Aid. 
united. —Ed.  Venet,  1546.    See  below,  p.  162.  — Ed.    [For 

2  See  De   Interjjretatione,  c.  10,  §  4.    "OTav  the  origin  of  this  distinction  see  Blemmidag ; 

8e  rb   tim    tpiTov  trpvffKaTiyyoprirai, an  (after  Aristotle),  Lo°-iea,  p.  186.] 

expression  to  which  may  be  traced  the  scho-  3  AnaX.  Prior.,  1. 1,  4.  — Ed. 

lastic  distinction  between  seeundi  and  tertii  ad-         ^  Anal.  Prior.  1. 15  16  25. El>. 

iacentis.    For  the  term  irpoaKKTifyopovnevov 

21  t 


162  LOGIC.  lect.  xm. 

notions  thought  as  subject  and  as  predicate,  the  one  does  or 
does  not  constitute  a  part-  of  the  other,  either  in  the  quantity 
of  Extension,  or  in  the  quantity  of  Comprehension. 

Thus  in  the  proposition,  iron  is  magnetic,  we  have  iron  for  the 
Subject,   magnetic  for  the   Predicate,  and   the 

Illustration.  .  ■i/.i>~,-,t 

substantive  verb  is  for  the  Copula.  In  regard  to 
this  last,  it  is  necessary  to  say  a  few  words.  "  It  is  not  always  the 
case,  that  in  propositions  the  copula  is  expressed  by  the  substantive 
verb  is  or  est,  and  that  the  copula  and  predicate  stand  as  distinct 
words.  In  adjective  verbs  the  copula  and  predicate  coalesce,  as  in 
the  proposition,  the  sun  shines,  sol  lucet,  which  is  equivalent  to  the 
stcn  is  shining,  sol  est  lucens.  In  existential  propositions,  that  is, 
those  in  which  mere  existence  is  predicated,  the  same  holds  good. 
For  when  I  say  I  am,,  Ego  sum,  the  am  or  sum  has  here  a  far 
higher  and  more  emphatic  import  than  that  of  the  mere  copula  or 
link  of  connection.  For  it  expresses,  lam  existing,  Ego  sum,  exist- 
ens.  It  might  seem  that,  in  negative  propositions,  when  the  copula 
is  affected  by  the  negative  particle,  it  is  converted  into  a  non- 
copula.  But  if  we  take  the  word  copula  in  a  wider  meaning,  for 
that  through  which  the  subject  and  predicate  are  connected  in  a 
mutual  relation,  it  will  apply  not  only  to  affirmative  but  to  negative, 
not  only  to  categorical  but  to  hypothetical  and  disjunctive,  proposi- 
tions."^    I  may  notice  that  propositions  with  the  subject,  predicate, 

and  copula,  all  three  articulately  expressed,  have 
Third^jacent"  been  Called  by  the  schoolmen  those  of  the  third 

adjacent  {propositiones  tertii  adjacentis,  or  tertii 
adjecti),  inasmuch  as  they  manifestly  contain  three  parts.  This  is 
a  barbarous  expression  for  what  the  Greeks,  after  Aristotle,  called 
Trporacrcis  (k  rpiTov  {l(m\  Kartffopovfi.i.vov.  For  the  same  reason,  prop- 
ositions with  the  copula  and  predicate  in  one,  were  called  those 
of  the  second  adjacent? 

"  What  has  now  been  said  will  enable  you  to  perceive  how  far 

concepts  and  judgments  coincide,  and  how  far 
Concepts  and  judg-       ^|^g    differ.   On  the  one  hand,  they  coincide  in  the 

mentEi,  —  how  far  they         /»  i ,        •  x       i       r>  ^  i 

coincide  and  differ.  followmg  respccts :  In  the  first  place,  the  concept 

and  the  judgment  are  both  products ;  the  one  the 
product  of  a  remote,  the  other  the  product  of  an  immediate,  act  of 
comparison.  In  the  second  place,  in  both,  an  object  is  determined 
by  a  character  or  attribute.     Finally,  in  the  third  place,  in  both, 

1  Knig,  Logik,  |  GS;  Anni.,  ii.,  pp.  I6S-4.—     Schnize,  Logik,  p.  74;  Crakaothovpa,  l^mfit^ 
—  Ed.    [Compare  Baobmann,  Logik,  p.  127;     pp.  160, 167.) 

!  Sec  above,  p.  161,  note  %  —  E». 


l^f£^T.  XIIL  LOGIC.  163 

things  relatively  different  in  existence  are  reduced  to  a  relative 
identity  in  the  unity  of  thought.  On  the  other  hand,  they  differ  in 
the  following  respects :  In  the  first  place,  the  determination  of  an 
object  by  an  attribute  is  far  more  express  in  the  judgment 
than  in  the  concept ;  for  in  the  one  it  is  developed,  in  the  other, 
only  implied.  In  the  second  place,  in  the  concept  the  unity  of 
thought  is  founded  only  on  a  similarity  of  quality;  in  the  judgment, 
on  the  other  hand,  it  is  founded  on  a  similarity  of  relation.  For  in 
the  notion,  an  object  and  its  characters  can  only  be  conceived  as 
one,  inasmuch  as  they  are  congruent  and  not  conflictive,  for  thus 
only  can  they  be  united  into  one  total  concept.  But,  in  the  judg- 
ment, as  a  subject  and  predicate  are  not  necessarily  thought  under  a 
similarity  of  quality,  the  judgment  can  comprehend  not  only  con- 
gruent, but  likewise  conflictive,  and  even  contradictory,  notions ;  for 
two  concepts  which  are  compared  together  can  be  I'ecognized  as 
standing  in  the  relation  either  of  congruence  or  of  repugnance. 
Such  is  the  sameness,  and  such  is  the  diversity,  of  concept  and 
judgment."' 

We  have  thus  seen  that  a  judgment  or  proposition  consists  of 
three  parts  or  correlative  notions, — the  notion  of  a  subject,  the 
notion  of  a  predicate,  and  the  notion  of  the  mutual  relation  of  these 
as  determined  and  determining. 

Judgments  may,  I  think,  be  primarily  divided  in  two  ways,  —  the 

divisions  being  determined  by  the  general  .dc- 
d-   d"/"^"  **'""  °^       pendencies  in  which  their  component  parts  stand. 

to  each  other,  —  and  the  classes  afforded  by 
these  divisions,  when  again  considered,  without  distinction,  in  the 
different  points  of  view  given  by  Quantity,  Quality,  and  Relation, 
will  exhaust  all  the  possible  forms  in  which  judgments  are  manifested 

%  XL VIII.  The  first  great  distinction  of  Judgments  is  taken 

from  the  relation  of  Subject  and  Predicate, 

Par.  xLvm.  First       as  rcciprocally  whole  and  part.     If  the  Sub- 

mlntl!-  comprehen-      j^ct  or  determined  notion  be  viewed  as  the 

Bive  and  Extensive.  Containing  wholc,  WO  havo  an  Intensive  or 

Comprehensive  proposition ;  if  the  Predicate 

or  determining  notion  be  viewed  as  the  containing  whole,  we 

have  an  Extensive  proposition. 

This  distinction  of  propositions  is  founded  on  the  distinction  of 
the  two  quantities  of  concepts,  —  their  Comprehension  and  their 

1  i^ser,  I-ogUe,  i  66,  p.  Ul. 


164  LOGIC.  Lect.  XftL 

Extension.      The   relation  of  subject    and  predicate  is  contained 

within  that  of  whole  and  part,  for  we  can  always 

Explication,  —  this      view  either  the  determining  or  the  determined 

distinction     founded       notion  as  the  whole  which  contains  the  other. 

on  tlie  Comprehension  -1,1  -i  •   i       1  i  • 

and  Extension  of  Con-      The  wholc,  howcvcr,  which  the  subject  consti- 
cepts.  tutes,  and  the  whole  which  the  predicate  consti- 

tutes, are  different,  —  being  severally  determined 
by  the  opposite  quantities  of  comprehension  and  of  extension  ;  and 
as  subject  and  predicate  necessarily  stand  to  each  other  in  the  re- 
lation of  these  inveree  quantities,  it  is  manifestly  a  matter  of  in- 
difference, in  so  far  as  the  meaning  is  concerned,  whether  we  view 
the  subject  as  the  whole  of  comprehension,  which  contains  the  pre- 
dicate, or  the  predicate  as  the  whole  of  extension,  which  contains 
the  subject.  In  point  of  fact,  in  single  propositions  it  is  rarely  ap- 
parent whTch  of  the  two  wholes  is  meant ;  for  the  copula  is,  est, 
etc.,  equally  denotes  the  one  form  of  the  relation  as  the  other. 
Thus,  in  the  proposition  man  is  two-legged,  —  the  copula  here  is 
convertible  with  comprehends  or  contains  in  it,  for  the  proposition 
means,  man  contains  in  it  two  legged;  that  is,  the  subject  man,  as  an 
.  intensive  whole  or  complex  notion,  comprehends  as  a  part  the 
.  predicate  two-legged.  Again,  in  the  proposition  m,an  is  a  biped,  the 
copula  corresponds  to  contained  under,  for  this  proposition  is  tanta- 
mount to  m,an  is  contained  under  biped,  —  that  is,  the  predicate 
biped,  as  an  extensive  whole  or  class,  contains  under  it  as  a  part  the 
subject  m,an..  But,  in  point  of  fact,  neither  of  the  two  propositions 
unambiguously  shows  whether  it  is  to  be  viewed  as  of  an  intensive 
or  of  an  extensive  purport ;  nor  in  a  single  proposition  is  this  of  any 
moment.  All  that  can  be  said  is,  that  the  one  form  of  expression 
is  better  accommodated  to  express  the  one  kind  of  proposition^  tlie 
other  better  accommodated  to  express  the  other.  It  is  only  when 
propositions  are  connected  into  syllogism,  that  it  becomes  evident 
whether  the  subject  or  the  predicate  be  the  whole  in  or  under 
which  the  other  is  contained;  and  it  is  only  as  thus  constituting 
two  different,  two  contrasted,  forms  of  reasoning,  —  forms  the  most 
general,  as  under  each  of  these  every  other  is  included,  —  that  the 
distinction  becomes  necessary  in  regard  to  concepts  and  proposi- 
tions. The  distinction  of  propositions  into  Extensive  and  Inten- 
sive, it  is  needless  to  say,  is,  therefore,  likewise  the  most  general; 
.•uid,  accordingly,  it  is  only  in  subordination  to  this  distinction  that 
the  other  distinctions,  of  which  we  are  about  to  treat,  are  valid. 

I  now  proceed  to  the  second  division  of  Judgments,  and  com- 
mence with  the  following  paragraph  : 


lect.  xni. 


LOGIC.  166 


%  XLIX.  The  second  division  of  Judgments  is  founded  on 
the  different  mode  in  which  the  relation  of 

Par.  XLIX.  Second  determination  may  subsist  between  the  sub- 
division    of      Judg-  •' 

ments,  -  Categorical  ject  and  predicate  of  a  proposition.     This 

and  Conditional. -the  ^^^^i^^^   jg   either   Simple   or    Conditional 

latter  of  whicli  is  sub-  ■>■ 

divided  into   Hypo-       (^propositio  simplcx^  pTopositio  condiUorir 
theticai.  Disjunctive,       ^^..^     q^  ^^^  formcr  alternative,  the  prop- 

and  Dilemmatic.  '  '  t.        i. 

osition  is  called  Categorical;^  on  the  latter, 
inasmuch  as  the  condition  lies  either  in  the  subject  or  in  the 
predicate,  or  in  both  the  subject  and  predicate,  there  are  three 
species  of  proposition.  In  the  first  case,  the  proposition  is 
Hypothetical,  in  the  second,  Disjunctive,  in  the  thii-d  Dilem- 
matic or  Hypothetico-disjunctive? 

I  shall  consider  these  in  their  order ;   and,  first,  of  Categorical 

propositions.     But  here  it  is  proper,  before  pro- 

ExpHcation,!.  Cate-       cccding  to  cxpound  what  is  designated  by  the 

eorical      Judgments.  ,  .  .      t    ^  -^i  i 

The  term  tatcorkax  term  cotegorxcal,  to  commence  with  an  explana- 

tion of  the  term  itself  This  word,  as  far  as  now- 
known,  was  first  employed  by  Aristotle  in  a  logical  signification.  I 
have  already  explained  the  meaning  of  the  term  category;  ^  but  you 
are  not  to  suppose  that  categorical  has  any  reference  to  the  ten 
summa  genera  of  the  Stagirite.  By  Aristotle  the  term  Ka-njyopiKos 
is  frequently  employed,  more  especially  in  the  books  of  the  J^riot 
Analytics,  —  and  in  these  books  alone  it  occurs,  if  I  am  correct  in 
my  estimate,  eighty-seven  times.  Now  you  will 
it«  signification  as       observe,  that  in  no  single  instance  is  this  word 

used  by  Aristotle.  7-     -i  i         »    •  i 

applied  by  Aristotle,  except  m  one  unambiguous' 

signification,  that  is,  the  signification  of  affirmative  ;  and  it  is  thus 

by  him  used  as  a  term  convertible  with  Kara^artKo?,  and  as  opposed 

to  the  two  synonyms  of  negation  he  indifferently  employs,  —  airof^a- 

TLKo<i  and  oT-epr/TtKos.*     Such  is  the  meaning  of  the 

Its  meaning  in  the       ^r^^^.^  jn  Avistotelic  usage.     Now  you  will  oh- 

writings  of  his  disci-       .  ,         .        ,       .        ,  n       TrC. 

ipg  serve,  that  it  obtained  a  totally  difierent  mean- 

ing in  the  writings  of  his  disciples.  This  new 
meaning  it  probably  obtained  from  Theophrastus,  the  immediate 
disciple  of  Aristotle,  for  by  him  and  Eudemus  we  know  that  it  was 
so  employed;  —  and  in  this  new  meaning  it  was  exclusively  applied 

1  [Categorical  had  better  be  called  Absolute,  2  Cf.  Krug,  Logik,  §  57.  —  Ed.    [MoceniCHS. 

Es  is  done  by  Gassendi,   Logica,  p.  287,  ed.  /oc.  rit. ;  Schulze,  X-og-i A;,  §§  45,  52,  60— 69.] 

Oxen;  or  Perfect,  as  by  Mocenicus,  who  has  3  See  above,  p.  139. —Ed. 

al>  o  Absolute.  See  Contemplaiiones  PeripateticeB,  4  Compare  Discussions,  p.  152.  —  Ed. 
ii   c.  2,  p.  Sdetseg.^ 


166  1.0 G I c.  Lbgt.  xni 

by -all  the  Greek  and  Latin  expositors  of  the  Peripatetic  philosophy, 
in  fact,  by  all  subsequent  logicians  without  exception.  In  this 
second  signification,  the  terra  categorical^  as  applied  to  a  proposi- 
tion, denotes  a  judgment  in  which  the  predicate  is  simply  affirmed 
or  denied  of  the  subject,  and  in  contradistinction  to  those  proposi- 
tions which  have  been  called  hypothetical  and  disjunctive.  In  this 
change  of  signification  there  is  nothing  very  re- 
This  difference   of       marlcable.    But   it   b  a   singular    circumstance 

signification  not  hith-  ,  t  i       i        *    •  t  i  />     i 

erto  obeerred.  that,  though  the  Anstotelio  employment  oi  the 

word  be  in  every  instance  altogether  clear  and  un- 
ambiguous, no  one,  either  in  ancient  or  in  modern  times,  should  ever 
have  made  the  observation,  that  the  word  was  used  in  two  different 
meanings ;  and  that  in  the  one  meaning  it  was  used  exclusively  by 
Aristotle,  and  in  the  other  exclusively  by  all  other  logicians.  I  find, 
indeed,  that  the  Greek  commentators  on  the  Organon  do,  in  refer- 
ence to  particular  passages,  sometimes  state,  that  Karriyopuccyi  is  there 
used  by  Aristotle  in  the  signification  of  affirmative  ;  but,  in  so  far 
as  I  have  been  able  to  ascertain,  no  one  has  made  the  general  ob- 
servation, that  the  word  was  never  applied  by  Aristotle  in  the  sense 
in  which  alone  it  was  understood  by  all  other  logical  writers.  So 
much  for  the  meaning  of  the  term  categorical ;  as  now  employed 
for  simple  or  absolute,  and  as  opposed  to  conditional^  it  is  used  in  a 
sense  difierent  from  its  original  and  Aristotelic  meaning. 

In  regard  to  the  nature  of  a  Categorical  Judgment  itself,  it  is 

necessary  to  say  almost  nothing.     For,  as  this 

Nature  of  a  Categor-      ju^jorment  is  that  in  M'hich  the  two  terms  stand 

ioalJudgment.  ,  ,  .        ,       .         ,  ,     .  ,  .   . 

to   each   other  simply   m   that   relation  which 

every  judgment  implies,  to  the  exclusion  of  all  extrinsic  conditions, 
it  is  evident,  that  what  we  have  already  said  of  the  essential  nature 
of  judgment  in  general,  affords  all  that  can  be  said  of  categorical 
judgments  in  particular.  A  categorical  proposition  is  expressed  in 
the  following  fornuil:e  — A  is  B,  or,  A  is  not  B.  I  proceed,  iherfforo, 
to  the  genus  of  propositions  as  opposed  to  categorical,  —  viz.,  tlio 
Conditional,  —  Conditioned.  This  genus,  as  stated  in  the  pnra- 
graph,  comprises  two  species,  according  as  the 
II.  —  Conditional       condition  lies  more  proximately  in  the  subject. 

Judgments.         These  .,  ..  ,.,.  ,  tt-i 

.i.^»i,«^..^i^       or  in  the  predicate,  to  which  is  to  be  added, 

eomprise  three  species.  r  ^  ' 

either  as  a  third  species  or  as  a  compound  of 
these  two,  those  propositions  in  which  there  is  a  twofold  condition, 
the  one  belonging  to  tlie  subject,  the  other  to  the  predicate.  The 
first  of  these,  as  stuted,  forms  the  class  Hypothetical,  the  second 
that  of  Disjunctive,  the  third  that  of  Dileramatic,  propositions.  I 
may  notice,  by  the  way,  that  there  is  a  good  deal  of  variation  in 


LBCT.Xm.  LOGIC.  167 

the  language  of  logicians  in  regard  to  the  terms  Conditional  and 

Hypothetical.    You  are  aware  that  conditionalis^ 

Variations  in  regard       jn  Latin,  is  commonly  applied  as  a  translation  of 

,0  the  application  of      ^^^^^^^^  i„  Q,^.^^\^.  and  bv  Boethius,  who  was 

the  terms   Conautonat  '  . 

&nd  Hypothetical.  t^e  first  amoug  the  Latins  who  elaborated  the 

logical  doctrine  of  hypotheticals,  the  two  terms 
are  used  convertibly  with  each  other.'  By  many  of  the  Schoolmen, 
liowever,  the  terra  hypothetical  {hypotheticus)  was  used  to  denote 
the  genus,  and  the  term  conditional.,  to  denote  the  species,  and  from 
them  this  nomenclature  has  passed  into  many  of  the  more  modern 
conipends  of  logic,  —  and,  among  others,  into  those  of  Aldrich  and 
Whately.  This  latter  usage  is  wrong.  If  either  term  is  to  be  used 
in  subordination  to  the  other,  conditional,  as  the  more  extensive 
term,  ouglit  to  be  applied  to  designate  the  genus ;  and  so  it  has  ac- 
cordingly been  employed  by  the  best  logicians.  But  to  pass  from 
words  to  things. 

I  said  that  Hypothetical  propositions  are  those  in  which  the  con- 
dition qualifying  the  relation  between  the  sub- 

I.  Hypothetical.  .  ?         /•  ,.  •  ,     •       , 

ject  and  predicate  lies  proximately  in  the  subject. 
In  the  proposition,  B  is  A,  the  subject  B  is  unconditionally  thought 
to  exist,  and  it  thus  constitutes  a  categorical  proposition.  But  if 
we  think  the  subject  B  existing  only  conditionally,  and  under  this 
conditional  existence  enunciate  the  judgment,  we  shall  have  the 
hypothetical  proposition  —  -(/^  B  is,  A  is,  —  or,  in  a  concrete  exam- 
ple —  Rainy  weather  is  wet  weather,  is  a  categorical  proposition,  — 
If  it  rains,  it  will  be  wet,  is  a  hypothetical.  In  a  hypothetical  prop- 
osition the  objects  thought  stand  in  such  a  mutual  relation,  that 
the  one  can  only  be  thought  in  so  far  as  the  other  is  thought ;  in 
other  words,  if  we  think  the  one,  we  must  necessarily  think  the 
other.  They  thus  stand  in  the  relation  of  Reason  and  Consequent. 
For  a  reason  is  that  which,  being  affirmed,  necessarily  entails  the 
affirmation  of  something  else ;  a  consequent  is  that  which  is  only 
affirmed,  inasmuch  as  something  previous  is  affirmed.  The  relation 
between  reason  and  consequent  is  necessary.  For  a  reason  followed 
by  nothing,  would  not  be  the  reason  of  anything,  and  a  consequent 
which  did  not  proceed  from  a  reason,  would  not  be  the  consequent 
of  anything.  An  hypothetical  proposition  must,  therefore,  contain 
a  reason  and  its  consequent,  and  it  thus  presents  the  appearance  of 
two  members  or  clauses.  The  first  clause —that  which  contains 
the  reason  —  is  called  the  Antecedent,  also  the  Jieaso?i,  the  Condi- 


1  Compare  Diseustions,  p.  160.    For  Boethius,  see  his  treatise  De  SyUogismo  Hypothetieo,  It 
L— Ed. 


168  XOGIC.  Lbct.  Xffl. 

tion,  or  the  Hypothesis  {hypothesis,  conditio,  ratio,  antecedeiis,- — 
i.  e.,  memhrum  siv e  propositio) ;  the  second,  which  contains  the  con- 
sequent necessitated  by  this  ground,  is  called  the  Conseq^ient,  also 
the  Thesis  (consequens,  thesis,  rationatum,  conditionatum).  The 
relation  between  the  two  clauses  is  called  the  Consequence  [couse- 
quentia),  and  is  expressed  by  the  particles  if  on  the  one  hand,  and 
then,  so,  therefore,  etc.,  on  the  other,  which  are,  therefore,  called  the 
Consecutive  particles  {particidoe  consecutive)}  These  are  frequently, 
however,  not  fonnally  expressed. 

"  This  consequence  (if  is  —  then  is)  is  the  copula  in  hypothetical 
jiropositions ;  for  through  it  the  concepts  are 
ment  not  composite.  brought  together,  80  as  to  make  up,  in  conscious- 
ness,  but  a  single  act  of  thought ;  consequently, 
in  it  lies  that  synthesis,  that  connection,  which  constitutes  the  hypo- 
thetical judgment.  Although,  therefore,  a  hypothetical  judgment 
appear  double,  and  may  be  cut  into  two  different  judgments,  it  is 
nevertheless  not  a  composite  judgment.  For  it  is  realized  through 
a  simple  act  of  thought,  in  which  if  and  then,  the  antecedent  and 
the  consequent,  are  thought  at  once  and  as  inseparable.  The  prop- 
osition, if  B  is,  then  A  is,  is  tantamount  to  the  proposition,  A  is 
ihrovgh  B.  But  this  is  as  simple  an  act  as  if  we  categorically 
judged  B  is  A,  that  is,  B  is  under  A.  Of  these  two,  neither  the 
one  —  If  the  sun  shines,  nor  the  other  —  then  it  is  day  —  if  thought 
apart  from  the  othei',  will  constitute  a  judgment,  but  only  the  two  in 
conjunction.  But  if  we  think — The  sun  shines,  and  it  is  day, 
each  by  itself,  then  the  whole  connection  between  the  two  thoughts 
is  abolished,  and  we  have  nothing  more  than  two  isolated  categori- 
cal judgments.  The  relatives  if  and  then,  in  which  the  logical  syn- 
thesis lies,  constitute  thus  an  act  one  luid  indivisible." 

"For  the  same  reason,  a  Hypothetical  judgment  cannot  be  con- 
verted into  a  Categorical.  For  the  thought, 
Not  convertible  into       ^   .^  through  B,  is  wholly   different  from  the 

a  Categorical.  t/  •  >i 

thought,  A  is  in  B.  The  judgment  —  If  God 
is  righteous,  then  will  the  tcicked  he  punished,  and  the  judg- 
ment—  A  righteous  God  punishes  the  wicked,  are  very  different, 
although  the  matter  of  thought  is  the  same.  In  the  former  judg- 
ment, the  punishment  of  t/ie  wicked  is  viewed  as  a  consequent  of 
the  righteousness  of  God ;  whereas  the  latter  considers  it  is  an  at- 
tribute of  a  righteous  God.  But  as  the  consequent  is  regarded  as 
something  dependent  from,  —  the  attribute,  on  the  contrary,  as  some- 
thing inhering  in,  —  it  is  from  two  wholly  different  points  of  view 

1  Knig,  Logik,  §  67,  Anna.  S,  p.  168.  —So. 


Lect.  Xm.  LOGIC.  169 

that  the  two  judgments  are  formed.  The  hypothetical  judgment, 
therefore,  A  is  through  B,  is  essentially  different  from  the  categori- 
cal judgment,  A  is  in  B  ;  and  the  two  judgments  are  regulated  by 
different  fundamental  laws.  For  the  Categorical  judgment  as  ex- 
pressive of  the  relation  of  subject  and  attribute,  is  determined  by 
the  laws  of  Identity  and  Contradiction  ;  the  Hypothetical,  as  ex- 
j)ressive  of  the  relation  of  Reason  and  Consequent,  is  regulated  by 
the  principle  of  that  name."  ^     So  much  for  Hypothetical. 

"Disjunctive  judgments  are  those  in  which  the  condition  qualify- 
ing the  relation  between  the  subject  and  predi- 

2.  Disjunctive.  =>        .  .  ,      .        ,  ^.  7        , 

cate,  lies  proximately  in  the  predicate,  as  in  the 
proposition,  D  is  either  B  or  C,  or  A.  In  this  class  of  judgments  a 
certain  plurality  of  attributes  is  predicated  of  the  subject,  but  in 
such  a  manner  that  this  plurality  is  not  predicated  conjunctly,  but  it 
is  only  judged  that,  under  conditions  some  one,  and  only  some  one, 
of  this  bundle  of  attributes  appertains  to  the  subject.  When  I  say 
that  Ifen  are  either  Black,  or  White,  or  Tawny,  —  in  this  proposi- 
tion, none  of  these  three  predicates  is  unconditionally  affirmed;  but 
it  is  only  assumed  that  one  or  other  may  be  affirmed,  and  that,  any 
one  being  so  affirmed,  the  others  must,  ec  ipso,  be  denied.  The  attri- 
butes thus  disjunctively  predicable  of  the  subject,  constitute  together 
a  certain  sphere  or  whole  of  extension ;  and  as  the  attributes  mutu- 
ally exclude  each  other,  they  may  be  regarded  as  reciprocally  reason 
and  consequent.  A  disjunctive  proposition  has  two  forms,  according 
as  it  is  regulated  by  a  contradictory,  or  by  a  contrary,  opposition. 
A  is  either  B  or  not  B,  —  This  mineral  is  either  a  metal  or  not,  —  are 
examples  of  the  former ;  A  is  either  B,  or  C,  orT>,  —  This  m,ineral  ^* 
either  lead,  or  tin,  or  zinc,  —  are  examples  of  the  latter.  The  oppo- 
site attributes  or  characters  in  a  disjunctive  proposition  are  called 
the  Disjunct  Members  {membra  disjuncta)  ;  and  their  relation  to 
each  other  is  called  the  Disjunction  (disjunctio),  which  in  English 
is  expressed  by  the  relative  particles  either,  or  {aut,  vel),  in  conse- 
quence of  which  these  words  constitute  the  Disjunctive  particles 
{particulce  disjunctive).  In  propositions  of  this  class  the  copula 
is  formed  by  either  is,  —  or  is,  for  hereby  the  concepts  are  brought 
together  so  as  to  constitute  a  single  object  of  consciousness,  and 
thus  a  synthesis  or  union  of  notions  is  effected." 

"  Now,  although  in  consequence  of  the  multiplicity  of  its  predi- 
cates, a  disjunctive  proposition  may  be  resolved  into  a  plurality  of 

1  Krug,  Logik,  f  57,  p.  168,  Anm.  2  —  Ed.  rule,  Propositio  Conditionalis  nihil  ponit  in  esse. 

[Hypotheticals  take  account  not  of  the  cor-  Christian  Weiss,  Lehrbuch  der  Logik,  p.  109,  ed. 

rectness  of  the  two  clauses,  but  only  of  their  1801.] 
connection  (consequentia).    Hence  the  logical 

22 


170  LOGIC.  Lect.  xm. 

judgments,  still  it  is  not  on  that  account  a  complex  or  composite 

judgment.     For  it  is  realized  by  one  simple  energy  of  thought,  in 

which  the  two  relatives  —  the  either  and  the  or 

A  Di^unctive  judg-       —  are  thought  together,  as  inseparable,  and  as 

ment,  not  in  reality       binding  up  the  Opposing  predicates  into  a  single 

composite,     and     not  ,  -,  /.    ^i  •  n-   •         ^' 

^■v.y  •  ^     />  i.        sphere.     In    consequence  ot    this,  a  disiunctive 

convertible  into  a  Cat-  ^  ^  ''  j 

egoricai.  proposition  cannot  be  converted  into  a  categor- 

ical. For  in  a  categorical  judgment  a  single 
predicate  is  simply  affirmed  or  denied  of  a  subject ;  wlicreas  in  a 
disjunctive  judgment  there  is  neither  affirmation  nor  negation,  but 
the  opposition  of  certain  attiibutes  in  relation  to  a  cei'tain  subject 
constitutes  the  thought.  Howbeit,  therefore,  that  a  disjunctive  and 
a  categorical  judgment  may  have  a  certain  resemblance  in  respect 
of  their  object  matter ;  still  in  each  the  form  of  thought  is  wholly 
different,  and  the  disjunctive  judgment  is,  consequently,  one  essenti- 
ally different  from  the  categorical.'" 

Dilemmatic  judgments  are  those  in  which  a  condition  is  found, 
both  in  the  subject  and  in  the  predicate,  and  as 

3.  Dilemmatic.  ...  n         i  »       .      i    /.  t 

thus  a  combmation  of  an  hypothetical  form  and 
of  a  disjunctive  form,  they  may  also  appropriately  be  denominated 
Hypothetico-disjunctwe.  If  X  is  A,  it  is  either  B  or  C  —  If  an 
action  be  prohibited,  it  is  prohibited  either  by  natural  or  by  positive 
law  —  If  a  cognition  be  a  cognition  of  fact,  it  is  giv^n  either 
through  ayi  act  of  external  perception  or  through  an  act  of  self- 
consciousness.  In  such  propositions,  it  is  not  necessary  that  the 
disjunct  predicates  should  be  limited  to  two ;  and  besides  what  are 
strictly  called  dilemmatic  judgments,  we  may  have  othei-s  that  would  . 
properly  obtain  the  names  of  trilemmatic,  tetralemmatic,  polylem- 
matic,  etc.  But  in  reference  to  propositions,  as  in  reference  to  syl- 
logisms, dilemma  is  a  word  used  not  merely  to  denote  the  cases 
where  there  are  only  two  disjunct  membei-s,  but  is,  likewise,  extended 
to  any  plurality  of  opposing  predicates.  There  remains  here,  how- 
ever, always  an  ambiguity  ;  and  perhaps,  on  that  account,  the  term 
hypothetico-disjunctive  might  with  propriety  be  substituted  for  dilem- 
matic. A  proj)Osition  of  this  class,  thougli  bear- 
A  Dilemmatic  judg-  ing  both  an  hypothetical  and  a  disjunctive  form, 
ment  indivisible,  and       cannot,  howevcr,  be  analvzed  into  an  hypotheti- 

not  reducible  to  a  pin-  i  -i        -i.   .  .         .     ,  t 

raiity  of  categorical       ^al  and  a  disjunctive  judgment.     It  constitutes 
propositions.  as  indivisible  a  unity  of  thought  as  either  of 

these;  and  can  as  little  as  these  be  reduced 
without  distinction  to  a  plurality  of  categorical  propositions. 

Every  form  of  Judgments  which  we  have  hitherto  considered, 

1  Krug,  Logik,  pp.  170, 171.    Compare  Kant,  Logik^ )  29.  —  £d. 


Lbct.  xhl  logic.  ITl 

has  its  corresponding  form  of  Syllogism ;  and  it  is  as  constituting 
the  foundations  of  different  kinds  of  reasoning,  that  the  considera- 
tion of  these  different  kinds  of  propositions  is  of  principal  impor- 
tance.   These  various  kinds  of  propositions  may, 
Judgments  consid-      however,  be  considered  in  the  different  points  of 

^nanwt  '*^*"°'"'  ^^      "^^^^  ^^  Quantity,  Quality,  and  Relation.     And 
firet  of  Quantity ;  in  reference  to  which  I  give 
you  the  following  paragraph. 

%  L.  The  Quantity  of  Judgments  has  reference  to  the  whole 

of  Extension,  by  the  number  of  the  objects 

Par.  li.  10.  The  com-       conccming  which  we  judc;e.      On   this   I 

mon   doctrine  of   the  ,     ,,  .11,0    ^r^^^        1  •  i» 

division     of    judg-       shall  State  articulately,  1  ,   Ihe  doctrme  ot 
menta   according  to       tjjg  Logiciaus ;  and,  2°,  The  doctrine  which 

their     Quantity.      2°.  _  .  ,  , 

The  doctrine  of  the       I  conccivc  to  be  the  morc  correct, 
author  on  this  point.  1°.  (The  doctrinc  of  the  Logicians.)    The 

common  doctrine,  which,  in  essentials,  dates 
from  Aristotle,^  divides  Propositions  according  to  their  Quan- 
tity into  four  classes ;  viz.,  (A)  the  Universal  or  General  {pr. 
universales,  generates,  Trporacrets  aX  koBoXov)  ;  (B)  the  Particular 
{pr.  particulares  irpoToicrcLi  /xcpiKai,  at  iv  fiipet) ;  (C)  the  Individ- 
ual or  Singular  {pr.  individuales,  singulares,  expositorice,  irpo- 
rao-cts  at  KoSt'  Ikoxttov,  to,  arofia)  ;  (D)  the  Indefinite  {pr.  imprcB- 
finitce,  indefitlitce,  Trporacrcis  dSiopio-rot,  ctTrpoo-Sto/ato-TOi) .  They 
mean  by  universal  propositions,  those  in  which  the  subject  is 
taken  in  its  whole  extension  ;  h^  particular  propositions,  those 
in  which  the  subject  is  taken  in  a  part,  indefinitely,  of  its  exten- 
sion ;  by  individual  propositions,  those  in  which  the  subject  is 
at  a  minimum  of  extension ;  by  indefinite  propositions,  those 
in  which  the  subject  is  not  articulately  or  overtly  declared  to 
be  either  universal,  particular,  or  individual. 

2°.  (The  doctrine  I  prefer.)  This  doctrine  appears  to  me 
untenable,  and  I  divide  Propositions  according  to  their  Quan- 
tity in  the  following  manner :  —  In  this  respect  their  differences 
arise  either  (A),  as  in  Judgments,  from  the  necessary  condition 
of  the  Internal  Thought;  or  (B),  as  in  Propositions,  merely 
from  the  accidental  circumstances  of  its  External  Expression. 

Under  the  former  head  (A),  Judgments  are  either  (a)  of 
Determinate  or  Definite  Quantity,  according  as  their  sphere  is 
circumscribed,  or  (b)  of  Quantity  Indeterminate  or  Indefinite, 
according  as  their  sphere  is  uncircumscribed.  —  Again,  Judg- 
ments of  a  Determinate  Quantity  (a)  are  either  (1)  of  a  Whole 

1  D«  Interp.,  o.  7.    Andt.  Prior,,  i.  1.  —  Ed. 


172 


LOGIC. 


lkct.  xm. 


Undivided,  in  which  case  they  constitute  a  Universal  or  Gerv- 
eral  Proposition  ;  or  (2)  of  a  Unit  Indivisible,  in  which  case, 
they  constitute  an  Individual  or  Singular  Proposition.  —  A 
Judgment  of  an  Indeterminate  Quantity  (b)  constitutes  a,  Par- 
ticular Proposition. 

Under  the  latter  head  (B),  Propositions  have  either,  as  prop- 
ositions, their  quantity,  determinate  or  indeterminate,  marked 
out  by  a  verbal  sign,  or  they  have  not ;  such  quantity  being 
involved  in  every  actual  thought.  They  may  be  called  in  the 
one  case  (a)  Predesignate ;  in  the  other  (b)  Preindesignate. 

Again,  the  common  doctrine,  remounting  also  to  Aristotle,' 
takes  into  view  only  the  Subject,  and  regulates  the  quantity  of 
the  proposition  exclusively  by  the  quantity  of  that  term.  The 
Predicate,  indeed,  Aristotle  and  the  logicians  do  not  allow  to  be 
affected  by  quantity ;  at  least  they  hold  it  to  be  always  Particu- 
lar in  an  Affirmative,  and  Universal  in  a  Negative  Proposition. 

This  doctrine  I  hold  to  be  the  result  of  an  incomplete  analy- 
sis; and  I  hope  to  show  you  that  the  confusion  and  multiplicity 
of  which  our  present  Logic  is  the  complement,  is  mainly  the 
consequence  of  an  attempt  at  synthesis,  before  the  ultimate  ele- 
ments had  been  fairly  reached  by  a  searching  analysis,  and  of  a 
neglect,  in  this  instance,  of  the  fundamental  postulate  of  the 
science. 


(Mental)  Jadgments 


of  a  Whole  Undivided  - 
a  \  Universal  or  General  Jadgments. 

of  Determinate  or , 
\  Definite  Quantity. 

of  a  Unit  Indivisible  — 
.  y  Individual  or  Singular  Judgments, 

of  Indeterminate  or 
Indefinite  Quantity  —  forming  Particular  Judgments. 


3  i  their  Quantity  Expressed  —  Predesignate. 

(Verbal)  Propositions  }  b 

/their  Quantity  Not  Expressed  — Preindesignate.' 


1  Of.  Inttrp  ,  c.  7.  —  Ed. 

'i  Vide  Th.  et  Am.  apud  Am  In  Dr.  Int., 
8vo,  ff.  72,  111—113.  [In  the  first  of  these 
pascaj^eB,  Ammoiiius,  proceeding  on  a  merely 
arithmetical  calculation,  enumerates  sixteen 
varieties  of  the  Proposition,  any  one  of  four 
(|uantities  in  the  subject,  —  [all  —  vot  nil,  none 
—  not  none  or  some),  being  capable  of  combi- 
iiatiuD  with  any  one  of  four  quantities  in  the 


predicate.  But  of  these  some  are  but  verbal 
varieties  of  the  same  judgment,  and  others 
are  excluded  on  material  grounds,  so  that  his 
division  Anally  coincides  with  Aristotle's.  In 
the  second  passage  Theophrastus  is  cited  in 
illustration  of  a  very  obscure  statement  con- 
cerning the  opposition  of  iudesignatc  propo- 
sitious.  — £d.] 


Lect.  Xm.  LOGIC.  173 

Universal  Judgments  are  those  in  which  the  whole  number  of 

objects  within  a  sphere  or  class  are  judged  of, — 

Explication.     Uni-       ^  ^^^  ^^^^  ^^^  mortaL  or  Every  man  is  mortal, 

versalJudgments.  ,  „   .        ,  •,    r>    ■  i  11  1 

the  all  in  the  one  case  denning  the  whole  col- 
lectively, —  the  evenj  in  the  other  defining  it  discretively.  In  such 
judgments  the  notion  of  a  determinate  wholeness  or  totality,  in  the 
form  of  omnitude  or  allness,  is  involved. 

Individual  Judgments  are  those  in  which,  in  like  manner,  the 

whole  of  a  certain  sphere  is  judged  of,  but  in 

Singular  or  indi-  j^j^^  sphere  there  is  found  only  a  single  object, 

vidual    Judgments,—  ^  ,  ^     .       ,        ,  .  %      .,.        . 

^ijj^t  or  collection  of  single  objects,  —  as   Cahline  ts 

amhitious,  —  The  ticelve  apostles  icere  inspired. 
In  such  judgments  the  notion  of  determinate  wholeness  or  totality 
in  the  form  of  oneness,  indivisible  unity,  is  involved.' 

Particular  Judgments   are   those  in  which,  among   the   objects 

within  a  certain  sphere  or  class,  we  judge  con- 

a  "C""      "  g       cerninff  some   indefinite  number  less  than  the 

ments,  —  what.  o 

whole,  —  as    Som,e  men   are  virtuous  —  Many 
hoys  are  courageous  —  Most  women  are  compassionate.     The  indef- 
inite plurality,  within  the  totality,  being  here  denoted  by  the  words 
some,    many,  m,ost.     There  are   certain  words 
Words  which  serve       which  scrve  to  mark  out  the  quantity  in  the  case 
to  mark  out  quantity       ^f  Universal,  Individual,  and  Particular  propo- 

in  Universal,  Individ-  .   .  _,  i  •    1       t      •  • 

uai,   and    ParUcuiar      sitions.      The   words   which   designate   univer- 
Propositions.  sality  are  all,  the  whole  of,  every,  both,  each,  none, 

no  one,  neither,  always,  everywhere,  etc.  The 
words  which  mark  out  pai;ticularity  are  som,e,  not  all,  one,  two,  three, 
etc.,  sometimes,  somewhere,  etc.  There  are  also  terms  which,  though 
they  do  not  reach  to  an  universal  whole,  approximate  to  it,  as  many, 
most,  almost  all,  the  greatest  part,  etc.,  few,  very  few,  hardly  any, 
etc.,  which,  in  the  common  employment  of  language,  and  in  refer- 
ence to  merely  probable  matter,  may  be  viewed  as  almost  tanta- 
mount to  marks  of  universality. 

By  logicians  in  general  it  is  stated,  that,  in  a  logical  relation, 

an  Individual  is  convertible  with  an  Universal 

Distinction  of  Uni-       proposition ;  as  in  both  something  is  predicated 

versai  and  Individual       ^^  ^  ^^j^^j^  subject,  and  neither  admits  of  any 

from  Particular  Judg-  .  -r,  i-i 

ments.  exception.       But  a  Particular  Judgment,  like- 

wise, predicates  something  of  a  whole  subject, 
and  admits  of  no  exception ;  for  it  embraces  all  that  is  viewed  as 
the  subject,  and  excludes  all  that  is  viewed  as  not  belonging  to  it. 

'  Individuum  (proprium )  signatum,  and  indi-     particulare  vagum.   The  former  of  each,  and  th» 
vidwum  vagum.    So  particulare  signatum,  and     latter  of  each,  corresponding.  —  Memoranda. 


174  LOGIC.  Lect.  xiu. 

The  whole  distinction  consists  in  this,  —  that,  in  Universal  and  in 
Individual  Judgments,  the  number  of  the  objects  judged  of  is 
thought  by  us  as  definite ;  whereas,  in  Particular  Judgments,  the 
number  of  such  objects  is  thought  by  us  as  iudefinite.  That  Indi- 
vidual Judgments  do  not  correspond  to  Universal  Judgments,  merely 
in  virtue  of  the  oneness  of  their  subject,  is  shown  by  this,  —  that,  if 
the  individual  be  rendered  iudefinite,  the  judgment  at  once  assumes 
the  character  of  particularity.  For  example,  the  propositions,  —  A 
German  invented  the  art  of  printing^  —  An  Englishman  generalized 
the  laxo  of  gravitation,  —  are  to  be  viewed  as  particular  propositions. 
But,  if  we  substitute  for  the  indefinite  expressions  a  German  and 
an  Englishman,  the  definite  expressions  Faust  and  Newton,  the 
judgment  obtains  the  form  of  an  universal. 

With  regard  to  quantity,  it  is  to  be  observed,  say  the  logicians,  that 
Categorical  Judgments  are  those   alone  which 

Categorical  Jadg-  admit  of  all  the  forms.  "  Hypothetical  and  Dis- 
ments  alone,  accord-      junctivc  propositions  are  always  universal.     For 

ing  to  logicians,  admit         .       ,  i       •      i       i  i  •   •  f 

of  all  the  forms  of  »»  hypotheticals,  by  the  position  of  a  reason, 
quantity.  there  is  posited  every  consequent  of  that  reason ; 

and  in  disjunctives  the  sphere  or  extension  of  the 
subject  is  so  defined,  that  the  disjunct  attributes  are  predicated  of 
the  whole  sphere.  It  may,  indeed,  sometimes  seem  as  if  in  such 
propositions  something  were  said  of  some,  and,  consequently,  that 
the  judgment  is  particular  or  indefinite.  For  example,  as  an  hypo- 
thetical, —  If  some  men  are  learned,  then  others  are  unlearned ;  as 
a  disjunctive,  —  Those  men  who  are  learned  are  either  philosophers 
or  not.  But  it  is  easily  seen  that  these  j lodgments  are  essentially  of 
a  general  character.  In  the  first  judgment,  the  real  consequent  is,  — 
then  all  others  are  unlearned;  and  in  the  second,  the  true  subject  is, 
—  all  learned  m,en,  for  this  is  involved  in  the  expression  —  Those 
men  tcho  are  learned,  etc."^ 

Such  is  the  doctrine  of  the  Logicians.  This  I  cannot  but  hold 
to  be  erroneous ;   for  we   can   easily  constnict 

This  doctrine  errone-  .  .  i     ^i_         i  ^i     ^'      i  j-  • 

proposition.s,  whether  hypothetical  or  disjuni-- 
tive,  which  cannot  be  construed  either  as  uni- 
vei*sal  or  singular.  For  example,  when  we  say,hypothetically,  —  If 
some  Dodo  is,  then  some  animal  is;  or,  disjunctively,  —  Som.e  men 
are  eit/ier  rogues  or  fools :  —  in  either  case,  the  proposition  is  indefi- 
nite or  particular,  and  no  ingenuity  can  show  a  plausible  reason  why 
it  should  be  viewed  as  definite,  —  as  general  or  individual. 

1  Krug,  Logik,  )  67,  Anm.  4,  p.  171  et  seq.  —  i.  §  122.    Schulze,  Logik,  S  60.     Conira  ,-  —  £»• 

Ed.     [Cf  liofTbaucr,  An/angsgrtinke  der  Logik,  ser,  Logik,  §  92,  p.  177.  — [See  below,    p.  887 

S  243.    Sigwart,  Lngik,  )  1G4  tt  seq.,ed.  1835.  note  L  — Ed.] 
Kiesewettcr,  Gruadriss  einer  allgrtneintn  Logik. 


LECTURE      XIV. 

STOICHEIOLOOY. 
SECTION    II.— OF   THE    PRODUCTS   OF   THOUGHT, 

II.  —  APOPHANTIC. 
JUDGMENTS.  — THEIR  QUALITY,  OPPOSITION,  AND  CONVERSION. 

The  first  part  of  our  last  Lecture  was  occupied  witli  the  doctrine 
of  Judgments,  considered  as  divided  into  Simple 
ecapi  u  a  ion.  ^^^  .^^^  Conditional ;  Simple  being  exclusively 

Categorical,  Conditional,  either  Hypothetical,  Disjunctive,  or  Hypo- 
thetico-disjunctive.  We  then  proceeded  to  treat  of  the  Quantity 
of  propositions,  and,  in  this  respect,  I  stated  that  they  are  either 
Definite  or  Indefinite  ;  the  Definite  comprising  the  two  subordinate 
classes  of  General  or  Universal,  and  of  Singular  or  Individual 
propositions,  while  the  Indefinite  are  correspondent  to  Particular 
propositions  alone.  In  regard  to  the  terms  definite  and  indefinite^  I 
warned  you  that  I  do  not  apply  them  in  the  sense  given  by  logical 
writers.  With  them.  Indefinite  propositions  denote  those  in  which 
the  quantity  is  not  explicitly  declared  by  one  of  the  designatory 
terms,  all,  every,  some,  many,  etc  Such  propositions,  however, 
ought  to  be  called  pre-hidesignate  {^prcB-indesignatm,  airpoaSiopLcrToi), 
that  is,  not  marked  oxit  by  a  prefix,  —  a  term  better  adapted  to  indi- 
cate this  external  accident  of  their  enunciation;  for,  in  point  of  fact, 
these  preindesignate  propositions  are  either  definite  or  indefinite, 
and  quite  as  definite  or  indefinite  in  meaning,  as  if  their  quantity 
had  been  expressly  marked  out  by  the  predesignatory  terms. 

,    ,  „  This  being  premised,  I  now  go  on  to  the  next 

Second    division   of  ...  ... 

Judgments,  or  that  ac-  division  of  Judgments  —  the  division  proceed- 
cording  to  tiieir  Quai-  ing  On  that  ground  which  by  Logicians  has  been 
'*y*  called  the  Quality  of  Judgments.     In  itself  the 

term  quality  is  here  a  very  vague  and  arbitrary  expression,  for  w« 


176  LOGIC.  Lect.  XIV. 

I 

might,  with  equal  propriety,  give  the  name  of  quality  to  several 
other  of  the  distinguishing  principles  of  propositions.  For  example 
the  truth  or  falsehood  of  propositions  has  been  also  called  their 
quality;  and  some,  logicians  have  even  given  the  n.ame  of  quality 
to  the  ground  of  the  distinction  of  judgments  into  categorical,  hypo- 
thetical, and  disjunctive.  What,  however,  has  been  universally,  if 
not  always  exclusively,  styled  the  quality  of  propositions,  both  in 
ancient  and  modern  times,  is  that  according  to  which  they  are  dis- 
tributed into  Affirmative  and  Negative. 

^  LI.  In  respect  of  their  Quality,  Judgments  are  divided  into 
two  classes.     For  either  the  Subject  and 

Par.  LL  Jndsrments,  -r»       ,.       ^  i_  •       j  „ 

in  respect  of  their       Jr  rcdicatc  may  be  recognized  as  reciprocally 
Quality,  are  Afflrma-       containing  and  contained,  in  the  opposite 

tlve  and  Negative.  ..  n    t\  •  i      i~^ 

quantities  of  Extension  and  Comprehen- 
sion ;  or  they  may  be  recognized  as  not  standing  in  this  rel.a- 
sion.  In  the  fomier  case,  the  subject  and  predicate  are  affirmed 
of  each  other,  and  the  proposition  is  called  an  Affirmative 
(Trporao-is  KaracfMTucq  or  Karqyopucr),  Judicium  affirmativum  or 
positivum) ;  in  the  latter  case,  they  are  denied  of  each  other, 
and  the  proposition  is  called  a  Negative  (irpOTao-is  d7ro<t>aTucq  or 
areprjTucq.,  Judicium  negativum). 

In  this  paragraph,  I  have  enounced  more  generally  than  is  done  by 

logicians  the  relation  of  predication,  in  its  affirmative  and  negative 

phases.     For  their  definitions  only  apply  cither  to  the  subject  or  to 

the  predicate,  taken  as  a  whole ;  whereas,  since 

Explication.    Gen-       ^g  jugy  indiffisrcntly  view  either  the  subject  as 

fr'^r**   A-^ .-^  "'        the  whole  in  relation  to  the  predicate,  or  the 

tion  of  predication  in  ^  .  . 

tiie  paragraph.  predicate  as  the  whole  in  relation  to  the  subject, 

according  as  we  consider  the  proposition  to  ex- 
press an  intensive  or  to  express  an  extensive  judgment,  —  it  is 
proper  in  our  definition,  whether  of  predication  in  general,  or  of 
affirmation  and  negation  in  particular,  to  couch  it  in  such  terms  that 
it  may  indifferently  comprehend  both  these  classes,  —  both  these 
phases,  of  propositions. 

As  examples  of  Affinnative  and  Negative  propositions,  the  follow- 
ing may  suffice :  —  A  is  B  —  A  is  not  B  —  God 
rma  i\ea eg        ^.^  merciful —  God  ts  uot  vindictive.     In  an  Af- 

ative  Propositions.  •' 

firmative  judgment,  there  is  a  complete  inclusion 
of  the  subject  within  the  predicate  as  an  extensive  whole ;  or  of 
the  predicate  within  the  subject  as  an  intensive  whole.  In  Nega- 
tive judgments,  on  the  contrary,  there  is  a  total  exclusion  of  the 


JjBCT.  XIV.  lOGlO.  ft*T 

subject  from  the  sphere  of  the  predicate  (extensively),  of  of  the 
predicate  from  the  comprehension  of  the  subject  (intensively).  In 
affirmative  propositions  there  is  also  distinctly  enounced  through 
what  predicate  the  notion  of  the  subject  is  to  be  thought,  that  is, 
what  predicate  must  be  annexed  to  the  notion  of  the  subject ;  in 
negative  propositions,  in  like  manner,  it  is  distinctly  enounced 
through  what  predicate  the  notion  of  the  subject  is  not  to  be 
thought,  that  is,  what  predicate  must  be  shut  out  from  the  notion  of 
the  subject.  In  negative  judgments,  therefore,  the  negation  essen- 
tially belongs  to  the  Copula ;  for  otherwise  all  propositions  without 
distinction  would  be  affirmative.  This,  however,  has  been  a  point 
of  controversy  among  modem  logicians ;  for  many  maintain  that  the 
negation  belongs  to  the  predicate,  on  the  follow- 
That  Negation  does  jng  grounds :  —  If  the  negation  pertained  to  the- 
not  belong  to  the  Cop-      p^,    ,j     ^jje^e  couM  be  no  synthesis  of  the  two 

tilft,  held  by  some  logi-  *  •' 

cjans.  terms,  —  the  whole  act  of  judgment  would  be 

subverted,  —  while  at  the  same  time  a  non-con- 
necting copula,  a  non-copulative,  is  a  contradiction  in  terms.     But 
a  negative   predicate,  that  is,  a  predicate  by  which  something  is- 
taken  away  or  excluded   from  the  Subject,  involves  nothing  con- 
tradictory ;   and,   therefore,  a  judgment  with  such  a  predicate  is  ■ 
competent.^ 

The  opposite  doctrine  is,  however,  undoubtedly  the  more  correct. 

For  if  we  place  the  negation  in  the  predicate, 

The  opposite  doctrine       negative  judgments,  as  already  said,  are  not  dif- 

maintainedbytheAu-         /.  ^     •        r.  j.  jn  .•  i.    •  i 

jjjop  lerent   in   lorm  Irom  affirmative,  being  merely 

affirmations  that  the  object  is  contained  within 
the  sphere  of  a  negative  predicate,  or  that  a  negative  predicate 
forms  one  of  the  attributes  of  the  subject.  This,  however,  the 
advocates  of  the  opinion  in  question  do  not  venture  to  assert.  The 
objection  frpm  the  apparent  contradiction  of  a  non-connecting  cop- 
ula is  valid  only  if  the  literal,  the  grammatical,  meaning  of  the 
term  copula  be  coextensive  with  that  which  it  is  applied  logically  to 
express.  But  this  is  not  the  case.  If  literally  taken,  it  indicates 
only  one  side  of  its  logical  meaning.     What  the 

True  import  of  the        j  7  .j  xij^-au 

word  copula  very  inadequately  denotes,  in  the 

form  of  the  relation  between   the  subject  and 

predicate  of  a  judgment.     Now,  in  negative  judgments,  this  form 

1  Krug,  Logik,  §  55,  Anm.  3.  —  Ed.  [Com-  Bardili,  Gntndriss  der  ersten  Logik,  §  12.  Der- 
pare  on  tlie  same  side  BuflBer,  Logique,  i.,  §75  odon,  Logiea,  p.  642.  Cf.  p.  515  tt  seq.  Com- 
et seq.  Bolzano,  Wiessenscha/tsle/tre,  Lagik,  voL  tra ;  —  Kant,  Logik,  f  ffi,  Anm.  3.  Baehmann, 
ii.,  H  127, 129, 136.    Schulze,  X^gii,  j  60,  p.  74.  iogi*, »  84,  p.  127.    Eager,  iog*, »  59,  p.  116-1 

23 


178  LOGIC.  Jjeot.  XIV. 

eesentially  consists  in  the  act  of  taking  a  part  out  of  a  whole, 

and   is  as  necessary  an  act  of  thought  as  the  putting  it  in.     The 

notion  of  the  one  contradictory  in  fact  involves  the  notion  of  the 

other.^ 

The  controversy  took  its  origin  in  this,  —  that  every  negative 

judgment   can   be  expressed   in   an  affirmative 

Origin  of  the  contro-      f^^^^  ^y^^^  ^^le  negation  is  taken  from  the  cop- 

pi«ce  of  negation  "'^  ^^^  placed  in  the  predicate.    Thus,  A  is  not 

B  may  be  changed  into,  —  A  is  not-3.  The  con- 
trast is  better  expressed  in  Latin,  A  non  est  B  —  A  est  non-B.  In 
fact,  we  are  compelled  in  English  to  borrow  the  Latin  Jion  to  make 
the  difference  unambiguously  apparent,  saying,  A  is  non-B,  instead 
of  A  is  7iot-B.  But  this  proves  nothing;  for  by  this  transposition 
of  the  negation  from  the  copula  to  the  predicate,  we  are  also  ena- 
bled to  express  every  affirmative  proposition  through  a  double  nega- 
tion. Thus,  A  is  B,  in  the  affirmative  form  is  equivalently  enounced 
by  A  is  not  non-B  —  A  non  est  non-B,  in  the  negative. 

This  possibility  of  enunciating  negative  propositions  in  an  afiSrma- 
j.,  tive,  and  affirmative  propositions  in  a  negative 

Negative  temw,—      form,  has  been  the  occasion  of  much  perverse 

how  designated  by  Ar-  _  i       •    •  »    •  ,    o    i 

j^^jyg  •       rennement  among  logicians.     Aristotle  *  denom- 

inated the  negative  terms,  such  as  7Jon  B,  non 
homo,  non  albus,  etc.  ovofjutm  aopurra,  literally,  indefinite  nou7is,  Boe- 
thius,'  however,  unhappily  translated  Aristotle's  Greek  term  aopur- 
Tos  by  the  Latin  infinitus,  reserving  the  term 
^   **    *"■  indefitiitus  to  render  d&dpioros  as  applied    to 

propositions,  but   of  which  the  notion  is  more  appropriately  ex- 
pressed, as  we  have  seen,  by  the  word  indesignate  (indesignatus), 
or  better  preindesignate  {prcBxndesignatus).     The  Schoolmen,  fol- 
:  >,  lowing  Boethius,  thus  called  the  ovofiara  aopwra 

of  Aristotle  nomina  infinita :  and  tjie  non  they 
Btyled   the  particula  infinitans.     Out  of  such  elements  they  also 
constructed  Propositiones  Infinites;   that  is,  judgments  in  which 
either  the  subject  or  the  predicate  was  a  nega- 
Propositum*s  infiniuB      ^j^^  notion,  as  non-homo  est  viridisy  and  homo 
of    the  achoolmen,—  .   .  ■,.  -,       ,  ,  •.•     •         •  i     j 

^,,,t  est  non-vtrtdis,  and    these  they  distinguished 

from  the  simple  negative,  homo  —  non  est  —  vir- 

idis.     Herein  Boethius  and  the  schoolmen  have  been  followed  by 

Kant,*  through  the  Wolfian  logicians ;  for  he  explains  Infinite  Judg- 

1  Bacbnann,  Logik,  p.  127.  — Ed.  4  Logtfc,  {  SS.    Compare  Wolf,  FkUo*.  Ro- 

S  D«  Ilerpretatione,  o.  2.  —  £d.  I»o«.,  }  209.  —  Ed. 

^  In  De  Inttrpretationtf  L.  il.  )  1.     Optra,  p. 
860.  — Ed. 


I 


Lect.  XIV.  LOGIC.  It9 

ihents  as  those  which  do  not  simply  indicate,  that  a  subject  is  not 

contained  under  the  sphere  of  a  predicate,  but  that  it  lies  out  of  its 

sphere,  somewhere  in  the  infinite  sphere.     He  has  thus  considered 

them  as  combining  an  act  of  negation  and  an 

On  this  point  foi-       ^^^^  ^f   affirmation,  inasmuch   as   one    thing  is 

lowed  by  Kant.  /«  -i    •         i  i  t        i  •  /• 

affirmed  m  them  through  the  negation  oi  an- 
other. In  consequence  of  this  view,  he  gave  them,  after  some 
Wolfians,  the  name  of  Limitatwe,  which  he  constituted  as  a  third 
form  of  judgments  under  quality,  —  all  propositions  being  thus 
either  Affirmative,  Negative,  or  Limitative.  The  whole  question 
touching  tiie  validity  of  the  distinction  is  of  no  practical  conse- 
quence ;  and  consists  merely  in  whether  a  greater  or  less  latitude  is 
to  be  given  to  certain  terms.  I  shall  not,  therefore,  occupy  your 
attention  by  entering  on  any  discussion  of  what  may  be  urged  in 

refutation  or  defence.  But  if  what  I  have  al- 
Kant'8  three-fold  di-       ready  Stated  of  the  nature  of  negation  and  its 

vision  of  Propositions  .  .  ,       ,  ,      ,  ,  . 

unfounded.  Connection  with  the  copula,  be  correct,  there  is 

no  ground  for  regarding  limitative  propositions 
as  a  class  distinct  in  form,  and  coordinate  with  Affirmative  and  Neg- 
ative judgments,' 

If  we  consider  the  quantity  and  quality  of  judgments  as  com- 
bined, there  emerges  from  this  juncture  four  separate  forms  of  prop- 
.ositions,  for  they  are  either  Universal  Affirmative,  or  Universal 
Negative,  Particular  Affirmative,  or  Particular  Negative.  These 
forms,  in  order  to  facilitate  the  statement  and  analysis  of  the  syllo- 
gism, have  been  designated  by  letters,  and  as  it  is  necessary  that 
you  should  be  familiar  with  these  symbols,  I  shall  state  them  in  the 
following  paragraph. 

^  LII.  In  reference  to  their  Quantity  and  Quality  together. 
Propositions  are  designated  by  the  vowels 
o/'prop^siti^rs'ae"  ^'  E,  I,  O.  The  Universal  Affirmative  are 
cording  to  their  dcuotcd  by  A ;  the  Universal  Negative  by 
urniUl'e?'^"'^  E;  the  Particular  Affirmative  by  I;  the 
Particular  Negative  by  O.  To  aid  the 
memory,  these  distinctions  have  been  comprehended  in  the 
following  lines : 

Asserit  A,  negat  E,  sed  universaliter  ambae, 
Asserit  I,  negat  0,  sed  particulariter  ambo.^ 

1  Compare  Kmg,  Logik,  f  65.    Anm.  2.  —  2  Petms  Hispanns,  SHmmulai,  Tract,  r.  par- 

Ed.   [Against  the  distinction,  see  Bachmann,  tic.  4,  f.  9.    Cf  Petrus  Tartaretns;  ExpoaitU 

Logik,  §  84,  p.  128.     Schulze,  Logik,  J    50.  in  5u»imui<M,  Tract  i.  f.  9  b.  — Ed. 
Drobisek,  (  42.] 


180 


Loorc. 


Lkct.  XIT. 


I  may  here,  likewise,  show  you  one,  and  perhaps  the  best,  mode, 
in  which  these  different  forms  can  be  expressed  by  diagrams. 


Tlie  first  employment 
of  circular  diagrams 
in  logic  improperly 
tMcribed  to  Euler.  To 
be  found  in  Christian 
Weise. 


The  invention  of  this  mode  of  sensualizing  by  circles  the  abstrac- 
tions of  Logic,  is  generally  given  to  Euler,  who 
employs  it  in  his  Letters  to  a  German  Princess 
071  different  Matters  of  Physics  ayid  Philosophy} 
But,  to  say  nothing  of  other  methods,  this  by 
circles  is  of  a  much  earlier  origin.  For  I  find 
it  in  the  JVudeus  Logicoe  Weisiance,  which  ap- 
peared in  1712;  but  this  was  a  posthumous  publication,  and  the 
author.  Christian  Weise,  who  was  Rector  of  Zittau,  died  in  1708. 
I  may  notice,  also,  that   Lambert's  method  of 

LBmberfs    method       accomplishing  the  same   end,  by  parallel  lines 
to  be  found  in  Aste-  «.,./«  /         ,       .  i       *»         i  •       ^       -r       • 

jj^g  of  different  lengths,  is  to  be  found  in  the  Liogxc 

of  Alstedius,  published  in  1614,  consequently 
above  a  century  and  a  half  prior  to  Lambert's  Neues  Organon?  Of 
Lambert's  originality  there  can,  however,  I  think,  be  no  doubt;  for 
he  was  exceedingly  curious  about,  and  not  overlearned  in,  the  his- 
tory of  these  subsidia,  while  in  his  philosophical  coiTcspondence 
many  other  inventions  of  the  kind,  of  far  inferior  interest,  are 
recorded,  but  there  is  no  allusion  whatever  to  that  of  Alstedius. 
Before  leaving  this  part  of  the  subject,  I  may  take  notice  of  another 


1  P«rtieii.,Lcttrexxxv.,ed.Coumot.— Ed.  Logieer,    S^atema    Harmonieum    of   AlMcdiofi 

*  A  rery  imperftct  diagram  of  this  kind,  (1614),  p.  395.    Lambert's  diagrams  (  A>ik«  O- 

with  the  lines  of  equal  length,  in  illustration  ganon,  vol.  i.  p.  Ill  tt  nq.)  are  muoh  nun 

of  the  first  syllogistic  figure,  is  given  in  the  complete.  —  Ed. 


I 


hmxK.  XIY.  LOGIC.  181 

cUvisioQ  of  Propositions,  made  by  all  logicians — viz.,  into  I^ure  and 
Modal.  Pure  propositions  are  those  in  wliich  the  predicate  is  cate- 
gorically affirmed  or  denied  of  the  subject,  simply,  without  any  qualifi- 
cation ;  Modal,  those  in  which  the  predicate  is  categorically  affirmed 
or  denied  of  the  subject,  under  some  mode  or 
Olgtinctiop  of  Fro-       qualifying  determination.     For  example,  —  ^^ejc- 

pfieltions    into     Pure  ,  t   t^       •         •  < »  7 

and  Modal  anoer  conquered  JJarius,  is  a  pure,  —  A.lexancler 

conquered  Darius  honorably,  is  a  modal  j^ropo- 

iution.^  Nothing  can  be  more  futile  than  this  distinction.  The 
mode  in  such  propositions  is  nothing  more  than 

This  distinction  futile. 

a  part  oi  the  predicate.  1  he  predicate  may  be 
a  notion  of  any  complexity,  it  may  consist  of  any  number  of  attri- 
butes, of  any  number  even  of  words,  and  the  mere  circumstance 
that  one  of  these  attributes  should  stand  prominently  out  by  itself^ 
can  establish  no  diffei-ence  in  which  to  originate  a  distinction  of  the 
kind.  Of  the  examples  adduced,  —  the  pure  proposition,  Alexander 
oonqticred  Darius,  means,  being  resolved,  Alexander  was  the  con- 
queror of  Darius,  —  Alexander  being  the  subject,  was  the  copula, 
and  the  conqueror  of  Darius  the  predicate.  Now,  if  we  take  the 
modal,  —  Alexander  conquered  Darius  honorably,  and  resolve  it  in 
like  manner,  we  shall  have  Alexander  teas  the  honorable  conquei-or 
of  Darius;  and  here  the  whole  difference  is,  that  in  the  second  the 
predicate  is  a  litle  more  complex,  being  the  honorable  conqueror  of 
Darius,  instead  of  the  conqueror  of  Darius. 

But  logicians,  after   Aristotle,-  have   principally   considered   as 

modal  propositions  those  that  are  modified  by 
ivision  o      o  a       ^^^  ^^^^  attributions  of  Necessity,  Impossibility, 

Propogitions  by  logi-  .  .  .1  >         l  rf> 

cians.  Medals  as  Contingence,  and  Possibility.  But,  in  regard  to 
involving  the  consid-  these,  the  case  is  precisely  the  same ;  the  mode 
eration  of  the  matter       jg  merely  a  part  of  the  predicate,  and  if  so, 

of   a   proposition    are  ,  .  ,  -  ,  . 

extra-logical.  nothing  can  be  more  un wan-anted  than  on  this 

accidental,  on  this  extra-logical,  circumstance  to 
establish  a  great  division  of  logical  propositions.  This  error  is  seen 
in  all  its  flagrancy  when  applied  to  practice.  The  discrimination  of 
propositions  into  Pure  and  Modal,  and  the  discriminatioja  of  Modal 
propositions  into  Necessary,  Impossible,  Contingent,  Possible,  and 
the  recognition  of  these  as  logical  distinctions,  rendered  it  impera- 
tive on  the  logician,  as  logician,  to  know  what  matter  was  neces- 
sary, impossible,  contingent,  and   possible.     For  rules   were   laid 

.^  These  medals  are  not  acknowledged  by  by  the  Schoolmen.    Compare  Ammonia?,  //» 

A  listotle,  who  allows  only  the  four  mentioned  Be  Interp.,  p.  148  b,  ed.  1546.— Ed. 

huiow.    They  appear,  however,  in  his  Greek  2  De  Interp.,  c.  12.    Compare  AnaL  Prior,,  i, 

commentators,  and  from  tli«m  were  adopted  2.  —  £i». 


182  LOGIC.  Lect.  xir. 

doTm  in  regard  to  the  various  logical  operations  to  which  proposi- 
tions were  subjected,  according  as  these  were  determined  by  a 
matter  of  one  of  these  modes  or  of  another,  and  this,  too,  when  the 
modal  character  itself  was  not  marked  out  by  any  peculiarity  or 
form  of  expression.  Thus,  to  take  one  of  many  passages  to  the 
same  effect  in  Whately;  speaking  of  the  quality 

Whately  quoted.  „  .  .  ,  ^  '     %_,       *'  ,  ,  ?  % 

oi  propositions,  he  says,  "  When  the  subject  of 
a  proposition  is  a  Common-term,  the  tmiverscU  sigiis  ('  all,  no,  every,') 
are  used  to  indicate  that  it  is  distributed  (and  the  proposition  con- 
sequently is  universal) ;  the  particular  signs  ('  some,  etc.'),  the  con- 
trary. Should  there  be  no  sign  at  all  to  the  common  term,  the 
quantity  o/  the  proposition  (which  is  called  an  Indefinite  proposi- 
tion) is  ascertained  by  the  matter;  i.e.,  the  nature  of  the  connec- 
tion between  the  extremes :  which  is  either  Necessary,  Impossible, 
or  Contingent.  In  necessary  and  impossible  matter,  an  Indefinite 
is  understood  as  a  universal;  e.  g.,  birds  have  wings ;  i.  e.,  aU :  birds 
are  not  quadrupeds;  i.e.,  none:  in  contingent  matter  (t.  e.,  where 
the  terms  partly  (t.  e.  sometimes)  agree,  and  partly  not),  an  Indefi- 
nite is  understood  as  a  particular ;  e.  g^  food  is  necessary  to  life ;  ». «., 
smne  food ;  birds  sing ;  ».  c,  some  do ;  birds  are  not  carnivorous ; 
I.  e.,  some  are  not,  or  all  are  not."  ^ 

Now  all  this  proceeds  upon  a  radical  mistake  of  the  nature  and 
domain   of  Logic.     Losjic   is  a  purely   formal 

Criticized. 

science ;  it  knows  nothing  of,  it  establishes  noth- 
ing upon,  the  circumstances  of  the  matter,  to  which  its  form  may 
chance  to  be  applied.     To  be  able  to  say  that  a 

On   the   supposition  ,  .         .         ^  .  ... 

that  LoRic  takes  cog-       ^^'"8  '^  of  necessary,  mipossible,  or  contingent 

ninnce  of  tiie  modal-       matter,  it  is  requisite  to  generalize  its  nature 

ity    of   object?,  this      from  an  extensive  observation ;  and  to  make  it 

scence  can  ia\e  no  incumbent  on  the  logician  to  know  the  modality 
existence.  _  .... 

of  all  the  objects  to  which  his  science  may  Ik; 

applied,  is  at  once  to  declare  that  Logic  has  no  existence;  for  this 
condition  of  its  existence  is  in  every  point  of  view  impossible.  It 
is  impossible  —  1°,  Inasmuch  as  Logic  would  thus  presuppose  a 
knowledge  of  the  whole  cycle  of  human  science ;  and  it  is  impossi- 
ble —  2°,  Because  it  is  not  now,  and  never  will  be,  determined  what 
things  are  of  necessary  or  contingent,  of  possible  or  impossible  exist- 
ence. Speaking  of  things  impossible  in  nature,  Sir  Thomas  Brown 
declared  that  it  is  impossible  that  a  quadruped  could  lay  an  e^^,  ot 
that  a  quadruped  could  possess  the  beak  of  a  bird  ;  and,  in  the  ago 
of  Sir  Thomas  Brown,  these  propositions  would  have  shown  as 

I  EUmenU  o/Logik,  book  U.  ohftp.  ii.  f  8,  pp.  68,  M. 


I 


Lect.  XIV.  LOGIC.  188 

(rood  a  title  to  be  regarded  as  of  impossible  matter  as  some  of  the 
examples  adduced  by  Dr.  Whately.  The  discovery  of  New  Hol- 
land, and  of  the  Ornithorhynchus,  however,  turned  the  impossible 
into  the  actual;  for,  in  that  animal,  there  is  found  a  quadruped 
which  at  once  lays  an  egg  and  presents  the  bill  of  a  duck.  On  the 
principle,  then,  that  Logic  is  exclusively  conversant  about  the  forms 
of  thought,  I  have  rejected  the  distinction  of  propositions  and  syl- 
lo<Tisms  into  pure  and  modal,  as  extra-logical.  Wliatever  cannot  be 
stated  by  A,  B,  C,  is  not  of  logical  import ;  and  A,  B,  C,  know 
nothing  of  the  necessary,  impossible,  and  contingent.^ 

It  maybe  proper,  however,  to  explain  to  you  the  meaning  of  three 

terms  which  are  used  in  relation  to  Pure  and 

Explanation  of  three       Modal   propositions.      A   proposition  is   called 

terms  used  in  reference       Assertory,  wheu  it  cnounccs  what  is  known  as 

actual :  Problematic,  when  it  enounces  what  is 

Propositions.  '  ' 

known  as  possible ;  Apodeictic  or  Deinonstror 
five,  when  it  enounces  what  is  known  as  ^necessary.  ^ 

The  last  point  of  view  in  which  judgments  are  considered,  is  their 

Relation  to  each  other.     In  respect  of  these  rela- 

Third  Division  of      tions,  propositions  havo  obtained  from  Logicians 

Judgments— Relation  .       ,  i  •    t     i  i 

each  other  particular  names,  which,  however,  cannot  be  un- 

derstood without  at  the  same  time  regarding  the 
matter  which  the  judgments  contain.  As  the  distinctions  of  Judg- 
ments and  of  Concepts  are,  in  this  respect,  in  a  great  measure  analo- 
gous, both  in  name  and  nature,  it  will  not  be  necessary  to  dictate 
them. 

When  the  matter  and  form  of  two  judgments  are  considered  as 
the  same,  they  are  called  Identical,  Convertible, 
Judgments  identi-       Equal  OX  Equivalent  {propositiones  identicce, 
pares,  convertibiles,  cequipollentes) ;  on  the  oppo- 
Different.  site  alternative,  they  are  called  Different  {pr. 

diverscB).     If  considered  in  certain  respects  the 
Relatively  Identical.       Same,  in  others  different,  they  are  called  Eela- 
tively  Identical,  Similar,  or   Cognate  {pr.  rela- 
tive identicce,  similes,  affines,  cognatCB).      This   resemblance   may 
be  either  in  the  subject  and  comprehension,  or  in  the  predicate  and 
extension.     If  they  have  a  similar  subject,  their 
ispara  e.  predicates  are  Disparate  (disparata),  if  a  simi- 

Disjunct.  ^ar  predicate,  their  subjects  are  Disjunct  (dis- 

Junctd). 

I  See  JDucu«ion»,  p.  145  «««?.  — Ed.    [Com-     Loffik,  {  19.  p.  72,  and  i  23,  p.  79;  Schnlaa^ 
pare  Bacbmann,  Logik,  f  73,  p.  115;  Richter,     Logik,  §  52,  p.  78.] 
2  Kant,  Logik,  f  30.— Ed. 


184  LOGIC.  L»ox.  XIV. 

When  two  judgments  diflfer  merely  in  their  quantity  of  exten- 
sion, and  the  one  is,  therefore,  a  particular,  the 
other  a  general,  they  are  said  to  be  subordinated, 

and  their  relation  is  called  Subordination  (sttbordinatio).  The 
subordinating  (or  as  it  might,  perhaps,  be  more 
properly  styled,  the  super  ordinate)  judgment,  is 

called  the  Suhalternant  {subaltemans) ;  the  subordinate  judgment 

is  called  the  Subalternate  {stibaltematum). 

When,  of  two  or  more  judgments,  the  one  affirms,  the  other  de- 
nies, and  when  they  are  thus  reciprocally  difier- 

^(^^witionof  Judg-      ^^^  jj^  quality,  they  are  said  to  be  Opposed  or 

CofiJHctive  (pr.  ojypositce,  oLvTucciyxcvai),  and  their 

relation,  in  this  respect,  is  called  Opposition  (opjyositio).     This  oj)- 

'-  position  is  either  that  of  Contradiciion  or  He- 

.JCantradiotion.  puqnance    (contradictio.    a.vr!.<i>axTi%),   or   that   of 

Contrariety.  ^^"^  ^  ^  .  ,  .       \ 

Contrarietif  {contrartetas,  evan-ion/s). 

If  neither  contradiction  nor  contrariety  exists,  the  judgments  are 

called  Congruent  (pr.  congruentes^  consonantes^ 

^ongruen       u  g-       consentientes) .     In  regard  to  this  last  statement, 

you  will  find  in  logical  books,  in  general,'  that 

^bcoDtrary  oppod-       ^j^^^.^  j^  ^^  opposition  of  what  are  called  Sub- 

contraries  (svbcontraria),  meaning  by  these  par- 
ticular propositions  of  different  quality,  as,  for  example,  some  A  are 
B,  some  A  are  not  B ;  or,  som,e  men  are  learned,  some  men  are 
not  learned;  and  they  are  called  Sitbcontraries,  as  they  stand  sub- 
ordinated to  the  universal  contrary  propositions,  —  All  A  are  B,  no 
A  t»  B ;  or.  All  men  are  learned,  no  man  is  learned.    But  this  is  a 

mistake,  there  is  no  opposition  between  Subcon- 
^^j*ot  a  real  opposi-      trarics ;  for  both  may  at  once  be  maintained,  a^ 

both  at  once  must  be  true  if  the  some  be  a  nega- 
tion of  all.  They  cannot,  however,  both  be  false.  The  opposition 
In  this  case  is  only  apparent;'  and  it  was  probably  only  laid  down 
fK)m  a  love  of  symmetry,  in  order  to  make  out  the  opposition  of  *11 
the  comers  in  the  square  of  Opposition,  which  you  will  find  in 
almost  every  work  on  Logic. 


t  Elements  of  Logik,  by  Dr.  Whately,  part  Com'mfcnwiMM  JVora  Z.o^Va,  Tract  iii.  DJ»p.iti., 

ti.  «twp.  ti.  i  S,  p.  68,  ad  edit.    But  see  Soheib-  f  2,  p.  124,  edit.  ITll.    Kant  expressly  rt^ects 

le|\  Ofrrn    I^jgica^  I'ars  iii.  c.  xi.  p,  48T,  ed.  Svtiicaiitrariety,  Logik,  f  50.  Aiim.    Compare 

lflG6.      Ulricli,  llnstit.    Log.  ft  Met,  i  1S3,  p.  Krug,  Logi^,  f  64,  Anm.  4.     Braiiiss,  Grundnss 

190.  —  Ed.]  dtr    Logile,   p.   W&.     Denzingur,   iHstitutionet 

t  For  which  reason  Aristotle  describes  it  as  Logica,  vol.  ii. }  713,  p.  138.    Cararauel,  p  38 


mk  oppoeition  ia  language,  hut  not  in  reality.      [RatienaUt  tt  Rtalis  PkiioMpkia 
Anal.  Prior.,  ii.  15.  —  Ed.    [Compare  Fonseea,      Caramutl  LaUeatoitx,  S.  1%.  Lavmtiamti 
JnstU.  DiaUet.,  L.  iii.  c.  6,  p.  129,  ed.  1604.      4M<U«  Mttfensi,  Lovanii,  1642.  —Ed  ] 


Lect.  XIV. 


LOGIC. 


196 


Terms  employed  to 
t'.euote  the  original 
and  converted  propo- 
sition. 

pfop.,  convertens). 


Finally,  various  relatioas  of  judgments  arise  from  what  is  called 

their  Conversion.     When  the  subject  and  predi- 

CooverBiou  of  Pro-       ^.^^^  jj^  g^  categorical  proposition  (for  to  this  wo 

positions.  t     ,  •  ^         •      \  -11 

now  limit  our  consideration)  are  transposed,  the 

proposition  is  said  to  be  converted  ;  the  propositiou  given  and  its 
|)rodnct  are  both  called  the  jadicia  conversa;  the  relation  itself  of 
reciprocation  in  which  the  judgments  stand  is  called  Conversion^ 
sometimes  Obversion  and  Transposition  {reciprocatio^  conversio, 
obversio,  transpositlo,  /icra^ccrts,  fieTa^oXrj,  avTUf- 
Tpo<f>^).  The  given  proposition  is  called  the 
Converted  or  Converse  (Judicium^  proposition 
prcejaeens,  conversum,  eonversa) ;  the  other,  into 
which  it  is  converted,  the  Converting  (Jud., 
There  is,  however,  much  ambiguity,  to  say  the 
least  of  it,  in  the  terms  commonly  employed  by  Logicians  to  des- 
ignate the  two  propositions,  —  that  given,  and  that  the  product  of 
tlic  logical  elaboration.  The  prejacent  and  subjacent  may  pass,  but 
they  have  been  very  rarely  employed.  The  term  2}ropositio  con- 
u<9rsflr,  the  converse  or  converted  judgment,  specially  for  the  original 
proposition,  is  worse  than  ambiguous ;  it  is  applied  generally  to  both 
judgments;  it  may,  in  fact,  more  appropriately  denote  the  other, — 
its  product, — to  which  indeed  it  has,  but  through  a  blunder,  been 
actually  applied  by  Aldrich,^  and  he  is  followed,  of  course,  by 
Whately.  The  original  proposition  ought  to  be  called  the  Convert- 
end  or  Convertible  {pr.  convertenda,  convertibilis)?  The  terra  CoTirr 
verting  {convertens)  employed  for  the  proposition,  the  product  of 
conversion,  marks  out  nothing  of  its  peculiar 
roposttxs  txposua—       eharactcr.     The  expression  pr.  exposita,  applied 

Its  use  by  Aid  rich  er-  „      .  '     »  i 

roneous.  by  Aldrich,"  without  a  word  of  comment,  to  this 

judgment,  is  only  another  instance  of  his  daring 
ignorance  ;  for  the  phrase  pr.  eocposita  had  nothing  to  recommend 
it  in  this  relation,  and  was  employed  in  a  wholly  different  meaning 
by  logicians  and  mathematicians.*    In  this  error  Aldrich  is  followed 


1  B-mlirnentt^  Logic«B,  L.  1.  c.  ii. 

2  [So  NoJdiug,  p.  263,  [LogUa  Recognita,  Haf- 
aiae,  1766.  —  Ed.] 

3  Crakanthorpe,  Sanderson,  and  Wallis  [de- 
nominate the  original  proposition  pr.  con.' 
versa,  its  product  pr.  convertens.  See  Crakan- 
tliorpe,  Logica,  L.  iii.  c.  10,  p.  179,  ed.  1677. 
Sanderson,  Logica,  L.  ii.  0.  7,  p.  76,  ed.  1741. 
Wallis,  Institutio  Logicce,  L.  ii.  c.  7,  p  113, 
edit.  1729,  Wallis  alsQ  uses  pr.  convtrtettda  as 
a  synonym  for  pr.  conversa.  —  Ed.] 

*  The  term  exposition  ((K^tffis)  is  employed 
by  Aristotle,  and  by  most  subseqaent  logi- 


cians, to  denote  the  seleotiou  of  an  individual 
instance  whose  qualities  may  be  perceived  by 
sense  (iKTi^tyai,  exponere,  objicere  sensui),  in 
order  to  prove  a  general  relation  between  no- 
tions apprehended  by  the  intellect-  Thici 
method  is  used  by  Aristotle  in  proving  the 
conversion  of  propositions  and  the  reduction 
of  syllogisms.  See  Anal.  Prior  .  i.  2;  i.  6;  i.  8. 
The  instance  selected  is  called  the  expasitum. 
(tJi  iKTtbiv);  and  hence  singular  propwitiona 
aad  syllagisKks  are  called  to^ositonj.  Compare 
Pacius  on  Anal.  Pr.,  i.  2,  and  Sir  W.  Hamil' 
ton's  note,  Reicfs  Works,  p.  696.  —  Ed. 


24 


186  LOGIC.  Lkct.  XIV. 

by  Whately,  who,  like  his  able  pi'edecessor,  is  wholly  unversed  iu 
the  literature  and  language  of  Logic. 

The  logicians  after  Aristotle  have  distinguished  two,  or,  as  we  may 
take  it,  three,  or  even  four,  species  of  Conver- 

Species  of  Conver-         gion 

logicUms!"^'*  *     ^  ^'  ^^^  ^^*'  which  is  called  Simple  or  Pure 

Conversion  (conver sio  simplex,  tois  opois  ttpoi;  eav- 
njv,  Aristotle,  *.  e^  curn  terminis  reciprocatis)^  is  when  the  quantity 
and  quality  of  the  two  judgments  are  the  same.  It  holds  in  Uni- 
versal Negative  and  Particular  Affirmative  propositions. 

2.  The  second,  which  is  called  Conversion  by  Accident  {c.  per  ac 
cidens^  iv  fj.€pei,  Kara  fiipo';,  Aristotle),  is  when,  the  quality  remaining 
unaltered,  the  quantity  is  reduced.  It  holds  in  Universal  Affirma- 
tives. These  two  are  the  species  of  the  conversion  of  propositions 
acknowledged  by  all ;  they  are  evolved  by  Aristotle,  not,  as  might 
have  been  expected,  in  his  treatise  On  £nounc€tne?it,  but  in  the  sec- 
ond chapter  of  the  first  book  of  his  Prior  Analytics? 

3.  The  third,  which  is  called  Conversion  by  Contraposition  (c. 
per  oppositioneniy  c.  per  contra  positionem^  both  by  Boethius,'  con- 
traposition avTL(jTpo<f}T^  <rvv  avTiSta-u,  Alexander),*  is  when,  instead  of 
the  subject  and  predicate,  the  quantity  and  quality  remaining  the 
same,  there  is  placed  the  contradictory  of  each.  This  holds  in  Uni- 
versal Affirmatives,  and  most  logicians  allow  it  in  Particular  Nega- 
tives. It  is  commemorated  by  Aristotle  in  the  eighth  chapter  of  the 
second  book  of  his  Topics  :  it  is  there  called  the  inverse  consecution 
from  contradictions. 

I  shall  here  mention  to  you  some  mnemonic  verses  in  which  the 
doctrine  of  conversion  is  expressed. 

Mnemonic  verses  ex-  loii  j*  •  i*-..!*.*! 

1  .  liegardmg   conversion  as    hmited  to  tlie 

pressing  conversion.  ,  °  . 

Simple  and  Accidental,  and  excluding  altogether 
Contraposition,  we  have  the  doctrine  contained  in  the  two  following 
verses. 

1  Toij  %pois  i.trruTrpi(ptiV,  Anal.  Pr.,  I.  2,  logismo  Categorico,!..  i.,  p.  5S7.  Thus Mnr<».«io 
i.e.,  when  each  term  is  the  exact  equivalent  *»  divided  primarily  into  c.  simpUx  and  c.  per 
of  the  other.  See  Trendelenburg,  EUi}xenia  contrapositionem.  Aristotle  does  not  use  iy 
Log.  Ari.U.,  iU;  In  De  Anima,  p.  408;  WaiU,  ^*^*'.  »«  subsequent  logicians,  for  c.  diminuta. 
In  Arist.  Org.,  vol.  i.  p.  373  —  Ed.  !*<=  "^^  '^  mainly  tor  particular  in  opposition 

2  [Boethius  seems  the  first  who  gave  the  to  univer.'ial.  (See  Anal.  Prior,  i.  2,  »  4.)  They 
name  of  Cont^rsio  prr  Accidens.  With  him  it  »'^  «hus  wrong  in  their  use  of  the  words  oe<-.-. 
Is  properly  both  Ampliative  and  Kestrictive.  ''"""^  »'><1  partial.] 

(So  Ridiger,  De  Sensu  Veri  et  FaUi,  pp.  250,  ,  j„troductio  ad  Syllogismos  Categorios,  and 

803,  2d  edit.,  1722.    Fischer  Logik,  p.  108.)    It  ^  Syttogismo  OUtgorico,  L.  1.  -  Ed. 

is  opposed  as  a  oonspecies  to  c.  genrralis,  and 

both  are  sjiecies  of  c.  simplex,  which  is  op-         *  In  Anal.  Prior.,  £  10  b,  edit.  Aid.  1620.  - 

posed  to  Contrapositioo.    See  Opera,  D*  Syl-  Eo. 


k 


Lect.  XIV.  LOGIC.  19i 

£,  I,  simpliciter  vertendo,  signa  manebont; 
Ast  A  cum  vertis,  signa  minora  cape.i 

O  is  not  convertible. 

2°.  Admitting  Contraposition  as  a  legitimate  species  of  conver- 
sion, the  whole  doctrine  is  embodied  in  the  following  verses  by 
Petrus  Hispanus: 

F  E  c  I  (F  E  s  I)  simpliciter,  convertitar  E  v  A  (E  p  A)  per  Acdd, 
Ast  O  (A  c  0)  per  Contrap.;  sic  fit  conversio  tota.2 

Or,  to  condense  the  three  kinds  of  conversion  with  all  the  propo- 
sitions, prejacent  and  subjacent,  in  a  single  line : 

"EccE,  TiBi,  Simp. ;  Abmi — geros,  4cc. ;  Arha,  bono,  Cont."^ 

It  may  be  proper  now  to  make  you  acquainted  with  certain  dis- 
tinctions of  judgments  and  propositions,  which, 
Distinction  of  Pro-      tj^Qugh  not  Strictly  of  a  logical  character,  it  is 

,  positions   not  strictly  i_iju  v 

,    j^jjjj  oi    importance   that   you   should   be   aware  oi. 

"Considered  in  a  material  point  of  view,  all 
judgments  are,  in  the  first  place,  distinguished  into  Theoretical  and 

Practical.     Theoretical  are  such  as  declare  that 

core  ica  an     rac-       ^  certain  character  belongs  or  does  not  belong 

tical.  *=  ^ 

to  a  certain  object;  Practical,  Bwch.  as  declare 

that  something  can  be  or  ought  to  be  done,  —  brought  to  bear." 

"Theoretical,  as  well  as  practical  judgments,  are  either  Indemorir- 

strable,  when  they  are  evident  of  themselves  — 

Indemonstrable  and  i  ^i,  j  j.  •  i        ^  ^\ 

^        ,   ^,  when  they  do  not  require,  and  when  thev  are 

Demonstrable.  ,  •'  ^  ^  « 

incapable  of  proof:  or  they  are  Demonstrable, 
when  they  are  not  immediately  apparent  as  true  or  false,  but  require 
some  external  reason  to  establish  their  truth  or  falsehood." 

"  Indemonstrable  propositions  are  absolute  principles  {apx^-h  pi'it^ 
cipia) ;  that  is,  from  which  in  the  construction  of  a  system  of 
science,  cognitions  altogether  certain  not  only  are,  but  must  be 
derived.  Demonstrable  propositions,  on  the  other  hand,  can,  at 
best,  constitute  only  relative  principles ;  that  is,  such  as,  themselves 
requiring  a  higher  principle  for  their  warrant,  may  yet  afford  the 
basis  of  sundry  other  propositions." 

1  [Given  by  Chauvin,  Lex  Phil.,  v.  Conversio.     Tartaretns,  Eipositio  in  Summulas  Petri  Hit- 
Denzinger,  Institutiones  Logica,  ii.  140.]  pani,  Tract,  i.,  f,  9  b.  —  Ed.] 

2  See   Petrus    Hispanus,  p.   9,  [Summuka, 

Tract  1.,  partic.  4,  f.  9,  ed  1505.    C£  Petrus        3  [Hispanus,  Summulat,  I.  e.    Chaarin,  I.  e.\ 


l.$8  LOGIC.  tKCT.  :ja  •. 

"  If  the  indemonstrable  propositions  be  of  a  theoretical  character, 

they  are  called  Axioms;  if  of  a  practical  churac- 

Axioms  and  Portu-  Postulates.      The  former  are  principles  of 

liites.  .  .       , 

immediate   certainty;   the  latter,  principles  of 

immediate  application.'* 

"  Demonstrable  propositions,  if  of  a  theoretical  nature,  are  called 
Theorems  (theoremata) ;  if  of  a  practical,  Prob- 

^^Theorems  and  Trob-  ^^^^^  {problemuta).  The  former,  as  propositions 
of  a   mediate   certainty,   require   proof;    they, 

therefore,  consist  of  a  Thesis  and  its  Demonstration/  the  latter,  as 

of  mediate  ajjplication,  suppose  a  Question  {qucestio)  and  its  iSolu- 

tiou  (resolidio).^^ 

"  As  species  of  the  foregoing,  there  are,  likewise,  distinguished 
Corollaries  (consectaria.  coroUaria),  that  is, 
propositions  which  flow,  without  a  new  proof, 

out  of  theorems  or  postulates  previously  demonstrated.  Proposi- 
tions whose  validity  rests  on  obsenatiou  or  ex- 

^pei^uneuui  Propp-  periment  are  called  Experiential,  Experimental 
propositions   {empiremata^  experienticBy  eacperi- 

menta).    Hypotheses^  that  is,  propositions  which  are  assumed  with 

probability,  in  order  to  explain  or  prove  some- 

jp    1C8C8.  thing  else  which  cannot  otherwise  be  explained 

or  proved.  lemmata,  that  is,  propositions  borrowed  from  another 
science,  in  oi'der  to  serve  as  subsidiary  proposi- 
tions  in  the  science  of  which  we  treat,    r  mally, 

SchoUa-y  that  is,  propositions  which  only  serve  as  illustrations  of 
what  is  considered  in  chief.  The  clearest  and 
most    appropriate    examples    of   these    various 

kinds  of  propositions  are  given  in  mathematics.'' ' 

,  LofU,  I  79,  pp.  liT,  M8.  — Kd.    [OompueKnig.LofOs  fi  87,66.] 


i  •>  .5  ,(;iVU.  (1-J 


0':t 


LECTURE     XV. 

STOICHEIOLOGY. 

SECTION    II.  — OF  THE    PRODUCTS   OF    THOUGHT 

in.  — THE  DOCTRINE    OF  REASONINGS. 

REASONING  IN  GENERAL— SYLLOGISMS— THEIR  DIVISIONS  AC- 
CORDING TO  INTERNAL  FORM. 

Iw  my  last  Lecture,  I  terminated  the  Doctrine  of  Judgments, 
and  now  proceed  to  that  of  Reasonings. 

"When  the  necessity  of  the  junction  or  separation  of  a  certain 

subject-notion  and  a  certain  predicate  notion  is 

•n,e  act  of  reasoning       ^^^  manifest  from  the  nature  of  these  notions 

—  what. 

themselves ;  but  when,  at  the  same  time,  we  are 
desirous  of  knowing  whether  they  must  be  thought  as  inclusive,  or 
as  exclusive  of  each  other,  —  in  this  case,  we  find  ourselves  in  a 
state  of  doubt  or  indecision,  from  our  ignorance  of  which  of  the 
two  contradictory  predicates  must  be  affirmed  or  denied  of  the  sub- 
ject. But  this  doubt  can  be  dissipated, — this  ignorance  can  be 
removed,  only  in  one  way,  —  only  by  producing  in  us  a  necessity 
to  connect  with,  or  disconnect  from,  the  subject  one  of  the  re- 
pugnant predicates.  And  since,  ex  hypothesis  this  necessity  does 
not  —  at  least,  does  not  immediately —  arise  from  the  simple  knowl- 
edge of  the  subject  in  itself,  or  of  the  predicate  in  itself,  or  of  both 
together  in  themselves,  it  follows  that  it  must  be  derived  from  some 
external  source,  —  and  derived  it  can  only  be,  if  derived,  from  some 
other  knowledge,  which  affords  us,  as  its  necessary  consequence,  the 
removal  of  the  doubt  originally  harbored.  But  if  this  knowledge 
has  for  its  necessary  consequence  the  removal  of  the  original  doubt, 
this  knowledge  must  stand  to  the  existing  doubt  in  the  relation  of 
a  general  rule ;  and,  as  every  rule  is  a  judgment,  it  will  constitute  a 
general  proposition.  But  a  general  rule  does  not  simply  and  of 
itself  reach  to  the  removal  of  doubt  and  indecision ;  there  is  re- 
quired, and  necessarily  required,  over  and  above  this  further  knowl- 


190  LOGIC.  Lect.  XV. 

edge  —  that  the  rule  has  really  an  application,  or,  what  is  the  same 
thing,  that  the  doubt  really  stands  under  the  general  proposition,  as 
a  case  which  can  be  decided  by  it  as  by  a  general  rule.  But  when 
the  general  rule  has  been  discovered,  and  when  its  application  to 
the  doubt  has  likewise  been  recognized,  the  solution  of  the  doubt 
immediately  follows,  and  therewith  the  determination  of  which  of 
the  contradictory  predicates  must  or  must  not  be  affirmed  of  the 
subject;  and  this  determination  is  accompanied  with  a  conscious- 
ness of  necessity  or  absolute  certainty." '  A  simple  example  will 
place  the  matter  in  a  clearer  light.  When  the 
.u  rat      yanex-       ^otion  of  the  subject  man  is  given  alonw  with 

ample  ^  "^         .  ®  '^ 

the  contradictory  predicates/rcc  agent  and  neces- 
sary agents  there  arises  the  doubt,  with  which  of  these  contradic- 
tory predicates  the  subject  is  to  be  connected ;  for,  as  contradictoiy, 
they  cannot  both  be  affirmed  of  the  subject,  and,  as  contradictory, 
the  one  or  the  other  must  be  so  affirmed ;  in  other  words,  I  doubt 
whether  man  be  a  free  agent  or  not.  The  notion  man^  and  the 
repugnant  notions  free  agent  and  necessary  agenty  do  not,  in  them- 
selves, affi^rd  a  solution  of  the  doubt;  and  I  must  endeavor  to  dis- 
cover some  other  notion  which  will  enable  me  to  decide.  Now, 
taking  the  predicate  free  agent,  this  leads  me  to  the  closely  con- 
nected notion  moraUy  responsible  agent,  which,  let  it  be  supposed 
that  I  otherwise  know  to  be  necessarily  a  free  agent,  I  thus  obtain 
the  proposition.  Every  moraUy  responsible  agent  is  a  free  agent. 
But  this  proposition  does  not  of  itself  contain  the  solution  of  the 
doubt ;  for  it  may  still  be  asked,  Does  the  notion  moraUy  responsible 
agent  constitute  a  predicate  which  appertains  to  the  notion  of  man, 
the  subject?  This  question  is  satisfied,  if  it  is  recognized  that  the 
notion  man  involves  in  it  the  notion  of  a  moraUy  responsible  agent, 
I  can  then  say,  Man  is  a  moraUy  responsible  agent.  These  two 
propositions  being  thus  formed  and  applied  to  the  subsisting  doubt, 
the  removal  of  this  doubt  follows  of  itself,  and,  in  place  of  the 
previous  indecision,  whether  man  be  a  free  agent  or  not,  there  fol- 
lows, with  the  consciousness  of  necessity  or  absolute  certainty,  the 
connected  judgment  that  Man  is  also  a  free  agent.  The  whole 
process  —  the  whole  series  of  judgments  —  will  stand  thus: 

Every  monjUy  rtspongibU  agmt  it  a  free  <tQeHt; 
Man  is  a  morally  responsible. agent ; 
Thenjore,  man  is  a  fret  agent. 

Let  as  consider  in  what  relation  the  different  constituent  parts  of 

1  Bner,  Lofikt  (  83,  p.  lU. 


Lect.  XV. 


LOGIC. 


191 


The  example  given 
is  a  Seasoning  in  the 
whole  of  Extension, 
i:ii<l  may  be  repre- 
sented by  three  circles. 


this  process  stand  to  each  other.  It  is  evident  that  the  whole  pro- 
cess  consists  of  three  notions  and  their  mutual 
relations.  The  three  notions  are,  free  agent, 
responsible  agent,  and  man.  Their  mutual  rela- 
tions are  all  those  of  whole  and  part,  and  whole 
and  part  in  the  quantity  of  extension ;  for  the 
notion  free  agent  is  seen  to  contain  under  it  the 
notion  responsible  agent,  and  the  notion  responsible  agent  to  contain 
under  it  the  notion  man.  Thus,  these  three  notions  are  like  tliree 
circles  of  three  various  extensions  severally,  contained  one  within 
another ;  and  it  is  evident,  that  the  process  by  which  we  recognize 
that  the  narrowest  notion,  man,  is  contained  under  the  widest 
notion,  responsible  agent,  is  precisely  the  same  by  which  we  should 
recognize  the  inmost  circle  to  be  contained  in  the  outmost,  if  we 
were  only  supposed  to  know  the  relation  of  these  together  by  their 
relation  to  the  middle  circle.     Let  ABC  denote  a 

the  three  circles.  Now,  ex  Jiypothesi,  we  know, 
and  only  know,  that  A  contains  B,  and  that  B  con- 
tains C ;  but  as  it  is  a  self-evident  principle,  that  a 
part  of  the  part  is  a  part  of  the  whole,  we  cannot, 
with  our  knowledge  that  B  contains  C,  and  is  con- 
tained in  A,  avoid  recognizing  that  C  is  contained  in  A.  This  is 
j)recisely  the  case  with  the  three  notions — free  agent,  responsible 
agent,  man ;  not  knowing  the  relation  between  the  notions  free 
agent  and  man,  but  knowing  that  free  agent  contained  under  it 
responsible  agent,  and  that  responsible  agent  contained  under  it 
m,an,  we,  upon  the  principle  that  the  part  of  a  part  is  a  part  of  the 
whole,  are  compelled  to  think,  as  a  necessary  consequence,  that 
free  agent  contains  under  it  man.  It  is  thus  evident,  that  the  pro- 
cess shown  in  the  example  adduced  is  a  mere  recognition  of  the 
relation  of  three  notions  in  the  quantity  of  extension,  —  our  knowl- 
edge of  the  relation  of  two  of  these  notions  to  each  other  being  not 
given  immediately,  but  obtained  through  our  knowledge  of  their 
relation  to  the  third. 

But  let  us  consider  this  process  a  little  closer.  The  relations  of 
the  three  notions,  in  the  above  example,  arc 
those  given  in  the  quantity  of  Breadth  or  Ex- 
tension. But  every  notion  has  not  only  an 
Extensive,  but  likewise  an  Intensive,  quantity, 
— not  only  a  quantity  in  breadth,  but  a  quan- 
tity in  depth ;  and  these  two  quantities  stand  to 
each  other,  as  we  have  seen,^  always  in  a  determinate  ratio,  —  the 


The  reasoning  of 
Kxtension  may  be 
exhibited  in  Compre- 
hension —  this  illus- 
trated. 


1  See  above,  p.  104.  —  £d. 


192  xoaio.  L«cT.  x\ 

ratio  of  inversion.  It  would,  therefore,  appear,  a  priori,  to  be  a 
necessary  presumption,  that  if  notions  bear  a  certain  relation  to 
each  other  in  the  one  quantity,  they  must  bear  a  counter  relation  to 
each  other  in  the  other  quantity ;  consequently,  that  if  we  are  able, 
under  the  quantity  of  extension,  to  deduce  from  the  relations  ot 
two  notions  to  a  third  their  relation  to  each  other,  a  correspondent 
evolution  must  be  competent  of  the  same  notions,  in  the  quantity 
of  comprehension.  Let  us  try  whether  this  theoretical  presumption 
bo  warranted  a  posteriori,  and  by  experiment,  and  whether,  in  tlie 
example  given,  the  process  can  be  inverted,  and  the  same  result 
obtained  with  the  same  necessity.  That  example,  as  in  extension, 
was : 

AU  responsible  agents  are  free  agents ; 

But  man  is  a  responsible  agent; 

Therefore,  man  is  a  free  agent. 

in  other  words,  —  the  notion  responsible  agent  is  contained  under 
the  notion yVee  agent;  but  the  notion  man  is  contained  under  the 
notion  responsible  agent;  therefore,  on  the  principle  that  the  part 
of  a  part  is  a  part  of  the  whole,  the  notion  man  is  also  contained 
under  the  notion /Vee  agent.  Now,  on  the  general  doctrine  of  the 
relation  of  the  two  quantities,  we  must,  if  we  would  obtain  the 
same  result  in  the  comprehensive  which  is  here  obtained  under  tlio 
extensive  quantity,  invert  the  whole  process,  that  is,  the  notions 
which  in  extension  are  wholes  become  in  comprehension  parts,  an<l 
the  notions  which  in  the  former  are  parts,  become  in  the  latter 
wholes.  Thus  the  notion  free  agent,  which,  in  the  example  given, 
was  the  greatest  whole,  becomes,  in  the  counter  process,  the  small- 
est part,  and  the  notion  man,  which  was  the  smallest  part,  now 
becomes  the  greatest  whole.  The  notion  responsible  agent  remains 
the  middle  quantity  or  notion  in  both,  but  its  relation  to  the  two 
oth<?r  notions  is  reversed ;  what  was  formerly  its  part  being  now 
its  whole,  what  was  formerly  its  whole  being  now  its  part.  The 
process  will,  therefore,  be  thus  explicitly  enounced  : 

The  fiction  man  comprehends  in  it  the  notion  responsible  agent  ; 
But  the  notion  responsible  agent  comfirebends  in  it  the  notion  free  agent ; 
ThereforefOn  the  principle  that  the  part  of  a  part  is  a  part  tf  the  whole,  tfie  notion  man 
also  comprehaids  in  it  the  notion  free  agent. 

Or,  in  common  language : 

Mdfn  is  a  responsible  agent  / 

But  a  responsible  agent  is  n  firm  ttgiM; 

Thertfore,  man  is  a  free  agent. 


Lect.  XV.  LOGIC.  196 

This  reversed  process,  in  the  quantity  of  comprehension,  gives,  it  is 
evident,  the  same  result  as  it  gave  in  the  quantity  of  extension. 
For,  on  the  supposition,  that  we  did  not  immediately  know  that  the 
notion  man  comprehended  free  agent,  but  recognized  that  man 
comprehended  responsible  agen%  and  that  responsible  agent  com- 
prehended free  agent,  we  necessarily  are  compelled  to  think,  in  the 
3vent  of  "his  rec':gni':ion^  Lhat  the  nction  m.a"^  comprehends  the 
notion  free  agent. 

It  is  only  necessary  further  to  observe,  that  in  the  one  process,  — 
that,  to  wit,  in  extension,  the  copula  is,  means  is 

The  copula  in  ex-  contained  under,  whereas,  in  the  other,  it  means 
tension  and  compre-       comprehends  hi.     Thus  the  proposition,  —  G^orf 

hension   of  a  counter  ./.t*  t  -i 

meaning.  **  mercxful,  Viewed  as  m  the  one  quantity,  sig- 

nifies God  is  contained  under  merciful,  that  is, 
the  notion  God  is  contained  under  the  notion  merciful;  viewed  as 
in  the  other,  means,  —  God  comprehends  merciful,  that  is,  the  notion. 
God  comprehends  in  it  the  notion  merciful. 

Now,  this  process  of  thought  (of  which  I  have  endeavored  to 
give  you  a  general  notion)  is  called  Reasoning;  but  it  has,  like- 
wise, obtained  a  variety  of  other  designations.  The  definition  of 
this  process,  with  its  principal  denominations,  I  shall  include  in  the 
following  paragraph. 

^  LIU.  —  Reasoning  is  an  act  of  mediate  comparison   or 
Judgment;    for  to  reason  is  to   recognize - 
Par.  Liii.  Definition      \^^2X  two  uotious  Stand  to  cach  othcr  in  the  ■ 

of     the     process    of  i..  r.  ■<     •%  -\    .  t  i 

Keasoning,  with  the       rclatiou  ot  a  wholc  and  its  parts,  through 
principal   denomina-       a  rccognition,  that  thcsc  notious  severally 

tions   of  process  and  .         i..,i  i..  .  .i.-i/-^. 

product.  stand  in  the  same  relation  to  a  third.    Con- 

sidered as  an  act.  Reasoning,  or  Discourse 
of  Reason  (to  Xoyt^co-^ai,  Xoywr/xo's,  Siavota,  to  Siavoetcr^ai),  is,  likC'- 
wise,  called  the  act  or  process  of  Argumentation  {argumenta- 
tionis),   of  Ratiocination   (ratiocinationis),   of   Inference  or~ 
Illation  (inferendi),  of  Collecting  (colligendi),  of  Concluding: 
(concludendi),  of  Syllogising   {tov   (rvAAoyt'^eor^ai,  barbarously 
syllogisandi).     The  term  Reasoning  is,  likewise,  given  to  the- 
product  of  the  act;    and  a  reasoning  in  this   sense  (ratioci- 
natio,   ratiocinium),   is,    likewise,    called    an   Argumentation- 
{argumentatio)  ;  also,  frequently,  an  Argument  (argumentum)., , 
an  Inference  or  Illation  (illatio) ;  a    Collection  (collectio),  a 
Conclusion  {conclusion  trvfnrepaafjM) ;  and,  finally,  a  Syllogism^ 
(crvXXoy  «r/Aos) . 

26 


194  LOfiBIC.  fjEcT.  XT- 

A.  few  words  in  explanation  of  these  will  suffice  ;  and,  first,  of 

the  thing  and  its  definition,  thereafter    of   its 
Explicatioir. 

names. 

In  regard  to  the  act  of  Reasoning,  nothing  can  be  more  eiToneous 
than  the  ordinary  distinction  of  this  process,  as 
^^LThe  Ai5t  of  Reas-       ^j^^  operation  of  a  faculty  different  in  kind  from 
those  of  Judgment  and   Conception.     Concep- 
tion, Judgment,  and  Reasoning,  are  in  reality  only  various  applica- 
tions of  the  same  simple  faculty,  that  of  Comparison  or  Judgment. 
I  have  endeavored  to  show  that  concepts  are  merely  the  results, 
rendered  permanent  by  language,  of  a  previous  process  of  compari- 
.Hon ;  that  judgment  is  nothing  but  comparison,  or  the  results  of 
comparison,  in  its  immediate  or  simpler  form  ;  and,  finally,  that  reas- 
oning is  nothing  but  comparison  in  its  mediate  or  more  complex 
application.^     It  is,  therefore,  altogether  erroneous  to  maintain^  as  is 
commonly  done,  that  a  reasoning  or  syllogism  is 
reason  ng      one       ^  mere  decompound  whole,  made  up  of  judg- 

organic  whole.  /  .  r  j       o 

ments ;  as  a  judgment  is  a  compound  whole, 
made  up  of  concepts*  This  is  a  mere  mechanical  mode  of  cleaving 
the  mental  phenomena  into  parts ;  and  holds  the  same  relation  to  a 
genuine  analysis  of  mind  which  the  act  of  the  butdier  does  to  that 
of  the  anatomist.  It  is  true,  indeed,  that  a  syllogism  can  be  sepa- 
rated into  three  parts  or  propositions ;  and  that  these  propositions 
have  a  certain  meaning,  when  considered  apart,  and  out  of  relation 
to  each  other.  But,  when  thus  considered,  they  lose  the  whole  sig- 
nificance which  they  had  when  united  in  a  reasoning;  for  their 
whole  significance  consisted  in  their  reciprocal  relation,  —  in  the 
light  which  they  mutually  reflected  on  each  other.  We  can  cer- 
tainly hew  down  an  animal  body  into  parts,  and  consider  its  mem- 
bers apait ;  but  these,  though  not  absolutely  void  of  all  meaning, 
when  viewed  singly  and  out  of  relation  to  their  whole,  have  lost  the 
principal  and  peculiar  significance  which  they  possesse<l  as  the  coef- 
ficients of  a  one  organic  and  indivisible  whole.  It  is  the  same  with 
a  syllogism.  The  parts  which,  in  their  organic  union,  possessed  life 
and  importance,  when  separated  from  each  other  remain  only  enun- 
ciations of  vague  generalities,  or  of  futile  identities.  Though,  when 
expressed  in  language,  it  be  necessary  to  analyze  a  reasoning  into 
parts,  and  to  state  these  parts  one  after  another,  it  is  not  to  be  sup- 
posed that  in  thought  one  notion,  one  proposition,  is  known  before 
or  after  another ;  for,  in  consciousness,  the  three  notions  and  their 
reciprocal  relations  constitute  only  one  identical  and  simultaneous 
cognition. 

1  6m  above,  pp.  88, 07.  — ft>. 


ElfcT.  xt.  to  ore.  f9S 

The  logicianis  have  indeed  all  treated  the  syllogisih  as  if  this 

were  not  the  case.     They  have  considered  one 

Error  of  logicians  in       proposition  as  naturally  the  last  in  expression, 

their  treatment  of  the  S   ,.        ,         ,  .  ,.       ,  „     -,      , 

Syllogism.  ^^^  ^"^^  ^"^y  have  accordingly  called  the  con- 

cluHon;  whilst  the  other  two,  as  naturally  goirig 
before  the  other  two,  they  have  styled  the  premises^  forming  to- 
gether what  they  call  the  antecedent.  The  two  premises  they  have 
also  considered  as  the  one  the  greater  (major).,  the  other  the  less 
(minor),  by  exclusive  reference  to  the  one  quantity  of  extension. 
AH  this,  however,  is,  in  my  view,  completely  erroneous.  For  we 
may,  in  the  theory  of  Logic,  as  we  actually  do  in  its  practical  appli- 
eationi5,  indifferently  enounce  what  is  called  the  conclusion  first  dr 
last.  In  the  latter  case,  the  conclusion  forms  a  thesis,  and  the  prem- 
ises its  groundis  or  reasons ;  and  instead  of  the  inferential  there- 
fore (ergo,  o^p°)i  we  would  employ  the  explicative /br.  The  whole 
diffbrence  consists  in  this,  —  that  the  common  order  is  synthetic, 
the  other  analytic;  and  as,  to  express  the  thought,  we  must  analyze 
it,  the  analytic  order  of  statement  appears  certainly  the  most  direct 
and  natural.*  On  the  subordinate  matter  of  the  order  of  the  prertl- 
ises,  I  do  not  here  touch.  , 

But  to  speak  of  thfe  process  in  general :  —  without  the  power  of 
reasoning  we  should  have  been  limited  in  our 
II  >o     epiocess      knowledge  (if  knowledge  of  such  a  limitation 

of  reasoning.  o       \  o 

would  deserve  the  name  of  knowledge  at  all), 
—  I  say  without  reasoning  we  should  have  been  limited  to  a  knowl- 
edge of  what  is  given  by  immediate  intuition;  we  should  have  been 
unable  to  draw  any  inference  from  this  knowledge,  and  have  been 
shut  out  from  the  discovery  of  that  countless  multitude  of  truths, 
which,  though  of  high,  of  paramount  importance,  are  not  self-evi# 
dent.  This  faculty  is,  likewise,  of  peculiar  utility,  in  order  to  pro- 
tect us,  in  our  cogitations,  from  eiTor  and  falsehood,  and  to  removfe 
these  if  they  have  already  crept  in.  For  every,  the  most  complex, 
web  of  thought  may  be  reduced  to  simple  syllogisms;  and  when 
this  is  done,  their  truth  or  falsehood,  at  least  in  a  logical  relation, 
flasiies  at  once  into  view. 

Of  the  terms  by  which  this  process  is  denoiti- 

2.  Terms  by  which       inated,  Reasoning  is  a  modification   from   the 

the  proce.8  of  Reason-      Preuch   roisonn^r  (and  this  a  derivation  from 

ing  18  denominated.  .  * 

the  Latm  ratio),  and  corresponds  to  ratioci?iatio, 
cination.  which  has  indeed  been  immediately  transferred 

iatd  Out  language  under  the  form  ratiocination. 
Ratiocination  denotes  properly  the  process,  but,  improperly,  also 

1  ArisMtte^  Analytics  are  Bynthetie^ 


196  LOGIC.  Lkct.  XY. 

the  product  of  reasoning ;  Jiatiocinium  marks  exclusively  the  pro- 
duct.    The  oriffinal  meaning  of  ratio  was  com- 

Discoiirsc 

putation,  and,  from  the  calculation  of  numbers, 
it  was  transferred  to  the  process  of  mediate  comparison  in  general. 
Discourse  {discursus^  hiavota)  indicates  the  operation  of  compari- 
son, the  running  backwards  and  forwards  between  the  characters  or 
no^es  of  objects  --  {(^iscu-rerc  inter  notas,  huur^wrBouL,  :  this  *3nn 
may,   therefore,  be  properly  applied   to  the   Elaborative   Faculty 
in  general,  which  I  have  just  called  the  Discursive.     The  terms 
discourse    and    discursics,   Sidvoia,   are,   liowever,   often,   nay   gen- 
erally, used  for  the  reasoning  process,  strictly  considered,  and  dis- 
imrsive  is  even  applied  to  denote  mediate,  in  opposition  to  intuitive, 
judgment,  as  is  done  by  Milton.^     The  compound  term,  discourse 
of  reason^  unambiguously  marks  its  employment   in   this   sense. 
Argumentation  is   derived  from    arffumentari, 
rgumen  a  on.       which  means  argttJnentis  uti,'  argument  again, 
argumentum,,  —  what   is   assumed   in   order   to 
argue  something,  —  is  properly  the  middle  notion  in  a  reasoning, — 
that  through  which  the  conclusion  is  established ;  and  by  the  Latin 
Rhetoricians  it  was  defined,  —  "probabile  inventum  ad  faciendam 
fidem." '    It  is  often,  however,  applied  as  coextensive  with  argu- 
mentation.    Inference  or  illation  (froui  infero). 

Inference.  ,     ,,  ,         "^         .  .  ,^    ,  "^         . 

indicates  the  carrying  out  into  the  last  proposi- 
tion what  was  virtually  contained  in  the  antecedent  judgments. 

To  conclude   (concludere).  again,  signifies  the 
To  conclude.  „  ^ .  -,,..,, 

act   of  connecting   and  shutting  into  the  last 

proposition  the  two  notions  which  stood  apart  in  the  two  first.     A 

conclusion  (conclusio)  is   usually  taken,  in    its 

Conclnsion.  .  .       .'1        . 

*  Strict  or  proper  signification,  to  mean  the  last 

proposition  of  a  reasoning ;  it  is  sometimes,  however,  used  to  express 
the  product  of  the  whole  process.    To  syllogize  means  to  form  syllo- 
gisms.  Syllogism  (trvXAoyw/io?)  seems  originally, 

To  Syllotrixe .  ,.,  .  t  i  ^  .. 

SyiioKtem  "^^  rotxo,  to  have  denoted  a  computation  —  an 

adding  up  —  and,  like  the  greater  part  of  the 

technical  terms  of  Logic  in  general,  was  borrowed  by  Aristotle  from 

the  mathematicians.*    This  primary  meaning  of  these  two  words 

J. I  ftni^ut  JLo*!,  r.  486,  —  reason,  aided  with  the  inflaenee  of  dirine 

"  Whence  thBioul  grace."  — Ed. 

Raaion  recelrea,  and  rctuon  U  her  bclDK,  '  Cicero,  OnUoria  PartitiomtM,  G.  2.     Cf.  D'S- 

;,! ,      Olscunivc  or  IntoitiTC;  ditconne  CMSIOIU,  p.  149.  —  Ed. 

Iione.tyoan."-ED.  4  [gee  Piccartus,   O^.  Arist.,  pp.  4«7,  46*. 

^  Shakspcare,  Hamlet,  act  1,  so.  2,—  Ammonins,  In  Qiiinqve  Voces,  f.  1.     l'hn<^M>- 

•'  nns, /n  jIk.  Pn'of ,  f.  li>.    raciiu, />«.  m  (ky.. 

" *  »*••*•  "»•*  '""'•  dl»eouF«.  of  remMn.  jjg   ^^     Bcrtiug,  Log.  Perip.  p.  119.    Bat 

Would  hare  mourned  lonnr."  nr   i.      ^               t        no.      ro   i.    <        r      •>. 

^^  ••«  Wait*,  OrgoHon  I.  p.  884.    [Schaln,  LogOt, 

Booker,  S.  F.,  ill.  8,  18  •>  •'  Bj  diaoowM  of     t  70,  p.  lOL    Ditctutitm*,  p.  607,  not*.  -«  Ed.] 


Lkct.  XV. 


LOGIC.  1§^ 


favors  the  theory  of  those  philosophers  who,  like  Hobbes  ^  and  Lei- 
denfrost,''  maintain  that  all  thought  is,  in  fact,  at  bottom  only  a  cal- 
culation, a  reckoning.  2wAAoy«r/xos  may,  however,  be  considered  as 
expressing  only  what  the  composition  of  the  word  denotes,  —  a  col- 
lecting together;  for  <rvXA.oyi^£o-^at  comes  from  oTjAAcyav,  which  signi- 
fies to  coUect?  Finally,  in  Latin,  a  syllogism  is 
called  collection  and  to  reason  coUigere.  This 
refers  to  the  act  of  collecting,  in  the  conclusion,  the  two  notions 
scattered  in  the  premises. 

.  "  From  what  has  already  been  said  touching  the  character  of  the 
reasoning  process,  it  is  easy  to  see  what  are  the 

The  general  coiidi-  ,  ,.   .  i  •   i  n       • 

-    ,,    .  general  conditions  which   every  syllogism  sup- 

tions  of  svllogism.  o  j       j       ts  f 

poses.  For,  as  the  essential  nature  of  reasoning 
consists  in  this,  —  that  some  doubt  should  be  removed  by  the  appli- 
cation to  it  of  some  decisive  general  rule,  there  are  to  every  syllo- 
gism three,  and  only  three,  requisites  necessary;  1°,  A  doubt, — 
which  of  two  contradictory  predicates  must  be  affirmed  of  a  certain 
subject,  —  the  problem  or  question  (problema,  quaesitum)  ;  2°,  The 
application  of  a  decisive  general  rule  to  the  doubt;  and,  3°,  The 
general  rule  itself.  But  these  requisites,  when  the  syllogism  is  con- 
structed and  expressed,  change  their  places ;  so  that  the  general  rule 
stands  first,  the  application  of  it  to  the  doubt  stands  second,  and  the 
decision  in  regard  to  the  doubt  itself  stands  last.  Each  of  these 
necessary  constituents  of  a  syllogism  forms  by  itself  a  distinct,  though 
a  correlative,  proposition  ;  every  syllogism,  therefore,  contains  three 
propositions,  and  these  three  propositions,  in  their  complement  and 
correlation,  constitute  the  syllogism."  *  It  will  be  proper,  however, 
here  to  dictate  a  paragraph,  expressive  of  the  denominations  techni- 
cally given  to  the  parts,  which  proximately  make  up  the  syllogism. 

^  LIV.  A  Reasoning  or  Syllogism  is  composed  of  two 
parts,  —  that  which  determines  or  precedes,  and  that  which 
follows  or  is  determined.  The  one  is  called  the  Antecedent 
(anteceilens) ;  the  other,  the  Consequent  (consequens).  The 
Antecedent  comprises  the  two  propositions,  tlie  one  of  which 

^  Leviathan, Vt.\.c.b\  Computatio  sive  Log-  avWoyifffJiSs     .      .      .      ws  ffvWtyov  rrjv  ip 

tea,  c.  1.    Cf.  Stewart,  EUments,  P.  ii.  c.  ii.  §  wa<rt    tois    opois    Si«nrapfxeirqv    dirdS*t|ij'!" 

3;   Works,  vol.  iii.  p.  132  et  seq.  —  Ed.  Cf.  Zabarella,  In  Anal.  Post.,  1.  1,  Optra  Log- 

2  D-'  Mfntr.  Humana,  c.  viii.  H  4, 10,  pp.  112,  tea,  p.  640.     "SfWoyKrixhi,  non  (rvWoyr)  rwv 

118,  ed.  1793.  —  Ed.  \6yeev,  sed  quasi  avWoy^  rod  \6yov,  coUfrrirt 

•"i  Euirenios,  AoyiKi],  p.  405,  et  ibi  Blemmi-  rationii;  ratio  autem  coUigi  dicitur,  dum  ci,i.- 

flae  [Kcu  rh  fxey  Syofia,  on  ffvWoyl]  ris  i<rr\  clusio  infertur;  quare  a  conclusione  potiue, 

\iyti)v   •ir\ei6uoiv   iv  avrtf     .     .     .     'O  Se  quam  a  propositionibus  dictus  est  8yllogi» 

BAfjUjulS.  iv  ''Evirofi.  Aoy.  Ke<p.  \d,  "Tlori  mus."  —  Ed.] 

5«  ;fol  avrh  rh  vvivwipaa^ui  KoKflToi  {^pr^al)  4  Eager,  Logik,  \  83,  p.  166. 


t^  hJOQW.  Lect.XV. 

enounces  the  general  rule,  and  the  other  its  application.    These, 
from  their  naturally  preceding  the  conae- 

na^uons^^'th^raru  q"<^"*'  »^®  ^^^^^^  ^hc  Frcmises  {proposi- 
which  proximately  tioncs  proEmissce^  sumptio7ies^  membra  atUe- 
^nu  ^^  ^^^  '^"°  cedentia,  Xi^/A/x«Ta).  Of  the  premises,  the 
one  which  enounces  the  general  rule,  or  the 
relation  of  the  greatest  quantity  to  the  lesser,  is  called  the  Major 
Premise^  or  Major  Proposition^  or  the  Proposition  simply 
{propositio  major^  propositio  pHma^  proposition  sumptuniy 
sumptio  major^  sumptio,  thesis^  expositio,  intentio,  vpoakriii/K, 
vporaais  rj  fiti^wv,  Xijfifia  to  iiei^ov).  The  other  premise,  which 
enounces  the  application  of  the  general  rule,  or  the  relation  of 
the  lesser  quantity  to  the  least,  is  called  the  Minor  Premise^ 
the  Minor  Proposition^  the  Assumptioiiy  or  the  Subsumption 
{propositio  minor,  propositio  altera,  assumptio,  siibsumptuniy 
SubsumptiOy  sumptio  minor,  Trporaais  ^  (Xd-n-wv,  X^/i^a  to  tXarrov). 
It  is  manifest  that,  in  the  counter  qualities  of  Breadth  and 
Depth,  the  two  premises  will  hold  an  opposite  relation  of 
major  and  minor,  of  rule  and  application.  The  Consequent  is 
the  final  proposition,  which  enounces  the  decision,  or  the  rela- 
tion of  the  greatest  quantity  to  the  least,  and  is  called  the  Con- 
clusion  (conclusio,  conclusum,  propositio  condusc^,  coUectiOy 
complexio,  summa,  connexio,  illatio,  iyitentio,  and,  in  Greek, 
crvyxTT^cur/xo,  to  (rvvayoyifvov}  ro  cm^cpd/xevoi') .  This  part  is  usu- 
ally designated  by  the  conjunction  Tlierefore  {ergo.  Spa),  and 
its  synonyms.  The  conclusion  is  the  Problem  {problema)^ 
Question  {qucBstio,  qv^situm),  which  was  originally  asked, 
stated  now  as  a  decision.'  The  problem  is  usually  omitted 
in  the  expression  of  a  syllogism,  but  is  one  of  its  essential 
parts.  The  whole  nomenclature  of  the  syllogistic  parts,  be  it 
observed,  has  reference  to  the  one-sided  views  of  the  logicians 
in  regard  to  the  process  of  reasoning.' 

The  Syllogism  is  divided  into  two  parts,  the 
ExpiioaUon.  Antecedent  and  the  Consequent :  —  the  autece- 

Antecedent  and  .  i         i<  >i  ... 

Consequent  "^"^^  Comprehending  the   two   propositions,  in 

which  the  middle  notion  is  compared  with  the 

two  notions  we  would  compare  together;  and  the  consequent  com- 

1  [Eugenics,  AoyiKii  passim.]  [t.  i.,  D*  Censura  Yeri,  L.  i\.  p.  (306  ft  teg.,  ed. 

«  [Se6  Alex.  AphrodisieiiRis, //>  j4fio/.  JVjor.,  1556.  —  Ed.]    Bachmann,  Z.opiJt,  p.  184.    Fao- 

V  0.  4,  f.  IV'.    Boethius,  In  Topica  Cictronis,  1.  ciolati,  Sextos  Empiricu8.    (Facciolati,  Rii^i- 

i ,  Opera,  p.  764.]  menta  Logica,  o.  iii.  p.  83,  ed.  1750.    Sextaa 

S  [See  R.  Agrioola,  D*  Invention*  Dialeetita,  Emplricua,  HypotypoMS,  L.  ii.  p.  86  *t  aKbi.  — 

I.,  ii.  0.  xir.  pp.  401,  417, «».    Tir^  Optra  E|>.I 


Lbct.  XY.  logic.  199 

prising  the  one  proposition,  which  explicitly  enounces  the  relation 
implicitly  given  in  the  prior  of  these  two  notious  to  each  other. 
The  two  propositions  which  constitute  the  antecedent  are  called, 
among  other  names,  the  Premises.     Of  these, 
the  proposition  expressing  the  relation  of  whole, 
which  one  of  the  originally  given  notions  holds  to  the  assumed  or 
middle  notion  as  its  part,  is  called,  among  other  appellations,  the 
Major  Proposition,  the  Major  Premise,  or  The 
^°^'  Pro2:)Osition,  Kar  i$6xrfv.     The  other  proposition 

of  the  antecedent  enouncing  the  relation  of  whole,  which  the  as- 
sumed or  middle  notion  holds  to  the  other  of  the  given  notions  as 
its  part   is   called,  among  other  appellations,  the  Minor  Proposi- 
tion, the  Minor  Premise,  the  Assumption,  or 
the  Suhsumption.     These,  as  terms  of  relation, 
vaj'y,  of  course,  with  the  relation  in  the  counter  quantities.     The 
one  proposition,  which  constitutes  the  consequent,  is  called,  among 
other  appellations,  the   Conclusion.     Perhaps  the  best  names  for 
these  three  relative  propositions  of  a  syllogism 
Sumption,  subsump-       ^^^^^  y^^  Sumption,  Subsumjition,  Conclusion, 

tjon,  and  Conclusion.  .      ■'  •*      ^ 

as  those  which  express,  most  briefly  and  natu- 
rally, the  nature  and  reciprocal  dependence  of  the  three  judgments 
of  a  syllogism.     In  the  first  place,  the  expressions  Sumption  and 

SvhsumpAion    are    appropriate    logical   expres- 

Grounds  of   their       sions,   in   conscquence   of   their  both   showing 

adoptionaBbestnames       ^^^^  j^ogic  Considers  them,  not  as  absolutely, 

for  the  three  proposi-  '^  .  .  '' 

tionsof  asyiiogism.         "ut  Only  as  hvpothetically  true  ;  for  Logic  does 
not  warrant  the  truth  of  the  premises  of  a  syl- 
logism ;  it  only,  on  the  supposition  that  these  premises  are  true, 
guarantees  the  legitimacy  of  the  inference,  —  the  necessity  of  the 
conclusion.     It  is  on  this  account  that  the  premises  have,  by  the 
Greek  logicians,  been  very  properly  styled  Ai;^ 
/Aara,^  corresponding  to  the  Latin  snmptiones ; 
and  were  there  any  necessity  to  resort  to  Greek,  the  Major  Propo- 
sition, which   I   would   call   Sumption  (sumptio),  might   be    well 
denominated  iemma  simply;  and  the  Minor  Proposition,  which  I 
would  call  the  Subsumption  (subsumpiio),  might  be  well  denomi- 
nated  the  Hypolem.m,a.     In  the  second  place, 

Hypolemma.  i  i      i       i  •  •  i 

though  both  premises  are  sumptions,  or  lem- 
mata, yet  the  term  sum,ption,  as  specially  applied  to  the  Major  Prer 
mise,  is  fully  warranted  both  by  precedent  and  principle.  For,  in 
like  manner,  the  major  proposition  —  the  major  lemma  —  has  always 

I  See  Alexander,  In  Anal.  Priori,  C  lA,  h.  Scholia,  ed.  Brsndis,  p.  150.  —  Ed. 


200  logic:  Lect.  xv. 

obtained  both  from  the  Greek  and  Latin  logicians  the  generic  term ; 
it  has  been  called,  The  Proposition^  The  Lemma  {propositio,  -fj  irpo- 
TOflTis,  TO  krjfxfia) ;  and  as  this  is  the  judgment  which  includes  and 
allows  both  the  others,  it  is  well  entitled,  as  the  principal  proposi- 
tion, to  the  style  and  title  of  the  proposition^  the  lemma,  the  sump- 
tion by  preeminence.  In  the  third  place,  the  term  subsumption  is 
preferable  to  the  term  assumption^  as  a  denomi- 
nation of  the  Minor  Premise ;  for  the  term 
subsumption  precisely  marks  out  its  relation  of  subordination  to 
the  m.'ijor  premise,  whereas  the  term  assumption  does  not.  ^5- 
tnimptton  would  indeed,  in  conti'ast  to  subsumption,  have  been  an 
unexce|)tionable  word  by  which  to  designate  the  major  proposition, 
had  it  not  been  that  logicians  have  very  genenUly  employed  it  to 
designate  the  minor,  so  that  to  revei-se  its  application  would  be  pro- 
ductive of  inevitable  confusion.  But  for  this  objection,  I  should 
certainly  have  preferred  the  term  assumption  to  that  of  sumption^ 
for  the  appellation  of  the  major  proposition  ;  not  that  in  itself  it  is 
a  preferable  expression,  but  simply  because  assumption  is  a  word 
of  familiar  usage  in  the  English  language,  which  sum,ption  and  sub- 
sumption  certainly  are  not. 

The  preceding  are  reasons  why  the  relative  terms  sumption  and 

subsumption  ought  to  be  employed,  as  being  pos- 

Objections  to   tiie       itively  good  expressions ;  but  the  expediency  of 

denominations  of  the       ^j^^j^  adoption  bccomcs  Still  moro  manifest,  when 

Propositions     of    the  i         •   i 

Syllogism  in  ordinary       "'^X  ^^^  Compared  and  Contrasted  with  corre- 

une.  sponding  denominations  in  ordinary  use.     For 

M«jor  Proposition       j^g  terms  m^ojor  proposition  and  major  premise, 

and   Premise.     Minor  .  ...-•. 

p        . .  ^        ,  .,  minor  proposition  and  m.inor  prem.ise,  are  cx- 

mSte.  posed  to  various  objections.     In  the  first  place, 

they  are  complex  and  tedious  expressions,  whereas 
sumption  and  subsumption  are  simple  and  direct.  In  the  second 
place,  the  abbreviations  in  common  use  (the  major  proposition  being 
called  the  major,  the  minor  proposition  being  called  the  minor)  arc 
ambiguous,  not  only  in  consequence  of  their  vagueness  in  general,  but 
because  there  are  two  other  parts  of  the  syllogism  to  which  these 
expressions,  tnajor  and  minor,  may  equally  apply.  For,  as  you  will 
soon  be  informed,  the  two  notions  which  we  compare  together 
through  a  third,  are  called  the  major  and  the  minor  terms  of  the 
syllogism ;  so  that  when  we  talk  of  majors  and  minors  in  reference 
to  a  syllogism,  it  remains  uncertain  whether  we  employ  th'?se  words 
to  denote  the  propositions  or  the  terms  of  a  reasoning.  Still  more 
objectionable  are  the  correlative  terms,  Proposition  and  Assump- 
tion, as  synonyms  for  the  major  and  minor  premises.    The  term 


Lect.  XV.  LOGIC.  201 

proposition  is  a  word  in  too  constant  employment  in  its  vagne  and 
general  sense,  to  be  unambiguously  used  in  a 
iToposition.  Assump-  signification  so  precise  and  special  as  the  one  in 
question ;  and,  in  consequence  of  this  ambigu- 
ity, its  employment  in  this  signification  has  been  in  fact  long  very 
generally  abandoned.  Again,  the  term  assumption  does  not  express 
the  distinctive  peculiarity  of  the  minor  premise,  —  that  of  being  a 
subordinate  proposition,  —  a  proposition  taken  or  assumed  under 
another ;  this  word  would  indeed,  as  I  have  noticed,  have  been  ap- 
plied with  far  greater  propriety,  had  it  been  used  to  denote  the  major 
in  place  of  the  minor  premise  of  a  syllogism. 

These  are  among  the  reasons  which  have  inclined  me  to  employ, 

at  least  along  with  the  more  ordinary  denomina- 

The  use  of  Sumption      tjons,  the  tcrms  sumptiou  and  subsumption.   Nor 

and  Subsumption  sane-         ...  i      i  i  •  •       t        • 

tioued  by  precedent.         ^^  ^^  *«  ^^  supposcd,  that  this  usagc  IS  destitute 

of  precedent,  for  I  could  adduce  in  its  favor  even 

the  high  authority  of  Boethius.^     In  general  and  without  reference  to 

Logic,  it  appears  marvellous  how,  in  English  philosophy,  we  could  so 

long  do  without  the  noun  subsumption,  and  the  verb  to  sicbsume,  for 

these  denote  a  relation  which  we  have  very  frequently  occasion  to  ex- 

])ress,  and  to  express  which  there  are  no  other  terms  within  our  reach. 

We  have  already  in  English  assumption  and  assume,  2>^^sumption 

and  presum,e,  consumption  and  consume,  and  there  is  no  imaginable 

reason  why  we  should  not  likewise  enrich  the  language,to  say  nothing 

o^  sumption,  by  the  analogous  expressions  subsumptioti.and  subsume. 

In   regard  to  the  proposition   constituting  the   consequent  of  a 

syllogism,  the  name  which  is  generally  bestowed 

The  Conclusion.  *    •  ,       ^        t      •  •  -, 

on  It,  —  the  Conclusion,  —  is  not  exposed  to  any 
serious  objections.  There  is  thus  no  reason  why  it  should  be  super- 
seded, and  there  is  in  fact  no  other  term  entitled  to  a  preference. 
So  much  in  reference  to  the  terms  by  which  the  proximate  parts  of 
a  syllogism  are  denoted.  I  now  proceed  to  state  to  you  in  general 
the  Division  of  Syllogisms  into  Species  determined  by  these  parts, 
and  shall  then  proceed  to  consider  these  several  species  in  detail. 
But  I  have  first  of  all  to  state  to  you  a  division  of  Syllogisms,  which, 
as  comprehending,  ought  to  precede  all  others.  It  is  that  of  Syllo- 
gisms into  Extensive  and  Comprehensive. 

%  LV.     The  First  Division  of  Syllogisms  is  taken  from  the 
different  kinds  of  quantity  under  which  the  reasoning  proceeds. 

I  "  Quoniam  enim    omniB  Byllogismus  ex      «io."    Boethios,  De  SyUogiamo  Hypothetico,  lib 
prupositionibus  texitur,  prima  vel  propositio,      i.  —  Ed. 
vel  sumptum  vocatur;  sccunda  vero  assump- 

26 


202  L-Q«i<;.  Leot.  XY. 

For  while  every  syllogism  infers  that  the  part  of  a  part  is  a 
part  of  the  whole,  it  does  this  either  iu  the 

Par.    LV.    First  ©i-  -^  .  . 

vision  of  Syllogisms  quantity  of  Extension,  —  the  Predicate  of 
into  Extensive  and  ^jje  two  notions  Compared  in  the  Question 
and  Conclusion  being  the  greatest  whole,  and 
the  Subject  the  smallest  part ;  or  in  the  counter  quantity  of 
Comprehension,  —  the  Subject  of  these  two  notions  being  the 
greatest  whole,  and  the  Predicate  the  smallest  pait. 

After  what  I  have  already  stated  in  regard  to  the  nature  of  these 
opposite  quantities,  under  the  doctrine  of  Concepts  and  Judg- 
ments,^ and  after  the  illustrations  I  have  given  you  of  the  possibility 
of  conducting  any  reasoning  in  either  of  these  quantities  at  will,*  — 
every  syllogism  in  the  one  quantity  being  convertible  into  a  syllo- 
gism absolutely  equivalent  in  the  other  quantity,  —  it  will  be  hero 
needless  to  enlarge  upon  the  nature  of  this  distinction  in  general. 
This  distinction  comprehends  all  others ;  and  its  illustration,  there- 
fore, supposes  that  the  nature  of  the  various  subordinate  classes  of 
syllogisms  should  be  previously  understood.  It  will,  therefore,  be 
expedient,  not  at  present  to  enter  on  any  distinct  consideration  of 
this  division  of  reasonings,  but  to  show,  when  treating  of  syllogisms 
under  their  various  subaltern  classes,  how  each  is  capable  of  being 
cast  in  the  mould  of  either  quantity,  and  not,  as  logicians  suppose, 
in  that  of  extensive  quantity  alone. 

The  next  distinction  of  Syllogisms  is  to  be  sought  for  either  in 

the  constituent  elements  of  which  they  are  corn- 
Matter  and  form  of  :,  .  ^ ,  i  •  i  .  i 
gyiio  isms  posed,  or  in  the  manner  m  which  these  are  con- 
nected. The  former  of  these  is  technically  called 
the  matter  of  a  syllogism,  the  latter  its  form.  You  must,  however, 
observe  that  these  terms  are  here  used  in  a  restricted  meaning.  Both 
matter  and  form  under  this  distinction  are  included  in  the  form  of  ^ 
syllogism,  when  we  speak  of  form  in  contrast  to  the  empirical  mat- 
ter which  it  may  contain.  This,  therefore,  is  a  distinction  under 
that  form  with  which  Logic,  as  you  know,  is  exclusively  conversant ; 
and  the  matter  here  spoken  of  should  be  called,  for  distinction's 
sake,  the  formal  or  necessary  matter  of  a  syllogism.  In  this  sense, 
then,  the  matter  of  a  syllogism  means  merely  the  propositions  and 
terms  of  which  every  syllogism  is  necessarily  made  up ; '  whereas, 

1  See  above,  p.  100  tt  seq.  —  Ed.  "  Materia  (syllogiemi)  alia  est  proxima,  alia 

2  See  abovr,  p  192  et  sfrj.  —  Ed.  remota.   Reinota  £uut  termini  propositionum, 
8  Proxiipat.e  pnd  (cmotc  matter.     Marginal     proxima  vero  sunt  propositioiies  ipsa,  quibni 

Jotting     [Sec  llurtudo  dc  yienAozs.,  Disput.     coftlescit  eyllogismuB." — Ed.] 
riiil.,   Disp.  Logita,  t.  i.  d.  x.  §  48,  p.  466. 


Lkct.  XV.  LOGIC.  203 

otherwise,  the  form  of  a  syllogism  points  out  the  way  in  which  these 
constituents  are  connected.^  This  being  understood,  I  repeat  that 
the  next  distinction  of  syllogisms  is  to  be  sought  for  either  in  their 
matter  or  in  their  form. 

"  Now  in  regard  to  their  matter,  syllogisms  cannot  differ,  for  every 
syllogism,  without  exception,  requires  the  same 

Their  form,  the  constituent  parts,  —  a  question,  the  subsumption 
ground  of  the  next       ^^  j^  ^^^^^  ^  general  rule,  and  the  sumption  of 

grand   distinction    of  /.  •   i 

syllogisms.  t^e  general  rule  itself;  which  three  constituents, 

in  the  actual  enunciation  of  a  syllogism,  change, 
as  I  have  already  noticed,  their  relative  situation;- — what  was  first 
in  the  order  of  thought  being  last  in  the  order  of  expression. 

"  The  difference  of  Syllogisms  can,  therefore,  only  be  sought  for 
in   their  different  forms  ;  so  that  their  distinc- 

The  form  of  Syllo-         ^^^^g  ^j.^  ^^^y  formal.      But  the   form  of  a  syllo- 
gism twofold,  internal  .  .  T  T   .      .,  ^      i  T^        •         r. 

nd  External  g^s^n?  Considered  in  its  greatest  generality,  is  oi  a 

twofold  kind,  viz.,  either  an  Internal  and  Essen- 
tial, or  an  External  and  Accidental.  The  former  of  these  depends 
on  the  relations  of  the  constituent  parts  of  the  syllogism  to  each 
other,  as  determined  by  the  nature  of  the  thinking  subject  itself; 
the  latter  of  these  depends  on  the  external  expression  of  the  con- 
stituent parts  of  the  syllogism,  whereby  the  terms  and  propositions 
are  variously  determined  in  point  of  number,  position,  and  consecu- 
tion. We  must,  therefore,  in  conformity  to  the  order  of  nature,  first 
of  all,  consider  what  classes  of  syllogism  are  given  by  their  internal 
or  essential  form ;  and  thereafter  inquire  what  are  the  classes 
afforded  by  their  external  or  accidental  modifications.  First,  then, 
in  regard  to  the  Internal  or  Essential  Form  of  Syllogism. 

"A  Syllogism  is  only  a  syllogism  when  the  conclusion  follows 
from  the  premises  with  an  absolute  certainty ;  and  as  this  certainty 
is  determined  by  a  universal  and  necessary  law  of  thought,  there 
must,  consequently,  be  as  many  kinds  of  Syllogism  as  there  are 
various  kinds  of  premises  affording  a  consequence  in  virtue  of  a 
different  law.  Between  the  premises  there  is  only  one  possible 
order  of  dependency,  for  it  is  always  the  sumption,  —  the  major 
premise,  which,  as  the  foundation  of  the  whole  syllogism,  must  first 
be  taken  into  account.  And  in  determining  the  difference  of  syl- 
logisms, the  sumption  is  the  only  premise  which  can  be  taken  into 
account  as  affording  a  difference  of  syllogism ;  for  the  minor  pre- 
mise is  merely  the  subsumption  of  the  lesser  quantity  of  the  two 

1  Krug,  Logik,  i  72,  Anm.,  i.  —  Ed.     [Cf.  Fries,  Logik,  $  44.]  3  Esser,  L(^,  i  85,  p 

159.  — Ed. 


204  LOGIC.  Leci.  X\ 

notions,  concerning  whose  relation  we  inquire,  under  the  question, 

and  this  premise  always  appears  in  one  and  the  same  form,  —  in 

that,  namely,  of  a  categorical  proposition.     The  same  is,  likewise, 

the  case  in  regard  to  the  conclusion,  and,  therefore,  we  can  no  more 

look  towards  the  conclusion  for  a  determination  of  the  diversity  of 

syllogism  than  towards  the  subsumption.     We  have  thus  only  to 

inquire  in  regard  to  the  various  possible  kinds  of  major  proposition."^ 

;  Now  as  all  sumptions  are  judgments,  and  as  we  have  already 

found  that  tlie   most  general  division  of  judg- 

y  ogiems    to  ments,  next  to  the  primary  distinction   of  in- 

divided  according   to  .  *^     ^        "'  . 
the  character  of  their  tensive    and    extensive,   is  into    simple    and    con- 
sumptions and  the  law  ditional,  this  division  of  judgments,  which,  when 
regulating  the  connec-  developed,  affords  the  classes  of  rategorical,  dis- 

tion  b«'tween  premises         .  .         ,  •,     .•      i  t  -,  i..         t. 

and  conclusion.  junctive,  hypothetical,  and  hypothetico-disjunct- 

ive  propositions,  will  furnish  us  with  all  the 
possible  differences  of  major  premises.  "  It  is  also  manifest  that  in 
any  of  these  aforesaid  propositions, —  (categorical,  disjunctive, 
hypothetical,  and  hypothetico-disjunctive),  —  a  decision  of  the  ques- 
tion, —  which  of  two  repugnant  predicates  belongs  to  a  certain  sub- 
ject,—  can  be  obtained  according  to  a  univereal  and  necessary  law. 
In  a  categorical  sumption,  this  is  competent  through  the  laws  of 
Identity  and  Contradiction ;  for  what  belongs  or  does  not  belong 
to  the  superordinate  notion,  belongs  or  does  not  belong  to  the  sub- 
prdinate.  In  disjunctive  sumptions,  this  is  competent  through  the 
law  of  Excluded  Middle ;  since  of  all  the  opposite  determinations 
one  alone  belongs  to  the  object;  so  that  if  one  isaflSrmed,  the  others 
must  be,  conjunctively,  denied  ;  and  if  one  is  denied,  the  others  must 
be,  disjunctively  at  least,  affirmed.  In  hypothetical  sumptions,  this 
is  competent  through  the  law  of  Reason  and  Consequent ;  for  where 
the  reason  is,  there  must  be  the  consequent,  and  where  the  conse- 
quent is,  there  must  be  the  reason."  -  There  are  thus  obtained  three 
or  four  great  classes  of  Syllogisms,  whose  essential  characteristics 
I  shall  comprise  in  the  following  paragraph : 

^  LVI.  Syllogisms  are  divided  into  different  classes,  accord- 
ing as  the  connection  between  the  premises  and  conclusion  is 

1  Esscr,  Logik,  f  85.  —  £d.  Baynes's  Eaay  on  the  ffnr  Analytic  of  Logical 

2  See  Esser,  Lo^ik,  i  8C,  p.  161.  This  clas-  Forms,  the  author's  later  view  is  expressed  as 
sification  of  syllogisms  cannot  be  regarded  as  follows :  "  All  Mtdiatt  inference  is  one  —  that 
expressing  the  author's  tinal  view;  according  incorrectly  called  Cattgorical ,•  for  the  Cm* 
to  which,  as  before  observed,  the  principle  of  junctive  and  Disjunctive  forms  of  Hypotkeiicti 
Reason  and  Consequent  is  not  admitted  as  a  reasoning  are  reducible  to  immediate  Infer- 
Uw  of  thought.  See  above,  p.  62,  uotcl.  In  enccs."  Compare  Discussions,  p.  661  wj. — 
•  note  by  Sir  W.  Hamilton,  appended  to  Mr.  Eo. 


I.ECT.  XV.  LOGIC.  205 

determined  by  the  different  fundamental  laws,  1",  of  Identity 

and  Contradiction ;  2°,  Of  Excluded  Mid- 

^":  .fT^    Tr^      die  ;  3",  Of  Reason  and  Consequent ;  these 

grand  division  or  Syl-  '        '  ^  ' 

logisms  -  according       Several   determinations  affording  the  three 
to  the  law  regulating       dagses  of  CategoHcal,  of  Disjunctive,  and 

the  laferenee.  a  ^  m 

of  Hypothetical  Syllogisms.  To  these  may 
be  added  «  fourth  claRs,  th--^  Hyp<thet^co-Hsjv^ctr:e  o\  Dilerz-' 
matic  Syllogism,  which  is  determined  by  the  two  last  laws  in 
combination. 

Before  proceeding  to  a  consideration  of  these  several  syllogisms 
in  detail,  I  shall,  first  of  all,  give  you  examples 
Examples    of    the       ^f  ^j^g  f^^^  species  together,  in  order  that  you 
four  species  of  syllo-  ,  i  m       ^        ^-  c  i,        >.    i        ^ 

may  have,  while   treating  oi   each,   at  least  a 

general  notion  of  their  differences  and  similarity. 


gism. 


1.  Categorical.  1.  — Of  a  Categorical  Syllogism. 

Sumption, AH  matter  is  created  ; 

Sabsnmption,  ....  But  the  heavenly  bodies  are  material ; 
Conclusion Therefore,  the  heavenly  bodies  are  created. 

2.  DisJanctiTO.  2. —Of  a  Dibjtjnctivb  Stllooism. 

Sumption, The  hope  of  immortality  is  either  a  rational  expectation  or  an  illusion  f 

Subsumption, . .  .  But  the  hope  of  immortality  is  a  rational  expectation; 
Conclusion, ....  Therefore,  the  hope  of  immortality  is  not  an  illusion. 

3.  Hypothetical.  3.  —  Of  an  Htpothktical  Syllogism. 

Sumption If  Logic  does  not  profess  to  be  an  instrument  of  invention,  the  r^roack 

that  it  discovers  nothing  is  unfounded ; 
Subsumption, .  .  .  But  Logic  does  not  profess  to  be  an  instrument  of  invention ; 
Conclusion,  ....  Therefore,  the  reproach  that  it  discovers  nothing  is  unfounded. 

4.   Hypothetico-dis-        4.  —  Of  the   Dilemma    ok    Hypothetico-disjunctivb 
junctive.  Syllogism. 

Sumption, If  man  were  suited  to  live  out  of  society,  he  would  either  be  a  god  or  a 

beast; 
Subsumption,  .  .  .  But  man  is  neither  a  god  nor  a  beast; 
Conclusion,  ....  Therefore,  he  is  not  suited  to  live  out  of  society. 


LECTURE      XVI. 

STOIOHErOLOG-Y. 

SECTION   II.— OF  THE   PRODUCTS  OF  THOUGHT 

ni— DOCTRINE  OF  REASONINGS. 

SYLLOGISMS.  — THEIR  DIVISIONS  ACCORDING  TO  INTERNAL 

FORM. 

A.  SIMPLE —CATEGORICAL.  — L    DEDUCTIVE  IN  EXTENSION. 

In  our  last  Lecture,  I  entered  on  the  Division  of  Syllogisms.  I 
first  stated  to  you  the  principles  on  which  this 
ecap  na  on.  division  must  proceed;  I  then  explained  the 
nature  of  the  first  great  distribution  of  Reasonings  into  those  of 
Intensive  and  those  of  Extensive  Quantity;  and,  thereafter, that  of 
the  second  great  distribution  of  reasonings  into  Simple  and  Condi- 
tional, the  Simple  containing  a  single  species,  —  the  Categorical ; 
the  Conditional  comprising  three  species, —  the  Disjunctive,  the 
ttypothetical^  and  Hypothetico-disjunctive.^  These  four  species 
I  showed  you,  were  severally  determined  by  different  fundamental 
Laws  of  Thought :  the  Categorical  reposing  on  the  laws  of  Identity 
and  Contradiction  ;  the  Disjunctive  on  thij  law  of  Excluded  Middle ; 
the  Hypothetical  on  the  law  of  Reason  and  Consequent ;  and  the 
Hypothetico-disjunctive  on  the  laws  of  Excluded  Middle  and  Rea- 
son and  Consequent  in  combination. 

I  now  go  on  to  the  special  consideration  of  the  first  of  these 
classes  of  Syllogism  —  viz.,  the  Syllogism  which 

.    mpe  y  ogsm.       has  been  denominated  Categorical.    And  in  re- 

The  Categorical.  ^  ,  ^ 

gard  to  the  meaning  and  history  of  the  term  cat- 
egorical, it  will  not  be  necessary  to  say  anything  in  addition  to  what 

1  Compare  above,  p.  187      Gi>< 


r^ECT.  XVI.  LOGIC.  207 

I  have  already  stated  in  speaking  of  judgments.^  As  used  originally 

by  Aristotle,  the  term  categorical  meant  merely  affirmative^  and 

was  opposed  to  negative.     By  Theophrastus  it  was  employed  in  the 

sense  absolute,  — simple, — direct,  and  as  opposed 

The  term  Categorical.  -     .  ,  j    •       ^u-        '•£-.•  •.    i 

to  conditional ;  and  m  this  signincation  it  has 
continued  to  be  employed  by  all  subsequent  logicians,  without 
their  having  been  aware  that  Aristotle  never  employed  it  in  the 
meaning  in  which  alone  they  used  it. 

%  LVII.  A  Categorical  Syllogism  is  a  reasoning  whose  form 

is  determined  by  the  laws  of  Identity  and 

Par.  Lvn.  The  Gate-       Contradiction,  and  whosc  sumption  is  thus 

gorioal      Syllogism.—  .  .  ,  t  r^  •      , 

what.  a  categorical  proposition^     In  a  Categorical 

Syllogism  there  are  three  principal  notions, 
holding  to  each  other  the  relation  of  whole  and  part ;  and  these 
are  so  combined  together,  that  they  constitute  three  proposi- 
tions, in  which  each  principal  notion  occurs  twice.  These 
notions  are  called  Terms  {termini^  opot),  and  according  as  the 
notion  is  the  greatest,  the  greater,  or  the  least,  it  is  called  the 
Major,  the  Middle,  or  the  Minor  Term.^  The  Middle  Term  is 
called  the  Argument  (argumentum,  Aoyo?,  iriarts);  the  Major 
and  Minor  Terms  are  called  Extremes  (extrema,  a/cpa).  If  the 
syllogism  proceed  in  the  quantity  of  Extension  (and  this  form 
alone  has  been  considered  by  logicians),  the  predicate  of  the 
conclusion  is  the  greatest  whole,  and,  consequently,  the  Major 
Tenii ;  the  subject  of  the  conclusion,  the  smallest  part,  and, 
consequently,  the  Minor  Term.  If  the  syllogism  proceed  in 
the  quantity  of  Comprehension,  the  subject  of  the  conclusion 
is  the  greatest  whole,  and,  consequently,  the  Major  Term;  the 
predicate  of  the  conclusion,  the  smallest  part,  and,  consequently, 
the  Minor  Term.  In  either  quantity,  the  proposition  in  which 
the  relation  of  the  major  term  to  the  middle  is  expressed,  is  the 
Sumption  or  Major  Premise,  and  the  proposition  in  which  is 
expressed  the  relation  of  the  middle  term  to  the  minor,  is  the 
Siihsumption  or  Minor  Premise.  The  general  forms  of  a  Cate- 
gorical Syllogism  under  the  two  quantities,  are,  consequently, 
the  following: 


1  See  above,  p.  165  fi  «?.  —  Ed.  L.  vi.  c.  xii.  p.  343.    Hnrtado  de  Mendoza,  p. 

2  [On  principle  of  name  of  Major  and  Ml-  469.]  [Disp'ut.  Fhilosophicce,  t.  i. ;  Disp.  Logicce, 
nor  terms,  see  Alex.  Aphrodisiensis,  In  An.  d.  x.  }  50  et  seg.  TolosjB,  1617.  See  also  JW* 
Prior.,  L.  i.  CO.  iv.  v.     Fliiloponus,  In  An.  eussions,  p.  66Q  et  seq.  —  Ed.] 

Prior.,  L.  i.  f  23  b.    Fonseca,  Instit.  Dialect., 


208  LOGIC.  Lkct.  XVL 

t 

AH  JEXTENSIVB  STI.LOaiSlC.  AN  IlfTKNSIVK  STUXXUSM. 

BisA  CtsB 

C  is  B  B  t  s  A 


Ct«A  CtsA 

AH  man  is  mortal ;  Caius  is  a  man  ; 

But  Caius  is  a  man ;  Bui  all  man  is  mortal; 

Therefore,  Caius  is  mortal.  Therefore,  Caius  is  nortaL 

In  these  examples,  you  are  aware,  from  what  has  previously  been 

said,'  that  the  copula  in  the  two  different  quan- 
£xplication.  .  .  •  ^  •       i 

titles  18  precisely  of  a  counter  meaning ;  in  the 

quantity  of  extension,  signifying  contained  under;  in  the  quantity 
of  comprehension,  signifying  contains  in  it.  Thus,  taking  the  sev- 
eral formulae,  the  Extensive  Syllogism  will,  when  explicitly  enounced, 
be  as  follows : 

The  Middle  term  B  is  contained  under  the  Major  term  A; 
Example  of  the  Ex-      ^^  ^^  ^^.^^  term  C  is  contained  under  the  Middle  term  B ; 
tensive        Categorical 
Svlloeism  There/ore,  the  Minor  term  C  is  also  contained  under  the  Major 

term  A. 

Or,  to  take  the  concrete  example  : 

The  Middle  term  aU  men  is  contained  under  the  Major  termmortal; 
But  the  Minor  term  Caius  is  contained  under  the  Middle  term  all  men ; 
Ther^ore,  the  Minor  term  Caius  is  also  contained  under  the  Major  term  mortal. 

On  the  contrary  the  Intensive  Syllogism,  when 

Of  the  Intensive.  ,.  ,    .  ^  „  J       o    "» 

explicated,  is  as  follows : 

The  Major  term  C  contains  in  it  the  Middle  term  B; 
But  the  Middle  term  B  contains  in  it  the  Minor  term  A ; 
Therefore,  the  Major  term  C  also  contains  in  it  the  Minor  term  A. 

Or,  in  the  concrete  example : 

The  Major  term  Caius  contains  in  it  the  Middle  term  man ; 
But  the  Middle  term  man  contains  in  it  the  Minor  term  mortal  ; 
Thertfore,  the  Major  term  Ccuus  also  contains  in  it  the  Minor  term  mortal. 

Thus  you  see  that  by  revereing  the  order  of  the  two  premises, 
and  by  reversing  the  meaning  of  the  copula,  we  can  always  change 
a  categorical  syllogism  of  the  one  quantity  into  a  categorical  syllo- 
gism of  the  other.* 

1  See  above,  p.  198.  —  Kd. 

s  Mot  in  Inductive  S^rllogisms.    Jauing.    [See  below,  p.  228.  —  Ed.] 


Lect.  XVI.  LOGIC.  209 

In  this  paragraph  is  enounced  the  general  nature  of  a  categorical 
syllogism,  as  competent  in  both  the  quantities  of  extension  and 
comprehension,  or,  with  more  propriety,  of  comprehension  and  ex- 
tension ;  for  comprehension,  as  prior  to  extension  in  the  order  of 
nature  and  knowledge  ought  to  stand  first.  But  as  all  logicians, 
with  the  doubtful  exception  of  Aristotle,  have  limited  their  consid- 
eration to  that  process  of  reasoning  given  in  the  quantity  of  exten- 
sion, to  the  exclusion  of  that  given  in  the  quantity  of  comprehension, 
it  will  be  proper,  in  order  to  avoid  misapprehension,  to  place  some 
of  the  distinctions  expressed  in  this  paragraph  in  a  still  more 
explicit  contrast. 

In  the  reasonings  under  both  quantities,  the  words  expressive  of 

the  relations  and  of  the  things  related  are  identi- 

The    reasoning    in       cal.     The  things  Compared    in   both   quantities 

comprehension     and       ^^^  ^^^  ^^^^  j^  ^^^^^^.^  ^^^  ^^  number.     In  each 

that  in  Extension  ex-  . 

pHcitiy  compared  and       there  are  three  notions,  three  terms,  and  three 
contrasted.  propositions,  combined  in  the  same  complexity  ; 

and,  in  each  quantity,  the  same  subordination  of 
a  greatest,  a  greater,  and  a  least.  The  same  relatives  and  the  same 
relations  are  found  in  both  quantities.  But  though  the  relations  and 
the  relatives  be  the  same,  the  relatives  have  changed  relations.  For 
while  the  relation  between  whole  and  part  is  the  one  uniform  rela- 
tion in  both  quantities,  and  while  this  relation  is  thrice  realized  in 
each  between  the  same  terms ;  yet,  the  term  which  in  the  one  quan- 
tity was  the  least,  is  in  the  other  the  greatest,  and  the  term  which  in 
both  is  intermediate,  is  in  the  one  quantity  contained  by  the  term 
which  in  the  other  it  contained. 

Now,  you  are  to  observe  that  logicians,  looking  only  to  the  reason- 
ing competent  under  the  quantity  of  extension. 
Narrow  and  errone-       and,  therefore,  looking  only  to  the  possibility  of 
ous  definitions  by  lo-       a  single  relation  between  the  notions  or  terms 

gicians  of  the  Major,  f  ^^       •  ^  •  n    -i  • 

Middle,  and  Minor  ^f  a  Syllogism,  have,  m  consequence  of  this  one- 
terms,  sided  consideration  of  the  subject,  given  defini-  - 
tions  of  these  relatives,  which  are  true  only 
when  limited  to  the  kind  of  reasoning  which  they  exclusively  con- 
templated. This  is  seen  in  their  definitions  of  the  Major,  Middle^ 
and  Minor  Terms. 

In  regard  to  the  first,  they  all  simply  define  the  Major  term  to  be 
the  predicate  of  the  conclusion.     This  is  true  of 

1.  Mfljor.  ^  . 

the  reasoning  under  extension,  but  of  that  ex- 
clusively.    For  the  Major  term,  that  is,  the  term  which  contains- 
both  the  others  —  in  the  reasoning  of  comprehension,  is  the  subject 
of  the  conclusion.     Again,  the  Minor  term  they  all  simply  define  to- 

27 


2X0  LQ&ia.  Lkct.  XVI 

be  th&  subject  of  the  conclusion ;  and  thia  is  likewise  true  only  of 
the  reasoning  under  extension :  for,  in  the  reasour 

2.  Minor.  .  ,,.,,,■  •       , 

ing  under  comprehension,  the  Minor  teirin  is  the 
predicate  of  the  conclusion.  Finally,  they  all  simply  define  the 
Middle  term  as  that  which  is  contained  under  the  predicate,  an4 

contains  under  it  the  subject  of  the  conclusion. 

3.  Middle.  ,.,„..  ,.i  , 

x>ut  this  definition,  like  those  of  the  two  other 
terms,  must  be  reversed  as  applied  to  the  reasoning  under  comprehen- 
sion. I  have  been  thus  tediously  expUcit,  in  order  that  you  should 
be  fully  aware  of  the  contrast  of  the  doctrine  I  propose,  to  what  you 
will  find  in  logical  books ;  and  that  you  may  be  prepared  for  the 
further  development  of  this  doctrine,  —  for  its  application  in  detail. 
In  regard  to  the  nomenclature  of  the  Major,  Minor,  and  Middle 

terms,  it  is  not  necessary  to  say  much.  The 
Nomenclature  of  Ma-  expression  term  (temiinuSy  opos),  was  first  em- 
term*  '"""^  "*  *      ployed  by  Aristotle,  and,  Hke  the  greater  part 

of  his  logical  vocabulary,  was,  as  I  have  observed, 
borrowed  from  the  language  of  Mathematics.^  You  are  aware  that 
the  word  term  is  applied  to  the  ultimate  constituents  both  of  propo>- 
sitlons  and  of  syllogisms.  The  terms  of  a  proposition  are  the 
subject  and  predicate.  The  terms  of  a  syllogism  are  the  three 
notions  which  in  their  threefi)ld(  combination  form  the  three  puopo- 

sitions  of  a  syllogism.     The  major  and  minor 

Arirtotie's  definition       terms  Aristotle,  by  another  mathematical  nieta- 

ofthc termsofasyllo-  ,  n      .i  ^  /•        \    ^i  •  j 

^^^  phor,  calls  the  extremes  {aLKpa)y  the   fnc^or  and 

m,mor  extremes/  and  his  definition  of  these  and 
of  the  middle  term  is,  unlike  those  of  the  subsequent  logicians,  so 
general,  that  it  will  apply  with  perfect  propriety  to  a  syllogism  in 
either  quantity.  "  I  call,"  he  says,  "  the  middle  term  that  which  is 
both  itself  in  another  and  another  in  it ;  and  which,  by  its  position, 
lies  in  the  middle  ;  the  extremes  I  call  both  that  which  is  in  another 
and  that  in  which  another  is."  *  And  in  another  place  ho  says,  "I  define 
the  major  extreme  that  in  which  the  middle  is  j  the  minor  extreme 
that  which  is  subordinated  to  the  middle."' 

I  may  notice  that  the  part  of  his  definitioa  of 
Hi«  definition  of  the       ^^^  middle  term,  where  he  describes  it  as  "  that 

Middle  term,  as  mid-  .  •  ^  ^^    n  n 

die  by  position,  not  whicli,  by  its  position,  lios  in  the  middle,  does  not 
applicable  to  tiiemode  apply  to  the  modc  in  which  subsequent  logicians 
in  which  subsequent      enounce  the  syllogism.    For  let  A  be  the  major, 

loiriclans  enounce  the         ni  .i-n  -ii-ii  •  .  f         i-i 

syiioirinik  ^  ^"^  middle,  and  C  the  minor  term  of  an  Kx 

tensive  Syllogism,  this  will  be  expressed  Uius: 

V  See  Scheibler,  [Opera  Logica,  Para.  iii.  o.  2,         >  ^mi^.  Prior..  L.  i.,  o.  i,  f  4. 
V  898,  and  abore,  p.  19G,  note 4.  —Ed.]  »  Ibid.,  ^  8. 


I 


Samptionv B'rts.A,i.«.  Bi  is  mntained  anderA. 

Snbsuraptibn,.  .  .  .  C  is  B",  i.  e.  €  is  oontcdned  under  B. 
Conclusion,  .  .  .  .  .  C  t»  A,  t.  c.  C  is  also  contained  under  A. 

In  this  syllogism  the  middle  term  B  stands  first  and  last  in  the 
premises,  and,  therefore,   Aristotle's   definition 

But  quite  applicable        ^^  ^^^   ^^j^^j^   ^  ^^^   ^^j      ^^   ^j^^j^   ^     ^^^ 

to    (he    reasoning    in  ... 

Comprehension.  ture,  containing  the  minor  and  contained  by 

the  major,  but  as  middle  by  position,  standing 
after  the  major  and  before  the  minor,  becomes  inept.  It  will  apply, 
however,  completely  to  the  reasoning  in  comprehension ;  for  the 
extensive  syllogism  given  above  being  converted  into  an  intensive, 
by  reversing  the  two  premises,  it  will  stand  as  follows : 

Sumption, C  w  B,,t.  e.  C  omtUdna  in  it  B. 

Subsumption,.  ...  B  is  A,  t.  e.  B  contains  in  it  A. 

Ck>ndusion, C  is  A,  i.  c.  C  also  contains  in  it  A.  ' 

It  does  not  follow,  however,  from  this,  that  Aristotle  either 

contemplated  exclusively  the  reasoning  in  comm- 
it does  not,  however,  \  "  '^ 
follow  that  Aristotle  prehension,  or  that  he  contemplated  the  reason- 
contemplated  exciu-  ings  in  both  quantities:  for  it  is  very  easy  to 
siveiy  the  reasoning  state  a  reasoning  in  extension,  so  that  the  major 
pre  nsion.  term  shall  stand  first,  the  middle  term  second^ 
and  the  minor  last.     We  can  state  it  thus : 


Sumption, A  is  B,  i.  e.  A  contains  under  it  B. 

Subsumption,.  .  .  .  B  is  C,  t.  e.  B  contains  under  it  C. 
Conclusion, A  is  C,  i.  e.  A  contains  under  it  C. 

This  is  as  good  a  syllogism  in  extension  as  the  first,  though  it  is 
not  stated  in  the  mode  usual  to  logicians.  We  may  also  convert  iiB 
into  a  comprehensive  syllogism,  by  reversing  its  premises  and  the 
meaning  of  the  copula,  though  here  also  the  mode  of  expression  will 
be  unusual : 

Sumption, B  is  C,  i.  c.  B  is  contained  in  C. 

Subsumption,.  ...  A  is  B,  t.  e.  A  is  contained  in  B. 
Conclusion, A  is  C,  i.  c.  A  is  contained  in  C. 

From  this  you  will  see,  that  it  is  not  to  the  mere  external 
arrangement  of  the  terms,  but  to  the  nature  of  their  relation,  that 
we  must  look  in  determining  the  character  of  the  syllogism. 

Before  leaving  the  consideration  of  the  terms  of  a  syllogism,  I 
may  notice  that  the  most  conA'enient  mode  of  stating  a  syllogism  in 


212 


LOGIC. 


Lkct.  XVI 


Most  convenient 
mode  of  stating  a  syl- 
logism in  an  abstract 
form. 


Categorical  Syllo- 
gisms divided  into 
special  classes  accord- 
ing to  the  applications 
of  the  laws  of  Iden- 
tity and  Contradiction 
under  the  relation  of 
whole  and  part- 


an  abstract  form,  is  by  the  letters  S,  P,  and  M,  —  S  signifying  tbo 
subject,  as  P  the  predicate,  of  the  conclusion, 
and  M  the  middle  term  of  the  syllogism.  This 
you  will  b§  pleased  to  recollect,  as  we  shall 
find  it  necessary  to  employ  this  notation  in 
showing  the  differences  of  syllogisms  from  the 
different  arrangement  of  their  terms. 

I  have  formerly  stated  that  categorical  syllogisms  are  regulated 
by  the  fundamental  laws  of  Identity  ^nd  Con- 
tradiction; the  law  of  Identity  regulating  Af- 
firmative, the  law  of  Contradiction,  Negative, 
Categoricals.  As,  however,  the  laws  of  Iden- 
tity and  Contradiction  are  capable  of  certain 
special  applications,  these  will  afford  the  ground 
of  a  division  of  Categorical  Syllogisms  into  a 
corresponding  number  of  classes.  It  has  been 
already  stated,  that  all  reasoning  is  under  the  relation  of  whole  and 
part,  and,  consequently,  the  laws  of  Identity  and  Contradiction 
will  find  their  application  to  categorical  syllogisms  only  under  this 
relation. 

But  the  relation  of  whole  and  part  may  be  regarded  in  two  pointa 
of  view ;  for  we  may  either  look  from  the  whole 
to  the  parts,  or  look  from  the  parts  to  the  whole. 
This  being  the  case,  may  we  not  apply  the  prin- 
ciples of  Identity  and  Contradiction  in  such  a 
way  that  we  either  reason  from  the  whole  to 
the  parts,  or  from  the  parts  towards  the  whole  ? 
Let  us  consider :  looking  at  the  whole  and  the 
parts  together  on  the  principle  of  Identity,  we  are  assured  that  the 
whole  and  all  its  parts  are  one,  —  that  whatever  is  true  of  the 
one  is  true  of  the  other,  — that  they  are  only  different  expressions 
for  the  different  aspects  in  which  we  may  contemplate  what  in  itself 
is  absolutely  identical.  On  the  principle,  therefore,  that  the  whole 
is  only  the  sum  of  the  parts,  I  am  entitled,  on  the  one  hand,  looking 
from  the  whole  to  its  parts,  to  say  with  absolute  certainty,  —  What 
belongs  to  a  whole  belongs  to  its  part;  and  what  does  not  belong 
to  a  whole  does  not  belong  to  its  part :  and  on  the  other,  looking 
from  the  parts  to  their  whole,  to  say,  — "What  makes  up  all  the  parts 
constitutes  the  whole ;  and  what  does  not  make  up  all  the  parts 
does  not  constitute  the  whole.  Now,  these  two  applications  of  the 
principles  of  Identity  and  Contradiction,  as  we  look  from  one  term 
of  the  relation  of  whole  and  part,  or  from  the  other,  determine  two 
different  kinds  of  reasoning.    For  if  we  reason  downwards,  from 


The  relation  of 
whole  and  part  may 
be  regarded  in  two 
pointa  of  view,  and 
thus  affords  two  class- 
es of  Reasonings. 


Lect.xvl  logic.  218 

a  containing  whole  to  a  contained  part,  we  shall  have  one  sort  of 
reasoning  which  is  called  the  Deductive;  whereas,  if  we  reason  up- 
wards, from  the  constituent  parts  to  a  constituted  whole,  we  shall 
have  another  sort  of  reasoning,  which  is  called  the  Inductive.  This 
I  shall  briefly  express  in  the  following  paragraph. 

%   LVIII.  —  Categorical   Syllogisms   are   Deductive^   if,   on 
the  principles  of  Identity  and   Contradic- 

P»r.  LVIlI.  Categor.  ,         *  '  •' 

icai  Syllogisms    di-       tion,  WO  rcason  downwards,  from  a  con- 
•■        vided  into  Deductive       taining  wholc  to  a  contained  part;    they 

and  Inductive.  t-^  t        .  •/•  •       •    / 

are  Inductive^  ii,  on  these  pnnciples,  we 
reason  upwards,  from  the  constituent  parts  to  a  constituted 
whole. 

This  is  sufficient  at  present  to  afford  you  a  general  conception 

of  the  difference  of  Deductive  and   Inductive 

.    ,."f,  "^     *  *"       Categoricals.     The  difference  of  these  two  kinds 

gorical  Syllogisms.  ^         .  . 

of  reasoning  will  be  properly  explained,  when, 
after  having  expounded  the  nature  of  the  former,  we  proceed  to 
consider  the  nature  of  the  latter.  We  shall  now,  therefore,  con- 
sider the  character  of  the  deductive  process,  —  the  process  which 
has  been  certainly  and  most  successfully  analyzed  by  logicians ;  for, 
though  their  treatment  of  deductive  reasoning  has  been  one-sided 
and  imperfect,  it  is  not  positively  erroneous;  whereas,  their  analy- 
sis of  the  inductive  process  is  at  once  meagre  and  incorrect.  And, 
first,  of  the  proximate  canons  by  which  Deductive  Categoricals 
ive  regulated. 

T  LIX.    In  Deductive  Categoricals  the   universal  laws  of 

Identity  and  Contradiction  take  two  modi- 

Par.  LIX.  Deductive       fied  forms,  accordiug  as  these  syllogisms 

Categoricals,  —  their  i  .       i  •  f  r-i  i  • 

proceed  in  the  quantity  oi  Comprehension  or 


canons. 


in  that  of  Extension.  The  peculiar  canon 
by  which  Intensive  Syllogisms  of  this  class  are  regulated,  is, — 
What  belongs  to  the  predicate  belongs  also  to  the  subject; 
what  is  repugnant  to  the  predicate  is  repugnant  also  to  the 
subject.  The  peculiar  canon  by  which  Extensive  Syllogisms 
of  this  class  are  regulated  is,  —  What  belongs  to  the  genus 
belongs  to  the  species  and  individual;  what  is  repugnant  to 
the  genus  is  repugnant  to  the  species  and  individual.  O:-, 
more  briefly.  What  pertains  to  the  higher  class  pertains  also 
to  the  lower. 


214 


LOGIC. 


Lect.  X¥I 


Both  these  laws  are  enounced  by  Aristotle,*  and  both,  from  hi™^ 
have  passed  into  the  writings  of  subsequent  logicians.  The  former, 
as  usually  expressed,  is,  —  JPrmdicatutn  prcth 
dicati  est  etiam  prcBdicatum  subjecti;  or,  Nota 
notce  est  etiam  nota  rei  ipsius.  The  latter  is  correspondent  to  what 
is  called  the  Dicta  de  Omni  et  de  Nvllo;  the  Dictum  de  Omniy 
when  least  ambiguously  expressed,  being, —  Quicquid  de  omni 
valet,  valet  etiam  de  quibusdem,  et  singidus;  —  and  tlie  Dictum  de 
Nulla  being, — Quicquid  de  nuUo  valet ^  nee  de  quibusdam  nee  do 
singulis  valet.  But  as  logicians  have  altogether  overlooked  tho 
reasoning  in  Comprehension,  they  have,  consequently,  not  perceived 
the  proper  apphcation  of  tl>e  former  canon ;  which,  therefore,  re- 
mained in  their  systems  either  a  mere  hors  d\euvre,  or  else  was 
only  forced  into  an  unnatural  connection  with  the  principle  of  the 
syllogism  of  extension. 

Before  stating  to  you  how  the  preceding  canons  are  again,  in 
their  proximate  application  to  categorical  syllo- 
gisms, for  convenience  sake,  still  more  explicitly 
enounced  in  certain  special  rules,  it  will  be 
proper  to  show  you  the  method  of  marking  the 
connection  of  the  propositions  and  terms  of  a 
categorical  syllogism  by  sensible  symbols.  Of 
these  there  are  various  kinds,  but,  as  I  formerly  noticed,  the  best 
upon  the  whole,  because  the  simplest,  is  that  by  circles.*  Accord- 
ing to  this  method,  syllogisms  with  affirmative  and  negative  con- 
dosions  would  be  thus  represented.' 


Connection  of  the 
propositions  and  terms 
of  tlie  Categorical  Syl- 
logism illustrated  by 
sensible  symbols. 


Ext. 


Int. 


AFFIRMATIVE. 


Int. 

S- 


Ext. 
-P 


-M 


-M 


1  Categ..  C  8.     Anal.  Prior.,  1.  1.  —Ed. 

*  [An  objection  to  the  mode  of  syllojfistio 
notation  by  circles  is,  that  \\c  cannot,  by  this 
mode,  show  that  the  contained  exhausts  the 
containing;  for  we  cannot  divide  the  area  of 
n  circle  between  any  number  of  contained 
circles,  representing  in  extension  all  ooUrdJ- 


nate  species,  in  oomprehensioa  all  the  imme- 
diate attributes]  [For  the  author's  fiiml 
scheme  of  notation,  sec  Tabular  Scheme  :  t 
end  of  volume.  —  Ed.] 

3  See  above,  p.  180.    C£  Krng  Logik,  i  1^ 
p.  245.  — Eo. 


LKicr.  ;XVL 


LOGIC. 


Proximate  Rules  of 
Categorical  Syllo- 
gisms.   1.  Extensive. 


You  are  now  prepared  for  the  statement  and  illustration  of  the 
various  proximate  rules  by  which  all  categorical 
syllogisms  are  regulated.  And,  first,  in  regard 
to  these  rules  in  relation  to  the  reasoning  of 
Extension. 

"  Aldrich,"  says  Dr.  Whately,  "  has  given  twelve  rules,  which  I 
find  might  be  more  conveniently  reduced  to  six.  No  syllogism  can 
be  faulty  which  violates  none  of  these  rules."  ^  This  reduction  of 
the  syllogistic  rules  to  six  is  not  original  to  Dr.  Whately ;  but  had 
he  looked  a  little  closer  into  the  matter,  he  might  have  seen  that  the 
six  which  he  and  other  logicians  enumerate,  may,  without  any  sac- 
rifice of  precision,  and  with  even  an  increase  of  perspicuity,  be 
reduced  to  three.  I  shall  state  these  in  a  paragraph,  and  then  illus- 
trate them  in  detail. 


^     ^^  ^  ^  H  LX.  An  Extensive   Categorical    Syllo- 

Par.  IiX.  The  Three  "  ^  o  j 

Buies  of  the  Exten-       gism,  if  regularly  and   fully   expressed,  is 
sive  Categorical  syi-       governed  by  the  three  following  rules : 

I.  It  must  have   three,  and  only  three, 
Terms,  constituting  three,  and  only  three,  Propositions. 

II.  Of  the  premises,  the  Sumption  must  in  quantity  be 
Definite  (i.  e.  universal  or  singular),  and  the  Subsumption  in 
quality  Afiirmative. 

III.  The  Conclusion  must  correspond  in  Quantity  with  tibe 
Subsumption,  and  in  Quality  with  the  Sumption.^ 


1  Elements  ofLogik,B.  ii.  c.  iii. }  2,  p.  85,  8th 
edit.  —  Ed. 

2  Krug,  Logik,  §  80.  —  Ed.  [Cf.  Alexander 
Aphrodisieusis,  In  An.  Prior.,  L.  I.,  f.  17,  Aid. 
Derodon,  Logica  Restituta,  p.  639  et  seg,    Hoff- 


bauer,  Anfangsgriinde  der  Logik,  S  317,  p.  164. 
Bachmann,  Logik,  i  122,  p.  187.  Esser,  Logik, 
H  88,  89.  Schulze,  Logik, }  79.  Fries,  LogU^ 
i55,p..224.] 


216  LOGIC.  Lect^  XVL 

These  three  simple  laws  comprise  all  the  rules  which  logicians 
lay  down  with  so  confusing  a  minuteness.'     The 
inurtration.     Firet      firgt  is :  —  A  Categorical  syllogism,  if  regular  and 
perfect,  must  have  three,  and  only  three,  prop- 
ositions, made  up  of  three,  and  only  three,  terms.     "The  necessity 
of  this  rule  is  manifest  from  the  very  notion  of  a  categoiical  syllo- 
gism.   In  a  categorical  syllogism  the  relation  of  two  notions  to  each 
other  is  determined  through  their  relation  to  a  third ;  and,  conse- 
(jnently,  ench  must  be  compared  once  with  the  intermediate  notion, 
and  once  with  each  other.     It  is  thus  manifest  that  there  must  be 
three,  and  cannot  possibly  be  more  than  three,  terms ;  and  that 
these  three  terms  must   in  their  threefold  comparison,  constitute 
three,  and  only  three,  propositions.     It  is,  however,  to  be  observed, 
that  it  may  often  happen  as  if,  in  a  valid  syllo- 
What  is  properly  to         -^^  ^j^^.^.g  ^^j.g  ^^^.g  ^^^^  ^^iree  principal  no- 
be  regarded  as  a  logi-  .  ,  t->        •       i  i 

^  jgj^  tions,  —  three  terms.    Uut,  in  that  case,  the  tenns 

or  notions  are  only  complex,  and  expressed  by  a 
plurality  of  words.  Hence  it  is,  that  each  several  notion  extant  in 
a  syllogism,  and  denoted  by  a  separate  word,  is  not  on  that  account 
to  be  viewed  as  a  logical  term  or  terminus,  but  only  those  which, 
either  singly  or  in  connection  with  others,  constitute  a  principal 
momentum  of  the  syllogism." '  Thus,  in  the  following  syllogism, 
there  are  many  more  than  three  several  notions  expressed  by  three 
several  words,  but  these,  we  shall  find,  constitute  in  reality  only 
three  principal  notions  or  logical  terms : 

Samption He  who  conscientiously  performs  his  duty  is  a  truly  good  man  ; 

Subsumption  . . .  Socrates  consrietitiously performs  his  duty; 
Conclusion Therefore,  Socrates  is  a  truly  good  man. 

Here  there  are  in  all  seven  several  notions  denoted  by  seven  sep- 
arate words: — 1.  Conscientiously,  2.  Performs,  3.  Duty,  4,  Truly, 
5.  Good,  6.  Man,  7.  Socrates ^  but  only  three  principal  notions  or 
logical  terms,  —  viz.,  1.  Conscientiously  performs  his  duty,  2.  Truly 
good  m.an,  3.  Socrates. 

"When,  on  the  other  hand,  the  expression  of  the  middle  term  in 
the  sumption  and  subsumption  is  used  in  two 
Significations,  there  may,  in  that  case,  appear  to 
be  only  three  terms,  while  there  are  in  reality  four ;  or  as  it  is  tech- 
nically styled  in  logic,  a  quaternio  term,inorum.^    On  this  account, 

1  See  Scheibler,  Opera  Logica,  pars,  iv.,  p.  S  Kmg,  Logik,  (  80,  p.  246.  Anm.  1.  —  Rd 
516.  Keckermann,  Systema  Logica  Minus,  S  [Cf.  Fonseoa,  [/luitt.  Dial.,  L.  rL  c.  20,  p 
Oi>ro.  t.  i.,  p.  239.  — Ed.  869.  — £d.] 


I 


lect.  xvl  logic.  217 

ihe  syllogism  is  vicious  in  point  of  form,  and,  consequently,  can 
afford  no  inference,  howbeit  that  the  several  propositions  may,  in 
point  of  matter,  be  all  true.  And  why  ?  —  because  there  is  here  no 
mediation,  consequently  no  connection  between  the  different  terms 
of  the  syllogism.     For  example : 

The  animals  are  void  of  reaaon; 

Man  is  an  animal ; 

Therefore,  man  is  void  of  reason. 

"  Here  the  conclusion  is  invalid,  though  each  proposition,  by  itself, 
and  in  a  certain  sense,  may  be  true.  For  here  the  middle  term,  ani- 
mal, is  not  taken  in  the  same  meaning  in  the  major  and  minor  prop- 
ositions. For  in  the  former,  it  is  taken  in  a  narrower  signification, 
as  convertible  with  brute,  in  the  latter  in  a  wider  signification,  as 
convertible  with  animated  organism.''^ ^ 

The  second  rule  is:  —  Of  the  premises,  the  sumption  must  in 
quantity  be  definite  (universal  or  singular),  the 
subsumption  must  in  quality  be  affirmative. — 
The  sumption  must  in  reference  to  its  quantity  be  definite ;  because 
it  affords  the  general  rule  of  the  syllogism.  For  if  it  were  indefi- 
nite, that  is,  particular,  we  should  have  no  security  that  the  middle 
terra  in  the  subsumption  comprised  the  same  part  of  the  sphere 
which  it  comprised  in  the  sumption.  p 

Thus:  ^^ ^ 

Some  M  are  P;  S 

^nSar«P; 


AU  S  are  P.  /""'m'^N. 

Or,  in  a  concrete  example : 


Some  tvorks  of  art  are  cubical; 
AU  pictures  are  vxrrks  of  art ; 
Therefore,  all  pictures  are  cubical ; 


kJl) 


In  regard  to  the  subsumption,  this  is  necessarily  affirmative.  The 
sumption  is  not  limited  to  either  quality,  because  the  proposition 
enouncing  a  general  rule  may  indifferently  declare  All  M  is  P,  and 
No  M  is  P.  The  assumption  is  thus  indeterminate  in  regard  to 
quality.  But  not  so  the  proposition  enouncing  the  application  of  a 
general  rule.  For  it  must  subsume,  that  is,  it  must  affirm,  that 
something  is  contained  under  a  condition  ;  and  is,  therefore,  neces- 
sarily affirmative.    We  must  say  S  is  M.    But  in  respect  of  quantity 

I  Knig,  LogiU.  p.  247.  —Ed. 

28 


218  LOGIC*  Lkct.  XVi. 

it  is  undetermined,  for  we  can  either  say  All  S  is  M,  or  Some  S  is 
M.  If  the  subsumption  is  negative,  there  is  no  inference;  for  it  ia 
not  necessary  that  a  genus  should  contain  only  things  of  a  certain 
species.    This  is  shown  in  the  following  example : 

All  men  are  animals; 

N»  horse  is  a  man  ; 

Therrfore,  no  hone  is  cm  ammaL 

Or,  as  abstractly  expressed : 

AUMaref; 
But  no  S  IS  II; 
JVoStsP. 

Thus  it  is,  that  in  a  regular  extensive  categorical  syllogism,  the 
sumption  must  be  always  definite  in  quantity,  the  subsumption 
always  affirmative  in  quality.^ 

I  have,  however,  to  add  an  observation  requisite  to  prevent  the 

possibility  of  a  misconception.    In  stating  it  as 

Misconception  in  re-       ^  ,.^lg  ^f  exrtensive  categoricals,  that  the  sump- 

gard  to  definiteness  of         ^.  ^   \        i    u    •,       /       ■  i  •  i\'^ 

sfmption  m  second  ^^^^  ™"«*  ^^  defanite  (universal  or  singular),  if 
rnie  obviated.  you  are  at  all  conversant  with  logical  books,  you 

will  have  noticed  that  this  rule  is  not  in  unison 
with  the  doctrine  therein  taught,  and  you  may,  accordingly,  be  sur- 
prised that  I  should  enounce  as  a  general  rule  what  is  apparently 
contradicted  by  the  fact  that  there  are  syllogisms  —  valid  syllo- 
gisms —  of  various  forms,  in  which  the  sumption  is  a  particular,  or 
the  subsumption  a  negative,  proposition.  In  explanation  of  this,  it 
is  enough  at  present  to  say,  that  in  these  syllogisms  the  premises 
are  transposed  in  the  €X}5ression.  You  will,  hereafter,  find  that  the 
sumption  is  not  always  the  proposition  which  stands  first  in  the 

enunciation,  as  the  conclusion  is  not  always  the 

The  mere  order  of       proposition  wliich  Stands  last.     Such  Iransposi- 

enunciation  does  not       tions  are,  however,  only  external  accidents,  and 

constitute   the   sump-         ,i  i         •  i_  •    i_    ^i_  •  j 

.        ,.  the  mere  order  in  which  the  premises  and  oon- 

tion   or   subsumption  ,  ^ 

in  a  reasoning.  clusion  of  a  Syllogism  are  enounced,  no  moru 

changes  their  nature  and  their  necessary  relation 
to  each  other,  than  does  the  mere  order  in  which  the  grammatical 
parts  of  a  sentence  are  expressed,  alter  their  essential  character  and 
reciprocal  dependence.  In  the  phrases- vir  bonus  and  bonus  vir, — • 
iu  both,  the  vir  is  a  substantive  and  the  bonus  an  adjective.     In  the 

1  Krug,  Logik,  f2iS     Bachmaon,  LoiUc,  i  124.  —  Ed. 


Lect   XVL  logic.  219 

sentence  variously  enounced,  —  Alexander  Ikirvum  vicit^  —  Alexanr- 
der  vicit  Darium,  —  Dariwm  Alexander  vicit^  —  Darium  vicit  Alex- 
ander ^ —  Vicit  Alexander  Daritian, —  Vicit  Darium  Alexander: — 
in  these,  a  difference  of  order  may  denote  a  difference  of  the  inter- 
est we  feel  in  the  various  constituent  notions,  but  no  difference  of 
tbeir  grammatical  or  logical  relations.  It  is  the  same  with  syllo- 
gisms. The  mere  order  of  enunciation  does  not 
What  truly  consti-       change  a  sumption    into  a  subsumption,  nor  a 

tutes  the  sumption  and  ,  .•        •    j.  ^'  t^  •     ^t_    • 

.        ,.     ,  subsumption  into  a  sumption.     It  is  their  essen- 

subsumption  in  a  rea-  ^  ^  ^  ^  ^ 

goning.  tial  relation  and  correlation  in  thought  which 

constitutes  the  one  proposition  a  major,  and  the 
other  a  minor  premise.  If  the  former  precede  the  latter  in  the 
expression  of  the  reasoning,  the  syllogism  is  technically  regular;  if 
the  latter  precede  the  former,  it  is  technically  irregular  or  trans- 
posed. This,  however,  as  you  will  hereafter  more  fully  see,  has  not 
been  attended  to  by  logicians,  and  in  consequence  of  their  looking 
away  from  the  internal  and  necessary  consecution  of  the  premises 
to  their  merely  external  and  accidental  arrangement,  the  science 
had  been  deformed  and  perplexed  by  the  recognition  of  a  multi- 
tude of  different  forms,  as  real  and  distinct,  which  exist  only,  and 
are  only  distinguished,  by  certain  fortuitous  accidents  of  expres- 
sion. This  being  understood,  you  will  not  marvel  at  the  rule  in 
regai'd  to  the  quantity  of  sumptions  in  extensive  syllogisms  (which, 
however,  I  limited  to  those  that  were  regularly  and  fully  expressed), 

—  that  it  must  be  definite.     Nor  will  you  marvel  at  the  counter 
canon  in  regard  to  the  quality  of  sumptions  in  intensive  syllogisms, 

—  that  it  must  be  affirmative.' 

The  necessity  of  the  last  rule  is  equally  manifest  as  that  of  the 
preceding.  It  is :  —  The  conclusion  must  corre- 
spond in  quantity  with  the  subsumption,  and  in 
quality  with  the  sumption.  "This  rule  is  otherwise  enounced  by 
logicians :  —  The  conclusion  must  always  follow  the  weaker  or  worser 
part,  —  the  negative  and  the  particular  being  held  to  be  weaker  or 
worser  in  relation  to  the  affirmative  and  universal.  The  conclusion, 
in  extensive  categoricals  (with  which  we  are  at  present  occupied) 
is  made  up  of  the  minor  term,  as  subject,  and  of  the  major  tenn,  as 
predicate.  Now,  as  the  relation  of  these  two  terms  to  each  other 
is  determined  by  their  relation  to  the  middle  term,  and  as  the  mid- 
dle term  is  compared  with  the  major  term  in  the  sumption ;  it  fol- 
lows that  the  major  term  must  hold  the  same  relation  to  the  minor 

1  [Se«  Bachmann,  Logik,  j  124,  pp.  192, 194.  Krng,  Logik,  {  82,  p.  249.  Cf.  J  83,  p.  264,  and 
Anm.  3.  Drobisch,  Logik,  i  73,  h.  65,  §§  42,  }  109,  p.  362.  Facciolati,  Rudimtnta  hogiea, 
44,  pp.  34,  36.     Sohulze,  Logik,  J  79,  p.  114.     P.  iii.  c.  iii.  p.  91.] 


220  1.0  GIC.  Lect.  XVL 

in  the  conclusion  which  it  held  to  the  middle  in  the  sumption.  If 
then  the  sumption  is  affirmative,  so  likewise  must  be  the  conclusion; 
on  the  other  hand,  if  the  sumption  be  negative,  so  likewise  must  be 
ilie  conclusion.  In  the  subsumption,  the  minor  term  is  compared 
with  the  middle ;  that  is,  the  minor  is  affirmed  as  under  the  middle. 
In  the  conclusion,  the  major  term  cannot,  therefore,  be  predicated 
of  more  things  than  were  affirmed  as  under  the  middle  tenn  in  the 
subsumption.  Is  the  subsumption,  therefore,  universal,  so  likewise 
must  be  the  conclusion ;  on  the  contrary,  is  the  former  particular,  so 
likewise  must  be  the  latter."^ 

I  Krag,  LogOe,  i  80,  p.  SCO-l.  — Sd. 


LECTURE     XVII. 

STOIOHEIOI.   OQY. 

SECTION    II.  — OF  THE    PRODUCTS   OF    THOUGHT. 

III.  — THE  DOCTRINE    OF  REASONINGS. 

SYLLOGISMS.  — THEIR  DIVISIONS   ACCORDING  TO   INTERNAL 

FORM. 

A.  SIMPLE.  —  CATEGORICAL.  —  IL  DEDUCTIVE  IN  COMPREHEN- 
SION —  IlL  INDUCTIVE  IN  EXTENSION  AND  COMPREHENSION. 
—  B.  CONDITIONAL.  — DISJUNCTIVE. 


In  my  last  Lecture,  after  terminating  the  consideration  of  the 
constituent  elements  of  the  Categorical  Syllo- 

Recapitulation.  .  .  i         t       i  •       ^i  .'j^  e- 

gism  in  general,  whether  in  the  quantity  or 
Comprehension  or  of  Extension,  I  stated  the  subdivision  of  Cate- 
gorical Syllogism  into  Deductive  and  Inductive  —  a  division  de- 
termined by  the  difference  of  reasoning  from  the  whole  to  the  parts, 
or  from  the  parts  to  the  whole.  Of  these,  taking  the  former  —  the 
Deductive  —  first  into  consideration,  I  was  occupied,  during  the 
remainder  of  the  Lecture,  in  giving  a  view  of  the  laws  which,  in 
their  higher  or  lower  universality  —  in  their  remoter  or  more  proxi- 
mate application,  govern  the  legitimacy  and  regularity  of  Deductive 
Categorical  Syllogisms.  Of  these  laws,  the  highest  are  the  axioms 
of  Identity  and  Contradiction,  by  which  all  Categorical  Syllogisms 
ai'e  controlled.  These,  when  proximately  applied  to  the  two  forms 
of  Deductive  Categoricals,  determined  by  the  two  quantities  of 
Comprehension  and  Extension,  constitute  two  canons,  —  the  canon 
of  the  Intensive  Syllogism  being:  What  belongs  to  the  predicate 
belongs  also  to  the  subject  —  what  is  repugnant  to  the  predicate  is 
repugnant  also  to  the  subject;  —  the  c'anon  of  the  Extensive  Syllo- 
gism being:  What  belongs  to  the  genus  belongs  also  to  the  species 
and  individual  —  what  is  repugnant  to  the  genus  is  repugnant  also 


222  LOGIC.  Lect.  XVII. 

to  the  species  and  individual.  Each  of  these,  however,  in  its  more 
proximate  application,  is  still  further  developed  into  a  plurality  of 
more  explicit  rules.  In  reference  to  Extensive  Syllogism,  the  gen- 
eral law,  or  the  Dictum  de  Omni  et  de  NuUo  (as  it  is  technically 
called)  is  evolved  into  a  series  of  rules,  which  have  been  multiplied 
to  twelve,  are  usually  recalled  to  six,  but  which,  throwing  out  of 
account  irregular  and  imperfect  syllogism,  may  be  conveniently 
reduced  to  three.  These  are,  I.  An  Extensive  Categorical  Deduc- 
tive Syllogism  must  have  three,  and  only  three,  terms  —  constitut- 
ing three,  and  only  three,  propositions.  II.  The  sumption  must  in 
quantity  be  definite  (t.  e^  universal  or  singular) ;  the  subsumption 
must  in  quality  be  affirmative.  III.  The  concIusioH  must  eorre* 
spond  in  quantity  with  the  subsumption,  and  in  quality  with  the 
sumption.  The  Lecture  concluded  with  an  explanation  of  these 
rules  in  detail. 

We  have  now,  therefore,  next  to  consider  into  what  rales  the 

law  of  Intensive  or  Comprehensive  Syllogism 

2.TbeintenBiTeC«te-       is  developed,  in  its  more  proximate  application. 

fforioal  Deductive  Sy I-         ^-p  ^.        •       '       •  -i         .         •  n       • 

J    .  J«Jow,  as  the  mtensive  and  extensive  syllogisms 

are  always  the  counterparts  of  each  other,  the 
proximate  rules  of  the  two  forms  must,  consequently,  be  either  pre- 
cisely the  same,  or  precisely  the  converse  of  each  other.  Accord- 
ingly, taking  the  three  rules  of  extensive  syllogisms,  we  find  that 
the  first  law  is  also,  without  difference,  a  rule  of  intensive  syllo- 
gisms; But  the  second  and  third,  to  maintain'  their  essential  iden- 
tity, must  be  externally  converted ;  for  to  change  an  extensive 
syllogism  into  an  intensive,  we  must  transpose  the  order  or  subor- 
dination of  the  two  premises,  and  reverse  the  reciprocal  relation  of 
the  terms.  The  three  general  rules  of  an  Intensive  Categorical 
Deductive  Syllogism  will,  therefore,  stand  as  follows: 

%  LXI.  An  Intensive  Categorical  Deductive  Syllogism,  that 

is,  one  of  Depth,  if  regularly  and  fully  ex- 

the*'nten»ivecat!go^      prcsscd,  is  govcmed  by  the  three  following 

loal  Dedaotiva  Syllo-         rulcS  \ 

I.    It  must  have  three,  and  only  three, 
terms,  —  constituting  three,  and  only  three,  propositions. 

II.  Of  the  premises,  the  Sumption  must  in  quality  be  Affir- 
mative, and  the  Subsumption  in  quantity  Definite  (that  is,  uni- 
versal or  singular). 

III.  The  Conclusion  must  not  exceed  the  Sumption  in  Quan> 
tity,  and  in  Quality  must  agree  with  the  Subsamptioiu 


Lect.  XVn.  LOGIC.  228 

In  regard  to  the  first  of  these  rules,  —  the  rule  which  is  identical 

for  syllogisms  whether  extensive  or  intensive,  it 

p  ication.  jg  needless  to  say  anything ;  for  all  that  I  stated 

First  Rule.  J        J  Ss ' 

in  regard  to  it  under  the  first  of  these  forms,  is 
valid  in  regard  to  it  under  the  second. 
I  proceed  to  the  second,  which  is,  —  The  sumption  must  in  qual- 
ity be  affirmative,  the  subsumption  must  in  quan- 
tity be  definite  (that  is,  universal  or  singular). 
And,  here,  we  have  to  answer  the  question,  — Why  in  an  intensive 
syllogism  must  the  sumption  be  affirmative  in  quality,  the  subsump- 
tion definite  in  quantity  ?     Let  us  take  the  following  syllogism  as 
explicated : 

S  comprehends  M ; 

H  does  not  comprehend  P ; 

Therefore,  S  does  not  comprehend  P. 

Prudence  comprehends  virtue; 

But  virtue  does  not  comprehend  blameworthy; 

Therefore,  prudence  does  not  comprehend  hlanuvxrrOiy. 

Here  all  goes  on  regularly.  We  descend  from  the  major  term  pru^ 
dence  to  the  middle  term  virtue.,  and  from  the  middle  term  virtue  td 
the  minor  term  blameworthy.  But  let  us  reverse  the  premises. 
We  at  once  see  that  though  there  is  still  a  discoverable  meaning, 
it  is  not  directly  given,  and  that  we  must  rectify  and  restoi-e  in 
thought  what  is  perverse  and  preposterous  in  expression.  In  the 
previous  example,  the  sumption  is  affirmative,  the  subsumption  neg. 
ative.     Now  let  us  take  a  negative  sumption : 

S  does  not  comprehend  M ; 
But  M  comprehends  P. 

Here  there  is  no  conclusion  competent,  for  we  can  neither  say  S 
comprehends  P,  nor  S  does  not  comprehend  P.  Or  to  take  a  con- 
crete example : 

Prudence  does  not  comprehend  learning; 
But  learning  comprehends  prca'seioorthy. 

We  can  draw,  it  is  evident,  no  concrusion  ;  for  we  can  neither  say, 
from  the  relation  of  the  two  propositions,  that  Prudence  compre- 
hends prcuiseworthyyX\ov  that  Prudence  does  not  comprehend  prawe^ 

worthy. 


224  LOGIC.  "  Lect.  XVIL 

The  reason  why  an  extensive  syllogism  requires  a  nniversal  sump- 
tion, and  an  intensive  syllogism  an  affirmative. 
Grounds  of  the  rules       and  why  the  One  requires  an  affirmative  and 
regarding    Sumption       ^j^g  ^^j^g^  ^  definite  subsumption,  is  the  follow- 

and   Subsumption   in         .  _,,  ,.   .  i       i        n       • 

Extensive  and  Com-  i°g  *  ^he  Condition  common  to  both  syllogisms 
prehensive  Syllogisms.  is  that  the  sumption  should  express  a  rule.  But 
in  the  extensive  syllogism  this  law  is  an  univer- 
sal rule,  that  is,  a  rule  to  which  there  is  no  exception ;  but  then  it 
may  be  expressed  either  in  an  affirmative  or  in  a  negative  form, 
whereas  in  the  intensive  syllogism  this  law  is  expressed  as  a  posi- 
tion, as  a  fact,  and,  therefore,  admits  only  of  an  affirmative  form, 
but,  as  it  is  not  necessarily  univei*sal,  it  admits  of  limitations  or 
exceptions.  This  opposite  character  of  the  sumptions  of  the  two 
forms  of  syllogisms  is  correspondent  to  the  opposite  character  of 
their  subsumptions.  In  the  extensive  syllogism,  the  subsumption 
is,  and  can  only  be,  an  affirmative  declaration  of  the  application  of 
the  sumption  as  a  universal  rule.  In  the  intensive  syllogism,  the 
subsumption  is  either  an  affirmation  or  a  negation  of  the  applica- 
tion of  the  sumption  as  a  positive  law.  Hence  it  is  that  in  an  in- 
tensive syllogism  the  major  premise  is  necessarily  an  affirmative, 
while  the  minor  may  be  either  an  affirmative  or  a  negative  propo- 
sition. 

In  regard  to  the  second  clause  of  the  second  rule,  the  reason 
why  the  subsumption  in  an  intensive  syllogism  must  be  definite  in 
quantity,  is  because  it  would  otherwise  be  impossible  to  affirm  or 
deny  of  each  other  the  minor  and  the  major  terms  in  the  conclu- 
sion.    For  example : 

Sumption Prudence  is  a  virtue  ;  i.  e.,  Prudence  comprthenda  virtue. 

Subsumption.  .  .  Some  virtue  is  praiaevoorthy ;  i.e.,  Some  virtue  comprehends  praiseworthy. 

From  these  we  can  draw  no  conclusion,  for  the  indefinite  some  vir- 
tue docs  not  connect  the  major  term  prudence  and  the  minor  term 
praiseworthy  into  the  necessary  relation  of  wliole  and  part. 

In   regard  to  the  third  rule,  —  The  conclusion   must  be  corre- 
spondent in  quantity  with  the  sumption,  and  in 
Third  Rule.  ,.  .  ,      ,  ,  .  .     . 

quality  with  the  subsumption,  —  it  is  not  neces- 
sary to  say  anything.  Here,  as  in  the  extensive  syllogism,  the  con- 
clusion cannot  be  stronger  than  the  weakest  of  its  antecedents,  that 
is,  if  any  premise  be  negative,  the  conclusion  cannot  but  be  negative 
.ilso ;  and  if  any  premise  be  particular,  the  conclusion  cannot  be  but 
particular  likewise ;  and  as  a  weaker  quality  is  only  found  in  the 
subsumption,  and  a  weaker  quantity  in  ihe  sunjption,  it  follows  that 


Lect.  XVII.  LOGIC.  225 

(as  the  rule  declares)  the  conclusion  is  regulated  by  the  sumption 
in  regard  to  its  quantity,  and  by  the  subsumption  in  regard  to  its 
quality.  It  is,  however,  evident,  that  though  warranted  to  draw  a 
universal  conclusion  from  a  general  sumption,  it  is  always  compe- 
tent to  draw  only  a  particular. 

So  much  for  the  proximate  laws  by  which  Categorical  Deductive 

Syllogisms  are   governed,  when  considered  as 

II.  Inductive  cate-       perfect  and  regular  in  external  form.    We  shall, 

gorieal  Syllogisms.  f  ^    ^  ^  -j        .i  •    i         i 

m  the  sequel,  have  to  consider  the  special  rules, 
by  which  the  varieties  of  Deductive  Categorical  Syllogisms,  as  de- 
termined by  their  external  form,  are  governed  ;  but  at  present  we 
must  proceed  to  the  general  consideration  of  the  other  class  of  cat- 
egorical syllogisms  afforded  by  their  internal  form,  —  I  mean  those 
of  Induction,  the  discussion  of  which  I  shall  commence  by  the 
following  paragraph : 

i[  LXII.  An  Inductive  Categorical  Syllogism  is  a  reasoning 

in  which  we  argue  from  the  notion  of  all 

Par.  Lxn.  Indue-      |^jjg  Constituent   parts  discretively,  to  the 

tlve  Categorical  Syl-  .  /.      ,  • 

io»i«in,-what.  notiou   of  ,  the   constituted   whole   collect- 

ively.    Its  general  laws  are  identical  Avith 
those  of  the  Deductive  Categorical  Syllogism,  and  it  may  be  ■ 
expressed,  in  like  manner,  either  in  the  form  of  an  Intensive  or 
of  an  Extensive  Syllogism. 

We  shall,  in  the  sequel,  have  to  consider  more  particularly  the 

nature  and  peculiarities  of  Logical  Induction, 

The  views  of  logi-       .^y^gn  we  come  to  treat  of  the  Figure  of  Syllo- 

cans    regar  ing      e       origm,  and  when  we  consider  the  nature  of  Logi- 

naturc  of  Logical  In-         o         '  ^  o 

duction  erroneous.  cal  or  Formal,  in  contrast  to  Philosophical  or 

Real  Induction,  under  the  head  of  Modified 
Logic.  At  present,  I  shall  only  say,  that  all  you  will  find  in  logical 
works  of  the  character  of  logical  induction  is  utterly  erroneous;; 
for  almost  all  logicians,  except  Aristotle,  consider  induction,  not  as 
regulated  by  the  necessary  laws  of  thought,  but  as  determined  by 
the  probabilities  and  presumptions  of  the  sciences  from  which  its  ■ 
matter  has  accidentally  been  borrowed.  They  have  not  considered 
it,  logically,  in  its  formal,  but  only,  extralogically,  in  its  material 
conditions.  Thus,  logicians  have  treated  in  Logic  of  the  inductive 
inference  from  the  parts  to  the  whole,  not  as  exclusively  warranted 
by  the  law  of  Identity,  in  the  convertibility  of  the  whole  and  all 
its  parts,  but  they  have  attempted  to  establish  an  illation  from  a  few 
of  these  parts  to  the  whole;  and  this,  either  as  supported  by  the 

29 


226  LOGIC.  Lkct.  XVll 

general  analogies  of  nature,  or  by  the  special  presumptions  afforded 
by  the  several  sciences  of  objective  existence.' 

Logicians,  with  the  exception  of  Aristotle,  who  is,  however,  very 
brief  and  unexplicit  in  his  treatment  of  this  sub- 
The  characters  of      ject,  have  thus  deformed  their  science,  and  per- 
d"^  rT*^!     "mL*        plexed  the  very  simple  doctrine  of  logical  in- 
riai,  Induction.  duction,  by  confounding  formal  with  material 

induction.  All  inductive  reasoning  is  a  reason- 
ing from  the  parts  to  the  whole;  but  the  reasoning  from  the  parts 
to  the  whole  in  the  various  material  or  objective  sciences,  is  very 
different  from  the  reasoning  from  the  parts  to  the  whole  in  the  one 
formal  or  subjective  science  of  Logic.  In  the  former,  the  illation  is 
not  simply  founded  on  the  law  of  Identity,  in  the  convertibility  of 
a  whole  and  all  its  parts,  but  on  certain  presumptions  drawn  from 
an  experience  or  observation  of  the  constancy  of  nature;  so  that,  in 
these  sciences,  the  inference  to  the  whole  is  rarely  from  all,  but 
generally  from  a  small  number  of^  its  constituent  parts;  conse- 
quently, in  them,  the  conclusion  is  rarely  in  truth  an  induction 
properly  so  called,  but  a  mixed  conclusion,  drawn  on  an  inductive 
presumption  combined  with  a  deductive  premise.  For  example, 
the  physical  philosopher  thus  reasons : 

This,  that,  and  the  other  magnet  attrad  iron  ; 

But  this,  that,  and  the  other  magnet  represent  all  magnets; 

Thertfore,  aU  magnets  attract  iron. 

Now,  in  this  syllogism,  the  legitimacy  of  the  minor  premise,  7%t», 
that,  and  the  other  magnet  represent  all  magnets,  is  founded  on  the 
principle,  that  nature  is  uniform  and  constant,  and,  on  this  gen- 
eral principle,  the  reasoner  is  physically  warranted  in  making  a  few 
parts  equivalent  to  the  whole.  But  this  process  is  wholly  incom- 
petent to  the  logician.  The  logician  knows  nothing  of  any  princi- 
ples except  the  laws  of  thought.  He  cannot  transcend  the  sphere 
of  necessary,  and  pass  into  the  sphere  of  probable,  thinking;  nor 
can  he  bring  back,  and  incorporate  into  his  own  formal  science,  the 
conditions  which  regulate  the  procedure  of  the  material  sciences. 
This  being  the  case,  induction  is  either  not  a  logical  process  differ- 
ent from  deduction,  for  the  induction  of  the  objective  philosopher, 
in  so  far  as  it  is  formal,  is  in  fact  deductive ;  or  there  must  be  an 
induction  governed  by  other  laws  than  those  which  warrant  the 
induction  of  the   objective  philosopher.     Now,  if  logicians  had 

I  Compare  Dittutimu,  p.  168. —KD. 


L.KCT.  XATl.  LOGIC.  227 

looked  to  their  own  sciences,  and  not  to  sciences  with  which,  as 

logicians,  they  had  no  concern,  they  would  have 

Canons  of  the  De-      seen  that  there  is  a  process  of  reasoning  from 

ductive  and  Inductive         ^^^  ^^    ^^    ^^^    ^j^^j        ^^    ^^^j    ^^    ly^^    ^^^ 

Syllogisms  —  equally  i     i  ,  .  i  • 

foTmai.  whole  to  the  parts,  that  this  process  it  governed 

by  its  own  laws,  and  is  equally  necessary  and 
independent  as  the  other.  The  rule  by  which  the  Deductive  Syllo- 
gism is  governed  is :  What  belongs,  or  does  not  belong,  to  the  con- 
taining whole,  belongs,  or  does  not  belong,  to  each  and  all  of  the 
contained  parts.  The  rule  by  which  the  Inductive  Syllogism  is 
governed  is :  What  belongs,  or  does  not  belong,  to  all  the  constitu- 
ent parts,  belongs,  or  does  not  belong,  to  the  constituted  whole. 
These  rules  exclusively  determine  all  fonnal  inference ;  whatever 
transcends  or  violates  them,  transcends  or  violates  Logic.  Both 
are  equally  absolute.  It  would  be  not  less  illegal  to  infer  by  the 
deductive  syllogism,  an  attribute  belonging  to  the  whole  of  some- 
thing it  was  not  conceived  to  contain  as  a  part ;  than  by  the  induc- 
tive, to  conclude  of  the  whole  what  is  not  conceived  as  a  predicate 
of  all  its  constituent  parts.  In  either  case,  the  consequent  is  not 
thought  as  determined  by  the  antecedent;  the  premises  do  not 
involve  the  conclusion.^ 

To  take  the  example  previously  adduced  as  an  illustration  of  a 
Tbese  reaMniDtrs        material  or  philosophical  induction,  it  would  be 
illustrated.  thus  expressed  as  a  formal  or  logical : 

This,  that,  and  the  other  magnet  attract  iron; 

But  this,  that,  and  the  other  magnet  are  all  tnagnets  ; 

Therefore,  all  magnets  attract  iron. 

Here  'the  inference  is  determined  exclusively  by  a  law  of  thought. 
In  the  subsumption,  it  is  said.  This,  that,  and  the  other  magnet  etc., 
are  all  magnets.  This  means.  This,  that,  and  the  other  magnet  are, 
that  is,  constitute,  or  rather,  are  conceived  to  constitute  all  magnets, 
that  is,  the  whole,  —  the  class,  —  the  genus  m.agnet.  If,  therefore, 
explicitly  enounced,  it  will  be  as  follows  :  This,  that,  and  the  other 
magnet  are  conceived  to  constitute  the  whole  class  magnet.  The 
conclusion  is  —  There/ore,  all  magnets  attract  iron.  This,  if  expli- 
cated, will  give  —  Therefore,  the  whole  class  m,agnet  is  conceived  to 
attract  iron.  The  whole  syllogism,  therefore,  as  a  logical  induc- 
tion, will  be : 

1  [Cf.  Krng,  Logik,  4§  166, 167.    Sanderson,     {QucBsiione$  in,  Ah.  Piior.^  X«  iL  4.  Till.  >  816. 
Compendium  Log.  Artis,  L.  iii.  c.  x.  p.   112.      ed.l610.  —  Ed.] 
Wolf.   PkU.  Rationalis,  H  477,  478.    Scotus. 


228  LOGIC.  lect.  xvn. 

This  that,  and  the  other  magnet  attract  iron; 

But  this,  that,  and  the  other  magnet,  etc.,  are  conceived  to  constitvte  the  germs  vtagnet; 

Therefore,  the  genus  magnet  attracts  iron. 

It  is  almost  needless  to  advert  to  an  objection  which,  I  see,  among 

othere,  has  misled   Whately.      It  may  be  said 
Objection  obviated.  ,  '  .  rm  .       t  t     ,  , 

that  tlie  mmor,  2ms,  that,  ana  the  other  maff- 

net  are  all  magnets,  is  manifestly  false.  This  is  a  very  superficial 
objection.  It  is  very  true  that  neither  here,  nor  indeed  in  almost 
any  of  our  inductions,  is  the  statement  objectively  correct,  —  that 
the  enumerated  particulars  are  really  equivalent  to  the  whole  or 
class  which  they  constitute,  or  in  which  they  are  contained.  But, 
as  an  objection  to  a  logical  syllogism,  it  is  wholly  incompetent,  as 
wholly  extralogical.  For  the  logician  has  a  right  to  suppose  any 
material  impossibility,  any  material  falsity ;  he  takes  no  account  of 
what  is  objectively  impossible  or  false,  and  has  a  right  to  assume 
what  premises  he  please,  provided  that  they  do  not  involve  a  con- 
tradiction in  terms.  In  the  example  in  question,  the  subsumption, 
This,  that,  and  the  other  magnet  are  all  magnets,  has  been  already 
explained  to  mean,  not  that  they  really  are  so,  but  merely  that  they 
are  so  thought  to  be.  It  is  only  on  the  supposition  of  this,  that,  and 
the  other  magnet,  etc.,  being  conceived  to  con- 
FonnnUe  for  Indue-  gtitutc  the  class  magnet,  that  the  inference  pro- 
l  ogisms     Ti       ceeds,  and,  on  this  supposition,  it  will  not  be 

Comprehension     and  _  '  _  . 

Kxtension.  denied  that  the  inference  is  necessary.    I  stated 

that  an  inductive  syllogism  is  equally  competent 
in  comprehension  and  in  extension.  For  example,  let  us  suppose 
that  X,  y,  z,  represent  parts,  and  the  letters  A  and  B  wholes,  and 
we  have  the  following  formula  of  an  inductive  syllogism  in 
Comprehension :  * 

X,  y,  z,  constitute  A ; 

A  compreitends  B ; 

Therefore,  x,  y,  z,  comprehend  B. 

This,  if  converted  into  an  extensive  syllogism,  by  transposing 
the  premises  and  revei'sing  the  copula,  gives  : 

A  is  contained  under  B ; 

X,  y,  z,  constitute  A ; 

Thertfore,  x,  y,  z,  are  contained  under  B. 

But  in  this  syllogism  it  is  evident  that  the  premises  are  in  an  un- 
natural order.  We  must  not,  therefore,  here  transpose  the  premises, 
as  we  do  in  converting  a  deductive  categorical  of  comprehension 


lect.  xvn. 


LOGIC. 


229 


into  one  of  extension.  We  may  obtain  an  inductive  syllogism  in 
two  different  forms,  and  in  either  comprehension  or  extension, 
according  as  the  parts  stand  for  the  major,  or  for  the  middle  term. 
If  the  minor  term  is  formed  of  the  parts,  it  is  evident  there  is  no 
induction  ;  for,  in  this  case,  they  only  constitute  that  quantity  of 
the  syllogism  which  is  always  a  part,  and  never  a  whole.  Let  x,  y, 
z  represent  the  parts;  where  not  superseded  by  x,  y,  z,  S  will  repre- 
sent the  major  term  in  a  comprehensive,  and  the  minor  term  in  an 
extensive  syllogism;  P  will  represent  the  major  term  in  an  exten- 
sive, and  the  minor  term  in  a  comprehensive  syllogism,  and  M  the 
middle  term  in  both.  I  shall  first  take  the  Inductive  Syllogism 
of  Comprehension. 


FiKST    Case,  —  (The  parts  holding  the 

place  of  the  m^or  term  S.) 
X,  y,  z  constitute  M ; 
M  comprehends  P; 
Therefore,  x,  y,  z  comprehend  P. 


Second  Case,  —  (The  parts  holdiug  the 

place  of  the  middle  term.) 
S  comprehends  x,  y,  z; 
X,  y,  z  constitute  P ; 
Therefore,  S  comprehends  P. 


Again,  in  the  Inductive  Syllogism  of  Extension : 


First    Case,  —  (The  parts   holding   the 

place  of  the  major  term  P.) 
X,  y,  z  constitute  M ; 
S  is  contained  under  M ; 
Therefore  S  is  contained  under  x,  y,  z. 


Second  Case,  —  (The  parts  holding  the 

place  of  the  middle  term.) 
X,  y,  z  are  contained  under  P; 
X,  y,  z  constitute  S; 
Theiffore,  S  in  contained  under  P. 


Before  leaving  this  subject,  I  may  notice  that  the  logical  indue 
tion  maintained  by  Whately  and  many  others, 
diverges  even  more  than  that  of  the  older  logi- 
cians from  the  truth,  inasmuch  as  it  makes  this 
syllogism  a  deductive  syllogism,  of  which  the 
sumption,  which  is  usually  understood  and  not 

expressed,  is  always  substantially  the  same,  namely,  "What  belongs 
(or  does  not  belong)  to  the  individuals  we  have 
examined,  belongs  (or  does  not  belong)  to  the 
whole  class  under  Avhich  they  are  contained." 

This  doctrine  was/first,  I    think,  introduced   by  Wolf,*   for  the 


Whately  and  others 
erroneously  make  the 
Inductive  Syllogism 
Deductive. 


Doctrine    of     the 
older  logicians. 


1  ICf.  Wolf.   Philosophta  Rationalis,  §    479,  (Entbymemate)  vel  major  vel  minor  prsemis- 

flrst  ed.  1728.    So,  before  Wolf,  Schramm,  sarum,  in    hoc  (Inductione)  semper  major 

AriMoi.  Philos.  Principia,  p.  27,  ed.  Helmst.,  propositio  subintelligitur."     Refers  as    lo,- 

1718.      "  Induct!  jue  ex  multis    siugularibus  lows  —  '■'■  De  Inductione^  Philos.  AUorf.,   Di.sp. 

c«>nigitur  universale  supposito  loco  majoris  xxvi.  p.  252  et  seg."    See  also  Crakanthorpe^ 

I'Fopositionis  hoc  canone :  Qufcquid  competit  iog-ica,  c.  xx.  p.  217,  ed.  1677.  [CL  Discussions, 

cmuibus  partibus,  hoc  competit  toti;  in  isto  p.  170,  note.  —  Ed.] 


2SQ  LOGIC.  Lkct.  xvu 

previous  logicians  viewed  the  subsumption  as  the  common,  and, 
therefore,  the  suppressed  premise,  this  premise  always  stating  that 
the  individuals,  or  particulars  enumei-ated,  made  up  the  class  under 
which  they  were  severally  contained.^  For  example,  in  the  instance 
from  the  magnet  we  have  already  taken,  the  subsumption  would  be, 
This^  tfiat,  and  the  other  magnet^  and  so  forth^  are  the  whole  class 
magnet.     This  doctrine  of  the  older  logicians  is 

Correct  as  far  as  it  ..  c  -^  j    ^  i       -^     i 

correct  as  lar  as  it  goes ;  and,  to  make  it  abso- 
lutely correct,  it  would  only  have  been  necessary 
to  have  established  the  distinction  between  the  logical  induction  as 
governed  by  the  a  priori  conditions  of  thought,  and  philosophical 
induction  as  legitimated  by  the  a  posteriori  conditions  of  the  mat- 
ter, about  which  the  inquiry  is  conversant.     This,  however,  was  not 
done,  and  the  whole  doctrine  of  logical  induction  was  corrupted 
and  confounded  by  logicians  introducing  into  their  science  the  con- 
sideration of  various  kinds  of  matter,  and  admitting  as  logical  an 
induction  supposed  imperfect,  that  is,  one  in  which  there  was  infer- 
ence to  the  whole  from  some  only  of  the  constituent  parts.     This 
Imperfect   Induction,  they  held   in  contingent 
oc  nne  o     mper-       matter  to  be  contingent,  in  necessary  matter  to 

feet  Induction.  ... 

be  necessary,  as  if  a  logical  inference  were  not, 
in  all  cases,  necessary,  and  only  necessary  as  governed  by  the  neces- 
sary laws  of  thought.  This  misapprehension  of  the  nature  of  logi- 
cal or  foiTnal  induction,  and  its  difference  from  philosophical  or 

material,  has  been  the  reason  why  Bacon  is  at 
Bacon  at  fault  in  his      fault  Jq  jjjg  criticism  of  Aristotlc's  doctriuc   of 

criticism  of  Aristotle's         -j^.  -»:,         ii-  i  .^•13.. 

.    ..      ,,  J    ..  induction.     Jbor,  looking   only  at  the  doctrine 

doctrine  of  Induction.  ^  '  ? 

of  the  inductive  syllogism  given  by  Aristotle 
in  the  Organon^  and  not  perceiving  that  the  question  there  was 
only  concerning  the  nature  of  induction  as  governed  by  the  laws  of 
thought,  he  forthwith  assumed  that  this  was  the  induction  practised 
by  the  Stagirite  in  his  study  of  nature,  and,  in  the  teeth  both  of 
the  precept  and  practice  of  the  philosopher,  condemned  the  Aris- 
totelic  induction  in  the  mass,  as  flying  at  once  to  general  principles 
from  the  hasty  enumeration  of  a  few  individual  instances.  Induc- 
tion, as  I  mentioned,  will,  however,  once  and  again,  engage  our 
attention  in  the  sequel ;  but  I  have  thought  it  proper  to  be  some- 
what explicit,  that  you  might  carry  with  you  a  clearer  conception 


i  [On  Indoetion  in  general,  sec  Zabarella,  xx.  p.  254     Keckermann,  Opera,  t.  i.  pp.  259, 

Tabula  in  An.  Prior,  p.  170  <<  sei]..  Optra  Log-  763.     Lambert,  Neuet  Organon,  i    H  286,  287, 

tea,  (Appendix)  Molin«ns,  EUtrtenta  Logica,  p.   183.      Kugenias  AoyiK)),   p.  410.    Jo.  Fr. 

L.  i.  c.  ii.  p.  99.    Isendoorn,  Cursus  Logieus,  Pious  Mirandulanus.]    [Opera,  Examen  DoU 

L.  iii.  q.  ii.  p.  361.    Crellius,  Isagoge,  L.  iii.  c.  Vonif.  Gent.  L.  r.  p  746  et  uq.  —  1Sd>.] 


Lkct.  XVIL  LOGIC.  231 

of  the  nature  of  this  process,  as  contrasted  with  the  process  of  the 
Deductive  Syllogism. 

Having  terminated  the  general  consideration  of  Categorical  Syl- 
logisms, Deductive  and  Inductive,  I  now  pro- 
B.  Conditional  Syi-       ^^^^  ^^  ^^^  ^^^^  ^j^^^  ^^  Reasonings  afforded 

1.  Difliunctive.  ^7  ^^^  internal  form ;  I  mean  the  class  of  Dis- 

junctive Syllogisms. 

%  LXIII.    A  Disjunctive  Syllogism  is  a  reasoning,  whose 
Par  Lxin   A  Dia-      forai  is  determined  by  the  law  of  Excluded 
jtmctive  ayiioKism,-      Middle,  and  whose  sumption  is  accordingly 
''^'"  a  disjunctive  proposition,  either  of  Contra- 

diction (as,  A  is  either  B  or  not  B)  —  or  of  Contrariety  (as,  A 
is  either  B,  or  C,  or  D).  In  such  a  judgment,  it  is  enounced 
that  B  or  not  B,  or  that  B,  C,  or  D,  as  opposite  notions  taken 
together  and  constituting  a  totality,  are  each  of  them  a  possi- 
ble, and  one  or  other  of  them  a  necessary,  predicate  of  A.  To 
determine  which  of  these  belongs,  or  does  not  belong  to  A,  the 
subsumption  must  either  affirm  one  of  the  predicates,  and  the 
conclusion,  eo  ipso,  consequently,  deny  the  other  or  others ;  or 
it  must  deny  one  or  more  of  them,  and  thus  necessitate  in  the 
conclusion,  either  the  determinate  affirmation  of  the  other,  or 
the  indeterminate  affirmation  of  the  others.  A  Disjunctive 
Syllogism  is  thus  either  Affirmative,  constituting  the  Modus 
ponens,  or  Modus  ponendo  tollens,  or  Negative,  constituting 
the  Modus  tollens,  or  Modus  tollendo  ponens. 

In  each  of  these  modes  there  are  two  cases,  which  I  compre- 
hend in  the  following  mnemonic  verses : 

(A)  Affirmative,  ok  Modus  ponendo  tollkns  :  — 

1.  Faileris  autfaUor ;  faJlor ;  non  fdUeris  ergo. 

2.  FaUeris  out  faUor ;  tu  faileris;  ergo  ego  nedum. 

(B)  Negative,  ok  Modus  tollendo  ponens:  — 

1.  Faileris  autfaUor ;  non  faUor;  faUeris  ergo.  ^ 

2.  FaUeris  aut  fallor ;  non  faUeris ;  ergo  ego  faUor. 

In  illustration  of  this  paragraph,  I  have  defined  a  'disjunctive 
syllogism,  one  whose  form  is  determined  by  the 

Explication.  J       a         ■>  J 

law  of  Excluded  Middle,  and  whose  sumption 
n,  accordingly,  a  disjunctive  proposition.  I  have  not,  as  logicians 
in  general  do,  defined  it  directly,  —  a  syllogism  whose  major  pre- 

I  This  line  is  from  Furehot,  Instit.  Phiios.  Logiea,  1. 1,  p.  I&i.    The  others  are  the  Anthor'k 
own.  —  Ed. 


232  LOGIC.  Lect.  XVIL 

mise  is  a  disjunctive  proposition.     For  though  it  be  tnie  that  every 

disjunctive    syllogism  has    a  disjunctive    major 

sy  ogism  \n         premise,  the  converse  is  not  true ;  for  every  syl- 

disjuuctive  major  pre-         *       ,  ...  . 

mise  is  not  necessarily  logism  that  has  a  disjunctive  sumption  is  not, 
a  disjunctive  reason-  on  that  account,  neccssanly  a  disjunctive  syllo- 
'"*■  gism.     For  a  disjunctive  syllogism  only  emerges, 

when  the  conclusion  has  reference  to  the  relation  of  reciprocal 
affirmation  and  negation  subsisting  between  the  disjunct  members 
in  the  m:!Jor  premise,  —  a  condition  not,  however,  contained  in  the 
mere  existence  of  the  disjunctive  sumption.^  For  example,  in  the 
syliogisra : 

B  is  either  C  or  D ; 

But  A  IS  B ; 

Therefore,  A  is  either  C  or  D. 

This  syllogism  is  as  much  a  reasoning  determined,  not  by  the  law 
of  Excluded  Middle,  but  solely  by  the  law  of  Identity,  as  the  fol- 
lowing : 

BisC. 

AtsB. 

There/ore,  A  is  C. 

For  in  both  we  conclude,  —  C  (in  one,  C  or  D)  is  an  attribute  of  B ; 
but  B  is  an  attribute  of  A  :  therefore^  C  (C  or  D)  is  an  attribute  of 
A,  —  a  process,  in  either  case,  regulated  exclusively  by  the  law  of 
Identity.^ 

This  being  premised,  I  now  proceed  to  a  closer  examination  of 
the  nature  of  this  reasoning,  and  shall,  fii*st,  give  you  a  general 
notion  of  its  procedure ;  then,  secondly,  discuss  its  principle ;  and, 
thirdly,  its  constituent  parts. 

,o  „        ,   .       ,  1°.  The  general  form  of  the  Disjunctive  Syl- 

1°.  General  view  of  =>  . 

the  Di^unctive  Syiio-  logism  may  be  given  in  the  following  scheme, 
«i»™-  in  which  you  will  observe  there  is  a  common 

sumption  to  the  negative  and  affirmative  modes : 

,    .  _         ,      -  A 15  either  B  or  C. 

(a.)  Formnla  for   a 

Syllogism  with  two  Affirmative,  or  Modus  Negative,  or  Modus  tol- 
disjunct  members.  ponekdo  tollens  — 

Now  A  IS  B ; 

Therefore,  A  is  not  C, 


LENDO  PONEK8  — 

Now  A  IS  tmt  B; 
Therefore,  A  is  C. 


1  Cf  Scheibler,  Opera  Lngiea,  Tars.  iv.  p.  553.  S  Sigwart,  pp.  164, 157.    I  Uandbuch  zur  For- 

'*  Neque  enim  syllogismus  disjunctus  semper  hsungfti  Ubr' die  Logik,voH  H.  C.  W.  Sigteartf 

eirt,  cum  propositio  est  disjuuctiva,  sed  cum  Sd  ed.  Tubingen,  idSft,  H  246, 248.  — £d.] 
totaquxstiodisponitur  in  propojiiionc."  £d. 


Lkct.  XVIL  logic.  233 

Or,  in  a  concrete  example  ; 

Sempronius  is  either  honest  or  dishonest. 
Affibmative,  or  Modus  poxendo       Negative,    or    Modus    tollendo 
tollen8  —  posen8  — 


Nau)  Sempronius  is  honest ; 


Now  Sempronius  is  not  honest ; 


Therefore,  Sempronius  is  not  dishonest.  Therefore,  Sempronius  is  dishonest. 

"  This  formula  is,  however,  only  calculated  for  the  case  in  which 

there  are  only  two  disjunct  members,  that  is,  for 

(b.)  Formula  for  a       i]^q  c^ge  of  negative  or  contradictory  opposition  : 

y  ogism  wi     ™ore       ^^^^  -j.  ^j^^  disjunct  members  are  more  than  two, 

than      two      disjunct  ... 

members.  that  is,  if  there  is  a  positive  or  contrary  opposi- 

tion, there  is  then  a  twofold  or  manifold  employ- 
ment of  the  Modus  ponendo  toUens  and  Modus  toUendo  ponens^ 
according  as  the  affirmation  and  negation  is  determinate  or  indeter- 
minate. I^  in  the  Modus  ponendo  tollens,  one  disjunct  member  is 
detenninately  affirmed,  then  all  the  others  are  denied  ;  and  if  sev- 
eral disjunct  members  are  indeterminately  affirmed  except  one,  then 
only  that  one  is  denied.  If,  in  the  Modu^  tollendo  ponens,  a  single 
member  of  the  disjunction  b6  denied,  then  some  one  of  the  others  is 
determinately  affirmed ;  and  if  several  be  denied,  so  that  one  alone 
is  left,  then  this  one  is  determinately  affirmed."  *  This  will  appear 
more  clearly  from  the  following  formulae.  Let  the  common  Sumption 
both  of  the  Modus  poneiido  tollens  and  Modus  toUendo  ponens  be  - 

A  is  either  B,  or  C  or  D. 

I.    The  Modus  Poxendo  Tou^ns — 
First  Case.        A  is  either  B  or  C  or  D  ; 
Now  A  is  B ; 
Therefore,  A  is  neither  C  nor  D. 

Second  Case.  A  is  either  B  or  C  or  D; 
Now  A  is  either  B  or  C ; 
Therefore,  A  is  notD. 

n.    The  Modus  Tollendo  Ponens  — 
First  Case.        Aiseitter  B  or  C  or  D; 
Now  A  is  not  B ; 
Therefore,  A  is  either  C  or  D. 

Second  Case.    A  iset</icr  B  or  Cor  D; 
Now  A  is  neither  B  nor  C; 
Ther^ore,  A  is  D. 

I  Eager,  L<«tfe,  {  93,  p.  180.— Ed. 

30 


234  LOGIC.  Lect.  xvn. 

Or,  to  take  these  in  concrete  examples,  let  the  Common  Sump- 
tion be : 

The  ancients  were  in  genius  either  superior  to  the  moderns,  or  inferior,  or  equal. 

I.    The  Modus  Ponendo  Tollens  — 
First  Case.        The  ancients  were  in  genius  either  superior  to  the  modems,  or  inferia, 
or  equal ; 
Now  the  ancients  were  superior ; 
Therefore,  the  ancients  were  neUher  inferior  nor  equal. 

Second  Case.    The  ancients  were  in  genius  either  superior  to  the  modems,  or  inferior, 
or  equal; 
Now  the  ancients  uxre  either  superior  or  equal ; 
Therefore,  the  ancients  uxre  not  inferior. 

n.    The  Modus  Tollendo  Ponens  — 
First  Case.        The  ancients  uxre  in  genius  either  superior  to  the  modems,  or  inferior, 
or  equal. 
Now  the  ancients  were  not  inferior  ; 
Therefore,  the  ancients  uxre  either  superior  or  equal. 

Second  Case.    The  ancients  uxre  in  genius  either  superior  to  the  modems,  or  inferior, 
or  equal.  • 

Now  the  ancients  uxre  neither  inferior  nor  equal ; 
Therefore,  the  ancients  uxre  superuA-. 

Such  is  a  general  view  of  its  procedure.    Now,  2*,  for  its  prin^ 

ciple. 
2°.  The  principle  of  «  jf  ^^e  essential  character  of  the  Disjunctive 

un    V     y  Syllogism  consist  in  this,  —  that  the  affirmation 

or  negation,  or,  what  is  a  better  expression,  the 
position  or  sublation,  of  one  or  other  of  two  contradictory  attributes 
follows  from  the  subsumption  of  the  opposite  ;  —  there  is  necessarily 
implied  in  the  disjunctive  process,  that,  when  of  two  opposite  predi- 
cates one  is  posited  or  affirmed,  the  other  is  sublated  or  denied ; 
and  that,  when  the  one  is  sublated  or  denied,  the  other  is  posited  or 
affirmed.  But  the  proposition,  —  that  of  two  repugnant  attributes, 
the  one  being  posited,  the  other  must  be  sublated,  and  the  one 
being  sublated,  the  other  must  be  posited,  —  is  at  once  manifestly 
the  law  by  which  the  disjunctive  syllogism  is  governed,  and  mani- 
festly only  an  application  of  the  law  of  Excluded  Middle.  For  the 
Modus  ponendo  tollens  there  is  the  special  rule,  —  If  the  one  charac- 
ter be  posited  tlie  other  character  is  sublated ;  and  for  the  Modus 
tollendo  ponens  there  is  the  special  rule,  —  If  the  one  character  be 
sublated,  the  other  character  is  posited.  The  law  of  the  disjunctive 
syllogism  is  here  enounced,  only  in  reference  to  the  case  in  which 


Lect.  XVn.  LOGIC.  236 

the  members  of  disjunction  are  contradictorily  opposed.  An  oppo- 
sition of  contrariety  is  not  of  purely  logical  concernment ;  and  a 
disjunctive  syllogism  with  characters  opposed  in  contrariety,  in  fact, 
consists  of  as  many  pure  disjunctive  syllogisms  as  there  are  opposing 
predicates."  ^ 

3°.  I  now  go  to  the  third  and  last  matter  of  consideration,  —  the 

several  parts  of  a  Disjunctive  Syllogism. 
8°.  The  several  parts  "The  question  concerning  the  special  laws  of 

of  aDisiunctire  St11o>  j*   •         x-  h      •  i     ^    •      ^i 

a  disjunctive  syllogism,  or,  what   is  the  same 

thing,  what  is  the  original  and  necessary  "form 
of  a  disjunctive  syllogism,  as  determined  by  its  general  principle  or 
law,  —  this  question  may  be  asked,  not  only  in  reference  to  the 
whole  syllogism,  but  likewise  in  reference  to  its  several  parts.  The 
original  and  necessary  form  of  a  disjunctive  syllogism  consists,  as 
we  have  seen,  in  the  reciprocal  position  or  sublation  of  contradictory 
characters,  by  the  subsumption  of  one  or  other.  Hence  it  follows, 
that  the  disjunctive  syllogism  must,  like  the  categorical,  involve  a 
threefold  judgment,  viz. :  1°,  A  judgment  in  which  a  subject  is 
determined  by  two  contradictory  predicates ;  2°,  A  judgment  in 
which  one  or  other  of  the  opposite  predicates  is  subsumed,  that  is, 
is  affirmed,  either  as  existent  or  non-existent;  and,  3°,  A  judgment 
in  which  the  final  decision  is  enounced  concerning  the  existence  or 
non-existence  of  one  of  the  repugnant  or  reciprocally  exclusive  pre- 
dicates. But  in  these  three  propositions,  as  in  the  three  proposi' 
tions  of  a  categorical  syllogism,  there  can  only  be  three  principal 
notions  —  viz.,  the  notion  of  a  subject,  and  the  notion  of  two  con- 
tradictory attributes,  which  are  generally  enounced  in  the  sumption, 
and  of  which  one  is  posited  or  sublated  in  the  subsumption,  in  order 
that  in  the  conclusion  the  other  may  be  sublatedor  posited.  The 
case  of  contrary  opposition  is,  as  we  have  seen,  easily  reconciled  and 
reduced  to  that  of  contradictory  opposition."  ^  The  laws  of  the 
several  parts  of  a  disjunctive  syllogism,  or  more  properly  the  origi- 
nal and  necessary  form  of  these  several  parts,  are  given  in  the 
following  paragraph: 

^  LXIV.     1".  A  regular  and  perfect  Disjunctive  Syllogism 

must  have  three  propositions,  in  which,  if 

Par.  iixiv.  The  laws       tj^e  sumptiou  be  simple  and  the  disjunction 

of     the     Dl8janotive  i       i       •      i  11  .       .       , 

syuogism.  purely  logical,  only  three  principal  notions 

can  be  found. 
2*,  The  Sumption,  in  relation  to  its  quantity  and  quality,  is 

lEsser,  Log^,  {94.  — Ed.  i 'Eaaer,  Logik,  i  %.~~Ed. 


236  LOGIC.  Lect.  xvii. 

always  uniform,  being  Univei-sal  and  AfBrmative ;  but  tlie  Sub- 
sumption  is  susceptible  of  various  forms  in  both  relations. 

3°,  The   Conclusion   corresponds  in  quantity  with  the  sub- 
sumption,  and  is  opposed  to  it  in  quality.* 

The  first  rule  is,  —  A  regular  and  perfect  disjunctive  syllogism 
must  have  three  propositions,  in  which,  if  the 
xp  ica  ion.  sumption  be  simple,  and  the  disjunction  purely 

logical,  only  three  principal  notions  can  be 
found.  "Like  the  categorical  syllogism,  the  disjunctive  consists  of 
a  sumption,  constituting  the  general  rule ;  of  a  subsumption,  con- 
taining its  application  ;  and  of  a  conclusion,  expressing  the  judg- 
ment inferred.  Disjunctive  syllogisms  are,  therefore,  true  and 
genuine  reasonings;  and  if  in  the  sumption  the  disjunction  be 
contradictory,  there  are  in  the  syllogism  only  three  principal  no- 
tions. In  the  case  of  contrary  disjunctions,  there  may,  indeed, 
appear  a  greater  number  of  notions ;  but  as  such  syllogisms  are  in 
reality  composite,  and  are  made  up  of  a  plurality  of  syllogisms  with 
a  contradictory  disjunction,  this  objection  to  the  truth  of  the  rule  is 
as  little  valid  as  the  circumstance,  that  the  subject  in  the  sumption 
is  sometimes  twofold,  threefold,  fourfold,  or  manifold ;  as,  for  exam- 
ple, in  the  sumption  —  John^  James^  Thomas^  are  either  virtuous  or 
vicious.  For  this  is  a  copulative  proposition,  which  is  composed  of 
three  simple  propositions  —  viz.  John  is,  etc.  If,  therefore,  there  be 
such  a  sumption  at  the  head  of  a  disjunctive  syllogism,  it  is  in  this 
case,  likewise,  composite,  and  may  be  analyzed  into  as  many  simple 
syllogisms  with  three  principal  notions,  as  there  are  simple  proposi- 
tions into  which  the  sumption  may  be  resolved."  * 

The. second  rule  is,  —  The  sumption  is,  in  relation  to  its  quantity 
and  quality,  always  uniform,  —  being  universal 

Second  Rule.  ,     V.  '  /  ,  ,  .        . 

and  affirmative ;  but  the  subsumption  is  suscep- 
tible of  different  forms  in  both  relations.  If  we  look,  indeed,  to  the 
subject  alone,  it  may  seem  to  be  possibly  equally  general  or  particu- 
lar ;  for  Ave  can  equally  say  of  some  as  of  all  A,  that  they  are  either 
B  or  C.  But  as  all  universality  is  relative,  and  as  the  sumption  is 
always  more  extensive  or  more  comprehensive  than  the  subsump- 
tion, it  is  thus  true  that  the  sumption  is  always  general.  Again, 
looking  to  the  predicate,  or,  as  it  is  complex,  to  the  predicates  alone, 
they,  as  exclusive  of  each  other,  appear  to  involve  a  negation.  But 
in  looking  at  the  Whole  proposition,  that  is,  at  the  subject,  the 
copula,  and  the  predicates  in  connection,  we  see  at  once  that  the 

1  Etser, ).  e.    Krug,  Logik,  {  80-  —  £^0.  *  Krug,  Logik,  I.  e.  —  £d. 


LiiCT.  XVII.  LOGIC.  237 

copula  is  affirmative,  for  the  negation  involved  in  the  predicates  is 
confined  to  that  term  alone.^ 

In   regard   to   the  third  rule,  which  enounces,  —  That  the  con- 
clusion should  have  the  same  quantity  with  the 

Third  Rule.  ,  .  ,  .  ,.  .      . 

subsumption,  but  an  opposite  quahty,  —  it  is 
requisite  to  say  nothing,  as  the  first  clause  is  only  a  special  applica- 
tion of  the  rule  common  to  all  syllogisms,  that  the  conclusion  can 
contain  nothing  more  than  the  premises,  and  must,  therefore,  follow 
the  weaker  j^art ;  and  the  second  is  self-evident,  as  only  a  special 
application  of  the  principle  of  Excluded  Middle,  for,  on  this  law,  if 
one  contradictory  be  affirmed  in  the  subsumption,  the  other  must  be 
denied  in  the  conclusion,  and  if  one  contradictory  be  denied  in 
the  subsumption,  the  other  must  be  affirmed  in  the  conclusion. 
The  Disjunctive,  like  every  other  species  of  syllogism,  may  be 

either  a  reasoning  in  the  quantity  of  Compre- 
The  Disjunctive  syi-       hgngjon    ^j.  ^  reasoning  in  the  quantity  of  Ex- 

logism  of  Comprehen-  •mi  i  ^     i 

sion  aud  Extension.  tension.  The  Contrast,  however,  of  these  two 
quantities  is  not  manifested  in  the  same  signal 
manner  in  the  disjunctive  as  in  the  categorical  deductive  syllogism, 
more  especially  of  the  first  figure.  In  the  categorical  deductive 
syllogism,  the  reasonings  in  the  two  counter  quantities  are  obtrusively 
distinguished  by  a  complete  conversion,  not  only  of  the  internal 
significance,  but  of  the  external  appearance  of  the  syllogism.  For 
not  only  do  the  relative  terms  change  places  in  the  relation  of 
whole  and  part,  but  the  consecution  of  the  antecedents  is  revereed; 
the  minor  premise  in  the  one  syllogism  becoming  the  major  premise 
in  the  other.  This,  however,  is  not  the  case  in  disjunctive  syllo- 
gisms. Here  the  same  proposition  is,  in  both  quantities,  always  the 
major  premise ;  and  the  whole  change  that  takes  place  in  convert- 
ing a  disjunctive  syllogism  of  the  one  quantity  into  a  disjunctive 
syllogism  of  the  other,  is  in  the  silent  reversal  of  the  copula  from 
one  of  its  meanings  to  another.  This,  however,  as  it  determines  no 
apparent  difference  in  single  propositions,  and  as  the  disjunctive 
sumption  remains  always  the  same  proposition,  out  of  which  the 
subsumption  and  the  conclusion  are  evolved,  in  the  one  quantity  ns 
in  the  other,  —  the  reversal  of  the  sumption,  from  extension  to  com- 
prehension, or  from  comprehension  to  extension. 

Examples.  ...  ,  , 

occasions  neither  a  real  nor  an  apparent  change 
in  the  syllogism.     Take,  for  example,  the  disjunctive  syllogism  : 

1  See  Krug,  Logik,  $   86,  Anm.  2.    Eb. —  quantitatemnisisnarumpartium  .    .    .  sicut 

[Bactimann,   Logik,  §   141,  p.   854.      Contra:  I'-onosilio  Hypothetica  habet  tantum  quan- 

Twesten,  Logik,  §  137,  ed.  1825,  p.  119.    Esser.  titatem  suarum  partium."    See  above,  p.  174. 

Lngik,  §  95.    Derodon,   Logira   R'stiiuta,  p.  and  note  1.  —  Ed.] 
676.]    [Propositio  Disjunctiva  nullani  habet 


238  LOGIC.  Lkct.  XVIl. 

Flato  is  either  learned  or  unlearned ; 

But  Plato  is  learned. 

Therefore,  Plato  is  not  unlearned. 

Now  let  us  explicate  this  into  an  intensive  and  into  an  extensive 
syllogism.    As  in  Intensive  Syllogism  it  will  stand : 

Plato  comprehends  either  the  attribute  learned  or  the  attribute  wnHeamed; 
But  Plato  comprehends  the  attribute  learned  ; 
Ther^ore,  etc. 

As  an  Extensive  Syllogism  it  will  stand ; 

Plato  is  contained  either  under  the  dass  learned  or  the  doss  uhleamed; 
But  Plato  is  contained  under  the  class  learned  ; 
Therefore,  etc. 

From  this  it  appears,  that,  though  the  difference  of  reasoning  in 
the  several  quantities  of  comprehension  and  extension  obtains  in 
disjunctive,  as  in  all  other  syllogisms,  it  does  not,  in  the  disjunctive 
syllogism,  determine  the  same  remarkable  change  in  the  external 
construction  and  consecution  of  the  parts,  which  it  does  in  categoric 
cal  syllogisms. 


LECTURE    XVIII. 

STOIOHEIOLOGY. 

SECTION   II.— OF  THE    PRODUCTS  OF    THOUGHT 

III.  — DOCTRINE    OF  REASONINGS. 

SYLLOGISMS.  — THEIR  DIVISIONS  ACCORDING  TO  INTERNAL 

FORM. 

B.  CONDITIONAL.  —  HYPOTHETICAL    AND   HYPOTHETICO- 
DISJUNCTIVE. 

Havtng  now  considered  Categorical  and  Disjunctive  Syllogisms, 
the  next  class  of  Reasonings  afforded  by  the  difference  of  Internal 
or  Essential  form  is  the  Hypothetical ;  and  the  general  nature  of 
these  syllogisms  is  expressed  in  the  following  paragraph : 

^  LXV.  An  Hypothetical  Syllogism  is  a  reasoning  whose 
form  is  determined  by  the  law  of  Reason 
Par.  LXV.  a.  Hypo-  and  Consequent.  It  is,  therefore,  reerulated 
ita  general  character.  by  the  two  pi'inciples  of  which  that  law  is 
the  complement,  —  the  one,  —  With  the 
reason,  the  consequent  is  affirmed;  the  other,  —  With  the 
consequent,  the  reason  is  denied :  and  these  two  princij^les 
severally  afford  the  condition  of  its  Affirmative  or  Constructive, 
and  of  its  N'egative  or  Destructive  form  (Modus  ponens  et 
Modus  tollens).  The  sumption  or  general  rule  in  such  a  syllo- 
gism is  necessarily  an  hypothetical  proposition  (^  A  is,  then  B 
is).  In  such  a  proposition  it  is  merely  enounced  that  the  prior 
member  (A)  and  the  posterior  member  (B)  stand  to  each  other 
in  the  relation  of  reason  and  consequent,  if  existing,  but  with- 
out it  being  determined  whether  they  really  exist  or  not. 
Such  determination  must  follow  in  the  subsumption  and  con- 
clusion ;    and  that,  either  by  the  absolute  affirmation  of  the 


240 


LOGIC. 


lect.  xvm. 


antecedent  in  the  subsuraption,  and  the  illative  affirmation  of 
the  consequent  in  the  conclusion  (the  modus  poneiu)  ;  or  by 
the  absolute  negation  of  the  consequent  in  the  subsuraption, 
and  the  illative  negation  of  the  antecedent  in  the  conclusion 
(the  modus  toUens)}  The  general  form  of  an  hypothetical 
syllogism^  is,  therefore,  the  following ; 

CokniDoa  SOinption  —  If  A  is,  thai  B  is; 
1,  2, 

Moons  PoxEKs:  Modus  Tolleks: 

But  A  IS ;  BtU  B  is  not ; 

Therefore,  B  is.  Therefore,  A  is  not. 

Or, 

A  B 

1)  Modus  Ponens  —  Si  poteris  possum ;  sed  tu  potes;  ergo  ego  possum. 

B  A 

2)  Modus  Tollens  —  Si  poteris  possum  ;  nan  possum;  nee  potes  ergo.^ 


1°.  Hypothetical  syl- 
lugism  ill  geueral. 
Contains  three  propo- 
■itions. 


In  illustrating  this  paragraph,  I  shall  consider,  1°,  This  species  of 
syllogism  in  general ;  2°,  Its  peculiar  principle ; 
^  '  and,  3",  Its  special  laws. 

1°,  "Like  every  other  species  of  simple  syllogism,  the  Hypothetical 
is  made  up  of  three  propositions,  —  a  sumption, 
a  subsuraption,  and  a  conclusion.  There  must, 
in  the  first  place,  be  an  hypothetical  proposition 
holding  the  place  of  a  general  rule,  and  from 
this  proposition  the  other  parts  of  the  syllogism 
must  be  deduced.  This  first  proposition,  therefore,  contains  a 
sumption.  But  as  this  proposition  contains  a  relative  and  correla- 
tive member,  —  one  member,  the  relative  clause,  enouncing  a  thing 
as  conditioning ;  the  other,  the  correlative  clause,  enouncing  a  thing 
as  conditioned  ;  and  as  the  whole  proposition  enounces  merely  the 
dependency  between  these  relatives,  and  judges  nothing  in  regard 
to  their  existence  considered  apart  and  in  themselves, — ^  this 
enonncement  must  be  made  in  a  second  proposition,  which  shall 
take  out  of  the  sumption  one  or  other  of  its  relatives,  and  categoii- 


'  [For  urc  of  terms  ponfns  and  toUens,  see 
I'-octhius,  De  SylloKismo  HypothetUo,  Opera,  p. 
i:il.  Wolf.  Phil.  Rat.,  i  403,  410.  Mark  Dun- 
can uses  the  terms  "  a  positlone  ad  posi- 
tionem,"  and  "  a  rt-motione  ad  remotioncm." 
[Iiiftitutionex  Logiccr,  L  iv.  c.  6,  4  4,  p.  240. 
Cf.  p.  243,  Salmurii,  1812.  —  Ed.] 

2  (On  the  Hypothetical  Syllogism  in  gen- 
eral, gee  Ammonius,  In  Dt  Int-rp.,  rrooom., 
f.   3,   Vcnetiis,    1648.      rhilopoiius,    In   AnaL 


Prior.,  I.  c.  23,  f.  60,  Venet.,  1536.  Magen- 
tinns.  In  Anal.  Prior.,  f.  16,  b.  Alex.  Aphro- 
disiensis.  In  An.jl.  Prior.,  ff.  87,  8S,  109,  130. 
Aid.  1520.  In  Topica,  f.  65,  Aid..  1513.  Anony- 
mous Author,  On  Syllogisms,  f.  44,  ed.  153  >. 
Schciblcr,  Opera  Logica,  pars  iv.  p.  643.  Bol- 
zano, W'issen.vha/liUfhre,  Logtk,  ii.  p.  510 
Waifz,  Organon,  In  An.  Prior.,  1.  c  23  ] 

■''  'I'heso  lines  are  the  Author's  own.  —  I'd 


I 


Lect.  XVm.  LOGIC.  241 

cally  enounce  its  existence  or  its  non-existence.  This  second  pro- 
position contains,  therefore,  a  subsumption  ;  and,  through  this  sub- 
sumption,  a  judgment  is  likewise  detemiiued,  in  a  third  proposition, 
with  regard  to  the  other  relative.  This  last  proposition,  therefore, 
contains  the  conclusion  proper  of  the  syllogism." 

"  But  as  the  sumption  in  an  hypothetical  syllogism  contains  two 
relative  clauses,  —  an  antecedent  and  a  conse- 

in  a  hypothetical       quent,  —  it,  therefore,  appears  double  ;    and  as 

syllogism  there  is  com-  .  ,  «  .  ,  i  i  .        i 

petent  a  twofold  kind  either  of  its  two  members  may  be  taken  m  the 
of  reasoning,— the  »wo-  subsumption,  there  is,  consequently,  competent 
rfiM  poneTis  and  modtu  ^  twofold  kind  of  reasoning.  For  we  can  either, 
°  ""'  in  the  first  place,  conclude  from  the  truth  of  the 

antecedent  to  the  truth  of  the  consequent ;  or,  in  the  second  place, 
conclude  from  the  falsehood  of  the  consequent  to  the  falsehood  of 
the  antecedent.  The  former  of  these  modes  of  hypothetical  infer 
ence  constitutes  what  is  sometimes  called  the  Constructive  Hypo- 
thetical,  but  more  properly  the  3fodus  JPonens :  —  the  latter  what 
is  sometimes  called  the  Destructive  hypothetical,  but  more  properfy 
the  Modu9  ToUensT^    As  examples  of  the  two  modes: 

HodOR  Ponens  —  If  Socrates  he  virtuous,  he  merits  esteem  ; 

But  Socrates  is  virtuous ; 

Therefore,  he  merits  esteem.  ^ 

Modus  Tollens  —  If  Socrates  be  virtuous,  he  merits  esteem  ; 

But  Socrates  does  not  merit  esteem  ; 

Therefore,  he  is  not  virtuous.^ 

So   much  for  the  character  of  the   Hypothetical  Syllogisnt   id  5 
general.     I  now  proceed  to  consider  its  peculiar  principle. 

2",  "  If  the  essential  nature  of  an  Hypothetical  Syllogism  consist 
in  this,  —  that  the  subsumption  affirms  or  denies  one  or  other  of  the 
two  parts  of  a  thought,  standing  to  each  other  in  the  relation 
of  the  thing  conditioning  and  the  thing  conditioned,  it  will  be  the 

1  Krug,  Logik,  §  81,  Anm.  1,  p.  254.    Com-  Here,  1/  it  be  day  is  called  ri  fryovnores-^  . 
pare  Esser,  Logik,  §  90,  p.  173.  —  Ed.  both  by  Peripatetics  and  by  Stoics;  the  sun  it 

2  [NomenelatBre  of  Tlieophrastus,   End©-  on  the  earth,  is  called  rh  iir^nevov  by  Teripa- 
mus,  and   other  PeripateUcs,  in    regard  to  tetics,  ih  \rjyoy  by  Stoics.    The  whole.  If  it 
Hypothetical  Syllogism,  in  contrast  with  that  be  day,  the  sun  is  on  the  earth,  is  called  ri,  - 
of  the  Stoics.  vwrififjifvov  by  Peripatetics,  rb  TpoiriK6v  by 

Upiytmra  yo^invra  <(>oryal  ( I'eripateUc),  gtoics :  But  it  is  day,  is  HfraX-q^is  to  Peri- 
are  called  by  the  Stoics  respectively,  rvy-  patetics,  icp6a\7j^is  to  Stoics.  Therefore,  the 
Xivoin-a  iK<popiKi,  Xficrd.  ,„„  ,-,  „„  the  earth,  is  av/iirepafffia  to  Peripa- 

Take  this  Hypothetical  Syllogism :  tetics,  iiri<f>opd  to  Stoics.     See  Philoponus, , 

Vit  he  day,  the  «a,  is  on  tJu:  earth:  ^"  ^"'^-  -^''^■'  ^-  '•  "•  ^'  ^    60  «.  e^.  VenCt 

Buiitisdav;  ^536.    Brandis,  Scholia,  p.  169.    Cf.  Anony- 

Thrr^ore,  the  tun  U  on  the  etertk.  "  ■  '  <       mous  Anthor,  On  Syllogisms,  f.  44.] 

31 


242  LOGIC.  Lect.  XVIIi. 

law  of  an  hypothetical  syllogism,  that,  —  If  the  condition  or  antece- 
dent be   affirmed,  so  also  must  be  the   eondi- 
2".  Its  peculiar  prin-      tioned  OF  consequent,  and  that  if  the  conditioned 

ciple,— the  law  of  Rea-  ,     i         t       •     i  ^^^         •  i 

■on  and  Consequent  ^^  consequent  be  denied,  so  likewise  must  be 
the  condition  or  antecedent.  But  this  is  mani- 
festly nothing  else  than  the  law  of  Sufficient  Reason,  or  of  Reason 
and  Consequent."  ^  The  principle  of  this  syllogism  is  thus  variously 
enounced,  —  JPosita  conditioner  ponitvr  conditionatvm  ;  sublato 
conditionato,  tollitur  conditio.     Or  otherwise, — 

How  enonnced.  •  .  i  .  ... 

A  rattone  ad  rationatum,  a  negatione  rationutt 
ad  negationem  ratio7iis,  valet  consequentia.  The  one  alternative  of 
either  rule  being  regulative  of  modus  ponens^  the  other  of  the  modus 
toUens? 

"  But  here  it  may  be  asked,  why,  as  we  conclude  from  the  truth 

of  the  antecedent  to  the  truth  of  the  consequent 

Why  we  cannot  con-       (^  ratione  ad  rationatum),  and  from  the  false- 

c  u  e   rom     e   ru         hood  of  the  Consequent  to  the  falsehood  of  the 

of  the  consequent  to  ^ 

the  truth  of  the  ante-  antecedent  (a  negatione  rationati  ad  negatio- 
cedent,  and  from  the  ncm,  vatiotiis).,  Can  wc  not  couverscly  conclude 
falsehood  of  the  ante-       ^^^^  ^^^  ^^^^^  ^^  ^j^^  Consequent  to  the  truth 

cedent   to    the    false-  ,01,1/., 

hood  of  the  oonse-  of  the  antecedent,  and  from  the  falsehood  of  the 
^nent  antecedent  to  the  falsehood  of  the  consequent? 

In  answer  to  this  question,  it  is  manifest  that 
this  could  be  validly  done,  only  on  the  following  supposition, 
namely,  if  every  consequent  had  only  one  possible  antecedent ;  and 
if,  from  an  antecedent  false  as  considered  absolutely  and  in  itself,  it 
were  impossible  to  have  consequents  true  as  facts. 

"Thus,  in  the  first  place,  it  is  incompetent  to  conclude  that  be- 
cause B  exists,  that  is,  because  the  consequent  member  of  the  sump- 
tion, considered  as  an  absolute  proposition,  is  true,  therefore  the 
supposed  reason  A  exists,  that  is,  therefore  the  alleged  antecedent 
member  must  be  true ;  for  B  may  have  other  reasons  besides  A, 
such  as  C  or  D.  In  like  manner,  in  the  second  place,  we  should 
not  be  warranted  to  infer,  that  because  the  sui)posed  reason  A  is 
unreal,  and  the  antecedent  member  filse,  therefore  the  result  B  is 
also  unreal,  and  the  consequent  member  false;  for  the  existence  of  B 
might  be  determined  by  many  other  reasons  than  A.'"  For  example: 

If  there  are  sharpers  in  the  company,  ux  ought  not  to  gambte; 
But  there  are  no  sharpers  in  the  company; 
Therefore,  we  ought  to  gamble, 

lEMer.Log^O:.  {91,p.l74.— Ed.  t  S««Kant,  Lo^  H  7S,76.  Krjxg, Legik, i  SI. —'Ed 

8  Krug,  Logik,  )  82,  p.  256.  —  Ed. 


■f^ 


Lkct.  XVm.  LOGIC.  248 

Here  the  conclusion  is  as  false  as  if  we  conversely  inferred,  that 
because  we  oxight  not  to  gamble^  the)'e  are  no  sharpers  in  the  room. 
"  Logicians  have  given  themselves  a  world  of  pains  in  the  dis- 
covery of  general  rules  for  the  conversion   of 
Conversion  of  Hy-       Hypothetical  Syllogisms  into  Categorical.^    But, 
pothetica  to   ategor-       j^  ^^^  g^,^^  place,  this  is  Unnecessary,  in  so  far  as 

ical  Syllogisms,  is  1°,  *  '  .    .      ' 

Unnecessary.  it  is  applied  to  manifest  the  validity  of  an  hypo- 

thetical syllogism;  for  the  hypothetical  syllo- 
gism manifests  its  own  validity  with  an  evidence  not  less  obtrusive 
than  does  the  categorical,  and,  therefore,  it  stands  in  no  need  of  a 
reduction  to  any  higher  form,  as  if  it  were  of  this  a  one-sided  and 
accidental  modification.  With  equal  propriety  might  we  inquire, 
how  a  categorical  syllogism  is  to  be  converted  into  an  hypothetical. 
In  the  second  place,  this  conversion  is  not 
21^,  Not  a  ways  pes-  always  possible,  and,  therefore,  it  is  never  ne- 
cessary. In  cases  where  the  sumption  of  an 
hypothetical  syllogism  contains  only  three  notions,  and  where,  of 
these  three  notions,  one  stands  to  the  other  two  in  the  relation  of 
:i  middle  term,  —  in  these  cases,  an  hypothetical  syllogism  may 
without  difficulty  be  reduced  to  categoricals.  Thus,  when  the 
formula — -5^  A  is,  then  B  is,  signifies — If  ^  is  C,  then  A  is  also  B; 
that  is,'  A  is  B,  inasmuch  as  it  is  C ;  —  in  this  case  the  categorical 
form  is  to  be  viewed  as  the  original,  and  the  hypothetical  as  the 
derivative."^    For  example: 

If  Caius  be  a  man,  then  he  is  mortal; 
But  Caius  is  a  man ; 
Therefore,  he  is  mortal 

Here  the  notion  man  is  regarded  as  comprehending  in  it,  or  a« 
contained  under,  the  notion  mortal;  and  as  being  comprehended 
in,  or  as  containing  under  it,  the  notion  Caius ;  it  can,  therefore, 
serve  as  middle  term  in  the  categorical  syllogism  to  connect  the 
two  notions  Caius  and  mortal.    Thus : 

Man  is  mortal; 
Caius  is  a  man ; 
Therefore,  Caius  is  mortal. 

1  [For  the  reduction  of  hypotheticals,  see  see  Krug,  Logik,  p.  356,  and  Lexikon,  iii.  p 

Wolf,   Philos.   Rat.,   §   412.    Reusch,  Systema  559.    Fries,  Logik,  §  62,  p.  267.    Baclimana 

Logicum,  §  663.     HollDaeus,  EUmenta    Logica,  Logik,   §   89,   Anm.  2.      (In  part),   Aristotle, 

L.  i.  tract,  iii.  c.  1,  p.  95.     Keckermann,  Opera,  Anal.  Prior.,  L.  i.  c.  44,  p.  274,  ed.  Pacii..    (lu 

t.  i.  pp.  266,  767.     Crellius,  Isagoge,  L.  iii.  c.  part),  Pacius,  Tn  Arist.,  Organon,  loc.  eit-,  p 

17,  p.  243       Kiesewetter,  Allgemeine  Logik,  i.  194] 

♦  239,  p.  115.   Esser,  Z.og^iAr,  §§  99, 100.    Against,  2  Krug,  I.og^ii,  p.  268,  Anm,  3.  —  Ed. 


S44  LOGIC.  Lkct.  xvm. 

"  In  such  cases  it  requires  only  to  discover  the  middle  term,  in 
order  to  reduce  the  hypothetical  syllogism  to  a  categorical  form; 
and  no  rules  are  requisite  for  those  who  comprehend  the  nature  of 
tlie  two  kinds  of  reasoning. 

"But  in  those  cases  where  the  gumption  of  an  hypothetical  syllo- 
gism contains  more  than  three  notions,  so  that  the  formula,  If  K 
iSy  then  B  is^  signifies,  If  A  is  C,  then  is  B  also  D,  —  in  such  cases, 
an  easy  and  direct  conversion  is  impossible,  as  a  categorical  syllo- 
gism admits  of  only  three  principal  notions.  To  accomplish  a 
reduction  at  all,  we  must  make  a  circuit  through  a  plurality  of  cat- 
egorical syllogisms  before  we  can  ariive  at  an  identical  conclusion, 
—  a  process  which,  so  far  from  tending  to  simplify  and  explain,  con- 
duces only  to  pei-plex  and  obscure.^ 

"  On  the  other  hand,  we  can  always  easily  convert  an  h j-potheti- 

cal  syllogism  of  one  form  into  another,  —  the 

Hypothetical  syiio-      modus  ponens   into   the   modus   toUeiis,  —  the 

^TT  °    °?lx  TT      modus  tollens  into  the  modus  ponens.    This  is 

Muily  convertible  into  ,  ,     ^ 

tbat  of  another.  done  by  a  mere  contraposition  of  the  antece- 

dent and  consequent  of  the  sumption.    Tb'is, 
the  Ponent  or  Constructive  Syllogism  : 

^  Socrates  be  virtmua,  then  he  merits  «tleem  {  •  ■ 

But  Socrates  is  virtuoas  ; 

Therefore,  he  merits  esteem,  ^ 

may  thus  be  converted  into  a  ToUent  or  Destructive  syllogism : 

Jff'  Socrates  do  not  merit  esteem,  then  he  is  not  virtuous; 
But  he  is  virtuous ; 
Tker^re,  he  merits  esteem. 

"This  latter  syllogism,  though  apparently  a  Constructive  syllc 
gism,  is  in  reality  a  Destructive.  For,  in  modo  ponente,  we  con- 
clude from  the  truth  of  the  antecedent  to  the  truth  of  the  conse^ 
<quent;  but  here  we  really  conclude  from  the  falsehood  of  the 
consequent  to  the  falsehood  of  the  antecedent."*  This  latter  syl- 
logism, if  fully  expressed,  would  indeed  be  as  follows  : 

If  Socrates  do  not  merit  esteem,  he  is  not  virtuous; 
But  Socrates  is  not  not  virtuous  ; 
Therefore,  he  does  not  not  merit  estesm. 

1  Compare  Mark  Duncan,  Jnstit.  Leg.,  L.  It.      [Boliano,  WtastnteA^/tsMrt,  L»gik,  IL  tHK,  p^ 
«.  6,  i  4,  p.  240  et  seq.     Derodon,  Logica  Re»li-      662.] 
(iita,Z)«  Jr^m«n<«iion«,  i  lOG,  p.  67S.  — Ed.         *  Kmg,  Logik,  p.  Wd,2B0.  —  KD. 


I,KCT.  xvm.  LOGIC.  246 

3**.   I  now  go  on  to  ^  statement  and  consideration  of  the  special 
rales  by  which  an  hypothetical  syllogism  is  governed. 

Par.  Lxvi.  3o,  spe-  ^   LXVI.   The  spccial  rules  by  which  an 

oiai  Kuies  of  Hypo-       Hypothetical  Syllogism  is  regulated  are  the 

thetloal  SyllogiBm.  .  -         »  o 

following; 
I.  A  regular  and  peifect  hypothetical  syllogism  must  have  three 

propositions,   in   which,  however,  more   than   three    principal 

notions  may  be  found. 
H.  The  Sumption  is,  in  regard  to  quantity  and  quality,  uniform, 

being  always  Definite  and  Affirmative ;  whereas  the  Subsurap- 

tion.  varies  in  both  relations. 
III.  The  Conclusion  is  regulated  in  quantity  and  quality  by  that 

member  of  the  sumption  which  is  not  subsumed;   in  modo 

ponente^  they  are  congruent;  in  modo  toUente,  they  are  opposed.' 

"The  question  touching  the  special  laws  of  the  hypothetical  syl- 
logism, or,  what  is  the  same  thing,  the  question 
Buie.^  Thto  reguiatl  touching  the  original  and  necessary  form  of  the 
the  general  form  of  hypothetical  syllogism,  as  determined  by  itfi 
the  hypothetical  syiio-  general  principle,  —  the  law  of  Reason  and 
Consequent,  —  this  question  may  be  referred 
both  to  the  whole  reasoning  and  to  its  several  parts.  The  original 
and  necessary  form  of  the  hypothetical  syllogism,  as  determined  by 
its  general  principle,  we  have  already  considered-  From  this,  as 
already  noticed,  it  follows  as  a  corollary,  that  the  hypothetical,  like 
every  other  syllogism,  must  contain  a  threefold  judgment:  1°,  A 
judgment  whose  constituent  members  stand  to  each  other  in  the 
relation  of  reason  and  consequent;  2°,  A  judgment  which  sub- 
sumes as  existent,  or  non-existent,  one  or  other  of  these  constituent 
members,  standing  to  each  other  in  the  relation  of  reason  and  con- 
sequent; and,  3°,  Finally,  a  judgment  decisive  of  the  existence  or 
non-existence  of  that  constituent  member  which  was  not  subsumed 
in  the  second  judgment.  In  these  three  propositions  —  sumption, 
subsumption,  and  conclusion  —  there  may,  however,  be  found  move 
than  three  principal  notions ;  and  this  is  always  the  case  when  tii© 
8ura[)tion  contains  more  than  three  principal  terms,  as  is  exemplified 
in  a  proposition  like  the  following :  Jf  God  reward  virtue,  then  will 
virtuous  men  be  also  happy.  Here,  however,  it  must,  at  the  same 
time,  be  understood,  that  this  proposition,  in  which  a  larger  plural- 
ity of  notions  than  three  is  apparent,  contains,  however,  only  the 

1  Krag,  Z.ogii,  J  83.  — Ed. 


246 


LOGIC. 


lect.  xvni 


Ground  on  which 
the  Hypothetical  Syl- 
logism has  been  re- 
garded as  having  only 
two  terms  and  two 
propositions. 


This  view  erroneous. 


thought  of  one  antecedent  and  of  one  consequent;  for  a  single  con- 
sequent supposes  a  whole  antecedent,  how  complex  soever  it  may 
be,  and  a  single  antecedent  involves  in  it  a  whole  consequent, 
though  made  up  of  any  number  of  parts.  Both  of  these  possibili- 
ties are  seen  in  the  example,  now  adduced,  of  an  hypothetical  judg- 
ment, in  which  there  occur  more  than  three  principal  notions.  I^ 
however,  an  hypothetical  proposition  involve 
only  the  thought  of  a  single  antecedent  and 
of  a  single  consequent,  it  will  follow  that  any 
hypothetical  syllogism  consists  not  of  more  th;:ii 
three,  but  of  less  than  three,  capital  .notions; 
and,  in  a  rigorous  sense,  this  is  actually  the 
case."*  On  this  ground,  accordingly,  some  logicians  of  great  acute- 
ness  have  viewed  the  hypothetical  syllogism  as  a  syllogism  of  two 
terms  and  of  two  propositions."*  This  is,  how- 
ever, eiToneous ;  for,  in  an  hypothetical  syllo- 
gism, there  are  virtually  three  terms."  "That  under  this  form  of 
reasoning  a  whole  syllogism  can  be  evolved  out  of  not  more  than 
two  capital  notions  depends  on  this,  —  that  the  two  constituent 
notions  of  an  hypothetical  syllogism  present  a  character  in  the 
sumption  altogether  different  from  what  they  exhibit  in  the  sub- 
sumption  and  conclusion.  In  the  sumption  these  notions  stand 
bound  together  in  the  relation  of  reason  and  consequent,  without, 
however,  any  detennination  in  regard  to  the  reality  or  unreality  of 
one  or  other;  if  one  be,  then  the  other  is,  is  all  that  is  enounced. 
In  the  subsumption,  on  the  other  hand,  the  existence  or  nou-exist- 
ence  of  what  one  or  other  of  these  notions  comprises  is  expressly 
asserted,  and  thus  the  concept,  expressly  affirmed  or  expressly  de- 
nied, manifestly  obtains,  in  the  subsumption,  a  wholly  different  sig- 
nificance from  what  it  bore  when  only  enounced  as  a  condition  of 
reality  or  unreality ;  and,  in  like  manner,  that  notion  which  the  sub- 
sumption left  untouched,  and  concerning  whose  existence  or  non- 
existence the  conclusion  ,  decides,  obtains  a  character  altogether 
different  in  the  end  from  what  it  presented  in  the  beginning.  And 
thus,  in  strict  propriety,  there  are  found  only  three  capital  notions 
in  an  hypothetical  syllogism,  namely,  1°,  The  notion  of  the  recipro- 
cal dependence  of  subject  and  predicate,  2",  The  notion  of  the 
reality  or  unreality  of  the  antecedent,  and,  3°,  The  notion  of  the 
reality  or  unreality  of  the  consequent."'    So  much  in  explanatiou 


1  Esser,  Logii,  f  92,  p.  175-6.  —  Ed. 

S  See  Kant,  Logik,  )  75.  Kant's  view  is 
combatted  by  Krug,  Logik,  i  83.— Ed.  [A 
view  similar  to  that  of  Kant  is  held  by  Weiss, 


Logik,  M  210,  251.    Herbart,  Logik,  }  6S.    Fl» 
Cher,  Logik,  i  100,  p.  137.] 

s  Eaier,  foe. «(.  — Ed 


Lkct.  xviii.  logic.  247 

of  the  first  special  law,  or  that  regulative  of  the  general  form  of  the 
hypothetical  syllogism. 

The  second  law  states  the  conditions  of  these  two  premises,  — 
that  the  sumption,  in  reference  to  its  quantity 

Second  Rule.  r^        •  -r  u    •  i  ^   £    •/ 

and  quality,  is  unitorm,  being  always  dennite, 
that  is,  singular  or  universal,  and  affirmative ;  while  the  subsump- 
tion,  in  both  relations,  remains  free. 

In  regard  to  the  sumption,  when  it  is  said  that  it  is  always  defi- 
nite, that  is,  singular  or  universal,  and   affirma- 
That  the  sumption       tive,  this   must   be   understood   in    a  qualified 

18   always   definite  to  mi-.i^  •.  •i-ii 

.         J.J-  sense.     1  ouching  the  former,  it  may  indeed  be 

be    understood    in    a  _  cj  '  .' 

qualified  sense.  Said  that   quantity  may  be  altogether  throsvn 

out  of  account  in  an  hypothetical  syllogism.* 
For  a  reason  being  once  supposed,  its  consequent  is  necessarily 
affirmed  without  limitation ;  and,  by  tlie  disjunction,  the  extension 
or  comprehension  of  the  subject  is  so  defined,  that  the  opposite 
determinations  must  together  wholly  exhaust  it.  It  may,  indeed, 
sometimes  appear  as  if  what  was  enounced  in  an  hypothetical  sump- 
tion were  enounced  only  of  an  indefinite  number,  —  of  some ;  and 
it,  consequently,  then  assumes  the  form  of  a  particular  proposition. 
For  instance.  If'  some  men  are  virtuous,  then  some  other  men  are 
vicious.  But  here  it  is  easily  seen  that  such  judgments  are  of  an 
universal  or  exhaustive  nature.  In  the  proposition  adduced,  the 
real  antecedent  is.  If  some  men  {only)  are  virtuous ;  the  real  con- 
sequent is,  then  all  other  men  are  vicious.  It  Avould,  perhaps,  have 
been  better  had  the  relative  totality  of  the  major  proposition  of  a 
hypothetical  syllogism  been  expressed  by  another  term  than  univer- 
sal? For  the  same  reason  it  is,  that  the  difierence  of  extensive  and 
comprehensive  quantity  determines  no  external  change  in  the  ex- 
pression of  an  hypothetical  syllogism  ;  for  every  hypothetical  syllo- 
gism remains  the  same,  whether  we  read  it  in  the  one  quantity  or 
in  the  other. 

In  regard  to  the  other  statement  of  the  rule,  that  the  sumption 
of  an   hypothetical   syllogism  must  be  always 

That  the  sumption  is  «?  .•  ^i  •      ti         •  i  i  j     i» 

_      ..  affirmative,  —  this,  likewise,  demands  a  word  of 

always  affirmative.  '  '  ' 

illustration.  It  is  true  that  the  antecedent  or 
the  consequent  of  such  a  sumption  may  be  negative  as  well  as 
affirmative ;  for  example.  If  Caius  he  not  virtnaus,  he  is  not  entitled 
to  respect;  If  the  sun  be  not  risen,  it  is  not  day.     But  here  the 

1  [See  Alexander  Apbrodisiensis,  In  Anal.         2  See  above  p.  188.    Compare  Esser,  lagtk. 
Prior.,   f.   5  a.     Scholia,  ed.  Brandis,  p.  144.      §  92,  p.  177.  —  Ed. 
Dcrodon,  Logica  Rmtitvta,  p,  688.]    [Compare 
above,  pp.  188, 236.  —  Ed.] 


li4S  LOGIC.  Lkct.  xvia 

jjroposition,  as  an  hypothetical  judgment,  is  and  must  be  affirmative. 
For  the  affirmative  in  such  a  judgment  is  contained  in  the  positive 
assertion  of  the  dependence  of  consequent  or  antecedent ;  and  if 
such  a  dependence  be  not  affirmed,  an  hypothetical  judgment  can- 
not exist. 

In  regard  to  what  is  stated  in  the  rule  concerning  the  conditions 
of  the  subsumption,  —  that  this  may  either  bo 

The  subsumption.  ,  •      ^  n-  • 

general  or  particular,  amrmative  or  negative,  — 
it  will  not  be  requisite  to  say  anything  in  illustration.  For,  as  the 
Hubsuinption  is  merely  an  absolute  assertion  of  a  single  member  of 
the  sumption,  and  as  such  member  may,  as  an  isolated  j)roposition, 
be  of  any  quantity  or  any  quality,  it  follows  that  the  subsumption 
is  equally  unlimited. 

•  In  reference  to  the  third  rule,  which  states  that  the  conclusion  is 
regulated  in  quantity  and  quality  by  that  mem- 
ber of  the  sumption  which  is  not  subsumed,  and 
this  in  modo  ponente  by  congruence,  in  modo  toUetUe  by  opposition, 
it  will  not  be  requisite  to  say  much. 

♦*In  the  conclusion,  the  latter  clause  of  the  sumption  is  affirmed 
in  modo  ponente^  because  the  former  is  affirmed  in  the  sub8um])tion. 
In  tliis  case,  the  conclusion  has  the  same  quantity  and  quality  as  the 
clause  which  it  affirms.  In  modo  tollente  the  antecedent  of  the 
sumption  is  denied  in  the  conclusion,  because  in  the  subsumption 
the  consequent  clause  had  been  denied.  There  thus  emerges  an 
opposition  between  that  clause,  as  denied  in  the  conclusion,  and 
that  clause  as  affirmed  in  the  sumption.  The  conclusion  is  thus 
always  opposed  to  the  antecedent  of  the  sumption  in  quantity,  or 
in  quality,  or  in  both  together,  according  as  this  is  diflerently  deter- 
mined by  the  diffiarent  constitution  of  the  propositions.  For 
example : 

Jtr  some  men  were  omniscient,  dim  would  Ouy  be  as  Oods ; 

BtU  no  man  is  a  God ; 

Therefore,  some  men  are  not  omnitcieni,  that  is,  no  man  is  omniscient."^ 

- 1  now  proceed  to  the  consideration  of  the  last  class  of  syllogisms 

a  Hypothetico-diiH       affiii'dod  by  the  Intemal  Form,  — the  class  of 

juDctive    or    Diiem-      Dilenunatic   or   Hypothetico-disjunctivo    SyUo* 

matic  Syllogisms.  gisms,  and  I  comprise  a  general  enunciatlop  of 

their  nature  in  the  following  paragraph. 

1  Krag,  Logik,  i  83,  p.  a6&  -^Ep. 


Lect.  XVIII.  LOGIC.  249 

^  LXVII.   If  the  sumption  of  a  syllogiRra  he  at  once  hypo- 
thetical and  disjunctive,  and  if,  in  the  sub- 
pothetioo-disjuaotive       suuiption,  the  wholc  disjuuctioH,  as  a  conse- 
Byiiogism     or     Di-       qucut,  be  sublatcd,  in  order  to  sublate  tlie 
^™™**  antecedent  in  the  conclusion  ;  such  a  rea- 

soning is  called   an  Hypothetico-disjunctive   /SyUogism,  or  a 
Dilemma.     The  form  of  this  syllogism  is  the  following : 

If  A  exist,  then  either  B  or  C  exists  f 
But  neither  B  nor  C  exists  ; 
Therefore,  A  does  not  exist.^ 

We  have  formerly  seen  that  an  hypothetical  may  be  combined 
.  with  a  disjunctive  judgment;  and  if  a  proposi- 

tion of  such  a  character  be  placed  at  the  head 
of  a  reasoning,  we  have  the  Hypothetico-disjunctive  Syllogism  or 
Dilemma.  This  reasoning  is  properly  an  hypothetical  syllogism,  in 
which  the  relation  of  the  antecedent  to  the  consequent  is  not  abso- 
lutely affirmed,  but  affirmed  through  opposite  and  reciprocally  ex- 
clusive predicates.  J^  A  exist,  then  either  B  or  C  exist.  The 
sumption  is  thus  at  once  hypothetical  and  disjunctive.  The  sub- 
sumption  then  denies  the  disjunctive  members  contained  in  the  con- 
sequent or  posterior  clause  of  the  sumption.  J8ut  neither  B  nor  C 
exist.  And  then  the  inference  is  drawn  in  the  conclusion,  that  the 
reason  given  in  the  antecedent  or  prior  clause  of  the  sumption  must 
likewise  be  denied.     Therefore  A  does  not  exist.^    For  example  ; 

Jf  man  he  not  a  morally  responsible  being,  he  jnust  tcant  either  the  power  of  recognizing 
moral  good  (as  an  intelligent  agent),  or  the  power  of  willing  it  (as  a  free  agent). 

But  man  wants  neither  the  power  of  recognizing  moral  good  (as  an  intelligent  agent),  nor 
the  power  of  wiUyig  it  (as  a  free  agent) ; 

Therefore,  man  is  a  morally  responsible  being. 

"An  hypothetico-disjunctive  syllogism  is  called  the  dilemma  or 

hotted  syllogism,  in  the  broader  acceptation  of 

Designations  of  the       i}^q  term  (dilem,ma,  ceraXimts,  comutus  sc.  syllo- 

xiyTs,yVo^\sm.  gismus).     We  must  not,  however,  confound  the 

cornutus  and  crocodilinus  of  the  ancients  with 

our  hypothetico-disjunctive  syllogism.     The  former  were  sophisms 

of  a  particular  kind,  which  we  are  hereafter  to  consider;  the  latter 

1  Kriig,   Logik,  (    87. —  Ed.      [Contra,    see  257.     Aldrich,  Rurfimenm  Z-og^icff,  c.  iv.  $  3,  p. 

Troxler,  iog^.i,  ii.  p.  103  n*.    That  the  Dilem-  107,    Oxford,   1852.      riatner,    PMlosophUch* 

ma  is  a  negative  induction,  see  Wallis,  Lo^iea,  Aphorismen,  i.  }  5S3,  p.  280.] 

L.  Hi.  c.  19,  p.  218.    Cf.  Fries,  Logik,  §  60,  p.  2  Krug,  toe.  rit.  — Ed. 

32 


250  LOGIC.  Lect.  XVIII. 

is  a  regular  and  legitimate  form  of  reasoning.  In  regard  to  the 
application  of  the  terms,  it  is  called  the  cornutus  or  horned  syllo- 
gism, because  in  the  sumption  the  disjunctive  members  of  the  con- 
sequent are  opposed  like  horns  to  the  assertion  of  the  adversary ; 
with  these,  we  throw  it  from  one  side  to  the  other  in  the  subsump- 
tion ;  in  order  to  toss  it  altogether  away  in  the  conclusion.  If  the 
disjunction  has  only  two  members,  the  syllogism  is  then  called  a 
dilemma  (bicortiis)  in  the  strict  and  proper  signification,  literally 
double  sumption.  Of  this  the  example  previously  given  is  an  in- 
stance. If  it  has  three,  four,  or  five  members,  it  is  called  trilemma 
(tricomis),  tetralem,ma  (quadrncortiis), pentalemma  (qmtiquecomis)  ; 
if  more  than  four,  it  is,  however,  usually  called  polylemma  (multi- 
comis).  But,  in  the  looser  signification  of  the  word.  Dilemma  is  a 
generic  expression  for  any  or  all  of  these."* 

"Considered  in  itself,  the  hypothetico-disjunctive  syllogism  is  not 
to  be  rejected,  for  in  this  form  of  reasoning  we 

u  eg  for  sifting  a       ^^^  conclude  with  cosTency,  provided  we  attend 

proposed  Dilemma.  '^         -i  '  r 

to  the  laws  already  given  in  regard  to  the  hypo- 
thetical and  disjunctive  syllogisms.  It  is  not,  however,  to  be  de- 
nied, that  this  kind  of  syllogism  is  very  easily  abused  for  the  purpose 
of  deceiving,  through  a  treacherous  appearance  of  solidity,  and  from 
terrifying  a  timorous  adversniry  by  its  horned  aspect.  In  the  sifting 
of  a  proposed  dilemma,  we  ought,  therefore,  to  look  closely  at  the 
three  following  particulars:  —  1°,  "Whether  a  veritable  consequence 
subsists  between  the  antecedent  and  consequent  of  the  sumption ; 
2°,  Whether  the  opposition  in  the  consequent  is  thorough-going  and 
valid  ;  and,  3",  "Whether  in  the  subsumption  the  disjunctive  mem- 
bers are  legitimately  sublated.  For  the  example  of  a  dilemma 
which  violates  these  conditionsi,  take  the  following : 

jfjr  virtue  xoere  a  habit  worth  acquiriry,  it  must  insure  either  j^pwer,  or  wealth,  or  honor, 

or  pleasure  ; 
But  virtue  insures  none  of  these  ; 
Ther^ore,  virtue  is  not  a  habit  worth  attaining. 

"  Here :  —  1°.  The  inference  in  general  is  invalid :  for  a  thing  may 
be  worth  acquiring,  though  it  does  not  secure  any  of  those  advanta- 
ges enumerated.  2°.  The  disjunction  is  incomplete;  for  there  are 
other  goods  which  virtue  insures,  though  it  may  not  insure  those 
here  opposed.  3°.  The  subsumption  is  also  vicious  ;  for  virtue  has 
frequently  obtained  for  its  possessors  the  very  advantages  hero 
denied." » 

1  Kin^'./o(r  cit.    Anm..2.  —  Ed.    (Cf.  Keck-         <  Krug,  Logik,  J  87.     Anm    8,  p.  281  - 
ermauii,  Optra,  t.  i.  pp.  26S,  76!)  ]  Ed. 


Lect.  XVm.  LOGIC.  251 

Before  leaving  this  subject,  it  may  be  proper  to  make  two  obser- 
vations.    The  first  of  these  is,  that  though  it  has 
Tbe  whole  of  the      been  Stated  that  Categorical  Syllogisms  are  gov- 
logicai  iawB,-iden-       ^^.^^^  ,      the'laws  of  Identity  and  Contradic- 

tity,       Contradiction,  •'  *' 

Excluded  Middle,  and  tion,  that  Disjunctive  Syllogisms  are  governed 
Reason  and  Conee-  by  the  law  of  Excluded  Middle,  and  that  Hypo- 
quent.-are  operative      thetical    Syllogisms  are   governed  by  the   law 

in  each  form  of  syllo-  .    _  i     ^  ,  . 

jgjjj  01    Keason    and    Consequent,  —  this   statement 

is  not,  however,  to  be  underetood  as  if,  in  these 
several  classes  of  syllogism,  no  other  law  were  to  be  found  in 
operation  except  that  by  which  their  peculiar  form  is  determined. 
Such  a  supposition  would  be  altogether  erroneous,  for  in  all  of  tliese 
difierent  kinds  of  syllogism,  besides  the  law  by  which  each  class  is 
principally  regulated,  and  from  which  it  obtains  its  distinctive  char- 
acter, all  the  othera  contribute,  though  in  a  less  obtrusive  manner,  to 
allow  and  to  necessitate  the  process.  Thus, 
This  illustrated  though  the  laws  of  Identity  and  Contradiction 

.    n     a  egonca        ^^.^  ^y^^   laws  which  preeminently  regulate  the 

Syllogisms.  ^  ^     ^  .  . 

Categorical  Syllogism,  —  still  without  the  laws 
of  Excluded  Middle,  and  Reason  and  Consequent,  all  inference  in 
these  syllogisms  would  be  impossible.  Thus,  though  the  law  of 
Identity  affords  the  basis  of  all  affirmative,  and  the  law  of  Contra- 
diction the  basis  of  all  negative,  syllogisms,  still  it  is  the  law  of 
Excluded  Middle  which  legitimates  the  implication,  that,  besides 
affirmation  and  negation,  there  is  no  other  possible  quality  of  predi- 
cation. In  like  ma^jner,  no  inference  in  categorical  reasoning  could 
be  drawn,  were  we  to  exclude  the  determination  of  Reason  and 
Consequent.  For  we  only,  in  deductive  reasoning,  conclude  of  a 
part  what  we  assume  of  a  whole,  inasmuch  as  we  think  the  whole  as 
the  reason,  —  the  condition,  —  the  antecedent,  —  by  which  the  part, 
as  a  consequent,  is  determined ;  and  we  only,  in  inductive  reason- 
ing, conclude  of  the  whole  what  we  assume  of  all  the  parts,  inasmuch 
as  we  think  all  the  parts  as  the  reason,  —  the  condition,  — the  ante- 
cedent, —  by  which  the  whole,  as  a  consequent,  is  determined.     In 

point  of  fact,  logically  or  formally,  the  law  of 

The  law  of  Identity       Identity  and  the  law  of  Reason  and  Consequent 

formally  the  same  with       j^^  j^^  affirmative  form,  are  at  bottom  the  same; 

that  of   Reason    and  ■,  •  •  /• 

Consequent  *"®  ^^^  of  Identity  Constitutes  only  the  law  of 

Reason  and  Consequent,  —  the  two  relatives 
being  conceived  simultaneously,  that  is,  as  subject  and  predicate ; 
the  law  of  Reason  and  Consequent  constitutes  only  the  law  of 
Identity,  the  two  relatives  being  conceived  in  sequence,  that  is,  as 


252  LOGIC.  Lbct.  XVIII. 

.antecedent  and  consequent.^    And  as  the  law  of  Reason  and  Con- 
Kcquent,  in  its  positive  form,  is  only  that  of  Identity  in  movement; 
kio,  in  its  negative  form,  it  is  only  that  of  Contradiction  in  movement. 
In  Disjunctive  Syllogisms,  again,  though  the  law   of  Excluded 
Middle  be  the  principle  which  bestows  on  them 
2.  In  Disjuncuve  Syi-       ^j^^j^.        yii^r  form,  Still  these  syllogisms  are  not 
independent  of  the  laws  of  Identity,  of  Contra- 
diction, and  of  Reason   and  Consequent.      The  law  of  Excluded 
Middle  cannot  be  conceived  apart  from  the  laws  of  Identity  and 
Contradiction  ;  these  it  implies,  and,  without  the  principle  of  Reason 
and  Consequent,  no  movement  from  the  condition  to  the  condi- 
tioned, that  is,  from  the  affirmation  or  negation  of  one  contradictory 
to  the  affirmation  or  negation  of  the  other,  would  be  possible. 
Finally,  in  Hypothetical  Syllogisms,  though  the  law  of  Reason 
and  Consequent  be  the  prominent  and  distinc- 
3   In  Hypothetical       ^j^.^  principle.  Still  the  laws  of  Identity,  Contra- 

Syllogisms.  . 

diction,  and  Excluded  Middle  are  also  there  at 
work.  The  law  of  Identity  affords  the  condition  of  Affirmative  or 
Constructive,  and  the  law  of  Contradiction  of  Negative  or  Destruc- 
tive, Hypotheticals ;  while  the  law  of  Excluded  Middle  limits  the 
reasoning  to  these  two  modes  alone. 

The  second  observation  I  have  to  make,  is  one  suggested  by  a 

difficulty  which   has  been  proposed   to  me  in 

Difficulty  in  regard       ^^  ^^j   ^^   ^j^^   doctiine,  that   all   reasoning   is 

to  the  doctrine,   that  .  /. 

all  reasoning  is  either  either  from  whole  to  part,  or  from  the  parts  to 
from  whole  to  part  or  the  wholc.  The  difficulty,  which  oould  only 
from  the  parts  to  the       j^j^^e  presented  itself  to  an  acute  and  observant 

whole,  —  obviated.  .        ,,  .  i  •   /•       •  i 

intellect,  it  gave  mo  much  satisfaction  to  hear 
proposed ;  and  I  shall  have  still  greater  gratification,  if  I  should 
be  able  to  remove  it,  by  showing  in  what  sense  the  doctrine 
advanced  is  to  be  understood.  It  was  to  this  effect: — In  Cate- 
gorical Syllogisms,  deductive  and  inductive,  intensive  and  exten- 
sive, the  reasoning  is  manifestly  from  whole  to  part,  or  from  the 
parts  to  the  whole,  and,  therefore,  in  regard  to  the  doctrine  in 
question,  as  relative  to  categorical  reasoning,  there  was  no  difficulty. 
But  this  was  not  the  case  in  regard  to  Hypothetical  Syllogisms. 
These  are  governed  by  the  law  of  Reason  and  Consequent,  and  it 
docs  not  appear  how  the  antecedent  and  consequent  stand  to  each 
other  in  the  relation  of  whole  and  pafrt. 

In  showing  how  the  reason  and  the  conseqaent  are  to  be  viewed 
as  whole  and  pait,  it  is  necessary,  first,  to  repeat,  that  the  reason 

I  [Compare  Kappen,  Daruettung  de$  Watn*  dtr  PhilosopU*,  p.  102  «  J(f .,  NUmberg,  1810.| 


Lect.  XVIlt  LOGIC.  25^ 

or  antecedent  means  tlie  condition^  that  is,  the  complement  of  all, 

without  which  something  else  would   not  be; 

This  difficulty  con-       a^f]  \\^q  consequent  means  the  conditioned,  that 

.idered  with  respect       j     ^,^^  complement  of  all  that  is  determined  to 

to  Hypothetical  8jllo-         ,        ,        ^,  -^  r  ^,  •  ,  v 

jj,jpg  be  by  the  existence  of   something  else.      You 

Antecedent  and  Con-       must  further  bear  in  mind,  that  we  have  nothing 

81-quent  are  equal  to       ^^  ^(j  ^.j^}^  things  Standing  in  the  relation  of 

Condition  and  Condi-  ,  ^      ,    •  ^  i 

jj^j^g^  reason  and  consequent,  except  in  so  lar  as  they 

are  thought  to  stand  in  that  relation ;  it  is  with 
the  ratio  co^noscendi,  not  Avith  the  ratio  essendi,  that  we  have  to 
do  in  Logic ;  the  former  is,  in  fact,  alone  properly  denominated 
reason  and  consequent,  while  the  latter  ought  to  be  distinguished 
as  cause  and  effect.  The  ratio  essendi,  or  the  law  of  Cause  and 
Effect,  can  indeed  only  be  thought  under  the  form  of  the  ratio  cog- 
noscendi,  or  of  the  principle  of  Reason  and  Consequent ;  but  as  the 
two  are  not  convertible,  inasmuch  as  the  one  is  far  more  extensive 
than  the  other,  it  is  proper  to  distinguish  them,  and,  therefore,  it  is 
to  be  recollected,  that  Logic  is  alone  convereant  with  the  ratio  cog- 
noscendi,  or  the  law  of  Reason  and  Consequent,  as  alone  conversant 
with  the  form  of  thought. 

This  being  underetood,  if  the  reason  be  conceived  as  that  which 

conditions,  in  other  words,  as  that  which  con- 

Hence  the  reason  or      ^.^j^g  ^^^  necessity  of  the  existence  of  the  con- 

condition    must   con-  .      .  .  .  ...  .        , 

tain  the  consequent.  Sequent;   It  IS  evident  that  it   is  conceived  as 

containing  the  consequent.  For,  in  the  first 
place,  a  reaaon  is  only  a  reason  if  it  be  a  sufficient  reason,  that  is,  if 
it  comprise  all  the  conditions,  that  is,  all  that  necessitates  the  exist- 
ence, of  the  consequent;  for  if  all  the  conditions  of  anything  arc 
present,  that  thing  must  necessarily  exist,  since,  if  it  do  not  exist, 
then  some  condition  of  its  existence  must  have  been  wanting,  that 
is,  there  was  not  a  sufficient  reason  of  its  existence,  which  is  con- 
trary to  the  supposition.  In  the  second  place,  if  the  reason,  the 
sufficient  reason,  be  conceived  as  comprising  all  the  conditions  of 
the  existence  of  the  consequent,  it  must  be  conceived  as  comprising 
the  consequent  together;  for  if  the  consequent  be  supposed  to  con- 
tain in  it  any  one  part  not  conceived  as  contained  in  the  reason,  it 
may  contain  two,  three,  or  any  number  of  parts  equally  uncontained 
in  the  reaaon,  consequently  it  may  be  conceived  as  altogether  un- 
contained in  the  reason.  But  this  is  to  suppose  that  it  has  no 
reason,  or  that  it  is  not  a  consequent;  which  again  is  contrary  to 
the  hypothesis.  The  law  of  Reason  and  Consequent,  or  of  the 
Condition  and  the  Conditioned,  is  only  in  fact  another  expression 
of  Aristotle's  law,  that  the  whole  is  necessaiily  conceived  aa  prior 


254 


LOGIC. 


Lect.  XVIIl 


The  Law  of  Reason 
and  Consequent  only 
another  expression  of 
Aristotle's  law.  that 
the  whole  is  necessa- 
rily conceived  as  prior 
to  the  part. 

Aristotle's  law  criti- 
cized. 


Whole  and  Parts  re- 
»pectively  may  be 
viewed  in  thought 
either  as  the  condi- 
tioning or  as  the  con- 
ditioned. 


to  the  part,  totum  parte  prius  esse,  necesse  est}  It  is,  however, 
more  accurate ;  for  Aristotle's  law  is  either 
inaccurate  or  ambiguous.  Inaccurate,  for  it  is 
no  more  true  to  say  that  the  whole  is  necessarily 
piior  in  the  order  of  thought  to  the  parts,  than 
to  say  that  the  parts  are  necessarily  prior  in  the 
order  of  thought  to  the  whole.  Whole  and 
parts  are  relatives,  and  as  such  are  necessarily 
coexistent  ir.  thought.  But  while  eaclf  implies 
the  other,  and  the  notion  of  each  necessitates 
the  notion  of  the  other,  we  may,  it  is  evident,  view  either,  in 
thought,  as  the  conditioning  or  antecedent,  or  as 
the  conditioned  or  consequent.  Thus,  on  the  one 
hand,  we  may  regard  the  whole  as  the  prior  and 
determining  notion,  as  containing  the  parts,  and 
the  parts  as  the  posterior  and  determined  notion, 
as  contained  by  the  whole.  On  the  other  hand, 
we  may  regard  the  parts  as  the  prior  and  determining  notion,  as  con- 
stituting the  whole,  and  the  whole  as  the  posterior  and  determined 
notion,  as  constituted  by  the  parts.*  In  the  former  case,  the  whole  is 
thought  as  the  reason,  the  parts  are  thought  as  the  consequent;  in 
the  latter,  the  parts  are  thought  as  the  reason,  the  whole  is  thought  as 
the  consequent.  Now,  in  so  far  as  the  whole  is  thought  as  the  rea- 
son, there  will  be  no  difficulty  in  admitting  that  the  reason  is  con- 
ceived as  containing  the  parts.  But  it  may  be  asked,  how  can  the 
parts,  when  thought  as  the  reason,  be  said  to  contain  the  whole? 
To  this  the  answer  is  easy.  All  the  parts  contain  the  whole,  just  as 
iViuch  as  the  whole  contains  all  the  parts.  Objectively  considered, 
the  whole  docs  not  contain  all  tlie  parts,  nor  do  all  the  parts  con- 
tain the  whole,  for  the  whole  and  all  the  parts  are  precisely  equiva- 
lent, absolutely  identical.  But,  subjectively  considered,  that  is, 
as  mere  thoughts,  we  rnay  either  think  the  whole  by  all  the  parts, 
or  think  all  the  parts  by  the  whole.  If  we  think  all  the  parts  by 
the  whole,  we  subordinate  the  notion  of  the  parts  to  the  notion  of 


1  Mftaphyfics,  iv.  11.  Aristotle,  however, 
allows  a  double  relation.  The  whole,  when 
conceived  as  actually  constituted,  must  be 
regarded  as  prior  to  the  parts;  for  the  latter 
only  exist  as  parts  in  relation  to  the  whole. 
Potentially,  however,  the  parts  may  be  re- 
garded as  prior;  for  the  whole  might  be 
destroyed  as  a  system  without  the  destruction 
of  the  parts.  Where  the  whole  is  not  con- 
ceived as  actually  constituted,  this  relation  is 
reversed.    Thus  Ariittotle'B  rule  may  be  re- 


garded as  coextensive  with  that  given  in  the 
text.    See  the  next  note.  —  Ed. 

2  This  is  substantially  expressed  by  Aris- 
totle, I.  c,  whose  distinction  is  applicable 
either  to  the  order  of  thought  or  to  that  of 
existence,  tcarii  yiy*<riy  (i.  «.,  regarded  as  a 
complete  system),  the  whole  is  actually,  the 
parts  arc  only  potentially,  existent ;  while,  on 
the  other  hand,  iforol  (ft^opdy  (i.  c,  regarded 
as  disorganized  elements),  the  parts  exist  ac- 
tually, the  whole  only  potentially.  —  Kd. 


Lect.  xviii.  logic.  255 

the  whole ;  that  is,  we  conceive  the  parts  to  exist,  as  we  conceive 
their  existence  given  through  the  existence  of  the  whole  containing 
them.  If  we  think  the  whole  by  all  the  parts,  we  subordinate  the 
notion  of  the  whole  to  the  notion  of  the  parts ;  that  is,  we  conceive 
the  whole  to  exist,  as  we  conceive  its  existence  given  through  the 
existence  of  the  parts  which  constitute  it.  Now,  in  the  one  case, 
we  think  the  whole  as  conditioning  or  comprising  the  parts,  in  the 
other,  the  parts  as  conditioning  or  comprising  the  whole.  In  the 
former  case,  the  parts  are  thought  to  exist,  because  their  whole 
exists ;  in  the  latter,  the  whole  is  thought  to  exist,  because  it§  parts 
exist.  In  either  case,  the  prior  or  determining  notion  is  thought  to 
comprise  or  to  contain  the  posterior  or  deter- 
Appiication  of  this       mined.     To  apply  this  doctrine:    On  the  one 

doctrine  to  the  solu-         ,         j  •  .      ,  ,  11    .^ 

r  *..    j«i    1*        hand,  every  science  is  true  only  as  all  its  sev- 

lion  of  the  difficulty  ^  J  ... 

previously  stated.  eral  rules  are  true ;  in  this  instance  the  science 

is  conceived  as  the  determined  notion,  that  is, 
as  contained  in  the  aggregate  of  its  constituent  rules.  On  the 
other  hand,  each  rule  of  any  science  is  true  only  as  the  science 
itself  is  true  ;  in  this  instance  the  rule  is  conceived  as  the  deter- 
mined notion,  that  is,  as  contained  in  the  whole  science.  Thus, 
every  single  syllogism  obtains  its  logical  legitimacy,  because  it  is  a 
consequent  of  the  doctrine  of  syllogism ;  the  latter  is,  therefore, 
the  reason  of  each  several  syllogism,  and  the  whole  science  of 
Logic  is  abolished,  if  each  several  syllogism,  conformed  to  this  doc- 
trine, be  not  valid.  On  the  other  hand,  the  science  of  Logic,  as  a 
whole,  is  only  necessary  inasmuch  as  its  complementary  doctrines 
are  necessary ;  and  these  are  only  necessary  inasmuch  as  their  indi- 
vidual applications  are  necessary;  if  Logic,  therefore,  as  a  whole,  be 
not  necessary,  the  necessity  of  the  parts,  which  constitute,  deter- 
mine, and  comprehend  that  whole,  is  subverted.  In  one  relation, 
therefore,  reason  and  consequent  are  as  the  whole  and  a  contained 
part,  in  another,  as  all  the  parts  and  the  constituted  or  comprised 
whole.  But  in  both  relations,  the  reason  —  the  determining  notion 
—  is  thought,  as  involving  in  it  the  existence  of  the  consequent  or 
determined  notion.  Thus,  in  one  point  of  view,  the  genus  is  the 
determining  notion,  or  reason,  out  of  which  are  evolved,  as  conse- 
quents, the  species  and  individual;  in  another,  the  individual  is  the 
determining  notion  or  reason,  out  of  which,  as  consequents,  are 
evolved  the  species  and  genus.^  In  like  manner,  if  we  regard  the 
subject  as  that  in  which  the  attributes  inhere,  —  in  this  view  the 
subjept  is  the  reason,  that  is,  the  whole,  of  which  the  attributes  are 

1  This  is  expressly  allowed    by  Aristotle,     W.  Hamilton  liimself,  Discussions,  p.  178.  — 
Metnph  ,  iv.  25,  and  is  quoted  from  I'.im  by  Sir     Ed. 


256 


LOGIC. 


Lbct.  xvm 


a  part ;  whereas  if  we  regard  the  attributes  as  the  modes  through 
which  alone  the  subject  can  exist,  in  this  view  the  attributes  are 
the  reason,  that  is,  the  whole,  of  which  the  subject  is  a  part.  In  a 
woi"d,  whatever  we  think  as  conditioned,  we  think  as  contained  by 
something  else,  that  is,  either  as  a  part.,  or  as  a  constituted  whole ; 
whatever  we  think  as  conditioning,  we  think  either  as  a  containing 
whole,  or  as  a  sum  of  constituting  parts.  What,  therefore,  the 
sumption  of  an  hypothetical  syllogism  denotes,  is  simply  this :  If  A, 
a  notion  conceived  as  conditioning,  and,  therefore,  as  involving  B, 
exist,  then  B  also  is  necessarily  conceived  to  exist,  inasmuch  as  it  is 
conceived  as  fully  conditioned  by,  or  as  involved  in,  A,  I  am  afraid 
that  what  I  have  now  said  may  not  be  found  to  have  removed  the 
difficulty,  but  if  it  suggest  to  you  a  train  of  reflection  which  may  lead 
you  to  a  solution  of  the  difficulty  by  your  own  eflfort,  it  will  have 
done  better. 

So  much  for  Hypothetico-disjunctive  syllogisms,  the  last  of  the 
four  classes  determined  by  the  internal  form  of  reasoning.  In  these 
four  syllogisms,  —  the  Categorical,  the  Disjunctive,  the  Hypothet- 
ical, and  the  Hypothetico-disjunctive,  —  all  that  they  exhibit  is  con- 
formable to  the  necessary  laws  of  thought,  and  they  are  each  dis- 
tinguished from  the  other  by  their  essential  nature ;  for  their 
sumptions,  as  judgments,  present  characters  fundamentally  differ- 
ent, and  from  the  sumption,  as  a  general  rule,  the  validity  of  syllo- 
gisms primarily  and  principally  depends. 


LECTURE      XIX. 

STOIOHEIOLOGY. 

SECTION   II.— OF  THE    PRODUCTS  OF  THOUGHT 

III.  — DOCTRINE  OF  REASONINGS. 

SYLLOGISMS.  — THEIR  DIVISIONS  ACCORDING  TO  EXTERNAL 

FORM. 

A.  COMPLEX,  — EPICHEIREMA  AND  SORITES. 

In*  our  treatment  of  Syllogisms,  we  have  hitherto  taken  note  only 
of  the  Internal,  or  Essential  Form  of  Reason- 
syiiogisms,  -  their      ■         g^^  besides  this  internal  or  essential  form, 

External  Form.  &  '  ,  .       . , 

there    is    another,   an    External   or  Accidental 

Form ;  and  as  the  former  was  contained  in  the  reciprocal  relations 
of  the  constituent  parts  of  the  syllogism,  as  determined  by  the 
nature  of  the  thinking  subject  itself,  so  the  latter  is  contained  in  the 
outer  expression  or  enouncement  of  the  same  parts,  whereby  the 
terms  and  propositions  are  variously  affected  in  respect  of  their - 
number,  position,  and  order  of  consecution.  The  varieties  of  Syl- 
logism arising  from  their  external  form  may,  I  think,  be  con- 
veniently reduced  to  the  three  heads  expressed  in  the  following: 
paragraph : 

if  LXVm.   Syllogisms,  in  respect  of  their  External  Form, 
admit   of   a  threefold   modification.      For 

Par.   IiXVm.    Divi-  i.-i  ,■.  .  o-         7 

8ioa  of  Syllogisms  ac-       ^^^^6,  as   purc,  they  are   at  once  Simple, 
cording  to  External       and  Complete,   and  Regular,   so,  as   quali- 
°''"'  fied,  they   are   either  Com,plex,  or  Income- 

plete,  or  Irregular;  the  two  former  of  these  modifications 
regarding  the  number  of  their  parts,  as  apparently  either  too 
many  or  too  few ;  the  last  regarding  the  inverted  order  in 
which  these  parts  are  enounced. 

S8 


258  LOGIC.  Lect.  XIX 

I  shall  consider  these  several  divisions  in  their 

ExpUcaUon.  order ;  and,  first,  of  the  syllogisms  which  vary 

A.  Complex  SyUo-        ^  \  .        ,       „  /  •  ,  ,     . 

giga^  fi'om  the   simple   form   of   reasoning  by  their 

apparent  complexity. 

But,  before  touching  on   the  varieties  of  syllogism  afforded  by 

their   apparent   complexity   of   composition,   it 

ation  o      y  o-      ^jjjjy  be  proper  to  premise  a  few  words  in  re- 
giams  to  each  other.  *'  '       "^         _     • 

gard  to  the  Illation  of  syllogisms  to  each  other. 

"Every  syllogism  may  be  considered  as  absolute  and  independent, 

inasmuch  as  it  always  contains  a  complete  and  inclusive  series  of 

thought.     But  a  syllogism  may  also  stand  to  other  syllogisms  in 

sach  a  relation   that,  along  with  these  correlative  syllogi^ii>  it 

makes  up  a  greater  or  lesser  series  of  thoughts,  all  holding  to  each 

other  the  dependence  of  antecedent  and  conseqnent.    And  such  a 

reciprocal  dependence  of  syllogisms  becomes  necessary,  when  one 

or  other  oi  the  predicates  of  the  principal  syllogism  is  destit«te  of 

complete  certainty,  and  when  this  certainty  must  be  established 

through  one  or  more  correlative  syllogisms."^   "A  syllo^sm,  viewed 

as  tin  isolated  and  independent  whole,  is  called 

Classes  and  desig-       a  MonosyUogtsm  {monosyllogismus),  that  is,  a 

DaUons  of  related  syi-      gj^jrle  i^asoning ;  whcfeas,  a  series  of  coTrelati\  e 

logisms.      Houo8yIIo-      -         '^  ^ 

gteth.  syllogisms,  following  each  other  in  the  recipro- 

„  ,     „  cal  relat^fi  of  antecfedeat  and   conseqtient,  is 

Poljrsyllogistn,    or  ^ 

Chain  of  Reasoning.         Called    ^  PolysyUogism  {polysyllogismus),  thzX. 

is,  a  multiplex  or  coinposite  reasoning,  and  may 
likewise  be  denominated  a  Chain  of  Reasoning  (series  syUogistica). 
Such  a  chain  —such  a  series  —  may,  however,  have  such  an  order  of 
tde^endence,  that  cither  each  successive  syllogism  is  the  reason  of 
iJiat  which  preceded,  of  the  preceding  syllogism  is  the  reason  of 

that  which  follows.  Iti  the  former  case,  we  con- 
ABaiyUo  Mid      ^lude  analytically  or  regressively ;  in  the  second, 

synthetically  or  progressively.  That  syllogism 
in  the  series  which  contains  the  reasoning  of  the  premise  of  another, 

is  called  a  Prosyllogisnt  (prosyllogismus) ;  and 
Prosyiiogism.  .jj^j^^  gyUogism  which  coTitatns  the  cotisequent  of 
Episyiiogism.  another,  is  called  an  Episyllogis7n  {episyUogiS' 

mils).  Eheiy  Oiain  of  Reasoning  must,  there-? 
fore,  be  made  np  both  of  Prosyllogisms  and  of  Episyllogisms."' 
'*When  the  series  is  composed  of  more  than  two  syllogisms,  the 
58ame  syllogism  may,  in  different  relations,  be  at  once  a  prosyllogism 
and  an  episyiiogism;  and  that  reasoning  which  contains  the  primary 

I  EMer.  Loftfc,  }104.  — £d.  t£  rag  I^vtlh  fill.  — Bd. 


I 


J^ifiCT.  XIX.  L 0<S  I C .  ^9 

or  highest  reason  'is  alone  exclusively  a  prosyllogism,  as  that  reason- 
ing which  enounces  the  last  or  low<?st  consequent  is  alone  exclu- 
sively an  episyllogism.  But  this  concatenation  of  syllogisms,  as 
antecedents  and  consequents,  may  be  either  manifest,  or  occult, 
according  as  the  plurality  of  syllogisms  may  either  be  openly  dis- 
played, or  as  it  may  appear  only  as  a  single  syllogism.  The  poly- 
syllogism  is,  therefore,  likewise  either  manifest  or  occult.  The 
occult  polysyllogism,  with  which  alone  we  are  at  present  con- 
cerned, consists  either  of  partly  complete  and  partly  abbreviated 
syllogisms,  or  of  syllogisms  all  equally  abbreviated.  In  the  former 
case,  there  emerges  the  complex  syllogism  called  Epicheirema;  in 
the  latter,  the  complex  syllogism  <;aUed  Soritt&r^  Of  these  in 
tlueir  order. 

T  LXIX.    A  syllogism  is  now  vulgarly  called  an  Epichei- 
rema  (iinx^Lprjfia),  when  to  either  of  the  two 

Par.    liXIX.      The  .  ^        i      ^i       .i_  •  j 

jEpiebeixema.  premises,  or  to  botfl,  thens  IS  annexed  a 

reason  for  its  support.    As : 

B  is  A; 

But  C  is  B;  for  it  is  J); 
Thertfore,  C  is  also  A.2 

Or, 

All  vice  is  odious  ; 

But  avarice  is  a  vice ;  for  it  makes  men  slaves; 

Thertfore,  avarice  is  odious.^ 

In  illustration  of  this  paragraph,  it  is  to  be  observed  that  the 
Epicheirema,  or  Reason-rendering  Syllogism, 
is  either  single  or  double,  according  as  one 
or  both  of  the  premises  are  furnished  with  an  auxiliaiy  reason. 
The  single  epicheii-ema  is  either  an  epicheirema  of  the  first  or  sec- 
ond order,  according  as  the  adscititious  proposition  belongs  to  the 
sumption  or  to  the  subsumption.  There  is  little  or  nothing  requi- 
•fiite  to  be  stated  in  regard  to  this  A'ai-iety  of  complex  syllogism,  as 
it  is  manifestly  nothing  more  than  a  regular  episyllogism  with  an 
abbreviated  prosyllogism  interwoven.    There  might  be  something 

lEsser,  Logik,  §  104.  — Ed.    [Cf.  Reusch,         3  In  full,— 
Sj/stema  Logicum,  §  578,  p.  664,  lenae,  1741.1  nr.  .      t  j       j     ^^ 

'  p  .   J.,  Bia  avarice  makes  men  slaves; 

_  .   _'  Therefore,  avarice  is  a  vice. 

D  u  B;    .  ^      ^ 

Thaxfore,  C  «  B.  v 


260 


LOGIC. 


Lect.  XLX. 


said  touching  the  name,  which,  among  the  ancient  rhetoricians,  was 
used  now  in  a  stricter,  now  in  a  looser,  signification.^  This,  how- 
ever, as  it  has  little  interest  in  a  logical  point  of  view,  I  shall  not 
trouble  you  by  detailing ;  and  now  proceed  to  a  far  more  important 
and  interesting  subject,  —  the  second  variety  of  complex  syllo- 
^sms, —  the  Sorites. 


Par.  XiXX.   Tbe  80. 
rites. 


^  LXX.  When,  on  the  common  principle  of  all  reasoning, 
—  that  the  part  of  a  part  is  a  part  of  the 
whole,  —  we  do  not  stop  at  the  second 
gradation,  or  at  the  part  of  the  highest 
part,  and  conclude  that  part  of  the  whole,  —  as  All  B  is  a  part 
of  the  whole  A,  and  aU  C  is  a  part  of  the  part  B,  therefore  cUl  C 
is  also  a  part  of  the  whole  A, —  but  proceed  to  some  indefinitely 
remoter  part,  as  D,  E,  F,  G,  H,  etc.,  which,  on  the  general  prin- 
ciple, we  connect  in  the  conclusion  with  its  remotest  whole, — 
this  complex  reasoning  is  called  a  Chain- Syllogism  or  Sorites. 
If  the  whole  from  which  we  descend  be  a  comprehensive  quan- 
tity, the  Sorites  is  one  of  Comprehension ;  if  it  be  an  extensive 
quantity,  the  Sorites  is  one  of  Extension.  The  formula  of  the 
first  will  be : 


1)  E  u  D;  that  is,  E  comprehends  D; 

2)  D  it  C;  that  is,  D  comprehends  C; 

3)  C  14  6;  that  is,  C  comprehends  B; 

4)  B  15  A ;  that  is,  B  comprehends  A ; 
Thertfore,  E  is  A;  in  other  words,  £  comprehends  A. 

The  formula  of  the  second  will  be : 

1 )  B  is  A ;  that  is,  A  contains  under  U  B ; 

2)  C  is  B;  that  is,  B  contains  under  it  C; 

3)  D  is  C ;  that  is,  C  contains  under  it  D; 

4)  E  is  D;  that  is,  D  contains  under  it  E; 
Therrfore,  E  i«  A ;  in  other  words,  A  contains  under  it  E. 

These  reasonings  are  both  Progressive,  each  in  its  several  quan- 
tity, as  descending  from  whole  to  part.  But  as  we  may  also,  argu- 
ing back  from  part  to  whole,  obtain  the  same  conclusion,  there  is 
also  competent  in  either  quantity  a  Regressive  Sorites.     However, 


I  For  some  notices  of  these  variations,  see  i  83;  Facciolati,  Aeroasrt,  De  Spiekirtmatt,  p. 

Qiilntilian,  Imt.  Oral  ,  v.  \0,  2,  \ .14,5.    Com-  127  etsftf.    In  Aristotle  the  term  is  uxetl  for  a 

pare  also  Scliweigh«;user  on  Epictctus,  i.  8;  dialectic  syllogism.     See  7Vp*c«,  Till.  11.— 

Trcndeienburg,  SUmenta  Logicu  AriMottUea,  £d. 


Lkct.  XIX. 


LOGIC. 


26t 


the  formula  of  the  Regressive  Sorites  in  the  one  quantity,  will  be 
only  that  of  the  Progressive  Sorites  in  the  other.^ 


Explication. 


As  a  concrete  example  of  these : 


I.  Progsessive  Comprehensive  Sorites. 


Concrete  examples 
ot  Sorites. 


Or  as  explicated; 


Bucephalus  is  a  horse  ; 
A  horse  is  a  quadruped ; 
A  quadruped  is  an  animal ; 
An  animal  is  a  substance ; 
Therefore,  Bucephalus  is  a  substance. 


The  representation  of  the  individual  Btuxphaius  comprehends  or  contains  in  it  tkt 

notion  horse ; 


1  [On  the  Sorites  in  general,  see  Crakan- 
tborpe,  Logica,.  L.  iii.  c.  22,  p.  219.  Valla, 
Dialect.,  L.  iii.  c.  54,  fol.  38,  ed.  1509.  M.  Dun- 
can, Instil.  Log.  L.  iv.  c.  vii.  §  6,  p.  255.  Fac- 
ciolati,  Acroases,  De  Sorite,  p.  15  et  seq.  Me- 
laiiclitlion,  Erotem.  Dial.,  L.  iii.  De  Sorite,  p. 
74.3.  Wolf,  Phil.  Rat.,  §  466,  et  seg.  Walch, 
i.  -.rilcon.  V.  "  Sorites."    Fries,  Logik,  }  64.] 

-'  Diagrams  Nos.  1  and  2  represent  the  afflr- 
rautive  Sorites  in  the  casein  which  the  con- 


cepts are  coextensive.  —  See  above,  p.  133, 
Diagram  2.  Diagrams  Nos.  3  and  4  represent 
the  Affirmative  Sorites  in  the  case  in  which 
the  concepts  are  subordinate.  —  See  above,  p- 
133,  Diagram  3.  Diagram  No.  5,  taken  in 
connection  with  No.  3,  represents  the  Negi..- 
tive  Sorites.  Thus,  to  take  the  Progressive 
Comprehensive  Sorites:  —  E  is  D,  D  is  C,  C 
M  B,  B  t«  A,  no  A  M  P;  there/ore,  »o  E  is  P.  — 
Ed. 


SK"  LOGIC.  L«CT.  XIX 

T%e  notitm  hone  comprehends  the  notion  qaadruped  ; 

The  notion  quadruped  cemprehends  the  iwtiim  amnnU  ; 

The  notion  animal  comprehends  the  notion  substance; 

Therefore  (<m  the  common  principle  that  the  pari  of  a  part  is  a  part  of  the  voheiU), 

the  r^resentation  of  the  individual,  BucepJudus,  comprehends  or  contains  im  it 

<Ae  notion  substance. 

n.  EbGbsssivs  Covpbchensive  Sobites. 

An  animal  is  a  substance  ; 

A  quadruped  is  an  animal ; 

A  horse  is  a  quadruped ; 

Bucephalus  is  a  horse ; 

Therefore,  Bucephalus  is  m  substance. 

Or  as  explicated : 

The  notion  animal  comprehends  the  notion  substance  ; 
The  notion  quadruped  comprehends  the  notion  animal; 
The  notion  horse  comprehends  the  notion  quadruped; 
The  representation,  Bucephalus,  comprehends  the  notion  horse ; 
Therefore  (on  the  common  principle,  etc.),  the  repremnUUUm,  Bucephalus,  cempn- 
hends  tie  notion  aubsta$tee. 

m.  Progressive  Extensive  Sorites  (which  is,  as  cnoanced  by  the  common 
copula,  identical  in  expression  with  the  Regressive  Comprehensive  Sorites, 

No.  n.): 

An  animal  ts  a  substance ; 

A  quadruped  is  an  animal ; 
A  horse  is  a  quadruped; 
Bucephalus  is  a  horse ; 
Thertfore,  Bucephalus  it  a  tubstaitee. 

Or  as  explicated : 

The  notion  animal  is  contained  tender  the  ruttion  substance; 
The  notion  quadruped  is  contained  under  the  notion  animal ; 
The  notion  horse  is  contained  under  the  notion  quadruped ; 
The  representation  Bucephalus  is  contained  under  the  notion  horse  ; 
Tkerrfore  {on  the  eemmon  principle,  etc.),  the  representation  BuoephcduM  ts  comlaimi 
under  the  notion  substance. 

foilY.  Tbb  Reoressivb  Exteksitb  Soritbs  (which  is,  as  expraned  by  the  an- 

bigaous  copola,  verbally  identical  with  the  Progressire  Comi»«beDsiv» 

Sorites, No.  I.): 

Bucephalus  is  a  horse; 

A  horse  is  a  <ftadrupeAf 

A  quadruped  is  an  animal ; 

An  animal  is  a  substance  ; 

Therrfore,  Bueephalut  ie  a  i 


Lkct  XIX  LOGIC.  263 

Or  as  explicated : 

The  representation  Bucephalus  is  contained  under  the  notion  horat; 

The  notion  horse  is  contained  under  tlie  notion  quadruped ; 

The  notion  quadruped  is  contained  under  the  notion  animal; 

The  notion  animal  is  contained  under  the  notion  substance; 

Therefore,  the  representation  Bucephalus  is  contained  under  the  notion  substance. 

There  is  thus  not  the  smallest  difficulty  either  in  regard  to  the 
peculiar  nature  of  the  Sorites,  or  in  regard  to 

1.  The  formal  inftr-       its  relation  to  the  simple  syllogism.     In  the  first 
ence  in  Sorites  equally         ,        j^.  -^  ^y-^^^^^^  tj^^t  the  formal  inference  in 

necessary  as  in  simple        *  o     • 

syllogism.  "^^   Sontcs   IS   equally   necessary   and   equally 

manifest  as  in  the  simple  syllogism,  for  the  prin- 
ciple—  the  part  of  a  part  is  a  part  of  the  whole  —  is  plainly  not 
less  applicable  to  the  remotest  than  to  the  most  proximate  link  in 
the  subordination  of  whole  and  part.     In  the  second  place,  it  is 
evident  that  the  Sorites  can  be  resolved  into  as 

2.  soritea  resolvable      ^         ^-^    j^  syllogisms  as   there  are   middle 

Into  simple  syllof^isms.  ,  i  i  . 

terms  between  the  subject  and  predicate  of  the 
conclusion,  that  is,  intermediate  wholes  and  parts  between  the 
greatest  whole  and  the  smallest  part,  which  the  reasoning  connects. 
Thus,  the  concrete  example  of  a  Sorites,  already  given,  is  virtually 
composed  of  three  simple  syllogisms.  It  will  be  enough  to  show 
this  in  one  of  the  quantities ;  and,  as  the  most  perspicuous,  let  us 
take  that  of  Comprehension. 

The  Progressive  Sorites  in  this  quantity  wae 
This  iUostnited.  as  follows   (and  it  is  needless,  I  presume^  to 

explicate  it) : 

Bucephalus  is  a  horse  ; 
A  horse  is  a  quadruped; 
A  quadruped  is  an  animal; 
An  animal  is  a  substance ; 
Therefore,  Bucephalus  is  a  substance. 

Here,  besides  the  major  and  minor  terms  (Bucephalus  and  sub- 
stance), we  have  three  middle  terms  —  horse,- — quadruped, —  ani- 
mal. We  shall,  consequently,  have  three  simple  syllogisms.  Thus, 
in  the  first  place,  we  obtain  from  the  middle  term  horse,  the  follow- 
ing syllogism,  concluding  quadruped  of  Bucephalus  : 

I. -^  Bucephalus  is  a  horse; 

•  But  a  hoj-se  is  a  quadruped  ; 
Therefore,  Bucephalus  is  a  quadruped. 


264  LOGIC.  Lect.  XIX. 

Having  thus  established  that  Bucephalus  is  a  quadruped^  we 
employ  quadruped  as  a  middle  term  by  which  to  connect  Bucephxi- 
lu8  with  animal.  We  therefore  make  the  conclusion  of  the  previous 
Byllogism  (No.  I.)  the  sumption  of  the  following  syllogism  (No.  II.) : 

II.  —  Buctphaltis  is  a  quadruped; 
But  a  quadruped  is  an  animal; 
Therefore,  Bucephalus  is  an  animal.    > 

Having  obtained  another  step,  we  in  like  manner  make  a?iimal, 
which  was  the  minor  term  in  the  precedmg  syllogism,  the  middle 
term  of  the  following;  and  the  conclusion  of  No.  II.  forms  the 
major  premise  of  No.  III. 

III.  —  Bucephalus  is  an  animal; 

But  an  animal  is  a  substance; 
Therefore,  Bucephalus  is  a  substattoe. 

In  this  last  syllogism,  we  reach  a  conclusion  identical  with  that 

of  the  Sorites. 

In  the  third  place,  it  is  evident  that  the  Sorites  is  equally  natural 

as  the  simple  syllogism ;  and,  as  the  relation  is 

8.   Sorites  equally       equally  cogcnt  and  equally  manifest  between  a 

natural  as  simple  syl-  i     t  -•  1111 

,    j^jj^  whole  and  a  remote,  and  a  whole  and  a  proxi- 

mate, part,  that  it  is*  far  less  prolix,  and,  conse- 
quently, far  more  convenient.  What  is  omitted  in  a  Sorites  is  only 
the  idle  repetition  of  the  same  self-evident  principle,  and  as  this  can 
tvithoat  danger  or  inconvenience  be  adjourned  until  the  end  of  a 
series  of  notions  in  the  dependence  of  mutual  subordination,  it  is 
plain  that,  in  reference  to  such  a  series,  a  single  Sorites  is  as  much 
preferable  to  a  number  of  simple  syllogisms,  as  a  comprehensive 
cipher  is  preferable  to  the  articulate  enumeration  of  the  units  which 
it  collectively  represents. 

Before  proceeding  to  touch  on  the  logical  history  of  this  form  of 
syllogism,  and  to  comment  on  the  doctrine  in  regard  to  it  main- 
tained by  all  logicians,  I  shall  conclude  what  it  is  proper  further  to 
state  concerning  its  general  character. 

IF  LXXI.  A  Sorites  may  be  either  Categorical  or  Hypothet- 
ical ;  and,  in  both  forms,  it  is  governed  by 
Par.  LXXI.  Sorites.       i\^q  following  laws :  —  Speaking  of  the  Com- 

—  Cater  or  ioal  and  Hy-  _-.  .  o       •.         /•  ■»  •    1 

pothetio*!.  "^on  or  Progressive  Sorites  (in  which  rea- 

soning you   will   observe   the  meaning  of 
tihe  word  progressive  is  reversed),  which  proceeds  from  the 


Lkot.  XIX.  LOGIC.  265 

individual  to  the  general,  and  to  which  the  other  form  may  be 
easily  reduced  :  —  1".  The  number  of  the  premises  is  unlimited. 
2°.  All  the  premises,  with  exception  of  the  last,  must  be  affir- 
mative, and,  with  exception  of  the  first,  definite.  3°.  The  first 
premise  may  be  either  definite  or  indefinite.  4*.  The  last  may 
be  either  negative  or  affirmative. 

Explication.  ^  havc  already  given  you  examples  of  the  cat- 

Kormuia  of  Hypo-       egorical  Soritcs.     The  following  is  the  formula 
theticai  Sorites.  ^f  tj^e  hypothetical ; 


Progressive. 

IfI>is,Cis; 
If  C  it,  B  is  ; 
If  B  IS,  A  is ; 
(In  modo  ponente), 
Now  D  IS  ; 
Therefore,  A  is  also. 
(Or  In  modo  tollente), 
Now  A  is  not ; 
Therefore,  D  is  not. 

Or,  to  take  a  concrete  example 


Regressive. 

If  Bis,  his; 
If  C  is,  Bis; 
If  D  IS,  C  is ; 
(In  modo  ponente). 
Now  D  is ; 
Therefore,  A  is. 
(Or  in  modo  toUcnte), 
Now  A  is  not ; 
Therefore,  D  is  not. 


Progressive. 

If  Harpagon  be  ainiricious,  he  is  intent  on  gam  ; 
If  intent  on  gain,  he  is  discontented; 
If  discontented,  he  is  unhappy ; 
Noio  Harpagon  is  avaricious  ; 
He  is,  therefore,  unhappy. 

Regressive. 

If  Harpagon  he  discontented,  he  is  unhappy; 
If  intent  on  gain,  he  is  discontented ; 
If  avaricious,  he  is  intent  on  gain  ; 
Now  Harpagon  is  avaricious ; 
Therefore,  he  is  unhappy. 

In  regard  to  the  resolution  of  the  Hypothetical  Sorites  into  simple 
Resolution  of  Hypo-      sy^ogisms,  it  is  evident  that  in  this  Progressive 
theticai   Sorites  into       Sorites  we  must  take  the  two  first  ])ropositions 
simple  syllogisms.  as  premises,  and  then  in  the  conclusion  connect 

I.  Progressive  Sorites.       ^j^^  antecedent  of  the  former  proposition  with 
the  consequent  of  the  latter.     Thus: 

34 


266  LOGIC.  Lrct.  XIX. 

I.  —  If  Harpagon  he  avaricious,  be  is  inteal  on  gain. 
If  intent  on  gain,  he  is  discontented  ,- 
Therefore,  if  Harpagon  be  avaricious^  he  is  discontented. 

We  now  establish  this  conclusion,  as  the  sumption  of  the 
following  syllogism : 

n.  —  If  Harpagon  be  avaricious^  he  is  discontented  ;  "> 
If  discontented,  he  is  unhappy  ; 
Therefore,  if  Harpagon  be  avaricious,  he  is  utAappjf. 

In  like  manner  we  go  to  the  next  syllogism : 

m.  —  If  Harpagon  lye  avaricious,,  he  is  unhappy ; 
Now  Harpagon  is  avaricious; 
Therefore,  he  is  unhappy. 

In  the  Regressive  Sorites,  we  proceed  in  the  same  fashion  ;  only 
that,  as  here  the  consequent  of  the  second  prop- 
^  osition  is  the  antecedent  of  the  first,  we  reverse 

the  consecution  of  these  premises.    Thus : 

I.  —  If  Harpagon  be  intent  on  gain,  he  is  discontented ; 
If  discontented,  he  is  unhaj^p ; 
Therefore,  if  Harpagon  be  intent  on  gain,  he  is  unhappy. 

We  then  take  the  third  proposition  for  the  sumption  of  the  next, 
—  the  second  syllogism,  and  the  conclusion  of  the  preceding  for  its 
subsumption : 

11.  —  ff  Harpagon  be  avaricious,  he  is  intent  on  gain  ; 
If  intent  on  gain,  he  is  unhappy; 
Therrfore,  if  Harpagon  be  avaricious,  he  is  unhappy. 

We  now  take  this  last  conclusion  for  the  sumption  of  the  last 
syllogism : 

III.  —  If  Harpagon  be  avaricious,  he  is  unAoppy; 
Now  Harpagon  is  avaricioue  ,* 
Therefore,  he  is  unhappy. 

But  it  may  be  asked,  can  there  be  no  Disjunctive  Sorites  ?    To 
this  it  may  be  answci-ed,  that  in  the  sense  in 

Disjunotlre  Sorites.  ,.    ,  "'  .      ,  '  ,       •      ,         ,,       . 

which  a  categorical  and  hypotJioticnl  syllogism 
is  possible,  —  viz.,  so  thut  n  term  of  the  prec<j|ding  iirojiosition 
biiuukl  bo  ihe  subject  or  j)iedicato  of  the  following,  —  in  this  sense, 


Lect.  XIX.  LOGIC.  267 

a  disjunctive  sorites  is  impossible :  since  two  opposing  notions, 
whether  as  contraries  or  contradictoiies,  exchide  each  other,  and 
cannot,  therefore,  be  combined  as  subject  and  predicate.  But 
when  the  object  has  been  determined  by  two  opposite  characters, 
the  disjunct  members  may  be  amplified  at  pleasure,  and  there  fol- 
lows certainly  a  correct  conclusion,  provided  that  the  disjunction 
be  logicaUy  accurate.    As : 


A.  is  either  B  or  C. 
Now, 


"B  is  either  D  or  E; 
D  is  either  H  or  I; 
E  is  either  K  or  L. 


C  is  either  ¥  or  G; 
F  t»  either  M  or  N; 
G  is  either  O  or  P. 


Thenefore,  A  is  either  H,  or  I,  or  K,  or  h,  or  M,  or  N,  or  0,  or  P. 

Although,  therefore,  it  be  true  that  such  a  Sorites  is  correct ; 
still,  were  we  astricted  to  such  a  mode  of  reason- 
omp  ex  j^^^  thought  would  be  so  difficult,  as  to  be  almost 

impossible.  But  we  never  are  obliged  to  employ 
such  a  reasoning;  for  when  we  are  once  assured  that  A  is  either  B 
or  C, —  and  assured  we  are  of  this  by  one  of  the  fundamental  laws  of 
thought,  —  we  have  next  to  consider  whether  A  is  B  or  C,  and  if  A  is 
B,  then  all  that  can  be  said  of  C,  and  if  A  is  C,  then  all  that  can  be 
said  of  B,  is  dismissed  as  wholly  irrelevant.  In  like  manner,  in  the 
case  of  B,  it  must  be  determined  whether  it  is  D  or  E,  and  in  the 
case  of  C,  whether  it  is  F  or  G ;  and  this  being  determined,  one  of 
the  two  members  is  necessarily  thrown  out  of  account.  And  this 
compendious  method  we  follow  in  the  process  of  thought  spon- 
taneously, and  as  if  by  a  natural  impulsion. 

So  much  for  the  logical  character  of  the  Sorites.  It  now  remains  to 
make  some  observations,  partly  historical,  partly  critical,  in  connec- 
tion with  this  subject. 

In  regard  to  the  history  of  the  logical  doctrine  of  this  form  of 

reasoning,  it  seems  taken  for  granted,  in  all  the 

Historical  notice  of      systems  of  the  Science,  that  both  the  name  Sorites^ 

the  logical  doctrine  of  t    j  .  i     •  ^^      •  j  .1  i      • 

as  apphed  to  a  cham-syllogism,  and  the  analysis 

of  the  nature  of  that  syllogism,  are  part  and  par- 
cel of  the  logical  inheritance  bequeathed  to  us  by  Aristotle.    Noth- 
ing can,  however,  be  more  erroneous.    The  name 
Neither  name  nor       Sorites  docs  not  occur  in  any  logical  treatise  of 
jgjQtjg  Aristotle ;  nor,  as  far  as  I  have  been  able  to  dis- 

cover, is  there,  except  in  one  vague  and  cursory 
allusion,  any  reference  to  what  the  name  is  now  employed  to  ex' 


268  LOGIC.  Lect.  XIX 

press.  ^     Nay,  further,  the  word  Sorites  is  never,  I  make  bold  to  say, 
applied  by  any  ancient  writer  to  designate  a  certain  form  of  reason- 
ing.    On  the  contrary,  Sorites,  though  a  word  in 
Sorites,  with  ancient       not  unfrequent  employment  by  ancient  author .<, 
authors,  used  to  des-       „o\vhere  occuiTS   in  any  other  logical  meanino 

i/jnate     a     particular  i  j? 

kit.d  of  sophism  t"^"  ^^^^  of  a  particular  kind  of  sophism,  of 

which  the  Stoic  Chrysippus  \vas  reputed  the  in- 
ventor.'^ 2<i»pos,  you  know,  in  Greek,  means  a  heap  or  pile  of  any 
aggregated  substances,  as  sand,  wheat,  etc. ;  and  Sorites^  literally  a 
heaper^  was  a  name  given  to  a  certain  captious  argument,  which 
obtained  in  Latin  fi'om  Cicero  the  denomination  of  acervalis.^  The 
nature  of  the  argument  was  this:  You  were  asked. 

The  nature  o    this      ^^^  example,  whether  a  certain  quantity  of  some- 
sophism.  ^  '■     \  ^     -*    •/ 

thing  of  variable  amount  were  large  or  small,  — 

say  a  certain  sum  of  money.  If  you  said  it  was  small,  the  adversary 
went  on  gi-adually  adding  to  it,  asking  you  at  each  increment 
whether  it  were  still  small ;  till  at  length  you  said  that  it  was  lai'ge. 
The  last  sum  which  yon  had  asserted  to  be  small,  was  now  compared 
Vith  that  which  you  now  asserted  to  be  large,  and  you  were  at 
length  forced  to  acknowledge  that  one  sum  which  you  maintained 
to  be  large,  and  another  which  you  maintained  to  be  small,  differed 
from  each  other  by  the  very  pettiest  coin,  —  or,  if  the  subject  were 
a  pile  of  wheat,  by  a  single  com.  This  sophism,  as  applied  by  Eubu- 
iides  (who  is  even  stated  by  Laertius*  to  be  the  inventor  of  the 
Sorites  in  general),  took  the  name  of  <^aAaxpo9,  calvus,  the  bald.  It 
was  asked,  —  was  a  man  bald  who  had  so  many  thousand  haira  ;  you 
answer.  No :  the  antagonist  goes  on  diminishing  and  diminishing 
the  number,  till  cither  you  admit  that  he  who  was  not  bald  with  a 
certain  number  of  hairs,  becomes  bald  when  that  complement  is 
diminished  by  a  single  hair ;  or  you  go  on  denying  him  to  be  bald, 
until  his  head  be  hypothetically  denuded.  Such  was  the  quibble 
which  obtained  the  name  of  Sorites,  —  acervalis,  climax,  gradatio, 
etc.  This,  it  is  evident,  had  no  real  analogy  with  the  form  of  rea- 
soning now  known  in  logic  under  the  name  of  Sorites'. 


"  Inrenta*.  Chrytippe,  tul  finltor  •eerri."  —  Ed. 


1  The  passage  referred  to  is  probably  AhoI.  >  Persius,  Sat.  vi.  80. 
Prior.,  i.  25.    But  there  was  no  need  of  a 
special   treatment    of   the  Sorites,   as  it    is 

merely   a    combination     of     ordinary   sy^-  [Cicero  applies  SoritM  to  an  argument  which 

Ipjfisms,  and  subject  to  the  game  rules.  —  Ed.  we  would  call  a  Sorius,  but  it  oould  also  be  a 

[The  principle  of  the  Sorites  is  to  be  found  in  Chr)-8ippean.     Dt  Finibus,  h.  iv.  c.  18.] 

Aristotle's   rule,  Catrg.,  c.  2.    "  Prcdicatum  S  D«  Divinatione,  ii.  4.    "  Quemadmodum 

prxdicati  est  prsdicatum  subjecti."  8ee  also,  Soriti  resistas?   quern,  si   necesse  sit,  Latino 

Anal.  Post.,  I.  23  tt  trg.  Cf.  Tticius,  Comment.,  verbo  llceat  af*rraif»n  appellare  "   Cf.  Facoio< 

p.  169.    Bertius,    Loglea   Prripatrtiea,  L    Hi  latl,  Acroasis,  ii.  p.  17  et  st^.  —  Ed. 

Appendix,  p.  179.]  4  L.  ii.  f  108.  —  Ed 


Lect.XIX.  logic.  !i69 

But  when  was  the  name  perverted  to  this,  its  secondary  significa- 
tion ?   Of  this  I  am  confident,  that  the  change  was 
Lanrentius  Valla  the      ^ot  older  than  the  fifteenth  century.     It  occurs  in 

first  to  use  Sorites  in  ^^^^  ^^  ^^^  logicians  previoUS  tO  that  period, 
its    present     accepta-  '^  '■  *  .    , 

tjQQ_  It  is  to  be  found  in  none  of  the  Greek  logicians 

of  the  Lower  Empire  ;  nor  is  it  to  be  met  with 
in  any  of  the  more  celebrated  treatises  on  Logic  by  the  previous 
Latin  schoolmen.  The  earliest  author  to  whose  writings  I  have  been 
able  to  trace  it,  is  the  celebrated  Laurentius  Valla,  whose  work  on 
Dialectic  was  published  after  the  middle  of  the  fifteenth  century. 
He  calls  the  chain-syllogism  —  "coacervatio  syllogismorum  (quem 
Graeci  <rwpbv  vocant").^  I  may  notice  that  in  the  Dialectica  of  his 
contemporary  and  rival,  George  of  Trebisond,  the  process  itself  is 
described,  but,  what  is  remarkable,  no  appropriate  name  is  given  to 
it.'  In  the  systems  of  Logic  after  the  commencement  of  the  six- 
teenth century,  not  only  is  the  form  of  reasoning  itself  described, 
but  described  under  the  name  it  now  bears. 

I  have  been  thus  particular  in  regard  to  the  history  of  the  Sorites, 

—  word  and  thing,  —  not  certainly  on  account 

The  doctrine  ofio-       ^^  ^^^  importance  of  this  history,  considered  in 

gicians  regarding  the         .       ,/.  ,  , 

Sorites  illustrates  their  itself,  but  because  it  Will  enable  you  the  better 
one-sided  view  of  the  to  ajiprehcnd  what  is  now  to  be  said  of  the  illus- 
nature  of  reasoning  in  tration  which  the  doctrine,  taught  by  logicians 
^*°^™  ■  themselves  of  the  nature  of  this  particular  pro- 

cess, afibrds  of  the  one-sided  view  which  they  have  all  taken  of  the 
nature  of  reasoning  in  general. 

I  have  already  shown,  in  regard  to  the  simple  syllogism,  that  all 
deductive  reasoning  is  from  whole  to  part ;  that  there  are  two  kinds 
of  logical  whole  and  two  kinds  of  logical  part,  —  the  one  in  the 
quantity  of  comprehension,  the  other  in  the  quantity  of  extension ;  — 
and  that  there  are  consequently  two  kinds  of  reasoning  corresponding 
to  these  several  quantities.  I  further  showed  that  logicians  had  in 
simple  syllogisms  marvellously  overlooked  one,  and  that  the  simplest 
and  most  natural,  of  these  descriptions  of  reasoning,  —  the  reason- 
ing in  the  quantity  of  comprehension ;  and  that  all  their  rules  were 
exclusively  relative  to  the  reasoning  which  proceeds  in  the  quantity 
of  extension.  Now,  in  to-day's  Lecture,  I  have  shown  that,  as  in 
simple  syllogisms,  so  in  the  complex  form  of  the  Sorites,  there  is 
equally  competent  a  reasoning  in  comprehension  and  in  extension, 
—  though  undoubtedly,  in  the  one  case  as  in  the  other,  the  reason- 

1  DiaUctuee  DisptOationes,  Lib.  iii.  C.  12.  See  2  See  Gtorgii  Trap'zuntii  De  Re  Dialectica 
Laurentii  YalU  Opera,  Basilese,  1540,  p.  742.—  LibeUus,  Coloniae,  1533,  f.  60».  Cf.  the  Scholia 
Ed.  of  Neomagus,  ibid.  f.  67'>.  —  Ed. 


270  LOGIC.  Lect.  XIX 

ing  in  comprehension  is  more  natural  and  easy  in  its  evolution  than 
the  reasoning  in  extension,  inasmuch  as  the  middle  term,  in  the 
former,  is  really  intermediate  in  position,  standing  between  th«  ma- 
jor and  the  minor  terms,  whereas,  in  the  latter,  the  middle  term  is 
not  in  situation  middle,  but  occupies  the  position  of  one  or  other  of 
the  extremes. 

Now,  if  in  the  case  of  simple  syllogisms,  it  be  man^ellous  that 

logicians  should  have  altogether  overlooked  the 

Logicians  have  over-       possibility  of  a  reasoning  in  comprehension,  it  is 

looked  the  Sorites  of         ,       ,  ,  ,,  ^i     ^        -.j     »i  •      .1     • 

_      ^^^  doubly  marvellous  that,  with  this  their  prepos- 

session, they  should,  in  Ihe  case  of  the  Sorites, 
have  altogether  overlooked  the  possibility  of  a  reasoning  in  exten- 
sion. But  so  it  is.  *  They  have  all  followed  each  other  in  defining 
the  Sorites  as  a  concatenated  syllogism  in  which  the  predicate  of 
the  proposition  preceding  is  ra^ade  the  subject  of  the  proposition  fol- 
lowing, until  we  arrive  at  the  concluding  proposition,  in  which  the 
predicate  of  the  last  of  the  premises  is  enounced  of  the  subject  of 
the  first.  This  definition  applies  only  to  the  Progressive  Sorites  in 
comprehension,  and  to  the  Regressive  Sorites  in  extension :  but 
that  they  did  not  contemplate  the  latter  form  at  all  is  certain,  both 
because  it  is  not  lightly  to  be  presumed  that  tliey  had  in  view  that 
artificial  and  recondite  forra^  and  because  the  cxaniples  and  illustra- 
tions they  supply  positively  prove  that  they  had  not. 

To  the  Progressive  Sorites  in  extension,  and  to  the  Regressive 
Sorites  in  comprehension,  tJiis  definition  is  iaap- 
Difference  between       pUcable  ;  for  in  these,  the  subject  of  the  premise 
the  two  forms  of  Sori-  -,•        •  .1  t  /»,  •,., 

,j^  precedmg  is  not  the  predicate  ol  the  premise  fol- 

lowing. But  the  diflerence  between  tlie  two 
forms  is  better  stated  thus:  —  In  the  Progressive  Sorites  of  com- 
prehensioiTand  the  Regressive  Sorites  of  extension,  the  middle  terms 
are  the  predicates  of  the  prior  premises,  and  the  subjects  of  the  pos- 
terior; the  middle  term  is  here  in  position  intermediate  between 
the  extremes.  On  the  contrary,  in  the  Progressive  Sorites  of  exten- 
.sion  and  in  the  Regressive  Sorites  of  comprehension,  the  middle 
terms  are  the  subjects  of  the  prior  premises  and  the  predicates  of 
the  posterior ;  the  middle  term  is  here  in  position  not  intermediate 
between  the  extremes. 

To  the  question,  —  why,  in  the  case  of  simple  syllogisms,  the 
logicians  overlooked  the  reasoning  in  comprehension,  and,  in  the 

1  (Ridiger  notices  tlic  error  of  those  wlio  rcripntelici.  ef  ciitn  his  (Jassendus,  qui  Sori- 

mnke  Sorites  only  of  compieltcntiive  wliole.  »itn  mlinii  ad  pricdicKtum  iK-rtinere  exisU- 

•tjee  hie  Dr  .Scmm(  Veri  tt  Falsi,,  i,  ii.  c.  10,  4  6_  niat^°— J£i>.] 
p.  400.    Ci.  p.  MS  u,i  iR.]    il-'4"jnaw»<  vuXgu 


I 


Lkct.  XIX.  LOGIC.  2X1 

case   of  the  Sorites,  the  reasoning  in  extension,  it  is,  perhaps,  im- 
possible   to    afford  a   satisfactory    explanation, 
ro  a  e    reason       g^^  ^_^  ^       plausibly  coniecture,  what  it  is  out 

why   logicians    over-  •'    ^  •>  •'  ' 

looked,  in  the  case  of  of  our  power  Certainly  to  prove.  In  regard  to 
simple  syllogisms,  the  simple  syllogisms,  it  was  an  original  dogma  of  the 
reasoning  iu  Compre-       pjat^nic  school,  and  an  early  dogma  of  the  Peii- 

liension.  .  ,  .  .      , 

patetic,  that  philosophy  —  that  science,  strictly 
so  called  —  was  only  conversant  with,  and  was  exclusively  con- 
tained in,  universals;  and  the  doctrine  of  Aristotle,  which  taught 
tliat  all  our  general  knowledge  is  only  an  induction  from  an  observa- 
tion of  particulars,  was  too  easily  forgotten  or  perverted  by  his  follow- 
ers. It  thus  obtained  almost  the  force  of  an  acknowledged  principle, 
that  everything  to  be  known  must  be  known  under  some  general 
form  or  notion.  Hence  the  exaggerated  importance  attributed  to 
definition  and  deduction ;  it  not  being  considered,  that  we  only  take 
out  of  a  general  notion  what  we  had  previously  placed  therein ; 
and  that  the  amplification  of  our  knowledge  is  not  to  be  sought  for 
from  above,  but  from  below,  —  not  from  speculation  about  abstract 
generalities,  biit  from  the  observation  of  concrete  particulars.  But, 
however  erroneous  and  ii'rational,  the  persuasion  had  its  day  and 
influence ;  and  it  perhaps  determined,  as  one  of  its  effects,  the  total 
neglect  of  one-half,  an<i  that  not  the  least  important  half,  of  the 
reasoning  process.  For,  while  men  thought  only  of  looking  up- 
wards to  the  more  extensive  notions,  as  the  only  objects  and  the 
only  media  of  science,  they  took  little  heed  of  the  more  compre- 
hensive notions,  and  absolutely  contemned  individuals,  as  objects 
which  could  neither  be  scientifically  known  in  themselves,  nor  sup- 
ply the  conditions  of  scientifically  knowing  aught  besides.  The 
logic  of  comprehension  and  of  induction  was,  therefore,  neglected 
or  ignored,  —  the  logic  of  extension  and  deduction  exclusively  cul- 
tivated, as  alone  affording  the  niles  by  which  we  might  evolve 
higher  notions  into  their  subordinate  concepts.  This  may  help  to 
explain  why,  subsequently  to  Aristotle,  Logic  was  cultivated  in  so 
partial  a  manner;  but  why,  subsequently  to  Bacon,  the  logic  of  com- 
prehension should  still  have  escaped  observation  and  study,  I  am 
altogether  at  a  loss  to  imagine.  But  to  the  question,  —  why,  when 
reasoning  in  general  was  viewed  only  as  in  the  quantity  of  exten- 
sion, the  minor  form  of  the  Sorites  should  have 
/. '!.  ^'  I"  x  ^      "been  viewed  as  exclusively  in  that  of  compre- 

case    of    the    Sorites,  •'  i        r  i 

they  ovcriooiced  the  hensiou,  may,  perhaps,  be  explained  by  the  fol- 
leasoning  in   Exten-       lovvinjT  consideratioTi :  this  form  was  not  origi- 


»ion 


nally  analyzed  and  expounded  by  the  acuteness 
of  Aristotle.     But  it  could  not  escape  notice  that  there  was  a  form 


272  LOGIC.  Lect.  XIX 

of  reasoning,  of  very  frequent  employment,  botli  by  philosophers 
and  rhetoricians,  in  which  a  single  conclusion  was  drawn  from  a 
multiplicity  of  premises,  and  in  which  the  predicate  of  the  forego- 
ing premise  was  usually  the  subject  of  the  following.  Cicero,  for 
example,  and  Seneca,  are  full  of  such  arguments ;  and  the  natural 
and  easy  evolution  of  the  reasoning  is  indeed  peculiarly  appropriate 
to  demonstration.  Thus,  to  prove  that  every  body  is  movable,  we 
have  the  following  self-evident  deduction.  Every  body  is  in  space ; 
what  is  in  space  is  in  some  one  part  of  space ;  what  is  in  one  part 
of  space  may  be  in  another;  what  may  be  in  another  part  of  space 
may  change  its  space;  what  may  change  its  space  is  movable; 
therefore,  every  body  is  movable.  When,  therefore,  Valla,  or  who- 
ever else  has  the  honor  of  first  introducing  the  consideration  of  this 
form  of  reasoning  into  Logic,  was  struck  with  the  cogency  ftnd 
clearness  of  this  compendious  argumentation,  he  did  not  attempt  to 
reduce  it  to  the  conditions  of  the  extensive  syllogism ;  and  subse- 
quent logicians,  when  the  form  was  onCe  introduced  and  recognized 
in  their  science,  were,  as  usual,  content  to  copy  one  from  another, 
without  subjecting  their  borrowed  materials  to  any  oiiginal  or 
rigorous  criticism. 

Ut  nemo  in  seso  tentat  descendere;  —  nemo ! 
Sed  prsecedenti  spectatur  mantica  tergo.^ 

Accordingly,  not  one  of  them  has  noticed,  that  the  Sorites  of  their 
systems  proceeds  in  a  different  quantity  from  that  of  their  syllo- 
gisms in  general,  —  that  their  logic  is  thus  at  variance  with  itself; 
far  less  did  any  of  them  observe  that  this,  and  all  other  forms  of 
reasoning,  are  capable  of  being  drawn  in  another  quantity  fi'om 
that  which  they  all  exclusively  contemplated.  And  yet,  had  they 
applied  their  observation  without  prepossession  to  the  matter,  they 
would  easily  have  seen  that  the  Sorites  could  be  cast  in  the  quan- 
tity of  extension,  equally  as  common  syllogisms,  and  that  common 
syllogisms  could  be  cast  in  the  quantity  of  comprehension,  equally 
as  the  Sorites.  I  have  already  shown  that  the  same  Sorites  may  be 
drawn  either  in  comprehension  or  in  extension ;  and  in  both  quan- 
tities proceed  either  by  progression  or  by  regres- 
Exampie  of  the  So-       gion.     But  the  example  given  may,  perhaps,  be 

rites    in    Comprehen-  .  .  i  -i        t  i  /»  ^    i 

.ion  and  Extension.  Viewed  as  Selected.     Let  us,  therefore,  take  any 

other;  and  the  first  that  occni-s  to  my  recollec- 
tion is  the  following  from  Seneca,'  which  I  shall  translate  : 

1  renins,  ir.  23.  -  Ed.  t  ^ritt.,  8S.  —  Ed. 


Lect.  XTX.  tOGta.  273 

Be  toho  is  prudent  is  temperate ; 

He  who  is  temperate  is  constant ; 

He  who  is  constant  is  iivpcrturbed ; 

He  who  is  unperturbed  is  without  sorrow ; 

He  who  is  without  sorrow  is  happy ; 

Therefore,  the  prudent  man  is  happ;/. 

In  tliis  Sorites,  everything  slirles  easily  and  smoothly  frojn  the 
whole  to  the  ]iarts  of  comprehension.  But,  tliough  the  process  will 
be  rattier  more  by  hitches,  the  descent  under  extension  will,  if  not 
quite  so  pleasant,  be  equally  rapid  and  certain. 

Be  who  is  vnthout  sorrow  is  happy; 
He  who  is  unperturbed  is  unthout  sorrow; 
Be  who  is  constant  is  unperturbed; 
Be  who  is  temperate  is  constant : 
Be  xvho  is  prudent  is  temperate; 
Therefore,  the  prudent  man  is  happy. 

I  do  not  think  it  necessary  to  explicate  these  two  reasonings, 
which  you  are  fully  competent,  I  am  sure,  to  do  without  difficulty 
for  yourselves. 

What  renders  it  still  more  wonderful  that  the  logicians  did  not 
evolve  the  competency  of  this  process  in  either 
e  oc  euian  o-  quantity,  and  thus  obtain  a  key  to  the  opening 
up  of  the  whole  mystery  of  syllogistic  reason- 
mg,  is  this  :  —  that  it  is  now  above  two  centuries  since  the  Inverse 
or  Regressive  Sorites  in  comprehension  was  discovered  and  signal- 
ized by  Rodolphus  Goclenius,  a  celebrated  philosopher  of  Marburg, 
in  which  university  he  occupied  the  chair  of  Logic  and  Meta- 
physics.^ This  Sorites  has  from  him  obtained  the  name  of  Gocle- 
nian;  while  the  progressive  Sorites  has  been  called  the  common  or 
Aristotelian.  This  latter  denomination  is,  as  I  have  previously 
noticed,  an  error;  for  Aristotle,  though  certainly  not  ignorant  of 
the  process  of  reasoning  now  called  /Sorites,  does  not  enter  upon  its  • 
consideration,  either  under  one  form  or  another.  This  observation 
by  Goclenius,  of  which  none  of  our  British  logicians  seem  aware,, 
was'  a  step  towards  the  explication  of  the  whole  process;  and  we 
are,  therefore,  left  still  more  to  marvel  how  this  explication,  so  easy 
and  manifest,  should  not  have  been  made.  Before  terminating  this 
subject,  I  may  mention  that  this  form  of  syllogism  has  been  some- 
times styled  by  logicians  not  only  /Sorites,  but  also  coacervatio,  con- 

1  Goclenii  Isagoge  in  Orgarium  ArL'itotcli's,  clenian  Sorites  before  Goclenius,  see  Pacius, 
Francof.,  1698,  p.  265  —Ed.     [For  the  Go-      Comment,  in  Anal.  Prior.,  1.  25.  p.  159] 

35 


,274 


LOGIC. 


Lkct.  XIX 


Epicheirema  and  So- 
rites, as  polysyllo- 
gisms,  comparatively 
simple,  and  not  pleon- 

«8tJC. 


fferies,  ffradatio,  climax,  and  deprimo  adtdtimum.  The  old  name, 
before  Valla,  which  the  process  obtained  among  the  Greek  logicians 
of  the  Lower  Empire,  was  the  vague  and  general  appellation  of 
complex  syllogism.,  —  cruXXoyw/jios  (ruv^crds.^ 

So  much  for  the  two  forms  of  reasoning  which  may  be  regarded 
as  composite  or  complex,-  and  which  logicians 
have  generally  considered  as  redundant.  But 
here  it  is  proper  to  remark,  that  if  in  one  point, 
that  is,  as  individual  syllogisms,  the  Epicheirema 
and  Sorites  may  be  viewed  as  comparatively 
complex,  in  another,  that  is,  as  polysyllogisms,  they  may  be  viewed 
as  comparatively  simple.  For,  resolve  a  Sorites  into  the  various 
syllogisms  afforded  by  its  middle  terms,  and  compare  the  multitude 
of  propositions  through  which  the  conclusion  is  thus  tedidusly 
evolved,  with  the  short  and  rapid  process  of  the  chain-syllogism 
itself,  and,  instead  of  complexity,  we  should  rather  be  disposed  to 
predicate  of  it  extreme  simplicity.'  In  point  of  fact,  we  might 
arrange  the  Epicheirema  and  Sorites  with  far  greater  propriety 
under  elliptical  syllogisms,  than,  as  is  commonly  done  by  logicians, 
under  the  pleonastic.  This  last  classification  is,  indeed,  altogether 
erroneous,  for  it  is  a  great  mistake  to  suppose  that  in  either  of  these 
fonns  there  is  aught  redundant. 


1  [Blemmidas,  Epitomt  Logiea,  o.  81.] 


*  [See  Leibnitz,  Nouveaux  Essais,  L.  ir. 
xtU.  i  4,  pp.  445, 446, 448,  ed.  Baspe.] 


LECTURE     XX. 

STOICHEIOLOOY. 

SECTION    II.— OF  THE    PRODUCTS   OF    THOUGHT 

III —DOCTRINE    OF  REASONINGS. 

SYLLOGISMS.  —  THEIR  DIVISIONS  ACCORDING  TO  EXTERNAL 

FORM. 

B.    DEFECTIVE,  — ENTHYMEME. 
C.     REGULAR  AND  IRREGULAR,  —  FIGURE  AND  MOOD. 

I  PEOCEED  now  to  the  Second  Class  of  Syllogisms,  —  those,  to 
wit,  whose  External  Form  is  defective.     This 

tive'i!Srte™"iFr^'  <'^««s  I  give  ill  Conformity  to  the  doctrine  of 
modern  logicians,  whose  unanimous  opinion  on 

the  subject  I  shall  comprehend  in  the  following  paragraph. 

%    LXXTI.    According  to  logicians,  in  general,  a  defective 

syllogism  is  a  reasoning  in  which  one  only 

Par.  Lxxn.    Tue       ^^  ^^^  premises  is  actually  enounced.     It 

Enthymeme.  i^  •' 

is,  therefore,  they  say,  called  an  Enthymeme 
{cvSvfx.Tjfia),  because  there  is,  as  it  were,  something  held  back  in 
the  mind  (cV  ^vfiwi).  But,  as  it  is  possible  to  retain  either  the 
sumption  or  the  subsuraption,  the  Enthymeme  is  thus  of  two 
kinds :  —  an  Enthymeme  of  the  First,  and  an  Enthymeme  of 
the  Second,  Order.  The  whole  distinction  is,  however,  errone- 
ous in  principle,  and,  even  if  not  erroneous,  it  is  incomplete ; 
for  a  Third  Order  of  Enthyraemes  is  competent  by  the  suppres- 
sion of  the  conclusion. 

Such,  as  it  is  stated  in  the  former  part  of  the  paragi'aph,  is  the 
doctrine  yon  will  find  maintained,  with  singular  unanimity,  by 
modern  logicians ;   and,  with  hardly  an  exception,  this  classification 


276  LOGIC.  Lect.  XX. 

of  syllogisms  is  stated  noi  only  without  a  suspicion  of  its  own  cor- 
rectness, but  as  a  division   established  on  the 

Explication.      The  . 

common  doctrine  of  authority  of  the  great  father  of  logic  himself, 
the  Enthymeme  futile,  In  both  assertions  they  are,  however,  wrong, 
and  erroneously   at-       foj.  ^^q  classification  itsclf  is  futile,  and  Aristotle 

tributed  to  Aristotle.  re     :i      '^  i  ••  ■■     ' 

anords  it  no  countenance ;  winle,  at  the  same 
time,  if  a  distinction  of  syllogisms  is  to  be  taken  from  the  ellipsis 
of  tlieir  propositions,  the  subdivision  of  enthymemcs  is  not  com- 
plete, inasmuch  as  a  syllogism  may  e.xist  with  both  premises  ex- 
pressed, and  the  conclusion  understood. 

I  shall,  therefore,  in  the  first  place,  show  that  the  Enth}Tneme,  as 
at  syllogism  of  a  defective  enouncement,  constitutes  no  special  form 
of  reasoning;  in  the  second,  that  Aristotle  does  not  consider  a  syl- 
logism of  such  a  character  as  such  a  special  form ;  and,  in  the  third, 
that,  admitting  the  validity  of  the  distinction,  the  restriction  of  the 
Enthymeme  to  a  syllogism  of  one  suppressed  premise  cannot  be 
competently  maintained. 

'  I.  In  regard,  then,  to  the  validity  of  the  distinction.     This  is 

disproved   on  the  following  grounds:   First  of 

I  T!;t.  Ertfiniht^me       j,|]^  ^■^^  discrimination  of  the  Enthymeme,  as  a 

i.ut  u  Fpecial  lot  m  of  n       •  n  i  .  ,. 

reasoning.  Syllogism  of  One  suppressed  premise,  from  the 

ordinary  syllogism,  would  involve  a  discrinii- 
hation  of  the  reasoning  of  Logic  from  the  reasoning  in  common 
use;  for,  in  general  reasoning,  we  rai*ely  express  ail  the  proposi- 
tions of  a  syllogism,  and  it  is  almost  only  in  the  treatises  on  Ab- 
stract Logic  that  we  find  examples  of  reasoning  in  which  all  the 
members  are  explicitly  enounced.  But  Logic  does  not  create  new 
f6fms  of  syllogism,  it  merely  expounds  those  which  are  already 
gi^en ;  and  while  it  shows  that  in  all  reasoning  there  are,  in  the 
mental  process,  necessarily  three  judgments,  the  mere  non-expres- 
sion of  any  of  these  in  language,  no  more  constitutes  in  Logic  a 
particular  kind  of  syllogism,  than  docs  the  ellipsis  of  a  term  consti- 
tute in  Grammar  a  particular  kind  of  concord  or  government.  But, 
secondly,  Syllogism  and  Enthymeme  are  not  distingnished  as  re- 
spectively an  intralogical  and  an  extralogical  form ;  both  are  sup- 
posed equally  logicah  Those  who  defend  the  distinction  are,  there- 
fore, necessarily  compelled  to  maintain,  that  Logic  regards  the 
R:<S(jident  of  the  external  expfession,  and  not  th«  essence  of  the 
internal  thought,  in  holding  that  the  Enthymeme  is  really  a  defec- 
tive reasoning.^ 

1  Cotnpore  Discussions,  p.  153  r«  srq.  — Ed.         Derodon,  Logiea  ReatittHa,  Pars  V.  tract,  i.  a 

2  [Thct  Syllogism  and  Enthymeme  are  not     1.,  p.  608.] 
properly  distinct  species  of  reasoning,  see 


I^,CT.  XX.  LOGIC  27t 

It  thus  appears!,  tii8t  to  eonstttate  ihe  E«thymerae  as  a  speeios 
of  reasoning  distinct  from  Syllogisms  Proper,  by  the  difference  of 
perfect  and  iinpei'fect,  is  of  all  absurdities  the  greatest.  But  is  this 
absurdity  the  work  of  Aristotle  ?  —  and  this  le^s  us  to  the  second 
bead. 

II.   Without  entering  upon  a  regular  examination  of  the  various 

passages  of  the  Aristotelic  treatises  relative  to 

II.   The  distinction       tjjjg  point,  I  may  observe,  in  the  first  place,  that 

of  the  Euthyrueme  as  a     •    ...    ^i  '    i        j       i  •  1^1^ 

a  special  form  of  rea-  AiistoUe  expressly  declares  m  general,  that  a 
Boning  not  made  by  syllogism  is  Considered  by  the  logician,  not  in  re- 
Aristotie.  latiou  to  jts  expression  (ou  tt/sos  tov  l^oi  Aoyov),  but 

exclusively  as  a  mental  process  (dAA.a  tt/ws  tov  €v 
rg  i/o^xS  ^o'yov).^  The  distinction,  therefore,  of  a  class  of  syllogisms, 
as  founded  on  a  verbal  accident,  he  thus  of  course,  implicitly  and  by 

anticipation,  condemns.  But  Aristotle,  in  the 
Aristode  —what  sccoud  place,  docs  distinguish  the  Enthymeme 

as  a  certain  kind  of  syllogism,  —  as  a  syllogism 
of  a  peculiar  matter,  —  as  a  syllogism  fi-om  signs  and  likelihoods.* 
Xow  if,  having  done  this,  it  were  held  that  Aristotle  over  and  above 
distinguished  the  Enthymeme  also  as  a  syllogism  with  one  sup- 
pressed premise,  Aristotle  must  be  8<jp^posed  to  define  the  Enthy- 
meme by  two  differences,  and  by  two  differences  which  have  no 
mutual  analogy ;  for  a  syllogism  from  signs  and  likelihoods  does  not 
more  naturally  fall  into  an  elliptical  form  than  a  syllogism  of  any 
other  mattei'.  Yet  this  absurdity  has  been  and  is  almost  universally 
believed  of  the  acutest  of  human  intellects,  and  on  grounds  which, 
when  examined,  afford  not  the  sliglitest  warrant  for  such  a  conclu- 
sion. On  the  criticism  of  these  grounds  it  would  be  out  of  place 
here  to  enter.  Suffice  it  to  say,  that  the  texts  in  the  Organon  and 
Rhetoric,  which  may  be  adduc^ed  in  support  of  the  vulgar  opinion, 
will  bear  no  such  interpretation ;  —  that  in  one  passage,  where  the 
word  arcX^s  {imperfect)  is  applied  to  the  Enthymeme,  —  this  word, 
if  genuine,  need  signify  only  that  the  reasoning  from  signs  and 
probabilities  affords  not  a  perfect  or  necessary  inference  ;  but  that, 
in  point  of  fact,  the  woi'd  arcX^s  is  there  a  manifest  interpolation, 
made  to  accommodate  the  Aristotelic  to  the  common  doctrine  of  the 
Enthymeme,  for  it  is  not  extant  in  the  oldest  manuscripts,  and  has, 
accordingly,  without  any  reference  to  the  present  question,  been 
ejected  from  the  best  recensions,  and,  among  others,  from  the  recent 
o<Ution  of  the  works  of  Aristotle  by  the  Academicians  of  Berlin,  — 
■^n  edition   founded   on  a  collation  of  the   principal   manuscripts 

1  Ancd.  Post.,  i.  10.  —  Ed.  2  Anal.  Prior.,  ii.  27.     RAet.,  i.  2.  —  Ed. 


278 


LOGIC. 


Lect.  XX 


Applications  of  the 
term  Enthymeme. 

By  Dionysius  of 
Ualicarnassus.  Au- 
thor of  Rhetoric  to  Alex- 
ander. Sopater.  Aulus 
Uellius.  Cicero.  Quin- 
tilian. 


tbrougliout  Europe.'  It  is  not,  however,  to  be  denied  that  the  term 
Enthymeme  was  applied  to  a  syllogism  of  some 
unexpressed  part,  in  very  ancient  times;  but, 
along  with  this  meaning,  it  was  also  employed  by 
the  Greek  and  Roman  rhetoricians  for  a  thought 
in  general,  as  by  Dionysius  the  Halicarnassian,^ 
and  the  author  of  the  Rhetoric  to  Alexander^  at- 
tributed to  Aristotle,^ — for  an  acute  dictum,  as 
by  Sopater  *  and  Aulus  Gellius,* —  for  a  reasoning 
from  contraries  or  contradictories,  as  by  Cicero.^  Quintilian  gives 
tbree  meanings  of  the  term ;  in  one  sense,  signifying  "  omnia  mente 
concepta^''  in  another,  '■'- sententia  cum,  rationed"*  in  a  third,  '■'•argu- 
menti  conclusio,  r)cl  ex  consequentihns,  vel  ex  repngnantihus?''^ 

Among  the  ancients,  who  employed  the  term  for  a  syllogism  with 
some  suppressed  part,  a  considerable  number 
held,  with  our  modern  logicians,  that  it  was  a 
syllogism  deficient  of  one  or  other  premise,  as 
Alexander  the  Aphrodisian,  Ammonius  Hermia>, 
Philoponus,*  etc.  Some,  however,  as  Pachy- 
meres,"  only  recognized  the  absence  of  the 
major  premise.  Some,  on  the  contrary,  thought, 
like  Quintilian,"^  that  the  suppressed  proposition 
ought  to  be  the  conclusion ;  —  nay,  Ulpian,  the  Greek  commentator 


Denoted,  with  some 
of  the  ancients,  a 
syllogism  with  some 
suppressed  part.  The 
Aphrodisian.  Am- 
monius. Fhiloponus. 
Pachymeres.  Quintil- 
ian. Ulpian.  Scholi- 
ast on  Hermogenes. 


1  For  a  fuller  history  of  this  interpolation, 
see  Discussions,  p.  164.  —  Ed.  [For  the  correct 
doctrine  of  the  Aristotelic  Enthymeme,  see 
Mariotte,  Essay  de  Logiquc,  P.  ii.  dljc.  iii.  p. 
168,  Paris,  1678.  —  Ed.  ] 

8  Epistola  ad  Cn.  Pomptium  de.  pracipuis  His- 
toricis,  c.  5.  Tfjj  ftiuToi  KoXXiXoyias  (Kfiyov 
Koi  70V  irKovrov  rwv  ivbvixfftArwy  Kwrh 
•KoKv  vffTfpfi,  The  expression  irKovroi  iv- 
dvfxendTup  is  rendered  by  J.  C.  T.  Ernesti, 
Gedankin  FiUle ;  see  his  Lexikon  Ttchnologicr 
Graeorum  Rhetoriea,  v.  ivbvufixa.  Tlie  same 
sentence  is  repeated  in  nearly  the  same  words 
by  Dionysius,  in  his  Veterum  Scriptorum  Cen- 
sura,  iii.  2.  —  Ed. 

*  3  The  author  of  the  Rhetorica  ad  AUxan- 
drum,  c.  8,  classes  the  enthymeme  among 
proofs  (iriffTtis),  and  in  c.  11,  defines  it  as  a 
proof,  drawn  from  any  kind  of  opposition. 
'''E.vbvft.iift.aTa  8'  iariv  oh  ix6vov  rh.  ry  \'by(f 
KoX  rij  -irpd^fi  ivavriovfifva,  oAXA  »ca)  ro7s 
iKKoii  &.ira<Tiv.  This  work  Is  attributed  by 
Victorias  to  Anaximenes  of  Lampsacus,  and 
this  conjecture  is  adopted  by  the  latest  editor, 
Spengcl.  —  Ed. 


<  Sopatri  Apameensis  Prolegomena  (n  Aristi- 
dem.  Aristidis  Op.  Omit.,  ed.  Jebb,  vol.  L  f.  d. 
S.  Kal  TTJ  rHy  iv^vfitiixdroiy  ruKvirriTi  8»j- 
fioffdfyl^fi.  In  Canter's  Prolegomena  this  ex- 
pression is  rendered  sentenliarum  densitas,  and 
the  word  iydufirifjMTiK6s  in  the  same  passage 
by  argutus  in  argumentis.  But  compare  Dis- 
cussions, p.  157.  —  Ed. 

i  Tfoctes  Attira,  vi.  13.  "  Qnserebantur 
autem  non  gravia  ncc  rcvercnda,  sed  ^I'^u- 
fx-finara  quxdam  lepida  et  miunta."  —  Ed. 

«  Topiea,  c.  13.  —  Ed. 

T  Jn.U.  Orat.,  v.  10,  1.  — Ed. 

8  See  Alexander,  In  Topiea,  pp.  6,  7,  ed. 
Aid.  1513.  Ammonius,  In  Quinque  Toees  Por- 
phyrii^  {.  5  a,  ed.  Aid.  1546.  Philoponus,  In 
Anal.  Post.,  {.  4  a,  ed.  Aid.  1534.  These  author- 
ities are  cited  in  the  author's  note,  Discussions, 
p.  156. —Ed. 

0  Epitome  I^gices  Aristotelis,  Oxon.,\G&3,  p. 
113.  See  also  his  Epito}ne  in  Universam  Aristo- 
telis  Disierendi  Artem,  appended  to  Rasarius's 
translation  of  Ammonius  on  Forpbyrj 
Lugd.,  1647,  p.  244.  —  Ed. 

lOiJut.  Orat.,  V.  14, 1.  —Ed. 


LrcT.  XX.  LOGIC.  279 

of  Demosthenes,  and  the  scholiast  on  Hei-mogenes  the  Rhetorician,^ 
absolutely  define  an  Enthymerae  —  "a  syllogism,  in  which  the  con- 
clusion is  unexpressed."^ 

III.   This  leads  us  to  the  third  head ;  for  on  no  principle  can  it  be 

shown,  that  our  modern  logicians  are  correct  in 

III.  Admitting  the       denying  or  not  contemplating  the  possibility  of 

validity  of  the  discrim-  ,*'r  ^     ,  ^,.  —ii  i'- 

iuation  of  the  Enthy-  the  reticcuce  of  the  conclusion.  The  only  prin- 
meme,  it  cannot  be  ciplc  On  which  a  sylloglsm  is  Competent,  with 
restricted  to  a  syiio-       q^q  qj.  ot^er  of  its  propositions  unexpressed,  is 

sismofoneBuppressed  ..  ^i^^i  ^  t-x  -r-    ^ 

this,  —  that  the  part  suppressed  is  too  manliest 

premise.  '  r  rjr 

to  require  enouncement.  On  this  principle,  a 
syllogism  is  not  less  possible  with  the  conclusion,  than  with  either 
of  the  premises,  understood;  and,  in  point  of  fact,  occurs  quite  as 
frequently  as  any  other.     The  logicians,  therefore,  to  complete  their 

doctrine,  ought  to  have  subdivided  the  Enthy- 

Exampiea  of  Enthy-       meme  not  -merely  into  Enthymemes  of  the  first 

memes  of  the.  First,       ^^^  second,  but  also  into  Enthymemes  of  the 

Second,    and    Third,  ,  •    ,         t  t  i  .  ,  -, 

Qy^gj.  third  order,  according  as  the  sumption,  the  sub- 

sumption,  or  the  conclusion  is  suppressed.'  Aa 
examples  of  these  various  Enthymemes,  the  following  may  suffice: 

The  Explicit  Syllogism. 

Every  liar  is  a  covoard ; 

Caius  is  a  liar ; 

Therefore,  Caius  is  a  coward. 

I.    Enthtmemb  of  the  First  Ordee — (the  Sumption  understood.) 
Caius  is  a  liar  ; 
Therefore,  Caius  is  a  couxtrd. 

n.    £nththehe  of  the  Second  Order  —  (the  Subsumption  understood.) 
Every  liar  is  a  coward ; 
Therefore,  Cains  is  a  coward. 

ni.    Enthtmeme  of  the  Third  Order  —  (the  Conclusion  understood.) 
Every  liar  is  a  coward ; 
And  Caius  is  a  liar. 

1  Ulpian,  Ad  Demosth.  Olynth.,  ii.  f.  7  b,  ed.     ities  on  this  question  is  given  by  the  author, 
Aid.,  1527.    Anonymi  ad  Hermogenem,  De      Discussions,  p.  Ibl .  —  Ed. 

Inventione,  lib.  iv.  See  RhHores  Grceci,  ed.  3  [That  the  Enthymeme  is  of  three  orders  is 
Aid.  1509,  vol.  ii.  p.  371.  In  the  same  work,  held  by  Victorinus  (in  Cassiodorus  Opera,  vol. 
p.  365,  the  scholiast  allows  that  either  premise-  ii.  p.  536,  ed.  1729.  Rhetores  Pithgei,  p.  3il,  ed. 
or  conclusion  may  be  omitted.  —  Ed.  1599),  or  rather  of  four  orders,  for  tliere  may 

be  an  Enthymeme  with  only  one  propositiOB 

2  An  enlarged  and  corrected  list  of  author-     enounced.    See  Victorinus,  as  above.] 


LOGIC. 


Lect.  XX. 


Epigrammatic  ex- 
amples of  Euthymeme 
witli  suppressed  con- 
elusiou. 


In  this  last,  you  see,  the  suppression  of  the  concduaion  is  i>ot  only 
not  yioUnit,  bat  its  expression  is  even  more  su- 
pei-fluous  than  that  of  either  of  the  premises. 
There  occure  to  rae  a  olever  epigram  of  tlie 
Greek  Anthology,  in  ^yhich  there  is  a  syllogism 
with  the  conclusion  supf^ressed.  I  shall  not 
quote  the  original,  but  give  you  a  Latin  and  English  imitation,  which 
will  serve  equally  well  to  illustrate  the  point  in  question.^  The 
Ijatin  imitation  is  by  the  learned  printer  Henricus  Stephanus,  and 
he  applies  his  epigram  to  a  certain  Petrns,  who,  I  make  no  doubt, 
was  the  Franciscan,  Petrus  a  Ccwnibus,  whom  Buchanan,  J5eza, 
Rabelais,  and  others  have  also  satiiized."  It  rcHis,  tk»  I  recollect, 
thus: 

"Sunt  mooachi  oeqaam;  nequara  uon  unas  ec  ultcrc 
Pr«cer  PeUiim  omnes :  est  8cd  et  hie  tooaachus." 

The  English  imitaUon  was  written  by  Porson  upon  Gottfried 
Hermann  (when  this  was  written,  confessedly  the  prince  of  Greek 
scholars),  who  when  hardly  twenty  had  attacked  Poi-son's  famous 
canons,  in  his  work,  J)e  Metris  Grcecoriim  et  JiotnaHortWi.  Tiw 
merit  of  the  epigram  does  not  certainly  lie  in  its  truth. 

"The  Germans  in  Greek, 
Are  sadiy  to  seek ; 
Not  five  in  five  score, 
Bot  ninety -five  more;  ^ 

All,  save  only  Hermann, 
And  Hermann  's  a  German." 

In  these  epigrams,  the  conclusion  of  the  syllogism  is  suppressed, 
yet  its  illative  force  is  felt  even  in  spite  of  the  express  exception  ; 
nay,  in  really  conquering  by  implication  the  apparent  disclaimer, 
consists  the  whole  point  and  elegance  of  the  epigram.  To  put  the 
former  into  a  syllogistic  shape,  — 


1  The  original  is  an  epigram  of  rhocyIi4.e!>, 
preserved  by  Strabo,  B.  x.  p.  487,  ed.  Casau- 
bon,  1620.  Compare  Anthologia  Grata,  1.  p. 
64,  ed.  Bruiick.  Lips  ,  1794.  Porta  Minores 
Groan,  ed.  Gaiefoj;d,i.  p.  444. 

Koi  rdSt  (f)aiKv\lSeu  '  A^piot  koxoI  '  o'jx 
6  ifXv,  hs  S'  o&  • 

Tlivjti,  jr\i)v  npoKKiovi  '  koI  Ilf»OK\tT}s 
/^ptoi. 

For  t^c  Latin  imitation  by  Stepliamis,  «ea 
THeod.  Bextt  Potmaia,  ittm  ex  Gmrgw  Ruchmt- 


CM«,  alii*qtu  variis  insignibus  pottis  excerpta  tor- 
mina. Excudebat  H.  Stephanus,  ex  tujut  etiatn 
Epigramtnalis  Gratis  et  Latinis  aliquot  eaieris 
adjecta  sunt,  1569,  p.  217. 

The  parody  by  Porsoo  is  f^reta  is  4  /^^f* 
AecouMt  qfth*  Uut  Mr  Riclu/trd  f'orspn,  M.  4., 
p.  14.  Loudou,  1S08.  The  oifgiiial  Grade. 
with  Porsou'e  imitation,  is  al^ugivc^  in  Dr. 
Wfillesley's  Aatkologia  Polygloita,  p.  438  — KP. 

-  Sec  BuoiMitan,  Fmneiseaays.  1.  i(H  fioi^ 
Poemata,  p.  86,  ed.  1569.  Rabelais,  L.  iii.  dk 
li.-fil^ 


Lect.  XX.  LOGIC.  281 

Sumption  —  The  monks,  one  and  all,  are  good-for-nothing  varlets,  excepting  POer; 
Subsumption  —  But  Peter  is  amonk. 

Now,  what  is,  what  must  be,  ufldergtood  to  complete  tiie  sense  ? 
—  Why,  the  conclusion,^ 

Therefore,  Peter  is  a  yoodfor-nothing  varlet  like  the  rest. 

There  is  recorded,  likewise,  a  dying  deliverance  of  the  philosopher 
Hegel,  the  wit  of  whicli  depends  upon  the  same  ambiguous  reason- 
ing. "  Of  all  my  disciples,"  he  said,  "  one  only  understands  my 
philosophy;  and  he  does  not."^  But  we  may  take  this  for  an  ad- 
mission by  the  philosopher  himself,  that  the  doctrine  of  the  Absolute 
transcends  human  comprehension. 

What  has  now  been  said,  may  suffice  to  show,  not  only  that  we 
may  have  enthymemes  with  any  of  the  three  propositions  under- 
stood, but  that  the  distinction  itself  of  the  enthymeme,  as  a  species 
of  syllogism,  is  inept. 

I  now  go  on  to  the.  Third  Division  of  Syllogisms,  under  the  head 
of  their  External  or  Accidental  form,  —  I  mean 

.     >  ogMins,    e-       ^^^    division    of   syllogisms    into   Regular   and 

gular  and  Irregular.  .'        o  o 

Irregular,  —  a  distinction  determined  by  the  or- 
dinary or  extraordinary  arrangement  of  their  constituent  parts.  I 
commence  this  subject  with  the  following  paragraph. 

*|[  LXXIII.     A  syllogism  is  Irregular  by  relation,  —  1°.  To 
the  transposed  order  of  its  Propositions;  2°. 

Par.  LXXIII.  Kinds  „         ,  ,  r-   •        rr. 

of   Irregular   syiio-       To  the  transposcd  Order  of  its  lerms;  and 
eisnis-  3°.  To   the   transposed   order    of  both   its 

Propositions  and  Terms.     Of  these  in  their  order. 

1".  A  syllogism  in  extension  is  Regular,  in  the  order  of  its 
Propositions,  when  the  subsumption  follows  the  sumption,  and 
the  conclusion  follows  the  subsumption.  In  this  respect  (dis- 
counting the  difference  of  the  quantities  of  depth  and  breadth), 
it,  therefore,  admits  of  a  fivefold  irregularity  under  three  heads, 
—  for  either,  1°.  The  two  premises  may  be  transposed;  m\  2°. 
The  conclusion  may  precede  the  premises,  and  here,  either  the 
sumption  or  the  subsumption  may  stand  first;  or,  3"*.  The  con- 
clusion may  be  placed  between  the  premises,  and  here  either 
the  sumption  or  the  subsumption  may  stand  first.  Thus,  repre- 
senting the  sumption,  subsumption,  ^ud  conclusion  by  the  letters 
A,  B,  C,  we  have,  besides  the  regular  order,  1°.  B,  A,  C,  —  2°.  C, 

J  See  Discussions,  p.  788.  —  Ed. 

36 


•282 


LOGIC. 


Lkct.  XX. 


A,  B,— 3°.  C,  B,  A,— 4°.  A,  C,  B,— 5».  B,  C,  A.  (This  doctaine 
of  the  logicians  is,  however,  one-sided  and  (erroneous.) 

2°.  A  syllogism  is  Regular  or  Irregular,  in  respect  to  the  or- 
der of  its  Terms,  according  to  the  place  which  the  middle  term 
holds  in  the  premises.  It  is  regular,  in  Comprehensive  Quan- 
tity, when  the  middle  term  is  the  predicate  of  the  sumption  and 
the  subject  of  the  subsumption; — in  Extensive  Quantity,  when 
the  middle  term  is  the  subject  of  the  sumption  and  the  predi- 
cate of  the  subsumption.  From  the  regular  order  of  the  terms 
there  are  three  possible  deviations,  in  either  quantity.  For  the 
middle  term  may  occur,  1°.  Twice  as  predicate ;  2°.  Twice  as 
^abject ;  and,  3°.  In  Comprehensive  Quantity,  it  may  in  the 
sumption  be  subject,  and  in  the  subsumption  predicate';  in  Ex- 
tensive Quantity,  it  may  in  the  sumption  be  predicate,  and  in 
the  subsumption  subject.  Taking  th«j  letter  M  to  designate  tho 
middle  term,  and  the  letters  S  and  P  to  designate  the  subject 
and  predicate  of  the  conclusion,  the  following  scheme  will  rep- 
resent all  the  possible  positions  of  the  middle  term,  both  in  its 
regular  and  its  irregular  arrangement.  The  Regular  constitutes 
tho  First  Figure  ;  the  Irregular  order  the  other  Three.* 

A. —  In  Comprehension. 


I. 

II. 

III. 

IV. 

S  is  M. 

S  is  M. 

M  is  S. 

M  isS. 

M  IS  P. 

P  tsM. 

M  is  P. 

Pis  M. 

S  is  P. 

S  IS  P. 

S  is  P. 

S  isP. 

B.  —  ly  Extension. 

I. 

II. 

III. 

rr. 

M  IS  P. 

P  isM. 

M  is  P. 

P«M. 

S  isM. 

S  if  M 

M  is  S. 

M  is  S. 

S  w  P. 

S  t»  P 

S  is  P. 

S  is  P. 

These  relative  positives  of  the  middle  term  in  the  premises, 
constitute,  I  repeat,  what  are  called  the  ^our  Syllogistic  Fig- 
ures {(TXTjiuvra,  Jigune)  ;  and  these  positions  I  have  comprised  in 
the  two  following  mnemonic  lines. 

In  Comprehension. 
Pns  sub  ;  turn  pne  prcs ;  turn  sub  sub  ;  deniqufi  sub  pros. 

In  Extension. 
Sub  prcE :  turn  prce  prce ;  turn  sub  sub ;  denique  pra  sub.* 


1  Cf.  Krug,  Logik,  4 104.  —  Ed. 

2  This  formula  for  Extension  is  taken  from 


Purchot,   Inst.  Phil.,  Logiea,  t.  I.  o.  iil.  p.  188 

Tl'.e  other  line  is  the  Author's  own.  —  Ed. 


Lect.  XX.  LOGIC.  S83 

Of  these  two  kinds  of  irregularity  in  the  external  form  of  syllo- 
gisms, the   former  —  that   of   propositions  —  is 
p  caion.  of  far  less  importance  than  the  latter  —  that  of 

Irregularity  in  the  t- 

external  form  of  syi-  terms;  and  logicians  have  even  thrown  it  alto- 
logism,  arising  from  gether  out  of  account,  in  their  consideration  of 
transposition   of  the       gyllogistic  Figure.     They  are,  however,  equally 

Propositions.  ''       °  .  .  "^  ,  . 

wrong  m  passmg  over  the  irregular  consecution 
of  the  propositions  of  a  syllogism,  as  a  matter  of  absolutely  no  mo- 
ment;   and  in  attributing  an   exaggerated  im- 
Thatasy  ogismcan       portance  to  every  variety  in  the  arrangement 

be   perspicuously   ex-  „  .  m 

pressed  by  any  of  the  ^f  its  terms.  They  ought  at  least  to  have  made 
live  irregular  consecu-  the  studcnt  of  Logic  aware,  that  a  syllogism  can 
tions  of  Its  Proposi-  jjg  perspicuously  expressed  not  only  by  the  nor- 
mal, but  by  any  of  the  five  consecutions  of  its 
propositions  which  deviate  from  the  regular  order.  For  example, 
take  the  following  syllogism : 

AU  virtue  is  praiseworthy  ; 
But  sobriety  is  a  virtue; 
Therefore,  sobriety  is  praiseworthy. 

This  is  the  regular  succession  of  sumption,  subsumption,  and  con- 
clusion, in  a  syllogism  of  extension ;  and  as  all  that  can  be  said,  on 
the  present  question,  of  the  one  quantity,  is  applicable,  mutatis 
mutandis,  to  the  other,  it  will  be  needless  to  show  articulately  that 
a  syllogism  in  comprehension  is  equally  susceptible  of  a  transposi- 
tion of  its  propositions  as  a  syllogism  in  extension.  Keeping  the 
same  quantity,  to  wit,  extension,  let  us  first  reverse  the  premises- 
leaving  the  conclusion  in  the  last  place  (B,  A,  C). 

Sobriety  is  a  virtue ; 

But  all  virtue  is  praiseworthy ; 

Therefore,  sobriety  is  praiseworthy. 

This,  it  will  be  allowed,  is  sufficiently  perspicuous.  Let  us  now 
enounce  the  conclusion  before  the  premises ;  and,  under  this  head 
let  the  premises  be  first  taken  in  their  natural  order  (C,  A,  B). 

Sobriety  is  praiseworthy  ; 
For  all  virtue  is  praiseworthy  ; 
And  sobriety  is  a  virtue. 

Now  let  the  premises  be  transposed  (C,  B,  A). 


^  LOGIC.  Ljxt.  x:^ 

Sobriety  is  praiseworthy  / 
For  sobriety  is  p.  virtue  ; 
4.nd  all  virtue  is  prvjsewoHhj/. 

The  regressive  reasoning  in  botti  these  pases  is  not  less  manifest 
than  the  progressive  reasoning  of  the  regular  order. 

In  the  last  place,  lot  us  inteqwlate  the  conclusion  betweea  th« 
premises  in  their  normal  consecation  (A,  C,  B). 

JLH  virtue  is  prcdsevcor^ ; 
Therefore,  sobriety  is  praittworthy  ; 
For  sobriety  is  a  virtue. 

Secondly,  between  the  premises  in  their  reversed  ot4er  (B,  C,  A). 

Sobriety  is  a  virtue; 

Therefore,  sobriety  is  praiseworthy ; 

For  aU  virtue  is  praiseworthyA 

In  these  two  cases  the  reasoning  is  not  obscure,  though  perhaps 
the  expression  be  inelegant;  for  the  judgment  placed  after  the  con- 
clusion had  probably  been  already  supplied  in  thought  on  the  enun- 
ciation of  the  conclusion,  and,  therefore,  when  subsequently  ex- 
pressed, it  Is  felt  as  superfluous.  But  this  is  a  circumstance  of  no 
logical  importance. 

It  is  thus  manifest,  that,  though  worthy  of  notice  in  a  system  of 
Logic,  the  transposition  of  the  propositions  of  a  syllogism  affords 
no  modifications  of  form  yielding  more  than  a  superficial  character. 
Logicians,  therefore,  were  not  wrong  in  excluding  the  order  of  the 
propositions  as  a  ground  on  which  to  constitute  a  difference  of  syl- 
logistic form:  but  we  shall  see  that  they  have  not  been  consistent, 
or  not  sufficiently  sharp-sighted,  in  this  exclusion ;  for  several  of 
their  recognized  varieties  of  form  —  several  of  the  moods  of  syllo- 
gistic figure  —  consist  in  nothing  but  a  reversal  of  the  premises. 

In  reality,  however,  there  is  no  irregular  order  of  the  syllogistic 

propositions,  except  in  the  single  case  where  the 

True  doctrine  of  con-       conclusion  is  placed  between  the  premises.     For 

'^k.^«m  either sy«.       *  syUogism  may  be  either  called  Sf/niAetic,  iu 

tnetio  or  Anal)  tic.  casc  thc  premises  come  first,  and  the  conclusion 

is  last  —  (the  case  alone  contemplated  by  thc 

logicians) ;  or  it  may  be  called  Analtftic^  the  proposition  styled  the 

conclusion  preceding,  the  proposiiious  called  the  premises  following, 

as  its  reasons — (a  case  not  contemplated  by  the  logicians).     The 

1  Cr.  Krag,  I^f  lA;, )  104,  Anmerk,  i.  —  Eo. 


Lect.  XX.  .LOGIC.  285 

Analytic  and  Synthetic  syllogisms  ttiay  again  be  each  considered 
as  in  the  quantity  of  Extension,  or  as  in  the  quantity  of  Compre- 
hension ;  in  which  cases,  we  shall  have  a  counter-order  of  the  prem- 
ises, but  of  which  orders,  as  indeed  of  such  quantities,  one  alone 
has  been  considered  by  the  logicians. 

I  now,  therefore,  go  on  to  the  second  and  more  important  ground 
of  regularity  and  irregularity  —  the  natural  and 

The   natural    and       transposed  order  of  the  Syllogistic  Terms.    The 

irsTiTogltrxerms"/      ^^^ms  deteiTuined  by  the^  different  position  of 

the  middle  term  by  relation  to  the  major  and 

minor  terms  in  the  premises  of  a  syllogism  are  called  Figures  ((txt 

uara,  fiqi(rm)  —  a  name  given  to  them  by  Aris- 
Figures  of  Syllogism.        ^  ,*^  ^^  _  /,  ,  v       ^     .    •  .,  ,      - 

totle.^     Of  these  the  nrst  is,  on  the  prevalent 
doctrine,  not  properly  a  figure  at  all,  if  by  figure  be  meant  in  Logic, 
as  in  Grammar  and  Rhetoric,  a  deviation  from  the  natural  and  reg- 
ular form  of  expression.     Of  these  figures  the 
h*ib^A**t  ti"*       ^^^*  three  were  distinguished  by  Aristotle,  who 
developed  their  rules  with  a  tedious  minuteness 
sometimes  obscure,  and  not  always  in  the  best  order,  but  altogether 
with  an  acuteness  which,  if  ever  equalled,  has  certainly  never  been 
surpassed.      The  fourth,  which  Whately  —  at 
Fourth  Figareattrib-      jg^g^  -^^  ^^^  former  editions  of  his  Elements  — 

uted  to  Galen,  but  on  ,        ,  /-v    /»      i    i       •    • 

slender  authority.  ^°^  Other  recent  Oxford  logicians  seem  to  sup- 

pose to  be,  like  the  others,  of  Aristotelic  origin, 
—  we  owe  perhaps  to  the  ingenuity  of  Galen.  I  say  perhaps,  for 
though  in  logical  treatises  attributed  without  hesitation  to  the  great 
physician,  as  if  a  doctrine  to  be  found  in  his  works,  this  is  altogether 
erroneous.  There  is,  I  am  certain,  no  mention  of  the  fourth  figure 
in  any  writing  of  Galen  now  extant,  and  no  mention  of  Galen's 
addition  of  that  figure  by  any  Greek  or  Lit'cin  authority  of  an  age 
approximating  to  his  own.  The  first  notice  of  this  Galenic  Figure 
is  by  the  Spanish  Arabian,  AveiToes  of  Cordova, 

First  ascribed  to  Ga-         •      i  •  x  ^i.       ^o  a       a     ^ 

...  in  his  commentary  on  the  Orqanon.'    Averroes 

Jen  by  Averroes.  _  *'   ,  "^ 

flourished  above  a  thousand  years  posterior  to 
Galen;  and  from  his  rejwrt  alone  (as  I  have  also  ascertained)  does 
the  ])revnlent  opinion  take  its  rise,  that  we  owe  to  Galen  this  ampli- 
fication (or  corruption,  as  it  may  be)  of  the  Aristotelic  doctrines  of 
logical  figure.  There  has  been  lately  published  from  manuscript, 
by  Didot  of  Paris,  a  new  logical  treatise  of  Galen.^  In  this  work, 
in  which  the  syllogistic  figures  are  detailed,  there  is  no  mention  of 

1  Anal.  Prior  ,  1.  4.  —  Ed.    [Of.  Pacing,  Com-  "  YaXiivov   EiVaycoT^    AtoAerrorii  —  i* 
mem.,  pp.  118,  122.]                                                    Uaoiaitf  au/JtS'  (1844)  —  Ed. 

2  Prior  Analytics,  [B.  i.  oh   8.  —  Ed.] 


286  LOGIC.  Lkct.  XX 

a  fourth  figure.  Galen,  therefore,  as  far  as  we  know,  affords  no 
exception  to  the  other  authors  upon  Logic.  In  these  circumstances, 
it  is  needless  to  observe  how  slender  isthe  testimony  in  favor  of  the 
report ;  and  this  is  one  of  many  others  in  which  an  idle  story,  once 
told  and  retailed,  obtains  universal  credit  as  an  established  fact,  in 
consequence  of  the  prevalent  ignorance  of  the  futility  of  its  foun- 
dation. Of  the  legitimacy  of  the  Fourth  Figure  I  shall  speak,  after 
having  shown  you  the  nature  of  its  reasoning. 

Before  proceeding,  further  in  the  considera- 
compiex  modifica-       tj^jj  ^f  ^^jg  Figure  of  Syllogism,  it  is,  however, 
tlon  of  the  Figure  of  ♦       ^  ♦  i  ;i-c     *•  * 

Syiioirism.  necessary  to  state  a  complex    modmcation    to 

which  it  is  subject,  and  which  is  contained  in 
the  following  paragraph. 

%  LXXrV.  The  Figure  of  Syllogism  is  modified  by  the 
Quantity  and  Quality  of  the  propositions 
sutioicoo^  ^'"*^  which  constitute  the  reasoning.  As  the 
combination  of  Quantity  and  Quality  af- 
fords four  kinds  of  propositions  —  Universal  Affirmative  (A), 
Universal  Negative  (E),  Particular  Affirmative  (I),  Particular 
Negative  (O) ;  and  as  there  are  three  propositions  in  each  syl- 
logism, there  are  consequently  in  all  sixty-four  arrangements 
possible  of  three  propositions,  differing  in  quantity  and  quality ; 
—  arrangements  which  constitute  what  are  called  the  Syllogis- 
tic Moods  (rpoTToi,  modi).  I  may  interpolate  the  observation : 
The  Greek  logicians  after  Aristotle,  looking  merely  to  the  two 
premises  in  combination,  called  these  Syzygies  (irwfvyuu,  juga- 
tiones,  conjugationes^  combinationes).  Aristotle  himself  never 
uses  TpoTTos  for  either  mood  or  modality  specially ;  nor  does  he 
use  (Tvi,vyla  in  any  definite  sense.  His  only  word  for  mood  is 
the  vague  expression  syllogism. 

The  greater  number  of  these  moods  are,  however,  incompe- 
tent, as  contradictory  of  the  general  rules  of  syllogism ;  and 
there  are  in  all  only  eleven  which  can  possibly  enter  a  legiti- 
mate syllogism.  These  eleven  moods  again  are,  for  the  same 
reason,  not  all  admissible  in  every  figure,  but  six  only  in  each, 
that  is,  in  all  twenty-four ;  and  again  of  these  twenty-four,  five 
are  useless,  and,  therefore,  usually  neglected,  as  having  a  par- 
ticular conclusion  where  a  universal  is  competent.  The  nine- 
teen useful  moods  admitted  by  logicians  may,  however,  by  the 
quantification  of  the  predicate,  be  still  further  simplified,  by 
superseding  the  significance  of  Figure. 


Lect.  XX.  LOGIC.  287 

In  entering  on  the  consideration  of  the  various  Moods  of  the 
Sylloffistic  Figures,  it  is  necessary  that  you  re- 
call  to  memory  the  three  laws  I  gave  you  ot  the 
Categorical  Syllogism,  and  in  particular  the  two  clauses  of  the  sec- 
ond law, —  That  the  sumption  must  be  definite  (general  or  singu- 
lar), and  the  subsumption  afiii-mative,  —  clauses  which  are  more 
vaguely  expressed  by  the  two  laws  of  the  logicians  —  that  no  con- 
clusion can  be  drawn  from  two  particular  premises  —  and  that  no 
conclusion  can  be  drawn  from  two  negative  premises.  This  being 
premised,  you  recollect  that  the  four  combinations  of  Quantity  and 
Quality,  competent  to  a  proposition,  were  designated  by  the  four 
letters,  A,  E,  I,  O,  —  A  denoting  a  universal  affirmative; — E  a 
universal  negative;  —  I,  a  particular  affirmative;  —  O,  a  particular 
negative. 

AsseritA;  negatE;  veram  universallter  amb»: 
Assent  I;  negatO;  sed  particulariter  ambo.l 

A,  it  afflrms  of  this,  these,  all ; 

As  E  denies  of  any : 
I,  it  affirms,  as  O  denies, 

Of  some,  or  few,  or  many. 
Thus  A  affirms  what  E  denies. 

And  definitely  either; 
Thus  I  affirms  what  O  denies. 

But  definitely  neither.* 

Now,   as  each  syllogism  has  two  premises, 

The  possib  e  com  i-       ^here  are,  consequently,  sixte'eu  different  corn- 
nations  of  premises.  -^  . 

binations  possible  of  premises  differing  in  quan- 
tity and  quality  —  viz. : 


A  A. 

2)EA. 

3)  I  A. 

4)0  A. 

AE. 

EE. 

IE. 

OE. 

AL 

EI. 

II. 

OL 

AO. 

EO. 

10. 

0  0. 

Now  the  question  ai'ises  —  are  all  of  these  sixteen  possible  com- 
binations of  different  premises  valid  towards  a  legitimate  conclu- 
sion?    In  answer  to  this,  it  is  evident  that  a  considerable  number 

1  See  above,  p.  180.  —  Ed.  —  Wilson,  RuU  of  Reason,  p.  27  a,  1551. 

2  [The  following  are  previous  English  met-  ..  ^  ,^y^  ^^^  ^  ^^^.^^,  ^^^  j^^^,,^ 
rical  versions  of  these  lines :  I  „y,  ^^^  q  denies,  both  partially." 

"  A  doeth  afflrme,  E  doeth  denigh,  which  are  bothe  .  _     ..        . 

universall:  —  Wallis,  Institutio  Logiae,  16S6,  L.  U.  C.  4,  p 

1  doeth  afflrme,  O  doeth  denigli,  which  wc  particn-      105.] 
Ur  call." 


LOGIC. 


Lkct.  XX. 


How  many  of  these 
are  syllogistically  val- 
M. 


of  these  ai*e  at  once  invalidated  by  the  first  claase  of  the  second 
law  of  the  categorical  syllogism,  in  so  far  as 
recognized  by  logicians,  by  which  all  moods  with 
two  particular  premises  are  excluded,  as  in  these 
there  is  no  general  rule.  Of  this  class  are  the 
four  moods,  I  I,  I  O,  O  I,  and  O  O.  And  the  second  clause  of 
the  same  law,  in  so  far  as  recognized  by  logicians,  invalidates  the 
moods  of  two  negative  premises,  as  in  these  there  is  no  subordina- 
tion. Of  this  class  are  the  four  moods  E  E,  E  O,  O  E,  and  O  O. 
Finally,  by  the  two  clauses  of  the  second  rule  in  conjunction,  the 
mood  I  E  is  said  to  be  excluded,  because  the  particuhir  sumption 
contains  no  general  rule,  and  the  negative  snbsumption  no  subordi- 
nation. (This,  I  think,  is  incorrect.)  These  exclusions  have  been 
admitted  to  be  valid  for  every  Figure;  there,  consequently,  remain 
(say  the  logicians)  as  the  possible  modes  of  any  legitimate  syllogism, 
the  eight  following  —  A  A,  A  E,  A  I,  A  O,  E  A,  E  I,  I  A,  O  A  ; ' 
but  some  of  these,  as  apparently  contradictory  of  the  second  rule  in 
its  more  definite  assertions,  —  that  the  suUiption  must  be  general 
and  the  subsuniption  affirmative,  —  I  shall,  after  stating  to  you  the 
common  doctrine  of  the  logicians,  show  to  be  really  no  exceptions. 
But  whether  each  of  the  moods,  though  a  jyriori  possible,  affords 
a  proper  syllogism  in  all  the  figures  —  this  de- 
pends on  the  definite  relations  of  the  middle 
term  to  the  two  others  in  the  several  figures. 
These,  therefore,  require  a  closer  investigation. 
I  shall  consider  them,  with  the  logicians,  princi- 
j)ally  in  the  quantity  of  extension,  but,  mutatie  mutandis^  all  that 
is  true  in  the  one  quantity  is  equally  true  in  the  other. 

Now  if,  in  the  first  figure,  we  consider  these  eight  moods  with 
reference  to  the  general  rules,  we  shall  find  that 
all  do  Aot  in  this  figure  afford  correct  syllogisms; 
but  only  those  which  are  constructed  in  conformity  to  the  follow- 
ing particular  rules,  which  are,  however,  in  this  figure,  identical  with 
those  we  have  already  given  as  general  laws  of  every  perfect  and 
regular  categorical  syllogism. 
The  symbol  of  the  First  Figure  is, — 


Whether  each  mood 
that  is  a  priori  possible 
affords  a  proper  syllo- 
gism in  ail  the  figures. 


First  Figure. 


S  M    I    for  Extension ;      ^  p'  |  for  Comprehension. 

The  first  rule  is,  —  "  The  sumption  must  be  universal.    Were  U 
particular,  and,  consequently,  the  subsumption  universal,  as; 


1  Cf.  Baobmaan,  Litgik,  ( 129.  —  Ed. 


Lect.  XX.  LOGIC.  289 

Some  M  are  P; 
ButaUSareH; 

we  could  not  know  whether  S  were  precisely  the  part  of  M  which 
lies  in  P,  and  it  might  be  altogether  out  of  P.  In  that  case,  a  uni 
versal  negative  conclusion  would  be  the  correct ;  but  this  cannot 
be  drawn,  as  there  is  no  negative  premise,  and  though  accident- 
ally perhaps  true,  still  it  is  not  a  necessary  consequence  of  the 
premises."  ^ 

"  The  second  rule  is,  —  The  subsumption  must  be  affirmative. 
Were  it  negative,  and  consequently  the  sumption  affirmative,  in 
that  case  S  would  be  wholly  excluded  from  the  sphere  of  M ;  and, 
consequently,  the  general  rule  under  which  M  stands  would  not  be 
applicable  to  S.    Thus : 

AUMareF; 

NoSisTA; 

No  S  i»  P. 
AH  colors  are  physical  pJuenomena  ; 
No  sound  is  a  color; 
Therefore,  no  sound  is  a  physical  phcenomenon. 

"Here  the  negative  conclusion  is  filse,  but  the  affirmative,  whioh- 
would  be  true,  —  all  sounds  are  physical  phcenomena^  —  cannot  be 
inferred  from  the  premises,  and,  therefore,  no  inference  is  competent 
at  all."  2 

Thus,  in  this  figure,  of  the  eight  moods  generally  admissible,  I  A 

and  O  A  are  excluded  by  the  first ;  A  E  and 

LegiUmate  moods  of      A  O  by  the  second  rule.     There  remain,  there- 

^'"xhlrsynibois.  ^•^'*^'  ^^^Y  ^^^^  legitimate  moods,  A  A,  E  A,, 

A  T,  and  E  I.     The  lower  Greek  logicians  de- 
noted them  by  the  terms,  — 

rpd/ifiaTUf  ''Eypa^f,  rpa(pi5i,  T€xytK6s ; ' 

the  Latin  schoolmen  by  the  terms  — 

Barbara,  Celareni,  DarU,  and  Ferio. 

1  Bachmann,  Logik,   t  130,  p.  203.  —  Ed.  2  Bachmann,  as  abore.  — Ed.    [Cf.  Dero- 

[So   Hollmann,  Phil.   Rationalis,  qutz   Logica  don,  Logica  Restiluta,'P.  ir.  p.  618.    Ulricb,  at 

vulgo  dicitur,  §  461,  Gottingse,  1V46.    Lovani-  above.     Lovanienses,  as  above.     Hollmann, 

enses,    Commentaria   in  hag.   Porphyrii  tt  in  Logica,  §  462.] 
ornnes  Libros  Arist.  de  DiaUctiea,  Anal.  Prior,  L. 

i.  p.  215,  Lovanii,  1547.    Ulrich,  Instit.  Log.  3  For  an    account  of  these   mnemonic^. 

et  Mel.,  f  191,  lense,  1785.     Fonseca,  Instit.  see  i>ucuMtoiu,  p.  671,  second  edition.  —  Ed. 
Dial.,  L.  vi.  c.  21,  p.  363.] 

37 


B90 


LOGIC. 


Lect.  XX. 


In  the  Latin  symbols,  which  are  far  more  ingenious  and  complete, 
and  in  regard  to  the  history  of  which  I  shall  say  something  in  the 
sequel,  the  vowels  are  alone  at  present  to  be  considered,  and  of 
these  the  first  expresses  the  sumption,  the  second  the  subsumption, 
and  the  third  the  conclusion.  The  correctness  of  these  is  shown 
by  the  following  examples  and  delineations. 

"  The  first  mood  of  this  figure : 


I.  Barbara. 


I.  Basbaba. 

AUiiartP; 
AUSareU; 
Thenfore,  afl  S  ar«  P. 

AU  that  »  composite  is  dismluble  ; 
AU  material  things  are  composite ; 
Ther^ore,  all  material  things  are  ditaobttiU. 


n.  Cclarant 


m.  DwlL 


W) 


IL  Cblakbht. 

AbMwP; 
AnSareJA; 
There/ore,  no  8  is  T. 

No  finite  being  is  exempt  from  emr; 

AU  men  are  finite  beings ; 

TTherrfore,  no  man  is  exenq>t  from  emr. 


m.  Darii. 

AUVLarePi 
Some  SoreM; 
Thertfore,  some  S  are  P. 

AU  virtues  are  laudMe; 
Some  habits  are  virtues ; 
Ther^ore,  some  habits  are  laudable. 


"This  diagram  makes  it  manifest  to  the  eye  why  the  conclusion 
can  only  be  particular.  As  only  a  part  of  the  sphere  S  lies  in  the 
gphero  M,  this  part  must  lie  in  the  sphere  P,  as  the  whole  of  M  lies 
therein ;  but  it  is  of  this  part  only  that  anything  can  be  affirmed  in 
the  conclusion.  The  other  part  of  S  can  cither  lie  wholly  out  of 
P,  or  partly  in  P  but  out  of  M;  but  as  the  premises  affirm  nothing 
of  this  part,  the  conclusion  cannot,  therefore,  include  \t. 


Lect.  XX. 
IV.  Feria 


LOGIC. 

IV.  Febio. 

NoUisF; 

Some  S  are  M ;  • 

Therefore,  some  S  are  not  P. 

No  virtue  is  reprehensible ; 

Some  habits  are  virtues  ; 

Thartfore,  some  habits  are  tiot  reprehensible. 


291 


0 


"  The  conclusion  in  this  case  can  only  be  particular,  as  only  a  part 
of  S  is  placed  in  the  sphere  of  M.  The  other  part  of  S  may  lie  out 
of  P  or  in  P,     But  of  this  the  premises  determine  nothing."  ^ 

Second  Figure.  The  symbol  of  the  Second  Figure  is  — 


PM, 

SM, 


for  Extension ; 


SM, 
PM, 


for  Comprehension. 


Itsmles. 


♦*  This  figure  is  governed  by  the  two  following 
rules.    Of  these  the  first  is  —  One  premise  must 
be  negative.*    For  were  there  two  affirmative  premises,  as : 


AUFareM; 
AUSareil; 

All  metals  are  minerals ; 
AU  pebbles  are  minerals  ; 


the  conclusion  would  be  —  All  pebbles  are  metals^  which  would  be 
false. 

"  The  second  rule  is :  —  The  sumption  must  be  universal.^     Were 


1  Bachmann,  Xofiik,  p.  204— 206.  —  Ed.  Scotns.]     [Quetstionts  in  Anal.  Prior.,  l„\.i^ 

2  [See  Derodon,  Lo^ka  Restituta,  P.  ir.  p.  20,  f.  268.  —  Ed.] 

637.    HoUmann,  Logiea,  §;  4G3,  464.    Lorani-  ,3  See  Uollmann,  and  Lovanienses,  asciteti 

enses,  Com.  in  Arist.  Anai.  Prior.,  h.  i.  p.  21B.  abov«.  —  £d. 


LOGIC. 


Lkct.  XX. 


the  sumption  particular,  the  snl^sumption  hehooved  to  be  uniyersal ; 
for  otherwise  no  conclusion  would  be  possible.     But  in  that  case  the 
gumption,  whether  affirmative  or  negative,  would  afibrd  only  aa 
absurd  conclusion.^ 
« If  affirmative,  as  — 

Some  P  are  M ; 

AbSwM; 

Therefore,  some  S  are  not  P. 

Some  ammcda  lay  eggs,  i.  e.  are  egg^ying  tJang$j 
No  horse  lays  eggs,  i.  e.  is  any  egg-laying  thing; 
Tlierefore,  some  horses  are  not  aniwkoU. 

"If  negative,  as  — 

Some  P  ore  tu3<  M; 

AMSare'U.; 

Ther^ore,  some  S  are  not  P. 

Some  minerals  are  not  precious  stones; 
An  topazes  are  precious  stones ; 
Ther^ore,  some  topazes  are  not  minerals  ; 

in  both  cases  the  conclusion  is  absurd. 

"There  thus  remain,"  say  the  logicians,  "only  the  moods  Cesar6f 
Camestresy  Festino^  JBaroco. 


I.  Cetare. 


I.  Cbsabb. 

AbPitH; 

JOS  ore  M; 
Therefore,  no  S  tf  P. 

Nothing  material  has  free  wHt; 
AH  spirits  have  free  will; 
Ther^ore,  no  spirit  is  materiaL 


n.  Camestica. 


H.  Camestrbs. 

AHFareM; 
NoSu  M; 
Uterrfore,  no  8  is  P. 

An  colors  are  visible  ; 
No  sound  is  visible  ; 
Thertfore,  no  sound  is  a  odor. 


I  [C£  Fonaeoa,  hutit.  DimL,  L.  tL  «.  »,  p.  9tS.} 


Lect.  XX- 


L06IC. 


29$ 


III.  Feetino. 

JVoPisM; 

Some  S  are  M; 

Therefore,  some  S  are  fu*  P. 


in.  Festiko. 


No  vice  is  praiseworthy; 
Some  actions  are  praiseworthy  ; 
Therefore,  some  actions  are  not  vten. 


"  The  diagram  here  is  alternative,  for  as  the  conclusion  can  only 
comprise  a  part  of  S,  as  it  is  only  the  consequence  of  a  partial  sub- 
ordination of  S  to  M,  the  other  parts  of  S  which  are  out  of  M  may 
either  lie  within  or  without  P.  —  The  conclusion  can,  therefore,  only 
be  particular. 


IV.  Baroco. 


rv.  baboco. 


AUTareyi; 
Some  S  are  not  M ; 
Therefore,  some  S  are  not  P. 

AU  birds  are  oviparous ; 

Some  animals  are  not  oviparous ; 

Therefore,  some  animals  are  not  birds."  * 


1  Bacbmann,  Logik,  as  above.  —  Bd. 


LECTURE      XXI. 

STOIOHEIOLOGY. 

SECTION    II.  — OF    THE    PRODUCTS  OF  THOUGHT 

ni,  — DOCTRINE   OF  REASONINGS. 

SYLLOGISMS.  — THEIR  DIVISIONS  ACCORDING  TO  EXTERNAL 

iX)RM. 

FIGURE  — THIRD  AND  FOURTH. 


In  our  last  Lecture,  after  terminating  the  general  consideration 
of  the  nature  of  Figure  and  Mood  in  Categorical 
Syllogisms,  we  were  engaged  in  a  rapid  survey 
of  the  nineteen  legitimate  and  useful  moods  belonging  to  the  four 
figures,  according  to  the  received  doctrine  of  logicians  (conse- 
quently, exclusively  in  Extension)  ;  and  I  had  displayed  to  you 
the  'laws  and  moods  of  the  First  and  Second  B'igures.  Before,  there- 
fore, proceeding  to  any  criticism  of  this  doctrine,  it  behooves  us  to 
terminate  the  view  of  the  two  remaining  figures. 

To  each  of  the  first  two  figures,  logicians  at- 
tribute four  moods ;  to  the  third  they  concede 
six ;  and  to  the  fourth  five.    The  scheme  of  the  Third  Figure,  in 

Extension,  is  — 

MP, 
M  S. 

This  figure  (always  in  extension)  is  governed  by  the  two  follow- 
ing   laws  :  —  the   first   is,   "  The    subsumption 
must  be  affirmative.^    Were  the  minor  premise  a 
negative,  as  in  the  syllogism,  — 


Third  rigure. 


It«  rules. 


AUJAareF; 
iVoMtsS; 


AU  fiddles  are  musical  instruments ; 
But  no  fiddle  is  a  flute; 


I  [Sm  Aristotle,  Anal.  Prior.,  i.  6,  (f  8|  16-    UoIImann,  Logiea,  f  466.    LoTanienaes,  Ik  Am. 
PHor.L.  i.  P.220.J 


Lkct.  XXI.  LOGIC.  295 

here  the  conclusion  would  be  ridiculous,  —  Therefore^  no  S  is  P,  — 
Therefore^  no  flute  is  a  musical  instrument.  For  M  and  S  can  both 
exclude  each  other,  and  yet  both  lie  within  the  sphere  of  P. 

"  The  second  law  is,  —  The  conclusion  must  be  particular,  and 
particular  although  both  premises  are  universal.*  This  may  be 
shown  both  in  affirmative  and  negative  syllogisms.  In  the  case  of 
affirmative  syllogisms,  as: 

^HMarcP; 
But  aU 'Hare  S; 

here,  you  will  observe,  M  lies  in  two  different  spheres  —  P  and  S, 
and  these  must  in  the  conclusion  be  connected  in  a  relation  of  sub- 
ordination. But  S  and  P  may  be  disparate  notions,^  and,  con- 
sequently, not  to  be  so  connected ;  an  absurd  conclusion  would, 
therefore,  be  the  result.     For  example,  — 

AU  birds  are  animals  with  feathers ; 

But  an  birds  are  animals  with  a  heart ; 

Therefore,  aU  animals  with  a  heart  are  animals  with  feathers. 

"  Again,"  say  the  logicians,  "  in  regard  to  negatives :  —  In  these 
only  the  sumption  can  be  negative,  as  the  subsumption  (by  the  first 
rule)  must  be  affirmative.     Thus : 

NoHisP;  No  silver  is  iron :  ' 

or, 
But  all  M  are  S ;  But  all  silver  is  a  mineral. 

"  Here  the  conclusion  —  No  S  is  P,  —  iVb  mineral  is  iron,  would 
be  false, 

"  Testing  the  eight  possible  moods  in  Extension  by  these  special 
rules,  there  remain  for  this  figure,  six,  which  by  the  Latin  logicians 
have  been  named,  Darapti,  Felapton,  Disamis,  Datisi^  Bocardo^ 
Ferison.     The  first  mood  of  this  figure  is : 


I  Darapti.  I.  Dabapti.' 

An.  M  are  P;  y»^ v 

ButaR  MareS; 

Therefore,  some  S  are  P; 
or. 
All  gilding  is  metallic ; 

AU  gilding  shines ;  \  / 

Therefore,  some  things  that  shine  are  metoBic.  X^^      _,,^ 


&:) 


1  [But  Bee  HollmaBD,  Logiea,  H  332,  458.     the  comprehension  of  their  common  Fubjeot 
Loranienses,  In  An.  Priar.^  L.  i.  p.  220.]  M.    See  above,  p.  158.  —  Ed. 

2  Disparate  notions,  i.  t.,  coordinate  parts  of        8  [Some  of   the  ancient  logicians,  among 


296 


LOGIC. 


Lect.  xxr. 


"  Here  it  Is  manifest  that  M  cannot  at  once  lie  in  two  different 
spheres,  unless  these  partially  involve,  partially  intersect  each  other. 
But  only  partially ;  for  as  both  P  and  S  are  more  extensive  than  M, 
and  are  both  only  connected  through  M  {i.  e.  through  a  part  of 
themselves),  they  cannot,  except  partially,  be  identified  with  each 
other. 

"  The  second  mood  of  this  figure  is,  — 

II.  Felapton.  II.  Felapto».* 

No  M  IS  P; 

ButaflMareS; 

Therefore,  some  S  are  not  P; 
or. 
No  mateiial  substance  is  a  moral  suttject ; 
But  all  that  is  material  is  extended  ; 
Therefore,  something  extended  is  not  a  moral  subject. 


"You  will  observe,  that  according  to  this  diagram,  the  conclusion 
ought  to  be  —  No  S  is  P,  because  the  whole  of  S  lies  out  of  the 
sphere  of  P;  and  as  in  the  concrete  example,  the  notion  extended 
is  viewed  as  out  of  the  notion  moral  subject,  we  might  conclude, — 
Nothing  extended  is  a  moral  subject.  But  this  conclusion,  though 
materially  correct,  cannot,  however,  be  formally  inferred  from  the 
premises.  In  the  sumption,  indeed,  the  whole  of  M  is  excluded 
from  the  sphere  of  P ;  but  in  the  subsumption  M  is  included  in  the 
sphere  S,  that  is,  we  think  that  the  notion  M  is  a  part  of  the  notion 
S.  Now  in  the  conclusion,  S  is  brought  under  P,  and  the  conclusion 
of  a  categorical  syllogism,  in  reference  to  its  quantity,  is,  as  you 
remember,  by  the  third  general  law  regulated  by  the  quality  of  the 
subsumption.  But  as  in  the  present  case  the  subsumption,  notwith- 
Btanding  the  universality  of  the  expression,  only  judges  of  apart  of 


others  Porphyry,  have  made  two  moods  of 
Dampti,  as  Aristotle  himself  docs  in  Cesare 
and  Cameittres,  in  Di.«amis  and  Datisi.  See 
Uocthiiifi,  Df  SyUngismo  Calrgnrifo,  L.  ii..  Op- 
em,  p  694  alibi.  Cf  Zabarella,  Opera  Logica, 
Df  Quarta  Figura  Si/Uog.,  pp.  119,  120  tt  srq. 
Alex.  Aphrodisiensis,  In  Anal.  Prior.,  i.  6,  ff. 


28,  24,  Aid.  1631.  Phlloponns,  In  Anal.  Pnor., 
L.  i.  C.  6,  f.  18  b.  Apulcius.  De  Habitwi.  Doct. 
Plat.,  L.  ill.  Opera,  p.  87,  88,  ed.  Elmenhorst.) 

1  [Aristotle  gives  Fapemo,  A-al.  Prior.  J.  7- 
(Burgersdyck,  Instit.  Logica,  L.  il  0.  7|  p- 
169,  Cantak,  1647.)] 


XXI. 


LOGIC. 


297 


S ;  the  conclusion  can,  in  like  manner,  only  judge  of  a  part  of  S. 
Of  the  other  parts  of  S  there  is  nothing  enounced  in  the  premises. 
The  relation  between  S  and  P  could  likewise  be  as  follows : 


No  M  is  P; 
But  all  M  arc  S; 

or, 
No  pigeon  is  a  hawk; 
But  ail  pigeons  are  birds  ; 


"  Here  the  conclusion  could  not  be  a  universal  negatise,  —  There- 
fore^ no  S  is  P,  —  Therefore,  no  bird  is  a  hawk  —  for  the  sphere  of 
S  (bird)  is  greater  than  that  of  either  M  (pigeon)  or  P  (hawk);  it 
may,  however,  be  a  particular  negative —  Therefore,  some  S  are  not 
P  (therefore,  some  birds  are  not  hawks),  —  because  the  sumption 
has  excluded  M  and  P  (pigeon  and  hawk)  from  each  other's  sphere, 
and,  consequently,  the  part  of  S  which  is  equal  to  M  is  diflferent 
from  the  part  of  S  which  is  equal  to  P.  — But  if  this  be  the  case 
when  the  subsumption  has  a  universal  expression,  the  same,  a  for- 
tiori, is  true  when  it  is  particular. 

"  The  third  mode  of  this  figure  is : 


III.  Disamis  III.  DiSAMis. 

Some.  M  are  P ; 
But  all  M  are  S ; 
Therefore,  some  S  are  P; 

or, 

Some  acts  of  homicide  are  laudable ; 
But  aU  acts  of  homicide  are  crtiel; 
Therefore,  some  cruel  acts  are  laudable. 


"  The  fourth  mood  of  this  figure  is  : 


IV.  Datisi.  IV.  Datisi. 

^ZZMareP; 

But  some  M  are  S ; 

Therefore,  some  S  are  P ; 
or, 
AU  acts  of  homicide  are  cruel ; 
Some  acts  of  homicide  are  laudable ; 
Therefore,  some  laudable  acts  are  cruel. 

38 


298 


LOGIC 


Lect.  XXL 


'  This  diagram  makes  it  manifest  that  more  than  a  single  case  is 
possible  in  this  mood.  As  the  subsumption  is  particular,  the  con- 
slusion  can  only  bring  that  part  of  S  which  is  M  into  identity  with 
P;  of  the  other  parts  of  P  there  can  be  nothing  determined,  and 
these  other  parts,  it  is  evident,  may  either  lie  wholly  out  o^  or 
partly  within,  P. 

"  The  fifth  mood  of  this  figure  is : 


V.  Bocardo. 


V.   BOCARIK). 

Some  M  are  not  P; 

But  da  in  are  S; 

Therefore,  some  S  are  not  P; 
or, 
Some  syllogisms  are  not  regular; 
But  all  syllogisms  are  things  important ; 
Thertifore,  some  important  things  are  not  things  regular. 


"  The  sixth  mood  of  this  figure  is : 

VI.  Ferison.  VL  FEBigOK. 

JVbMisP; 
But  some  M  are  S ; 
Therefore,  some  S  ore  not  P; 
or, 

No  truth  is  wUhout  result  ; 

Some  truths  are  misunderstood ; 

Therefore,  some  things  misunderstood  are  not  without  reguU. 


or, 


"Here,  as  in  the  premises,  only  that  part  of  S  which  is  M  is 
excluded  from  P,  consequently  the  other  parts  of  S  may  either  like- 
wise lie  wholly  out  of  P,  or  partially  in  P."  ^  ' 

So  much  for  the  moods  of  the  third  fiffure. 


1  Bacbmann,  LosUc,  i  132,  p.  211— 218.  — £d. 


Lect.  XXL  LOGIC.  299 

Fourth  Figure.  "  The  formula  of  the  Fourth  Figure  is : 

M  S. 

Its  Laws.  «  Tijis  figure  is  regulated  by  three  laws. 

"  I.  Of  these  the  first  is,  —  If  the  sumption  be  affirmative,  the 
subsumption  must  be  universal.  The  necessity  of  this  law  is  easily 
seen.    For  if  we  had  the  premises : 

AUFareii; 
But  some  M  are  S; 

in  this  case  M  may,  or  may  not,  be  ^  notion  superior  to  P. 

"  On  the  former  alternative,  if  M  be  higher  than  P,  and  likewise 
higher  than  S,  then  the  whole  of  S  might  be  contained  under  P. — 
In  this  case,  the  proper  conclusion  would  be  a  universal  affirmative ; 
which,  however,  cannot  follow  from  the  premises,  as  the  subsump- 
tion, ex  hypothesi,  is  particular.  On  the  latter  alternative,  even  if  M 
were  not  superior  to  S,  still,  since  P  is  only  a  part  of  M,  we  could 
not  know  whether  a  part  of  S  were  contained  under  P  or  not.  For 
example : 

AU  men  are  animals ; 

But  some  animals  are  amphibious. 

"  From  these  premises  no  conclusion  could  be  drawn. 
"II.  The  second  rule  by  which  this  figure  is  governed  is  —  If 
either  premise  be  negative,  the  sumption  must  be  universal. 
"Suppose  we  had  the  premises  — 

Some  P  are  not  M ; 

But  aU 'ill  are  Si 

Therefore,  some  S  are  not  P; 
or. 
Some  animals  are  not  feathered; 
But  all  feathered  aniinals  are  birds  ; 
Therefore,  some  birds  are  not  animals. 

"  In  this  case  the  whole  of  S  lies  within  the  sphere  of  P ;  there 
cannot,  therefore,  follow  a  particular  negative  conclusion,  and  if 
not  that,  no  conclusion  at  all.  The  same  would  happen  were  the 
sumption  a  particular  affirmative,  and  the  subsumption  a  universal 
negative. 

"  III.  The  third  rule  of  the  fourth  figure  is  —  If  the  subsumption 


300 


LOGIC. 


Lect.  XXL 


he  affirmative,  the  conclusion  must  be  particular.  This  (the  logi- 
cians say)  is  manifest.  For  in  this  figure  S  is  higher  than  M,  and 
higher  than  P,  consequently  only  a  part  of  S  can  be  P. 

"  If  we  test  by  these  rules  the  eight  possible  moods,  there  are  m 
this  figure  five  found  competent,  which,  among  sundry  other  names, 
have  obtained  the  following:  ^ramantip,  Camenes^  DimariSy 
JP^esapo,  Fresison. 

"  Of  these  moods  the  first  is : 


I   Bramantip. 


I.  Bbahantip,  otherwise  Bahalip,  etc 

All  U  arc  S; 
Therefore,  sonve  S  ore  P; 


AU  greyhounds  are  dogs ; 

But  all  dogs  are  quadrupeds ; 

Therefore,  some  quadrupeds  are  grei/hounds. 


"  The  second  mood  is  called : 


II.  Camenea.  n.  Camehes,  Calehes,  or  Calektes,  etc 

AUFareU; 
BiUnoJtlisS; 
Therrfore,  no  S  if  P; 

or, 
AU  ruminating  animals  hatx  four  stomachs  ; 
But  no  animal  with  four  stomachs  is  camivorotu  ; 
Thertfore,  no  carnivorous  animal  ruminates. 

"The  third  mood  in  the  fourth  figure  is  variously  denominated: 


III.  Dimaria. 


in.  DiMARis,  or  DiHATis,  Of  DiBATis,  etc 

Some  P  are  M ; 
ButaUUareS; 
Therefore,  some  8  are  P; 

or, 

Some  practicaUy  virtuous  men  are  necessitmriaiu ; 

All  necessitarians  speculatively  subvert  the  distinction  of  vice  and 

virtue ; 
Therefore,  some  who  speculativdy  subvert  the  distinction  qf  via 

and  virtue  are  practically  virtuous  men. 


"The  fourth  mood  of  this  figure  is: 


Lkct.  XXI. 
rV.  Fesapo. 


LOGIC. 

IV.  Fbsapo. 
iVoPisM; 
All  M  are  S; 

Therefore,  some  S  are  not  P; 
or, 
No  negro  is  a  Hindoo ; 
But  aO  Hindoos  are  blacks; 
Therefore,  some  blacks  are  not  negroes ; 


301 


O© 


or, 


"  According  to  the  first  of  these  diagrams,  all  S  is  excluded  from 
P,  and  thus  the  conclusion  would  seem  warranted  that — No  S  is 
P.  This  conclusion  cannot,  however,  be  inferred ;  for  it  would  vio- 
late the  third  rule  of  this  figure.  For  while  we,  in  the  sumption, 
have  only  excluded  M,  that  is,  a  part  of  S,  from  P,  and'as  the  other 
parts  of  S  are  not  taken  into  account,  we  are,  consequently,  not 
entitled  to  deny  these  of  P.  The  first  diagi-am,  therefore,  which 
sensualizes  only  a  single  case,  is  not  coadequate  with  the  logical 
formula,  and  it  is  necessary  to  add  the  second  in  order  to  exhaust 
it.  The  second  diagram  is,  therefore,  likewise  a  sensib^le  represen- 
tation of  Fesapo ;  and  that  diagram  makes  it  evident  that  the  con- 
clusion can  only  be  a  particular  negative. 

"  The  fifth  and  last  mood  is  ; 

V.  Fresiion.  V.  Fresison. 

•    iVbPisM; 

But  some  "Mare  S; 
Thertfore,  some  S  are  not  P; 
or, 
JVo  moral  principle  is  an  animal  impulse ; 
But  some  animal  impulses  are  principles  of  action ; 
Therefore,  some  principles  of  action  are  not  moral  prindplet. 


or, 


30B  LOGIC.  Lect.  XXI. 

"  The  demonstration  is  here  the  same  as  in  the  former  mood. 
Since  the  subsuniption  only  places  a  part  of  M  in  the  sphere  of  S, 
the  conclusion,  whose  quantity  is  determined  by  the  subsumption, 
can  only  deny  P  of  that  part  of  S  which  is  likewise  a  part  of  M."' 

Having  thus  concluded  the  exposition  of  the  various  Figures  and 
Moods  of  Syllogisms,  as  recognized  by  logicians. 

0  an      ignre  in       j^  reference  to  Extensive  Quantity,  it  will  not 

Comprehension.  . 

be  necessary  to  say  more  than  a  word  in  general, 
touching  these  figures  and  moods  in  reference  to  Comprehensive 
Quantity.  Whatever  mood  and  figure  is  valid  and  regular  in  the 
one,  is  valid  and  regular  in  the  other ;  and  every  anomaly  is  equally 
an  anomaly  in  both.  The  rules  of  the  various  figures  which  we 
have  considered  in  regard  to  syllogisms  in  Extension,  are  all,  with- 
out exception  or  qualification,  applicable  to  syllogisms  in  Compre- 
hension, with  this  single  proviso,  that,  as  the  same  proposition  forms 
a  different  premise  in  the  several  quantities,  all  that  is  said  of  the 
sumption  in  extension,  should  be  understood  of  the  subsumption  in 
comprehension,  and  all  that  is  said  of  the  sumption  in  comprehen- 
sion, shoul(f  be  understood  of  the  subsumption  in  extension.  What, 
therefore,  has  hitherto  been,  or  may  hereafter  be,  stated  of  the  mood 
and  figure  of  one  quantity,  is  to  be  viewed  as  applicable,  mutatis 
mutandis,  to  the  other.  This  being  understood,  I  proceed,  in  the 
fii"st  place,  to  show  you  that  the  complex  series 

Criticism  of  the      ^f  logical  forms  which  I  have  enumerated  may 

loeicai' forms  '  "  ^^  Considerably  diminished,  and  the  doctrine  of 

syllogism,  consequently,  reduced   to    a  higher 

simplicity.    In  doing  this  I  shall  consider,  firet,  the  Figures,  and, 

secondly,  their  Moods. 

Now,  as  regards  the  number  of  the  Figures,  you  are  aware,  from 

1  The  FiKures.  what  I  formerly  stated,  that  Aristotle  only  con- 

templated the  three  first,  and  that  the  fourth, 
which  is,  by  those  who  do  not  mistake  it  for  an 
Aristotelic  form,  referred  with  little  probability  to  Galen,  was  wholly 
unnoticed  until  the  end  of  the  twelfth  or  tjie  beginning  of  the  thir- 
teenth century,  when  it  was  incidentally  communicated,  as  an  inno- 
vation of  the  physician  of  Pergamus,  by  the  celebrated  Averroes,  in 
his  commentary  on  the  Prior  Analytics  of  Aristotle,  but  by  Aver- 
roes himself  rejected  as  an  illegitimate  novelty.*  The  notice  of  this 
figure  by  the  commentator  was,  however,  enough  ;  and  though  re- 
pudiated by  the  great  majority  of  the  rigid  Aristotelians,  the  author- 


1  Bacbmann,  Logik,  i  188,  p.  218—223.—         2  In  Anal   Prior,  1%.     Opaa  ilmtwtdi*,  t.  i> 
£o.  f .  78.  VenctUs,  1600.  —  £d. 


Lkct.  XXI.  LOGIC.  303 

ity  of  Scotus,  by  whom  it  was  defended/  secured  for  it  at  last,  if  not 
a  universal  approval,  at  least  a  very  general  toleration,  as  a  legiti- 
mate though  an  awkward  form.  The  arguments  indeed  by  which 
it  was  attempted  to  evince  the  incompetency  of  this  figure,  were 
not  of  a  character  calculated  to  enforce  assent ;  for  its  inference  is 
not  less  valid  than  that  of  any  other,  —  however  tortuous  and  per- 
verse it  may  be  felt  to  be.  In  fict,  the  logicians,  in  consequence  of 
their  exclusive  recognition  of  the  reasoning  in  extension,  were  not  in 
possession  of  the  means  of  showing,  that  this  figure  is  a  monster  un- 
deserving of  toleration,  fur  less  of  countenance  and  favor.  I  shall  not, 
therefore,  trouble  you  with  the  inconclusive  reasoning  on  the  part 
either  of  those  who  have  assailed  or  of  those  who  have  defended 
this  figure,  but  shall  at  once  put  you  in  possession  of  the  ground  on 
which  alone,  I  think,  its  claim  to  recognition  ought  to  be  disallowed. 
In  the  first  place,  then,  you  are  aware  that  all  reasoning  is  either 
in   the   quantity  of  comprehension,  or   in    the 

Grounds  on  winch  quantity  of  extension.  You  are  aware,  in  the 
ou'ht  to  be  disallowed  sccoud,  that  thcsc  quantities  are  not  only  differ- 
ent, but,  as  existing  in  an  inverse  ratio  of  each 
other,  opposed.  Finally,  in  the  third  place,  you  are  aware  that, 
though  opposed,  so  that  the  maximum  of  the  one  is  the  minimum 
of  the  other,  yet  the  existence  of  each  supposes  the  existence  of  the 
other ;  accordingly  there  can  be  no  extension  without  some  compre- 
hension, —  no  comprehension  without  some  extension. 

This  being  the  case,  it  is  evident  that,  besides  the  definite  reason- 
ing from  whole  to  part,  and  from  parts  to  whole, 

A  cross    inference       \^rithin  the  Several  quantities  and  in  their  per- 

possible  from    Exten-  f      ^        i-  ^i  •        i  ^       ^ 

.      .     „         ,  pendicular  lines,  there  is  also  competent  an  in- 

8ion    to    Comprehen-         ^  '  ^  ^ 

sion  and  vice  versa.  definite  inference  across  from  the  one  quantity  to 

the  other.  For  if  the  existence  of  the  one  quan- 
tity be  only  possible  under  the  condition  of  the  other,  we  may 
always,  it  is  self-evident,  in  the  first  place,  from  the  afiirmation  of 
anything  in  extension,  indefinitely  aflSrm  it  in  comprehension,  as, 
reciprocally,  from  the  affirmation  of  anything  in  comprehension,  we 
may  indefinitely  affirm  it  in  extension ;  and,  in  the  second  place, 
from  the  negation  of  anything  in  extension,  we  may  absolutely  deny 

1  This  statement  is  marked  as  doubtful  in  conclusionis:  per  consequens  nee  diversitas 

the  Author's  Common-place  Book.    Scotus  figures." 

( Qti^st.  in  Anal.  Prior.,  i.  q.  34)  expressly  re-  The  Fourth  Figure  is,  however,  said  by 

jects  the  Fourth  Figure.    He  says:    "  Solum  Ridiger  {De  Sensu  Yeri  et  Falsi,  p.  337)  to  have 

tribus  modis  potest  fieri  debita  ordinatio  re-  been  introduced  by  Galen  and  Scotus.    IIos- 

Fpectu  e.xtremorum  secundum  subjictionem  pinianus  (De  Controversiis  Dinlecticis,  c.  xix.) 

et  prasdicationem ;  igltur  tres  figuraj  et  non  attributes  (erroneously)  the  invention  of  this 

plurcs  ....  quia  per  solam  transpositionem  figure   to   Scotus.     Compare    also  Noldius, 

r.on  pervenit  diversitas  allcujus  pra-missa:  nee  Logica  Recognita,  c.  xiii.  i  4,  p.  277-  —  Ed. 


304 


LOGIC. 


Lect.  XXI 


This  the  nature  of 
the  inference  in  the 
Fourth  Figure. 


it  in  compreh<^nsion,  as,  reciprocally,  from  the  negation  of  anything 
in  comprehension,  we  may  absolutely  deny  it  in  extension. 

Now,  what  has  not  been  observed,  such  is  exclusively  the  infer- 
ence in  the  Fourth  Figure  ;  its  two  last  rules 
are  in  fact  nothing  but  an  enunciation  of  these 
two  conditions  of  a  cross  inference  from  the  one 
quantity  to  the  other ;  and  the  first  rule  will  be 
hereafter  shown  to  be  only  an  error,  the  result  of  not  observing  that 
certain  moods  are  only  founded  on  the  accident  of  a  transposed 
order  of  the  premises,  and,  therefore,  constitute  no  subject  for  a  logi- 
cal legislation. 

To  prove  this  statement  of  the  nature  of  the  inference  in  the 
Trored  and  iiiustra-       fourth  figure,  it  is  only  necessary  to  look  at  its 
ted.  abstract  formula.     In  extension  this  is  — 

P  is  M; 
M  ts  S; 


8  IS  P. 


Here  in  the  premises  P  is  contained  under  M,  and  M  is  contained 
under  S ;  that  is,  in  the  premises  S  is  the  greatest  whole  and  P  the 
smallest  part.  So  far,  this  syllogism  in  extension  is  properly  a  syl- 
logism in  comprehension,  in  which  the  subject  of  the  conclusion  is 
the  greatest  whole,  and  its  predicate  the  smallest  part.  From  such 
premises  we,  therefore,  expect,  that  the  conclusion  carrying  out  what 
was  established  in  the  antecedent,  should  affirm  P  as  the  part  of  S. 
In  this,  however,  our  expectation  is  disappointed;  for  the  reasoning 
suddenly  turns  round  in  the  conclusion,  and  affirms  S  as  a  part  of  P. 
And  how,  it  may  be  asked,  is  this  evolution  in  the  conclusion  com- 
petent, seeing  that  it  was  not  prepared,  and  no  warrant  given  for  it 
in  the  premises.  To  this  the  answer  is  prompt  and  easy.  The  con- 
clusion in  this  figure  is  solely  legitimated  by  the  circumstance,  that 
from  an  identity  between  the  two  terms  in  one  quantity,  we  may 
always  infer  some  identity  between  them  in  the  other,  and  from  a 
non-identity  between  them  in  one  quantity,  we  can  always  infer  a 
non-identity  in  the  other.  And  that  in  this  figure  there  is  always 
a  transition  in  the  conclusion  from  the  one  quantity,  is  evident ;  for 
that  notion  which  in  the  premises  was  the  greatest  whole,  becomes 
in  the  conclusion  the  smallest  part ;  and  that  notion  which  in  the 
premises  was  the  smallest  part,  becomes  in  the  conclusion  the  great- 
est whole.  Now,  how  is  this  manoeuvre  possible?  —  how  are  we 
entitled  to  say  that  because  A  contains  all  B,  therefore  B  contains 
some  A  ?  Only,  it  is  clear,  because  there  is  here  a  change  from  the 
containing  of  the  one  quantity  to  the  containing  of  the  other ;  and 


Lect.  XXI.  LOGIC.  305 

because,  each  quantity  necessarily  implying  the  indefinite  existence 
of  the  other,  we  are  consequently  permitted  to  render  this  necessary 
implication  the  ground  of  a  logical  inference. 

It  is  manifest,  however,  in  the  first  place,  that  such  a  cross  and 

hybrid    and    indirect    reasoning   from   the   one 

This  hybrid  infer-       quantity  to   the   other,  in  the  fourth  figure,  ia 

ence  is,  1.  Unnatural.  ^  •'  '  -,  ^ 

wholly  oi  a  different  character  and  account  from 
the  reasoning  in  the  other  three  figures,  in  which  all  inference, 
whether  upwards  or  downwards,  is  equable  and  homogeneous 
within  the  same  quantity.  The  latter  in  short  is  natural  and  easy; 
the  former,  unnatural  and  perverse. 
In  the  second  place,  the  kind  of  reasoning  competent  in  the  fourth 

figure  is  wholly  useless.     The  chanjje  from  the 
2.  Useless.  .  . 

one  quantity  to  the  other  in  the  course  of  a  syl- 
logism is  warranted  by  no  necessity,  by  no  expediency.  The  reason- 
ing in  each  quantity  is  absolute  and  complete  within  itself,  and  all 
that  can  be  accomplished  in  the  one  process  can  equally  well  be  ac- 
complished in  the  other.  The  jumping,  therefore,  from  extension  to 
comprehension,  or  from  comprehension  to  extension,  in  the  conclu- 
sion of  the  fourth  figure,  is  a  feat  about  as  reasonable  and  useful  in 
Logic,  as  the  jumping  from  one  horse  to  another  would  be  reason- 
able and  useful  in  the  race-course.  Both  are  achievements  possible  ; 
but,  because  possible,  neither  is,  therefore,  a  legitimate  exercise  of 
skill. 

We  may,  therefore,  on  the  ground  that  the  fourth  figure  involves 
a  useless  transition  from  one  quantity  to  another,  reject  it  as  a  logi- 
cal figure,  and  degrade  it  to  a  mere  logical  caprice. 

But,  in  the  third  place,  there  is  a  better  ground ;  the  inference, 

though  valid  in  itself,    is  logically,  is  scientifi- 

3.  Logically  invalid.  n       •         t  i        -n         ,i        •    r-  •  i      i       ••• 

cally,  invalid.  J^or  the  inference  is  only  legiti- 
mated by  the  occult  conversion  of  the  one  quantity  into  the  other, 
which  takes  place  in  the  mental  process.  There  is  thus  a  step  taken 
in  the  reasoning  which  is  not  overtly  expressed.  Were  the  whole 
process  stated  in  language,  as  stated  it  logically  ought  to  be,  instead 
of  a  simple  syllogism  with  one  direct  conclusion,  we  should  have  a 
complex  reasoning  with  two  conclusions ;  one  conclusion  direct  and 
immediate  (the  inference,  to  wit,  of  conversion),  and  from  that  im- 
mediate conclusion  another  mediate  and  indirect,  but  which,  as  it 
stands,  appears  as  the  one  sole  and  exclusive  conclusion  from  the 
premises.  This  ground,  on  which  I  think  the  fourth  figure  ought  to 
be  specially  abolished,  is  stated  with  the  requisite  details  in  the  Logi- 
cal Appendix  contained  in  the  second  edition  of  my  Discussions  on 
Philosophy} 

39  1  p.  663.  —  Ed. 


LECTURE    XXII. 

STOICHEIOI.   OOY. 

SECTION   II.— OF    THE    PRODUCTS   OF  THOUGHT 
III.  —  DOCTRINE   OF  REASONINGS. 

SYLLOGISMS.  — THEIR  DIVISIONS  ACCORDING  TO  EXTERNAL 

FORM. 

C.    REGULAR  AND   IRREGULAR. 

FIGURE  —  REDUCTION. 

In  my  last  Lecture,  after  terminating  the  view  of  the  nineteen 
Moods  of  the  Four  Syllogistic  Figures,  accord- 
ing to  the  doctrine  of  logicians,  I  entered  on  the 
consideration, —  how  far  their  doctrine  concerning  the  number  and 
legitimacy  of  these  various  figures  and  moods  was  correct.  In  the 
conduct  of  this  discussion,  I  proposed,  firet,  to  treat  of  the  Figures, 
and,  secondly,  to  treat  of  the  Moods.  Commencing,  then,  with  the 
Figures,  it  is  manifest  that  no  exception  can  possibly  be  taken  to 
the  first,  which  is,  in  point  of  fact,  no  figure  at  all,  but  the  one  reg- 
ular,—  the  one  natural  form  of  ratiocination.  The  other  three  fig- 
ures divide  themselves  into  two  classes.  The  one  of  these  classes 
comprehends  the  fourth ;  the  other,  the  second  and  third  figures. 
The  fourth  figure  stands,  on  the  common  doctrine  of  the  logicians, 
in  a  more  unfavorable  situation  than  the  second  and  third.  It  was 
not  recognized  by  Aristotle  ;  it  obtained  admission  into  the  science 
at  a  comparatively  recent  period ;  it  has  never  in  fact  been  univer- 
sally recognized  ;  and  its  progress  is  manifestly  more  perverse,  cir- 
cuitous, and  unnatural,  than  that  of  any  other. 

In  regard  to  this  fourth  figure,  I  stated  that  the  controversy  among 
logicians  touching  its  legitimacy  had  been  without  result ;  its  op- 
ponents failing  to  show  that  it  ought  to  be  rejected ;  its  defenders 
failing  to  show  that  it  was  deserving  of  recognition.  I  then  stated 
that  the  logicians,  in  their  one-sided  view  of  the  reasoning  pi'ocess, 


I 


Lect.  XXn.  LOGIC.  307 

had  let  slip  the  one  great  principle  on  which  the  legitimacy  of  this 
jSgure  was  to  be  determined,  I  then  explained  to  you  that  the  pecu- 
liarity of  the  fourth  figure  consists  in  this,  —  that  the  premises  are 
apparently  the  premises  of  a  syllogism  in  one  kind  of  quantity,  while 
its  conclusion  is  the  converted  conclusion  of  a  syllogism  in  the  other. 
It  is  thus  in  every  point  of  view  contorted  and  preposterous.  Its 
premises  are  transposed,  and  the  conclusion  follows  from  these,  not 
directly,  but  through  the  medium  of  a  conversion.  I  showed  how, 
and  how  far,  this  kind  of  reasoning  was  competent,  and  that  though 
the  inference  in  the  fourth  figure  is  valid,  it  is  inconvenient  and  use- 
less, and  therefore,  that  the  form  itself,  though  undoubtedly  legiti- 
mate, is  still  only  a  legitimate  monster.  Herewith  the  Lecture  ter- 
minated. 

Now,  looking  superficially  at  the  matter,  it  might  seem,  from  what 

has  now  been  said,  that  the  fourth  ought  to  be 

General  character  of      ^^  q^qq  expunged  from  the  series  of  logical  fig- 

the  Second,  Third,  and  t-»    ,  i  •       .•  mi      v 

r,    _,,  ^.  ures.      But  a  closer  exammation  will  show  us 

Fourth  Fij»ures. 

that  this  decision  would  be  rash.  In  point  of 
fact,  all  figure  properly  so  called,  that  is,  every  figure,  with  the  ex- 
ception of  the  first,  must  be  rejected  equally  with  the  fourth,  and  on 
the  following  ground,  —  that  they  do  not,  in  virtue  of  their  own 
expressed  premises,  accomplish  their  own  inference,  but  that  this  is 
done  by  the  mental  interpolation  of  certain  complementary  steps, 
without  which  no  conclusion  in  these  figures  could  be  drawn.  They 
.ire  thus  in  fact  reasonings  apparently  simple,  but  in  reality  complex ; 
and  when  the  whole  mental  process  is  expressed,  they  are  found  to 
be  all  only  syllogisms  in  the  first  figure,  with  certain  corollaries  of 
the  different  propositions  intermingled.*  This  doctrine  corresponds 
with  that  of  the  logicians,  in  so  far  as  they,  after  Aristotle,  have 
allowed  that  the  last  three  figures  are  only  valid  as  reducible  to  the 
first ;  and,  to  accomplish  this  reduction,  they  have  supplied  us  with 
a  multitude  of  empirical  rules,  and  lavished  a  world  of  ingenuity  in 
rendering  the  working  of  these  complex  rules  more  easy.  From 
Whately  and  the  common  books  on  Logic,  you 
Latin  and  Greek  are  of  course  acquainted  with  the  import  of  the 
mnemonics,-theirau-       consonants  in  the  cabalistical  verses,  Barbara, 

thor8.  . 

Celarent,  etc. ;  ^  and  it  must  be  confessed  that, 
taking  these  verses  on  their  own  ground,  there  are  few  human 
inventions  which  display  a  higher  ingenuity.     Their  history  is  ap- 


1  This  doctrine  of  Figure,  which  is  devel-  Werke,  i.  p.  55,  ed.  Rosenkranz  and  Schubert 

oped   in   paragraph   Ixxv.,  is   mainly  taken  —  Ed. 
from  Kant.    See  his  Essay,  Die  Falsche  Spitz- 

findigkeit  der  vitr  Syllogistischen  Figuren,  1762.  2  See  Discussions,  p.  666.— Ed. 


308 


LOGIC. 


Lect.  XXH 


parently  altogether  unknown  to  logicians.  They  were,  in  so  fer  as 
they  relate  to  the  three  first  or  Aristotelic  figures,  the  invention  oi 
Petrus  Hispanus,  who  died  in  1277,  Pope  John  XXII.  (or  as  he  is 
reckoned  by  some  the  XXI.,  and  by  others  the  XX.).  He  was  a 
native  of  Lisbon.  It  is  curious  that  the  corresponding  Greek  mne- 
monics were,  so  far  as  I  can  discover,  the  invention  of  his  contem- 
porary Nicephorus  Blemmidas,  who  was  designated  Patriarch  of 
Constantinople.^  Between  them,  these  two  logicians  thus  divided 
the  two  highest  places  in  the  Christian  hierarchy ;  but  as  the  one 
had  hardly  begun  to  reign  when  he  was  killed  by  the  downfall  of 
his  palace,^  so  the  other  never  entered  on  his  ofiice  by  accepting  his 
nomination  at  all.  The  several  works  of  the  Pope  and  the  Patri- 
arch were  for  many  centuries  the  great  text-books  of  Logic,  —  the 
one  in  the  schools  of  the  Greek,  the  other  in  the  schools  of  the 
Latin  church. 

The  Greek  symbols  are  far  less  ingenious  than  the  Latin,  as  they 
only  mark  the  consecution,  quantity,  and  quality 
The  Greek  symbols  of  the  different  propositions  of  the  Various  moods 
^ mgenious  an  e  ^^  ^^^  three  generally  admitted  figures,  Mithout 
showing  to  what  mood  of  the  first  the  moods  of 
the  other  two  figures  are  to  be  reduced,  far  less  by  what  particular 
process  this  is  to  be  done.  All  this  is  accomplished  by  the  symbols 
of  the  Roman  Pontiff".  As  to  the  relative  originality,  or  the  j^riority 
in  point  of  date,  of  these  several  inventions,  I  am  unable  to  speak 
with  certainty.  It  is  probable,  however,  that  the  Blemmidas  was 
the  first,  both  because  his  verses  are  the  simpler  and  ruder,  and  be- 
cause it  is  not  known  that  he  was  acquainted  with  the  writings  of 
the  Western  logicians :  whereas  I  find  that  the  Summulce  of  His- 
panus are  in  a  great  measure  taken,  not  indeed  from  the  treatise  of 
Blemmidas  upon  Dialectic,  but  from  the  Synopsis  of  the  Organon 
of  his  somewhat  earlier  contemporary  Michael  Psellus.' 

But  the  whole  of  the  rules  given  by  logicians  for  the  Reduction 
of  Syllogisms  are  unphilosophical,  for  they  are 
merely  the  empirical  statements  of  the  opera- 
tion of  a  principle  in  detail,  which  principle  it- 
self has  been  overlooked,  but  which,  when  once 
rationally  explicated,  supersedes  the  whole  com- 
plex apparatus  of  rules  for  its  mechanical  application. 

If  I  succeed,  therefore,  in  explaining  to  you  how  the  last  three 


The  Kulcs  of  logi- 
cians for  the  Keduction 
of  Syllogisms  unphil- 
osophical. 


1  Bat  see  Discussions,  p.  672.  —  Ed. 

2  See  riatina  [Historia  de   Yitis  PonHficutn 
Ri)manonim,p.  181,  ed.  1572.  — Ed]. 

i  The  reverse  is  probabl/  the  truer  account; 


the  work  which  goes  by  the  name  of  Psellus 
being  in  all  probability  a  translation  from  His- 
panus, the  mnemonics,  with  one  exception« 
being  omitted.    See  Discussions,  p.  128.  —  Ed 


Lfxt.  XXII.  LOGIC.  809 

Figures  arc   only  the  mutilated   e.vprcssion?  of  a  complex   mental 
process,  I  shall  not  only  subvert  tlieir  existence 

The   last   tliree  Fig-  „        '  -,  .       "■  .  ,,        .  ,  . 

,  .,        ...  .   ,        as    lorms    oi    reasoninLT    nut    \irtuailv    nlentical 

ures  only  the  mutilated  -^ 

expressions  of  a  coin-  witli  the  first  figure.  —  I  shall  nut  only  relie\'e 
piex  mental  proce.-?,  you  from  the  necrs>it\-  <jf  stuilviniT  the  tediuus 
and  virtually  identical  ^^^j  dh^usUuiS  rule>  ' vf  tlieir  reduction,  hut  in 
with  the  first.  .     '   .  '- 

fiict  vindicate  the   gruat   jirinciples   of  rr:;>uiiing 

from  apparent  anomaly.  For,  in  the  lirst  place,  if  the  thix'e  last  fig- 
ures are  admitted  as  genuine  and  original  f  ;rms  of  reasuning,  the 
principle  that  all  reasoning  is  the  recognition  of  the  relation  of  a 
least  part  to  a  greatest  whole,  tlirough  a  k'Sser  whule  dv  greater 
part,  is  invalidated.  For,  in  the  three  latter  fig'are>.  the  middle 
term  does  not  really  hold  the  relation  tif  an  intermediate  wh^le  or 
part  to  the  sidiject  and  [iredicate  of  the  conclusion  ;  fir  rilln.r,  in 
the  second  figure,  it  contains  them  both,  iir,  in  the  third,  is  euiitained 
by  them  lioth,  ur.  in  the  fourth,  at  once  contains  the  greatest  whole 
(that  is,  the  predicate  in  extensi\'e,  the  subjeet  in  cum]irLdifii>i\-e, 
quantity),  and  is  containeil  Ijy  tlie  smallest  part  (that  is,  the  subject 
in  extensi\-e.  the  predicate  in  co!inii-ehensi\e,  cjuantity).  In  the  sec- 
ond place,  if  these  three  figures  are  admitted  as  inde]iende!it  and 
legitimate  lurms,  tlie  second  general  ride  I  ga\e  you  f u'  cateL:()rical 
syllogisms  is  invalidated  iu  both  its  clauses.  Fur  it  \vill  nut  hold 
true,  that  every  categorical  sylloQ-ivm  mu>t  lun'e  an  universal  sump- 
tion and  an  afiirmati\-e  subsunq.tiun.  The  h-n\-  (4'  the  univei-sal 
quantity  of  the  sumption  is  violatetl  in  the  third  tiii-uye.  by  ])is;uins 
and  Bocardo,  in  the  fourth,  by  Dimari.-:  the  law  tif  the  afiirina.tive 
quality  of  the  subsumption  is  viulatch  in  tlie  second  figure,  by  C'a- 
mestres  ami  IJaroco ;  and.  in  the  fourth,  by  C'amenes.  I,  therefore. 
proceed  to  reconcile  all  these  anomalies  by  the  extinction  of  the 
hist  three  figures,  as  more  than  accidental  modifications  of  the  lirst, 
and  commence  with  the  followins:  parairraph. 

1i   LXXV.     The  three  last    (that  is.  Second.  Third.  Fourth) 
Figures  are  mcrelvhvbrid  or  mixed  reasuii- 

Par.     LXXV.     The  •      ^      .  ,..,''  ,     , 

Second,     Th.rd.     and  1"?^'  1"   ^^"'i't'^^  ^^>'-"'    ^^^'S    Ot    tllC    l-rOCCSS    are 

Fourth  Figures  only       ouly  partially  cxprcsscd.     The  unexpressed 

accidental      modifica-  ,  ■  i  •  •     x- 

^,^   „.    ,  Steps  are,  m  ixencral.  conversive  mterences. 

tions  of  the  First.  I  '  r- 

which  we  are  entitled  to  make.  1°,  From  the 
absolute  negation  of  a  first  notion  as  predicated  of  a  second,  to 
the  absolute  negation  of  the  second  notion  as  predicated  of  tl;j 
first  —  if  >iO  A  /.•*  B;  thin  no  B  is  A:  2°.  From  the  total  or 
partial  affirmation  of  a  lesser  class  or  notion  of  a  greater,  to  the 
partial  affirmation  of  that  greater  notion  of  that  lesser,  —  if  all 
(or  soyne)  A  is  B  ;  then  some  B  is  A. 


310  LOGIC.  Lect.  xxn, 

Taking  the  figures  and  moods  in  their  common  order;  in  the 
Second  Figure   the 

Moods   of    Second  ,  .   ,      ,       ^  i     • 

Figure.  1.  Cesare.  which  the  formula  IS 


Second  Figure   the   first   mood   is   Cesare,   of 

Moods   of    Second  ® 


JVbPtsM; 

But  oZZ  S  are  M; 
Therefore,  no  S  is  P. 

Here  the  ostensible  or  expressed  sumption,  No  P  is  M,  is  mentally 
converted  into  the  real  sumption  by  the  inference,  —  Then  no  M  is 
P.     The  other  propositions  follow  regularly,  —  viz. : 

But  aOSare  M; 
Therefore,  no  S  is  P. 

In  reality  Ceiarent.      The  real  syllogism,  fully  expressed,  is  thus : 

Real  SamptioD,  ....  No  M  ts  P; 

Subsumption, But  all  S  are  M ; 

Ck>nclusion, Ergo,  no  S  is  P. 

To  save  time,  I  shall  henceforward  state  the  complementary  prop- 
ositions which  constitute  the  real  and  proximate  parts  of  the  syl- 
logism, by  the  name  of  real,  proximate,  or  interpolated  sumption, 
subsumption,  or  conclusion ;  and  those  who  take  notes  may  simply 
mark  these,  by  placing  them  within  brackets.  To  avoid  confusing 
the  conversive  inference  with  the  ostensible  conclusion  of  the  syl- 
logism, I  shall  mark  the  former  by  the  illative  conjunction  then; 
the  latter  by  the  illative  conjunction  therefbre.  I  shall  take  the 
concrete  examples  which  I  chanced  to  give  in  illustration  of  the 
various  moods.    In  Cesare  the  concrete  example  was : 

Ostensible  Sumption, Nothing  that  it  material  has  free  will; 

Real,  Interpolated,  Sumption,    ....  (  Then  nothing  that  has  free  vnU  is  material;) 

Subsumption, But  nil  spirits  have  freewill; 

Conclusion, Therefore,  no  spirit  is  material. 

Throwing  out  of  account  the  ostensible  sumption,  and  considering 
the  syllogism,  in  its  real  nature,  as  actually  evolved  out  of  the  sump- 
tion mentally  understood  ;  we  have  thus,  instead  of  a  syllogism  in 
Cesare  of  the  second  figure,  a  syllogism  in  Ceiarent  of  the  first. 
The  seeming  irregularity  is  thus  reduced  to  real  order. 

The  second  mood  of  the  second  figure,  viz.  Camestres,^  is  rather 

1  [That  Cesare  and  Camestres  are  the  same      Syllo^.,  p.  Ill,  and  authorities  cited  abore,  p 
(yllogism  with  accidental  order  of  premises,     296,  note.] 
see  Zabarella,  Opera  Logiea,  Dt  Quarto  Figura 


Lect.  XXn.  LOGIC.  311 

more  irregular,  and,  therefore,  the  process  of  redressing  it,  though 
equally  easy,  is  somewhat  more  complex.     The 
2.    Camestres.  formula  is  : 

All  T  are  M.; 
ButnoSts'il; 
Therefore,  no  S  is  P. 

Here,  in  the  first  place,  the  premises  are  transposed,  for  you  re- 
member by  the  second  general  law  of  syllogisms, 

In  reality  Celareut.  .  .  •        i  •  i  i 

the  sumption  must  in  extension  be  universal,  and 
the  subsuraption  affirmative.  By  a  preliminary  operation,  their  ap- 
parent consecution  must,  therefore,  be  accommodated  to  their  real. 
The  premises  being  restored  to  order,  there  is  yet  a  further  intricacy 
to  unravel.  The  sumption  and  the  conclusion  are  neither  of  them 
proximate ;  for  we  depart  from  a  conversive  sumption,  and  primarily 
obtain  a  conclusion  which  only  gives  us  the  ostensible  conclusion,  in 
the  second  instance,  through  an  inference.     Thus  : 

Ostensible  Sumption, iVb  S  «  M ; 

Proximate  or  Real  Sumption,  .     .     .  (  Then  no  M.  is  S;) 

Subsumption, AUF  are  M ; 

Proximate  or  Real  Conclusion,      .    .  ( Therefore,  no  P  is  S;) 

Ostensible  Conclusion, Therefore,  no  S  is  P. 

The  concrete  example  given  was : 

All  colors  are  visible  ; 
But  no  sound  is  visible ; 
Therefore,  no  sound  is  a  color. 

Reveraing  the  premises,  we  have : 

Apparent  Sumption No  sound  is  visible ; 

Proximate  or  Real  Sumption,  .  (  Then  nothing  visBle  is  a  sovnd;) 

Subsumption, All  colors  are  visible  ; 

Proximate  or  Real  Conclusion,  ( Therefore,  no  color  is  a  sourtd;) 

which  gives,  as  a  conversive 

inference,  the 

Expressed  Conclusion, ....  Then  no  sound  is  a  color. 

Thus  it  is  evident  that  Camestres,  in  the  second  figure,  is  only  a 
modification  of  Celarent  in  the  first.^ 

1  Cf.  Krug,  Logik,  J  109,  p.  363.    Mark  Dun-      [Derodon,    Logica   Restit.,  Pare.  iv.   p.  6t8L 
can,  Instit.  LogUce,  L.  iv.  c.  4,  p.  229.  —  Ed.      Eeusch,  Systema  Logicum,  i  439,  p.  613.] 


312  LOGIC.  Lkct.  XXII 

The  third  mood  of  the  Second  Figure,  Festino,  presents  no  diffi- 
3    Festino.  culty.     We  have  only  to  interpolate  the  real 

sumjDtion,  to  which  the  subsumption  and  conclu- 
In  reality  Ferio.  .  .        ^   ,  «  rm 

sion  proximately  refer.     Ihus: 

Expressed  Samption,      .    .     .  JVo  P  w  M  ; 

Real  or  Proximate  Sumption,  ( TTien ttoMisP); 

Subsumption, But  some  S  are  M; 

Conclusion, Therefore,  some  S  are  not  P. 

Our  concrete  example  was  : 

Expressed  Sumption,    .    .    .    No  vice  is  laudable ; 

Some  actions  are  laudable  ; 
Therrfort,  $ome  actions  art  not  vtm. 

Here  we  have  only  to  intci-polate,  as  the  real  sumption  : 

Nothing  laudable  is  a  vice. 

Festino,  in  the  second  figure,  is  thus  only  Ferio  in  the  firet,  with  its 
sumption  converted. 

The  fourth  mood,  Baroco,  is   more   troublesome.     In   fact,  this 

mood   and   Bocardo,  in   the  third   figure,  have 

been  at  once  the  cruces  and  the  opprobria  of 
logicians.     They  have,  indeed,  succeeded  in  reducing  these  to  the 

first  figure  by  what  is  called  the  reductio  ad 
^^  "*  "    jinpos-       {mj)ossibile,  that  is,  by  circuitously  showing  that 

if  you  deny  the  conclusion  in  these  syllogisms, 
the  contradictory  inference  is  absurd  ;  but  as  of  two  contradictories 
one  or  other  must  be  true,  it,  therefore,  remains  that  the  original 
conclusion  shall  be  admitted.  This  process  is  awkward  and  perplex- 
ing ;  it  likewise  only  constrains  assent,  but  does  not  .afford  knowl- 
edge ;  while  at  the  same  time  we  have  here  a  syllogism  with  a  neg- 
ative subsumption,  which,  if  legitimate,  invalidates  the  universality 
of  our  second  general  rule.  Now,  on  the  principle  I  have  proposed 
to  you,  there  is  no  difficulty  whatever  in  the  reduction  of  this  or  of 
any  other  mood.  Here,  however,  we  do  not,  as  in  the  other  moods 
of  the  second  figure,  find   that  the  syllogism  proximately   departs 

from  an  unexpressed  sumption,  but  that  the  prox- 
Tn  reality  Daril.  ,  ,        ^      .  ,      ,  •  , 

imate  subsumption  and  the  proximate  conclu- 
sion have  been  replaced  by  two  derivative  propositions.  The 
formula  of  Baroco  is : 


Lkct.  XXII.  LOGIC.  J?ll 

AUFareJ/L; 

But  some  S  are  notM; 
Therefore,  some  S  are  not  P. 

But  the  following  is  the  full  mental  process  : 

Sumption, AUP  aretl; 

Real  Snbsumption, {Some  not-M.  are  S;) 

which  gives  the  (  TTien,  some  S  are  noi-M; 

Expressed  Subsumption, (  Ov,  some  S  are  not  ^; 

Real  Conclusion, (  Therefcyre,  some  nol-F  are  S; 

which  gives  the  {  Tlien,  some  S  are  not-P; 


(  The 
(Or, 


Expressed  Conclusion, (  Or,  some  S  are  not  P. 

Or,  to  take  our  concrete  example  : 

All  birds  are  oviparous ; 

But  some  animals  are  not  oviparous ; 

There/ore,  some  animals  are  not  birds. 

Of  this  the  explicated  process  will  stand  as  follows : 

Sumption, .      All  birds  are  oviparous; 

Real  subsumption, {Some  things  not  oviparous  art, atdrntds;) 

which  gives  the  {  Then,  some  animals  are  not-oviparous  ; 

Expressed  Subsumption, (  Or,  are  not  oviparous  ; 

_,_,..    ^       ,     .  (  ( Therefore,  some  things  not  birds  are  ani- 

Real  or  Proximate  Conclusion,    ....  J  ^  j      >  •> 

,  .  ,      .        ^,  (.  mals:) 

which  gives  the  ' 

„              J  /^       1     •  (  Then,  some  animals  are  not-birds; 

Expressed  Conclusion, J  ' 

(.  Or,  are  not  birds. 

Now,  in  this  analysis  of  the  process  in  Baroco,  we  not  only  re> 
solve  the  whole  problem  in  a  direct  and  natural  and  instructive 
way;  but  we  get  rid  of  the  exception  which  Baroco  apparently 
affords  to  the  general  rule,  that  the  subsumption  of  a  categorical 
must  be  affirmative.  Here  you  see  how  the  real  subsumption  is 
affirmative,  and  how,  from  having  a  negative  determination  in  its 
SMbject,  it  by  conversion  assumes  the  appearance  of  a  negative  pro]>- 
osition,  the  affirmative  proposition  —  some  things  not-birds  are  ani- 
mals, being  legitimately  converted,  first  into  —  some  animals  are 
no^-Wrc?5,  and  this  again  being  legitimately  converted  into  —  some 
animals  are  not  birds.  You  recollect  that,  in  the  doctrine  of  Prop- 
ositions,^ I  showed  you  how  every  affimiative  proposition  could  be 
adequately  expressed  in  a  negative,  and  every  negative  in  an  affir- 
m*ative  form ;  and  the  utility  of  that  observation  you  now  see,  as  it 

1  See  above,  p.  178.  —  Ed. 

40 


314 


LOGIC, 


Lect.  XXU 


Third  Figure. 


enables  us  simply  to  solve  the  problem  of  the  reduction  of  Baroco, 
and,  as  we  shall  also  see,  of  Bocardo.  Baroco  is  thus  directly  re- 
duced to  Darii  of  the  first  figure,  and  not,  as  by  the  indirect  process 
of  logicians  in  general,  to  Barbara.^  On  this  doctrine  the  name 
Baroco  is  also  improper,  and  another,  expressive  of  its  genuine 
affinity,  should  be  imposed. 

We  proceed  now  to  the  Third  Figure.  You  will  observe  that, 
as  in  the  Second  Figure,  with  the  exception  of 
Baroco,  it  was  the  sumption  of  the  two  premises 
which  was  affected  by  the  conversion,  so  in  the  third  it  is  the  sub- 
sumption.  For  in  Camestres  of  the  second,  and  in  Disamis  and 
Bocardo  of  the  third,  figure,  the  premises  are  transposed.  This 
understood  subsumption  is  a  conversive  inference  from  the  expressed 
one,  and  it  is  the  proxininte  antecedent  from  which  the  real  con- 
clusion is  immediately  inferred. 

In  the  first  mood  of  this  figure,  Darapti,  the  subsumption  is  a 
1.  Darapti.  universal  affirmative  ;  its  convei-sion  is,  therefore, 

In  reality  Darii.         into  a  particular  affirmative.    Its  formula  is  — 


Sumption, AUMareF; 

Expressed  Subsumption,    .     .     .  Bui  all  IS.  are  S; 

which  {^ives  the 

Really  Proximate  Subsumption,  .  (  Then  some  S  are  M;) 

from  which  directly  flows 

The  Conclusion Therefore,  tome  S  are  P. 


1  There  seems  to  be  an  error  in  the  text 
here.  The  syllogism,  as  finally  reduced,  is 
not  in  Darii,  nor  in  any  legitimate  mood ; 
and  its  natural  reduction,  according  to  the 
method  adopted  by  the  Author,  is  not  to  Da- 
rii, but  to  Ferio,  by  means  of  an  unexpressed 
sumption.    Thus  — 

AttTcBreJA; 
Then  no  no/-M  are  P; 
Some  S  are  noNM; 
Ther^ore,  some  S  are  not  P. 

This  is  the  method  adopted  by  the  following 
logicians,  referred  to  by  the  Author  in  his 
Common-Place  Book,  viz. :  —  Noldius,  who 
calls  Baroco,  Facrono,  Logica  Recognita,  cap. 
xii.  }  12,  p.  300,  1666;  Reusch  (who  follows 
Noldius),  Systema  Logicum,  §  631).  p.  611.  2d 
ed.,1741;  Wolf,  Phil.  Rationalis,  }  384;  Bach- 
mann,  Logik,  §  133,  Anni.,  i.  p.  224.  Before 
any  of  the  above-mentioned  writers,  Mark 
Duncan  gives  the  reduction  of  Camestres  to 
<.'elnri-nt,  and  of  Baroco  to  Fcrio,  by  coun- 
terjiosition.  He  adds,  with  special  reference 
to  the  reduction  of  Baroco  to  Ferio  by  this 
method,  —  "  Hanc  reductionis  speciem  exist- 


imo  a  scholasticis  perspectam  Aiisse:  sed  de.<>. 
pcctam;  quia  in  prima  figura  propositio  mi- 
nor aflirmans  attributi  iniiniti,  quam  primo 
intuitu  videatur  esse  negans,  formx  eviden- 
tiam  obscurat:  atqui  syllogismorum  reductio 
comparata  est  non  ad  formse  bonitatem  ob- 
scurandam,  sed  illustraiidam."  InUitutionei 
Logica,  L.  ir.  c.  3,  S  4,  p.  230.  Salmurii,  1612 
The  syllogism  of  the  text  may  also  be  ex- 
hibited morecircuitously.as  Darii,  by  retain- 
ing the  affirmative  quality  in  the  converted 
proposition.    Thus ;  — 

\ 
An  not-il  are  not-P; 
Some  S  are  not  Ml 
Ther^ore,  tome  8  cart  iio^P. 

This  is  the  method  of  reduction  employed 
by  Derodon,  who,  in  the  same  way,  would 
reduce  Camestres  to  Barbara,  Logica  Restituia, 
P.  iv.  tract,  i.  c  2,  art.  6,  p.  648.  The  error 
here  noticed  seems  to  have  originated  in  a 
momentary  confusion  of  the  reduction  of 
Baroco  with  that  of  Bocardo;  which,  hoV- 
ever,  could  not  be  rectified  without  greater 
alterations  in  the  text  than  the  Editors  con- 
sider tliemselves  Justified  in  making  —Ed 


Lect.  XXn.  LOGIC.  315 

Our  concrete  example  was  — 

Sumption, All  gilding  is  metallic ; 

Expressed  Subsiimption, Bui  all  <jildin<j  shines; 

which  jiivcs,  as  a  conversion,  the 

Real  Subsuniption, 7'hen,  some  things  that  shine  are  (jilding ; 

and  from  this  last  immediately  pro- 
ceeds the 

Conclusion, Therefore,  some  things  that  shine  are  vietaliic. 

Thus  Darapti,  in    the   third  figure,  is  nothing  but   a  one-sided 
derivative  of  Darii  in  the  first.' 

The  second  mood  of  the  Tliird  Figure  is  Fe- 

2.  Felapton.  ,  t       i--  i 

lapton.     Its  lormula  — 

Sumption,       No  M  i's  1'; 

Expressed  Sinni)ti(jn 1// M  areS; 

The  Ileal  Subsuniption,    .     .     .     {Thtn,  some  S  are  "^l;) 

from  which 
The  Conclusion, Therefore,  some  S  are  not  P. 

Our  example  was  — 

Sumption, Nothing  material  is  a  free  acjcnt; 

Expressed  Subsumption, But  eceryfhing  material  is  extended; 

Of  which  the  Real   Subsumption  is   the  )  ,  ^,  , .  ,   ,  .  .  ,  , 

r  ( Iken,  something  extended  is  material;) 
converse, > 

^  Therefore,  something  extended  is  not  a  free 

From  which  the  Conclusion, -; 

(  agent. 

Felapton,  in  the  third  Figure,  is  thus  only  a  modification  of  Ferio 
in  the  first. 

The  third  mood  in  this  figure  is  Disamis.     Its 

3.  Disamis.  ^  , 

lormula  — 

Some  M  are  P; 
But  all  M  are  S; 
Therefore,  some  S  are  P. 

Here  the  premises  are  transposed.     Their  or- 

In  reality  Darii.  t       i     •  -r.    -, 

der  bemg  rectified : 

Sumption, AlllslareS; 

Expressed  Subsumption But  some 'M  are  P ; 

1  [Eeusch,  Systema  Logicum,  §  539,  p.  614.] 


316  LOGIC.  '  Lect.  XXII. 

Which,  by  conversive  inference,  gives  the  ^ 

T.       .      .    c  w          ^-  f  ( I'hen,  some  P  are  M;) 

Proximate  Subsumption, ) 

From  which  proceeds  the  Real  Conclusion,     (Therefore,  tome  V  are  &;) 

Whichfby  conversion,  gives  the  Expressed  > 

„       ,     .  y  Then,  some  S  are  P. 

Conclusion, )  ' 

Our  example  was  (the  reversal  of  the  premises  being  rectified) : 


Samption, All  acts  of  homicide  are  cruel; 

Expressed  Subsumption, But  some  acts  of  homicide  are  laudable ; 

Which  {fives,  as  a  conversive  inference,  7  ( Then,  some  laudable  acts  art  acts  of  homi- 

the  Proximate  Subsumption,     .     .    .)         cide;) 

From  this  Proximate  Conclusion,     .    .    .     (  Therefore,  some  laudable  acts  are  cruel;) 

Which  ainiin  gives,  as  its  converse,  the )  _,       ,  ,  ,     ,  , . 

>-  Therefore,  some  cruel  acts  are  laudable. 
Expressed  Conclusion, > 

Thus  Disamis  in  the  third  is  only  Darii  in  the  first  figure. 
The  fourth  mood  of  the  Third  Figure  is  Datisi,  which  is  only 
Disamis,  the  premises  not  being  revereed,  and 
-       ,.,  r^   ,.  the  conclusion  not  a  conversive  inference.     It 

In  reality  Darii. 

requires,  therefore,  only  to  interpolate  the  prox- 
imate subsumption.     Thus: 

Sumption, -iWMnreP; 

Expressed  Subsumption, But  some  "M.  are  S; 

Giving  by  conversion, {TTien,  some  S  are  }ti;) 

From  which  last  the  Conclusion,      .    .    .  Therefore,  some  S  are  P. 


Sumption, All  acts  of  homicide  are  erue* , 

Expressed  Subsumption, But  some  acts  of  homicide  are  laudable; 

Which  gives,  by  conversion,  the  Proxi-  )  ( TTien,  tome  laudable  acts  are  acta  of  homi- 

mate  Subsumption, >         cide;) 

From  which  the  Conclusion, Therefore,  tome  laudable  acts  are  crueL 


Thus,  Datisi  likewise  is  only  a  distorted  Darii. 

The  fifth  mood  of  the  Third  Figure  is  the  famous  mood  Bocardo, 
which,  as  I  have  mentioned,  with  Baroco,  but 
far  more  than  Baroco,  was  the  opprobrium  of 
the  scholastic  system  of  reduction.  So  intricate,  in  fact,  was  this 
mood  considered,  that  it  was  looked  upon  as  a  trap,  into  which  if 
you  once  got,  it  was  no  easy  matter  to  find  an  exit.  Bocardo  was, 
during  the  middle  ages,  the  name  given  in  Oxford  to  the  Academi- 
cal Jail  or  Career  —  a  name  which  still  remains  as  a  rolique  of  the 
ancient  logical  glory  of  that  venerable  seminary.    Rejecting,  then. 


Lect.  XXn.  LOGIC.  317 

the  perplexed  and  unsatisfactory  reduction  by  the  logicians  of  Bo- 
cardo  to  Barbara  by  an  apagogical  exposition,  I  commence  by  stat- 
ing, that  Bocardo  is  only  Disamis  under  the  form  of  a  negative 
affirmative ;  its  premises,  therefore,  are  transposed.  Removing  the 
transposition,  its  formula  is  — 

All  M  are  S ; 

But  some  M  are  not  P ; 

Therejbre,  some  S  are  nofP; 

which  is  thus  explicated,  like  Baroco  — 

Sumption, AUilareS; 

Expressed  Subsumption, Some  M  are  tiof  P; 

Which  gives,  by  conversive  inference,      .     (Then,  some noi-V  are  ilL;) 
From  this  Real  Subsumption  proceeds  the  ) 

Proximate  Conclusion, 
Which  again 

Expressed 
Whence  again, Some  S  are  not  P; 


>•  (  There/ore,  some  not-P  are  S;) 


iin  gives,  by  conversion,  the  )  ^  „  _ 

y  Then,  some  S  are  not-P ; 
ised  Conclusion, ) 


Our  concrete  example  was  —  the  order  of  the  premises  being 
redressed ; 

Sumption, All  syllogisms  are  important ; 

Expressed  Subsumption, But  some  syllogisms  are  not  regttlar ; 


\  ( Then,  some   things  not  regular  are  syllo- 


From  which,  by  conversive  inference.         . 

1.  gisms;) 

And  from  this  Proximate  Subsumption  )  Therefore,  some  things  not  regular  are  im- 

proceeds  the  Proximate  Conclusion,  .  J        poriant  ; 

From  whence,  by  conversion,  the    Ex- ) 

,  „       ,     .  f  Then,  some  important  things  are  not-regular  < 

pressed  Conclusion, > 

^,^  J  Whence,  some  important  things  are  not  regit- 

(.         lar. 

Bocardo  is  thus  only  a  perverted  and  perplexed  Darii.^ 

The  last  mood  of  the  Third  Figure  is  Ferison, 
In  reality  Ferio  whicli  is  without  difficulty  —  it  Only  being  re- 

quired to  interpolate  the  real  subsumption,  from 
which  the  conclusion  is  derived.     Its  formula  is  — 

Sumption, iVo  MwP; 

Expressed  Subsumption, But  some  M  are  S ; 

1  (See  Noldins,  Log.  Rec.  c.  xii. )  12,  p.  301.    Bocardo  is  called  Docamroc  by  Koldius.    Cf 
Reusch,  Syst.  Log.,  i  539,  p.  611.] 


818  LOGIC.  Lect.  xxn 

Which  gives,  by  conversive  inference,  the ") 

r  Then,  some  S  are  M;      • 
Subsumption j 

From  which  immediately  flows  the  Con-} 

>  Therefore, 


,   _,_..,  some  S  are  ikX  P. 

elusion, 


Snmption, No  truth,  is  without  resuU  ; 

Expressed  Sabsnmption, But  some  truths  are  misunderstood; 

The  Conversive  Inference  from  which  is,      ITien  some  things  misunderstood  are  truths ; 
And  from  this  Implied  Subsumption  im-  >  There/ore,  some  things  misunderstood  are  not 


im-  > 
»    •  f 


mediately  proceeds  the  Conclusion,    .  )         tdthout  result. 

Ferison  ^  is  thus  only  Ferio,  jfringed  with  an 
Fourth  Figure.  •  t      .      /. 

accident  oi  conversion. 

The  Fourth  Figure  is  distinguished  from  the  two  former  in  this 
—  that  in  the  Second  and  Third  Figures  one  or  other,  but  only  one 
or  other,  of  the  premises  requires  the  interpolation  of  the  mental 
inference  ;  whereas,  in  the  Fourth  Figure,  either  both  the  premises 
require  this,  or  neither,  but  only  the  conclusion.  The  three  first 
moods  (Bamalip,  Calemes,  Dimatis)  need  no  conversion  of  the  prem- 
ises ;  the  two  last,  Fesapo  and  Fresison,  require  the  conversion 
of  both. 

The  result  of  the  foregoing  discussion  is  thus  accordingly  that,  in 

rigid  truth,  there  is  no  figure  entitled  to  the  dig- 

The  First  Figure  the       nity  of  a  simple  and  independent  form  of  rea- 

onysimpe  an    in  e-       goning,  cxccpt  that  which  has  improperly  been 

pendent  form  of  rea-  i     i       -r^.  r      r       ^ 

goning.  termed  the  First ;  the  three  latter  figures  being 

only  imperfect  or  elliptical  expressions  of  a  com- 
plex process  of  inference,  which,  when  fully  enounced,  is  manifestly 
only  a  reasoning  in  the  first  figure.     There  is  thus  but  one  figure, 
or,  more  properly,  but  one  process  of  categorical  reasoning;  for  the 
term  figure  is  abusively  applied  to  that  which  is  of  a  character  reg- 
ular, simple,  and  essential. 
Having,  therefore,  concluded  the  treatment  of  figure  in  respect 
of  Categorical   Syllogisms,  it  remains  to  con- 
Figure  of  Hypcthet-       sidcr  how  far  the  other  species  of  Simple  Syllo- 
icai,  Disjunctive,  and         -^^  _  ^^^  hypothetical,  the  disjunctive,  and 

Hypotlietico-Disjunct-         °  ...  .  .  '. 

ive  Syllogisms  ^^^  hypothetico-disjunctive  —  are  subject  to  this 

accident  of  form.  In  regard  to  the  Hypothetical 
Syllogism,  this  kind  of  reasoning  is  not  liable  to  the  affection  of 
figure.  It  is  true  indeed  that  we  may  construct  a  syllogism  of  three 
hypothetical  propositions,  which  shall  be  susceptible  of  all  the  fig- 

1  [Scotus  says  that  Ferison,  Bocardo,  and  Felapton,  are  useless,  as  concluding  indirectly 
QuantionfS,  In  Anal.  Prior.y  L.  i.  q.  24.] 


Lkct.  XXII.  LOGIC.  319 

ures  incident  to  a  categorical  reasoning ;  but  this  is  itself  in  fact 
only  a  categorical  syllogism  hypothetically  expressed.    For  example : 

If  K  is,  then  B  is; 
But  if  S  is,  then  Ais  ; 
Therefore,  if  S  is,  then  B  ts. 

This  syllogism  may  certainly  be  varied  through  all  the  figures, 
but  it  is  not  an  hypothetical  syllogism,  in  the  proper  signification 
of  the  term,  but  manifestly  only  a  categorical ;  and  those  logicians 
who  have  hence  concluded,  that  a  hypothetical  reasoning  was  ex- 
posed to  the  schematic  modifications  of  the  categorical,  have  only 
shown  that  they  did  not  know  how  to  discriminate  these  two  forms 
by  their  essential  diflfcrences. 

In  regard  to  the  Disjunctive  Syllogism  the  case  is  different;  for 
as  the  disjunctive  judgment  is  in  one  point  of  view  only  a  categor- 
ical judgment,  whose  predicate  consists  of  logically  opposing  mem- 
bers, it  is  certainly  true  that  we  can  draw  a  disjunctive  syllogism 
in  all  the  four  figures. 

I  shall  use  the  letters  P,  M,  and  S ;  but  as  the  disjunction  requires 
at  least  one  additional  letter,  I  shall,  where  that  is  necessary,  take 
the  one  immediately  following. 

Figure  I. 
M  ts  either  P  or  Q ; 
*  StsM; 

Therefore,  S  is  either  P  or  Q. 

Figure  II. 
First  case — 

P  is  either  M  or  N; 
S  is  neither  M  nor  N; 
Therefore,  S  is  not  P.  . 

Second  case — 

P  is  neither  M  nor  Nj 
S  is  either  M  or  N; 
Therefore,  S  is  not  P. 

Figure  HI. 
M  is  either  P  or  Q ; 
MtsS; 
Therefore,  some  S  is  either  P  or  Q. 


^20  LOGIC.  Lect.  xxa 

FionRE  rv. 
First  case  — 

P  is  eiUier  M  or  N; 
Both  M.  and  E  are  8; 
Therefore,  some  S  uP. 

Second  case  — 

P  is  either  M  or  N; 
Neither  M  nor  N  i«  S; 
Therefore,  S  is  not  P.* 

Of  Composite  Syllogisms  —  I  need  say  nothing  concerning  the 

Epicheirema,  which,  it  is  manifest,  may  be  in 

jgnreo    omposi  e       ^^^  figure  equally  as  another.     But  it  is  less  evi- 

Syllogisms.  °  . 

dent  that  the  Sorites  may  be  of  any  figure;  and 
logicians  seem,  in  fact,  from  their  definitions,  to  have  only  contem- 
])lated  its  possibility  in  the  first  figure.  It  is,  however,  capable  of 
all  the  four  schematic  accidents  by  a  little  contortion ;  but  as  this 
at  best  constitutes  only  a  logical  curiosity,  it  is  needless  to  spend 
any  time  in  its  demonstration."^ 

So  much  for  the  Form  of  reasoning,  both   Essential  and  Acci 
dental,  and  the  Divisions  of  Syllogisms  which  are  founded  thereon. 

1  See  Chr.  J.  Braniss,  Grundruw  der  Log-it,  }      difiTerent    figures,  see  Uerbart,  Lehrbueh  zur 
394,  p.  146.   Compare  Knig,Logiit,  p.  387  e/ if?.      Einleitung  in  die  Philosophie,  i  70.    Drobisch, 

2  For  a  complicated  theory  of  Sorites  in     Neue  Darstellung  der  Logik, }{  80 — 84.  —  Eo. 


LECTURE     XXIII. 

STOICHEIOLOGY. 

SECTION   II.— OF  THE    PRODUCTS  OF    THOUGHT. 

III.  — DOCTRINE    OF  REASONINGS. 

SYLLOGISMS.  — THEIR  DIVISIONS  ACCORDING  TO   VALIDITY. 

FALLACIES. 

All  the  varieties  of  Syllogism,  whose  necessary  laws  and  oontirr- 
pfent  modifications  we  have  hitherto  considered,  are,  taken  together, 
divided  into  classes  by  reference  to  their  Validity ;  and  I  shall  com- 
prise the  heads  of  what  I  shall  afterwards  illustrate,  in  the  follow- 
ing paragraph. 

%  LXXVI.   Syllogisms,  by  another  distribution,  are  distin- 
guished, by  respect  to  their  Validity,  into 
Par.  LXXVI.  syuo-       Corvect  ov   True,  and  Incorrect  or  False. 

glsms,  — Correct    and  mi        t  tt    i  •        ^  i  i 

Incorrect.  I  he  lucorrcct  or  liaise  are  agam  (though 

not  in  a  logical  point  of  view)  divided,  by 
reference  to  the  intention  of  the  reasoner,  into  Paralogisms, 
Faulty,  and  into  Sophisms,  or  Deceptive,  Reasonings.  The 
Paralogism  {paralogisnius)  is  properly  a  syllogism  of  whose 
falsehood  the  employer  is  not  himself  conscious;  the  Sophism. 
{sophisma,  captio,  cavillatio)  is  properly  a  false  syllogism,  fab- 
ricated and  employed  for  the  purpose  of  deceiving  others. 
The  term  ^aZ^acy  may  be  applied  indifferently  in  either  sense. 
These  distinctions  are,  however,  frequently  confounded ;  nor  in 
a  logical  relation  are  they  of  account.  False  Syllogisms  are, 
again,  vicious,  either  in  respect  of  their  form  or  of  their  matter,, 
or  in  respect  of  both  form  and  matter.* 


1  Krug,  Logik,  J  115.— Ed. 

41 


^22  LOGIC.  '  Lect.  XXlli 

In  regard  to  the  first  distinction  contained  in  this  paragraph,  — 
of  Syllogisms  into  Con-ect  or  True  and  Incor- 
Explication.  rector  False, —  it  is  requisite  to  say  a  few  words. 

iut^'Trulh  ""discrimt  ^^  '^^  nccessary  to  distinguish  logical  truth,  that  is, 
nated.  the  truth  which  Logic  guarantees  in  a  reasoning, 

from  the  absolute  truth  of  the  several -judgments 
of  which  a  reasoning  is  composed.  I  have  frequently  inculcated  on 
you  that  Logic  does  not  w}»aTant  the  truth  of  its  premises,  except 
in  so  far  as  these  may  be  the  formal  conclusions  of  anterior  reason- 
ings,—  it  only  warrants  (on  the  hypothesis  that  the  premises  are 
truly  assumed)  the  truth  of  the  inference.  In  this  view  the  conclu- 
sion may,  as  a  separate  proposition,  be  true,  but  if  this  truth  be  not 
a  necessary  consequence  from  the  premises,  it  is  a  false  conclusion, 
that  is,  in  fact,  no  conclusion  at  all.  Now,  on  this  point  there  is  a 
<loctrine  prevalent  among  logicians,  which  is  not  only  erroneous, 
but,  if  admitted,  is  subversive  of  the  distinction  of  Logic  as  a 
purely  formal  science.  The  doctrine  in  question  is  in  its  result  this, 
—  th^nt  if  the  conclusion  of  a  syllogism  bo  true,  the  pi'emises  may 
be  either  true  or  false,  but  that  if  the  conclusion  be  false,  one  or 
both  of  the  premises  must  be  false ;  in  other  woi'ds,  that  it  is  possi- 
ble to  infer  true  from  false,  but  not  false  from  true.  As  an  example 
of  this  I  have  seen  given  the  following  syllogism ;  * 

Aristotle  is  a  Ronum  ; 
A  Roman  is  a  European ; 
Therefore,  Aristotle  is  a  European- 

The  inference,  in  so  far  as  expressed,  is  true ;  but  I  would  remark 
that  the  whole  inference  which  the  premises  necessitate,  and  which 
the  conclusion,  therefore,  virtually  contains,  is  not  true,  —  is  false. 
For  the  premises  of  the  preceding  syllogism  gave  not  only  the 
conclusion,  Aristotle  is  a  European^  but  also  the  conclusion,  Aris- 
totle is  not  a  Greek;  for  it  not  merely  follows  from  the  premises 
that  Aristotle  is  conceived  under  the  universal  notion  of  which  the 
concept  Roman  forms  a  particular  spliere,  but  likewise  that  he  is 
conceived  as  excluded  from  all  the  other  particular  spheres  which 
are  contained  under  thr.t  univereal  notion.  The  consideration  of 
the  truth  of  the  premise,  Aristotle  is  a  Jioman^  is,  however,  more 
properly  to  be  regarded  as  extralogical ;  but  if  so,  then  the  consid- 
eration of  the  conclusion,  Aristotle  is  a  European,  on  any  other 
view  than  a  mere  formal  inference  from  certain  given  antecedents, 
is,  likewise,  extralogical.  Logic  is  only  concerned  with  the  formal 
truth  —  the  technical  validity  —  of  its  syllogisms,  and   anything 


I 


Lect.  XXm.  LOGIC.  823 

beyond  the  legitimacy  of  the  consequence  it  draws  from  certain 
hypothetical  antecedents,  it  does  not  profess  to  vindicate.  Logic:;! 
truth  and  falsehood  are  thus  contained  in  the  correctness  and 
incorrectness  of  logical  inference ;  and  it  was,  therefore,  with  no 
impropriety  that  we  made  a  true  or  correct,  and  a  false  or  incorrect 
syllogism  convertible  expressions.^ 

In  regard  to  the  distinction  of  Incorrect  Syllogisms  into  Paralo- 
gisms   and    Sophisms,   nothing    need   be   said. 

The    distinction    of        —.u  ^    ^  ^     •  ix;    •       ^i  -c    ^ 

Incorrect  Syllogisms  ^^^  "^^''^  Statement  IS  Sufficiently  manifest; 
into  Paralogisms  and  and,  at  the  same  time,  it  is  not  of  a  logical 
Sophisms, not ofiogi-  import.  For  logic  does  not  regard  the  inten- 
*^  '™P<""  •  tion  with  which  reasonings  are  employed,  but 

considers  exclusively  their  internal  legitimacy.  But  while  the  dis- 
tinction is  one,  in  other  respects,  proper  to  be  noticed,  it  must  be 
owned  that  it  is  not  altogether  without  a  logical  value.  For  it 
behooves  us  to  discriminate  those  artificial  sophisms,  the  criticism 
of  which  requires  a  certain  acquaintance  with  logical  forms,  and 
which,  as  a  play  of  ingenuity  and  an  exercise  of  acuteness,  are  not 
without  their  interest,  from  those  paralogisms  which,  though  not  so 
artificial,  are  on  that  account  only  the  more  frequent  causes  of  error 
and  delusion. 

The  last  distinction  is,  however,  logically  more  important,  viz.,  1°, 
Of  reasonings  into  such  as  are  materially  falla- 

Formal  and  material  .  i         •        i  i      i  -i  •  f    ^     ' 

Fallacies  cious,  that  IS,  through  the  object-matter  or  their 

t  propositions  ;  2°,  Into  such  as  are  formally  falla- 

cious, that  is,  through  the  manner  or  form  in  which  these  proposi- 
tions are  connected  ;  and,  3°,  Into  such  as  are  at  once  materially  and 
formally  fallacious.  Material  Fallacies  lie  beyond  the  jurisdiction 
of  Logic.  Formal  Fallacies  can  only  be  judged  of  by  an  a2:)plica- 
tion  of  those  rules,  in  the  exposition  of  which  we  have  hitherto 
been  engaged. 

The  application  of  these  rules  will  afford  the  opportunity  of  ad- 
ducing and  resolving  some  of  the  more  capital 

Ancient  Greek   So-  j.>  ^u  o       t,*  i  •   i,  ^.i-    •  •    •       ^ 

jj.  oi  those  Sophisms,  Avhich  owe  their  origin  to 

the  ingenuity  of  the  ancient  Greeks.  "Many 
of  these  sophisms  appear  to  us  in  the  light  of  a  mere  play  of  wit 
and  acuteness,  and  we  are  left  to  marvel  at  the  interest  which  they 
originally  excited,  —  at  the  celebrity  which  they  obtained,  and  at 
the  importance  attached  to  them  by  some  of  the  most  distinguished 
thinkers  of  antiquity.  The  marvel  will,  however,  be  in  some  degree 
abated,  if  we  take  the  following  circumstances  into  consideration. 

1  Cf.  Esser,  Logik,  i  109.  —  £d. 


824  LOGIC.  Lkct.  xxiil 

"In  the  first  place,  in  the  earlier  ages  of  Greece,  the  method  of 
science  was  in  its  infancy,  and  the  laws  of  thought  were  not  yet 
investigated  with  the  accuracy  and  minuteness  requisite  to  render 
the  detection  of  these  fallacies  a  very  easy  matter.  Howbeit,  there- 
fore, men  had  an  obscure  consciousness  of  their  fallacy,  they  could 
not  at  once  point  out  the  place  in  which  the  error  lay;  they  were 
thus  taken  aback,  confounded,  and  constrained  to  silence. 

"In  the  second  place,  the  treatment  of  scientific  subjects  was 
more  oral  and  social  than  M'ith  us;  and  the  form  of  instruction 
principally  that  of  dialogue  and  conversation.  In  antiquity,  men 
did  not  isolate  themselves  so  much  in  the  retirement  of  their 
homes ;  and  they  read  far  less  than  is  now  necessary  in  the  mod- 
ern world ;  consequently,  with  those  who  had  a  taste  for  science, 
the  necessity  of  social  communication  was  greater  and  more  urgent. 
In  their  converse  on  matters  of  scientific  interest,  acuteness  and 
profundity  were,  perhaps,  less  conducive  to  distinction  than  vivac- 
ity, wit,  dexterity  in  questioning,  and  in  the  discovery  of  objec- 
tions, self-possession,  and  a  confident  and  uncompromising  defence 
of  bold,  half-ti'ue,  or  even  erroneous  assertions.  Through  such 
means,  a  very  superficial  intellect  can  frequently,  even  with  us, 
puzzle  and  put  to  silence  another  far  acuter  and  more  profound. 
But,  among  the  Greeks,  the  Sophists  and  Megaric  philosophers  were 
accomplished  masters  in  these  arts. 

"  In  the  third  place,  as  we  know  from  Aristotle  and  Diogenes 
Laertius,^  it  was  the  rule  in  their  didlogical  disputations,  that  every 
question  behooved  to  be  answered  by  a  yes  or  a  no,  and  thus  the 
interrogator  had  it  in  his  power  to  constrain  his  adversary  always 
to  move  in  a  foreseen,  and,  consequently,  a  determinate  direction. 
Thus  the  Sophisms  were  somewhat  similar  to  a  game  of  forfeits,  or 
like  the  passes  of  a  conjurer,  which  amuse  and  astonish  for  a  little, 
but  the  marvel  of  which  vanishes  the  moment  we  understand  the 
principle  on  which  they  are  performed."  ^ 

As  the  various  fallacies  arise  from  secret  violation  of  the  logical 
laws  by  which  the  different  classes  of  syllogisms  are  governed,  and 
as  syllogisms  arc  Categorical,  or  Hypothetical,  or  Disjunctive,  or 
Hypothetico-disjunctive,  we  may  pi'operly  consider  Fallacies  under 
these  four  heads,  and  as  transgressions  of  the  syllogistic  laws  \n 
their  special  application  to  these  several  kinds  of  syllogism. 

^  LXXVII.  The  Syllogistic  Laws  determine,  in  reference  to 
all  the  classes  of  Syllogism,  the  three  following  principles ;  and 


I  Arist.  Soph.  Elench.,  c.  17.    Laertius,  L.  ii.  c.  18,  i  135.    Tlie  references  are  giren  bjr  Bacb- 
mann.  —  Ed.  2  Baohmann,  Logik,  i  884,  p.  613. 


I 


Lecx  XXIII.  LOGIC.  826 

all  Fallacies  are  violations  of  one  or  other  of  these  principles, 
in  relation  to  one  or  other  class  of  syllogism. 

I.  If  both  the  Looical  Form  and  the  Mat- 

Par.  liXXVII.  Palla-  _  ^ 

oies, -their  division       tcr  of  a  syllogism  bc   correct,  then  is  the 

andclassifleation.  Conclusion  trUC. 

II.  If  the  syllogism  be  Materially  Correct,  but  Formally  In- 
correct, then  the  Conclusion  is  not  (or  only  accidentally)  true. 

III.  If  the  syllogism  be  Formally  Correct,  but  Materially 
Incorrect,  then  the  Conclusion  is  not  (or  only  accidentally) 
true. 

Fallacies,  as  violations  of  these  principles  in  more  immediate 
reference  to  one  or  other  of  the  Four  Classes  of  Syllogism, 
must  again  be  vicious  in  reference  either  to  the  form,  or  to  the 
matter,  or  to  both  the  form  and  matter  of  a  syllogism.  Falla- 
cies are  thus  again  divided  into  Formal  and  Material^  under 
which  classes  we  shall  primarily  arrange  them. 

%  LXXVIII.  Of  Formal  Fallacies,  the  Categorical  are  the 
Par  Lxxviii  For-      "^ost  frcqucnt,  and  of  these,  those  whose 
mai  Paiiaeiea   Gate-       vicc  lies  in  having  four  in  place  of  three 
goncai.  terms  {quaternione  termino'rum.) ;  for  this, 

in  consequence  of  the  ambiguity  of  its  expression,  does  not 
immediately  betray  itself.  Under  this  genus  are  comprised 
three  species,  which  are  severally  known  under  the  names  of, 
1°,  Fallacia  sensus  compositi  et  divisi ;  2°,  Fallacia  a  dicto 
secundum  quid  ad  dictum  sim,pliciter,  et  vice  versa  /  3°,  Fallct- 
ciafigurce.  dictionis. 

"-  That  in  a  categorical  syllogism  only  three  terms  are  admissible, 
„    ,.     .  has  been   already  shown,     A  categorical  syllo- 

Explication.  _  .  . 

Fallacies  arising  gism,  Avith  four  Capital  notions,  has  no  connec- 
from  a  Quaternio  Ter-  tion  ;  and  is  Called,  by  way  of  jest,  the  logical 
"""""""■  quaUruped  {animal  quadrupes  logicum).     This 

vice  usually  occurs  when  the  notions  are  in  reality  different,  but 
when  their  difference  is  cloaked  by  the  verbal  identity  of  the  terms; 
for,  otherwise,  it  would  be  too  transparent  to  deceive  either  the 
reasoner  himself  or  any  one  else.  This  vice,  may,  however,  be  of 
various  kinds,  and  of  these  there  are,  as  stated,  three  principal 
epecics." 

"  The  first  is  the  Fallacia  sensus  compositi  et  divisi,  —  the  Fal- 
lacy of  Composition  and  Division}  This  arises  when,  in  the  same 

1  [See  Fonseca,  Instit.  Dial.,  L.  viii.  c.  v.  p.  106,  Ingolstadii,  1604-] 


32«  LOGIC.  Lect.  XXIH 

syllogism,  we  employ  words  now  collectively,  now  distributively, 

so  that  what  is  true  in  connection,  we  infer  must 

i.FaUactasensuseom-       ^^  ^-^^^  tr\ie  in  Separation,  and  vice  versa;  as,  for 

ponti  et  divisi.  .  x>    •  •  t 

example:  —  All  must  sin/  Cams  sins;  there- 
fore^ Caius  must  sin."^  Here  we. argue,  from  the  unavoidable  lia- 
bility in  man  to  sin,  that  this  particular  sin  is  necessary,  and  for 

this  individual  sinner.  "  This  fallacy  may  arise 
^^Modes  of  this  Fai-       -^^  different  ways.     F,  It  may  arise  when  the 

predicate  is  joined  with  the  subject  in  a  simple 
and  in  a  modal  relation,  for  example :  White  can  be  (i.  e.  become) 
Uack,  therefore  white  can  be  black.  2°,  It  may  arise  from  the  con- 
fusion of  a  copulative  and  disjunctive  combination.  T^ius  9  co)i- 
ststs  or  is  m,acle  up  q/*  7  -{-  2,  which  are  odd  and  even  numbers, 
therefore  9  is  odd  and  even.  3°,  It  may  arise,  if  words  connected 
in  the  premises  are  disjoined  in  the  conclusion.  Thus :  Socrates  is 
dead,  therefore  Socrates  is" ^ 

An  exam2)le  of  the  first  of  these  contingencies  —  that  which  is 
the  most  frequent  and  dangerous  —  occurs  when,  from  its  univer- 
sality, a  proposition  must  be  interpi-eted  with  restriction.  Thus, 
when  our  Saviour  says,  —  The  blind  shall  see,  — The  deof  shall  hear, 
—  he  does  not  mean  that  the  blind,  as  blind,  shall  see,  —  that  the 
deaf,  as  deaf,  shall  hear,  but  only  that  those  who  had  been  blind 
and  deaf  should  recover  the  use  of  these  senses.  To  argue  the 
opposite  would  be  to  incur  the  fallacy  in  question. 

The  second  fallacy  is  that  A  dicto  secundum  quid  ad  dictum  sim- 

pliciter,  and  its  converse,  A  dicto  simpliciter  ad 

2.  FaUacia  a  dicto  x-       dictum  secundum  quid.    The  former  of  these 

urn  qui   a     letum      —  ^j^^  fallacy  A  dicto  secundum,  quid  ad  dictum 

umplicitrr^  and  its  con-  "^         .  ■  ■* 

ygtBb.  simpliciter  —  arises   when,  from   what  is  tnie 

only  under  certain  modifications  and  relations, 
we  infer  it  to  be  true  absolutely.  Thus,  if,  from  the  fact  that  some 
Catholics  hold  the  infallibility  of  the  Pope,  we  should  conclude 
that  the  infallibility  of  the  Pope  is  a  tenet  *of  the  Catholic  Church 
in  general.  The  latter  —  the  fallacy  a  dicto  simpliciter  ad  dictum 
secundum  quid  —  is  the  opposite  sophism,  where  from  what  is  true 
absolutely  we  conclude  what  is  true  only  in  cei-tain  modifications 
and  relations,  as,  for  example,  when  from  the  premise  that  Man  is  a 


I  Krug,  Logik,  S  116,  p.  420.  —  Ed.    [On  the  Alrarez,  in  Gale,  Pkilosophia  Generalis,  L.  iii 

distinction  of  Scnsus  Compositi  ft  Divisi,  so  C.  iii.  sect.  2,  }  8,  p.  468.] 
famous  in  the  question  of  foreknowledge  and 

liberty,  see   its  history  in  Kuiz,  Conimtnt'irii         3  [Denzin-^r,]    [Die  Logik    als  Wisienschnft 

ae  Disfiututiones,  de   Scientia,  de  Ideis,  dt  Yeri-  dtr  Denkkmut,  dargestellt,  i  558,  Bamberg,  183& 

late,  ae  de  Vita  Dei,  Disp.  xxxiii.  p.  261  et  ug.  —  Ed.] 


Lbct.  xxni.  LOGIC.  32T 

Kmng  organism^  we  infer  that  A  painted  or  sculptured  man  is  a 
living  organism} 

The  third  fallacy  —  the  Sophisma  Jigurm  dictionis  —  arises  when 
we  merely  play  with  the  ambiguity  of  a  word.  The  well-known 
syllogism,  3fus  syllaba  est ;  Mus  caseum  rodit/  Ergo^  syllaba  ca- 
seum  rodit^  is  an  example ;  or, 

Herod  is  a  fox; 

A  fox  is  a  quadruped ; 

Therefore,  Herod  is  a  quadruped. 

To  this  fallacy  may  be  reduced  what  are  called  the  Sophisma  equtv- 
ocationis,  the  Sophisma  amphibolice,  and  the  Sophisma  accentus* 
which  are  only  contemptible  modifications  of  this  contemptible 
fallacy. 

^  LXXIX.  Of  Material  Fallacies,  those  are  of  the  most  fre- 
quent  occurrence,  where,  from    a   premise 
_^f ^' ^,^'^^^'  ^^^^'       which  is  not  in  reality  universal,  we  con- 

rial  Fallacies.  ^  .  . 

elude  universally ;  or  from  a  notion  which 
is  not  in  reality  a  middle  term,  we  infer  a  conclusion.  Under 
this  genus  there  are  various  species  of  fallacies,  of  which  the 
most  remarkable  are,  1°,  the  Sophisma  cum  hoc  (vel  post  hoc)^ 
ergo  propter  hoc ;  2°,  Sophisma  pigrum^  or  ignava  ratio ;  3°> 
Sophisma polyzeteseos ;  and  4°,  Sophisma  heterozeteseos* 

In  this  paragraph  you  will  observe  that  there  are  given  two 

genera  of  Material  Fallacies,  —  those  of  an  Un- 

Expiication.  YGTiX  Universality  (sophismata  Jictce  universali- 

<a  a  les  o  an     n-       fatis),  and  thosc  of  an  Illusive  Reason  (sophis- 

real  Universality,  and  '  \     l 

of  an  Illusive  Keason.  mata  falsi  medH,  —  or  7i07i  caiisce  ut  causce).  1 
must  first  explain  the  nature  of  these,  consid- 
ered apart,  then  show  that  they  both  fall  together,  the  one  being 
only  the  categorical,  the  othel-  only  the  hypothetical,  expression  of 
the  same  vice  ;  and,  finally,  consider  the  various  species  into  which 
the  generic  fallacy  is  subdivided. 

"  Our  decisions  concerning  individual  objects,  in  so  far  as  they 

belong  to  certain    classes,  are   very  frequently 

1.    Of  an  Unreal       fallacies  of  the  former  kind ;    that  is,  conclu- 

Universality.  '  .  . 

sions  from  premises  of  an   unreal  universality. 
For  example  :  — The  Jews  are  rogues,  —  The  Carthaginians,  faith- 

1  Cf.  Denzinger,  iMgik, }  564.  —Ed.  S  On  these  fallacies,  see  Denzinger,  Logik, 

H  559,  560,  561.  —  Ed. 

2  Seneca,  !>«< ,  48.  —  B».  4  Ct  Krug,  hog}k^ }  117. — Ep, 


328  LOGIC.  Lect.  XXll! 

less,  —  The  Cretans,  liars,  —  The  French,  hragadocios, —  TJie  Ger- 
mans, iny sties, — The  rich,  purse-proud,  —  The  noble,  haughty, — 
Women,  frivolous, — The  learned,  pedants.  —  These  and  similar 
judgments,  which  in  general  are  true  only  of  many,  —  at  best  only 
of  the  majority,  of  the  subjects  of  a  class,  often  constitute,  how- 
ever, the  grounds  of  the  opinions  we  form  of  individuals ;'  so  that 
these  opinions,  with  their  grounds,  when  expressed  as  conclusion- 
and  premises,  are  nothing  else  than  fallacies  of  an  unreal  generality, 
—  sophisrnata  fictce  universalitatis.  It  is  impossible,  however,  to 
decide  by  logical  rales  whether  a  proposition,  such  as  those  above 
stated,  is  or  is  not  universally  valid ;  in  this,  experience  alone  can 
instruct  us.  Logic  requires  only,  in  general,  that  every  sumption 
should  be  universally  valid,  and  leaves  it  to  the  several  sciences  to 
pronounce  whether  this  or  that  particular  sumption  does  or  does 
not  fulfil  this  indispensable  condition." '  The  sophisma  fictoe  uni- 
versalitatis is  thus  a  fallacious  syllogism  of  the  class  of  categoricals. 
But  the  second  kind  of  material  fallacies,  the  sophisms  of  Unreal 
Middle,   are   not   less   frequent   than   those   of 

2.  Of  Unreal  Middle.  ,  .  ,.  ,„,  „  i       -.     • 

unreal  universality.  When,  for  example,  it  is 
argued  (as  was  done  by  ancient  philosophers)  that  the  magnet  is 
animated,  because  it  moves  another  body,  or  that  the  stars  arc 
animated,  because  they  move  themselves;  —  here  there  is  assumed 
not  a  true,  but  merely  an  apparent,  reason ;  there  is,  consequently, 
no  real  mediation,  and  the  sophisma  falsi  medii  is  committed. 
F'or,  in  these  cases,  the  conclusion  in  the  one  depends  on  the 
sumption,  —  If  a  body  moves  another  body,  it  is  animated;  in 
the  other,  on  the  sumption,  —  If  a  body  m,oves  itself,  it  is  ani- 
mated/hut  as  the  antecedent  and  consequent  in  neither  of  these 
sumptions  are  really  connected  as  reason  and  consequent,  —  or  as 
cause  and  effect,  —  there  is,  therefore,  no  valid  inference  of  the 

conclusion.^    The  sophisma  non  causes  ut  caiiscB 
The  fallacies  of  Un-       jg  t^u^  an  hypothetical  syllogism  ;  but,  as  it  may 

real    Reason    and    of        i  .  •      n  i    .^i,*     .£»  ii  r-  i 

,     ,,  .       ,.,        be  categorically  enounced,  this  fallacy  of  unreal 

Unreal      Uuiversahty  9  j  '  j      ^ 

coincide.  reason  will  coincide  with  the   categorical   fal- 

lacy of  unreal  universality.     Thus,  the  second 
example  above  alleged : 

If  (he  Stan  move  themsdves,  they  are  animated', 
But  the  stars  do  move  themselves ; 
Therefore,  the  stars  are  animated :  — 

is  thus  expressed  by  a  categorical  equivalent  — 

1  Krug,  Logik,  i  117.    Anm.,  p.  422.  —  Ed.  «  Cf.  Krug,  Logik,  p.  423.  —  Elk 


Lkct.  xxiii.  logic.  329 

All  bodi.es  that  move  themselves  are  animated; 
But  the  stars  move  themselves ; 
Therefore,  the  stars  are  animated. 

In  the  one  case,  the  sumption  ostensibly  contains  the  subsumption 
and  conclusion,  as  the  correhitive  parts  of  a  causal  whole ;  in  the 
other,  as  the  correlative  parts  of  an  extensive  whole,  or,  had  the 
categorical  syllogism  been  so  cast,  of  an  intensive  whole.  The  two 
genera  of  sophisms  may,  therefore,  it  is  evident,  be  considered  as 
one,  —  taking,  however,  in  their  particular  manifestation,  either  a 
categorical  or  an  hypothetical  form. 

I  may  notice  that  the  sophism  of  Unreal  Generality,  or  Unreal 

Reason,  isTiardly  more  dangerous  in  its  positive 

Fallacy  of   Unreal       than  in  its  negative  relation.     For  we  are  not 

Keason  as  dangerous       ^^^^.^  disposed"  lightly  to  assume  as  absolutely 

ill  its  negative  as  in  its  .  .  .  ,    .  ,      . 

positive  form  universal  what  IS  universal  m  relation  to  our 

experience,  than  lightly  to  deny  as  real  what 
comes  as  an  exception  to  our  factitious  general  law.  Thus  it  is 
that  men  having  once  generalized  their  knowledge  into  a  compact 
system  of  laws,  are  found  uniformly  to  deny  the  reality  of  all  phe- 
nomena which  cannot  be  comprehended  under  these.  They  not 
only  pronounce  the  laws  they  have  generalized  as  veritable  laws 
of  nature,  which,  haply,  they  may  be,  but  they  pronounce  that 
there  are  no  higher  laws;  so  that  all  which  does  not  at  once  find 
its  place  within  their  systems,  they  scout,  without  examination,  as 
visionary  and  fictitious.  So  much  for  this  ground  of  fallacy  in  gen- 
eral ;  we  now  proceed  to  the  species. 

Now,  as  unreal  reasons  may  be  conceived  infinite  in  number,  the 

minor  species  of  this  class  of  sophisms  cannot 

Species  of  the  fai-       y^^   enumerated;    I    shall,  therefore,  only   take 

lacy  of  Unreal  Reason.  '  ^ 

notice  of  the  more  remarkable,  and  which,  in 
consequence  of  their  greater  notoriety,  have  been  honored  with 
distinctive  appellations. 

Of  these,  the  first  is  the  Sophisma  cum,  hoc  {vel  post  hoc),  errjo 

propter  hoc.     This  fallacy  arises  when,  from  the 

(■a.)  Sophisma  cum  hoc       contingent  consecution  of  certain  phenomena  in 

(vel  post  hoc),  ergo  prop-  ^  •    />       xu    •  ...       i    j  A 

t^i^^g  the  order  oi  time,  we  inter  their  mutual  depend- 

ence as  cause  and  effect.  When,  for  example, 
among  the  ancient  Romans,  a  general,  without  carefully  consulting 
the  augurs,  engaged  the  enemy,  and  suffered  a  defeat,  it  was  in- 
ferred that  the  cause  of  the  disaster  was  the  unfavorable  character 
of  the  auspices.  In  like  manner,  to  this  sophism  belongs  the  con- 
clusion, so  long  •  prevalent  in  the  world,  that  the  appearance  of  a 

42 


830  LOGIC.  ^  Lect.  XXUI 

comet  was  the  harbinger  of  famine,  pestilence  and  war.     In  fact, 
the  greater  number  of  the  hypotheses  which  constitute  the  history 
of  physics  and  philosophy,  are  only  so  many  examples  of  this  fal- 
lacy.    But  no  science  has  exhibited,  and  exhibits,  so  many  flagrant 
instances  of  the  sophism  cum  hoc,  ergo  propter  hoc,  as  that  of  med- 
icine ;  for,  in  proportion  as  the  connection  of  cause  and  efiect  is 
peculiarly  obscure  in  physic,  physicians  have  only  been  the  bolder 
in  assuming  that  the  recoveries  which  followed  after  their  doses, 
were  not  concomitants,  but  effects.     This  sophism  is,  in  practice,  of 
great  influence  and  very  frequent  occurrence ;  it  is,  however,  in  tlie- 
ory,  too  perspicuous  to  require  illustration. 
The  second  fallacy  is  that  which  has  obtained  the  npime  o^Ignava  ra- 
tio, or  Sophisma  pigrum.,  —  in  Greek,  dpyos  Aoyos.^ 
ignata    a  lo.         ^j^^  excogitation  of  this  argument  is  commonly 
attributed  to  the  Stoics,  by  whom  it  was  employed  as  subsidiary  to 
their  doctrine  of  fate.     "It  is  an  argument  by  which  a  man  endeav- 
ors to  vindicate  his  inactivity  in  some  particu- 
lar   relation,   by   the    necessity   of   the   conse- 
quence.    It  is  an  hypothetico -disjunctive  syllogism,  and,  when  fully 
expressed,  is  as  follows  : 

Sumption.  ......  If  I  ought  to  exert  myself  to  effect  a  certain  event,  this  event  either  must 

take  place  or  it  must  not ; 
Snbsumptlon  .  ...  If  it  must  take  place,  my  exertion  is  superfluous;  if  it  inust  not  take 

place,  my  exertion  is  of  no  avail ; 
Ck>nclasion Therefore,  on  either  alternative,  my  exertion  is  useless."  2 

Cicero,  in  tjie  twelfth  chapter  of  his  book,  De  Fato,  thus  states  it : 

If  it  be  fated  that  you  recover  from  your  present  disease,  whether  you  call  in  a  doctor  or  not, 
you  will  recover ;  again,  if  it  be  fated  that  you  do  not  recover  from  your  present  dis- 
ease, whether  you  caM  in  a  doctor  or  not,  you  will  not  recover; 

But  one  or  other  of  the  contradictories  is  fated; 

Therefore,  to  call  in  a  doctor  is  of  no  consequence. 

Others  have  enounced  the  sumption  in  various  forms,  for  ex- 
ample :  If  it  be  impossible  but  that  yov.  recover  from,  the  present 
disease,  etc.,  —  or  —  If  it  be  true  that  you  loiU  recover  from  this 
disease,  —  or  —  If  it  be  decreed  by  God  thai 

ts  various   esigna-         ^^^  ^^.^  ^^^  ^.^  ^r,  ^^^.^  disease,  and  so  likewise 

tlons.  ^  ''  ,       ., 

in   different  manners;  according  to  which  like- 
wise the  question  itself  has  obtained  various  titles,  as  Argument 

1  See  Mennjre  on  Diogenes  Lnertius,  L.  ii.      Gassendi,  OptTa,X.  i.  Bt  Log.  Orig.  €t  Tmr.,  It 
p.  123. —  Ed.     [FaccJolati,  Acroasis,  v.  p.  55.      i.  c.  6.  p   51] 

2  Krug,  Logik,  i  117,  p.  424.  —  Ed. 


I 


L 


Lkct.  XXIIL  logic.  331 

De  Fato  — De  Possihilihus  — De  JOibero  Arbitrio  — De  Promden- 
tia — De  Divinis  Decretis — De  Futuris  Contingentibus — DePhys- 
ica  Prcedeterminatione,  etc.  No  controversy  is  more  ancient, 
none  more  universal,  none  has  more  keenly  agitated  the  minds  of 
men,  none  has  excited  a  greater  influence  upon  religion  and  morals ; 
it  has  not  only  divided  schools,  but  nations,  and  has  so  modified 
not  only  their  opinions,  but  their  practice,  that  whilst  the  Turks,  as 
converts  to  the  doctrine  of  Fate,  take  not  the  slightest  precaution 
in  the  midst  of  pestilence,  other  nations,  on  the  contrary,  who  admit 
the  contingency  of  second  causes,  carry  their  precautionary  policy 
to  an  opposite  excess. 

The  common  doctrine,  that  this  argument  is  an  invention  of  the 
Stoics,  and  a  ground  on  which  they  rested  their 

Its  history.  ,  .  ^     ■,         ^       ■      ^  • 

doctrme  oi  the  physical  necessitation  oi  human 
action,  is,  however,  erroneous,  if  we  may  accord  credit  to  the  testi- 
mony of  Diogenes  Laertius,  who  relates,  in  the  Life  of  Zeno,  the 
founder  of  this  sect,  that  he  bestowed  a  sum  of  two  hundred  minae 
on  a  certain  dialectician,  from  whom  he  had  learned  seven  species  of 
the  argument  called  the  Xoyos  ■^epl^wv,  metens,  or  reaper,  which  diffei-s 
little,  if  at  all,  from  the  ignava  ratio}  For  how  this  sophism  is 
constructed,  and  with  what  intent,  I  find  recorded  in  the  commen- 
tary of  Ammonius  on  the  book  of  Aristotle  Ilept  "Etpfxrjvda'i?  Of 
the  same  character,  likewise,  is  the  argument  called  the  Xoyos  Kvpi- 
cwQjv,  the  ratio  dominans,  or  controlling  reason,  the  process  of  which 
Arrian  describes  under  the  nineteenth  chapter  of  the  second  book 
of  the  sayings  of  Epictetns.''  The  lazy  reason, — the  reaper, — and  the 
controlling  reason,  are  t!)us  only  various  names  for  the  same  process. 
In  regard  to  the  vice  of  this  sophism,  "it  is  manifest  that  it  lies  in 
the  sumption,  in  which  the  disjunct  members 
e   vice  o       js      ^^^  imperfectly  enounced.     It  ought   to   have 

sophism.  . 

been  thus  conceived  :  If  I  ought  to  exert  my- 
self to  effect  a  certain  event,  which  I  cannot,  however,  of  myself 
effect,  this  event  must  either  take  place  from  other  causes,  or  it 
must  not  take  place  at  all.  It  is  only  under  such  a  condition  that 
my  exertion  can,  on  either  alternative,  be  useless,  and  not  if  the 
event  depend  wholly  or  in  part  for  its  accomplishment  on  my  exer- 
tion itself,  as  the  conditio  sine  qua  non."  *    It  is  plain,  however,  that 

1  See  Laertins,  vii.  25.  The  observation  in  ered  from  Arrian,  but  not  the  nature  of  the 
the  text  is  from  Facciolati,  Acroasis,  v.  p.  57,  argument  itself.  It  is  also  mentioned,  though 
ed.  1750.  —  Ed.  not  explained,  by  Lucian,  Vit.  Auct.,  c.  22 

Plutarch,  Sympos.,  i.  1,  5.    Gellius,  N.  A.,  i.2 


2  F.  91  b,  ed.  Aid.  Tenet.,  1546.  — Ed 


Compare  Facciolati,  Acroasis,  v.  p.  67.  —  Eu 


uompare  facciolati,  >ieroasis,  1 
8  The  purpose  of  this  sophism  may  be  gath-        •*  Krug,  Logik,  p.  424.  —  Ed. 


832  LOGIC.  Lect.  XXIII. 

the  refutation  of  this  sophism  does  not  at  all  affect  the  doctrine  of 
necessity  ;  for  this  doctrine,  except  in  its  very  absiirdest  form, — the 
Fatum  Turcicum^  —  makes  no  use  of  such  a  reasoning. 

"  The  third  fallacy  is  the  Sophisma  polyzeteseos  or  qucestionis  dit- 
plicis^,  —  the  sophism  of  cofitinuous  questioning^ 

(c)  Sophisma  polyze-  i  •    u      a^  ..      £•  xi        •  -UM-^         c 

which  attempts,  trom  the  impossibility  oi  assign- 
ing the  limit  of  a  relative  nbtiou,  to  show  by 
continued  interrogation  the  impossibility  of  its  determination  at 
all.     There  are  certain  notions  which  are  only  conceived  as  relative, 

—  as  proportional,  and  whose  limits  we  cannot,  therefore,  assign  by 
the  gradual  addition  or  detraction  of  one  determination.  But  there 
is  no  consequence  in  the  proposition,  that,  if  a  notion  cannot  be 
determined  in  this  manner,  it  is  incapable  of  all  determination,  and, 
therefore,  absolutely  inconceivable  and  null."^     Such  is  the  Sorites, 

the  nature  of  which  I  have  already  explained  to 
Its  various  designa-       ^^^      rpj^j^  reasoning,  as  applied  to  various  ob- 

tions.  ^  _  o'  rr 

jects,  obtained   various   names,  as,  besides   the 
Sorites  or  Acervus,  we  have  the  crescens^  —  the  <^taXaKp6%  or  calvus^ 

—  the  virepSeTiKo^,  superpositus  or  superlativiis*  —  the  rjo-vxaZoyv  or 
qviescens,  etc.,  etc.*  The  Sorites  is  Avell  defined  by  Ulpian,*'  a  soph- 
ism in  which,  by  very  small  degrees,  the  disputant  is  brought  from 
the  evidently  true  to  the  evidently  false.  For  example,  I  ask,  Does 
one  grain  of  corn  make  up  a  heap  of  grain  ?  My  opponent  answers,  — 
No.  I  then  go  on  asking  the  same  question  of  two,  three,  four,  and 
so  on  ad  infimtuin^  nor  can  the  respondent  find  the  number  at  which 
the  grains  begin  to  constitute  a  heap.  On  the  other  hand,  if  we 
depart  from  the  answer,  —  that  a  thousand  grains  make  a  heap,  the 
interrogation  may  be  continued  downward  to  unity,  and  the  answerer 
be  unable  to  determine  the  limit  where  the  grains  cease  to  make  uj) 
a  heap.  The  same  process  may  be  performed,  it  is  manifest,  upon 
all  the  notions  of  proportion,  in  space  and  time  and  degree,  both  in 
continuous  and  discrete  quantity.' 

The  fourth  and  last  fallacy  of  this  class  is  the  sophisma  hetero- 
zeteseos,  or  sophism  of  counter-questioning^  and  as  applied  to  vari- 

1  Krng,  Logik,  S  H"-  —  Ed.  «  Leg',  177.  De  Verb  Signif.  "Natnra  cavil- 

2  Wyttenbacli,  ilrf  Ptut.  De  Sera  Num.  Vind.,  Jationis,  quam  Graeci  (ru>p(iT7{v  appellarnnt, 
p.  559;  Pra-cepia  Phil.  Log  ,  p.  iii.  c.  9,  §  4. —  Ed.  haec  est,  ut  ab  ea  ab  evidenter  veris  per  brev- 

3  Diog.  Laert.,  ii.  103.  Cf.  Gasseudi,  De  issimas  mutationes  disputatio  ad  ea  quas  evi- 
Log.  Orig.,  c.  3.  —  Ed.  dentur  falsa  sunt  perducatur."    Quoted  by 

4  Epictetus,  Dissert.,  iii.  2, 2.  As  interpreted  Gassendi,  De  Logieee  Origine  et  Yarittate.,  L.  i. 
by  Gassendi,  De  Log.  Orig.,  c.  6.  But  Ibe  c.  3,  p.  41,  aud  by  Menage,  Ad  Laert.,  ii.  108. 
true  reading  is  probably  inro^eTtKOVs.    See  —  Ed. 

Scbweigbasuser's  note.  —  Ed.  7  Krug,  Logik,  {  117.  —  Ed. 

«  Cicero,  Acwl.,  ii.  29.  Epictetus,  Dissert.  8  [See  Gassendi,  Opera,  1. 1.  De  Log.  Orig 
ii.  18, 19.  —  Ed.  et  Var.  L.  i.  c.  6,  p.  61] 


Lkct.  XXm.  LOGIC.  •  383 

ous  objects,  it  obtained,  among  tlie  ancients,  tlic  names  of  the  Di- 
lemma^ —  tJic  Cornidus^'  —  the  TAti(jiosus^  —  the 
(d)  sophisma  hctero.       ^^^.j.m,^.^  _  fj^,,  ^lentkus^  —  the  Fulhuis^  —  the 

z'teseos. 

I^JlectraS'  —  the  Obeekitus^  —  the  liec'njrocns,^ — • 
Its  vunous  names.  '  i  i  ^ 

tlie    Crocodilinifsj''  —  the  oiJrt?,-'^  —  the    Induct io 

imperfecta /^^  and  to  tliis  should  also  be  refei-rcd  the  Ass  of  Buri- 

danus.^-     "It    is  a  hvj^otlielico-disjunctivo    rea- 

Its  character.  .  i  •    i  '  •  •   •  i 

soning,  wlncii  rests  on  a  certain  suj)])osition,  and 
which,  through  a  reticence  of  this  supposition,  deduces  a  fallacious 
inference.  To  take,  for  an  exaini)le  of  tliis  fdlacy,  tlie  /cspanro?  or 
Cornutus:  —  it  is  asked:  —  Have  }ou  east  your  horns":'  —  If  you 
answer,  I  have;  it  is  rejoined,  Then  you  have  had  horns:  if  you 
answer,  I  have  not,  it  is  rejoined.  Then  you  have  them  still.'"' — To 
this  question,  and  to  the  inferences  from  it,  the  disjunctive  ])roposi- 
tion  is  suj)}iosed,  —  A  certain  subject  has  either  had  horns  or  has 
theni  still.  This  disjunction  is,  however,  only  coi'rcct  il'llie  question 
is  concerning  a  subject  to  which  horns  preA'iously  belonged.  If  I 
<lo  not  suppose  this,  the  ilisjmiction  is  f  ilse ;  it  must,  (■(jiiseipiently, 
thus  run  :  —  a  certain  subject  has  cither  had  or  not  had  horns.  In 
the  latter  case  they  could  not  of  course  be  cast.  The  alternative 
inferences  (thai  you  hare  hud  ththt,  or  then  you  linn:  thrin  .it ill) 
liave  no  longer  ground  or  plausibility."     To  take  anotlicr  instance  in 

the   LUiqiofius   or  jRecip/'OCu.s.     Of  ihc    history 

rhe  Litigiosus.  . 

of  this  iinnous  dilemma  there  are  two  accounts, 
the  Greek  and  the  Konum.  The  Iionum  account  is  gi\-en  us  by 
Aulus  Gellius,'"'  and  is  there  told  in  rehition  to  an  .'u-tiou  l^etween 

I'rotagoras,  the  prince  of  the  Sophists,  and 
The  case  of  Protag-       E^.^tlilus,  a  voung  uiau,  his  disciidc.     The  disci- 

oras  and  Luatlilus.  '        '  ■-  _  _    ^ 

pie  had  covenanted  to  give  Iiis  master  a  lai-ge 
sum  to  accomplish  him  as  a  legal  rhetorician;  the  one  half  of  the 
siuii  was  paid  down,  uvA  the  other  vras  to  be  paid  on  the  day  when 
Kuathliis    should    plerul    ;ind  gain    his    first  cause.     But   when  the 

i  IlcrmoErciies,  /)>■  Ln-nii..  L.  iv.,  and   Pro-  "^  Anius  (A'Uius,  N.  A.,  L.  v.  c.  10.  11  —  il;>^ 

l'-^^    ail    H-r!noi;nirm.      See    Walz's    IVi^tnrni  n  Liician,  /   c.     (;ninti;i:iii,  I.i.^:.  Om,'.,  i.  IT 

I'Vwc/,  vol.  iii.  p.  107,  iv.  j).  11.  —  Kd.  ;".     (T.  >Ienr._<re,  .4-/  Xl/w;'.  L«fr;.,  L.  ii    lOS.   - 

-'  Si^neca,  Epi.^t.,  l.j.     3Ie)iage,  Ad  Dlog;    Ln-  Kd. 

cr«.,  L.ii   108.  — Ki).  1"  Aminonin.s,   Ad  Arisi.   C<it.^..  f.  r,<.     Cf. 

•' Diop;.   Laert.,  L.  ix.  23.     Aristotle,  P/jt/,'!.,  Meua.trc, /or.  c/j.  —  I.'.n, 

vi.  9.     Soph.  Ecnri,.,  24.  —  Kl).  H  Cicero,  /)-;  In  rnninnr.  L.  i.  c.  SI.  -     Kn. 

•»  5Ienajre.  yl  /  Dii^s:.  Lneit.,  1^  ii.lO,'^.    Cicero,  I- See  DenzinL'er.  Ln-^iL-.  \  r,71,  IVoiri  \vliom 

.IfO'/.,  ii.  29.  —  En.  tliese  de.<iLri;ntions   are  taken.     llei'J's    Works, 

■>  Diojr.  Laert.,  ii.  108.  — Kd.  p.  2,38.  —  Kd. 

•5  Luc i an,  Vit.  And.,  5  22.     Cf.  Menage,  .W  ].'!  Diog.  Laert.,  vii.  187.— Kd. 

Diog.  Laert..,  L.  ii.  108.  —  Kd.  l-I  Krug,  Losik,  \).  ^'I'o.  —  Ed. 

^  Menage,  ibid.  —  Ed.  15  L.  v.  c.  10. 


334  LOGIC.  Lect.  XXIU 

scholar,  after  the  due  course  of  preparatory  instractioB,  was  not  in 
the  same  hurry  to  commence  pleader  as  the  master  to  obtain  the 
remainder  of  his  fee,  Protagoras  brought  Euathlus  into  court,  and 
addressed  his  opponent  in  the  following  reasoning :  —  Learn,  most 
foolish  of  young  men,  that  however  matters  may  turn  up  (whether 
the  decision  to-day  be  in  your  favor  or  against  you),  pay  me  my 
demand  you  must.  For  if  the  judgment  be  against  you,  I  shall 
obtain  the  fee  by  decree  of  the  court,  and  if  in  your  favor,  I  shall 
obtain  it  in  terms  of  the  compact,  by  which  it  became  due  on  the 
very  day  you  gained  your  first  cause.  You  thus  must  fail,  either  by 
judgment  or  by  stipulation.  To  this  Euathlus  rejoined: — Most 
sapient  of  masters,  learn  from  your  own  argument,  that  whatever 
may  be  the  finding  of  the  court,  absolved  I  must  be  from  any  claim 
by  you.  For  if  the  decision  be  favorable,  I  pay  nothing  by  the  sen- 
tence of  the  judges,  but  if  unfavorable,  I  pay  nothing  in  virtue  of 
the  compact,  because,  though  pleading,  I  shall  not  have  gained  my 
cause.  The  judges,  says  Gellius,  unable  to  find  a  ratio  decidendi, 
adjourned  the  case  to  an  indefinite  day,  and  ultimately  left  it  unde- 
termined. T  find  a  parallel  story  told,  among  the  Greek  writers,  by 
Arsenius,  by  the  Scholiast  of  Hermogenes,  and 
^'^,1.*!°**        "*       by  Suidas,^  of  the    rhetorician  Corax  (anqlice 

rax  and  Tisias.  •'  '        ■  .  ^      ^f 

Crow)  and  his  scholar  Tisias.  In  this  case,  the 
judges  got  off  by  delivering  a  joke  against  both  parties,  instead  of  a 
decision  in  favor  of  either.  We  have  here,  they  said,  the  plaguy 
Qgg  of  a  plaguy  crow,  and  from  this  circumstance  is  said  to  have 
originated  the  Greek  proverb,  kokov  K6paKo<s  kukov  wov. 

Herewith  we  terminate  the  First  Great  Division  of  Pure  Logic,— 
Stoicheiology,  or  the  Doctrine  of  Elements. 

1  [Prolegomena  to  Hermogenes,  in  Walz's  313, 314.  Quoted  by  Sigwart,  LogiU,  f  333,  p 
Rhttores  Graci,  torn.  iv.  pp.  13,  14.  Arsenii  211,  3d  edit.  Suidaa,  quoted  by  Schottua 
Tioletum,  edit.    Walz,  Stuttgard,  1832,  pp.     Adagia  Gracorum,  p.  4£0, 1612.] 


LECTURE    XXIV. 

PURE    LOGIC. 

PART     II.-METHODOLOOY. 

SECTION  I.  —  METHOD   IN   GENERAL. 

SECTION  IL  —  METHOD  IN  SPECIAL,  OR  LOGICAL  METHODOLOGY 

L  — DOCTRINE   OF  DEFINITION, 

Gentlemen,  —  We  concluded,  in  our  last  Leetui'e,  the  considera- 
tion of  Syllogisms,  viewed  as  Incorrect  or  False ; 
e  10  o  ogy.  .^  other  words,  the  doctrine  of  Fallacies,  in  so 

far  as  the  fallacy  lies  within  a  single  syllogism.  This,  however,  you 
will  notice,. does  not  exhaust  the  consideration  of  fallacy  in  general, 
for  there  are  various  species  of  fjxlse  reasoning  which  may  affect  a 
Avhole  train  of  syllogisms.  These  —  of  which  the  Petitio  Prin- 
cipii,  the  Ignoratio  Elenchi,  the  Circnlus,  and  the  Saltits  in  Con- 
cludendo,  are  the  principal- — will  be  appropriately  considered  in 
the  sequel,  when  we  come  to  treat  of  the  Doctrine  of  Probation  or 
Demonstration.  With  Fallacies  terminated  the  one  Grand  Division 
of  Pure  Logic,  —  the  Doctrine  of  Elements,  or  Stoicheiology, — 
and  I  open  the  other  Grand  Division,  —  the  Doctrine  of  Method,  or 
Methodology,' —  with  the  following  paragraph. 

^  LXXX.  A  Science  is  a  complement  of  cognitions,  having, 
^^^^  „  .^  ^       in  point  of  Form,  the  character  of  Logical 

Par.  IiZXZ.  Method  i  '  C 

in  general.  Perfection ;  in  point  of  Matter,  the  charac- 

ter of  Real  Truth. 

The  constituent  attributes  of  Logical  Perfection  are  the  Per- 
spicuity, the  Completeness,  the  Harmony,  of  Knowledge.  But 
the  Perspicuity,  Completeness,  and  Harmony  of  our  cognitions 
are,  for  the  human  mind,  possible  only  through  Method. 

Method  in  general  denotes  a  procedure  in  the  treatment  of 
an  object,  conducted  according  to  determinate  rules.     Method, 


336  LOGIC.  Lect.  XXIV. 

in  reference  to  Science,  denotes,  therefore,  the  arrangement 
and  elaboration  of  cognitions,  according  to  definite  rules,  with 
the  view  of  conferring  on  these  a  Logical  Perfection.  The 
Methods  by  which  we  proceed  in  the  treatment  of  the  objects 
of  our  knowledge  are  two  ;  or  rather  Method,  considered  in  its 
integrity,  consists  of  two  processes,  —  Analysis  and  Synthesis. 

I.  The  Analytic  or  Regressive ;  —  in  which,  departing  from 
the  individual  and  the  determined,  we  ascend  always  to  the 
more  and  more  general,  in  order  finally  to  attain  to  ultimate 
principles. 

II.  The  Synthetic  or  Progressive ;  —  in  which  we  depart 
from  principles  or  univereals,  and  from  these  descend  to  the 
determined  and  the  individual. 

Through  the  former  we  investigate  and  ascertain  the  reality 
of  the  several  objects  of  science ;  through  the  latter  we  con- 
nect the  fragments  of  our  knowledge  into  the  unity  of  a  system. 

In  its  Stoicheiology,  or  Doctrine  of  Elements,  Logic  considers 

the  conditions  of  possible  thought ;  for  thcnght 

Explication.  ^^^  ^^^    y^^  exerted  under  the  general  laws  of 

Possibility  and  Per-  •  r^  -,•      •  -niin     nr- -i -ii  i 

cection  of  Thought.  Identity,  Contradiction,  ll<xcluded  Middle,  and 

Reason  and  Consequent ;  and  through  the  gen- 
eral forms  of  Concepts,  Judgments,  and  Reasonings.  Xl^ese,  there- 
fore, may  be  said  to  constitute  the  Elements  of  thought.  But  we 
may  consider  thought  not  merely  as  existing,  but  as  existing  well ; 
that  is,  we  may  consider  it  not  only  in  its  possibility,  but  in  its  per- 
fection ;  and  this  perfection,  in  so  far  as  it  is  dependent  on  the  form 
of  thinking,  is  as  much  the  object-matter  of  Logic  as  the  mere  pos- 
sibility of  thinking.  Now  that  part  of  Logic  which  is  conversant 
with  the  .  Perfection,  with  the  Well-being  of  thought,  is  the  Doc- 
trine of  Method,  —  Methodology. 

Method  in  general  is  the  regulated  procedure  towards  a  certain 

end  ;  that  is,  a  process  governed  by  rules,  which 

-what         ^        '      g"itle  us  by  the  shortest  way  straight  towards 

a  certain  point,  and  guard  us  against  devious 

aberrations.^     Now  the  end  of  thought  is  truth,  —  knowledge, — 

1  [On  Method,  see  Alex.  Aphrod.,  In  Anal,  nesius,  De  Cnnstitvtiorie  Artis  Diahctlca,  p.  43 

Prior.,  f.  3b,  Aid.  1520.    Ammonius, //» /Voosm.  et  scq.,  cA.  1554,  with  relative  comraentarr. 

Porphyrii,  f.  21b,  Aid.  1546.     Philoponus,  In  Timpler,  Stjstima  Logicft,  L.  iv.  c.  viii.  p.  716 

An.  Prior.,  f.  4.     /«  An.  Post.,  f.  94.     Eustra-  et  seq.    G.  Downam.  Commentarii  in  P.  Rami 

tins,  III  An.  Post.  ff.  lb,  53b.     See  also  Molin-  Dialecticam,  L.  ii.  c.  17,  p.  472  et  seq.  -On  the 

jcus,   Zabarella,   Nunne.«ius,   Timpler,    Dow-  distinction  between  Method  and  Order,  see 

nam.]    [Slolin.-cus,  Logica,  L.  ii.,  De  Methodo,  lectures  on   Metaphysics,  lecL.  rl.  p    6S,  and 

p.  245  et  seq.     Zaharella,    Oj)era  Lngica,   De  note. —  Ed.) 
Metho'lis,  L.  i.  c.  2,  p.  131.    Peter  John  Nun-  * 


Lect.  XXIV.  LOGIC.  337 

science,  —  expressions  whicli  may  here  be  considered  as  convertible. 
Science  may,  therefore,  be  rejjarded  as  the  per- 

Science,  —  what,  n       •  r 

lection  of  thought,  and  to  the  accomphshment 
of  this  perfection  the  Methodology  of  Logic  must  be  accommodated 
and  conducive.     But  Science,  that  is,  a  system  of  true  or  certain 
knowledge,  supposes  two  conditions.     Of  these,  the  first  has  a  rela- 
tion to  the  knowing  subject,  and  supposes  that 
i  nd'siateriai  ^^        what  is  known  is  known  clearly  and  distinctly, 
completely,  and  in  connection.     The  second  has 
a  relation  to  the  objects  known,  and  supposes  that  what  is  known 
has  a  true  or  real  existence.     The  former  of  these  constitutes  the 
Formal  Perfection  of  science,  the  latter  is  the  Material. 

Now,  as  Logic  is   a  science  exclusively  conversant  about  the 

form  of  thought,  it   is   evident   that   of  these 

gicaesmoac-       ^^^^   conditions, —  of  these    two   elements,   of 

count  only  the  formal 

perfection  of  science.  scienco  or  perfect  thinking,  Logic  can  only  take 
into  account  the  formal  perfection,  which  may, 

therefore,  be  distinctively  denominated  the  logical  perfection  of 
thought.     Logical   Methodology  will,  therefore,. 

Logical    Methodol-         ,        ^,  ...  c   ^,  {  n  i 

.  ,  be  the  exposition    oi   the   rules    and   ways    by 

ogy,  —  what.  ^  j  •/ 

which  we   attain    the  formal  or  logical  perfec- 
tion of  thought. 

But   Method,  considered   in   general,  —  considered   in  its  unre-  - 
stricted  universality,  —  consists  of  two  proces.ses,. 
Method  in  general       correlative  and  complementary  of  each   other. 

consists    of  two    cor-  -,         .  i  n  T  i     i  i 

relative  and  compie-      For  it  proceeds  Cither  from  the  whole  to  the 

mentary  processes,—  parts,  or  from  the  parts  to  the  whole.  As  pro- 
Analysis  and  synthe-  ceeding  from  the  whole  to  the  parts,  that  is,  as 
resolving,  as  unloosing,  a  complex  totality  intO' 
its  constituent  elements,  it  is  Analytic ;  as  proceeding  from  the 
parts  to  the  whole,  that  is,  as  recomposing  constituent  elements- 
into  their  complex  totality,  it  is  Synthetic.  These  two  processes 
are  not,  in  strict  propriety,  two  several  methods,  but  together  con- 
stitute only  a  single  method.  Each  alone  is  imperfect ;  —  each  is 
conditioned  or  consummated  by  the  other ;  and,  as  I  formerly  ob- 
served,^ Analysis  and  Synthesis  are  as  necessary  to  themselves  and 
to  the  life  of  science,  as  expiration  and  inspiration,  in  connection,, 
are  necessary  to  each  other,  and  to  the  possibility  of  animal 
existence.  • 

It  is  here  proper  to  make  you  aware  of  the  confusion  which 
prevails  in  regard  to  the  application  of  the  terms  Analysis  and 


1  See  Lecture*,  on  Metaphysics,  p.  70-  — £)I>. 

43 


LOGIC. 


Lkct.  XXIV. 


ConfUsion  in  regard 
to  the  application  of 
the  terms  Analysis 
and  Synthesis. 


abuse. 


These  counter  pro- 
cesses as  applied  to 
the  countet-  wholes  of 
Coniprelifusion  and 
Kxtensioii,  correspond 
with  each  other. 


Synthesis}  It  is  manifest,  in  general,  from  the  meaning  of  the 
words,  that  the  term  analysis  can  only  be  applied 
to  the  separation  of  a  whole  into  its  parts,  and 
that  the  term  synthesis  can  only  be  aj^plied  to 
the  collection  of  parts  into  a  whole.  So  far, 
no  ambiguity  is  possible,  no  room  is  left  for 
But  you  are  aware  that  there  are  different  kinds  of  whole 
and  parts;  and  that  some  of  the  wholes,  like 
the  whole  of  Comprehension  (called  also  the 
Metaphysical)^  and  the  wliole  of  Extension, 
((ialled  also  the  Logical),  are  in  the  invei-se  ratio 
of  each  other:  so  that  what  in  the  one  is  a  part, 
is  necessarily  in  the  other  a  whole.  It  is  evi- 
dent, then,  that  the  counter  processes  of  Analysis  and  Synthesis,  as 
applietl  to  these  counter  wholes  and  parts,  should  fall  into  one,  (xr 
correspond ;  inasmuch  as  each  in  the  one  quantity  should  be  dia- 
metrically opposite  to  itself  in  the  other.  Thus  Analysis,  as  applied 
to  Comprehension,  is  the  reverse  process  of  Analysis  as  applied  to 
Extension,  but  a  corresponding  process  with  Synthesis ;  and  vice 
versa.  Now,  should  it  happen  that  the  existence  and  opposition  of 
the  two  quantities  are  not  considered,  —  that  men,  viewing  the 
whole  of  Extension  or  the  whole  of  Comprel\ension,  each  to  the 
exclusion  of  the  other,  must  define  Analy!5is  and  Synthesis  with 
reference  to  that  single  quantity  which  they  exclusively  take  into 
account;  —  on  this  supposition,  I  say,  it  is  manifest  that,  if  dif- 
ferent philosophers  regard  different  wholes  or 
quantities,  we  may  have  the  terms  analysis  and 
synthesis  absolutely  used  by  different  philoso- 
phers in  a  contraiy  or  reverse  sense.  And  this 
has  actually  happened.  The  ancients,  in  gen- 
eral, looking  alone  to  the  whole  of  Extension,  use  the  terms  analysis 


Ueiice  the  terms 
Analysis  and  Synthe- 
sis used  in  a  contrary 
sense. 


1  [Zaba  pel  la.  Opera  Logica,  Liber  de  Regressu, 
pp.  4S1,  489.  See  also,  In  Anal.  Poster..  L.  ii. 
te.\t  81,  pp.  1212,  1213.  Molinseus,  Logica,  L. 
ii.  Appendix,  p.  241  et  seq.,  who  notices  that 
both  the  Analytic  and  Synthetic  order  may 
proceed  from  the  general  to  the  particular. 
See  also,  to  the  same  effect,  HofFbauer,t/6fr 
rf(>  Analysis  in  dtr  Phitosophie.  p.  41  et  seg., 
Halle,  1810.  Ga.«sendi,  P/iysica,  Scctio  iii. 
Memb.  Part,  L.  ix.  Opera,  t.  il  p.  460.  Vic- 
torUi,  iVei«t  natHrlickere  Darstellung  der  Logik, 
I  214.  Trendelenburg,  Elementa  Logicrs  Aris- 
tntelirrr,  p.  89.  Troxler,  Logik,  ii.  p.  100.  n.  *». 
Knig,  Lo^'ik,  §  114.  p.  406,  n.  **,  and  §  120,  p. 
431.  Wyttenbach  makes  Synthetic  method 
pngivss  from  particulars  to  universals ;  other 


logicians  generally  the  reverse.]  —  (See  bib 
Prarrpta  Phil.  Logi.-er,  T.  Ill  c.  i.  S  3,  p.  84, 
1781.  —  "Mentem  suaptc  natura  Syntheticarr, 
Mctliodum  sequi,  eaque  ad  universales  idea» 

pervenire Contrarium  est  iter  An? 

lyticaj  Methodi,  quae  ab  universalibus  initiuro 
ducit  et  ad  peculiaria  progreditur,  dividends 
Genera  in  suas  Formas.-'  ''Contra  commw 
nem  sensum  et  vcrborum  naturara,  Synthet- 
icam  vocani  Jlcthodnm,  qua;  dividit,  Anj. 
lyticam  contra,  quae  componit."  Pra;f  sub 
Jin.  In  the  edition  of  the  Pr/rcepta  by  Miaa, 
Wyttenbach  is  made  to  say  precisely  tho  re 
verse  of  what  he  lays  down  in  the  origins' 
edition.  See  Prcec.  Phil.  Log.,  ed.  Maafis,  j 
64.  — Ed.] 


Lkct.  XXIV.  LOGIC.  339 

and  analkjtic  simply  to  denote  a  division  of  the  genus  into  species, 
—  of  the  species  into  individuals  ;  the  moderns,  on  the  other  hand, 
in  general,  looking  only  at  the  whole  of  Comprehension,  employ 
these  terms  to  express  a  resolution  of  the  individual  into  its  varions 
attributes.^  But  though  the  contrast  in  this  respect  between  the; 
ancients  and  moderns  holds  in  general,  still  it  is  exposed  to  sundry 
exceptions ;  for,  in  both  |>criods,  there  are  philosophers  found  at  the 
same  game  of  cross-purposes  with  tlicir  contemporaries  as  the  an- 
cients and  moderns  in  general  are  with  each  other.  This  difference, 
Avhicli  has  never,  as  far  ts,  I  know,  been  fully  observed  and  stated, 
is  the  cause  of  great  confusion  and  mistake.  It  is  pi'oper,  therefore, 
when  we  use  these  terms,  to  use  them  not  in  exclusive  relation  to 
one  whole  more  than  to  another;  and,  at  the  same  time,  to  take 
care  that  we  guard  again.s;t  the  misapprehension  that  might  arise 
from  the  vague  and  one-sided  view  which  is  now  universally  preva- 
lent. So  much  for  the  meaning  of  the  words  analytic  and  synthetic, 
which,  by  the  way,  I  may  notice,  ait;,  like  most  of  our  logical  terms, 
laken  from  Geometry.^ 

The  Synthetic  Method  is  likewise  called  the  Progressive ;  the 

Analytic   is  called  the  Rerjressive.     Now  it  is 

TijeSyntiieticMetii.       plain  that  this  application  of  the  terms  progres- 

od  has  been  called  the       ^^^^  ^^^^^  regressive  is  altogether  arbitrary.     For 

I'rogressive,   and    the  .  r^  '' 

Analytic  the  Regres-  the  unport  of  these  words  expresses  a  relation 
.-ive.  Tiicse  desigiia-  to  a  certain  point  of  departure,  —  a  termintis  o 
(ions  wholly  arbitrary,       quo,  Vir\(\  to  a  certain  point  of  termination,  —  a 

;ind  of  various  appli-  .  ,  i    •  <»     i  i  ^ 

^jjj^^  terminus  ad  quern;  and  it  these  have  only  an 

arbitrary  existence,  the  correlative  words  will, 
consequently,  only  be  of  an  arbitrary  application.  But  it  is  mani- 
fest that  the  point  of  departure,  —  the  point  from  which  the  Pro- 
gressive process  starts,  —  may  be  either  the  concrete  realities  of  our 
experience,  —  the  principiata,  —  the  notiora  nobis;  or  the  abstract 
generalities  of  intelligence,  —  the  principia,  —  the  notiora  natura. 
Each  of  these  has  an  equal  right  to  be  regarded  as  the  starting- 
point.  The  Analytic  process  is  chronologically  first  in  the  order  of 
knowledge,  and  we  may,  therefore,  reasonably  call  it  the  progres- 
sive, as  starting  from  the  primary  data  of  our  observation.  On  the 
other  hand,  the  Synthetic  process,  as  following  the  order  of  consti- 
tution, is  first  in  the  order  of  nature,  and  we  may,  therefore,  like- 
wise reasonably  call  it  the  progressive,  as  starting  from  the  primary 
elements  of  existence.     The  application  of  these  terms  as  synonyms 

1  [See  Aristotle,  Fkysica,  Ii..iv.  c.  3.    Timp-      Analysis  of  Geometry,  see  Plotinus.  ^tinead:.. 
ler,  Logicm  Systema,  L.  ii.  c.  i.  qu.  11.  p.  24S.]       iv.  L.  ix.  c.  5.    Philoponus,  la  An.  Post.r  f 

2  See  above,  p.  196,  u.  4.  —  Ed.      [On  the     36a,Venet.  1534.1 


840  LOGIC.  Lect.  xxrv. 

of  the  analytic  and  synthetic  processes,  is,  as  wholly  arbitrary,  man- 
ifestly open  to  confusion  and  contradiction.  And  such  has  been 
the  case.  I  find  that  the  philosophers  are  as  much  at  cross-purposes 
in  their  application  of  these  terms  to  the  Analytic  and  Synthetic 
processes,  as  in  the  application  of  analysis  and  synthesis  to  the  dif- 
ferent wholes. 

In  general,  however,  both  in  ancient  and  modern  times,  Sj-nthesis 

has  been  called  the  Progressive^  Analysis  the 

In  general,  Synthe-       Regressive^  process ;    an   application   of   terms 

si8  has  been  desig-       which  has  probably  taken  its  rise  from  a  passage 

Dated  the  Progressive,         .       »    .  i  ,  i  , 

and  Analysis  the  Kc-  ^^  Aristotle,  who  says  that  there  are  two  ways 
gressive  Process.  \  of  scientific  procedure,  —  the  one  from  princi- 

ples (aTTo  ruiv  a.pywv\  the  Other  to  principles  {IttX 
Tas  apx^s).  From  this,  and  from  another  similar  passage  in  Plato,  (?) 
the  term  progressive  has  been  applied  to  the  process  of  Comprehen- 
sive Synthesis  {progrediendi  a  principiis  ad  principiata)^  the  term 
regressive^  to  the  process  of  Compi*ehensive  Analysis  {progrediendi 
a  principiatis  ad  principia.y 

So  much  for  the  general  relations  of  Method  to  thought,  and  the 
general  constituents  of  Method  itself.     It  now 

Method  in  special.  .         .  '       .  ,  ,     .  . .  .      , 

remains  to  consider  what  are  the  particular  ap- 
plications of  Method,  by  which  Logic  accomplishes  the  Formal  Pei- 
fection  of  thought.  In  doing  this,  it  is  evident  that,  if  the  formal 
perfection  of  tliought  is  made  up  of  various  virtues,  Logic  must 
accommodate  its  method  to  the  acquisition  of  these  in  detail ;  and 
that  the  various  processes  by  which  these  several  virtues  are  ac- 
quired, will,  in  their  union,  constitute  the  system  of  Logical  Method- 
ology.    On  this  I  will  give  you  a  paragra^ih. 

^  LXXXI.  The  Formal  Perfection  of  thought  is  made  up  of 
„     ,^^^  the   three   virtues   or   characters:  —  1°,  Of 

Par.  IiXXXI.    Logi-  ^  ' 

cai Methodology,- its  Clearness;  2°,  Of  Distinctness^  involving 
Three  Parts.  Completmess  ;  zndi,  Z"" ,  0^  Ilarmouy .     The 

character  of  Clearaess  depends  principally  on  the  determination 
of  the  Comprehension  of  our  notions ;  the  character  of  Dis- 
tinctness depends  principally  on  the  development  of  the  Exten- 
sion  of  our   notions ;  and  the  character  of  Harmony,  on  the 

\  Elk.  Nie,\.2(i).    The  reference  to  Plato,  quoted  in  Is.  Casaubon's  note.    On  the  views 

whom  Aristotle  mentions  as  making  a  similar  of  Method  of  Aristotle  and  Plato,  see  Schcib- 

distinction,  is  probably  to  be  found  by  com-  ler  and  Downam.]    [Scheibler,  Op«ra  Logicn,  ■ 

paring  two  separate  passages  in  the  Republic,  Pars,  iv..  Tract.  Syllog.,  c.  xvii.,  Dt  Methodn, 

B.  Iv.  p.  435,  vi.  p.  504.  —  Ed.    [Plato  is  said  tit.  7,  p.  603.    Downam,  Cowj.  in  P.  Rami  Dia- 

to  have  taught  Analysis  to  Leodamas  the  Ucticam,  L.  U.  c.  17,  p.  482.  —  £d.] 
rhasian.  See  Laertlus,  L.  lii.  24,  and  Proclus, 


Lkct.  XXIV.  LOGIC.  341 

mutual  Concatenation  of  our  notions.  The  rules  by  which 
these  three  conditions  are  fulfilled,  constitute  the  Three  Parts 
of  Logical  Methodology.  Of  these,  the  first  constitutes  the 
Doctrine  of  Definition  ;  the  second,  the  Doctrine  of  Division ,' 
and  the  third,  the  Doctrine  of  Probation} 

"When  we  turn  attention  on  our  thoughts,  and  deal  with  thera 
to  the  end  that  they  may  be  constituted  into  a 
scientific  whole,  we  must  perform  a  three-fold 
operation.  We  must,  first  of  all,  consider  what  we  think,  that  is, 
what  is  comprehended  in  a  thought.  In  the  second  place,  we  must 
consider  how  many  things  we  think  of,  that  is,  to  how  many  objects 
the  thought  extends  or  reaches,  that  is,  how  many  are  conceived 
under  it.  In  the  third  place,  we  must  consider  why  we  think  so 
and  so,  and  not  in  any  other  manner;  in  other  words,  how  the 
thoughts  are  bound  together  as  reasons  and  consequents.  The  first 
consideration,  therefore,  regards  the  comprehension  ;  the  second,  the 
extension  ;  the  third,  the  concatenation  of  our  thoughts.  But  the 
comprehension  is  ascertained  by  definitions ;  the  extension  by  divi- 
sions; and  the  concatenation  by  probations."^  We  proceed,  there- 
fore, to  consider  these  Three  Parts  of  Logical  Methodology  in 
detail ;  and  first,  of  Declaration  or  Definition,  in  regard  to  which  I 
give  the  following  paragraph. 

f  LXXXII.  How  to  make  a  notion  Clear,  is  shown  by  the 

logical  doctrine  of  Declaration^  or  Defini- 

par.  LXXXII.  1.  The       fi^jj^  j^  its  widcr  scnsc.     A  Declaration  (or 

Doctrine   cf   Deolara-  t\    n     •    '  •       •  •  -t  •  .^ 

tion  or  Definition.  Definition  in  its  Wider  sense)  is  a  Categori- 

cal Proposition,  consisting  of  two  clauses  or 
members,  viz.,  of  a  Subject  Defined  (menihruni  definitum)  and 
of  the  Defining  Attributes  of  the  subject,  that  is,  those  by  which 
it  is  distinguished  from  other  things  {membrum  definieyis).  This 
latter  member  really  contains  the  Definition,  and  is  often  itself 
so  denominated.  Simple  notions,  as  containing  no  plurality  of 
attributes,  are  incapable  of  definition.' 

1  Krug,  Logilc,  §  121a.  —  Ed.    [Ramus  was  68,  and  makes  four  special  logical  methods, 

the  first  to  introduce  Metliod  as  a  part  of  Division,    Definition,  Analysis,  Demonstra- 

I-ogic  under  Syllogistic  (see  his  Dialectica,  L.  tion.     Eustachius    treats    of  Method  under 

ii  c  17),  and  the  Port  Royalists  (1S62)  made  Judgment,  and  Scheibler  under  Syllogistic.J 

if  ix  fourth  part  of  logic.     See  La  Logique.  ou  [Eustachius,  Summa  Philosophice,  Logica,  P.  ii- 

/.■  Art  de  denser,  Prem.  Dis.,  p.  26,  pp.  47,  50.  Tract.  2.     De  Methodo,  p.  106,  ed.  Lugd.  Ba- 

(;uat.  Part.,  p.  445  (t  seq.  ed.  1775.    Gassendi,  tav.,  1747.      First  edition,  1609.      Scheibler, 

I..  Iii.s  liiititiitio  Logica^  has  Pars  iv.,  De  Meth-  Opera  Logica,  Pars  iv.  C.  xviii.  p.  595  et  seg.—> 

<■'■'■    Ue  died   in  1655;    his    Logic  appeared  Ed] 

pu-thnmously  in  1658.     John  of  Damascus  2  Krug,  Log^i/fc,  §121*.  —  Ed. 

»-,  e.>k8  sti  ongly  of  Method  in  his  Dialectic,  ch.  8  Krug,  Logik,  {  1216.  —  Ed. 


342  LOGIC.  Lect.  XXTV. 

The  terras  declaration  and  definition^  which  are  here  used  as  appli- 
cable to  the  same  process,  express  it,  however, 
p  ica  jon.  .^  different  asi)ects.     The  term  declaration  (dec- 

The  terms  Declara-  ^  ^ 

tion  and  Definition  laratio)  is  a  wofd  somcwhat  vaguely  employed 
express  the  same  pro-  in  English  ;  it  is  here  used  strictly  in  its  proper 
cess  in  difierent  as-  g^^^g^  ^^  throwing  light  upon,—- cleaHng  up. 
The  terra  definition  {definition  is  employed  in  a 
more  general,  and  in  a  more  special,  signification.  Of  the  latter  we 
are  soon  to  speak.  At  present,  it  is  used  simply  in  the  meaning  of 
an  enclosing  within  limits^  —  the  separating  a  thing  from  others. 
Were  the  terra  declaration  not  of  so  vague  and  vacillating  a  sense, 
it  would  be  better  to  employ  it  alone  in  the  moi'e  general  accepta- 
tion, and  to  reserve  the  term  definitiojt  for  the  special  signification. 

%  LXXXIII.  The  process  of  Definition  is  founded  on  the 

logical  relations  of  Subordination,   Coordi- 

par.  LXXXIII.  Defl-      nation,  and  Congruence.     To  this  end  we 

nition  in  its  stricter       discriminate  the  constituent  characters  of  a 

•ense,  —  wbat. 

notion  into  the  Essential^  or  those  which 
belong  to  it  in  its  unrestricted  univereality,  and  into  the  Unes- 
sential, or  those  which  belong  to  some  only  of  its  species.  The 
Essential  are  again  discriminated  into  Original  and  Derivative^ 
a  division  which  coincides  with  that  into  Internal  or  Proper, 
and  Exteiwial.  In  "-ivinf;  the  sum  of  the  original  characters 
constituent  of  a  notion,  consists  its  Definition  in  the  stricter 
sense.  A  Definition  in  the  stricter  sense  must  consequently 
afford  at  least  two,  and  properly  only  two,  original  character, 
viz.,  that  of  the  Genus  immediately  superior  {genus  proximum)y 
and  that  of  the  Difference  by  which  it  is  itself  marked  out 
from  its  coordinates  as  a  distinct  species  {nota  specialise  differ- 
entia specifica)} 

Declarations  (or  definitions  in   the  wider  sense)  obtain  various 
denominations,  according  as  the  process  is  per- 
Expiication.  formed  in  different  manners  and  degrees.      A 

Declaration  is  called  an  Explication  {explication, 
Explication.  when  the  predicate  or  defining  member  indcter- 

Exposition.  minately  evolves  only  some   of  the  characters 

belonging  to  the  subject.    It  is  called  an  Exposi- 
tion {exposiCio),  when  the  evolution  of  a  notion  is  continued  through 

I  [Cf.  Aristotle,  rop»>a,  i.  6.    Keckermann,      pp.  199,656.    Scheibler, 7l>p>ca,  c  30.    Riohter, 
SyMema  Loj^ica  Minus,  L  i.  c.  17.     Optra.t    i.      Logik,  p.  94.] 


L;:ci.  XXIV.  LOGIC.  8^3 

several  explications.     It  is  called  a  Description  (<kscriptio),  when 
the  subject  is  made  known  through  a  number 

Description.  .      .  _,.       ,,        •      •  t        n     t 

„  „  ...       „  „  ,  or  concrete  characteristics.     J^  mally,  it  is  called 

Definition  proper.  •' ' 

.1  Dejinition  Proper,  when,  as  I  have  said,  two 
of  the  essential  and  original  attributes  of  the  defined  subject  are 
given,  whereof  the  one  is  common  to  it  with  the  various  species  of 
the  same  genus,  and  the  other  discriminates  it  from  these.^ 

"Definitions  are  distinguished  also  into  Verbal  or  Nominal,  into 

Real,  and  into  Genetic  {dejinitiones  noniinales. 

Definitions,  —  jJom-       reulcs,  geneticce),  diCcovdim^  as  they  are  conver- 

inai,  Keai,  and  Gene-       ^^^^  ^^-^j^  ^j^^  meaning  of  a  term,  with  the  nature 

tic.  ^ . 

of  a  thing,  or  with  its  rise  or  production."  Nom- 
inal Definitions  are,  it  is  evident,  merely  explications.  They  are, 
therefore,  in  geiicnd  only  used  as  preliminary,  in  order  to  prepare 
the  way  for  more  perfect  declarations.  In  Real  Definitions  the 
thing  defined  is  eousiJered  a^  already  there,  as  existing  (ov),  and 
the  notion,  therefore,  as  given,  precedes  the  definition.  They  are 
thus  merely  analytic,  that  is,  nothing  is  given  explicitly  in  the  predi- 
cate or  defining  member,  which  is  not  contained  implicitly  in  the 
subject  or  member  defined.  In  Genetic  Definitions  the  defined 
subject  is  considered  as  in  tlie  progress  to  be,  as  becoming  yiyvo/*c- 
vqv,  the  notion,  therefore,  has  to  be  made,  and  is  the  result  of  the 
definition,  which  is  consequently  synthetic,  that  is,  ])laces  in  the 
predicate  or  defining  member  more  than  is  given  in  the  subject  or 
member  defined.  As  examples  of  these  three  species,  the  following 
three  definitions  of  a  circle  may  suftice  '.- —  1.  The  Nominal  Defini- 
tion,—  The  word  circle  signifies  a  uniformly  curved  liiie.  2.  Thti 
Real  Definition,  —  A  circle  is  a  line  returning  upon  itself,  of  which 
all  the  parts  are  equidistant  from  a  given  point.  3.  The  Geiietio 
Definition, — A  circle  is  formed  when  we  draw  around,  and  always 
at  the  same  distance  from,  a  fixed  point,  a  movable  point  which 
leaves  its  trace,  until  the  termination  of  the  movement  coincides 
witli  the  commencement.''  It  is  to  be  observed  that  only  those 
notions  can  be  genetically  defined,  which  relate  to  quantities  repre- 
sented in  time  and  space.  Mathematics  are  principally  conver- 
sant with  such  notions,  and  it  is  to  be  noticed  that  the  mathematician 
usually  denominates  such  genetic  definitions  real  definitions,  while 
the  others  he  calls  without  distinction  nominal  definitions"* 
The  laws  of  Definition  are  given  in  the  following  paragraph. 


1  Cf.  Krug,  Logik,  §  122.  —  Ep.  tion,  from  Wolf,  Philosopkia  RcUionalis,  i  19L 

2  [Cf.   Reasch,    Systema   Lo^eum,   §   309  et  — Ed. 

«7l  *  K^rug)  Logik,  §  122.    Anpi.  3,  pp.  443,  44a 

3  This  example  is  taken,  with  some  altera-  —  Ed. 


344  LOGIC.  Lect.  XXIV. 

%  LXXXIV.  A  definition  sliould  be  Adequate  (adequata), 

that  is,  the  subject  defined,  and  the  predi- 

.^  ^  cate  dofinint;,  should  be  equivalent  or  ot  the 

nition,  —  its  Laws.  o'  T. 

same  extension.  If  not,  the  sphere  of  the 
predicate  is  either  less  than  that  of  tlie  subject,  and  the  defini- 
tion Too  Narrow  {angustior),  or  greater,  and  the  definition 
Too  Wide  {latior). 

II.  It  should  not  define  by  Negative  or  Divisive  attributes 
{Ne  sit  negans,  ne  fiat  per  disjunc(a). 

III.  It  should  not  be  Tautological,  —  what  is  contained  ia 
the  defined,  should  not  be  repeated  in  the  defining  clause  (Ne 
sit  circidus  vel  diallelon  in  defi?iiendo). 

IV.  It  should  be  Precise,  that  is,  contain  nothing  unessential, 
notliing  superfluous  (Definitio  ne  sit  abundans). 

V.  It  should  be  Perspicuous,  that  is,  couched  in  terms  intel- 
ligible, and  not  figurative,  but  proper  and  compendious.'^ 

The  First  of  these  rules:  —  That  the  definition  should  be   ade- 
quate, that  is,  that  the  definiens  and  definitum 
pica  ion.  should  be  of  the  same  extension,  is  too  manifest 

First  Rule.  ,  ... 

to  require  much  commentary.  Is  the  definition 
too  wide  ?  —  then  more  is  declared  than  ought  to  be  declared  ;  is  it 
too  narrow  ? —  then  less  is  declared  than  ought  to  hv  declared  ;  — 
and,  in  either  case,  the  definition  does  not  fully  accotnpllsh  the  eiid 
which  it  proposes.  To  avoid  this  defect  in  definition,  we  must 
attend  to  two  conditions.  In  the  firet  place,  that  attribute  should 
tie  given  which  the  thing  defined  has  in  common  with  others  of  the 
same  class;  and,  in  the  second  place,  that  attribute  should 'be  given 
which  not  only  distinguishes  it  in  general  from  all  other  things,  but 
proximately  from  things  which  are  included  with  it  under  a  couitnon 
class.  This  is  expressed  by  Logicians  in  the  rule  —  Definitio  con- 
stet  genere  proximo  et  differentia  ultima,  —  Let  the  definition  consist 
of  the  nearest  genus  and  of  the  lowest  difference.  But  as  the  no- 
tion and  its  definition,  if  this  rule  be  obeyed,  are  necessarily  i<lentical 
or  convertible  notions,  they  must  necessarily  have  the  s:mie  extent ; 
consequently,  everything  to  which  the  definition  ap[)lies,  and  noth- 
ing to  which  it  does  not  apply,  is  the  thing  defined.  Thus  :  —  if 
the  definition,  Man  is  a  rational  animal,  be  adequate,  we  shall  be 
able  to  say  —  Every  rational  animal  is  human:  — nothing  lohich  is 
not  a  rational  animal  is   human.     But  we    cannot   say  this,  for 

1  Cf.  KruR,  Logik,  §  12.3. —  Ed.  [Victorin.  Definitione,  Oiiera,  p.  (H8  ft  ieq.  Buffier.  Vrri- 
Logik,  i  22S  ft  sfq.  Sig-wa.rt,  Ham/buck  zuVor-  ttz  de  Consfqutnce,  \  Ab-b\.  Goclenius,  L«x»- 
tfungrn  iibrr  die  Logik,  J  371.     Boetbius,  De      con  Phitosopkicum,  f.  Definitio,  p.  600.] 


Lect.  XXIV.  LOGIC.  345 

though  this  may  be  true  of  this  earth,  we  can  conceive  in  other 
worlds  rational  animals  which  are  not  human.  The  definition  is, 
therefore,  in  this  case  too  wide  ;  to  make  it  adequate,  it  will  be  nec- 
essary to  add  terrestrial  or  some  such  term  —  as,  Man  is  a  rational 
animal  of  this  earth.  Again,  were'  we  to  define  Man,  —  a  ration- 
ally acting  animal  of  this  earth,  —  the  definition  would  be  too 
narrow ;  for  it  Avould  be  false  to  say,  7io  animal  of  this  earth  not 
acting  rationally  is  human,  for  not  only  children,  but  many  adult 
persons  would  be  excluded  by  this  definition,  which  is,  therefore,  too 
narrow.^ 

The  Second  Rule  is,  —  That  the  definition  should  not  be  made  by 
negations,  or  disjunctions.    In  regard  to  the  for- 

SecondBuIe.  ,.  ^i     ^  i,       u     j    ii 

mer,  —  negations,  —  that  we  should  define  a 
thing  hj  what  it  is,  and  not  by  what  it  is  not,  —  the  reason  of  the 
rule  is  manifest.  The  definition  should  be  an  afiirmative  proposition, 
for  it  ought  to  contain  the  positive,  the  actual,  qualities  of  the  no- 
tion defined,  that  is,  the  qualities  which  belong  to  it,  and  which 
must  not,  therefore,  be  excluded  from  or  denied  of  it.  If  there  are 
characters  which,  as  referred  to  the  subject,  afford  purely  negative 
judgments;  —  this  is  a  proof  that  we  Iiave  not  a  proper  comprehen- 
sion of  the  notion,  and  have  only  obtained  a  precursory  definition 
of  it,  enclosing  it  within  only  negative  boundaries.  For  a  definition 
wiiich  contains  only  negative  attributions,  affords  merely  an  empty 
notion,  —  a  notion  which  is  to  be  called  a  nothing;  for,  as  some 
think,  it  must  at  least  possess  one  positive  character,  and  its  defini- 
tion cannot,  tlierefore,  be  made  up  exclusively  of  negative  attri- 
butes. If,  however,  a  notion  stands  opposed  to  another  which  has 
already  been  declared  by  positive  characters,  it  may  be  defined  by 
negative  characters,  —  provided  always  that  the  genus  is  positively 
determined.  Thus  Cuvier  and  other  naturalists  define  a  certain  or- 
der of  animals  by  the  negation  of  a  spine  or  back-bone,  —  the  inver- 
tebrata  as  opposed  to  the  vertebrata  /  and  many  such  definitions 
occur  in  Natural  History. 

For  a  similar  reason,  the  definition  must  not  consist  of  divisive  or 
disjunctive  attributions.  The  end  of  a  definition  is  a  clear  and  dis- 
tinct knowledge.  But  to  say  that  a  thing  is  this  or  that  or  the 
other,  affords  us  either  no  knowledge  at  all,  or  at  best  only  a  vague 
and  obscure  knowledge.  If  the  disjunction  be  contradictoiy,  its 
enunciation  is,  in  fact,  tantamount  to  zero ;  for  to  say  that  a  thing 
either  is  or  is  not  so  and  so,  is  to  tell  us  that  of  which  we  required 
no  assertion  to  assure  us.    But  a  definition  by  disparate  alternatives 

1  Cf.  Krug,  Logilc,  §  123.    Anna,  i  —  Ed. 

44 


346  LOGIC.  Lect.  XXIV. 

is,  though  it  may  vaguely  circumscribe  a  notion,  only  to  be  consid- 
ered as  a  prelusory  definition,  and  as  the  mark  of  an  incipient  and 
yet  imperfect  knowledge.  We  must  not,  however,  confound  de- 
finitions by  divisive  attributes  with  propositions  expressive  of  a 
division. 

The  Third  Rule  is,  —  "  The  definition  should  not  be  tautological ; 
that  is,  what  is  defined  should  not  be  defined  by 

^  ^    "  ,  "  *!   ,         itself.     This  vice  is  called  defining  in  a  circle. 
Defining  in  a  circle.  .  ^  " 

This  rule  may  be  violated  either  immediately  or 
mediately.  The  definition,  —  Law  is  a  lawful  command,  —  is  an 
example  of  the  immediate  circle.  A  mediate  circle  requires,  at 
least,  two  correlative  definitions,  a  principal  and  a  subsidiary.  For 
example,  —  Law  is  the  expressed  xcish  of  a  ruler,  and  a  rtder  is  one 
who  establishes  laics.  The  circle,  wliether  immediate  or  mediate,  is 
manifest  or  occult  according  as  the  thing  defined  is  repeated  in  the 
same  terms,  or  with  other  synonymous  words.  In  the  previous  ex- 
ample it  was  manifest.  In  the  following  it  is  concealed  :  —  Grati- 
tude is  a  virtue  of  acknnioledgm,ent,  —  Might  is  the  competence  to  do 
or  not  to  do.  Such  declarations  may,  however,  be  allowed  to  stand 
as  prelusory  or  nominal  definitions.  Concealed  circular  definitions 
are  of  very  frequent  occurrence,  when  they  are  at  the  same  time 
mediate  or  remote  ;  for  we  are  very  apt  to  allow  ourselves  to  be 
deceived  by  the  difference  of  expression,  and  fimcy  that  we  have 
declared  a  notion  when  we  have  only  changed  the  language.  We 
ought,  therefore,  to  be  strictly  on  our  guard  against  this  besetting 
vice.  The  ancients  called  the  circular  definition  also  by  the  name 
of  DiaUdon,  as  in  this  case  we  declare  the  definUum  and  the 
defyiiens  reciprocally  by  each  other  {hC  aKX.r,\<jiv)}  In  probation 
there  is  a  similar  vice  which  bears  the  same  names."  ^  We  may,  I 
think,  call  them  by  the  homely  English  appellation  of  the  Seesaw. 
The  Fourth  Rule  is,  —  ".That  the  definition  should  be  precise; 

that  is,  contain  nothing  unessential,  nothing  su- 
FonrthRuIe.  „  t^  .   ,  .  ., 

perfluous.  Unessential  or  contmgent  attributes 
are  not  sufficiently  characteristic,  and  as  they  are  now  present,  now 
absent,  and  may  likewise  be  met  with  in  other  things  which  are  not 
comprehended  under  the  notion  to  be  defined,  they,  consequently, 
if  admitted  into  a  definition,  render  it  sometimes  too  wide,  some- 
times too  narrow.  The  well-known  Platonic  definition,  —  '■Man  is 
a  two-legged  animal  without  feathers,'  —  could,  as  containing  only 
unessential  characters,  be  easily  refuted,  as  was  done  by  a  plucked 


1  Compare  Sextns  Empiricus,  Pt/rrk.  Hyp.,        »  Krug,  Logik,  {  123-    Anm.  3.  —  Ed. 
J  169,  ii.  68.  —  Ed. 


Lect.  XXIV.  LOGIC.  347 

cock.^  And  when  a  definition  is  not  wholly  made  np  of  such  attri- 
butes, and  when,  in  consequence  of  their  intermixture  with  essen- 
tial characters,  the  definition  does  not  absolutely  fail,  still  there  is  a 
sin  committed  against  logical  purity  or  precision,  in  assuming  into 
the  declaration  qualities  such  as  do  not  determinately  designate  what 
is  defined.  On  the  same  principle,  all  derivative  characters  ought 
to  be  excluded  from  the  definition ;  for  although  they  may  neces- 
sarily belong  to  the  thing  defined,  still  they  overlay  the  declaration 
with  superfluous  accessories,  inasmuch  as  such  characters  do  not 
designate  the  original  essence  of  the  thing,  but  are  a  mere  conse- 
quence thereof.  This  fault  is  committed  in  the  following  defini- 
tion :  —  The  Circle  is  a  curved  line  returning  upon  itself,  the  paints 
of  which  are  at  an  equal  distance  from  the  central  point.  Hero 
l)recision  is  violated,  though  the  definition  be  otherwise  correct.  For 
that  every  line  returning  upon  itself  is  curved,  and  that  the  point 
from  which  all  the  paits  of  the  line  are  equidistant  is  the  central 
point,  —  these  are  mere  consequences  of  the  returning  on  itself,  and 
of  the  equidistance.  Derivative  characters  are  thus  mixed  up  witli 
the  original,  and  the  definition,  therefore,  is  not  j^recise."  ^ 

The  Fifth  rule  is,  —  "That  the  definition  should  be  perspicuous, 
that  is,  couched  in  terms  intelligible,  not  figura- 

Fifth  Kule.  .  '  ,.  _,  r  ^    .  .  °     , 

tive,  and  compendious..  Ihat  definitions  ought 
to  bo  perspicuous,  is  self-evident.  For  why  do  we  declare  or  define 
at  air?     The  perspicuity  of  the  definition  depends,  in  the  first  place, 

on  the  intelligible  character  of  the  language,  and 
III  Older  to  perspi-       i\i[^  again  depends  on  the  employment  of  words 

cuity     in    Definition,         •      ^i,    •  •       j  t  •       'u      ^'  mi 

,  .,.,    ,  '       m  their  received  or  ordinary  signification.     1  he 

1.  J  he  language  must  _  . 

be  intelligible.  meaning  of  words,  both  separate  and  in  con- 

junction, is  already  determined  by  conventional 
usage ;  when,  therefore,  we  bear  or  read  these,  we  naturally  asso- 
ciate with  them  their  ordinary  meaning.  Misconceptions  of  every 
kind  must,  therefore,  arise  from  a  deviation  from  the  accustomed 
usage ;  and  though  the  definition,  in  the  sense  of  the  definer,  may 
be  correct,  still  false  conceptions  are  almost  inevitable  for  others. 
If  such  a  deviation  becomes  necessary,  in  consequence  of  the  com- 
mon meaning  attached  to  certain  words  not  corresponding  to  cer- 
tain notions,  there  ought  at  least  to  be  appended  a  couiment 
or  nominal  definition,  by  which  we  shall  be  warned  that  such 
words  are  used  in  an  acceptation  wider  or  more  restricted  than  they 
obtain  in  ordinary  usage.  But,  in  the  second  place,  words  ought 
not  only  to  be  used  in  their  usual  signification,  —  that  signification, 

1  Diog.  Laert ,  vi.  40.  —  Ed.  9  Krng,  Logik,  4  123.    Anm.  2.  —  Ed. 


348  LOGIC.  Lect.  XXIV. 

if  the  definition  be  perspicuous,  must  not  be  figurative  but  proper. 
Tropes  and  figures  are  logical  hieroglyphics,  and  themselves   re- 
quire a  declaration.     They  do  not  indicate  tlie 
2.  The meaniDg must       t^ing  itself,  but  Only  Something  similar."^    Such, 

be  not  figurative,  but  «  ,  .^  -i    r-    ■   ■  i  r- 

tor   example,  are   the   definitions   we    have    of 

proper.  i^     ' 

Logic  as  the  Pharus  Intellectus^  —  the  Light- 
house of  the  Understanding,  —  the  Cynosura  Veritatis,  —  the  Cy- 
nosure of  Truth,  —  the  Medicina  Mentis,  —  the  Physic  of  the 
Mind,  etc.^ 

"However,  many   expressions,  originally   metaphorical  (such  as 

conception,  imagination,  comprehension,  representation,  etc.  etc.), 

have  by  usage  been  long  since  reduced  from  figurative  to  proper 

terms,  so  that  we  may  employ  these  in  definitions  without  scruple, 

—  nay  frequently  must,  as  there  are  no  others  to  be  found. 

"  In  the  third  place,  the  perspicuity  of  a  definition  depends  upon 
its  brevity.     A  long  definition  is  not  only  bur- 

3.    The    definition  ,  .       ,-,  i  i-i         •  i 

must  be  brief.  thensome  to  the  memory,  but  likewise  to  the 

understanding,  which  ought  to  comprehend  it  at 
a  single  jet.  Brevity  ought  not,  however,  to  be  purchased  at  the 
expense  of  perspicuity  or  completeness."^ 

"The  rules  hitherto  considered  proximately  relate  to  Definitions 

in  the  stricter  sense.     In  reference  to  the  other 

The  other  kinds  of      kinds  of  Declaration,  there  are  certain  modifica- 

Deciaration.  ^j^^^g  ^^^  exceptions  admitted.    These  Dilucida- 

Dilucidations  orEx-  .  . 

plications.  tions  or  Explications,  as  they  make  no  pretence 

to  logical  perfection,  and  are  only  subsidiary  to 
the  discovery  of  more  perfect  definitions,  are  not  to  be  very  rigidly 
dealt  with.  They  are  useful,  provided  they  contain  even  a  single 
true  character  by  which  we  are  conducted  to  the  apprehension  of 
others.  They  may,  therefore,  be  sometimes  too  wide,  sometimes  too 
narrow.  A  contingent  and  derivative  character  may  be  also  useful 
for  the  discovery  of  the  essential  and  original. 

Circular  Definitions.         t-<  d~i-        ^         t^   i'    '^-  ^    \  i 

Even  Circular  Dennitions   are  not  here    abso- 
lutely to  be  condemned,  if  thereby  the  language  is  rendered  simpler 
and  clearer.     Figurative  Expressions   are  like- 

ligurative    Expres-         ^j^^,    j,j     ^^^^^    j^^^     f^^^^.        ^^^^^     j^    definitions 
liions.  .  •  1  1 

])roper,  inasmuch  as  such  expressions,  by  the 
analogies  they  suggest,  contribute  always  something  to  the  illustra- 
tion of  the  notion. 

"  In  regard  to  Descriptions,  these  must  be  adequate,  and  no  circle 


1  Krug,  Logik,  {  123.    Anm.  4.  —  Ed .  S  S«e  above,  p.  26.  —  Ed. 

3  Krug,  »6k/.  —  Ed. 


Lect.  XXIV.  LOGIC.  349 

is  permitted  in  them.  But  they  need  not  be  so  precise  as  to  ad- 
mit of  no  derivative  or  contingent  characters. 
For  descriptions  ought  to  enumerate  the  char- 
acters of  a  thing  as  fully  as  possible  ;  and,  consequently,  they  cannot 
be  so  brief  as  definitions.  They  cannot,  however,  exceed  a  certain 
measure  in  point  of  length."' 

1  Krag,  Logik,  i  123.    Anm.  5.  ~  Ed. 


LECTURE     XXV. 

METHODOLOGY. 

SECTION    II.  — LOGICAL    METHODOLOGY. 

IL  — DOCTRINE  OF  DIVISION. 

I  NOW  proceed  to  the  Second  Chapter  of  Logical  Methodology, — 

the  Doctrine  of  Division,  —  the  doctrine  which 

affords  us  the  rules  of  that  branch  of  Method, 

by  which  we  render  our  knowledge  more  distinct  and  exhaustive. 

I  sliall  preface  the  subject  of  Logical  Division  by  some  observations 

on  Division  in  general. 

"Under  Division  (divisio,  Siat/ieo-is)  we  understand  in  general  the 

sundering  of  the  whole  into  its  parts.*     The 
Division  in  general.  ,  .      .        ....       .,..,,.  n    -•      i  -       t    .  t    ■, 

object  which  is  divided  is  called  the  divided 

whole  {totxim  divisiim),  and  this  whole  must  be  a  connected  many, 
—  a  connected  multiplicity,  for  otherwise  no  division  would  be  pos- 
sible. The  divided  whole  must  comprise  at  least  one  character, 
affording  the  condition  of  a  certain  possible  splitting  of  the  object., 
or  through  which  a  certain  opposition  of  the  object  becomes  recog- 
nized ;  and  this  character  must  be  an  essential  attribute  of  the 
object,  if  the  division  be  not  aimless  and  without  utility.  This 
point  of  view,  from  which  alone  the  division  is  possible,  is  called 
the  j!9rt/?c?/:)^e  of  the  division  {principium  sive  fundaraentum  divisi- 
onis) ;  and  the  parts  which,  by  the  distraction  of  the  whole,  come 
into  view,  are  called  the  divisive  members  (membra  dividentia). 
When  a  whole  is  divided  into  its  ])arts,  these  parts  may,  either  all 
or  some,  be  themselves  still  connected  multiplicities;  and  if  these 
are  again  divided,  there  results  a  sid)division  {subdivisio),  the  sev- 
eral parts  of  which  are  called  the  subdivisive  members  (membra 
std)dividentia).  One  and  the  same  object  may,  likewise,  be  differ- 
ently divided  from  different  points  of  view,  whereby  condivisions 

1  [Oo  DIrision  and  its  vnrioue  kinds,  see  Ammouius,  De  Quinque  Voeibtu,  f.  6*,  AM.  IMS.] 


Lect.  XXV.  LOGIC.  851 

{condivisiones)  nrise,  which,  taken  together,  arc  all  reciprocally 
coordinatetl.  If  a  division  has  only  two  members,  it  is  called  a 
dichotomy  {dichotomia)  ;  if  three,  a  trichotomy  (trichotomia)  ;  if 
four,  a  tetrachotom,y ;  if  many,  2l  polytomy,  etc. 

"Division,  as  a  genus,  is  divided  into  two  species,  according  to 

the  different  kind  of  whole  which  it  sunders  into 

Division  of  two  8p€-       parts.^     These  parts  are  either  coi)tained  in  the 

^"'^'    ,  r^-  •  •  divided  whole,  or  they  are  contained  under  it. 

Logical  Division.  '  •' 

In  the  former  case  the  division  is  called  a  parti- 
tion {partitio^airapiSix-qaL^)^  in  the  latter,  it  is  named  a  logical  divi- 
sion? Partition  finds  an  application  only  when  the  object  to^  be 
divided  is  a  whole  compounded  of  parts,  —  consequently,  where 
the  notion  of  the  object  is  a  complex  one;  Logical  Division,  on  the 
other  hand,  finds  its  application  only  where  the  notion  contains  a 
plurality  pf  characters  under  it,  and  where,  consequently,  the  notion 
is  a  universal  one.  The  simple  notion  is  thus  the  limit  of  Parti- 
tion ;  and  the  individual  or  singular  is  thus  the  limit  of  Division. 

Partition  is  divided  into  ^physical  or  real,  when 

Partition  cither  Eoal         ^,  ^  ^       ii       i  ^     i    j?  i 

the  parts  can  actually  be  separated  irom  each 
other;  and  into  a  metaphysical  or  ideal,  when 
the  parts  can  only  be  sundered  by  Abstraction.*  It  may  be  applied 
in  order  to  attain  to  a  clear  knowledge  of  .the  whole,  or  to  a  clear 
knowledge  of  the  parts.  In  the  former  case,  the  parts  are  given 
and  the  whole  is  sought;  in  the  latter,  the  whole  is  given  and  the 
parts  are  sought.  If  the  whole  be  given  and  the  parts  sought  out, 
the  object  is  first  of  all  separated  into  its  proximate,  and,  thereafter, 
into  its  remoter  parts,  until  either  any  further  partition  is  impossible, 


1  [On  various  kinds  of  Wlioles,  see  Cara-  By  Division,  triangle  is  distinguished,  1°, 

muel,  Rationaiis  et  Healis  Pkilosopliia,  L.  iv.  Into  the  two  species  of  rectilinear  and  curvi- 

sect.  iii.  disp.  iv.  p.  277,]  [and  above,  Lectures  linear.     '2°,  Both  of  these  are  again  subdi- 

cn  Metaphysics, -p.  f^l;    Lectures  on   Logic,  p.  vided  (A)  by  reference  to  the  sides,  (B)  by 

142.  — Ed.]  reference  to  the  angles.    By  reference  to  the 

^  ' ATraplb/i7](Tis  is  properly  a  rhetorical  sides,  triangles  are  divided    into    the    three 

term,  and  signifies  tlie  division  of  a  subject  species  of  equilateral,  isosceles,  and  scalene, 

into  successive  heads,  first,  second,  etc.    See  (The  dichotomic  division  would,  however,  be 

Uermogenes,  Ilepl  iSeoi/'.    Rhetores  Gr^ci,  i.  p.  here  more  proper.)    By  reference  to  the  an- 

104,  cd.  Aid.  —  Ed.  gles,  they  are  divided  into  the  three  species  of 

3  [See  Keckermaun,  Systema  Logicce,  L.  i.  rectangular,  t  e.  triangle  which  has  one  of 

0.  3.     Opera,  t.  i.  p.  6G7.    Drobiscli,  New  Bar-  its  angles  right;  into  amblygon,  or  triangle 

stellung  der  Logik,  §  112.    Krug,  Logik,  §  124.  which  has  one  of  its  angles  obtuse;  and  into 

Anm.  2  ]  oxygon,   /.  e.   triangle  which  has  its  three 

•*  By  I'artition,  triangle  may  be  distinguished,  angles  acute. 

1°,  Into  a  certain  portion  of  space  included  By  Definition,  triangle  is  distinguislied  into 

within  certain  boundaries;  2°,  Into  sides  and  figure   of   three    sides,  equal    to    triangular 

angles;  3°,  Into  two  triangles,  or  into  a  tra-  figure;    that  is,  into  figure,  the    proximate 

pezium  and  a  triangle.    The  first  two  parti-  genus,  and  trilateral  or  three-sided,  the  differ- 

tions  are  ideal,  they  cannot  be  actually  ac-  ential  quality, 
complished.    The  last  is  real,  it  may. 


352  LOGIC.  Lect.  XXV. 

or  the  partition  has  attained  its  end.  To  this  there  is,  however,  re- 
quired an  accurate  knowledge  of  the  object,  of  its  parts  proximate 
and  remote,  and  of  the  connection  of  these  parts  together,  as  con- 
stituting the  whole.  We  must,  likewise,  take  heed  whether  the 
partition  be  not  determined  from  some  particular  point  of  view,  in 
consequence  of  which  the  notions  of  more  proximate  and  more 
remote  may  be  very  vague  and  undetermined.  If  the  parts  be 
given,  and  from  them  the  whole  sought  out,  this  is  accomplished 
when  we  have  discovered  the  order,  —  the  arrangement,  of  the 
parts;  and  this  again  is  discovered  when  the  principle  of  division 
is  discovered  ;  and  of  this  we  must  obtain  a  knowledge,  either  from 
the  general  nature  of  the  thing,  or  from  the  particular  end  we  have 
in  view.  If,  for  example,  a  multitude  of  books,  of  every  various 
kind,  are  arranged  into  the  whole  of  a  well-ordered  library, —  in 
this  case  the  greater  or  lesser  similarity  of  subject  will  afford,  either 
exclusively  or  mainly,  the  principle  of  division.  It  happens,  how- 
ever, not  unfrcquently,  that  the  parts  are  ordered  or  arranged 
according  to  different  rules,  and  by  them  connected  into  a  whole ; 
an<l,  in  this  case,  as  the  different  rules  of  the  arrangement  cannot 
together  and  at  once  accomplish  this,  it  is  proper  that  the  less 
important  arrangement  should  yield  to  the  more  important ;  as,  for 
example,  in  the  ordering  of  a  library,  when,  besides  the  contents 
of  the  books,  we  take  into  account  their  language,  size,  antiquity, 
binding,  etc."' 

I  now  proceed  to  Logical  Division,  on  which  I  give  you  the 
following  pai'agraph : 

%    LXXXV.    The   Distinctness   and    Completeness   of  our 

^  knowledge  is  obtained  by  that  logical  pro- 

par  LXXXV.  Logi-       ^^^^   which    is    tcrmcd   Division    (divisio, 

oal  Division.  ''  ' 

8taipc<ns).  Division  supposes  the  knowl- 
edge of  the  whole  to  be  given  through  a  foregone  process  of 
Definition  or  Declaration  ;  and  proposes  to  discover  the  parts 
of  this  whole  which  are  found  and  determined  not  by  the 
development  of  the  Comprehension,  but  by  the  development 
of  the  Extension.  As  Logical  Definition,  therefore,  proposes 
to  render  the  characters  contained  in  an  object,  that  is,  the 
comprehension  of  a  reality  or  notion,  Clear ;  Logical  Division 
proposes  to  render  the  characters  contained  under  an  object, 
that  is,  the  extension  of  a  notion.  Distinct  and  Exhaustive. 
Division   is,  therefore,  the   evolution   of  the   extension   of  a 


1  Esser,  1.0^ lit,  H  134, 135,  p.  261-«4.  —  Ed. 


Lect.  XXV.  LOGIC.  3,')8 

notion  :  .and  it  is  expressed  in  a  disjunctive  proposition,  of 
wlucli  the  notion  (li\  iiled  constitutes  tlie  subject,  and  tlio 
notions  coutaine(|  under  it,  tlie  jiredicate.  It  is,  tliereforo, 
regulated  by  tlie  law  Avhicli  o()\ei-iis  Disjunctive  Judgnient.s, 
(the  Pi'inciple  of  Kxchnled  Middk'),  aUliough  it  is  usually 
expresse(l  in  the  I'oiMii  of  a  Copulative  ( 'atcgoi'ical  Judgment. 
The  I'ules  by  which  this  ])rocess  is  I'cgulateil  are  seven  : 

1°.  iMery  I)i\ision  shoidd  be  governed  by  some  pi'inciple, 
{Dirixlo  itc.  (u(r<'(it  funJjntn  nfa). 

2°.  Every  J)ivision  should  be  governed  by  oidy  a  singl(> 
principle. 

o*.  Tlie  piMii('i]ile  of  I)i\i>ioii  should  be  an  actual  ;in(l  essen- 
tial character  of  the  <livided  notion,  and  the  division,  therefore, 
neitlier  complex  nor  without  a  juirpose. 

4°.  Xo  di^•iding  member  of  the  predicate  must  l)y  itself 
exhaust  the  subject. 

5°.  The  dividing  iiu'inbers,  taken  together,  must  exhaust,  but 
only  exhaust,  the  subject. 

0°.  The  di\isive  members  must  be  reciprocal! v  exclusive. 

7°.  The  di\'isioiis  must  ]>roceed  continuouslv  from  immediat(! 
to  mediate  d'iiei'eiices  (/Jin'sio  ne  Jidt  per  aaltinn). 

In  this  paragraph   are  contained,  first,  the  general   Princi]»les   of 
Logical    Division,  and,  secondly,  the    l^aws    by 
which    it   IS    governed.      1    shall    now    illustrate 
these  in  detail. 

In  the  iirst  place,  it  is  stated  that  "the  distinctness  and  complete- 
ness of  our  knowledge  is  obtaiiie<l  by  that  logical  ])rocess  which  is 
termed  Division  [divisio,  8t(u'/jerjt?).  Di\  ision  supposes  the  knowl- 
edge of  the  whole  to  be  given  through  a  tbregone  jirocess  of  defini- 
tion, and  projioscs  to  discover  the  parts  of  this  whole  which  art; 
found  and  determined  not  by  the  development  ol'  the  comjirehen- 
sion,  but  by  tlie  develojiment  of  the  extension.  As  logical  defini- 
tion, therefore,  proposes  to  render  the  characters  contained  in  a 
notion,  that  is,  its  comprehension,  clear;  logical  division  pr(>poses 
to  render  the  characters  contained  under  an  object,  that  is,  the 
extension  of  a  notion,  distinct.  Division  is,  therefore,  the  evolution 
of  the  extension  of  a  notion,  and  it  is  expresse<l  in  a  disjunctive 
proi)osition,  of  which  the  notion  divided  constitutes  the  subject, 
and  the  notions  contained  under  it,  the  predicate.  It  is,  therefore, 
regulated  by  the  law  which  go\erns  disjunctive  judgments  (tho 
princi])le  of  excluded  middle),  although  it  be  usually  expressed  in 
the  form  of  a  copulative  categorical  judgment." 

45 


>354  1.0 G I C.  Lect.  XXV. 

The  special  virtue,  the  particular  element,  of  perfect  thinking, 

which  Division   enables  us  to  acquire,  is  Dis- 

End  of  Division  is       tinctucss,  but,  at  the  same  time,  it  is  evident 

Distinctness,  which  in-  ...  ,.,,..,  , 

voives  Completeness.  ^^^^  ^^  Cannot  accomplish  this  without  render, 
ing  our  thinking  more  complete.  This,  how- 
ever, is  only  a  secondary  and  collateral  result ;  for  the  problem 
which  division  proximately  and  principally  proposes  to  solve  is, — 
to  afford  us  a  distinct  consciousness  of  the  extension  of  a  given 
notion,  through  a  complete  or  exhaustive  series  of  subordinate  or 
coordinate  notions,  Tiiis  utility  of  Division,  in  rendering  our 
knowledge  more  complete,  is,  I  find,  stated  by  Aristotle,'  though 
it  has  been  -overlooked  by  subsequent  logicians.  He  observes  that 
it  is  only  by  a  regular  division  that  we  can  be  assured  that  nothing 
has  been  omitted  in  the  definition  of  a  thing. 

"As  it  is  by  means  of  division  that  we  discover  what  are  the 
characters   contained   under  the   notion    of  an 

As  many  kinds  of  •      /•  n 

Division  possible  as  objcct,  it  follows  that  there  must  be  as  many 
there  are  characters  kinds  of  division  possiblc  as  there  are  chai-ac- 
aflbrdinfi  a  Principle       ^q^^  contained  Under  the  notion  of  an   object, 

which  may  afford  the  principle  of  a  different 
division.  If  the  characters  which  afford  the  principle  of  a  division 
are  only  external  and  contingent,  there  is  a  division  in  the  wider 
sense ;  if,  again,  they  are  internal  and  constant,  there  is  a  division 
in  the  stricter  sense  ;  if,  finally,  they  are  not  only  internal  but  also 
essential    and'  original,  there  is  a  division  in  the  strictest   sense. 

From  the  very  conception  of  logical  division,  it 

A  universal  notion       j^  manifest  that  it  can  only  be  applied  where 

Lo  ica" Division  ^'^^  objcct  to  be  divided  is  a  universal  notion, 

and  that  it  is  wholly  inapplicable  to  an  individ- 
ual ;  for  as  the  individual  contains  nothing  under  it,  consequently  it 
is  not  susceptible  of  an  ulterior  division.     The  general  problem  of 

which  division  affords  the  solution  is,  —  To  find 
General  problem  of      ^^^  subordinate  genera  and  species,  the  higher 

Division.  ^^  .  ,    ^         ^  =* 

or  generic  notion  being  given.  The  higher 
notion  is  always  something  abstracted,  —  something  generalized 
from  the  lower  notions,  with  which  it  agrees,  inasmuch  as  it  con- 
tains all  that  is  common  to  these  inferior  concepts,  and  from  which 
it  differs,  inasmuch  as  they  contain  a  greater  number  of  determin- 
ing charactei-s.  There  thus  subsists  an  internal  connection  between 
the  higher  and  the  lower  concepts,  and  there  is  thus  afforded  a  tran- 
sition from  the  superior  notion  to  the  subordinate,  and,  conse- 
quently, an  evolution  of  the  lower  notions  from  the  higher. 

1  Anat.  Pott.,  L.  ii.  0. 1& 


Lect.  XXV.  LOGIC.  366 

order  to  discover  the  inferior  genera  and  species,  we  have  only  to 
discover  those  characters  which  afford  the  proximate  determina- 
tions, by  which  the  spliere  or  extension  of  the  higher  notion  is 
circumscribed.  But  to  find  what  characters  are  wanted  for  the 
thoroug])-g()ing  determination  of  a  higher  notion,  we  must  pre- 
viously know  what  characters  the  higher  notion  actually  contains, 
and  this  knowledge  is  only  attainable  by  an  analysis,  —  a  sundering 
of  tlie  higher  notion  itself  In  doing  this,  the  several  characters 
must  be  separately  drawn  forth  and  considered  ;  and  in  regard  to 
each,  we  must  ascertain  how  far  it  must  still  be  left  undetermined, 
and  how  fiir  it  is  capable  of  opposite  determinations.  But  whether 
a  character  be  still  undetermined,  and  of  what  opposite  determina- 
tions it  is  capable,  —  on  these  points  it  is  impossible  to  decide  a 
priori^  but  only  a  2^osteriori,  through  a  knowledge  of  this  particular 
character  and  its  relations  to  other  notions.  And  the  accomplish- 
ment of  this  is  rendered  easier  by  two  circumstances;  —  the  one, 
that  the  generic  notion  is  never  altogether  abstract,  but  always 
realized  and  held  fast  by  some  concrete  form  of  imagination;  —  the 
other,  that,  in  general,  we  are  more  or  less  acquainted  with  a  greater 
or  a  smaller  number  of  special  notions,  in  which  the  generic  notion 
is  comprehended,  and  these  are  able  to  lead  us  either  mediately  or 
immediately  to  other  subordinate  concepts. 

"  But  the  determinations  or  constituent  characters  of  a  notion 
Avhich  we  seek  out,  must 'not  only  be  completely,  but  also  precisely, 
opposed.  Completely,  inasmuch  as  all  the  species  subordinate  to 
the  notions  ougfit  to  be  discovered ;  and  precisely,  inasmuch  as 
whatever  is  not  a  subordinate  species,  ought  to  be  absolutely 
excluded  from  the  notion  of  the  genus. 

"In  regard  to  the  completeness  of  the  opposition,  it  is  not,  how- 
ever, required  that  the  notion  should  be  determined  through  every 
possible  contradictory  opposition ;  for  those  at  least  ought  to  be 
omitted,  concerning  whose  existence  or  non-existence  the  notion 
itself  decides.  In  regard  to  the  opposition  itself,  it  is  not  required 
that  the  division  should  be  carried  through  by  contradictory  oppo- 
sitions. The  only  opposition  necessary  is  the  reciprocal  exclusion 
of  the  inferior  notions  into  which  the  higher  notion  is  divided."' 
In  a  mere  logical  relation,  indeed,  as  we  know  nothing  of  the  nature 
of  a  thing  more  than  that  a  certain  character  either  does  or  does 
not  belong  to  it,  a  strictly  logical  division  can  only  consist  of  two 
contradictory  members,  for  example,  —  that  angles  are  either  ri(/ht 
or  not  riffht,  —  that  men  are  either  white  or  7iot  lohite.  But  looking 
to  the  real  nature  of  the  thing  known,  either  a  priori  or  a  posteri- 

1  Esser,  Logik,  5  136.  —  Ed. 


366  LOGIC.  Lect.  XXVv 

on,  the  division  may  be  not  only  dichotomous  but  polytomous,  as 
for  example,  —  angles  are  rights  or  acute,  or  obtuse  ;  men  are  tohite^ 
or  blade,  or  copper-colored,  or  olive-colored,  etc. 

We  now  come,  in  the  second  place,  to  the 

Rales  of  Logical  Di-  ,         t    ^    ^    j  ^      x        ■      i  ta-    •   • 

rules  dictated  tor  Losrical  Division. 

vision.  _    °     _ 

These  Rnles  spring  either,  1°,  From  the  Prin- 
ciple of  Division  ;  or,  2°,  From  the  Relations  of  the  Dividing  Mem- 
bers to  the  Divided  Whole;  or,  3°,  From  the  Relations  of  the 
several  Dividing  Members  to  each  other;  or,  4°,  From  the  relations 
of  the  Divisions  to  the  Subdivisions. 

The  first  of  these  heads  —  the  Principle  of  Division  —  compre- 
hends the  three  first  rules.     Of  these  the  firet  is 
ose  springing,    .       self-evident,  —  There   must  be  some  principle, 

From  the  rnuciple  of  '  ...  i  r     ' 

Divwion.   First  Kuie.       somc  reason,  for  every  division ;   for  otherwise 
there  would  be  no  division  determined,  no  divi- 
sion carried  into  effect. 

In  regard  to  the  second  rule,  —  That  every  division  should  have 
only  a  single  principle,  —  the  propriety  of  this  is 
likewise  stifiiciently  apparent.     In  every  division 
we  should  depart  from  a  definite  thought,  which  has  reference  either 
to  the  notion  as  a  unity,  or  to  some  single  character.     On  the  con- 
trary, if  we  do   not  do  this,  but  carry  on  the  process  by  different 
principles,  the  series  of  notions  in  which  the  division  is  realized  is 
not  orderly  and  homogeneous,  but  heterogeneous  and  perplexed. 
The  Third  rule,  —  That  the  principle  of  div*ision  should   be  an 
actual   and  essential  charact<?r  of  the   divided 

Third.  .  .  ,  .^  ^        , 

notion,  —  IS  not  Ies3  manitest.  "  As  the  ground 
of  division  is  that  \vj)ich  principally  regulates  the  correctness  of  the 
whole  process,  that  is,  the  completenesj*  and  opposition  of  the  divi- 
sion, —  it  follows  that  this  ground  niuH  be  of  notoriety  and  impor- 
tance, and  accommodated  to  the  end  for  the  sake  of  which  the 
division  is  instituted.  Those  characters  of  an  object  are  best 
adapted  for  a  division,  whose  own  determinations  exert  the  great- 
est influence  on  the  determinations  of  otlier  characters,  and,  con- 
sequently, on  tliose  of  the  notion  itself;  but  suchCare  inanift-stly  not 
the  external  and  contingent,  but  the  internal  and  essential,  charao- 
ters,  and,  of  these,  those  have  the  preeminence  through  whose  deter- 
mination the  greater  number  of  otheis  are  determined,  or,  what  is 
the  same  thing,  from  which,  as  fundamental  and  original  attributes, 
the  greater  number  of  the  others  arc  derived.  The  choice  of  char- 
acter is,  however,  for  the  most  part,  regulated  by  some  particular 
end;  so  that,  under  certain  circumstances,  external  and  contingent 
characters  may  obtain  a  preponderant  importance.     Such  ends  can 


Lkct.  XXV.  LOGIC. 

not,  however,  be  enumerated.  The  character  afFording  the  principle 
of  division  must  likewise  be  capable  of  being  clearly  and  definitely 
brought  out ;  for  unless  this  be  possible,  we  can  have  no  distinct 
consciousness  of  the  completeness  and  contrast  of  the  determination 
of  which  it  is  susceptible.  We  ought,  therefore,  always  to  select 
those  characters  for  principles  of  division,  which  are  capable  of  a 
clear  and  distinct  recognition."' 

The  second  part  of  the  rule,  —  That  the  division  be  not,  therefore, 
too  complex,  and  without  a  purpose,  —  is  a  corollary  of  the  fii*st. 
"  In  dividing,  we  may  go  on  to  infinity.  For  while,  as  was  formerly 
shown,  there  is,  in  the  series  of  higher  and  lower  notions,  no  one 
which  can  be  conceived  as  absolutely  the  lowest ;  so  in  subdividing, 
there  is  no  necessary  limit  to  the  process.  In  like  manner,  the 
coordinations  may  be  extended  ad  infinitum.  For  it  is  impossible 
to  exhaust  all  the  possible  relations  of  notions,  and  each  of  these 
may  be  employed  as  the  principle  of  a  new  division.  Thus  we  can 
divide  men  by  relation  to  their  age,  to  their  sex,  to  their  color,  to 
their  stature,  to  their  knowledge,  to  their  riches,  to  their  rank,  to 
their  manner  of  life,  to  their  education,  to  their  costume,  etc.,  etc. 
It  would,  however,  be  ridiculous,  and  render  the  divisions  wholly 
useless,  if  we  multiplied  them  in  this  fashion  without  end.  We, 
therefore,  intentionally  restrict  them,  that  is,  we  make  them  com- 
paratively limited,  inasmuch  as  we  only  give  them  that  completeness 
which  is  conducive  to  a  -certain  end.  In  this  manner,  divisions 
become  relatively  useful,  or  acquire  the  virtue  of  adaptation.  In 
the  selection  of  a  principle  of  division,  we  must  take  heed  whether 
it  be  fertile  and  pertinent.  A  ground  of  division  is  fertile,  when  it 
affords  a  division  out  of  which  again  other  important  consequences 
may  be  drawn ;  it  is  pertinent,  when  these  consequences  have  a 
proximate  relation  to  the  end,  on  account  of  which  we  were  origi- 
nally induced  to  develop  the  extension  of  a  concept,  A  principle 
of  division  may,  therefore,  be  useful  with  one  intent,  and  useless 
with  another.  Soldiers^  for  example,  may  be  conveniently  divided 
into  cavalry  and  infantry^  as  this  distinction  has  an  important  influ- 
ence on  their  determination  as  soldiers.  But  in  considering  man  in 
general  and  his  relations,  it  would  be  ludicrous  to  divide  men  into 
foot  and  horsemen  ;  while,  on  the  contrary,  their  division  would  be 
here  appropriate  according  to  principles  which  in  the  former  case 
would  have  been  absurd.  Seneca^  says  well,  —  'Quicquid  in  majus 
crevit  facilius  agnoscitur,  si  discessit  in  partes;  quas  innumerabilcH 
esse  ct  parvas  non  oportet.     Idem  enim  vitii  habet  nimia,  quod  null.i 

1  EBSer,  Logik, }  137.  —  Ed-  2  Epist.,  90. 


358  LOGIC.  Lect.  XXV. 

divisio.     Simile  confuso  est,  quicquid  usque  in  pulverem  sectum 
est.'"^ 

Under  the  second  head,  that  is,  as  springing  from  the  relations  of 

the  Dividing  Members  to  the  Divided  Wholes, 

II.  From  the  reia-       ^jj^^.g   ^re  included   the  fourth  and  fifth  laws. 

tions  of  the  Dividing         ,,   a      j.\  •  t      i  •  •  i  •    i      . 

Members  to  the  Divid-      "^sthe  notion  and  the  notions  into  which  it 
ed  Wholes.    Fourth.        is  divided  Stand  to  each  other  in  the  relation  of 
whole  and  parts,  and  as  the  whole  is  greater 
than  the  part,  the  fourth  rule  is  manifestly  necessary,  viz..  That  no 
dividing  member  of  the  predicate  must  by  itself  exhaust  the  sub- 
ject.    When  this  occurs,  the  division  is  vicious,  or,  more  properly* 
there  is  no  division.     Thus  the  division  of  man  into  rational  ani- 
mals and  uncultivated  nations^  would  be  a  violation  of  this  law. 
"  On  the  other  hand,  as  the  notions  into  which  a  notion  is  divided, 
stand  to  each  other  in  the  relation  of  constitut- 

Fifth. 

mg  parts  to  a  constituted  whole,  and  as  the 
whole  is  only  the  sum  of  all  the  parts,  the  necessity  of  the  fifth  rule 
is  manifest,  —  That  the  dividing  members  of  the  predicate,  taken 
together,  must  exhaust  the  subject.  For  if  this  does  not  take  place, 
then  the  division  of  the  principal  notion  has  been  only  partial  and 
imperfect.  We  transgress  this  law,  in  the  first  place,  when  we  leave 
out  one  or  more  membci's  of  division  ;  as  for  example.  —  Tlie  actions 
of  men  are  either  good  or  had,  — for  to  these  we  should  have  adde'd 
or  indifferent.  And  in  tho  second  place,  we  transgress  it  when  wc 
coordinate  a  subdivision  with  a  division  ;  as  for  example,  —  Philos- 
ophy is  either  theoretical  philosophy  or  moral  philosophy  :  here  the 
proper  opposition  would  have  been  theoretical  philosophy  and  jororc- 
ticol philosophy r^  On  the  other  hand,  the  dividing  members,  taken 
together,  must  not  do  more  than  exhaust  the  subject.  The  defini- 
tion of  the  whole  must  apply  to  every  one  of  its  parts,  but  this  con- 
dition is  not  fulfilled  if  there  be  a  dividing  member  too  much,  that 
is,  if  there  be  a  notion  brought  :is  a  dividing  member,  which,  Iiow- 
ever,  does  not  stand  in  subordination  to  the  divided  whole.  For 
example,  —  Mathematical  figures  are  either  solids  or  surfaces  [or 
lines  or  2)oints\  Here  the  last  two  members  {lines  and  points)  are 
redundant  and  erroneous,  for  lines  and  points,  though  the  elements 
of  mathematical  figures,  are  not  themselves  figures. 
-  Under  the  third  head,  as  springing  from  the  relations  of  the  sev- 
eral Dividing  Members  to  Each  Other,  there  is  a  single  law,  —  the 
sixth,  —  which  enjoins,  —  That  the  dividing  members  be  recipro- 
cally exclusive. 

1  Knig,  Logik,  i  126.     Anm.  4.  —  Ed.  S  Esaer,  Lagik,  )  187.  —  £d. 


Lkct.  XXV.  LOGIC.  359 

"  As  a  division  does  not  present  the  same  but  the  different  deter- 
minations of  a  single  notion   (for  otherwise  one 

III.  From  the  reia-       and  the  same  determination  would  be  presented 
tions  of  the  several       ^^^j^.^)  tj^^  dividing  members  must  be  so  consti- 

Dividing  Members  to  '  ^  ,,  .       .  , 

Kaoh  Other.  Sixth.  tuted  that  they  are  not  mutually  comcident,  so 
that  they  either  in  whole  or  in  part  contain 
each  other.  This  law  is  violated  when,  in  the  first  place,  a  subdi- 
vision is  placed  above  a  division,  as,  —  Philosophy  is  either  theoret- 
ical philosophy,  or  moral philosojihy,  or  2iractical philosophy  ;  here 
moral  philosophy  falls  into  practical  philosophy  as  a  subordinate 
part;  or  when,  in  the  second  place,  the  same  thing  is  divided  in 
different  points  of  view,  as,  —  Human  actions  are  either  necessary^ 
or  free,  or  useful,  or  detrimentaV  ^ 

Under  the  fourth  and  last  head,  as  arising  from  the  relations  of 
the  Divisions  to  the  Subdivisions,  there  is  con- 

IV.  From  the  reia-       taiued  One  law,  the  seventh,  which  prescribes,  — 
tions  of  the  Divisions       rj.}^^^   ^^^    divisions  proceed  continuously  from 

to    the    Subdivisions.  .  .  , -r\-    •    • 

Seventh.  immediate  to  mediate  differences   {Utvtsto  ne 

fat  per  salttan  vel  hiatum). 
"  As  divisions  originate  in  the  character  of  a  notion,  capable  of 
an  opposite  determination,  receiving  this  determination,  and  as  the 
subdivisions  originate  in  these  opposite  determinations  being  them- 
selves again  capable  of  opposite  determinations,  in  which  gradual 
descent  we  may  proceed  indefinitely  onwards,  —  from  this  it  is  evi- 
dent, that  the  divisions  should,  as  far  as  possible,  be  continuous,  that 
is,  the  notion  must  first  be  divided  into  its  proximate,  and  then  into 
its  remoter  parts,  and  this  without  overleaping  any  one  part  ;  or  in 
other  words,  each  part  must  be  immediately  subordinated  to  its 
whole."  ^  Thus,  when  some  of  the  ancientsdivided  j(?Ai7osq/9Ay  into 
rational,  and  natural,  and  moral,  the  first  and  second  members  are 
merely  subdivisions  of  theoretical  philosophy,  to  which  m,oral  as 
practical  philosophy  is  opposed.  Sometimes,  however,  such  a 
spring  —  such  a  saltus  —  is,  for  the  sake  of  brevity,  allowed  ;  but 
this  only  under  the  express  condition,  that  the  omitted  members 
are  interpolated  in  thought.  Thus,  many  mathematicians  say,  angles 
are  either  right,  or  acute,  or  obtuse,  although,  if  the  division  w^ere 
continuous,  witl)out  hiatus,  it  would  run,  angles  are  either  righi 
or  oblique;  and  the  oblique,  again,  either  acuta  or  obtuse. 

1  Esser,  Logik,  §  137-  —  Ed.  2  Esser,  Logile,  §  137.  —  Ed. 


LECTURE    XXVI. 

METHODOLOOY. 

SECTION    II.  — LOGICAL    METHODOLOGY. 

in— DOCTRINE  OF  PROBATION. 

We  now  proceed  to  the  Third  Part  of  Pure  Methodology,  that 
which  guides  us  to  the  third  character  or  virtue 
of  Perfect   Thinking,  —  the   Concatenation   of 
Thought;  —  I  mean  Probation,  or  the  Leading  of  Proof.     I  com- 
mence with  the  following  paragraph. 

%   LXXXVI.    When  there  are  propositions  or  judgments 

which  are  not  intuitively  manifest,  and  the 

Par.  LXXXVI.  Pro-       ^,.^^1^  ^f  ^hich  Is  not  admitted,  then  their 

bation.-iti      Nature  ,,.,,» 

and  Elements.  Validity  can  Only  be  established  when  we 

evolve  it,  as  an  inference,  from  one  or  more 
judgments  or  propositions.  This  is  called  frohation,  Proving, 
or  the  Leading  of  Proof  (probatio,  argitmentatio,  or  demoiX' 
stratio^  in  its  wider  sense).  A  Probation  is  thus  a  series  of 
thoughts,  in  which  a  plurality  of  different  judgments  stand  to 
each  other,  in  respect  of  their  validity,  in  the  dependence  of 
determining  and  determined,  or  of  antecedents  and  conse- 
quents. In  every  Probation  there  are  three  things  to  be  dis- 
tinguished,—  1°.  The  Judgment  to  be  proved,  (thesis) ;  2°.  The 
Ground  or  Principle  of  Proof,  (argumentum) ;  and,  3°.  Tl>e 
Cogency  of  this  principle  to  necessitate  the  connection  of 
antecedents  and  consequents  (vis  demonstrationis  or  nervus 
probandi).  From  the  nature  of  Pivbation,  it  is  evident  that 
Probation  without  inference  is  impossible ;  and  that  the  Thesis 
to  be  proved  aird  Principles  of  Proof  stand  to  each  other  as 
conclusion  and  premises,  with  this  difference,  that,  in  Proba- 
tion, there  is  a  judgment  (the  thesis)  expressly  supposed, 
which,  in  the  Syllogism,  is  not,  ?it  least  necessarily,  the  case.' 

1  Esscr,  Logik,  S  138.    Cf.  Krug,  Logik,  S  127.  —  Ed.    [Cf.  Richter,  Vber  den  Gegenstand  w 
fttH  Vn{fang  der  Logik,  iS2  el  seq.] 


Lkct.  XXVI.  LOGIC.  361 

In  regard  to  the  terms  here  employed,  it  is  to  be  noticed  that  the 

term  argumentation  {argumentatio)  is  applied 

Explication.  not  only  to  a  reasoning  of  many  syllogisms,  but 

Terms  employed.         likewise  to  a  reasoning  of  one.    The  term  argu- 

Argumentation.  .      ti 

Argument.  mcnt  [argumentum)  in  like  manner  is  employed 

not  only  for  the  ground  of  a  consecutive  reason- 
ing, but  for  the  middle  term  of  a  single  syllogism.     But  it  is,  more- 
•over,  vulgarly  employed  for  the  whole  process  of  argumentation.^ 
The  term  demonstration  (demonstratio)  is  used  in  a  looser  and 
in  a  stricter  signification.     In  the  former  sense, 

DemonPtration.  .      .  .       ,       ' 

It  IS  equivalent  to  probation,  or  argumentation 
in  general;  in  the  latter,  to  necessary  probation,  or  argumentation 
from  intuitive  principles. 

The  expression  leading  q/'j!?roo/' might,  perhaps,  be  translated  by 

the   term  deduction,  but  then  this  term    must 

lugo     roo  o        1^^  ^^  such  a  latitude  as  to  include  induction,  to 

two  sorts. 

which  it  is  commonly  opposed ;  for  Probation 
may  be  either  a  process  of  Deduction,  that  is,  the  leading  of  proof 
out  of  one  higher  or  more  general  proposition,  or  a  process  of 
Induction,  that  is,  the  leading  of  proof  out  of  a  plurality  of  lower 
or  less  general  judgments. 

To  prove,  is  to  evince  the  truth  of  a  proposition  not  admitted  to 
be  true,  from  other  propositions  the  truth   of 

I'robalion  in  general.  i  •    i      •         i  i  i  t  i       i        x 

which  IS  already  established.  In  every  proba- 
tion there  are  three  things  to  be  distinguished  :  —  1°.  The  Proposi- 
tion to  be  proved,  —  the  Thesis ;  2°.  The  Grounds  or  Principle  of 
Proof, —  the  Argument;  and,  3°.  The  Degree  of  Cogency  with 
which  the  thesis  is  infeiTed  by  the  argumentum  or  argumenta,  ■ — 
the  vis  or  nervus  probandi.     All  probation  is  thus  syllogistic ;  but 

all  syllogism  is  not  probative.  The  peculiarity 
ow    ismguisie         ^^  probation  consists  in  this,  —  that  it  expressly 

from  Syllogism.  ^  .  '  I  . 

supposes  a  certain  given  proposition,  a  certain 
thesis,  to  be  true ;  to  the  establishment  of  this  proposition  the 
proof  is  relative ;  this  proposition  constitutes  the  conclusion  of  the 
syllogism,  or  series  of  syllogisms,  of  which  the  probation  is  made 
up ;  whereas,  in  the  mere  syllogistic  process,  this  supposition  is  not 

necessarily  involved.  It  is  also  evident  that  the 
Whereon   depends       logical  Value  of  a  probation  depends,  1°.  On  the 

tbe  logical  value  of  a         j.      ..t         j?    '^  •       •    i  .,00/^ 

probation  truth   oi   its   principles   or   argumenta,    z  .    Un 

their   connection  with  each  other,  and  with  the 

thesis  or  proposition  to  be  proved,  and,  3°.   On  the  logical  foi*- 

1  See  above,  p.  196.  —  Ed. 
46 


862  LOGIC.  Lkct.  XXVI. 

mality  of  the  inference  of  the  thesis  from  its  arguinenta.  No  prop- 
osition can  be  for  another  the  principle  of  proof,  which  is  not  itself 
either  immediately  or  mediately  certain.  A  proposition  is  imme- 
diately certain,  or  evident  at  first  hand,  when,  by  the  very  nature 
of  thought,  we  cannot  but  think  it  to  be  true,  and  when  it,  there- 
fore, neither  requires  nor  admits  of  proof.  A  proposition  is  medi- 
ately certain,  or  evident  at  second  hand,  when  it  is  not  at  once  and 
in  itself  thought  as  necessarily  true,  but  when  we  are  able  to  deduce* 
it,  with  a  consciousness  of  certainty,  from  a  proposition  which  is 
evident  at  first  hand.  The  former  of  these  certainties  is  called  self- 
evident,  intuitive,  original,  jyrimary,  ultimate,  etc,  and  the  latter, 
demonstrative,  derivative,  secondary,  etc. 

According  to  this  distinction,  the  Ground  or  Principle  of  Proof 
is  either  an  absolute  or  a  relative.    Absolute, 

Ground  of  Proof       ^yhen   it  is  an  intuitive;  relative,  when  it  is  a 

either      Absolute     or  .,  .  •   •  rm     x 

g^j^y^g  demonstrative  proposition.     Ihat  every  propo- 

sition must  ultimately  rest  on  some  intuitive 
truth,  on  some  judgment  at  first  hand,  is  manifest,  if  the  fact  of 
probation  itself  be  admitted ;  for  otherwise  the  regress  would 
extend  to  infinity,  and  all  probation,  consequently,  be  impossible. 
When,  for  example,  in  the  series  of  grounds  H,  G,JF,  E,  D,  C,  B, 
there  is  no  ultimate  or  primary  A,  and  when,  consequently,  every  A 
is  only  relatively,  in  respect  of  the  consequent  series,  but  not  abso- 
lutely and  in  itself,  first;  —  in  this  case,  no  suflScient  and  satisfactory 
probation  is  possible,  for  there  always  remains  the  question  concern- 
ing a  still  higher  principle.  But  positively  to  show  that  such  pri- 
mary judgments  arc  actually  given,  is  an  exposition  which,  as 
purely  metaphysical,  lies  beyond  the  sphere  of  Logic.^ 

To  the  general  form  of  a  system  of  Proof  belong  the  following 
distinctions  of  propositions,  to  which  I  fomierly 

Distinction  of  Prop-  iiiioji-i_t  •  11^ 

....  .    -      alluded,^  and  which  1  may  again  recall  to  vour 

ositions  in  respect  of  '  ./      o  . 

the  general  form  of  a       remembrance.     Propositions  are  either  Theoret- 

fystem  of  Proof.  {f.Qi  or  Practical.    Practical,  when  they  enounce 

Theoretical     and       ^j^^  j^  ^^^j^j^,^  j^  j^  possible  to  effectuate  or 

produce  something;  Theoretical,  when  they  sim- 
ply enunciate  a  truth,  without  respect  to  the  way  in  which  this  may 
be  realized  or  produced.'    A  Theoretical  proposition,  if  a  primary 

or  intuitive  principle,  is  styled  an  Axiom.  Ex- 
''"*'"'  amples  of  this  are  given  in   the  four   Funda- 

mental Laws  of  Logic,  and  in  the  mathematical  common  notions  — 

*  Compare  Esser,  Logik,  i  138  —  Kd.  2  See  above,  p.  18".  —Ed. 

3  [Fries,  Sn-Atm  iltr  Logik,  i  73.] 


Lect.  XXVI.  LOGIC.  363 

The  whole  is  greater  than  Us  part,  — J^  equals  be  added  to  equals, 

the  wholes  are  equal,  etc.     A  Practical  proposition,  if  a  primary  or 

intuitive  principle,  is  styled  a  Postulate.     Thus 

Geometry  postulates  the  possibility  of  drawing 

lines,  —  of  producing  them  ad  infinitum,  of  describing  circles,  etc. 

A  Theoretical  proposition,  if  mediate  and  demonstrable,  is  called 

a  Theorem.     This  is  laid  down  as  a  Thesis, — 

Theorem.  . 

as  a  judgment  to  be  proved,  —  and  is  proved 
from  intuitive  principles,  theoretical  and  practical.     A  Practical 

proposition,   if   mediate    and    demonstrable,  is 

called  a  Problem,.  In  the  probation,  the  Prob- 
lem itself  is  firet  enounced ;  it  is  then  shown  in  the  solution  how 
that  which  is  required  is  to  be  done,  —  is  to  be  efiected ;  and, 
finally,  in  the  proof,  it  is  demonstrated  that  througli  this  procedure 
the  solution  of  the  problem  is  obtained.  For  examj:)^,  in  the  geo- 
raeti'ical  problem,  —  to  describe  an  equilateral  triangle  on  a  given 
straight  line,  —  there  this  problem  is  first  stated  ;  the  solution  then 
shows  that,  with  this  given  line  as  a  semi-diameter,  we  are  to 
describe  from  each  of  its  points  of  termination  a  circle ;  the  two 
circles  will  intersect  each  other,  and  we  are  then,  from  the  point 
of  intersection,  to  draw  straight  lines  to  each  point  of  termination ; 
this  being  done,  the  proof  finally  demonstrates  that  these  circles 
must  intersect  each  other,  that  the  drawn  straight  lines  necessarily 
constitute  a  triangle,  and  that  this  triangle  is  necessarily  equilateral. 
Corollaries  or  Consectaries  are  propositions  which,  as  flowing 

immediately  as  collateral  results  of  others,  re- 
oro  anes.       m-       quji-g  jjq  separate  proof     Empeiremata  or  Em- 

peiremata.  •*  *  *•  ■*    . 

pirical  Judgments  are  propositions,  the  validity 
of  which  reposes  upon  observation  and  experience.      Scholia  or 
Comments  are  propositions  which  serve  only  for 
'^  °  '^'  illustration.    Lemmata  or  Sumptions  are  propo- 

sitions, borrowed  either  from  a  different  part  of 
the  system  we  treat  of,  or  from  sciences  other  than  that  in  which 
we  now  employ  them.     Finally,  Hypotheses  are 

Hypotheses.  ^/  ,■•.,•  -r. 

propositions  oi  two  dmerent  significations,  x*  or, 
in  the  first  place,  the  name  is  sometimes  given  to  the  arbitrary 
assumption  or  choice  of  one  out  of  various  means  of  accomplishing 
an  end ;  when,  for  example,  in  the  division  of  the  periphery  of  the 
circle,  we  select  the  division  into  360  degrees,  or  when,  in  Arith- 
metic, we  select  the  decadic  scheme  of  numeration.  But,  in  the 
second  place,  the  name  of  hypothesis  is  more  emphatically  given  to 
provisory  suppositions,  which  serve  to  explain  the  phenomena  in  so 
far  as  observed,  but  which  are  only  asserted  to  be  true,  if  ultimately 


364  LOGIC.  LtCT.  XXVI 

confirmed  by  a  complete  induction.  For  example,  the  supposition 
of  the  Copernican  solar  system  in  Astronomy,^ 

Now  these  various  kinds  of  propositions  are  mutually  concat- 
enated into  system  by  the  Leading  of  Proof,  —  by  Probation. 

So  much  for  the  character  of  this  process  in  general.  The  para- 
graph already  dictated  contains  a  summary  of  the  various  particu- 
lar characters  by  which  Probations  are  distinguished.  Before  con- 
sidering these  in  detail,  I  shall  offer  some  preparatory  observations. 

"The  differences  of  Probations  are  dependent  partly  on  their 
Matter,  and  partly  on  the  Form  in  which  they 

The    differences   of  j 

,.   u  ..  J,       J       are  expressed. 

FroDBtions        depend  '^ 

paiiiy  on  their  Matter  "  I"  respect  of  the  former  ground  of  differ- 

and  partly  on  their  cnco,  —  the    Matter,  —  Probations    are    distin- 

*^"'^™"  guished  into  Pure  or  a  priori,  and  into  Empir- 

1.  In  respect  of  their  ical    Or    a  posteriori,   according    as    they   are 

Matter,  Probations  founded  on  principles  which  we  must  recog- 
are  Pure  and  Empir-  .  ... 

jg^j  nize  as  true,  as  constitutmg  the  necessary  con- 

ditions   of    all    experience,   or   which    we    do 

2.  In  respect  of  their  .  ,  .      ,  ,  . 

y  recognize   as   true,   as   particular  results   given 

by  certain  applications  of  exfiorience.  In  re- 
spect of  the  latter  ground  of  difference,  —  the  Form, —  Probations 
fall  into  various  classes  according  to  the  difference  of  the  form 
itself,  which  is  cither  an  External  or  an  Internal. 

"  In  relation  to  the  Internal  Form,  probations  are  divided  into 

Direct  or  Ostensive  and  into  Indirect  or   Apa- 

(a)  In  relation  to      gogical,  according  as  they  are  drawn  from  the 

the  Internal  Form,  ^^-  .^^^jf  ^^  f^.^^  j^^  opposite,  in  Other  WOrds, 
Probations  are  Direct  "  ..,_  ,. 

or  Ostensive  and  indi-       according  as  the  principles  of  probation  are  posi- 

rect  or  Apagogicai.  tivc  or  are  negative."  *    Under  the  same  relation 

Synthetic  or  Pro-      ^f  Internal  Form,  they  are  also  distinguished  by 

grossive  and  Analytic  -,  ^       ^i     •  i  /•  j  ^i_- 

or  ReirreBsive.  reierencc   to   their  order  oi    procedure,  —  this 

order  being  either  Essential  or  Accidental.  The 
essential  order  of  procedure  regards  the  nature  of  the  inference 
itself^  as  either  from  the  whole  to  the  part,  or  from  the  parts  to  the 
whole.  The  former  constitutes  Deductive  Probation,  the  latter 
Inductive.  The  accidental  order  of  procedure  regards  only  our 
point  of  departure  in  considering  a  probation.  If,  commencing 
with  the  highest  principle,  we  descend  step  by  step  to  the  conclu- 
sion, the  process  is  Synthetic  or  Progressive ;  here  the  conclusion  is 
evolved  out  of  the  priuoiple.     If^  again,  starting  from  the  conclu- 


1  rrin,  St/Ufm  tttr  Logik,  {  7S.    Kmg,  L^ik,  H  VI,  68.] 

2  £«scr,  Logik,  i  Ul.  —  £0. 


I 


Lkct.  XXVJ.  logic.  365 

sion,  we  ascend  step  by  step  to  the  highest  principle,  the  process 
is  Analytic  or  Regressive ;  here  the  principle  is  evolved  out  of  the 
conclusion. 

In    respect   to   the   External   Form,  Probations   are   Simple   or 

Monosyllogistic,    if   they    consist    of   a    single 

Prob  tionr°re  simT       reasoning,  Composite  or  Polysyllogistic  if  they 

and  Composite.  consist   of  a  plurality  of  reasonings.      Under 

Regular  and  irregu-       the  Same  relation    of  external   form,  they  ai-e 

lar    Perfect  und  im-       ^j^^  divided  into  Regular  and  Irregular,  into 

p€ri6Ct«  ,^ 

Perfect  and  Imperfect. 
Another  division  of  Probations  is  by  reference  to  their  Cogency, 
or  the  Degree  of  Certainty  with  which   their 
their  deg*i^'^o7cl-       inference  is  drawn.     But  their  cogency  is   of 
g^ncy,  Probations  are      various  degrees,  and  this  either  objectively  con- 
Apodeictic  and  Proba-       sidered,  that  is,  as  determined  by  the  conditions 
of  the  proof  itself,  or  subjectively  considered, 
that  is,  by  reference  to  those  on  whom  the  proof  is  calculated  to 
operate  conviction.     In  the  former,  or  objective  relation,  probations 
are  partly  Apodeictic,  or  Demonstrative  in  the  stricter  sense  of  that 
term,  —  when  the  certainty  they  necessitate  is  absolute  and  com- 
plete, that  is,  when  the  opposite  alternative  involves  a  contradic- 
tion ;  partly  Probable,  —  when  they  do  not  produce  an  invincible 
assurance,  but  when  the  evidence  in  favor  of  the  conclusion  pre- 
ponderates over  that  which  is  opposed  to  it.     In  the  latter  or  sub- 
jective relation,  probations  are  either  Universally 
nirerga  y    an        Valid,  when  they  are  calculated  to  operate  con- 

Particularly  Valid.  .     .  ♦'  ,  ^ 

viction  on  all  reasonabliB  minds,  or  Particularly 
Valid,  when  they  are  fitted  to  convince  only  certain  individual 
minda. 

Par     i-xxxvn  ^  LXXXVII.  Probations  are  divided  by 

Brob»tions,  tiieir  Di.  reference  to  their  Matter,  to  their  Form, 
'*'*°'*^'  and  to  their  Degree  of  Cogency. 

In  relation  to  their  Mattel-,  they  are  partly  I*ure  or  a  priori, 
partly  Empirical  or  a  posteriori. 

As  to  their  Form,  —  this  is  either  Internal  or  External.  In 
respect  to  their  Internal  Form,  they  arc,  1°,  By  j-eference  to  the 
Manner  of  Inference,  Direct  or  Ostensive  (SetKriKat,  ostensivm), 
and  Indirect  or  Apagogical  {jyrohationes  apayogicm  reductiones 
ad  absurduvi)  ;  2°,  By  reference  to  their  Essential  or  Internal 
Order  of  Procedure,  they  are  either  Deductive  or  Inductive,' 
3°,  By  reference  to  their  Accidental  or  External  Order  of  Pro- 
cedure, they  are  partly  Synthetic  or  Progressive,  partly  Atia- 


366  LOGIC.  Lect.  XXVI. 

lytic  or  Hegressive.  In  respect  to  their  External  Form,  tbey 
are,  1°,  Simple  or  Monosylloyistic,  and  Composite  or  P oly syllo- 
gistic ;  2°,  Perfect  and  Imperfect;  3°,  Regular  and  Irregular. 
In  respect  to  their  Degree  ot  Cogency,  they  are,  1°,  As 
objectively  considered,  either  Apodeictic  or  Demonstrative  in 
the  stricter  signification  of  the  term  (aTrdScifcts,  demonstrationes 
stride  dictce),  or  Probable  (probationes  sensu  latiori)  ;  2**,  As 
subjectively  considered,  they  are  either  Universally  Valid  (/car 
aXrj^eLav,  secundum  veritatem)^  or  Particularly  Valid  (kot  a»^ 
Bponrov,  ad  hominem,)} 

To  speak  now  of  these  distinctions  in  detail.     In  the  first  place, 

"  Probations,"  we  have  said,  "  in  relation  to  their 

T>   K^J    '  1°  T  matter,  are  divided  into  Pure  or  a  priori,  arfd 

Probations,  1.  In  re-  '  ■»  ' 

epect  of  their  Matter,  into  Empirical  or  a  posteriori.  Pure  or  a  priori 
are  Pure  and  Empiri-  proofs  are  thosc  that  Tcst  on  principles  which, 
although  rising  into  consciousness  only  on  occa- 
sion of  some  external  or  internal  observation,  of  some  act  of  expe- 
rience, are  still  native,  are  still  original,  contributions  of  the  mind 
itself,  and  a  contribution  without  which  no  act  of  experience 
becomes  possible.  Proofs  again  are  called  Empirical  or  a  pos- 
teriori, if  they  rest  on  principles  which  are  exclusively  formed  from 
experience  or  observation,  and  whose  validity  is  cognizable  in  no 
other  way  than  that  of  experience  or  observation.  When  the  prin- 
ciples of  Probation  are  such  as  are  not  contingently  given  by  expe- 
rience, but  spontaneously  engendered  by  the  mind  itself,  these 
principles  are  always  characterized  by  the  qualities  of  necessity 
and  universality ;  consequently,  a  proof  supported  by  them  is  ele- 
vated altogether  above  the  possibility  of  doubt.  When,  on  the 
other  hand,  the  Principles  of  Probation  ai*e  such  as  liave  only  the 
guarantee  of  observation  and  experience  for  their  truth,  —  (suppos- 
ing even  that  the  observation  be  correct  and  the  experience  stable 
and  constant),  —  these  principles,  and,  consequently,  the  probation 
founded  on  them,  can  pretend  neither  to  necessity  nor  univei*sality ; 
seeing  that  what  produces  the  observation  or  experience  has  only  a 
relation  to  individual  objects,  and  is  only  competent  to  inform  us 
of  what  now  is,  but  not  of  what  always  is,  of  what  necessarily  must 
be.  Although,  however,  these  empirical  principles  are  impressed 
with  the  character  neither  of  necessity  nor  of  universality,  they 
play  a  very  important  part  in  the  theatre  of  human  thought."' 


1  Cf.  KruB,  Logik,  H  128,  129,  130,  131,  132.     Esser,  Logik,  s  139— Ed.    [Cf.  Degeranda 
Vts  Signts,  t.  iv.  ch.  7,  p.  234.]  3  Esser,  Logik,  )  140.—  £d. 


Lect.  XXVI.  LOGIC.  367 

This  distinction  of  Proofe,  by  reference  to  the  matter  of  our  knowl- 
edge, is  one,  indeed,  which  Logic  does  not  take 
This  distinction  of      [^^q  account,      Logic,  in  fact,  considers  every 

Probations  not  taken         .     „  -,  ^  „  ^  i       ^ 

^,    _     .         inierence  ot  a  consequent  irom  an  antecedent  as 

nito  account  by  Logic.  _  i 

an  inference  a  2^^iori,  supi^osing  even  that  the 
antecedents  themselves  are  only  of  an  empirical  character.  Thus 
Ave  may  say,  that,  from  the  general  relations  of  distance  found  to 
hold  between  the  planets,  Kant  and  Olbers  proved  a  priori  that 
between  Mars  and  Jupiter  a  planetary  body  must  exist,  before 
Ceres,  Pallas,  Juno,  and  Vesta,  were  actually  discovered.^  Here, 
however,  tlie  a  priori  principle  is  in  reality  only  an  empirical  rule, 
—  only  a  generalization  from  experience.  But  with  the  manner 
in  which  these  empiiical  rules  —  (Bacon  would  call  them  axi- 
oms) —  are  themselves  discovered  or  evolved  —  with  this.  Pure 
Logic  has  no  concern.  This  will  fall  to  be  considered  in  Modified 
Logic,  when  we  treat  of  the  concrete  Doctrine  of  Induction  and 
Analogy. 

In   the   second  place,  "in  respect  of  their  Form,  and  that  the 
Internal,  Probations  are,  as  we  said,  first  of  all, 
2.  In  respect  of  their       divided  into  Direct  or  Ostensive,  and  into  Indi- 
anHndirect. '     "^^        ^®^*  ^^*  Apagogical.     A  proof  is  Direct  or  Os- 
tensive, when  it  evinces  the  truth   of  a  thesis 
through  positive  principles,  that  is,  immediately ;  it  is  Indirect  or 
Apagogical,  when  it  evinces  the  truth  of  a  thesis  through  the  false- 
hood of  its  opposite,  that  is,  mediately.     The  indirect  is  specially 
Jled  the  apagogical  {argumentatio  apagogica  sive  deductio  ad 
impossibile),  because  it  shows  that  something  cannot  be  admitted, 
since,  if  admitted,  consequences  would  necessarily  follow  impossible 
or  absurd.     The  Indirect  or  Apagogical  mode  of  proof  is  estab- 
lished on  the  principle,  that  that  must  be  con- 
nncipeo    n  irec        ceded  to  be  true  whose  contradictory  opposite 
contains   within   itself   a    contradiction.      This 
principle  manifestly  rests, on  the  Law  of  Contradiction,  and  on 
the  Law  of  Excluded  Middle ;   for  what  involves  a  contradiction 
it  is  impossible  for  us  to  think,  and  if  a  character  must  be  denied 
of  an  object,  —  and  that  it  must  be  so  denied  the  probation  has  to 
show,  —  then   the  contradictory   opposite   of  that  character  is  of 
necessity  to  be  affirmed  of  that  object.     The  Direct  mode  of  proba- 
tion has  undoubtedly  this  advantage  over  the  Indirect,  —  that  it  not 
only  furnishes  the  sought-for  truth,  but  also  truly  develops  its  neces- 
sary connection  with  its  ultimate  principles;  whereas  the  Indirect 
demonstrates  only  the.  repugnance  of  some  proposition  with  certain 

1  See  Kant's  Vorlesungen  iJfter  Pkysische  Geographie,  1802;   Werke,  vi.  p.  449 — Ed. 


LOGIC.  Lect.  XXVI. 

truths,  without,  however,  positively  evincitig  the  truth  of  its  oppo- 
site, and  thereby  obtaining  for  it  a  full  and  satisfactory  recognition. 
It  is,  therefore,  usually  enaployed  only  to  constrain  a  troublesome 
opponent  to  silence,  by  a  display  of  the  absurdities  which  are 
implied  in,  and  which  would  flow  out  of,  his  assertions.  Never- 
theless, the  indirect  probation  establishes  the  proposition  to  be 
proved  not  less  certainly  than  the  direct;  nay,  it  still  more  pre- 
cisely excludes  the  supposition  of  the  opposite  alternative,  and, 
consequently,  affords  an  intenser  consciousness  of  necessity.  We 
ought,  however,  to  be  on  our  guard  against  the  paralogisms  to 
which  it  is  peculiarly  exposed,  by  taking  care  —  1°,  That  the  oppo- 
sites  are  contradictory  and  not  contrary;  and  2°,  That  an  absurdity 
really  is,  and  not  merely  appears  to  be.  The  differences  of  Apa- 
gogical  Probations  correspond   to   the   different 

Diflerences  of  indi-       kinds  of  propositions  whlch  may  be  indirectly 
i*robation8      ^  ^  demonstrated ;    and  these  are,  in   their  widest 

generality,  either  Categorical,  or  Hypothetical, 
or  Disjunctive.  Is  the  thesis  a  categorical  proposition  ?  Its  con- 
tradiclory  opposite  is  supposed,  and  from  this  counter  proposition 
conclusions  are  deduced,  until  we  obtain  one  of  so  absurd  a  charac- 
ter, that  we  are  able  to  argue  back  to  the  falsehood  of  the  original 
proposition  itself.  Again,  is  the  thesis  an  hypothetical  judgment? 
The  contradictory  opposite  of  the  consequent  is  assumed,  and  the 
same  process  to  the  same  end  is  performed  as  in  the  case  of  a  cate- 
gorical proposition.  Finally,  is  the  thesis  a  disjunctive  proposi- 
tion ?  In  that  case,  if  its  membra  disjuncta  are  contradictorily 
op})osed,  we  cannot,  either  directly  or  indirectly,  prove  it  false  as  a 
whole  ;  all  that  we  can  do  being  to  show  that  one  of  these  disjunct 
members  cannot  be  affirmed  of  the  subject,  from  which  it  necessa- 
rily follows  that  the  other  must." ' 

Under  the  Internal  Form,  Probations  are,  in  the  second  place,  in 
respect  of  their  Essential  or  Internal  Order  of 

(b)   Deductive   an        procedure,  either  Deductive  or  Inductive,  accord- 

Inductive.  t  '  -%  ' 

ing  as  the  thesis  is  proved  by  a  process  of  reason- 
ing descending  from  generals  to  particulars  and  individuals,  or  by  a 
process  of  reasoning  ascending  from  individuals  and  particular  to 
generals.  On  this  subject  it  is  not  necessary  to  say  anything,  as  the 
rules  which  govern  the  formal  inference  in  these  processes  have 
been  already  stated  in  the  Doctrine  of  Syllogisms ;  and  the  consid- 
eration of  Induction,  as  modified  by  the  general  conditions  of  the 
matter  to  which  it  is  applied,  can  only  be  treated  of  when,  in  the 
sequel,  we  come  to  Modified  or  Concrete  Methodology. 

1  Esser,  Logik,  f  142.  —  Ed 


Lect.  XXVI.  logic:  369 

"  Under  the  Internal  Form,  Probations  are,  however,  in  the  third 
place,  in  respect  of  their  External  or  Accidental 
aIeI  tfj"*^^"*'  ""'^  Order  of  procedure,  Synthetic  or  Progressive, 
and  Analytic  or  Regressive.  A  probation  is 
called  synthetic  or  progressive,  when  the  conclusion  is  evolved  out 
of  the  principles,  —  analytic  or  regressive,  when  the  principles  are 
evolved  out  of  the  conclusion.  In  the  former  case,  the  probation 
goes  from  the  subject  to  the  predicate;  in  the  latter  case,  from  the 
predicate  to  the  subject.  "Where  the  probation  is  complex, —  if 
synthetic,  the  conclusion  of  the  preceding  syllogism  is  the  subsump- 
tion  of  that  following;  if  analytic,  the  conclusion  of  the  preceding 
syllogism  is  the  sumption  of  that  following.  In  respect  of  certainty, 
both  procedures  are  equal,  and  each  has  its  peculiar  advantages ;  in 
consequence  of  which  the  combination  of  these  two  modes  of  proof 
is  highly  expedient.  But  the  Analytic  Procedure  is  often  compe- 
tent where  the  Synthetic  is  not;  whereas  the  Synthetic  is  never 
possible  where  the  Analytic  is  not,  and  tliis  is  never  possible  whei-e 
we  have  not  a  requisite  stock  of  propositions  already  verified. 
When  the  Probation  is  partly  analytic,  partly  synthetic,  it  is  called 
Mixed:" 

If  LXXXVIII.    The  Formal  Legitimacy  of  a  Probation  is- 
determined  by  the  following  rules, 
po^rmai    If^ullfy  1%  Nothing  is  to  be  begged,  borrowed,  or 

of  a  Probation,  -  its       stolcn  ;  that  is,  nothing  is  to  be  presupjDosed 
as  proved,  which  itself  requires  a  demon- 
stration.    The  violation    of  this  rule   afibrds   the  vice   called 
the  Petitio  principii,  or  Fallacia  qucesiti  medii  (to  iv  apx^- 
aiTCio-^at).^ 

2°,  No  proposition  is  to  be  employed  as  a  principle  of  proof, 
the  truth  of  which  is  only  to  be  evinced  as  a  consequence  of 
the  proposition  which  it  is  employed  to  prove.     The  violation . 
of  this  rule  is  the  vice  called  varepov  -Trporepov. 

3",  No  circular  probation  is  to  be  made;  that  is,  the  propo- 
sition which  we  propose  to  prove  must  not  be  used  as  a  princi- 
ple for  its  own  probation.     The  violation  of  this  rule  is  called 
the    Orbis   vel  circulus  in  demonstrando,  —  diallelus,  —  6  St?/ 
aXKriXwv  rpoTros.^ 

1  Ksser,  Lo^A,  5 142.  —  Ed  qnod  initio  fuit  propositum  et  in  disquisi^ 

2  [On  error  of  this  term,  see  Pacius,  Cow-      tionem  vocatum."    Ibid,  ii,  24.  —  Ed.] 
menlariux  in  Org  ]  [In  Anal.  Prior  iL  16.   "  Non 

est  petitio  t^s  o-PX'l^t  id  est,  principii,  vel  3  See  Sextus  Empiricus,  Fyrrh.  Hyp.,  i.  169, 

iv  Tf  apxfj,  id  est,  in  principio;  sed  tov  iv     ii.  68.    Laertius,  L.  ix.  H  88,  89.    [Cf.  Faocio- 
^PXV  TrpoKeiixfvov,  id  est,  ejus   probleraatis,      lati,  Acroasi.^,  v.  pi.  69  et  seq.] 

47 


870  LOGIC.  Lect.  XXVI. 

4**,  No  leap,  no  hiatus,  must  be  made;  that  is,  the  syllogisms 
of  which  the  probation  is  made  up  must  stand  in  immediate  or 
continuous  connection.  From  the  transgression  of  this  rule 
results  the  vice  called  the  Saltus  vel  Hiatus  in  demonstrando. 

5°,  The  scope  of  the  probation  is  not  to  be  changed ;  that  is, 
nothing  is  to  be  proved  other  than  what  it  was  proposed  to 
prove.  The  violation  of  this  rule  gives  the  JSeterozetesis,  I(/tio- 
ratio  vel  Mutatio  elenchi,  and  the  Transitus  in  aliud  genus  vel 
a  genere  ad  genits,  —  /xcTaySao-i?  dt  oAAo  ycvos.^ 

In  this  paragraph,  I  have  given,  as  different  rules,  those  canons 
which  are  opposed  to  vices  not  absolutely  iden- 
,Qj^.^  tical,  and  which  have  obtained  different  denom- 

inations. But  you  must  observe,  that  the  first 
three  rules  are  all  manifestly  only  various  modifications  —  only 
special  cases,  —  of  one  general  law.  To  this  law,  likewise,  the 
fourth  rule  may  with  perfect  propriety  be  reduced,  for  the  saltus  or 
hiatus  in  probanda  is,  in  fact,  no  less  the  assumption  of  a  proposi- 
tion as  a  principle  of  probation  which  itself  requires  proof,  than 
either  the  petitio  principii,  the  hysteron  proteron,  or  the  circulus  in 
probanda.  These  five  laws,  therefore,  and  the  correspondent  vices, 
may  all  be  reduced  to  two;  ono  of  which  regards  the  means,  —  the 
principles  of  proof;  the  other  the  end,  —  the  proposition  to  be 
proved.  The  former  of  these  laws  prescribes,  —  That  no  proposition 
be  employed  as  a  principle  of  probation  which  stands  itself  in  want 
of  proof;  the  lattei*,  —  That  nothing  else  be  proved  than  the  propo- 
sition for  whose  proof  the  probation  was  instituted.  You  may, 
therefore,  add  to  the  last  paragraph  the  following  supplement : 

%  LXXXIX.  These  rules  of  the  logicians  may,  however,  all 

be  reduced  to  two. 
Par.       LXXXIX.  jo^  That  no  proposition  be  employed  as 

Sules     of    Probation  -r-k'-i  f>  tt      i        •  i-i  i> 

reduced  to  two.  ^  Principle  of  Probation    which  stands  it- 

self in  need  of  proof 
2**,  That  nothing  else  be  proved  than  the  Proposition  for 
whose  proof  the  Probation  was  instituted. 

Of  these  two,  the  former  comprehends  the  first 
four  rules  of  the  logicians,  —  the  latter  the  fifth. 
I  shall  now,  therefore,  proceed  to  illustrate  the  five  rules  in  detail. 

I  [See  Reinhold,  Die  Logik  oder  die  altga-      1827]    [Cf.  Krug,  Logik,  i  133.    Esser,  Logik 
mtiae    Denk/ormenlthre,  i  160,  p.   407,  Jena.      {  144.  —  Ed.] 


Lect.  XXVI.  LOGIC.  371 

The  First  Rule  —  Nothing  is  to  be  begged,  borrowed,  or  stolen  ; 
that  is,  notliinir  is  to  be  presupposed  as  proved, 

First  Rule.  .        '  »      .  \  ^  ^  .  '     .        . 

which  itself  requires  a  demonstration,  —  is,  in 
/act,  an  enunciation  of  tha  first  general  rule  I  gave  you,  and  to  this, 
therefore,  as  we  shall  see,  the  second,  third,  and  fourth  are  to  be 
reduced  as  special  applications.     But,  in  considering  this  law  in  its 

universality,  it  is  not  to  be  understood  as  if 
Limitation     under       (3^.^,.^  probation  Were  at  once  to  be  rejected  as 

which  this  Rule  is  to  *    '  .  ,  .    ,  ,  .         .  t         i 

be  understood.  woithlcss,  in  which  anything  IS  presupposed  ana 

not  proved.  Were  this  its  sense,  it  would  be 
necessary  in  every  probation  to  ascend  to  the  highest  principles 
of  human  knowledge,  and  these  themselves,  as  immediate  and, 
consequently,  incapable  of  proof,  might  be  rejected  as  unproved 
assumptions.  Were  this  the  meaning  of  the  law,  there  could  be  no 
probation  whatever.  But  it  is  not  to  be  understood  in  this  extreme 
rigor.  That  probation  alone  is  a  violation  of  this  law,  and,  conse- 
quently, alone  is  vicious,  in  which  a  pi'oposition  is-  assumed  as  a 
principle  of  proof,  which  may  be  doubted  on  the  ground  on  which 
the  thesis  itself  is  doubted,  and  where,  therefore,  we  prove  the  un- 
certain by  the  equally  uncertain.  The  probation  must,  therefore, 
depart  from  such  principles  as  are  either  immediately  given  as  ulti- 
mate, or  mediately  admit  of  a  proof  from  other  sources  than  the 
proposition  itself  in  question.  When,  for  example,  it  was  argued 
that  the  Newtonian  theory  is  false,  which  holds  colors  to  be  the 
result  of  a  diversity  of  parts  in  light,  on  the  ground,  admitted  by 
the  ancients,  that  the  celestial  bodies,  and,  consequently,  their  ema- 
nations, consist  of  homogeneous  elements;  —  this  reasoning  was 
inept,  for  the  principle  of  proof  was  not  admitted  by  modern  phi- 
losophers. Thus,  when  Aristotle  defends  the  institution  of  slavery 
as  a  natural  law,  on  the  ground  that  the  barbai-ians,  as  of  inferior 
intellects,  are  the  born  bondsmen  of  the  Greeks,  and  the  Greeks,  as 
of  superior  intellect,  the  born  masters  of  the  barbarians '  —  (an 
argument  which  has,  likewise,  been  employed  in  modern  times  in 
the  British  Parliament,  with  the  substitution  of  negroes  for  barba- 
rians, and  whites  for  Greeks),  —  this  argument  is  invalid,  as  assuming 
what  is  not  admitted  by  the  opponents  of  slavery.  It  would  be  a 
petitio  principii  to  prove  to  the  Mohammedan  the  divinity  of 
Christ  from  texts  in  the  New  Testament,  "for  he  does  not  admit  the 
authority  of  the  Bible ;  but  it  would  be  a  valid  argumentum  ad 
hominem  to  prove  to  him  from  the  Koran  the  prophetic  mission  of 
Jesus,  for  the  authority  of  the  Koran  he  acknowledges. 

The  Second  Rule,  That  no  proposition  is  to  be  employed  aa  .a 

1  Folit.,  i.  2.  —  Ed. 


ST2  LOGIC.  Lect.  XXVL 

principle  of  proof,  the  truth  of  which  is  only  to  be  evinced  as  a 
consequence  of  the  proposition  which  it  is  em- 
ployed to  prove,  —  is  only  a  special  case  of  the 
preceding.  For  example,  if  we  were  to  argue  that  man  is  a  fi-ee 
agent,  on  the  ground  that  he^  is  morally  responsible  for  his  actions, 
or  that  his  actions  can  be  imputed  to  him,  or  on  the  ground  that 
vice  and  virtue  are  absolutely  different,  — in  these  cases,  the  hysteron 
proteron  is  committed ;  for  only  on  the  ground  that  the  human  will 
18  free,  can  man  be  viewed  as  a  morally  responsible  agent,  and  his 
actions  be  imputed  to  him,  or  can  the  discrimination  of  vice  and 
virtue,  as  more  than  a  merely  accidental  relation,  be  maintained. 
But  we  must  pause  before  we  reject  a  reasoning  on  the  ground  of 
hi/stero7i  2yroteron  ;  for  the  reasoning  may  still  be  valid,  though  this 
logical  fault  be  committed.  Nay,  it  is  frequently  necessary  for  us 
to  reason  by  sucli  a  regress.  In  the  very  example  given,  if  we  be 
unable  to  prove  directly  that  the  will  of  man  is  free,  but  are  able  to 
prove  that  he  is  a  moral  agent,  responsible  for  his  actions,  as  sub- 
jected to  the  voluntary  but  unconditioned  Law  of  Duty,  and  if  the 
fact  of  this  law  of  duty  and  its  unqualified  obligation  involve,  as  a 
postulate,  an  emancipation  from  necessity,  —  in  that  case,  no  com- 
petent objection  can  be  taken  to  this  process  of  reasoning.  This, 
in  fact,  is  Kant's  argument.  From  what  he  calls  the  categorical 
imperative,  that  is,  from  the  fact  of  the  unconditioned  law  of  duty 
feS  obligatory  on  man,  he  postulates,  as  conditions,  the  liberty  of  the 
human  will,  and  the  existence  of  a  God,  as  the  moral  governor  of  a 
moral  universe.' 

The  Thii'd  Law,  —  That  no  circular  probation  is  to  be  made,  that 

is,  the  proposition  which  we  propose  to  prove 
Third  Kale.  ,  -  .      .    ,     ^      . 

must  not  be  used  as  a  prmciple  tor  its  own  pro 

bation, — this,  in  like  manner,  is  only  a  particular  case  of  the  fii-st. 
"To  the  Circle  there  are  required  properly  two  probations,  which 
are  so  reciprocally  related  that  the  antecedent  in  the  one  is  prove<l 
by  its  own  consequent  in  the  other.  The  proposition  A  is  true  be- 
cause the  proposition  B  is  true;  and  the  proposition  B  is  true 
because  the  proposition  A  is  true.  A  circle  so  palpable  as  this 
would  indeed  be  committed  by  no  one.  The  vice  is  usually  con- 
cealed by  the  interpolation  of  intermediate  propositions,  or  by  a 
change  in  the  expression."^  Thus  Plato,  in  his  PAopf^o,^  demon- 
strates the  immortality  of  the  soul  from  its  simplicity  ;  and,  in  the 
Hepiiblic*  he  demonstrates  its  simplicity  from  its  immort.ality. 

1  Kriiik  det  reintn  YttnuAfl,  Methodenlebre,         2  Krug,  Logik,  }  183.     Anm.  8.  —El*. 
Hauptst.,  ii.  Abschn.,  2.    Kritik  iler  praktischr.n         3  p  78.  —  Ed. 
ftntun/t,  p.  274,  ed.  Rosenkranz.  —  Ed.  *  B.  x.  p.  611.  —  Ed. 


I 


hacr.  XX VL  LOCxic.  378 

In   relation  to  the   Ilysteron    Proteron  and  the   Circfe,  I  must 

observe  that  these  present  some  peculiar  diffi- 

Kegressive  and  Pro-       culties   for  the  Systematic  arrangement  of  our 

gressive  Proofs  not  to       knowledge.     Through  the  Circle  (the  result  of 

be    confounded    with  ,  .    ,      •  ,  ,  c       c  ^-       \ 

the  tautological  Cir.       ^hich    IS   Only   the   proof  of  au    assertion),— 
Ola  through  the  circle  by  itself,  nothing  whatever  is 

gained  for  the  logical  development  of  our  knowl- 
edge. But  we  njust  take  care  not  to  confound  the  connection  of 
Regressive  and  Progressive  Proofs  with  the  tautological  Circle. 
When,  in  the  treatment  of  a  science  out  of  the  observed  facts,  we 
wish  to  generalize  universal  laws,  we  lead,  in  the  first  place,  an  in- 
ductive probation,  that  {oti)  certain  laws  there  are.  Having  assured 
ourselves  of  the  existence  of  these  laws  by  this  regressive  process, 
we  then  place  them  in  theory  at  the  head  of  a  progressive  or  syn- 
thetic probation,  in  which  the  facts  again  recur,  reversed  and  illus- 
trated from  the  laws,  which,  in  the  antecedent  process,  they  had 
been  employed  to  establish  ;  that  is,  it  is  now  shown  why  (Sion) 
these  facts  exist. 

The  Fourth  Rule,  —  No  leap,  no  gap,  must  be  made,  that  is,  the 
syllogisms  of  which  the  probation  is  made  up 

Fourth  Rule.  ,».      .  ,.  . 

must  stand  m  mimediate  or  contmuous  connec- 
tion,—  may  be,  likewise,  reduced  to  the  first.  For  here  the  only 
vice  is  that,  by  an  ellipsis  of  an  intermediate  link  in  the  syllogistic 
chain,  we  use  a  proposition  which  is  actually  without  its  proof,  and 
it  is  only  because  this  j^roposition  is  as  yet  unproved,  that  its  employ- 
ment is  illegitimate.  The  Saltus  is,  therefore,  only  a  special  case 
of  the  Petitio. 

The  Saltus  is  committed  when   the  middle  term  of  one  of  the 

syllogisms  in  a  probation  is  not  stated.     If  the 

The  Saltus  in  demon-  •  i  j  i       a.  i_       j.  t     j.    j.  •  j.    a. 

middle  term  be  too  manifest  to  require  state- 

timntlo.  _  *■ 

ment,  then  is  the  saltus  not  to  be  blamed,  for  it 
is  committed  only  in  the  expression  and  not  in  the  thought.  If  the 
middle  term  be  not  easy  of  discovery,  then  the  saltus  is  a  fault;  but 
if  there  be  no  middle  term  to  be  found,  then  the  saltus  is  a  vice 
whieh  invalidates  the  whole  remainder  of  the  probation.  The 
proper  saltus^ — the  real  violation  of  this  law,  is,  therefore,  when 
we  make  a  transition  from  one  proposition  to  another,  the  two  not 
being  connected  together  as  reason  and  consequent.^  The  (vulgar) 
Enthymeme  and  the  Sorites  do  not,  therefore,  it  ia  evident,  involve 
violations  of  this  law. 

The    Fifth   Rule,  —  The  scope  of  the   probation   is  not   to   bo 
changed,  that  is,  ftothing  is  to  be  proved  other  than  what  was  pro- 

1  Cf.  Krug,  Logik,  S  133.    Anm.  4.  —  Ed. 


3T4  LOGIC.  Lect.  XXVI. 

posed   to  be  jjroved,  coi*responds  to  the  second  of  the  two  niles 
which  I  gave,  and  of  which  it  is  only  a  less 
Fifth  Bnie.  explicit  Statement.    It  evidently  admits  of  three 

A  nuts  oft  ree  e-  jjjjj^g  or  degj-ces.  In  the  first  case,  the  proposiT_ 
tion  to  be  proved  is  changed  by  the  change  of 
its  subject  or  predicate  into  different  notions.  Again,  the  propo- 
sition may  substantially  remain  the  same,  but  may  be  changed  into 
oue  either  of  a  wider  or  of  a  narrower  extension,  —  the  second  and 
third  cases. 

The  first  of  these  cases  is  the  Mutatio  Elenchi,  or  Transitus  ad 

alhid  genus,  properly  so  called.     "  When  a  pro- 

irs     egree,—    «-       Nation  docs  uot  demonstrate  what  it  ought  to 

tatio  Elenchi.  ^  ,  ° 

demonstrate,  it  may,  if  considered  absolutely  or 
in  itself,  be  valid ;  but  if  considered  relatively  to  the  proposition 
which  it  behooves  us  to  prove,  it  is  of  no  value.  We  commute  by 
this  procedure  the  whole  scope  or  purport  of  the  probation ;  we 
desert  the  proper  object  of  inquiry,  —  the  point  in  question.  If  a 
person  would  prove  the  existence  of  ghosts,  and  to  this  end  prove 
by  witness  the  fact  of  unusual  noises  and  appearances  during  the 
night,  he  would  prove  something  very  different  from  what  he  pro- 
posed to  establish  ;  for  this  would  be  admitted  Mithout  difficulty  by 
those  who  still  denied  the  apparition  of  ghosts;  it,  therefore,  be- 
hooved him  to  show  that  the  unusual  phenomena  were  those  of  a 
spirit  good  or  bad."' 

The  two  other  cases,  —  when  the  proposition  actually  proved  is 

either  of  a  smaller  or  of  a  greater  extension 

Second  Degree,— in       than  the  proposition  which  ought  to  have  been 

which    too     little    is  .  .,        ...         ^, 

.  proved,  —  are  not.  necessarily,  like   the   prece- 

ding, altogether  irrelevant.  They  are,  however, 
compared  together,  of  various  degrees  of  relevancy.  In  the  former 
case,  where  too  little  is  proved,  —  here  the  end  proposed  is,  to  a 
certain  extent  at  least,  changed,  and  the  probation  results  in  some- 
thing different  from  what  it  was  intended  to  accomplish.  For 
example,  if  we  propose  to  prove  that  Sempronius  is  a  virtuous  char- 
acter, and  only  prove  the  legality  of  his  actions,  we  here  prove 
something  less  than,  something  different  from,  what  we  professed  to 
do ;  for  we  proposed  to  prove  the  internal  morality,  and  not  merely 
the  external  lawfulness,  of  his  conduct.  Such  a  proof  is  not  abso- 
lutely invalid;  it  is  not  even  relatively  null,  for  the  external  legality 
is  always  a  concomitant  of  internal  morality.  But  the  existence  of 
the  latter  is  not  evinced  by  that  of  the  former,  for  Sempronius 

I  Krug,  Loglk,  (  133.    Anm.  2.  —  Ei>. 


Lect  XXVI.  LOGIC.  375 

may  conform  his  actions  to  the  law  from  expediency  and  not  from 
duty.* 

In  the  other  case,  in  which  there  is  proved  too  much,  the  proba- 
tion is  lawful,  and  only  not  adequate  and  pre- 

rhird  Degree,— in       ^jgg^     Yov  example,  if  We  propose  to  prove  that 

which    too   much    is^,  ,.,  .i-iii-i  i 

^^^gj  the  soul   does  not  perish  with   the  body,  and 

actually  prove  that  its  dissolution  is  absolutely 
impossible,  —  here  the  proof  is  only  superabundant.  The  logical 
rule,  —  Qui  nimium  prohat^  nihil  prohat,  is,  therefore,  in  its  univer- 
sal, or  unqualified  expression,  incorrect.  The  proving  too  much  is, 
however,  often  the  sign  of  a  saltus  having  been  committed.  For 
example,  —  when  a  religious  enthusiast  argues  from  the  strength  of 
his  pei-suasion,  that  he  is,  therefore,  actuated  by  the  Holy  Spirit, 
and  his  views  of  religion  consequently  true,  —  there  is  here  too 
much  proved,  for  there  is  implied  the  antecedent,  omitted  by  a 
saltus,  that  whoever  is  strongly  persuaded  of  his  inspiration  is 
really  inspired,  —  a  proposition  too  manifestly  absurd  to  bear  an 
explicit  enouncement.  In  this  case,  the  apparent  too  much  is  in 
reality  a  too  much  which,  when  closely  examined,  resolves  itself 
into  a  nothing.^ 

We  have  thus  terminated  the  consideration  of  Pure  or  Abstract 
Logic,  in  both  its  Parts,  and  now  enter  on  the  Doctrine  of  Modified 
or  Concrete  Logic. 

1  Cf.  Krug,  Logik,  f  133.    Anm.  5.  —  Ed. 

S  [Cf.  Sigwart,  Handbuch  zu  VorUsungtn  iiber  die  Logik,  {  407,  p.  252.] 


LECTURE    XXVII. 

MODIFIED  LOGIC. 

PAPT    I. -MODIFIED    STOICHEIOLOGY. 

SECTION    I.— DOCTRINE    OF    TRUTH    AND    ERROR. 
TRUTH.  — ITS   CHARACTER  AND   KINDS. 

Having  now  terminated  the  Doctrine  of  Pure  or  Abstract  Logic, 
we   proceed   to  that  of  Modified   or   Concrete 

Jiodified  Logic,  -       L     .^^     j^  entering  on  this  subject,  I  have  to 
its  object. 

recall  to  your  memory  what  has  formerly  been 

stated  in  regard  to  the  object  which  Modified  Logic  proposes  for 
consideration.  Pure  Logic  takes  into  account  only  the  necessary 
conditions  of  thought,  as  founded  on  the  nature  of  the  thinking 
process  itself.  Modified  Logic,  on  the  contrary,  considers  the  con- 
ditions to  which  thought  is  subject,  arising  from  the  empirical  cir- 
cumstances, external  and  internal,  under  which  exclusively  it  is  the 
will  of  our  Creator  that  man  should  manifest  his  faculty  of  think- 
ing. Pure  Logic  is  thus  exclusively  conversant  with  the  form ; 
Modified  Logic  is,  likewise,  occupied  with  the  matter,  of  thought. 
And  as  their  objects  are  different,  so,  likewise,  must  be  their  ends. 
The  end  of  Pure  Logic  is  formal  truth,  —  the  harmony  of  thought 
with  thought;  the  end  of  Modified  Logic  is  the  harmony  of  thought 
with  existence.  Of  these  ends,  that  which  Pure  Logic  proposes  is 
less  ambitious,  but  it  is  fully  and  certainly  accomplished ;  the  end 
which  Modified  Logic  proposes  is  higher,  but  it  is  far  less  perfectly 
attained.     The  problems  which  Modified  Logic  has  to  solve  may  be 

reduced  to  three:  1**,  What  is  Truth  and  its  con- 
*  d  f^th  *"*  ~  "*        tradictory  opposite,  —  Error?    2°,  Whatare  the 

Causes  of  Error,  and  the  Impediments  to  Truth, 
by  which  man  is  beset  in  the  employment  of  his  faculties,  and 
what  are  the  Means  of  their  Removal?  And,  3°,  What  are  the 
f^ibsidiaries  by  which  Human  Thought  may  be  strengthened  and 
guided  in  the  exercise  of  its  functions? 


Lect.  XXVII.  LOGIC.  377 

From  this  statement  it  is  evident  that  Concrete  Logic  might,  like 

Pure  Logic,  have  been  divided  into  a  Stoicheiol- 

And  distributed  be-       ogy  and  a  Methodologv,  —  the  former  conipris- 

tvvoeu    its   Stolcheiol-         ■         ^j^^   ^^.^^   ^^^.^   j^^^^^^g^  _  ^^^   j.^^^^,,.  ^^j^^   ^jjjj.,| 
o;:y  and  its  Methodol-  "  -.^     t  r.     i     r.      •    i     •    i  ^        .i 

j,^y  }*  or  it   to  Modmed   Stoicheiology  we  refer  the 

consideration  of  the  nature  of  concrete  truth 
:;nd  error,  and  of  the  conditions  of  a  merely  not  erroneous  employ- 
ment of  thought,  —  this  will  be  exhausted  in  the  First  and  Second 
Chapters ;  whereas,  if  we  refer  to  Methodology  a  consideration  of 
the  means  of  employing  thought  not  merely  without  error,  but  with 
a  certain  positi\'c  perfection,  —  this  is  what  the  Third  Chapter  pro- 
fosses  to  expound. 

I  commence  the  P^'irst  Chapter,  which  proposes  to  answer  the 
question, — What  is  Truth?  with  its  correlatives,  ^- by  the  dict.t- 
tion  of  the  following  paragraph  : 

1[  XC.    The  end  which  all  our  scientific  efforts  are  exerted 

to     accomplish,   is    Truth    and    Certainty. 

Par.  XC.  Truth  and       Tiuth  is  the  Correspondence  or  agreement 

Certainty,  —  what.  _  '      _  p  _ 

of  a  cognition  with  its  object ;  its  Crite- 
rion is  the  necessity  determined  by  the  laws  which  govern  our 
faculties  of  knowledge  ;  and  Certainty  is  the  consciousness  of 
this  necessity.^  Certainty,  or  the  conscious  necessity  of  knowl- 
edge, absolutely  excludes  the  admission  of  any  opposite  sup- 
position. Where  such  appeal's  admissible,  doubt  and  uncer- 
tainty arise.  If  we  consider  truth  by  relation  to  the  degree 
and  kind  of  Certainty,  we  have  to  distinguish  Itnowledge, 
Belief.,  and  Opinion.  Knowledge  and  Belief  differ  not  only  in 
degree,  but  in  kind.  Knowledge  is  a  certainty  founded  upon 
insight;  Belief  is  a  certainty  founded  upon  feeling.  The  one 
is  perspicuous  and  objective ;  the  other  is  obscure  and  subjec- 
tive. Each,  however,  supposes  the  other ;  and  an  assurance  is 
said  to  be  a  knowledge  or  a  belief,  according  as  the  one  element 
or  the  other  preponderates.  Opinion  is  the  admission  of  some- 
thing as  true,  where,  however,  neither  insight  nor  feeling  is  so 
intense  as  to  necessitate  a  perfect  certainty.  What  prevents 
the  admission  of  a  proposition  as  certain  is  called  Doubt,  The 
approximation  of  the  imperfect  certainty  of  opinion  to  the  poi-- 
fect  certainty  of  knowledge  or  belief  is  called  Prohability. 

If  we  consider  Truth  with  reference  to  Knowledge,  and  t<» 
the  way  in  which .  this  knowledge  arises,  we  must  distinguish 

I  Cf.  Twcsten.  Die  I.n;;lkJnsbesondereili';  Analytik,  {  306.  —  El>. 
4« 


B78  LOGIC.  Lect.  XXVIl 

Empirical  or  a  2^osterioriy  from  J°ure  or  a  priori  7Vuth.  Thfi 
former  has  left-rence  to  cognitions  which  have  their  source  in 
the  presentations  of  Perception,  External  and  Internal,  and 
which  obtain  their  form  by  the  ehiboration  of  the  Underetand- 
ing  or  Faculty  of  Relations  (Siavoia).  The  latter  is  contained 
in  the  necessary  and  universal  cognitions  afforded  by  the  Reg- 
ulative Faculty  —  Intellect  Proper  —  or  Common  Sense  {voW) 

This  paragraph,  after  stating  that  Truth  and  Certainty  constitute 
the  end  of  all  our  endeavors  after  knowledije. 

Explication.  /•  i     •        ,  •  ^  ,  t 

tor  only  m  the  attainment  of  truth  and  certainty 
can  we  possibly  attain  to  knowledge  or  science; — I  say,  after  the 
statement  of  this  manifest  proposition, —  it  proceeds  to  define  what 
is  meant  by  the  two  terms  Truth  and  Certainty;  and,  to  commence 
with  the  former,  —  Truth  is  defined,  the  corresi)ondence  or  agree- 
ment of  a  cognition  or  cognitive  act  of  thought  with  its  object. 
The  question  —  What  is  Truth  ?  is  an  old  and  celebrated  prob- 
lem.    It  was  proposed  by  the  Roman  Governor 

Truth,  — what.  .      ^^.,  ~      . 

—  by  Pontius  Pilate  —  to  our  Saviour;  and  it 
is  a  question  which  still  recurs,  and  is  still  keenly  agitated  in  the 
most  recent  schools  of  Philosophy.     In  one  respect,  all  are  nearly 

agreed  in  regard  to  the  definition  of  the  term,  for 
tem^^°'"°°   °^  **"*       all  ^^^^^  that  by  truth  is  understood  a  liarmony, 

—  an  agreement,  a  correspondence  between  our 
thought  and  that  which  we  think  about.  This  definition  of  truth 
we  owe  to  the  schoolmen.  "Veritas  intellectus,"  says  Aquinas, 
"est  adaequatio  intellectus  et  rei,  secundum  quod  intellectus  dicit 
esse,  quod  est,  vel  non  esse,  quod  non  est."  *  From  the  schoolmen, 
this  definition  has  been  handed  down  to  modern  philosophers,  by 
whom  it  is  currently  employed,  without,  in  general,  a  suspicion  of 
its  origin.  It  is  not,  therefore,  in  regard  to  the  meaning  of  the 
tei-m  truth,  that  there  is  any  diflference  of  opinion  among  philoso- 
phers.    The  questions  which  have  provoked  dis- 

Questions  in    e  ate       cussion,  and  which  remain,  as  heretofore,  without 

rej^arding  Truth. 

a  definitive  solution,  are  not  whether  truth  be 
the  harmony  of  thought  and  reality,  but  whether  this  harmony,  or 
truth, be  attainable,  and  wliether  we  possess  any  criterion  by  which 
we  can  be  assured  of  its  attainment.  Considering,  however,  at 
present  only  the  meaning  of  the  terra,  philosophers  have  divided 
Truth   (or  the  harmony  of  thought  and  its  object)  into  different 

1  [Contra  GtntiUs,  lib.  i.  c.  59.    See  Biunde,      general,  see  Ruiz,  Commmt.rfe  Seientia^itt  Uttt 
'UO>r  Wahr/ifit  in  Eikenntn,  p.  11.     Ou  Trutli  in      t/«-  Vrritatf,  etc     Disp.  Ixxxv.,  p.  871  et  stq] 


Lect.  XXVII.  LOGIC.  379 

species,  to  which  they  have  given  diverse  names ;  but  they  are  at 
one  neither  in  the  division  nor  in  the  nomenclature. 

It  is  plain  that  for  man  there  can  only  be  conceived  two  kinds  of 
Truth,   because   there   are  for   human   thought 
For  man  only  two       ^j^iy  ^^^^  spccics  of   object.      For   that   about 
mai  and  Real '  which  WO  think  must  either  be  a  thought,  or 

something  which  a  thought  contains.  On  this 
is  founded  the  distinction  of  Formal  Knowledge  and  Real  Knowl- 
edge, —  of  Formal  Truth  and  Real  Truth.  Of  these  in  their 
order. 

I.   In  regard  to  the  former,  a  thought  abstracted  f^jom  what  it 
contains,  that  is,  from  its  mjftter  or  what  it  is 

I.  Formal  Truth.  ,  .       ,  />  o    ■,  ■, 

conversant  about,  is  the  mere  lorm  oi  thought. 
The  knowledge  of  the  form  of  thought  is  a  formal  knowledge,  and 
the  harmony  of  thought  with  the  form  of  thought  is,  consequently, 

Foi-mal  Truth.  *  Now  Formal  Knowledge  is  of 

Formal   Truth   of      ^^.^  kinds ;  for  it  regards  either  the  conditions 

lldMa'thematkar"       ^^  ^hc  Elaborative  Faculty,  — the  Faculty  of 

Thought  Proper,  —  or  the  conditions  of  our 
Presentations  or  Representations  of  external  things,  that  is,  the 
intuitions  of  Space  and  Time.  The  former  of  these  sciences  is 
Pure  Logic,  —  the  science  which  considers  the  laws  to  which  the 
Underetanding  is  astricted  in  its  elaborative  operations,  without 
inquiring  what  is  the  object,  —  what  is  the  matter,  to  which  these 
operations  are  applied.  The  latter  of  these  sciences  is  Mathe- 
matics, or  the  science  of  Quantity,  which  considers  the  relations 
of  Time  and  Space,  without  inquiring  whether  there  be  any  actual 
reality  in  space  or  time.  Formal  truth  will,  therefore,  be  of  two 
kinds,  —  Logical  and  Mathematical.     Logical  truth  is  the  harmony 

or  agreement  of  our  thoughts  with  themselves 

Logical  Truth.  ,  ,  •  ,  i        , 

as  thoughts,  m  other  words,  the  correspondence 
of  thought  with  the  universal  laws  of  thinking.  These  laws  are 
the  object  of  Pure  or  General  Logic,  and  in  these  it  places  the  cri- 
terion of  truth.  This  criterion  is,  however,  only  the  negative  con- 
dition —  only  the  conditio  sine  qua  non,  of  truth.  Logical  truth  is 
supposed  in  supposing  the  possibility  of  thought ;  for  all  thought 
presents  a  combination,  the  elements  of  which  are  repugnant  or 
congruent,  but  which  cannot  be  repugnant  and  congruent  at  the 
same  time.  Logic  might  be  true,  although  we  possessed  no  truth 
beyond  its  fundamental  laws ;  although  we  knew  nothing  of  any 
real  existence  beyond  the  formal  hypothesis  of  its  possibility. 

But  were  the  Laws  of  Logic  purely  subjective,  that  is,  were  they 
true  only  for  our  thought  alone,  and  without  any  objective  validity, 


810  LOGIC.  Lect.  XXVII. 

oil  human  sciences  (and  Mathematics  among  the  rest)  would  bo 
]iurely  subjective  likewise;  for  we  are  cognizant  of  objects  only 
under  the  forms  and  rules  of  which  Logic  is  the  scieutifio  develop- 
ment. If  the  true  character  of  objective  validity  be  universality, 
the  laws  of  Logic  are  really  of  that  character,  for  these  laws  con- 
strain us,  by  their  own  authority,  to  regard  them  as  the  universal 
laws  not  only  of  human  thought,  but  of  universal  reason. 

The  case  is  the  same  with  the  other  formal  science,  the  science  of 
„   ^       .    ,^     ^        Quantity,  or  Mathematics,     Without   inquiring 

Mathematical  Truth  .  .  . 

into  the  reality  of  existences,  and  without  bor- 
rowing fron^  or  attributing  to  them  anything,  Arithmetic,  the  science 
of  Discrete  QuantRy,  creates  its  numbers,  and  Geometry,  the  science 
of  Continuous  Quantity,  creates  its  figures  ;  and  both  operate  upon 
these  their  objects  in  absolute  independence  of  all  external  actuality. 
The  two  mathematical  sciences  are  dependent  for  their  several 
objects  only  on  the  notion  of  tJIne  and  the  notion  of  space,  —  no- 
tions under  which  alone  matter  can  be  conceived  as  possible,  for  all 
matter  supposes  space,  and  all  matter  is  moved  in  space  and  in  time. 
But  to  the  notions  of  space  and  time  the  existence  or  non-existence 
of  matter  is  indifferent;  indifferent,  consequently,  to  Geometry  and 
Arithmetic,  so  long  at  least  as  they  remain  in  the  lofty  regions  of 
pure  speculation,  and  do  not  descend  to  the  practical  application  of 
their  principles.  If  matter  had  no  existence,  nay,  if  space  and  time 
existed  only  in  our  minds,  mathematics  would  still  be  true ;  but 
their  truth  would  be  of  a  purely  formal  and  ideal  character,  — 
would  furnish  us  with  no  knowledge  of  objective  realities.* 

So  much  for  Formal  Truth,  under  its  two  species  of  Logical  and 
Mathematical. 

The  other  genus  of  truth — (the  end  which  the  Real  Sciences 
propose)  —  is  the  harmony  between  a  thought 

II.  Ileal  Truth.  ^    -.^ .  mi        t^      i    o    •  , 

and  Its  matter.     Ihe  Keal  feciences  are  those 
Real    and    Formal       ^hich  have  a  determinate  reality  for  their  ob- 

Sciences.  .  -,       j  •   ■,  i 

ject,  and  which  are  conversant  about  existences 
other  than  the  forms  of  thought.  The  Formal  Sciences  have  a 
superior  certainty  to  the  real ;  for  they  are  simply  ideal  combina- 
tions, and  they  construct  their  objects  without  inquiring  about  their 
objective  reality.    Tlie  real  sciences  are  sciences  of  fact,  for  the 

point  from  which  they  depart  is  always  a  fact, — 
Under  the  Real  Sci.       always  a  presentation.     Some  of  these  rest  on 
enccs  arc  included  the  ,  .  /•    r<   if  •  ^v. 

Mental  and  Material       ^"^   presentations  ot   belt-consciousness,  or  the 

facts  of  mind  ;  others  on  the  presentations  of 
{Sensitive  Perception,  or  the  facts  of  nature.     The  former  are  the 

1  Cf.  Esaer.  Logik,  ♦  172.  —  Ep.    [Fries,  Logik,  i  124.^ 


Lkct.  XXVII.  LOGIC.  S8l 

Mental  Sciences,  the  latter  the  Material.  The  facts  of  mind  are 
given  partly  as  contingent,  partly  as  necessary  ;  the  latter  —  the 
necessary  facts  —  are  universal  virtually  and  in  themselves  ;  the 
former — the  contingent  facts  —  only  obtain  a  fictitious  universality 
by  a  process  of  generalization.  The  facts  of  nature,  however  neces- 
sary in  themselves,  are  given  to  us  only  as  contingent  and  isolated 
phenomena;  they  have,  therefore,  only  that  conditional,  that  empir- 
ical, generality,  which  we  bestow  on  them  by  classification. 

Real  truth  is,  therefore,  the  correspondence  of  our  thoughts  with 

the   existences   which  constitute  their   objects. 

How  can  wo  know       But  here  a  difficulty  arises ;  —  How  can  we  know 

that  there  is  a  corre-  ^Jj^t  there  is,  that  there  can  be,  such  a  corre- 
spondence      between  -,  n       ah.i^  i  r- ^-i         ^  '      ^     ' 

,,      ,.       .  .,        spondence?     All  that  we  know  of  the  obiects  is 

our  thought    and   its  ^  _  *' 

Object?  through  the  presentations  of  our  faculties ;  but 

whether  these  present  the  objects  as  they  are  in 
themselves,  we  can  never  ascertain,  for  to  do  this  it  would  be  requi- 
site to  go  out  of  ourselves, — out  of  our  faculties,  —  to  obtain  a 
knowledge  of  the  objects  by  other  faculties,  and  thus  to  compare 
Our  old  presentations  with  our  new.  But  all  this,  even  Were  the 
supposition  possible,  would  be  incompetent  to  afibrd  us  the  certainty 
required.  For  were  it  j^ossible  to  leave  our  old,  and  to  obtain  a 
new,  set  of  faculties,  by  which  to  test  the  old,  still  the  veracity  of 
these  new  faculties  would  be  equally  obnoxious  to  doubt  as  the 
veracity  of  the  old.  For  what  guarantee  could  we  obtain  for  the 
credibility  in  the  one  case,  which  we  do  not  already  possess  in  the 
other?  The  new  faculties  could  only  assert  their  own  truth;  but 
this  is  done  by  the  old ;  and  it  is  impossible  to  imagine  any  presen- 
tations of  the  non-ego  by  any  finite  intelligence,  to  which  a  doubt 
might  not  be  raised,  whether  these  presentations  were  not  merely 
subjective  modifications  of  the  conscious  ego  itself.  All  that  could 
be  said  in  answer  to  such  a  doubt  is,  that  if  such  were  true,  our 
whole  nature  is  a  lie,  —  a  supposition  which  is  not,  without  the 
strongest  evidence,  to  be  admitted ;  and  the  argument  is  as  compe- 
tent against  the  skeptic  in  our  present  condition,  as  it  would  be  were 
we  endowed  with  any  other  conceivable  form  of  Acquisitive  and 
Cognitive  Faculties.  But  I  am  here  trenching  on  what  ought  to  be 
reserved  for  an  explanation  of  the  Criterion  of  Truth. 

Suoh,  as  it  appears  to  me,  is  the  only  rational  division  of  Truth 

according  to  the  different  character  of  the  ob- 

snbdivisiou™  ''•"  '  ^      jects  to  which  thought  is  relative,  —  into  Formal 

and   itito   Real   Truth.     Formal   Truth,  as  we 

have  seen,  is  subdivided  into  Logical  and  into  Mathgmatical.     Real 

Truth  miglit  likewise  be  subdivided,  were  this  requisite,  into  vaiious 


382  LOGIC.  Lect.  xxvn. 

species.   For  example,  Metaphysical  Truth  might  denote  the  harmony 

of  thought    with  the  necessary  facts  of  mind; 

Metaphyseal.  Psychological  Truth,  the  harmony   of  thought 

^^jj^g^^'j***  '  with  the  contingent  facts  of  mind  ;  and  Physical 

Truth,  the  harmony  of  thought  with  the  phae- 

nomena  of  external  experience. 

It  now  remains  to  say  a  word  in  regard  to  the  confusion  which 

has   been  introduced  into  this  subject,  by  the 

Various  applications      ^,.^^^^^1^^^   distinctions   and   contradictions   of 

of  the  term  Trutk.  ° 

philosophere.  Some  have  absurdly  given  the 
name  of  truth  to  the  mere  reality  of  existence,  altogether  abstracted 
from  any  conception  or  judgment  relative  to  it,  in  any  intelligence 
human  or  divine.  In  this  sense  physical  truth  has  been  used  to 
denote  the  actual  existence  of  a  thing.  Some  have  given  the  name 
of  metaphysical  truth  to  the  congruence  of  the  thing  with  its  idea 
in  the  mind  of  the  Creator.  Others  again  have  bestowed  the  name 
of  metaphysical  truth  on  the  mere  logical  possibility  of  being 
thought;  while  they  have  denominated  hy  logical  truth  the  meta- 
physical or  physical  correspondence  of  thought  with  its  objects. 
Finally,  the  term  moral  or  ethical  truth  has  been  given  to  veracity, 
or  the  correspondence  of  thought  with  its  expression.  In  this  last 
case,  truth  is  not,  as  in  the  others,  employed  in  relation  to  thought 
and  its  object,  but  to  thought  and  its  enouncement.  So  much  for 
the  notion,  and  the  principal  distinctions  of  Truth. 

But,  returning  to  the  paragraph,  I  take  the  next  clause,  which  is, 

—  "The  Criterion  of  truth  is  the  necessity  de- 
er tenon    o        termincd  by  the  laws  which  govern  our  faculties 
rruth.  •'  * 

of  knowledge ;    and  the  consciousness  of  this 

necessity  is  certainty."  That  the  necessity  of  a  cognition,  that  is, 
the  impossibility  of  thinking  it  other  than  as  it  is  presented,  —  that 
this  necessity,  as  founded  on  the  laws  of  thought,  is  the  criterion  of 
truth,  is  shown  by  the  circumstance  that  where  such  necessity  is 
found,  all  doubt  in  regard  to  the  correspondence  of  the  cognitive 
thought  and  its  object  must  vanish ;  for  to  doubt  whether  what  we 
necessarily  think  in  a  certain  manner,  actually  exists  as  we  conceive 
it,  is  nothing  less  than  an  endeavor  to  think  the  necessary  as  the 
not  necessary  or  the  impossible,  which  is  contradictory. 

What  has  just  been  said  also  illustrates  the  truth  of  the  next  sen- 
tence of  the  paragraph,  —  viz.,  "  Certainty  or  the  conscious  necessity 
of  a  cognition  absolutely  excludes  the  admission  of  any  opposite 
supposition.  When  such  is  found  to  be  admissible,  doubt  and  un- 
certainty arise."  This  sentence  requiring  no  explanation,  I  proceed 
to  the  next  —  viz.,  "  If  we  consider  truth  by  relation  to  the  degree 


Lect.  XXVII.  logic.  383 

and  kind  of  Certainty,  we  have  to  distinguish  Knowledge,  Belief, 
and  Opinion.     Knowledge  and  Belief  differ  not  only  in  degree  but 
in  kind.     Knowledge  is  a  certainty  founded  on  intuition.     Belief  is 
a  certainty  founded  upon  feeling.     The  one  is  perspicuous  and  ob- 
jective, the  other  is  obscure  and  subjective.     Each,  however,  sup- 
poses the  other,  and  an  assurance  is  said  to  be  a  knowledge  or  a 
belief,  according  as  the  one  element  or  the  other  preponderates." 
In  reference  to  this  passage,  it  is  necessary  to  say  something  in 
regard  to  the  difference  of  Knowledge  and  Be- 
Knowiedge  and  Be-       j-^f.     j^  common  language  the  word  Belief  is 

lief,  —  their  difference.  ,  ,  ?         . 

often  used  to  denote  an  inferior  degree  of  cer- 
tainty.    We  may,  however,  be  equally  certain 

That   the    certainty  •'  ^     ^.  r. 

of  all  knowledge  is  ^^  what  We  bclieve  as  of  what  we  know,  and  it 
ultimately  resolvable  has,  uot  without  grouud,  been  maintained  by 
into  a  certainty  of  Be-       many  philosophers,  both  in  ancient  and  in  mod- 

lief.    maintained     by  ^.  1,^1  •  /.     1,  1  1     t         • 

j^jjjjjgj.  em  times,  that  the  certainty  of  all  knowledge  is, 

in  its  ultimate  analysis,  resolved  into  a  certainty 
of  belief  "All  things,"  says  ^lUther,  "stand  in  a  belief,  in  a  faith, 
which  we  can  neither  see  nor  comprehend.  The  man  who  would 
make  these  visible,  manifest,  and  comprehensible,  has  vexation  and 
heart-grief  for  his  reward.  May  the  Lord  increase  Belief  in  you 
and  in  others."^  But  you  may  perhaps  think  that  the  saying  of 
Luther  is  to  be  taken  theologically,  and  that,  philosophically  con- 
sidered, all  belief  ought  to  be  founded  on  knowledge,  not  all  knowl- 
edge in  belief  But  the  same  doctrine  is  held  even  by  those  phi- 
losophers who  are  the  least  disposed  to  mysticism  or  blind  faith. 
Amonsc  these  Aristotle  stands  distinsruished.   He 

AristoUe.  °       .  .  * 

defines  science,  strictly  so  called,  or  the  knowl- 
edge of  indubitable  truths,  merely  by  the  intensity  of  our  convic- 
tion or  subjective  assurance  ;^  and  on  a  primary  and  incomprehen- 
sible belief  he  hangs  the  whole  chain  of  our  comprehensible  or 
mediate  knowledge.  The  doctrine  which  has  been  called  The  Phi- 
losophy of  Common  Sense,  is  the  doctrine  which  founds  all  our 
knowledge  on  belief;  and,  though  this  has  not  been  signalized,  the 
doctrine  of  Common  Sense  is  perhaps  better  stated  by  the  Stagirite 
than  by  any  succeeding  thinker.  "What,"  he  says,  "appears  to  all 
men,  that  we  affirm  to  be,  and  he  who  rejects  this  belief  (Trtcrris)  will 
assuredly  advance  nothing  better  worthy  of  credit."  This  passage 
is  from  his  Nicomachean  Ethics?  But,  in  his  Physical  Treatises,  he 
founds  in  belief  the  knowledge  we  have  of  the  reality  of  motion, 

1  Weiahth,  Th.  iii.  Abth.,  2.    Quoted  by  Sir     effect  are  cited  by  the  Author,  RtiO's  TTorii, 
W.  Hamilton,  K^/rf's  Works,  pi  778.  —  Ed.  p.  771.  —  Ed. 

2  Various  passages  from  Aristotle  to  this         3  B.  x.  c.  2.  —  Ed. 


.384  LOGIC.  Lect.  XXVIL 

< 
and  by  this,  as  a  source  of  knowledge  paramount  to  the  Understand- 
ing, he  supersedes  the  contradictions  which  are  involved  in  our  con- 
ception of  motion,  and  which  had  so  acutely  been  evolved  by  the 
Eleatic  Zeno,  in  order  to  show  that  motion  was  impossible.^  In 
like  manner,  in  his  Logical  Treatises,  Aristotle  shows  that  the 
primr.ry  or  ultimate  principles  of  knowledge  must  be  incomprehen- 
sible ;  for  if  comprehensible,  they  must  be  comprehended  in  some 
higher  notion,  and  this  again,  if  not  itself  incomprehensible,  must 
be  again  comprehended  in  a  still  higher,  and  so  on  in  a  progress  ad 
infinititm,  which  is  absurd.''  But  what  is  given  as  an  ultimate  and 
incomprehensible  principle  of  knowledge,  is  given  as  a  fact,  the 
existence  of  which  wo  must  admit,  but  the  reasons  of  whose  exist- 
ence we  cannot  know,  —  we  cannot  understand.  But  such  an  ad- 
mission, as  it  is  not  a  knowledge,  must  be  a  belief;  and  thus  it  is 
that,  according  to  Aristotle,  all  our  knowledge  is  in  its  root  a  blind, 
a  passive  faith,  in  other  words,  a  feeling.  The  same  doctrine  was 
subsequently  held  by  many  of  the  acutest  think- 
ers  oi  ancient  tigies,  more  especially  among  the 
Platonists ;  and  of  these  Proclus  is  perhaps  the 
j)hilosoi)her  in  whose  works  the  doctrine  is  turned  to  the  best 
account.^  In  modem  times  we  may  trace  it  in  silent  operation, 
though  not  explicitly  proclaimed,  or  placed  as  the  foundation  of  a 
system.  It  is  found  spontaneously  i*ecognized  even  by  those  who 
might  be  supposed  the  least  likelv  to  acknowl- 

Hume.  *      .  .   /  ^  ,   .  -^-.  - 

edge  It  without  compulsion.  Hume,  tor  exam- 
ple, against  whose  philosophy  the  doctrine  of  Common  Sense  was 
systematically  arrayed,  himself  pointed  out  the  weapons  by  which 
his  adversnries  subsequently  assailed  his  skepticism;  for  he  himself 
was  possessed  of  too  much  philosophical  aciiteness  not  to  perceive 
that  the  root  of  knowledge  is  belief.  Thus,  in  his  Inquiry^  he  says 
■*—  "  It  seems  evident  that  men  are  carried  by  a  natural  instinct  or 
prepossession  to  repose  foith  in  their  senses:  and  that,  without  any 
reasoning,  or  even  almost  before  the  use  of  reason,  we  always  sup- 
pose an  external  universe  which  depends  not  on  our  preception,  but 
would  exist  though  we  and  every  sensible  creature  were  absent  or 
annihilated.  Even  the  animal  creation  are  governed  by  a  like 
ojjinion,  and  preserve  this  belief,  —  the  belief  of  external  objects,  in 

all  their  thoughts,  designs,  and  actions This  very  table, 

which  we  see  white,  and  whioh  we  feel  hard,  is  believed  to  exist 


1  U.  viii.  c.  3.  SeeiJeirf'4  Worts,  p.  773.— Ed.  ^  In.   Platonis   Vuologiam,  i.e.  25.     Quoted 

,   S  Mftaphys.,  iii.  (iv.)    4.  Cf.  Anal.  P»st.,  i.  3,      in  HtiW*  (Tarvb,  p.  77C.  —  Ed. 
3. —  Ed 


lect.  xxvil  logic.  385 

independent  of  our  perception,  and  to  be  something  external  to  our 
mind  which  perceives  it."  ^ 

But,  on  the  other  hand,  the  manifestation  of  this  belief  necessa- 
rily involves  knowledge  ;  for  we  cannot  believe 

The  manifestation       without   somc  cousciousness  or  knowledge   of 

of     Belief      involves         ^i       i     t    r>  -,  ,i  -^i        ^ 

^jg^  g  the  beher,  and,  consequently,  without  some  con- 

sciousness or  knowledge   of  the   object  of  the 
belief.     Now,  the  immediate  consciousness  of  an  object  is  called  an 
intxiUion,  —  an  insight.     It  is  thus  impossible  to 
separate   belief  and   knowledge,  —  feeling   and 
intuition.     They  each  suppose  the  other. 

The    consideration,   however,   of   the    relation    of   Belief   and 

Knowledge  does  not  properly  belong  to  Logic,. 

Tiie  question  as  to       except   in  SO  far  as  it  is  necessary  to  explain i 

,  „      ,  ,  the   nature   of  Truth    and  Error.      It   is   alto- 

and  Knowledge  prop- 
erly metaphysical,  gether  a   metaphysical  discussion;    and   one  of 

the    most    difficult    problems   of   which   Meta- 
physics attempts  the  solution. 

The  remainder  of  the  paragraph  contains  the  statement  of  cer- 
tain distinctions  and  the  definition  of  certain  terms,  which  it  was- 
necessary  to  signalize,  but  which  do  not  requii'e  any  commentary 
for  their  illustration.     The  only  part  that  might  have  required  an- 
explanation  is  the  distinction  of  Truth  into  Pure,  or  a  priori,  and 
into  Empirical,  or  a  posteriori.     The  explanation  of  this  division ; 
has  been  already  given  more  than  once  in  the  course  of  the  Lec- 
tures,^ but  the  following  may  now  be  added. 

Experience  presents  to  us  only  individual  objects,  and  as  these 
individual    objects   might   or   might    not    have 

ure  an      mpinc         come   within    our   sphere    of   observation,   our 

Truth.  ' 

whole  knowledge  of  and  from  these  objects 
might  or  might  not  exist;  —  it  is  merely  accidental  or  contingent. 
But  as  our  knowledge  of  individual  objects  affords  the  possibility,, 
as  supplying  the  whole  contents,  of  our  generalized  or  abstracted 
notions,  our  generalized  or  absttacted  notions  are,  consequently,  not 
more  necessary  to  thought,  than  the  particular  observations  out  of 
which  they  are  constructed.  For  example,  every  horse  I  have  seen;; 
I  might  not  have  seen ;  and  I  feel  no  more  necessity  to  think  the- 
reality  of  a  horse  than  the  reality  of  a  hippogriff;  I  can,  therefore, 
easily  annihilate  in  thought  the  existence  of  the  whole  species.  I 
can  suppose  it  not  to  be,  —  not  to  have  been.     The  case  is  the  same 

1  Inquiry  concfrning  the  Human  Undtntand-  2  See  above,  Lectures  on  Metnphijsics,  p.  403- 
>ng.  sect.  12.  PhilosophiccU  Works,  iv.  p.  177.  et  seq.  Cf.  Esser,  Logik,  H  4,  171.  —  Ed. 
—  Ed.  [Fries,  Logik,  }  124.] 

.49 


8S6  LOGIC.  Lect.  xxvii. 

with  every  other  notion  which  is  mediately  or  immediately  the 
datum  of  observation.  We  can  think  away  each  and  every  part 
of  the  knowledge  we  have  derived  fi-om  experience ;  our  whole 
empirical  knowledge  is,  therefore,  a  merely  accidental  possession 
of  the  mind. 

But  there  are  notions  in  the  mind  of  a  very  different  character, — 
notions  which  we  cannot  but  think,  if  we  think  at  all.  These, 
therefore,  are  notions  necessary  to  the  mind;  and,  as  necessary, 
they  cannot  be  the  product  of  experience.  For  example,  I  perceive 
something  to  begin  to  be.  I  feel  no  necessity  to  think  that  this 
thing  must  be  at  all,  but  thinking  it  existent,  I  cannot  but  think 
that  it  has  a  cause.  The  notion,  or  rather  the  judgment,  of  Cause 
and  Effect,  is,  therefore,  necessary  to  the  mind.  If  so,  it  cannot  be 
derived  from  experience. 


LECTURE     XXVIII. 

MODIFIED      STOIOHEIOLOQY. 

SECTION  I.  — DOCTRINE  OF  TRUTH  AND  ERROR. 

« 

SECTION   II.  —  ERROR,  —  ITS   CAUSES   AND   REMEDIES. 

A.  — GENERAL   CIRCUMSTANCES  —  SOCIETY. 

I  NOW  proceed  to  the  consideration  of  the  opposite  of  Truth,  —^ 
Erroi",  and,  on  this  subject,  give  you  the  following  paragraph  : 

%  XCI.    Error  is  opposed  to  Truth ;   and  Error  arises,  I*, 

From  the  commutation  of  what  is  Subjec* 

Par.  xcr.  Error,-       tivc  with   what   is  Objcctive   in   thought; 

2°,  From  the  Contradiction  of  a  supposed 


sources. 


knowledge  with  its  Laws ;    or,  3",  From  a 
want  of  Adequate  Activity  in  our  Cognitive  Faculties. 

Error  is  to  be  discriminated  from  Ignorance  and  from  lUu- 
sion  ;  these,  however,  along  with  Arbitrary  Assumption,  afford 
the  most  frequent  occasions  of  error.' 

This  paragraph  consists  of  two  parts,  and  these  I  shall  succes- 
sively consider.     The  first  is  :  '  Error  is  opposed 

fixpiication.  ,  ,    _  .  ,  „    -n  , 

to  truth;  and  Error  arises,  1°,  trom  the  com- 
mutation of  what  is  subjective  with  what  is  objective  in  thought; 
2°,  From  the  contradiction  of  a  supposed  knowledge  with  its  laws; 
or,  3°,  From  a  want  of  adequate  activity  in  our  cognitive  faculties.' 
"  In  the  first  place,  we  have  seen  that  Truth  is  the  agreement  of 
a  thought  with  its  obiect.     Now,  as  Error  is  the 

Error,- what.  •  ^  ,  t, 

opposite  oi  truth,  —  Error  must  necessarily  con- 
sist in  a  want  of  this  agreement.     In  the  second  place,  it  has  been 

J  Twesten,  Die  Logik,insbesondere  die  Analytik,  §§  308,  309.  —  Ed.    [Cf.  Ruiz,  Commentarius  «*»■ 
Scienlia,  etc.     Disp.  xcii.  p.  925.] 


888  LOGIC.  Lkct.  XXVUl 

shown  that  the  criterion  or  standard  of  truth  is  the  necessity 
founded  on  the  laws  of  our  cognitive  faculties;  and  from  this  it 
follows  that  the  essential  character  of  error  must  be,  either  that  it 
is  not  founded  on  these  laws,  or  that  it  is  repugnant  to  them.  But 
these  two  alternatives  may  be  viewed  as  only  one ;  for  inasmuch  as, 
in  the  former  case,  the  judgment  remains  undecided,  and  can  make 
no  pretence  to  certainty,  it  may  be  thrown  out  of  account  no  less 
than  in  the  latter,  where,  as  positively  contradictory  of  the  laws  of 
knowledge,  it  is  necessarily  false.  Of  these  statements  the  firet, 
that  is,  the  non-agreement  of  a  notion  with  its 

As  Material.  ...  .  ,  . 

object,  IS  error  viewed  on  its  material  side ;  and 
as  a  notion  is  the  common  product,  —  the  joint  result  aflTorded  by 
the  reciprocal  action  of  object  and  subject,  it  is  evident  that  what- 
ever the  notion  contains  not  correspondent  to  the  object,  must  be  a 
contribution  by  the  thinking  subject  alone,  and  we  are  thus  war^ 
ranted  in  saying  that  Material  Error  consists  in  the  commuting  of 
what  is  subjective  with  what  is  objective  in  thought ;  in  other 
words,  in  mistaking  an  ideal  illusion  for  a  real  representation.     The 

second  of  these  statements,  that  is,  the  incon- 
As  Formal.  o      ^  -,  ... 

gruence   of   the   supposed   cognition   with   the 

Jaws  of  knowledge,  is  error  viewed  on  its  formal  side.     Now  here 

the  question  at  once  presents  itself,  —  How  can  an  act  of  cognition 

contradict  its  own  laws  ?     The  answer  is  that  it  cannot ;  and  error, 

when  more  closely  scrutinized,  is  found  not  so 

Arises    from    the       much  to  consist  in  the  contradictory  activity  of 

want  of  adequate  ac-  ...         n        i^-  •      .i_    •  .      r       ^• 

r  .X.    r>      •       our  cognitive  faculties  as  in  their  want  oi  act:v- 

tivlty  of  the    Cogni-  »  ^ 

tire  Faculties.  ity.     And  this  may  be  in  consequence  of  one  or 

other  of  two  causes.  For  it  may  arise  from 
some  other  mental  power,  —  the  will,  for  example,  supei^seding, — 
taking  the  place  of,  the  defective  cognition,  or,  by  its  intenser  force, 
turning  it  aside  and  leading  it  to  a  false  result ;  or  it  may  arise  from 
borne  want  of  relative  perfection  in  the  object,  so  that  the  cognitive 
faculty  is  not  determined  by  it  to  the  requisite  degree  of  action. 

"What  is  actually  thought,  cannot  but  be  correctly  thought- 
Error  first  commences  when  thinking  is  remitted,  and  can  in  fact 
only  gain  admission  in  virtue  of  th6  truth  which  it  contains;  — 
dvery  error  is  a  perverted  truth.  Hence  Descartes*  is  justified  in 
the  establishment  of  the  principle,  —  that  we  would  never  admit 
the  false  for  the  true,  if  we  would  only  give  assent  to  what  we 
clearly  and  distinctly  apprehend.  'Nihil  nos  unquam  falsum  pro 
vero  admissuros,  si  tantum  iis  assensum  praebeamus,  quaj  clare  et 

1  Principia  Philosophia,  i.  4a     Cf.  Med.  Ir.  De  Vero  et  Fatso. 


Lect.  XXVUI.  LOGIC.  38Ji 

distincte  perciijimus.' " ^     In  this  view  the  saying  of  the  Roman' 
poet  — 

"Nam  neqae  decipitur  ratio,  nee  decipit  unqnam,"2 

-7- is  no  longer  a  paradox;   for  the  condition  of  error  is  not  the 
activity  of  intelligence,  but  its  inactivity. 

So  much  for  the  first  part  of  the  paragraph.     The  second  is  — . 
'  Error  is  to  be  discriminated  from  Ignorance  and 
Error  discriminated       f^.^^  Illusion,  which,  howcver,  along  with  Avbi- 
jjj^gj^j,  trary  Assumption,  afford  the  usual  occasions  of. 

Error.' 
.  "Ignorance  is  a  mere  negation,  —  a  mere  not-knowledge ;  whereas  . 
in  error  there  lies  a  positive  pretence  to  knowl- 

Ignorance.  .... 

edge.     Hence  a  representation,  be  it  imperfectv, 
be  it  even  without  any  correspondent  objective  reality,  is  not  in 
itself  an  error.     The  imagination  of  a  hippogriflf  is  not  in  itself  . 
false ;  the  Orlando  Fnrioso  is  not  a  tissue  of  errors.     Error  only  ; 
arises  when  we  attribute  to  the  creations  of  our  minds  some  real  • 
object,  by  an  assertory  judgment;  we  do  not  err  and  deceive  either 
ourselves  or  others,  when  we   hold  and  enounce  a  subjective  or , 
problematic   supposition    only   for   what   it   is.      Ignorance,  —  not' 
knowledge,  —  however,  leads  to  error,  when  we  either  regard  the  • 
unknown  as  non-existent,  or  when  we  falsely  fill  it  up.     The  latter 
is,  however,  as  much  the  result  of  Will,  of  arbitrary  assumption,  as 
of  ignorance  ;  and,  frequently,  it  is  the  result  of  both  together.     In 
general,  the  will  has  no  inconsiderable  share  in  the  activity  by 
which  knowledge  is  realized.     The  will  has  not  immediately  an 
influence  on  our  judgment,  but  mediately  it  has.     Attention  is  an 
act  of  volition,  and  attention  furnishes  to  the  Understanding  the 
elements  of  its  decision.     The  will  determines  whether  we  shall 
carry  on  our  investigations,  or  break  them  off,  content  with  the  first 
apparent  probability ;  and  whether  we  shall  apply  our  observations 
to  all,  or,  only  partially,  to  certain,  momenta  of  determination. 
"  The  occasions  of  Error  which  lie  in  those  qualities  of  Present;:- 

tion.  Representation,  and  Thought  arising  from 

Illusion.  '  \.    .  '.      -  r.       1  1   ■     ^   ' 

the  conditions  and  influences  of  the  thinking 
subject  itself,  are  called  Illusions.  But  the  existence  of  illusion 
does  not  necessarily  imply  the  existence  of  error.  Illusion  becomes 
error  only  when  we  attribute  to  it  objective  truth  ;  whereas  illusion 
i-:  no  error  when  we  regard  the  fallacious  appearance  as  a  mere  sub- 
jiH'tive  affection.  In  the  jaundice,  we  see  everything  tinged  with 
yullow,  in  consequence  of  the  suffusion  of  the  eye  with  bile.     lu 

1  Twesten,  Logik,  }  308.  -'  Ed.  2  Manilius,  ii.  131.  —Ed. 


390  LOGIC.  Lkct.  xxvm. 

this  case,  the  yellow  vision  is  illusiou ;  and  it  would  become  error, 
were  we  to  suppose  that  the  objects  we  perceive  were  really  so  col- 
ored.   All  the  powei-s  which  cooperate  to  tlie  formation   of  our 
judgments,  may  become  the  sources  of  illusion, 

lis  sources.  i  i         i  •  c-  mi 

and,  consequently,  the  occasions  of  error.  1  he 
Senses,^  the  Presentative  Faculties,  External  and  Internal,  tho 
Representative,  the  Retentive,  the  Reproductive,  and  the  Elab- 
orative,  Faculties,  are  immediate,  the  Feelings  and  the  Desires 
are  mediate,  sources  of  illusion.  To  these  must  be  added  the 
Faculty  of  Signs,  in  all  its  actual  manifestations  in  language. 
Hence  we  speak  of  sensible,  psychological,  moral,  and  symbolical, 
illusion."^  In  all  these  relations  the  causes  of  illusion  are  partly 
general,  partly  particular;  and  though  they  proximately  manifest 
themselves  in  some  one  or  other  of  these  forms,  they  may  ulti- 
mately be  found  contained  in  the  circumstances  by  which  tho 
mental  character  of  the  individual  is  conformed.  Taking,  there- 
fore, a  general  view  of  all  the  possible  Sources  of  Error,  I  think 
they  may  be  reduced  to  the  following  classes,  which,  as  they  consti- 
tute the  heads  and  determine  the  order  of  the  ensuing  discussion,  I 
shall  comprise  in  the  following  paragraph,  with  which  commences 
the  consideration  of  the  Second  Chapter  of  Mt>dified  Logic.  Be- 
fore, however,  proceeding  to  consider  these  several  classes  in  their 
order,  I  may  observe  that  Bacon  is  the  first  phi- 
Bacon  a  ciassifica-  losopher  who  attempted  a  systeniatio  enumera- 
tion of  tUe  gources  of  .  „  ,,  .  ^  «  i  ,  • 
„  „_                            lion  or  the  various  sources  oi   error;'  and  hia 

error.  ' 

quaint  classification  of  these,  nnder  the  signifi- 
cant name  of  idols,  into  the  four  genera  of  Idols  of  the  Tribe  {idola 
tribiis).  Idols  of  the  De?)  {idola  specus).  Idols  of  the  Forum  {idola 
fori),  which  may  mean  either  the  market-place,  the  bar,  or  the 
place  of  public  assembly,  and  Idols  of  the  Theatre  {idola  theatri), 
he  thus  briefly  characterizes. 

\  XCII.  The  Causes  and  Occasions  of  Eiror  are  compre- 
hended in  one  or  other  of  the  four  foUow- 

ar.  rror,-       -^     classcs.     For  thcv  are  found  either,  l". 

In  the  General  Circumstances  which  mod- 
ify the  intellectual  character  of  the  individual ;  or,  2°,  In  the 

I  La  Fontaine.    See  Maznre,  Court  de  Phi-     g^rent.    C'est  ce  que  La  Fontaine  a  tiia  bien 

losopMe,  ii.  241.    [Toutcs  )es  sciences  natnr-      exprim^  dans  les  vers  suiraat: 

dies  ne  sont  autre  cliose  qn'une  j{uerre  ou- 

verte  dc  la  raison  contre  lis  deceptions  de  Is  "  **""""*  '' '""  '^"""'^  °°  **^°'  "•  "'*•''  "  ~ 

^     ,..,..,  ,    i       ,-  ,  ,1  .  drcM*,"  etc.  —  Ed. 

M!n8ibiIit<S e'est-a-dire,    qu'elles    ont 

pour  objet  de  rifornerles  erreurs  de  noa  sens,         S  [Twesten,  Logik,  f  309,  pp.  288.  289.    Ci 

et  dc  substituer  les  rialites  de  la  .science  aux      Sigwart,  Logik,  ^  484,  485.] 

apparences  factices  que  uos  i>eu8  nous  sug-         3  Novum  Orgaautn,  l  Aph.  xxxix.  —  Eo> 


Leer.  XXVin.  LOGIC.  391 

Constitution,  Habits,  and  Reciprocal  Relations  of  his  powers 
of  Cognition,  Feeling,  and  Desii^e  ;  or,  3°,  In  the  Language 
which  he  employs,  as  an  Instrument  of  Thought  and  a  Medium 
of  Communication ;  or,  4°,  In  the  nature  of  the  Objects  them- 
selves, about  which  his  knowledge  is  conversant. 

• 
%  XCIII.   Under  the  General  Circumstances  which  modify 
the  character  of  the  individual,  are  compre- 
-,,t'*  „«^„.,^.t»«rr.       bended,  1°.  The  particular  degree  of  Culti- 

eral       circumstances  '  i  o 

which  modify  the  vatiou  to  which  his  natiou  has  attained ; 
vduai  ^'^°  ^^^  ^  ^*^''  ^^^  I'udeness,  the  partiality  of  its  civili- 
zation, and  its  over-refinement  are  all  mani- 
fold occasions  of  error ;  and  this  cultivation  is  expressed  not 
merely  in  the  state  of  the  arts  and  sciences,  but  in  the  degree 
of  its  religious,  political,  and  social  advancement;  2°.  The 
Stricter  Associations,  in  so  far  as  these  tend  to  limit  the  free- 
dom of  thought,  and  to  give  it  a  one-sided  direction ;  such 
are  Schools,  Sects,  Orders,  Exclusive  Societies,  Corporations, 
Castes,  etc.^ 

In  the  commen<;nment  of  the  Course,  I  had  occasion  to  allude  to 

the  tendency  there  is  in  man  to  assimilate   in 

Explication.    Man       opinions  and  habits  of  thoucrht  to  those  with 

by  nature  isocial,  and  i  i       ,  <>■««■•      i       "^ 

influenced  by  the  vvhom  he  lives.  Man  IS  by  nature,  not  merely 
opinions  of  his  fellows.  by  accidental  necessity,  a  social  being.  For 
only  in  society  does  he  find  the  conditions 
which  his  diflferent  ficulties  require  for  their  due  development  and 
application.  But  society,  in  all  its  forms  and  degrees,  from  a  fam- 
ily to  a  State,  is  only  possible  under  the  condition  of  a  certain  har- 
mony of  sentiment  among  its  members;  and  as  man  is  by  nature 
destined  to  a  social  existence,  he  is  by  nature  determined  to  that 
analogy  of  thought  and  feeling  which  society  supposes,  and  out  of 
which  society  springs.  There  is  thus  in  every  association,  great 
and  small,  a  certain  gravitation  of  opinions  towards  a  common 
centre.  As  in  our  natural  body  every  part  has  a  necessary  sympathy 
with  every  other,  and  all  together  form,  by  their  harmonious  con- 
spiration, a  healthy  whole ;  so,  in  the  social  body,  there  is  always  a 
strong  predisposition  in  each  of  its  members  to  act  and  think  in 
unison  with  the  rest.  This  universal  sympathy  or  fellow-feeling  is 
the  principle  of  the  different  spirit  dominant  in  different  ages, 
countries,  ranks,  sexes,  and  periods  of  life.  It  is  the  cause  why 
fashions,  why  political  and  religious  enthusiasm,  why  moral  example 

1  Bachniann,  Logik,  \\  402,  403.  —  Ed.  2  See  Lectures  on  Mitap/iysics,  p.  59.  —Ed. 


392  LOGIC.  Lect.  xxvm. 

either  for  good  or  evil,  spread  so  rapidly  and  exert  so  powerful  an 
influence.  As  men  are  natur.'tlly  prone  to  imitate  others,  they,  con- 
sequently, regai'd  as  important  or  insignificant,  as  honorable  or  dis- 
graceful, as  true  or  false,  as  good  or  bad,  what  those  around  them 
consider  in  the  same  light.* 

Of  the  various  testimonies  ?  formerly  quoted,  of  the  strong  as- 
similating influence  of  man  on  man,  and  of  the 

PaFcal  quoted  on  the  r  i.  j.  iii,^  *  x 

,  power  of  custom  to  make  that  apT)ear  true,  nat- 

power  of  custom.  ^  ... 

ural,  and  necessary,  which  in  reality  is  false,  un- 
natural, and  only  accidentally  suitable,  I  shall  only  adduce  that  of 
Pascal.  "In  the  just  and  the  unjust,"  says  he,  "  we  find  hardly  any- 
thing which  does  not  change  its  character  in  changing  its  climate. 
Three  degrees  of  an  elevation  of  the  pole  reverses  the  whole  of 
jurisprudence.  A  meridian  is  decisive  of  truth,  and  a  few  years,  of 
possession.  Fundamental  laws  change.  Right  has  its  epochs.  A 
pleasant  justice  which  a  river  or  a  mountain  limits  !  Truth  on  this 
side  the  Pyrenees,  error  on  the  other  !"*  It  is  the  remark  of  an  in- 
genious philosopher,  "  that  if  we  take  a  survey  of  the  universe,  all 
nations  will  be  found  admiring  only  the  reflection  of  their  own 
qualities,  and  contemning  in  others  whatever  is  contrary  to  what 
they  are  accustomed  to  meet  with  among  themselves.  Here  is  the 
Englishman  accusing  the  French  of  frivolity;  and  here  the  French- 
man reproaching  the  Englishman  with  selfishness  and  brutality. 
Here  is  the  Arab  persuaded  of  the  infallibility  of  his  Caliph,  and 
deriding  the  Tartar  who  believes  in  the  immortality  of  the  Grand 
Lama.  In  every  nation  we  find  the  same  congratulation  of  their 
own  wisdom,  and  the  same  contempt  of  that  of  their  neighbors. 

"  Were  there  a  sage  sent  down  to  earth  from  heaven,  who  regu- 
lated his  conduct  by  the  dictates  of  pure  reason  alone,  this  sage 
would  be  universally  regarded  as  a  fool.  He  would  be,  as  Socrates 
says,  like  a  physician  accused  by  the  pastry-cooks,  before  a  tribunal 
of  children,  of  prohibiting  the  eating  of  tarts  and  cheese-cakes ;  a 
crime  undoubtedly  of  the  highest  magnitude  in  the  eyes  of  his 
judges.  In  vain  would  this  sage  support  his  opinions  by  the  clear- 
est arguments,  —  the  most  irrefragable  demonstrations ;  the  whole 
world  would  be  for  him  like  the  nation  of  hunchbacks,  among 
whom,  as  the  Indian  fabulists  relate,  there  once  upon  a  time  ap- 
peared a  god,  young,  beautiful,  and  of  consummate  symmetry.  This 
god,  they  add,  entered  the  capital;  he  was  there  forthwith  sur- 
rounded by  a  crowd  of  natives;  his  figure  appeared  to  them  extra- 


I  [Melners,   Untersuchungen  Mer  die    Drnlc-        2  P^twrfes,  partie  i.  art.  vi.  4  8  (vol.  il.  p  126,ed 
icidfte  undf.  WiUtnskrifle  dti  Menschen,  ii.  322.]        Faugere).     Comp.  Leet.  on  Metaphysics,  p.  00 


Lect.  XXVm.  LOGIC.  393 

ordinary ;  laughter,  hooting,  and  taunts  manifested  their  astonish- 
ment, and  they  were  about  to  carry  their  outrages  still  further,  had 
not  one  of  the  inhabitants  (who  had  undoubtedly  seen  other  men), 
in  order  to  snatch  him  from  the  danger,  suddeijly  cried  out  —  'My 
friends !  my  friends !  What  are  we  going  to  do  ?  Let  us  not  insult 
this  miserable  monstrosity.  If  heaven  has  bestowed  on  us  the  gene- 
ral gift  of  beauty,  —  if  it  has  adorned  our  backs  with  a  mount  of 
flesh,  let  us  with  pious  gi'atitude  repair  to  the  temple  and  render 
our  acknowledgment  to  the  immortal  gods.' "  This  fable  is  the  his- 
tory of  human  vanity.  Every  nation  admires  its  own  defects,  and 
contemns  the  opposite  qualities  in  its  neighbors.  To  succeed  in  a 
country,  one  must  be  a  bearer  of  the  national  hump  of  the  people 
among  whom  he  sojourns. 

There  are  few  philosophers  who  undertake  to  make  their  country- 
men aware  of  the  ridiculous  figure  they  cut  In 
The  art  of  doubting       ^]jg  gyg  ^f  reason  ;  and  still  fewer  the  nations 

well  diflScult  to  teach  ,  ^  -i      .  r>.  i       .1  i    •  a  ^^ 

and  10  learn  ^^  ^^®  *°  pront  by  the  advicc.    All  are  so 

punctiliously  attached  to  the  interests  of  their 
vanity,  that  none  obtain  in  any  country  the  name  of  wise,  except 
those  who  are  fools  of  the  common  folly.  There  is  no  opinion  too 
absurd  not  to  find  nations  ready  to  believe  it,  and  individuals 
prompt  to  be  its  executioners  or  its  martyrs.  Hence  it  is  that  the 
philosopher  declared,  that  if  he  held  all  truths  shut  up  within  his 
hand,  he  would  take  especial  care  fiot  to  show  them  to  his  fellow- 
men.  In  fact,- if  the  discovery  of  a  single  truth  dragged  Galileo  to 
the  prison,  to  what  punishment  would  he  not  be  doomed  who  should 
discover  all  ?  Among  those  who  now  ridicule  the  folly  of  the  human 
intellect,  and  are  indignant  at  the  persecution  of  Galileo,  there  are 
few  who  would  not,  in  the  age  of  that  philosopher,  have  clamored 
for  his  death.  They  would  then  have  been  imbued  with  difierent 
opinions ;  and  opinions  not  more  passively  adopted  than  those 
which  they  at  present  vaunt  as  liberal  and  enlightened.  To  learn 
to  doubt  of  our  opinions,  it  is  sufficient  to  examine  the  powers  of 
the  human  intellect,  to  survey  the  circumstances  by  which  it  is  af- 
fected, and  to  study  the  history  of  human  follies.  Yet  in  modem 
Europe  six  centuries  elapsed  from  the  foundation  of  Universities 
until  the  appearance  of  that  extraordinary  man,  —  I  mean  Des- 
cartes, —  whom  his  age  first  persecuted,  and  then  almost  worship- 
ped as  a  demi-god,  for  initiating  men  in  the  art  of  doubting,  —  of 
doubting  well,  —  a  lesson  at  which,  however,  both  their  skepticism 
and  credulity  show  that,  after  two  centuries,  they  are  still  but  awk- 
ward scholars.     Socrates  was  wont  to  say  —  "  All  that  I  know  is 

50 


S94  LOGIC.  Lect.  XX VUI 

that  I  know  nothing."^  In  our  age  it  would  seem  that  men  know 
everything  except  what  Socrates  knew.  Our  errors  would  not  be 
80  frequent  were  we  less  ignorant ;  and  our  ignorance  more  curable, 
did  we  not  believe  ourselves  to  be  all-wise. 

Thus  it  is  that  the  influence  of  Society,  both  in  its  general  form 

of  a  State  or  Nation,  and  jn  its  particular  forms  of  Schools,  Sects, 

etc.,  determines  a  multitude  of  opinions  in  its  menibei*s,  which,  as 

they  are  passively  received,  so  they  are  often  altogether  erroneous. 

Among  the  more  general  and  influential  of  these  there  are  two, 

which,  though   apparently   contrary,  are,  how- 
oftiie  influence  of  ex-       ever,  both,  in  reality,  founded  on  the  same  in- 
ample,  capacity  of  independent  thouglit,  —  on  the  same 
1.  Prejudice  in  fa-       influence  of  example,  —  I  mean  the  excessive 

admiration  of  the  Old,  and  the  excessive  admi- 
ration of  the  New.  The  former  of  these  prejudices,^  —  under  which 
may  be  reduced  the  prejudice  in  favor  of  Authority,  —  was  at  one 
time  prevalent  to  an  extent  of  which  it  is  difficult  for  us  to  form  a 
conception.     This  prejudice  is  prepared  by  the  very  education  not 

only  which  we  do,  but  which  Ave  all  must  re- 
pare     y     uca-       ceive.     The  child  necessarily  learns  everything 

at  first  on  credit,  —  he  believes  upon  authority. 
But  when  the  rule  of  authority  is  once  established,  the  habit  of  pas- 
sive acquiescence  and  belief  is  formed,  and,  once  formed,  it  is  not 
again  always  easily  thrown  off.  .When  the  child  has  grown  up  to 
an  age  in  which  he  might  employ  his  own  reason,  he  has  acquired  a 
large  stock  of  ideas ;  but  who  can  calculate  the  number  of  errora 
which  this  stock  contains  ?  and  by  what  means  is  he  able  to  dis- 
criminate the  true  from  the  false  ?  His  mind  has  been  formed  to 
obedience  and  uninquiry ;  he  possesses  no  criterion  by  which  to 
judge ;  it  is  painful  to  suspect  what  has  been  long  venerated,  and  it 
is  felt  even  as  a  kind  of  personal  mutilation  to  tear  up  what  has  be- 
come irradicated  in  his  intellectual  and  moral  being.  Poiiere  diffi- 
cile est  quoB placuere  diu.  The  adult  doea  not,  therefore,  often  judge 
for  himself  more  than  the  child  ;  and  the  tyranny  of  authority  and 
foregone  opinion  contiimes  to  exert  a  sway  during  the  whole  course 
of  his  life.  In  our  infancy  and  childhood  the  credit  accorded  to  our 
parents  and  instructors  is  implicit;  and  if  what  wo  have  learned 
from  them  be  confirmed  by  what  we  hear  from  others,  the  opinions 

1  riafo,  Apol ,  p  23.  —  Ed.  ft  dm  Prejuges  repandus  dans  la  Socidc,  Paris, 

2  [On  Prejudice  in  pencral  see  the  IbllowmR  1810—1813,  3  vols.  8va  J.  L.  Cnstillon,  Essai 
works:  —  Diiinarsais,  E^sai  sur  Us  Prcjuges,  siir  U.t  Errrurs  et  Us  superstitions  Ancieunes  M 
new  ed.,  Pnri.«,  1822.  Examen  ilt  V  Esun  sur  Moiitmrs,  Amsterdam,  1705;  l^aris,  1767.  Sir 
/',«  ^([/'/i'J.t,  l?oiJ.  1777.  K^tni  sur  let  Prejii!i<is,  Thomas  Brown,  Vulgar  Errors,  lilauvil,  £t- 
Neucbttel,   179G.    J.  11.  .Suliiuvs,    U-s   Err>urs  suys.\ 


Lect.  XXVIII.  LOGIC.  395 

thus  recommended  become  at  length  stamped  in  almost  indelible 
characters  uj^on  the  mind.  This  is  the  cause  why  men  so  i-arely 
abandon  the  opinions  which  vulgarly  pass  current ;  and  why  what 
comes  as  new  is  by  so  many,  for  its  very  novelty,  rejected  as  false. 
And  hence  it  is,  as  already  noticed,  that  truth  is  as  it  were  geo- 
graphically and  politically  distributed ;  what  is  truth  on  one  side 
of  a  boundary  being  error  and  absui'dity  on  the  other.  What  has 
now  been  said  of  the  influence  of  society  at  large,  is  true  also  of  the 
lesser  societies  which  it  contains,  all  of  which  impose  with  a  stronger 
or  feebler,  a  wider  or  more  contracted,  authority,  certain  received 
opinions  upon  the  faith  of  the  members.  Hence  it  is  that  whatever 
has  once  obtained  a  recognition  in  any  society,  large  or  small,  is  not 
rejected  when  the  reasons  on  which  it  was  originally  admitted 
have  been  proved  erroneous.  It  continues,  even  for  the  reason  that 
it  is  old  and  has  been  accepted,  to  be  accepted  still ;  and  the  title 
wliich  was  originally  defective,  becomes  valid  by  continuance  and 
prescription. 

But  opposed  to  this  cause  of  error,  from  the  prejudice  in  favor  of 

the  Old,  there  is  the  other,  directly  the  reverse, 

reju  ice  in  avor       — ^j^^   prejudice   in   favor  of  the   New.     This 

of  the>ew.  . 

prejudice  may  be,  in  part  at  least,  the  result  of 
sympathy  and  fellow-feeling.  This  is  the  cause  why  new  opinions, 
however  erroneous,  if  they  once  obtain  a  certain  number  of  con- 
verts, often  spread  with  a  rapidity  and  to  an  extent,  which,  after 
their  futility  has  been  ultimately  shown,  can  only  be  explained  on 
the  ])rinciple  of  a  kind  of  intellectual  contagion.  But  the^  principal 
cause  of  the  prejudice  in  favor  of  novelty  lies  in  the  Passions,  and 
the  consideration  of  these  does  not  belong  to  the  class  of  causes 
with  which  we  are  at  present  occupied. 

Connected  with  and  composed  of  both  these  prejudices,  —  that  in 

favor  of  the  old  and  that  in  favor  of  the  new,  — 

AuZrur^*^'"'"'**  *^®'"^  ^^  ^^®  prejudice  of  Learned  Authority; 
for  this  is  usually  associated  with  the  prejudices 
of  Schools  and  Sects.  "As  often  as  men  have  appeared,  who,  by  the 
force  of  their  genius,  have  opened  up  new  views  of  science,  and  thus 
contributed  to  the  progress  of  human  intellect,  so  often  have  they, 
likewise,  afforded  the  occasion  of  checking  its  advancement,  and  of 
turning  it  from  the  sti'aight  path  of  improvement.  Not  that  this 
result  is  to  be  imputed  as  a  reproach  to  them,  but  simply  because  it 
is  of  the  nature  of  man  to  be  so  affected.  The  views  which  influ- 
enced these  men  of  genius,  and  which,  consequently,  lie  at  the 
foundation  of  their  works,  are  rarely  comprehended  in  their  totality 
by  those  who  have  the  names  of  these  authors  most  frequently  in 


896  LOGIC.  Lect.  XXVIIL 

their  mouths.  The  many  do  not  concern  themselves  to  seize  the 
ideal  which  a  philosopher  contemplated,  and  of  which  his  actual 
works  are  only  the  imperfect  representations ;  they  appropriate 
to  themselves  only  some  of  his  detached  apothegms  and  proposi- 
tions, and  of  these  compound,  as  they  best  can,  a  sort  of  system 
suited  to  their  understanding,  and  Avhich  they  employ  as  a  talisman 
in  their  controversies  with  others.  As  their  reason  is  thus  a  captive 
to  authority,  and,  therefore,  unable  to  exert  its  native  freedom,  they, 
consequently,  catch  up  the  true  and  the  false  without  discrimina- 
tion, and  remain  always  at  the  point  of  progress  where  they  had 
been  placed  by  their  leaders.  In  their  hands  a  system  of  living 
truths  becomes  a  mere  petrified  organism ;  and  they  require  that  the 
whole  science  shall  become  as  dead  and  as  cold  as  their  own  idol. 
Such  was  Plato's  doctrine  in  the  hands  of  the  Phitonists ;  such  was 
Aristotle's  philosophy  in  the  hands  of  the  Schoolmen  ;  and  the  his- 
toiy  of  modern  systems  affords  equally  the  same  result."* 

So  much  for  the  first  genus  into  which  the  Sources  of  Error  are 
divided. 

I  BacbinaoD,  Logii,  S  404,  p.  560-  —  Ed. 


LECTURE    XXIX. 

MODIFIED     S  T  O  I  C  H  E  I  O  L  O  O  Y. 

SECTION  II.  — ERROR  — ITS  CAUSES  AND  REMEDIES 

A.  —  GENERAL  CIRCUMSTANCES  —  SOCIETY. 

B.  —  AS  IN  POWERS   OF  COGNITION,  FEELING,  AND  DESIRE. 

L  — AFFECTIONS.  — PRECIPITANCY— SLOTH  — HOPE  AND  FEAR- 
SELF-LOVE. 

In   our  last   Lecture,  we  entered  on  the  consideration  of  the 
various  sources  of  Error.     These,  I  stated,  may 

Recapitulation.  .        i  t  i  ,.         i        t  t 

be  conveniently  reduced  to  tour  heads,  and  con- 
sist, 1°.  In  the  General  Circumstances  which  modify  tlie  intellectual 
character  of  the  individual ;  2°.  In  the  Constitution,  Habits,  and 
Reciprocal  Relations  of  his  powers  of  Cognition,  Feeling,  and 
Desire ;  3°.  In  the  Language  which  he  employs  as  an  Instrument 
of  Thought  and  a  Medium  of  Communication ;  and,  4°.  In  the 
nature  of  the  Objects  themselves  about  which  his  knowledge  is 
conversant. 

Of  these,  I  then  gave  you  a  general  view  of  the  nature  of  those 
occasions  of  Error,  which  originate  in  the  circumstances  under  the 
influence  of  which  the  character  and  opinions  of  man  are  deter- 
mined for  him  as  a  member  of  society.  Under  this  head  I  stated, 
that,  as  man  is  destined  by  his  Creator  to  fulfil  the  end  of  hia 
existence  in  society,  he  is  wisely  furnished  with  a  disposition  to 
imitate  those  among  whom  his  lot  is  cast,  and  thus  conform  himself 
to  whatever  section  of  human  society  he  may  by  birth  belong,  or 
of  which  he  may  afterwards  become  a  member.  The  education  we 
receive,  nay  the  very  possibility  of  receiving  education  at  all,  sup- 
poses to  a  certain  extent  the  passive  infusion  of  foreign  and  tradi- 
tionary opinions.  For  as  man  is  compelled  to  think  much  earlier 
than  he  is  able  to  think  for  himself,  —  all  education  necessarily 
imposes  on  him  many  opinions  whicli,  whether  in  themselves  true 


398  LOGIC.  Lect.  XXIX. 

or  false,  are,  in  reference  to  the  recipient,  only  prejudices;  and  it  is 
even  only  a  small  number  of  mankind  who  at  a  later  period  are 
able  to  bring  these  obtruded  opinions  to  the  test  of  reason,  and  by 
a  free  exercise  of  their  own  intelligence  to  reject  them  if  found 
false,  or  to  acknowledge  them  if  proved  true. 

But  while  the  mass  of  mankind  thus  remain,  during  their  whole 
lives,  only  the  creatures  of  the  accidental  circumstances  which  have 
concuiTcd  to  form  for  them  their  habits  and  beliefs;* the  few  who 
are  at  last  able  to  form  opinions  for  themselves,  are  still  dependent, 
in  a  great  measure,  on  the  unreasoning  judgment  of  the  many. 
Public  opinion,  hereditary  custom,  despotically  impose  on  us  the 
capricious  laws  of  propriety  and  manners.  The  individual  may 
possibly,  in  matters  of  science,  emancipate  himself  from  their  servi- 
tude ;  in  the  affaii-s  of  life  he  must  quietly  submit  himself  to  the 
yoke.  The  only  freedom  he  can  here  prudently  manifest,  is  to 
resign  himself  Avith  a  consciousness  that  he  is  a  slave  not  to  reason 
but  to  conventional  accident.  And  while  he  conforms  himself  to 
the  usages  of  his  own  society,  he  will  be  tolerant  to  those  of  others. 
In  this  respect  his  maxim  will  be  that  of  the  Scythian  prince  : 
"With  you  such  may  be  the  custom,  —  with  us  it  is  different." 

So  much  for  the  general  nature  of  the  infln- 
Means  by  which  ihe      ence  to  wliicli  we  are  exposed  from  the  circum- 

Infliience  of  society,  as  ,  f  c<      •    ^         '^  •        ^  i.^ 

-     ■  stances  of  bociety :  it  now  remams  to  sa3'  what 

a    source    of    error,  .  .       . 

may  be  counteracted.        f"*e   the   means  by  which   this   influence,  as   a 

source  of  error,  may  be  counteracted. 

It  has  been  seen  that,  in  consequence  of  the  manner  in  which 

our  opinions  are  formed  for  us  by  the  accidents 

Necessary  to  insti-       of  society,  our  imposed  and  supposed  knowledge 

tute  a  critical  examin-         .  j?i  31  o  ^      ^\  3  tt 

,  ^        ,    .        IS  a  contused  medley  or  truths  and  erroi-s.    Here 

atlon  of  the  contcuts        ^      ^  •' 

of  our  knowledge.  it  is  evidently  necessary  to  institute  a  critical 

examination  of  the  contents  of  this  knowledge. 
Descartes  proposes  that,  in  order  to  discriminate,  among  our  preju- 
diced opinions,  the  truths  from  the  errors,  we  ought  to  commence 
by  doubting  all.*     This  has  exposed  him  to  much  obloquy  and 
clamor,  but  most  unjustly.     Tlie  doctrine  of  Descartes  has  nothing 
skeptical   or  offensive ;   for  he   only  maintains 
Descartes, -his pre-       ^^^^  j^  behooves  US  to  examine   all  that   has 
been  inculcated  on  us  from  infancy,  and  under 
the  masters  to  whose  authority  we  have  been  subjected,  with  the 
same  attention  and  circumspection  which   we   accord  to  dubious 
questions.     In  fact  there  is  nothing  in  the  precept  of  Descartes, 
which  bad  not  been  previously  enjoined   by  other  philosophers. 

1  Discours  de  la  Mitkodt,  Partie  ii.  —  Ed. 


Lect.  XXIX.  LOGIC.  399 

Of  these  I  formerly  quoted  to  you  several,  and  among  others  tho 

remarkable  testimonies  of  Aristotle,  St.Augustin,  and  Lord  Bacon.^ 

But  although  there  be  nothing  reprehensible  in  the  precept  of 

Descartes,  as  enounced  by  him,  it  is  of  less  prac- 

Conditions    winch       iiQal  Utility  in  cousequencc  of  no  account  being 

taken  of  the  circumstances  which  condition  and 

tion. 

modify  its  application.  For,  in  the  first  place, 
the  judgments  to  be  examined  ought  not  to  be  taken  at  random, 
but  selected  on  a  principle,  and  arranged  in  due  order  and  depend- 
ence. But  this  requires  no  ordinary  ability,  and  the  distribution  of 
things  into  their  proper  classes  is  one  of  the  last  and  most  difficult 
fruits  of  philosophy.  In  the  second  place,  there  are  among  our 
prejudices,  or  pretended  cognitions,  a  great  many  hasty  conclusions, 
the  investigation  of  which  requires  much  profound  thought,  skill, 
and  acquired  knowledge.  Kow,  from  both  of  these  considerations, 
it  is  evident  that  to  commence  philosophy  by  such  a  review,  it  is 
necessary  for  a  man  to  be  a  philosopher  before  he  can  attempt  to 
become  one.  The  precept  of  Descartes  is,  therefore,  either  unrea- 
sonable, or  it  is  too  unconditionally  expressed.  And  this  latter 
alternative  is  true. 

What  can  be  rationally  requii'ed  of  the  student  of  philosophy,  is 
not  a  preliminary  and  absolute,  but  a  gradual 

A  j^radual  and  pro-  ^  .        •'  ,  «  .     ,.  t^ 

gressive  abrogation  of  '^^^^  progressive  abrogation,  of  prejudices.  It 
prejudices  all  that  can  can  onlv  be  required  of  him,  that,  when,  in  the 
be  required  of  the  stu-       course  of  his  Study  of  philosophy,  he  meets  with 

dent  of  philoeophy.  .,.  i-ii  ,i  i         i  a? 

a  proposition  which  has  not  been  already  sutn- 
ci en tly  sifted, —  (whether  it  has  been  elaborated  as  a  principle  or 
admitted  as  a  conclusion),  —  he  should  pause,  discuss  it  without 
prepossession,  and  lay  aside  for  future  consideration  all  that  has  not 
been  subjected  to  a  searching  scrutiny.  The  precept  of  Descartes, 
when  rightly  explained,  corresponds  to  that  of  St.  Paul  -J  "If  any 
man  among  you  seemeth  to  be  wise  in  this  world,  let  him  become  a 
fool,  that  he  may  be  wise ; "  that  is,  let  him  not  rely  more  on  the 
opinions  in  which  he  has  been  brought  up,  and  in  favor  of  which  he 
and  tljose  around  him  are  prejudiced,  than  on  so  many  visions  of 
imagination  ;  and  let  him  examine  them  with  the  same  circumspec- 
tion as  if  he  were  assured  that  they  contain  some  truth  among 
much  falsehood  and  many  extravagances.^ 
Proceeding  now  to  the  second  class  of  the  Sources  of  Error, 


1  See  Leet.  on  Metaphysics,  p.  63  et  seq.  —  Ed.      is,   with  some   slight    changes,   taken    from 

2  1  Cor.  iii.  18.  Crousaz,  Logique,  t.  ill.,  part  ii.,  ch.  6,  p.  263 

3  This  criticism  of  the  precept  of  Descartes      et  uq.  —  Ed. 


400  LOGIC.  Lect.  XXIX. 

which  are  found  in   the  Mind  itself,  I  shall  commence  with  the 
following  paragraph  : 

%  XCIV.   The  Sources  of  Error  which  arise  from  the  Con- 
stitution, Habits,  and  Reciprocal  Relations 

Par.  XCIV.  II.  Source  i»^i  ^^-i--  -ni-  i 

of  Error  arising  from  ^^  ^hc  powcrs  of  Cognition,  Feeling,  and 
the  powers  of  cogni-  Dcsire,  may  be  subdivided  into  two  kinds, 
ion,    ee  mg,  an      e-       rpj^^  g^.^^  of  thcsc  consists  in  the  uuduc  pre- 

sire,  —  of  two  Kinds.  i 

ponderance  of  the  Affective  Elements  of 
mind  (the  Desires  and  Feelings)  over  the  Cognitive;  the  sec- 
ond, in  the  weakness  or  inordinate  strength  of  some  one  or 
other  of  the  Cognitive  Faculties  themselves. 

AiFection  is  that  state  of  mind  in  which  the  Feelings  and  Desires 

exert  an  influence  not  under  the  control  of  rea- 

KxpHcation.  gQ^ ;  in  Other  words,  a  tendency  by  which  the 

1.  Preponderance  of         •    .    n      .    •      •  j     i    •       -x  j  ^      ai_'    i 

.„    .  „  intellect  is  impeded  in  its  endeavor  to  think  an 

Affection  over  Cogui-  ^  '  _ 

tion.  object  as  that  object  really  is,  and   compelled 

to  think  it  in  conformity  with  some  view  pre- 
scribed by  the  passion  or  private  interest  of  the  subject  thinking. 
The  human  mind,  when  unruffled  by  passion,  may  be  compared 
to  a  calm  sea.     A  calm '"sea  is  a  clear  mirror,  in 

Influence  of  Passion  i-t-ii_  ji       j*  i-t-^i-i? 

..    ...  .  which  the  sun  and  clouds,  in  which  the  forms 

on  the  Mind.  ' 

of  heaven  and  earth,  are  reflected  back  pre- 
cisely as  tliey  are  presented.  But  let  a  wind  arise,  and  the  smooth, 
clear  surface  of  the  water  is  lifted  into  billows  and  agitated  into 
foam.  It  no  more  reflects  the  sun  and  clouds,  the  forms  of  heaven 
and  earth,  or  it  reflects  them  only  as  distorted  and  broken  images. 
In  'like  manner,  the  tranquil  mind  receives  and  reflects  the  world 
without  as  it  truly  is ;  but  let  the  wind  of  passion  blow,  and  every 
object  is  represented,  not  as  it  exists,  but  in  the  colore  and  aspects 

and  partial  phases  in  which  it  pleases  the  sub- 

Uoethjus  quoted.  '■  ^  . 

ject  to  regard  it.  The  state  of  passion  and  its 
influence  on  the  Cognitive  Faculties  are  truly  pictured  by  Boethius.' 

"  Nubibus  atris  Parqne  serenls 

Condita  nullum  Utuhi  dicbus, 

Fnnderc  possunt  Mox  resoluto 

Sidcm  lumen.  Soj-dida  cocno, 

Si  marc  volvcns  Visibus  obstat. 
Turbidus  austcr 

Misccat  acstum,  Tu  quoqiic  si  vis 

Vitrea  dudum,  Lumino  claro 

1  De  Consol.  Phil.,  L.  i  ,  Metr  7-  —  Ko. 


Lkct.  XXIX.  LOGIC.  401 

Cernero  verum,  Spenique  fugato, 

Tramite  recto  Nee  doloi-  adsit, 

Carpere  callem :  Nubila  mens  est, 

Gaudia  pelle,  Vinctaque  frenis, 

Pelle  timorem,  Ha;c  ubi  regnant." 

Every  error  consists  in  this,  —  that  we  take  something  for  non- 
existent, because  we  have  not  become  aware  of 
Error    limited    to       -^^  existence,  and  that,  in  place  of  this  existent 

Probable  Keasoning.  .  ^ 

something,  we  fill  up  the  premises  of  a  probable 
reasoning  with  something  else. 

I  have  here  limited  the  possibility  of  error  to  Probable  Reason- 
ing, for,  in  Intuition  and  Demonstration,  there  is  but  little  possi- 
bility of  important  error.  Hobbes  indeed  asserts  that  had  it  been: 
contrary  to  the  interest  of  those  in  authority,  that  the  three  angles 
of  a  triangle  should  be  equal  to  two  right  angles,  this  truth  would 
have  been  long  ago  proscribed  as  heresy,  or  as  high  treason.^  Tiiis 
may  be  an  ingenious  illustration  of  the  blind  tendency  of  the  pas- 
sions to  subjugate  intelligence;  but  we  should  take  it  for  more  than 
was  intended  by  its  author,  were  we  to  take  it  as  more  than  an  inge- 
nious exaggeration.  Limiting,  therefore,  error  to  probable  inference 
(and  this  constitutes,  with  the  exception  of  a  comparatively  small  - 
department,  the  whole  domain  of  human  reasoning),  we  have  to 
inquire,  How  do  the  Passions  influence  us  to  the  assumption  of 
false  premises  ?  To  estimate  the  amount  of  probability  for  or 
against  a  given  proposition,  requires  a  tranquil,  an  unbiassed,  a 
comprehensive  consideration,  in  order  to  take  all  the  relative  ele- 
ments of  judgment  into  due  account.  But  this  requisite  state  of 
mind  is  disturbed  when  any  interest,  any  wish,  is  allowed  to 
interfere. 

%  XCV.   The  disturbing  Passions  may  be  reduced  to  four : 
Precipitancy,  Sloth,  Hope  and  Fear,  Self— 

Par.  XCV.    The  Pas-  t  ."  '1  ' 

sions,   as    sources    of  lOVC. 

Error.- reduced    to  jo^  ^  Tcstlcss  anxicty  for  a  dccisiou  be- 

four.  .  .  .        •'  . 

gets  impatience,  which  decides  before  the 
preliminary  inquiry  is  concluded.     This  is  precipitancy. 

2°.  The  same  result  is  the  eflect  of  Sloth,  which  dreams  on 
in  conformity  to  custom,  without  subjecting  its  beliefs  to  the 
test  of  active  observation. 

3°.  The  restlessness  of  Hope  or  F"ear  impedes  observation^ 
distracts  attention,  or  forces  it  only  on  what  interests  the  pas- 

I  Leviathan,  Fart  I.  ch.  11.  — £lX 

51 


402  LOGIC.  Lkct.  XXIX 

sion  ;  —  the  sanguine  looking  on  only  what  harmonizes  with 
his  hopes,  the  diffident  only  on  what  accords  with  his  fears. 

4°.  Self-love  perverts  our  estimate  of  probability  by  causing 
us  to  rate  the  grounds  of  judgment,  not  according  to  their  real 
influence  on  the  truth  of  the  decision,  but  according  to  their 
bearing  on  our  personal  interests  therein. 

In  regard  to  Impatience  or  Precipitation,  — "  all  is  the  cause  of 

this  which  determines  our  choice  on  one  side 

Explication.  rather   than    another.     An  imagination  excites 

1.  Precipitancy.  .  . 

pleasure,  and  because  it  excites  pleasure  we 
yield  ourselves  up  to  it.  We  suppose,  for  example,  that  we  are  all 
that  we  ought  to  be,  and  why?  Because  this  supposition  gives  us 
pleasure.  This,  in  some  dispositions,  is  one  of  the  greatest  obsta- 
cles to  improvement ;  for  he  who  entertains  it,  thinks  there  is  no 
necessity  to  labor  to  become  what  he  is  already.  '  I  believe,'  says 
Seneca,^  'that  many  had  it  in  their  power  to 
have  attained  to  wisdom,  had  they  not  been 
impeded  by  the  belief  that  wisdom  they  had  already  attained.' 
'Multos  puto  ad  sapientiam  potuisse  pervenire,  nisi  putassent  se 

pervenisse.' "  ^     Erasmus  gives  the  following  as 
Erasmus.  i  •      •      i      &    •  />  i 

the  principal  a«vice  to  a  young  votaiy  oi  learn- 
ing in  the  conduct  of  his  studies:  "To  read  the  most  learned  books, 
to  converse  with  the  most  learned  men ;  but,  above  all,  never  to 
conceit  that  he  himself  was  learned."' 

"From  the  same  cause,  men  flatter  themselves  with  the  hope  of 
dying  old,   although    few   attain   to   longevity. 

Illustrations.  mi        i  i     i  i        i  .     .i  ^      .    • 

Ihe  less  probable  the  event,  the  more  certain 
are  they  of  its  occurrence  ;  and  why  ?  Because  the  imagination  of 
it  is  agreeable.     '  Decrcpiti  senes  pnucorum  annorum  accesslonem 

votis    mendicant ;    minores    natu    seipsos    esse 

From  Seneca.  _  ,..,.,,,.  ,. 

nngunt;  mendacio  sibi  blandiuntur;   et  tarn  ii- 

benter  fallunt,  quam  si  fata  una   decipiant.'"*     "Preachers,"  says 

Montaigne,  "are  aware  that  the  emotion  which 

From  Montaigne.  .  ,      .  ,     .  .  ,  , 

arises  during  their  sennons  animates  themselves 
to  belief,  and  we  are  conscious  that  when  roused  to  anger  we  apply 


1  De  Thinquillilnte  Animi,  c.  1.  — Ed.  doctos  diligenter  ediiiceret,  deniqne  si  fe  doc- 

2  Crousaz,  Logiqut,  t.  iil  ,  part  il.  ch.  7,  p.  turn  nunquam  pntaret."    Motto  to  G.  J.  Vos- 
29".  —  Ed.  sius,    Opuscula    de    Studiorum     linlicne.       See 

8  "Joannes  Alexander  Brassicanns  rogavit  Crenlus,  Consiliaet  Metkodus,  etc.,  p.  686, 169i 

Erasmum,  qua  ratione  doctus   posset   fieri,  — Ed. 

respond  it  ex  tempore:  si  doctis  assidue  con-  4  Seneca,  De  Brevitale  Vita,  ch.  11.    Cron- 

viveret,  si  doctos  audiret  non  minus  submisse  saz,  Logiqut^  t.  iii.  p.  ii.  oh.  7,  p.  297,  ed.  1T2& 

quam  honoriflce,  ei  doctos  strenue  legeret,  si  —  Ed. 


1 


J.ECT.  XXIX.  LOGIC.  403 

ourselves  more  intently  to  the  defence  of  our  thesis,  and  embrace  it 
with  greater  vehemence  and  approbation,  than  we  did  when  our 
mind  was  cool  and  unruffled.  You  simply  state  your  case  to  an 
advocate;  he  replies  with  hcvsitation  and  doubt;  you  are  aware  that 
it  is  indifferent  to  him  whether  he  undertakes  the  defence  of  the  one 
side  or  of  the  other ;  but  have  you  once  fee'd  him  well  to  take  your 
case  in  hand ;  he  begins  to  feel  an  interest  in  it ;  his  will  is  ani- 
mated. His  reason  and  his  science  become  also  animated  in  pro- 
portion. Your  case  presents  itself  to  his  understanding  as  a 
manifest  and  indubitable  truth ;  he  now  sees  it  in  a  wholly  dif- 
ferent light,  and  really  believes  that  you  have  law  and  justice  on 
your  side."^  It  is  proper  to  observe  that  Montaigne  was  him- 
self a  lawyer,  —  he  had  been  a  counsellor  of  the  Parliament  of 
Bordeaux. 

It  might  seem  that  Precipitate  Dogmatism  and  an  inclination  to 

Skepticism  were  opposite  characters  of  mind. 

Precipitate  Dogma-       They  are,  howcver,  closely  allied,  if  not  merely 

lism  and   Skepticism,  ,  /?  .1  j-  '.•  fth.*      •      •     j       j 

,  ,,  phases  of  the  same  disposition,     ihis  is  indeed 

phases    of    the    same         '■  '^ 

disposition.  coufessed    by   the   skeptic  Montaigne.^      "The 

most  uneasy  condition  for  me  is  to  be  kept  in 
suspense  on  urgent  occasions,  and  to  be  agitated  between  fear  and 
^hope.  Deliberation,  even  in  things  of  lightest  moment,  is  very 
Itroublesome  to  me;  and  I  find  my  mind  more  put  to  it,  to  undergo 
|the  various  tumbling  and  tossing  of  doubt  and  consultation,  than  to 
'set  up  its  rest,  and  to  acquiesce  in  whatever  shall  happen,  after  the 
Mie  is  thrown.  Few  passions  break  my  sleep  ;  but  of  deliberations, 
lihe  least  disturbs  me." 

Precipitation  is  no  incurable  disease.     There  is  for  it  one  suni 

and   simple  remedy,  if  properly  applied.     It  is 

tat^ir*^^  ^°'  ^''"^'"       °"^y  required,  to  speak  with  Confucius,  manfully 

to  restrain  the  wild  horse  of  precipitancy  by  the 

curb  of  consideration,  —  to  weigh  the  reasons  of  decision,  each  and 

I  all,  in  the  balance  of  cool  investigation,  —  not  to  allow  ourselves  to 

decide  until  a  clear  consciousness  has  declared  these  i-easons  to  be 

true,  —  to  be  sufficient;  and,  finally,  to  throw  out  of  account  the 

'Suffrages  of  self-love,  of  prepossession,  of  passion,  and   to   admit 

only  those  of  reflection,  of  experience,  and  of  evidence.      This 

remedy  is  certain   and  effectual.     In  theory  it  is  satisfactory,  but 

its  practical  application  requires  a  moral  resolution,  for  the  acquisi- 

r  tion  of  which  no  precept  can  be  given. 

In  the  secoiKJ  place,  "  Sloth  is  likewise  a  cause  of  precipitation, 
and  it  deserves  the  more  attention  as  it  is  a  cause  of  error  extremely 

1  Essais,  L.  ii.  ch.  12.   Quoted  by  Crousaz,  I.  c.  —  Ed.  2  Esaais,  L.  ii.  c.  17.  —  Ed. 


404  LOGIC.  Lkct.  XXIX 

fiequent,  and  one  of  which  we  are  ourselves  less  aware,  and  which 

is  less  notorious  to  others.     We  feel  it  fatiguing 
2.  Sloth.  .  .  .        .  ,         ^  , 

to  continue  an  investigation,  therefore  we  do 

not  pursue  it ;  but  as  it  is  mortifying  to  think  that  we  have  la- 
bored in  vain,  we  easily  admit  the  flattering  illusion  that  Ave  have 
succeeded.  By  the  influence  of  this  disposition  it  often  happens, 
that,  after  having  rejected  what  first  presented  itself,  —  after  having 
rejected  a  second  time  and  a  third  time  what  subsequently  turned 
up,  because  not  sufficiently  applicable  or  certain,  we  get  tired  of  the 
investigation,  and  perhaps  put  up  with  the  fourth  suggestion,  which 
is  not  better,  haply  even  worse,  than  the  preceding;  and  this 
simply  because  it  has  come  into  the  mind  when  more  exhausted 
and  less  scrupulous  than  it  was  at  the  conmiencement."^  "The 
volition  of  that  man,"  says  Seneca,  "is  often 

Seneca  quoted.  t       i  i  i  i         .  i 

frustrated,  who  undertakes  not  what  is  easy,  but 
who  wishes  what  he  undertakes  to  be  easy.  As  often  as  you 
attempt  anything,  compare  together  yourself,  the  end  which  you 
propose,  and  the  means  by  which  it  is  to  be  accomplished.  For  the 
repentance  of  an  unfinished  work  will  make  you  rash.  And  here  it 
is  of  consequence  whether  a  man  be  of  a  fervid  or  of  a  cold,  of  an 
aspiring  or  of  a  humble,  disposition."  ^ 

To  remedy  this  failing  it  is  necessary,  in  conformity  with  this 

advice  of  Seneca,  to  consult  our  forces,  and  the 
^".  tune  we   can    afford,  and    the  difficulty  of  the 

subjects  on  which  we  enter.  We  ought  to  labor  only  at  intervals, 
to  avoid  the  tedium  and  disquiet  consequent  on  unremitted  appli- 
cation ;  and  to  adjourn  the  consideration  of  any  thought  which 
may  please  us  vehemently  at  the  moment,  until  the  preposses- 
sion in  its  favor  has  subsided  with  the  animation  which  gave  it 
birth. 

The   two   Causes   of  premature  judgment  —  the   affections   of 

Impatience   and    Sloth  —  being    considered,   I 

3.  Hope  and  Fear.  . 

pass  on  to  the  third  principle  of  Passion,  by 
which  the  intellect  is  turned  aside  from  the  path  of  truth,  —  I 
mean  the  disturbing  influence  of  Hope  and  Fear.  These  passions, 
though  reciprocally  contrary,  determine  a  similar  effect  upon  the 
deliberations  of  the  Underetanding,  and  are  equally  unfavorable  for 
the  interest  of  truth.  In  forming  a  just  conclusion  upon  a  question 
of  probable  reasoning,  that  is,  where  the  grounds  of  decision  are 
not  few,  palpable,  and  of  determinate  effect,  —  and  such  questioi 


1  Crousaz,  Logique,  t.  iii.  part  ii.  oh.  7,  pt,         9  De  Ira,  L.  iii,  c.  7.    Quoted  by  Crou8a%j 
302.  —  Ed.  Logiqut,  t  iii.  p.  302.  —  Ed. 


Lkct.  XXIX.  LOGIC.  406 

may  be  said  to  be  those  alone  on  which  differences  of  opinion  may 
arise,  and  are,  consequently,  those  alone  which  require  for  their 
solution  any  high  degree  of  observation  and  ingenuity,  —  in  such 
questions  hope  and  fear  exert  a  very  strong  and  a  very  unfavorable 
influence.  In  these  questions  it  is  requisite,  in  the  first  place,  to 
seek  out  the  premises ;  and,  in  the  second,  to  draw  the  conclusion. 
Of  these  requisites  the  first  is  the  more  important,  and  it  is  also  by 
far  the  more  difficult. 

Now  the  passions  of  Hope  and  Fear  operate  severally  to  prevent 

the  intellect  from  discovering  all  the  elements 

How  Hope  and  Fear       of  decision,  which   ought  to  be  considered  in 

oj)erate    unfavorably       forming  a  coH'ect  Conclusion,  and  cause  it  to 

on    the    Understand-         .    i        •    .  ^^i  i  i-ii 

take  into  account  those  only  which  harmonize 
with  that  conclusion  to  w-hich  the  actuating 
passion  is  inclined.  And  here  the  passion  operates  in  two  ways. 
In  the  first  place,  it  tends  so  to  determine  the  associations  of 
thought,  that  only  those  media  of  proof  are  suggested  or  called 
into  consciousness,  which  support  the  conclusion  to  which  the 
passion  tends.  In  the  second  place,  if  the  media  of  proof  by 
which  a  counter  conclusion  is  supported  are  brought  before  the 
mind,  still  the  mind  is  influenced  by  the  passion  to  look  on  their 
reality  with  doubt,  and,  if  such  cannot  be  questioned,  to  undervalue 
their  inferential  importance;  whereas  it  is  moved  to  admit,  without 
hesitation,  those  media  of  proof  which  favor  the  conclusion  in  the 
interest  of  our  hope  or  fear,  and  to  exaggerate  the  cogency  with 
which  they  establish  this  result.  Either  passion  looks  exclusively 
to  a  single  end,  and  exclusively  to  the  means  by  which  that  single 
end  is  accomplished.  Thus  the  sanguine  temperament,  or  the 
mind  under  the  habitual  *  predominance  of  hope,  sees  only  and 
magnifies  all  that  militates  in  favor  of  the  wished-for  consum- 
mation, which  alone  it  contemplates ;  whereas  the  melancholic 
temperament,  or  the  mind  under  the  habitual  predominance  of 
fear,  is  wholly  occupied  with  the  dreaded  issue,  views  only  what 
tends  to  its  fulfilment,  while  it  exaggerates  the  possible  into  the 
probable,  the  probable  into  the  certain.  Thus  it  is  that  whatever 
conclusion  we  greatly  hope  or  greatly  fear,  to  that  conclusion  we 
are  disposed  to  leap ;  and  it  has  become  almost  proverbial,  that 
men  lightly  believe  both  what  they  wish,  and  what  they  dread,  to 
bo  true. 

But  the  influence  of  Hope  on  our  judgments,  inclining  us  to  find 
whatever  we  wish  to  find,  in  so  far  as  this  arises  from  the  illusion 
of  Self-love,  is  comprehended  in  this,  —  the  fourth  cause  of  Error, 
—  to  which  I  now  proceed. 


41f6  LOGIC.  Lect.  XXIX- 

Self-love,  under  which  I  include  the  dispositions  of  Vanity,  Pride, 
and,  in  general,  all  those  which   incline  us  to 

4.  Self-love.  ',  ,  •    i  .   .      .1 

attribute  an  undue  weight  to  those  opinions  in 
which  we  feel  a  personal  interest,  is  by  far  the  most  extensive  and 
influential  in  the  way  of  reason  and  truth.  In  virtue  of  this  princi- 
ple, whatever  is  ours  —  whatever  is  adopted  or  patronized  by  us, 
whatever  belongs  to  those  to  whom  we  are  attached  —  is  either 
gratuitously  clothed  with  a  character  of  truth,  or  its  pretensions  to 
be  accounted  true  are  not  scrutinized  with  the  requisite  rigor  and 
impartiality.  I  am  a  native  of  this  country,  and,  therefore,  not  only 
is  its  history  to  me  a  matter  of  peculiar  interest,  but  the  actions 
and  character  of  my  countrymen  are  viewed  in  a  very  difierent 
light  from  that  in  which  they  are  regarded  by  a  foreigner.  I  am 
born  and  bred  a  member  of  a  religious  sect,  and  because  they  con- 
stitute my  creed,  I  find  the  tenets  of  this  sect  alone  in  conformity 
to  the  Word  of  God.  I  am  the  partisan  of  a  philosophical  doc- 
trine, and  am,  therefore,  disposed  to  reject  whatever  does  not  har- 
monize with  my  adopted  system. 

It  is  the  part  of  a  philosopher,  says  Aristotle,  inasmuch  as  he  is  a 

philosopher,  to  subjugate  self-love,  and  to  refute, 
Aristotle, -his  pre-       -^  contrary  to  truth,  not  only  the  opinions  of 

his  friends,  but  the  doctrines  which  he  himself 
may  have  professed.*  It  is  certain,  however,  that  philosophera  — 
for  philosophers  are  men  —  have  been  too  often  found  to  regulate 
their  conduct  by  the  same  opposite  principle.     That  man  pretended 

to  the  name  of  philosopher,  who  scrupled  not  to 
Illustrations  of  the       declare  that  he  would  rather  be  in  the  wrong 

influence  of  Self-love  •  1      -r-^i  1  •         i  •    1  •  i      i  • 

on  our  opinions.  "^^^^  ^^^^^  ^^^"  1"   ^^^   light  With   his  Oppo- 

nents." "Gisbert  Vo^tius  urged  Mersennus  to 
refute  a  work  of  Descartes  a  year  before  the  book  appeared,  and 
before  he  had  himself  the  means  of  judging  whether  the  opinions  it 
contained  were  right  or  wrong.  A  certain  professor  of  philoso))hy 
in  Padua  came  to  Galileo,  and  requested  that  he  would  explain  to 
him  the  meaning  of  the  term  parallaxis  ;  which  he  wished,  he  said, 
to  refute,  having  heard  that  it  was  opposed  to  Aristotle's  doctrine 
touching  the  relative  situation  of  the  comets.  What!  answered 
Galileo,  you  wish  to  controvert  a  word  the  meaning  of  which  you 
do  not  know !  Redi  tells  us  that  a  sturdy  Peripatetic  of  his 
acquaintance  would  never  consent  to  look  at  the  heavens  through 
a  telescope,  lest  he  should  be  compelled  to  admit  the  existence  of 
the  new  stars  discovered  by  Galileo  and  othei-s.  The  same  Redi 
informs  us  that  he  knew  another  Peripatetic,  a  staunch  advocate  of 

1  JEM.  mc,  1. 4  (6).  —  Ed.  «  Cicero,  lV*t.  Qimbsi.,  i.  17. 


i 


Lect.  XXIX.  LOGIC.  407 

the  Aristotelian  doctrine  of  equivocal  generation  (a  doctrine,  by 
the  way,  which  now  again  divides  the  physiologists  of  Europe),  and 
who,  in  particular,  maintained  that  the  green  frogs  which  appear 
upon  a  shower  come  down  with  the  rain,  who  would  not  be 
induced  himself  to  select  and  examine  one. of  these  frogs.  And 
Avhy?  Because  he  was  unwilling  to  be  convicted  of  his  error,  by 
Redi  showing  him  the  green  matter  in  the  stomach,  and  its  feculae 
in  the  intestines  of  the  animal."  ^  The  spirit  of  the  Peripatetic 
philosophy  was,  however,  wholly  misunderstood  by  these  mistaken 
followers  of  Aristotle ;  for  a  true  Aristotelian  is  one  who  listens 
rather  to  the  voice  of  nature  than  to  the  precept  of  any  master, 
and  it  is  well  expressed  in  the  motto  of  the  great  French  anatomist, 
—  Riolanus  est  Peripateticus ;  credit  ea,  et  ea  tantum,  quae  vidit. 
From  the  same  principle  proceeds  the  abuse,  and  sometimes  even 
the  persecution,  which  the  discoverers  of  new  truths  encounter  from 
those  who  cherished  opinions  these  truths  subvert. 

In  like  manner,  as  we  are  disposed  to  maintain  our  own  opinion, 
we  are  inclined  to  regard  with  favor  the  opin- 

Self-love  leads  us  to         .  ^  '■ 

regard  with  favor  the  ^^"S  of  thosc  to  whom  we  are  attached  by  love, 
opinions  of  those  to  gratitude,  and  Other  conciliatory  affections.  "We 
xvhom  we  are  in  any       ^^  ^^^^  j^j^j^  q^.  attachment  to  the  pcrsous  of 

way  attached.  „  .        ,  ,  .  .  n     i 

our  iriends,  —  we  love  m  a  certam  sort  all  that 
belongs  to  them ;  and  as  men  generally  manifest  sufficient  ardor  in 
support  of  their  opinions,  we  are  led  insensibly  by  a  kind  of  sym- 
pathy to  credit,  to  approve,  and  to  defend  these  also,  and  that  even 
more  passionately  than  our  friends  themselves.  We  bear  affection 
to  others  for  various  reasons.  The  agreement  of  tempers,  of  incli- 
nations, of  pursuits ;  their  appearance,  their  manners,  their  virtue, 
the  partiality  which  they  have  shown  to  us,  the  services  we  have 
received  at  their  hands,  and  many  other  particular  causes,  determine 
and  direct  our  love. 

"It  is  observed  by  the  great  Malebranche,^  that  if  any  of  our 

friends,  —  any  even  of  those  we  are  disposed 
a  e  ranciie    a  -       ^^   love,  —  advance  an   opinion,  we   forthwith 

duced  to  this  effect.  .  ' 

lightly  allow  ourselves  to  be  persuaded  of  its 
truth.  This  opinion  we  accept  and  support,  without  troubling  our- 
selves to  inquire  whether  it  be  conformable  to  foct,  frequently  even 
against  our  conscience,  in  conformity  to  the  darkness  and  confusion 


1  Reimarus,  p.  389.    [Die  VernunftUhre,  von     published  in  1756.    The  above  four  anecdotes 
H.    S.    R.      (Hermann    Samuel    Reimarus),      are  all  taken  from  this  work.  —  Ed.] 
dritte  Auflage,  Hamburg,  1766,  §  332.     First         2  Recherche  dt  la  Verite,  L.  iv.  ch.  13.  —  Ed. 


408  LOGIC.  Lect.  XXnL 

of  our  intellect,  to  the  corruption  of  our  heart,  and  to  the  advan- 
tages which  we  hope  to  reap  from  our  facility  and  comphiisance."^ 

The  influence  of  this  principle  is  seen  still  more  manifestly  Avhen 
the   passion    changes ;    for   though   the   things 

rius  ghown   egpe-       themselves    remain    unaltered,    our  judgments 

ciallv    when   the  pas-  .  ,  ,  i         tt 

sion "  chauees  concernmg   them    are    totally   reversed.      How 

often  do  we  behold  persons  who  cannot,  or  will 

not,  recognize  a  single  good  quality  in  an  individual  from  the  mo- 

inent  he  has  chanced  to  incur  their  dislike,  and  who  are  even  ready 

to  adopt  opinions,  merely  because  opposed  to  others  maintained  by 

the   object  of  their  aversion?     The  celebrated 

Arnault!  iioids  that       Arnauld "  gocs  SO  far  even  as  to  assert,  that  men 

man  isnaturaJIv  euvi-  .  i  .      i  ,         .     .         .   , 

^^^  '  are  natui'ally  envious  and  jealous;  that  it  is  with 

pain  they  endure  the  contemplation  of  othera  in 
the  enjoyment  of  advantages  which  they  do  not  themselves  possess; 
and,  as  the  knowledge  of  truth  and  the  power  of  enlightening  man- 
kind is  of  one  of  these,  that  they  have  a  secret  inclination  to  de- 
prive them  of  that  glory.  This  accordingly  often  determines  them 
to  controvert  without  a  ground  the  opinions  and  discoveries  of 
others.  Sell-love  accordingly  often  argues  thus  :  —  '  This  is  au 
opinion  which  I  have  originated,  this  is  an  opinion,  therefore,  which 
is  true;'  whereas  the  natural  malignity  of  man  not  less  frequently 
suggests  such  another:  '  It  is  another  than  I  who  has  advanced  this 
doctrine ;  this  doctrine  is,  therefore,  false.' 

We  may  distinguish,  however,  from  malignant  or  envious  contra- 
diction  another  passion,    which,    though    more 
e  ove  o      ispu-       generous  in  its  nature  and  not  simply  a  mode  of 
Self-love,  tends,  nevertheless,  equally  to  divert 
ns  from  the  straight  road  of  truth,  —  I  mean  Pugnacity,  or  the  love 
of  Disputation.     Under  the  influence  of  this  passion,  we  propose 
as  our  end  victory,  not  truth.     We  insensibly  become  accustomed 
to  find  a  reason  for  any  opinion,  and,  in  placing  ourselves  above  all 
reasons,  to  surrender  our  belief  to  none.     Thus  it  is  why  two  dis- 
putants so  rarely  ever  agree,  and  why  a  question  is  seldotn  or  never 
decided  in  a  discussion,  where  the  combative  dispositions  of  the  rea- 
soners  have  once  been  roused  into  activity.     In  controversy  it  is 
always  easy  to  find  wherewithal  to  reply;  the  end  of  the  parties  is 
not  to  avoid  erroi",  but  to  impose  silence ;  and  they  are  less  ashamed 
of  continuing  wrong  than  of  confessing  that  they  are  not  right.'  •• 

1  Vtiro,IfouvtlU  Logiqut,  part  ii.,  ch.  viii.,  p.  3  V  Art  de  Ptntrr,  p.  iii.  ch.  20.    Cf.  CarCk 
288.  —  Ed.  NouveUe  Logiqut,  part  ii.,  ch.  9,  p.  811,  Pari* 

2  /,'  Art  de  Ptnser  {Port  Royal  Logic),  p.  iii.  1820.  —  Ed. 
efa.  20.  —  Ed. 


Lkct.  XXIX. 


LOGIC, 


409 


These  affections  the 
immediate  causes  of 
all   error. 

rieliminary  condi- 
tions requisite  for  tlie 
efficiency  of  precepts 
against  the  sources  of 
error. 


These  affections  may  be  said  to  be  the  immediate  causes  of  all 
error.  Other  causes  there  are,  but  not  immedi- 
ate. In  so  far  as  Logic  detects  the  sources  of 
our  false  judgments  and  shows  their  remedies, 
it  must  carefully  inculcate  that  no  precautionary 
precept  for  particular  cases  can  avail,  unless  the 
inmost  principle  of  the  evil  be  discovered,  and 
a  cure  applied.  You  must,  therefore,  as  you 
would  remain  free  from  the  hallucination  of 
fjilse  opinion,  be  convinced  of  the  absolute  necessity  of  following 
out  the  investigation  of  every  question  calmly  and  without  passion. 
You  must  learn  to  pursue,  and  to  estimate,  truth  without  distraction 
or  bias.  To  this  there  is  required,  as  a  primary  condition,  the  un- 
shackled freedom  of  thought,  the  equal  glance  which  can  take  in 
the  whole  sphere  of  observation,  the  cool  determination  to  pursue 
the  truth  whithersoever  it  may  lead  ;  and,  what  is  still  more  impor- 
tant, the  disposition  to  feel  an  interest  in  truth  and  in  truth  alone. 
If  perchance  some  collateral  interest  .may  first  prompt  us  to  the 
inquiry,  in  our  general  interest  fortnith  we  must  repress,  —  we  must 
forget,  this  interest,  until  the  inquiry  be  concluded.  Of  what 
account  are  the  most  venerated  opinions  if  they  be  untrue  ?  At 
best  they  are  only  venerable  delusions.  He  who  allows  himself  to 
be  actuated  in  his  scientific  procedure  by  any  partial  interest,  can 
never  obtain  a  comprehensive  survey  of  the  whole  he  has  to  take 
into  account,  and  always,  therefore,  remains  incapable  of  discrimi- 
nating, with  accuracy,  error  from  truth.  The  independent  thinker 
must,  in  all  his  inquiries,  subject  himself  to  the  genius  of  truth, — 
must  be  prepared  to  follow  her  footsteps  without  faltering  or  hesita- 
tion. In  the  consciousness  that  truth  is  the  noblest  of  ends,  and 
that  he  pursues  this  end  with  honesty  and  devotion,  he  will  dread 
no  consequences,  —  for  he  relies  upon  the  truth.  Does  he  compass 
the  truth,  he  congratulates  himself  upon  his  success  ;  does  he  fall 
short  of  its  attainment,  he  knows  that  even  his  present  failure  will 
ultimately  advance  him  to  the  reward  he  merits.  Err  he  may,  and 
that  perhaps  frequently,  but  he  will  never  deceive  himself  We 
cannot,  indeed,  rise  superior  to  our  limitary  nature,  we  cannot, 
therefore,  be  reproached  for  failure  ;  but  we  are  always  responsible 
for  the  calnjness  and  impartiality  of  our  researches,  and  these  alone 
render  us  worthy  of  success.  But  though  it  be  manifest,  that  to 
attain  the  truth  we  must  follow  whithersoever  the  truth  may  lead, 
still  men  in  general'  are  found  to  yield  not  an  absolute,  but  only  a 
restricted,  obedience  to  the  precept.  They  capitulate,  and  do  not 
unconditionally  surrender.     I  give  up,  but  my  cherished  dogma  in 

52 


410  LOGIC.  Lect.  XXIX. 

religion  must  not  be  canvassed,  says  one  ;  —  my  political  principles 
are  above  inquiry,  and  must  be  exempted,  says  a  second  ;  —  my 
country  is  the  land  of  lands,  this  cannot  be  disallowed,  cries  a  thii-d; 
—  my  order,  my  vocation,  is  undoubtedly  the  noblest,  exclaim  a 
fourth  and  fifth  ;  —  only  do  not  require  that  we  should  confess  our 
having  erred,  is  the  condition  which  many  insist  on  stipulating. 
Above  all,  that  resolve  of  mind  is  difficult,  which  is  ready  to  sur- 
render all  fond  convictions,  and  is  prepared  to  recommence  investi- 
gation the  moment  that  a  fundamental  error  in  the  foriner  system 
of  belief  has  been  detected.  These  are  the  principal  grounds  why, 
among  men,  opinion  is  so  widely  separated  from  opinion ;  and  why 
the  clearest  demonstration  is  so  frequently  for  a  season  frustrated 
of  victory. 

Par.  xcvi.    Holes  ^  XCVI.  Agaiust  the  Errors  which  arise 

against  Errors  from       from  the  Affcctions,  there  may  be  given 
the  Affections.  ^y^^  ^^^.^^  following  rulcs : 

1°.  When  the  error  ,has  arisen  from  the  influence  of  an 
active  affection,  the  decisive  judgment  is  to  be  annulled  ;  the 
mind  is  then  to  be  freed,  as  far  as  possible,  from  passion,  and 
the  process  of  inquiry  to  be  recommenced  as  soon  as  the  requi- 
site tranquillity  has  been  restored. 

2°.  When  the  error  has  arisen  from  a  relaxed  enthusiasm  for 
knowledge,  we  must  reanimate  this  interest  by  a  vivid  repre- 
sentation of  the  paramount  dignity  of  truth,  and  of  the  lofty 
destination  of  our  intellectual  nature. 

3°.  In  testing  the  accuracy  of  our  judgments,  we  must  be 
particularly  suspicious  of  those  results  which  accprd  with  our 
private  inclinations  and  predominant  tendencies. 

These  rules  require  no  comment. 


LECTURE    XXX, 

MODIFIED    STOICHEIOLOaY. 
SECTION  II.— ERROR— ITS  CAUSES  AND  REMEDIES. 

B.  — AS  IN  THE   COGNITIONS,  FEELINGS,  AND   DESIRES. 

II. —  WEAKNESS    AND    DISPROPORTIONED    STRENGTH    OF    THE 
FACULTIES   OF   KNOWLEDGE. 

I  NOW  go  on  to  the  Second  Head  of  the  class  of  Errors  founded 

on  the  Natural  Constitution,  the  Acquired  Hab- 

Weakness  and  Dis-       j^g^  ^j^d  the  Reciprocal  Relations  of  our  Cogni- 

propor  lone    treng         ^j^^  ^^^  AiFective  Powers,  that  is,  to  the  Causes 

of    the    Faculties    of  .... 

Knowledge.  of  Error  which  originate  in  the  Weakness  or 

Disproportioned  Strength  of  one  or  more  of 
our  Faculties  of  Knowledge  themselves. 

Here,  in  the  first  place,  I  might  consider  the  errors  which  have 

arisen  from  the  Limited  Nature  of  the  Human 

Neglect  of  the  Lim-       Intellect  in  general,  —  or  rather  from  the  mis- 

ited    Nature    of    the         ,-,  iiii  t.  ii-r-i  t_ 

^  ,  „   ,  takes  that  have  been  made  by  philosophers  m 

Human     Intellect     a  _  ^  ...  . 

source  of  error.  denying  or  not  taking  this  limited  nature  into 

account.^    The  illustration  of  this  subject  is  one 

which  is  relative  to,  and  supposes  an  acquaintance  with,  some  of 

the  abstrusest  speculations  in  Philosophy,  and  ■which  belong  not  to 

Logic,  but  to  Metaphysics,     I  shall  not,  therefore,  do  more  than 

simply  indicate  at  present,  what  it  will  be  proper  at  another  season 

fully  to  explain.      It   is   manifest,  that,  if  the 

.     losop  yo     e       human  mind  be  limited,  —  if  it  only  knows  as 

Absolute.  ... 

it  is  conscious,  and  if  it  be  only  conscious,  as  it 
is  conscious  of  contrast  and  opposition,  —  of  an  ego  and  non-ego, — 
if  this  supposition,  I  say,  be  correct,  it  is  evident  that  those  philoso- 
phers are  in  error,  who  virtually  assume  that  the  human  mind  is 

1  [On  this  subject  see  Crusjus.]     [Christian      verldssigkeit  der  menschlichen  Erkenntniss,  $  443, 
August  Crusius,  Weg  zur  Gewissheit  und  Zu-     1st  ed.  1747.  —  Ed- 


412  LOGIC.  Lect.  XXX. 

unlimited,  that  is,  that  the  human  mind  is  capable  of  a  knowledge 
superior  to  consciousness,  —  a  cognition  in  which  knowledge  and 
existence  —  the  Ego  and  non-Ego  —  God  and  the  creature  —  are 
identical ;  that  is,  of  an  act  in  which  the  mind  is  the  Absolute,  and 
knows  the  Absolute.  This  philosophy,  the  statement  of  which,  as 
here  given,  it  would  require  a  long  commentary  to  make  you  under- 
stand, is  one  which  has  for  many  years  been  that  dominant  in  Ger- 
many ;  it  is  called  the  Philosophy  of  the  Absolute,  or  the  Philoso- 
phy of  Absolute  Identity.  This  system,  of  which  Schelling  and 
Hegel  are  the  great  representatives,  errs  by  denying  the  limitation 
of  human  intelligence  without  proof,  and  by  boldly  building  its 
edifice  on  this  gratuitous  negation.^ 

But  there  are  other  forms  of  philosophy  which  err  not  in  actually 

postulating  the  infinity  of  mind,  but  in  taking 

2.  A  one-sided  view       ^^-^^  j^  one-sided  view  of  its  finitude.     It  is  a 

of    the    finitude     of  i     /.     ,  i  •   i  ^  ^ 

^^^^  general   tact,  which    seems,   however,   to   have 

escaped   the  observation   of  philosophers,  that 

whatever  we  can  positively  compass  in  thought,  —  whatever  we  can 

conceive  as  possible,  —  in  a  word,  the  omne  cogitabile,  lies  between 

two  extremes  or  poles,  contradictorily  opposed,  and  one  of  which 

must  consequently  be  true,  but  of  neither  of  which  repugnant  oppo- 

sites  are  we  able  to  represent  to  our  mind  the  possibility .'^    To  take 

one  example  out  of  many :  we  cannot  construe 

iiiurtrfttcd  by  refer.      ^^  ^^^  ^.^^  ^^  possiblc  the  absolutc  commcncc- 

ence  to  the  two  con-  «      •  i 

tradictorie8,-theab-  "^^nt  of  time;  but  wc  are  equally  unable  to 
solute  commencement,  think  the  possibility  of  the  counter  alternative, 
and  the  iniinite  nou-       —  jjg  infinite  or  absolute  non-commencement,  in 

commenceme&t        of  .,  t      .^        •    t*    •,  f  .•  -v-r 

.pjjj^^  other  words,  the  mnmte  regress  of  time.     Now 

it  is  evident,  that,  if  we  looked  merely  at  the 
one  of  these  contradictory  opposites  and  argued  thus :  whatever  is 
inconceivable  is  impossible,  the  absolute  commencement  of  time  is 
inconceivable,  therefore  the  absolute  commencement  of  time  is 
impossible;  but,  on  the  principles  of  Contradiction  and  Excluded 
Middle,  one  or  other  of  the  two  opposite  contradictories  must  be 
true  ;  therefore,  as  the  absolute  commencement  of  time  is  impossi- 
ble, the  absolute  or  infinite  non-commencement  of  time  is  neces- 
t?ary:  —  I  say,  it  is  evident  that  this  reasoning  would  be  incompe- 
tent and  one-sided,  because  it  might  be  converted ;  for,  by  the  same 
one-sided  process,  the  opposite  conclusion  might  be  drawn  in  favor 
of  the  absolute  commencement  of  time. 


1  See  Discussions^  p.  19.  —  Ed. 

3  See  Discussions,  p.  601  et  seq.,  Lectures  on  Metapkysies,  p.  S27  et  uq.  —  Ex>. 


Lkct.  XXX.  LOGIC.  413 

Now,  the  unilateral  and  incompetent  reasoning  which  I  have  here 

supposed  in  the  case  of  time,  is  one  of  which 

^  ,^^™^  pnncip  e       ^^^  Necessitarian  is  guilty  in  his  arfjument  to 

exemplified  in  the  case  ^  ...  .  . 

of  the  Necessitarian  prove  the  impossibility  of  human  volltions  being 
Argument  against  the  free.  He  correctly  lays  down,  as  the  foundation 
Freedom  of  the  Hu-  ^£  j^j^  reasoning,  two  propositions  which  must 
at  once  be  allowed :  1°,  That  the  notion  of  the 
liberty  of  volition  involves  the  supposition  of  an  absolute  com- 
mencement of  volition,  that  is,  of  a  volition  which  is  a  cause,  but  is 
not  itself,  qua  cause,  an  effect.  2°,  That  the  absolute  commence- 
ment of  a  volition,  or  of  aught  else,  cannot  be  conceived,  that  is, 
cannot  be  directly  or  positively  thought  as  possible.  So  far  he  is 
correct ;  but  when  he  goes  on  to  apply  these  principles  by  arguing 
(and  be  it  observed  this  syllogism  lies  at  the  root  of  all  the  reason- 
ings for  necessity).  Whatever  is  inconceivable  is  impossible  ;  but  the 
supposition  of  the  absolute  commencement  of  volition  is  inconceiva- 
ble,'  therefore^  the  sxipp)osition  of  the  absolute  commencement  of 
volition  {the  condition  of  free  will)  is  impossible,  —  we  may  here 
demur  to  the  sumption,  and  ask  him,  —  Can  he  positively  conceive 
the  opposite  contradictory  of  the  absolute  commencement,  that  is, 
an  infinite  series  of  relative  non-commencements?  If  he  answers, 
as  he  must,  that  he  cannot,  we  may  again  ask  him,  —  By  what  right 
he  assumed  as  a  self-evident  axiom  for  his  sumption,  the  proposition, 
—  that  lohatever  is  inconceivable  is  im.possible,  or  by  Avhat  right  he 
could  subsume  his  minor  premise,  when  by  his  own  confession  he 
allows  that  the  opposite  contradictory  of  his  minor  premise,  that  is, 
the  very  proposition  he  is  apagogically  proving,  is,  likewise,  incon- 
ceivable, and,  therefore,  on  the  principle  of  his  sumption,  likewise 
impossible. 

The  same  inconsequence  would  equally  apply  to  the  Libertarian, 

who  should  attempt  to  prove  that  free-will  must 

And  in  the  case  of      be  allowed,  ou  the  ground  that  its  contradictory 

the  Libertarian  Arcu-  'j.       •       •  -i  i        i  •  •       i  i 

^    .     ,  ,  ,„     „       opposite   IS   impossible,    because    inconceivable. 

ment    in    behalf    of  ^  ^  .  . 

Free-will.  He  cannot  prove  his  thesis  by  such  a  process; 

in  fact,  by  all  speculative  reasoning  from  the 
conditions  of  thought,  the  two  doctrines  are  in  mqiiilibrio ;  —  both 
are  equally  possible,  —  both  are  equally  inconceivable.  It  is  only 
when  the  Libertarian  descends  to  arguments  drawn  from  the  fact 
of  the  Moral  Law  and  its  conditions,  that  he  is  able  to  throw  in 
reasons  which  incline  the  balance  in  his  favor. 

On  these  matters,  I  however,  at  present,  only  touch,  in  order  to 
show  you  under  what  head  of  Error  these  reasonings  would  natu 
rally  fall. 


414 


LOGIC. 


Lect.  XXX 


Weakness  or  di?pro- 
portioned  strength  of 
the  several  Cognitive 
Faculties,  —  a  source 
of  Error. 

Cognitive  Faculties 
of  two  classes,  a  Lower 
and  a  Higher. 


Leaving,  therefore,  or  adjourning,  the  consideration  of  the  imbe- 
cility of  the  human  intellect  in  general,  I  shall 
now  take  into  view,  as  a  source  of  logical  error, 
the  Weakness  or  Disproportioned  Strength  of 
the  several  Cognitive  Faculties.  Now,  as  the 
Cognitive  Faculties  in  man  consist  partly  of 
certain  Lower  Powers,  which  he  possesses  in 
common  Avith  other  sensible  existences,  namely, 
the  Presentative,  the  Retentive,  the  Representa- 
tive and  the  Reproductive  Faculties,  and  partly  of  certain  Higher 
Powers,  in  virtue  of  which  he  enters  into  the  rank  of  intelligent 
existences,  namely,  the  Elaborative  and  Regulative  Faculties,  —  it 
will  be  proper  to  consider  the  powers  of  these  two  classes  severally 
in  succession,  in  so  far  as  they  may  afford  the  causes  or  occasions 
of  error. 

Of  the  lower  class,  the  first  faculty  in  order  is  the  Presentative 
or  Acquisitive  Faculty.  This,  as  you  remember, 
is  divided  into  two,  viz.,  into  the  faculty  which 
presents  us  with  the  phenomena  of  the  outer 
world,  and  into  the  foculty  which  presents  us 
with  the  phenomena  of  the  inner.^  The  former  is  External  Per- 
ception, or  External  Sense ;  the  latter  is  Self-consciousness,  Inter- 
nal Perception,  or  Internal  Sense.  I  commence,  therefore,  with  the 
Faculty  of  Extenial  Perception,  in  relation  to  which  I  give  you  the 
following  paragraph. 


L  The  Lower  Class, 
—  1.  The  Presentative 
Faculty. 


1   XCVII.   When  aught  is  presented   through  the  outer 

senses,  there  are  two  conditions  necessary 

Par.  xcvn.  (a)  Ex-       f^j.  j^g  j^dequatc  perception  :  —  1%  The  rela- 

temal    Perception,  —  ^  n  i  i 

a8  a  source  of  Error.  tivc  OrgQus  must  be  prcscut,  and  in  a  con- 
dition to  discharge  their  functions ;  and  2°, 
The  Objects  themselves  must  bear  a  certain  relation  to  these 
organs,  so  that  the  latter  shall  be  suitably  affected,  and  thereby 
the  former  suitably  apprehended.  It  is  possible,  therefore, 
that,  partly  through  the  altered  condition  of  the  organs,  partly 
through  the  altered  situation  of  the  objects,  dissimilar  pre- 
sentations of  the  same,  and  similar  presentations  of  different, 
objects,  may  be  the  result.* 

"In  the  jBrst  place,  without  the  organs  specially  subservient  to 


1  See  Lectures  on  MetapAysi'cs,p.  282  et  seq. — Ed.      Kouvelle  Logique,  part  ii.  ch.  rl.  p.  278.    Bacb 
*  Krug,  Logik,  i    1.  83.  —  Ed.     [Cf.  Caro,     mann,  Logik,  i  407,  p.  668.1 


Lect.  XXX.  LOGIC.  415 

External  Pei'ception,  —  without  the  eye,  the  ear,  etc.,  sensible  per- 
ceptions of  a  precise  and  determinate  character, 
Explication.  Ruch,  for  example,  as  color  or  sound,  are  not 

Conditions   of   the  ^       .    .  r      xi  i      i  x 

^.  .^      „      competent  to  man.     In  the  second  place,  to  per- 

adequate    activity    of  ^  . 

External  Perception.        form  their  functions,  these  organs  must  be  in 
a  healthy  or  normal  state;  for  if  this  condition 
be  not  fulfilled,  the  presentations  which  they  furnish  are  null,  incom- 
plete, or  false.     But,  in  the  third  place,  even  if  the  organs  of  sense 
are  sound  and  perfect,  the  objects  to  be  presented  and  perceived 
must  stand  to  these  organs  in  a  certain  relation,  —  must  bear  to 
them  a  certain  proportion;  for,  otherwise,  the  objects  cannot  be  pre- 
sented at  all,  or  cannot  be  perceived  without  illusion.     The  sounds, 
for  example,  which  we  are  to  hear,  must  neither  be  too  high  nor  too 
low  in  quality ;  the  bodies  which  we  are  to  see,  must  neither  be  too 
near  nor  too  distant,  —  must  neither  be  too  fee- 
0K81  e  1  usjons  o        ^^j     ^^j.  ^^^  intensely  illuminated.     In  relation 

the  Senses.  ''  .   •     , 

to  the  second  condition,  there  are  given,  in  con- 
sequence of  the  altered  state  of  the  organs,  on  the  one  hand,  differ- 
ent presentations  of  the  same  object;  —  thus  to  a  person  who  has 
waxed  purblind,  his  friend  appears  as  an  utter  stranger,  the  eye 
now  presenting  its  objects  with  less  clearness  and  distinctness.  On 
the  other  hand,  there  are  given  the  same,  or  undistinguishably  simi> 
lar,  presentations  of  different  objects;  —  thus  to  a  person  in  the 
jaundice,  all  things  are  presented  yellow.  In  relation  to  the  third 
condition,  from  the  altered  position  of  objects,  there  are,  in  like 
manner,  determined,  on  the  one  hand,  different  presentations  of  the 
same  objects,  —  as  when  the  stick  which  appears  straight  in  the  air 
appears  crooked  ^h en  partially  immersed  in  water;  and,  on  the 
other  hand,  identical  presentations  of  different  objects,  as  when  sx 
man  and  a  horse  appear  in  the  distance  to  be  so  similar,  that  thb 
one  cannot  be  discriminated  from  the  othex\  In  all  these  cases, 
these  illusions  are  determined,  —  illusions  which  may  easily  become 
the  occasions  of  false  judgments."^ 

"In  regard  to  the  detection  of  such  illusions  and  obviating  the 

error  to  which  they  lead,  it  behooves  us  to  take 

Precautions  with    a  i         /-  n        •  ,•  -»tt  ^      •       ^l 

,    ^,     .  »   ,.  the  followmg  precautions.      We  must,  m  the 

view  to  the  detection  =>    ^  ' 

of  illusions  of  the  fii'st  placc,  examine  the  state  of  the  organ.  If 
Senses,  and  obviating  found  defective,  wc  must  endcavor  to  restore  it 
the  errors  to  which       ^^  perfection ;  but  if  this  cannot  be  done,  we 

they  lead.  ^  /  r      -u 

must  ascertain  the  extent  and  nature  of  tna 
evil,  in  order  to  be  upon  our  guard  in  regard  to  quality  and  degree 
of  the  false  presentation. 

1  Krug,  Logik,  i  138.    Anm.  —  £•». 


416  LOGIC.  Lect.  XXX 

"  In  the  second  place,  we  must  examine  the  relative  situation  of 
the  object,  and  if  this  be  not  accommodated  to  the  organ,  we  must 
either  obviate  the  disproportion  and  remove  the  media  which  occa- 
sion the  illusion,  or  repeat  the  observation  under  different  circum- 
stances, compare  these,  and  thus  obtain  the  means  of  making  an 
ideal  abstraction  of  the  disturbing  causes."  * 

In  regard  to  the  other  Presentative  Faculty,  —  the  Faculty  of 
Self-consciousness,  —  Internal  Perception,  or  Internal  Sense,  as  we 
know  less  of  the  material  conditions  whicli  modify  its  action,  we 
are  unable  to  ascertain  so  precisely  the  nature  of  the  illusions  of 
which  it  may  be  the  source.  In  reference  to  this  subject  you  may 
take  the  following  paragraph. 

%  XCVIII.   The  faculty  of  Self-consciousness,  or  Internal 

Sense,  is  subject  to  various  changes,  which 

Par.  xcnn.    (b)       either  modify  our  apprehensions  of  objects, 

Self-oonsoiousness,  —  ._  ,  .,.,  ., 

aa  a  source  of  Error.         <>>"  uiflucnce  the  manner  HI  which  we  judge 
concerning  them.     In  so  far,  therefore,  as 
felse  judgments   are  thus  occasioned.  Self-consciousness   is   a 
source  of  error.* 

It  is  a  matter  of  ordinary  observation,  that  the  vivacity  with 

which  we  are  conscious  of  the  various  phenom- 

Expiication.  ^^^  ^f  p^j^d,  differs  not  only  at  different  times, 

Sclf-coiisciousncss 

varies  in  intensity.  ^"  different  States  of  health,  and  in  different  de- 

grees of  mental  freshness  and  exhaustion,  but,  at 
the  same  time,  differs  in  regard  to  the  different  kinds  of  these  phe- 
nomena themselves.  According  to  the  greater  (^"  less  intensity  of 
this  faculty,  the  same  thoughts  of  which  we  are  conscious  are,  at 
one  time,  clear  and  distinct,  at  another,  obscure  and  confused.  At 
one  time  we  are  almost  wholly  incapable  of  reflection,  and  every 
act  of  self-attention  is  forced  and  irksome,  and  differences  the  most 
marked  pass  unnoticed  ;  while,  at  another,  our  self-consciousness  is 
alert,  all  its  applications  pleasing,  and  the  most  faint  and  fugitive 
phenomena  arrested  and  observed.  On  one  occasion,  self-conscious- 
ness, as  a  reflective  cognition,  is  strong ;  on  another,  all  reflection  is 
extinguished  in  the  intensity  of  the  direct  consciousness  of  feeling 
or  desire.  In  one  state  of  mind  our  representations  are  feeble  ;  in 
another,  they  are  so  lively  that  they  are  mistaken  for  external  reali- 
ties. Our  self-consciousness  may  thus  be  the  occasion  of  frequent 
error ;  for,  according  to  its  various  modifications,  we  may  form  the 
most  opposite  judgments  concerning  the  same  things,  —  pronouno- 

1  Krug,  Losik,  j  166.  —  Ed.  «  Knig,  Logik,  J 139.  —  Ed. 


Lect.  XXX.  LOGIC.  417 

ing  them,  for  example,  now  to  be  agreeable,  now  to  be  disagreeable, 
according  as  our  Internal  Sense  is  variously  affected. 

The  next  is  the  Retentive  or  Conservative  Faculty,  —  Memory 
Btrictly  so  called  ;  in  reference  to  which  I  give  you  the  following 
paragraph. 

%   XCIX.    Memory,  or  the   Conservative   Faculty,   is   the 

occasion  of  Error,  both  when  too  weak  and 

Par.  XCIX.  2.  Mem-       whcu    too   stroug.      Whcu    too  wcak,  the 

ory,  —  as  a  soupae  of  ,  ,        „  ,   .  i  •    i      • ,  .    • 

j,j,ygp  complement  oi  cognitions  which  it  retains 

is  small  and  indistinct,  and  the  Under- 
standing or  Elaborative  Faculty  is,  consequently,  unable  ade- 
quately to  judge  concerning  the  similarity  and  differences 
of  its  repi'csentations  and  concepts.  When  too  strong,  the 
Understanding  is  overwhelmed  with  the  multitude  of  acquired 
cognitions  simultaneously  forced  upon  it,  so  that  it  is  unable 
calmly  and  deliberately  to  compare  and  discriminate  these.' 

That  both  these  extremes, —  that  both  tlie  insufficient  and  the 
supei-fluous  vigor  of  the   Conservative  Faculty 

Explication.  ,,         ,  /.  .  .„ 

are  severally  the  sources  or  error,  it  will  not 
require  many  observations  to  make  apparent. 

In  regard  to  a  feeble  memory,  it  is  manifest  that  a  multitude  of 
false  judgments  must  inevitably  arise  from  an 

Feeble  memory.  .  ..,.„,  ,         , 

incapacity  in  this  faculty  to  preserve  the  obser- 
vations committed  to  its  keeping.  In  consequence  of  this  incapac- 
ity, if  a  cognition  be  not  wholly  lost,  it  is  lost  at  least  in  part,  and 
the  circumstances  of  time,  place,  persons  and  things  confounded 
with  each  other.  For  example,  —  I  may  recollect  the  tenor  of  a 
passage  I  have  read,  but  from  defect  of  memory  may  attribute  to- 
one  author  what  really  belongs  to  another.  Thus  a  botanist  may 
judge  two  different  plants  to  be  identical  in  species,  having  for- 
gotten the  differential  characters  by  which  they  were  discriminated  ;. 
or  he  may  hold  the  same  plant  to  be  two  different  species,  having 
examined  it  at  different  times  and  places.- 

Though  nothing  could   be  more  erroneous  than  a  general  and 
unqualified    decision,  that   a   great   memory   is- 

Strong  memory.  .      ^  -,     .     ^  ■ 

incompatible  with  a  sound  judgment,  yet  it 
is  an  observation  confirmed  by  the  experience  of  all  ages  and  coun- 
tries, not  only  that  a  great  memory  is  no  condition  of  high  intellect- 
ual talent,  but  that  great  memories  are  very  frequently  found  in  com- 

1  [Cf.  Bacbmann,  Logik,  i  408.]  3  Krng,  Logik,  i  141.    Anm.  —  Ed, 

53 


418 


LOGIC. 


Lect.  XXX. 


bination  with  comparatively  feeble  powers  of  thought.^  The  truth 
seems  to  be,  that  where  a  vigorous  memory  is  conjoined  with  a 
vigorous  intellect,  not  only  does  the  force  of  the  subsidiary  faculty 
not  detract  from  the  strength  of  the  principal,  but,  on  the  contrary, 
tends  to  confer  on  it  a  still  higher  power;  whereas  when  the  infe- 
rior faculty  is  disproportionately  strong,  that  so'  far  from  nourishing 
and  corroborating  the  superior,  it  tends  to  reduce  this  faculty  to  a 
lower  level  than  that  at  which  it  would  have  stood,  if  united  with 
a  less  overpowering  subsidiary.  The  greater  the  magazine  of  vari- 
ous knowledge  which  the  memory  contains,  the  better  for  the  un- 
derstanding, provided  the  understanding  can  reduce  this  various 
knowledge  to  order  and  subjection.  "A  great  memory  is  the  prin- 
cipal condition  of  bringing  before  the  mind  many  different  repre- 
sentations and  notions  at  once,  or  in  rapid  succession.  This  simul- 
taneous or  nearly  simultaneous  presence  disturbs,  however,  the 
tranquil  comparison  of  a  small  number  of  ideas,  which,  if  it  shall 
judge  aright,  the  intellect  must  contemplate  with  a  fixed  and  steady 
attention."^  Now,  where  an  intellect  possesses  the  power  of  concen- 
tration in  a  high  degree,  it  will  not  be  harassed  in  its  meditations 
by  the  officious  intrusions  of  the  subordinate  faculties,  however  vig- 
orous these  in  themselves  may  be,  but  will  control  their  vigor  by  ex- 
hausting in  its  own  operations  the  whole  applicable  energy  of  mind,  'j 
Whereas  where  the  inferior  is  more  vigorous  than  the  superior,  it  will, 
in  like  manner,  engross  in  its  own  function  the  disposable  amount  of 
activity,  and  overwhelm  the  principal  faculty  with  materials,  many 
even  in  proportion  as  it  is  able  to  elaborate  few.  This  appears  to  me 
the  reason  why  men  of  strong  memories  are  so  often  men  of  propor- 
tionally weak  judgments,  and  why  so  many  errors  arise  from  the 
possession  of  a  faculty,  the  perfection  of  which  ought  to  exempt] 
them  from  many  mistaken  judgments. 

As  to  the  remedy  for  these  opposite  extremes.  The  former  — 
the  imbecility  of  Memory  —  can  only  be  allevi- 
ated by  invigorating  the  capacity  of  Retention  | 
through  mnemonic  exercises  and  methods ;  the 
latter,  —  the  inordinate  vigor  of  Memory,  —  by  cultivating  the 
Understanding  to  the  neglect  of  the  Conservative  Faculty.  It 
will,  likewise,  be  necessary  to  be  upon  our  guard  against  the  errors 
originating  in  these  counter  sources.  In  the  one  case  distrusting 
the  accuracy  of  facts,  in  the  other,  the  accuracy  of  their  elaboration.*  j 
The  next  faculty  is  the  Reproductive.     This,  when  its  operation 


Remedies  for  these 
opposite  extremes. 


1  Compare  Lecturet  on  Metaphysics,  p.  424.  —     quoted  by  Stewart,  Mem.,  Part  iii.  ch.  i.  sect 
Ed  vi.     ColUeted  Works,  vol.  iv.p.249i 

2  Diderot.  Ltttrt  nr  **s  Sourds  tt   Muets,        »  C(.  Krug,  Loeik,  ^  16&    Anm.  —  Eix 


Lkct.  XXX.  I.GGIC.  '  419 

is  voluntarily  exerted,  is  called  Recollection  ov  Jteminiscence ;  when 

it  energizes  spontaneously  or  without  volition,  it 

3.  The  Reproductive       j^  ^.^jj^^^  Suoqestion.     The  laws  by  which  it  is 

Faculty.  ,    .  .  ,  ,  .    ,,       .         , 

governed  in  either  case,  but  especially  in  the 
latter,  are  called  the  Laws  of  Mental  Association.  This  Repro- 
ductive Faculty,  like  the  Retentive,  is  the  cause  of  error,  both  if  its 
vigor  be  defective,  or  if  it  be  too  strong.  I  sliall  consider  Recollec- 
tion and  Suggestion  severally  and  apart.  In  regard  to  the  former  I 
give  you  the  following  paragraph, 

^  C.   The  Reproductive  Faculty,  in  so  far  as  it  is  volunta- 
rily exercised,  as  Reminiscence,  becomes  a 
par.c.  (a)Reminis.       soUTCc  of  EiToi',  as  it  is  either  too  slug- 

cence,  —  as  a  source  of  .  .      ,  ^  i  t-> 

jjrror.  g^^"  or  too  pi'onipt,  precisely  as  the  Re- 

tentive   Faculty,  combined  with  which   it 
constitutes  Memory  in  the  looser  signification. 

It  is  necessary  to  say  very  little  in  special  reference  to  Reminis- 
cence, for  what  was  said  in  regard  to  the  Con- 
Explication.  servative    Faculty   or    Memory   Proper   in   its 

Reminiscence,  —  its         •,  •    ^       .        •  tiix  :i     •        r     ^ 

undue  activity.  highest  vigor,  was  applicable   to,  and   in   fact 

supposed  a  corresponding  degree  of,  the  Re- 
productive. For,  however  great  may  be  the  mass  of  cognitions 
retained  in  the  mind,  that  is,  out  of  consciousness  but  potentially 
capable  of  being  called  into  consciousness,  these  can  never  of  them- 
selves oppress  the  Understanding  by  their  simultaneous  crowding 
or  rapid  succession,  if  the  faculty  by  which  they  are  revoked  into 
consciousness  be  inert ;  whereas  if  this  revocative  faculty  be  com- 
paratively alert  and  vigorous,  a  smaller  magazine  of  retained  cogni- 
tions may  suffice  to  harass  the  intellect  with  a  ceaseless  supply  of 
materials  too  j^rofuse  for  its  capacity  of  elaboration. 

On  the  other  hand,  the  inactivity  of  our  Recollection  is  a  source 
of  error,  precisely  as  the  weakness  of  our  Mem- 
ory proper ;  for  it  is  of  the  same  effect  in  rela- 
tion to  our  judgments,  whether  the  cognitions  requisite  for  a  deci- 
sion be  not  retained  in  the  mind,  or  whether,  being  retained,  they 
are  not  recalled  into  consciousness  by  Reminiscence. 

In  regard  to  Suggestion,  or  the  Reproductive  Faculty  operating 
spontaneously,  that  is,  not  in  subservience  to  an  act  of  Will,  —  I 
shall  give  you  the  following  paragraph. 

%    CI.   As  our  Cognitions,  Feelings,  and  Desires  are  con- 
nected together  by  what  are  called  the  Laws  of  Association, 


420  ^  LOGIC.  Lect.  XXX 

and  as  each  link  in  the  chain  of  thought  suggests  or  awakens 

into  consciousness  some  other  in  conformity 

Par.  CI.  (b)  sugges-       ^q  thcse  Laws,  —  thesc  Laws,  as  they  be- 

tion,— as  a  source  of  ... 

Error.  stow   a    Strong    subjective    connection    on 

thoughts  and  objects  of  a  wholly  arbitraFy 

union,  frequently  occasion  great  confusion   and  error  in  our 

judgments. 

* 

"  Even    in   methodical    thinking,   we   do   not   connect   all   onr 
thoughts  intentionally  and  rationally,  but  many 

Explication.  °  \  .  .,.  "^ 

press  forward  into  the  tram,  either  m  conse- 
quence of  some  external  impression,  or  in  virtue  of  certain  internal 
relations,  which,  however,  are  not  of  a  logical  dependency.  Thus, 
thoughts  tend  to  suggest  each  other,  which  have  reference  to  things 
of  which  we  were  previously  cognizant  as  coexistent,  or  as  immedi- 
ately consequent,  which  have  been  apprehended  as  bearing  a  resem- 
blance to  each  other,  or  which  have  stood  together  in  reciprocal 
and  striking  contrast.  This  connection,  though  precaiious  and 
non-logical,  is  thus,  however,  governed  by  certain  laws,  which  have 
been  called  the  Laws  of  Association^  *  These  laws,  which  I  have 
just  enumerated,  viz.,  the  Law  of  Coexistence  or  Simultaneity,  the 
Law  of  Continuity  or  Immediate  Succession,  the  Law  of  Similarity, 
and  the  Law  of  Contrast,  are  all  only  special  modifications  of  one 
general  law,  which  I  would  call  the  Law  of  Redintegration ;^  that 
is,  the  principle  according  to  which  whatever  has  previously  formed 
a  part  of  one  total  act  of  consciousness,  tends,  when  itself  recalled 
into  consciousness,  to  reproduce  along  with  it  the  other  parts  of 
that  original  whole.  But  though  these  tendencies  be  denominated 
Imos^  the  influence  which  they  exert,  though  often  strong  and  somo- 
times  irresistible,  is  only  contingent ;  for  it  frequently  happens  that 
thoughts  which  have  previously  stood  to  each  other  in  one  or  other 
of  the  four  relations  do  not  suggest  each  other.  The  Laws  of 
Association  stand,  therefore,  on  a  very  different  footing  from  the 
laws  of  logical  connection.  But  those  Laws  of  Association,  contin- 
gent though  they  be,  exert  a  great  and  often  a  very  pernicious 
influence  upon  thought,  inasmuch  as  by  the  involuntary  intrusion 
of  representations  into  the  mental  chain  which  are  wholly  irrele- 
vant to  the  matter  in  hand,  there  arises  a  perplexed  and  redundant 
tissue  of  thought,  into  which  false  characters  niny  easily  find  admis- 
sion, and  in  which  true  characters  may  easily  be  overlooked.'    But 


t  Krng,   Logik,  f  144.     Anra.  —  Ed.  >  See  Lect.  on  Metaphysics,  p.  481  cl  leq.  —  Kd- 

3  Krug,  Logik,  i  144.    Anm.  —  £i>. 


I 


LkgT.  XXX  LOGIC.  421 

this  is  not  all.  For,  by  being  once  blended  together  in  our  con- 
seiousness,  things  really  distinct  in  their  nature  tend  again  naturally 
to  reassooiate,  and,  at  every  repetition  of  this  conjunction,  this  ten- 
dency is  fortified,  and  their  mutual  suggestion  rendered  more  cer- 
tain and  irresistible. 

It  is  in  virtue  of  this  principle  of  Association  and  Custom,  that 
things  are  clothed  by  us  with  the  precarious  attri- 

inflnence  of  Asso        butcs  of  deformity  or  beauty ;  and  some  philos- 

eiatioD  in  matters  of  ,  ,  />  '  •         •        i     , 

-.  ophers  have  gone  so  far  as  to  mamtain  that  our 

principles  of  Taste  are  exclusively  dependent 
on  the  accidents  of  Association.  But  if  this  be  an  exaggeration,  it 
is  impossible  to  deny  that  Association  enjoys  an  extensive  jurisdic- 
tion in  the  empire  of  taste,  and,  in  particular,  that  fashion  is  almost 
wholly  subject  to  its  control.  . 

On  this  subject  I  may  quote  a  few  sentences  from  the  first  volume 
of  Mr.  Stewart's  Elements.      "In   matters   of 

Stewart  quoted.  i  /*.  .  •   i  .  t 

laste,  the  effects  which  we  consider  are  pro- 
duced on  the  mind  itself^  and  are  accompanied  either  with  pleasure 
or  with  pain.  Hence  the  tendency  to  casual  association  is  much 
stronger  than  it  commonly  is  with,  respect  to  physical  events  ;  and 
when  such  associations  are  once  formed,  as  they  do  not  lead  to  any 
important  inconvenience,  similar  to  those  which  result  from  phys- 
ical mistakes,  they  are  not  so  likely  to  be  corrected  by  mere  experi- 
ence, unassisted  by  study.  To  this  it  is  owing  that  the  influence 
of  association  on  our  judgments  concerning  beauty  and  deformity, 
is  still  more  remarkable  than  on  our  speculative  conclusions;  a  cir- 
cumstance which  has  led  some  philosophers  to  suppose  that  associa- 
tion is  sufficient  to  account  for  the  origin  of  these  notions,  and  that 
there  is  no  such  thing  as  a  standard  of  taste,  founded  on  the  princi- 
ples of  the  human  constitution.  But  this  is  undoubtedly  pushing 
the  theory  Ji  great  deal  too  far.  The  association  of  ideas  can  never 
account  for  the  origin  of  a  wo^^  notion,  or  of  a  pleasure  essentially 
<lifferent  from  all  the  others  which  we  know.  It  may,  indeed, 
enable  us  to  conceive  how  a  thing  indifferent  in  itself  may  become 
a  source  of  pleasure,  by  being  connected  in  the  mind  with  some-. 
thing  else  which  is  naturally  agreeable ;  but  it  presupposes,  ift 
every  instance,  the  existence  of  those  notions  and  those  feelings 
which  it  is  its  province  to  combine  ;  insomuch  that,  I  apprehend,  it 
will  be  found,  wherever  association  produces  a  change  in  our  judg- 
ihents  on  matters  of  taste,  it  does  so  by  cooperating  with  some  n:;:- 
ural  i)rinciple  of  the  mind,  and  implies  the  existence  of  certaia 
original  sources  of  pleasure  and  uneasiness. 

"A  mode  of  dress,  which  at  first  appeared  awkward,  acquires,  in 


422  LOGIC.  Lect.  XXX. 

a  few  weeks  or  months,  the  appearance  of  elegance.  By  being 
accustomed  to  see  it  worn  by  those  whom  we  consider  as  models 
of  taste,  it  becomes  associated  with  the  agreeable  impressions 
which  we  receive  from  the  ease  and  grace  and  refinement  of  their 
manners.  When  it  pleases  by  itself,  the  effect  is  to  be  ascribed, 
not  to  the  object  actually  before  us,  but  to  the  impressions  with 
which  it  has  been  generally  connected,  and  which  it  naturally 
recalls  to  the  mind. 

"This  observation  points  out  the  cause  of  the  perpetual  vicissi- 
tudes in  dress,  and  in  everything  whose  chief  recommendation 
arises  from  fashion.  It  is  evident  that,  as  fir  as  the  agreeable  effect 
of  an  ornament  arises  from  association,  the  effect  will  continue  only 
while  it  is  confined  to  the  higher  orders.  When  it  is  adopted  by 
the  multitude,  it  not  only  ceases  to  be  associated  with  ideas  of 
taste  and  refinement,  but  it  is  associated  with  ideas  of  affectation, 
absurd  imitation,  and  vulgarity.  It  is  accordingly  laid  aside  by  the 
higher  orders,  who  studiously  avoid  every  circumstance  in  external 
appearance  which  is  debased  by  low  and  common  use ;  and  they 
are  led  to  exercise  their  invention  in  the  introduction  of  some  new 
peculiarities,  which  firet  become  fiishionable,  then  common,  and  last 
of  all,  are  abandoned  as  vulgar." ' 

"Our  moral  judgments,  too,  may  be  modified,  and  even  perverted 
to  a  certain  degree,  in  consequence  of  the  operation  of  the  same 
principle.  In  the  same  manner  in  which  a  pereon  who  is  regarded 
as  a  model  of  taste  may  introduce,  by  his  example,  an  absurd  or 
fantastical  dress ;  so  a  man  of  splendid  virtues  may  attract  some 
esteem  also  to  his  imperfections ;  and,  if  placed  in  a  conspicuous 
situation,  may  render  his  vices  and  follies  objects  of  general  imita- 
tion among  the  multitude. 

"'In  the  reign  of  Charles  II.,'  says  Mr.  Smith,*  'a  degree  of  licen- 
tiousness was  deemed  the  characteristic  of  a  liberal  education.  It 
was  connected,  according  to  the  notions  of  those  times,  with  gen- 
erosity, sincerity,  magnanimity,  loyalty;  and  proved  that  the  person 
who  acted  in  this  manner  was  a  gentleman,  and  not  a  puritan.  Se- 
verity of  manners,  and  regularity  of  conduct,  on  the  other  hand, 
were  altogether  unfashionable,  and  were  connected,  in  the  imagina- 
tion of  that  age,  with  cant,  cunning,  hypocrisy,  and  low  mannere. 
To  superficial  minds  the  vices  of  the  great  seem  at  all  times  agree- 
able. They  connect  them  not  only  with  the  splendor  of  fortune, 
but  with  many  superior  virtues  which  they  ascribe  to  their  superiors; 


I  EUmentt,  vol.  i.,  Part  i.  chap.  r.    CoUttUd        «  ntory  of  Moral  Sentiments,  Part  t.  o.  2.  — 
Works,  ii.  p.  322  tt  srq.  £d. 


LiXT.  XXX.  LOGIC.  428 

with  the  spirit  of  freedom  and  independency  ;  with  frankness,  gen- 
erosity, humanity,  and  politeness.     The  virtues  of  the  inferior  ranks 
of  people,  on   the  contrary,  —  their   parsimonious   frugality,  their 
painful  industry,  and  rigid  adherence  to  rules,  seem  to  them  mean 
and  disagreeable.     They  connect  them  both  with  the  meanness  of 
the  station  to  which  these  qualities  commonly  belong,  and  with 
many  great  vices  which  they  suppose  usually  accompany  them; 
such  as  an  abject,  cowardly,  ill-natured,  lying,  pilfering  disposition.'"* 
"  In  general,"  says  Condillac,  "  the  impression  we  experience  in  the 
ditt"eren^''cn'cumstances  of  life,  makes   "s  asso- 
Condiiiac  quoted  on-       cJate  ideas   with   a   force   which    renders'  them 

tlie  influence  of  Asso-  '  ^         c  •     t        i    i  i  tt-  /> 

ever  alter  for  us  indissoluble.     \V  e  cannot,  for 


example,  frequent  the  society  of  our  fellow-men 
without  insensibly  associating  the  notions  of  c.ertain  intellectual  or 
moral  qualities  with  certain  corporeal  characters.  This  is  the  reason 
why  persons  of  a  decided  pliysiognomy  please  or  displease  us  more 
than  otiiers  ;  for  a  physiognomy  is  only  an  assemblage  of  charac- 
tere,  with  which  W'e  have  associated  notions  which  are  not  sug- 
gested without  an  accompaniment  of  satisfaction  or  disgust.  It  is 
not,  therefore,  to  be  marvelled  at  that  we  judge  men  according  to 
their  physiognomy,  and  that  we  sometimes  feel  towards  thein  at 
first  sight  aversion  or  inclination.  In  consequence  of  these  associa- 
tions, we  are  often  vehemently  prepossessed  in  favor  of  certain  indi- 
viduals, and  no  less  violently  disposed  against  others.  It  is  because 
all  that  strikes  us  in  our  friends  or  in  our  enemies  is  associated  with 
the  agreeable  or  the  disagreeable  feeling  which  we  severally  experi- 
ence; and  because  the  faults  of  the  former  borrow  always  something 
pleasing  from  their  amiable  qualities ;  whereas  the  amiable  qualities 
of  the  latter  seem  always  to  participate  of  their  vices.  Hence  it  is 
that  these  associations  exert  a  powerful  influence  on  our  whole  con- 
duct. They  foster  our  love  or  hatred ;  enhance  our  esteem  or  con- 
tempt ;  excite  our  gratitude  or  indignation ;  and  produce  those 
sympathies,  —  those  antipathies,  or  those  capricious  inclinations, 
for  which  we  are  sometimes  sorely  puzzled  to  render  a  reason. 
Pescartes  tells  us  that  through  life  he  had  always  found  a  strong 
predilection  for  squint  eyes,  —  which  he  explains  by  the  circum« 
stance,  that  the  nursery-maid  by  whom  he  had  been  kindly  tended^ 
and  to  whom  as  a  child  he  was,  consequently,  much  attached,  had 
this  defect."^  'S.Gravesande,  I  think  it  is,  who  tells  us  he  knew  a 
man,  and  a  man  otherwise  of  sense,  who  had  a  severe  fall  from  a 


1  Elements,  vol.  i.  c.  v,  §  3.     Collected  Works,         2  Origine  Ues   Connoissances  HumaiTUS,  sect 
vol.  ii.  p.  335.  ii.  ch.  ix.  i  80.  —Ed. 


424  LOGIC.  Lect.  XXX 

wagon ;  and  thereafter  he  could  never  enter  a  wagon  without 
fear  and  trembling,  though  he  daily  used,  without  apprehension, 
another  and  far  more  dangerous  vehicle.^  A  girl  once  and  again 
sees  her  mother  or  maid  fainting  and  vociferating  at  the  appearance 
of  a  mouse  ;  if  she  has  afterwards  to  escape  from  danger,  she  will 
rather  pass  through  flames  than  take  a  patent  way,  if  obstructed  by 
a  ridicidus  mus.  A  remarkable  example  of  the  false  judgments 
arising  from  this  principle  of  association,  is  recorded  by  Herodotus 
and  Justin,  in  reference  to  the  war  of  the  Scythians  with  their 
slaves.  The  slaves,  after  they  had  repeatedly  repulsed  several 
attacks  with  arms,  were  incontinently  put  to  flight  when  their  mas- 
ters came  out  against  them  with  their  whips.* 

I  shall  now  offer  an  observation  in  regard  to  the  appropriate 
remedy  for  this  evil  influence  of  Association. 

The  only  mean  by  which  we  can* become  aware  of,  counteract, 

and  overcome,  this  besetting  weakness  of  our 

Only  remedy  for  th«      nature,  is  Philosophy, —  the  Philosophy  of  the 

influence   of  Associa-         tt  ■»!••     j  j     ^i  •         ^     j-     i     l    ,.l     •        ^i. 

.    ,    ,„ .,       ,         Human   Mind ;    and   this  studied   both   m   the 

tiou  IS  the  I  liilosopliy  ^  ' 

of  theHutnun  Mind.  cousciousncss  of  the  individual,  and  in  the  his- 
tory of  the  species.  The  philosophy  of  mind, 
as  studied  in  the  consciousness  of  the  individual,  exhibits  to  us  the 
source  and  nature  of  the  illusion.  It  accustoms  us  to  discriminate 
the  casual,  from  the  necessary,  combinations  of  thought ;  it  sharp- 
ens and  corroborates  our  faculties,  encourages  our  reason  to  revolt 
against  the  blind  jncformations  of  opinion,  and  finally  enables  us  to 
break  through  the  enchanted  circle  within  which  Custom  and  Asso- 
ciation had  enclosed  us.  But  in  the  accomplishment  of  this  end, 
we  are  greatly  aided  by  the  study  of  man  under  the  various  circum- 
stances which  have  concurred  in  modifying  his  intellectual  and 
moral  character.  In  the  great  spectacle  of  history,  we  behold  in 
different  ages  and  countries  the  predominance  of  different  systems 
of  association,  and  these  ages  and  countries  are,  consequently, 
distinguished  by  the  prevalence  of  different  systems  of  opinions. 
But  all  is  not  fluctuating;  and,  amid  the  ceaseless  changes  of  acci- 
dental circumstances  and  precarious  beliefs,  we  behold  some  princi- 
ples ever  active,  and  some  truths  always  commanding  a  recognition. 
We  thus  obtain  the  means  of  discriminating,  in  so  far  as  our  unas- 
sisted reason  is  conversant  about  mere  worldly  concerns,  between 
what  is  of  universal  and  necessary  certainty,  and  what  is  only  of 


»  Inirnrtihtio  art  Philnsophiam.  Los'rn.  c.  26.      which  follow  are  also  from  >S  (iravesande.  — 
Tile  example,  bowever.  is  piven  as  a  t^tipiK^cd      Ei>. 
cRre,  and  not  as  a  fuct.    Tlte  two  iuatauces         >  Herod  ,  iv.  8.    JusUu.,  ii.  6.  —  B»> 


Lkct.  XXX.  LOGIC.  425 

local  and  temporary  acceptation ;  and,  in  reference  to  the  latter,  in 
witnessing  the  influence  of  an  arbitrary  association  in  imposing  the 
most  irrational  opinions  on  our  fellow-men,  our  eyes  are  opened, 
and  we  are  warned  of  the  danger  from  the  same  illusion  to  our- 
selves. And  as  the  philosophy  of  man  affords  us  at  once  the  indi- 
cation and  the  remedy  of  this  illusion,  so  the  philosophy  of  man 
does  this  exclusively  and  alone.  Our  irrational  associations,  our 
habits  of  groundless  credulity  and  of  arbitrary  skepticism,  Snd  no 
medicine  in  the  study  of  aught  beyond  the   domain  of  mind  itself 

As  Goethe  has  well  observed,  "Mathematics  rem.ove  no  preju- 
dice; they  cannot  mitigate  obstinacy,  or  temper  party-spirit;"^  in  a 
word,  as  to  any  moral  influence  upon  the  mind,  they  are  absolutely 
null.  Hence  we  may  well  explain  the  aversion  of  Socrates  for 
these  studies,  if  carried  beyond  a  very  limited  extent. 

The  next  faculty  in  order  is  the  Representative,  or  Imagination 
proper,  which   consists   in   the  greater  or  less 

The  Representative       power   of  holding   up   an   ideal  object   in  the 

Faculty,   or  Imagina-         r    i*      ^  •  rpi  r  r> 

tiou  Proper  light  01  consciousuess.     I  he  energy  or  Kepre- 

sentation,  though  dependent  on  Retention  and 
Reproduction,  is  not  to  be  identified  with  these  operations.  For 
though  these  three  functions  (I  mean  Retention,  Reproduction,  and 
Representation)  immediately  suppose,  and  are  immediately  depend- 
ent on,  each  other,  they  are  still  manifestly  discriminated  as  differ- 
ent qualities  of  mind,  inasmuch  as  they  stand  to  each  other  in  no 
determinate  proportion.  We  find,  for  example,  in  some  individuals 
the  capacity  of  Retention  strong,  but  the  Reproductive  and  Repre- 
sentative Faculties  sluggish  and  weak.  In  others,  again,  the  Con- 
servative tenacity  is  feeble,  but  the  Reproductive  and  Representa- 
tive energies  prompt  and  vivid ;  while  in  others  the  power  of 
Reproduction  may  be  vigorous,  but  what  is  recalled  is  never  pic- 
tured in  a  clear  and  distinct  consciousness.  It  will  be  generally, 
indeed,  admitted,  that  a  strong  retentive  memory  does  not  infer  a 
prompt  recollection ;  and  still  more,  that  a  strong  memory  and  a 
prompt  recollection  do  not  infer  a  vivid  imagination.  These,  there- 
fore, though  variously  confounded  by  philosophers,  we  are  war- 
ranted, I  think,  in  viewing  as  elementary  qualities  of  mind,  which 
ought  to  be  theoretically  distinguished.  Limiting,  therefore,  the 
term  Imagination  to  the  mere  Faculty  of  Representing  in  a  more 
or  less  vivacious  manner  an  ideal  object,  —  this  Faculty  is  the 
source  of  errors  which  I  shall  comprise  in  the  following  paragraph. 

1  Wtrke,  xxii.  p.  258.    Quoted  by  Scheidler,  Psychologic,  p.  146. 

54 


426  LOGIC.  Lect.  XXX. 

T  CII.   Imagination,  or  the  Faculty  of  Representing  with 

more  or  less  vivacity  a  recalled  object  of 

Par.cii.4.imaeina.       cognition,   is   the   sourcB   of   Errors,   both 

tion,  —  as  a  source  of  ... 

Error.  whcn   it   IS   too   languid    and   when    it    is 

too  vigorous.  In  the  former  case,  the  ob- 
ject is  represented  obscurely  and  indistinctly ;  in  the  latter, 
the  ideal  representation  affords  the  illusive  appearance  of  a 
sensible  presentation. 

A  strong  imagination,  that  is,  the  power  of  holding  up  any  ideal 

object  to  the  mind  in  clear  and  steady  colors,  is 

Explication.  g,  faculty  necessary  to  the  poet  and  to  the  artist ; 

ecessj  y  o     mag  -      ^^^^  ^^^  ^^  them  alone.     It  is  almost   equally 

nation     m     scieutifio  _   _  ^         J 

pursuits.  requisite  for  the  successful  cultivation  of  every 

scientific  pureuit;  and,  though  differently  .ij)- 
plied,  and  different  in  the  character  of  its  representation,  it  may 
well  be  doubted  whether  Anstotle  did  not  possess  as  powerful  an 
imagination  as  Homer.  The  vigor  and  perfection  of  this  faculty  is 
seen,  not  so  much  in  the  representation  of  individual  objects  and 
fiJigmentary  sciences,  as  in  the  representation  of  systems.  In  the 
better  ages  of  antiquity  the  perfection,  the  beauty,  of  all  works 
of  taste,  whether  in  Poetry,  Eloquence,  Sculp- 

Diveree  characteris-         .  !->•.•  -nr      •  •      •      n 

.  .  ,  .  ture,  Painting,  or   Music,  was  pi-incipally  esti- 

tics  of  Art  in  ancient  '  ®  ^  r  r      j 

and  modirn  times.  mated  from  the  Symmetry  or  proportion  of  all 

the  parts  to  each  other,  and  to  the  whole  which 
they  together  constituted ;  and  it  was  only  in  subservience  to  this 
general  harmony  that  the  beauty  of  the  several  parts  was  appreci- 
ated. In  the  criticism  of  modern  times,  on  the  contrary,  the  reveree 
is  true ;  and  we  are  disposed  to  look  more  to  the  obtrusive  qualities 
of  details,  than  to  the  keeping  and  unison  of  a  whole.  Our  works 
of  art  are,  in  general,  like  kinds  of  assorted  patch-work ;  —  not  sys- 
tems of  parts  all  subdued  in  conformity  to  one  ideal  totality,  but 
coordinations  of  independ-ent  fragments,  among  which  a  '■'■  2:>urpureu8 
pannus''^  seldom  comes  amiss.  The  reason  of  this  difference  in 
taste  seems  to  be,  what  at  first  sight  may  seem  the  reverse,  that  in 
antiquity  not  the  Reason  but  the  Imagination  was  the  more  vigor- 
ous;—  that  the  Imagination  was  able  to  represent  simultaneously  a 
more  comprehensive  system;  and  thus  the  several  parts  being  re- 
garded and  valued  only  as  conducive  to  the  general  result,  —  these 
])arts  never  obtained  that  individual  importance,  which  would  have 
fallen  to  them  had  they  been  only  created  and  only  considered  for 
themselves.  Now  this  power  of  representing  to  the  mind  a  com- 
plex system  in  all  its  bearings,  is  not  less  requisite  to  the  philosopher. 


Lkct.  XXX.  LOGIC.  427 

than  to  the  poet,  though  the  representation  be  different  in  kind ; 
and  the  nature  of  the  philosophic  representations,  as  not  concrete 
and  palpable  like  the  poetical,  supposes  a  more  arduous  operation, 
and,  therefore,  even  a  more  vigorous  faculty.     But  Imagination,  in 
the  one  case  and  in  the  other,  requires  in  proportion  to  its  own 
power   a   powerful   intellect ;    for   imagination   is   not   poetry  nor 
philosophy,  but  only  the  condition  of  the  one  and  of  the  other. 
But  to  speak  now  of  the  Errors  which  arise  from  the  dispropor- 
tion between   the  Imagination    and   the  Judg- 
Errors  which  arise       ment ;  —  they  originate  either  in  the  weakness, 

from    the    dispropor-  ...  ,.      ""  i         ,.     i       r' 

.i„„Kot„o^„T™o  i  „        or  m  the  mordinate  strength,  ot  the  lormor. 

t  ion  between  Imagma-  »      ' 

tion  and  Judgment.  In  regard  to  the  errors  which  arise  from  the 

Those  arising  from      imbecility  of  the  Representative  Faculty,  it  is 

the  weakness  of  Imagi-  .      t/v.      i.     .  •  i  ^i,"       •     -l      'Tx 

"         not    dimcult   to   conceive    how   this   imbecility 

nation.  _  •' 

may  become  a  cause  of  erroneous  judgment. 
The  Elaborative  Faculty,  in  order  to  judge,  requires  an  object, — 
requires  certain  diiferences  to  be  given.  Now,  if  the  imagination 
be  weak  and  languid,  the  objects  represented  by  it  will  be  given  in 
such  confusion  and  obscurity,  that  their  differences  are  either  null 
or  evanescent,  and  judgment  thus  rendered  either  impossible,  or 
possible  only  with  the  jji-obability  of  error.  In  these  circumstances, 
to  secure  itself  from  failure,  the  intellect  must  not  attempt  to  rise 
above  the  actual  presentations  of  sense ;  it  must  not  attempt  any 
ideal  analysis  or  synthesis,  —  it  must  abandon  all  free  and  self- 
active  elaboration,  and  all  hope  of  a  successful  cultivation  of 
knowledge. 

Again,  in  regard  to  the  opposite  errors,  those  arising  from  the 

disproportioned  vivacity  of  imagination,  —  these 

From/ its  dispropor-       ^^.^  equally  apparent.     In  this  case  the  renewed 

tionate  vivacity.  i         •'      i  i 

or  newly-modified  representations  make  an  equal 
impression  on  the  mind  as  the  original  presentations,  and  are,  con- 
sequently, liable  to  be  mistaken  for  these.  Even  during  the  percep- 
tion of  real  objects,  a  too  lively  imagination  mingles  itself  with  the 
observation,  which  it  thus  corrupts  and  falsities.  Thus  arises  what 
is  logically  called  the  vitium  subreptionis}  This  is  frequently  seen 
in  those  pretended  observations  made  by  theorists  in  support  of 
their  hypotheses,  in  which,  if  even  the  possibility  be  left  for  imagi- 
nation to  interfere,  imagination  is  sure  to  fill  up  all  that  the  senses 
may  leave  vacant.  In  this  case  the  observers  are  at  once  dupes  and 
deceivers,  in  the  words  of  Tacitus,  '■'■  Fingxmt  simul  creduntque^^ 


1  Krug,  Logik,^  142.    Anm.  —  Ed. 

3  Hist.  lib.  ii  c.  8.    See  Lectures  on  Metaphysics,  p.  64. — Ed. 


428  LOGIC.  LiccT.  XXX. 

In  regard  to  the  remedies  for  these  defects  of  the  Representative 

Faculty  ;  —  in  tlie  former  case,  the  only  allevia- 

ICeroedies  for  these       ^j^,^  ^j^.^^  ^^^  ^^  proposed  for  a  feeble  Imagina- 

(k'Cccts  of  the  I  magi-  .  .  .  •      i         i  i      •  i 

„^^■^Q^  tion,  IS  to  animate  it  by  the  contemplation  and 

study  of  those  works  of  art  which  are  the  jiro- 
ducts  of  a  strong  Phantasy,  nnd  which  tend  to  awaken  in  the  stu- 
dent a  corresponding  energy  of  that  fiiculty.  On  the  other  hand,  u 
too  powerful  imaginntion  is  to  be  quelled  and  regulated  by  abstract 
thinking,  and  the  »tudy  of  philosophical,  perhaps  of  mathematical, 
science.^ 

The  faculty  wliich  next  follows,  is  the  Elaborative  Faculty,  Com- 
parison, or  the  Faculty  of  Relations.  This  is  the  Understanding, 
in  its  three  functions  of  Conception,  Judgment,  and  Reasoning. 
On  this  faculty  take  the  following  paragraph. 

^  cm.    The  Affections  and  the  Lower  Cognitive  Faculties 

afford  the  sources  and  occasions  of  error; 

par.ciii.oEiabora-       fcut  [^  jg  i\^q  Ehiborativc  Faculty,  Under* 

tive     Faculty,  —  as    a  t  /-^  •  t      i  i  •    i 

source  of  Error.  Standing,  Comparison,  or  Judgment,  which 

truly  errs.  This  faculty  does  not,  however, 
eiT  from  strength  or  over-activity,  but  from  inaction ;  ami  this 
inaction  arises  either  from  natural  weakness,  from  want  of 
exercise,  or  from  the  impotence  of  attention.^ 

I  formerly  olwerved  that  error  does  not  lie  in  the  conditions 

of    our   higher   faculties   themselves,   and    that 

Kxpiication.  ^j^^.^^.  faculties  are  not,  by  their  own  laws,  deter- 

Error  does  not  lie  in  •        i  />  i         •     -i  i      • 

the  conditions  of  our       "ii"^'*!  ^o  fulsc  judgments  or  conclusions: 

Higher  Faculties,  but 

in  po^f^ible  iu  tlie  ap.  "  Nam  neque  dccfpitur  ratio,  noc  decipit  unquam.''^ 

plication  of  the  laws 

of   tlioFc    faculties  to         _,.     ,  .  ,  .  „    ,  ,     ,  i  i    i 

determinate  c.*e«.  ^^  ^^^^  ^^*^''^  Otherwise,  all  knowledge  would  be 

impossible, —  the  root  of  our  nature  would  be  a 
lie.  "But  in  the  application  of  the  laws  of  our  higher  faculties  to 
determinate  cases,  many  errore  are  possible ;  and  these  errors  may 
actually  be  occasioned  by  a  variety  of  circumstances.  Thus,  it  is  a 
law  of  our  intelligence,  that  no  event,  no  phenomenon,  can  be 
thought  as  absolutely  beginning  to  be ;  we  cannot  but  think 
'Jiat  all  its  constituent  elements  had  a  virtual  existence  prior 
X)   th«ir  concurrence,  to   necessitate  its  manifestation  to  us;    w« 

1  Cr.  Krnr;,  Logik,i  lb6.    Anm.  — Ed. 

i  Kra-,  Logils,  {  148.  —  Ed.    [Cf  Fries,  Logik,  1 108.    B«chm»nn,  Ligik, }  411.] 

^  Sec  above,  p.  889  —  Ed. 


Lkct.  XXX. 


LOGIC. 


429 


are  thus  unable  to  accord  to  it  more  than  a  relative  commencement, 
in  other  words,  we  are  constrained  to  look  upon  it  as  the  effect  ol" 
antecedent  causes.  Now  though  the  law  itself  of  our  intelligence 
—  that  a  cause  there  is  for  every  event  —  be  altogether  exempt 
from  error,  yet  in  the  application  of  this  law  to  individual  cases, 
that  is,  in  the  attribution  of  determinate  causes  to  determinate 
effects,  we  are  easily  liable  to  go  wrong.  For  we  do  not  know, 
except  from  experience  and  induction,  what  particular  antecedents 
are  the  causes  of  particular  consequents  ;  and  if  our  knowledge  of 
this  relation  be  imperfectly  generalized,  or  if  we  extend  it  by  a 
false  analogy  to  cases  not  included  within  our  observation,  error  is 
the  inevitable  consequence.  But  in  all  this  there  is  no  fault,  no 
failure,  of  intelligence,  there  is  only  a  deficiency,  —  a  deficiency  in 
the  activity  of  intelligence,  while  the  Will  determines  us  to  a  de- 
cision before  the  Understanding  has  become  fully  conscious  of  cer- 
tainty. The  defective  action  of  the  Under- 
standing may  arise  from  three  causes.  In  the 
first  place,  the  faculty  of  Judgment  may  by 
nature  be  too  feeble.  This  is  the  case  in  idiota 
and  weak  persons.  In  the  second  place,  though 
not  by  nature  incompetent  to  judge,  the  intel- 
lect may  be  without  the  necessary  experience, 
—  may  not  possess  the  grounds  on  which  a  cor- 
rect judgment  must  be  founded.  In  the  third  place,  —  and  this  is 
the  most  frequent  cause  of  error,  —  the  failure  of  the  understanding 
is  from  the  incompetency  of  that  act  of  will  which  is  called  Atten- 
tion. Attention  is  the  voluntary  direction  of  the  mind  upon  an 
object,  with  the  intention  of  fully  apprehending  it.  The  cognitive 
(energy  is  thus,  as  it  were,  concentrated  upon  a  single  point.  We, 
therefore,  say  that  the  mind  collects  itself,  when  it  begins  to  be 
attentive ;  on  the  contrary,  that  it  is  distracted,  when  its  attention 
is  not  turned  upon  an  object  as  it  ought  to  be.  This  fixing  — this 
concentration,  of  the  mind  upon  an  object  can  only  be  carried  to  a 
wrtain  degree,  and  continued  for  a  certain  time.  This  degree  and 
.his  continuance  are  both  dependent  upon  bodily  circumstances;  and 
they  are  also  frequently  interrupted  or  suspended  by  the  intrusion 
of  certain  collateral  objects,  which  are  forced  upon  the  mind,  either 
from  without,  by  a  strong  and  sudden  impression  upon  the  senses,  or 
from  within,  through  the  influence  of  Association ;  and  these,  when 
once  obtruded,  gradually  or  at  once  divert  the  attention  from  the 
|)4'iginal  and  principal  object.  If  we  are  not  sufficiently  attentive, 
r  if  the  effort  which  accompanies  the  concentration  of  the  mind 
upon  a  single  object  be  irksome,  there  arises  hurry  and  thoughtless- 


Defective  action  of 
-tbe  Understanding 
I  may  arise  from  three 
I  Muses. 

(a)  Natural  feeble- 
ness, (b)  Want  of  ne- 
cessary experience,  (c) 
[Incompetency  of  at- 
ation. 


480 


LOGIC. 


Lect.  XXX 


ness  in  judging,  inasmuch  as  we  judge  either  before  we  have  fully 
Bought  out  the  grounds  on  which  our  decision  ought  to  proceed,  or 
have  competently  examined  their  validity  and  effect.  It  is  hence 
manifest  that  a  multitude  of  erroi-s  is  the  inevitable  consequence." ' 

In  regard  to  the  Regulative  Faculty,  —  Common  Sense,  —  Intel- 
ligence,—  vovs,  —  this  is  not  in  itself  a  source 

6.  Regulative  Fac-       ^f   error.      Errors   may,  however,  arise   either 

ulty,— not  properly  a         „  i      i  •  4.1       i  •      • 

eource  of  Error.  iroxYi  overlooking  the  laws  or  necessary  princi- 

ples which  it  does  contain ;  or  by  attributing  to 
it,  as  necessary  and  original  data,  what  are  only  contingent  general- 
izations from  experience,  and,  consequently,  make  no  part  of  its 
complement  of  native  truths.  But  these  errors,  it  is  evident,  are 
not  to  be  attributed  to  the  Regulating  Faculty  itself,  which  is  only 
a  place  or  source  of  principles,  but  to  the  imperfect  operations  of 
the  Understanding  and  Self-consciousness,  in  not  properly  observ- 
ing and  sifting  the  phenomena  which  it  reveals. 

Besides  these  sources  of  Error,  which  immediately  originate  in 
the  several  powers  and  faculties  of  mind,  there 
are  othere  of  a  remoter  origin  arising  from  the 
different  habits  which  are  determined  by  the 
differences  of  sex,^  of  age,'  of  bodily  constitu- 
tion,* of  education,  of  rank,  of  fortune,  of  pro- 
fession, of  intellectual  pursuit.  Of  these,  how- 
ever, it  is  impossible  at  present  to  attempt  an  analysis ;  and  I  shall 
only  endeavor  to  afford  you  a  few  specimens,  and  to  refer  you 
for  information  in  regard  to  the  others  to  the  best  sources. 

Intellectual  pursuits  or  fivorite  studies,  inasmuch  as  these  deter- 
mine the  mind  to  a  one-sided  cultivation,  that 
is,  to  the  neglect  of  some,  and  to  the  dispropor- 
tioned  development  of  other,  of  its  faculties,  are 
among  the  most  remarkable  causes  of  error. 
This  partial  or  one-sided  cultivation  is  exempli- 
fied in  three  different  phases.  The  first  of 
these  is  shown  in  the  exclusive  cultivation  of 
the  powers  of  Observation,  to  the  neglect  of 
the  higher  faculties  of  the  Understanding.  Of 
this  type  are  your  men  of  physical  science.  In  this  department  of 
knowledge  there  is  chiefly  demanded  a  patient  habit  of  attention  to 
details,  in  order  to  detect  phenomena,  and,  these  discovered,  their 


Remote  sources  of 
Error  in  the  different 
habits  determinated 
by  sex,  age,  bodily 
constitution,  educa- 
tion, etc. 


Selected  examples 
of  these. 

A  one-sided  cultiva- 
tion of  the  intellectual 
lowers. 

This  exemplified  in 
three  difTercnt  phases. 
Exclusive  cultivation. 
1.  Of  the  powers  of 
Observation. 


1  Krug,  Logilc,  i  148.   Anm.   In  some  places 
iliglvtly  changed.  —  Ed. 

2  [See  Stewart,  Elements,  vol.  iii.  part  iii. 
s«ct.  V.  chap.  i.     Works,  vol.  ir.  p.  238  et  stq.  ] 


3  [Aristotle,  Rhtt.,  L.  il.  c.  12.     Crousaz. 
Logique,  t.  i.  part  i.  sect.  i.  ch.  v.  f  15,  p.  104.] 

4  [See  Crousax,  Logique,  t.  i.  p.  i.  sect.  i.  cb. 
v.  p.  91  et  ftq.] 


Lect.  XXX.  LOGIC.  431 

generalization  is  usually  so  easy  that  there  is  little  exercise  afforded 
to  the  higher  energies  of  Judgment  and  Reasoning.  It  was  Bacon's 
boast,  that  Induction,  as  applied  to  nature,  would  equalize  all  tal- 
ents, level  the  aristocracy  of  genius,  accomplish  marvels  by  coopera- 
tion and  method,  and  leave  little  to  be  done  by  the  force  of  individ- 
ual intellects.  This  boast  has  been  fulfilled.  Science  has,  by  the 
Inductive  Process,  been  brought  down  to  minds,  who  previously 
would  have  been  incompetent  for  its  cultivation,  and  physical  knowl- 
edge now  usefully  occupies  many  who  would  otherwise  have  been 
without  any  rational  pursuit.  But  the  exclusive  devotion  to  such 
studies,  if  not  combined  with  higher  and  graver  speculations,  tends 
to  wean  the  student  from  the  more  vigorous  efforts  of  mind, 
which,  though  unamusing  and  even  irksome  at  the  commencement, 
tend,  however,  to  invigorate  his  nobler  powers,  and  to  prepare  him 
for  the  final  fruition  of  the  highest  happiness  of  his  intellectual 
nature. 

A  partial  cultivation  of  the  intellect,  opposite  to  this,  is  given 
in  the  exclusive  cultivation  of  Metaphysics  and 

2.  Of  Metaphysics.         ^f  Mathematics.     On  this  subject  I  may  refer 

3.  Of  Mathematics.  ^  ,  ^.  ^-m-o^  j.     • 

Stewart  referred  to.  y^^^  ^°  ^'^^^  obscrvations  of  Mr.  Stcwart,  m 
two  chapters  entitled  The  3fetaphysician  and 
The  Mathematician,  in  the  third  volume  of  his  Elements  of  the 
Philosophy  of  the  Human  Mind,  —  chapters  distinguished  equally 
by  their  candor  and  their  depth  of  observation.  On  this  subject 
Mr.  Stewart's  authority  is  of  the  highest,  inasmuch  as  he  was  dis- 
tinguished in  both  the  departments  of  knowledge,  the  tendency  of 
which  he  so  well  develops. 


LECTURE    XXXI. 

MODIFIED    STOICHEIOLOG  Y. 

SECtlON  II.  — ERROR— ITS  CAUSES  AND  REMEDIED. 

C  — LANGUAGE.  — D.  — OBJECTS  OF  KNOWLEDGE. 

In  my  last  Lecture,  I  concluded  the  survey  of  the  En-oi*s  which 

have  their  origin  in  tlie  conditions  and  circnm- 

. -.aiiguusre,  — lu       g^anccs  of  the  several  Cosinitive  Faculties,  and 

!i  souic'i;  ot  Error.  *-^  ' 

now  proceed  to  that  source  of  false  judgment 
wliich   lies  in  the  imperfection  of  the  Instrument  of  thought  and 
Coininnnicntion, —  I  mean  Language. 
Much  controversy  has  arisen  in  regard  to  the  question,  —  Has 
man  invented  Language?     But  ihe  differences 
Has  man  Invented       ^,f  opinion  have  in  a  great  measure  arisen  from 
itv..f  the  question.  ^'^^.  ambiguity  or  complexity  of  the  terms,  m 

which  the  problem  has  been  stated.  By  lan- 
f/n«/r/e  we  may  mean  cither  the  power  which  man  possesses  of  asso- 
ciating his  thought  with  signs,  or  the  particular  systems  of  signs 
with  which  different  portions  of  mankind  have  actually  so  associ- 
ated their  thoughts. 

Taking  language  in  the  former  sense,  it  is  a  natural  faculty,  an 

original  tendency  of  mind,  and,  in  this  view, 

In  what  sense  Lan-       ^^^   -^^^  ^^  more  invented  language  than  he 

liuagc    is    natural    to         ,  .  i       i  i  x       /»  i  p 

^g^  has  invented   thouglit.     \w  fact,  the  power  oi 

thought  and  the  power  of  language  are  equally 
entitled  to  be  considered  as  elementary  qualities  of  intelligence; 
foi-  while  they  are  so  different  that  they  cannot  be  identified,  they 
are  still  so  reciprocally  necessary  that  the  one  cannot  exist  .without 
the  other.  It  is  true,  indeed,  that  presentations  and  representations  - 
of  given  individual  objects  might  have  taken  place,  although  there 
were  no  signs  with  which  they  were  mentally  connected,  and  by 
which  they  could  be  overtly  expressed  ;  but  all  complex  and  facti- 
tious constructions  out  of  these  given  individual  objects,  in  other 


Lkct.  XXXI. 


LOGIC 


483 


words,  nil  notions,  concepts,  goner.il  idcns,  or  thoughts  proper, 
would  have  been  impossible  without  an  association  to  certain  signs, 
by  which  their  scattered  elements  might  be  combined  in  unity, 
and  their  vague  and  evanescent  existence  obtain  a  kind  of  definite 
and  fixed  and  palpable  reality.  Speech  and  cogitation  are  thus  the 
relative  conditions  of  each  other's  activity,  and  both  concur  to  the 
accomplishment  of  the  same  joint  result.  The  Faculty  of  Think- 
ing—  the  Faculty  of  forming  General  Notions  —  being  given,  this 
necessarily  tends  to  energy,  but  the  energy  of  thinking  depends 
upon  the  coactivity  of  the  Faculty  of  Speech,  which  itself  tends 
equally  to  energy.  These  faculties, — these  tendencies,  —  these 
energies,  th-us  coexist  and  have  always  coexisted ;  and  the  result  of 
their  combined  action  is  thought  in  language,  and  language  in 
thought.  So  much  for  the  origin  of  Language,  considered  in  gen- 
eral as  a  faculty. 

But,  though  the  Faculty  of  Speech  be  natural  and  necessary, 
that  its  manifestations  are,  to  a  certain  extent, 
contingent  and  artificial,  is  evident  from  the 
simple  fact,  that  there  are  more  than  a  single 
language  actually  spoken.  It  may,  therefore, 
be  asked,  —  Was  the  first  language,  actually 
spoken,  the  invention  of  man,  or  an  inspiration, 
of  the  Deity  ?  The  latter  hypothesis  cuts,  but 
does  not  loose  the  knot.  It  declares  that  ordi- 
ary  causes  and  the  laws  of  nature  are  insufiicient  to  explain  the 
henomenon,  but  it  does  not  prove  this  insufficiency ;  it  thus  vio- 
tes  the  rule  of  Parcimony,  by  postulating  a  second  and  hypothet- 
cause  to  explain  an  effect,  which  it  is  not  shown  cannot  be 
ccounted  for  without  this  violent  assumption.  The  first  and 
eatest  difficulty  in  the  question  is  thus :  —  It  is  necessary  to  think  , 
in  order  to  invent  a  language,  and  the  invention 
of  a  language  is  necessary  in  order  to  think; 
for  we  cannot  think  without  notions,  and  no-- 
lions  are  only  fixed  by  words.^  This  can  only  be  solved,  as  I  have 
aid,  by  the  natural  attraction  between  thought  and  speech,  —  by 
iheir  secret  afl^nity,  which  is  such  that  they  suggest  and,  pari 
<assv,  accompany  each  other.  And  in  regard  to  the  question, — 
hy,  if  speech  be  a  natural  faculty,  it  does  not  manifest  itself  like 
ther  natural  principles  in  a  uniform  manner,  —  it  may  be  answered 


Was  the  first  lan- 
guage, actually  spo- 
ken, the  invention  of 
man,  or  an  inspiratioa 
of  the  Deity  r 

The  latter  hypothe- 
I  considered. 


Difficulty    of    the 
uestion. 


1  See  Rousseau,  Discours  svr  V  Origine  de  P      pour  apprendre  Si  penser,  ils  ont  en  bien  plus 
)K^aliti  partni  Us  Hommes.    Premiere  Tartie.      besoin  encore  de  savoir  penser  pour  trouver 
PSi  le$  hommes  ont  eu  besoin  de  la  parole     )-art  de  la  parole."— Ed. 

55 


484  LOGIC.  Lect.  XXXT. 

that  the  Faculty  of  Speech  is  controlled  and  modified  in  its  exer- 
cise by  external  circumstances,  in  consequence  of  which,  though  its 
exertion  be  natural  and  necessai-y,  and,  therefore,  identical  in  all 
men,  the  special  forms  of  its  exertion  are  in  a  great  degree  conven- 
tional and  contingent,  and,  therefore,  different  among  different  por- 
tions of  mankind. 

Considered  on  one  side,  languages  are  the  results  of  our  intelli- 
gence and  its  immutable  laws.     In  consequence 
Language  has  a  gen-       ^f  ^.j^jg^  ^^ley  exhibit  in  their  progress  and  devel- 

eral     and     a     special  ,  ,  ,  , 

character  opment   resemblances  and    common   characters 

which  allow  us  to  com  pure  and  to  recall  them 
to  certain  primitive  and  essential  forms,  —  to  evolve  a  system  of 
Universal  Grammar.  Considered  on  another  side,  each  language  ia 
the  olF-<pring  of  particular  wants,  of  special  circumstances,  physical 
and  moral,  and  of  chance.  Hence  it  is  that  every  language  has 
particular  forms  as  it  has  peculiar  words.  Language  thus  bears 
the  impress  of  human  intelligence  only  in  its  general  outlines. 
There  is,  therefore,  to  be  found  reason  and  philosophy  in  all  lan- 
guages, but  we  should  be  wrong  in  believing  that  reason  and  phi- 
losophy have,  in  any  language,  determined  everything.  No  tongue, 
how  pei-fect  soever  it  may  appear,  is  a  corn- 
No  language  is  a       pj^^g  ^nd  perfect  instrument  of  human  thought. 

perfect  instrument  of        -,,  .  •,.  .  , 

thoucht  J^rom  its  vei'y  conditions  every  language  must 

be  imperfect.  The  human  memory  can  only 
compass  a  limited  complement  of  words,  but  the  data  of  sense,  and 
still  more  the  combinations  of  the  undei-standing,  are  wholly  un- 
limited in  numbei-.  No  language  can,  therefore,  be  adequate  to 
the  ends  for  which  it  exists;  all  are  imperfect,  but  some  are  far  less 
incompetent  instruments  than  othei*s. 

From  what  has  now  been  said,  you  will  be  prepared  to  find  in 
Language  one  of  the  principal  sources  of  Error;  but  before  I  go  on 
to  consider  the  particular  modes  in  Avhich  the  Imperfections  of 
Language  are  the  causes  of  false  judgments,  —  I  shall  comprise  the 
general  doctrine  in  the  following  paragraph. 

%  CIV.    As  the  human  mind  necessarily  requires  the  aid 

of  signs  to  elaborate,  to  fix,  and  to  commu- 

par.  CIV.  Language,       nicatc  its  uotious,  and  as  Articulate  Sounds 

—  as  a  source  of  Error.  ' 

are  the  species  of  signs  which  most  effect- 
ually afford  this  aid.  Speech  is,  therefore,  an  indispensable 
instrument  in  the  higher  functions  of  thought  and  knowledge. 
But  as  speech  is  a  necessary,  but  not  a  j^erfect,  instrument,  its 
imperfection  must  react  upon  the  mind.     For  the  Multitude 


Lkct.  XXXI.  LOGIC.  486 

of  Languages,  the  Difficulty  of  their  Acquisition,  their  neces- 
sary Inadequacy,  and  the  consequent  Ambiguity  of  Words, 
both  singly  and  in  combination,  —  these  are  all  copious  sources 
of  Illusion  and  Error.^ 

We  have  already  sufficiently  considered  the  reason  why  thought 

is  dependent  upon  some  system  of  sign.s  or  sym- 

Expiication.  )3Q|g  both  for  its  internal  perfection  and  external 

Signs  necefsary  for  •        9      mi  i  i  ^1  ^1 

the  internal  operation  expression.-  The  analyses  and  syntheses,  -  the 
of  Thought.  decompositions  and  compositions,  —  in  a  word, 

the  elaborations,  performed  by  the  Understand- 
ing upon  the  objects  presented  by  External  Perception  and  Self- 
Consciousness,  and  represented  by  Imagination,  —  these  operations 
are  faint  and  fugitive,  and  would  have  no  existence,  even  for  the 
conscious  mind,  beyond  the  moment  of  present  consciousness,  were 
we  not  able  to  connect,  to  ratify,  and  to  fix  them,  by  giving  to 
their  parts  (which  would  otherwise  immediately  fall  asunder)  a 
permanent  unity,  by  associating  them  with  a  sensible  symbol,  which 
we  may  always  recall  at  pleasure,  and  which,  when  recalled,  recalls 
along  with  it  the  characters  which  concur  in  constituting  a  notion 
or  factitious  object  of  intelligence.  So  far  signs  are  necessary  for 
the  internal  operation  of  thought  itself  But  for  the  communica- 
tion of  thought  from  one  mind  to  another,  signs  arc  equally  indis- 
pensable.    For  in  itself  thought  is  known,  —  thought  is  knowable, 

only  to  the  thinking  mind  itself;  and  were  we 

And  for  the  commu-  ,  ui     i    i  ^  *    •  1  i     _«" 

not  enabled  to  connect  certain  complements  of 

iiiciitiun  of  1  liought.  .  .  * 

thought  to  certain  sensible  symbols,  and  by 
their  means  to  suggest  in  other  minds  those  complements  of 
thought  of  which  we  were  conscious  in  ourselves,  we  should  never 
be  able  to  communicate  to  others  what  engaged  our  interest,  and 
man  would  remain  for  man,  if  an  intelligence  at  all,  a  mere  isolated 
intelligence. 

In  regard  to  the  question,  —  What  may  these  sensible  symbols 
be,  by  which  we  are  to  compass  such  memorable  effects,  —  it  is 
needless  to  show  that  mien  and  gesture,  which,  to  a  certain  extent, 
afford  a  kind  of  natural  expression,  are  altogether  inadequate  to  the 
double  purpose  of  thought  and  communication,  which  it  is  here 
required  to  accomplish.     This  double  purpose  can  be  effected  onl^ 


1  Krug,  Lo^j'i:,  §  145. —  Ed.    [Cf.  Ernesti,  Logi'Jfc,  J  109.    Care,  Lo^ig«c,  Part.  i.  ch.  i.  art. 

Inkia  DnctrincB  Solirlioris:  Pars  Alttra;  Dialec-  9,  p.  121.     Crousaz,  Toussaint.]   [Crousaz,  Lo- 

tica,  c.  2,  i   24.     Wyttenbach,  Pra-cepta   Phil,  giguf,  t.  iii.  part  i.  tect.  iil.  c.  2,  p.  63  et  setf 

Log.  P.  iii.  c.  iii.  p.  98.    Tittcl,  Logik,  p.  292.  Toussaint,  De  la  Ptnsie.    Chs.  viii.  x.  — Ed.} 

Eirwan,   Logick,    i.   214.    Fries,   System    tier  a  See  above,  p.  430.  —  Err. 


486 


LOGIC. 


Lect.   XXXL 


Intonations  of  the 
voice  tlie  only  ade- 
quate sensible  symbols 
of  thouj;ht  and  its 
communication. 

Tliese  inarticulate 
and  articulate. 

The  latter  constitute 
Language  Proper. 

How  Language  is  a 
(Ource  of  Error. 


by  symbols,  which  express,  through  intonations  of  the  Aoiee,  what 
is  passing  in  the  mind.  The.se  vocal  intonations 
are  either  inarticulate  or  articulate.  The  for- 
mer are  mere  sounds  or  cries ;  and,  as  Buch,  an 
expression  of  the  feelings  of  which  the  lower 
animals  are  also  capable.  The  latter  ( onstitute 
words,  and  these,  .is  the  expression  of  thoughts 
or  notions,  constitute  Language  Proper  or 
Speech,^  Speech,  as  we  have  said,  as  the  in- 
strument of  elaborating,  fixing,  and  commu- 
nicating our  thoughts,  is  a  principal  mean  of 
knowledge,  and  even  the  indispensable  condition  on  which  depen<is 
the  exercise  of  our  higher  cognitive  faculties.  But,  at  the  same  time, 
in  consequence  of  this  very  dependence  of  thought  upon  language, 
inasmuch  as  language  is  itself  not  perfect,  the  underatanding  is  not 
only  restrained  in  its  operations,  and  its  higher  development,  conse- 
quently, checked,  but  many  occasions  are  given  of  positive  error. 
For,  to  say  nothing  of  the  impediment  presented  to  the  free  com- 
munication of  thought  by  the  multitude  of  tongues  into  which 
human  language  is  divided,  in  consequence  of  which  all  speech 
beyond  their  mother-tongue  is  incomprehensible  to  those  who  do 
not  make  a  study  of  other  languages,  —  even  the  accurate  learning 
of  a  single  language  is  attended  with  such  difficulties,  that  perhaj>8 
there  never  yet  has  been  found  an  individual  who  was  thoroughly 
acquainted  with  all  the  words  and  modes  of  verbal  combination  in 
any  single  language,  —  his  mother-tongue  even  not  excepted.  But 
the  circumstance  of  principal  importance  is, 
that  how  copious  and  expressive  soever  it  may 
be,  no  language  is  competent  adequately  to 
denote  all  possible  notions,  and  all  possible  rela- 
tions of  notions,  and  from  this  necessary  jioverty 
of  language  in  all  its  different  degrees,  a  certain  inevitable  ambigu- 
ity arises,  both  in  the  employment  of  single  words  and  of  words  in 
mutual  connection. 

As  this  is  the  ])rincipai  source  of  the  error  originating  in  Lan- 
guage, it  will  be  proper  to  be  a  little  more 
explicit.  And  here  it  is  expedient  to  take  into 
accoimt  two  circumstances,  which  mutually  af- 
fect each  other.  Tlie  first  is,  that  as  the  vocab- 
ulary of  every  language  is  necessarily  finite,  it 
is  necessarily  disproportioned  to  the  multiplicity,  not  to  say  infinity, 
of  thought ;  and  the  second,  that  the  complement  of  words  in  any, 


The  ambiguity  of 
words  the  principal 
source  of  error  origi- 
nating in  Language. 


Two  circumstances 
%Mtiderthi8  bead,  which 
mutually    affect   each 
other. 


1  Cf.  Krug,  Logik,  i  146.    Anm.  —  Eo. 


» 


r«KCT.  XXXL  LOGIC.  43T 

given  language  has  been  always  filled  up  with  terms  significant  of 
objects  and  relations  of  the  external  world,  before  the  want  was 
experienced  of  words  to  express  the  objects  and  relations  of  the 
internal. 

From  the  first  of  these  circumstances,  considered  exclusively 
and  by  itself,   it  is   manifest  that  one  of  two 

The  vocabulary  of      alternatives  must  take  place.     Either  the  word* 

every  latiKuatre  ncces-  ^       i  ,     n      •  ,  .       , 

.,     «   „      r^  of  a  language  must  each  designate  only  a  smgle 

rarily    finite.     Conse-  .  Jo 

qnencee  of  this.  notion,  —  a  single  fasciculus  of  thought,  —  the 

multitude  of  notions  not  designated  being  al- 
lowed to  perish,  never  obtaining  more  than  a  momentary  exist- 
ence in  the  mind  of  the  individual ;  or  the  words  of  a  language 
must  each  be  employed  to  denote  a  plurality  of  concepts.  In 
the  former  case,  a  small  amount  of  thought  would  be  expressed, 
but  that  precisely  and  without  ambiguity;  in  the  latter,  a  large 
amount  of  thought  Avould  be  expressed,  but  that  vaguely  and 
equivocally.  Of  these  alternatives  (each  of  which  has  thus  its 
advantages  and  'disadvantages),  the  latter  is  the  one  which  has 
universally  been  preferred ;  and,  accordingly,  all  languages  by  the 
same  word  express  a  multitude  of  thoughts,  more  or  less  differing 
from  each  other.  Nov.',  what  is  the  consequence  of  this?  It  i« 
plain  that  if  a  word  has  more  than  a  single  meaning  attached 
to  it,  when  it  is  employed  it  cannot  of  itself  directly  and  per- 
emptorily suggest  any  definite  thought;  —  all  that  it  can  do  is 
vaguely  and  hypothetically  to  suggest  a  variety  of  different  no- 
tions ;  and  we  are  obliged  from  a  consideration  of  the  context, 
—  of  the  tenor,  —  of  the  general  analogy,  of  the  discourse,  to  sur- 
mise, wifh  greater  or  less  assurance,  with  greater  or  less  precision, 
what  p;uticular  bundle  of  characters  it  was  intended  to  convey. 
Words,  in   fact,  as   languages   are   constituted, 

Words  are   mcrclv  i  j.t  •  ^i,  j.  ii  • 

,     ■        do  nothing  more  than  suggest,  —  are  nothing 

liintK  to  the  nund  *  trJ5        i  » 

more  than  hints ;  hints,  likewise,  which  leave 
the  principal  part  of  the  process  of  interpretation  to  be  performed 
by  the  mind  of  the  hearer.  In  this  respect,  the  effect  of  words 
resembles  the  effect  of  an  outline  or  shade  of  a  countenance 
with  which  we  are  familiar.  In  both  cases,  the  mind  is  stimulated 
to  fill  up  what  is  only  hinted  or  pointed  at.  Thus  it  is  that  the 
function'  of  language  is  not  so  much  to  infuse  knowledge  from 
one  intelligence  to  another,  as  to  bring  two  minds  into  the  same 
train  of  thinking,  and  to  confine  them  to  the  same  track.  In  this 
procedure  what  is  chiefly  wonderful,  is  the  rapidity  with  which  the 
mind  compares  the  word  with  its  correlations,  and  in  general,  with- 
out the  slightest  effort,  decides  which  among  its  various  meanings 


438  LOGIC.  .     Li^ci.  XXXL 

is  the  one  which  it  is  here  intended  to  convey.  But  liow  marvel-- 
lous  soever  be  the  ease  and  velocity  of  this  process  of  selection,  it 
cannot  always  be  performed  with  equal  certainty.  Words  are  often 
employed  with  a  plurality  of  meanings ;  several  of  which  may 
quadrate,  or  be  supposed  to  quadrate,  with  the  general  tenor 
of  the  discourse.  Error  is  thus  possible  ;  and  it  is  also  proba- 
ble, if  we  have  any  prepossession  in  fixvor  of  one  interpreta- 
tion rather  than  of  another.  So  copious  a  source  of  error  is 
the  ambiguity  of  language,  that  a  very  large  jDroportion  of  human 
controversy  has  been  concerning  the  sense  in  which  ceilain  terms 
should  be  understood;  and  many  disputes  have  even  been  fiercely 
waged,  in  consequence  of  the  disputants  being  unaware  that 
they  agreed  in  opinion,  and  only  differed  in  tlie  meaning  they 
attached  to  the  words  in  which  that  opinion  was  expressed. 
On  this  subject  I  may  refer  you  to  the  very  amusing  and  very 
instructive  treatise  of  Werenfelsias,  entitled  De  LogomacMis 
Eruditorum. 

"In  regard  to  a  remedy  for  this  description  of  error,  —  this  lies 
exclusively  in  a  thorough  study  of  the  language 

Remedy  for  error       employed  in  the  communication  of  knowledge, 

arising      from     Lan-  ,    .  .  •  >       i  »  »>  /-i  •  • 

g  and  m  an  acquaintance  with  the  rules  ot  Criti- 

cism and  Interpretation.  The  stuuy  of  lan- 
guages, when  rationally  pursued,  is  not  so  unimportant  as'manjr 
fondly  conceive ;  for  misconceptions  most  frequently  ai"ise  solely 
from  an  ignorance  of  words ;  and  eveiy  language  may,  in  a  cer- 
tain sort,  be  viewed  as  a  commentary  upon  Logic,  inasmuch  as 
every  language,  in  like  manner,  mirrors  in  itself  the  laws  of 
thought. 

"In  reference  to  the  rules  of  Criticism  and  Interpretation, — 
these  especially  should  be  familiar  to  those  who  make  a  study 
of  the  writings  of  ancient  authors,  as  these  writings  have  de- 
scended to  us  often  in  a  very  mutilated  state,  and  are  composed 
in  languages  which  are  now  dead.  How  many  theological  errors, 
for  example,  have  only  arisen  because  the  divines  were  either 
ignorant  of  the  principles  of  Criticism  and  Hermeneutic,  or 
did  not  properly  apply  them!  Doctrines  originating  in  a  cor* 
rupted  lection,  or  in  a  figurative  expression,  have  thus  arisen-j 
and  been  keenly  defended.  Such  errora  are  best  combated  bj 
philological  weapons ;  for  these  pull  them  up  along  with  their 
roots. 

"  A  thorough  knowledge  of  languages  in  general  accustoms  th« 
mind  not  to  remain   satisfied  with  the  husk,  but  to  penetrate  io,^ 
oven  to  the  kernel.     With  this  knowledge  we  shall  not  so  easiljri 


Lect.  XXXI.  LOGIC.  439 

imagine  'that  we  understand  a  system,  when  we  only  possess 
the  language  in  which  it  is  expressed ;  we  sliall  not  conceive 
that  we  truly  reason,  when  we  only  employ  certain  empty  words 
and  formulae ;  we  shall  not  betray  oui-selves  into  unusual  and 
obscure  expressions,  under  which  our  meaning  may  be  easily  mis- 
taken ;  finally,  we  shall  not  dispute  with  others  about  words,  when 
we  are  in  fact  at  one  with  them  in  regard  to  things."  ^  So  much 
for  the  errors  which  originate  in  Language. 

As  to   the   last   source   of   Error   which   I   enumerated,  —  the 

Objects  themselves  of  our  knowledge,  —  it  is 

IV.  Source  of  Error,      hardly  necessary  to  say  anything.     It  is  evident 

—  the  Objects  of  our         ^i     ^  ^^  i  i       i     , 

..      ,  ,  that   some   matters   are  obscure   and   abstruse. 

Knowledge.  '. 

while  others  are  clear  and  palpable  ;  and  that» 
consequently,  the  probability  of  error  is  greater  in  some  studies 
than  it  is  in  others.  But  as  it  is  impossible  to  deliver  any  special 
rules  for  these  cases,  different  from  those  which  are  given  for  the 
Acquisition  of  Knowledge  in  general,  concerning  which  we  are 
soon  to  speak,  —  this  source  of  error  may  be,  therefore,  passed  over 
in  silence. 

We   have   now  thus  finished   the   consideration  of  the  various 
Sources  of  Error,  and  — 

%  CV.   The   following   rules   may  be  given,  as  the  results 
of  the  foregoing  discussion,  touching  the 

Par.     CV.       Kules  &         O  '  & 

touching  the  Causes       Causcs  and  Remedies  of  our  False  Judg- 

and  Semedies  of  our  mentS 

False  Judgments.  __, 

1°.  Endeavor  as  far  as  possible  to  obtain 
a  clear  and  thorough  insight  into  the  laws  of  the  Understand- 
ing, and  of  the  Mental  Faculties  in  general.  Study  Logic  and 
Psychology. 

2°.  Assiduously  exercise  your  mind  in  the  application  of 
these  laws.     Learn  to  think  methodically. 

3°.  Concentrate  your  attention  in  the  act  of  Thinking ; 
and  principally  employ  the  seasons  when  the  Intellect  is 
alert,  the  Passions  slumbering,  and  no  external  causes  of 
distraction  at  work. 

4°.  Carefully  eliminate  all  foreign  interests  from  the  objects 
of  your  inquiry,  and  allow  yourselves  to  be  actuated  by  the 
interest  of  Truth  alone. 

5".  Contrast  your  various  convictions,  your  past  and  present 
judgments,  with  each  other ;  and  admit  no  conclusion  as  cer- 

iKrug,  Logik,  i  157.    Anm.  —  Ed. 


440 


LOGIC. 


Lrct.  XXXI 


tain,  until  it  has  been  once  and  again  thoroughly  e^famined, 
and  its  correctness  ascertained. 

6°.  Collate  your  own  persuasions  with  those  of  others; 
attentively  listen  to  and  weigh,  without  prepossession,  the 
judgments  formed  by  others  of  the  opinions  which  you  your- 
selves maintain.^ 


1  Cf.  Krug,  Logik,  { 16a    BacbmaDn,  Logik,  i  416-  —Ed. 


LECTURE    XXXII. 

MODIFIED     METHODOLOGY. 


Means  by  which  oar 
knowledge  obtains  the 
character  of  Perfec- 
tion, viz.,  the  Acquisi- 
tion and  the  Commu- 
nication of  Knowl- 
edge. 


SECTION  I.— OF  THE  ACQUISITION  OF  KNOWLEDGR 

I.  EXPERIENCE.  — A.  PERSONAL:  —  OBSERVATION- 
INDUCTION  AND  ANALOGY. 

In  our  last  Lecture,  having  concluded  the  Second  Department 
of  Concrete  Logic,  —  that  which  treats  of  the 
Causes  of  Error,  we  now  enter  upon  the  Third 
part  of  Concrete  or  Modified  Logic,  —  that 
which  considers  the  Means  hy  which  our 
Knowledge  obtains  the  character  of  Perfec- 
tion.  These  means  may,  in  general,  be  re- 
garded as  two,  —  the  Acquisition  and  the 
Communication  of  knowledge,  —  and  these  two  means  we  shall, 
accordingly,  consider  consecutively  and  apart. 

In  regard  to  the  Acquisition  of  Knowledge,  —  we  must  consider 
this  by  reference  to  the  different  kinds  of  knowl- 
edge of  which  the  human  intellect  is  capable. 
And  this,  viewed  in  its  greatest  universality,  is 
of  two  species. 

Human  knowledge,  I  say,  viewed  in  its  greatest  universality,  is 
of  two  kinds.     For  either  it  is  one  of  which  the 
uman     now  e  ge       objects  are  given  as  contingent  phaenomena,  or 
one  in  which  the  objects  are  given  as  necessary 
&cts  or  laws.     In  the  former  case,  the  cognitions  are  called  empir- 
ical^ experiential,  or  of  experience;   in   the  latter,  puT^,  intuitive, 
rational,  or  of  reason,  also  of  common  sense.     These  two  kinds 
of  knowledge   are,  likewise,  severally  denominated   cognitions  a 
posteriori  and  cognitions  a  2>}'iori.     The  distinction  of  these  two 
species  of  cognitions  consists  properly  in  this,  —  that  the  former 
are  solely  derived  frotn  the  Pi-esentations  of  Sense,  External  and 
Internal ;  whereas  the  ktter,  though  first  manifested  on  the  occasion 

56 


The   acquisition    of 
Knowledge. 


442  LOGIC  Lect.  XXXIL 

of  such  Presentations,  are  not,  however,  mere  products  of  Sense; 
on  the  contrary,  they  are  laws,  principles,  forms,  notions,  or  by 
whatever  name  they  may  be  called,  native  and  original  to  the  mind, 
that  is,  founded  in,  or  constituting  the  very  nature  of.  Intelligence ; 
:in<l,  accordingly,  out  of  the  mind  itself  they  must  be  developed, 
.'tnd  not  sought  for  and  acquired  as  foreign  and  accidental  acquisi- 
tions. As  the  Presentative  Faculties  inform  us  only  of  what  exists 
and  what  happens,  that  is,  only  of  facts  and  events,  —  such  empir- 
ical knowledge  constitutes  no  necessary  and  universal  judgment; 
all,  in  this  case,  is  contingent  and  particular,  for  even  our  general- 
ized knowledge  has  only  a  relative  and  precarious  universality. 
The  cognitions,  on  the  other  hand,  which  are  given  as  Laws  of 
Mind,  are,  at  once  and  in  .themselves,  universal  and  necessary.  We 
cannot  but  think  them,  if  we  think  at  all.  The 
Doctrine  of  the  Ac-      doctnne,  therefore,  of  the  Acquisitiou'of  Knowl- 

fiuisition    of    Knowl-  ■,  .  '   ^      c  j.  ^  ^i       ii     ^  ^        ^ 

,  .  .     ,  „  edge,  must  consist  of  two  parts,  —  the  nrst  treat- 

edge  consists  ol  two        . 

parts.  iHg  of  the  acquisition  of  knowledge  through  the 

data  of  Experience,  the  second,  of  the  acquisi- 
tion of  knowledge  through  the  data  of  Intelligence.^ 

In  regard  to  the  first  of  these  sources,  viz..  Experience,  —  this  is 
either  our  own  experience  or  the  experience  of 
I.  The  Doctrine  of  others,  and  in  either  case  it  is  for  lis  a  mean  of 
encror'two  kinds!*"  knowledge.  It  is  manifest  that  the  knowledge 
we  acquire  through  our  jjersonal  experience,  is 
far  superior  in  degree  to  that  which  we  obtain  through  the  experi- 
ence of  other  men ;  inasmuch  as  our  knowledge  of  an  object,  in 
the  fonner  case,  is  far  clearer  and  more  distinct,  far  more  complete 
and  lively,  than  in  the  latter;  while  at  the  same  time  the  latter 
also  affords  us  a  far  inferior  conviction  of  the  correctness  and  cer- 
tainty of  the  cognition  than  the  former.  On  the  other  band,  for- 
eign is  far  superior  to  our  propei  experience  in  this,  —  that  it  is 
much  more  comprehensive,  and  that,  without  this,  man  would  be 
deprived  of  those  branches  of  knowledge  which  are  to  him  of  the 
most  indispensable  importance.  Now,  as  the  principal  distinction 
of  ex))erience  is  thus  into  our  own  experience  and  into  the  experi- 
ence of  others,  we  must  consider  it  more  closely  in  this  twofold 
relation.''     First,  then,  of  our  Personal  Experience. 

Experience  necessarily  supposes,  as  its  primary  condition,  certain 
presentations  by  the  faculties  of  External  or  of  Internal  Perception, 


1  See  F.sf'er,  Lngik,  i  145  —  Ed.    In  regard      ocquired  cither,  1°,  By  experience;  or, 2°,  On 
to  tlic  nciiuisition  of  kno\vlcd;re,  — nil  knowl-      occasion  of  expericixc. 
ccigc  may  be  called  acquired,  inasmuch  as  it  is         2  Esfcr,  Lo^ik,  J  146.  —  'Ej>, 


Lect.  XXXII.  LOGIC.  443 

and  is,  therefore,  of  two  kinds,  according  as  it  is  conversant  about 

the  objects  of  the  one  of  these  faculties,  or  the 

1.  Personal  Expert-       objects  of  the  Other.     But  the  presentation  of  a 

ence.  ''  ^ 

fact  of  the  external  or  of  the  internal  M^orld  is 
not  at  once  an  experience.  To  this  there  is  required  a  continued 
series  of  such  presentations,  a  comparison  of  these  together,  a  men- 
tal separation  of  the  different,  a  mental  combination  of  the  similar, 
and  it,  therefore,  over  and  above  the  operation  of  the  Presentative 
Faculties,  requires  the  cooperation  of  the  Retentive,  the  Repro- 
ductive, the  Representative,  and  the  Elaborative  Faculties.  In 
regard  to  Experience,  as  the  first  means  by  which  we  acquire 
knowledge  through  the  legitimate  use  and  application  of  our  Cog- 
nitive Faculties,  I  give  you  the  following  pai*agraph : 

%  CVI.   The  First  Mean  towards  the  Acquisition  of  Knowl- 
edge  is  JExperience  {experientia^  ifnreLpia). 
Par.  CVI.    Ezperi-       Experience  may  be,  rudely  and  generally, 

ence;  what,  —  in  een-  .  . 

erai.  described  as  the  apprehension  of  the  phse- 

nomena  of  the  outer  world,  presented  by 
the  Faculty  of  External  Perception,  and  of  the  phsenomena  of 
the  inner  world,  presented  by  the  Faculty  of  Self-conscious- 
ness ;  —  these  phjenomena  being  retained  in  Memory,  ready  for 
Reproduction  and  Representation,  being  also  arranged  into 
order  by  the  Understanding. 

This  paragraph,  you  will  remark,  affords  only  a  preliminary  view 
of  the  general  conditions  of  Experience.     In 

Explication.  ir>i  ••  •  ^  ■,  •  i 

the  first  place,  it  is  evident,  that  without  the 
Presentative,  or,  as  they  may  with  equal  propriety  be  called,  the 
Acquisitive,  Faculties  of  Perception,  External  and  Internal,  no 
experience  would  be  possible.  But  these  faculties,  though  afford- 
ing the  fundamental  condition  of  knowledge,  do  not  of  themselves 
make  up  experience.  There  is,  moreover,  required  of  the  phaa- 
nomena  or  appearances  the  accumulation  and  retention,  the  repro- 
duction and  representation.  Memory,  Reminiscence,  and  Imagina- 
tion must,  therefore,  also  cooperate.  Finally,  unless  the  phajnoraena 
be  compared  together,  and  be  arranged  into  classes,  according  to 
their  similarities  and  differences,  it  is  evident  that  no  judgments, — 
no  conclusions,  can  be  formed  concerning  them  ;  but  without  a 
judgment  knowledge  is  impossible;  and  as  experience  is  a  knowl- 
edge, consequently  experience  is  impossible.  The  Understanding 
or  Elaborative  Faculty  must,  therefore,  likewise  cooperate.     Mani- 


444  LOGIC.  Lkct.  XXXIL 

ilus  has  well  expressed  the  nature  of  experience  in  the  following 
lines. 

"  Per  varies  usus  artem  experientia  fecit, 
Exemplo  monstrante  viam."  l 

And  Afranius  in  the  others: 

"Usus  me  Rcnuit,  mater  peperit  Memoria; 
Sophiam  voeant  me  Graii,  vo>  Sapientiam."' 

"  Our  own  observation,  be  it  external  or  internal,  is  either  with, 
or  without,  intention  ;  and  it  consists  either  of  a 

( 'ointnon  and  Scien-  •  i»-o  **•  i  au^^- 

.„   ^       .  series   ot    Presentations   alone,  or   Abstraction 

tine  Lxperieuce. 

and  Reflection  supervene,  so  that  the  presenta- 
tions obtain  that  completion  and  system  which  they  do  not  of 
themselves  possess.  In  the  former  case,  the  cxpericrrce  may  be 
called  an  Unlearned  or  a  Common;  in  the  latter,  a  Learned  or 
Scientific  Experieyice.    Intentional  and  reflective  experience  is  called 

Observation.  Observation  is  of  two  kinds;  for 
Observation, -what.       either  the   objects   which    it    considers   remain 

Of  two   kinds, —  Ob-  ,  j  ■  ^       .  t      .•         .1 

„  .       unchan2:ed,  or,  previous  to  its  application,  they 

Kcrvutio!)  i  roper,  sua  o       '        '   1  ^  11  i  j 

Kx|.».-i iincut.  •'ii'e  made  to  undergo  certain  arbitrary  changes, 

or  are  placed  in  certain  factitious  relations.  In 
the  latter  case,  the  observation  contains  the  specific  name  of  Ex- 
periment. Observation  and  ex[)erimcnt  do  not,  therefore,  constitute 
opposite  or  two  difierent  procedures,  —  the  latter  is,  in  propriety, 
only  a  certain  subordinate  modification  of  the  former ;  for,  while 
observation  may  accomplish  its  end  without  experiment,  experi- 
ment without  observation  is  impossible.  'Observation  and  experi- 
ment are  manifestly  exclusively  competent  upon  the  objects  of  our 
emiiincal  knowledge ;  and  they  cooperate,  equally  and  in  like  man- 
ner, to  the  progress  of  that  knowledge,  partly  by  establishing, 
partly  by  correcting,  partly  by  amplifying  it.  Under  observation, 
therefore,  is  not  to  be  undei*stood  a  common  or  unlearned  experi- 
ence, which  obtrudes  itself  upon  every  one  endowed  with  the 
ordinary  faculties  of  Sense  and  Understanding,  but  an  intentional 
and  continued  application  of  the  faculties  of  Perception,  combined 
with  an  abstractive  and  reflective  attention  to  an  object  or  class  of 
objects,  a  moixj  accurate  knowledge  of  jvhich,  it  is  proposed,  by  the 
observation,  to  accomplish.  But  in  order  that  the  observation 
sliould  accomplish  this  end,  —  more  especially  when  the  objects  are 

8  Fragmentum  t  Silla.    Vide  Corpus  Poetarum  Latinorum,  vol.  ii.  p.  1G18,  Loud.    1713.  — £o 


I.KCT.  XXXU.  LOGIC.  446 

numerous,  and  a  systematic  complement  of  cognitions  is  the  end 
proposed,  —  it  is  necessary  that  we  should  know 
praecognita  of  Ob-       certain   prjBCOi^nita,  —  1°.   What   we    ought   to 
observe  ;  2°.  How  we  ought  to  observe  ;  and  S". 
By  what  means  are  the  data  of  observation  to  be  reduced  to  sys- 
tem.    The  first  of  these  concerns  the  Object;  the  second,  the  Pro- 
cedure ;  the  third,  the  scientific  Completion,  of  the  observations. 
It  is  proper  to  make  some  general  observations  in  regard  to  these, 
in  their  order;  and  first,  of  the  Object  of  observation, —  the  what 
we  ought  to  observe. 

"The  Object  of  Observation  can  only  be  some  given  and  deter- 
minate phjenomenon,  and  this  phsenomenon  ei- 
Firet,  — The  Object       thcr  an  external  or  an  internal.  Thnough  observa- 
T-u-  r  I  ij  tion,  whether  external  or  internal,  there  are  four 

Th»  fourfold.  '  ' 

several  cognitions  which  we  propose  to  compass, 

—  viz.,  to  ascertain —  1°.  What  the  Phaenomena  themselves  are;  2". 

What  are  the  Conditions  of  their  Reality ;  3°.  What  are  the  Causes 

of  their  Existence ;  4°.  What  is  the  Order  of  their  Consecution. 

"In  regard  to  what  the  phaenomena  themselves  are  (quid  sint), 

that  is,  in  regard  to  what  constitutes  their  pecu- 

1°.  What  the  Phaj-       jj^^,   nature,  —  this,  it  is  evident,  must  be  the 

nomena  are.  .  „.,..,. 

primary  matter  of  consideration,  it  being  always 
supposed  that  the  fact  (the  an  sit)  of  the  phsenomenon  itself  has 
been  established.^  To  this  there  is  required,  above  all,  a  clear  and 
distinct  Presentation  or  Representation  of  the  object.     In  order  to 

obtain  this,  it  behooves  us  to  analyze,  —  to  dis- 

in  their  individual       member,  the   constituent  parts   of  the   object, 

pecu  lan  es  an    con.       ^^^  ^^  take  into  proximate  account  those  char- 

trasta.  \ 

acters  which  constitute  the  object,  that  is,  which 
make  it  to  be  what  it  is,  and  nothing  but  what  it  is.  This  being 
performed,  we  must  proceed  to  compare  it  with  other  objects,  and 
with  those  especially  which  bear  to  it  the  strongest  similarity, 
taking  accurate  note  always  of  those  points  in  which  they  recipro- 
cally resemble  and  in  which  they  reciprocally  disagree. 

"But  it  is  not  enough  to  consider  the  several  phaenomena  in  their 

individual  peculiarities  and  contrasts,  —  in  what 

As  under  determi-         ^j^gy  ^^,^^  ^^^    J^  ^,\^^^   ^j^py  are  not,  —  it   is   also 
nate  genera  and  spe-  .   .  ,     .  ,  i         ^    ^  •      .. 

gj^  requisite  to  bring  them  under  determinate  gen- 

era and  species.  To  this  end  we  must,  having 
obtained  (as  previously  prescribed)  a  clear  and  distinct  knowledge 
of  the  several  phaenomena  in  their  essential  similarities  and  differ- 
ences, look  away  or  abstract  from  the  latter,  —  the  differenc^is,  and 

I  Better  the  Aristotelic  questions,  —  ^n  Sit,  etc.   [See  Lectures  on  Metaphysics,  p.  4V    -  Ed.] 


446  LOGIC.  Lect.  xxxn. 

comprehend  the  former,  —  the  similarities,  in  a  compendious  and 
characteristic  notion,  under  an  appropriate  name. 

"  When  the  distinctive  peculiarities  of  the  }>haBnomena  have  been 

thus  definitively  recognized,  the   second   ques- 

*•        *•'.!.    'LT/'       tion    emerges,  —  What  are   the   Conditions  of 

tions  of  their  Reality.  .  . 

their  Reality.  These  conditions  are  commonly 
called  Requisites,  and  under  requisite  we  must  understand  all  that 
must  have  preceded,  before  the  phaenomena  could  follow.  In  order 
to  discover  the  requisites,  we  take  a  number  of  analogous  cases,  or 
cases  similar  in  kind,  and  inquire  what  arc  the  circumstances  under 
which  the  phasnomenon  always  arises,  if  it  does  arise,  and  what  are 
the  circumstances  under  which  it  never  arises;  and  then,  after  a 
competent  observation  of  individual  cases,  we  construct  the  general 
judgment,  that  the  phaenomenon  never  occurs  unless  this  or  that 
other  phaenomenon  has  preceded,  or  at  least  accompanied,  it.  Here, 
however,  it  must  be  noticed,  that  nothing  can  be  viewed  as  a  requi- 
site which  admits  of  any,  even  the  smallest,  exception. 

"The  requisite  conditions  being  discovered,  the  third  question 
arises,  —  What  are  the  Causes  of  the  Phaenom- 

3"  What  the  Causes       ^^^^    According   to   the   current   doctrine,  the 

of  the  rhsenomena.  ^ 

causes  of  phaenomena  are  not  to  be  confounded 
with  their  requisites;  for  although  a  phaenomenon  no  more  occurs 
without  its  requisite  than  without  its  cause,  still,  the  requisite  being 
given,  the  phaenomenon  does  not  necessarily  follow,  and,  indeed, 
very  frequently  does  not  ensue.  On  the  contrary,  if  the  cause 
occurs,  the  phaenomenon  must  occur  also.  In  other  words,  the 
requisite  or  condition  is  that  without  which  the  phaenomenon  never 
is ;  the  cause,  on  the  other  hand,  is  that  through  which  it  always  is. 
Thus  an  emotion  of  pity  never  arises  without  a  knowledge  of  the 
misfortune  of  another;  but  so  little  does  this  knowledge  necessitate 
that  emotion,  that  its  opposite,  a  feeling  of  rejoicing,  complacency, 
at  such  suffering  may  ensue ;  whereas  the  knowledge  of  another's 
misfortune  must  be  followed  by  a  sentiment  of  pity,  if  we  are  pre- 
disposed in  favor  of  the  person  to  whom  the  misfortune  has  oc- 
curred. In  this  view,  the  knowledge  of  another's  misfortune  is 
only  a  requisite;  whereas  our  favorable  predisposition  constitutes 
the  cause.  It  must,  however,  be  admitted,  that  in  different  rela- 
tions one  and  the  same  circutnstance  may  be  both  requisite  and 
cause ;"^  and,  in  point  of  fact,  it  would  be  more  correct  to  consider 
the  cause  as  the  whole  sura  of  antecedents,  without  which  the  phae- 
nomenon never  does  take  place,  and  with  which  it  always  must. 

1  Easer,  Logik,  { 148.  — Ed. 


Lect.   XXXII.  LOGIC.  447 

What  are  commonly  callecl  requisites,  are  thus,  in  truth,  only  partial 
causes ;  what  are  callecl  causes,  only  proximate  requisites. 

"In  the  fourth  place,  having  ascertained  the  essential  qualities, — 

•  the  Conditions  and  the  Causes  of  pluEnomena, 

4».  What  the  Order       _^    ^^^^    question    emerges,  —  What    is    the 

of  tlieir  Consecution.  r^    -,         •  i-ii  .^  ,«  ti- 

Order  in  which  they  are  manifested  ?  and  this 
being  ascertained,  the  observation  has  accomplished  its  end.  This 
question  applies  either  to  a  phaenomenon  considered  in  itself^  or  to  a 
j)ha?nomenon  considered  in  relation  to  others.  In  relation  to  itself, 
(ho  question  concerns  only  the  time  of  its  origin,  of  its  continuance, 
and  of  its  termination ;  in  relation  to  others,  it  concerns  the  recip' 
rocal  consecution  in  which  the  several  phaenomena  api^ear." ' 

"We  now  go  on  to  the  Second  Pra9cognitum,  —  the  Manner  of 

Observation,  —  How  we  are  to  observe.     What 
Second,  -  The  Man-       ^^  ^^^^,^  hitherto  spoken  of  —  the  Object  —  can 

ner  of  Observation.  '■  n    • 

be  known  only  in  one  way,  —  the  way  of  Scien- 
tific Observation.  It  therefore  remains  to  be  asked,  —  How  must 
the  observation  be  instituted,  so  as  to  afford  us  a  satisfactory  result 
in  regard  to  all  the  four  sides  on  which  it  behooves  an  object  to  be 

observed  ?  In  the  first  place,  as  preliminary  to 
.     roper  g  ate  o        observation,  it   is  required  that  the    observins: 

the  observing  mind.  ,  ,  -^  ^ 

mind  be  tranquil  and  composed,  be  exempt 
from  prejudice,  partiality,  and  prepossession,  and  be  actuated  by 
no  other  interest  than  the  discovery  of  truth.  Tranquillity  and 
composure  of  mind  are  of  peculiar  importance  in  our  observation  of 
the  phaenomena  of  the  internal  world;  for  these  phrenomena  are  not, 
like  those  of  the  external,  perceptible  by  sense,  enclosed  in  space, 
continuous  and  divisible;  and  they  follow  each  other  in  such  num- 
bers, and  with  such  a  rapidity,  that  they  are  at  best  observable  with 
difficulty,  often  losing  even  their  existence  by  the  interference  of 
the  observing,  —  the  reflective  energy,  itself.  But  that  the  obser- 
vation should  be  always  conducted  in  the  calm  and  collected  state 
of  mind  required  to  purify  this  condition,  we  must  be  careful  to 
obtain,  more  and  more,  a  mastery  over  the  Attention,  so  as  to  turn 
it  with  full  force  upon  a  single  aspect  of  the  phenomena,  and,  conse- 
quently, to  abstract  it  altogether  from  every  other.  Its  proper  func- 
tion is  to  contemplate  the  objects  of  observation  tranquilly,  continu- 
ously, and  without  anxiety  for  the  result ;  and  this,  likewise,  without 
too  intense  an  activity  or  too  vigorous  an  application  of  its  forces. 
Bi;t  the  observation  and  concomitant  energy  of  attention  will  be 
without  result,  unless  we  previously  well  consider  what  pi-ecise 
object  or  objects  we.  are  now  to  observe.     Nor  will  our  experience 

1  Esser,  Logik,  §  148.  —  Ed. 


44s  LOGIC.  Lect.  XXXIL 

obtain  an  answer  to  the  question  proposed  for  it  to  solve,  unless 

that  question  be  of  such  a  nature  as  will  animate 

2^,  Conditions  of  the       i]^q  observing  faculties  by  some  stimixlus,  and 

question  to  be  deter-  .         ,,  ,    .  •       .       t        ,•  -nxi  i  • 

.     . ,    ^.     .  give  them  a  determinate  dirc^'tion.     Where  this 

mined  by  the  observa-        p 

tioM.  is  not  the  case,  attention  does  not  effect  any- 

thing, nay,  it  does  not  operate  at  all.  On  this 
account  such  psychological  questions  as  the  following  :  What  takes 
place  in  the  process  of  Self-consciousness,  —  of  Perception,  —  of 
Vision,  —  of  Hearing,  —  of  Imagination,  etc.,  —  cannot  be  an- 
swered, as  thus  absolutely  stated,  that  is,  without  reference  to 
some  determinate  object.  But  if  I  propose  the  problem, —  What 
takes  place  when  I  see  this  or  that  object,  or  better  still,  when  I  •seo 
this  table,  —  the  attention  is  stimulated  and  directed,  and  oven  a 
child  can  give  responses,  which,  if  properly  illustrated  and  ex- 
plained, will  afford  a  solution  to  the  problem.  If,  therefore,  the 
question  upon  the  object  of  observation  be  too  vague  and  general, 
so  that  the  attention  is  not  suitably  excited  and  applied,  —  thia 
question  must  be  divided  and  subdivided  into  others  more  par- 
ticular, and  tliis  process  must  bo  continued  until  wc  reach  a  ques- 
tion which  affords  the  requisite  conditions.  We  should,  therefore, 
detoiinine  as  closely  as  possible  the  object  itself  and  the  phases  in 
whicii  we  wish  to  observe  it,  separate  from  it  all  foreign  or  adventi- 
tious parts,  resolve  every  question  into  its  constituent  elements, 
enunciate  each  of  these  as  specially  as  ])ossible,  and  never  couch  it 
in  vague  and  general  expressions.  But  here  we  must  at  tlie  same 
time  take  care  that  the  object  be  not  so  torn  and  mangled  that  the 
attention  feels  no  longer  any  attraction  to  the  several  parts,  or  that 
the  several  parts  can  no  longer  be  viewed  in  their  natural  connec- 
tion. So  much  it  is  possible  to  say  in  general,  touching  the  Man- 
ner in  which  observation  ought  to  be  carried  on ;  what  may  further 
be  added  under  this  head,  depends  upon  the  particular  nature  of 
tlve  objects  to  be  observed."  * 

"In  this  manner,  then,  must  we  proceed,  until  all  lias  been 
accomplished  wjiich  the  problem,  to  be  answered  by  the  observa- 
tion, pointed  out.  When  the  observation  is  concluded,  an  accurate 
)('<'ord  or  notation  of  what  has  been  observed  is  of  use,  in  order  to 
I'liable  us  to  supply  Avhat  is  found  wanting  in  our  subsequent  obser- 
\  :ition.  If  we  have  accumnlated  a  considerable  apparatus  of  re- 
sults, in  relation  to  the  object  we  observe,  it  is  proper  to  take  a 
survey  of  these ;  from  what  is  found  defective,  new  questions  must 
be  evolved,  and  an  answer  to  these  sought  out  through  new  obser- 

1  Esser,  Logik,  f  149.  —  Ed 


Lkct.  :: :ixii.  logic.  449 

vations.  When  the  inquiry  lias  nttnined  its  issue,  a  tabular  view  of 
all  the  observations  made  upon  the  subject  is  convenient,  to  afford 
a  conspectus  of  the  whole,  and  as  an  aid  to  the  memory.  But  how 
(and  this  is  the  Third  Precognition)  individual 
Third,  — The  means  observations  are  to  be  built  up  into  a  systematic 
by  which  the  data  of      ^j^^j^^  j^  ^^  ^^  sou^ht  for  partly  from  the  nature 

Observation  are  to  be  /.       •  .  ,  i      /^  i  /> 

rwiuced  to  System.  ^^  science  in  general,  partly  from  the  nature  of 

the  particular  empirical  science  for  the  constitu- 
tion of  which  the  observation  is  applied.  Nor  is  what  is  thus  sought 
difficult  to  find.  It  is  at  once  evident,  that  a  synthetic  arrangement 
is  least  applicable  in  tlje  empirical  sciences.  For,  anterior  to  obser- 
vation, the  object  is  absolutely  unknown  ;  and  it  is  only  through 
observation  that  it  becomes  a  matter  of  science.  We  can,  therefore, 
only  go  to  work  in  a  problematic  or  interrogative  manner,  and  it 
is  impossible  to  commence  by  assertory  propositions,  of  which  we 
afterwards  lead  the  demonstration.  We  must,  therefore,  determine 
the  object  on  all  sides,  in  so  far  as  observation  is  competent  to  this;; 
we  must  analyze  every  question  into  its  subordinate  questions,  and 
each  of  these  must  find  its  answer  in  observation.  The  systematic 
order  is  thus  given  naturally  and  of  itself;  and  in  this  procedure  it 
is  impossible  that  it  should  not  be  given.  But  for  a  comprehensive 
and  all-sided  system  of  empirical  knowledge,  it  is  not  sutficienl  to- 
possess  the  whole  data  of  observation,  to  have  collected  these  to- 
gether, and  to  have  arranged  them  according  to  some  external  prin- 
ciple ;  it  is,  likewise,  requisite  that  we  have  a  thorough-going  prin- 
ci])le  of  explanation,  even  though  this  explanation  be  impossible  in 
the  way  of  observation,  and  a  power  of  judging  of  the  data,  ac- 
cording to  universal  laws,  although  these  universal  laws  may  not  be 
discovered  by  experience  alone.  These  two  ends  are  accomplished 
by  different  means.  The  former  we  compass  by  the  aid  of  Hypoth- 
esis, the  latter,  by  the  aid  of  Induction  and  Analogy."^  Of  theso 
in  detail.  In  regard  to  Hypothesis,  I  give  you  the  following, 
paragraph. 

%.  CVII.   When  a  phsenomenon  is  presented,  which  can  be- 
explained  by  no  principle  afforded  through 
Par.  CVII.  Hypoth-       Experience,' We   feel  discontented  and  un- 

esia,  —  what.  *  ^ 

easy ;  and  there  arises  an  effort  to  discover  • 
gome  cause  which  may,  at  least  provisorily,  account  for  the 
outstanding  phaenomenon ;  and  this  cause  is  finally  recognized 
as  valid  and  true,  if,  through   it,  the  given  phaenomenon  is- 

1  Esser,  Logik,  J  150.  —  Ed. 

57 


450  LOGIC.  Lect.  XXXlL 

found  to  obtain  a  full  and  perfect  explanation.  The  judgment 
in  which  a  phaenomenon  is  referred  to  such  a  problematic 
cause,  is  called  an  Hypothesis} 

Hypotheses  have  thus  no  other  end  than  to  satisfy  the  desire  of 

the  mind  to  reduce  the  objects  of  its  knowledge 

\p  ication.  ^^  unity  and  system  :  and  they  do  this  in  recall- 

Hypothesis, — its  end.         .  ■'  ^  '  •/     ^      ^ 

ing  them,  ad  interim,  to  some  principle,  through 

which  the  mind  is  enabled  to  comprehend  them.  From  this  view 
of  their  nature,  it  is  manifest  how  far  they  are  permissible,  and  how 
far  they  are  even  useful  and  expedient ;  throwing  altogether  out  of 
account  the  possibility,  that  what  is  at  first  assumed  as  hypothetical, 
may,  subsequently,  be  proved  true. 

When  our  experience  has  revealed  to  us  a  certain  correspondence 
among  a  number  of  objects,  we  are  determined,  by  an  origmal  prin- 
ciple of  our  nature,  to  suppose  the  existence  of  a  more  extensive 
conespondence  than  our  observation  has  already  proved,  or  may 
ever  be  able  to  establish.  This  tendency  to  generalize  our  knowl- 
edge by  the  judgment,  —  that  where  mucli  has  been  found  accord- 
ant, all  will  be  found  accordant,  —  is  not  properly  a  conclusion 
deduced  from  premises,  but  an  original  principle  of  our  nature, 
which  we  may  call  that  o^  Logical^  or  perhaps  better,  that  of  I* hila- 
sophical,  Presumption.  This  Presumption  is  of  two  kinds;  it  i? 
either  Induction  or  Analogy,  which,  though  usually  confounded, 
are,  however,  to  be  carefully  distinguished.  I  shall  commence  th<» 
consideration  of  these  by  the  following  paragraph. 

%  CVIII.    If  we  have  uniformly  observed  that  a  number  of 

objects  of  the  same  class  (genus  or  species) 

Par.  cviii.   Indue-       posscss  in  couimon  a  certain  attribute,  we 

tlon  and  Analogy.  ' 

are  disposed  to  conclude  that  this  attribute 
is  possessed  by  all  the  objects  of  that  class.  This  conclusion  is 
properly  called  an  Inference  of  Induction.  Again,  if  we  have 
observed  that  two  or  more  things  agree  in  several  internal  and 
essential  characters,  we  are  disposed  to  conclude  that  they 
agree,  likewise,  in  all  other  essential  characters,  that  is,  that 
they  are  constituents  of  the  same  class  (genus  or  species). 
This  conclusion  is  properly  called  an  Inference  of  Analogy. 
The  principle  by  which,  in  cither  case,  we  are  disposed  to 
extend  our  inferences  beyond  the  limits  of  experience,  is  a  nat- 
ural or  ultimate  principle  of  intelligence ;  and  may  be  called 

I  EsMr,  Logik,  i  151      Ci.  Ltcturti  on  Xtiaphysics,  p  117  et  aeq.  —  Ed 


Lect.  XXXII.  LOGIC.  451 

the  principle  of  Logical^  or,  more  properly,  of  Philosophicai 
Presumption} 

"The  reasoning  by  Induction   and  the  reasoning   by  Analogy 

have  this  in  common,  that  they  both  conclude 

Explication.  from  something  observed  to  something  not  ob- 

Induction  and  Anal-  i        /•  ^i  •  -.i  •        ^  ^i  • 

,   .  served  ;    from   somethmi;   within    to    something 

ogy,  —  their       agree-  ^  o  o 

ment and  diiTerence.  beyond  the  Sphere  of  actual  experience.     They 

differ,  however,  in  this,  that,  in  Induction,  that 
which  is  observed  and  from  which  the  inference  is  drawn  to  that 
which  is  not  observed,  is  a  unity  in  plurality  ;  whereas,  in  Analogy, 
it  is  a  plurality  in  unity.  In  other  words,  in  Induction,  we  look  to 
the  one  in  the  many ;  in  Analogy  we  look  to  the  many  in  the  one : 
and  while  in  both  we  conclude  to  the  unity  in  totality,  we  do  this, 
in  Induction,  from  the  recognized  unity  in  plurality,  in  Analogy, 
from  the  recognized  plurality  in  unity.  Thus,  as  induction  rests 
upon  the  principle,  that  what  belongs  (or  does  not  belong)  to 
many  things  of  the  same  kind,  belongs  (or  does  not  belong)  to  all 
things  of  the  same  kind;  so  analogy  rests  upon  the  principle, — 
that  things  which  have  many  observed  attributes  in  common,  have 
other  not  observed  attributes  in  common  likewise."^  It  is  hardly 
necessary  to  remark  that  we  are  now  speaking  of  Induction  and 
Analogy,  not  as  principles  of  Pure  Logic,  and  as  necessitated  by 
the  fundamental  laws  of  thought,  but  of  these  as  means  of  acquir- 
ing knowledge,  and  as  legitimated  by  the  conditions  of  objective 
reality.  In  Pure  Logic,  Analogy  has  no  place,  and  only  that  induc- 
tion is  admitted,  in  which  all  the  several  parts  are  supposed  to 
legitimate  the  inference  to  the  whole.  Applied  Induction,  on  the 
contrary,  rests  on  the  constancy,  —  the  uniformity  of  nature,  and 
on  the  instinctive  expectation  we  have  of  this  stability.  This  con- 
stitutes what  has  been  called  the  principle  oi  Logical  Presumption^ 
though  perhaps  it  might,  with  greater  propriety,  be  called  the  prin- 
ciple of  Philosophical  Presumption.  We  shall  now  consider  these 
severally  ;  and,  first,  of  Induction. 

An  Induction  is  the  enumeration  of  the  parts,  in  order  to  /egiti- 
mate  a  iudsrment  in  regard  to  the  whole.^   Now, 

Induction,— what.  ,  J       &  f      .     ^.    . -,      .  . 

the  parts  may  either  be  individuals  or  particu- 
lars, strictly  so  called.     I  say  strictly  so  called,  for  you  are  aware 

1  Cf.  Esser,  Logik,  §J  140, 152.  Krug,  hogik,  H  3  [Cf.  Ahu  AU  (Avicenncp)  Viri  Docti,  De  Log- 

166,167,168.— Ed.  [Wolf,  Pkil.  Kationalis,  §  479.  ica,  Poema,  1.  190.    (In  Schmcilders,  Documenla 

Reusch,  Systfma  Logicum,  §§  572,573.  Nunne-  P/iilosophicF:  Arabum,  p. 36-)  Bonn!B,18S&.  Zaba- 

Siu8,  De  Constitutione  Artis  DiaUctica,  p.  126.]  rella.  Opera  Logica,  De  Natura  Logica,  Li.  i.  « 

a  Esser,  Logik,  i  152.  —  Ed.  18,  p.  46.] 


452 


LOGIC. 


lkct.  xxxn. 


Of  two  kinds,  —  In- 
dividual and  Special. 

vidual   Induction 


that  the  term  particular  is  very  commonly  employed,  not  only  to 
denote  the  species,  as  contained  under  a  genus,  but,  likewise,  to 
denote  the  individual,  as  contained  under  a  species.  Using,  how- 
ever, the  two  terms  in  their  proper  significations,  I  say,  if  the  parts 
are  individual  or  singular  things,  the  induction  is  then  called  Indi- 
vidual; whereas  if  the  parts  be  species  or  subal- 
tern genera,  the  induction  then  obtains  the 
name  of  Special.  An  example  of  the  Indi- 
is  given,  were  we  to  argue  thus,  —  Mercury^ 
Venus,  the  Earth,  Mars,  etc.,  are  bodies  in  themselves  o^yaque,  and 
which  borroio  their  light  from  the  sun.  But  Mercury,  Venus,  etc., 
are  planets.  Therefore,  all  planets  are  opaque,  and  borroio  their 
ligMfrom  the  sun.  An  example  of  the  special  is  given,  were  we  to 
argue  as  follows,  —  Quadrupeds,  birds,  fishes,  the  amphibia,  etc,  ctO 
have  a  nervous  system,.  But  quadrupeds,  birds,  etc.,  are  animah. 
Therefore  all  animals  (though  it  is  not  yet  detected  in  some)  have 
»  nervous  systein.  Xow,  here  it  is  manifest  that  Sj^ecial  rests  upon 
Individual  induction,  and  that,  in  the  last  result,  all  induction  is 
individual.  For  we  can  assert  nothing  concerning  species,  unless 
what  we  assert  of  them  has  been  previously  observed  in  their  con- 
•tituent  singulars.' 

For  a  legitimate  Induction  there  are  requisite  at  least  two  condi- 
tions.- In  the  fii-st  place,  it  is  necessary.  That 
the  partial  (and  this  word  I  use  as  including 
both  the  terms  individual  and  particular), —  I 
say,  it  is  necessary  that  the  partial  judgments 
out  of  which  the  total  or  general  judgment  is  inferred,  be  all  of  the 
same  quality.  For  if  one  even  of  the  partial  judgments  had  an 
opposite  quality,  the  whole  induction  would  be  subverted.  Hence 
it  is  that  we  refute  universal  judgments  founded  on  an  imperfect 
induction,  by  bringing  what  is  called  an  instance  {instantia),  that 
is,  by  adducing  a  thing  belonging  to  the  same  class  or  notion,  in 
reference  to  which  the  opposite  holds  true.  For  example,  the 
general  assertion,  All  dogs  bark,  is  refuted  by  the  instance  of  th« 
dogs  of  Labrador  or  California  (I  forget  which),  —  these  do  not 
bark.  In  like  manner,  the  general  assertion,  No  quadruped  is  ovi- 
parous, is  refuted  by  the  instance  of  the  Ornithorhynchus  Para- 
doxus. But  that  the  universal  judgment  must  have  the  same 
quality  as  the  partial,  is  self-evident;  for  this  judgment  is  simply 
the  assertion  of  something  to  be  true  of  all  which  is  true  of 
many. 

The  second   condition  required  is,  That  a  competent  number 


The  two  conditions 
of  legitimate  Induc- 
tion,—.First. 


1  Krng,  Logik,  (  167.    Anm.  —  Bd. 


»  Esser,  Logik,  f  IfiS.  —  £l>. 


Jtwer.  xxxu.  LOGIC.  45$ 

<rf  the  partial  objects  from  which  the  induction  departs  should  have 
been  observed,  for  otherwise  the  comprehensioo 
of  other  objects  «nder  the  total  judgment  would 
be  rash.'  What  is  the  number  of  such  ylyects,  vvliich  amounts  to  u 
Competent  induction,  it  i,s  not  jxjssible  to  say  in  general.  In  some 
ca«e«,  the  observation  of  a  very  few  parti<;ular  or  individual  exam- 
pleaB  is  sufficient  to  warrant  an  assertion  in  regard  to  the  whole 
class;  in  others,  the  total  judgment  is  hardly  cotnpctent,  until  our 
observation  has  gone  through  each  of  its  constituent  parts.  This 
distinction  is  founded  on  the  difference  of  essential  and  unessential 
characters.  If  the  character  be  essential  to  the  several  objects,  a 
eomparatively  limited  observatic*  is  necessary  to  legitimate  our 
geBei^al  conclusion.  For  example,  it  would  require  a  far  less  induc- 
tion to  prove  that  all  animals  breathe,  than  to  prove  that  the  mam- 
malia, and  the  mammalia  alone,  have  lateral  lobes  to  the  cerebellum. 
For  the  one  is  seen  to  be  a  function  necessary  to  animal  life ;  the 
other,  as  far  as  our  present  knowledge  reaches,  appears  only  as  an 
arbitrary  concomitant.  The  difference  of  essential  and  accidental 
]&,  however,  one  itself  founded  on  induction,  and  varies  according 
to  the  greater  or  less  perfection  to  which  this  has  been  carried.  In 
the  progress  of  science,  the  lateral  lobes  of  the  cerebellum  may 
appear  to  future  physiologists  as  necessary  a  condition  of  the  func- 
tion of  suckling  their  young,  as  the  organs  of  breathing  appear  to 
UB  of  circulation  and  of  life. 

To  sum  up  the  Doctrine  of  Induction,  —  "This  is  more  certain, 

1°,  In  proportion  to  the  number  and  diversity 

I  ummary   o     t  e       ^^  ^^^  objccts  observed  :  —  2°,  In  proportion  to 

doctrine  of  Induction.  *^  .  _  . 

the  accuracy  with  which  the  observation  and 
©omparison  have  been  conducted;  —  3°,  In  proportion  as  the  agree^ 
ment  of  the  objects  is  clear  and  precise  ;  —  and,  4°,  In  proportion 
a«  it  has  been  thorouglily  explored,  whether  there  exist  exception* 
or  not."  ^ 

Almost  all  induction  is,  however,  necessarily  imperfect;  and 
L^ic  can  inculcate  nothing  more  important  on  the  investigatoiis 
of  nature  than  that  sobriety  of  mind,  which  regards  all  its  'past 
observations  only  as  hypothetically  true,  only  as  relatively  com- 
plete, and  which,  consequently,  holds  the  mind  open  to  every  new 
observation,  which  may  correct  and  limit  its  former  judgments. 

So  much  for  Induction  ;  now  for  Analogy.  Analogy,  in  genei-al, 
means  proportion,  or  a  similarity  of  relation^^-. 

Analogy, -what.  ^,  .     ,  ,       .      „ 

Ihus,  to  judge  analogically,  or  accordmg  to 
aaalogy,  is  to  judge  things  by  the  eimilarity  of  their  relations. 

I  Esser,  Logik.  i  152—  Ed.  2  Esser.  Logik,  {  162.  — Ed. 


454  LOGIC.  lect.  xxxn. 

Thus  when  we  judge  that  as  two  is  to  four,  so  is  eight  to  sixteen, 
we  judge  that  they  are  analogically  identical ;  that  is,  though  the 
sums  in  other  respects  are  different,  they  agree  in  this,  that  as  two 
18  the  half  of  four,  so  eighths  the  half  of  sixteen. 

In  common  language,  however,  this  propriety  of  the  term  is  not 
preserved.  For  hy  analogy  is  not  always  meant  merely  hy  propor- 
tion^ but  frequently  hy  comparison  —  hy  relation,  or  simply  by  simi- 
larity. In  so  far  as  Analogy  constitutes  a  particular  kind  of  rea- 
soning from  the  individual  or  particular  to  the  universal,  it  signifies 
an  inference  from  the  partial  similarity  of  two  or  more  things  to 
their  complete  or  total  similarity.  For  example,  —  This  disease 
corresponds  in  many  symptoms  with  those  we  have  observed  in 
typhus  fevers ;  it  will,  therefore^  con'espond  in  all,  that  is,  it  is  a 
typhus  fever} 

Like  Induction,  Analogy  has  two  essential   requisites.     In  the 

first  place,  it  is  necessary  that  of  two  or  more 

-    ..^.    ^°  !f^"  '*        things  a  certain  number  of  attributes   should 

oonditions,  —  First.  ° 

have  been  observed,  in  oi-der  to  ground  the 
inference  that  they  also  agree  in  those  other  attributes,  which  it 
has  not  yet  been  ascertained  that  they  possos.s.  It  is  evident  that 
in  proportion  to  the  number  of  points  observed,  in  which  the 
things  compared  together  coincide,  in  the  same  proportion  can  it 
be  with  safety  assumed,  that  there  exists  a  common  principle  in 
these  things,  on  which  depends  the  similarity  in  the  points  known 
»s  in  the  points  unknown. 

In  the  second  place,  it  is  required  that  the  predicates  already 
observed  should  neither  be  all  negative  nor  all 
contingent ;  but  that  some  at  least  should  bo 
positive  and  necessary.  Mere  negative  characters  denote  only  what 
the  thing  is  not ;  and  contingent  characters  need  not  be  present  in 
the  thing  at  all.  In  regard  to  negative  attributes,  the  inference, 
that  two  things,  to  which  a  number  of  qualities  do  not  belong,  and 
which  are,  consequently,  similar  to  each  other  only  in  a  negative 
point  of  view,  —  that  these  things  are,  therefore,  absolutely  and 
positively  similar,  is  highly  improbable.  But  that  the  judgment  in 
reference  to  the  compared  things  (say  A  and  X)  must  be  of  the 
same  quality  (i.  e.  either  both  affirmative  or  both  negative),  is  self- 
evident.  For  if  it  be  said  A  is  B,  X  is  not  B,  A  is  not  C,  X  is  C; 
their  harmony  or  similarity  is  subverted,  and  we  should  rather  bo 
warranted  in  arguing  their  discord  and  dissimilarity  in  other  points. 


I  Of.  Krug,  Z/>^,  (  168.  Anm.  —  Ed.  [Con-      Avicenna   (in    Schmbldera,   Doeumenta    PkiL 

riillno,  VArt  de  Raisonner,  L.  iv.  ch.  3,  p.  159.      Arabum,  p.  36.)    Whately,  Rhetoric,  p.  74.] 


Lkct.  XXXn.  LOGIC.  455 

And  here  it  is  to  be  noticed  that  Analogy  diifers  from  Induction  in 
this,  that  it  is  not  limited  to  one  quality,  but  that  it  admits  of  a 
mixture  of  both. 

In  regard  to  contingent  attributes,  it  is  equally  manifest  that  the 
analogy  cannot  proceed  exclusively  upon  them.  For,  if  two  things 
coincide  in  certain  accidental  attributes  (for  example,  two  men  in 
respect  of  stature,  age,  and  dress),  the  supposition  that  there  is  a 
common  principle,  and  a  general  similarity  founded  thereon,  is  very 
unlikely. 

To  conclude :  Analogy  is  certain  in  proportion,  1°,  To  the  num- 
ber of  congruent  observations ;  2°,  To  the  num- 

Summary   of  the       ^^^  ^^  congruent  characters  observed:  3°,  To 

doctrine  of  Analogy.  . 

the  importance  of  these  characters  and  their 
essentiality  to  the  objects;  and,  4",  To  the  certainty  that  the  char- 
acters really  belong  to  the  objects,  and  that  a  partial  correspond- 
ence exists.*  Like  Induction,  Analogy  can  only  pretend  at  best  to 
a  high  degree  of  probability ;  it  may  have  a  high  degree  of  cer- 
tainty, but  it  never  reaches  to  necessity. 

Comparing  these  two  processes  together:  —  " The  Analogical  is 

distinguished  from  the  Inductive  in  this  —  that 

Induction  and  Anal-       Induction   regards  a  single  predicate  in   many 

.  Subjects  as  the  attribute  Z  in  A,  in  B,  in  C,  in 

D,  in  E,  in  F,  etc. ;  and  as  these  many  belong 
to  one  class,  say  Q ;  it  is  inferred  that  Z  will,  likewise,  be  met  with 
in  the  other  things  belonging  to  this  class,  that  is,  in  all  Qs.  On 
the  other  hand.  Analogy  regards  many  attributes  in  one  subject 
(say  m,  n,  o,  p,  in  A) ;  and  as  these  many  are  in  part  found  in 
another  subject  (say  m,  and  n,  in  B),  it  is  concluded  that,  in  that 
second  thing,  there  will  also  be  found  the  other  attributes  (say  o 
and  p).  Through  Induction  we,  therefore,  endeavor  to  prove  that 
one  character  belongs  (or  does  not  belong)  to  all  the  things  of  a 
certain  class,  because  it  belongs  (or  does  not  belong)  to  many 
things  of  that  class.  Through  Analogy,  on  the  othep  hand,  we 
seek  to  prove  that  all  the  characters  of  a  thing  belong  (or  do  not 
belong)  to  another  or  several  others,  because  many  of  these  charac- 
ters belong  to  this  other  or  these  others.  In  the  one  it  is  pro- 
claimed,—  One  in  many,  therefore  one  in  all.  —  In  the  other  it  is 
proclaimed,  —  Many  in  one,  therefore  all  in  one."  ^ 

"By  these  processes  of  Induction  and  Analogy,  as  observed,  we 
are  unable  to  attain  absolute  certainty ;  —  a  great  probability  is  all 


1  EsBer,  Logik,  S  152.    Cf  Krug,  Logik,  }  168.    Anm.  —  Ed. 

2  Krug,  Log-ii,  {  168.    Anm.  —  E©. 


466 


LOGIC. 


LarcT.  XXXII. 


Indnction  and  Anal 
ogy  do  not  &3brd  ab- 
solute certainty. 


that  tre  can  reach,  and  this  for  the  simple  reason,  that  it  is  impossi- 
ble, under  any  condition,  to  infer  the  unob- 
served from  the  observed,  —  the  whole  from 
any  proportion  of  the  parts,  —  in  the  way  of 
any  rational  necessity.  Even  from  the  requi- 
sites of  Induction  and  Analogy,  it  is  manifest  that  they  bear  the 
stamp  of  tincertainty ;  inasmuch  as  they  are  unable  to  determine 
liow  many  objects  or  how  many  characters  must  be  observed,  m 
order  to  draw  the  conclusion  that  the  case  is  the  same  with  all  the 
otiier  objects,  or  with  all  the  other  characters.  It  is  possible  only 
in  one  way  to  raise  Induction  and' Analogy  from  mere  probability 
to  complete  certainty,  —  viz.,  to  demonstrate  that  the  principles 
which  lie  at  the  root  of  these  processes,  and  which  we  have  already 
stated,  are  either  necessary  laws  of  thought,  or  necessaiy  laws  of 
nature.  To  demonstrate  that  they  are  necessary  laws  of  thought  is 
impossible  ;  for  Logic  not  only  does  not  allow  inference  from  many 
to  all,  but  expressly  rejects  it.  Again,  to  demonstrate  that  they 
are  necessary  laws  of  nature  is  equally  impossible.  This  has  in- 
deed been  attempted,  from  the  uniformity  of  nature,  but  in  vain. 
For  it  is  incompetent  to  evince  the  necessity  of  the  inference  of 
Induction  and  Analogy  from  the  fact  denominated  the  laio  (^ 
nature ;  seeing  that  this  law  itself  can  only  be  discovered  by  the 
way  of  Induction  and  Analogy.  In  this  attempted  demonstration 
there  is  thus  the  most  glaring  petitio  principii.  The  result  which 
has  been  previously  given  remains,  therefore,  inUict:  —  Induction 
and  Analogy  guarantee  no  perfect  certainty,  but  only  a  high  degree 
of  probability,  while  all  probability  rests  at  best  upon  Induction 
and  Analogy,  and  nothing  else."  * 


1  Eeser,  Logik,  §  162.—  Ed.  [On  history  and 
doctrine  of  tlus  Logic  of  Probabilities,  see 
Leibnitz,  Nouceaux  Essais.  L.  iv.  ch.  xv.  p. 
425,  «d.  Raspe.  Wolf,  Phil.  Rat.  f  564  <(  stg. 
riatner,  Phil.  Aphorismen,  f  701  (old  edit.)  f 
694  (new edit.).  Zedler,  Lexikon.  v.Wahrschein- 
Hek.  Walch,  Lfxikon,  Ibid.  Lambert,  iVirK** 
Orgtmon,  ii.  p.  818  et  seq.  Reusch,  SysUma  Log- 
tctttn,  i  653  et  seq.    Hollmann,  Lo^iea,  i  215  et 


seq.  Uoffbauer,  Anfangsgr^tnde  der  LogiJc,  ^ 
422  et  seq.  Bolzano,  Logii,  vol.  ii.  i  161,  vol. 
iii.  §  317.  Bachmann,  Logik,  $  229  et  stq. 
Fries,  Logik,  f  96  «t  ieq.  Frevost,  Essais  ile 
Philosophie,  ii.  L.  i.  part  iii.  p.  56.  Kant,  Logik, 
Einleitung  x.  Jacob,  Grundriss  drr  AUgemei- 
nen  Logik,  }  358,  p.  181  et  sfq.,  1800,  Halle. 
Metz,  IiistUutioiui  Lqgita,  i  280  et  seq.fp.  171, 
1796.] 


LECTURE    XXXIII. 

MODIFIED     METHODOLOGY. 
SECTION  I.  — OF  THE  ACQUISITION  OF  KNOWLEDGE 

I.   EXPERIENCE.  — B.  FOREIGN :  — ORAL   TESTIMONY  — 
ITS   CREDIBILITY. 

Having,  in  our  last  Lecture,  terminated  the  Doctrine  of  Empiri- 
cal Knowledsre,  considered  as  obtained  Iramedi- 

Fomgn  Experience.  i         .        i  •  r 

ately,  —  that  is,  through  the  exercise  of  our  own 
powers  of  Observation,  —  we  are  now  to  enter  on  the  doctrine  of 
Empirical  Knowledge  considered  as  obtained  Mediately,  —  that  is, 
through  the  Experience  of  Other  Men,  The  following  paragraph 
will  afford  you  a  general  notion  of  the  nature  and  kinds  of  this 
knowledge. 

^l'  CIX.  A  matter  of  Observation  or  Empirical  Knowledge 
can  only  be  obtained  Mediately,  that  is,  by 

Bar.  CIX.  Testimony.  •     j-    -j       i     r  *l,  .il,  u 

one  individual  irom  another,  through  an 
enouncement  declaring  it  to  be  true.  This  enouncement  is 
called,  in  the  most  extensive  sense  of  the  word,  a  Witnessing 
or  Testimony  {testimojiiitm)  ;  and  the  person  by  whom  it  is 
made  is,  in  the  same  sense,  called  a  Witness,  or  Testifier 
(testis).  The  object  of  the  testimony  is  called  the  J^act  (fac- 
tum) ;  and  its  validity  constitutes  what  is  styled  Historical 
Credibility  (credibilitas  historica).  To  estimate  this  credi- 
bility, it  is  requisite  to  consider — 1°,  The  Subjective  Trust- 
worthiness of  the  Witnesses  (fides  testium),  and  2°,  The  Ob- 
jective Probability  of  the  Fact  itself.  The  former  is  founded 
partly  on  the  Sincerity,  and  paitly  on  the  Competence,  of  the 
Witness.  The  latter  depends  on  the  Absolute  and  Relativ<; 
Possibility  of  the  Fact  itself.  Testimony  is  either  Immediate 
or  Mediate.     Immediate,  where  the  foct  reported  is  the  object 

d8 


458  LOGIC.  lect.  xxxm. 

of  a  Personal  Experience ;  Mediate,  where  the  fact  reported  is 
the  object  of  a  Foreign  Experience.* 

"It  is  manifest  that  Foreign  Experience,  or  the  experience  of 
other  men,  is  astricted  to  the  same  laws,  and  its 

Explication.  .  i    i         i  ... 

certainty  measured  by  the  same  criteria,  as  the 
experience  we  carry  through  oui-selves.  But  the  experience  of  the 
individual  is  limited,  when  compared  with  the  experience  of  the 
species;  and  if  men  did  not  possess  the  means  of  communicating 
to  each  other  the  results  of  their  several  observations,  —  were  they 
unable  to  cooperate  in  accumulating  a  stock  of  knowledge,  and  in 
carrying  on  the  progress  of  discovery,  —  they  would  never  have 
risen  above  the  very  lowest  steps  in  the  acquisition  of  science. 
But  to  this  mutual  communication  they  are  competent ;  and  each 
individual  is  thus  able  to  appropriate  to  his  own  benefit  the  experi- 
ence of  his  fellow-men,  and  to  confer  on  them  in  return  the  advan- 
tages which  his  own  observations  may  supply.  But  it  is  evident 
that  this  reciprocal  communication  of  their  respective  experiences 
among  men,  can  only  be  effected  inasmuch  as  one  is  able  to  inform 
another  of  what  he  has  himself  observed,  and  that  the  vehicle  of 
this  information  can  only  be  some  enouncement  in  conventional 
signs  of  one  character  or  another.  The  enouncement  of  what  has 
been  observed  is,  as  stated  in  the  paragraph,  called  a  witnessing^ — a 
hearing  witness,  —  a  testimony,  etc.,  these,  terms  being  employed  in 
their  wider  acceptation  ;  and  he  by  whom  this  declaration  is  made, 
and  on  whose  veracity  it  rests,  is  called  a  witness,  voucher,  or  testi- 
fier  {testis)^^  The  term  testhnony,  I  may  notice,  is  sometimes,  by 
an  abusive  metonym,  employed  for  witness ;  and  the  word  evidence 
is  often  ambiguously  used  for  testimony,  and  for  the  bearer  of  testi- 
mony, —  the  witness. 

"  Such  an  enouncement,  —  such  a  testimony,  is,  however,  neces- 
sary for  others,  only  when  the  experience  which 
The  proper  object  of      j^  communicates  is  beyond  the  compass  of  their 

festimony.  ,  "  .      « 

own  observation.  Hence  it  follows,  that  mat- 
ters of  reasoning  are  not  proper  objects  of  testimony,  since  mattera 
of  reasoning,  as  such,  neither  can  rest,  nor  ought  to  rest,  on  the 
observations  of  othei-s  ;  for  a  proof  of  their  certainty  is  equally 
comj)etent  to  all,  and  may  by  all  be  obtained  in  the  manner  in 
which  it  was  originally  obtained  by  those  who  may  bear  witness  to 
their  truth.  And  hence  it  further  follows,  that  mattei-s  of  experi- 
ence alone  are  proper  objects  of  testimony;  and  of  mattere  of 
experience  tlionisclves,  such  only  as  are  beyond  the  si)here  of  our 

1  Kmg,  Logik,  S  172.  —  Ed.    [Cf.  Scheibler,  ibpica,  c.  31.]     8  Esser,  Logik,  |  153.  —  Ed. 


Lect.  XXXin.  LOGIC.  459 

personal  experience.  Testimony,  in  the  strictest  sense  of  the  term, 
therefore,  is  the  communication  of  an  experience,  or,  what  amounts 
to  the  same  thing,  the  report  of  an  observed  phaenomenon,  made 
to  those  whose  own  experience  or  observation  has  not  reached  so 
far. 

"The  object  of  testimony,  as  stated  in  the  paragraph,  is  called 

the  fact;  the  validity  of  a  testimony  is  called 

The  Fact.  historical  credibility.     The  testimony  is  either 

Historical    credibil-         •  j-^  ^•    .  t  t^  i  ^i 

immediate   or  mediate.     Immediate,  when   the 

ity.  .  .  ' 

witness  has  himself  observed  the  fact  to  which 
he  testifies ;  mediate,  when  the  witness  has  not  himself  had  experi- 
ence of  this  fact,  but  has  received  it  on  the  testimony  of  others. 

The  former,  the  immediate  witness,  i?  com- 
ye-witness.  tnonly  Styled    an  eye-ioitness   (testis  oculatus)  ; 

Ear-witness.  J         J  it ,  \  /  ■> 

and  the  latter,  the  mediate  witness,  an  ear- 
witness  {testis  auritas).  The  superionty  of  immediate  to  mediate 
testimony  is  expressed  by  Plautus,  '  Pluris  est  oculatus  testis  unus, 
quam  auriti  decem.'  ^  These  denominations,  eye  and  ear  witness, 
are  however,  as  synonyms  of  immediate  and  mediate  witness,  not 
always  either  applicable  or  correct.  The  person  on  whose  testi- 
'    mony  a  fact  is  mediately  reported,  is  called  the 

The  Guarantee.  *'  ,         ^  '    .         . 

guarantee,  or  he  on  whose  authority  it  rests; 
and  the  guarantee  himself  may  be  again  either  an  immediate  or  a 
mediate  witness.  In  the  latter  case  he  is  called  a  second-hand  or 
intermediate  witness;  and  his  testimony  is  commonly  styled  hearsay 
evidence.     Further,  Testimony,  whether  immediate  or  mediate,  is 

either  partial  or  complete;  either  consistent  or 

Testimonies  —  Par-       contradictory.      These    distinctions   require   no 

1  ,     ^""P  *^  ^'     "'"■       comment.     Finally,  testimony  is  either  direct  or 

sistenl,  Contradictory.  •"  •' 

indirect;  direct,  when  the  witness  has  no  mo- 
tive but  that  of  making  known  the  fact ;  indirect,  when  he  is  actu- 
ated to  this  by  other  ends,"  ^ 

The   only   question    in   reference   to   Testimony  is   that   which 

regards  its  Credibility ;   and  the  question  con- 

Division  of  the  sub-       ceming  the  credibility  of  the  witness  may  be 

ject:  I.  Credibility  of  ,  -,     i  -,  ,  ,  .  y        r^       ^^ 

Testimony  in  general.  Comprehended  Under  that  touching  the  Credi- 
II.  Credibility  of  Tea-  bility  of  Testimony.  The  order  I  shall  follow 
timony  in  its  particu-       j^  ^^iQ  subsequent  observations  is  this,  —  I  shall, 

ate andMediatl!"'^'^''       ^"  *^®  ^^'^^  P^^^®'  Consider  the  Credibility  of 
Testimony  in  general ;  and,  in  the  second,  con- 
sider the  Credibility  of  Testimony  in  its  particular  forms  of  Imme- 
diate and  Mediate, 

1  IVufu&ntiw,  II.  vi.  9.    Cf.  Krug,  LogOr,  §  172.    Anm.  — Ed.    3  Esser,  iofft*,  §  153.  —  Ed. 


460  LOGIC.  Lect.  XXXIIL 

FtfBt,  then,  in  regard  to  the  Credibility  of  Testimony  in  general  j 
—  When  we  inquire  whether  a  certain  testimony  is,  or  is  not, 
deserving  of  fixKlit,  there  are  two  tilings  to  be  considered :  1°,  The 
Object  of  the  Testimony,  that  is,  the  feet  or  facts  for  the  truth  of 
whicli  tlie  Testimony  vouches;  and,  2°,  Tlie  Subject  of  the  Testi- 
mony, tbat  is,  the  jKirson  or  persons  by  wliom  the  testimony  is 
borne.  Th«  question,  thercfoi'e,  concerning  the  Credibility  of  Tes- 
timony, thus  naturally  subdivides  itself  into  two.  Of  these  ques- 
tions, the  first  asks,  —  What  are  the  conditions  of  the  credibility 
of  a  testimony  by  reference  to  what  is  testified,  that  is,  in  relation 
to  the  Object  of  the  testimony  ?  The  second  asks,  —  What  are  the 
conditions  of  the  credibility  of  a  testimony  by  i-eferenoe  to  him 
who  testifies,  that  is,  in  relation  to  the  Sijbject  of  the  testimony?^ 
Of  these  in  their  order. 

On  the  first  question.  —  "  In  regard  to  the  matter  testified,  that 

is,  in  regard  to  the  object  of  the  testimony  ;  it 

.      re  1  1 1  >    o        .     g^^  ^^  ^jj  ^  requisite  condition,  that  what  is 

li'Stiraony  in  general.  '  ^  ♦  _ 

1°,  Hie  Object  of  Uie  reported  to  be  true  should  be  possible,  both 
Testimony.  absolutely,  or  as  an  object  of  tlie   Elaborative 

J'',.  ^^'''^''^^  ^**''"       Fr.culty,  'and  relatively,  or  as  an  object  of  the 

Piesentative  Faculties,  —  Perception,  External 
CM*  Internal,  A  thing  is  possible  absolutely,  or  in  itself,  when  it 
can  be  construed  to  thought,  that  is,  when  it  is  not  inconsistent 
with  the  logical  laws  of  thinking ;  a  tiling  is  relatively  possible  as 
an  object  of  Perception,  External  or  Internal,  when  it  can  affect 
Sense  or  Self-consciousness,  and,  through  such  affection,  determine 
its  apprehension  by  one  or  oth<H'  of  these  faculties.  A  testimony 
is,  therefore,  to  be  unconditionally  rejected,  if  the  fact  which  it 
rejiorts  be  eitlicr  in  itself  impossible,  or  impossible  as  an  object  of 
the  Presentative  Faculties.     But  the  impossibility  of  a  thing,  as  an 

object  of  these  faculties,  must  be  decided  either 

riivficai  and  Jieta-       upon  ])hysical,  or  upon  metaphysical,  principles. 

1  iy«M5a       ni|>oi-8i  i-       ^  tiijng  js  physically  impossible  as  an  object  of 

sense,  when  the  existence  itself,  or  its  percep- 
t«»n  fey  ««,  M,  by  the  laws  of  the  mateiial  woi-ld,  impossible.  It  is 
mctaphysicaMy  impossible,  when  the  object  itself,  or  its  perception, 
i«  possible  neither  through  a  natural,  nor  through  a  supei-natural, 
ageiicy.  But,  to  establish  the  iiRta]ihysical  impossibility  of  a 
thing,  it  is  not  fiuflicient  that  its  existence  cannot  be  explained  by 
tbe  ordinary  laws  of  natui-e,  or  even  that  its  existence  should 
appear  reptigtiant  wifh  these  laws ;  it  is  requisite  that  an  universal 
and  immutable  law  of  nature  should  have  been  demonstrated  to 

i  or.  Emet,  Moe*,  f  Mt — Bd. 


Lkct.  XXXm.  LOGIC.  461 

exist,  and  that  this  law  would  be  subverted  if  the  fact  in  question 
were  admitted  to  be  physically  possible.  In  like  manner,  to  consti- 
tute the  metaphysical  impossibility  of  a  thing,  it  is  by  no  means 
enough  to  show  that  it  is  not  explicable  on  natural  laws,  or  even 
that  any  natural  law  stands  opposed  to  it ;  it  is  further  requisite  to 
prove  that  the  intervention  even  of  supernatural  agency  is  incom- 
petent to  its  production,  that  its  existence  would  involve  the  viola- 
tion  of  some  necessary  principle  of  reason. 

"To  establish  the  credibility  of  a  testimony,  in  so  far  as  this  is 
regulated  by  the  nature  of  its  object,  there  is, 

Relative   Possibility        ijggj^jgg   ^^^  f  ^f  ^^e   absolute  possibilitv  of 

of  an  object.  .  ^        .  ^  • 

this  object,  required  also  a  proof  of  its  relative 
possibility ;  that  is,  there  must  not  only  be  no  contradiction  be 
tween  its  necessary  attributes,  —  the  attributes  by  which  it  must  be 
thought,  —  but  no  contradiction  between  the  attributes  actually 
assigned  to  it  by  the  testimony.  A  testimony,  therefore,  which, 
qua  testimony,  is  self-contradictory,  can  lay  no  claim  to  credibility ; 
for  what  is  self-contradictory  is  logically  suicidal.  And  here  the 
only  question  is, —  Does  the  test'imonj,  qtia  testimony,  contradict 
itself?  for  if  the  repugnancy  arise  from  an  opinion  of  the  witness, 
apart  from  which  the  testimony  as  such  would  still  stand  undis- 
proved, in  that  case  the  testimony  is  not  at  once  to  be  repudiated 
as  false.  For  example,  it  would  be  wrong  to  reject  a  testimony  to 
the  existence  of  a  thing,  because  the  witness  had  to  his  evidence 
of  its  observed  reality  annexed  some  conjecture  in  regard  to  its 
origin  or  cause.  For  the  latter  might  well  be  shown  to  be  absurd, 
and  yet  the  former  would  remain  unshaken.  It  is,  therefore, 
always  to  be  observed, —  that  it  is  only  the  self-contradiction  of 
a  testimony,  qua  testimony,  that  is,  the  self-contradiction  of  the 
fact  itself,  which  is  peremptorily  and  irrevocably  subversive  of  its 
eredibility. 

"  We  now  proceed  to  the  second  question ;  that  is,  to  consider  in 

general  the  Credibility  of  a  Testimony  by  ref- 
20,  The  Subject  of      gj-g^ce  to  j^g  Subject,  that  is,  in  relation  to  the 

the  Testimony,  or  per-  "^ 

sonai  trustworthiness  Personal  Trustworthiuess  of  the  Witness.  The 
of  the  Witness.  This  trustworthiness  of  a  witness  consists  of  two  ele- 
ceawsts  of  two   eie-       ments  or  conditions.    In  the  first  place,  he  must 

ments:  — (a)  Honesty         ,  .„.  .        ,  t       1  ,  ,         »  i 

or  Veracity.  "^  Willing,  in  the  sccond  place,  he  must  be  able, 

to  report  the  truth.  The  first  of  these  elements 
the  Honesty,  —  the  Sincerity,  —  the  Veracity  ;  the  second  is  the 
Competency  of  the  Witness.  Both  are  equally  necessary,  and  if 
one  or  other  be  deficient,  the  testimony  becomes  altogether  null. 
These  constituents,  likewise,  do  not  infer  each   other;   for  it  fre- 


462  •  LOGIC.  Lect.  XKXm 

quently  happens  that  where  the  honesty  is  greatest  the  compe- 
tency is  least,  and  Avhere  the  competency  is  greatest  the  honesty  is 
least.  But  when  the  veracity  of  a  witness  is  established,  there  is 
established  also  a  presumption  of  his  competency;  for  an  honest 
man  will  not  bear  evidence  to  a  point  in  regard  to  which  his  recol- 
lection is  not  231'ecise,  or  to  the  observation  of  which  he  had  not 
accorded  the  requisite  attention.  In  truth,  when  a  fact  depends  on 
the  testimony  of  a  single  witness,  the  competency  of  that  witness 
is  solely  guaranteed  by  his  honesty.  In  regard  to  the  honesty  of  a 
witness,  —  this,  though  often  admitting  of  the  highest  probability, 
never  admits  of  absolute  certainty  ;  for,  though,  in  many  cases,  we 
may  know  enough  of  the  general  character  of  the  witness  to  rely 
with  perfect  confidence  on  his  veracity,  in  no  case  can  we  look  into 
the  heart,  and  observe  the  influence  which  motives  have  actually 
had  upon  his  volitions.  We  are,  however,  compelled,  in  many  of 
the  most  important  concerns  of  our  existence,  to  depend  on  the 
testimony,  and,  consequently,  to  confide  in  the  sincerity,  of  others. 
But  from  the  moral  constitution  of  human  nature,  we  are  war- 
ranted in  presuming  on  the  honesty  of  a  witness;  and  this  pre- 
sumption is  enhanced  in  proportion  as  the  following  circumstances 
concur  in  its  confirmation.  In  the  first  place,  a  witness  is  to  be  pre- 
sumed veracious  in  this  case,  in  proportion  as  his  love  of  truth  is 
already  established  from  others.  In  the  second  place,  a  witness  is 
to  be  presumed  veracious,  in  proportion  as  he 
The  presumption  of  jjgg  fewer  and  weaker  motives  to  falsify  his  tes- 
ones  y  o   a    '  *       timouv.     In  the  third  place,  a  witness  is  to  be 

new  enhanced  by  cer-  •  '^  '        _ 

tain  circumstances.  presumed  veracious,  in  proportion  to  the  like- 

lihood of  contradiction  which  his  testimony 
would  encounter,  if  he  deviated  from  the  truth.  So  much  for  the 
Sincerity,  Honesty,  or  Veracity  of  a  witness. 

"In  regard  to  the  Competency  or  Ability  of  a  witness,  —  this,  in 
general,  depends  on  the  supposition,  that  he  has 

(b)  Competency  of  a         j^^^   j^  ^^  j^j^      ^^^,^^  COlTCCtly  tO  obscrve  the  foct 
5  itness.  '■  "' 

to  which  he  testifies,  and  correctly  to  report  it. 
The  presumption  in  favor  of  the  competence  of  a  witness  rises  in 

proportion  as  the  following  conditions  are  ful- 

Circumstances   by       filled:  —  In   thc   first  place,   he   must  be   pre- 

^•hich  the  presump-       ^^^^^^  competent  in   reference  to  the  case  in 

tiou  of  competency  js  ^  ,  . 

enhanced.  hand,  in   proportion    as  his   general   ability^to 

observe  and  to  communicate  his  observation 
nas  been  established  in  other  cases.  In  the  second  place,  the 
competency  of  a  witness  must  be  presumed,  in  proportion  as  in 
the  particular  case  a  lower  and  commoner  amount  of  ability  is 


Lkct.  XXXIII.  LOGIC.  ,  463 

requisite  rightly  to  observe,  and  rightly  to  report  the  observation. 
In  the  third  place,  the  competency  of  a  witness  is  to  be  presumed, 
in  proportion  as  it  is  not  to  be  presumed  that  his  observation  was 
made  or  communicated  at  a  time  when  he  was  unable  correctly  to 
make  or  correctly  to  communicate  it.  So  much  for  the  Competency 
of  a  witness. 

"Now,  when  both  the  good  will  and  the  ability,  that  is,  when 

both  the  Veracity  and  Competence  of  a  witness 

e  ere  i  iiy  jjave  been  sufficiently  established,  the  credibility 

Testimony  not  invali-  j  ^  j 

dated  because  the  fact  of  his  testimony  is  not  to  be  invalidated  because 
testified  is  one  out  of  tijg  fact  Avhich  it  goes  to  provc  is  one  out  of 
the   ordinary  course       ^j^^  ordinary  course  of  experience."  ^     Thus  it 

of  experience.  *'  '■ 

would  be  false  to  assert,  Avith  Hume,  that  mira- 
cles, that  is,  suspensions  of  the  ordinary  laws  of  nature,  are  incapa- 
ble of  proof,  because  contradicted  by  what  we  have  been  able  to 
observe.  "  On  the  contrary,  where  the  trustworthiness  of  a  witness 
or  witnesses  is  unimpeachable,  the  very  circumstance  that  the  ob- 
ject is  one  in  itself  unusual  and  marvellous,  adds  greater  weight  to 
the  testimony  ;  for  this  very  circumstance  would  itself  induce  men 
of  veracity  and  intelligence  to  accord  a  more  attentive  scrutiny  to 
the  fact,  and  secure  from  them  a  more  accurate  report'  of  their 
observation. 

"  The  result  of  what  Jias  now  been  stated  in  regard  to  the  credi- 
bility of  Testimony  in  general,  is  :  —  That  a  tes- 
Summary  regarding  timony  is  entitled  to  Credit  when  the  requisite 
timony^in  gener*li.  *"'  Conditions,  both  on  the  part  of  the  object  and 
on  the  part  of  the  subject,  have  been  fulfilled. 
On  the  part  of  the  object  these  are  fulfilled  when  the  object  is 
absolutely  possible,  as  an  object  of  the  higher  faculty  of  experience, 
—  the  Understanding,  —  the  Elaborative  Faculty,  and  relatively 
possible,  as  an  object  of  the  lower  or  subsidiary  faculties  of  experi- 
ence, —  Sense,  and  Self-consciousness.  In  this  case,  the  testimony, 
qua  testimony,  does  not  contradict  itself.  On  the  part  of  the  sub- 
ject the  requisite  conditions  are  fulfilled  when  the  trustworthiness, 
that  is,  the  veracity  and  competency  of  the  witness,  is  beyond  rea- 
sonable doubt.  In  regard  to  the  veracity  of  the  witness,  —  this 
cannot  be  reasonably  doubted,  when  there  is  no  positive  ground  on 
which  to  discredit  the  sincerity  of  the  witness,  and  when  the  only 
ground  of  doubt  lies  in  the  mere  general  possibility  of  deception. 
And  in  reference  to  the  competency  of  a  witness,  —  this  is  exposed 
to  no  reasonable  objection,  when  the  ability  of  the  witness  to 
observe  and  to  communicate  the  fact  in  testimony  cannot  be  dis- 

1  Esser,  Logik^  §  154.  —  Ed. 


464 


LOGIC. 


Lect    XXXill. 


II.  Testimony  in 
ipeeial,  as  Immediate 
aiid  Mediate. 

1°,  Immediate  Testi- 
mony. 


Conditions    of    its 
Credibility. 


allowed.  Having,  therefore,  concluded  the  consideration  of  testi- 
mony in  general,  we  proceed  to  treat  of  it  in  special,  that  is,  in  so 
far  as  it  is  viewed  either  as  Immediate  or  as  Mediate."  *  Of  these 
in  their  order. 

The  special  consideration  of  Testimony,  when  that  testimony  is 
Immediate.  —  "An  immediate  testimony,  or  tes- 
timony at  first  hand,  is  one  in  which  the  fact 
reported  is  an  object  of  the  proper  or  personal 
experience  of  the  reporter.  Now  it  is  manifest, 
that  an  immediate  witness  is  in  general  better 
entitled  to  credit  than  a  witness  at  second  hand  ;  and  his  testimony 
rises  in  probability,  in  proportion  as  the  requisites,  already  speci- 
fied, both  on  the  part  of  its  object  and  on  the  pai't  of  its  subject, 
are  fulfilled.  An  immediate  testimony  is,  therefore,  entitled  to 
credit,  —  1°,  In  proportion  to  the  greater  ability  with  which  the 
observation  has  been  made ;  2°,  In  proportion 
to  the  less  impediment  in  the  way  of  the  obser- 
vation being  perfectly  accomplished ;  3",  In 
))roportion  as  what  was  observed  could  be  fully  and  accurately 
rt'membeved ;  and,  4°,  In  proportion  as  the  facts  observed  and 
remembered  have  been  communicated  by  intelligible  and  unambig- 
uous signs. 

"Now,  whether  all  these  conditions  of  ♦a  higher  credibility  be 
fulfilled  in  the  case  of  any  immediate  testimony, 
—  this  cannot  be  directly  and  at  once  ascer- 
tained ;  it  can  only  be  inferred,  with  greater  or 
less  certainty,  from  the  qualities  of  the  witness ; 
and,  consequently,  the  validity  of  a  testimony 
can  only  be  accurately  estimated  from  a  critical 
knowledge  of  the  personal  character  of  the  witness,  as  given  in  his 
intellectual  and  moral  qualities,  and  in  the  circumstances  of  his  life, 
which  have  concurred  to  modify  and  determine  these.  The  verac- 
ity of  a  witness  either  is,  or  is  not,  exempt  from  doubt ;  and,  in  the 
latter  case,  it  may  not  only  lie  open  to  doubt,  but  even  be  exposed 
to  suspicion.  If  the  sincerity  of  the  witness  be  indubitable,  a 
direct  testimony  is  always  preferable  to  an  indirect ;  for  a  direct 
testimony  being  made  with  the  sole  intent  of  establishing  the  cer- 
tainty of  tlie  fact  in  question,  the  competency  of  the  witness  is  less 
exposed  to  objection.  If,  on  the  contrary,  the  sincerity  of  the  wit- 
ness be  not  beyond  a  doubt,  and,  still  more,  if  it  be  actually  sus- 
pected, in  that  case  an  indirect  testimony  is  of  higher  cogency 
than  a  dii'ect;  for  the  indirect  testimony  being  given  with  another 


Whether  all  these 
conditions  are  fulfilled 
in  tlK!  case  of  any  im- 
mediate testimony, 
cannot  be  directly  as- 
certained. 


1  Esser.  Logik,  f  154.  —  Ed. 


Lscr.  XMXIIL  LOGIC.  465 

view  tlinn  merely  to  establish  the  fact  in  questir>ft,  the  intention  of 
the  witness  to  falsify  the  truth  of  the  fact  has  not  so  strong  a  pre- 
tjuinption  in  its  favor.     If  both  the  sincerity  and  the  compotenoy 
of  the  witness  are  altogether  indubitable,  it  is  then  of  no  impor- 
tance whether  the  truth  of  the  fact  be  vouched  for  by  a  single  wit- 
ness, or  by  a  plurality  of  witnesses.     On  the   other  hand,  if  the 
sincerity  and   competency  of  the   witness  be  at  all  doubtful,  the 
credibility  of  a  testimony  will  be  greater,  the  greater  the  number 
of  the  witnesses  by  whom  the  flict  is  corrob- 
when  testimony  at-       orated.     But  here  it  is  to  be  considered,  that 
le   ''g  e-^  when  there  are  a  plurality  of  testimonies  to  the 

gree  of  probability.  ^  J 

same  fact,  these  testimonies  are  either  consistent. 
or  inconsistent.  If  the  testimonies  be  consistent,  and  the  sincerity 
and  competency  of  all  the  witnesses  complete,  in  that  case  the  taa- 
timony  attains  the  highest  degree  of  probability  of  which  any  testi- 
mony is  capable.  Again,  if  the  witnesses  be  inconsistent,  —  on  this 
hypothesis  two  cases  are  possible  ;  for  either  their  discrepancy  is 

negative,    or   it   is   positive.      A   negative   dis- 

Neeative  and  Posi-  •  r  •. 

^  crepancy  arises,  where  one  witness  passes  over 

tive  Discrepancy.  ',         •  .  .   . 

in  silence  what  another  witness  positively  avera. 
A  positive  discrepancy  arises,  where  one  witness  explicitly  affirms 
something,  which  something  another  witness  explicitly  denic*3. 
When  the  difference  of  testimonies  is  merely  negative,  we  may 
suppose  various  causes  of  the  silence ;  and,  therefore,  the  positive 
averment  of  one  witness  to  a  fact  is  not  disproved  by  the  mere  cir- 
cumstance that  the  same  fact  is  omitted  by  another.  But  if  it  be 
made  out,  that  the  witness  who  omits  mention  of  the  fact  could 
not  have  been  ignorant  of  that  fact  had  it  taken  place,  and,  at  the 
same  time,  that  he  could  not  have  passed  it  over  without  violating 
every  probability  of  human  action,  —  in  this  case,  the  silence  of 
the  one  witness  manifestly  derogates  from  the  credibility  of  the 
other  witness,  and  in  certain  circumstances  may  annihilate  it  alto- 
gether. Where,  again,  the  difference  is  positive,  the  discrepancy 
is  of  greater  importance,  because  (though  there  are  certainly  excep- 
tions to  the  rule)  an  overt  contradiction  is,  in  general  and  in  itself, 
of  stronger  cogency  than  a  mere  non-confirmation  by  simple  silence. 
Now  the  positive  discrepancy  of  testimonies  either  admits  of 
conciliation,  or  it  does  not.  In  the  former  case,  the  credibility 
of  the  several  testimonies  stands  intact ;  and  the  discrepancy 
among  the  witnesses  is  to  be  accounted  for  by  such  circum stall ces 
as  explain,  without  invalidating,  the  testimony  considered  in  itself. 
In  the  latter  case,  one  testimony  manifestly  detracts  from  the  cred- 
ibility of  another;  for  of  incompatible  testimonies,  while  both  can- 

d9 


466 


LOGIC. 


lect.  xxxm. 


2°,    Mediate    Testi 
mbuy. 


not  be  tnie,  the  one  must  be  false,  when  reciprocally  con  trad  ictorv, 
or  they  may  both  be  false,  when  reciprocally  contrary.  In  this 
case,  the  whole  question  resolves  itself  into  one  of  ^the  greater  or 
less  trustworthiness  of  the  opposing  witnesses.  Is  the  trustworthi- 
ness of  the  counter-witnesses  equally  great  ?  In  that  case,  neither 
of  the  conflictive  testimonies  is  to  be  admitted.  Again,  is  the 
trustworthiness  of  the  witnesses  not  upon  a  par?  In  that  case,  the 
testimony  of  the  witness  whose  trustworthiness  is  the  greater,  ob- 
tains the  preference,  —  and  this  more  especially  if  the  credibility 
of  the  other  witnesses  is  suspected."  * 

So  much  for  the  Credibility  of  Testimony,  considered  in  Special, 
in  so  far  as  that  testimony  is  Immediate  or  at  First  Hand ;  and  I 
now,  in  the  second  place,  pass  on  to  consider,  likewise  in  special, 
the  Credibility  of  Testimony,  in  so  far  as  that  testimony  is  Medi- 
ate, or  at  Second  Hand. 

"A  Mediate  Testimony  is  one  where  the  fact  is  an  object  not  of 
Personal,  but  of  Foreign  Experience.  Touch- 
ing the  credibility  of  a  mediate  testimony,  this 
supposes  that  the  report  of  the  immediate,  and 
that  the  report  of  the  mediate,  witness  are  both  trustworthy. 
Whether  the  report  of  the  immediate  witness  be  trustworthy, — 
this  we  are  either  of  ourselves  able  to  determine,  viz.,  from  our 
personal  acquaintance  with  his  veracity  and  competence ;  .or  we  are 
unable  of  oui-selves  to  do  this,  in  which  case  the  credibility  of  the 
i?nmediate  must  be  taken  upon  the  authority  of  the  mediate  wit- 
ness. Here,  however,  it  is  necessary  for  us  to  be  aware,  that  the 
mediate  witness  is  possessed  of  the  ability  requisite  to  estimate  the 
credibility  of  the  immediate  witness,  and  of  the  honesty  to  commu- 
nicate the  truth  without  retrenchment  or  falsification.  But  if  the 
trustworthiness  both  of  the  mediate  and  of  the  immediate  witness 
be  sufficiently  established,  it  is  of  no  consequence,  in  regard  to  the 
credibility  of  a  testimony,  whether  it  be  at  firet  hand  or  at  second. 
Nay,  the  testimony  of  a  mediate  may  even  tend  to  confirm  the  tes- 
timony of  an  immediate  witness,  when  his  own  competence  fiurly 
to  appreciate  the  report  of  the  immediate  witness  is  indubitable. 
If,  however,  the  credibility  of  the  immediate  witness  be  unimpeach- 
able, but  not  so  the  credibility  of  the  mediate,  in  that  case  the 
mediate  testimony,  in  respect  of  its  authority,  is  inferior  to  the 
immediate,  and  this  in  the  same  proportion  as  the  credibility  of 
the  second  hand  witness  is  inferior  to  that  of  the  witness  at  first 
hand.  Further,  mediate  witnesses  are  either  Proximate  or  Remote; 
and,  in  both  cases,  either  Independent  or  Dependent.     The  trust- 


1  Esser,  Ugik,  f  166.  —  Ed. 


Lect.  XXXIII.  LOGIC.  467 

worthiness  of  proximate  witnesses  is,  in  general,  greater  than  the 
trustworthiness  of  remote ;   and  the  credibility 

Mediate    Witnesses  n  •     •>  i  ■  i  i  j 

are  either  Proximate  ©^  independent  Witnesses  greater  than  the  cred- 
or  Remote,  and  either  ibility  of  dependent.  The  remote  witness  is 
Independent  or  De-  unworthy  of  belief;  when  the  intermediate  links 
^'^  ^°  ■  are  wanting  between  him  and  the  original  wit- 

ness ;  and  the  dependent  witness  deserves  no  credit,  when  that 
on  which  his  evidence  depends  is  recognized  as  false  or  unestab- 
lished.  Mediate  testimonies  are,  likewise,  either  direct  or  indirect; 
and,  likewise,  when  more  than  one,  either  reciprocally  congruent  or 
conflictive.  In  both  cases  the  credibility  of  the  witnesses  is  to 
be  determined  in  the  same  manner  as  if  the  testimonies  were 
immediate. 

"  The  testimony  of  a  plurality  of  mediate  witnesses,  where  there 

is  no  recognized  immediate  witness,  is  called  a 

Rumor,  — what.  rumor.  if  the  , witnesses   be  contemporaneous; 

Tradition.  '  , 

and  a  tradition^  if  the  witnesses  be  chronolog- 
ically successive.  These  are  both  less  entitled  to  credit,  in  propor- 
tion as  in  either  case  a  fiction  or  falsification  of  the  fact  is  compara- 
tively easy,  and,  consequently,  comparatively  probable."  * 

1  Eaeer,  Logik,  i  156.  —Ed. 


LECTUEE    XXXIV. 

,  MODIFIED     METHODOLOOY. 

SECTION  I.— OF  THE  ACQUISITION  OF  KNOWLEDGBL 

t.  EXPERIENCE.  —  B.  FOREIGN :  — RECORDED    TESTIMONY 
AND  WRITINGS  m  GENERAL. 

II.  SPECULATION. 

lir  our  last  Lecture,  we  were  engaged  in  the  consideration  of 
Testimony,   and    the    Principles   by   which   its 
Criticism   of  Re-       Credibility  is   governed,  —  on   the   supposition 
and  ^  f  w  ^/"°"r^       always  that  we  possess  the  veiitable  report  of 
general.  the  witness  whose  testimony  it  professes  to  be, 

and  on  the  supposition  that  we  are  at  no  loss  to 
understand  its  meaning  and  purport.  But  questions  may  arise  in 
regard  to  these  points,  and,  therefore,  there  is  a  further  critical  pro- 
cess requisite,  in  order  to  establish  the  Authenticity,  —  the  Integ- 
rity, and  the  Signification,  of  the  documents  in  which  the  testi- 
mony is  conveyed.  This  leads  to  the  important  subject,  —  the 
Criticism  of  Recorded  Testimony,  and  of  Writings  in  general.  T 
shall  comprise  the  heads  of  the  following  observations  on  this  sub- 
ject in  the  ensuing  paragraph. 

%  ex.   The  examination  and  judgment  of  Writings  profess- 
ing to   contain    the    testimony   of   certain 
Par.  ex.  Criticism       witucsscs,  and  of  Writings  in  General  pro- 

and  Interpretation.  _  '  . 

fessing  to  be  the  work  of  certain  authors,  \a 
of  two  parts.  FoV  the  inquiry  regards  either,  1°,  The  Authen- 
ticity of  the  document,  that  is,  whether  it  be,  in  whole  or  ii 
part,  the  product  of  its  ostensible  author;  for  ancient  writing 
in  particular  are  frequently  supposititious  or  interpolated ;  or 
2°,  It  regards  the  Meaning  of  the  words  of  which  it  is  com«| 
posed,  for  these,  especially  when  in  languages  now  dead, 


Legt.  XXXIV.  LOGIC.  4^9 

frequently  obscure.  The  forrner  of  these  problems  is  resolved 
by  the  Art  of  Criticism  (Critica),  in  the  stricter  sense  of  the 
term  ;  the  latter  by  the  Art  of  Interjvetation  {Exegetica  or 
Uernxeneutica).  Criticism  is  of  two  kinds.  If-it  be  occupied 
with  the  criteria  of  the  authenticity  of  a  writing  in  its  totality, 
or  in  its  principal  parts,  it  is  called  the  Higher^  and  sometimes 
the  Interlude  Criticism.  If,  again,  it  consider  only  the  integ- 
rity of  particular  words  and  phrases,  it  is  called  the  Low^^ 
and  sometimes  the  External,  Criticism.  The  former  of  thes^ 
may  perhaps  be  best  styled  the  Criticism,  of  Authenticity  j — - 
the  latter,  the  Criticism  of  Integrity. 

The  problem  which  Interpretation  has  to  solve  is,  —  To 
discover  and  expound  the  meaning  of  a  writer,  from  the 
words  in  which  his  thoughts  are  expressed.  It  departs  from 
the  principle,  that  however  manifold  be  the  possible  meanings 
of  the  expressions,  the  sense  of  the  writer  is  one.  Interpreta- 
tion, by  reference  to  its  fsoui'ces  or  subsidia,  has  been  divided 
into  the  Gramrriaticaly  the  Historical,  and  the  Philosophical, 
Exegesis} 

"Testimonies,  especially  when  the  ostensible  witnesses  themselves 
can  no  longer  be  interrosrated,  may  be  subiected 

Explication.  '^  .         .  °  .       *^     „  "^       ' 

to  an  examination  under  various  lorms ;  ana 
this  examination  is  in  fact  indispensable,  seeing  not  only  that  a 
false  testimony  may  be  subiftituted  for  a  true,  and  a  testimony  true 
upon  the  whole  may  yet  be  falsified  in  its  parts,  —  a  practice  which, 
prevailed  to  a  great  extent  in  ancient  times ;  while  at  the  same 
time  the  meaning  of  the  testimony,  by  reason  either  of  the  foreign 
character  of  the  language  in  which  it  is  expressed,  or  of  the  foreign 
character  of  thought  in  which  it  is  conceived,  may  be  obscure  and 
undetermined.     The  examination  of  a  testimony  is  twofold,  inag* 

much  as  it  is  either  an  examination  of  its  Au- 

•The  examination  of  ^  .  .         .      ■       „ 

a  te^tiraouy  twofold,  thenticity  and  Integrity,  or  an  examination  of 
—  of  its  Autiieiiticity  its  Meaning.  This  twofold  process  of  examina- 
atid  Integrity,  and  of  ^Jqjj  jg  applicable  to  testimonies  of  every  kind, 
but  it  becomes  indispensable  when  the  testi- 
mony has  been  recorded  in  writing,  and  when  this,  from  its  anti- 
qiiity,  has  come  down  to  us  only  in  transcripts,  indefinitely  removed 
fropi  the  original,  and  when  the  witnesses  are  men  differing  greatly 
from  ourselves  in  language,  niaimers,  customs,  and  associations  of 


}  Qt  Krug,  Lagifc,  *  177  «t  seg.  ^  Eo.    {gn*ll,  IfOgH;,  P-  »•  ♦  6  p.  196.    Kiesewetter.I^gi'^  P 

ii.  }  185  et  seq.] 


470 


LOGIC. 


Lect.  XXXIV. 


Criticism. 


Its  problems. 


thought.     The  solution  of  the  problem,  —  By  what  laws  are  the 

authenticity   or   spuriousness,  the   integrity   or 

corruption,  of  a  writing  to   be   determined, — 

constitutes  the  Art  of  Criticism,  in  its  stricter  signification  [Crit- 

ica) ;  and  the  solution  of  the  problem, —  By  what  law  is  the  sense 

or  meaning  of  writing  to  be  determined,  —  con- 
interpretation.  .  °    ^        ^,®  .  _,.. 

stitutes  the  Art  oi  Interpretation  or  Exposition 

{ITermeneuticayExegetica).  In  theory,  Criticism  ought  to  precede 
Interpretation,  for  the  question,  —  Who  has  spoken,  naturally  arises 
before  the  question,  —  How  what  has  been  spoken  is  to  be  under- 
stood. But  in  practice,  criticism  and  interpretation  cannot  be  sepa- 
rated ;  for  in  application  they  proceed  hand  in  hand."  * 

"  First,  then,  of  Criticism  ;  and  the  question  that  presents  itself  iii 
the  threshold  is,  —  What  are  its  Definition  and 

I.   Criticism.  t>.-    •   •  o        xt     t         y-.  •  •    •  •  i  i 

Divisions/  Under  Criticism  is  to  be  under- 
stood the  complement  of  logical  rules,  by  which  the  authenticity  or 
spuriousness,  the  integrity  or  interpolation,  of  a  writing  is  to  be 
judged.  The  problems  which  it  proposes  to 
answer  are  —  1°,  Does  a  writing  really  proceed 
from  the  author  to  whom  it  is  ascribed ;  and,  2°,  Is  a  writing,  as  we 
possess  it,  in  all  its  parts  the  same  as  it  came  from  the  hands  of  its 
author.  The  system  of  fundamental  rules,  which  are  supposed  in 
judging  of  the  authenticity  and  integrity  of  every  writing,  consti- 
tutes what  is  called  the  Doctrine  of  Universal 
Criticism;  and  the  system  of  particular  rules, 
by  which  the  authenticity  and  integrity  of  writings  of  a  certain 
kind  are  judged,  constitutes  the  doctrine  of  what  is  called  Special 
Criticism.  It  is  manifest,  from  the  nature  of 
Logic,  that  the  doctrine  of  Universal  Criticism 
is  alone  within  its  sphere.  Now  Universal 
Criticism  is  conversant  either  with  the  authen- 
ticity or  spuriousness  of  a  writing  coiJsider»'<l  a.s 
a  whole,  or  with  the  integrity  or  interpolation  of  certain  parts.  In 
the  foimer  case  it  is  called  Higlier^  in  the  latter, 
Lower^  Criticism ;  but  these  denominations  are 
inappropriate.  The  one  criticism  has  also  been  styled  the  Internaly 
the  other  the  External;  but  these  appellations  are,  likewise,  excep- 
tionable ;  and,  perhaps,  it  would  be  preferable  to  call  the  form6^ 
the  Criticism,  of  the  Authenticity,  the  latter,  the  Criticism  of  th^ 
Integrity,  of  a  work.  I  shall  consider  these  in  particular;  and,  first, 
of  the  Criticism  of  Authenticity. 
.'.'A  proof  of  the  authenticity  of  a  writing,  more  especially  of  an 


Universal  Criticism. 


Bpecial  Criticism. 

Universal  Criticism 
alone  within  the 
sphere  of  Logic. 


Its  Divisions. 


1  EaMf,  Logik,  §  157.  —  Ed. 


Lkct.  XXXIV.  LOGIC.  471 

ancient  writing,  can  be  rested  only  upon  two  grounds,  —  an  Intev'- 
nal    and    an    External,  —  and   on    these   either 

1.   Criticism  of  Au-  .  •  t  •       ^-  -o       •    ^  7  7 

apart  or  in  combination.     By  internal  qrounds. 

fbenticity.  ^  .        .  ^  .    .  .    , 

we  mean  those  indications  of  authenticity  which 
the  writing  itself  affords.  By  external  grounds^  we  denote  the  tes- 
timony borne  by  other  works,  of  a  corresponding  antiquity,  to  the 
authenticity  of  the  writing  in  question. 

"  In  regard  to  the  Internal  Grounds  ;  —  it  is  evident,  without 

entering   upon    details,   that    these   cannot    of 

(a) Internal  Grounds. 

These  of  themselves  theiiiselves,  that  IS,  apart  from  the  external 
not  sufficient  to  cstab-  grounds,  afford  evidence  capable  of  establish- 
lish  the  authenticity       j^g  beyoud  a  doubt  the  authenticity  of  an  an- 

of  a  writing.  .       ,  .  .  „  .,  '         ^\     .. 

cient  writing;  lor  we  can  easily  conceive  that 
an  able  and  learned  forger  may  accommodate  his  fabrications  both 
to  all  the  general  circumstances  of  time,  place,  pecjple,  and  lan- 
guage, under  which  it  is  supposed  to  have  been  written,  and  even 
to  all  the  particular  circumstances  of  the  style,  habit  of  thought, 
personal  relations,  etc.,  of  the  author  by  whom  it  professes  to  have 
been  written,  so  that  everything  may  militate  for,  and  nothing  mili- 
tate :igainst,  its  authenticity. 

"  But  if  our  criticism  from  the  internal  grounds  alone  be,  on  the 

one  hand,  impotent  to  establish,  it  is,  on  the 
u    omnipo  en     o       other,  omnipotent  to  disprove.     For  it  is  suffi- 

disprove  thi.s.  _  '  '  .... 

cient  to  show  that  a  writing  is  in  essential  parts, 
that  is,  parts  which  cannot  be  separated  from  the  whole,  in  opposi- 
tion to  the  known  manners,  institutions,  usages,  etc.,  of  that  people 
with  which  it  would,  and  must,  have  been  in  harmony,  were  it  the 
product  of  the  writer  whose  name  it  bears ;  that,  on  the  contrary, 
it  bears  upon  its  face  indications  of  another  country  or  of  a  later 
age ;  and,  finally,  that  it  is  at  variance  with  the  personal  circum- 
stances, the  turn  of  mind,  and  the  pitch  of  intellect,  of  its  pre- 
tended author.  And  here  it  is  to  be  noticed,  that  these  grounds 
are  only  relatively  internal ;  for  we  become  aware  of  them  origi- 
nally only  through  the  testimony  of  others,  that  is,  through  exter- 
nal grounds."* 

In  regard  to  the  External  Grounds ;  —  they,  as  I  said,  consist 

in  the   testimony,  direct  or    indirect,  given   to 

(b)  External  Grounds.  •        ,  ,  ....  .   .  .  .  , 

the  authenticity  or  the  writing  in  question  by 
other  works  of  a  competent  antiquity.  This  testimony  may  bo 
contained  either  in  other  and  admitted  writings  of  the  supposed 
author  himself;  or  in  those  of  contemporary  writers ;  or  in  those 
of  writers  approximating  in  antiquity.    This  testimony  may  also  be 

1  Esser,  Log^i't,  S 158—160.  —  Ed. 


472  LOGIC.  Lect.  XXXIV. 

given  either  directly,  by  attribution  of  the  disputed  writing  by 
title  to  the  author ;  or  indirectly,  by  quoting  as  his  certain  pas- 
sages which  are  to  be  found  in  it.  On  this  subject  it  is  needless  to 
go  into  detail,  and  it  is  hardly  necessary  to  observe,  that  the  proof 
of  the  authenticity  is  most  complete  when  it  proceeds  upon  the 
internal  and  external  grounds  together.  I,  therefore,  pass  on  to 
the  Criticism  of  Integrity.^ 

"  When  the  authenticity  of  an  ancient  work  has  been  established 
on  external  grounds,  and  been  confirmed  on 
X.  t-"tic»sm  o  n-  internal,  the  integrity  of  this  writing  is  not 
therewith  proved  ;  for  it  is  very  ])ossible,  and 
in  ancient  writings  indeed  very  probable,  that  particular  passages 
are  either  interpolated  or  corrupted.  The  authenticity  of  particu- 
lar passages  is  to  be  judged  of  precisely  by  the  same  laws  which 
regulate  our  criticism  of  the  authenticity  of  the  whole  work.  The 
proof  most  pertinent  to  the  authenticity  of  particular  passages  is 
drawn  — "1°,  From  their  acknowledgment  by  the  author  himself  in 
other,  and  these  unsuspected,  works ;  2°,  From  the  attribution  of 
them  to  the  author  by  other  writers  of  competent  information ; 
and,  3°,  From  the  evidence  of  the  most  ancient  MSS.  On  the 
other  hand,  a  passage  is  to  be  obelized  as  spurious,  —  1°,  When 
found  to  be  repugnant  to  the  general  relations  of  time  and  place, 
and  to  the  personal  relations  of  the  author ;  2",  When  wanting  in 
the  more  ancient  codices,  and  extant  only  in  the  more  modern. 
A  passage  is  suspicious,  when  any  motive  for  its  interpolation  is 
manifest,  even  should  we  be  unable  to  establish  it  as  spurious. 
The  differences  which  different  copies  of  a  writing  exhibit  in  the 
particular  passages,  are  called  various  readings  (varicB  lectiones  or 
lectiones  variantes).  Now,  as  of  various  readings  only  one  can  be 
the  true,  while  they  may  all  very  easily  be  false,  the  problem  which 
the  criticism  of  Integrity  proposes  to  solve  is, —  How  is  the  genu- 
ine reading  to  be  made  out;  and  herein  consists  what  is  tech- 
nically called  the  Recension^  more  properly  the  Emendation^  of  the 
text. 

"The  Emendation  of  an  ancient  author  may  be  of  two  kinds; 
the  one  of  which  may  be  called  Historical,  the 

Emendation  of  the  other  the  Conjectural.  The  former  of  these 
\    '~^,°.  ^"i  '"  1'       founds  upon   historical  data  for  its  proof;  the 

vj?,,    Historical     anji  »  '  ' 

coiijccfuiai.  latter,    again,   proceeds    on   grounds    which   lie 

beyond   the  sphere  of  historical  fiict,  and   this 

fbr  the  very  reason  that  histoncnl  fact  is  found  incompetent  to  tho 

ivfttoration  of  the  text  to  its   original   integrity,      The  historical 

1  See  Esser,  Logik,  {(161, 162.  —  Eo. 


Lect.  XXXIV.  LOGIC.  473 

emendation  necessarily  precedes  the  conjectural,  because  the  object 
itself  of  emendation  is  wholly  of  an  historical  character,  and  be- 
cause it  is  not  permitted  to  attempt  any  other  than  an  emendation 
on  historical  grounds,  until,  from  these  very  grounds  themselves,  it 
be  shown  that  the  restitution  of  the  text  to  its  original  integrity 
cannot  be  historfcally  accomplished.  Historical 
Historical  Emenda-  Emendation  is  again  of  two  kinds,  according  as 
tion  of  two  kiuds,—       j|.g  judgment  proceeds  on  external  or  on  inter- 

External  .  and    Inter-  ,  i  t^    />         i  .1  1 

nal  grounds.  It  founds  upon  external  grounds, 
when  the  reasons  for  the  truth  or  falsehood  of 
a  reading  are  derived  from  testimony ;  it  founds  upon  internal 
grounds,  when  the  reasons  for  the  truth  or  falsehood  of  a  reading 
are  derived  from  the  writing  itself.  Historical  emendation  has  thus 
a  twofold  function  to  perform  (and  in  its  application  to  practice, 
these  must  always  be  performed  in  conjunction),  viz.,  it  has  care- 
fully to  seek  out  and  accurately  to  weigh  both  the  external  and 
internal  reasons  in  support  of  the  reading  in  dispute.  Of  external 
grounds  the  principal  consists  in  the  confirmation  afforded  by  MSS., 
by  printed  editions  which  have  immediately  emanated  from  MSS., 
by  ancient  translations,  and  by  passages  quoted  in  ancient  authors. 
The  internal  grounds  are  all  derived  either  from  the  form,  or  from 
the  contents,  of  the.  work  itself.  In  reference  to  the  form,  —  a 
reading  is  probable,  in  proportion  as  it  corresponds  to  the  general 
character  of  the  language  prevalent  at  the  epoch  when  the  work 
was  written,  and  to  the  peculiar  character  of  the  language  by  which 
the  author  himself  was  distinguished.  In  reference  to  the  contents, 
—  a  reading  is  probable,  when  it  harmonizes  with  the  context,  that 
is,  when  it  concurs  with  the  other  words  of  the  particular  passage  in 
which  it  stands,  in  affording  a  meaning  reasonable  in  itself,  and  con- 
formable with  the  author's  oj^inions,  reasonings,  and  general  charac- 
ter of  thought."  ^ 

"  It  frequently  happens,  however,  that,  notwithstanding  the  uni- 
formity of  MSS.,  and  other  external  subsidia,  a 
conjectura  Emen-       reading  cannot  be  recognized   as  genuine.     In 

datioQ.  ®  00 

this  case,  it  must  be  scientifically  shown  from 
the  rules  of  criticism  itself  that  this  lection  is  corrupt.  If  the 
demonstration  thus  attempted  be  satisfactory,  and  if  all  external 
subsidia  have  been  tried  in  vain,  the  critic  is  permitted  to  con- 
sider in  what  manner  the  corrupted  passage  can  be  restored  to 
its  integrity.  And  here  the  conjectural  or  divinatory  emenda- 
tion  comes   into   play ;    a   puocess   in  which  the  power  and  effi- 

J  Esser,  Logik.  §  1G3.  -Ed. 

GO 


474 


LOGIC. 


Lect.  XXXIV. 


II.  Interpretation. 


General  and  Special. 


ciency  of  criticism  and  the  genius  of  the  critic  are  principally 
manifested."  ^ 

So  much  for  Criticism,  in  its  applications  both  to  the  Authen- 
ticity and  to  the  Integrity  of  Writings.  We  have  now  to  consider 
the  general  rules  by  which  Interpretation,  that  is,  the  scientific  pro- 
cess of  expounding  the  Meaning  of  an  author,  is  regulated. 

"By  the  Art  of  Interpj'etation,  called  likewise  technically  JTer- 
meneutic  or  JEJxegetic,  is  meant  the  complement 
of  logical  laws,  by  which  the  sense  of  an  ancient 
writing  is  to  be  evolved.  Hermeneutic  is  either  General  or  Spe- 
cial. General,  when  it  contains  those  laws 
which  ajDply  to  the  interpretation  of  any  writ- 
ing whatever;  Special,  when  it  comprises  those  laws  by  which 
writings  of  a  particular  kind  are  to  be  expounded.  •The  former 
of  these  alone  is  of  logical  concernment.  The  problem  proposed 
for  the  Art  of  Interpretation  to  solve,  is,  —  How  are  we  to  proceed 
in  order  to  discover  from  the  words  of  a  writing  that  sole  meaning 
which  the  author  intended  them  to  convey  ?  In  the  interpretation 
of  a  work,  it  is  not,  therefore,  enough  to  show  in  what  signification 
its  words  may  be  underetood ;  for  it  is  required  that  we  show  in 
what  signification  they  must.  To  the  execution  of  this  task  two 
conditions  are  absolutely  necessary  ;  1°,  That  the  interpreter  should 
be  thoroughly  acquainted  with  the  language  itself  in  general,  and 
with  the  language  of  the  writer  in  particular ;  and,  2°,  That  the 
interpreter  should  be  familiar  with  the  subjects  of  which  the  writing 
treats.  But  these  two  requisites,  though  indispensable,  are  not  of 
themselves  suflicient.  It  is  also  of  importance  that  the  expositor 
should  liave  a  competent  acquaintance  with  the  author's  personal 
circumstances  and  character  of  thought,  and  with  the  history  and 
spirit  of  the  age  and  country  in  which  he  lived.  In  regard  to  the 
intei"pretation  itself,  —  it  is  to  be  again  observed,  that  as  a  writer 
could  employ  expressions  only  in  a  single  sense,  so  the  result  of  the 
exposition  ought  to  be  not  merely  to  show  what  meaning  may  pos-" 
sibly  attach  to  the  doubtful  terms,  but  what  meaning  necessarily 
must.  When,  therefore,  it  appears  that  a  passage  is  of  doubtful 
import,  the  best  preparative  for  a  final  determination  of  its  mean- 
ing is,  in  the  first  place,  to  ascertain  in  how  many  diflferent  significa- 
tions it  may  be  construed,  and  then,  by  a  process  of  exclusion,  to 
arrive  at  the  one  veritable  meaning.  When,  however,  the  obscu- 
rity cannot  be  removed,  in  that  case  it  is  the  duty  of  the  expositor, 


1  F^sser,  LosH',  i  10(>-  —  1^-    [Pan/iasiana,  i.  859—365,  2d  ed.  1701.    Gcnuensis,  Ars  Ijogico- 
Cfitica,  L.  iv.  C.  vi.  ft  srq.] 


Lect.  XXXIV.  LOGIC.  475 

before  abandoning  his  task,  to  evince  that  an  interpretation  of 
the  passage  is,  without  change,  absolutely  or  relatively  impossible. 

"As  to  the  sources  from  whence  the  Interpretation  is  to  be 
drawn,  —  these  are  three  in  all,  —  viz.,  1°,  The 

ourceso    n  rpre-       Tractus   lUerarum.   the   words    themselves,   as 

tation.  '  ' 

they  appear  in  MSS. ;  2°,  The  context,  that  is, 
the  passage  in  immediate  connection  with  the  doubtful  term ;  3°, 
Parallel  or  analogous  passages  in  the  same,  or  in  other  writings."  ^ 
How  the  interpretation  drawn  from  these  sources  is  to  be  applied,  I 
shall  not  attempt  to  detail ;  but  pass  on  to  a  more  generally  useful 
and  interesting  subject. 

So   much   for  Experience   or   Observation,  the   first   mean   of 

scientific    discovery,    that,    viz.,   by    which    we 

Specaiation  the  Sec-       apprehend    what    is    presented    as    contingent 

ond  Means  of  Knowl-  ,  -t     ^  ■,  n   x     t 

gjj  phaenomena,  and    by  whose  process  oi   Induc- 

tion and  Analogy  we  cany  up  individual  into 
general  facts.  We  have  now  to  consider  the  other  mean  of  sci- 
entific discovery,  that,  viz.,  by  which,  from  the  j^haenomena  pre- 
sented as  contingent,  we  separate  what  is  really  necessary,  and 
thus  attain  to  the  knowledge,  not  of  merely  generalized  facts, 
but  of  univei-sal  laws.  This  mean  may,  for  distinction's  s.ike, 
be  called  Speculation^  and  its  general  nature  I  comprehend  in  the 
following  i^aragraph. 

^    CXI.    When    the   mind    does   not   rest   contented   with 

observing   and   classifying   the   objects   of 

Par.  CXI.  Specula-       j^g  experience,  but,  by  a  reflective  analy- 

tion,  —  as  a  means  °^  .  -,  ,  ,      ,  ■» 

'  Knowledge.  SIS,  suudci's  the  concrctc  wholes  presented 

to  its  cognition,  throws  out  of  account 
all  that,  as  contingent,  it  can  think  away  from,  and  con- 
centrates its  attention  exclusively  on  those  elements  which, 
as  necessary  conditions  of  its  own  acts,  it  cannot  but  think ; 
—  by  this  process  it  obtains  the  knowledge  of  a  certain 
order  of  facts,  —  facts  of  Self-consciousness,  which,  as  essen- 
tial to  all  Experience,  are  not  the  result  of  any ;  consti- 
tuting in  truth  the  Laws  by  which  the  possibility  of  our 
cognitive  functions  is  determined.  This  process,  by  which 
we  thus  attain  to  a  discriminative  knowledge  of  the  N'eces- 
aary^  Native,  and,  as  they  are  also  called,  the  Noetic,  Pure, 
a  priori,  or  Transcendental,  Elements 'of  Thought,  may  be 
styled  Speculative  Analysis,  Analytic  Speculation,  or  Specu- 

1  Esser,  Logik,  i  167.  —  Ed.    [Cf.  Snell,  Logik,  p.  ii.  i  6,  p.  200.] 


476  LOGIC,  Lect.  XXXIV. 

lation  simply,  and  is  carefully  to  be  distinguished  from  Inducr 
tion,  with  which  it  is  not  unusually  confounded. 

**  The   em{>irical   knowledge   of  which   we   have   hitherto   been, 
speaking,  does  not,  however  varied  and  exten- 

Kxplicatioii.  ,  .  ,  „,  •    />        i  i  •    i  • 

give  It  naay  be,  suffice  to  satisfy  the  thinking 
niind  as  such  ;  for  our  empirical  knowledge  itself  points  at  certain 
higljer  cognitions  from  which  it  may  obtain  completion,  and  which 
me  of  a  very  different  character  from  that  by  which  the  mere  em- 
pirical cognitions  themselves  are  distinguished.  The  cognitions  are 
styled,  among  other  names,  by  those  of  noetic^  pure,  or  rational, 
and  they  are  such  ns  cannot,  though  manifested  in  experience, 
be  derived  from  experience;  for,  as  the  conditions  under  which 
experience  is  possible,  they  must  be  viewed  as  necessarj'  con- 
stituents of  the  nature  of  the  thinking  principle  itself.  Philos- 
ophers have  indeed  been  found  to  deny  the  reality  of  such  cog- 
nitions native  to  the  mind ;  and  to  confine  the  whole  sphere 
of  human  knowledge  to  the  limits  of  experience.  But  in  this 
c.ise  philosophers  have  overlooked  the  important  circumstance, 
that  the  acts,  that  is,  the  apprehension  and  judgment,  of  expe- 
rience, ;;ro  themselves  impossible,  except  under  the  supposition 
of  cert:;|n  potential  cognitions  previously  existent  in  the  think- 
.ng  subject,  and.  which  become  actual  on  occasiop  of  an  object 
being  piesented  to  the  external  or  internal  sense.  As  an  exam- 
ple of  a  poetic  cognition,  the  following  propositions  may  suf- 
fice:.-^ An  object  and  all  its  attributes  are  convertible;  —  All 
that   is    has   its   sufficient   cause.       The   principal   distinctions    of 

Empirical  and  Rational  Knowledges,  or  rather 
I'rincipai   distinc-       Empirical  and  Noetic  Cognitions,  are  the  fol- 

fions     of      Empirical         i        •  -lo      x?         •   •      i  •*•  •    •       ^ 

Noetic    c  lowing  :  —  1  ,   Empirical    cognitions    originate 

jiong.  exclusively  in   experience,  whereas  noetic  cog- 

nitions are  virtually  at  least  before  or  above 
all  experience,  —  all  experience  being  only  possible  through  them. 
'Z°,  Empirical  cognitions  come  piecemeal  and  successively  into  exist- 
cM^p,  (jnd  may  again  gradually  fade  and  disappear;  whereas  noetic 
cognitions,  like  Pallas,  armed  and  immortal  from  the  head  of  Jupi- 
ter, spring  at  once  into  existence,  complete  and  indestructible.  3°, 
P^mpirical  cognitions  find  only  an  application  to  those  objects  from 
which  they  were  originally  abstracted,  and,  according  a»  things 
obtain  a  different  form,  they  also  may  become  differently  fash- 
ioned ;  noetic  cognitions,  on  the  contrary,  bear  the  character  im- 
pressed on  them  of  necessity,  universality,  sameness.  Whether 
a  cognition  be  t'Uipirical  or  noetic,  can   only  be  determined  by 


Lect.  XXXIV. 


LOGIC. 


477 


P 


considering  whether  it  can  or  cannot  be  presented  in  a  sensible 
perception ;  —  whether  it  do  or  do  not  stand  forward  clear,  dis- 
tinct, and  indestructible,  bearing  the  stamp  of  necessity  and  abso- 
lute universality.  The  noetic  cognitions  can  be  detected  only  by  a 
critical  analysis  of  the  mental  phenomena  proposed  for  the  purpose 
of  their  discovery;"^  and  this  analysis  may,  as  I  have  said,  be 
styled  Speculation,  for  want  of  a  more  appropriate  appellation. 

1  Esser,  Logik,  f  171.  —  Ed. 


LECTURE    XXXV. 


MODIFIED     METHODOLOOY. 


SECTION  I.  — OF  THE  ACQUISITION  OF  KNOWLEDGE 


III.   COMMUNICATION   OF  KNOWLEDGE.  — A.  INSTRUCTION 

—  ORAL  AND  WRITTEN.  — B.  CONFERENCE  — 

DIALOGUE  AND  DISPUTATION. 

I  NOW  go  on  to  the  last  Mean  of  Acquiring  and  Perfecting  our 
knowledge ;  and  commence  with  the  following  paragraph  : 

^  CXII.  An  important  mean  for  the  Acquisition  and  Per- 
fecting of  Knowledge  is  the  Communica- 
tion of  Thought.     Considered  in  general, 
the   Communication   of  thought   is   either 
One-sided,  or  Mutual.    The  former  is  called 
Instruction  (mstitutio),  the  latter,  Confer- 
ence (coHocutio) ;  but  these,  though  in  theory  distinct,  are  in 
practice  easily  combined.     Instruction  is  again  either  Oral  or 
Written;  and  Conference,  as  it  is  interlocutory  and  familiar,  or 
controversial  and  solemn,  may  be  divided  into  Dialogue  (col- 
loqimim^  dialoffus),  and   Disjmtation   (disputatio,  concertatid). 
The  Corninunication  of  thought  in  all  its  forms  is  a  means  of 
intellectual  imj)rovement,  not  only  to  him  who  receives,  but  to 
him  who  bestows,  information  ;  in  both  relations,  therefore,  it 
ought  to  be  considered,  and  not,  as  is  usually  done,  in  the 
former  only.^ 


Par.  CXII.  The 
Communication  of 
Thought,  —  as  a  m  eans 
of  Acquiring  and  Per- 
fecting Knowledge. 


In  illustrating  this  paragraph,  I  shall  commence  with  the  last 
sentence,  and,  before  treating  in   detail  of  In- 

Explication.  •  i    ^       /.  /.  i 

struction  and  Conference,  as  means  ot  extend- 
ing the  limits  of  our  knowledge  by  new  acquisitions  derived  from 

1  Cf.  Krug,  Logik,  s  181  e«  je?.— Ed 


Lect.  XXXV. 


LOGIC. 


479 


The  Communication 
of  Thought  an  impor- 
tant mean  towards  the 
perfecting  of  Knowl- 
edge in  the  mind  of 
the  communicator. 


the  communication  of  others,  I  shall  endeavor  to  show,  that  the 
Communication  of  thought  is  itself  an  impor- 
tant mean  towards  the  perfecting  of  knowledge 
in  the  mind  of  the  communicator  himself.  In 
this  view,  the  communication  of  knowledge  is 
like  the  attribute  of  mercy,  twice  blessed,  — 
"  blessed  to  him  that  gives  and  to  him  that 
takes;"  in  teaching  others  we  in  tact  teach  ourselves. 

This  view  of  the  reflex  eifect  of  the  communication  of  thought 
on  the  mind,  Avhether  under  the  form  of  Instruction  or  of  Confer- 
ence, is  one  of  high  importance,  but  it  is  one  which  has,  in  modern 
times,  unfortunately  been  almost  wholly  overlooked.  To  illustrate 
it  in  all  its  bearings  would  require  a  volume ;  at  present  I  can 
only  contribute  a  few  hints  towards  its  exposition. 

Man  is,  by  an  original'tendency  of  his  nature,  determined  to  com- 
municate to  others  what  occupies  his  thoughts, 
and  by  this  communication  he  obtains  a  clearer 
understanding  of  the  subject  of  his  cogitations 
than  he  could  otherwise  have  compassed.  This 
fact  did  not  escape  the  acuteness  of  Plato.  In 
the  Protagoras,  —  "  It  has  been  well,"  says 
Plato  (and  he  has  sundry  passages  to  the  point),  —  "It  has  been 
well,  I  think,  observed  by  Homer  — 


Man  naturally  de- 
termined to  communi- 
cation. 

This  fact  noticed  by 
Plato. 


'  Through  mutual  intercourse  and  mutual  aid, 
Great  deeds  arc  done  and  great  discoveries  made; 
The  wise  new  wisdom  on  the  wise  bestow, 
Whilst  the  lone  thinlvcr's  thoughts  come  slight  and  slow.'l 


For  in  company  we,  all  of  us,  are  more  alert,  in  deed  and  word 
and  thought.  And  if  a  man  excogitate  aught  by  himself,  forthwith 
he  goes  about  to  find  some  one  to  whom  he  may  reveal  it,  and  from, 
whom  he  may  obtain  encouragement,  aye  and  until  his  discovery  be 
completed."^  The  same  doctrine  is  maintained 
by  Aristotle,  and  illustrated  by  the  same  quota- 
tion ;  ^  (to  which,  indeed,  is  to  be  referred  the 
adage,  —  "Unus  homo,  nullus  homo.") — "We 
rejoice,"  says  Themistius,  "in  hunting  truth  in 
company,  as  in  hunting  game."*  Lucilius, — 
"Scire  est  nescire,  nisi  id  me  scire  alius  scierit;*  —  paraphrased  in 


Aristotle. 


Themistius. 


Lucilius. 


1  Altered  from  Pope's  Homer,  Book  x.  266. 

2  Protag.,  p  348.     Compare  Lectures  on  Met- 
aphysics, p.  261. 

8  Etk.  Nie.,  viil.  1. 


4  Orat.,xxi.   Erplorator  aut  Philosophus,  Ora- 
tiones,  p.  254,  ed.  Harduin,  Paris,  1684.  —  Ed. 

5  Fragm.,  25,  in  the  Bipont  edition  of  Per- 
sius  and  Juvenal,  p.  176.  —  Ej>. 


4B0 


LOGIC. 


LiXT.  XXXV. 


the  compacter,  though  far  inferior,  verse  of  Peisius,  —  " Scire  tuum 

nihil  est,  nisi  te  scire  hoc  sciat  alter."'  —  Cicero's 

persins.  Cato  testiiRes  to  the  same  truth  :  —  "  Non  facile 

Cicero.  cst   invenire,  qui    quod   sciat   ipse,  non    trad;it 

Seneca.  alteri."  ^    And  Seneca :  —  "  Sic  cum  hac  excep- 

tione  detur  sapientia,  ut  illam  inclusam  teneam 

nee  enunciem,  rejiciam.     Nullius  boni,  sine  socio,  jucunda  possessio 

est."« 

"  Condita  tabescit,  vulgata  scientia  cre8eit."4 


Modes  in  which 
Communication  is 
conducive  to  the  Ter- 
fecting  of  Thought 
are  two. 


"  In  hoc  gaudeo  aliquid  discere,  ut  doceam  :  nee  me  ulla  res  deleo- 
tabit,  licet  eximia  sit  et  salutaris,  quam  mihi  uni,  sciturus  sim."* 
"Ita  non  solum  ad  discendum  propensi  suraus,  verum  etiam  ad 
docendum."  '^ 

The  modes  in  which  the  Communication  of  thought  is  conducive 
to  the  perfecting  of  thought  itself,  are  two ;  for 
the  mind  may  be  determined  to  more  exalted 
energy  by  the  sympathy  of  society,  and  by  the 
stimulus  of  opposition  ;  or  it  may  be  necessi- 
tated to  more  distinct,  accurate,  and  orderly 
thinking,  as  this  is  the  condition  of  distinct,  accurate,  and  orderly 
communication.  Of  these  the  former  requires  the  presence  of 
otliers  during  the  act  of  thought,  and  is,  therefore,  only  manifested 
in  oral  instruction  or  in  conference  ;  whereas  the  latter  is  operative 
both  in  our  oral  and  in  our  Written  communications.  Of  these  in 
their  t)rder. 

In  the  first  place,  then,  the  influence  of  man  on  man  in  recipro- 
cally determining  a  higher  energy  of  the  facul- 
ties, is  a  phaenomenon  sufficiently  manifest.  By 
nature  a  social  being,  man  has  powers  which 
are  relative  to,  and,  consequently,  find  their  de- 
velopment in,  the  company  of  his  fellows  ;  and 
this  is  more  particularly  shown  in  the  energies 
of  the  cognitive  faculties.  "As  iron  sharpeneth  iron,"  says  Solo- 
mon, "so  a  man  sharpeneth  the  understanding  of  his  friend."" 
This,  as  I  have  said,  is  effected  both  by  fellow-feeling  and  by  oppo- 
sition.    We  see  the  efiects  of  fellow-feeling  in  the  necessity  of  an 


1.  By  reciprocally 
determining  a  higher 
energy  of  the  facul- 
ties. 

(a)  Through  Sympa- 
thy. 


II.  27.  — Ed. 

S  Cato  apud  Cicero,  De  Fin.,  iii.  c.  20,  ( 
66. 

*  Seiioca,  JE/7.,  vi. 

*  Quoted  al80  in  Dismssions.  p.  778  This 
line  nppearg  to  have  been  taken  from  a  ntnall 
volume  entitled  Carminum  Proverbiaiium  Loti 


Communes,  p.  17,  Lond.  1583;  but  the  author 
is  not  named.  —  Ed. 
fi  Seneca,  Epift.,  vi.  —  Ed. 

6  Cicero,  De  Fin.,  iii.  20.  — Ed. 

7  Proverbf,  xxvii.  17.  The  authorized  ver- 
sion is,  countenance  of  his  friend.  CompM* 
Lectures  on  Mttaphysics,  p.  261.  —  ED. 


L:;CT.  ::XXV.  LOGIC.  481 

aadicuce    to   cull   forth   the   exertions   of   the    orator.     Eloquence 
requires  numbers  ;  and  oratory  has  only  flourished  where  the  con- 
dition  of  large   audiences   has   been   supplied. 
.         '""^   opposi-       g^^^  opposition  is  perhaps  still  more  powerful 
than   mere    sympathy   in    calling    out    the   re- 
sources of  the  intellect. 

In  the  mental  as  well  as  in  the  material  world,  action  and  i-eac- 
tion   are  ever  equal ;    and   Plutarch  ^  well   ob- 

Plutarch.  ,  ^       .' 

seiTCS,  that  as  motion  would  cense  were  con- 
tention to  be  taken  out  of  the  physical  universe,  so  progress  in 
improvement  would  cease  were  contention  taken  out  of  the  moral ; 
•troXjifWi  dirdvTwv  TraTrjp? 

"It  is  maintained,"  says  the  subtle  Scaliger,  "  by  Vives,  that  we 

profit  more  by  silent   meditation  than  by  dis- 

Scaliger,  J.  C  •  ,  mi   •       •  ,  -ry  r-  •  ^•     •         -,■ 

pute.  1  his  IS  not  true,  bor  as  fare  is  elicited 
by  the  collision  of  stones,  so  truth  is  elicited  by  the  cpllision  of 
minds.  I  myself  (he  adds)  frequently  meditate  by  myself  long 
and  intently  ;  but  in  vain ;  unless  I  find  an  antagonist,  there  is  no 
hope  of^  a  saccessful  issae.  By  a  master  we  are  more  excited  than 
by  a  book;  but  an  antagonist,  whether  by  his  pertinacity  or  his  mis- 
dom,  is  to  me  a  double  master."' 

But,  in  the  second  place,  the  necessity  of  communicating  a  piece- 

of  knowledge  to  others,  iinijoses  upon  us  the 

%.  By  imposing  tl.e  %        /  u*    •    •  V  11  •  C 

necessity  of  obtaining  necessity  ot  obtaining  a  fuller  consciousness  of 
a  fiiiJer  coiisciousjiess  that  knowledge  for  oureelves.  BThis  result  is  to 
of  knowledge  for  qui:-  ^  certain  extent  secured  by  the  very  process  of 
clothing  our  cogitations  in  words.  For  speech 
is  an  analytic  process;  and  to  express  our  thoughts  in  language,  it 
is  requisite  to  evolve  them  from  the  implicit  into  the  explicit,  from 
the  confused  into  the  distinct,  in  order  to  bestow  on  each  part  of 
the  organic  totality  of  a  thought  its  precise  and  appropriate  sym- 
bol. But  to  do  this  is  in  fact  only  to  accomplish  the  first  step 
towards  the  perfecting  of  our  cognitions  or  thoughts. 

But  the  communication  of  thought,  in  its  higher  applications,, 
iaiposes  on  us  far  more  than  this  ;  and  in  so  doing  it  reacts  with  a 
»tiM  more  beneficial  influence  on  our  habits  of  thinking.  Suppose 
Ihat  we  are  not  merely  to  express  our  thoughts  as  they  spontane- 
«>u&ly  arise;  suppose  that  we  are  not  merely  extemporaneously  to 
speak,  but  deliberately  to  write,  and  that  what  we  are  to  communi- 


IVita  AgesMai,  Opera^  1599,  vol.  i.  p.  598.— Ed.         3  Exercit.,  f.  420.    [For  a  criticism  of  Seal- 
2  Heraclitus.  Cf  Tiiitarch,  De  Is.et  Osir.,p.      iger's  remark  as  regards  Vires,  see  DiscuS' 
870.   Brandis,  Gesch.  der  Philo*.,  i.  p.  1^8.  —El),      sions,  p.  773.  —  Ed.] 

61 


482 


LOGIC. 


Lect.  XXXV. 


Influence  of  Compo- 
sition and  Instruction 
in  perfecting  our 
Knowledge. 

Godwin  quoted. 


cate  is  not  a  simple  and  easy,  but  a  complex  and  difficult,  matter. 
In  this  case,  no  man  will  ever  fully  understand 
his  subject  who  has  not  studied  it  with  the  view 
of  communication,  while  the  power  of  commu- 
nicating a  subject  is  the  only  competent  crite- 
rion of  his  fully  understanding  it.  "When  a 
man,"  says  Godwin,  "  writes  a  book  of  method- 
ical investigation,  he  does  not  write  because  he 
undei-stands  the  subject,  but  he  understands  the  subject  because  he 
has  written.  He  was  an  uninstructed  tyro,  exposed  to  a  thousand 
foolish  and  miserable  mistakes,  when  he  began  his  work,  compared 
with  the  degree  of  piofieiency  to  which  he  has  attained  when  he 
has  finished  it.  He  who  is  now  an  eminent  philosopher,  or  a  sub- 
lime poet,  was  formerly  neither  the  one  nor  the  other.  Many  a 
man  has  been  overtaken  by  a  premature  death,  and  left  nothing 
behind  him  but  compositions  worthy  of  ridicule  and  contempt, 
who,  if  he  had  lived,  would  perhaps  have  risen  to  the  highest  lite^ 
rary  eminence.  If  we  could  examine  the  school  exercises  of  men 
who  have  afterwards  done  honor  to  mankind,  we  should  often  find 
them  inferior  to  those  of  their  ordinary  competitors.  If  we  could 
dive  into  the  portfolios  of  their  early  youth,  we  should  meet  with 
abundant  matter  for  laughter  at  their  senseless  incongruities,  and 
for  contemptuous  astonishment."  ^ 

"  The    one    exclusive    sign,"   says   Aristotle, 
"that  a  man  is  thoroughly  cognizant  of  any-v 
thing,  is  that  he  is  able  to  teach  it ; "  ^  and  Ovid,^  — 


Aristotle. 


'  Quodqae  parum  novit  nemo  docere  potest." 


In  this  reiictive  effect  of  the  communication  of  knowledge  in 
determining  the  perfection  of  the  knowledge  communicated,  origi- 
nated the  scholastic  maxim  Doce  ut  discas,  —  a  maxim  which  has 
unfortunately  been  too  much  overlooked  in  the  schemes  of  modern 
education.  In  former  ages,  teach  that  you  may  learn  always  con- 
stituted one  at  least  of  the  great  means  of  intel- 
lectual cultivation.  "To  teach,"  says  Plato,  "is 
the  way  for  a  man  to  learn  most  and  best."* 
"Homines  dum  docent  discunt,"  says  Seneca.*    "In  teaching,"  says 


riato. 

Seneca. 


1  Enquirer,  part  i.  Essay  iv.  pp.  23,  24,  ed.  S  Tristia,  ii.  348.  - 
1797.  — Ed.  4  rseudo-l'lnto, 

2  Metaphyi.,  i.  1.    Quoted  in  Discussions,  p.  Ed. 

765.  —  Ed.  «  Epist.,  7.  —  Ed. 


Ed. 
Epinomis,     p. 


Lect.  XXXV. 


LOGIC. 


483 


Clement  of  Alexandria,^  "  the  instructor  often  learns  more  than  his 
pupils."  "  Disce  sed  a  doctis ;  indoctos  ipse 
doceto,"  is  the  precept  of  Dionysius  Cato ;  ^ 
and  the  two  following  were  maxims  of  au- 
thority in   the   discipline  of  the   middle   ages. 


Clement  of  Alexan 
dria. 
Dionysius  Cato. 


The  first 


The  second 


"  Multa  rogare,  rogata  tencre,  retenta  docere, 
Haec  tria,  discipuium  faciunt  superare  magistrum."  8 

"Discere  si  quaeris  doceas;  sic  ipse  doceris; 
Nam  studio  tali  tibi  profids  atque  sodali."  * 


Vive8. 


This  truth  is  also  well  enforced  by  the  great  Vives.  "Doctrina  est 
traditio  corum  quae  quis  novit  ei  qui  non  novit. 
DLsciplina  est  illius  traditionis  acceptio ;  nisi 
quod  mens  accipientis  impletur,  dantis  vero  non  exhauritur,  —  imo 
coramunicatione  augetur.eruditio,  sicut  ignis,  motu  atque  agitatione. 
Excitatur  enim  ingenium,  et  discurrit  per  ea  quae  ad  praesens  nego- 
tiuin  jsertinent :  ita  invenit  atque  excudit  multa,  et  quae  in  mentera 
non  veniebant  cessanti,  docenti,  aut  disserenti  oecurrunt,  calore 
acuente  vigorem  ingenii.  Idcirco,  nihil  est  ad  magnam  eruditio- 
nem  perinde  conducens,  ut  docere."'  The  celebrated  logician,  Dr. 
Robert  Sanderson,  used  to  say:  "I  learn  much 
from  my  master,  more  from  my  equals,  and  most 
of  all  from  my  disciples."* 

But  I  have  occupied  perhaps  too  much  time  on  the  influence  of 
the  communication  of  knowledge  on  those  by 
whom  it  is  made  ;  and  shall  now  pass  on  to  the 
consideration  of  its  influence  on  those  to  whom 
it  is  addressed.  And  in  treating  of  communica- 
tion in  this  respect,  I  shall,  in  the  first  place, 
consider  it  as  One-sided,  and,  in  the  second,  as  Reciprocal  or 
Bilateral. 

The  Unilateral  Communication  of  knowledge,  or  Instruction,  is 
of  two  kinds,  for  it  is  either  Oral  or  Written ;  but  as  both  these 


Sanderson. 


Influence  of  the 
communication  of 
Knowledge  on  those 
to  whom  it  is  ad- 
dressed. 


1  Stromata,  lib.  i.  p.  275,  edition  Sjih., 
&ki5i<TKwv  Tis  fiav&dvfi  ■ir\e7oy,  Ka\  \eyuy 
vvvoKpoarai  iroAXiKis  rois  iiraKoiovtnv  av- 
rov,  —  Ed. 

2IV.  29.  — Ed. 

8  [Crenius,  p.  581.]  [  Gabridis  Naudai  Syn- 
tagma de  Studio  Liberali.  Included  in  the 
Consilia  et  Methodi  Aureee  studiorum  optime 
autituendorum,  collected  by  Th.  Crenius,  Bot- 


terdam,  1692.    The  lines  are  quoted  as  from 
an  anonymous  author.  —  Ed.] 

-*  <jiven  without  author's  name  in  the  Car- 
minum  Proverbialum  Loci  Communes,  Lond. 
1683,  p.  17.    See  above,  p.  480,  note  *.  —  Ed. 

5  De  Anima,  p.  89. 

6  [Reason  and  Judgment,  or  Special  Remarks 
of  the  Life  of  the  Renowned  Dr.  Sanderson,  p.  lO- 
London:  1663.] 


484  LOGIC.  Lect   XXXV. 

species  of  instruction  propose  the  same  end,  they  are  both,  to  a  cer- 
tain extent,  subject  to  the  same  laws. 
1.    instructioD,-  Oral  and  Written  Instruction  have  cach  their 

Oral  and  Written. 

peculiar  advantages. 
In  the  first  place,  instruction  by  the  living  voice  has  this  advan- 
tage over  that  of  books,  that,  as  more  natural. 

Oral  instruction, —         .      .  .  •  tt         •  ^i  ^ 

.,    ^      ,  it  IS  more  impressive.     Hearing  rouses  the  at- 

its  advantages.  _  *  _  _  ° 

(a)  More  natural,  tcution  and  keeps  it  alive  far  more  effectually 
therefore  more  im-  than  reading.  To  this  we  have  the  testimony 
pressive.  ^^  ^^^  niost  competent  observers.     "Hearing," 

Theophrastus.  i       •         /. 

says  Theophrastus,^  "is  of  all  the   senses   the 
most  pathetic,"  that  is,  it  is  the  sense  most  intimately  associate4 
with  sentiment  and   passion.     "Multo   magis,"  says  the   younger 
Pliny,  "multo   magis   viva   vox   afficit.      Nam, 
'  licet  acriora  sunt   quae   legas,  altius   taraeu   in 

animo  sedent  quae  pronuntiatio,  vultus,  habitus,  gestu^  etlam  dicen- 
tisadfigit."2 

"  Plus  prodest,"  says  Valerius  Maximus,  "  docentem  atidirey  quam 
in  librls  studere ;  quia  vehementior  fit  impressio 

Valerias  M  aximns.  .  . ,  ^ .         .  .... 

in    mentibus    audientium,   ex   visu   doctoris   et 
audita,  quara  ex  studio  et  libro." ' 
And  St.  Jerome  —  "Habet  nescio  quid  latentis  energiae  viva  vox; 
et  in  aures  discipuli  de  doctoris  ore  transfusa, 

8t  Jerome.  n     ^-  ^nt. 

fortius  sonat.  * 
A  second  reason  why  our  Attention  (and  Memory  is  always  in 
the   ratio   of   Attention)    to    things    spoken   is 

(b)  Less  permanent,       greater  than  to   things  read,  is   that  what   is 

therefore      more     at-  .^^  i 

.  ,  written  we  regard  as  a  permanent  possession 

to   which    we    can    always   recur   at   pleasure ; 

whereas  we  are  conscious  that  the  "winged  words"  are  lost  to  us 

forever,  if  we  do  not  catch  them  as  they  fly.     As  Pliny  hath  it : 

"  Legendi  semper  est  occasio  ;  audiendi  non  semper."  ^ 

A  third  cause  of  the  superior  efficacy  of  oral  instruction  is  that 
man  is  a  social  animal.  He  is  thus  naturally  disposed  to  find  pleas- 
ure in  society,  and  in  the  performance  of  the  actions  performed  by 
those  with  whom  he  consorts.     But  reading  is  a  solitary,  hearing  is 

^  Qjw  tan  iaifim  8*  o2)uai  (r«  vpovoKQvaai  fat  the  JF^^  of  Tboinas  Hijtienuco?,  as4  jn 

wtp\  Tijs  itKovirriKris,  aiV^<r*a.s,  ^u  6  et6-  ^^^  Anthologia  of  Langius,  under  the  article 

.               ,          _               ..  Doetrina.    It  is  not,  however,  to  be  found  in 

I:          ,                         I             r  /  ijjjjt  a^tho^■  —  Ed-J 
Plutarch,  De  Audilione,  sub  intt.  —  Ed. 

«  Ernst.,  ii.  8  —  Ed.  *  Epist.,  oiii.     Optm,  Antt  1679,  torn.  Hi  p 

3  [Thom«8  HiberuicuB^  p.  330.]    [The  above  ^37.  —  Ed. 

passage  is  quoted  as  from  Valerius,  lib.  viii.,  <  fyist.  ii.  3.  —  Ed 


LfeCT.  XXXV.  LOGIC.  48S 

a«t<ydal  act.    In  reading,  we  are  not  d^ermiw6fd  to  attend  by  any* 
fellow-feeling  with  oth'^rs  attending;    whereas 
(c)    earing  a  socia        -^  hearing,  our  attention  is  not  only  engaged  by 
our  sympathy  with  the  speaker,  but  by  our  sym- 
pathy with  the  other  attentive  auditors  around  us. 

Suoh  are  the  causes  which  contnir  in  rendering  Oral  Instruction 

more   effectual   than   Written.      "M.  Varillas," 

^       '         says  Menage  (and  Vaiillas  was  one  of  the  most 

learned   of   modern   historians,  —  and   Menage   one   of   the   most 

learned  of  modern  scholars),  "  M.  Varillas  himself  told  me  one 

day,  that  of  every  ten  things  he  knew,  he  had  learned  nine  of  them 

in  conversation.     I  myself  might  say  nearly  the  same  thing."  ^ 

On  the  other  hand,  Reading,  though  only  a  substitute  for  Oral 

Instruction,  has  likewise  advantages  peculiar  to 

Reading,  -  its  ad-  -^g^if.  j^  ^j^g  gj.g^  |g^g^  j^  j^  ^^^^.^  ^j^^-j  '^^^ 
vantages.  .1  -i  t        i  t    •     • 

(a)  More  easily  ac-       cessible.     In  the  second,  it  IS  more  comprehen- 
c(Bssib)e.  sive  in  its  sphere  of  operation.     In  the  third,  it 

(b)  More  compre-       jg  j^^^  transitory  with  the  voice,  but  may  again 
,  ,  .,*  .        and  again  be  taken  up  and  considered,  so  that 

(c)  More  permanent.  »  _      "  ' 

the  object  of  the  instruction  may  thus  more 
fully  be  examined  and  brought  to  proof.  It  is  thus  manifest,  that 
oral  and  written  instruction  severally  supply  and  sevei-ally  support 
each  other;  and  that,  where  this  is  competent,  they  ought  always 
to  be  employed  in  conjunction.  Oral  instruction  is,  however,  in 
the  earlier  stages  of  education,  of  principal  importance ;  and  writ- 
ten ought,  therefore,  at  first  only  to  be  brought  in  as  a  subsidiary. 
A  neglect  Of  the  oral  instruction,  and  an  exclusive  employment  of 
the  written,  —  the  way  in  which  those  who  are  self-taught  (the 
atitodidacti)  obtain  their  education,  —  for  the  most  part  betrays  its 
One-sided  influence  by  a  contracted  cultivation  of  the  intellect, 
with  a  deficiency  in  the  power  of  communicating  knowledge  to 
others. 

Oral  instruction  nece«sarily  supposes  a  speaker  and  a  hearer;  and 
written  instruction  a  writer  and  a  reader.  In  these,  the  capacity 
of  the  speaker  and  of  the  writer  must  equally  fulfil  certain  common 
requisites.  In  the  first  place,  they  should  be  fully  masters  of  the 
subject  with  which  their  instruction  is  conversant ;  and  in  the  sec- 
ond, they  should  be  able  and  willing  to  communicate  to  Others  the 
knowledge  which  they  themselves  possess.  But  in  reference  to 
these  several  Jspecies  of  instruction,  there  are  various  special  rul-s 
that  ought  to  be  attended  to  by  those  who  would  reap  the  advan- 
tages they  sfevierally  afford.     I  shall  commence  with  Written  Irt- 

1  Menagiana,  torn.  ir.  p.  Ill,  ed.  1715. —  Ed. 


486  LOGIC.  Lkct.  XXXV. 

struction,  and  comprise  the  rules  by  which  it  ought  to  be  regulated, 
in  the  following  paragraph. 

%  CXIII.  In  regard  to  Written  Instruction,  and  its  profit- 
able employment  as  a  means  of  intellectual 
in^struct^  Tna'Ts      improvement,  there  are  certain  rules  which 
employment     as    a       ought  to  be  observed,  ahd  which  together 
means  of  inteuectuai       gonstitute  the  Proper  Method  of  Reading. 

improvement.  i  o 

These  may  be  reduced  to  three  classes,  as 
they  regard,  1**,  The  Quantity,  2°,  The  Quality,  of  what  is  to 
be  read,  or,  3°,  The  Mode  of  reading  what  is  to  be  read. 

I.  As  concerns  the  Quantity  of  what  is  to  be  read,  there 
is  a  single  rule,  —  Read  much,  but  not  many  works  (multum 
non  multa). 

II.  As  concerns  the  Quality  of  what  is  to  be  read,  —  there 
may  be  given  five  rules.  1°,  Select  the  works  of  principal 
importance,  estimated  by  relation  to  the  several  sciences  them- 
selves^ or  to  your  particular  aim  in  reading,  or  to  your  individ- 
ual disposition  and  wants.  2%  Read  not  the  more  detailed 
works  upon  a  science,  until  you  have  obtained  a  rudimentary 
knowledge  of  it  in  general.  3°,  Make  yourselves  familiar  with 
a  science  in  its  actual  or  present  state,  before  you  proceed  to 
study  it  in  its  chronological  development.  4°,  To  avoid  errone- 
ous and  exclusive  views,  read  and  compare  together  the  more 
imjiortant  works  of  every  sect  and  party.  5°,  To  avoid  a  one- 
sided development  of  mind,  combine  with  the  study  of  works 
which  cultivate  the  Understanding,  the  study  of  works  which 
cultivate  the  Taste. 

III.  As  concerns  the  Mode  or  Manner  of  reading  itselti 
there  are  four  principal  rules.  1°,  Read  that  you  may  accu- 
rately remember,  but  still  more,  that  you  may  fully  understand. 
2°,  Strive  to  compass  the  general  tenor  of  a  work,  before  you 
attempt  to  judge  of  it  in  detail.  3°,  Accommodate  the  inten- 
sity of  the  reading  to  the  importance  of  the  work.  Some 
books  are,  thei-efore,  to  be  only  dipped  into ;  others  are 
to  be  run  over  rapidly ;  and  others  to  be  studied  long  and 
sedulously.  4°,  Regulate  on  the  same  principle  the  extracts 
which  you  make  from  the  works  you  read.* 

I.   In  reference  to  the  head  of  Quantity,  the  single  rule  is  — 

1  Cf.  Krng,  Logik,  i  180.  ~  Ed.    [Figchaber,      der  Hodegetik,  §  63  p.  196;  1832.    Magirus  v. 
Logik,  p.  188,  ed.  1818.    Scheidler,    Grundriss      Lectio.] 


Lect.  XXXV.  LOGIC.  48T 

Read  much,  but  not  many  works.     Though  this  golden  rule  has 

risen  in  importance,  since  tlie  world,  by  the  art 

Explication.  ^^  printing,  has  been  overwhelmed  by  the  mul- 

I.    Quantity  to   be  '^  ^  .       r  •       i    i 

j.ga^  titude  of  books,  it  was  still  fully  recognized  by 

Rule.  the   great   thinkers   of   antiquity.      It   is   even 

Solomon.  hinted   by   Solomon,  when   he    complains   that 

Quintiiian.  "  of  making  many  books  there  is  no  end."^     By 

Younger  Pliny.  Quintiiian,  by  the  younger  Pliny,  and  by  Seneca, 

®®°^*'"'  the  maxim,  "multum  legend um  esse,  non  multa," 

Luther  quoted.  ^^  laid  down  as  the  great  rule  of  study.^    "All," 

says  Luther,  in  his  Table  Talk,''  "  who  would 

study  with  advantage  in  any  art  whatsoever,  ought  to  betake  them, 

selves  to  the  reading  of  some  sure  and  certain  books  oftentimes  over; 

for  to  read  many  books  produceth  confusion,  rather  than  learning, 

like  as  those  who  dwell  everywhere,  are  not  anywhere  at  hoine." 

He  alludes  here  to  the  saying  of  Seneca,  "  Nusquam  est  qui  ubique 

est."  *     "  And  like  as  in  society,  we  use  not  daily  the  community  of 

all  our  acquaintances,  but  of  some  few  selected  friends,  even  so 

likewise  ought  we  to  accustom  ourselves  to  the  best  books,  and  to 

make  the  same  fimiliar  unto  us,  that  is,  to  have  them,  as  we  use  to 

say,  at  our  fingers'  ends."     The  great  logician, 

Sanderson.  ,   ,  ,,        ,  i  t  p  i  /•  t 

Jiishop  banderson,  to  Avhom  1  lormerly  reierred, 
as  his  friend  and  biographer  Isaac  Walton  informs  us,  said  "  that  he 
declined  reading  many  books ;  but  what  he  did  read  were  well 
chosen,  and  read  so  often  that  he  became  very  familiar  with  them. 
They  were  principally  three,  —  Aristotle's  Rhetoric^  Aquinas's  Se- 
cunda  Secrindce,  ^xi(\  Cicero,  particularly  his  Offices."^     The  great 

Lord  Burleigh,  we  are  told  by  his  biographer, 

Lord  Burk'igli.  .     ,   ^~,  T-v>^/r»..  •   ^      a-  ii      tu 

carried  Cicero  JJe  O^ffims,  with  Aristotle  s  lihet- 
oric,  always  in  his  bosom ;  these  being  complete  pieces,  "  that 
would  make  both  a  scholar  and  an  honest  man." 
"Our  age,"  says  Herder,  "is  the  reading  age;" 
and  he  adds,  "it  would  have  been  better,  in  my  opinion,  for  the 
world  and  for  science,  if,  instead  of  the  multitude  of  books  which 
now  overlay  us,  we  possessed  only  a  few  works  good  and  sterling, 
and  which,  as  few,  would,  therefore,  be  more  diligently  and  pro- 
foundly studied."  *     I  might  quote  to  you  many  other  testimonies 

1  Eccles.  xii.  12.  —  Ed.  *  Epist.,  ii.  —  Ed. 

2  Quintiiian,  x.  1,  59.  Pliny,  Ep.,  vii.  9.  5  See  Walton's  Lives  of  Donne,  Wotton, 
Seneca,  De  TranquiU.  Animi,  C.  9.  Epist.,  2,  Hooker,  Herbert,  and  Sanderson,  vol.  ii.,  p.  287, 
45.  —  Ed.  ed.  Zouch,  York,  1817.  —  Ed. 

3  No.  DCCCXLIV.  Of  Learned  Men.  —  6  Briefe  ilber  das  Stud,  der  Theol.  B.  xlix., 
Ed.  Werke,  xiv.  267,  ed.  1829.  —  Ed. 


4^  LOGIC.  Lect.  XXXV. 

to  the  same  effect;  but  testimonies  are  useless  in  support  of  so 
manifest  a  truth. 

For  what  purpose,  — -  with  what  intent,  do  we  read  ?  We  read 
not  for  the  sake  of  reading,  but  we  read  to  the 
ing.  ^^^^j  ^^^^  ^^  may  think.  Reading  is  valuable 
only  as  it  may  supply  to  us  the  materials  which  the  mind  itself 
elaborates.  As  it  is  not  the  largest  quantity  of  any  kind  of  food, 
taken  into  the  stomach,  that  conduces  to  health,  but  such  a  quan- 
tity of  such  a  kind  as  can  be  best  digested ;  so  it  is  not  the  greatest 
complement  of  any  kind  of  information  that  improves  the  mind, 
but  such  a  quantity  of  such  a  kind  as  determines  the  intellect  to 
most  vigorous  energy.  The  only  profitable  reading  is  that  in 
which  we  are  compelled  to  think,  and  think  intensely  ;  whereas 
that  reading  which  serves  only  to  dissipate  and  divert  our  thought, 
is  either  positively  hurtful,  or  useful  only  as  r.n  occasional  relaxa- 
tion from  severe  exertion.  But  the  amount  of  vigorous  thinking 
is  usually  in  the  inverse  ratio  of  multifarious  reading.  Multifarious 
reading  is  agreeable  ;  but,  as  a  habit,  it  is,  in  its  way,  as  destructive 
to  the  mental  as  dram-drinking  is  to  the  bodily  health. 

II.  In  reference  to  the  quality  of  what  is  to  be  read,  the  First  of  the 
five  rules  is  —  'Select  the  works  of  principal  im- 

ir.  Quality  of  what       portauce,  in  accommodation  either  to  the  several 

iK  to  be  read.  *    .  .... 

-,.  ,„  ,  sciences  themselves,  to  your  iiarticnlar  ami  m 

First  Rnle.  ,  ... 

reading,  or  to  your  individual  disposition  and 
wants.'  This  rule  is  too  manifestly  true  to  require  any  illustration  of 
its  truth.  No  one  will  deny  that  for  the  accomplishment  of  an  end 
you  ought  to  employ  the  means  best  calculated  for  its  accomplish- 
ment. This  is  all  that  the  rule  inculcates.  But  while  there  is  no 
difficulty  about  the  expediency  of  obeying  the  rule,  there  is  often 
wjnsiderable  difficulty  in  obeying  it.  To  know  what  books  ought 
to  be  read  in  order  to  learn  a  science,  is  in  fact  frequently  obtained 
after  the  science  has  been  already  learned.  On  this  point  no  gen- 
eral advice  can  be  given.  We  have,  on  all  of  the  sciences,  works 
which  profess  to  supply  the  advice  which  the  student  here  requires. 
But  in  general,  I  must  say,  they  are  of  small  assistance  in  pointing 
oat  what  books  we  should  select,  however  useful  they  may  be  in 
showing  us  what  books  exist  upon  a  science.  In  this  respect,  the 
British  student  also  labors  under  peculiar  disadvantages.  The  libra- 
ries in  this  country  are,  one  and  all  of  them,  wretchedly  imperfect ; 
and  there  are  feW  departments  of  science  in  which  they  are  not  des- 
titute even  of  the  works  of  {irimary  necessity,  —  works  which,  from 
their  high  price,  but  more  frequently  from  the  difficulty  of  proCuT' 
ing  them,  ai:e  beyond  the  reach  of  ordinary  readers. 


Lkct.  XXXT.  LOCfliC.  489 

Under  the  head  of  Quality  the  Second  Rule  is  — 'Read  not  the 
more  detailed  works  upoh  a  science,  until  you 
have  obtained  a  rudimentary  knowledge  of  it  in 
general.'  The  expediency  of  this  rule  is  sufficiently  apparent.  It 
is  altogether  impossible  to  read  ipith  advantage  an  extensive  work 
on  any  branch  of  knowledge,  if  we  are  not  previously  atvare  of  its 
general  bearing,  and  of  the  relations  in  which  its  several  parts 
stand  to  each  other.  In  this  case,  the  mitod  is  overpowered  aftd 
oppressed  by  the  mass  of  details  presented  to  it,  ^^  details,  the  sig- 
nificance and  subordination  of  which  it  is  as  yet  unable  to  recog- 
nize. A  conspectus,  —  a  survey  of  the  Science  as  a,  whole,  Oxight, 
therefore,  to  precede  the  !*tudy  of  it  in  its  pa'ttS ;  Ive  should  be 
aware  of  its  distribution,  before  we  attend  to  what  is  distributed,  ^- 
We  should  possess  the  empty  frame-work,  before  we  collect  the 
materials  with  which  it  is  to  be  filled.  Hence  the  utility  of  an  ency- 
clopgedical  knowledge  of  the  sciences  in  general,  preliminary  to  a 
study  of  the  several  sciences  in  particular ;  that  is,  a  summary 
knowledge  of  their  objects,  their  extent,  their  connection  with  each 
other.  By  this  means  the  student  is  enabled  to  steer  his  Way  on 
the  wide  ocean  of  science.  By  this  means  he  always  knows  where- 
abouts he  is,  and  becomes  aware  of  the  point  towards  which  his 
author  is  leading  him. 

In  entering  upon  the  study  of  such  authors  as  Plato,  Aristotle, 
Descartes,  Spinoza,  Leibnitz,  Locke,  Kant,  etc.,  it  is,  therefore, 
proi>er  that  we  first  obtain  a  preparatory  acquaintance  tvith  the 
scope,  both  of  their  philosophy  in  general,  and  of  the  particular 
Work  on  which  we  are  about  to  enter.  In  the  case  of  writers  of 
such  ability  this  is  not  difl[icult  to  do,  as  there  are  abundance  of 
subsidiaiy  works,  affording  the  preliminary  knowledge  of  which  we 
are  in  quest.  But  in  the  case  of  treatises  where  similar  assistance 
is  not  at  hand,  we  may  often,  in  some  degree,  prepare  ourselves  for 
a  i-egular  perusal,  by  examining  the  table  of  contents,  and  taking  a 
cursory  inspection  of  its  several  departments.  In  this  respect,  and 
also  in  others,  the  following  advice  of  Gibbon  to  young  students  is 
highly  deserving  of  attention.  "After  a  rapid 
on  quo  e  .  gJance  (I  translate  from  the  original  French)  — 
after  a  rapid  glance  on  the  subject  and  distribution  of  a  new  book, 
I  suspend  the  reading  of  it,  which  I  only  resume  after  having  my- 
self examined  the  subject  in  all  its  relations,  —  after  having  called 
up  in  my  solitary  walks  all  that  I  have  read,  thought,  or  learned  in 
regard  to  the  subject  of  the  whole  book,  or  of  some  chapter  in  })ar- 
licular.  I  thus  place  myself  in  a  condition  to  estimate  what  the 
author  may  add  to  my  general  stock  of  knowledge  ;  and  I  am  thus 

62 


490 


LOGIC. 


Lect.  XXXV 


Third  Bale. 


Fourth  Bale. 


sometimes  favorably  disposed  by  the  accordance,  sometimes  armed 
by  the  opposition,  of  our  views."  ^ 

The  Third  Rule  under  the  head  of  Quality  is  —  'Make  your- 
selves familiar  with  a  science  in  its  present 
state,  before  you  proceed  to  study  it  in  its 
chronological  development.'  The  propriety  of  this  procedure  is 
likewise  manifest.  Unless  we  be  acquainted  with  a  science  in  its 
more  advanced  state,  it  is  impossible  to  distinguish  between  what 
is  more  or  less  important,  and,  consequently,  impossible  to  deter- 
mine what  is  or  is  not  wortliy  of  attention  in  the  doctrines  of  its 
earlier  cultivators.  We  shall  thus  also  be  overwhelmed  by  the 
infinitude  of  details  successively  presented  to  us ;  all  will  be  confu- 
sion and  darkness,  where  all  ought  to  be  order  and  light.  It  is 
thus  improper  to  study  philosophy  historically,  or  in  its  past  prog- 
ress, before  we  have  studied  it  statistically,  or  in  its  actual  results. 
The  Fourth  Rule  under  the  same  head  is — 'To  avoid  erroneous 
and  exclusive  views,  read  and  compare  together 
the  more  important  works  of  every  party.'  In 
proportion  as  different  opinions  may  be  entertained  in  regard  to  the 
objects  of  a  science,  the  more  necessary  is  it  that  we  should  weigh 
with  care  and  impartiality  the  reasons  on  which  these  different 
opinions  rest.  Such  a  science,  in  particular,  is  philosophy,  and  such 
sciences,  in  general,  are  those  which  proceed  out  of  philosophy.  In 
the  philosophical  sciences,  we  ought,  therefore,  to  be  especially  on 
our  guard  against  that  partiality  which  considers  only  the  argu- 
ments in  favor  of  particular  opinions.  It  is  true  that  in  the  writ- 
ings of  one  party  we  find  adduced  the  reasons  of  the  opposite 
party ;  but  frequently  so  distorted,  so  mutilated,  so  enervated,  that 
their  refutation  occasions  little  effort.  We  must,  therefore,  study 
the  arguments  on  b.oth  sides,  if  we  would  avoid  those  one-sided 
and  contracted  views  which  are  the  result  of  party-spirit.  The 
precept  of  the  Apostle,  "Test  all  things,  hold  fast  by  that  which  is 
good,"  is  a  precept  which  is  applicable  equally  in  philosophy  as  in 
theology,  but  a  prece})t  that  has  not  been  more  frequently  neglected 
in  the  one  study  than  in  the  other. 

The  Fifth  Rule  under  the  head  of  Quality  is  —  '  To  avoid  a  one- 
sided development  of  mind,  combine  with  the 
study  of  works  which  cultivate  the  Understand- 
ing, the  study  of  works  which  cultivate  the  Taste.'     The  propriety 


Fifth  Bule. 


1  The  substance  of  the  abovo  pnssa;;e  is 
given  in  English,  in  Gibbon's  Mewoirx  o/my 
Life   and  Writingf,  pp.  54,  5o;   I'd.  1837.     The 


French  original  is  quoted  bf  Scheidler,  Hod*- 
getik,  i  66,  p.  204.  —  Ed. 


Lect.  XXXV.  LOGIC.  491 

of  this  rule  requires  no  elucidation ;  I,  therefore,  pass  on  to  the 
third  head  ■ —  viz.,  the  Manner  of  reading  itself; 

III.      Manner     of        ^^^^^    ^j^.^j^    ^^^    p-^.^^    j^^j^    is— 'Read    that 
Reading.  .  , 

.     „  you  may  accurately  remember,  but  still  more 

First  Rule.  -^  •'  ^  „  ,  .  , 

that  you  may  fully  understand. 
This  also  requires  no  comment.  Reading  should  not  be  a  learn- 
ing by  rote,  but  an  act  of  reflective  thinking.  Memory  is  only  a 
subsidiary  faculty,  —  is  valuable  merely  as  supplying  the  materials 
on  which  the  understanding  is  to  operate.  We  read,  therefore, 
principally,  not  to  remember  facts,  but  to  understand  relations.  To 
commit,  therefore,  to  memory  what  we  read,  before  we  elaborate  it 
into  an  intellectual  possession,  is  not  only  useless  but  detrimental ; 
for  the  habit  of  laying  up  in  memoiy  what  has  not  been  digested 
by  the  undei"standing^  is  at  once  the  cause  and  the  eflect  of  mental 
weakness. 

The  Second  Rule  under  this  head  is  —  'Strive  to  compass  the 
general  tenor  of  a  work,  before  you  attempt  to 
judge  of  it  in  detail.'  Nothing  can  be  more 
absurd  than  the  attempt  to  judge  a  part  before  comprehending  the 
whole;  but  unfortunately  nothing  is  more  common,  especially 
among  professional  critics,  —  reviewers.  This  proceeding  is,  how- 
ever, as  frequently  the  effect  of  wilful  misrepresentation,  as  of 
unintentional  error. 

The  Third  Rule  under  this  head  is  — '  Accommodate  the  inten- 
sity of  the  reading  to  the  importance  of  the 
work.     Some  books  are,  therefore,  to  be  only 
dipped  into ;  others  are  to  be  run  over  rapidly ;  and  others  to  be 
studied  long  and  sedulously.'     All  books  are  not  to  be  read  with 
the  same   attention  ;  and,  accordingly,  an  ancient  distinction  was 
taken  of  reading  into  lectio  cursoria  and  lectio  stataria.     The  for- 
mer of  these  we  have  adopted  into  English,  cur- 
,    .  sory  readmg  bemg  a  lammar  and  correct  trans- 

Lectio  stalarta.  ^  ^  " 

lation  of  lectio  cursoria.  But  lectio  stataria 
cannot  be  so  well  rendered  by  the  expression  of  stationary  read- 
ing. "  Read  not,"  says  Bacon,  in  his  Fiftieth  Essay  —  "  read  not  to 
contradict  and  confute,  nor  to  believe  and  take 
for  granted,  nor  to  find  talk  and  discourse,  but 
*;0  weigh  and  consider.  Some  books  %re  to  be  tasted,  others  are  to 
be  swallowed,  and  some  few  to  be  chewed  and  digested ;  tliat  is, 
some  books  are  to  be  read  only  in  parts ;  others  to  be  read,  but  not 
curiously ;  and  some  few  to  be  read  wholly  and  with  diligence  and 
attention.  Some  books  also  may  be  read  by  deputy,  and  extracts 
made  of  them  by  others ;  but  that  would  be  only  in  the  less  impor- 


492  LOGIC.  Lect.  XXXV. 

tant  arguments,  and  the  raean^  sort  of  books  >  else  distilled  books 
are,  like  common  distilled  waters,  fleshy  things."  "  One  kind  of 
books,"  says  the  great  historian,  Johann  von  Mullet,^  "  I  fead  witli 
great  rapidity,  for  in  these  there  is  much  4rosi^ 
to  throw  aside,  and  little  gold  to  be  found; 
some,  however,  there  are  all  gold  and  diamonds,  and  he  who,  for 
example,  in  Tacitus  can  read  more  than  twenty  pages  in  four  boars, 
certainly  does  not  understand  him." 

Rapidity  in  reading  depends,  however^  greatly  on  our  acquaint- 
ance with  the  subject  of  discussion.  At  first,  upon  a  science  we 
can  only  read  with  profit  few  books,  and  laboriously.  By  degrees, 
however,  our  knowledge  of  the  mattere  treated  expands,  the  reason- 
ings appear  more  manifest^  —  we  advance  more  easily,  until  at 
length  we  ai'e  able,  without  overlooking  anything  of  importance, 
to  read  with  a  velocity  which  appears  almost  incredible  for  those 
who  are  only  commencing  the  study. 

The  Fourth  Rule  under  this  head  is  —  'Regulate  on  the  same 
principle  the  extracts  which  you  make  from  the 

Fourth  fiiile.  ,  ■,  , 

works  you  read. 

So  much  for  the  Unilateral  Communication  of  thouglit,  as  a 
meaA  of  knowledge.  We  now  proceed  to  the  Mutual  Communica- 
tion of  thought,  —  Conference. 

This  is  either  mere  Convei-sation,  —  mere  Dia- 

kh.dr'^"'^"*''^""       logue,  or  Formal  Dispute,  and  at  present  we 

consider  both  of  tliese  exclusively   only   as  a 

means  of  knowledge,  —  only  as  a  means  for  the  conimnnicntion  of 

truth. 

The  employment  of  Dialogue  as  such  a  mean,  requires  great  skill 
and  dexterity ;  for  presence  of  mind,  confidence, 
laogue.  ^^^^  ^^j  pliability  are  necessary  for  this,  and 

these  are  only  obtained  by  exercise,  independently  of  natural  talent. 
This  was  the  metliod  which  Socrates  almost  exclusively  employed 
in  the  communication  of  knowledge ;  and  he  called  it  his  art  of 
inteliectiial  midwifery,  because  in  it«  application  truth  is  not  given 
over  by  the  master  to  the  disciple,  but  the  master,  by  skilful  ques- 
tioning; only  helps  the  disciple  to  deliver  himself  of  the  truth  explic- 
itly, whicl)  his  mind  had  before  held  imi)licitly.  This  method  is  not, 
however,  applicable  to  all  kiilds  of  knowledge,  but  only  to  those 
which  the  human  intellect  is  able  to  evolve  out  of  itself,  that  is, 
only  to  the  j.'ognitions  of  Pure  Reason.  Disputation  '\%  of  two  prin- 
cipal kinds^  inasmuch  as  it  is  oral  or  written;  and  in  botli  cases,  the 
controversy  may  be  conducted  either  by  the  rules  of  strict  logical 

J  W'Tke,  Iv  177     Cf.  xvii.  263.    Quoted  by  Scheldler,  Hodegttik. »  66,  p.  204  —  Ed 


Lect.  XXXV.  LOGIC.  493 

disputation,  or  left  to  the  freedom  of  debate.    Without  entering  on 

details,  it  may  be  sufficient  to  state,  in  regard  to 

2.   Disputation,—       Logical   Disputation,  that   it   is   here   essential 

Oral  and  Written.  ^i,    ^    ^u  •    .    •  ^-  ^i         ^    ^ 

Academical  dis  u-  pomt  m  question,  —  the  status  contro- 

tation.  versice,  —  the  thesis,  should,  in  the  first  place,  be 

accurately  determined,  in  order  to  prevent  all 
logomachy,  or  mere  verbal  wrangling.  This  being  done,  that  dis- 
putant who  denies  the  thesis,  and  who  is  called  the  opponent,  may 
either  call  upon  the  disputant  who  affirms  the  thesis,  and  who  is 
called  the  defendant,  to  allege  an  argument  in  its  support,  or  he 
may  at  once  himself  produce  his  countei'-argument.  To  avoid, 
however,  all  misunderstanding,  the  opponent  should  also  advance 
an  antithesis,  that  is,  a  proposition  conflictive  with  the  thesis,  and 
when  this  has  been  denied  by  the  defendant  the  process  of  argu- 
mentation commences.  This  proceeds  in  regular  syllogisms,  and  is 
governed  by  definite  I'ules,  which  are  all  so  calculated  that  the  dis- 
cussion is  not  allowed  to  wander  from  the  point  at  issue,  and  each 
disputant  is  compelled,  in  reference  to  every  syllogism  of  his  adver- 
sary, either  to  admit,  or  to  deny,  or  to  distinguish.'  These  rules 
you  will  find  in  most  of  the  older  systems  of  Logic ;  in  particular 
I  may  refer  you  to  them  as  detailed  in  Heerebord's  Praxis  Logica, 
to  be  found  at  the  end  of  his  edition  of  the  Synopsis  of  Burgersdi- 
cius.  The  practice  of  disputation  was  long  and  justly  regarded  as 
the  most  important  of  academical  exercises ;  though  liable  to  abuse, 
the  good  which  it  certainly  ensures  greatly  surpasses  the  evil  which 
it  may  accidentally  occasion. 

1  Cf.  KruK,  Logik,  §  186.    Amu.  2.    Scbeidler,  Hbdegetik,  {  45,  p.  138.  —  £» 


APPENDIX. 


I. 


THE  CHARACTER  AND  COMPREHENSION  OF  LOGIC— A 
FRAGMENT. 

(See  page  3.) 

In  the  commencement  of  a  course  of  academical  instruction,  there  are 
usually  two  primary  questions  which  obtrude  themselves ;  and  with  the  answer 
to  these  questions  I  propose  to  occupy  the  present  Lecture. 

The  first  of  these  questions  is,  —  What  is  the  character  and  comprehension 
of  the  subject  to  be  taught?  The  second,  —  What  is  the  mode  of  teaching 
it?  In  regard  to  the  former  of  these,  the  question,  —  What  is  to  be  taught, — 
in  the  present  instance  is  assuredly  not  superfluous.  The  subject  of  our  course 
is  indeed  professedly  Logic ;  but  as  under  that  rubric  it  has  been  too  often  the 
practice,  in  our  Scottish  Universities,  to  comprehend  almost  everything  except 
the  science  which  that  name  properly  denotes,  it  is  evident  that  the  mere  inti- 
mation of  a  course  of  Lectures  on  Logic  does  not  of  itself  definitely  mark  out 
what  the  professor  is  to  teach,  and  what  the  student  may  rely  on  learning. 

I  shall,  therefore,  proceed  to  give  you  a  general  notion  of  what  Logic  is,  and 
of  the  relation  in  which  it  stands  to  the  other  sciences ;  for  Logic  —  Logic 
properly  so  called  —  is  the  all-important  science  in  which  it  is  at  once  my  duty 
and  my  desire  fully  and  faithfully  to  instruct  you. 

The  very  general  —  I  may  call  it  the  very  vague  —  conception  which  I  can 
at  present  attempt  to  shadow  out  of  the  scope  and  nature  of  Logic,  is  of  course 
not  intended  to  anticipate  what  is  hereafter  to  be  articulately  stated  in  regard 
to  the  peculiar  character  of  this  science. 

All  science,  all  knowledge,  is  divided  into  two  great  branches ;  for  it  is 
either,  1°,  Conversant  about  Objects  Known,  or,  2°,  Conversant  about  the 
Manner  of  knowing  them,  in  other  words,  about  the  laws  or  conditions  under 
which  such  objects  are  cognizable.  The  former  of  these  is  Direct  Science,  or 
Science  simply;  the  latter.  Reflex  Science,  —  the  Science  of  Science,  or  the 
IVIethod  of  Science. 

Now  of  these  categories  or  great  branches  of  knowledge,  Simple  Science,  or 
Science  directly  conversant  about  Objects,  is  again  divided  into  two  branches  j 


496.  APPENDIX. 

for  it  is  either  conversant  about  the  phaenomcria  of  the  internal  world,  as  re- 
vealed to  us  in  consciousness,  or  about  the  phasnomena  of  the  external  world, 
as  made  known  to  us  by  sense.  The  former  of  these  constitutes  the  Science 
of  Mind,  the  latter  the  Science  of  Matter;  and  each  is  again  divided  and  sub- 
divided into  those  numerous  branches,  which  together  make  up  nearly  the 
whole  cycle  of  human  knowledge. 

The  other  category  —  the  Sciene*  of  Science^  or  the  Methodology  of  Sci- 
ence—  falls  likewise  into  two  branches,  according  as  tlie  conditions  which  it 
considers  are  the  laws  which  determine  the  possibility  of  the  mind,  or  subject 
of  science,  knowing,  or  the  laws  which  determine  the  possibility  of  the  exist- 
ence, or  object  of  science,  being  known ;  Science,  I  repeat,  considered  as 
reflected  upon  its  own  conditions,  is  twofold,  for  it  either  considers  the  laws 
under  which  the  human  mind  can  knpw,  or  the  laws  under  which  what  is  pro- 
T)osed  by  the  human  mind  to  know,  can  be  known.  Of  these  two  sciences  of 
scipnce,  tjie  former  —  that  which  treats  of  those  conditiofls  of  k.upwledge  which 
lie  in  the  nature  of  thought  itself — is  Logic,  properly  so  called;  the  latter, — 
that  which  treats  of  those  conditions  of  knowledge  which  lie  in  the  nature,  not 
of  thought  itself,  but  of  that  which  we  thinlc  about,  —  this  has  as  yet  obtained 
no  recognized  appellation,  no  name  by  which  it  is  universally  and  familiarly 
known.  Various  deqomiijations  have  indeed  been  given  to  it  in  its  several 
parts,  or  in  its  special  relations ;  thus  it  has  been  called  Heuretic,  in  so  fai-  as  it 
expoimds  the  rules  of  Invention  or  Discovery,  Architectonic,  in  so  far  as  it  treats 
of  the  method  o.f  building  up  our  observations  into  system;  but  hitherto  it  has 
obtained,  as  a  whole,  no  adequate  and  distiuctive  title.  The  consequence,  or 
perhaps  the  cause,  of  this  wapt  of  a  peculiar  name  to  mark  out  the  second 
science  of  science,  as  distinguished  from  the  first,  is  that  the  two  have  fre- 
quently been  mixed  up  together,  and  that  the  naiue  o( Logic  has  been  stretched 
so  as  to  comprehend  the  confused  assemblage  of  their  doctrines.  Of  these  two 
sciences  of  the  conditions  of  knowledge,  the  one  owes  its  systematic  develop- 
ment principally  to  Aristotle,  the  other  to  Bacon  ;  though  neither  of  these 
philosophers  has  precisely  marked  or  rigidly  observed  the  limits  which  separati» 
them  from  each  other ;  and  from  the  circumstance,  that  th<^  latter  gave  to  his 
great  Treatise  the  name  of  Organum,  —  the  name  which  has  in  later  times 
been  applied  to  designate  the  complement  of  the  Logical  Treatises  of  the  for- 
mer, —  from  this  circumstance,  I  say,  it  has  often  been  supposed  that  the  aim 
of  JJacon  was  to  build  up  a  Logic  of  his  own  upon  the  ruins  of  the  Aristotelic. 
Nothing,  however,  can  be  more  erroneous,  either  as  to  Bacon's  views,  or  as  to 
the  relation  in  which  the  two  sciences  nmtually  stand.  These  are  not  only  not 
inconsistent,  they  are  in  fact,  as  correlative,  each  necessary  to»  each  dependent 
on,  the  other ;  and  although  they  constitute  two  several  doctrines,  which  must 
be  treated  in  the  first  instance  each  by  and  for  itself,  they  are,  however,  in  the 
last  resort  oiily  two  phases,  —  two  members,  of  one  great  doctrine  of  method, 
which  considers,  in  the  counter  relations  of  thought  to  the  object,  and  of  the 
object  to  thought,  the  universal  conditions  by  which  the  possibility  of  bum^n 
knowledge  is  regulated  and  defined. 

But  allowing  th^P  term  Logic  to  be  extended  so  as  to  denote  the  genus  of 
which  these  opposite  doctrines  of  Method  »re  the  species,  it  will,  however,  be 
necessary  to  add  a  difference  by  which  these  special  Logics  may  be  distin- 


APPENDIX.  497 

guished  from  each  other,  and  from  the  generic  science  of  ■which  they  are  the 
constituents.  The  doctrine,  therefore,  which  expounds  the  laws  by  which  our 
scientific  procedure  should  be  governed,  in  so  far  as  these  lie  in  the  forms  of 
thought,  or  in  the  conditions  of  the  mind  itself,  which  is  the  subject  in  which 
knowledge  inheres,  —  this  science  may  be  called  Formal,  or  Subjective,  or  Ab- 
stract, or  Pure  Logic.  The  science,  again,  which  expounds  the  laws  by  which 
our  scientific  procedure  should  be  governed,  in  so  far  as  these  lie  in  the 
contents,  materials,  or  objects,  about  which  knowledge  is  conversant,  —  this 
science  may  be  called  Material,  or  Objective,  or  Concrete,  or  Applied  Logic. 

Now  it  is  Logic,  taken  in  its  most  unexclusive  acceptation,  which  will  con- 
stitute the  object  of  our  consideration  in  the  following  course.  Of  the  two 
branches  into  which  it  falls.  Formal  Logic,  or  Logic  Proper,  demands  the 
principal  share  of  our  attention,  and  this  for  various  reasons.  In  the  first 
place,  considered  in  reference  to  the  quantity  of  their  contents.  Formal  Logic 
is  a  far  more  comprehensive  and  complex  science  than  Material.  For,  to  speak 
first  of  the  latter :  —  if  we  abstract  from  the  specialities  of  particular  objects 
and  sciences,  and  consider  only  the  rules  which  ought  to  govern  our  procedure 
in  reference  to  the  object-matter  of  the  sciences  in  general,  —  and  this  is  all 
that  a  universal  logic  can  propose,  —  these  rules  are  few  in  number,  and  their 
applications  simple  and  evident  A  Material  or  Objective  Logic,  except  in 
special  subordination  to  tlie  circumstances  of  particular  sciences,  is,  therefore, 
of  very  narrow  limits,  and  all  that  it  can  tell  us  is  soon  told.  Of  the  former, 
on  the  other  hand,  the  reverse  is  true.  For  though  the  highest  laws  of  thought 
be  few  in  number,  and  though  Logic  proper  be  only  an  articulate  exposition  of 
the  universal  necessity  of  these,  still  the  steps  through  which  this  exposition 
must  be  accomplished  are  both  many  and  multiform. 

In  the  second  place,  the  doctrines  of  Material  Logic  are  not  only  far  fewer 
and  simpler  than  those  of  Formal  Logic,  they  are  also  less  independent ;  for 
the  principles  of  the  latter  once  established,  those  of  the  other  are  either  im- 
plicitly confirmed,  or  the  foundation  laid  on  which  they  can  be  easily  rested. 

In  the  third  place,  the  study  of  Formal  Logic  is  a  more  improving  exercise ; 
for,  as  exclusively  conversant  with  the  laws  of  thought,  it  necessitates  a  turn- 
ing back  of  the  intellect  upon  itself,  which  is  a  less  easy,  and,  therefore,  a  more 
invigoi-ating,  energy,  than  the  mere  contemplation  of  the  objects  directly  pre- 
sented to  our  observation. 

In  the  fourth  place,  the  doctrines  of  Formal  Ix)glc  are  possessetl  of  an  in- 
trinsic and  necessary  evidence  ;  they  shine  out  by  their  native  light,  and  do  not 
require  any  proof  or  corroboration  beyond  that  which  consciousness  itself  sup- 
plies. They  do  not,  therefore,  require,  as  a  preliminary  condition,  any  ap- 
paratus oi  acquired  knowledge.  Formal  Logic  is,  therefore,  better  fitted  than 
Material  for  the  purposes  of  academical  instruction;  for  the  latter,  primarily 
ctmversant  with  the  conditions  of  the  external  world,  is  in  itself  a  less  invig- 
orating exercise,  as  determining  the  mind  to  a  feebler  and  more  ordinary 
exertion,  and,  at  the  same  time,  cannot  adequately  be  understood  without  the 
previous  possession  of  such  a  ctMnplement  of  information  as  it  would  be  unrea- 
sonable to  count  upon  in  the  case  of  those  who  are  only  commencing  their 
philosophical  studies. ' 

68 


498  APPENDIX. 

II. 

GENUS   OF  LOGIC. 

(Seepage?.) 
I.  —  Science. 

A.  Affirmative.  —  Stoici  (v.  Alexander  Aphrod.  In  Topica,  Prooem. ;  Diog- 
enes Laertius,  Vita  Zenonis,  L.  vii.,  §  42).  "  Plato  et  Platonici  et  Academici 
omues"  (v.Camerarius,  Selectee  Disput.  Philos.     Pars,  i.,  qu.  3,  p.  30). 

(a)    SPECULATIVE  SCIENCE. 

Toletus,  In  Un.  Arist.  Log.,  De  Dial,  in  Comniuni,  Qu.  ii.,  iv.  Suarez,  Disp. 
Metaph.,  Disp.  i.  §  iv.  26  ;  Disp.  xliv.  §  xiii.  64.  "  Comniuniter  Thomistse,  ut 
Capreolus,  Sotus,  Masius,  Flandra,  Soncinas,  Javellus :  Omnes  fere  Scotist89 
cum  Scoto,  ut  Valera,  Antonius  Andreas,  etc."  (v.  Udephonsus  de  Penafiel, 
LogiccB  Disputationes,  Disp.  i.  qu.  4.  Cursus,  p.  79.)  For  Aquinas,  Durandus, 
Niphus,  Canariensis,  see  Antonius  Ruvio,  Com.  in  Arist.  Dialect.,  Prooem.  qu. 
5.  For  Bacchonus,  Javellus,  Averroes,  see  Conimbricenses,  In  ArisL  Dial. 
Prooem.  Q.  iv.  art.  5.  Lalemandet,  Cursus  Phil.,  Logica,  Disp.  iii.  part  iii. 
Derodon,  Logica  Restit.,  De  Genere,  p.  45.  Camerarius,  Disp.  Phil.,  Pars  i., 
qu.  3,  4.  (That  Logica  docens  a  true  science.)  For  Pseudo-Augustinus,  Av- 
icenna,  Alpharabius,  see  Conimbricenses,  Com.  in  Arist.  Dial.  Prooem.  Qu.  iv. 
art.  3.  For  Boethius,  Mercado,  Vera  Cruce,  Montanesius,  see  Masius,  Com.  in 
Porph.  et  in  Universam  Aristotelis  Logicam,  Sect,  i.,  Prooem.  qu.  v.  et  seq. 
Poncius,  De  Nat.  Log.,  Disp.  ii.,  concl.  2.  For  Rapineus,  Petronius,  Faber, 
see  Camerarius,  Sel.  Disp.  Phil.,  Pars  i.,  qu.  4,  p.  44. 

(b)    rSACTICAL  SCIENCE. 

Conimbricenses,  In  Universam  Aristotelis  Dialecticam.  Prooem.  Qu.  iv.,  art. 
5.  Fonseca,  In  Metaph.  L.  ii.  c.  3,  qu.  1,  §  7.  For  Vcnetus,  Albertus  Magnus, 
Jandunus,  see  Ruvio,  I.  c.  Schuler,  Philosophia  nova  Methodo  Explicata,  Pars 
Prior,  L.  v.  ex.  i.,  p.  306.  (1603).  D'Abra  de  Raconis,  Summa  Totius  Philoso- 
phice.  Log.  Prcel.,  c.  i.  Isendoorn,  Cursus  Logicus,  L.  i.,  c.  2,  qu.  7.  Biel,  In 
Sentent.,  L.  ii.  Prol.  Occam,  Sumina  Totius  Logicce,  D.  xxxix.  qu.  6.  For 
Aureolus,  Bern.  Mirandulanus,  see  Conimbricenses,  I.  c.  For  Mathisius,  Murcia, 
Vasquez,  Eckius,  see  Camerarius,  Sel.  Disp.  Phil.  Pars  i.,  qu.  4,  p.  44.  Ude- 
phonsus de  Penafiel,  Log.  Disp.  D.  i.  qu.  4,  sect.  2.  Oviedo,  Cursus  Philo- 
sophicus,  Log.,  Contr.  Prooem.  ii.  5.    Arriaga,  Cursus  Philosophicus,  Disp.  iii.  §  4. 

(c)    SPECULATIVE  AND  PRACTICAL. 

Hurtado  de  Mendoza,  Log.  Disp.  D.  ii.  §  2. 

B.  Negative.  —  For  almost  all  the  Greek  commentators,  see  Zabarella,  Opera 


APPENDIX.  499 

Logica,  De  Nat.  Log.,  L.  i,  c.  5,  and  Smiglecius,  Logica,  D.  ii.  qu.  5.     See  also 
Ildephonsus  de  Penafiel,  Disp.  Log.  D.  i.  qu.  1,  §  1,  p.  67. 

II.  —  Art. 

Scheiblcr,  Opera  Logica,  Pars.  i.  c.  1,  p.  49.  J.  C.  Scaliger,  Exercitationes, 
Exerc.  i.  3.  G.  J.  Vossius,  De  Natura  Arfium,  L.  iv.,  c.  2,  §  4.  Balforeus,  In 
Org.  Q.  V.  §  G,  Prooem.,  p.  31.  Burgersdicius,  Instilutiones  LogiccE.  Lib.  i.  c. 
1.  Paoius,  Comm.  in  Org.  p.  1.  Sanderson,  Log.  Artis  Compendium,  L.  i.  c.  1, 
p.  1,  Cf.  p.  1!)2.  Aldrich,  Artis  Log.  Compendium.  L.  i.  c.  1,  p.  1.  Hildenius, 
Qucestiones  et  Commentaria  in  Orgunon,  p.  579  (1.585).  Goclenius,  Problemata 
Logica  et  Philosopfiica.  Pars.  i.  qu.  3.  Bamus,  Dialectica.  L.  i.  c.  1.  Augus- 
tinus,  De  Ordine,  ii.  c.  15.  Cicero,  De  Claris  Oralorihus,  c.  41.  De  Oratore,  L. 
ii.,  c.  38.  Lovanienses,  Com.  in  Arist.  Dial.  Praef.  p.  3.  Rodolphus  Agricola,  De 
Dialecticce  Invenlione,  L.  ii.  p.  255.  Monlorius  (Bapt.),  Comm.  in  Anal.  Pr. 
Prajf.  Nunnesius,  De  Constitut.  Dial.,  p.  43.  Downam  (Ramist),  Comm.  in  Ram. 
Dial.,  L.  i.  c.  1.  p.  3.  Paraeus,  Ars  Logica,  p.  1,  1670.  For  Horatius  Corna- 
chinus.  Ant.  Bernardus  Mirandulanus,  Flammiaius  Nobilius,  see  Camerarius, 
-Se/.  Disp.  Phil.     Pars.  i.  q.  3,  p.  30. 

III.  —  SciExcK  AND  Art. 

Lalemandet,  L/)g.,  Disp.  iii.  Part  iii.  el.  4.  (Logica  tUens,  an  art ;  Logica  do- 
cens,  a  speculative  science.)  Tartaretus,  In  P.  Hispannm,  f.  2  (Practical  Sci- 
ence and  Art.)  P.  Hispanus,  Copulata  Omn.  Tractat.  Pet.  Hisp.  Parv.  Logical, 
T.  i.  f.  10,  1490.  Philosopkia  Vetus  et  Nova  in  Regia  Burgundia  olim  Pertrac- 
taia,  Logica,  T.  I.,  pp.  58.  59.  4th  ed.  London,  1685.  Tosca,  Comp.  Phil. 
Log.,  Tr.  i.  1.  iv.  c.  4,  p.  208  (Practical  Science  and  Art).  Purchot,  Instit. 
Phil.,  T.  L  Prooem.  p.  36.  Eugenius,  Aojikt},  pp.  140,  141.  Dupleix,  Logique, 
p.  37.  Facciolati,  Rudimenta  Logical,  p.  5.  Schmier,  Philosophia  Quadripartita 
(v.  Henmannus,  Acta  Philosoph.  iii.  p.  67).  Aquinas  (in  Caramuel,  Phil.  Realis 
el  Rationalis,  Disp.  ii.  p.  3). 

IV.  —  Neither   Science  nor   Art,  but  Instrument,  Organ,  or  Habit,  or 
Instrumental  Discipline. 

Philoponus,  In  An.  Prior.,  initio.  For  Ammonius  (Prcef.  in  Prced.'),  Alex- 
ander (In  Topica,  i.  c.  4  ;  Metaph.  ii.  t.  15).  Simplicius,  (Prcef.  in  Prced.}, 
Zabarella  (De  Natura  Logicce,  L.  i.  c.  10.),  Zimara  (In  Tabula  v.  Absurdum), 
Averroes,  see  Smiglecius,  Logica,  Disp.  ii.  qu.  6,  p.  89.  Aegidius,  In  An.  Post. 
L.  i.  qu.  1.  For  Magnesius,  Niger  (Petrus),  Villalpandeus,  see  Ruvio,  In  Aritt. 
Dial.,  prooem.  qu.  2.  F.  Crellius,  Isagoge  Logica,  L.  i.  c.  1,  p.  5.  P.  Vallius, 
Logica,  T.  I.  prooem.  c.  i.  et  alibi.  Bartholinus,  Janitores  Logici,  II.  pp.  25  and 
76.  Bertius,  Logica  Peripatetica,  pp.  6,  10.  Themistius,  An.  Post.  i.  c.  24. 
Aquinas,  Opuscula,  70,  qu.  De  Divisione  Sciential  Specidativce,  —  sed  alibi  sci- 
entiam  vocat.  (See  Conimbricenses,  In  Arist.  Dial.,  T.  I.  qu.  iv.  art.  5,  p.  42.) 
Balduinus,  In  Qucesito  an  Logica  sit  Scientia.  Scaynus,  Paraphrasis  in  Organo'' 
Prief.  p.  9. 


500 


APPENDIX. 


"V.  —  That,  looselt  takiwo  the  terms,  Logic  is  either  Art  or  Sctbscs, 

OR  both. 

Zabarella,  Opera  Logica,  De  Nat,  Log.,  L.  i.  c.  viii.  D'Abra  de  Raconis, 
Summa  Tot.  Phil.  Prcel.  Log.,  L.  iii.,  c.  1,  p.  8,  ed.  Colon.  (Practical  Science). 
Balforeus,  In  Organon,  Q.  v.  §§  1,  6,  pp.  20,  32.  (Art).  Dero<lon,  Logica  RestiL 
De  Procem.  Log.,  p.  49,  (Speculative  Science).  Crellius,  Isogoge,  pp.  1,  4. 
Bertius,  Logica  Peripatetica,  pp.  11,  13.  Aldrich,  Art.  Log.  Comp.,  L.  ii.  c.  8, 
T.  i.  (Art).  Sanderson,  Log.  Art.  Comp.  Append.  Pr.,  c.  2,  page  192.  (Art). 
Conimbricenses,  In  Arift.  Dial.,  T.  I.,  p.  33  (Practical  Science).  Philosophia 
Burgundia,  T.  I.  pp.  56,  59.  Eustachius,  Summa  Philosophice,  Dialectica  Quosit. 
Prooem.,  i.  p.  4.  Nunnesius,  De  Constit.  Dial.,ff,  43,68.  Scheibler,  Opera  Log- 
ica, pp.  48,  49.  Scaynus,'  Par.  in  Org.,  pp.  11,  12.  Camerarius,  Sel.  Disp.  PhU^ 
Pars.  i.  qu.  3,  pp.  31,  38  (Speculative  Science).  B.  Pereira,  De  Commun.  Prut- 
dp.  Omn.  Rer.  Natural,  h.  l  De  Phil.  c.  18,  p.  60,  1618. 

VI.  —  That  at  once  Scibkcs  (fast  of  Philosophy)  and  Iksthcment  or 

PhIIXJSOI'HY. 

Boethius,  Prtef.  in  Porphyr.  (a  Victorino  Transl.)  Opera,  p.  48.  Eustachius, 
Summa  Philosophice,  p.  8  (Scientia  organica  et  practica).  For  Simplicius,  Al- 
exander, Philoponus,  etc.,  see  Camerarius,  Sel.  Disp.  PhiL,  p.  SO.  Pacius,  Com.  in 
Arist.  Org.,  p.  4, 

Vn.  —  That  Qcestion,  whether  Logic   part  of  Philosophy  or  not,  aw 

Idle  Question. 

Pacius,  Com.  in  Arist.  Org.,  p.  4.  Avicenna  (in  Conimbricenses,  In  ArisL 
Dial.,  Qu.  iv.  art.  4,  T.  I.  p.  38). 


Vni.  —  That   Question    of   whether  Art,  Sciekce,  etc..  Idle  —  only 

Verbal. 

Buffier,  Cours  des  Sciences,  Seconde  Logique,  §  421,  p.  887. 

Eugenius,  'H  AcryiKi],  p.  140,  has  the  following: 

'*  From  what  has  been  said,  therefore,  it  clearly  appears  of  what  character 
are  the  diversities  of  Logic,  and  what  its  nature.  For  one  logic  is  Natural, 
another  Acquired.  And  of  the  Natural,  there  is  one  sort  according  to  Faculty, 
another  according  to  Dispa4tion.  And  of  the  Acquired,  there  is  again  a 
kind  according  to  Art,  and  a  kind  according  to  Science.  And  the  Native 
Logic,  according  to  Faculty,  is  the  rational  faculty  itself  with  which  every  hu- 
man individual  is  endowed,  through  which  all  are  qualified  for  the  knowledgt-. 
and  discrimination  of  truth,  and  which,  in  proportion  as  a  man  employs  tbt*. 
le~ss,  the  less  is  he  removed  from  irrationality.  But  the  Native  Logic,  according 
to  Disposition,  is  the  same  faculty  by  which  some,  when  they  rt-ason,  are  wont 
to  exert  their  cogitations  with  care  and  attention,  confusedly,  indeed,  and  un- 
critically, still,  however,  in  pursuit  of  the  truth.  The  Acquired,  according  to 
Art,  is  the  correct  and  corrected  knowledge  of  the  Rules,  through  which  the 
intellectual  energies  are,  without  fault  or  failure,  accomplished.     But  the  Ae- 


APPENDIX. 


601 


qaired,  according  to  Science,  is  the  exact  and  perfect  knowledge  both  of  the 
enei^es  themselves,  and  also  of  the  causeij  through  which,  and  through  which 
exclusively,  they  are  capable  of  being  directed  towards  the  truth." 


Logic. 


(  N**'^^'  according  to      j  ^tspo^ion. 


(.  Acquired,  according  to  ]  o  ! 


Art. 
Science. 


"  And  thus  Disposition  adds  to  Faculty  consuetude  and  a  promptness  to  en- 
eigize.  Art,  again,  adds  to  Disposition  a  refinement  and  accuracy  of  Energy 
Finally,  Science  adds  to  Art  the  consciousness  of  cause,  and  the  power  of  ren- 
dering a  reason  in  the  case  of  all  the  Rules.  And  the  natural  logician  may  be 
able,  in  lils  random  reason,  to  apprehend  that,  so  to  speak,  one  thing  has  deter- 
mined another,  although  the  nature  of  this  determinatiou  may  be  beyond  his 
ken.  But  he  whose  disposition  is  exercised  by  reflection  and  imitation,  being 
able  easily  to  connect  thought  with  thought,  is  cognizant  of  the  several  steps  of 
the  reasoning  process,  howbeit  this  otherwise  may  be  confused  and  disjointed. 
But  he  who  is  disciplined  in  the  art,  knows  exactly  that,  in  an  act  of  inference, 
there  are  required  three  terms,  and  that  these  also  should  be  thus  or  thus  con- 
nected. Finally,  the  scientific  logician  understands  the  reason,  —  why  three 
terms  enter  into  every  syllogism,  —  why  there  are  neither  more  nor  fewer, — 
and  why  they  behoove  to  be  combined  in  this,  and  in  no  other  fashion. 

'*  Wherefore  to  us  the  inquiry  appears  ridiculous,  which  is  frequently,  even 
to  nausea,  clamorously  agitated  concerning  Logic  —  Whether  it  should  be  re- 
garded as  an  Art  or  as  a  Science." 


III. 


DIVISIONS,  VARIETIES,  AND   CONTENTS  OF  LOGIC.     . 

(See  p.  49.) 

/v.  Timpler,  Logicce  Systema,  L.  i.   c.  i. 

Docens  I  quaest.  2,  3.     Isendoom,  Effaia,  Cen- 

,X»f>ls»pa7jiM{Tft)i'.  )  turia,   i.   EfF.  55.      Crellius,   Isagoge, 

J  J  Pars  Prior,  L.  i.  c.  i.  p.  12.     Noldius, 

L  LooiCA.N  Utens,  \  Z^ica  TJeco^nifa,  Procem.  p.  13. 

4v    XP^vu    icol    yvtwcuTiefJ  philoponus,  In.  An.  Pr.,  f.  4.     Alstedius, 

wpayndrwv.  i  Encydopcedia,   pp.  29   and   406.      v. 

\  Aristotle,  Metaph.,  Li  vii.  text,  23. 


IL   LOGICA, 


Doctrinalis    i         [Objec- 
Systematica  )  tiva] . 

Habitualis    [Subjectiva]. 


I V.  Timpler,  Sgst.  Log.,  Appendix,  p. 
877.  Noldius,  Ijog.  Becog.,  Prooem., 
p.  13. 


502 


APPENDIX. 


5  Pare    Communis,    Gene- 
ralis. 
Pare  Propria,  Specialis. 


''Adopted  in  different  significations  by 
Timpler,  Si/st.  Loi.,  q.  19,  p.  55. 
Theoph.  Gale,  Lacficxi,  pp.  6,  246, 
et  seq.  (1681).  Crellius,  Isagoge,  P.  i. 
L.  i.  c.  1,  p.  3.  Alstedius,  Encyclop., 
pp.  29  and  406. 


(Para. 
IV.  LooicA,  W  ppiicata. 


N.  B.  —  Averroes  (Pacins,  Com.  p.  2) 
has  Logica  appropriata  sen  particalaris, 
and  Logica  communis  =  Unirereal,  Ab- 
stract Logic. 


V.  Logica, 


Abstracta. 
Concreta. 


Pare  Communis. 

VI.  Logica,  <(  -p&n  Pro-  ( ■A^P<xi>ctica. 

}  Dialectica. 
pna,     i 

(  Sophistica. 


^  T.  Timpler,  Sifst.  Log  ,  p.  42.    Isendoom. 
Efata,  Cent.  i.    ES.  56. 


Vn.  Logica," 


^EvpfTtic^  TCl  Tonrucif. 
,  Inventio. 

I  KpiTllcfl. 

Judicium. 
^Dispositio. 


V.  Timpler,  Si/s.  Log.,  p.  44.  Crellius, 
Isagoge,  pp.  10,  11,  and  Isendoom, 
Effata,  Cent.  i.  Eff".  51.  Adopted 
by  Agricola,  Lk  Inv.  Died.,  L.  i. 
p.  35.  Melanchthon,  Erot.  Dial.,  p. 
10.  Ramus,  Schol.  Dialect.  L.  i.  t. 
i.,  and  L.  ii.  c.  i.  p.  351  et  seq. 
Spencer,  Log.,  p.  1 1 .  Downam,  In 
Rami  Dial.,  L.  i.  c.  2,  p.  14.  Peri- 
onius,  De  Dialectica,  L.  i.  p  6 
(1544).  Vossius,  De  Nat.  Artium 
sive  Logica,  L.  ir.  c.  ix.  p.  217. 


VIIL  Logica, 


Pars  de  Propositio. 
Pare  de  Judicio. 


V.  Timpler,  Si/st.  Log.,  p.  49. 


IX.  Logica, 


Doctrina  Dividendi. 
'  Doctrina  Definiendi. 
Doctrina  Argumeiitandi. 


v.  Timpler,  Syst.  Log.,  p.  51.  Isen- 
doom, Effata,  Cent.  i.  Eff".  57. 
Boethius,  (Augustin,  Fonseca,  etc) 


APPENDIX. 


503 


X.  LOOICA, 


Simplicis    Apprehensi- 

onis. 
Judicii. 
Batiocinatioois . 

NoStica  {melius  Noema-| 
Synthetica.  tica). 

Dianoetica. 


fv.  Timpler,  S^/st.  Log.,  52.     Isendoorn, 

Effata,  Cent.  i.  Eff.  .58. 
> Isendoorn,  Cursus  Logicus,  p.  31,  and 

Effata,  Cent.  i.  §  59.    Noldius,  Log. 

Bee.,  p.  9.    Aquinas. 


XL   LOGICA, 


1.  Ideas  (notions).  ^  L'  Ai-t  de  Penser,   Part  i.      Clericus, 

2.  Judgment.  /  Logica,    adopts    this    division,   but 

3.  Reasoning.  (  makes    Method    third,    Reasoning 

4.  Method.  j  fourth. 


XII.  Logica, 


■i: 


Doctrine  of  Elements. 
Doctrine  of  Method. 


Kant,  Logik ;  Krug,  Logik. 


1st.  Called  Analytic  by  Metz,  Instit.  Log,  Twesten,  Die  Logik, 
inshesondere  die  Analytik,  p.  lii.     Esser,  Logik     Part  i. 

2d.  Called  Systematic  or  Architectonic  by  Bachmann,  Logik, 
Part  ii. 

Called  Synthetic  by  Esser  (who  includes  under  it  also  Applied 
Logic),  ZyO^i'A;,  Part  ii. 

/Thematica  —  de   materia\ 
Xm   Logics  )  operationi    Logicae  /Mark    Duncan,    Institutiones    Logicce, 

'  partes       )  subjecta.  \      Proleg.  c.  iii.  §  2,  p.  22.    Burgersdi- 

/  Organica  —  de       instm-  \       cius,  Instit.  Log.,  L.  i.  c.  i.  p.  5. 
\  mentis  sciendi.         J 


Communis, 
Generalis. 


XIV.  LogicaX    Specialis. 


Genetiea. 


1.  De  ordinibus  rerum  generalibus" 
et  attributis  communissimis. 

2.  De  Vocibus  et  Oratione. 

3.  De  Ideis  siniplicibus  et  appre- 
hensione  simplici 'dirigenda. 

4.  De  Judicio  et  Propositione. 

5.  De  Discursu. 

6.  De  Dispositioue  seu  Methodo. 


Genesis 

sen 
Inventio. 

Analysis. 


f  Genesis  stricta. 
(  Genesis  didactica. 

<■  Hermeneutica. 

(  Analy  tica  and  Critica. 


Analytica. 


In    ordine    ad    mentem  —  Logica 

stricte  dicta. 
In  ordine  ad  alios — Interpretativa 

vel  Hermeneutica  genetiea. 
Hermeneutica  analytica. 
Analytica  stricta  vel  in  specie. 


Theophilus 
Gale  {Logica, 
1681)  follows 
(besides  Kec- 
kermann  and 
Burgersdyk) 
principally 
Clauberg  and 
L'Art  de  Pen- 
of  Port 
Royal. 


504 


APPENDIX- 


Theoretica  pars. 

,,,   ^  J  Practica  pare  —  (this  in-,     ^rr  ,i.  t,.  ..      -r,    ■      ,■    -^ 

XV.  LogicaX  ,  j.       r,     Iff  »i.  J  >  Wolf,  PAitos. /cafebnofjs.  Pare  1.  and  11. 

'  ^        eluding  the  Method- A  ' 

ology    and    Applied ' 

Logic  of  S^ant., 


XVI. 


On  Adrastean  order,  etc.  of  the  books  of  the  Organon,  rtrfc 
Ramus,  Sdidte  Dial.,  L.  ii.,  c.  8.,  p.  354.  Piccartus,  In 
Organum,  Prolegomena,  p.  1  et  seq. 


1.  Xlfpl  tfjs  wpiirTis  iyvoias,  or^ 


irfio\ii\f/fais. 

partes.      )  ^-  ^'P]  "P^"'"'' 

4.  Tlepi  Suwotas. 

5.  Tlepl  fi(d6iov. 


Eugenius  Diacooos,  Aajutitf  f, 
144. 


■SGenoTCsi.    A  division  different  in  some 

1 .  Emendatrice.  I  respects  is  given  in  his  Latin  Logic, 

2.  Inventrice.                   f  Proleg.   §  51,  j).  22.     The  fourth 
XVU.  LoGiCA,'<(  3.  Giudicatrice.                V  part  of  the  division  in  the  Latin 

4.  Rogionatrice.  y  Logic  is  omitted  in  the  Italian,  or 

5.  Ordinatrice.                   1  rather  reduced  to  the  second;  and 
/  the  fifth  divided  into  two. 


XVm.  LooiOA,^ 


SPorphyrii  Isag.  •  •  •  ) 

Praed. \  Isendoom,   Effata,    Cent   1. 

Interpret )  Eff.  52. 

(  ^""(W  ^ y  Reason  of  terms,  Pacius,  Com 

NoTa.      )  ^"^y^-  P'^ (        numt  in  Org.,  In  Porph.  Isag 

/  ^<^ \        p.  3. 


MX.  LooiCA,<  rApodictica. 

/  ^vSXoyunucfi.  <  Topica. 
\  ( Sopfaifitica. 


Isendoom,  Effata,  Cent,  i 
Eff.  56.  ( From  John  Ho» 
pinian,  De  Ckmtrovenrh 
Dialecticis.) 


•  'SroixtioXoyiK^i. 

^ 

. 

(  Prior.          j 

Yoesius,    De  Natura 

XX.  LooiCA,  ^ 

\                         {   Analytica. 

\  Posterior,    v 

,         Artium  sive  tie  Lo- 

/ 

1  XvWayttrrur^.  J 

J  Dialectica. 

(  Topica.        I 

gica,  L.  iv.  c.  ix. 

^                          ^ 

(  Sophistic*.  ] 

p.  220. 

(  Analytica. 


XXL  LoGicA/ 


\ 


APPENDIX.  505 

C  prodromus    de  Interpretatione.     \ 
}  universe        de  Syllogismo.  \ 

(^  speciatem      de  Demonstratione.   f  Vossius,  De  Na- 

z'    tura  Artium,  p. 
(  prodromus  de  Categoriis.  (      220. 


-r»-  1  __•       -\  de  Syll.  Terisimili. 
Dialectica.   ^  ■' 


(^  de  Syll.  sophistico  sive  pirastico. 


\   Dialectica. 
XXIL  LOGICA,  -j   Analytica. 


)  Aristotle,  in  Laertius  v.  Vossius, 
r  De  Nat.  Art.  sive  De  Logica,  L. 
)        iv.  c.  ix.  §  11,  p.  219. 


__-.,^   ^               r -,  ,                 .     ...              I  Stoicorum,  see   \ossius,  De  Nat. 

XXIII.  Logica   S  Rebus  quae  signincantur.  f  .        .      ,^    ^     •      t    • 

.•<„.,                   ...            >-  Art.  sive  De  Loqica,  L.  IV.  c.  IX. 

de   i  Vocibus  quae  significant.  ^ 


Loquendo. 
XXIV.  LooiCJB    }  Eloquendo. 
partes  de    )  Proloquendo. 


Proloquiorom  summa. 


Varro,  vide  Vossius,  De  Nat.  Art., 
L.  iv.  c.  ix.  §  8,  p.  219. 


(  nphs  tSpeffiy. 

XXV.  Logica,  <  upbs  Kplaw. 


Logicse 
partes. 


)  Aristotle  (?)  in  Laertius,  L.  v.  §  28, 
>•  p.  284.  Alexander  Aphrod.  in 
y       nota  Aldobrandini. 


i'NoTiTucfi,  Apprehensiva.    \ 
Kpiaifios  vel  Kpirufff,         t  Caramuel  Lobkowitz,   Batioualii  et 
Judicativa.  /        Realis    Phihsophia,    Logica    seu 

AioXfKTucfi,   Argumenta-  V        PAH.  Bat.  Disp.  ii.  p.  3. 


\      tiva. 

.  r  Divisio. 

^"^        ^  Definitio. 
partes,  ) 

(_  Argnmentatio. 


r  Apodictica. 
J  Dialectica. 


•  V.  Crellius,  Isagoge,  Pars,  prior,  c.  i.  p.  10. 


T.  Crellius,  Isagoge,  Pars,  prior,  c.  i.  p.  10. 
Isendoom,  Effata,  Cent.  i.  Eflf.  54. 


(  Sophistica. 

<  ^     .  r  Crellius,  Isanoge,  Pars,  prior,  c.  i.  p.  10 

partes,  |  Topica.  i  ^'^  '  f      >         r 


Stoicheiology  (pure)  should  contain  the  doctrine  of  Syllogism,  without  dis- 
tinction of  Deduction  or  Induction.    Deduction,  Induction,  Definition,  Division, 

64 


506  APPENDIX. 

from  the  laws  of  thought,  should  come  under  pure  Methodology.  All  are  pro- 
cesses (v.  Caesalpinus,  Qucest.  Perip.  sub  init.) 

Perhaps,  1°,  Formal  Logic  (from  the  laws  of  thought  proper)  should  be 
dlstin»uished  from,  2°,  Abstract  Logic  (material,  but  of  abstract  general  mat- 
ter) ;  and  then,  3°,  A  Psychological  Logic  might  be  added  as  a  third  part, 
considering  how  Reasoning,  etc.,  is  affected  by  the  constitution  of  our  minds. 
Applied  Logic  is  properly  the  several  sciences. 

Or  may  not  Induction  and  Deduction  come  under  abstract  Material  Logic  ? 


LAWS    OF    THOUGHT. 

(Seep.  60.) 


C  is  either  r  or  uon  r. 

The  laws  of  Identity  and  Contradiction,  each  infers  the  other,  but  only 
through  the  principle  of  Excluded  Middle;  and  the  principle  of  Excluded 
Middle  only  exists  through  the  supposition  of  the  two  others.  Thus,  the  prin- 
ciples of  Identity  and  Contradiction  cannot  move,  —  cannot  be  applied,  except 
through  supposing  the  principle  of  Excluded  Middle ;  and  this  last  cannot  be 
conceived  existent,  except  through  the  supposition  of  the  two  former.  They 
are  thus  coordinate  but  inseparable.  Begin  with  any  one,  the  other  two 
follow  as  corollaries. 

I.  —  Primary  Laws  of  Thought,  —  in  general. 

See  the  following  authors  on :  —  Dreier,  Dbput.  ad  Ph'dosophiam  Primam, 
Disp.  V.  Aristotle,  Anali/t.  Pout.  i.  c.  11,  §§  2,  3,  4,  5,  6,  7.  Schramm,  Philoso- 
phia  Aristotelica,  p.  36.  Lippius,  Metaphjsica  Magna,  L.  i.  c.  i.,  p.  71  et  seq. 
Stahl,  Rer/ulce  Philosophicce,  Tit.  i.,  reg.  i.  p.  2  et  seq.,  reg.  ii.  p.  8  et  seq.,  Tit, 
xix.  reg.  viii.,  p.  520  et  seq.  Chauvin,  Lexicon  PhUosophicum,  v.  Metaphysica. 
Bisterfeld  evolves  all  out  of  ens,  —  ens  est.  See  PhUosophia  Prima,  c.  ii.  p.  24 
et  seq,     Bobrik,  System  der  Loyik,  §  70,  p.  247  et  seq. 


APPENDIX.  607 

Laws  of  Thought  are  of  two  kinds :  —  1".  The  laws  of  the  Thinkable,  — 
Identity,  Contradiction,  etc.  2°.  The  laws  of  Thinking  in  a  strict  sense  —  viz. 
laws  of  Conception,  Judgment,  and  Reasoning.  See  Scheidler,  Psychologic,  p. 
15,  ed.  1833. 

That  they  belong  to  Logic  :  —  Ramus,  ScJid.  Dial.,  L.  ix.,  p.  549. 

Is  Affirmation  or  Negation  prior  in  order  of  thought  ?  and  thus  on  order  and 
mutual  relation  of  the  Laws  among  themselves,  as  coordinate  or  derived ;  (see 
separate  Laws).  Fracastorius,  Opera,  De  Intellecdone,  L.  i.  f.  125  b.,  makes 
negation  an  act  prior  to  affirmation  ;  therefore,  principle  of  Contradiction  prior 
to  principle  of  Identity.  —  Fisser,  Logik,  §  28,  p.  57.  Sigwart,  Ilandhuch  zu 
Vorlesungen  ilber  die  Logik,  §  38  et  seq.  Piccolomineus,  De  Mente  Humana,  L. 
iii.,  c.  4,  p.  1301,  on  question  —  Is  affirmative  or  negative  prior  ?  Schulz,  Prilf. 
der  Kant.  Krit.  der  reinen  Vemunft,  I.  p.  78,  2d  ed.  Weiss,  Lehrbuch  der  Logik, 
§  81  et  seq.  pp.  61,  62,  1805.  Castillon,  Memoires  de  I'Acade'mie  de  Berlin 
(1803)  p.  8  (Contradiction  and  Identity  coordinate).  A.  Andreas,  In  Arist. 
Metaph.  iv.  Qu.  5.  p.  21.  (Affirmative  prior  to  negative.)  Leibnitz,  CEuvres 
Philosophiques,  Nouv.  Essais,  L.  iv.  ch.  2,  §  1,  p.  327,  ed.  Raspe.  (Identity  prior 
to  Contradiction.)  Wolf,  Ontologia,  §§  55,  288  —  (Contradiction  first.  Identity 
second).  Derodon,  Metapliysica,  c.  iii.,  p.  75  et  seq.  1669.  (Contradiction  first. 
Excluded  Middle  second,  Identity  third).  Fonseca,  In  Metaph.,  1. 849.  Biunde, 
Psychologie,  Vol.  I.,  part  ii.,  §  151,  p.  159.  (That  principle  of  Contradiction 
and  principle  of  Reason  and  Consequent  not  identical,  as  Won  and  Reimarus 
holdi)  Nic.  Taurellus,  Philosophice  Triumphus,  etc.,  p.  124.  Arnheim,  1617, 
"  Cum  simplex  aliqua  sit  affirmatio,  negatio  non  item,  banc  illam  sequi  conclu- 
dimus,"  etc.     Chauvin,  Lexicon  Philosophicum,  v.  Metaphysica. 

By  whom  introduced  into  Logic:  —  Eberstein  (^Uber  die  BescTiaffenheit  der 
Logik  und  Metaphysik  der  reinen  Peripatetiker,  p.  21,  Halle,  1800)  says  that 
Darjes,  in  1737,  was  the  first  to  introduce  Principle  of  Contradiction  into 
Logic.  TKat  Buffier,  ami  not  Reimarus,  first  introduced  principle  of  Identity 
into  Logic,  see  Bobrik,  Logik,  §  70,  p.  249. 

II.  —  Primary  Laws  of  Thought,  —  in  particular. 

1.  Principle  of  Identity.  "  Omne  ens  est  ens."  Held  good  by  Antonius 
Andreas,  In  Metaph.  iv.,  qu.  5.  (apud  Fonsecam,  In  Metaph.  I.  p.  849 ;  melius 
apud  Suarez,  Select.  Disp.  Metaph.  Disp.  iii.  sect.  iii.  n.  4.)  Derodon,  Meta- 
physica, c.  iii.,  p.  77.  J.  Sergeant,  Method  to  Science,  pp.  133 — 136  and  after. 
(Splits  it  absurdly.)  Boethius  —  "  Nulla  propositio  est  verior  ilia  in  qua  idem 
praedicatur  de  seipso."  (Versor,  In  P.  Hispani  Sum7nulas  Logicales,  Tr.  vii., 
p.  441  (1st  ed.  1487);  et  Buridanus,  In  Sophism.')  "  Propositiones  illas  oportet 
esse  notissimas  per  se  in  quibus  idem  de  se  ipso  prsedicatur,  ut '  Homo  est 
homo,'  vel  quarum  prjedicata  in  definitionibus  subjectarum  includuntur,  ut 
'  Homo  est  animal.'"  Aquinas,  Contra  Gentiles,  L.  i.  c.  10.  Opera  T.  XYHI. 
p.  7,  Venet.  1786.  Pjior  to  principle  of  Caalradiction  —  Leibnitz,  Nouveaux 
Essais,i).  377,    Buffier,  Principes  du  Raissonnement,  H.  art.  21,  p.  204.    Rejected 


608  APPENDIX. 

as  identical  and  nugatory  by  Fonseca,  he.  eit.  Suarez,  loc.  cU.  Wolf,  Onlolo- 
ffla,  §§  55,  288,  calls  it  Principium  Certitudinis,  and  derives  it  from  Principium 
Cloatradictionis. 

2.  Principle  of  Contradiction  —  oliw/ta  t^s  iLvrnpiffeus. 

Aristotle,  Metaph.^  L.  iii.  3 ;  x.  5.  (Fonseca^  In  Metaph.  T.  I^  p,  860,  L.  iv. 
(iii.)  c.  iii.)  Anal.  Post.  L.  i.  c.  11  c.  2,  §  13.  (On  Aristotle  and  Plato,  see 
Mansel's  Prolegomena,  pp,  236,  237.)  Stahl,  Reguloe  Philosophiea^  Tit  i.  r^.  i. 
Suarez,  Selecl  Disp.  Phil.,  Disp.  iii.  §  3.  Timpler,  Metaph.  L.  L,  c.  8  qu.  14. 
DoiXKion,  Aletaphysica,  p.  75  etc.  Lippius,  MtUiphi/sica,  L.  i.  c.  i.,  p.  73.  Ber- 
nardi,  Thes.  Arv^tot.^  vv.  Principium,  Contrail ict to.  Leibnitz,  (Euvres  Philoso- 
phiqueSy  Nouv.  Ess.,  L.  iv.  c.  2.  Ramus,  "  Axioma  Contradictionis,"  Scholee 
DiaL  L.  ix.  c.  i.,  L.  iv.  c.  2,  §  1,  p.  548.  Gul.  Xylander,  In.<itihitiones  Aphori^iat 
Logices  Aristot.,  p.  24  (1577),  "Principium  priucipiorum  hoc.  est,  lex  Contra- 
dictionis." Fhiloponus,  iftw/Mi  t^j  ayrt<pcurt<es,  v.  In  Post.  An.  f.  30  b.  et  seq. 
Ammonius,  i^lv»jia  t^j  tuni^Jurftts,  In  De  Interpret,  f.  94,  Aid.  1503  ;  but  princi- 
pium Exclusi  Medii,  Scheibler,  T'opica^c.  19.  On  Definition  of  Contradictories, 
V.  Scheibler,  Ibid.  On  Two  Principles  of  Contradiction,  —  Negative  and 
Positive,  V.  Zabarella,  Opera  Logica,  In  An.  Post.  i.  t  83,  p.  807. 

Conditions  of.  —  Aristotle,  Metaph.,  L.  iv.,  c.  6.  Bernardi,  Thesartrus  Arist.^ 
V.  Contrad.,  p.  300. 

Proof  attempted  by  —  Claubei^,  Ontosophitt,  §  26  (Degerando,  iSstoire  de 
Philosophic,  T.  II.  p-  67),  through  Excluded  Middle. 

3.  Principle  of  Excluded  Middle  —  i^it^fta  ttcuprrucSf. 

"*A^/wfi«  8iaifKTiic({i/,  divisivum,  dicitur  a  Gr«cis  principium  contradictionis 
affirmativum  ;  '  Oportet  de  omni  re  affirmare  aut  negare,'  "  Groelenius,  Lexicon 
Philogophicum.  Lat.  p.  136.  Zabarella,  In  An.  Post.,  L.  i.,  text  83,  Opera 
Logica,  p.  807.  Conimbricenses,  In  Org.,  II.  125.  Lucian,  Opera,  II.  p.  44 
(cd.  Henisterhuis).  Aristotle,  Metapli.,  L.  iv.  (iii.)  c.  7  ;  An.  Post.,  L.  i.  2 ;  ii. 
18  (Mansel's  Prolegomena,  p.  286).  Joannes  Philoponus  (v.  Bernardi,  Thes.  r. 
ConiraiL,  p.  300).  Piccartus,  Isagoge,  pp.  290,  291.  Javelins,  In  Metaph.,  L. 
iv.  qu.  9.  Suarez,  Disp.  Metaph.,  Disp.  iii.,  sect.  3,  §  5.  Stahl,  Regulce  Pkilos., 
Tit.  i.  reg.  2.  Wolf,  Ontologia,  §§27,  29,  56,  71,  498.  Fonseca,  In  Metaph., 
L.  iv.  c.  iii.  qu.  1.  et  seq.,  T.  I.  p.  850.  (This  principle  not  first)  Timpler, 
Metaphysica.  L.  ii.  c.  8,  qu.  15.  Derodon,  Metaph.,  p.  76.  (Secundum  princi- 
pium.) Lippius,  Metaphysica,  L.  L  c.  i-,  pp.  72,  75.  Chauvin,  Lexicon  Philo- 
foi^ncum,  V.  Metaphysica.  Scheibler,  Topica,  c.  19.  Hurtado  de  Mendoza,  Z)i!ip. 
Meuijh.,  Disp.  iii,,  §  3  (Caramuel,  Rat.  et  ReaL  Phil.,  §  462,  p.  68). 

^\niether  identical  with  Principle  of  Contradiction, 

AfTirmative,  —  Javcllus,  /.  c.  Mendoza,  Disp.  Metaph.,  D.  iii.  §  3,  Leibnitz, 
(Euvres  Philosophiques,  Nouv.  Es.'i.,  L.  iv.  c.  2,  p,  327. 

Negative,  —  Fonseca,  Di<<p.  Met.  Disp,  iv.  c.  3,  9.  Suarez,  Disp.  Metaph., 
Disp.  ni.  §  3.     Stahl,  Reg.  Phil.  Tit.  i.  reg.  2. 

Whether  a  valid  and  legitimate  Law. 
Fischer,  Logii;  ^  64  el  seq.  (Negative),  —  Made  first  of  all  principles  by 
Alexander  do  Ales,  Metaph.,  xiv.  text  9 :    "  Conceptus  onmes  simplices,  ut 


1 


APPENDIX.  609 

resolvtintur  ad  ens,  ita  omnes  conceptus  compositi  resolvtintur  ad  hoc  princi- 
pium  —  De  quolibet  affirmatio  vel  negado."  J.  Picas  Mirandulanus  (after  Aris- 
totle), Conclusiones,  Opera,  p.  90.  Philoponus,  In  An.  Post.  i.  f.  9  b,  (Brandis, 
Scholia,  p.  199).  Th  8'  iircw  (pdvai  ^  airo((>duai,  fi  tls  rh  aSvyaTOf  air6Set^is  Aanfidyfi. 
Aristotle,  An.  Post.  i.  c.  11.  §  3.  ^AyTtpcuris  5«  am-ldtais  f;s  ovk  effri  fiera^v  ko^ 
oMff.  An,  Post.  i.  c.  2,  §  13.  McTa|ii  ijm<f»i(r&i>s  ovk  ivStx^^"*  ov^tv.  Metaph. 
L.  iii.  C.  7.  'Eire!  aini(paafas  ouSci/  avk  fiiaov,  ^Kwtpbv  on  4v  rols  ivamlois  tarai  ri 
(xtra^i.  Physica,  L.  v.  c.  3,  §  5.  See  also  Post.  An.  L.  i.  c.  i.  §  4,  p.  414  j  c.  2 
§  13,  p.  417 ;  c.  11,  §  3,  p.  440.  (vide  Scheibler,  Topica,  c.  19 ;  and  Mansel'i 
Prolegomena,  p.  236,  on  Aristotle). 

4.  Principle  of  Reason  and  Consequent 

That  can  be  deduced  from  Principle  of  Contradicticm. 
Wolf,  Oniologia,  §  70.     Baumgarten,  Metaphysik,  §  18. 

Jakob,  Grundri-is  der  allgemeinen  Logik  und  Kritische  Angfangsgriinde  der      ] 
allgemeinen  Metaphysik,  p.  38,  3d  ed.,  1794.     (See  Kiesewetter,  I.  c.)  J 

That  not  to  be  deduced  from  Principle  of  Contradiction. 
Kiesewetter,  Allgemeine  Logik ;  Weitere  Auseinandersetzung,  P.  I.  ad  §§  20, 
21,  p.  57  et  seq.     Hume,  On  Human  Nature,  Book  i.  part  iii.  §  8.     Schulze, 
Logik,  §  18,  5th  ed.,  1881. 


V. 

NEW  ANALYTIC  OF  LOGICAL  FORMS  —  GENERAL  RESULTS 

—  FRAGMENTS. 

/ 

L  —  Extract  fboh  Pkospectus  of  "Essay  towards  a  New  Analytic  of 

Logical  Forms." 

(First  published  in  1846.1    See  pp.  102,  172.  —  Ed.) 

"  Now,  what  has  been  the  source  of  all  these  evils,  Tpi-oceed  to  relate,  and  shall  clearly  con- 
vince those  who  have  an  intellect  and  a  will  to  attend,  —  that  a  trivial  slip  in  the  elementary 
precepts  of  a  Logical  Theory  becomes  the  cause  cf  mightiest  errors  in  thai  Theory  itself."  — 
Galen.    {De  Temper amentis,  1.  i.  c.  5.) 

"  This  New  Analytic  is  intended  to  complete  and  simplify  the  old  ;  —  to 
place  the  keystone  in  the  Aristotelic  arch.  Of  Abstract  Logic,  the  theory,  in 
particular  of  Syllogism  (bating  some  improvements,  and  some  errors  of  detail), 
remains  where  it  was  left  by  the  genius  of  the  Stagirite  ;  if  it  have  not  receded. 


1  An  extract,  corresponding  in  part  with  is  republished  in  the  Discustions  on  Philosopht/., 
that  now  given  from  the  I'roepectus  of"  Essay  p.  650.  To  this  extract  tlie  Author  has  pre- 
towards  a  New  Analytic  of  Logical  Forms,"      fixed  the  following  notice  regarding  the  dat« 


610 


APPENDIX. 


still  less  has  it  advanced.  It  contains  the  truth ;  but  the  truth,  partially,  and 
not  always  correctly,  developed,  —  in  complexity,  —  even  in  confusion.  And 
why  ?  Because  Aristotle,  by  an  oversight,  marvellous  certainly  in  him,  was 
prematurely  arrested  in  his  analysis ;  began  his  synthesis  before  he  had  fully 
sifted  the  elements  to  be  recomposed;  and,  thus,  the  system  which,  almost 
spontaneously,  would  have  evolved  itself  into  unity  and  order,  he  laboriously, 
and  yet  imperfectly,  constructed  by  sheer  intellectual  force,  under  a  load  of 
limitations  and  corrections  and  rules,  which,  deforming  the  symmetry,  has  seri- 
ously impeded  the  usefulness,  of  the  science.  This  imperfection,  as  I  said,  it  is 
the  purpose  of  the  New  Analytic  to  supply. 

"  In  the  first  place,  in  the  Essay  there  will  be  shown,  that  the  Syllogism 
proceeds,  not  as  has  hitherto,  virtually  at  least,  been  taught,  in  one,  but  in  the 
two  correlative  and  counter  wholes  (Metaphysical)  of  Comprehension,  and 
(Logical)  of  Extension  ;  the  major  premise  in  the  one  whole  being  the  minor 
premise  in  the  other,  etc.  —  Thus  is  relieved  a  radical  defect  and  vital  inconsis- 
tency in  the  present  logical  system. 

"  In  the  second  place,  the  self-evident  truth,  —  That  we  can  only  rationally 
deal  with  what  we  already  understand,  determines  the  simple  logical  postulate, 
— To  state  explicitly  what  is  thought  implicitly.  From  the  consistent  application 
of  this  postulate,  on  which  Logic  ever  Insists,  but  which  Logicians  have  never 
fairly  obeyed,  it  follows :  —  that,  logically,  we  ought  to  take  into  account  the 
quantity,  always  understood  in  thought,  but  usually,  and  for  manifest  reasons, 
elided  in  its.  expression,  not  only  of  the  subject,  but  also  of  the  predicate,  of 
a  judgment  This  being  done,  and  the  necessity  of  doing  it  will  be  proved 
against  Aristotle  and  his  repeaters,  we  obtain,  inter  alia,  the  ensuing  results : 

'•  1°.  That  the  preinrlcsignate  terms  of  a  proposition,  whether  subject  or  predi- 
cate, are  never,  on  that  account,  thought  as  indejinite  (or  indeterminate)  in 
quantity.  The  only  indefinite,  is  particular,  as  opposed  to  dejinite,  quantity ; 
and  this  last,  as  it  is  either  of  an  extensive  maximum  undivided,  or  of  an  exten- 
sive minimum  indivisible,  constitutes  quantity  universal  (general),  and  quantity 
singular  (individual).  In  fact,  dejinite  and  indefinite  are  the  only  quantities  of 
which  we  ought  to  hear  in  Logic ;  for  it  is  only  as  indefinite  that  particular,  it 
is  only  as  definite  that  individual  and  general,  quantities  have  any  (and  the 
same)  logical  avail. 

"  2°.  The  revocation  of  the  two  Terms  of  a  proposition  to  their  true  relation  ,- 
a  proposition  being  always  an  equation  of  its  subject  and  its  predicate. 

"3o.  The  consequent  reduction  of  the  Conversion  of  Propositions  from  three 
species  to  one,  —  that  of  Simple  Conversion. 

"  4°.  The  reduction  of  all  the  General  Laws  of  Categorical  Syllogisms  to  a 
Single  Canon. 


of  his  doctrine  of  the  Qnantiflcation  of  the 
Predicate: — "Touching  the  principle  of  an 
explicitly  Quantified  Predicate,  I  had,  by  1833, 
become  convinced  of  the  necessity  to  extend 
and  correct  the  logical  doctrine  upon  this 
point.  In  the  article  on  Logic  (in  the  Edin- 
burgh Review)  first  published  in  1833,  the  theory 
of  Induction  there  maintained  proceeds  on 


a  thorough  quantification  of  the  predicate,  in 
affirmative  propositions. 

"  Before  1840, 1  had,  however,  become  con- 
vinced that  it  was  necessary  to  extend  the 
principle  equally  to  negatives;  for  I  find,  by 
academical  documents,  that  in  that  year,  tt 
latest,  I  had  publicly  taught  the  unejcolusive 
doctrine."  —  Discussions,  p.  650.  —  Ed. 


APPENDIX.  511 

"  5°.  The  evolution  from  that  one  canon  of  all  the  Species  and  varieties  of 
Syllogism. 

"  6°.  The  abrogation  of  all  the  Special  Laws  of  Syllogism. 

"  7°.  A  demonstration  of  the  exclusive  possibility  of  Three  syllogistic  Figures  . 
and  (on  new  grounds)  the  scientific  and  final  abolition  of  the  Fourth. 

"  8°.  A  manifestation  that  Figure  is  an  unessential  variation  in  syllogistic 
form ;  and  the  consequent  absurdity  of  Reducing  the  syllogisms  of  the  other 
figures  to  the  first. 

"  9°.  An  enouncement  of  one  Organic  Principle  for  each  Figure. 

"  1 0°.  A  determination  of  the  true  number  of  the  legitimate  Moods  ;  with 

"  1 1°.  Their  amplification  in  number  (thirty-six)  ; 

"  12°.  Their  numerical  equality  under  all  the  figures;  and, 

"  13°.  Their  relative  equivalence,  or  virtual '  identity,  throughout  every  sche- 
matic difference. 

"  14°.  That,  in  the  second  and  third  figures,  the  extremes  holding  both  the 
same  relation  to  the  middle  term,  there  is  not,  as  in  the  first,  an  opposition  and 
subordination  between  a  term  major  and  a  term  minor,  mutually  containing  and 
contained,  in  the  counter  wholes  of  Extension  and  Comprehension. 

"16°.  Consequently,  in  the  second  and  third  figures,  there  is  no  determinate 
major  and  minor  premise,  and  there  are  two  indifferent  conclusions  ;  whereas, 
in  the  frst  the  premises  are  determinate,  and  there  is  a  single  proximate  con- 
clusion. 

"  16°.  That  the  third,  as  the  figure  in  which  Comprehension  is  predominant,  is 
more  appropriate  to  Induction. 

"  1 7°.  That  the  second,  as  the  figure  in  which  Extension  is  predominant,  is 
more  appropriate  to  Deduction. 

"  18°.  That  the^rs^,  as  the  figure  in  which  Comprehension  and  Extension  are 
in  equilibrium,  is  common  to  Induction  and  Deduction,  indifferently. 

"In  the  third  place,  a  scheme  of  Symbolical  Notation  will  be  given,  wholly 
different  in  principle  and  perfection  from  those  which  have  been  previously 
proposed ;  and  showing  out,  in  all  their  old  and  new  applications,  the  proposi- 
tional  and  syllogistic  forms,  with  even  a  mechanical  simplicity. 

"This  Essay  falls  naturally  into  two  parts.  There  will  be  contained,  —  in 
the_^rs/,  a  systematic  exposition  of  the  new  doctrine  itself;  in  the  second,  an 
historical  notice  of  any  occasional  anticipations  of  its  several  parts  which  break 
out  in  the  writings  of  previous  philosophers. 

"  Thus,  on  the  new  theory,  many  valid /orms  of  judgment  and  reasoning,  in 
ordinary  use,  but  which  the  ancient  logic  continued  to  ignore,  are  now  openly 
recognized  as  legitimate ;  and  many  relations,  which  heretofore  lay  hid,  now 
come  forward  into  the  light.  On  the  one  hand,  therefore,  Logic  certainly 
becomes  more  complex.  But,  on  the.  other,  this  increased  complexity  proves 
only  to  be  a  higher  development.  The  developed  Syllogism  is,  in  effect, 
recalled,  from  multitude  and  confusion,  to  order  and  system.  Its  laws,  ere- 
while  many,  are  now  few,  —  we  might  say  one  alone,  —  but  thoroughgoing.  Tlie 
exceptions,  formerly  so  perplexing,  have  fallen  away ;  and  the  once  formidable 
array  of  limitary  rules  has  vanished.  The  science  now  shines  out  in  the  true 
character  of  beauty,  —  as  One  at  once  and  Various.     Logic  thus  accomplishes 


512 


APPENDIX. 


its  final  destination ;  for  as  '  Thrice-greatest  Hermes,'  speaking  in  the  mind  of 
Plato,  has  expressed  it,  — '  The  end  of  Philosophy  is  the  intuition  of  Unity.' " 


II.  —  Logic,  —  Its  Postulates. 
(November  1848  —  See  p.  81.) 

I.  To  state  explicitly  what  is  thought  implicitly.  In  other  words,  to  deter- 
mine what  is  meant  before  proceeding  to  deal  with  the  meaning.  Thus  in  the 
proposition  Men  are  animals,  we  should  be  allowed  to  determine  whether  the 
term  men  means  all  or  some  men,  —  whether  the  term  animals  means  all  or  some 
animals  ;  in  sliort,  to  quantify  both  the  subject  and  predicate  of  the  proposition. 
This  postulate  applies  both  to  "Propositions  and  to  Syllogisms.^ 

II.  Throughout  the  same  Proposition,  or  Immediate  (not  mediate)  Reason- 
ing, to  u.se  the  same  words,  and  combinations  of  words,  to  express  the  same 
thought  *  (that  is,  in  the  same  Extension  and  Comprehension),  and  thus  iden- 
tity to  be  presumed. 

Thus  a  particular  in  one  (prejaeent)  proposition  of  an  immediate  reasoning, 
though  indefinite,  should  denote  (he  same  part  in  the  other.  This  postulate 
applies  to  inference  immediate,  e.  g.  Convei-sion- 

Predcsignate  in  same  logical  unity  (proposition  or  syllogism),  in  same  sense, 
both  Collective  or  both  Distributive.  That  one  term  of  a  proposition  or  syllo- 
gism should  not  be  used  distributively  and  another  collectively. 

III.  And,  e  contra,  throughout  the  same  logical  unity  (inunediate  reasoning), 
to  denote  and  presume  denoted  the  same  sense  (notion  or  judgment)  by  the 
same  term  or  terms." 

This  does  not  apply  to  the  ditTerent  propositions  of  a  Mediate  Inference. 

IV.  (or  V.)  To  leave,  if  necessary,  the  thought  undetermined,  as  subjectively 
uncertain,  but  to  deal  with  it  only  as  far  as  certain  or  determinable.     Thus  a 


1  See  (quoted  by  Wallis,  Logka,  p.  291),  Ar- 
istotle, An.  Prior.,  L.  i.,  c.  33  (I'acius,  c.  32,  H 
2,  3.  4,  p.  261),  and  Ramns  (from  Downam,  In 
P.  Rami  Dialect.,  L.  ii.,  c  9.  p.  410) :  What  is 
utiderstoud  to  be  supplied;  IRamus  Hial.,Jj, 
ii.,  c.  9.  "  Si  qua  [de  argumeutationis  conse- 
qnentia  propter  crypsin]  dubitatio  fuerit,  ex- 
pleiida  quae  desunt;  ampotanda  qnas  «uper- 
i<uitt;  et  pars  qusclib«t  in  locum  redigenda 
situ  est."]  [Cf.  rioucquet,  Elemrnta  Philoso- 
phirp  Contemptativcr,  5  29,  p.  5.  Stutgardise, 
1778.  "  Secundum  sensum  logicum  cum  omni 
teimino  Jungendum  est  signum  quantitatis." 
—  Ed.  J 

-  That  words  must  be  used  in  the  same 
sense  Sec  Aristotle,  Anal.  Prior.,  L.  i.,  cc.  33. 
84,  85.  8«,  37,  etc 

3  If  these  postulates  (II.  and  III.)  were  not 
cogent,  we  could  not  convert,  at  least  not  use 


the  converted  proposition  (un!e.ss  tlie  I.  were 
cogent,  the  convntemla  would  be  false).  All 
man  is  (an)  animal,  is  converted  into  Some  an- 
imal 13  {alt)  man.  But  if  the  .'ome  animal  here 
were  not  thought  in  and  limited  to  the  sense 
of  the  convertend,  it  would  be  false.  So  in 
the  hypothetical  proposition,  //  tlie  Chinrse 
are  Mohammedans,  they  are  (some)  infidels  ;  the 
word  infidel,  unless  thought  iu  a  meaning 
limited  to  and  true  of  Mohammedans,  is  inept. 
But  if  it  be  so  limited,  we  can  (contrary  to 
the  doctrines  of  the  logicians)  argue  baclc 
from  the  jMisition  of  the  consequent  to  the 
position  of  the  antecedent,  and  from  tlie  snb- 
lation  of  the  antecedent  to  the  sublation  of 
the  consequent,  though  false.  If  not  grauted. 
Logic  is  a  mere  childish  play  with  the  vague- 
ness and  ambiguities  of  language.  fCf  Titius, 

Arx  Cogitandi,  C.  xii.,  }  26   —  ED.] 


APPENDIX.  513 

whole  may  be  truly  predicable,  though  we  know  only  the  truth  of  it  as  a  part. 
Therefore,  we  ought  to  be  able  to  say  some  at  least  when  we  do  not  know,  and 
cannot,  therefore,  say  determinately,  either  that  some  only  or  that  all  is  true. 

(January  1850.) 

III.  (or  IV.)  To  be  allowed,  in  an  immediate  reasoning,  to  denote,  that  an- 
other part,  other,  or  some,  is  used  in  the  conclusion,  fromwhatwasin  the  antece- 
dent.    Inference  of  Sub-contrariety. 

That  the  some,  if  not  otherwise  qualified,  means  some  only,  —  this  by  pre- 
sumption. 

That  the  Term  (Subject,  or  Predicate)  of  a  Proposition  shall  be  converted 
with  its  quantity  unchanged,  i.  e.  in  the  same  extension.  This  violated,  and 
violation  cause  of  error  and  confusion.  No  per  accidens,  for  the  real  terms 
compared  are  the  quantified  terms,  and  we  convert  only  the  terms  compared  in 
the  prejacent  or  convertenda. 

That  the  same  terms,  apart  from  the  quantity,  i,  e ,  in  the  same  comprehen- 
sion, should  be  converted.     As  before  stated,  such  terms  are  new  and  different. 
No  Contraposition,  for  contraposition  is  only  true  in  some  cases,  and  even  in 
these  it  is  true  accidentally,  not  by  conversion,  but  through  contradiction  ;  i.  e., , 
same  Comprehension. 

That  we  may  see  the  truth  from  the  necessary  validity  of  the  logical  process, . 
and  not  infer  the  validity  of  the  logical  process  from  its  accidental  truth.    Con- 
version per  accidens,  and  Contraposition,  being  thus  accidentally  true  in  some  - 
cases  only,  are  logically  inept  as  not  true  in  all. 

To  translate  out  of  the  complexity,  redundance,  deficiency,  of  common  lan- 
guage into  logical   simplicity,  precision,  and  integrity.* 

(December  1849.) 

As  Logic  considers  the  form  and  not  the  matter,  but  as  the  form  is  only  man- 
ifested in  application  to  some  matter,  Logic  postulates  to  employ  any  matter  in. 
its  examples. 

(January  1850.) 

That  we  may  be  allowed  to  translate  into  logical  language  the  rhetorical  ex-- 
pressions  of  ordinary  speech.     Thus  the  Exceptive  and  Limitative  proposi- 
tions in  which  the  predicate  and  subject  are  predesignated,  are  to  be  rendered 
into  logical  simplicity. 

(May  1850.) 

As  Logic  is  a  formal  science,  and  professes  to  demonstrate  by  abstract  for-- 
mulae,  we  should  know,  therefore,  nothing  of  the  notions  and  their  relations 
except  ex  facie  of  the  propositions.  This  implies  the  necessity  of  overtly  quan- 
tifying the  predicate. 

1  See  p.  512,  note  1.  —  Ed. 

65 


514  APPENDIX. 


in.  —  Quantification  of  Predicate, — Ihmediatb  Infehence,  —  Cos- 
VERSION,  —  Opposition.^ 

(See  pp.  172,  185.) 

We  how  proceed  to  what  has  been  usually  treated  under  the  relation  of 
Propositions,  and  previously  to  the  matter  of  Inference  altogether,  but  which  I 
think  it  would  be  more  correct  to  consider  as  a  species  of  Inference,  or  Rea- 
soning, or  Argumentation,  than  as  merely  a  preparatory  doctrine.  For  in  so 
far  as  these  relations  of  Propositions  warrant  us,  one  being  given,  to  educe 
irom  it  another,  —  this  is  manifestly  an  inference  or  reasoning.  Why  it  has 
not  always  been  considered  in  this  light  is  evident.  The  inference  is  immedi- 
ate ;  that  is,  the  conclusion  or  second  proposition  is  necessitated,  directly  and 
without  a  medium,  by  the  first.  There  are  only  two  propositions  and  two 
notions  in  this  species  of  argumentation ;  and  the  logicians  have  in  general 
limited  reasoning  or  inference  to  a  mediate  eduction  of  one  proposition  out  of 
the  correlation  of  two  others,  and  have  thus  always  supposed  the  necessity  of 
three  terms  or  collated  notions. 

But  they  have  not  only  been,  with  few  exceptions,  unsystematic  in  their  pro- 
cedure, they  have  all  of  them  (if  I  am  not  myself  mistaken)  been  fundamen- 
tally erroneous  in  their  relative  doctrine- 
There  are  various  Immediate  Inferences  of  one  proposition  from  another. 
Of  these  some  have  been  wholly  overlooked  by  the  logicians ;  whilst  what  they 
teach  in  regard  to  those  which  they  do  consider,  appears  to  me  at  variance  with 
the  truth. 

1  shall  make  no  previous  enumeration  of  all  the  possible  species  of  Immedi- 
ate Inference  ;  but  shall  take  them  up  in  this  order :  I  shall  consider,  1*,  Those 
which  have  been  considered  by  the  logicians ;  and,  2°,  Those  which  have  not 
And  in  treating  of  the  first  group,  I  shall  preface  what  I  tliink  the  true  doctrine 
by  a  view  of  that  which  you  will  find  in  logical  books. 

The  first  of  these  is  Conversion.  When,  in  a  categorical  proposition  (for  to 
this  we  now  limit  our  consideration),  the  Subject  and  Predicate  are  transposed, 
that  is,  the  notion  which  was  previously  the  subject  becomes  the  predicate,  and 
the  notion  which  was  previously  the  predicate  becomes  the  subject,  the  propo- 
sition is  said  to  be  converted.*  The  proposition  given,  and  its  product,  are 
together  called  the  judicia  conversa,  or  propositiones  conversce,  which  I  shall  not 
attempt  to  render  into  English.  The  relation  itself  in  which  the  two  judgments 
stand,  is  called  concersion,  reciprocation,  transposition,  and  sometimes  obversion, 
(conversio,  reciprocatio,  transpositio,  obversio). 

1  Appendix  III.,  from  p.  514  to  p.  527,  was  ffiiiiv  Kara  robs  opovs  avdvaXiv  rt^f/xfyovs, 

usually  delivered  by  the  author  as  a  Lecture,  jutra  tov  ffvva\ridfufiy.     Alexander,  /*  An. 

supplementary  to  the  doctrine  of  ConTersion  Pr.  i.  c.  4,  f.  15  b.    See  the  same  in  difTerent 

as  given  p.  185.  —  Ed.  word*,  by  Philoponus  (Ammonias),/*  An. 

2  [Definitions  of  conversion  in  general.  Pr.  i.  c.  2,  f.  11  b.,  and  copied  from  him  by 
'AvTi(rTpo<pri  iffnv  \aoffrpo<pi\  rts,  Philopo-  Mafjentinus,  In  An.  Pr.,  t.  3  b.  Cf.  Boethius, 
nus  (or  Ammonius),  In  An.  Pr.  i.  c.  2,  f.  11  b.  Opera,  Introditctio  ad  Sytlogistnos,  p.  574-  We- 
So  Magentinus,  In  An.  Pr.  i.  c.  2,  f.  3  b  gelin,  in  Gregorii  Aneponymi  Phil.  Syniag. 
Anonymug,  De  Syllogismo,  f.  42  b.  Tlpord-  (circa  1260),  L.  v.,  c.  12,  p.  621.  Kicephorus 
atws  ayri(rrpo<pi}  tan  Kowwvia  Buo  irpoTa-  Blemmidas,  Epit.  Log.,  c.  31,  p.  221.] 


APPENDIX.  615 

The  original  or^ven  proposition  Is  called  the  ConversCy  or  Converted,  some- 
times the  Prcejaceno,  Judgment  (Judicium,  or  propositio,  conversum,  conversa, 
prcejacens)  ;  the  other,  that  into  which  the  first  is  converted,  is  called  the  Con- 
vertinff,  and  sometimes  the  Subjacent,  Judgment  (propositio,  or  Jud.  convertens, 
subjacens).  It  would  be  better  to  call  the  former  the  Convertend  (pr.  conver- 
tenda),  the  latter  the  Converse  (pr.  conversa).     This  language  I  shall  use.* 

Such  is  the  doctrine  touching  Conveision  taught  even  to  the  present  day. 
This  in  my  view  is  beset  with  errors ;  but  all  these  errors  originate  in  two,  as 
these  two  are  either  the  cause  or  the  occasion  of  every  other. 

The  First  cardinal  error  is,  —  That  the  quantities  axe  not  converted  with  the 
quantified  terms.  For  the  real  terms  compared  in  the  Convertend,  and  which, 
of  course,  ought  to  reappear  without  change,  except  of  place,  in  the  Converse, 
are  not  the  naked,  but  the  quantified  terms.  This  is  evident  from  the  follow- 
ing considerations : 

1°,  The  Terms  of  a  Proposition  arc  only  terms  as  they  are  terms  of  relation  ; 
and  the  relation  here  is  the  relation  of  comparison. 

2°,  As  the  Propositional  Terms  are  terms  of  comparison,  so  they  are  only 
compared  as  Quantities,  —  quantities  relative  to  each  other.  An  Affirmative 
Proposition  Is  simply  the  declaration  of  an  equation,  a  Negative  Proposition  Is 
simply  the  declaration  of  a  non-equation,  of  Its  terms.  To  change,  therefore, 
the  quantity  of  either,  or  of  both  Subject  and  Predicate,  is  to  change  their  cor- 
relation, —  the  point  of  comparison  ;  and  to  exchange  their  quantities,  if  dif- 
ferent, would  be  to  invert  the  terminal  interdependence ;  that  is,  to  make  the 
less  the  greater,  and  the  greater  the  less. 

3°,  The  Quantity  of  the  Proposition  in  Conversion  remains  always  the  same ; 
that  is,  the  absolute  quantity  of  the  Converse  must  be  exactly  equal  to  that  of 
the  Convertend.     It  was  only  fcom  overlooking  the  quaittlty  of  the  predicate 


1  See  p.  185.  —  Ed.  or  exponens,  quite  different  as  used  by  Logi- 

[Xames  for  the  two  propositions  in  Conver-         cians,  v.  Scliegkius,  In  Arist.  Org.  162  (and 
sion.  above,  p.  186.) 

I.  Name  for  the  two  correJative   proposi-  g)  Convertenda,  Corvinus,  lot.  at.  Eichter, 
tions  —  Conversa,  Twesfen,  Lo^ik,  §  87,  Con-         loc.  cit. 

traposita,  Id.  ibid.  h)  Contraponens,  Twesten,  Ibid. 

II.  Original,  or  Given  Proposition.  i)  Prior,  Boethius,  De  Syllog.  Categ.  L.  I.  Op- 

a)  ■^  irporiyovneirrj,  rpoKei/xfinn,  avTiarpe^o-       '  era,  p.  588. 

liiirq   Trp6Tacns  —  Ct.    Strigelius    In    Me-  k)  Priiicipium,  Darjes,  Wa  arf  rerifa/ejn,  }  23i. 
landiih.  Erot.  Dial.,  L.  ii.,  jS.  581.  Ill-  Product  of  Conversion. 

^Ain-t<TTpe<povirca   irpordtreis,    Philoponus,  a)  V  avTicrrpfipovffa.    See  Strigelius,  loe.  cit. 

(quoted  by  Wegelin,  I.  e.)  b)  Convertens,  Subjacens,  Scotus,  Quastiones, 

b)  Conversa  (=  Convertenda)  vulgo.  Scotus,  In  An.  Prior.,  i.d,2i,{.  216,(1  passim.  Krug, 
Quastiones  in  An.  Prior.,  i  q.  12.  Corvinus,  Logik,  §  65,  p.  205,  and  logicians  in  general. 
Instil.  Pliil..  i  510.  Richter,  De  Conversione,  c)  Conversa,  Boethius,  Opera,  IntroU.  ad  Syll., 
1740.  Halae  Magdeb.  Baumgarten,  Lo^ica,  pp.  575  <•«  .v?.,  587  f«  .'<?.;  Melanchthon,  iV- 
§  278.  Ulrich,irt.<tit.  Log.  et  Met.,  ^  182,  p.  188.  otemata,  L.  ii.  p.  581,  and  Strigelius,  ad  loe. 

C)  Convertibilis  (raro).  Micraelius,  Lex.  Phil.,  v.  Conversio.     Nold- 

d)  Convertens,  Micraelius,  Lex.  Phil.  «.  Con-  ius,  Logica  Recognita,  p.  263,  says  that  the 
versio.  Twesten,  Logik,  }  87.  Antecedens,  first  should  more  probably  be  called  Con- 
Scotus,  I.  c.    StrigeJiup,  L  c.  vertibilis,  or  Convertenda,  and  the  second 

e)  Prjejacens,  Scheibler,  Opera  Logica  De  Prop-         Conversa. 

ositionibus,  Pars  iij.  c.  x.  p.  479.  d)  Conversi^m,  Twesten,  loe.  cit. 

f )  Exposita,    AJdrich,    Comp.,    L.    i.    c.    2.  e)  Contrapositum,  Id.  ibid. 

Whately,  Logxt^  p.  69.     Propositio 'exposita  f )  Conclusio,  Darjes,  Tia  ad  Veritatem,  {  23i 


516 


APPENDIX. 


(the  second  error  to  which  we  shall  immediately  advert)  that  two  propositions, 
exactly  equal  in  quantity,  in  fact  the  same  proposition,  perhaps,  transposed, 
were  called  the  one  universal,  the  other  particular,  by  exclusive  reference  to  the 
quantity  of  the  subject. 

4°,  Yet  was  it  of  no  consequence,  in  a  logical  point  of  view,  which  of  the 
notions  collated  were  Subject  or  Predicate ;  and  their  comparison,  with  the 
consequent  declaration  of  their  mutual  inconclusion  or  exclusion,  that  is,  of  af- 
firmation or  negation,  of  no  more  real  difference  than  the  assertions,  — London 
is  four  hundred  miles  distant  from  Edinburgh, — Edinburgh  is  four  hundred  miles 
distant  from  London.  In  fact,  though  logicians  have  been  in  use  to  place  the 
subject  first,  the  predicate  last,  in  their  examples  of  propositions,  this  is  by  no 
means  the  case  in  ordinary  language,  where,  indeed,  it  is  frequently  even  diffi- 
cult to  ascertain  which  is  the  determining  and  which  the  determined  notion. 
Out  of  logical  books,  the  predicate  is  found  almost  as  frequently  before  as  after 
the  subject,  and  this  in  all  languages.  You  recollect  the  first  words  of  the 
First  Olympiad  of  Pindar,  "KfjiaTov  yiev  vSup, "  Best  is  water ; "  and  the  Vulgate 
(I  forget  how  it  is  rendered  in  our  English  translation)  has,  "  Magna  est  Ver- 
itas, et  praevalebit."^  Alluding  to  the  Bible,  let  us  turn  up  any  Concordance 
under  any  adjective  title,  and  we  shall  obtain  abundant  proof  of  the  fact.  As 
the  adjective  great,  magtius,  has  last  occurred,  let  us  refer  to  Cruden  under  that 
simple  title.  Here,  in  glancing  it  over,  I  find  —  "  Great  is  the  wrath  of  the 
Lord — Great  is  the  Lord  and  greatly  to  be  praised  —  Great  is  our  God  — 
Great  are  thy  works  —  Great  is  the  Holy  One  of  Israel  —  Great  shall  be  the 
peace  of  thy  children  —  Great  is  thy  faithfulness  —  Great  is  Diana  of  the 
Ephesians  —  Great  is  my  boldness  —  Great  is  my  glorying  —  Great  is  the 
mystery  of  godlines?,"  etc. 

The  line  of  Juvenal, 

"  Nobilitas  sola  est  atque  unica  virtus," 

is  a  good  instance  of  the  predicate  being  placed  first. 

The  Second  cardinal  error  of  the  logicians  is,  the  not  considering  that  the 
Predicate  has  always  a  quantity  in  thought,  as  much  as  the  Subject;  although 
this  quantity  be  frequently  not  explicitly  enounced,  as  unnecessary  in  the  com- 
mon employment  of  language  ;  for  the  determining  notion  or  predicate  being 
always  thought  as  at  least  adequate  to,  or  coextensive  with,  the  subject  or  de- 
termined notion,  it  is  seldom  necessary  to  express  this,  and  language  tends  ever 
to  elide  what  may  safely  be  omitted.  But  this  necessity  recurs  the  moment 
that,  by  conversion,  the  predicate  becomes  the  subject  of  the  proposition  ;  and 
1o  omit  its  formal  statement  is  to  degrade  Logic  from  the  science  of  the  neces- 
sities of  thought,  to  an  idle  subsidiary  of  the  ambiguities  of  speech.  An  un- 
biassed consideration  of_the  subject  will,  I  am  confident,  convince  you  that 
tliis  view  is  correct. 

1°,  Tliat  the  predicate  is  as  extensive  as  the  subject  is  easily  shown.  Take 
the  proposition,  —  All  animal  is  man,  or.  All  animals  are  men.     This  we  arc 


1  III.  Esdras  ir.  41 :  "  Magna  est  Veritas  et     ir.  41),  "  Great  is  truth,  aud  mighty  above  all 
pnevalet  "    In  the  iCuglish  rereiou  (I.  Esdras     things."  — £d. 


APPENDIX.  617 

conscious  is  absurd,  though  we  maJce  the  notion  man  or  men  as  wide  as  possible ; 
for  it  does  not  mend  the  matter  to  say,  —  All  animal  is  all  man,  or,  All  animals 
are  all  men.  We  feel  it  to  be  equally  absurd  as  if  we  said,  —  All  man  is  all 
animal,  or,  All  men  are  all  animals.  Here  we  are  aware  that  the  subject  and 
predicate  cannot  be  made  coextensive.  If  we  would  get  rid  of  the  absurdity, 
we  bring  the  two  notions  into  coextension,  by  restricting  the  wider.  If  we  say, 
—  Man  is  animal  (^Homo  est  animal),  we  think,  though  we  do  not  overtly 
enounce  it,  AU  man  is  animal.  And  what  do  we  mean  here  by  animal  ?  We 
do  not  think,  —  All,  but  Some,  animal.  And  then  we  can  make  this  indiffer- 
ently either  subject  or  predicate.  AVe  can  think,  —  we  can  say,  Some  animal 
ts  man,  that  is.  Some  or  All  Man ;  and,  e  converso,  —  J\Ia7i  (some  or  all)  is 
animal,  viz.,  some  animal. 

It  thus  appears  that  there  is  a  necessity  in  all  cases  for  thinking  the  predicate, 
at  least,  as  extensive  as  the  subject  Whether  it  be  absolutely,  that  is,  out  of 
relation,  more  extensive,  is  generally  of  no  consequence ;  and  hence  the 
common  reticence  of  common  language,  which  never  expresses  more  than 
can  be  understood,  —  which  always,  in  fact,  for  the  sake  of  brevity,  strains  at 
ellipsis. 

2'^,  But,  in  fact,  ordinary  language  quantifies  the  Predicate  so  often  as  this 
determination  becomes  of  the  smallest  import.  This  it  does  directly,  by  adding 
all,  some,  or  their  equivalent  predesignations,  to  the  predicate ;  or  it  accom- 
pUshes  the  same  end  indirectly,  in  an  exceptive  or  limitative  form. 

»)  Directly,  —  as  Peter,  John,  James,  etc.,  are  all  the  Apostles  —  Mercury, 
Venus,  etc.,  are  all  the  planets. 

b)  But  this  is  more  frequently  accomplished  indirectly,  by  the  equipollent 
forms  o? Limitation  or  Inclusion,  and  Exception.^ 

For  example,  by  the  limitative  designations,  alone  or  only,  we  say, —  God 
alone  is  good,  which  is  equivalent  to  saying,  —  God  is  all  good,  that  is,  God  is 
all  that  is  good ;  Virtue  is  the  only  nobility,  that  is.  Virtue  is  all  noble,  that  is,  all 
that  is  nohle.^     The  symbols  of  the  Catholic  and  Protestant  divisions  of  Chris- 


1  By  the  ]o},'icians  this  is  called  simply  Ex-  subject  alone.  As,  Man  alone  philosophizes 
elusion,  and  the  particles,  tantu7n,  etc.,  panic-  (though  not  all  do).  The  dog  alone  barks,  or, 
ulfr,  fxclusivrr.  This,  I  think,  is  inaccurate;  dogs  alone  bark  (though  some  do  not).  '  Man 
for  it  is  inclusion,  limited  by  an  exclusion,  only  is  mtional,  or.  No  animal  but  man  is  ra- 
that  is  meant.  —  [See  Seheibler,  Opera  Logica,  tional.  Nothing  but  rational  is  risible.  Of  ma- 
1*.  iii.  C.  vii.  tit.  3,  p.  457  et  seq.]  terial    things   there  is  nothing  living  {but)    not 

2  (February  1850.)  Ou  the  Indirect  Predes-  organized,  and  nothing  organized  not  living. 
ignation  of  the  Predicate  by  what  are  called  God  alone  is  to  be  ivorskipped.  God  is  th* 
the  Exclusive  and  Exctptive  particles.  single,  —  sole  object  of  vjorship.     Some  men  only 

Names  of  the  particles.  are  elect. 

Latin,  —  unus,  vnicus,  unice ;   solus,  solum,  II.    Annexed  to  the  Predicate,  they  limit 

solummodo,   tantum,    tantummodo;    duntaxat ;  the  subject  to  the  predicate,  but  do  not  define 

pracise;  adequate.    Nihil  pr<p.ter, — prceterquam,  its  quantity,  or  exclude  from  it  other  sub- 

—  ni  nisi  non.  jects.    As,   Peter  only  plays.     The  sacraments 

English,  —  one,  only,  alone,  exclusively,  pre-  are  only  two.    John  drinks  only  water, 

cisely.  just,  sole,  solely,  nothing  but,  not  except,  III.     Sometimes   the    particles  sole,  sole!-; 

not  beyond.  single,  alone,  only,  etc.,  are   annexed  to  t..? 

I.  These  particles  annexed  to  the  Subject  Predicate  as  a  predesignation  tantamount  {», 

prcdesignate  the  Predicate  universally,  or  to  all.    As,  God  is  the  single,  —  one,  —  alone.  — 

its  whole  extent,  denying  its  j)articularity  or  only,  —  exclusive,  —  adequate,  object  of  worship. 

indefinitude,  and  definitely  limiting  it  to  the  On  the  relation  of  Exclusive  propositions 


518 


APPENDIX. 


tianitj  may  afford  us  a  logical  illustration  of  the  point.  Tlie  Catholics  say,-^ 
Faith,  Hope,  and  Charity  alone  justify  ;  that  is,  the  three  heavenly  virtues  together 
are  all  Justifying,  that  is,  all  that  justifies  ;  omne  juslifcans,  justum  faciens.  The 
Protestants  say,  —  Faith  alone  justifies  ;  that  is,  Faith,  which  they  hold  to  com- 
prise the  other  two  virtues,  is  all  justifying,  that  is,  all  that  justifies  ;  omne  justi- 
ficans.  In  either  case,  if  we  translate  the  watchwords  into  logical  simplicity, 
the  predicate  appears  predesignated. 

Of  animals  man  alone  is  rational ;  that  is,  Man  is  all  rational  animal.  WheU  is 
rational  is  alone  or  only  risible ;  that  is,  All  rational  is  all  risible,  etc. 

I  now  pass  on  to  the  Exceptive  Form.  To  take  the  motto  overhead, —  "On 
earth  there  is  nothing  great  but  man."  What  does  this  mean  ?  It  means, 
Man  —  is  —  all  earthly  great.  —  Homo  —  est  — omne  magnum  terrestre.  And  the 
second  clause  —  "  In  man  there  is  nothing  great  but  mind  " —  in  like  manner 
gives  as  its  logical  equipollent  —  Mind  —  is  —  all  humanly  great,  that  is,  all  that 
is  great  in  man.     (J/e/is  est  omne  magnvm  hwnanum.y 


to  those  in  which  the  predicate  is  predesig- 
nated, sec  Titius,  Ars  Cogitandi,  c.  vi.  H  66, 
67-  Hollman,  Philoaophia  Ralionalis,  J  475. 
Kreil,  Handbwh  der  Lo^ik.  S  62.  Derodon, 
Logica  Restituta,  De  Enunciationey  C.  v.  p.  569 
ft  $eq.  Keckermann,  Systema  Logica,  lib.  iii., 
C.  11.     Opera,  t.  i.  p.  763. 

The  doctrine  held  by  the  logicians  as  to  the 
exdusum  pradieatum,  exdusum  3ubjectuvi,  and 
exclusum  signum,  is  erroneous.  See  Scheibler, 
Opera  Logica,  P.  iii.  c.  vii.  tit.  3,  p.  457  et  Sfq. 
Jac.  Thomasius,  Erutem.  Lo^.,  c  xxx.  p.  67  ft 
teq.  [Cf.  Fonseca,  Inftlt.  Dial ,  L.  III.  c.  23. 
For  a  detailed  exposition  of  this  doctrine  by 
Scheibler,  see  below,  note  1.  —  Ed.] 

1  Vide  Scheibler,  Opera  Logica,  P.  iii.  c.  vii. 
pp.  458,  460,  where  his  exnnii)le.«,  with  the  ex- 
position of  the  Logicians,  may  be  well  con- 
trasted with  mine. 

[Scheibler,  after  referrin/f  to  the  Porra  Logi- 
etdia  of  the  schoolmen,  as  containing  a  pro- 
posed.supplement  of  the  doctrines  of  Aris- 
totle, proceeds  to  expound  the  Propositioius 
ExpnnibiU.%  of  those  treatises.  "  Exclusiva 
enunciatio  est,  quic  habet  particulain  exciu- 
sivam,  ut.  Solus  homo  est  rationalis.  .  .  . 
Porro  excluslvae  ennnciationos  sunt  duplicis 
generis.  Alia;  sunt  exclusivae  prsedicati :  aliae 
exclusive  subjecti ;  hoc  est,  in  aliis  particula 
exclusiva  excludit  a  subjecto,  in  aliis  excludit 
a  pra:dicato,  velnti  h«c  propositio  exclusiva 
est;  Deus  taatum  est  immortalis.  Estque  ex- 
clusiva a  subjecto,  hoc  sensu,  Dens  tantum,  et 

non  homo  vel  lapis,  etc Omnes 

propositiones  exclusivie  ambiguae  sunt,  si 
habeant  particulam  exclusivam.  post  snbjec- 
tum  propositionis,  ante  vinculum,  ut  erat  in 
proposito  exeroplo.  Carent  autem  propositi- 
ones exclusivse  ilia  ambiguitate,  si  vel  exclu- 
Hva  particula,  ponatur  ante  subjectum  prop- 


ositionis.  vel  etiam  seqnatnr  copnlam.  Ibl 
enim  indicatur  esse  propositio  exclusiva  snb- 
jecti,  ut,  solus  homn  discurrit  Hie  autem  in- 
dicatur, esse  propositio  exclusiva  pi-aedicat^ 
nt,  Sacramenta  Nofi  Testaiiienii  suvt  tatttuin 
duo.     Praniicamtnta  tantum  drcem.'-'' 

Scheibler  then  proceeds  to  give  the  follow- 
ing general  and  special  rules  of  Exclusion : 

"I.  Generaliter  tenendum  est,  quod  aliter 
sini  expon-rulft  txclusira  a  pradicalo,  el  alitet 
exclusifa  a  subjecto. 

'*  II.  Exclusiva  propo^tio  non  exdudit  toncom- 
itantia 

"III.  Otnnis  exclusiva  rtsolcititr  in  duos srm- 
plicex,  alteram  nffinnatam,  alteram  negatam. 
Atquc  hoc  est  quod  vulgo  dicitur,  quod 
omnis  exclusiva  sit  hypothetica.  Hypotb^tica 
enim  propositio  est  quae  includit  duas  alias  in 
virtute,  vel  dispositione  sua.  Veluti  haec. 
Solus  homo  est  ral'onalis,  squivalet  bis  dua> 
bus,  Homo  est  rationalis,  et  quod  non  est  homo, 
non  est  rationale.  £t  in  specie,  Bestia  non  rsl 
rationalis.  Plnnta  non  est  rationalis.  .... 
Atque  hse  du;c  propositiones  vocautur  ejpo- 
nentes,  sicut  propositio  exclusiva  dicitur  rx- 
ponibilis. 

''  Speciales  antem  regnlie  explicandi  excln- 
sivas  sunt  octo:  sicut  et  octo  sunt  genera 
locutionum  exclusivarum. 

"  I.  Propositio  f-xclusiva  univrrsalis  a_fffrtna~ 
tiva,  citjus  signum  non  negotur,  ut,  Tantum 
omnis  homo  turrit,  exponitur  sic,  Omnis  homo 
currit,  et  nihil  aliud  ab  hotnine  ctirrit.     Vocari 

solet  luec  expositio  Pater,  quia  prior  ejus 
pars  est  universalis  affirmativa,  quod  notnt 
A.  Et,  alterae  pars  est  universalis  negativa. 
quod  indicat  in  posteriori  syllaba  litera  E 

"II.  Propositio  particularism  vel  indeftnita  of- 
firmativa,  in  qua  signum  non  negatur,  ut  Tan- 
tum homo  currit,  exponitur  sic,  Homo  ctmit,  tl 


APPENDIX.  519 

We  ought,  indeed,  as  a  corollary  of  the  postulate  already  stated,  to  require 
to  be  allowed  to  translate  into  equivalent  logical  terms  the  rhetorical  enounce- 
ment  of  common  speech.  We  should  not  do  as  the  logicians  have  been  wont, 
—  introduce  and  deal  with  these  in  their  grammatical  integrity ;  for  this  would 
be  to  swell  out  and  deform  our  science  with  mere  grammatical  accidents  ;  and 
to  such  fortuitous  accrescences  the  formidable  volume,  especially  of  the  older 
Logics,  is  mainly  owing.  In  fact,  a  large  proportion  of  the  scholastic  system  is 
merely  grammatical. 

3o,  The  whole  doctrine  of  the  non-quantification  of  the  predicate  is  onlj' 
another  example  of  the  passive  sequacity  of  the  logicians.  They  follow  obedi- 
ently in  the  footsteps  of  their  great  master.  We  owe  this  doctrine  and  its  preva- 
lence to  the  precept  and  authority  of  Aristotle.  He  prohibits  once  and  again  the 
annexation  of  the  universal  predesignation  to  the  predicate.  For  why,  he  says, 
such  predesignation  would  render  the  proposition  absurd;  giving  as  his  only  exam- 
ple and  proof  of  all  this,  the  judgment  — All  man  is  all  animal.  This,  however, 
is  only  valid  as  a  refutation  of  the  ridiculous  doctrine,  held  by  no  one,  that  any 
predicate  may  be  universally  quantified  ;  for,  to  employ  his  own  example,  what 
absurdity  is  there  in  saying  that  some  animal  is  all  man  !  Yet  this  nonsense 
(be  it  spoken  with  all  reverence  of  the  Stagirite)  has  imposed  the  precept  on 
the  systems  of  Logic  down  to  the  present  day.  Nevertheless,  if  could  be  shown 
by  a  cloud  of  instances  from  the  Aristotellc  writings  themselves,  that  this  rule  is 
invalid ;  nay,  Aristotle's  own  doctrine  of  Induction,  which  is  far  more  correct 
than  that  usually  taught,  praceeds  upon  the  silent  abolition  of  the  erroneous 
canon.  The  doctrine  of  the  logicians  is,  therefore,  founded  on  a  blunder; 
which  is  only  doubled  by  the  usual  avennent  that  the  predicate,  in  what  are 
technicall}'  called  reciprocal  propositions,  is  taken  universally  vi  materia;  and 
not  vi  formce. 

But,  4°,  The  non-quantification  of  the  predicate  in  thought  is  given  up  by 
the  logicians  themselves,  but  only  in  certain  cases  where  they  were  forced  to 
admit,  and  to  the  amount  which  they  could  not  possibly  deny.     The  predicate, 


nihil  aliud  ab  homine  currit.    Vocatur  hacc  ex-  aliquid   aliiid  ab  homine    non   curril,    vocatur 

positio  XisK.  Fecit. 

"III.  Propositio  exdttsiva,  in  qua  signum  non  "  VII.  Exdusica,  in  qua  signum  negatur,  ex- 

negatur,  universalis  negativa,  ut,  TantuTn  nuUus  isiens  particularis  qffirmativa,  ut,  Non   tantuni 

homo  currit,  exi)Onitur  sic,  NuUui  homo  currit.  aliquis  homo  currit,  expositur  sic,  Aliquis  homo 

tt  quodlibet  aliud  ab  homine  currit,  vocatur  Te-  currit,  aliquia  aliud  ab  homine  currit,  vocatur 

WAX.  I'lLOS. 

"IV.  Exrlusivacujus  signum  non  negatur  par-  "VIII.  Negativa  particularis  exclusivm  prop- 

'.ieularis  vet  indefinita  negativa,  ut,  Tantum  homo  ositiones,  cvjus  signum  negatur,  ut,  Non  tantuni 

non  cnrrit,  exponitur   sic,   Homo  non   currit,  aliqais  homo  non  ctirrit,  exponitur  sic,  Aliquis 

tt   quodlibet  cUiutl    ab    homine    currit,   vocatur  homo  non  currit,  et  aliquid  aliud  ab  homine  non 

STORAX.  currit,  vocatur  NOBIS. 

"V.   Exclusiva,  in  qua  signum  negatur,  affir-  '•  Differentia  autem  propositionis  exclusivas 

mativa  et  universalis,  ut,  Non  tantum  omnis  et  exceptivae  est  evidens.    Nempe  exclusiva 

homo  currit,  exponitur  sic,  Omnis  homo  currit,  praedicatum  vendicat  uni  subjecto,  aut  a  sub- 

(t    aliquod   aliud   ab    homine    currit,  vocatur  jecto  excludit  alia  praedicata,  ut,  Solus  Devs 

Canos.  bonus  est.    Exceptiva  autem  statuit  universale 

*^  y I.  In  qua  signum  negatur,  txistensuniver-  subjectum,  iudicatque  aliquid  contineri   sub 

salis  affirmativa,  ut,  Non  tantum  nullus  homo  isto  universali,  de  quo  nou  dicatur  prasdica- 

currit,  sic    exponitur,   Nullus    homo  currit,  et  turn,  ut,    Omne  anim<d  est  irrationals,  preeter 

hominem.''^  —  ED.] 


620 


APPENDIX. 


they  confess,  is  quantified  by  particularity  in  affirmative,  by  universality  in  nega- 
tive, propositions.  But  why  the  quantification,  formal  quantification,  should 
be  thus  restricted  in  thought,  they  furnish  us  with  no  valid  reason. 

To  these  two  errors  I  might  perhaps  add,  as  a  third,  the  confusion  and  per- 
plexity arising  from  the  attempt  of  Aristotle  and  the  logicians  to  deal  with  in- 
definite (or,  as  I  would  call  them,  indesignale)  terms,  instead  of  treating  them 
merely  as  verbal  ellipses,  to  be  filled  up  in  the  expression  before  being  logically 
considered ;  and  I  might  also  add,  as  a  fourth,  the  additional  complexity  and 
perplexity  introduced  into  the  science  by  viewing  propositions,  like>vise,  as 
affected  by  the  four  or  six  modalities.     But  to  these  I  shall  not  advert. 

These  are  the  two  principal  errors  which  have  involved  our  systems  of  Lc^ic 
in  confusion,  and  prevented  their  evolution  in  simplicity,  harmony,  and  com- 
pleteness ;  —  which  have  condemned  them  to  bits  and  fragments  of  the  science, 
and  for  these  bits  and  fragments  have  made  a  load  of  rules  and  exceptions 
indispensable,  to  avoid  falling  Into  frequent  and  manifest  absurdity.  It  was  In 
reference  to  these  two  errors  chiefly  that  I  formerly  gave  aou  as  a  self-evident 
Postulate  of  Logic  —  "  Explicitly  to  state  what  hats  been  implicitly  thought ; " 
in  other  words,  that  before  dealing  logically  with  a  proposition,  we  are  entitled 
to  undei-stand  it ;  that  Is,  to  ascertain  and  to  enounce  its  meaning.  This  quali- 
fication of  the  predicate  of  a  judgment  Is,  Indeed,  only  the  beginning  of  the 
application  of  the  Postulate ;  but  we  shall  find  that  at  every  step  it  enables  us 
to  cast  away,  as  useless,  a  multitude  of  canons,  which  at  once  disgust  the  student, 
and,  if  not  the  causes,  are  at  least  the  signs,  of  imperfection  in  the  science. 

I  venture,  then,  to  assert  that  there  is  only  one  species  of  Convoreion,  and  that 
one  thorough-going  and  self-sufficient.  I  mean  Pure,  or  Simple  Conversion. 
The  other  species  —  all  are  admitted  to  be  neither  thorough-going  nor  self- 
sufficient —  they  are  In  fact  only  other  logical  processes,  accidentally  combined 
with  a  transposition  of  the  subject  and  predicate.  The  conversio  per  accidens 
of  Boetnlus,  as  an  ampliative  operation,  has  no  logical  existence  ;  it  is  material 
and  precarious,  and  has  righteously  been  allowed  to  drop  out  of  science.  It 
is  now  merely  a  historical  curiosity.  As  a  Restrictive  operation,  in  which  re- 
lation alone  It  still  stands  in  our  systems,  it  Is  either  merely  fortuitous,  or 
merely  possible  through  a  logical  process  quite  distinct  from  Conversion ;  I 
mean  that  of  Restriction  or  Subalternatlon,  which  will  be  soon  explained. 
Converaio  per  contrapositionem  is  a  change  of  terms,  —  a  substitution  of  new 
elements,  and  only  holds  through  contradiction,^  being  just  as  good  without  as 


I  [See  Aristotle,  Topica,  L.  ii.  c.  8.  Scotus, 
Bannes,  Mendoza,  silently  following  each 
other,  have  held  that  contraposition  is  only 
mediate,  inflnitation,  requiring  Constantia, 
etc.  Wholly  wrong.  See  Arringa.  Cursus 
PMlnsophicvs,  D.  II  s.  4.  p.  18.  "Observan- 
dum  est  prwdictas  C(>n8e(iueiitias  (per  contra- 
positionem) malas  esse  et  instiibilcB,  nisi  r.c- 
cesscrit  alia  jiropositio  in  antecedenii  qua; 
impartit  existentiam  subjecti  consequeiitis. 
Tunc  enim  firma  erit  consequentia,  e.  s- 
Omnis  homo  est  albus  et  non  alburn  est,  er^o 
otnne  non  album  est  non  homo.    Alioquin   si 


eonstantiam  illam  uon  posueris  in  antecedenti, 
instabitur  illi  consequentia;  iu  eveutu,  in  quo 
nihil  sit  non  album,  et  omnis  homosit  albus.'' 
Baunes,  Instit.  Min.  Dial.  L.  vi.  c.  2,  p.  590. 
—  Ed.] 

Rule  for  Finite  Prejacents  given. 

With  the  single  exception  of  E  n  E  ( A  n  A), 
the  other  seven  propositions  may  be  converted 
by  Counterposifion  under  tlic  following  rule, 
— '  Let  the  terms  be  inlinitated  and  transposed, 
the  predesignations  remaining  as  before  ' 

With  the  two  additional  e.Kceptions  of  the 
two  convertible  propositions,  A  f  I,  and  I  f 


APPENDIX. 


521 


with  conversion.  The  Contingent  Conversion  of  the  lower  Greeks^  is  not.  a 
conversion,  —  is  not  a  logical  process  at  all,  and  has  been  worthily  ignored  by 
the  Latin  world.  But  let  us  now  proceed  to  see  that  Simple  Conversion,  as  I 
have  asserted,  is  thorough-going  and  all-sufficient.  Let  us  try  it  in  all  the 
eiglit  varieties  of  categorical  propositions.  But  I  shall  leave  this  explication  to 
yourselves,  and  in  the  examination  will  call  for  a  statement  of  the  simple  con- 
version, as  applied  to  all  the  eight  propositional  forms. 

It  thus  appears  that  this  one  method  of  conversion  has  every  advantage 
over  those  of  the  logicians.  1°,  It  is  Natural ;  2°,  It  is  Imperative ;  3°,  It  is 
Simple ;  4°,  It  is  Direct ;  5°,  It  is  Precise  ;  6°,  It  is  thorough-going :  Whereas 
their  processes  are  —  1°,  Unnatural;  2°,  Precarious;  3°,  Complex;  4°,  Cir- 
cuitous ;  5°,  Confused ;  6°,  Inadequate :  breaking  down  in  each  and  all  of 
their  species.  The  Greek  Logicians,  subsequent  to  Aristotle,  have  well  and 
truly  said,  a.vTi<TTpo<pT]  i<mv  i(To<TTpo<l>^  ns, "  omnis  conversio  est  aequiversio;  "  *  that 
is,  all  conversion  is  a  conversion  of  equal  into  equal ;  and  had  they  attended 
to  this  principle,  they  would  have  developed  conversion  in  its  true  unity  and 
simplicity.     They  would  have  considered,   1°,  That  the  absolute  quantity  of 


A,  the  inflnitated  propositions  hold  good 
without  the  transposition  of  the  terms. 

Rule  for  Iiiflulte  Prejacents  given. 

With  the  single  exception  of  n  I  f  n  I  (nE 
=  u  =  uE  being  impossible),  the  other  six 
propositions  may  be  converted  by  Counter- 
position  under  the  following  rule,  —  '  Let  the 
terms  be  unintinitated  and  transposed,  the 
predesignations  remaining  as  before.' 

Contraposition  is  not  explicitly  evolved  by 
Aristotle  in  Prior  Analytics,  but  is  evolved 
from  his  Topics,  L.  ii.  cc.  1,  8,  alibi.  De  Inter' 
pretatione,  c.  14.  See  Conimbricenses,  In  Arist. 
Dial.,  An.  Prior.,  L.  i.  q.  i.  p.  271.  Bannes, 
Instit.  Minoris  Dialectics,  L.  v.  c.  2,  p.  532. 
Burgersdicius,  Instit.  Log-  L.  i.  c.  32. 

First  explicitly  enounced  by  Averroes,  ac- 
cording to  Molinaeus  (Elementa  Logica,  L.  i. 
c.  4,  p.  54).  1  cannot  tlnd  any  notice  of  it  in 
Averroes.  Ue  ignores  it,  name  and  thing. 
It  is  in  Anonymus,  De  Syllogismn,  f.  42  b.,  in 
Kicephorus  Blemmidas,  Epit.  Log.,  c.  xxxi. 
p.  222 ;  but  long  before  him  Boethius  has  all 
the  kinds  of  Conversion, —  Simplex,  Per  Acci- 
dens,  et  Per  Opposilionem  (Introdnctio  ad  SyUo- 
gismos,  p.  576),  what  he  calls  Per  Contraposi- 
tionem  [De  Syllogismo  Calegorico,  L.  i.  589). 
Is  he  the  inventor  of  the  name?  It  seems  so. 
Long  before  Boethius,  Apuleius  (in  second 
century)  has  it  as  one  of  the  five  species  of 
Conversion,  but  gives  it  no  name  —  only  de- 
scriptive; sec  De  HabitwI.  Doct.  Plat.,  L.  iii.  p. 
33.  Alexander,  In  An.  Pr..  i.  c.  2.  f.  10  a,  has 
it  as  of  propositions,  not  of  terms,  which  is 
conversion  absolutely.  Vide  I'hiloponus.  In 
An.  Pr.,  I.  f.  12  a.  By  tliem  called  ai/rto-TpofpT; 
oliv  OLfT i^(<Tfi.  So  Magentinus,  In  An.  Prior  , 
i.  2,  f.3b. 


That  Contraposition  is  not  properly  Con 
version  —  (this  being  a  species  of  consequence) 

—  an  aequipoUence  of  propositions,  not  a  con- 
version of  their  terms. 

Noldius,  Logica  Recognita,  c.  xii.  p.  299 
Crakanthorpe,  Logica,  L.  iii.  c.  10,  p.  180. 
Bannes,  Instit.  Min.  Dial.,  L.  v.  c.  2,  p.  530. 
Eustachius,  Summa  Pkilosopkice,  Logica,  P.  II 
tract,  i.  q.  3,  p.  104.  Ilerbart,  Lehrbuch  der 
Logik,  p.  78.  Scotus,  Quastiones,  In  An.  Prior., 
L.  i.  q.  lo,  f.  258  b.  Chauvin,  v.  Conversio. 
Isendoorn,  Cursus  Logicus,  p.  308. 

That  Contraposition  is  useless  and  perplex- 
ing. See  Chauvin,  v.  Conversio.  Arriaga, 
Cursus,  Philosopliicus,  p.  18.  Titius,  Ars  Cogi- 
tandi,  c.  viii.  §  19  et  seq.  D"Abra  de  Kaconis, 
Tot.  Phil.  Tract.,  Logica,  ii.  qu.  4,  p.  315. 
Bannes,  Instit.  Min.  Dial.,  p.  529] 

1  [Blemmidas.]  [Epitoine  Logica,  c.  31,  p. 
222.  The  following  extract  will  explain  the 
nature  of  this  conversion.  'H  S'  iu  Trpora- 
aeai  yivofj.fi/y)  auicTTpo^^,  r]  T'})*'  fieu  ra^iu 
Twi/  '6pwv  (pvKarrfi,  rhv  avThu  rripovaa  kut- 
riyopovfj,(vov  koI  rhv  avThv  vwoKfifievou ' 
ix6vtiv  8*  TTjc  'iroi6T7YTa  fiSTu^aWfi,  iroiovcra 
T7)j/  airo<paTiKi]v  ir^ioTeaiv  KaracpaTiKTqv,  koI 
Kara<pa,riicr}v  a.ito(pariKi)v.  Ko2  Ae-yerai 
oSttj  ^j/SexoMfVij  a.vTi<TTpo<pi],  ws  ^nl  ixoinjs 
T^y  ^fSexOiUfVes  KAtjs  (TwitTTafJifvi)  '  oiov, 
Tts  iv^pojiroi  Koverai,  tis  w^pKinros  ov  \ov- 
T]Tcu'  avTT)  S'  ovK  tiu  €^7)  Kvp'iws  afTiarpocpr}. 
This  so-called  contingfnt  conversion  is  in  fact 
nothing  more  than  the  assertion,  ippeatcd  by 
many  Latin  logicians,  that  in  contingent  mat- 
ter subcontrary  propositions  are  both  tru«. 

—  Kd.] 

2  See  p.  515.  —  Ed. 

6G 


522 


APPENDIX. 


the  propositioi>,  be  it  convertend  or  converse,  remains  always  identicjd ;  2', 
That  the  several  quantities  of  the  t-ollated  notions  remain  always  identical,  tho 
whole  change  being  the  transposition  of  the  (juantified  notion,  which  was  in  the 
subject  place,  into  the  place  of  predicate,  and  tnce  versa. 

Aristotle  and  the  logicians  were,  therefore,  wrong ;  1°,  In  not  considering 
the  proposition  simply  as  the  complement,  that  is,  as  the  etjuation  or  non-equa- 
tion, of  two  compared  notions,  but,  on  the  contrary,  considering  it  as  de- 
termined in  its  quantity  by  one  of  these  notions  more  than  by  the  other.  2°, 
They  were  wrong  in  according  too  great  an  importance  to  the  notions  con- 
sidered as  propositional  terms,  that  is,  as  subject  and  predicate,  independently 
of  the  import  of  these  notions  in  themselves.  3°,  They  were  wiong  in  ac- 
cording too  preponderant  a  weight  to  one  of  these  terms  over  the  other;  but 
differently  in  different  parts  of  the  system.  For  they  v.ore  wrong,  in  the  doc- 
trine of  Judgment,  in  allowing  the  quantity  of  the  proposition  to  be  determined 
exclusively  by  the  quantity  of  the  subject  term ;  whereas  they  were  wrong,  as 
we  shall  see,  in  the  doctrine  of  Reasoning,  in  considering  a  syllc^sm  as  ex- 
clusively relative  to  the  quantity  of  the  predicate  (extension).  So  mui;h  for 
the  theory  of  Conversion.  Before  concluding,  I  have,  however,  to  observe,  as 
a  correction  of  the  prevalent  ambiguity  and  vacillation,  that  the  tw'o  oroposi- 
tions  of  the  process  together  might  be  called  the  coiwertenl  or  converting  (pro- 
positiones  convertentes)  ;  and  whilst  of  these  the  original  proposition  is  named 
the  convertend  (propositio  convertenda),  its  product  would  obtain  the  title  of 
converse,  converted  (propositio  conversa)} 

The  other  species  of  Immediate  Inference  will  not  detain  us  long.  Of  these, 
there  are  two  noticed  by  the  logicians. 

The  first  of  these,  Equipollence  (cequipollentia),  or,  as  I  would  term  it.  Double 
Negation,  is  deserving  of  bare  mention.  It  is  of  mere  grammatical  relevancy. 
The  negation  of  a  negation  is  tantamount  to  an  affirmation,  li  is  not  not-A,  is 
manifestly  only  a  roundabout  way  of  saying  B  is  A ;  and,  vice  versa,  we  may 
express  a  position,  if  we  perversely  choose,  by  sublating  a  sublation.  The 
immediate  inference  of  Equipollence  is  thus  merely  the  grammatical  translation 
of  an  affirmation  into  a  double  negation,  or  of  a  double  negation  into  an 
affirmation.  Non-nxiUus  and  non-nemo,  for  example,  are  merely  other  gram- 
matical expressions  for  aliquis  or  quidam.  So  Nonnihil,  Nonnunquam,  Nonnus- 
quam,  etc. 

The  Latin  tongue  is  almost  peculiar  among  languages  for  such  double  negjt- 
tives  to  express  an  affirmative.  Of  course  the  few  which^  have  found  their  place 
in  Lofflc,  instead  of  being  despised  or  relegated  to  Grammar,  liave"beeii  fondly 
commented  on  by  the  ingenuity  of  tbc  scholastic  logicians.  In  English,  some 
authors  are  fond  of  this  inilirect  and  idle  way  of  speaking ;  they  prefer  saying 
—  "'I  entertain  a  not  unfavorable  opinion  of  such  a  one,"  to  saying  directly,  I 
entertain  of  him  a  favorable  opinion.     Neglecting  this,  I  pass  on  to 

The  third  sj)ecics  of  Immediate  Inference,  notii;ed  by  tlie  logicians.  This 
they  call  Siibalternation,  but  it  may  be  more  unambiguously  styled  Restrictipn. 
If  I  have  £100  at  my  credit  in  the  bank,  it  is  evident  that  I  may  draw  for  £5  or 
£lO.     In  like  manner,  if  I  can  say  unexclusively  that  all  men  are  aninutls,  I  can 


1  Sec  p.  185. —  Ed. 


APPENDIX.  523 

say  restrictively,  that  negroes  or  any  other  fraction  of  mankind  are  animals.    This 
restriction  is  Bilateral,  when  we  restrict  both  subject  and  predicate,  as : 

AU  Triangle  is  all  trilateral.  All  rational  is  all  risible. 

.'.Some  triangle  is  some  trilateral.  .■.Some  rational  is  some  risible. 

It  is  Unilateral,  by  restricting  the  omnitude  or  universality  either  of  the  Subject 
or  of  the  Predicate. 


Of  the  Subject  — 
Of  the  Predicate,  as- 


AH  man  is  some  animal ; 
.Some  man  is  some  animal. 

Some  animal  is  all  risible  ; 
.Some  animal  is  some  risible. 


It  has  not  been  noticed  by  the  logicians,  that  there  is  only  an  inference  by 
this  process,  if  the  some  in  the  inferred  proposition  means  some  at  least,  that  is, 
some  not  exclusive  of  all ;  for  if  we  think  by  the  some,  some  only,  that  is,  some, 
not  all,  so  far  from  there  being  any  competent  inference,  there  is  in  fact  a  real 
opposition.  The  logicians,  therefore,  to  vindicate  their  doctrine  of  the  Opposi- 
tion of  Subalternation,  ought  to  have  declared  that  the  some  was  here  in  the 
sense  of  .tome  only ;  and  to  vindicate  their  doctrine  of  the  Inference  of  Subal- 
ternation, they  ought,  in  like  manner,  to  have  declared,  that  the  some  was  here 
taken  in  the  counter  sense  of  some  at  least.  It  could  easily  be  shown  that 
the  errors  of  the  logicians  in  regard  to  Opposition  are  not  to  be  attributed  to 
Aristotle. 

Before  leaving  this  process,  it  may  be  proper  to  observe  that  we  might  well 
call  its  two  propositions  together  the  restringent  or  restrictive  (propositiones 
restringentes  vel  restrict ivce)  ;  the  given  proposition  might  be  called  the  restrin~ 
gend  (propositio  restringenda),  and  the  product  the  restrict  or  restricted  (propo- 
sitio  restricta). 

So  much  for  the  species  of  Immediate  Inference  recognized  by  the  logicians. 

There  is,  however,  a  kind  of  immediate  inference  overlooked  by  logical 
writers.  I  have  formerly  noticed  that  they  enumerate  (among  the  species  of 
Opposition)  Subcontrariety  (subcontrarietas,  vTr€vavTi6ri\s),  to  wit, — some  is, 
some  is  not ;  but  that  this  is  not  in  fact  an  opposition  at  all  (as  in  truth  neither 
is  Subalternation  In  a  certain  sense).  Subcontrariety,  in  like  manner.  Is  with 
them  not  an  opposition  between  two  partial  somes,  but  between  different  and 
different;  in  fact,  no  opposition  at  all.  But  if  they  are  thus  all. wrong  by 
commission,  they  are  doubly  wrong  by  omission,  for  they  overlook  the  Immediate 
Inference  which  the  relation  of  propositions  in  Subcontrariety  affords.  This, 
however.  Is  sufficiently  manifest.  If  I  can  say.  All  men  are  some  animals,  or 
Some  animals  are  all  men,  I  am  thereby  entitled  to  say,  —  All  men  are  not  some 
animals,  or  Some  animals  are  not  .some  men.  Of  course  here  the  some  In  the 
inferred  propositions  means  some  other,  as  in  the  original  proposition,  some 
ordy ;  but  the  inference  Is  perfectly  legitimate,  being  merely  a  necessary 
explication  of  the  thought;  for,  inasmuch  as  I  think  and  say  that  all  men  are 


524 


APPENDIX. 


some  animals,  I  can  think  and  say  that  they  are  some  animals  only,  which 
implies  that  they  are  a  certain  some,  and  not  any  other  animals.^  This  infer- 
ence is  thus  not  only  to  some  others  indefinitely,  but  to  all  others  definitely.  It 
is  further  either  affirmative  from  a  negative  antecedent,  or  negative  from  an 
affirmative.  Finally,  it  Is  not  bilateral,  as  not  of  subject  and  predicate  at  once; 
but  it  Is  unilateral,  either  of  the  subject  or  of  the  predicate.  This  Inference 
of  Subcontrarlety  I  would  call  Integration,  because  the  mind  here  tends  to 
determine  all  the  parts  of  a  whole,  whereof  a  part  only  has  been  given.  The 
two  propositions  together  might  be  called  the  integral  or  integrant  (propositiones 
intcgrales  vel  integrantes).  The  given  proposition  would  be  styled  the  integrand 
(propositio  integranda)  ;  and  the  product,  the  integrate  (proposUio  integrata)} 

I  may  refer  you,  for  various  observations  on  the  Quantification  of  the  Predi- 
cate, to  the  collection  published  under  the  title,  Discussions  on  Philosophy  and 
Literature. 


The  grand  general  or  dominant  result  of  the  doctrine  on  which  I  have 
already  partially  touched,  but  which  I  will  now  explain  consecutively  and  more 
in  detail,  is  as  follows  :  —  Touching  Propositions,  —  Subject  and  Predicate ;  — 
touching  Syllogisms,  —  In  Categoricals,  Major  and  Minor  Tei-ms,  Major  and 
Minor  Premises,  Figures  First,  Second,  Third,  Fourth,  and  even  what  I  call 
No  Figure,  are  all  made  convertible  with  each  other,  and  all  conversion  re- 
duced to  a  simple  etjuation ;  whilst  in  Hypothetlcals,  both  the  species  (viz., 
Conjunctive  and  Disjunctive  reasonings)  are  shown  to  be  forms  not  of  mediate 
argumentation  at  all,  but  merely  complex  varieties  of  the  immediate  inference 
of  Restriction  or  Subalternation,  and  are  relieved  of  a  load  of  perversions, 
limitations,  exceptions,  and  rules.  The  differences  of  Quantity  and  Quality, 
etc.,  thus  alone  remain ;  and  by  these  exclusively  are  Terms,  Propositions,  and 
Syllogisms  foimally  distinguished.  Quantity  and  Quality  combined  constitute 
the  only  i-eal  discrimination  of  Syllogistic  Mood.  Syllogistic  Figure  vanishes, 
with  Its  perplexing  apparatus  of  special  rules ;  and  even  the  General  Laws  of 
Syllogism  proper  are  reduced  to  a  single  compendious  canon. 

This  doctrine  is  founded  on  the  postulate  of  Logic  :  —  To  state  In  language 
what  is  efficient  in  thought ;  in  other  woixls,  Before  proceeding  to  deal  logically 
with  any  proposition  or  syllogism,  we  must  be  allowed  to  determine  and  express 
what  it  means. 

First,  then,  in  regard  to  Propositions  :  In  a  proposition,  the  two  terms,  the 
Subject  and  Predicate,  have  each  their  quantity  in  thought  This  quantity  is 
not  always  expressed  in  language,  for  lariguage  tends  always  to  abbreviation  ; 
but  it  is  always  understood.  For  example,  in  the  proposition,  Men  are  animals, 
what  do  we  mean  ?    We  do  not  mean  that  some  men,  to  the  exclusion  of  others, 


1  If  we  gay  some  animal  is  all  man,  and 
fome  animal  is  not  any  man.  —  in  that  case,  we 
<nu8t  hold  some  as  meaaiug  some  only.  We 
ir.uy  have  a  mediate  syllogism  on  it,  as  : 

Somr;  animnU  are  aU  nten  ; 

Some  aniinob  are  not  any  man  : 

Xher^ort,  tome  atunivfk  art  not  souie  animals. 


2  Mem.  Immediate  inference  of  Contradic- 
tion omitted.  Also  of  Relation,  which  would 
come  under  Equipollence.  [For  Tabular 
Schemes  of  Prepositional  Forms,  and  of 
their  Mutual  Relations,  see  pp.  629,  630.  -» 
Ed.] 


APPENDIX.  525 

are  animals,  but  we  use  the  abbreviated  expression  7n«n  for  the  thought  aZZ  Tnen. 
Logic,  therefore,  in  virtue  of  its  postulate,  warrants,  nay  requires^  us  to  state 
this  explicitly.  Let  ais,  therefore,  overtly  quantify  the  subject,  and  say,  All 
men  are  animals.  So  far  we  have  dealt  with  the  proposition,  —  we  have  quan- 
tified in  language  the  subject,  as  it  was  quantified  in  thought. 

But  the  predicate  still  remains.  We  have  said  —  All  men  are  animals.  But 
what  do  we  mean  hy  animals?  Do  we  mean  aZ^  animals,  ov  some  animals  f 
Not  the  former ;  for  dogs,  horses,  oxen,  etc.,  are  animals,  as  well  as  men ;  and 
dogs,  horses,  oxen,  etc.,  are  not  men.  Men,  therefore,  are  animals,  but  exclu- 
sively of  dogs,  horses,  oxen,  etc.  All  men,  therefore,  are  not  equivalent  to  all 
animals  ;  that  is,  we  cannot  say,  as  we  cannot  think,  that  all  men  are  all  ani- 
mals. But  we  can  say,  for  in  thought  we  do  affirm,  that  all  men  are  some  animals. 

But  if  we  can  say,  as  we  do  think,  that  all  men  are  some  animals,  we  can,  on 
the  other  hand,  likewise  say,  as  we  do  think,  that  some  animals  are  all  men. 

If  this  be  true,  it  is  a  matter  of  indifference,  in  a  logical  point  of  view 
(whatever  it  may  be  in  a  rhetorical),  which  of  the  two  terms  be  made  the 
subject  or  predicate  of  the  proposition ;  and  whichsoever  term  is  made  the 
subject  in  the  first  instance,  may,  in  the  second,  be  converted  into  the  predi- 
cate ;  and  whichsoever  term  is  made  the  predicate  in  the  first  instance,  may,  in 
the  second,  be  converted  into  the  subject 

From  this  it  follows  — 

1°,  That  a  proposition  is  simply  an  equation,  an  identification,  a  bringing 
into  congruence,  of  two  notions  in  respect  to  their  Extension.  I  say,  in  re- 
spect to  their  Extension,  for  It  Is  this  quantity  alone  which  admits  of  ampliation 
or  restriction,  the  Comprehension  of  a  notion  remaining  always  the  same, 
being  always  taken  at  its  full  amount. 

2*,  The  total  quantity  of  the  proposition  to  be  converted,  and  the  total 
quantity  of  the  proposition  the  product  of  the  conversion,  is  always  one  and 
the  same.  In  this  unexcluslve  point  of  view,  all  conversion  is  merely  simple  con- 
version ;  and  the  distinction  of  a  conversion,  as  it  is  called,  hy, accident,  arises 
only  from  the  partial  view  of  the  logicians,  who  have  looked  merely  to  the 
quantity  of  the  subject.  They,  accordingly,  denominated  a  proposition  univer- 
sal or  particular,  as  Its  subject  merely  was  (quantified  by  the  predeslgnation 
some  or  all ;  and  where  a  proposition  hke,  All  men  are  animals  (In  thought, 
some  animals),  was  converted  into  the  proposition,  Some  animals  are  men  (In 
thought,  all  men),  they  erroneously  supposed  that  It  lost  quantity,  was  restricted, 
and  became  a  particular  proposition. 

It  can  hardly  be  said  that  the  logicians  contemplated  the  reconversion  of 
such  a  proposition  as  the  preceding;  for  they  did  not  (or  rarely)  give  the  name 
of  conversio  per  accidens  to  the  case  In  which  the  proposition,  on  their  theory, 
was  turned  from  a  particular  into  a  universal,  as  when  we  reconvert  the  prop- 
osition. Some  animals  are  men,  Into  the  proposition,  All  men  are  animals.'^      They 


1  See  above,  p.  186.  —  Ed.  [A  mistake  by  For  Aristotle  uses  the  terms  universal,  and 
logicians  in  general,  that  partial  conversion,  partial  conversion^  simply  to  express  whether 
^M  jtis'pcj,  is  the  mere  synonym  of  per  awiVenj,  the  convertens  is  a  universal  or  particular 
and  that  the  former  is  so  used  by  Aristotle,  proposition.  See  §  4  of  the  chapter  on  Con- 
See  Vallius,  Logica,  t.  ii.  1    t.  q.  i.  c.  2,  p.  32.  version  (An.  Prior.,  i.  2),  where  particular  af 


h 


52G  APPENDIX. 

Kkcwisc  neglected  such  affirmative  propositions  as  Iiad  in  thought  both  subjecx 
and  predicate  quantified  to  their  whole  extent;  ?cS,  AH  triangular  Jigure  is  trilate- 
ral, that  is,  if  expressed  iis  understood,  All  trkintju'ar  is  all  trilateral  figure^  — 
AH  rational  is  risible,  that  is,  if  explicitly  enounced,  All  ralional  is  all  rmhle 
animals.  Aristotle,  and  subsequent  logicians,  had  indeed  frequently  to  do  with 
propositions  in  which  the  predicate  was  taken  in  its  full  extension.  In  these 
the  logicians  —  but,  be  it  observed,  not  Aristotle — attempted  to  remedy  the 
imperfection  of  the  Aristotelic  doctrine,  which  did  not  allow  the  quantification 
of  the  predicate  to  be  taken  logically  or  formally  into  account  in  affirmative 
propositions,  by  asserting  that  in  the  obnoxious  cases  the  predicate  was  dis- 
tributed, that  is,  fully  quantified,  in  virtue  of  the  matter,  and  not  in  virtue  of 
the  form  (^vi  materia,  non  ralione  formce).  But  this  is  altogether  erroneous. 
For  in  thought  we  generally  do,  nay,  often  must,  fully  quantify  the  predicate. 
In  our  logical  conversion,  in  fact,  of  a  proposition  like  All  men  are  animals, — 
some  animals,  we  must  formally  retain  in  thought,  for  we  cannot  formally 
al)olish,  the  universal  quantification  of  the  predicate.  We,  accordingly,  must 
formally  allow  the  proposition  thus  obtained,  Some  animals  we  all  men. 

The  error  of  the  logicians  is  further  shown  by  our  most  naked  logical  nota- 
tion ;  for  it  is  quite  as  easy  and  quite  as  natural  to  quantify  A,  B,  or  C,  as  pre- 
dicate, as  to  quantify  A,  B,  or  C,  as  subject.  Thus,  All  B  is  some  A  5  Some  A 
is  all  B. 


A, 


:B 


I  may  here  also  animadvert  on  the  counter  defect,  the  counter  error,  of  the 
logicians,  in  their  doctrine  of  Negative  Propositions.  In  negative  propositions 
they  say  the  predicate  is  always  distributed,  —  always  taken  in  its  full  exten- 
sion. Now  this  is  altogether  untenable.  For  we  always  can,  and  frequently 
do,  think  the  predicate  of  negative  propositions  as  only  partially  excluded  from 
the  sphere  of  the  subject.  For  example,  we  can  think,  as  our  naked  diagrams 
can  show, —  All  men  are  not  some  animals,  that  is,  not  irrational  animals.  In 
point  of  fact,  so  often  as  we  think  a  subject  as  partially  included  within  the 
sphere  of  a  predicate,  co  ipso  we  think  it  as  partially,  that  is,  particularly, 
excluded  therefrom.  Logicians  are,  therefore,  altogether  at  fault  in  their 
doctrine,  that  the  predicate  is  always  distributed,  t.  «.,  always  universal,  in 
negative  propositions.^ 


firmatives  arc  said    to   be  necessarily  con- 
verted, 4v  /ut'pfi. 

Conversio  per  acculrns  is  in  two  forms  differ- 
ently defliied  by  different  logicians.  Tlie  first 
by  Doetliiim,  by  v.lioin  the  nume  was  origin- 
ally given,  is  that  in  which  the  quantity  of 
the  proposition  is  contingently  changed 
either  from  greater  to  less,  or  from  less  to 
greater,  na'.va.  xcriktte,  the  quality  of  the  terms 


and  propositions  remaining  always  the  same. 
So  Kidiger,  De  Sensu  Veri  et  Falti,  p.  SOS. 
The  second  is  that  of  logicians  in  general, 
where  the  quantity  of  the  proposition  is  di- 
minished, the  quality  of  tlic  propositions  and 
terms  remaining  the  same,  salva  xfritatf.] 

1  Melanchthon  I  Erotetnaln.  L.  ii.  i>  Con- 
veninnf,  p.  516),  followed  by  his  pupil  and 
commentator  Strigelius    (/»  EroUtiuUa,  p^ 


APPENDIX. 


527 


But,  3°,  If  the  preceding  theory  be  true,  —  if  it  be  true  that  subject  and 
predicate  are,  as  quantified,  always  simply  convertible,  the  proposition  being 
in  fact  only  an  enouncement  of  their  equation,  it  follows  (and  this  also  is  an 
adequate  test)  that  we  may  at  will  identify  the  two'  terms  by  making  them  both 
the  subject  or  both  the  predicate  of  the  same  proposition.  And  this  we  can 
do.  For  we  can  not  only  say  —  as  A  in  B,  so  conversely  B  «  A,  or  as  All  men 
are  some  animals,  so,  conversely,  Some  animals  are  all  men;  but  equally  say  — 
A  and  B  are  convertible,  or,  Convertible  are  B  and  A ;  AU  men  and  some  ani- 
mals are  convertible  (that  is,  some  convertible  things),  or.  Convertible  (that  is,- 
some  convertible  things)  are  some  animals  and  all  men.  By  convertible,  I  mean 
the  same,  the  identical,  the  congruent,  etc.^. 


576,  581),  and  by  Kcckermann  (Syst.  Log. 
Minus,  L.  ii.  c.  3,  Op.  p.  222),  and  others, 
thinks  that  "there  is  a  greater  force  of  the 
particle  none  {niiUiis,  not  any),  than  of  the 
I)article  all  (oninis).  For,  in  a  universal  neg- 
ative, the  force  of  the  negation  is  so  spread 
over  the  whole  proposition,  that  in  its  con- 
version the  same  sign  is  retained  (as  —  No 
star  is  ronsumeci ;  therefore,  no  flame  which,  is 
consumed  is  a  ftar):  whereas  such  conversion 
does  not  take  place  in  a  universal  affirma- 
tive." This  Strigelius  compares  to  the  dif- 
fusion of  a  ferment  or  acute  poison;  adding 
that  the  affirmative  particle  is  limited  to  the 
subject,  whilst  the  negative  extends  to  both 
subject  and  predicate,  in  other  words,  to  the 
whole  proposition. 

This  doctrine  is  altogether  erroneous.  It  is 
an  erroneous  theory  devised  to  explain  an 
erroneous  practice.  In  thg  first  place,  we 
have  here  a  commutation  of  negation  with 
quantification;  and,  at  the  same  time,  con- 
verj;ion.  direct  conversion  at  least,  will  not 
be  said  to  change  the  quality  cither  of  a  neg- 
ative or  affirmative  proposition.  In  the  sec- 
ond place,  it  cannot  be  pretended  that  nega- 
tion has  an  exclusive  or  even  greater  affinity 
to  universal  than  to  particular  quantification. 
VTe  can  equally  well  say  not  some,  not  all,  not 
antj ;  and  the  reason  why  one  of  these  forms 
is  preferred  lies  certainly  not  in  any  attrac- 
tion or  afiSnity  to  the  negative  particle] 

1  [With  the  doctrine  of  Conversion  taught 
In  the  text,  compare  the  following  authori- 
ties: Laurentius  Valla,  Dialeciica,  L.  ii.  c. 
24,  f  3".  Titius,  Ars  Coeilif^\di  (v,  Ridigerj  fla 
Sensu  Veri  tt  Falsi,  L  ii.  c.  i.  p  232).  Rcusch, 
Systema  Logicum,  §  380,  p.  413  ft  stg.,  ed.  1741. 
Uollmann,  Logica,  §  89,  p.  172.  riouc<iuet. 
Fries,  Logik,  §  S3,  p.  146.  R.  Reinhold,  Logik, 
§  117,  p.  286.  Arcients  referred  to  by  Ammo- 
nius.  In  De  Interp  ,  c.  vii.  §  4,  f.  .  .  .  .  Faulus 
Vallius,  Lo!;ica,  t.  ii..  In  An.  Prior.,  L.  i.  q.  ii. 
c.  iv.]  [Valla  I.  c.  says:  "  Xon  amplius  ac 
latius  accipitur  prjedicatum  quam  subjectum. 
Idcoque  cum  illo  converti  potest,  ut  omnis 


homo  est  animal:  non  utique  totum  genus  ani- 
mal, sed  aliqua  pars  hujus  generis.  .  .  .  ergo, 
Aliqua  pars  animrdis  est  in  ontni  honiine.  Item, 
Quidam  homo  e^t  animal,  scilicet  est  queEiiatn 
pars  anitnalis,  ergo,  Qumdam  pars  aninialis  est 
quidam  homo,  etc."  Gottlieb  Gerhard  Titius, 
Ars  Cogitandi,  c.  vii.  §  3  ^ f  seq.,  p.  125.  LipsiJE, 
1723  (first  ed.  1701).  "  Nihil  autem  aliud  agit 
Conversio,  quam  nt  simpliciter  pradicatum 
et  subjectum  transponat,  hinc  nee  qualitatem 
nee  quantitatem  lis  largitur,  aut  eas  niutat, 
sed  prout  reperit,  ita  convertit.  Ex  quo  neces- 
sario  sequitur  conversionem  esse  uniformem 
ac  omnes  propositiones  eodem  plane  moJe 
converti.  Per  exempla,  (1),  NuUus  homo  est 
lapis,  ergo,  Nullus  lapis  est  homo.  (2),  Quidam 
homo  non  est  medinis  (omnis),  ergo,  JMedicus 
non  est  homo  quidam,  seu  Nullus  medicus  est 

homo  quidain (3),   Hie  Petrus  7ion 

est  doctus  (omnis),  ergo,  Omnis  doctiis  non  est 
hie  Petrus.  ....  (4),  Omnis  homo  est  ani- 
mal (quoddam),  ergo,  Quoddam  animal  est 
hon.o.  (5),  Quidavi  homo  currit  [parti culariter), 
ergo,  Quidam  currens  est  homo.  (6),  Hie  Paulus 
est  doctus  (quidam),  ergo,  Quidam  doctus  est  hie 
Paulus.  In  omnibus  his  exemplis  subjectum 
cum  sua  quantitate  in  locum  prasdicati,  et 
hoc,  eodem  modo,  in  illius  sedem  transponi- 
tur,  ut  nulla  penitus  ratio  solida  appareat, 
quare  conversionem  in  diversas  species  divel- 
lere  debeamus.  Vnlgo  tamen  aliter  sentiunt 
quando  triplicem  conversionem,  nempe  sim- 
plicem,  per  accidens,  acper  eontrapositionem,  ad- 

struunt Enimvero   conversio  per 

accidens  et  per  eontrapositionem  gratis  asseritur, 
nam  conversio  propositionis  affirmantis  uni- 
versalis perinde  simplex  est  ac  ea  qua  univer- 
salis negans  convertitur,  licet  post  eam  sub- 
jectum sit  particulare;  conversionis  enim  hie 
nulla  culpa  est,  quae  quantitatem,  quse  non 

adcst,  largiri  nee  potest  nee  debet 

Error  vulgaris  doctrinas,  nisi  fallor,  inde  est, 
quod  existimaverint  ad  conversionem  simpli- 
cem  requiri,  ut  prctdicatum  assumat  signu7n  et 

quantitatem  subjecti Conversionem 

per  eontrapositionem  quod  attinet,  facile  ostendi 


5-28 


APPENDIX 


The  general  errors  in  regard  to  Conversion,  —  the  errors  from  which  all  the 
rest  proceed,  arc  — 

1^,  The  omission  to  quantify  the  predicate  throughout. 

2°,  The  conceit  that  the  quantities  did  not  belong  to  the  terms. 

3°,  The  conceit  that  the  quantities  were  not  to  be  transposed  with  their 
relative  terms. 

4°,  The  one-sided  view  that  the  proposition  was  not  equally  composed  of  the 
two  terms,  but  was  more  dependent  on  the  subject  than  on  the  predicate. 

5°,  The  consequent  error  that  the  quantity  of  the  subject  term  determines 
the  quantity  of  the  proposition  absolutely. 

G°,  The  consequent  error  that  there  was  any  increase  or  diminution  of  the 
total  quantity  of  the  proposition. 

7°,  That  thorough-going  conversion  could  not  take  place  by  one,  and  that 
the  simple,  form. 

8°,  That  all  called  in  at  least  the  form  of  Accidental  Conversion ;  all  admit- 
ting at  the  same  time  that  certain  moods  remain  inconvertible. 

9°,  Tliat  the  majority  of  logicians  resorted  to  Contraposition  (which  is  not 
a  conversion  at  all)  ;  some  of  them,  however,  as  Burgersdyk,  admitting  that 
certain  moods  still  remained  obstinately  inconvertible. 

10°,  That  they  thus  introduced  a  form  which  was  at  best  indirect,  vague, 
and  useless,  in  fact  not  a  conversion  at  all. 

11°,  That  even  admitting  that  all  the  moods  were  convertible  by  one  or 
other  of  the  three  forms,  the  same  mood  was  convertible  by  more  than  one. 

1 2°,  That  all  this  mass  of  error  and  confusion  was  from  their  overlookiiig 
the  necessity  of  one  simple  and  direct  mode  of  conversion ;  missing  the  one 
straight  road. 

We  have  shown  that  a  judgment  (or  proposition)  is*  only  a  comparison  re- 
sulting in  a  congruence,  an  equation,  or  non-equation  of  two  notions  in  the 
quantity  of  Extension ;  and  that  these  compared  notions  may  stand  to  each 


potest  (1)  exempla  heic  Jactari  solita,  posse 
converti  simpHciter;  (2)  conversionem  per 
contrapositiciiem,  revera  non  esse  conversio- 
nem; interim  (3)  putativam  istam  conver- 
sionem non  in  universali  affirmante,  et  partic- 
ular! ne^ante  solum,  sed  in  omnibus  potius 
propositionibus  locum  habere,  .  .  .  e.  g., 
Qtio'liJam  animal  non  est  guadrupes,  ergo.  Nul- 
lum quaihupes  est  animal  guodUam.'^  See  the 
criticism  of  the  doctrine  of  Titius  by  Ridiger, 
quoted  below,  p.  555.  Ploucquet,  Methodus 
CaUulandi  in  Logicis,  p.  49  (1763).  "  Intellec- 
tic  identitatis  subject!  et  prsedicati  est  affirma- 

lio Omnis  circulus  est  linea  curva. 

Qua;  propositio  logice  expressa  haec  est :  — 
Omnis  circulus  est  quirdam  linea  rurva.  Quo 
pacto  id,  quod  intelligitur  in  pra?dicato  iden- 
tificatur  cum  eo  quod  intelligitur  in  subjecto. 
Sive  norim,  sive  non  norim  praiter  circulum 
dar!  quoque  alias  ciirvnriim  species,  verum 
tamen    est  quondam    lineam   curvam    sensu 


comprehensivo  sumtam,  esse  omnem  circulnm, 
seu  omnem  circulum  esse  quandam  lineam 
curvam."  Vallius, /.  c.  '•  Xegativas  vero  con- 
vertuntur  et  in  particulares  et  in  univer- 
sales  negatives;  ut  si  dicamus,  Socrates  non 
est  lapis,  convertens  illius  erit,  Aliquis  lapis 
non  est  Socrates,  et  NuUus  lapis  est  Socrates,  et 
idem  dicendum  erit  de  omni  alia  simili  prop- 
ositione.''  —  Ed.] 

[That  Universal  Affirmative  Propositions 
may  be  converted  simply,  if  their  predi- 
cates are  reciprocating,  see  Corvinus,  Instit, 
Phil.  Rat.,  §  514  Jens,  1742.  Baumgartcn, 
Logica,  §  280,  1765.  Scotus,  In  An.  Pr.,  L. 
i.  qu.  14.  Ulrich,  Instit.  Log.  et.  Met.,  |  1.2, 
177  (1785).  Kreil,  Logik,  §§  46,  62  (1789).  Is- 
endoom,  Logica  Perlpatetica,  L.  iii.  c.  8,  pp. 
430,  431.  Wallis,  Logica,  L.  ii.  c  7.  Zabar- 
ella,  In  An.  Prior.  TdbuUr.,  p.  148.  Lambert, 
X)3  Vnivirsaliori  Calculi  Idea,  (  24  et  seq.] 


APPENDIX. 


529 


other  as  the  one  subject  and  the  other  predicate,  as  both  the  subject,  or  as 
both  the  predicate  of  the  judgment.  If  this  be  true,  the  transposition  of  the 
terms  of  a  proposition  sinks  in  a  very  easy  and  a  very  simple  process ;  whilst 
the  whole  doctrine  of  logical  Conversion  is  superseded  as  operose  and  imper- 
fect, as  useless  and  erroneous.  The  systems,  new  and  old,  must  stand  or  fall 
with  their  doctrines  of  the  Conversion  of  propositions. 

Thus,  according  to  the  doctrine  of  the  logicians,  conversion  applies  only  to 
the  naked  terms  themselves :  —  the  subject  and  predicate  of  the  prejacent 
interchange  places,  but  the  quantity  by  whi(;h  each  was  therein  affected  is 
excluded  from  the  movement;  remaining  to  aifect  its  correlative  in  the  subja- 
cent proposition.  This  is  altogether  erroneous.  In  conversion  we  transpose 
the  compared  notions,  —  the  correlated  terms.  If  we  do  not,  eversion,  not 
conversion,  is  the  result. 

If  (as  the  Logicians  suppose)  in  the  convertens  the  subject  and  predicate 
took  each  other's  quantity,  the  proposition  would  be  not  the  same  relation  of 
the  same  notions.  It  makes  no  difference  that  the  converse  only  takes  place- 
when  the  subject  chances  to  have  an  equal  amount  or  a  less  than  the  predicate. 
There  must  be  at  any  rate  a  reasoning  (concealed  indeed)  to  warrant  it:  in 
the  former  case  —  that  the  predicate  is  entitled  to  take  all  the  quantity  of  the 
subject,  being  itself  of  equivalent  amount ;  in  the  second  (a  reasoning  of  sub- 
alternation),  that  it  is  entitled  to  take  the  quantity  of  the  subject,  being  less 
than  its  own.  All  this  is  false.  Subject  and  predicate  have  a  right  to  their 
own,  and  only  to  their  ov/n,  which  they  carry  with  them,  when  they  become 
each  other. 

IV. — Application  of  Doctrine  of  Quantified  Pkedigate  to  Propc>sition8. 

(a)    SEW  PROI'OSiriONAL   FOKMS- NOTATION. 

Instead  of  four  species  of  Proposition  determined  by  the  Quantity  and 
Quality  taken  together,  the  Quantity  of  the  Subject  being  alone  considered, 
there  are  double  that  number,  the  Quantity  of  the  Predicate  being  also  taken 
into  account. 


Irma 

tive. 

(1) 

[AfA] 

C 

(") 

[Afl] 

C 

(3) 

[If  A] 

A 

(iv) 

[If  I] 

C 

r  All  Triangle  is  all  Trilateral  [fig.  1]. 
A  All  Triangle  is  some  Figure  (A)  [fig.  2], 
C  Some  Figure  is  all  Triangle  [fig.  2]. 
B  Some  Triangle  is  some  Equilateral  (I) 
[fig.  4]. 
67 


530 


APPENDIX. 


Negative. 

(v)     [EnE]     C:i 

(A)  (A) 
(6)     [E  n  O]     C  : . 

(A)  (I) 
(vii)    [OnE]     B,, 

(I)  (A) 
(8)     [OnO]     C,. 

(I)  (I) 


:  D  Any  Triangle  is  not  any  Square  (E)  [fig.  3}. 

• ,  B  Any    Triangle    is    not    some    Equilateral 

[fig.  4]. 
• :  C  Some  Equilateral  is  not  any  Triangle  (O) 

[fig;  4]. 
,  B  Some   Triangle  is  not   some  Equilateral 

[fig.  4].^ 


(6)    QUANTITY  OF  PROPOSITIONS  -  DEFINTWDE  AND  INDEFINTTUDS. 

Nothing  can  exceed  the  ambiguity,  vacillation,  and  uncertainty  of  logicians 
foncerning  the  Quantity  of  Propositions. 

I.  As  regards  what  are  called  indefinite  (^iSi6pi(TToi)  more  properly  indesignate 
or  preindesignate propositions.  The  absence  of  overt  quantification  applies  only 
to  the  subject ;  for  the  predicate  was  supposed  always  in  aflirmatives  to  be 
particular,  in  negatives  to  be  universal.  Referring,  therefore,  only  to  the 
indesignation  of  the  subject :  —  indefinites  were  by  some  logicians  (as  the 
Greek  commentators  on  Aristotle  (?),  Apuleius  apud  Waitz,  In  Org.  i.  p.  338, 
but  see  Wegelin,  In  An'eponymi  Phil.  Sgn.,  p.  588)  made  tantamount  to  par- 
ticulars; by  others  (as  Valla,  Dialectica,  L.  ii.  c.  24,  f.  37),  made  tantamount 


1  [In  this  table  the  Roman  numerals  dis- 
tinguish such  prepositional  forms  as  arc  rec- 
ognized in  the  AristoteliC  or  common  doc- 
trine, whereas  the  Arabic  ciphers  mark  those 
(halt*  of  the  whole)  which  I  think  ought  like- 
wise to  be  recognized.  In  the  literal  symbols, 
I  simplify  and  disintricate  the  scholastic  nota- 
tion ;  taking  A  and  I  for  universal  and  par- 
ticular, but,  extending  them  to  either  quality, 
marking  affirmation  by  f,  negation  by  u,  the 
two  first  consonants  of  the  verbs  affirmo  and 
K,ego.  —  verbs  from  which  I  have  no  doubt 
that  Petrus  Uispanus  drew,  respectively,  the 
two  first  vowels,  to  denote  his  lour  complica- 
tions of  quantity  and  quality.]  —  Discussions, 
p.  686. 

[In  the  notation  employed  above,  the 
comma  ,  denotes  some ;  the  colon  :  all ;  the 
line  m  denotes    the  affirmative  copula, 

and  negation  is  expressed  by  drawing  a  line 
through  the  affirmative  copula  ■  [  ;  the 
thick  end  of  the  line  denotes  the  subject,  the 
thin  end  the  predicate,  of  Extension.  In  In- 
tension the  thin  end  denotes  the  subject,  the 
thick  end  the  predicate.  Thus :  —  C :  »  , 
A  is  read.  AU  C  is  some  A.  C  :  »^ —  :  D  is 
read,  No  C  is  any  D.  The  Table  given  in  the 
text  is  from  a  copy  of  an  early  scheme  of  the 
author's  new  Propositional  Forms.  For  some 


time  after  his  discovery  of  the  doctrine  of  a 
quantified  predicate.  Sir  W.  Hamilton  seems 
to  have  used  the  vowels  E  and  O  in  the  for- 
mulae of  Negative  Propositions;  and  the  full 
period  {.)  as  the  symbol  of  some  (indefinite 
quantity).  In  the  college  session  of  1845-46, 
he  had  adopted  the  comma  (,)  as  the  symbol 
of  indefinite  quantity.  As  the  period  ap- 
pears in  the  original  copy  of  this  Table" as  the 
symbol  of  some,  its  date  cannot  be  later 
than  1845.  The  comma  (,)  has  been  substi- 
tuted by  the  Editors,  to  adapt  the  Table  to 
the  Author's  latest  form  of  notation.  The 
translation  of  its  symbols  into  concrete  prop- 
ositions, affords  decisive  evidence  of  the 
meaning  which  the  Author  attached  to  them 
on  the  new  doctrine.  That  this,  moreover, 
was  the  uniform  import  of  Sir  W.  Hamil- 
ton's propositional  notation,  from  the  earli- 
est development  of  the  theory  of  a  quantified 
predicate,  is  placed  beyond  doubt  by  numer- 
ous passages  in  papers  (not  printed),  and  by 
marginal  notes  on  books,  written  at  various 
\)eriods  between  1839-40,  and  the  date  of  his 
illness,  July  1844,  when  he  was  compelled  to 
employ  an  amanuensis.  The  letters  in  round 
brackets  (A)  and  (I)  are  the  vowels  finally 
adopted  by  the  Author,  in  place  of  E  and  O 
See  p.  534.  —  Ed.] 


APPENDIX.  631 

to  universals.     They  ought  to  have  been  considered  as  merely  elliptical,  and  to 
be  definitely  referable  either  to  particulars  or  universals.^ 

II.  A  remarkable  uncertainty  prevails  in  regard  to  the  meaning  of  particu- 
larity and  its  signs,  —  some,  etc.  Here  some  may  mean  some  only, — some  not 
all.  Here  some,  though  always  in  a  certain  degree  indefinite,  is  definite  so  far 
as  it  excludes  omnitude,  —  is  used  in  opposition  to  all.  This  I  would  call  its 
Semi-definite  meaning.  On  the  other  hand,  some  may  mean  some  at  least, — 
some,  perhaps  all.  In  this  signification  some  is  thoroughly  indefinite,  as  it  does 
not  exclude  omnitude  or  totality.     This  meaning  I  would  call  the  Indefinite. 

Now  of  these  two  meanings  there  is  no  doubt  that  Aristotle  used  particularity 
only  in  the  second,  or  thoroughly  Indefinite,  meaning.  For,  1°,  He  does  not 
recognize  the  incompossibility  of  the  superordinate  and  subordinate.  2°,  He 
makes  all  and  oh  vu.%,  or  particular  negative,  to  be  contradictories ;  that  is,  one 
necessarily  true,  the  other  necessarily  false.  But  this  is  not  the  case  in  the 
Semi-definite  meaning.  The  same  holds  good  in  the  Universal  Negative  and 
Particular  Affirmative. 

The  particularity  —  the  some  —  is  held  to  be  a  definite  some  when  the  other 
term  is  Definite,  as  in  ii.  and  3,  in  6  and  vii.  On  the  other  hand,  when  both 
terms  are  Indefinite  and  Particular,  as  in  iv.  and  8,  the  some  of  each  is  left 
wholly  indefinite. 

The  quantification  of  definitude  or  non-particularity  (:)  may  designate  am- 
biguously or  indifferently  one  or  other  of  three  concepts.  1°,  It  may  designate 
explicit  omnitude  or  totality ;  which,  when  expressed  articulately,  may  be 
denoted  by  (: :).  Thus —  All  triangles  are  all  trilalerals.  2°,  It  may  designate 
a  class  considered  as  undivided,  though  not  positively  thought  as  taken  in  its 
whole  extent ;  and  this  may  be  ai'ticulately  denoted  by  (: .).  Thus —  The  iri- 
ancfle  is  the  trilateral; —  The  dor/  is  the  latrant.  (Here  note  the  use  of  the  def- 
inite'article  in  English,  Greek,  French,  German,^  etc.)    3°,  It  may  designate  not 

1  [That  Indefinite  propositions  are  to  be  re-  Ramus,   Scliol.   Dial.,  L.  vii.    c.    2, .  p.    457. 

lerred  to  universals,  see  Purcliot,  Instit.  Pliil.  Downam,  In  Rami  Dialect.,  L.  ii.  c.  4,  p.  850. 

Logica,  I.  ^  ii.  c.  2,  pp.  124,  125,  126.    Itottt'n-  Facciolati,  Rud.  Log.  p.  ii.  c.  iii.,  p.,  67.    De- 

beccius,  Logica  Contracta,  c.  vi.  p.  92  (1660).  lariviere,  Nouvelle  Logique    Classique,  L.  ii.  s. 

Baumeister,  Inst.  Phil.  Rat.,  §  213.   J.  C.  Seal-  ii.  c.  3,  s.  580,  p.  334. 

iger,  Exerciiatiows,  Ex.  212,  5   2.    Drobisch,  That  Indeflnitude  has  sometimes  a  logical 

Logik,  ^  39.    Neomagus,  Ad  Trapezunlium ,  f.  import,  when  we  do  not  know  whether  aK. 

10.    To  be  referred  to  particular;   see  Lovan-  or  some,  of  the  one  be  to  be  affirmed  or  de- 

ienses,  Com.  in  Arist.  Dial.  p.  161.    Molinaeus,  nied  of  the  other:    E.  Reinhold,  Logik,  §  88. 

Elemenla  Logica,  L.  I.  c.  2.    Alex.  Aphrod.,  Anm.  2,  pp.   193,  194.     Ploucquet,   Metkodiis 

In  An.  Prior.,  c.  ii.  p.  19.     Denzinger,  Logica,  Calculandi,   pp.   48,   53,   ed.   1773.      Lambert, 

S  71.    Either  universal  or  particular,  Keeker-  Neues  Organon,  I.,  §  235,  p.  143.] 

mann,  Opera,  p.  220.    Aristotle  doubts;  see  2  [On  effect  of  the  definite  article  and  its 

An.  Prior.,  L.  \.  c.  27,  f  7,  and  De  Interp.  c.  7.  absence  in  different  languages,  in  reducing 

That  Indefinitude  is  no  separate  species  of  the  definite  to  the  indefinite,  see  Delarivi6re, 

quantity,  see  Scheibler,  Opera  Logica,  p.  iii.  c.  Logique,  ^  580,  581. 

6,  p.  443.    Graecus  Anonymus,  De  Syllogismo,  On  the  Greek  article,  see  Ammonius,  In  De 

L.  i.  c.  4,  f.  42.     Leibnitz,  Opera,  t.  iv.  p.  iii.  Interp.  c.  vii.  f.  67  b. 

p.  123.    Fries,  SijMetn  der  Logik,  }  30,  p.  137.  On  use  of  the  Arabic  article  in  quantifica* 


532 


APPENDIX. 


what  IS  merely  undivided,  thoi/gh  divisible,  —  a  class,  but  what  Is  indivisible, — 
an  individual ;  and  this  may  be  marked  by  the  small  letter  or  by  (:  •)  —  Thus 
—  Socrates  is  the  husband  of  Xanthippe ;  —  This  horse  is  Bucephalus. 

In  like  manner  particularity  or  indefinitude  (,),  when  we  wish  to  mark  it  as 
thoroughly  indefinite,  may  be  designated  by  (' ,),  whereas  when  we  would 
mark  it  as  definitely  indefioite,  as  excluding  all  or  not  any,  may  be  marked 

by(")- 

The  indefinites  (a<$pHrTo)  of  Aristotle  correspond  sometimes  to  the  particular, 
sometimes  to  one  or  other,  of  the  two  kinds  of  univcrsals.^ 

The  designation  of  indefinitude  ov  particularitij,  some  (,  or  ,)  may  mean  one 
or  other  of  two  very  different  things. 

1**,  It  may  mean  some  and  some  only,  being  neither  all  nor  none,  and  in  tlils 
sense  it  will  be  both  affirmative  and  negative  (,r). 

2°,  It  may  mean,  negatively,  not  all, perhaps  none,  some  at  most;  affirmatively, 
ROt  none,  perhaps  all,  — some  at  least  (, ,). 

Aristotle  and  the  logicians  contemplate  only  the  second  moaning.  The 
reason  of  this  perhaps  is,  that  this  distinction  only  emerges  In  the  conslderatlosi 
of  Opposition  and  Immediate  Inference,  which  were  less  elaborated  In  the 
former  theories  of  Logic  ;  and  does  not  obtrude  itself  in  the  consideration  of 
Mediate  Inference,  which  is  there  principally  developed."  On  the  doctrine  of 
the  logicians,  there  Is  no  ojiposltlon  of  subalternatlon  ;  and  by  Aristotle  no 
opposition  of  subalternatlon  is  mentioned.  By  other  logicians  it  was  errone- 
ously Introduced.  The  opposition  of  Subcontraries  Is,  likewise,  improper, 
being  precarious  and  not  between  the  same  things.  Aristotle,  though  he 
enumerates  this  opposition,  was  quite  aware  of  its  impropriety,  and  declares  it 
to  be  merely  verbal,  not  real.* 


tion,  see  Averrofes,  De  Intcrp  ,  p.  39,  edition 
1552: 

"4i  in  the  Arabic  tongue,  and  Ha  in  tbe 
Hebrew,  and  iu  lilce  mauuer  the  articles  in 
other  languages,  sometimes  have  tlu;  power 
of  universal  predesiguations,  sometimes  of 
particular.  If  the  former,  then  they  have 
the  force  of  contraries;  if  the  latter,  tlien  the 
force  of  sub-contraries.  For  it  is  true  to  say, 
al,  that  is,  ipse  homo  is  white,  and  a/,  that  is, 
ipse  homo  is  not  white ;  tliat  is,  wljcn  the  arti- 
cle ai  or  ha,  that  is,  ipse,  denotes  the  designa- 
tion of  particularity.  They  may,  however, 
be  at  once  false,  when  the  article  al  or  ha  has 
the  force  of  the  universal  predesignation." 
(See  also  p.  52  of  the  same  book.) 

In  Knglish  the  definite  article  always  de- 
fines, —  renders  definite,  — but  sometimes  in- 
dividuahzes,  and  sometimes  generalizes.  If 
wo  would  use  man  generally,  we  must  not 
prefix  tiie  article,  as  iu  Greek,  German, 
French,  etc  ;  so  wealth,  government,  etc.  But 
in  definition  of  horse,  etc.,  the  reverse,  as  the 
dog  {l«  chien,  6  Kvaiv,  etc.).  A  in  English  is 
often  equivalent  to  anji^l 


1  [Logicians  who  have  marked  the  Quanti- 
ties by  Definite,  Indefinite,  etc. 

Aristotle,  An.  Pr.,  c.  iv.  §  21,  and  there  Al- 
exander, Pacius.  Theophrasfus  (Facdolati, 
Kud.  Log.,  p.  i.  c.  4,  p.  39).  Ammonius,  In 
De  Inter.,  f.  72  b.  (Brandis,  Scholia,  p.  113) 
Stoics  aud  Non-peripatetic  Logicians  in  gen- 
eral, see  Sext.  Empiricus,  4</f.  Ln^.,  §  98<Xie?  , 
p.  476,  ed.  Fabricii;  Diog.  Laert.  Lib.  vii.  .teq. 
71,  «bi  Meuagius.  Downam,  In  Rami  Dialeo- 
ticam,  L  ii.  c.  4,  p.  363,  notices  that  a  partior 
ular  proposition  "  was  called  by  the  Stoic* 
indefinite  [aiptaTov)  ;  by  some  latins,  aud 
sometimes  by  Ramus  himself,  infinite;  be- 
cause it  does  not  designate  some  certain 
species,  but  leaves  it  uncertain  and  intiefi- 
nite."  Hurtado  de  Mcndoza,  Di.^p.  Lo^.  »« 
Met.,  t.  i.  d.  iv.  i  2,  p.  114.  Lovaniense.*,  la 
Ari.1t.  Dial.,  p.  161.  HoUmann,  Logita,  p.  173. 
Boethius,  Opera,  p.  345.  Reusch,  Syst.  Log., 
p  424.  Esser,  Log-i/fc,  5  58.  Weiss,  Zx)g^it,  H  149, 
150.    So  Kiesewetler,  I^g-k,  §§  102,  103.] 

2  On  both  forms  of  Opposition,  see  Scheib- 
ier,lOpera  Logica,  ^  iii.,  rfe  Propositi/inibus,^^ 
xt  p.  487,  and  above,  p.  134.  -^  £»■] 


APPENDIX.  633 

By  the  introduction  of  the  first  meaning  of  some,  we  obtain  a  veritable 
opposition  in  Subalternation ;  and  an  inference  in  Subcontrariety,  which  I 
would  call  Integration. 

(c)    OPPOSITION  OF  PnOPOSlTJONS. 

Propositions  may  be  considered  under  two  views ;  according  as  their  par- 
ticularity, or  indefinitude,  is  supposed  to  be  thoroughly  indefinite,  unexclusivc 
even  of  the  definite :  some,  meaning  some  at  least,  some,  perhaps  all,  some,  per- 
haps not  any ;  or  definite  indefinitude,  and  so  exclusive  of  the  definite ;  smne, 
meaning  some  at  most, — some  only,  —  some  not  all,  etc.  The  latter  thus  excludes 
omnitude  or  totality,  positive  or  negative ;  the  former  does  not.  The  former  is 
the  view  promulgated  as  alone  contemplated  by  Aristotle;  and  has  been 
inherited  from  him  by  the  Logicians,  without  thought  of  increase  or  of  change. 
The  latter  is  the  view  which  I  would  introduce ;  and  though  it  may  not  super- 
sede, ought,  I  think,  to  have  been  placed  alongside  of  the  other. 

Causes  of  the  introduction  of  the  Aristotelic  system  alone : 

1°,  To  allow  a  harmony  of  Logic  with  common  language  ;  for  language 
eliding  all  that  is  not  of  immediate  interest,  and  the  determination  of  the 
subject-notion  being  generally  that  alone  intended,  the  predicate  is  only  con- 
sidered in  so  far  as  it  is  thought  to  cover  the  subject ;  that  is,  to  be  at  least 
coextensive  with  it  But  if  we  should  convert  the  terms,  the  inadequacy  would 
be  brought  to  light 

2°,  A  great  number  of  notions  are  used  principally,  if  not  exclusively,  as 
attributes,  and  not  as  subjects.  Men  are,  consecjuently,  very  commonly  igno- 
rant of  the  proportion  of  the  extension  between  the  subjects  and  predicates, 
which  they  are  in  the  habit  of  combining  into  propositions. 

3°,  In  i"cgard  to  negatives,  men  naturally  preferred  to  attribute  positively  a 
part  of  one  notion  to  another  than  to  deny  a  part  Hence  the  unfrequency  of 
negative?  with  a  particular  predicate. 

On  the  doctiine  of  Semi-definite  Particularity,  I  would  thus  evolve  the 
Opposition  or  Incompossibility  of  propositions,  neglecting  or  throwing  aside 
(with  Aristotle)  those  of  Subalternation  and  Sub-contrariety,  but  introducing 
that  of  InconsiMency, 

Incompossibility  is  either  of  propositions  of  the  same,  or  of  different,  quality. 
Incompossible  propositions  differing  in  quality  are  either  Contradictories  without 
a  mean,  —  no  third,  —  that  is,  if  one  bo  true  the  other  must  be  false,  and  if  one 
be  false  the  other  must  be  true  ;  or  Contraries  with  a  mean,  —  a  third,  —  that 
is,  both  may  be  false,  but  both  cannot  be  true.  Incompossible  propositions  of 
the  same  quality  are  Inconsistents,  and,  like  Contraries,  they  have  a  mean  ;  that 
is,  both  may  be  false,  but  both  cannot  be  true. 

Contradictories  are  again  either  simple  or  complex.  The  simple  are  either, 
1°,  Of  Universals,*as  undivided  wholes;  or,  2",  Of  Individuals,  as  indivisible 
parts.* 

1  General  tenlis,  used  as  individual  teHnd,     So  that  there  are  three  kinds  of  contradic- 
wbtiii  opposed  to  each  other,  may  be  contra-     tories. 
dictories,  as  Man  is  mortal,  Man  is  not  mortal. 


534 


APPENDIX. 


The  complex  are  of  universals  divided,  as  4 — 5. 

Contraries,  a«;ain,  which  are  only  of  divided  universals,  are,  1°,  Bilateral,  aa 
1—5  ;  or,  2°,  Unilateral,  as  1 — 6,  1—7,  2—5,  3 — 5;  or,  3°,  Cross,  as  2—7,  S— 6. 

Inconsistents  are  either,  1°,  Affirmatives ;  or,  2°,  Negatives.  Affirmatives,  as 
1 — 2,  1 — 3,  2 — 3.  Negatives,  as  5 — 6, 5 — 7,  The  propositions  6 — 7  are  some- 
times Inconsistents,  sometimes  Consistents. 

All  the  other  propositional  forms,  whether  of  the  same  or  of  different  quali- 
ties, are  Compossible,  or  Unopposed. 

The  differences  in  compossibility  of  the  two  schemes  of  Indefinite  and  Defi- 
nite particularity  lies,  1°,  In  the  whole  Inconsistents ;  2°,  In  two  Contraries  for 
Contradictories.  1°,  According  to  the  former,  all  affirmative  and  all  negativo 
propositions  are  consistent,  whereas  in  the  latter  these  are  inconsistent,  1 — 2, 
1 — 3,  2 — 3;  among  the  affirmatives,  and  among  the  negatives,  5 — 6,  5 — 7. 
(As  said  before,  6 — 7  is  in  both  schemes  sometimes  compossible,  and  sometimes 
incompossible.)  2°,  Two  incompossibles,  to  wit,  2 — 7,  3 — 6,  which,  on  the 
Aristotelic  doctrines,  are  Contradictories,  are  in  mine  Contraries. 

The  propositional  form  4  is  consistent  with  all  the  affirmatives ;  8  Is  not  only 
consistent  with  all  the  negatives,  but  is  compossible  with  every  other  form  in 
universals.  It  is  useful  only  to  divide  a  class,  and  is  opposed  only  by  the 
negation  of  divisibility. 

By  adopting  exclusively  the  Indefinite  particularity,  logicians  threw  away  some 
important  Immediate  inferences;  those,  to  wit,  1°,  From  the  affirmation  of  one 
tome  to  the  negation  of  another,  and  vice  versa  :  and,  2°,  From  the  affirmation 
of  one  inconsistent  to  the  negation  of  another.  1°,  Thus,  on  our  system,  but 
not  on  theirs,  affirming  all  wan  lo  be  some  animal,  we  have  a  right  to  Infer  that 
no  man  is  some  (other)  animal ;  affirming  that  some  animal  is  all  man,  we  have 
a  right  to  infer  that  some  (other)  animal  is  not  any  man  ;  affirming  some  men  are 
tome  blacks  (Nerp-oes),  we  are  entitled  to  say  that  (same)  some  men  are  not  some 
(other)  blacks  (Hindoos),  and  also  that  (other)  some  men  are  not  the  (same)  some 
blacks.  And  so  backwards  from  negation  to  affirmation.  This  inference  I 
would  call  that  of  [Integration]. 

2°,  Affirming  a//  men  are  some  animab,  we  are  entitled  to  infer  the  denial  of 
the  propositions,  all  men  are  all  animalSy  some  men  are  all  animals.  And  so  iu 
the  negative  inconsistents. 

Affirmatives. 

1.)  Toto-total  =  Afa=  All      —  Is  all      — . 

ii.)  Toto-partial  =  Afi  =  All      —  Is  some  — .  (A) 

S.)  Parti-total  =  Ifa  =  Some  —  Is  all       — . 

iv.)  Parti-partial  =  Ifi    ^  Some  —  is  some  — .  (I) 


V.)  Toto-total 

6.)  Toto-partial 

vil.)  Parti-total 

8.)  Parti-partial 


Negatives. 

Ana  =  Any    —  is  not  any    — .    (E) 
An  I  =  Any    —  Is  not  some  — . 
Ina  ^  Some  —  Is  not  any     — .  (O) 
In  I    =  Some  —  is  not  some  — . 


APPENDIX, 


536 


TABLE  OF  THE  Mutual  Relations  of  the  Eight  Propositional  Forms  oh 
Either  System  of  Pakticularity.     (For  Generals  only.) 


> 

<:                     t2! 

> 

« 

<  <  <  <  03Wwco3:3:s:3:i-'h-(— ►-'Elj 

1  1  1  1  1  1  1  1  M  M  1  1  1  1  ;^ 

■z:<^Zi<  <  ■<!  " 

1    1    1    1    1    l=g 
00  00  <_  00  ;<_  0  r' 

ml 

fl 

— -1 

p. 

3  =  3 

- - 

!i  =  S 

!    1    1    1    1    1    1    1    i    1    1    1    1    1    1    1 

5*>>  >»>>-> 

!=;>;>  !>>!> 

o!!«5 

P   3  3   3   3  3 

1    1    1    1    1    1 

?3>3-. 

1    1    1 

1  1  1 

t 

1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 

1    1    1    1    1    1 

1    1    1 

1  1  1 

s 

5*   • 

E.S33C.g33=.S33--p33 

3*  3' 3*  3^  3*^ 

—  —  P>  —  P  s. 

33^ 

a 

5d        jcr::'    w    o    ceo 

0 

„ 

<D            reO       n>       O       OOO 

0 

0 

•o        'H='S     g.     SxS 

c 

"1 

CR            Jjp        Jjj        p        ppp 

p        3;^     3     ^     rr'r' 

C            0*3        cr       3        3  =  3* 

1 

3      S> 

1- 

r-         r-  3      r-     3      33  .— 

Q 

^  1 

3-2  0 

p.         2  '       2      " 

C^      3 

re  -  2 

r^        r*        r* 

* 

"l-i« 

9      00   0   0   990 

p        33     3     3     5  =  2. 

0    5-5^ 

1  §s 

C        B   3 

3 
0 
0 

^-3 

0  0 

3  3 

2     H- 

£0  f* 

p        0p     p     p     ppp 

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alEs- 

SS.-^ 

bi. 

un. 
un. 

un. 

bi.  cr. 

un. 
.  bi.  cr. 

bi.  di. 

--*       C  3 
0        ?? 
71 

3 
3 

0 
7! 

3  3 
3  3 

fl 

a 

0 

3 

__ 

►-.-5"_. 

<  1  < 

\k\      ^.^        -.     -.    ^ 

00  3:p      M-J^           T      T      T 

=:o      -J  <!  «« 
II        III 

Tf 

TTT 

Is 

00-^  0>       00  ^_             00       0>       00 

II        III 

00  00        00  <.  Oi 

►L  J. 

^F 

g" 

1   7'  1             ""■ 

""■ 

g 

^  J..< 

§• 

■§ 

•^       3 

•^ 

fdW     WWW 

WW 

www 

g-      §■ 

^o* 

0   fD          0   ffi    <D 

fll    tB 

a  a  a 

3         31 

*   "    V 

ce   M         en  CK  en 

Zfi    rji 

»?l 

0         * 

c»  rt-          r*  rt   r» 

T'' 

7.  ^     7!  r^  r- 

?  ? 

r"  r*  r" 

oSg-« 

03°  «^ 

C  3        c-C  3 

3  S 

0*3  3 

3  3        r-3  3 

3  3 

23  3 

(t  0  ta 

g 

=<WW     W=<         W     5*     w 

3<B<t        <ti3.            0        5       <» 

WW     w 

WW 

w 

M 

3 
0 

0   <p         0 

0  a 

s 

r-  » 

3 

ffS"?'???            ?"???■ 

rt-  S-      "' 

«■  ?♦ 

&  §■ 

r  g^g*    ^        8=    ?     8= 

?  ?      ? 

r*  r* 

>1 

^?l 

5 

£".33        bS             3        S        3 

c  3      cr 
33      r- 

3  3 
3  3 

0; 

=  ."  3 

r^^rt         c.r3               «-         3         f^ 

i    S- 

CSC                      C                      C* 

5  1 

3  3        3                   3                   r- 

Abbreviations:  —  bi.  =  &i7a<era/ ;  cr.=  cross;  Contrar.  =  Contraries;  di.  =  direct; 
Incons.  =  Inconsistents ;  Int.  or  Integr.  =  Integration;  Repugn.  =  Mepugnants,  Con- 
tradictories; Res.  or  Restr.  =  Restriction,  Subalternation ;  un.  =  unilatei'al.  Blanks: 
in  I.  =  Compossibles ;  in  II.  =  No  inference.  —  ( Unilateral,  bilateral,  cross,  direct,  refer 
to  the  Extreme.?.) 

The  preceding  Table  may  not  be  quite  accurate  in  details. 


536  APPENDIX. 


V.  —  Syllogisms. 

OBSEBVATIOKS   ON   THB    MUTUAL  RELATIONS  OF   SYLLOGISTIC    TEEMS  .IN   QUAN- 
TITY   AND    QCAUTT. 

General  Canon.  — What  worst  relation  of  subject  and  predicate  subsists  between 
either  of  two  terms  and  a  common  third  term,  with  which  one,  at  least,  is  positively 
related ;  that  relation  subsists  between  the  two  terms  themselves. 

There  are  only  three  possible  relations  of  Terms  (notions,  representations, 
presentations). 

1°,  The  relation  of  Toto-total  Colnclusion  (cdidentity,  absolute  convertibility 
or  reciprocation)  (AfA). 

2",  The  relation  of  Toto-total  Coexclusion  (non-identity,  absolute  inconverti- 
bility or  non-reciprocation)  (AnA). 

3°,  The  relation  of  Incomplete  Colnclusion,  which  involves  the  counter-reljt- 
tion  of  Incomplete  Coexclusion  (partial  identity  and  non-identity,  relative  con- 
vertibility and  non-convertibility,  reciprocation,  and  non-reciprocation).  This 
is  of  various  orders  and  degrees. 

a)  Where  the  whole  of  one  term  and  the  part  of  another  are  coinclusive  or 
coideiitical  (Afl).  This  I  call  the  relation  of  ioto-partial  coinclunion,  as,  All 
men  are  some  animals.  This  necessarily  involves  the  counter-relation  of  toto- 
partial  coexclusion  (AnI),  as,  Any  man  is  not  some  animal.  But  the  converse 
of  this  afllrmative  and  negative  affords  the  relations  of 

b)  Parti-lotal  Colnclusion  (IfA)  and  Coexclusion  (InA),  as,  Some  animal  is 
all  man,  Some  animal  is  not  any  man. 

c)  There  is  still  a  third  double  relation  under  this  head,  when  two  tenns 
partially  include  and  partially  exclude  each  other  (If  I  Inl),  as,  Some  women  are 
some  authors,  and  Some  women  are  not  some  authors.  This  relation  I  call  that 
of  Parti-partial  Colnclusion  and  Parti-partial  Coexclusion. 

Of  these  three  general  relations,  the  first  is  [technically  stj'led]  the  best ;  the 
second  is  the  worst ;  and  the  third  is  intermediate. 

Former  logicians  knew  only  of  two  worse  relations,  —  a  particular,  worse 
than  a  universal,  affirmative,  and  a  negative  worse  than  an  affirmative.  As  to 
a  better  and  worse  in  negatives,  they  knew  nothing;  for  as  two  negative 
premises  were  inadmissible,  they  had  no  occasion  to  determine  which  of  two 
negatives  was  the  worse  or  better.  But  in  quantifying  the  predicate,  in  con- 
necting positive  and  negative  moods,  and  in  generalizing  a  one  supreme  canon 
of  syllogism,  we  are  compelled  to  look  further,  to  consider  the  inverse  proced- 
ures of  affirmation  and  negation,  and  to  show  (e.  (/.,  in  v.  a.  and  vi.  b.,  ix.  a. 
and  X.  b.)  how  the  latter,  by  reversing  the  former,  and  turning  the  best  quan- 
tity of  affirmation  into  the  worst  of  negation,  annuls  all  restriction,  and  thus 
apparently  varies  the  quantity  of  the  conclusion.  It  thus  becomes  necessary  to 
show  the  whole  order  of  best  and  woi-st  quantification  throughout  the  two 


APPENDIX. 


63T 


qualities,  and  how  affirmation  commences  with  the  whole  in  Inclusion  and 
Negation,  with  the  parts  in  Exclusion.^ 


Toto-total, 

Toto-partial, 

Parti-total, 

Parti-partial. 

Parti-partial, 

Parti-total, 

Toto-partial, 

Toto-total. 


Identity  or  Clomclosion. 


Non-identity  or  coexclosion. 


As  the  negation  always  reduces  the  best  to  the  worst  relation,  in  the  inter- 
mediate relations  determining  only  a  commutation  from  equal  to  equal,  whilst 
in  both  the  symbols  of  quantity,  in  their  inverse  signification,  remain  externally 
the  same ;  it  is  evident  that  the  quantification  of  the  conclusion  will  rarely  be 
apparently  different  in  the  negative  from  what  it  is  in  the  corresponding 
positive  mood.  There  are,  indeed,  only  four  differences  to  be  found  in  the 
negative  from  the  positive  conclusions,  and  these  all  proceed  on  the  same 
principle  —  viz.,  in  v.  a.  and  vi.  b.,  in  ix.  a.  and  x.  b.  Here-  the  particular 
quantification  of  the  positive  conclusions  disappears  in  the  negative  moods. 
But  this  is  in  obedience  to  the  general  canon  of  syllogism,  —  "  That  the  worst 
relation  subsisting  between  either  extreme  and  the  middle,  should  subsist 
between  the  extremes  themselves."  For  what  was  the  best  relation  in  the 
former,  becomes  the  worst  in  the  latter ;  and  as  affirmation  comes  in  from  the 
greatest  whole,  while  negation  goes  out  from  the  least  part,  so,  in  point  of  fact, 
the  some  of  the  one  may  become  the  not  any  of  the  other.  There  is  here, 
therefore,  manifestly  no  exception.  On  the  contrary,  this  affords  a  striking 
example  of  the  universal  applicability  of  the  canon  under  every  change  of 
circumstances.  The  canon  would,  in  fact,  have  been  invalidated,  had  the 
apparent  anomaly  not  emerged. 


I.  Terms  each  totally  co'inclusive  of 
a  third,  are  totally  coinclusive  of  each 
other. 


n.  Terms  each  parti-totally  coinclu- 
sive of  a  third,  are  partially  coinclusive 
of  each  other. 


a)  A  term  totally  coexclusive,  and 
a  term  totally  coinclusive,  of  a  third, 
are  totally  coexclusive  of  each  other. 

b)  A  term  totally  coinclusive,  and 
a  term  totally  coexclusive,  of  a  third, 
are  totally  coexclusive  of  each  other. 

a)  A  term  parti-totally  coexclusive, 
and  a  term  parti-totally  coinclusive, 
of  a  third,  are  partially  coexclusive  of 
each  other. 

b)  A  term  parti-totally  coinclusive^ 
and  a  term  parti-totally  coexclusive, 
of  a  third,  are  partially  coexclusive  of 
each  other. 


1  See  Magentious  (in  Brandis,  Scholia,  p.  113,  and  there  the  FIatonics> 

G8 


638 


APPENDIX. 


III.  A  term  totally,  and  a  term  par- 
ti-totally,  coinclusive  of  a  third,  are 
toto-partially  coinclusive  of  each  other. 


rV.  A  term  partl-totally,  and  a  term 
totally,  coinclusive  of  a  third,  are  parti- 
totally  coinclusive  of  each  other. 


V.  A  term  totally,  and  a  term  toto- 
partially,  coinclusive  of  a  third,  are 
parti-totally  coinclusive  of  each  other. 


VI.  A  term  toto-partially,  and  a 
term  totally,  coinclusive  of  a  third,  are 
toto-partially  coinclusive  of  each  other. 


Vli.  A  term  parti-totally,  and  a 
term  partially,  coinclusive  of  a  third, 
are  partially  coinclusive  of  each  other. 


Vni.  A  term  partially,  and  a  term 
parti-totally,  coinclusive  of  a  third,  are 
partially  coinclusive  of  each  other. 


a)  A  term  totally  coexclusive,  and 
a  term  parti-totally  coinclusive,  of  a 
third,  ^i-e  toto-partially  coexclusive  of 
each  other. 

b)  A  term  totally  coinclusive,  and 
a  term  parti-totally  coexclusive,  of  a. 
third,  are  toto-partially  coexclusive  of 
each  other. 

a)  A  term  parti-totally  coexclusive, 
and  a  term  totally  coinclusive,  of  a 
third,  are  parti-totally  coexclusive  of 
each  other. 

b)  A  term  parti-totally  coinclusive, 
and  a  term  totally  coexclusive,  of  a 
third,  are  parti-totally  coexclusive  of 
each  other. 

a)  A  term  totally  coexclusive,  and 
a  term  toto-partially  coinclusive,  of  a 
third,  are  totally  coexclusive  of  each 
other. 

b)  A  term  totally  coinclusive,  and 
a  term  toto-partially  coexclusive,  of  a 
third,  are  parti-totally  coexclusive  of 
each  other. 

a)  A  term  toto-partially  coexclu- 
sive, and  a  term  totally  coinclusive,  of 
a  third,  are  toto-partially  coexclusive 
of  each  other. 

b)  A  term  toto-partially  coinclusive, 
and  a  term  totally  coexclusive,  of  a 
third,  are  totally  coexclusive  of  each 
other. 

a)  A  term  parti-totally  coexclusive, 
and  a  term  partially  coinclusive,  of  a 
third,  are  partially  coexclusive  of  each 
other. 

b)  A  term  parti-totally  coinclusive, 
and  a  term  partially  coexclusive,  of  a 
third,  are  partially  coexclusive  of  each 
other. 

a)  A  term  partially  coexclusive,  and 
a  term  parti-totally  coinclusive,  of  a 
third,  are  partially  coexclusive  of  each 
other. 

b)  A  term  partially  coinclusive,  and 
a  tenn  parti-totally  coexclusive,  of  a 
third,  are  partially  coexclusive  of  each 
other. 


APPENDIX. 


639 


IX.  A  tema  totally,  and  a  term  par- 
tially, coinclusive  of  a  third,  are  par- 
tially coinclusive  of  each  other. 


X.  A  term  partially,  and  a  term 
totally,  coinclusive  of  a  third,  are  par- 
tially coinclusive  of  each  other. 


XL  A  term  parti-totally,  and  a  term 
toto-partially,  coinclusive  of  a  third, 
are  parti-totally  coinclusive  of  each 
other. 


XH.  A  term  toto-partially,  and  a 
term  parti-totally,  coinclusive  of  a  third, 
are  toto-partially  coinclusive  of  each 
other. 


a)  A  term  totally  coexclusive,  and 
a  term  partially  coinclusive,  of  a  third, 
are  totally  coexclusive  of  each  other. 

b)  A  term  totally  coinclusive,  and  a 
term  partially  coexclusive,  of  a  third, 
are  partially  coexclusive  of  each  other. 

a)  A  term  partially  coexclusive,  and 
a  term  totally  coinclusive  of  a  third, 
are  partially  coexclusive  of  each  other. 

b)  A  term  partially  coinclusive,  and 
a  term  totally  coexclusive,  of  a  third, 
are  toto-partially  coexclusive  of  each 
other. 

a)  A  term  parti-totally  coexclusive, 
and  a  term  toto-partially  coinclusive,  of 
a  third,  are  parti-totally  coexclusive  of 
each  other. 

b)  A  term  parti-totally  coinclusive, 
and  a  term  toto-partially  coexclusive, 
of  a  third,  are  parti-totally  coexclusive 
of  each  other. 

a)  A  term  toto-partially  coexclusive, 
and  a  term  toto-partially  coinclusive,  of 
a  third,  are  toto-partially  coexclusive 
of  each  other. 

b)  A  term  toto-partially  coinclusive, 
and  a  term  parti-totally  coexclusive,  of 
a  third,  are  toto-partially  coexclusive 
of  each  other. 


VI.  —  Objections  to  the  Doctbine  of  a  Quantified  Predicate  Con- 
sidered. 

(a)  GENERAL. 
HATERIAL   and   formal.  —  THEIR  DISTINCTION. 


But  it  is  requisite,  seeing  that  there  are  such  misconceptions  prevalent  on 
the  point,  to  determine  precisely  what  is  the  formal  which  lies  within  the 
jurisdiction  of  Logic,  and  which  Logic  guarantees,  and  what  the  material  which 
lies  without  the  domain  of  Logic,  and  for  which  Logic  is  not  responsible.  This 
is  fortunately  easy. 

Logic  knows  —  takes  cognizance  of — certain  general  relations;  and  from 
these  it  infers  certain  others.  These,  and  these  alone,  it  knows  and  guarantees ; 
and  these  are  formal.  Of  all  beyond  these  forms  or  general  relations  it  takes 
no  cognizance,  affords  no  assurance ;  and  only  hypothetically  says,  —  If  the 
several  notions  applied  to  these  forms  stand  to  each  other  in  the  relation  of 


6|d  APPENDIX. 

tlteee  forms,  then  so  and  so  is  the  result  Bat  whether  these  notions  arte  rightly 
ajjplied,  that  is,  do  or  do  not  bear  a  certain  reciprocal  dependence,  of  this 
I^>{j:ic,  as  IvOgic,  knows  nothing.  Let  ABC  represent  three  notions,  A  con- 
(.lining  B,  and  B  containing  C;  in  that  case  Logic  assures  us  that  C  is  a  part 
of  B,  and  B  a  part  of  A ;  that  A  contains  C ;  that  C  is  a  part  of  B  and  A. 
Xow  all  is  formal,  the  letters  being  supposed  to  be  mere  abstract  sj-mbols.  But 
if  we  apply  to  them  —  fill  them  up  by  —  the  tliree  determinate  notions, — 
Animal,  —  Man,  —  Negro,  we  introduce  a  certain  matter,  of  which  Logic  is 
not  itself  cognizant ;  Lo^c,  therefore,  merely  says,  —  If  these  notions  hold 
to  each  other  the  relations  represented  by  ABC,  then  the  same  results  will 
follow ;  but  whether  they  do  mutually  hold  these  relations,  —  that,  as  material, 
is  extra-logical.  Logic  is,  therefore,  bound  to  exhibit  a  scheme  of  the  forms, 
that  is,  of  the  relations  in  their  immediate  and  mediate  results,  which  are  deter- 
mined by  the  mere  necessities  of  thinking,  —  by  the  laws  of  thought  as  thought ; 
but  it  is  bound  to  nought  beyond  this.  That,  as  material,  is  beyond  its  juris- 
diction. However  manifest,  this  has,  however,  been  frequently  misunderstood, 
and  the  material  has  been  currently  passed  off  in  Logic  as  tha  formal. 

But  further,  L(^ic  is  bound  to  exhibit  this  scheme  full  and  unexclusive.  To 
lop  or  limit  this  in  conformity  to  any  circumstance  extrinsic  to  the  bare  condi- 
tions, the  mere  form,  of  thought,  is  a  material,  and,  consequently,  an  illegiti- 
mate curtailment.  To  take,  for  instance,  the  aberrations  of  common  language 
as  a  model,  would  be  at  once  absurd  in  itself,  and  absurd  as  inconsistent  even 
with  its  own  practice.  And  yet  this  double  absurdity  the  Logic  now  realized 
actually  commits.  For  while  in  principle  it  avows  its  allegiance  to  thought 
alone,  and  in  part  it  has  overtly  repudiated  the  elisions  of  language;  in  part  it 
has  accomnKxlateil  itself  to  the  usages  of  speech,  and  this  also  to  the  extent 
from  which  even  (jiammar  has  maintained  its  freedom.  Grammar, the  science 
proper,  the  nomology,  of  language,  has  not  established  ellipsis  as  a  third  law 
beside  Concord  and  Giovemment ;  nor  has  it  even  allowed  Concord  or  Govern- 
ment to  be  superseded  by  ellipsis.  And  why  ?  Because  tlie  law,  though  not 
externally  expressed  in  language,  was  still  internally  operative  in  thought. 
J^ogic,  on  the  contrary,  the  science  proper,  the  nomology,  of  thought,  has 
established  an  imperative  ellipsis  of  its  abstract  forms  in  conformity  to  the 
precarious  ellipses  of  outward  speech ;  and  this,  although  it  professes  to  look 
exclusively  to  the  internal  process,  and  to  explicate,  —  to  fill  up  what  is  implied, 
but  not  stated,  in  the  short  cuts  of  ordinary  language.     L<^c  has  neglected, 

—  withheld,  —  in  fact  openly  suppressed,  one-half  of  its  forms  (the  quantifica- 
tion of  the  predicate  universally  in  affirmatives,  particularly  in  negatives), 
btK.'auso  these  forms,  though  always  operative  in  thought,  were  usually  passed 
over  as  superfluous  in  the  matter  of  expression. 

Thus  has  Logic,  the  science  of  the  form,  been  made  hitherto  the  slave  of 
the  matter,  of  thought,  both  in  what  it  has  received  and  in  what  it  has  rejected. 
And  well  has  it  been  punished  in  its  servitude.  More  than  half  its  value  has 
at  once  been  lost,  confusion  on  the  one  hand,  imperfection  on  the  other,  it&  lot ; 
disgust,  contempt,  comparative  neglect,  the  con8e<iuencc.  To  reform  Logic,  we 
must,  therefore,  restore  it  to  freedom;  —  emancipate  the  form  from  the  matter; 

—  wc  must,  1°,  Admit  nothing  material  under  the  name  of  formal,  and,  2°, 


APPENDIX.  541 

Reject  nothing  formal  under  the  name  of  material.  When  this  is  done,  Logic, 
stripped  of  its  accidental  deformity,  walks  forth  in  native  beauty,  simple  and 
complete ;  easy  at  once  and  useful. 

It  now  remains  to  show  that  the  quantities  of  the  Predicate  denounced  by 
logicians  are  true  logical  forms. 

******* 

The  logicians  have  taken  a  distinction,  on  which  they  have  defended  the 
Aristotelic  prohibition  of  an  overt  quantification  of  the  predicate  5  the  distinc- 
tion, to  wit,  of  the  formal,  in  opposition  to  the  material,  —  of  what  proceeds  vi 
formce,  in  contrast  to  what  proceeds  vi  materice.  It  will  be  requisite  to  deter- 
mine explicitly  the  meaning  and  application  of  these  expressions ;  for  every 
logical  process  is  formal,  and  if  the  logicians  be  correct  in  what  they  include 
under  the  category  of  material,  the  whole  system  which  I  would  propose 
in  supplement  and  correction  of  theirs  must  be  at  once  surrendered  as 
untenable. 

In  the  first  place,  the  distinction  is  not  established,  in  terms  at  least,  by 
Aristotle.  On  the  contrary,  although  the  propositional  and  syllogistic  relations 
which  he  recognizes  in  his  logical  precept  be  all  formal,  he,  as  indeed  all 
others,  not  unfrequently  employs  some  which  are  only  valid,  say  the  logicians, 
171  materice,  and  not  ratione  forma;,  that  is,  in  spite  of  Logic. 

But  here  it  is  admitted  that  a  distinction  there  truly  is ;  it  is,  consequently, 
only  necessary,  in  the  second  place,  to  ascertain  its  import.  What  then  is 
meant  by  these  several  principles  ? 

The  answer  is  easy,  peremptory,  and  unambiguous.  All  that  is  formal  is 
true  as  consciously  necessitated  by  the  laws  of  thought ;  all  that  is  material  is 
true,  not  as  necessitated  by  the  laws  of  thought,  but  as  legitimated  by  the 
conditions  and  probabilities  discoverable  in  the  objects  about  which  we  chance 
to  think.  The  one  is  a  priori,  the  other  a  posteriori;  the  one  is  necessary, 
the  other  contingent;  the  one  is  known  or  thought,  the  other  unknown  or 
unthought. 

For  example  :  if  I  think  that  the  notion  triangle  contains  the  notion  trilateral, 
and  again  that  the  notion  trilateral  contains  the  notion  triangle ;  in  other  words, 
if  I  think  that  each  of  these  is  inclusively  and  exclusively  applicable  to  the 
other ;  I  formally  say,  and,  if  I  speak  as  I  think,  must  say  —  All  triangle  is  all 
ti-ilateral.  On  the  other  hand,  —  if  I  only  think  that  all  triangles  are  trilateral, 
but  do  not  think  all  trilaterals  to  be  triangular,  and  yet  say,  —  All  triangle  is  all 
trilateral,  the  proposition,  though  materially  true,  is  formally  false. 

Again,  if  I  think,  that  this,  that,  and  the  other  iron-attracting  stones  are  some 
magnets,  and  yet  thereon  overtly  infer,  —  All  magnets  attract  iron  ;  the  infer- 
ence is  formally  false,  even  though  materially  not  untrue.  Whereas,  if  I  think 
that  this,  that,  and  the  other  iron-attracting  stones  are  all  magnets,  and  thence 
conclude, — All  magnets  attract  iron;  my  conclusion  is  formally  true,  even 
should  it  materially  prove  false. 

To  give  the  former  example  in  an  abstract  notation  :  If  I  note  C  :  "  :  V, 

I  may  formally  convert  the  proposition  and  state  T  :  ■!  :  C.     But  if  I  note 

C  :  11  r,  I  cannot  formally  convert  it,  for  the  F  may  mean  either  :  F  or 


:42 


APPENDIX. 


,  r ;  and  if  I  do,  the  product  may  or  may  not  be  true,  according  as  it  is  acci- 
dentally applied  to  this  or  that  particular  matter.     As  to  the  latter  example  : 

C, — :  (m  m'  m",  etc.)  :  m  :  T 

II   :ia.ika&i-, ' 

This  syllogism  is  formally  legitimate.  But,  to  take  the  following  antecedent : 
this,  if  formally  drawn,  warrants  only,  (1),  a  particular  conclusion  ;  and  if,  (2), 
a  universal  be  drawn,  such  is  logically  null : 


C,- 
1. 
2. 


(m  m'  m",  etc.)  : 


,r 


This  being  the  distinction  of  formal  and  material,  —  that  what  is  formally 
true,  is  true  by  a  subjective  or  logical  law  ;  —  that  what  is  materially  true,  is 
true  on  an  objective  or  extra-logical  condition  ;  the  logicians,  with  Aristotle  at 
their  head,  are  exposed  to  a  double  accusation  of  the  gravest  character.  For 
they  are  charged :  —  1°,  That  they  have  excluded,  as  material,  much  that  is 
purely  formal.  2°,  That  they  have  included,  as  formal,  much  that  is  purely 
material.     Of  these  in  their  order. 

1°,  I  shall  treat  of  this  under  the  heads  of  Affirmative  and  of  Negative 
propositions. 

Of  the  four  Affirmative  relations  of  concepts,  as  subject  and  predicate ;  to 
wit  — 1.  The  Tolo-lotal  ;  2.  The  Toto-partial ;  3.  The  Parti-Toicd  ;  4.  The 
Parti-Partial ;  one  half  (1,  3)  are  arbitrarily  excluded  from  logic.  These  are, 
however,  relations  equally  necessarj',  and  equally  obtrusive  in  thought,  with 
the  others ;  and,  as  formal  realities,  equally  demand  a  logical  statement  and 
consideration.  Nay,  in  this  partial  proceeding,  logicians  are  not  even  self-con- 
FJstent.  They  allow,  for  example,  the  toto-partial  dependency  of  notions,  and 
they  allow  of  their  conversion.  Yet,  though  the  terms,  when  converted,  retain, 
and  must  retain,  their  original  relation,  that  is,  their  reciprocal  quantities ;  we 
find  the  logicians,  aft^'r  Aristotle,  declaring  that  the  predicate  in  affirmative 
propositions  is  to  be  regarded  as  particular ;  howbeit,  in  this  instance,  where  the 
tuto-purlial  is  converted  into  the  parti-total  relation,  their  rule  is  manifestly 
false.  When  I  enounce,  — All  man  is  animal,  I  mean,  —  and  the  logicians  do 
not  gainsay  me,  — All  man  is  some  animal.  I  then  convert  this,  and  am  allowed 
to  say,  —  Some  animal  is  man.  But  I  am  not  allowed  to  say,  in  words,  though 
I  say,  indeed  must  say,  in  thought,  —  Some  animal  is  all  man.  And  why  ? 
Simply  because  there  is  an  old  traditionary  rule  in  Logic  which  prohibits  us 
in  all  cases,  at  least  of  affirmative  propositions,  to  quantify  the  predicate  univer- 
sally;  and  to  establish  a'reason  for  this  exclusion,  the  principle  of  materiality 
has  been  called  in.  But  if  all  is  formal  which  is  necessitated  by  thought,  and 
if  all  that  is  formal  ought  to  find  an  expression  in  Logic,  in  that  case  the  uni- 
versal quantification  of  the  notion,  when  it  stands  as  predicate,  may  be,  ought, 
indeed,  on  demand,  to  be,  enounced,  no  less  explicitly  than  when  it  stood  as 


1  For  an  explanation  of  the  notation  here  employed,  in  reference  to  Syllogism,  see 
Apiteiidix  XI.  —  Eu. 


APPENDIX.  643 

subject.  The  quantification  is  no  more  material  on  tlie  one  alternative  than 
on  the  other ;  it  is  formal  in  both. 

In  like  manner,  the  toto-total  relation  is  denounced.  But  a  similar  exposi- 
tion shows  that  notions,  thougbt  as  reciprocating  or  coequal,  are  entitled,  as 
predicate,  to  have  a  universal  quantification,  no  less  than  as  subject,  and  this 
formally,  not  materially.^ 

In  regard  to  the  four  Negative  relations  of  terms,  —  1.  The  Toto-total, —  2. 
The  Toto-partial, —  3.  The Paiti-total,  —  4.  The  Parti-partial ;  in  like  manner, 
one  half,  but  these  wholly  different  classes  (3,  4),  are  capriciously  abolished.  I 
say  capriciously ;  for  the  relations  not  recognized  in  Logic  are  equally  real  in 
thought,  as  those  which  arc  exclusively  admitted.  Why,  for  example,  may  I 
say,  as  I  think,  —  Some  animal  is  not  any  man ;  and  yet  not  say,  convcrtibly,  as 
I  think,  — Any  man  is  not  some  animal  f  For  this  no  reason,  beyond  the  caprice 
of  logicians,  and  the  elisions  of  common  language,  can  be  assigned.  Neither 
can  it  be  shown,  as  I  may  legitimately  think,  —  Some  animal  is  not  some  animal 
(to  take  an  extreme  instance),  that  I  may  not  formally  express  the  same  in  the 
technical  language  of  i-easoning. 

In  these  cases,  to  say  nothing  of  others,  the  logicians  have,  therefore,  been 
guilty  of  extruding  from  their  science  much  that  is  purely  formal ;  and  this  on 
the  untenable  plea  that  what  is  formal  is  material. 

(6)   SPECIAL. 

Two  objections  have  been  taken  to  the  universal  quantification  of  the  pred' 
icate.     It  is  said  to  be  —  1°,  False  ;  2°,  If  not  false,  useless. 

I.  The  first  observation  may  be  subdivided  into  two  heads,  inasmuch  as  it 
may  be  attempted  to  establish  it,  a),  on  material;  b),  on  formal,  grounds.  Of 
these  in  their  order :  — 

a).  This  ground  seems  to  be  the  only  one  taken  by  Aristotle,  who,  on  three 
(perhaps  on  four)  different  occasions  denounces  the  universal  quantification  of 
the  predicate  (and  he  but  implicitly  limits  it  to  affirmative  propositions)  as 
"  always  untrue."  ^  The  only  proof  of  this  unexclusive  denunciation  is,  how- 
ever, one  special  example  which  he  gives  of  the  falsity  emerging  in  the  propo' 
sition,  — All  man  is  all  animal.  This  must  be  at  once  confessed  false ;  but  it  is 
only  so  materially  and  contingently,  —  argues,  therefore,  nothing  for  the  formal 
and  necessary  illegitimacy  of  such  a  quantification.  As  extra-logical,  this 
proof  is  logically  incompetent ;  for  it  is  only  because  we  happen,  through  an 
external  knowledge,  to  be  aware  of  the  relations  of  the  concepts,  man  and 
animal,  that  the  example  is  of  any  import.  But,  because  the  universal  quanti- 
ficatioa  of  the  predicate  is,  in  this  instance,  materially  false,  is  such  quantifica- 
tion, therefore,  always  formally  illegal  ?  That  this  i^  not  the  case,  let  us  take 
other  material  examples.  Is  it,  then,  materially  false  and  formally  incompe- 
tent to  think  and  say,  — All  human  is  all  rational,  — All  rational  is  all  risible,  — 

1  It  is  hardly  requisite  to  notice  the  blun-  nounced  by  the  acuter  logicians,  when  they 

dering  doctrine  of  some  autliors,  tliat  the  have  chanced  to  notice  the  absurdity.      See 

predicate  is  materially  quantified,  even  when  Fonseca,  Insiit.  Dial.  1.  vi.  c.  20. 

predesignated  as  universal.    It  is  sufficient  to  2  See  p.  546.  —  Kd. 
observe  that  this    opiuion  is  explicitly  re- 


544 


APPENDIX. 


AU  risible  vi  all  capab'e  of  a'lmiraiion,  —  All  trilateral  is  all  triangular,  —  ,421 
triangular  is  all  figure  with  its  angles  equal  to  two  right  angles,  etc.  ?  Or,  em- 
ploying Aristotle's  material  example,  is  it  untrue,  as  he  asserts,  to  say, —  Some 
animal  is  all  man  ;  and  this  either  collectively,  —  A  part  of  the  class  animal  i.< 
the  whole  of  the  class  man,  —  or  distribuiively,  —  Some  several  animal  is  ever^ 
several  man  ? 

But  the  absurdity  of  such  a  reasoning  is  further  shown  by  the  fact,  that  if  it 
were  cogent  at  all,  it  would  equally  conclude  against  the  validity  of  the  uni- 
versal quantification  of  the  subject  For  this  proposition  is  equally  untrue 
(employing  always  Aristotle's  own  material  example), — All  animal  is  man. 

After  this,  it  may  the  less  surprise  us  to  find  that  Aristotle  silently  abandons 
his  logical  canon,  and  adheres  to  truth  and  nature.  In  fact,  he  fre(}uently  does 
in  prartice  virtually  quantify  the  predicate,  his  conmion  reasonings  often  pro- 
ceeding on  the  reciprocation  or  coextension  of  subject  and  predicate.  Nay, 
in  his  logical  system,  he  expressly  rccc^nizes  this  coextension  ;  unless,  indeed, 
we  overtly  supply  the  quantification  of  the  predicate,  his  doctrines  of  Induc- 
tion and  of  Demonstration  proper  have  no  logical  notation  ;  and,  unless  we 
covertly  suppose  it,  they  are  actually  arrested.  His  definitions  of  the  Univer- 
sal, as  severally  given  in  his  Prior  and  Posterior  Attalylics,  are,  in  this  respect, 
conllictive.  In  the  former,  his  universal  (known  in  the  schools  as  the  Universale 
Prioristicum)  explicitly  forbids,  whereas  the  latter  (the  Universale  Posterior- 
isticum  of  the  schoolmen)  implicitly  postulates,  the  quantification  of  the 
predicate. 

b)..  The  defect  in  the  polemic  of  their  master  was  felt  by  his  followers. 
They,  accordingly,  in  addition  to,  but  with  no  correction  of,  Aristotle's  doc- 
trine, argue  the  question  on  broader  ground ;  and  think  that  they  disprove  the 
formal  validity  of  such  quantification  by  the  following  reasoning.  Overlooking 
the  case,  Avhere  the  subject  is  particularly,  the  predicate  universally,  quanti- 
fied, as  in  the  instance  I  have  just  given,  they  allege  the  case  of  Avhat  are 
called  reciprocating  propositions,  where  both  subject  and  predicate  are  taken 
in  their  utmost  extension,  vi  materia,  as  subsequent  logicians^  say,  but  not 
Aristotle.  In  this  case,  then,  as  in  the  example.  All  man  is  all  nsible,  they 
assert  that  the  overt  quantification  of  the  predicate  is  inept,  because,  the  all  as 
applied  to  the  subject  being  distributively  taken,  every  individual  man,  as 
Socrates,  Plato,  etc.,  would  be  all  (that  is,  the  whole  class)  risible.  This  ob- 
jection is  only  respectable  by  authorit;^',  through  the  great,  the  all  but  unex- 
clusive,  number  of  its  altegers ;  in  itself  it  is  futile. 

Terms  and  their  quantifications  are  used  either  in  a  distributive,  or  in  a  col- 
Iwlive,  se!»se.  It  will  not  be  asserted  that  any  quantification  is,  per  se,  neces- 
sirtly  collective  or  necessarily  distributive ;  and  it  remains  to  ascertain,  by  rule 
an<l  relation,  in  which  signification  it  is,  or  may  be,  employed.  Now  a  general 
rule  or  postulate  of  logic  is,  —  That  in  the  same  logical  unity  (proposition  or 
syllogism),  the  same  term  or  quantification  should  not  be  changed  in  imjwrt* 
If,  therefore,  we  insist,  as  insist  we  ought,  that  the  quantification  here,  all, 
should  be  used  in  the  sam^  proposition  in  the  same  meaning,  that  is,  as  applied 


1  [Sci',  for  example,  Pacius,  //i  An.  Prior,  L.  i.  c.  6,  p.  134. 
9,  and  above,  p.  527,  note  1,  sub.  fin.] 


Alexander,  In  An.  Prior,  L.  i.  c. 
2  Seep.  612.— Ed. 


APPENDIX.  545 

to  the  one  term,  collectively  or  distributivelyj  it  should  be  so  applied  likewise 
to  the  otlier,  the  objection  fails.  Thus  taken  collectively :  — All  (that  is,  the 
whole  class)  man  is  all  (that  is,  the  whole  class)  risih'e,  the  proposition  is  valid. 
Again,  taken  distributively : — All  (that  is,  every  several)  man  is  all  (that  is, 
every  several)  risible,  the  proposition  is,  in  like  manner,  legitimate.  Jt  is  only 
by  violating  the  postulate,  —  That  in  the  same  logical  unity  the  same  sign  or 
ivord  >>hould  be  used  in  the  same  sense,  that  the  objection  applies ;  whereas,  if  the 
postulate  be  obeyed,  the  objection  is  seen  to  be  absurd. 

It  is  hardly  necessary  to  say  anything  in  confutation  of  the  general  doctrine, 
that  in  Reciprocating  propositions  the  predicate  is  taken  in  its  full  extent,  vi 
materice.  In  the  first  place,  this  doctrine  was  not  promulgated  by  Aristotle; 
who,  frequently  allowing,  —  frequently  using,  —  such  propositions,  implicitly 
abandons  the  rule  which  he  explicitly  lays  down  in  regard  to  the  non-pre- 
designation  of  the  predicate  by  a  universal.  In  the  second  place,  apart  from 
authority,  such  doctrine  is  in  itself  unfounded.  For  as  form  is  merely  the  ne- 
cessity of  thought,  it  is  as  easy  to  think  two  notions  as  toto-totally  coinciding, 
(say,  triangle  and  trilateral),  as  two  notions  toto-partially  and  parti-totally  co-- 
inciding  (say,  triangle  and  figure).  Accordingly,  we  can  equally  abstractly 
represent  their  relations  both  by  geometric  quantities  (lines  or  figures),, 
and  by  purely  logical  symbols.     Taking  lines: — the  former   |  ;   the 

latter  (  .     Taking  the  symbols,  the  former  C  :  m     <         :  T  ;  the  latter 

A,  ■■  I  —  :  B.  But  if  the  reciprocation  were  determined  by  the  mere  matter,.^ 
by  the  object  contingenfly  thought  about,  all  abstract  representation  would  bo^ 
impossible.  So  much  for  the  first  objection,  —  that  the  universal  quantification  i 
of  the  predicate  would,  at  least  in  affirmative  propositions,  be  false. 

11.  As  to  the  second  objection,  that  such  quantification  would  be  useless  and 
superfluous,  dicorderly,  nay  confusive,  this  only  manifests  the  limited  and  one- 
sided view  of  the  objectors,  even  though  Aristotle  be  at  their  head. 

Is  it  useless  in  any  case,  theoretical  or  practical,  that  error  be  refuted,  truth 
established  ?     And  in  this  case  — 

1°,  Is  it  disorderly  and  confusive  that  the  doctrine  of  Exponibles,  as  they- 
are  called,  should  be  brought  back  from  anomaly  and  pain  to  ease  and  order;, 
that  propositions  Exclusive  and  Exceptive,  now  passed  over  for  their  difficulty, 
and  heretofore  confessedly  studied  as  "  opprobria  and  excruciations,"  should 
he  shown  to  be,  hot  merely  reducible  by  a  twofold  and  threefold  tortuosity, 
through  eight  genera  and  eight  rules,  but  simple,  though  misunderstood,  mani- 
festations of  the  universal  quantification  of  the  predicate  ?^ 

2°,  Is  it  useless  to  demonstrate  that  every  kind  of  proposition  may  be  con- 
verted, and  not  some  only,  as  maintained  by  Aristotle  and  the  logicians  ?  And 
is  it  disorderly  and  confur^ivc,  in  all  cases,  to  abolish  the  triple  (or  quadruple)) 
confusion  ift  the  triple  (or  quadruple)  processes  of  Conversion,  and  to  show,, 
that  of  these  proeesees  there  is  only  one  legitimate,  and  that,  the  one  simple  of. 
the  whole  ? 

3",  Is  it  disorderly  and  confusive  to  abolish  the  complex  confusion  of  Mood 
And  Figure,  with  all  their  array  of  rules  and  exceptions,  general  and  special ;, 
and  thlis  to  recall  the  science  of  reasoning  to  its  real  tmity  ? 

gg       1  See  p.  617.  —Ed. 


.'>46 


APPENDIX. 


4°,  Is  it  useless  and  superfluous  to  restore  to  the  science  the  many  forms 
of  reasoning  which  had  erroneously,  ineffectually,  and  even  inconsistently, 
been  proscribed  ? 

5°,  Is  it  useless  or  superfluous  to  prove  that  all  judgment,  and,  consequently, 
all  reasoning,  is  simply  an  equation  of  its  terms,  and  that  the  difference  of  sub- 
ject and  predicate  is  merely  arbitrary  V 

6°,  In  fine,  and  in  sum,  is  it  useless  or  superfluous  to  vindicate  Logic  against 
the  one-sided  views  and  errors  of  logicians,  to  reconcile  the  science  with  truth 
and  nature,  and  to  reestablish  it  at  once  in  its  amplitude  and  simplicity  ? 

VII,  —  Historical  Notices  of  Doctrine  of  Quantified  Fredicatk. 

(a)    ASISTOTLB. 

It  will  be  sufficient  to  make  one  extract  from  Aristotle  in  illustration  of  his 
doctrine  upon  this  point,  and  I  select  the  following  passage  from  his  Categories^ 
c.  v.,  §  7. 

"  Further,  the  primary  substances  [vpSnai  ohaiai,  —  individual  existences], — 
because  they  are  subjects  to  all  the  others,  and  as  all  the  others  are  predicated 
of,  or  exist  in,  them,  —  are,  for  this  reason,  called  substances  by  preeminence. 
And  as  the  primary  substances  stand  to  all  the  others,  so  stands  the  Species  to 
the  Genus.  For  genera  are  predicated  of  species,  but  not,  conversely,  species  of 
genera ;  so  that  of  these  two,  the  species  is  more  a  substance  than  the  genus." 

Ammonius,  who  has  nothing  in  his  Commentary  on  the  Categories  relative  to 
the  above  passage  of  Aristotle,  states,  however,  the  common  doctrine,  with  its 
reasonsj  in  the  following  extract  from  his  Commentary  on  Porphyry's  Introdxic- 
tion  (f  29,  ed.  Aid.  1546). 

"  But  confining  ourselves  to  a  logical  consideration,  it  behooves  us  to  inquire, 
—  of  these,  which  are  subject  to,  which  predicated  of,  the  others ;  and  to  be 
aware  that  Genera  are  predicated  of  Differences  and  Species,  but  not  con- 
versely. These,  as  we  have  said,  stand  in  a  certain  mutual  order,  —  the  genus, 
the  difference,  and  the  species ;  the  genus  first,  the  species  last,  the  difference 
in  the  middle.  And  the  superior  must  be  predicated  of  the  inferior ;  for  to 
predicate  the  inferior  of  the  superior  is  not  allowable.  If,  for  example,  we 
say,  — All  man  is  animal,  the  proposition  is  true ;  but  if  we  convert  it,  and  say, — 
All  animal  is  man,  the  enouncement  is  false.*  Again,  if  we  say, — All  horse  is 
irrational,  we  are  right ;  but  if  conversely  we  say,  — All  irrational  is  horse,  we 
are  wrong.  For  it  is  not  allowed  us  to  make  a  subject  of  the  accidental. 
Hence  it  is  incompetent  to  say  that  Animal  is  man,  as  previously  stated." 

[^Categ.  ch.  ii.,  §  1. 

"  When  one  thing  is  predicated  of  another  as  of  its  subject,  all  that  is  said 
[truly]  of  the  predicate  will  be  said  [truly]  also  of  the  subject     Thus  man  is 


1  The  converse  of  a  true  proposition  is  al- 
ways true;  but  the  false  propositions  which 
are  here  given,  as  conversions  of  the  true, 
are  not  conversions  at  all.  The  true  proposi- 
tions, if  explicitly  stated,  SiTe,  —  Alt  man  is 


some  animal,  and,  All  horse  is  some  irrational. 
Convert  these,  —  Some  animal  is  all  man,  and, 
Some  irrational  is  all  horse  ;  the  truth  remains, 
but  the  one-sided  doctrine  of  the  logicians  li 
exploded. 


APPENDIX.  647 

predicated  of  this  and  that  man,^  and  animal  of  man  ;  animal  will  therefore  be 
predicated  of  this  and  that  individual,  for  this  and  that  individual  is  both  man 
and  animal." 

De  Interpret.,  c.  vii.,  §  2-4 ;  see  also  c.  x. 

"  To  enounce  something  of  a  universal  universally,  I  mean  as.  All  or  every 

man  is  white,  No  man  u>  white To  enounce  something  of  universals  not 

universally,  I  mean  as,  Man  is  while,  Man  is  not  tchite :  for  whilst  the  term  man 
is  universal,  it  is  not  used  in  these  enouncements  as  universal.  For  all  or  every 
(iros)  does  not  indicate  the  universal  [itself],  but  that  [it  is  applied  to  a  sub- 
ject] universally.  Thus,  in  reference  to  a  universal  predicate,  to  predicate 
the  universal,  is  not  true.  For  no  affirmation  is  true  in  which  the  universal  is 
predicated  [of  a  universal  predicate],  as,  All  or  every  man  is  all  or  every  ani- 
vial."     (See  Ammonius,  Boethius,  Psellus,  Magentinus,  etc.) 

Pritjr  Analytics,  Bk.  I.  c.  27,  §  9.  "  The  consequent  [i.  e.  the  predicate]  is 
not  to  be  taken  as  if  it  Avholly  followed  [from  the  antecedent,  or  subject,  ex- 
clusively]. I  mean,  for  example,  as  if  all  [or  every"]  animal  [were  consequent] 
on  man,  or  all  [or  every]  science  on  music.  The  consequence  simply  [is  to  be 
assumed],  as  in  our  propositions  has  been  done  ;  to  do  otherwise  (as  to  say  that 
all  [or  evei-y]  man  ts-  all  [or  every]  animal,  or  tha,t  justice  is  all  [or  every]  good), 
is  useless  and  impossible ;  but  to  the  antecedent  [or  subject]  the  all  [or  ex'ery] 
is  prefixed." 

Posterior  Analytics,  B.  I.  c.  xii.,  §  10.  "  The  predicate  is  not  called  aZ/"  [or 
every]  ;  [that  is,  the  mark  of  universality  is  not  annexed  except  to  the  subject 
of  a  proposition]. 

In  refutation  of  Aristotle's  reasoning  against  the  universal  predesignation 
of  the  predicate  —  it  will  equally  disprove  the  universal  predesignation  of  the 
subject.  For  it  is  absurd  and  impos-siblc  to  say.  All  animal  is  man  ;  All  (every) 
immortal  iv  the  soul;  All  pleasure  is  health  ;  All  science  is  music  ;  All  motion  is 
pleasure.'^  But  in  point  of  fact  such  examples  disprove  nothing  ;  for  all  universal 
predesignations  are  applicable  neither  to  subject  rtor  predicate,  nor  to  both  sub- 
ject and  predicate  —  are  thoughts,  not  things ;  and  so  are  a\\  j^redesignations  ; 
therefore,  etc.  It  is  only  marvellous  that  such  examples  and  such  reasoning 
could  satisfy  the  acutest  of  intellects ;  that  his  authority  should  have  imposed 
on  subsequent  logicians  is  less  wonderful.*] 


1  [For  the  rls  here,  as  elsewhere,  denotes  of  the  definition  elevated  into  a  two-fold 
the  individuum  signatum,  not  the  individumn  axiom,  the  esse  t'n  toto,  etc.,  and  diet  de  omni, 
vagvm.]  etc.,  toward  the  conclusion  of  the  first  chap- 

2  Examples  from  'Wegelin,  In  Greg.  Ane-  ter  of  the  first  boolc  of  the  Prior  Analytics, 
ponymi  Comp.  Phil.  Synt.  L.  iv.  c.  1,  p.  473;  Tb  S4  4v  o\<i)  tlyou  erepov  kripw  Kai  rb 
L.  vi.  c.  1,  p.  673.  Kara   irayThs    Korriyoftfia^ai    bartpov    dd- 

3  And  here  I  may  correct  an  error,  as  I  con-  repov  ravT6v  iffTiv.  This,  with  its  ambi- 
ceive  it  to  be,  which  has  descended  from  the  guity,  may  be  thus  literally,  however  awk- 

'  oldest  to  the  most  recent  interpreters  of  the  wardly,  translated :  —  "  But  [to  say]  that  one 

Organon,   and   been    adopted   implicitly  by  thing  it  in  a  uiAoZe  otAer,  and  [to  say]  that  one 

logicians  in  general.    It  is  found  in  Alexan-  thing  is  predicated  of  all  another,  are  identicai." 

der  and   Ammonius,  as  in  Trendelenburg,  — Now,  the    question    arises,  —  What   does 

Saint-Hilaire,  and  Waitz;  nor  indeed,  as  far  Aristotle  here  mean  by  "a  whole  other?'"  for 

afi  I  know,  has  it  ever  been  called  in  question  it  may  signify  either  the  class  or  higher  no- 

during  the  interval.    It  regards  the  meaning  tion  under  which  an  inferior  concept  cornea. 


548 


APPENDIX. 


Quantification  of  Predicate — Aristotle. 

1.  Admits  that  syllogism  mental  not  oral  (An.  Posl.l.  10).  This  to  be  borne 
in  mind. 

2.  That  individual  is  never  predicated  (Cat.  c.  2),  refuted  by  reciprocation  of 
singular  (An.  Pr.  ii.  23,  §  4). 

3.  That  affirmative  universal  not  [to]  be  added  to  predicate,  incompatible  with 
what  he  says  of  reciprocation  (in  ^4)1.  Pr.  ii.,  cc.  22  and  23  alibi).  That  his 
custom  to  draw  universal  conclusions  in  Third  Figure  and  affirmative  in 
Second*  with  allowance  of  simple  conversion  in  certain  universal  affirma- 
tives. 

4.  That  particular  not  in  negative  predicate,  absurd  in  oi  «-os,  non  omnis. 

Aristotle's  doctrine  of  Prcdcsignation. 

1"*,  How  can  Aristotle,  on  his  doctrine,  make  universal  terms  taken  indif- 


or  the  inferior  concept  itself,  of  which,  as  of 
a  subject,  the  higher  is  predicated.  Tlie  for- 
mer is  tlie  sense  given  by  all  the  commenta- 
tors; the  latter,  the  sense  which,  I  am  confi- 
dent, was  intended  by  Aristotle. 

There  are  only  two  grounds  of  interpreta- 
tion. The  rule  must  be  expounded  in  cousi:^ 
tency  —  1°,  With  itself;  2°,  Must  be  with  the 
analogy  of  Aristotelic  usage. 

P.  On  the  former  ground,  the  ecmman 
doctrine  seems  untenable;  for  what  Arislotle 
declares  to  be  identical,  by  that  doctrine  be- 
comes diflferent,  nay,  opposed.  An  inferior 
concept  may  be  in  a  higher  whole  or  class, 
either  partially  or  totally;  and  tlie  definition 
on  the  prevalent  interpretation  virtually  runs 
—  *'To  say  that  one  thing  is  all  or  part  in  the 
whole  of  another,  and  to  say  that  this  other 
is  predicated  of  it  nnexclu.«ivcly;  are  convert- 
ible." Had  Ari.stotle,  therefore,  u.sed  the  ex- 
pression in  the  signification  attributed  to  him, 
he  must,  to  avoid  the  contradiction,  have 
raid  —  TJ>  8i  itaf  iripov  iy  8Xo>  tlyai  irtpa, 
K.T.\.  ("  But  to  say  that  one  thing  is  all  >a 
a  whole  other,"  etc.) 

2°.  On  the  second  ground,  it  may,  however, 
be  answered,  that  the  ambiguity  of  the  word, 
R8  it  stands,  is  superseded,  its  signification 
being  determined  by  other  passages.  I  join 
i»ne;  and  on  this  ground  am  well  content  to 
let  the  question  be  decided. 

In  flie  first  place,  the  meaning  I  attribute 
to  the  expression,  '^whole  oth^r"  —  that  is, 
whole  SHbject  or  Inferior  notion  —  is,  in  short, 
h>  nfrict  conformity  with  Aristotle's  ordinary 
langunge.  There  are,  I  admit,  sundry  pas- 
rages  in  his  logical  writings  where  the  term 
voAolf  is  clearly  used  as  synonymous  with  class, 
or  higher  notion ;  as,  to  limit  ourselves  to  the 
Prior  Analytics,  In  Hook  I.  iv.  §  2;  and  II.  i. 
t  4.  But,  every  single  text,  in  which  the  term 
ftkoU  appears  in  this  relation,  Is  overruled  by 


more  than  five  others,  hi  whicli  H  is  no  less 
clearly  applied  to  denote  the  totaiity  of  a  lower 
noiion,  of  which  a  higher  is  predicated  — 
pasj-ages  in  winch  the  word  whole  {o\os)  is 
itsed  conveilibly  with  all  {"Kai).  See  for  ex- 
ample. An.  Pr.  JI  ii.  i  5.  »  16— iii.  i  5,  }  7 
{bis  ),  i  14.  ^  15  — iv.  i  6  (6m.),  §  8,  i  10,  i  12 
{his  )  — xxii   i  1.  i  8  — xxiii.  ^  i. 

Lnt  in  the  si-cond  place  (and  this  is  directly 
cobversive  of  the  conuter-opinion,  even  iu 
tl;u  prii!ci])al  of  the  few  passages  where  the 
term  iciioU  is  u..oil  lor  class),  the  lower  notion 
mny  bo  in  or  under  the  higher,  only  particu- 
larly; and  this  manifestly  shows  that  Aris- 
totle could  not  possibly  mean,  by  merely  say- 
ing that  one  thing  is  another,  as  in  a  cla.ss, 
that  it  is  so  uneidusivtly,  or  universally.  Com- 
pare .in.  Pr.  I  iv.  {(  2,  3,  10.  On  this  inter- 
pretation, Darii  and  Feno  would  then  b(! 
annulled;  a  special  result  which  ought  to 
have  startled  the  logicians  into  a  doubt  of 
the  accuracy  of  the  received  doctrine  in  gen- 
eral. (See.  instar  omnium,  Facias,  in  his  rela- 
tive Kotes  and  Commentary.) 

That  doctrine  must,  therefore,  be  aban- 
doned, and  the  rule,  reduced  to  a  defini'ion, 
read  iu  the  following  signification:  —  "But 
to  say  that  one  thing  is  in  the  whole  of  anotlier, 
as  in  o  iub;ect,  and  to  preJicate  one  thing  tmiver- 
scUiy  oj  another,  are  merely  various  expression:! 
of  the  same  meaning."  This,  in  tact,  is  juft 
the  preliminary  explanation  of  the  two  orUi- 
nary  modes  of  stating  a  proposition,  subsi-- 
quently  used  by  Aristotle.  Here,  in  bot^i 
convertibles,  he  descends  from  extension  to 
comprehension,  from  the  predicate  to  the 
subject;  and  the  ingenious  exposition  by  the 
commentators,  old  and  new,  of  the  inverse 
intention  of  tlic  philosopher  in  the  two 
clauses,  must  be  regarded  as  erroneous. 

1  8«ep.  681.  — Ed 


¥ 


APPEMDIX.  d40 

ferently,  or  without  predesignation,  be  tantamount  to  particulars  ?  (^An.  Prior, 
I.  c.  4,  §  13 ;  Org.  Pacii,  p.  135,  alibi). 

2°,  An.  Prior,  I.  c-  27,  §  7,  He  says,  as  elsewhere,  "  A  proposition  being  in- 
definite £preindesignate],  it  is  not  clear  whether  it  be  universal ;  when,  however, 
it  is  definite  [predesignate],  that  is  manifest."  Contrast  this  statement  with  hii 
doctrine  of  the  all. 

3°,  There  are  syllogisms  in  Aristotle  which  are  only  valid  through  the  quaoi 
tity  of  the  predicate.^ 

4",  Aristotle  requires,  though  he  does  not  admit,  the  universal  predesigna- 
tion  of  the  predicate  in  his  syllogism  of  Induction.  (Vide  An.  Prior,  L.  ii.  c. 
23,  §  4  ;  Organon  Pacii,  p.  399.     Compare  also  his  doctrine,  p.  396.) 

(b)    ALEXANDER  APHRODISIENSIS. 

Alexander  Aphrodlsiensis,  in  his  commentary  on  the  first  book  of  the  Prior 
Analytics,  in  reference  to  the  second  passage  of  Aristotle,  states  as  follows : 

*'  And  in  the  book  of  Enouncement  Aristotle  explains  why  he  there  says  :  — • 
*  that  to  predicate  the  universal  of  a  universal  predicate  is  not  true  ;  for  there 
will  be  no  proposition,  if  in  it  we  predicate  the  universal  of  the  universal,  as, 
All  man  is  all  animal.'  He  repeats  the  same  also  here ;  showing  how  it  is 
useless  to  attempt  thus  to  express  the  consecution  [of  higher  from  lower 
notions]  ;  and  adds,  that  it  is  not  only  useless,  but  impossible.  For  it  is  impos- 
sible that  all  men  should  be  all  animal,  as  ^useless  to  say  (axfiv<rroy  etirtiy  must 
have  dropt  out)],  that  all  man  is  all  risible.  We  must  not,  therefore,  apply  the 
all  to  the  subsequent  [or  predicate],  but  to  that  from  which  it  follows  [or  sub* 
jectj.  For  man  .is  to  be  taken  universally,  as  that  from  which  animal  follows, 
supposing  this  to  be  the  consequent  of  all  man.  Thus  shall  we  obtain  a  stock 
of  universal  propositions.  The  process  is  tiie  same  in  making  man  the  con8e> 
(jueut  on  its  proper  all;  but  man  is  not  consequent  on  all  biped,  but  on  all 
rational. 

"  The  words, '  aa  we  express  ourselves,'  mean  —  as  we  express  ourselves  in 
common  usage-  For  we  say,  that  all  man  is  simply  animal,  and  not  all  animal, 
and  that  all  pleasure  is  natural,  not  all  natural ;  prefixing  the  aU,  not  to  the 
consequent,  but  to  the  subject  from  which  the  predicate  follows."  (Edd.  Aid., 
f.  100  a ;  Junt.,  f.  122  a ;  compare  Aid.,  f.  86  a ;  JunL,  f.  105  a.) 

(c)    AJlUOmUS  HBRMIJS. 

Ammonlus  Henniae,  In  de  Jnterp.  c.  vii.  §  2.  (Aldine  editions,  of  1503,  sig. 
C.  vii.  59,  of  1546,  fi".  70,  74.) 

"  In  these  words  Aristotle  inquires,  —  Whether,  as  the  annexation  of  the 
affirmative  predesignation  (irp<j<ThopuyfjL6s)  to  the  subject  constitutes  one  distinct 
class  of  propositions,  the  same  annexation  to  the  predicate  may  not,  likewise, 
constitute  another;  and  he  answers,  that  the  supposition  is  absolutely  groun  '.- 
less.  Thus  the  enouncement  —  all  (or  every)  man  is  all  (or  every)  animal 
(vais  iufApttros  T&r  (»»"  ^<""«)>  ^serts  that  each  man  is  all  animal,  as  horse,  ox,  etc 

1  Seep.  681.  — Ed. 


550 


APPENDIX. 


But  this  proposition  is  impossible ;  as  is  shown  by  Aristotle  in  his  here  omitting 
the  word  '  true.'  For  no  affirmation  can  be  true  in  which  the  universal  is 
predicated  of  a  universal  predicate ;  that  is,  in  which  the  universal  predesignate 
is  added  to  a  universal  predicate ;  as  when  we  say  that  man  (of  whom  all,  or, 
as  he  says,  universally,  animal  is  predicated)  is  not  simply  animal,  but  all 
animal.  He,  therefore,  teaches  that  such  an  affirmation,  as  utterly  untrue,  is 
utterly  incompetent 

"  Neither  does  Aristotle  allow  the  predesignation  some  to  be  annexed  to  the 
predicate,  that  propositions  may,  thereby,  become  true  always  or  occasionally. 
For  logicians  (as  they  do  not  propose  to  tliemselves  every  superfluous  variety 
of  enunciation)  are  prohibited  from  considering  propositions  (not  only  thoje 
always  true  or  always  false),  but  those  which  express  no  difference  in  reference 
to  necessary  or  impossible  matter,  and  afford  us  absolutely  no  discrimination  of 
truth  from  falsehood.  Thus,  particular  propositions,  which  may  be  alternatively 
true  and  false,  ought  not  to  have  a  prodesignated  predicate.  For  in  a  proposi- 
tion which  has  all  their  power,  without  any  predesignation  of  its  predicate, 
why  should  we  prefer  to  the  simpler  expression  that  which  drags  about  with 
it  a  sui>erfluous  additament  ?  Why,  for  example,  instead  of —  All  man  is  some 
animal  [I  read,  n  ^Sioy],  or.  All  man  in  not  all  animal,^  sliould  we  not  say, — AU 
man  w.  animal,  and  in  place  of  All  man  is  no  stone,  not  say, — All  man  is  not 
tlone :  or,  what  is  a  simpler  and  more  natural  enouncement  still,  —  No  man 
is  stone  ? 

"  And  when  we  find  some  of  the  ancients  teaching  that  the  particular  affirma- 
tive predesignation  is  to  be  connected  with  the  predicate,  as  when  Aristotle 
himself  styles  the  soul  a  certain  (some)  entelechy  (ivrfXtxttdf  rtva),  and  Plato, 
rhetoric,  a  certain  (some)  experience  (fus-tipcW  tii/o)  ;  it  is  to  be  observed  that 
the  some  is  there  added  for  the  sake  of  showing,  that  the  predicate  is  not  con- 
vertible Avith  the  subject,  but  is  its  genus,  and  requires  the  adding  on  of  certain 
differences  in  order  to  render  it  the  subject's  definition. 

"  But,  add  they,  is  not  the  reasoning  of  Aristotle  refuted  by  fact  itself,  seeing 
that  we  say,  All  man  is  capable  of  all  science :  thus  truly  connecting  the  uni- 
versal predesignation  with  the  universal  predicate?  The  answer  is  this:  — 
that,  in  truth,  it  is  not  the  predicate  to  which  we  here  annex  the  all.  For  what 
is  predicated,  is  what  is  said  of  the  subject.  But  what  is  here  said  of  mail  iv< 
not  that  he  is  science,  but  that  be  is  capable  of  science.  If,  therefore,  the  <M 
were  conjoined  with  the  capable,  and  the  p7X)position  then  to  remain  true,  as 
when  we  say  —  all  man  is  all  capable  of  science  ;  in  that  case  the  reasoning  of 
Aristotle  would  be  refuted.  But  this  proposition  is  necessarily  false.  It,  in 
fact,  asserts  nothing  less  than  that  of  men,  each  individual  is  all  the  kind :  — 
that  Socrates  is  not  Socrates  only,  but  also  Plato,  Alcibiades,  and,  in  short, 
every  other  man.  For,  if  all  man  is  all  capable  of  science,  Socrates  being 
one  of  the  all,  is,  therefore,  himself  all  capable  of  science;  so  that  Socrates 
will  be  Plato,  Alcibiades,  etc.,  since  they  also  are  capable  of  science.     For  if 


1  It  will  be  observed  that  Ammonias  does 
not  attempt  an  equivalent  for  this  proposi- 
tion.   In  fact  it  is  impossible  on  the  common 


or  Aristotclic  doctrine;  and  this  impoesibilitjr 
itself  ought  to  have  opened  his  eyes  upon  the 
insufficiency  of  the  view  be  maintained. 


APPENDIX.  551 

Socrates  be  not,  at  once,  Plato,  Alcibiades,  etc.,  neither  will  he  be  all  capable 
of  science. 

"  Now,  that  we  ought  not  to  prefix  the  universal  affirmalive  predesignation 
to  the  predicate  (whether  the  predicate  be  more  general  than  the  subject,  as 
All  man  is  all  animal,  or  whether  they  be  coadequate,  as  All  man  is  all  risible), 
this  is  manifest  from  what  has  been  said.  Even  when  the  terms  ai-e  coadequate 
or  reciprocating,  the  proposition  runs  into  the  absurd.  For,  declaring  that 
all  man  is  all  risible,  it  virtually  declares  that  each  individual  man  is  identical 
with  all  men  ;  that  Socrates,  in  that  he  is  a  man,  Is  all  risible,  consequently,  all 
man 

"  But  why  is  it  that  the  predicate  is  intolerant  of  the  predesignation  all, 
though  this  be  akin  to  the  counter-predesignation  no  or  none  ?  Is  it  because 
the  affirmative  predicate,  if  predicated  universally,  tends  always  to  contain 
under  it  the  subject,  and  this  not  only  when  itself  coadequate  with  the  subject, 
but  when  transcending  the  subject  in  extension ;  while,  moreover,  through  a 
participation  in  its  proper  nature,  it  is  suited  to  bind  up  and  reduce  to  unity 
the  multitude  of  individuals  of  which  the  subject  is  the  complement  ?  For,  as 
Aristotle  previously  observed  —  '  the  all  does  not  indicate  the  universal,  but 
that  [the  universal  predicate  Inheres  in,  or  is  attributed  to,  the  subject]  uni- 
versally.' If,  therefore,  the  affirmative  predicate  thus  tend  to  collect  into  one 
what  are  by  nature  distracted,  in  virtue  of  having  been  itself  previously  recog- 
nized as  simple ;  in  this  case,  the  all  [superadded  to  this  universal  predicate, 
in  fact]  enounces  not  a  unity,  but  a  multitude  of  several  things,  —  things  which 
it  is  manifestly  unable  to  complicate  Into  reciprocity.  But,  on  the  other  hand, 
since  what  is  negatively  predicated  of,  is  absolutely  separated  from,  the  subject; 
we  are,  consequently,  enabled  to  deny  of  the  subject  all  under  the  predicate, 
as  in  saying,  All  man  is  no  stone.  We  may  indeed  condense  this  proposition, 
and  say  more  simply.  All  man  is  not  stone;  or,  more  simply  still.  No  man  is  stone; 
thus  dispensing  with  the  affirmative  predesignation  in  a  negative  proposition." 

fd;    BOETUWS. 

Boethius,  In  Librum  de  Interpretatione,  editio  secunda,  et  in  textum  lauda- 
tum.     Opera,  p.  348. 

"  What  he  says  Is  to  this  purport :  —  Every  simple  proposition  consists  of  two 
terms.  To  these  there  is  frequently  added  a  determination  either  of  univer- 
sality or  of  particularity ;  and  to  which  of  the  two  parts  these  determinations 
are  to  be  added,  he  expounds.  It  appears  to  Aristotle  that  the  determination 
ought  not  to  be  conjoined  to  the  predicate  term  ;  for  In  this  proposition,  Man  is 
animal — (Homo  est  animal).  It  is  inquired  whether  the  determination  ought 
to  be  coupled  with  the  subject,  so  that  It  shall  be  —  (Omnis  homo  animal 
est)  — All  (or  every)  man  is  animal ;  or  with  the  predicate,  so  that  it  shall  be  — 
(Homo  omne  animal  est)  —  Man  is  all  (or  every)  animal ;  or  with  both  the  one 
and  the  other,  so  that  it  shall  be.  All  (or  every)  man  is  all  (or  every)  animal 
—  (Omnis  homo  omne  animal  est).  But  neither  of  these  latter  alternatives  is 
competent.  For  the  determination  is  never  joined  to  the  predicate,  but  ex- 
clusively to  the  subject ;  seeing  that  all  predication  is  either  greater  than  the 


552  APPENDIX. 

itubject,  or  equal.  Thus  in  this  proposition  —  All  (or  every)  man  is  animal 
(omnis  homo  animal  est),  animal  [the  predicate]  is  greater  than  man  [the  sub- 
ject] ;  and,  again,  in  the  proposition  —  Man  is  risible  (homo  risibilis  est),  risible 
[the  predicate]  is  equated  to  man  [the  subject]  ;  but  tliat  the  predicate  should  be 
less  and  narrower  than  the  subject  is  impossible.  Therefore,  in  those  predicates 
which  are  greater  than  the  subject,  as,  for  example,  where  the  predication  is 
animal,  the  proposition  is  manifestly  false,  if  the  determination  of  universality 
be  added  to  the  predicate  term.  For  if  we  say,  Man  is  animal  {homo  est 
animal),  we  <  ontract  animal,  which  is  greater  than  man,  by  this  determination 
to  [an  identity  of  extension  with]  man,  the  subject,  although  the  predicate. 
animal,  may  be  applied  not  only  to  man,  but  to  many  other  objects.  Moreover, 
in  those  [subjects  and  predicates]  which  are  equal,  the  same  occurs ;  for  if  I 
say.  All  (or  even/)  man  if  all  (or  every)  ritible  (omnis  homo  omne  risibile  est), — 
in  the  first  place,  in  reference  to  the  nature  of  man  itself,  it  is  superfluous  to 
adject  the  determination  ;  and,  again,  if  it  be  added  to  all  several  men,  the 
proposition  becomes  false,  for  when  I  say,  All  (or  every)  man  u  all  (or  every) 
risible,  by  this  I  seem  to  signify  that  the  several  men  are  [each  of  them]  all  or 
every  risible,  which  is  absurd.  The  determination  is,  therefore,  to  be  placed 
not  to  the  predicate  but  to  the  subject.  But  the  words  of  Aristotle  are  thus 
reduced  to  the  following  import:  —  In  those  predicates  which  are  universal,  to 
add  to  them  aitf/ht  universal,  so  that  the  universal  predicate  may  be  predicated  uni- 
versally, is  not  true.  For  this  is  what  he  says  —  "  In  the  case  of  a  universal 
predicate "  (that  is,  in  a  proposition  which  has  a  universal  predicate),  "  to 
predicate  the  universal  itself  universally,  is  not  true."  For  in  a  universal 
predicate,  that  is,  which  is  universal  and  is  itself  predicated,  in  this  case  uni- 
versally to  predicate  the  predicate  which  is  universal,  that  is,  to  adject  to  it  a 
determination  of  universality,  is  not  true  ;  for  it  cannot  be  that  any  affirmation 
riiould  be  true  in  which  a  universal  determination  is  predicated  of  a  predicate 
universally  distributed ;  and  he  illustrates  the  conception  of  the  matter  by  the 
example,  "  All  or  every  man  is  all  (or  every)  anitnal  (omnis  homo  omne  animal 
est).,  of  the  incompetency  of  which  we  have  already  spoken." 

Boethius,  In  Librum  de  luterpretatione,  editio  prima.  Opera,  p.  236.  (Text 
so  wretchedly  printed  that  the  sense  must  be  constituted  by  the  reader.) 

[^Aristotle,  c.  vii.  §  4].  " '  In  what  is  predicated  as  a  universal,  to  predicate 
the  universal  universally  is  not  true.' 

"  In  this  sentence  he  instructs  us  what  is  the  place  to  which  the  determina- 
tion of  universality  should  be  rightly  added.  For  he  teaches  that  the  univer- 
sality, which  we  call  the  universal  determination,  is  to  be  connected  with  the 
subject  term,  never  with  the  predicate.  For  were  we  to  say  —  All  (or  every) 
man  is  animal  (omnis  homo  animal  est),  we  should  say  rightly,  annexing  the  all 
(or  every)  to  the  subject,  that  is,  to  the  term  man.  But  if  we  thus  speak  —  All 
or  every  man  is  all  or  every  animal  (omnis  homo  omne  animal  e.'st),  we  should 
speak  falsely.  He,  thercfbro,  docs  not  say  this  [in  the  words]  — '  in  what  is 
predicated  as  a  universal,' as  animal  of  man;  for  animal  is  universal,  being 
predicated  of  all  or  every  man.  [But  he  says]  —  To  predicate  this  universal 
itself,  animal,  to  wit,  universally,  so  that  we  enounce  —  All  (or  every)  animal  is 


APPENDIX.  653 

man  (omne  animal  esse  hominem),  is  not  true;  for  he  allows  this  to  be  rightly 
done  neither  in  these  nor  in  any  other  affirmation.'  He  adds,  therefore :  — 
*  For  no  affirmation  will  be  true  in  which  a  universal  predicate  shall  be  univer- 
eally  predicated,  as  All  or  every  man  is  all  or  evert/  animal  (omnis  homo  est  omne 
animal).' 

"  Why  this  hapjiens,  I  will  explain  in  a  few  words.  "Hie  predicate  is  always 
greater  than  the  subject,  or  equal  to  it.  Greater,  as  when  I  say,  Man  is  animal 
(homo  animal  est)  ;  here  animal  is  predicated,  man  is  subjected,  for  animal  is 
predicated  of  more  objects  than  man.  Again,  it  is  equal  when  we  thus  speak 
—  Alan  is  rhtihle  (homo  risibilis  est)  :  here  man  is  the  subject,  risible  the  pred- 
icate. But  man  and  risible  are  equal ;  for  it  is  proper  to  man  to  be  a  risible 
animal.  But  that  the  predicate  should  be  found  less  than  the  subject,  is  impos- 
sible. Is  the  predicate  the  greater  ?  Then,'  to  adject  the  universal  to  the 
predicate,  is  false,  as  in  the  example  he  himself  has  given  —  All  (or  every)  man 
is  all  (or  every)  animal  (omnif  homo  omne  animal  est).  Is  it  equal  ?  Then,  the 
adjection  is  superfluous,  as  if  one  should  say,  All  every  man  is  all  or  every  risible 
(omnis  homo  omne  risibile  est).  Wherefore,  to  predicate  a  universal  predicate 
universally  is  incompetent." 

(e)    AVERROES. 

Averroes,  Perihermenias,  L.  I.,  c.  v. 

"  Propositions  are  not  divided  from  the  conjunction  of  the  predesignatlon 
(clausurae)  with  the  predicate  ;  because  the  predesignatlon,  when  added  to  the 
predicate,  constitutes  a  false  or  a  superfluous  proposition  :  —  False,  as  All  or 
every  man  is  all  (or  every)  animal  (omnis  homo  est  omne  animal)  ;  superfluous, 
as  All  (or  every)  man  is  some  or  a  ccviain  animal  (omnis  homo  est  quoddam  ani- 
mal)."    Vide  Conimbricenses,  In  Arist.  Dial.  ii.  158. 

CO    AlBERTUS  MAQlfUS. 

Albertus  Magnus,  Periherminias,  L.  I.,  Tractdtus,  v.  c.  1  {Op.  ed-  Lugd- 
1651,  t.  I.,  p.  261), 

["  Ly  '  omnis '  non  est  universale,  sed  signum  universalitatis,  Quare  ly 
'  omnis '  et  hujusmodi  signa  distributiva  non  sunt  universalia,  secundum  Avicen- 
nam."]  Hoc  enim  signum  distributivum,  quod  est  omnis,  non  est  universale, 
proprie  loquendo ;  sed  est  signum  per  quod  stat  pro  particularibus  universaliter 
universale,  cui  tale  signum  est  adjunctum.  Causa  autem,  quare  non  sit  univer- 
sale, est :  —  quia,  quamvis  secundum  grammaticum  sit  nomen  appellativum,  hoc 

I  The  Coimbra  Jesuits  (Sebastianus  Contus,  his  mighty  Logic  {art  locum).    With  Boethius 

1606)  erroneously  make  Boctliius  and  Aver-  he  joins    LcvigcrsouiUes  ;  —  lio    means    li.e 

roes  oppoHe  Aristotle,  "  thinking  fliat  the  sign  liabbi  Levi  Ben  Gerson,  of  Catalonia,  wiio 

of  uiiiverbalitv-  may  be  annexed  to  tlie  prodi-  died   at  Perpignan    in  1370,  who  wrote  on 

c«t«  of  It  univoifal  proposition  when  jt  is  Theology,     I'hjlosophy,    Mathematics,    und 

coextensive  with  the  subject"  tad  locum  ii.,  p.  Logic.    See  Jocher  v.  Levi,  from  Bartoloccj 

lo8)     This,  a  mistake,  has  l)een  copied  by  and  Wolf, 
their  brother  Jesuit,  P.  Vallius,  of  Rome,  in 

70 


554 


APPENDIX. 


est,  multis  secundum  naturae  suas  aptitudinem  conveniens ;  tamen  est,  secun* 
dum  fornaam,  infinitum,  nullam  enim  naturam  unam  dicit  Propter  quod  omnis 
naturae  communis  est  distributivum.  Universale  autem  est,  quod  est  in  multis 
et  de  multis,  suae  naturae,  suppositis.  Ideo  omnis,  et  nullus,  et  hujusmodi  signa 
universalia  esse  non  possunt;  sed  sunt  signa  designantia  utrum  universale  sit 
acceptum  universaliter  vel  particulariter,  secundum  sua  supposita.  Et  haec 
sunt  verba  Avicennae. 

["  Quare  signum  universale  non  sit  ponendum  a  parte  praedicati.]  In  sub- 
jecto  universali  signum  distributivum  ordinandum  :  quia  per  divisionem  subjecti, 
praedicatum  partibus  attribuitur  subjecti,  ut  divisim  participent  id  per  praedica- 
tionem,  et  non  in  praedicato  ponendum :  quia  quum  praedicatum  formaliter  sit 
acceptum,  non  proprie  dividitur,  nisi  alterius,  hoc  est,  subjecti  divisione :  sed 
inaequaliter  redditur  subjecto  et  partibus  ejus.  Unde  id  quod  est  universale, 
praedicari  potest,  ut  Omnis  homo  est  animal;  sed  universale  universaliter  ac- 
ceptum non  potest  praedicari :  nulla  enim  vera  affirmatio  esse  potest,  in  qua  de 
universali  aliquo  prsedicato  predicetur  sive  praedicatio  fiat ;  quoniam  universal- 
iter sic  patet,  quod  falsum  est,  Omnis  homo  est  omne  animal,  ct  si  ponatur,  quod 
Nullum  animal  sit  nisi  homo.  Cum  enim  hoino  subjiciatur  gratia  partium  suarum, 
et  praedicata  fi)rmaliter  accipiantur,  oportet  quod  Quilibet  homo  esset  omne  ani- 
mal, quod  falsum  est." 

(f)  LEVI  BEN  OERSOir. 

Levi  Ben  Gerson  (or  Levi  Gersonides),  a  Jewish  philosopher,  who  died  in 
1370,  at  Perpignan,  wrote  commentaries  on  Averroes'  Commentary  upon  the 
logical  books  of  Aristotle.  The  following  is  what  he  says  on  Averroes'  doctrine 
touching  the  quantification  of  the  predicate,  as  it  is  found  (f.  39)  of  the  Venice 
edition,  in  folio,  of  1552,*  of  the  works  of  Aristotle  and  Averroes: — "Al- 
though it  be  not  necessary  that  when  the  quantitative  note  is  attached  to  the 
predicate,  this  should  be  false  or  superfluous,  seeing  that  it  may  be  neither,  as 
when  we  say.  All  man  is  all  rational ;  and  the  same  holds  good  in  all  other 
reciprocating  propositions;  —  nevertheless,  as  in  certain  matters  it  may  so  hap- 
pen, Aristotle  has  declared  that  the  quantitative  note  is  not  to  be  joined  to  the 
predicate  in  any  language.  But  it  may  be  here  objected,  that  if  this  be  the 
case,  the  quantitative  note  should  not  be  annexed  even  to  the  subject,  since 
there  too  it  may  be  either  false  or  superfluous.  Superfluous,  —  as  when  we 
say,  Some  animal  is  rational.  For  the  very  same  follows  here,  as  if  we  simply 
say.  Animal  is  rational ;  the  some,  therefore,  is  superfluous.  False,  —  as  when 
we  say.  All  animal  is  rational.  The  reason,  therefore,  assigned  by  Aristotle 
why  the  quantitative  note  should  not  be  annexed  to  the  predicate,  is  futile,  see- 
ing that  for  the  same  reason  it  should  not  be  connected  with  the  subject.  To 
this  we  may  answer :  That  the  cause  why  the  quantitative  note  is  not  usually 
conjoined  with  the  predicate,  is,  that  there  would  thus  be  two  qusesita  at 
once,  —  to  wit,  whether  the  predicate  were  afiirmed  of  the  subject,  and,  more- 
over, whether  it  were  denied  of  everything  beside.     For  when  we  say,  All  man 


2  Not  in  the  8vo  edition  of  these  works.    Venice,  15Q0. 


APPENDIX.  555 

is  all  rational,  we  judge  that  all  man  is  rational,  and  judge,  likewise,  that  ra- 
tional is  denied  of  all  but  man.  But  these  are  in  reality  two  different  quaesita ; 
and  therefore  it  has  become  usual  to  state  them,  not  in  one,  but  in  two  several 
propositions.  And  this  is  self-evident ;  seeing  that  a  quaBsitum,  in  itself,  asks 
only  —  Does,  or  does  not,  this  inhere  in  that  V  and  not  —  Does  this  inhere  in 
that,  and,  at  the  same  time,  inhere  in  nothing  else  ?  " 

(h)   THE  MASTERS  OF  LOUVAIK. 

Factdtatis  Artium  in  Academia  Lovaniensi  Commentaria  in  Aristotelis  Libros 
de  Dialectica  (1535),  Tr.  iii.  c.  1,  p.  162,  ed.  1547. 

Speaking  of  the  text  in  the  De  Interpretatione,  the  Masters,  inter  alia,  allege : 
"  But  if  it  be  even  elegantly  said  by  a  poet  — '  Nemo  est  omnis  homo,'  — 
'  Non  omnes  omnibus  artes '  —  [proverb,  '  Unus  homo  nuUus  homo  '],  why  may 
we  not  contradict  this  aptly,  howbeit  falsely,  — '  Aliquis  est  omnis  homo '  ?  Why 
(they  say)  do  you  determine  the  predicate  by  the  note  of  universality,  seeing 
that  the  quantity  of  the  proposition  is  not  to  be  sought  from  the  predicate,  but 
from  the  subject  ?  We  answer,  because  we  wish  to  e.xpress  a  certain  meaning 
in  words,  which  by  no  others  can  be  done.  But  if  the  mark  of  universality 
could  only  be  employed  in  changing  the  quantity  of  propositions,  it  would 
not  be  lawful  to  annex  It  to  the  part  of  the  predicate.  We  have,  therefore, 
thought  these  few  cautions  requisite  to  evince  that  what  Is  condemned  by  these 
critics  for  its  folly,  is  not  incontinently  sophistical  or  foolish  babbling.  But  as 
to  the  universal  rule  which  Aristotle  enounces,  —  '  No  affirmation  will  be  true,* 
etc.,  —  it  is  sufficient  if  it  hold  good  in  the  majority  of  cases  ;  whether  the 
predicate  exceed  the  subject,  as.  All  man  is  all  animal,  —  be  its  equal,  as,  All 
man  is  all  risible,  or  its  inferior,  as,  \^Some']  animal  is  all  man.  In  a  few  cases, 
however,  the  exception  is  valid;  as, —  This  sun  is  every  sun,  One  phoenix  is  all 
phcenix,^nd  some  others.  Nor  are  these  futile  subtleties,  since  reason  herself 
approves." 

(i)  Trrms  and  ridiger. 

The  only  notice  of  these  speculations  of  Titius^  which  I  have  met  with  in 
any  subsequent  philosopher  (and  I  speak  from  an  inspection  of  several  hundred 

1  [Titins,  Ars  Cogitandi,  c.  vi.,  has  the  fol-  totam  qnidem    suam    comprekensionem,  non 

lowing  relative  to  the  quantification  of  the  vero  extemionem.    §  39 :  E  contrario  in  propo- 

predicate:  —  }    36:   "Licet    autem    Proposi-  sitionibus  negativis,  licet  particularibus,  ple- 

tiouum  quantitas  ex  Subjecto  sestimetur,  at-  rumque  prsedicatum  est   vniversale,  ac   tam 

tamen  Prasdicatum  non  peuitus  uegligendum  secundum    comprebensionem   quam    exten- 

videbatur,  ceu  vulgo  in  hoc  tractatioue  fieri  sionem  guam  totam,  a  subjecto  removetur- 

solet,  nam  et  hujus  quantitatem  observasse  §  41,  Interim  non  putarem  affirmationem  vel 

utile  est,  et  crediderim  et  disquisitionis  hujus  negationem  ipsam  diversam  illam  praedicati 

neglectu  varios  errores  tam  in  doctrina  Con-  quantitatem  necessario  postulare,  sed  credi- 

versionis,  quam  Syllogistica  esse  exortos,  quos  derim  potius,  id  omne  a  diverse  rerum  et  idea- 

suis  locis  videbimus.    j  37:  Breviter  itaque  rum  habitu  oriri,  aflSrmationi  vero  et  nega- 

observandum,  in  propositionibus  afiirmativis,  tioni  prasdicati  quantitatem  esse  velut  indif- 

licet   uuiversalibus,  prsedicatum  plerumque  ferentem.    i  42:  Nam  plerumque  prasdicata 

esse  particulare,  tribuique  subjecto  secundum  subjectis  suntlatiora;  quodsiigitur  ilia  cum 


556 


APPENDIX. 


logical  systems,  principally  by  Germans),  is  his  friend  J^J^gWr's i  '*f ^o»  in  hk 
elaborate  work,  De  Sensu  Veri  et  Falsi,  first  published  some  eight  yearssubee- 
"quently  (in  1709,  but  I  have  only  the  second  edition  of  1722},  attempts  a 
formal  refutation  of  the  heresy  of  a  quantified  predicate.  It  was  only,  how- 
ever, after  "  the  most  manifest  demonstrations  of  the  falsehood  of  this  novel 
prejudice  had  been  once  and  again  privately  communicated  to  his  very  learned 
friend"  (Titius?),  that  Ridiger  became  at  length  tired,  as  he  expresses  it,  "of 
washing  a  brick,"  and  laid  the  polemic  before  the  public.  It  was  not  certainly 
the  cogency  of  this  refutation  which  ought  to  have  thrown  the  counter  opinion 
into  oblivion  ;  but  this  refutation,  such  as  it  is,  though  with  nothing  new,  is 
deserving  attention,  as  presenting  the  most  elaborate  discussion  of  the  question 
to  be  met  with,  after  Ammonius,  and  in  modern  times.  But  the  whole  ai^u- 
ment  supposes  certain  foundations ;  and  it  will  be  sufficient  to  show  that  these 
are  false,  to  dispose  of  the  whole  edifice  erected  upon  them.  I  ought  to  men- 
tion, that  it  was  Ridiger's  criticism  which  first  directed  my  attention  to  the 
original  of  Titius. 

"  Origo  autem  hujus  erroris  neglectus  notissimse  acquivocationis  signorum 
omnis  et  quidam  esse  videtur,  qua  haec  signa,  vel  collective  sumi  possunt,  vel  dis- 
tributive. Priori  modo,  quantitas  in  praedicato  concepta  sensum  quidem  infert 
non  penitus  absurd um,  ca^terum  propositionem  constituit  identicam  et  frus- 
traneam."  Ridiger  then  goes  on  to  a  more  detailed  statement  of  what  he  eup- 
poses  to  be  the  groun<ls  on  which  the  erroneous  opinion  proceeds.^ 

First  Case.  —  "  Verbi  gratia,  Quoddam  animal  est  omnis  homo;  hoc  est.  Species 
qucedam  anhnalif,  homo  nempe  omne  id,  quod  homo  est :  quod  aliuin  sensum, 
habere  nullum  potest,  quam,  quod  omnis  homo  sit  homo :  sic  autem  collective 
Bumitur  et  signum  snbjecti  et  signum  praidicali."  This  objection  is  absunl,  for 
it  is  suicidal ;  applying  equalJy  to  the  proposition  which  the  objector  holds  for 
good,  and  to  that  which  he  assails  as  bad.  All  man  is  (sovie^  animxil.  Heie, 
is  not  animal  or  some  animal  just  a  certain  species  of  animal,  and  is  not  this 
species,  man,  to  wit,  all  that  is  man,  and  nothing  else  ?  There  is,  consequently, 
the  same  tautology  in  the  one  case  as  in  the  other ;  and  if  we  are  blamed  for 
only  virtually  saying,  by  the  former,  All  man  is  man,  does  the  objector  say  a 
whit  more  than  this  by  the  latter  ?  Ridiger  goes  on  :  "  Quodsi  vel  alterum 
signum,  vel  utrumque,  distributive  sumatur,  semper  absurdus  erit  propositionis 
pensus." 


l:is  componas,  non  poterit  non  praedicatum 
)ii«rticulRr«  ind«  «at«rgere,  dum  uuioa  kd 
i-'ubjccttini  restringi  nequit,  scd  ad  aliaquoquQ 
cxf*)iidi  apfiim  nmnet.  {  43:  A8t  si  praedica- 
tum a  subjecto  rfmovca^,  universale  illud 
urit,  cum  quicquid  iu  cjue  vel  comprelicnsione 
vul  extcnsiuiie  i-'Kt  ab  lioc  cejuii^atur,  iitic  iin- 
miiiuit  uuivcrsalitntuin,  quod  idem  ab  aliis 
fulijecti»i  quoque  rvtnoveatur,  ufim  *i  praedica- 
tum aliix  ctiam  conveniat,  turn  quidem  uni 
Kubjecto  non  jtoteft  dici  univprsaliter  tribu- 
tiun,  vorum  ni  de  multis  refretur.  pote8t  iiihil- 
oniiuiis  de  corto  Hiiniio  subjecto  unlver»iiliter 
qnuqtio  ne<;ari,  S  4) :  Quodsi  habitus  attributi 
{Mirinittat,  poterit  uliquando  propoaitio  afiir- 
mativa  prscdicntum  universale,  et  ncgativa 


particulare  habere;  nihil  enim  obstat,  quo 
minus  aliquando  totum  alteri  jungere,  vel 
I>artem  ab  eodem  removero  queaa.  (  46:  Uteo 
itaque  propositio: —  Omnis  homo,  est  risibilU, 
habet  pri«dicatum  universale, °8i  risibilitatem 
pro  liominis  proprio  habeas;  eioiit  hae,  —  JVni- 
lus  Turca  fit  homo  (Soil.  Chritiinnus),  vel  Qui- 
dam  mtilicvs  no*  est  homo  quidam,  preedicatum 
particulare  continent,  dum  part)  Folum  com- 
preheusionia  et  extenrionis  removetur.''  For 
the  application,  by  Titius.  of  the  principle  of 
a  quantified  predicate  to  the  doctrine  ot'Con- 
ver(<ion.  see  above,  pp.  628  fi29;  and  to  the 
theory  of  Syllo^iKm,  see  below,  p.  60S,  and 
Appendix.  X.  — Ed] 
1  Second  Editioo,  pp.  232,  S02. 


APPENDIX.  J55T 

Second  Case.  —  "  Verb!  gratia,  sumatur  utrumque  signum  distributive,  sensus 
erit,  Qubddam  individuum  animalis  (v.  g.  Petrus),  est  omne  individuum  hominis 
(v.  g.  Datms,  Oedipus)."  This  is  a  still  higher  flight  of  absurdity;  for,  to  re- 
fute the  proposition,  it  is  first  falsely  translated  into  nonsense.  Its  true  mean- 
ing, both  quantified  terms  being  taken  distributively,  is  :  — All  several  men  are 
some  several  animals,  or,  Every  several  man  is  some  several  animal. 

In  these  two  cases,  therefore,  all  is  correct,  and  the  objection  from  the 
identity  or  absurdity  of  a  quantified  predicate,  null. 

Third  Case.  —  "  Sumatur  signum  subjecti  distributive,  signum  praedicati  col- 
lective, sensus  erit :   Quoddam  individuum  animalis  est  universa  species  hominis." 

Fourth  Case.  —  "  Sumatur,  denique,  signum  subjecti  collective,  signum  prrodi- 
cati  distributive,  sensus  erit :  Qucedam  species  animalis,  ut  universale  et  prcedi- 
cabile,  est  omne  individuum  hominis." 

In  regard  to  these  last  two  cases,  it  is  sufficient  to  refer  to  what  has  been 
already  said  in  answer  to  Ammonius  (p.  549) ;  or  simply  to  recall  the  postulate, 
tbat  in  the  same  logical  unity  (proposition  or  syllogism)  the  terms  should  be 
supposed  in  the  same  sense.  If  this  postulate  be  obeyed,  these  two  cases  are 
inept,  and,  consequently,  the  objections  superfluous. 

Ridiger  then  proceeds  to  treat  us  with  four  long  "  demonstrations  a  priori," 
and  to  one  elaborate  "demonstration  a  posteriori ;"  but  as  these  are  all 
founded  on  the  blunders  now  exposed,  it  would  be  idle  to  refute  them  in 
detail. 

Ridiger,  it  may  Well  surprise  US,  howbeit  the  professed  champion  of  "  the  old 
and  correct  doctrine,"  is  virtually,  perhaps  unconsciously,  a  confessor  of  the 
truth  of  "the  new  and  false  prejudice;"  for  I  find  him  propounding  four 
several  syllogistic  forms,  three  of  which  are  only  valid  through  the  universal 
quantification  of  the  predicate  in  affirmatives,  and  two  (including  the  other 
one)  proceed  on  a  correct,  though  partial,  view,  opposed  to  that  of  the  logi- 
cians, touching  the  conclusion  of  the  Second  Figure  (L.  II.  c.  iv).  I  shaU 
insert  the  quantities,  operative  but  not  expressed. 

In  the  First  Figure  —  "At,  aut  ego  nihil  video,  aut  longe  naturalior  est  hic 
processus: —  Quoddam  Jluidum  est  {jjuoddani]  leve;  quoddam  corpus  est  {^omne^ 
Jluidum;  ergo  quoddam  corpus  est  quoddam  leve ;  quam  si  dicas,  etc.  (§  34).  — 
Here  the  middle  term  is,  and  must  be,  afiirmatively  distributed  as  predicate. 


In  the  Second  Figure.  —  "  Verbi  gratia:  —  Quoddam  ens  est  [omne'}  animal: 
omnis  homo  est  [quoddam}  animal :  ergo,  omnis  homo  est  [qv^ddam}  ens.  Haec 
conc^usio  verissima,"  etc.  (§  39.)  In  like  manner  the  middle  is  here  universally 
quantified  in  an  affirmative.     C,  i— — —  :  M,      ■«■ :  F- 


The  following,  Ridiger  (p.  330)  gives,  as  "  Two  new  moods,  which  cannot 
be  dispensed  with." —  "  Quoddam  animal  est  {omnis}  homo  :  nullum  brutum  est 
[ullus}  homo  :  ergo,  quoddam  animal  non  est  [ullum}  brutum.  Item :  —  Quod- 
dam animal  non  est  [uUus}  homo  ;  omnis  civis  est  [qtndam}  homo  ;  ergo,  quoddam 
animal  non  est  [ullus}  civis."  In  the  first  of  these,  the  middle,  as  predicate, 
is  affirmatively  distribtrted ;  and  in  both  syDogisms,  one  conclusion,  denied  by 


658 


APPENDIX, 


the  logicians,  is  asserted  by  Ridiger,  although  the  other,  which  involves  a  pred* 
icate,  particular  and  negative,  is  recognized  by  neither. 


a)  aODFRET  PLOUCQUET. 


Godfrey  Ploucquet,  a  philosopher  of  some  account,  Professor  of  Logic  and 
^letaphysics  in  the  University  of  Tubingen,  by  various  writings,  from  the  year 
1759,  endeavored  to  advance  the  science  of  reasoning;  and  his  failure  was 
perhaps  owing  more  to  the  inadequacy  and  limitation  of  his  doctrine,  than  to 
its  positive  error.'  To  jajLaQthing  about  his  attempt  to  -reduce  Logic  to  a 
species  of  computation,  in  which  his  one-sided  views  came  into  confliction  with 
the  one-sided  views  of  Lambert,  he  undoubtedly  commenced  auspiciously,  on 
the  principle  of  a  quantified  predicate.  This,  like  a  few  preceding  logicians, 
he  certainty  saw  aRbrdod  a  mean  of  simplifying  the  conversion  of  proposi- 
tions;'  but  he  did  not  see  that  it  could  accomplish  much  more,  if  properly 
applied,  in  the  theory  of  syllogism.  On  the  contrary,  in  syllogistic,  he  profes- 
sedly returns,  on  mature  consideration,  to  the  ordinary  point  of  view,  and 
thinks  himself  successful  in  recalling  the  common  doctrine  of  inference  to 
a  single  canon.  That  canon  is  this  :  —  "  The  terms  in  the  conclusion  are  to  be 
taken  absolutely  in  the  same  extension  which  they  hold  in  the  antecedent."  — 
"  In  conclusione  sint  termini  plane  iidem,  qui  in  praemissis,  intuitu  quantitatis." 
(Methodus  tarn  demonslrandi  directe  omnes  syllogismorum  species,  guam  viiia 
fomim  deter/endi,  ope  unius  regulce ;  —  Methodus  calculandi  in  Logicis ;  passim. 
Both  in  1763.)  This  rule,  as  applied  to  his  logical  calculus,  he  thus  enounces: 
"  Arrange  the  terms  in  syllogistic  order ;  strike  out  the  middle ;  and  the  ex- 
tremes then  afford  the  conclusion." —  "  Deleatur  in  prasmissis  medius ;  id  quod 
restat  indicat  conclusionem."  (Methodus  calculandi,  passim :  Elementa  PhUoso- 
phioe  Contemplatixice,  Logica,  §  122,  1778.)  This  rule  is_simple  eflQugh^-but, 
unfortunately,  it  is  both  inadequate  and  false.  Inadequate  (and  this  was  always 
sufficiently  apparent) ;  for  it  does  not  enable  us  to  ascertain  (and  these  the 
principal' q"'^gfi""'>s)  Imw  mapyT^xpis"^^' prwhat  identity  —  of  what  quantity  — 
and  of  what  quality,  can  be  legitimately  placed  in  the  antecedent.  But  it  is 
not  true  (though  this  was  never  signalized) ;  for  its  peculiar  principle  is  falsi- 
fied by  eight  of  the  thirty-six  moods,  to  wit,  in  affirmatives,  by  ix.,  x.,  xi.,  xii., 
and  in  negatives,  by  ix.  b,  x.  a,  xi.  b,  xii.  a.*  In  all  these,  the  quantity  of  an 
extreme  in  the  conclusion  is  less  than  its  quantity  in  the  antecedent.  We  can 
hardly,  therefore,  wonder  that  Ploucquet's  logical  speculations  have  been 
neglected  or  contemned  ;  although  their  author  be  an  independent  and  learned 
thinker,  and  his  works  all  well  worthy  of  perusal.  But,  though  dismissed  by 
Hegel  and  other  German  logicians,  not  for  its  falsity,  with  supreme  contempt, 
Ploucquet's  canon  has,  however,  found  its  admirers  in  England,  where  I  har\'e 
lately  seen  it  promulgated  as  original. 


1  An  extract  from  liis  Funriamtnta  Philoso- 

phi<r.  S/iectdntifrr,  1T59,  containing  I'loucquet's 

octrine  touching  tLo  quantification  of  tbe 


predicate,   will  be    found   in    Mr.    Baynes' 
Esiay,  p.  128. 
St  See  Table  of  Moods,  Appendix  XI.  —  ^ 


APPENDIX. 

(k)  ULKICH. 


669 


Institutiones  Logicce  et  Metaphysicce,%  171,  1785.  — "  Non  tantum  subjecto 
sed  et  pradicato,  ad  subjectum  relatio,  sua  constat  quantitas,  suumque  igitur 
signum  quantitatis  praefigere  Ik-et.  Sed  haec  praedicati  quantitas  ex  veterum 
praeceptis  saepe  justo  minor  invenitur.  In  loco  de  conversione  distinctius  de  eo 
exponetur."     In  that  place,  however,  nothing  of  the  kind  appears."  * 


YI. 

CANONS   OF   SYLLOGISM;    GENERAL   HISTORICAL  NOTICES 
AND  CRITICISM. 

A.  — HISTORICAL   NOTICES. 

I.  —  Quotations  fkom  Various  Logicians. 
(Collected  and  Translated  Autumn  1844.    See  p.  213.  —  Ed.) 

(a)  DAVID  DERODON. 

David  Derodon  (who  died  at  Geneva  in  1664,  and  had  been  previously 
Professor  of  Philosophy  at  Die,  Orange  and  Nismes)  was  a  logician  of  no 
httle  fame  among  the  French  Huguenots;  the  study  of  his  works  was  (if  I 
recollect  aright)  even  formally  recommended  to  the  brethren  of  their  com- 
munion by  one  of  the  Gallican  Synods.  "  Either  the  Devil  or  Doctor  Dero- 
don," was  long  a  proverbial  expression  in  France  for  the  authorship  of  an 
acute  argument;  and  the  "  Sepulchre  of  the  Mass"  has  been  translated  into  the 
vernacular  of  every  Calvinist  country.     Derodon  has  left  two  systems  of  Logic ; 


1  [That  the  Extension  of  Predicate  is  always 
reduced  to  Extension  of  Subject,  j.  c,  is 
equivalent  to  it,  see  Purchot,  Instil.  Phil., 
Logica,  i.  pp.  123, 125.  Tracy,  Siemens  rf'  Idc- 
ologif,  t.  iii.  Disc.  Prel.,  pp.  99, 100.  Crousaz, 
Logique,  t.  iii.  p.  190.  Derodon,  Logica  Resti- 
tuta,  P.  ii.  c.  V.  art.  4,  p.  224.  BoAhius, 
Opera,  p.  348  (see  above,  p.  551).  Sergeant, 
Method  to  Science,  b.  ii.,  less.  i.  p.  127.  Beneke, 
Lehrbuch  der  Logik,  f  156,  p.  100.  Stattler, 
Logica,  §  196. 

That  the  Predicate  has  quantity,  and  po- 
tential designation  of  it  as  well  as  the  Sub- 
ject, see  HolTbauer,  Analytic  der  Urtheile  und 
Scldusse,  ^  31  el  seq.  Lambert, 2)ci/«5cApr  Gelehrter 
Briefwechsel,  Brief  vi.  vol.  i.  p.  S95.  Platner, 
Philosophische  Aphorismen,  i.  §  546.  Corvinus, 
Listit.  Phil.  Rat.,  i  413.  Conimbricenses,  In 
Arist.  Dial.,'t.  ii.  pp.  158,  283.     Scotus,  In  An. 


Prior.  L.  i.  qn.  4,  f.  240;  qu.  13,  fT.  254^,  255»; 
qu.  14,  f  256b;  qu.  23,  f.  273». 

For  instances  of  Aristotle  virtually  using 
distributed  predicate,  see  An.  Post.,  i.  6,  i  1 
Cf.  Zabarella,  ad  loc.  Opera  Logica,  p.  735 
The  same.  In  An.  Post.,  I.  2.  Opera,  p.  827 
and  De  Quarto  Figura  Syllog.  Op.,  p.  123. 
The  adding  mark  of  universality  to  predicate 
is,  Aristotle  says,  "useless  and  impossible' 
(An.  Prior.,  i.  c.  27,  §  9);  yet  see  ii.  c.  22,  §}  1 
8;  c.  23,  §§  4,  5.  On  this  question,  see  Bol 
zano,  Logik,  §  131,  p.  27,  (and  above,  pp.  543 
648,549.) 

That  the  predesignation  of  the  predicate  by 
aU  collectively,  in  fact,  reduces  the  universal 
to  a  singular  proposition,  see  Purchot,  Instit. 
Phil.,i.  p.  124.  Cf  Logica  Contracta  Trajeetina. 
P.  ii.  C.5.    (1707.  U 


560  APPENDIX. 

a  larger  (Logica  Restztttta,  1659)  and  a  smaller  (Logica  Contracta,  1664),  both 
published  in  4to.^     I  shall  quote  only  from  the  former. 

It  is  impossible  to  deny  Derodon's  subtlety,  but  his  blunders  unibrtunately 
outweigh  his  originality.  Leaving  Conversion  as  he  found  it,  after  repeatins. 
with  approbation,  the  old  rules,  —  that  the  predicate  is  not  lo  be  overtly  quan- 
tified universally  (p.  573),  but  to  be  taken,  in  affirmative  propositions  particu- 
larly, as  in  negative  propositions  universally  (p.  623)  ,  we  are  surprised  to  find 
him  controverting,  in  detail,  the  special  rules  of  syllogism.  This  polemic,  r.s 
might  be  expected,  is  signally  unsuccessful;  for  it  is  frequently  at  variance  wilii 
all  principle,  and  uniformly  in  contradiction  of  his  own.  It  is,  indeed,  only 
interesting  as  a  manifestation,  that  the  old  logical  doctrine  was  obscurely  felt 
by  so  original  a  thinker  to  be  erroneous ;  for  the  corrections  attempted  by 
Derodon  are,  themselves,  especially  on  the  ground  which  he  adopts,  only  so 
many  errors.  He  unhappily  starts  with  a  blunder;  for  he  gives,  as  rectus,  an 
cxatBpIe  of  syllogism,  in  whicli  the  middle  term  is,  even  of  neeessity,  undis- 
tributed; and  he  goes  on  (pp.  627,  628,  636,  637,  638,  639,  649)  either  lo 
stumble  in  the  same  fashion,  or  to  adduce  reasonings,  which  can  only  be  vindi- 
cated as  inferential  by  ftupplpng  a  universal  quantity  to  the  predicate  in  affir- 
mative propositions,  or  by  reducing  it  to  particularity  in  negatives;  both  in  the 
teeth  of  Derodon's  own  laws.  I  have,  however,  recorrled,  in  my  Table  of  Syl- 
logisms, some  of  his  examples,  both  the  two  forms  which  he  has  named,  and 
four  others  which  he  only  enounces ;  according,  by  liberal  construction,  what 
was  requisite  to  give  them  sense,  and  which,  without  doubt,  the  author  would 
liimself  have  recognized. 

(b)  KAPttr. 

Rapin,  Rdflexions  sur  la  Loffiqu^,  §  4,  1684. 

"  Before  Aristotle  there  had  a])pcared  nothing  on  lo^c  systematic  and  estab- 
lished. His  genius,  so  full  of  rea*on  and  intelligence,  penetrated  to  the  recesses 
of  the  mind  of  man,  and  laid  open  all  its  secret  workings  in  the  accurate 
analysis  which  he  made  of  its  operations.  The  depths  of  human  thought  had 
not  as  yet  been  fathomed.  Aristotle  was  the  first  who  discovered  the  new  way 
of  attaining  to  science,  by  the  evidence  of  demonstration,  and  of  proceeding 
geometrically  to  demonstration,  by  the  infallibility  of  the  syllogism,  the  most 
accomplishe<l  work  and  mightiest  effort  of  the  human  mind,"  etc. 

Rapin  errs  in  making  Aristotle  lay  the  rule  of  proportion  along  with  the 
Dictum  de  Omni  as  a  principle  6f  Syllogism. 

(e)  LEIBinTZ. 

Leibnitz,  De  la  conformile  de  la  Foi  avec  la  liaison,  §  22.     Op.  t  i.,  p.  81. 
^"  Hence  the  facihty  of  some  writers  is  too  great,  in  conceding  that  the  doctrine 

1  Derodon  seems  wholly  unknown  to  the  number  in  the  same  binding  must  h«ve  been 

titrman  logicians,  and,  I  need  Itardly  add,  to  imported  at  once,  probably  in  consequence  of 

those  of  other  countries.    In  Scotland,  his  the  synodical  recommendation, 
works  are  not  of  the  rarest;   a  considerable 


APPENDIX.  561 

of  tbc  Holy  Trinity  is  repugnant  with  that  great  principle  which  enounces  — 
What  are  the  same  loith  the  same  third,  are  the  same  with  each  other ;  that  is,  if  A 
be  the  same  with  B,  and  C  be  the  same  with  B,  it  is  necessary  that  A  and  C 
should  also  be  the  same  with  one  another.  For  this  principle  flows  immediately 
from  the  principle  of  Contradiction,  and  is  the  ground  and  basis  of  ali  Logic ; 
if  that  fail,  there  is  no  longer  any  way  of  reasoning  with  certainty." 


(d)  REUSCH. 

Reusch,  Systema  Logicum,  1 734. 

§  506.  "  That  dictum  of  the  Aristotehans  de  Omni  et  Nulla  (503)  evinces, 
indeed,  a  legitimate  consequence,  but  it  only  regulates  one  species  of  syllogisms, 
at  least  immediately.  By  this  reaso^^  therefore,  looric.ians  ^ftye  been  inducedJCL, 
Y>rnvo  tha  ..r>n«pq.i<.»P<.  nf  |]^p  ^\]\er  specjes  by  means  of  the  first,  to  which  they 
are  reduced.  But,  that  we  may  be  able  to  supersede  this  labor,  I  have  en- 
deavored to  give  a  broader  basis  to  the  Dictum  de  Omni  et  NuUo,  or  by  what- 
ever name  that  rule  is  called,  to  which,  in  the  construction  of  syllogisms,  the 
order  of  thought  is  conformed. 

§  507.  "For  the  whole  business  of  ordinary  reasoning  is  accomplished  by 
the  substitution  of  ideas  in  place  of  the  subject  or  predicate  of  the  fundamental 
proposition.  This  some  call  the  equation  of  thoughts.  Now,  the  fundamental ; 
proposition  may  be  either  affirmative  or  negative,  and  in  each  the  ideas  of  the 
terms  may  be  considered  either  agreeing  or  diverse,  and  according  to  this  various  : 
relation  there  obtains  a  various  substitution,  which  we  shall  clearly  illustrate 
before  engaging  with  our  doctrine  of  the  Dictum  de  Omni  et  NuUo."  £Having 
done  this  at  great  length,  he  proceeds.] 

§  510.  "  From  what  has  been  now  fn))j^  de/r-l/^fprl^  ^Ka Jhllfimliig  Dietom-de' 
Omni_et  Nullo  may  be  formed,  which  the  definition  itself  of  reasoning  and 
syllogism  (§  502)  supports,  and  to  which  all  syllogisms  in  every  figure  and 
mood  may  be  acconmiodated. 

"//■  ttvo  irieas  (two  terms)  have,  through  a  iudgmrnt  rprnpnsitinn),  receintA  n 
relation  to  each  other,  either  affirmative  or  negative.,  in  that  case  it  is  alloioable,  in 
place  of  either  of  these  (that  is,  the  subject  or  predicate  of  that  judgment  or 
proposition),  to  substitute  another  idea  (term),  according  to  the  rules  given  of 
Equipollence  or  Reciprocation  (§  508,  s.  9),  of  Subordination,  of  Coordination."' 
(See  Waldin,  below,  p.  565.) 

(e)  cuasms. 

Crusius,  Weg  zur  Gewissheit.     Ed.  i.  1747;  Ed.  ii.  1762. 

§  256.  "  The  supreme  law  of  all  syllogism  is.  What  we  cannot  otherwise  think 
than  as  true,  is  true,  and  what  we  absolutely  cannot  think  at  all,  or  cannot  thirJc 
but  as  false,  is  false." ' 

1  Kaut  ( f/6er  die  Evidenz  in  inetaphysischen  gard  to  the  supreme  rule  of  all  certainty 
Wissenrhnftrn,  17G3,  Yerm.  Schrifl  ii.  43)  has  wbich  tliis celebrated  mau  thought  of  placiii<; 
liereon  tlie  following  observation  :  —  "In  re-      as  the  principle  of  all  knowledge,  and,  couM' 

71 


662 


APPENDIX. 


§  259.  Of  necessary  judgments,  of  judgments  which  we  cannot  but  think, 
"  which  are  not  identical,  and  which  constitute,  in  the  last  result,  the  positive  or 
the  kernel  in  our  knowledge  ;  to  which  we  apply  the  principle  of  Contradiction, 
and  thereby  enrich  the  understanding  with  a  knowledge  of  real  judgments,"  — 
such  judgments  are  principally  the  following :  Every  potoer  or  force  is  inherent 
in  a  subject;  All  that  arises  (begins  to  be),  arises  in  virtue  of  a  sufficient 
cause  ;  All  whose  non-existence  cannot  he  thought,  has  its  cause,  and  has  at  some 
time  arisen  (begun  to  be)  ;  Every  substance  exists  somewhere  ;  All  that  exists, 
exists  at  some  time  ;  Two  material  things  cannot  exkt  at  the  same  time,  and  in  pre- 
cisely the  same  place.  There  are  also  many  other  propositions,  which  treat  of 
ihe  determinate  qualification  of  things  as  present;  for  example —  The  same 
point  of  a  body  cannot  be  at  once  red  and  green ;  A  man  cannot  be  in  two  places 
at  once,  and  so  forth.  • 

§  261.  "  All  the  judgments  previously  alleged  (§  259)  may  be  compre- 
hended under  these  two  general  propositions,  —  What  cannot  in  thought  be  sepa- 
rated from  each  other,  cannot  be  separated  from  each  other  in  reality  ;  and,  What 
cannot  in  thought  be  connected  into  a  notion,  cannot  in  reality  be  connected ;  to 
wit,  although  no  contradiction  shows  itself  between  the  notions,  but  we  are 
only  conscious  of  a  physical  necessity  to  think  the  thing  so  and  so,  clearly  and 
after  a  comparison  of  all  the  circumstances  with  each  other.  For  we  now 
speak  of  propositions  which  are  not  identical  with  the  Principle  of  Contradic- 
tion, but  of  such  as  primarily  afford  the  matters  on  which  it  may  be  applied. 
Hence  we  see  that  the  supreme  principle  of  our  knowledge  given  above 
(§  256)  has  two  determinations ;  inasmuch  as  the  impossibility  to  think  a 
something  arises  either  because  a  contradiction  would  ensue,  or  because  we 
are  positively  so  compelled  by  the  physical  constitution  of  our  thinking 
faculties. 

§  262.  "  The  highest  principle  of  all  syllogism  thus  resolves  itself  into  the 
three  capital  propositions : 

1.  Nothing  can  at  once  be  and  not  be  in  the  same  point  of  view. 

2.  Things  which  cannot  be  thought  without  each  other,  without  each  other  cannot 
exist. 

3.  What  cannot  be  thought  as  with  and  beside  each  other,  cannot  exist  with  and 
beside  each  other,  on  the  supposition  even  that  between  the  notions  there  is  no  con- 
tradiction. 

"  The  second  of  these  capital  propositions  I  call  the  Principle  of  Insepara- 
bles (principium  inseparabilium)  ;  and  the  third  the  Prtncipfe  of  Inconjoinables 
( principium  inconjungibilium).  They  may  be  also  termed  the  three  Principles 
of  Reason." 

Ch.  VIII.     Of  the  different  species  of  .syllogisms,  he  says  (§  272),  "  Among 


qnently,  also  of  the  metaphysical,  — What  I 
cannot  otherwise  think  than  as  true,  is  true,  etc. ; 
it  is  maiiilest  that  this  proposition  can  never 
be  0  principle  of  truth  for  any  knowledge 
whatover.  For  if  it  be  agreed  that  no  other 
principle  of  truth  is  possible  than  inasmuch 
as  we  are  incapable  of  holding  a  thing  not 
for  true,  in  this  case  it  is  acknowledged  that 


no  other  principle  of  truth  is  competent,  and 
that  knowledge  is  indemonstrable.  It  is  in- 
deed true  that  there  are  many  indemonstrable 
knowledges,  but  the  feeling  of  conviction  in 
regard  to  them  is  a  confession,  but  not  a 
ground  of  proof,  that  they  are  true."'  See 
also  Keid,  Intelleetual  Poteen,  Essay  iv.  ch.  4. 


APPENDIX.  563 

the  higher  principles  of  syllogisms  it  is  needful  only  to  enumerate  the  Ptinciple 
of  Contradicfion,  and  the  Principle  of  Sufficient  Reason,  which  is  subsumed 
from  the  principle  of  Inseparables  (§  262).  We  shall  state  the  laws  of  syllo- 
gism in  this  order, — Consider  those  which  flow,  1°,  From  the  Principle  of 
Contradiction ;  2°,  From  the  Principle  of  Sufficient  Reason  ;  and,  3°,  From 
both  together." 

(f)    FRANCIS    nUTCHESON. 

[Francisci  Hutcheson.]  Logicce  Compendium.  Glasguce,  in  cedibus  academ- 
icis,  excudebant  Robertus  et  Andreas  Foulis,  Academioe  Typographi.     1 764. 

Part  III.,  Ch.  ii.,  p.  58. 

"  The  whole  force  of  syllogism  may  be  explicated  from  the  following  axioms. 

"  First  Axiom.  — Things  which  agree  in  the  same  third,  agree  among  themselves. 

"  Second  Axiom. — Things  irhereof  the  one  agrees,  the  other  does  not  agree,  in 
one  and  the  same  third,  these  things  do  not  agree  among  themselves. 

"  Third  Axiom. — Things  which  agree  in  no  third,  do  not  agree  among  them- 
selves. 

"  Fourth  Axiom. —  Things  which  disagree  in  no  third,  do  not  disagree  among 
themselves." 

"  Hence  are  deduced  the  general  rules  of  syllogisms. 

"  Of  these  the  three  first  regard  the  Quality  [not  alone]  of  Propositions. 

"  Rule  1 .  —  Jf  one  of  the  premises  be  negative,  the  conclusion  will  be  negative 
(by  Ax.  2). 

"  Rule  2.  —  If  both  premises  be  affirmative,  the  conclusion  will  be  affirmative 
(by  Ax.  1). 

'•  Rule  3.  —  If  both  premises  be  negative,  nothing  follows  :  because,  of  things 
mutually  agreeing  and  mutually  disagreeing,  both  may  be  different  from  a  third 
thing  (by  Ax.  3,  4). 

"  Two  Rules  regard  the  Quantity  of  Terms. 

"  Rule  4.  —  Let  the  middle  be  once  at  least  distributed,  or  taken  universally ; 
for  the  common  term  frequently  contains  two  or  more  species  mutually  opposed, 
of  which  it  may  be  predicated  according  to  various  parts  of  its  extension  ;  these 
[specific]  terms  do  not,  therefore,  truly  agree  in  one  third,  unless  one  at  least 
of  them  agrees  with  the  whole  middle  (by  Ax.  3,  4). 

"  Rule  5.  —  No  term  ought  to  be  taken  more  universally  in  the  conclusion  than 
in  the  premises:  because  no  consequence  is  valid  from  the  particular  to  the 
universal.  [Because  we  should,  in  that  case,  transcend  the  agreement  or  diss^- 
greement  of  the  two  terms  in  a  third,  on  which,  ex  hypothesi,  we  found.] 

"  [In  like  manner  there  are  two  rules]  concerning  the  Quantity  of  Proposi- 
tions. 

"  Rule  6.  —  If  one  of  the  premises  be  particular,  the  conclusion  will  also  be  par- 
ticular. 

"  For,  Case  I.  —  If  the  conclusion  be  affirmative,  therefore  both  premises  will 
be  affirmative  (by  Rule  1).  But,  in  a  particular  proposition,  there  is  no  term 
distributed ;  the  middle  is,  therefore,  to  be  distributed  in  one  or  other  of  the 
premises  (by  Rule  4).  It  will,  therefore,  be  the  subject  of  a  universal  affirma- 
tive proposition ;  but  the  other  extreme  is  also  taken  particularly,  when  it  i* 


564 


APPENDIX. 


the  predicate  of  an  affirmative  proposition,  the  conclusion  will,  therefore,  be 
particular  (by  Rule  5). 

"  Case  II.  —  Let  the  conclusion  be  negative ;  its  predicate  is,  therefore, 
distributed :  hence,  in  the  premises,  the  major  and  the  middle  terms  are  to  be 
distributed  (by  Rules  5  and  4). 

"  But  when  one  of  the  premises  is  negative,  the  other  is  affirmative  (by  Rule 
3).  If  one  premise  be  particular,  these  two  terms  only  can  be  distributed; 
since  one  premise  affirms,  whilst  the  other  is  particular.  The  minor  extreme, 
the  subject  of  the  conclusion,  is  not,  therefore,  distributed  in  the  premises;  it 
cannot,  therefore  (by  Rule  5),  be  distributed  in  the  conclusion. 

"  Rule  7.  —  From  two  particular  premises  nothing  follows ;  at  least  according 
to  the  accustomed  mode  of  speaking,  where  the  predicate  of  a  negative  propo- 
sition is  understood  to  be  distributed.  For,  1°,  If  the  conclusion  affirm,  both 
premises  will  affirm,  and,  consequently,  no  term  is  distributed  in  the  premises; 
contrary  to  Rule  4.  2°,  Let  the  conclusion  be  negative,  its  predicate  is  there- 
fore distributed ;  but  in  particular  premises  there  is  only  distributed  the  predi- 
cate of  a  negative  proposition ;  there  is,  therefore,  necessarily  a  vice  (either 
against  Rule  4  or  Rule  6)."' 

(a)  SAVOyAROLA. 

Savonarola,  Compemlium  Logices,  L.  iv.  p.  115,  ed.  Venetiis,  1542.  — "  In 
whatever  syllogism  any  proj)osition  can  be  concluded,  there  may  also  be  con- 
cluded every  other  proposition  which  follows  out  from  it."  On  this  he  remarks : 
"  When  any  syllogism  infers  a  conclusion  flowing  from  its  immediate  conclu- 
sion, it  is  not  to  be  called  one  syllogism,  but  two.  For  that  other  conclusion  does 
not  follow  simply  in  virtue  of  the  premises,  but  in  virtue  of  them  there  first 
follows  the  proper  conclusion,  and  from  this  conclusion  there  follows,  by  another 
syllogism,  the  conclusion  consequent  on  it.  Hence  there  are  tacitly  two  syllo- 
^sms ;  otherwise  the  moods  of  syllogisms  wbuld  be  almost  infinite." 

(h)  BAUltGARTEHr. 

Baumgarten,  Acroasis  Logica.     Ed.  Tollncr.     Ed.  I.  1765. 

§  297.  "  Every  reasoning  depends  on  this  proposition  :  —  A  and  B  connected 


A  B 

Some  Frenchmen  are  [wme]  learned  ; 
C  B 

Some  EnnJidtmcn  are  not  [any]  Icnrneii ;  Thax/hn, 
lome  Englithmen  are  not  some  Frenchmen." 


1  "Rules  1  and  7  are  thus  contracted  into 
one :  The  conclusion  follows  the  weaker  part ; 
that  is,  tlie  negative  or  the  particular.  All 
these  Rules  are  included  in  the  loUowing 
verses: 

Distribuat  mtdium,  nee  qnartui  terniinut  addt, 
Utraquc  ncc  prseinissa  ncgans,  ncc  particiilaris. 
Sicti'tur  partem  coiicliisio  di'ttiiorem; 
IZt  uoa  diatribuat  niii  cum  praemina,  n^jstre. 


In  an  unusual  mode  of  speaking,  a  certain  (What  arc  within  [    ]  arc  by  me).    [Written 

negative  conclusion  may  be  effected  with  a  Autumn,  1844.    In  the  latest  notation  (,)  i> 

non-distributive  predicate.     As  iu  thia  ex-  substituted  for  (.),ihh1  (:)  for  (:.).  SeeAppeu- 

mmple^  dixXI     -Ed.] 


APPENDIX.  666 

with  a  third  C,  are  connected  mlh  each  other :  in  affirmation  immediately,  in 
negation  mediately.  This  proposition  is,  therefore,  the  foundation  and  princi- 
ple of  all  reasoning ;  which,  however,  is  subordinate  to  the  principle  of  Con- 
tradiction. 

§  324.  "  Every  ordinary  syllogism  concluding  according  to  the  Dictum^  either 
de  Omni,  or  de  Nulla.  This  Dictum  is  thus  the  foundation  of  all  ordinary  syllo- 
gisms."    (It  had  been  previously  announced,  §§  31D,  321.) 

"  AVhatever  is  truly  affirmed  of  a  notion  universally,  is  also  truly  affirmed 
of  all  that  is  contained  under  it  Whatever  is  truly  denied  of  a  notion  univer- 
sally, is  also  truly  denied  of  all  that  is  contained  under  it." 

(i)  REIMARUS, 

Reimarus,  Vernunftlehre.     1766. 

§  176.  "  The  fundamental  rules  of  syllogism  are,  consequently,  no  other  than 
the  rules  of  Agreement  [Identity]  and  of  Contradiction.  For  what  the  geometer 
in  regard  to  magnitudes  takes  as  the  rule  of  equality  or  inequality,  that  the 
reasoner  here  adopts  as  the  universal  rule  of  all  mediate  insight :  —  If  two  things 
be  identical  with  a  third,  they  are  also  in  so  far  identical  with  each  other.  But  if 
the  ovc  he,  and  the  other  be  not,  identical  with  the  third,  then  they  are  not  mutuaUy 
identical,  but  rather  mutually  repugnant." 

§  177.  Here  he  notices  that  the  Dictum  de  Omni  et  NuUo  is  not  properly  a 
rule  for  all  figures,  but  for  the  first  alone. 

(j)  WALDUf. 

Waldin,  Novum  Logiae  Systcma.     17G6. 

§  335.  "  Since  the  syllogism  rc(iuires  essentially  nothing  but  a  distinct  cogni- 
tion of  the  sufiicient  rea?on  of  some  proposition,  the  most  universal  rule  of  all 
syllogisms  is,  —  The  sufficient  reason  of  a  given  proposition  is  to  he  distinctly 
rognized. 

§  864.  "  The  most  general  rule  of  all  reasonings  (§  335)  remains  also  the 
rule  of  all  reasonings  as  well  in  synthesis  as  in  analysis.  But  in  the  synthesis  of 
the  ordinary  syllogism  the  middle  term  in  the  major  proposition  is  referred  to 
the  major  term,  in  the  minor  proposition  to  the  minor  term.  (§  360.)  Where- 
fore, from  this  relation  we  must  judge  whether  the  middle  term  be  or  be  not 
the  sufficient  reason  of  the  conclusion.  Wherefore,  the  synthesis  of  the  ordi- 
nary syllogism  is  to  be  cognized  from  the  relation  of  its  ideas.  This  you  may 
tiius  express : 

"  1.)  After  the  true  proposition,  the  relation  of  whose  extremes  you  distinctly 
apprehend ; 

"  2.)  Add  to  its  subject  or  predicate  another  idea  different  from  bothf  tokether 
agreeing  or  disagreeing  ; 

"  3.)  Inquire  into  Hie  relation  of  the  added  idea,  to  the  end  that  you  may  know 
wliether  the  middle  term  in  the  given  relation  infer  the  conclusion  ;  and  this  .  •• 
known  by  the  application  of  the  rules  of  Reciprocation,  Subordination,  Coordina- 
tion, and  Opposition.  If  any  one  wish  to  call  this  the  Dictum  de  Omni  et  Nullo 
I  have  no  objections." 


5(66  APPENDIX. 

"Observation. — ^This  they  call  the  Dictum  de  Omni  et  Nullo  of  the  celebrated 
Reasch.  It  stands  true  indeed,  but  is  beset  with  difficulties,  inasmuch  as  it  is 
rather  a  complexus  of  all  rules  than  one  ohly,  which  as  yet  is  to  be  referred 
to  the  class  of  pia  desideria.  Logicians  have,  indeed,  taken  pains  to  dis- 
cover one  supreme  rule  of  all  ordinary  reasonings ;  but  no  one  has  as  yet 
been  so  happy  as  to  find  it  out"  Then  follows  a  criticism  of  the  attempts 
by  the  Port  Royal  and  Syrbius. 


(t)  STATTLSS. 

Stattler,  Philosophia,  P.  I.  Logica,  1 769. 

§  237.  "  In  this  comparison  of  two  ideas  with  a  third,  six  different  cases  may 
in  all  occur :  for,  either, 

I.)  "One  of  the  two  ideas  contains  that  same  third,  which  again  contains  the 
other;  or, 

2.)  "  Both  of  the  two  are  contained  in  the  third ;  or, 

S.)  "  Each  of  the  two  contains  the  third;  or, 

4.)  "  One  of  the  two  contains  the  third,  the  other  being  repugnant  with  it ; 
or, 

5.)  "One  of  the  two  is  contained  in  the  third,  with  which  the  other  is  repugnant ; 
or, 

6.)  "  Both  of  the  two  are  repugnant  to  the  third. 

•'  The  former  three  cases  generate  an  affirmative  conclusion,  the  latter  three 
a  negative."  In  a  note  Stattler  eliminates  a  seventh  case,  in  which  neither  may 
contain,  and  neither  be  repugnant  to  the  third. 

§  244.  General  Law  of  all  Reasonings.  "  In  all  reasonings,  as  often  as  a  con- 
sequent is,  by  legitimate  form,  inferred  from  an  antecedent,  so  often  is  there 
included  in  the  antecedent  what  the  consequent  enounces  ;  either  the  congruity  and 
reciprocal  containment,  or  the  repugnance  of  A  and  C ;  and  if  such  be  not 
included  in  one  or  other  of  the  antecedents,  whatever  is  inferred  in  the  consequent 
is  void  of  legitimate  form." 

(I)  SAOTSK. 

Sauter,  Institutiones  Logica:,  1798. 

§  1 23.  "  Foundations  of  Syllogism.  —  In  ^verj'  syllogism  there  are  two  notions 
compared  with  a  third,  to  the  end  that  it  may  appear  whether  they  are  to  be 
conjoined  or  sejoined.  There  are,  therefore,  here,  three  possible  cases.  For 
there  agree  with  the  assumed  third,  either  both  notions,  or  one,  or  neither.  In 
i-easoning,  our  mind,  therefore,  reposes  on  these  axioms,  as  on  fundament&l 
principles. 

1.)  "Wliere  txoo  notions  agree  with  the  same  third,  they  agree  with  one  another. 

2.)  '•  Where  one  is  contained  by  the  third,  with  which  the  other  is  repugnant, 
they  are  mutually  repugnant. 

8.)  "  When  neither  notion  agrees  mth  the  third,  there  is  between  them  neither 
agreement  nor  repugnance." 


APPENDIX.  567 


(m)  SUTEli. 

Suter,  Logica. 

§  61.  "  Quae  eidem  tertio  conveniunt  vel  disconveniunt,  etiam  coaveniunt 
vel  discouveniunt  inter  se." 

(n)  SEGUT. 

Seguy,  Philosophia  ad  Usum  Scholarum  Accommodata,  T.  I.  Logica.  Paris, 
1771. 

P.  1 75,  ed.  1 785.     "  Concerning  the  rule  of  recent  philosophers." 

Having  recited  the  general  rule  of  the  Port  Royal  Logic,  he  thus  comments 
on  it  : 

"1°,  This  is  nothing  else  than  the  principle  of  reasoning;  therefore,  it  is 
improperly  adduced  as  a  neV  discovery,  or  a  rule  strictly  so  called. 

"  2°,  It  may  be  useful,  to  the  rude  and  inexperienced,  to  recognize  whether 
a  syllogism  be  legitimate  or  illicit. 

"  But  the  principal  fault  of  this  rule  is,  that  it  contains  no  certain  method 
whereby  we  may  know  when,  and  when  not,  one  of  the  premises  contains  a 
conclusion ;  for  the  discovery  of  which  we  must  frequently  recur  to  the  general 
rules."! 

P.  1 78.  Seguy  exposes  Father  Buflier's  error  in  saying,  "  that,  according  to 
Aristotle  and  the  common  rules  of  Logic,  the  middle  term  ought  absolutely  to 
be  the  predicate  in  the  first  or  major  proposition  ;  "  seeing  that  the  middle  term 
is  not  the  predicate  in  the  first  and  third  Figures.  This  must  be  a  mistake  ;  for 
I  cannot  find  such  a  doctrine  in  Buffier,  who,  in  this  respect,  in  many  places 
teaches  the  correct. 

(o)  HOFFBACER. 

Hoffbauer,  Anfangsgriinde  der  Logik,  1794,  1810. 

"  §  317.    Fundamental  Principles. 

"  I.  1.)  An  attribute  which  belongs  to  all  and  every  of  the  objects  contained 
under  a  notion,  may  also  be  aflii'med  of  these  objects  so  contained.  (Dictum 
de  Omni.) 

"  2.)  An  attribute  which  belongs  to  none  of  the  objects  contained  under  a 
notion,  must  also  be  denied  of  these  objects  so  contained.     (Dictum  de  NuUo.) 

"II.  When,  of  the  objects  X  and  Z,  the  one  contains  an  attribute  which  the 
other  does  not  contain,  and  they  are  thus  different  from  each  other,  then  X  is 
not  Z,  and  Z  is  not  X. 

"III.  1.)  When  objects  which  are  contained  under  a  notion  a  are  also  con- 
tained under  another  notion  b,  then  this  last  notion  contains  under  it  some  at 
least  of  the  objects  which  are  contained  under  the  first. 

"  2.)  If  certain  objects  which  are  not  contained  under  a  notion  a  are  con- 

1  Followed  by  Larroque,  Elcmrns  de  Philo-  Metqfisica,  1.  47,  i.  348.  E  contra,  Philosophia 
tophie,  p.  231;  Galluppi,  Lezioni  di  Logica  e  di      Lugdunensis,  i.  159.    Troxler,  Logik,  ii.  41. 


568  APPENDIX. 

tained  under  &,  tlien  b  contains  under  it  some  at  least  of  the  objects  which  are 
not  contained  under  a. 

"IV.  1.)  If  objects  which  are  contained  under  a  notion  a  belong  to  those 
which  are  contained  under  another  notion  b,  then  this  second  notion  b  contains 
under  it  some  at  least  of  the  objects  which  are  contained  under  a. 

"  2.)  If  all  objects  which  are  contained  under  a  notion  a  belong  to  those 
which  are  not  contained  under  a  certain  other  notion  i,  then  this  noUon  b  con- 
tains under  it  no  object  which  is  contained  under  tJie  notion  a. 

"  3.)  If  all  the  objects  contained  under  a  certain  Aotion  a  are  different  from 
certain  other  objects  contained  under  b,  then  b  contains  under  it  at  least  some 
objects  which  are  not  contained  under  a." 

(p)  KAST.  0 

Kant,  Lor/ik.     1800-6.     II.  Syllogisms. 

"  §  56.  Syllogism  in  General.  —  A  syllogism  is  the  cognition  that  a  certain 
proposition  is  necessary,  through  the  subsumption  of  its  condition  under  a  given 
general  rule. 

"§  57.  General  principle  of  all  Syllogisms.  —  The  general  principle  whereon 
tlie  validity  of  all  inference,  through  the  reason,  rests,  may  be  determiriately 
enounced  in  the  following  formula  : 

"  What  stands  under  the  condition  of  a  rule,  that  stands  also  under  the  rule 
itself. 

"Ol)servatinn. —  The  syllogism  premises  a  General  Rule,  and  a  Subsumption 
under  its  Condition.  Hereby  we  understand  the  conclusion  a  priori,  not  as 
manifested  in  things  individual,  but  as  universally  maintained,  and  as  necessary 
under  a  certain  condition.  And  this,  that  all  stands  under  the  universal,  and  is 
determinable  in  universal  laws,  is  the  Principle  itself  of  Rationality  or  of  Neces- 
sity (principium  rationalitatis  seu  necessitatis). 

"  §  58.  Essetitial  constituents  of  the  Syllogism.  —  To  every  syllogism  there 
belong  the  three  following  parts : 

"  1.)  A  general  rule,  styled  the  Major  proposition  (propositio  major,  Obersatz). 

"  2.)  The  proposition  which  subsumes  a  cognition  under  the  condition  of  the 
general  rule,  called  the  Minor  proposition  (propositio  minor,  Untersatz) ;  and, 
finally, 

"  3.)  The  proposition  which  affirms  or  denies  the  predicate  in  the  rule  of  the 
subsumed  cognition,  —  the  Concluding  proposition,  or  Conclusion  ( Conclusio, 
Sehlussatz). 

"  The  two  first  propositions,  taken  in  connection  with  each  other,  are  called 
the  Antecedents,  or  Premises  (  Vordersdtze). 

"Observation.  —  A  rule  is  the  assertion  of  a  general  condition.  The  relation 
of  the  condition  to  the  assertion,  how,  to  wit,  this  stands  under  that,  is  the  Ex- 
ponent of  the  rule.  The  cognition,  that  the  condition  (somewhere  or  other) 
takes  place,  is  the  Subsumption. 

**  TTic  nexus  of  what  is  subsumed  under  the  condition,  with  the  assertion  of 
the  rule,  is  the  Conclusion." 

Having  shown  the  distribution  of  syllogisms  into  Categorical ,  Hypothetical, 
and  Diy'unctive,  he  proceeds  to  speak  of  the  first  class. 


APPENDIX.  569 

"  §  63.  Principle  of  Categorical  Syllogisms.  —  The  principle  whereon  the 
possibility  and  validity  of  Categorical  Syllogisms  is  this,  —  What  pertains  to  the 
attribute  of  a  thing,  that  pertains  to  the  thing  itself;  and  what  is  repugnant  to 
the  attribute  of  a  thing,  that  is  repugnant  to  the  thing  itself  (Nola  nolcc  est 
nota  ret  ipsius  ;  Repugnans  notoe,  repugnat  rei  ipsi). 

*^  Observation.  —  From  this  principle,  the  so-called  Dictum  de  Omni  et  Nullo 
is  easily  deduced,  and  cannot,  therefore,  be  regarded  as  the  highest  principle 
either  of  the  Syllogism  in  general,  or  of  the  Categorical  Syllogism  in  particular. 
Generic  and  Specijic  Notions  are  in  fact  the  general  notes  or  attributes  of  all 
the  things  which  stand  under  these  notions.  Consequently  the  rule  is  here 
valid  —  What  pertains  or  is  repugnant  to  the  genus  or  species,  that  also  pertains 
or  is  repugnant  to  all  the  objects  tohich  are  contained  under  that  genus  or  species. 
And  this  very  rule  it  is  which  is  called  the  Dictum  de  Omni  et  Nullo." 


(q)  CHRISTIAN  WEISS. 

Christian  Weiss,  Logifc,  1801. 

"  §  216.  Principle  for  all  Syllogisms.  —  The  principle  of  every  perfect  Syllo- 
gism consists  in  the  relation  of  one  of  the  notions  contained  in  the  conclusion  to  a 
third  notion  (terminus  medius),  to  ivhich  the  other  notion  of  the  conclusion  belongs. 
Now  the  relation  which  the  first  of  these  holds  to  the  middle  notion,  the  same  must 
hold  to  the  second,  just  because  the. second  coincides  with  the  middle  notion  to  the 
same  extent  as  the  first. 

"  Remark.  —  ^Relation  to'  means  only  any  determinately  thought  relation 
expressed  in  a  judgment 

"  The  older  logicians  adopt,  some  of  them,  the  principle  Nota  noice  est  nota 
rei  ipsius,  —  quod  repugnat  notes,  repugnat  ipsi  rei ;  this,  however,  is  only  prop- 
erly applicable  to  the  first  figure.  The  expression  of  others  is  preferable, 
Qucecumque  conveniunt  (vel  di-isentiunt)  in  uno  tertio,  eadem  conveniunt  (vel 
dissentiunt)  inter  se.  Others,  in  fine,  among  whom  is  Wolf,  give  the  Dictum  de 
Omni  et  Nullo  (cf.  §  233)  as  the  principle  of  syllogisms  in  general ;  compare 
Philosophical  Aphorisms  [of  Platner],  P.  i.  §  546.  All  inference  takes  place 
according  to  a  universal  rule  of  reason,  here  only  expressed  in  reference  to 
syllogism,  to  which,  however,  some  have  chosen  to  give  a  more  mathematical 
expression :  —  If  ttoo  notions  be  equal  to  a  third,  they  are  also  equal  to  each 
other. 

[iVoto  bene.  —  Weiss's  mistake  (§  231)  in  supposing  that  Aristotle  "  desig- 
nated the  syllogistic  moods  with  words,  like  his  learned  followers."] 

"§231.  Categorical  Syllogisms,  Figure  1. — The  first  figure  concludes  by 
means  of  a  subordination  of  the  minor  term  in  the  conclusion  under  the  subject 
of  another  judgment. 

"  §  233.  This  takes  place  under  the  general  principle  : 

"  1.)  What  pertains  to  all  objects  contained  under  a  notion,  that  pertains  also  to 
some  and  to  each  individual  of  their  number  among  them. 

"  2.)  What  belongs  to  none  of  the  objects  contained  under  a  notion,  that  also 
does  not  jwrtain  to  some  or  to  any  individual  of  their  number  among  ihem. 

*'  These  are  the  celebrated  Dicta  de  Omni  and  de  Nullo,  —  Qaidquid  prce' 

12, 


570  APPENDIX. 

dicatur  de  omni,  idem  etiam  de  aliquo,  and,  Quidquid  prcedicatur  de  nuUo,  id  n9» 
de  aliquo prmdicatur" 

(r)  FRIES. 

Fries,  System  der  Logik. 

"  §  52.  Hitherto  we  have  maintained  two  views  of  the  Syllo^sm  in  connec- 
tion. The  end  in  view  of  reasoning  is  this,  —  that  cases  should  be  subordinated 
to  general  rules,  and  through  them  become  determined.  For  example,  the 
general  law  of  the  mutual  attraction  of  all  heavenly  bodies  has  its  whole  signi- 
ficance, for  my  knowledge,  in  this,  that  there  are  given  individual  heavenly 
bodies,  as  Sun  and  Earth,  to  which  I  apply  it.  To  enounce  these  relations,  it 
is,  in  the  first  place,  necessary  that  I  have  a  general  rule,  as  Major  Proposition 
(Obersatz) ;  in  the  second,  a  Minor  Proposition  (Untersatz),  which  subordi- 
nates cases  to  the  rule ;  and,  finally,  a  Concluding  Proposition,  which  determines 
the  cases  through  the  rule.  On  the  other  hand,  we  see  that  every  Conclusion 
is  an  analytico-hypothetic  judgment,  and  this  always  flows  from  the  Dictum  de 
Omni  et  Nullo,  inasmuch  as  the  relation  of  subordination  of  particular  under 
universal  notions,  is  the  only  relation  of  Reason  and  Consequent  given  in  the 
form  of  thought  itself  Now,  if  the  conclusion,  as  syllogism,  combines  a  plu- 
rality of  judgments  in  its  premises,  in  this  case  the  principle  of  the  inference 
must  lie  in  a  connection  of  the  thoughts,  —  a  connection  which  is  determined 
by  the  matter  of  these  judgments.  In  the  simplest  case,  when  taking  into  ac- 
count only  a  single  syllogism,  I  thus  would  recognize  in  the  premises  the  rela- 
tion of  subordination  between  two  notions  by  reference  to  the  same  third 
notion,  and  therethrough  perceive  in  the  conclusion  the  relation  of  these  two 
notions  to  each  other.  I  know,  for  example,  that  all  men  are  mortal,  and  that 
Caius  is  a  man.  Consequently,  through  the  relation  of  the  notion  of  mortality , 
and  of  my  imagination  of  Caius,  to  the  notion  man,  the  relation  of  Caius  to 
mortality  is  likewise  determined  :  —  Caius  is  mortal.  The  first  of  these  views 
is  a  mere  postulate ;  but  in  conformity  to  the  second  we  are  enabled  imme- 
diately to  evolve  the  general  form  of  syllogisms,  and  from  this  evolution  does 
it  then  become  manifest  that  all  possible  syllogisms  satisfy  the  postulate.  We, 
therefore,  in  the  first  instance,  attach  oui-selves  to  the  second  view.  Through 
this  there  is  determined  as  follows : 

"  1.)  Here  the  determination  of  one  notion  is  carried  over  to  another,  super- 
ordinate  or  subordinate  to  itself.  To  every  syllogism  there  belong  three 
notions,  called  its  terms  (termini).  (We  say  notions  (Begriff),  because  they 
are,  in  general,  such,  and  when  individual  reprt^sentations  [or  images]  appear 
as  terms,  in  that  case  there  is  no  inter-commutation  possible.)  A  major  term, 
or  superior  notion  (Oberbegriff),  P,  is  given  as  the  logical  determination  of  a 
middle  term  or  notion  (Mittelbegriff),  M,  and,  through  this,  it  is  positively  or 
negatively  stated  as  the  determination  of  a  minor  term  or  notion  .(Unlerbeg- 
riff),S. 

*'  2.)  If,  then,  we  regard  the  propositions  in  which  these  relations  are 
enounced,  there  is,  firstly,  in  the  conclusion  (Schlussatz),  the  minor  term,  or 
inferior  notion,  subordinated  to  the  major  term,  or  superior  notion  (S  is  P). 
Further,  in  one  of  the  premises,  the  middle  must  be  connected  with  the  major 
term  or  notion  (M  is  P).     This  is' called  the  major  propositio/i  (Obersatz).     lu 


APPENDIX.  571 

the  other,  again,  the  minor  is  connected  with  the  major  term  or  notion  (S  is 

M)  ;  this  is  called  the  minor  proposition  (Untersatz). 
"  The  form  of  every  syllogism  is  therefore  — 

Major  Proposition,  M  is  P. 

Minor  Proposition,  S  is  M. 


Conclusion,  S  i«  P. 

"  In  the  example  given  above,  man  is  the  middle  term ;  mortality  the  major 
term ;  and  Caius  the  minor  term.     The  syllogism  is  — 

Major  Proposition,  All  men  are  mortal; 

Minor  Proposition,  Cuius  is  a  many- 


Conclusion,  Caius  is  mortal. 

"  The  fundamental  relation  in  all  syllogisms  is  that  of  the  middle  term  to 
the  major  and  minor  terms ;  in  other  words,  that  of  the  carrying  over  of  a 
logical  determination  from  one  notion  to  another,  through  certain  given  sub- 
ordinations. For,  howbeit  the  Dictum  de  Omni  et  NuUo,  as  a  common  princi- 
ple of  all  syllogisms  in  the  formula,  —  What  holds  good  of  the  universal,  holds 
also  good  of  the  particulars  subordinate  thereto,  and  still  more  in  that  other, — 
The  attribute  of  the  attribute  is  also  the  atiribute  of  the  thing  itself  —  is  proxi- 
mately only  applicable  to  the  categorical  subordination  of  a  representation  [or 
notion]  under  a  notion;  still,  however,  the  law  of  mental  connection  is  alto- 
gether the  same  in  syllogisms  determined  by  the  subordination  of  consequence 
under  a  reason  [Hypothetic  Syllogisms],  or  of  the  complement  of  parts  under 
a  logical  whole  [Disjunctive  Syllogisms].  The  displayed  form  is  the  form  of 
every  possible  syllogism.  In  fact,  it  also  coincides  with  the  first  requirement 
that,  in  the  syllogism,  a  case  should  always  be  determined  by  a  rule,  inasmuch 
as  every  syllogism  proposes  a  universal  premise,  in  order  rigorously  to  infer 
its  conclusion.  This  will  be  more  definitely  shown  when  we  treat  of  syllo- 
gisms in  detail.  Only  the  declaration,  that  the  rule  is  always  the  major  proposi- 
tion, is  sometimes  at  variance  with  the  declaration,  that  the  major  proposition 
contains  the  relation  of  the  middle  term  to  the  major  term.  We  must,  however, 
in  the  first  place,  always  follow  the  determination  of  the  latter.  For  every 
syllogism  properly  contains  the  three  processes :  —  1).  The  subordination  of  a 
particular  under  a  universal ;  this  is  the  function  of  the  minor  proposition,  ^^^ 
the  relation  between  the  minor  and  major  terms ;  2).  Postulate  of  a  logical 
determination  for  one  of  these  two ;  this  is  the  function  of  the  major  proposi- 
tion, and  the  relation  of  the  middle  to  the  major  term;  3).  The  carrying  over 
this  determination  to  that  other ;  this  is  the  function  of  the  conclusion  and  the 
relation  of  the  minor  to  the  major  terms. 

"  §  53.  The  subordination  of  a  particular  to  a  universal  must,  therefore,  in 
every  syllogism,  be  understood  wholly  in  general.  Here  either  a  particular 
may  be  determined  through  the  superordinated  universal,  and  such  an  in- 
ference from  universal  to  particular  we  shall  call  a  syllogism  in  the  first  figure; 
or  there  Is  a  universal  known  through  its  subordinated  particular,  and  this 
inference  from  the  particular  to  the  universal  is  called  a  syllogism  in  the  second 
Ithird']  figure.    If,  for  example,  the  subordination  is  given  me,  —  All  gold  is 


572  APPENDIX. 

metal;  I  can  either  transfer  an  attribute  of  metal,  for  instance  fusibility,  to  the 
gold,  or  enounce  an  attribute  of  gold,  ductility,  for  instance,  of  some  metal.  In 
the  first  case,  I  draw  a  conclusion  in  the  first  figure,  from  the  universal  to  the 
particular : 

AU  metal  is  fusible  ; 

All  gold  is  metal; 


AU  gold  is  fusible. 


"  In  the  other  case,  I  conclude  in  the  second  [third]  figure  from  the  par- 
ticular to  the  general : 

All  gold  is  ductile ; 
AU  gold  is  metal; 


Some  metal  is  ductile. 


Then,  after  distribution  of  the  Syllogism  into  Categorical,  Hj'pothetical,  and 
Divisive  (Disjunctive),  he  proceeds  with  the  first  class. 

($)   KIESEWETTER. 

BLiesewetter,  Allgemeine  Logik,  1801,  1824.     I.  Theil. 

"  §  228.  —  All  pure  Categorical  Syllogisms,  whose  conclusion  is  an  affirma- 
tive judgment,  rest  on  the  following  principle :  —  What  pertains  to  the  attribute 
of  an  object,  pertains  to  the  object  itself.  All  syllogisms,  whose  conclusion  is  a 
negative  judgment,  are  based  upon  the  principle: — What  is  repugnant  to  the 
attributes  of  an  object,  is  repugnant  to  the  object  itself.  Two  principles  which 
can  be  easily  deduced,  —  the  first  from  the  principle  of  Identity,  the  second 
from  the  principle  of  Contradiction. 

"  §  229.  —  If  we  take  into  consideration  that  the  major  proposition  of  every 
categorical  syllogism  must  be  a  universal  rule, —  from  this  there  flow  the  fol- 
lowing rules : 

"  1.  Whatever  is  universally  affirmed  of  a  notion,  that  is  also  affirmed  of 
everything  contained  under  it.     The  Dictum  de  Omni. 

"  2.  What  is  universally  denied  of  a  notion  is  denied  also  of  everything  con- 
tained under  it.     The  Dictum  de  Nullo. 

"  These  rules  are  also  thus  expressed : 

"  What  pertains  to  the  genus  or  species,  pertains  also  to  whatever  is  con- 
tained under  them.  What  is  repugnant  to  the  genus  or  species,  is  repugnant 
also  to  whatever  is  contained  under  them." 

See  also  the  Weitere  Auseinandersetzung  on  the  paragraphs. 

(I)    LARROQUE. 

Larroque,  Eltmeng  de  Philosophie,  Paris,  18S0.  Logique,  ch.  i.,  p.  202. 
"The  attribute  of  an  affirmative  proposition  is  taken  sometimes  particularly, 
Kometimes  universally.  It  is  taken  particularly  when  it  has  a  greater  extension 
than  the  subject;  universally,  when  it  has  not  a  greater  extension,  which  oc- 
curs in  every  proposition  where  the  two  terms  are  identical.     The  reason  of 


APPENDIX.  573 

this  difference  is  palpable.  If  the  attribute  be  a  term  more  general  than  the 
subject,  we  affirm  that  the  subject  is  a  species  or  individual  contained  in  the 
extension  of  the  attribute  :  —  Man  is  mortal ;  Paul  is  learned  ;  —  that  is,  man  is 
one,  and  not  the  only,  species  contained  in  the  extension  of  the  term  mortal; 
Paul  is  an  individual,  and  not  every  individual,  contained  in  the  extension  of 
the  term  learned.  If,  on  the  contrary,  the  attribute  be  not  more  general  than 
the  subject,  the  attribute  is  the  same  thing  with  the  subject,  and,  consequently, 
we  affirm  that  the  subject  is  all  that  is  contained  in  the  extension  of  the  at- 
tribute:— A  circle  is  a  plane  surface,  which  has  all  the  points  in  [a  line  calledj 
its  circumference  at  an  equal  distance  from  a  point  called  its  centre,  —  that  is, 
«  circle  is  all  or  every  plane  surface,  etc. 

"  The  attribute  of  a  negative  proposition  is  always  taken  universally.  When 
we  deny  an  attribute  of  a  subject,  "we  deny  of  this  subject  everything  that  has 
the  nature  of  that  attribute,  that  is  to  say,  all  the  species,  as  all  the  individuals, 
contained  in  its  extension :  The  soul  is  not  extended;  to  wit  the  soul  is  not  any 
of  the  species,  not  any  of  the  individuals  contained  in  the  extension  of  the  term 
extended." 

Ch.  ii.,  p.  230.  "  We  have  supposed,  in  the  demonstration  of  these  rules 
[the  general  rules  of  the  Categorical  Syllogism],  that  the  attribute  of  an  affirm- 
ative premise  is  always  taken  particularly.  It  would,  therefore,  seem  that  the 
calculations  on  which  this  demonstration  rests  are  erroneous,  whensoever  the 
attribute  is  not  a  term  more  general  than  the  subject,  for  we  have  seen  that, 
in  these  cases,  the  attribute  can  be  taken  universally.  But  it  is  to  be  observed, 
that  when  the  two  terms  of  a  proposition  are  identical,  if  the  one  or  the  other 
may  be  taken  nniversally,  they  cannot  both  be  so  taken  at  once ;  and  that,  if  it 
be  the  attribute  which  is  taken  universally,  it  ought  to  be  substituted  for  the 
subject,  which  then  affords  a  particular  attribute.  A  triangle  is  a  figure  which 
has  three  sides  and  three  angles.  We  cannot  say.  All  triangle  is  all  figure, 
which,  etc. ;  but  we  can  say.  All  triangle  is  some  figure,  which,  etc. ;  or,  All  figure 
which  has  three  sides  and  three  angles  it  some  triangle.  Now,  in  adopting  either 
of  these  last  expressions  of  the  proposition,  the  attribute  is  particular." 

Ch.  iL,  p.  231.  "We  have  seen  that  the  Syllogism  inferred  from  its  prem- 
ises a  proposition  to  be  proved ;  now  this  conclusion  cannot  be  inferred  from, 
unless  it  be  contained  in,  the  premises.  From  this  incontestable  observation 
the  author  of  the  Port  Royal  Logic  has  endeavored  to  draw  the  following  pre- 
tended rule,  by  aid  of  which  we  may  detect  the  vice  of  any  fallacious  reasoning 
whatsoever :  7'hus  sJwuld  one  of  the  premises  contain  the  conclusion,  and  the 
other  show  (hat  it  is  so  contained.  A  great  many  treatises  on  Logic  call  this 
the  single  rule  of  the  moderns.  This  pompous  denomination  seems  to  point  at 
some  marvellous  discovery,  of  which  the  ancients  had  no  conception,  —  at 
some  consummative  result  of  the  efforts  of  the  human  intellect.  It  is  true, 
indeed,  that  a  syllogism  is  invalid  if  the  conclusion  be  not  contained  in  the 
premises ;  but  a  fine  discovery  forsooth  !  This  all  the  world  already  knew,  — 
Aristotle  among  the  rest ;  but  he  justly  noted  that  it  is  not  always  easy  to  see 
whether  the  conclusion  be  contained  in  the  premises,  and  it  is  to  assure  our- 
selves of  this  that  he  laid  down   his  rules.     The  pretended  rule  of  the  Port 


)74 


APPENDIX 


Royal  is,  therefore,  not  one  at  all ;  it  enounces  only  an  observation,  true  but 
barren." 

(uj   GALLUP VI. 

Galluppi,  Lezioni  di  Logica  e  di  Metafisica.  1832.  Lez.  xlvii.,  p.  353,  ed. 
1841. 

"  In  a  reasoning  there  must  be  an  idea,  common  to  the  two  premises ;  and  a 
judgment  which  affirms  the  identity,  either  partial  or  perfect,  of  the  other  two 
ideas." 

In  the  same  Lecture  (p.  348)  he  shows  that  he  is  ignorant  of  the  law 
<luoted  from  the  Philosophia  Luffdunensis,  being  by  the  authors  of  the  L'  Art  de 
Penser. 

(V)  BUTFIER. 

Buffier,  Premiere  Logique,  about  1725.  The  following  is  from  the  Recapitu- 
lation, §  109: 

The  Syllogism  is  defined,  a  tissue  of  three  propositions,  so  constituted  that 
if  the  two  former  be  true,  it  is  impossible  but  that  the  third  should  be  true 
also.     (§  63.) 

The  first  Proposition  is  called  the  Major:  the  second  the  Minor;  the 
third  the  Conclusion,  which  last  is  the  essential  end  in  view  of  the  s>'ll(^sm. 
(§  65.) 

Its  art  consists  in  causing  a  consciousness,  that  In  the  conclusion  the  idea  of 
the  subject  comprises  the  idea  of  the  predicate  ;  and  this  is  done  by  means  of  a 
third  idea,  called  the  Middle  Term  (because  it  is  intermediate  between  the  sub- 
ject and  predicate),  in  such  sort  that  it  is  comprised  in  the  subject,  and  com- 
prises the  predicate.     (§  67.) 

If  the  first  thing  comprise  a  second,  in  which  a  third  is  comprised,  the  first 
comprises  the  third.  If  a  fluid  comprise  chocolate,  in  which  cocoa  is  comprised, 
the  fluid  itself  comprises  cocoa.     (§  68.) 

To  reach  distant  conclusions,  there  is  required  a  plurality  of  syllogisms. 
(§  71.) 

Our  rule  of  itself  suffices  for  all  syllogisms,  even  for  the  negative ;  for  every 
negative  syllogism  is  equivalent  to  an  affirmative.     (§  77.) 

Hypothetical  syllogisms  consist  in  the  enouncement,  by  the  major  premise, 
that  a  proposition  is  true  in  case  there  be  found  a  certain  condition ;  and  the 
minor  premise  shows  that  this  condition  is  actually  found.     (§  70.) 

Disjunctive  syllogisms,  to  admit  of  an  easy  verification,  ought  to  be  rednced 
to  hypothetical.     (§  81.) 

Although  the  single  rule,  which  is  proposed  for  all  syllogisms,  be  subject  to 
certain  changes  of  expression,  it  is  nevertheless  always  the  most  easy ;  in  feet, 
all  logical  laws  necessarily  suppose  this  condition.     (§  87.) 

The  employment  of  Grammar  is  essential  for  the  practice  of  Logic.     (§  90.) 

By  means  of  such  practice,  which  enables  us  to  estimate  accurately  the  value 
of  the  terms  in  every  proposition,  we  shall  likewise  obtain  the  rule  for  the  dis- 
covery of  all  sophisms,  which  consist  only  of  the  mere  equivocation  of  words, 
and  of  the  ambiguity  of  propositions.     (§  92  et  s«g.) 


APPENDIX.  576 

(w)  VTCTORiy. 

Victorin,  Neue  naturVichere  Darstellung  der  Logik,  Vienna,  1835. 

II.  Simple  Categorical  Syllogisms.  §  94.  The  fundamental  rule  of  all  such 
syllogisms : 

"  In  what  relation  a  concept  stands  to  one  of  two  reciprocally  subordinate  con- 
cepts, in  the  same  relation  does  it  stand  to  the  other." 

§  94.  First  Figure  ;  fundamental  rule:  —  "As  a  notion  determines  the  higher 
notion,  so  does  it  det^nnine  the  lower  of  the  same : "  or,  "  In  what  relation  a 
notion  stands  to  one  notion,  in  the  same  relation  it  stands  to  the  lower  of  the  same." 

§  96.  Second  Figure ;  fundamental  rule :  — "  When  two  notions  are  oppo- 
sitely determined  by  a  third  notion,  they  aire  also  themselves  opposed;"  or,  "7/" 
two  notions  stand  to  a  third  in  opposed  relations,  they  also  themselves  stand  in  a 
relation  of  opposition." 

§  98.  Third  Figure ;  fundamental  rule  :  —  "As  a  notion  determines  the  one  of 
two  l_to  jV]  subordinate  notions,  so  does  it  determine  the  other;"  or,  "In  what 
relation  a  notion  stands  to  the  one  of  two  \to  tV]  subordinate  notions,  in  the  same 
relation  stands  it  also  to  the  other." 

§  100.  Fourth  Figure;  fundamental  rule:  —  "As  a  notion  is  determined  by 
the  one  of  two  subordinate  notions  [^tico  notions  in  the  relation  to  each  other  of 
subordination'],  so  does  it  determine  the  other;"  or,  "In  what  relation  one  of  two 
subordinated  notions  [^notions  reciprocally  subordinate  or  superordinate]  stands  as 
to  a  third,  in  the  same  relation  stands  it  also  to  the  other." 


II.  —  Fundamental  Laws  of   Syllogism.  —  References. 

(See  Galluppi,  Lezioni  di  Logica  e  di  Metafisica,  Lez.  xlvii.,  vol.  i.  p.  345 
et  seq. ;  Troxler,  Logik,  i.  p.  33  ;  Bolzano,  Wissenschaftslehre,  Logik,  vol.  ii. 
§  263,  p.  543.) 

I.  Logicians  who  confound  the  Nota  notse  and  the  Dictum  de  Omni,  being 
ignorant  of  their  several  significances ;  making  them  — 

a)  Coordinate  laws  without  distinction. 

Jiigcr,  Handb.  d.  Logik,  §  68  (1839)  ;  Prochazka,  Gesetzb.,f  d.  Denken,  §  217 
(1842)  ;  Calker,  Denklehre,  §  143  (1822).     Troxler,  Logik,  ii.  p.  40. 

b)  Derivative  ;  the  Dictum  de  Omni,  to  wit,  from  the  Nota  notae.  This 
supreme  or  categorical. 

Wenzel,  Elem.  Philos.  Log.,  §§  253,  256.  Canonik,  §  64.  Kant,  Diefalsche 
Spitzf.,^3.  Logik,  ^63.  Krug,  Logik,  §  70.  Bachmann,  io^r*,  §  123.  Jakob, 
Logik,  §  262,  4th  ed.  1800  ;  1st  ed.  1788. 

II.  Logicians  who  enounce  the  law  of  Identity  (Proportion),  in  the  same 
third,  by  the  mathematical  expression  Equality. 

Reimarus,  Vernunftlehre,  §  176.  Mayer,  Vemunftschlusse,  i.  p.  290.  Arriaga, 
In.  Sum.,  D.  III.  §  3,  p.  23. 

III.  Logicians  who  make  the  Dictum  de  Omni  the  fundamental  rule  of  syl- 
logisms in  general. 

Aristot.,  An.  Prior.,  L.  i.  c.  1,  §  4.  Wolf,  Phil.  Rat.,  §  353.  Scheibler,  Op. 
P.  iv.     De  Syll.  c.  ii.  §  12.     Jac.  Thomasius,  Erot.  Log.,  c.  395.     Buttner,  Cur- 


676  APPENDIX. 

sus  PhUos.,  Log.,  §  146.  Conimbricenses,  In  Arist.  Dial.,  An.  Prior.,  L,  i.  c.  2, 
p.  204. 

IV.  Logicians  "who  confound  or  make  coordinate  the  law  of  Proportion  or 
Analogj',  and  the  Dictum  de  Omni. 

Wvttenbach,  Pr(ec.  Philos.  Log.,  P.  iii.  c.  6,  §  4.  Whately,  Logic,  Intr.,  eh. 
II.  p.  iii.,  §  2.  Leechman,  Logic,  P.  III.  ch.  2.  Keckermann,  Sj/stema  Logicce 
Minus,  L.  iii.  c.  2.     Syst.  Log.  Majus.,  L.  iii.  c.  5. 

V.  Logicians  who  make  the  Law  of  Identity  the  one  supreme. 

Suter,  Logica,  §  61,  calls  this  the  principle  of  Identity  and  Contradiction. 
Aldrich,  Comp.,  L.  i.  c.  3,  §  3,  p.  2.  Hutcheson,  Log.  Comp.,  P.  iii.  c.  2. 
Arriaga,  Cur.  Phil.,  In.  Sum.,  D.  iii.  §§  16-22,  pp.  23,  24.  Larroque,  Logique, 
p.  224.  Mayer,  Vemunftschusse,  i.  p.  293.  Troxler,  Logik,  ii.  pp.  33,  40. 
Reimarus,  Vemunftlehre,  §  176.  Mendoza,  Disp.  Log.  et  Met.,  I.  p.  470. 
Derodou,  Log.  Rest.,  De  Log.,  pp.  639,  644.  Darjes,ria.,  etc.,  §  271,  p.  97. 
Smiglecius,  Logica,  D.  xiii.  p.  517,  qu.  etc.  Fran.  Bonae  Spei,  Com.  Prim,  in 
Log.  Arist.,  D.  vii.  d.  2,  p.  25.  Cursus  Complut.,  De  Arg.,  L.  iii.  c.  4,  p.  57. 
Alstedius,  Enc.  Logica,  §  ii.  c.  10,  p.  435.  Havichonet,  Inst.  Log.,  §  324. 
Poncius,  Cursus  Philos.  In  An.  Prior.,  D.  xx.  qu.  5,  p.  282. 

VI.  Logicians  who  restrict  the  Dictum  de  Omni  to  the  First  Figure  (im- 
mediately). 

Aldrich,  Comp.  1.  1,  c.  3,  §  7.  Noldius,  Log.  Rec,  c.  xii.  p.  290.  Grosser, 
Pknrus  Intellectus,  §  iii.  p.  1,  memb.  iii.  p.  13  7. 

VII.  Logicians  who  make  the  Dicta  de  Omni  et  Nullo  the  supreme  canons 
for  Universal  Syllogisms  ;  the  law  of  Proportion  for  Singular  Syllogisms. 

Burgersdicius,  Inst.  Log.,  L.  ii.  c.  8,  p.  171.  Melancthon,  EroL  Dial.,  De 
Syll.  Expos.,  L.  iii.  p.  172,  ed.  1586.  Fonseca,  Instil.  Dial,  L.  vi.  cc.  21,  24, 
pp.  363,  373. 

VIII.  What  name  given  by  what  logicians  to  the  Law  of  Proportion,  etc. 
Law  of  Proportion,  or  of  Analogy,  Keckermann,  Syst.  Log.  L.  iii.  c.  5,  Op., 

p.  746.  Alstedius,  Encycl.,  p.  435,  -rh  i.ya\oyias.  Dictum  de  Omni  et  Nullo 
Majus,  Noldius,  Log.,  p.  288.  Of  Identity,  Zedler's  Lex.  Pr.  convenienticB. 
Darjes,  Via  ad  Verit,  §  270,  p.  96.  Law  of  Proportional  Identity  and  Non- 
Identity,  Self. 

IX.  Ix)gicians  erroneously  supposing  Aristotle  to  employ,  besides  the  Dictum 
de  Omni,  the  rule  of  Proportion  as  a  fundamental  law  of  syllogism. 

Rapin,  Reflexions  sur  la  Logique,  §  4. 

X.  Terms  under  which  the  law  of  Proportion  has  been  enounced. 

Agree  with.  Coincide  with.  The  same  with.  Cohere  (Syrbius).  Coexist 
(bad).  Cdidentical  with.  Equal  to  (No.  ii.).  In  combination  with,  Darjes,  Via 
ad  Ver.,  p.  97  (includes  negative).     Convertible. 

III.  —  Enunciations   or  thk  HiOBEa  Laws  of  Stllogism. 

Law  of  Proportion. 

Aristotle,  Elench,  c.  vi.  §  8.  "  Things  the  same  with  one  and  the  same,  are 
the  same  with  one  another."  Compare  Topica,  L.  vii.  c.  1,  §  6.  Thus  Scotus, 
In  An.  Prior.,  L.  i.  qu.  9,  f.  248. 


APPENDIX.  577 

Some  say,  "  Uni  tertio  indivisihili" — some  others,  "  Uni  tertio  indivisibiii, 
indivisiblliter  sumpto."  Others,  in  fine,  say,  "  Uni  tertio,  adequate  sumpto." 
See  Irenaeus,  Integ.  Philos.  Log.,  §§  3,  5.  Some  exj>ress  it,  "  Things  that  are 
equal  to  the  same  tliird  are  equal  to  each  other."  See  Irenaeus,  ih.  So  Reinv 
arus,  Mayer. 

Some  express  it,  "  Quaecunque  conveniunt  (vel  dissentiunt)  in  uno  tertio, 
eadem  conveniunt  (vel  dissentiunt)  inter  se." 

"  Quffi  duo  conveniunt  cum  uno  quodam  tertio,  eatenus  conveniunt  inter  se; 
quando  auteni  duorum  unum  convenit  cum  tertio,  et  alterum  huic  repugnat, 
repugnant  quoque  eatenus  sibi  invicem."  Wynpersse,  Inst.  Logicce,  §  272,  Lug. 
Bat.  3d  ed.  1806. 

Noldius  (Logica,  p.  288)  calls  these  the  Dicta  de  Omni  et  de  Nullo.  The 
former  is,  "  Quaecunque  affirmantur  in  aliquo  tertio  (singulari  identice,  univer- 
sali  et  identice  et  complete  distributive),  affirmantur  inter  se."  The  latter, 
"  Quorum  unum  [totaliter]  affirmatur  in  aliquo  tertio,  alterum  negatur,  ea  inter 
86  negantur." 

Noldius. — "Whatever  is  affirmed  essentially  of  a  subject,  is  affirmed  of  all 
that  is  inferior  or  reciprocal  to  that  subject.  Whatever  is  denied  of  a  subject, 
is  denied  of  all  inferior  or  reciprocal."  (See  Noldius  against  the  universal 
application  of  these  Dicta,  Log.  Rec,  p.  290.) 

Reusch  (Syst.  Logicum,  ed.  i.  1734,  §  503)  makes  the  Dicta  de  Omni  et 
NuUo  the  rule  of  ordinary  syllogisms,  and  thus  enunciates  them :  "  Si  quid 
praedicatur  de  omni,  illud  etiam  praedicatur  de  aliquo :  et,  Si  quid  predicatur 
de  nuUo,  illud  etiam  non  praedicatur  de  aliquo.  Sensus  prioris  est,  Quidquid 
de  genere ,  vel  specie  omni  prsedicari  potest,  illud  etiam  prsedicatur  de  quovis . 
sub  illo  genere,  vel  sub  ilia  specie,  contento ;  Item,  —  Cuicunque  competit 
definitio,  illi  quoque  competit  definitum."    (And  so  vice  versa  of  the  other.) 

Syrbius  gives  these  two  rules : 

1)  "  If  certain  ideas  cohere  with  a  one-third,  they  also  cohere  in  the  same 
manner  with  each  other." 

2)  "  Ideas  which  do  not  cohere  with  the  same  one-third,  these  do  not  cohere 
with  each  other."  (Given  in  the  original  by  Waldin,  Sysiema,  p.  162.  See 
also  Acta  Eruditorum,  1718,  p.  333.)  Syrbius  thinks  that  the  law  of  Propor- 
tion, unless  limited,  is  false. 

Darjes,  Via  ad  Veritatem  (1755),  §  270,  p.  96,  2d  ed.  1764.  "Two  [things  or 
notions]  in  combination  with  the  same  third,  may  be  combined  together  in  the 
same  respect  (ea  ratione)  wherein  they  stood  in  combination  with  that  third." 
(See  further;  shows  that  other  rules  are  derived  from  this.) 

Dictum  de   Omni,  etc. 

Aristotle,  Anal.  Pr.,  L.  i.  c.  i.  §  11. 

"  To  be  predicated,  de  Omni,  universally,  is  when  we  can  find  nothing  under 
the  subject  of  which  the  other  [that  Is,  the  predicate]  may  not  be  said  ;  and  to. 
be  predicated  de  Nullo,  In  like  manner." 

Jac.  Thomasius,  Erotemata  Logica.,  1670. 

"  40.  What  do  you  call  the  foundation  of  syllogism  ?  —  The  Dictum  de 
Omni  et  Nullo. 

"41.  What  is  the  Dictum  de  Omni? — When  nothing  can  be  subsumed. 

73 


§78  APPENDIX. 

under  the  subject  of  the  major  proposition  of  which  its  predicate  may  not  be 
affirmed. 

"  42.  What  is  the  Dictum  de  Nullo  ?  — When  nothing  can  be  subsumed 
under  the  subject  of  the  major  proposition  of  which  its  predicate  is  not 
denied." 

Thomasius  notices  that  the  first  rule  applies  only  to  the  aflirmative  moods  of 
the  first  figure,  Barbara  and  Darii ;  the  second  only  to  the  negative  moods  of 
the  same  figure,  Celarent  and  Ferio. 


IV.  —  Objections  to  the  Dictom  de  Omni  et  Nullo. 

I.  As  a  principle  of  syllogism  in  general. 

n.  As  a  principle  of  the  First  Figure,  as  enounced  by  Aristotle. 

1°,  Only  applies  to  syllogisms  in  extension. 

2°,  Does  not  apply  to  individual  syllogisms ;  as,  Peter  is  running  ;  hut  $ome 
man  is  Peter;  there/ore,  some  man  is  running. 

(Arriaga,  In.  Surnm.,  p.  24.) 

3°,  Does  not  apply  to  coextensive  reasonings ;  as.  All  trilateral  is  (all)  tri- 
angular ;  but  all  triangular  has  three  angles  equal  to  two  right  angles ;  ergo,  etc. 
Arriaga,  t6. 

Dictum  de  Omni  et  Niillo  does  not  apply, 

1°,  To  the  other  Figures  than  the  First. 

2°,  Not  to  all  the  moods  of  First  Figure,  for  in  many  of  these  the  higher 
class  is  subjected  to  the  lower. 

3°,  The  form  of  the  First  Figure  does  not  depend  upon  the  principle  of  the 
Dictum  de  Omni  et  Nullo.  This  imperfect ;  not  upon  the  thorough-going  prin- 
ciple, that  in  this  figure  one  notion  is  compared  to  a  second,  and  this  second 
with  a  third. 

V.  —  General  Laws  of  Stllooism  in  Verse. 

(1)  Partibus  ex  puris  sequitur  nil  (2)  sive  negatis. 

(3)  Si  qua  prasit  partis,  sequitur  conclusio  partis. 

(4)  Si  qua  negata  praeit,  conclusio  sitque  negata. 

(5)  Lex  generalis  erit,  medium  concludere  nescit.' 

(6)  Univocusque  ;  (7)  triplex;  (8)  ac  idem  terminus  esto.* 
'(1)  DIstribuas  medium ;  (2)  nee  quartus  terminus  adsit 

(3)  Utraque  nee  praemissa  negans ;  (4)  nee  particularis. 

(5)  Sectetur  partem  conclusio  deteriorem  ; 

(6)  Et  non  distribuat  nisi  cum  prsemissa,  (7)  negetve.* 


1  Petrus  Hispanns,  Summula.    [Tr.  iv.  c.  8,         2  Campanella,  DiaUet.,  p.  384. 
f  46  b.  —  Ed.]  3  Hutcbeson,  Log.  Comp.  [P.  iii.  c.  8,  p.  58.— 

Ed.] 


APPENDIX. 


679 


Terminus  csto  triplex  :  medius,  majorque,  minorque  : 

Latins  hunc  quam  prjemissse,  conclusio  non  vult, 

Nequaquam  medium  capiat  conclusio  oportet. 

Aut  semel  aut  itcrum  medium  generaliter  esto. 

Nil  sequitur  geminis  ex  particularibus  unquam. 

Utraque  si  praemissa  neget,  nihil  inde  sequetur. 

Ambae  afRrmantes  nequeunt  generare  negantem. 

Est  parti  similis  conclusio  deteriori.  ^ 

Pejorem  sequitur  semper  conclusio  partem.         ) 

Terminus  est  geminus,  mediumque  accedit  utrique. 

Prsemissis  dicat  ne  finis  plura,  caveto. 

Aut  semel,  aut  iterum  medium  genus  omne  capessat ; 

Officiique  tenax  rationem  daudere  nolit. 

Terminus  est  triplex.     (2)  Medium  conclusio  vitet. 
Hoc  ex  prseniissis  altera  distribuaL 

Si  praemissa  simul  fuit  utraque  particularis, 
Aut  iitrin(jue  negans,  nulla  sequela  veniL 

Particulare  praeit  V  sequitur  conclusio  partis. 
Ponitur  ante  negans  ?     Clausula  talis  erit. 

Quod  non  prascessit,  conclusio  nulla  requirit.* 

Tum  re,  tum  sensu,  triplex  modo  terminus  esto. 
(  Argumentari  non  est  ex  particulari. 
I  Neque  negatlvis  recte  concludere  si  vis. 
j  Nunquam  complecti  medium  conclusio  debet. 
I  Quantum  praemissae,  referat  conclusio  solum. 
(  Ex  falsis  falsum  verumque  aliquando  sequetur; 
(  Ex  veris  possunt  nil  nisi  vera  sequi.' 


VI.  —  Special  Laws  of  Syllogism  in  Veesb. 

1 .  Fig.  Sit  minor  affirmans,  nee  major  particularis. 

2.  Fig.  Una  negans  esto,  major  vero  generalis, 

3.  Fig.  Sit  minor  affirmans,  conclusio  particularis. 

4.  Fig.  a)  Major  ubi  affirmat,  generalem  sume  minorem. 

b)  Si  minor  affirmat,  conclusio  sit  speclalis. 

c)  Quando  negans  modus  est,  major  generalis  habetur.* 


B.— CRITICISM. 
L  —  Chiticism  of  the  Special  Laws  op  Syllogism. 

The  Special  Laws  of  Syllogism,  that  is,  the  rules  which  govern  the  several 
Figures  of  Categorical  Reasonings,  all  emerge  on  the  suspension  of  the  logical 


1  Purchot,  with  variations  of  Seguy,  Ph. 
Lugd.,  Galluppi.  [Purchot,  Inst.  Phil.,  vol. 
i.,  Logicn,  P.  iii.  c.  3,  p:  171.  —  Ed.] 

a  Isendoorn,  Logica,  L.  iii.  c.  8,  p.  427,  8°, 
(1652).    Chauvin  and  Walch,  Lex.  v.  Syttog. 


3  Crakanthorpe,  Logica,  L.  iii.  c.  15,  p.  210. 

4  Ubaghs,  LogicBR  Elementa,  §  225.  Sancru- 
cius,  Dialeetiea  ad  Mentem  Doet.  SubtUis,  L.  i. 
c.  3,  p.  103.    Lend.  1673. 


S§0  APPENDIX. 

postulate,  —  To  be  able  to  state  in  language  what  is  operative  in  thought 
They  all  emerge  on  the  refusal  or  neglect  to  give  to  the  predicate  that  quantity 
in  overt  expression  which  it  possesses  in  the  internal  operations  of  mind.  The 
logicians  assert,  1°,  That  in  affirmative  propositions  the  predicate  must  be 
always  presumed  particular  or  indefinite,  though  in  this  or  that  proposition  it 
be  known  and  thought  as  universal  or  definite ;  and,  2°,  That  in  negative 
propositions  this  same  predicate  must  be  always  presumed  absolutely  (i.  e., 
universally  or  definitely)  excluded  from  the  sphere  of  the  subject,  even  though 
in  this  or  that  proposition  it  be  known  and  thought  as  partially  (i.  e.,  partic- 
ularly or  indefinitely)  included  therein.  The  moment,  however,  that  the  s^d 
postulate  of  Logic  is  obeyed,  and  we  are  allowed  to  quantify  the  predicate  in 
language,  as  the  predicate  is  quantified  in  thought,  the  special  rules  of  syllo- 
gism disappear,  the  figures  are  all  equalized  and  reduced  to  unessential  modi- 
fications ;  and  while  their  moods  are  multiplied,  the  doctrine  of  syllogism  itself 
is  carried  up  to  the  simplicity  of  one  short  canon.  Having  already,  shown  that 
the  general  laws  of  syllogism  are  all  comprised  and  expressed  in  this  single 
canon,^  it  now  only  remains  to  point  out  how,  on  the  exclusive  doctrine  of  the 
logicians,  the  special  rules  became  necessary,  and  how,  on  the  unexclnsive  doc- 
trine which  is  now  propounded,  they  became  at  once  superfluous  and  even 
erroneous.  It  is  perhaps  needless  to  observe,  that  the  following  rules  have 
reference  only  to  the  whole  of  Extension. 

The  double  rule  of  the  First  Figure,  that  is,  the  figure  in  which  the  middle 
term  is  subject  in  the  sumption,  and  predicate  in  the  subsumption,  is,  —  SU 
minor  affirmans ;  nee  major  particularis.  Here,  in  the  first  place,  it  is  prescribed 
that  the  minor  premise  must  be  aflfirmative.  The  reason  is  manifest  ;  because, 
if  the  minor  premise  were  negative,  the  major  premise  behooved  to  be  affirma- 
tive. But  in  this  figure,  the  predicate  of  the  conclusion  is  the  predicate  of  the 
major  premise ;  but  if  affirmative,  the  predicate  of  that  premise,  on  the  doctrine 
of  the  logicians,  is  presumed  particular,  and  as  the  conclusion  following  the 
minor  premise  is  necessarily  negative,  a  negative  proposition  thus,  contrary  to 
logical  law,  has  a  particular  predicate.  But  if  we  allow  a  negative  proposition 
to  have  in  language,  as  it  may  have  in  thought,  a  particular  or  indefinite  predi- 
cate, the  rule  is  superseded. 

The  second  rule,  or  second  part  of  the  rule,  of  this  First  Figure,  is,  that  the 
major  premise  should  be  universal.  The  reason  of  this  is  equally  apparent 
For  we  have  seen  that,  by  the  previous  rule,  the  minor  premise  could  not  be 
negative,  in  which  case  certainly,  had  it  been  allowable,  the  middle  term  would, 
as  predicate,  have  been  distributed.  But  whilst  it  behooved  that  the  middle 
term  should  be  once  at  least  distributed  (or  taken  universally),  and,  as  being 
the  subject  of  the  major  premise,  it  could  only  be  distributed  in  a  universal 
.proposition,  the  rule,  on  the  hypothesis  of  the  logicians,  was  compulsory.  But 
as  we  have  seen  that  the  former  rule  is,  on  our  broader  ground,  inept,  and  that 
the  middle  term  may  be  universally  quantified,  as  the  predicate  either  of  an 
affirmative  or  negative  subsumption,  it  is  equally  manifest  that  this  rule  is,  in 
like  manner,  redundant,  and  even  false. 

In  the  Second  Figure,  that  is,  the  figure  in  which  the  middle  term  is  predica^ 

1  See  pp.  636and  A88.  — Bd. 


APPENDIX.  581 

both  in  sumption  and  subsumption,  the  special  rule  is,  —  Una  negans  esio ; 
major  vero  generalis. 

In  regard  to  the  first  rule^  or  first  half  of  the  rule,  —  That  one  or  other  of 
the  premises  should  be  negative,  —  the  reason  is  manifest.  For,  on  the  doc- 
trine of  the  logicians,  the  predicate  of  an  afiirmative  proposition  is  always 
presumed  to  be  particular ;  consequently,  in  this  figure  the  middle  term  can, 
on  their  doctrine,  only  be  distributed  (as  distributed  a£  least  once  it  must  be) 
in  a,  negative  judgment.  But,  on  our  doctrine,  on  which  the  predicate  is  quan- 
tified In  language  as  in  thought,  this  rule  Is  abolished.^ 

The  second  rule,  or  second  moiety  of  the  rule,  —  That  the  sumption  should 
be  always  univei"sal,  —  the  reason  of  this  is  equally  clear.  For  the  logicians,  not 
considering  that  both  extremes  wei'e  in  equlllbrio  in  the  same  whole  of  exten- 
sion, and,  consequently,  that  neither  could  claim  [in  either  quantity]  the  place 
of  major  or  minor  term,  and  thereby  constitute  a  true  major  or  a  true  minor 
premise ;  -^  the  logicians,  I  say,  arbitrarily  drew  one  instead  of  two  direct  con- 
clusions, and  gave  the  name  of  major  term  to  that  extreme  which  formed  the 
predicate  in  that  one  conclusion,  and  the  name  of  major  premise  to  that  ante- 
cedent proposition  which  they  chose  to  enounce  first.  On  their  doctrine, 
therefore,  the  conclusion  and  one  of  the  premises  being  always  negative,  it 
behooved  the  sumption  to  be  always  general,  otherwise,  contrary  to  their  doc- 
trine, a  negative  proposition  might  have  a  particular  predicate.  On  our 
doctrine,  however,  this  difficulty  does  not  exist,  and  the  rule  is,  consequently, 
superseded. 

In  the  Third  Figure,  that  is,  the  figure  in  which  the  middle  term  is  subject 
of  both  the  extremes,  the  special  rule  Is,  —  Sil  minor  riffirwans ;  conclusio  par- 
tictdaris. 

Here  (he  first  half  of  the  rule,  —  That  the  minor  must  not  be  negative, — 
is  manifestly  determined  by  the  common  doctrine.  For  (mnjor  and  minor 
terms,  major  and  minor  propositions,  being  in  this  figure  equally  arbitrary  as  in 
the  second)  here  the  sumption  behooving  lo  be  affirmative,  its  predicate,  con- 
stituting the  major  term  or  predicate  of  the  conclusion,  behooved  to  be  partic- 
ular also.  I>ut  (he  conclusion  following  the  minor  premise  would  necessarily 
be  negative  ;  and  It  would  have  —  what  a  negative  proposition  is  not  allowed 
on  the  common  doctrine  —  an  undistributed  predicate. 

The  second  half  of  the  rule,  —  That  the  conclusion  must  be  particular,— 
is  detennined  by  the  doctrine  of  the  logicians,  that  the  particular  antecedent, 
which  they  choose  to  call  the  minor  term,  should  be  affirmative.  For,  in  this 
case,  the  middle  term  being  the  subject  of  both  premises,  the  predicate  of  the 
aubsumption  is  the  minor  extreme  ;  and  that,  on  their  doctrine,  not  being  dis- 
tributed in  an  affirmative  proposition,  it  consequently  forms  the  undistributed 


1  [For  examples  from  Aristotle  of  affirma-  ositions  in  Second  Figure,  and  does  not  give 

live  coiiclus)oii*i.iu  the  Second  Figure,  see  De  the  reason  why  the  inference  is  good  or  bad 

Olio,  L.  ii.  c.  4,  i  4,  text  23,  ibi  Averroes.  in  such  syllogism.    Cf.  Ammonius  and  Philr- 

Pi'iys.  L.  ii.  c.  2,  §  12,  text  23,  ibi  Averroes;  c.  ponus  ad.  loc.    An.  Prior,  L.  ii.  c.  22,  §}  7,  >*. 

4.  i  8,  text  38,  ibi  Averroes.     Jb.c.  7,  §  1,  text  An.  Post  ,  L.  i.   c.  6,  §   1,  et  ibi,  Themistiu:, 

42,  ibi  Averroes.    An.  Post,  L.  i.  c.  12,  §  12,  Pacius,  Zabarella.     Cf.    also   Zabarella,  Df 

text  92,  ibi  Averroes  et  Pacius.    Argues  him-  Quarta  Fig.  Syll.,  c.  x.] 
fcelf,  like  Cseneus,  from  two  affirmative  prop- 


582  APPENDIX. 

subject  of  the  conclusion.  The  conclusion,  therefore,  having  a  particular  aulx 
ject,  is,  on  the  common  doctrine,  a  particular  proposition.  But  as,  on  our 
doctrine,  the  predicate  of  an  affirmative  proposition  may  have  a  universal 
quantification,  the  reason  fails. 

n.  —  Laws  of  Second  Figure — Additional.^ 

By  designating  the  quantity  of  the  predicate,  we  can  have  the  middle  term 
(which  in  this  figure  is  always  a  predicate)  distributed  in  an  affirmative  propo- 
ntiou.     Thus : 

AUPisaUM; 

AU  S  x$  some  M ; 

Therefore,  all  S  is  some  P. 

AU  the  things  that  are  orgnnized  are  all  the  tilings  that  are  endowed  with  Ufe  ; 
Btft  all  plants  are  some  things  endowed  with  life; 
Therefore,  aU  plants  are  some  things  organized. 

This  first  rule  (see  above,  p.  291)  must,  therefore,  be  thus  amplified:  —  The 
middle  term  must  be  of  definite  quantity,  in  one  premise  at  least ;  that  is,  it 
must  either,  1"*,  Be  a  singular,  —  individual,  —  concept,  and,  therefore,  identi- 
cal in  both  premises ;  or,  2°,  A  universal  notion  presumptively  distributed  by 
negation  in  a  single  preuiise ;  or,  3"*,  A  univei"sal  notion  expressly  distributed 
by  designation  in  one  or  both  premises. 

But  the  second  rule,  which  has  come  down  from  Aristotle,  and  is  adopted 
into  every  system  of  Logic,  with  only  one  exception,  an  ancient  scholiast,  is 
altogether  erroneous.  For,  1°,  There  is  properly  no  sumption  and  subsump- 
tion  in  this  figure ;  for  the  premises  contain  quantities  which  do  not  stand  to 
each  other  in  any  reciprocal  relation  of  greater  or  less.  Each  premise  may, 
therefore,  stand  first.  The  rule  ought  to  be,  "  One  premise  must  be  definite  ; " 
but  such  a  rule  would  be  idle  ;  for  what  is  here  given  as  a  special  canon  of  this 
figure,  was  already  given  as  one  of  the  laws  of  syllogism  in  general.  2°,  The 
error  in  the  principle  is  supported  by  an  error  in  the  illustration.  In  both  the 
syllogisms  given,*  the  conclusion  drawn  is  not  that  which  the  premises  warrant- 
Take  the  first  or  affirmative  example.  The  conclusion  here  ought  to  liavo 
been.  No  S  is  some  P,  or.  Some  P  is  »)o  S ;  for  tliere  are  always  two  eijuivalent 
conclusions  in  this  figure.  In  the  concrete  example,  the  legitimate  conclusions, 
as  necessitated  by  the  premises,  are,  —  No  horse  is  some  animal,  and.  Some 
animal  is  no  horse.  This  is  shown  by  my  mode  of  explicating  the  quantity  of 
the  predicate,  —  combined  with  my  symbolical  notation.  In  like  manner,  in 
the  second  or  negative  syllogism,  the  conclusion  ought  to  have  been  either 
of  the  two  following:  In  the  abstract  formula,  —  All  S  are  not  some  P,  or. 
Some  P  are  not  all  H;  —  in  the  concrete  example,  AU  topazes  are  not  some  min- 

I  What  follows  to  paj;e  583  was  on  early  The  iuterpolation  apjiears  in  students'  notes 

written  interpolation  by  the   author  in  Lr.c-  of  the  Lectures  of  session  1841-12,  and   was 

tures  (p.  291),  being  an  application  of  the  prin-  probably  given  still  earlier.—  Ed. 

•iple  of  a  quantified  predicate  to  syllogism.  ii  See  p.  292.  —  Rd. 


APPENDIX.  583 

erah,  i.  c,  No  topazes  are  some  minerals,  or,  Some  minerals  are  not  all  topazes, 
i.  e.,  Some  minerals  are  no  topazes. 

The  moods  Cesare  and  Camestres  may  be  viewed  as  really  one,  for  they 
are  only  the  same  syllogism,  with  premises  placed  first  or  second,  as  is  always 
allowable  in  this  [Figure],  and  one  of  the  two  conclusions,  which  are  always 
legitimately  consequential,  assigned  to  each. 

A  syllogism  in  the  mood  Festiuo  admits  of  either  premise  being  placed  first ; 
it  ought,  therefore,  to  have  had  another  mood  for  its  pendant,  with  the  affirma- 
tive premise  first,  the  negative  premise  second,  if  we  are  to  distinguish  moods 
in  this  figure  by  the  accidental  arrangement  of  the  premises.  But  this  was 
prohibited  by  the  second  Law  of  this  Figure,  —  that  the  Sumption  must  always 
be  universal.  Let  us  try  this  rule  in  the  formula  of  Festino  now  stated,  revers- 
ing the  premises. 

Some  S  are  M  (i,  e.,  some  M); 
JVoPtsM; 


INoF  is  some  S.      1 
(  Some  S  are  no  P.    ) 

Some  actions  are  praiseworthy  ,• 

No  vice  is  praiseiDorihy ; 
(  No  vice  is  some  action. 
I  Some  action  is  no  nee. 

From  what  I  have  now  said,  it  will  be  seen  that  the  Dictum  de  Omni  et  de 
Nullo  cannot  afford  the  principle  of  the  Second  Figure. 

The  same  errors  of  the  logicians,  on  which  I  have  already  commented,  in 
supposing  that  the  sumption  or  major  premise  in  this  figure  must  always  be 
universal,  —  an  error  founded  on  another  error,  that  there  is  (properly  speak- 
ing) either  sumption  or  subsumption  in  this  figure  at  all,  —  this  en  or,  I  say, 
has  prevented  them  recognizing  a  mood  corresponding  to  Baroco,  the  firs* 
premise  being  a  particular  negative,  the  second  a  universal  affirmative,  i. «., 
Baroco  with  its  premises  reversed.  That  this  is  competent  is  seen  from  the 
example  of  Baroco  now  given.     Reversing  it  we  have : 

\^Some  a  are  not  B ;  Some  animals  are  not  (any)  oviparous ; 

All  a  are  B.  All  birds  are  (some)  oviparous. 

No  a  IS  some  d ;  No  bird  is  some  animal; 

Some  a  are  no  a.]  Some  animal  is  no  bird. 

m.  —  Author's  Supreme  Canoxs  of  Categorical  Syllogisms. 

[The  supreme  Canon  or  Canons  of  the  Categorical  Syllogism,  finally  adopted 
by  Sir  W.  Hamilton,  are  as  follows  :] 

L  "  For  the  Unfigured  Syllogism,  or  that  in  which  the  terms  compared  do 
not  stand  to  each  other  in  the  reciprocal  relation  of  subject  and  predicate, 
being,  in  the  same  proposition,  either  both  si>bjects  or  (possibly)  both  predicates. 


684  APPENDIX. 

—  the  canon  is :  —  In  so  far  as  ttco  notions  (notions  proper,  or  individuals) 
either  both  agree,  or  one  agreeing,  the  other  does  not,  with  a  common  third  nation  ; 
m  so  far,  these  notions  do  or  do  not  agree  tcitk  each  other. 

11.  "  For  the  Figured  Syllogism,  in  which  the  terms  compared  are  severally 
subject  and  predicate,  consequently,  in  reference  to  each  other,  containing  and 
contained  in  the  counter  wholes  of  Intension  and  Extension,  —  the  canon  is : 

—  What  worse  relation  of  subject  and  predicate  subsists  between  either  of  two 
terms  and  a  common  third  term,  with  which  one,  at  least,  is  positively  related  ;  that 
relation  subsvits  between  the  two  terms  themselms. 

"■  Each  Figure  has  its  own  Canon. 

f*  First  Figure :  —  What  worse  relation  of  determining  (predicate)  and  of 
determined  (subject)  is  held  by  either  of  two  notums  to  a  third,  with  which  one  at 
least  is  j^ositirely  related ;  that  relation  do  they  immediately  (directly)  hold  to 
each  other,  and  indirectly  (mediately)   its  converse. 

"  Second  Figure :  —  What  worse  relation  of  determined  (subject)  is  held  by 
either  of  ttco  notions  to  a  third,  with  which  one  at  least  is  positively  related  ;  that 
relation  do  they  hold  indifferently  to  each  other. 

"  Third  Figure :  —  What  icorse  relation  of  determining  (predicate)  is  held  by 
either  of  two  notions  to  a  third,  with  which  one  at  least  is  positively  related  ;  that 
relation  do  they  hold  indifferently  to  each  other."  * 

IV.  —  Ultra-Total  Qdantification  op  Middle  Term. 

(a)  LAMBERTS  DOCTRINE. 

Lambert,  Neues  Organon. 

Dianoiologie,  §  193.  "  If  it  be  indetermined  how  far  A  does,  or  does  not, 
coincide  with  B,  but,  on  the  other  hand,  we  know  that  A  and  B,  severally, 
make  up  more  than  half*  the  individuals  under  C,  in  that  case  it  is  manifest 
that  a  [linear]  notation  is  possible,  and  that  of  the  two  following  kinds : 

C c. 


B- b, 

A. 

"  For  since  B  and  A  are  each  greater  than  the  half  of  C,  A  is  consequently 
greater  than  C  less  by  B ;  and  in  this  case,  it  is  of  necessity  that  some  A  are 
B,  and  some  B  are  A.*    We  may  accordingly  so  delineate : 


.B b. 


seeing  that  it  is  indifferent  whether  we  commence  with  A  or  with  B.  I  may 
add,  that  the  case  which  we  have  here  considered  does  not  frequently  occur, 
inasmuch  as  the  couiparative  extension  of  our  several  notions  is  a  relation 

1  Dhcussiotis,  pp.  654,  665.  —  Ed.  I  have  elsewhere  had  occasion  to  show.    See 

Sit  is  enough  if  either  A  or  B  exceed  the  below,  p.  688. 

b*]f  ;  the  other  need  be  only  half.     This,  3  In  the  original,  for  A  tbere  is,  by  a  tjrpo- 

wbich  Lambert  liere  and  hereafter  overlooks,  graphical  erratum,  C.    See  Ph. }  206. 


APPENDIX.  685 

which  remains  wholly  unknown.^  I,  consequently,  adduce  this  only  as  an  exam- 
ple, that  a  legitimate  employment  may  certainly  be  made  of  these  relations." 

Phanomenologie,  §  v.     Of  the  probable  — 

"  §  188.  In  so  far  as  such  propositions  are  particular,  they  may,  like  all  other 
particular  propositions,  be  syllogistically  employed ;  but  no  farther,  unless  we 
look  to  their  degree  of  particularity,  or  other  proximate  determination,  some 
examples  of  which  we  have  adduced  in  the  Dianoiologie  (§  235  et  seq.).  Thus 
the  degree  of  particularity  may  render  a  syllogism  valid,  which,  without  this, 
would  be  incompetent.     For  example  : 

Three-fourths  of  A  are  B; 
Ttco- thirds  of  A  are  C ; 
Therefore,  some  C  are  B. 

The  inference  here  follows,  because  three-fourths  added  to  two-thirds  are 
greater  than  unity ;  and,  consequently,  there  must  be,  at  least,  five-twelfths  of 
A  which  are  at  once  B  and  C. 

"  §  204.  In  the  Third  Figure  we  have  the  middle  term,  subject  in  both 
premises,  and  the  conclusion,  particular.  If,  now,  the  subjects  of  the  two 
premises  be  furnished  with  fractions  [?'.  e.,  the  middle  term  on  both  sides],  both 
premises  remain,  indeed,  particular,  and  the  conclusion,  consequently,  indeter- 
mined.  But,  inasmuch  as,  in  both  premises,  the  degree  of  particularity  is 
determined,  there  are  cases  where  the  conclusion  may  be  drawn  not  only  with 
probability,  but  with  certainty.  Such  a  case  we  have  already  adduced  (§  188.) 
For,  if  both  premises  be  affirmative,  and  the  sum  of  th^  fractions  with  which 
their  subjects  are  furnished  greater  than  unity,  in  that  case  a  conclusion  may 
be  drawn.     In  this  sort  we  infer  with  certainty : 

Threefourths  of  A  are  B ; 
Two-thirds  of  A  are  C ; 
Therefore,  some  C  are  B. 

"  §  205.  If,  however,  the  sum  of  the  two  fractions  be  less  than  unity,  as  -^ 

One  fourth  of  A  are  B ; 
One-third  of  A  are  C, 

1  In  reference  to  this  statement,  see  above,  tive  amount.    For   Logic   and   Philosophy 

Dion,  i  179,  and  below,  Ph.  §  157,  where  it  is  tend  always  to  an  unexclusive  generality ; 

repeated    and    confirmed.      Lambert    might  and    a    general    conclusion    is    invalidated 

have  added  that,  as  we  rarely  can  employ  equally  by  a  single  adverse  instance  as  by  a 

this  relation  of  the  comj>arative  extension  of  thousand.    It  is  only  in  the  concrete  or  real 

our  notions  it  is  still  more  rarely  of  any  im-  whole,  —  the  whole  quantitative  or  integrate, 

port  that  we  should.  For  in  the  two  abstract,  an^,   whether    continuous    or    discrete,    the 

or  notional,  wholes,  —  the  two  wholes  correl-  whole  in  which  mathematics  are  exclusively 

ative  and  counter  to  each  other,  with  which  conversant,  but  Logic  and  Philosophy  little 

Lo^ic  is  always  conversant  (the  Universal  and  interested,  —  that  this  relation  is  of  any  avail 

Formal ),  —  if  the  extension  be  not  complete,  or  significance, 
it  is  of  no  consequence  to  note  its  compara- 

74 


586  APPENDIX. 

in  that  case  there  is  no  certainty  in  any  affirmative  conclusion  [indeed  in  any 
conclusion  at  all].     But  if  we  state  the  premises  thus  determinately, — 

Three-fourths  of  A  are  not  B; 
Tioo-thirds  of  A  are  not  C ; 

in  that  case,  a  negatiye  conclusion  may  be  drawn.    For,  from  the  propositions, 

Three-fourths  of  A  are  not  B ; 
One-third  of  A  are  C; 

there  follows  —  Some  C  are  not  B.  And  this,  again,  because  the  sum  of  the 
two  fractions  (three-fourths  added  to  one-third)  is  greater  than  unity."  And 
so  on.    See  the  remainder  of  this  section  and  those  following,  till  §  211. 

(t)  AOTHOIPS  DOCTRINE. 

Aristotle,  followed  by  the  logicians,  did  not  introduce  into  his  doctrine  of 
syllogism  any  quantification  between  the  absolutely  universal  and  the  merely 
particular  predesignations,  for  valid  reasons.  —  1°,  Such  quantifications  were 
of  no  value  or  application  in  the  one  whole  (the  universal  potential,  logical), 
or,  as  I  would  amplify  it,  in  the  two  correlative  and  counter  wholes  (the  logical 
and  the  formal,  actual,  metaphysical),  with  which  Logic  is  conversant.  For 
all  that  is  out  of  classification,  —  all  that  has  no  reference  to  genus  and  species, 
is  out  of  Logic,  indeed  out  of  Philosophy ;  for  Philosophy  tends  always  to  the 
universal  and  nccessjrry.  Thus  the  highest  canons  of  deductive  reasoning,  the 
Dicla  de  Omni  et  de  Nullo,  were  founded  on,  and  for,  the  procedure  from  the 
universal  whole  to  the  subject  parts ;  whilst,  conversely,  the  principle  of  in- 
ductive reasoning  was  established  on,  and  for,  the  (real  or  presumed)  collection 
of  all  the  subject  parts  as  constituting  the  universal  whole.  —  2°,  The  integrate 
or  mathematical  whole,  on  the  contrary  (whether  continuous  or  discrete),  the 
philosophers  contemned.  For  whilst,  as  Aristotle  observes,  in  mathematics 
genus  and  species  are  of  no  account,  it  is,  almost  exclusively,  in  the  mathemat- 
ical whole  that  quantities  are  compared  together,  through  a  middle  term,  in 
neither  premise,  equal  to  the  whole.  But  this  reasoning,  in  which  the  middle 
term  is  never  universal,  and  the  conclusion  always  particular,  is,  as  vague, 
partial,  and  contingent,  of  little  or  no  value  in  philosophy.  It  was  accord- 
ingly ignored  in  Logic  ;  and  the  predesignations  more,  most,  etc.,  as  I  have 
said,  referred  to  universal,  or  (as  was  most  common)  to  particular,  or  to  neither, 
/quantity.*  This  discrepancy  among  logicians  long  ago  .attracted  my  attention ; 
rtnd  I  saw,  at  once,  that  the  possibility  of  inference,  considered  absolutely,  de- 
pended exclusively  on  the  (juantifications  of  the  middle  term,  in  both  premises, 
!)eing,  together,  more  than  its  possible  totality  —  its  distribution,  in  anyone. 
At  the  same  time  I  was  impressed  —  1°,  With  the  almost  utter  inutility  of 

1  [Cf.  Corvinus,  Tnstit.  Phil.  c.  v.  f  876,  p.      Syst.  Log.  i  360.    W.allis,  Instit.  Log.  L.  il  0. 
123.    leiije,  1742.    Rcusch,  WalU?.)    [Keufch,     4,  p.  100.    6th  ed.  —  Ed  ] 


APPENDIX.  587 

such  reasoning,  in  a  philosophical  relation  ;  and,  2°,  Alanned  with  the  load  of 
valid  moods  which  its  recognition  in  Logic  would  introduce.  The  mere  quan^ 
tification  of  the  predicate,  under  the  two  pure  quantities  of  definite  and  indefi- 
nite, and  the  two  qualities  of  affirmative  and  negative,  gives  (abstractly)  in  each 
figure  thirty-six  valid  moods ;  which  (if  my  present  calculation  be  correct) 
would  be  multiplied,  by  the  introduction  of  the  two  hybrid  or  ambiguous  quan- 
tifications of  a  majority  and  a  half,  to  the  fearful  amount  oi  four  hundred  and 
eighty  valid  moods  for  each  figure.  Though  not,  at  the  time,  fully  aware  of  the 
strength  of  these  objections,  they,  however,  prevented  me  from  breaking  down 
the  old  limitation  ;  but  as  my  supreme  canon  of  Syllogism  proceeds  on  the 
mere  formal  possibility  of  reasoning,  it  of  course  comprehends  all  the  legitimate 
forms  of  quantification.  It  is :  —  What  worst  relation  of  subject  and  predicate 
subsists  between  either  of  two  terms  and  a  common  third  term,  tvith  which  one,  at 
least,  is  positively  related;  that  relation  subsists  between  the  two  terms  themselves: 
in  other  words,  —  In  as  far  as  two  notions  both  agree,  or,  one  agreeing,  the  other 
disagrees,  with  a  common  third  notion;  insofar  those  notions  agree  or  disagree 
with  each  other.  This  canon  applies,  and  proximately,  to  all  categorical  syllo- 
gisms,—  in  extension  and  comprehension, —  affirmative  and  negative,  —  and 
of  any  figure.  It  determines  all  the  varieties  of  such  syllogisms  :  is  developed 
into  all  their  general,  and  supersedes  all  their  special,  laws.  In  short,  without 
violating  this  canon,  no  categorical  reasoning  can,  formally,  be  wrong.  Now, 
this  canon  supposes  that  the  two  extremes  are  compared  together  through  the 
same  common  middle  ;  and  this  cannot  but  be  if  the  middle,  whether  subject  or 
predicate,  in  both  its  quantifications  together,  exceed  its  totality,  though  not 
taken  in  that  totality  in  either  premise. 

But,  as  I  have  stated,  I  was  moved  to  the  reconsideration  of  this  whole  mat- 
ter ;  and  it  may  have  been  Mr.  De  Morgan's  syllogism  in  our  correspondence 
(p.  /1 9)  which  gave  the  suggestion.  The  result  was  the  opinion,  that  these  two 
quantifications  should  be  taken  into  account  by  Logic,  as  authentic  forms,  but 
then  relegated,  as  of  little  use  in  practice,  and  cumbering  the  science  with  a 
superfluous  mass  of  moods.' 

A  UTHOS'S  DOCTRIXE  -  continved. 

No  syllogism  can  be  formally  wrong  in  which  (1°),  Both  premises  are  not 
negative;  and  (2°),  The  quantifications  of  the  middle  term,  whether  as  sub- 
ject or  predicate,  taken  together,  exceed  the  quantity  of  that  term  taken  in  its 
whole  extent.  In  the  former  case,  the  extremes  are  not  compared  together ;  in 
the  latter,  they  are  not  necessarily  compared  through  the  same  third.  These 
two  simple  rules  (and  they  both  flow  from  the  one  supreme  law)  being  obeyed, 
no  syllogism  can  be  bad,  let  its  extremes  stand  in  any  relation  to  each  other 
as  major  and  minor,  or  in  any  relation  to  the  middle  term.  In  other  words,  its 
premises  may  hold  any  mutual  subordination,  and  may  be  of  any  Figure. 

On  my  doctrine.  Figure  being  only  an  unessential  circumstance,  and  every 
proposition  being  only  an  ecjuation  of  its  terms,  we  may  discount  Figure,  etc., 

I  Extract  from  A  Letter  to  A.  tie  Morgan,  Esq.,  from  Sir  W.  Hamilton,  p.  41.  —  Ed. 


688 


APPENDIX. 


altogether ;  and  instead  of  the  symbol  (mm*- — •)  marking  sijbject  %ed  predi' 
cate,  we  might  use  the  algebraical  sign  of  e<[uaUty  (=?=)• 

The  rule  of  the  logicians,  that  the  middle  term  should  be  once  at  le^t  di^^ 
tributed  [or  indistributable]  (i.  e.,  taken  universally  or  singularly  =  definitely), 
is  untrue.  For  it  is  sufficient  if,  in  both  the  premises  together,  its  quantification 
be  more  than  its  quantity  as  a  whole  (Ultratotal).  Therefore,  a  major  part  (a 
viore  or  most)  in  one  premise,  and  a  half  in  the  other,  are  sufficient  to  make  it 
effective.  It  is  enough,  for  a  valid  syllogism,  that  the  two  extreme  notion9 
should  (or  should  not),  of  necessity,  partially  coincide  in  the  third  or  middle 
notion ;  and  this  is  nei.'essarily  shown  to  be  the  case  if  the  one  extreme  coin-i 
cide  with  the  middle  to  the  extent  of  a  half  (Dimidiate  Quantification) ;  and 
the  other  to  the  extent  of  aught  more  than  a  half  (Ultradieiidiate  Quantifica- 
tion). The  first  and  highest  quantification  of  the  middle  term  ( : )  •*  sufficient, 
not  only  in  combination  with  itself,  but  with  any  of  all  the  three  inferior.  The 
second  ( . , )  suffices  in  combination  with  the  highest,  with  itself,  and  with  the 
third,  but  not  with  the  lowest.  The  third  ( . )  suffices  in  combination  with 
either  of  the  higher,  but  not  with  itself,  far  less  with  the  lowest  The  fourth  and 
lowest  ( ,  )  suffices  only  in  combination  with  the  highest.  [1.  Definite ;  2.  In- 
definito-definito ;  3.  Semi-definite ;  4.  Indefinite.] 


(\at  March,  1847.  —  Yery  carefully  authenticated.) 

There  are  4  quantities  ( ,  |  .  |  .,  |  :),  affording  (4x4)  16  possible  double  quan- 
tifications of  the  middle  term  of  a  syllogism. 


S 


M. 


,,M.  I  :M 


,M: 


Of  these  10  are  legitimate  equivalents  (:  M ; 
4  6 

:  M  ,  I  ,  M  :  |  . ,  M  . ,  j  .  ,  M  .  |  .  M  . , )  ;  and  6  illegitimate,  as  not,  together,  nece*- 
sarilv  exceeding  ilio  quantity  of  that  term,  taken  once  in  its  full  extent  ( .  ,M  , 
|,M.,|.M.|.M,l,M.|,]vi,). 

Each  of  these  16  quantified  middle  terms  affords  64  possible  moods;  to  wit, 
16  affirmative,  48  negative  ;  legitimate  and  illegitimate. 

Altogether,  these  16  middle  terms  thus  give  256  affirmative  and  768  negative 
moods  ;  which,  added  together,  make  up  1024  moods,  legitimate  and  illegitimate, 
(or  each  figure.     For  all  three  figures  =  3072. 

The  10  legitimate  quantifications  of  the  middle  term  afford,  of  legitimate 
moods,  160  affirmative  and  320  negative  (=480),  i.  e.,  each  16  affirmative  and 
32  negative  moods  (=48);  besides  of  illegitimate  moods,  from  double  nega- 
tou,  160,  L  e.,  each  16.  The  6  illegitimate  quantifications  afford,  of  affirmative 
moods,  96  ;  of  simple  negative  moods,  192 ;  of  double  negative  mood$,  96  (= 
384).     Adding  all  the  illegitimates  =  544. 

The  1024  moods,  in  each  figure,  thus  afford,  of  legitimate,  480  moods  (1440 
for  all  3  Figs.);  being  of  affirmative  160(480  for  3  Figs.),  of  negative  320 
(960  for  3  Figs.),  of  illegitimate  544  pioods ;  there  being  excluded  in  each, 
from  inade<|uate  distribution  alone  (§),  288  moods  (viz.,  96  affirmative,  192 
negative)  ;  from  double  negation  alone  (J),  160  moods;  from  inadequate  dis- 
tribution and  double  negation  together  (§J),  96  moods. 


APPENDIX.  589 

(e)  MNEMONIC  VERSES. 

A  it  affirms  of  this,  these,  all  — 

Whilst  E  denies  of  any: 
I,  it  affli-ms,  whilst  O  denies, 

Of  some  (or  few  or  many). 

Thus  A  affirms,  as  E  denies. 

And  definitely  either: 
Thus  I  affirms,  as  O  denies. 

And  definitely  neither. 

A  half,  left  semi-definite, 

Is  worthy  of  its  score; 
U,  then,  affirms,  as  Y  denies, 

This,  neither  less  nor  more. 

Indefinito-definites, 

To  IJI  and  YO  we  come ; 
And  that  affii-ms,  and  tliis  denies. 

Of  more,  most  (half  plus  some). 

"Dl  iand  YO  may  be  called  Indefinite-definite,  either  (1*).  Because  they  ajy- 
proximate  to  the  whole  or  definite,  [forming]  more  than  its  moiety,  or  (2*^), 
Because  they  include  a  half,  which,  in  a  certain  sense,  maybe  regarded  as 
definite,  and  something,  indefinite,  over  and  above. 


YII. 

INDUCTION    AND    EXAMPLE. 

(See  p.  225.) 
I.  -^  Quotations  from  Authors. 

(a)   ARISTOTLE. 

Aristotle,  Prior  Analytics,  B.  ii.  c.  23.  After  stating  that  "  we  believe  all 
things  either  through  [deductive]  Syllogism  or  from  Tnductioi»,"  he  goes  on  to 
expound  the  nature  of  this  latter  process. 

"  Now,  Induction,  and  the  Syllogism  from  Induction,  is  the  inferring  one 
extreme  [the  major]  of  the  middle  through  the  other;  if,  for  instance,  B  is  the 
middle  of  A  C,  and,  through  C,  we  show  that  A  inheres  in  B.  Thus  do  we 
institute  Inductions.  In  illustration  :  —  I^et  A  be  long-lived,  B,  icanting-bile, 
and  C,  individual  long-lived  animals,  as  vian,  horse,  mule,  etc.  A,  then,  inheres 
in  the  whole  of  C  (for  all  animal  without  bile  is  [at  least  some]  long-lived)  ;  but 


o90 


APPENDIX. 


B,  wanting  hile,  also  [partially,  at  least]  inheres  in  all  C.^  If  now  C  reciprocate 
with  B,  and  do  not  go  beyond  that  middle  [if  C  and  B,  subject  and  predicate, 
are  each  all  the  other],  it  is  of  necessity  that  A  [some,  at  least]  should  inhere 
in  [all]  B.  For  it  has  been  previously  shown,*  that  if  any  two  [notions]  inhere 
in  the  same  [remote  notion],  and  if  the  middle'  reciprocate  with  either  [or 


1  I  have,  however,  doubts  whether  the  ex- 
ample which  now  stands  in  the  Organon  be 
tliat  wliich  Aristotle  himself  proposed.  It 
appears,  at  least,  to  have  been  considerably- 
modified,  probably  to  bring  it  nearer  to  wliat 
was  subsequently  supposed  to  be  the  truth. 
This  I  infer  as  likely  from  the  Commentary 
of  Ammoiiius  on  the  Prior  Analytics,  occa- 
sionally interpolated  by,  and  thus  erroneously 
quoted  under  the  name  of  a  posterior  critic, 

—  Joannes,  surnamed  Philoponus,  etc.  His 
words  aie,  in  reference  to  Aristotle,  as  fol- 
lows: ^'"  He  wishes,  through  an  example,  to 
illustrate  the  Inductive  process;  it  is  of  this 
intent.  Let  A  be  long-lived ;  B,  wanting  bile; 
C,  as  crow,  and  the  like.  Now,  he  says,  that 
t.'ie  rrow  and  the  stag,  being  animals  without 
bile  and  long-lived,  therefore,  animal  want- 
ing bile  is  long-lived.  Thus,  through  the  last 
[or  minor]  do  we  connect  the  middle  terra 
with  the  [major]  extreme.    For  I  argue  thus: 

—  the  individual  animals  wanting  bile  are 
[all]  long-lived;  consequently,  [all]  animals 
wanting  bile  are  long-lived."  F.  107,  a.  ed. 
Aid.  Compare  also  the  greatly  later  Leo 
Magentinus,  on  the  Prior  Analytics,  f.  41,  a. 
cd.  Aid.  On  the  age  of  Magentinus,  histori- 
ans (as  Saxius  and  Fabricius)  vary,  from  the 
teventli  century  to  the  fourteentli.  He  was 
certainly  subsequent  to  Michael  Psellus,  ju- 
nior, whom  he  quotes,  and,  therefore,  not 
before  the  end  of  the  eleventh  century ;  whilst 
his  ignorance  of  the  doctrine  of  Conversion, 
introduced  by  Boethius,  may  show  that  he 
could  hardly  have  been  so  recent  as  the  four- 
teenth. 

Aristotle,  De  Part.  Anitfial  (L.  iv.  c.  2),  says, 
"In  some  animals  the  gall  [bladder]  is  abso- 
lutely wanting,  as  in  the  horse,  mule,  ass, 
stag,  and  roe."  ....  "  It  is,  therefore,  evi- 
dent that  the  gall  serves  no  useful  purpose, 
but  is  a  mere  excretion.  Wherefore  those  of 
the  ancients  say  well,  who  declare  that  the 
cause  of  longevity  is  the  absence  of  the  gall; 
and  this  from  their  observation  of  the  soli- 
dungula  and  deer,  for  animals  of  these  classes 
want  the  gall,  and  are  long-lived."  —  Hist. 
An.,L.  ii  c.  11,  Schn.  18,  Seal.  15vul.  Notices 
that  some  animals  have,  others  want,  the 
gall-bladder  (xoA.^j.v.  Schn.iii.  p.  106),  at  the 
liver.  Of  the  latter,  among  viviparous  quad- 
rupeds, he  notices  stag,  roe,  horse,  mule,  ass, 
etc.     Of  birds  who   have  the    gall-bladder 


aparl  from  the  liver"  and  attached  to  the  in- 
testines, lie  notices  the  pigeon,  crow,  etc. 

-  Aristotle  refers  to  the  chapter  immedi- 
ately preceding,  which  treats  of  the  Kecipro- 
cation  of  Terms,  and  in  that  to  the  fifth  rule 
which  he  gives,  and  of  the  following  purport: 
"Again,  when  A  and  B  inhere  in  all  C  [t.  e., 
all  C  is  A  and  is  B],  and  when  C  reciprocate* 
[i.  e.,is  of  the  same  extension  and  comprehen- 
sion] with  B,  it  is  necessary  that  A  should 
inhere  in  all  B  [i.  e.,  that  all  B  should  be  A]." 

3  For  &Kpov,  1  read  fieffov;  but  perhaps  the 
true  lection  is  —  irphs  tovto  ^irepoi'  abrijov 
avriffrpf(pri  rwu  &Kpa)v.  The  necessity  of  an 
emendation  becomes  manifest  from  the  slight- 
est consideration  of  the  context.  In  fact,  the 
common  reading  yields  only  nonsense,  and 
this  on  sundry  grounds.  —  1°,  There  are  three 
things  to  which  ^artpoy  is  here  applicable, 
and  yet  it  can  only  apply  to  two.  But  if  lim- 
ited, as  limited  it  must  be,  to  the  two  inhe- 
rents,  two  absurdities  emerge.  2°,  For  the 
middle,  or  common,  notion,  in  which  both 
the  others  inhere,  that,  in  fact,  here  exclu- 
sively wanted,  is  alone  excluded.  3°,  One, 
too,  of  the  inherents  is  made  to  reciprocate 
with  either;  that  is,  with  itself,  or  other.  i°, 
Of  the  two  inlierents,  the  minor  extreme  is 
that  whicli,  on  Aristotle's  doctrine  of  Induc- 
tion, is  alone  considered  as  reciprocating  with 
the  middle  or  common  term.  But,  in  Aris- 
totle's language,  to  &Kpoy,  "  The  Extreme,"  is 
(lilce  f]  Tt-p6Taaii,  The  Proposition  in  the  com- 
mon language  of  the  logicians)  a  synonyme 
for  the  major,  in  opposition  to, -and  in  exclu- 
sion of,  the  minor,  term.  In  the  two  short 
correlative  chapters,  tlie  present  and  that 
which  immediately  follows,  on  Induction 
and  on  Example,  the  expression,  besides  the 
instance  in  question,  occurs  at  least  seven 
times ;  and  in  all  as  the  major  term.  —  5°,  The 
emendation  is  required  by  the  demonstration 
itself,  to  which  Aristotle  refers.  It  is  found 
in  the  chapter  immediately  preceding  (J  5), 
and  is  as  follows:  —  "  Again,  when  A  and  B 
inhere  in  all  C,  and  when  C  reciprocates  with 
B,  it  necessarily  follows  that  A  should  [par- 
tially, at  least]  inhere  in  all  B.  For  whilst  A 
[some,  at  least]  inheres  in  all  C,  and  [all]  C, 
by  rea.«on  of  their  reciprocity,  inheres  in  [ali] 
B;  A  will  also  [some,  at  least]  inhere  in  all  B." 
The  mood  here  given  is  viii.  of  our  Table. 
{See  Appendix  XI.) 


( 


APPENDIX.  591 

with  both],  then  will  the  other  of  the  predicates  [the  syllogism  being  in  the 
third  figure]  inhere  in  the  co-reciprocating  extreme.  But  it  behooves  us  to 
conceive  C  as  a  complement  of  the  whole  individuals ;  for  Induction  has  its 
inference  through  [as  it  is  of]  all.^ 

"  This  kind  of  syllogism  is  of  the  primary  and  immediate  proposition.  For 
the  reasoning  of  things  mediate  is,  through  their  medium,  of  things  immediate, 
through  Induction.  And  in  a  certain  sort.  Induction  is  opposed  to  the  [Deduc- 
tive] Syllogism.  For  the  latter,  through  the  middle  term,  proves  the  [major] 
extreme  of  the  third  [or  minor] ;  whereas  the  former,  through  the  third  [or 
minor  term,  proves]  the  [major]  extreme  of  the  middle.  Thus  [absolutely], 
in  nature,  the  syllogism,  through  a  medium,  is  the  prior  and  more  notorious ; 
but  [relatively]  to  us,  that  through  Induction  is  the  clearer."  • 

An.  Pr.,  L.  ii.  c.  24.  Of  Example.  —  §  1.  "  Example  emerges,  when  it  is 
shown  that  the  [major]  extreme  inheres  in  the  middle,  by  something  similar  to         \ 

the   third   [or   minor   term] §  4.     Thus   it  is  manifest  that  the  / 

Example  does  not  hold  the  relation  either  of  a  whole  to  part  [Deduction],  nor  '^ 
of  a  part  to  whole  [Induction],  but  of  part  to  part;  when  both  are  contained 
under  the  same,  and  one  is  more  manifest  than  the  other.  §  5.  And  [Example] 
differs  from  Induction,  in  that  this,  from  all  the  individuals,  shows  that  the 
[major]  extreme  inheres  in  the  middle,  and  does  not  [like  Deduction]  hang  the 
syllogism  on  the  major  extreme ;  whereas  that  both  hangs  the  syllogism  [on  the 
major  extreme],  and  does  not  show  from  all  the  individuals  [that  the  major 
extreme  is  inherent  in  the  minor.]  " 

An.  Post.,  L.  i.  c.  1,  §  3.  —  "  The  same  holds  true  in  the  case  of  reasonings, 
whether  through  [Deductive]  Syllogisms  or  through  Induction ;  for  both  ac- 
complish the  instruction  they  afford  from  information  foreknown,  the  former 
receiving  it  as  it  were  from  the  tradition  of  the  inteUigent,  the  latter  manifest- 
ing the  universal  through  the  light  of  the  individual."  (Pacii,  p.  413.  See  the 
rest  of  the  chapter.) 

An.  Pos.,  L.  i.  c.  18,  §  1.  —  "  But  it  is  manifest  that,  if  any  sense  be  want- 
ing, some  relative  science  should  be  wanting  likewise,  this  it  being  now  impos- 
sible for  us  to  apprehend.  For  we  learn  everything  either  by  induction  or  by 
demonstration.  Now,  demonstration  is  from  universals,  and  induction  from 
particulars ;  but  it  is  impossible  to  speculate  the  universal  unless  through  in- 
duction, seeing  that  even  the  products  of  abstraction  will  become  known  to  us 
by  induction." 

A.     Aristotle's  Errors  regarding  Induction. 

Not  making  Syllogism  and  its  theory  superior  and  common  to  both  Deduc- 
tive and  Inductive  reasonings. 

A  corollary  of  the  preceding  is  the  reduction  of  the  genus  Syllogism  to  its 
species  Deductive  Syllogism,  and  the  consequent  contortion  of  Induction  to 
Deduction. 

I  This   requisite  of  Logical  Induction,  —  immediately  following,  in  which  he  treats  the 

that  it  should  be  thought  as  the  result  of  an  reasoning  from  Example.  See  passage  quoted 

agreement  of  all  the  individuals  or  parts,  —  on  page  590  (j  6). 
is  further  shown  by  Aristotle  in  the  chapter 


592 


APPENDIX. 


B.  Omissions. 
Omission  of  negatives. 

Of  both  terms  reciprocating. 

C.  Ambiguities. 

Confusion  of  Individuals  and  Particular.  See  Scheibler  [_Opera  Logica,  P. 
iii.  De  Prop.,  c.  vi.,  tit.  3,  5.  —  Ed.]. 

Confusion  or  non-distinction  of  Major  or  Minor  extremes. 

The  subsequent  observations  are  intended  only  to  show  out  Aristotle's  au- 
thentic opinion,  which  I  hold  to  be  substantially  the  true  doctrine  of  Induction ; 
to  eipose  the  multiform  errors  of  his  expositors,  and  their  tenth  and  ten  times 
tenth  repeaters,  would  be  at  once  a  tedious,  superfluous,  and  invidious  labor. 
I  shall,  first  of  all,  give  articulately  the  correlative  syllogisms  of  Induction  and 
Deduction  which  Aristotle  had  in  his  eye  ;  and  shall  employ  the  example  which 
now  stands  in  the  Organon,  for,  though  physiologically  false,  it  is,  nevertheless 
(as  a  supposition),  valid,  in  illustration  of  the  logical  process. 

ABIBTOTLE'S   CORSEUITIVE   SYLLOGISMS, 
(a)  Ol-  INDUCTIOH.  (6)  Of  DEDUCnOIf. 

AU  C  {man,  horse,  mule,  etc. )  is  some  A  {long-  AU  A  {rcanting-bile)  is  some  A  {long-lived) ; 

lived) ;  All  C  {man,  horse,  mule,  etc.)  is  all  B  {uxmt- 
AU  C  {man,  horse,  mtde,  etc.)  is  all  B  {uxznt-  ing-bUe); 

ing-bile) ;  AU  C  {man,  horse,  mule,  etc. )  is  some  A  {long- 
All  B  {waniing-bile)  is  some  A  {long^ved).  lived). 


A, 


C  (p,  q,  r,  etc.) ; 


•:B     A,  ■;B:  it  C  (p, q, r,  etc.) 


These  syllogisms,  though  of  different  figures,  fall  in  the  same  mood ;  in  our 
table  they  are  of  the  eighth  mood  of  the  third  and  first  Figures.  Both  un- 
allowed.    (See  Ramus,  quoted  below,  p.  593.) 

The  Inductive  syllogism  in  the  first  figure  given  by  Schegkius,  Pacius,  the 
Jesuits  of  Coimbra,  and  a  host  of  subsequent  repeaters,  is  altogether  incompe- 
tent, so  far  as  meant  for  Aristotle's  correlative  to  his  Inductive  syllogism  in  the 
tliird.  Neither  directly  nor  indirectly  does  the  philosopher  refer  to  any  Induc- 
tive reasoning  in  any  other  figure  than  the  third.  And  he  is  right;  for  the 
third  is  the  figure  in  which  all  the  inferences  of  Induction  naturally  run.  To 
reduce  such  reasonings  to  the  first  figure,  far  more  to  the  second,  is  felt  as  a 
contortion,  as  will  be  found  from  the  two  following  instances,  the  otie  of  which 
is  Aristotle's  example  of  Induction,  reduced  by  Pacius  to  the  first  figure,  and 
the  other  the  same  example  reduced  by  me  to  the  second.  I  have  taken  care 
also  to  state  articulately  what  are  distinctly  thought,  —  the  quantifications  of 
the  predicate  in  this  reasoning,  ignored  by  Pacius  and  logicians  in  general,  and 


APPENDIX.  593 

aduiittcd  only  on  compulsion,  among  others,  by  Derodon  (below,  p.  594),  and 
the  Coimbra  commentator.' 


ARISTOTLE  S    INDUCTIVE    SYLLOGISM    IN    FIGURES. 

(e)    Fio.  I.  (rf)    Fio.  II. 

All  C  (man,  horse,  mule,  etc.)  is  some  A  (long-  Some  A  (long-lived)  is  all  C  (man,  horse, 

lived);  mule,  etc.); 

AH  B   (wanting-bile)  is  all  C  (man,  horse,  AU  B  (imnting-bile)  is  all  C  (man,  horse, 

mule,  etc. ) ;  mtde,  etc. ) ; 

All  B  (toanttng-bile)  is  some  A  (long-lived).  All  B  (uxinting-bile)  is  some  A  (long-lived). 

(b)  PACHYMERES. 

Pachymeres,  Epitome  of  Aristotle's  Logic  (Title  viii.  ch.  3,  c.  1280).  —  "  In- 
duction, too,  is  celebrated  as  another  instrument  of  philosophy.  It  is  more 
persuasive  than  Deductive  reasoning,  for  it  proposes  to  infer  the  universal 
from  singulars,  and,  if  possible,  from  all.  But  as  this  is  frequently  impossible, . 
individuals  being  often  in  number  infinite,  there  has  been  found  a  method 
through  which  we  may  accomplish  an  Induction,  from  the  observation  even  of 
a  few.  For,  after  enumerating  as  many  as  we  can,  we  are  entitled  to  call  on 
our  adversary  to  state  on  his  part,  and  to  prove,  any  opposing  instances. 
Should  he  do  this,  then  [for,  'data  instantia,  cadit  inductio']  he  prevails;  but  . 
should  he  not,  then  do  we  succeed  in  our  Induction.  But  Induction  is  brought 
to  bear  in  the  third  figure  ;  for  in  this  figure  is  it  originally  cast.  Should,  then, , 
the  minor  premise  be  converted,  so  that  the  middle  be  now  predicated  of  all 
the  minor  extremes,  as  that  e.xtreme  was  predicated  of  all  the  middle  ;  in  that 
case,  the  con<lusion  will  be,  not  of  some,  but  of  all.  [In  induction]  the  first 
figure,  therefore,  arises  from  conversion,  —  from  conversion  of  the  minor  prem- 
ise, —  and  this,  too,  converted  into  all,  and  not  into  sojyie.  But  [an  inductive 
syllogism]  is  drawn  in  the  third  figure,  as  follows  :  —  Let  it  be  supposed  that 
we  wish  to  prove,  —  every  animal  moves  the  lower  jaw.  With  that  intent,  we 
place  as  terms :  —  the  major,  moves  the  under  jaw;  the  minor,  [a//]  animal; 
and,  lastly,  the  middle,  all  contained  under  animal,  so  that  these  contents  recip- 
rocate with  all  animal.  And  it  is  thus  perfected  [?]  in  the  first  figure,  as 
follows: — To  move  the  lower  jato  is  predicated  of  all  individual  animals;  these 
all  are  predicated  of  all  animal;  therefore,  moving  the  lower  jaw  is  predicated 
of  all  animal.     In  such  sort  induction  is  accomplished." 

(e)  RAMUS. 

Ramus,  Scholce  Dialecticce,  L.  viii.  (?".  11.  "  Quid  vero  sit  inductio  perobscure- 
[Aristoteli]  declaratur  :  nee  ab  interpretibus  intelligitur,  quo  modo  syllogisinus 
I)er  medium  concludat  majus  extremum  de  minore  :  inductio  majus  de  medio 

?. 
1  [In  An.  Prior,  L.  ii.  p.  403.    Cf.  I'erionius,  DidUctica,  L.  iii.  p.  366  (1544).    Tosca,  Comp^. 
riiU   Logica,  t.  I.  1.  iii.  c.  1,  p.  115  ] 

75 


^ 


APPENDIX. 


per  minus."     Kamus  has  confirmed  his  doctrine  by  his  example.     For,  in  his 
expositions,  he  himself  is  not  correct. 


(d)    DERODON. 

Derodon,  Logica  Restituta,  1659,  p.  602.  Philosophia  Contracta,  IGGi,  Logica, 
p.  91.  "  Induction  is  the  argumentation  in  which,  from  all  the  particulars, 
their  universal  is  inferred ;  as  —  Fire,  air,  water,  earth,  are  bodies ;  therefore, 
every  element  is  body.  It  is  recalled,  however,  to  syllogism,  by  assuming  all  the 
particulars  [including  singulars]  for  the  middle  term,  in  this  manner  :  — Fire, 
air,  water,  and  earth  are  bodies;  Imt  jire,  air,  water,  and  earth  are  every  element; 
there/ore,  every  element  is  body.  Again  :  —  The  head,  chest,  feet,  etc.,  are  dis- 
eased ;  but  the  head,  chest,  feet,  etc.,  are  the  whole  animal ;  therefore,  the  whole 
animal  i.v  diseased.  Thus  induction  is  accomplished  when,  by  the  enumeration 
of  all  the  individuals,  we  conclude  of  the  species  what  holds  of  all  its  mdi- 
viduals ;  as  —  Peter,  Paul,  James,  etc.,  are  rational;  therefore,  all  man  is 
rational ;  or  when,  by  the  enumeration  of  all  the  species,  we  conclude  of  the 
genus  what  holds  of  all  its  species ;  as  —  Man,  ass,  horse,  etc.,  are  sensitive ; 
therefore,  all  animal  is  sensitive ;  or  when,  by  the  enumeration  of  all  the  parts, 
we  conclude  the  same  of  the  whole  ;  as  —  Head,  chest,  feet,  etc.,  art  diseased ; 
Oierefore,  the  whole  animal  is  diseased." 


(*)  THE  COLLEGE   OFALCALA. 

A  curious  error  in  regard  to  the  contrast  of  the  Inductive  and  the  Deductive 
syllogism  stands  in  the  celebrated  Cursus  ■Complutensv*,  —  in  the  Disputations 
on  Aristotle's  Dialectic,  by  the  Carmelite  College  of  Alcala,  1624  (L.  iii.  c.  2). 
"We  there  find  surrendered  Aristotle's  distinctions^  as  accidental.  Induction 
and  Deduction  are  recognized,  each  as  both  ascending  and  descending,  as  both 
from,  and  to,  the  whole ;  the  essential  diflTerence  between  the  processes  being 
taken,  in  the  existence  of  a  middle  term  for  Deduction,  in  its  non-existence 
lor  Induction.  The  following  is  given  as  an  example  of  the  descending  syllo- 
gism of  Induction  :  — All  men  are  animals ;  therefore,  tliis,  and  this,  and  thit, 
etc.,  man  is-  an  animal.  An  ascending  Inductive  syll(^sm  is  obtained  from  the 
preceding,  if  reversed.  Now  all  this  is  a  mistake.  The  syllogism  here  stated 
h  Deductive  ;  the  middle,  minor,  and  major  terms,  the  minor  premise  and  the 
conclusion  being  confounded  together.  Expressed  as  it  ought  to  be,  the  syllo- 
gism is  as  follows  :  — All  men  are  (some)  aniinals ;  thu<,  and  this,  and  this,  etc., 
arc  (constitute)  all  men ;  therefore,  this,  and  thuf,  and  thit,  etc.,  are  (some) 
animal.  Here  the  middle  term  and  three  propositions  reappear ;  whilst  the 
Deductive  syllogism  in  the  first  figure  yields,  of  course,  on  its  reversal,  an 
Inductive  syllogism  in  the  third. 

The  vulgar  errors,  those  till  latterly,  at  least,  prevalent  in  this  country,  — 
that  Induction  is  a  syllogism  in  the  Mood  Barbara  of  the  first  figure  (with  the 
minor  or  the  major  premise  usually  suppressed)  ;  and  still  more  that  from  a 
some  in  the  antecedent  we  can  logically  induce  an  all  in  the  conclusion,  — 
these,  on  their  own  account,  are  errors  now  hardly  deserving  of  notice,  and 


APPENDIX.  ^8fe 

have  been  already  sufficiently  exposed  by  me,  upon  another  occasion  (Edin- 
burgh Review,  LVII.  p.  224  et  seq.).     \^Discussions,  p.  158  et  seq.  —  Ed.] 

(/)  FACCIOLATI. 

Facciolati,  Rudimenta  Logica,  P.  iii.  c.  3,  defines  Induction  as  "  a  reasoning 
without  a  middle,  and  concluding  the  universal  by  an  enumeration  of  the  sin- 
gulars of  which  it  is  made  up."  His  examples  show  that  he  took  it  for  an 
Enthymeme.  —  '■'■Prudence,  Temperance,  Fortitude,  etc.,  are  good  habits  [these 
constitute  all  virtue"]  ;  there/ore  [a^Z]  virtue  is  a  habit." 

(g)    LAMBERT. 

Lambert,  Neues  Organon,  i.  §  287.  "When,  in  consequence  of  finding  a 
certain  attribute  in  all  things  or  cases  which  pertain  to  a  class  or  species 
[genus  (V)],  we  are  led  to  affirm  this  attribute  of  the  notion  of  the  class  or 
genus ;  we  are  said  to  find  the  attribute  of  a  class  or  genus  through  induction. 
There  is  no  doubt  that  this  succeeds  so  soon  as  the  induction  is  complete,  or 
80  soon  as  we  have  ascertained  that  the  class  or  species  A  contains  under  it  no 

other  cases  than  C,  D,  E,  F, M,  and  that  the  attribute  B  occurs  in  each 

of  the  cases  C,  D,  E,  F, M.    This  process  now  presents  a  formal  syllo- 
gism in  Caspida.     For  we  thus  reason  — 

C,  as  M!cR  as  D,  E,  F, MareoKB; 

But  A  IS  either  C,  or  D,  or  E,  or  F or  M; 

Consequently,  all  A  are  B. 

"  The  example  previously  given  of  the  syllogistic  mood  Caspida  may  here 
serve  for  illustration.  For,  to  find  whether  every  syllogism  of  the  Second 
Figure  be  negative,  we  go  through  its  several  moods.  These  are  Cesare, 
Camestres,  Festino,  Baroco.  Now  both  the  first  conclude  in  E,  both  the  last  in 
O.  But  E  and  O  are  negative,  consequently  all  the  four,  and  herewith  the 
Second  Figure,  in  general,  conclude  negatively.^  As,  in  most  cases,  it  is  very 
difficult  to  render  the  minor  proposition,  which  has  the  disjunctive  predicate 
for  its  middle  term,  complete,  there  are,  therefore,  competent  very  few  perfect 
inductions.  The  imperfect  are  [logically]  worthless,  since  it  is  not  in  every 
case  allowable  to  argue  from  some  to  all.  And  even  the  perfect  we  eschew, 
whensoever  the  conclusion  can  be  deduced  immediately  from  the  notion  of  the 
genus,  for  this  inference  is  a  shorter  and  more  beautiful." 

Strictures  on  Lambert's  doctrine  of  Induction. 
1°,  In  making  the  minor  proposition  disjunctive. 
2°,  In  making  it  particular. 

3°,  In  making  it  a  minor  of  the  First  Figure  instead  of  the  Third. 
Better  a  categorical  syllogism  of  the  Third  Figure,  like  Aristotle,  whom  he 
does  not  seem  to  have  been  aware  of     Refuted  by  his  own  doctrine  in  §  230- 

1  It  Js  given  in  §  285,  as  follows:  "Now  every  syllogism  of  the  Second  Figure  ii  either  in 

Cesare,  or  Camestres,  or  Festino,  or  Baroeo  ; 
"7%e  syllogisms,  03  well  in  Cesare  as  m  Camestres,  "Consegitently  every  tyllogism  in  the  Second  Flgan  is 

Festino,  and  Baroco,  are  all  negative ;  Jfeaative," 


596 


APPENDIX. 


The  recent  German  Logicians,^  following  Lambert  (iV.  Org.  i.  §  287),  mako 
the  inductive  syllogism  a  byword.      Lambert's  example :  —  "  C,  as  well  as  D, 

E,  F M,  all  are  B ;  but  A  is  either  C,  or  D,  or  E,  or  F, or  M  ; 

there/ore,  all  A  is  B."  Or,  to  adapt  it  to  Aristotle's  example  :  —  Man,  as  well 
as  horse,  mule,  etc.,  all  are  long-lived  animals ;  hut  animal  I'oid  of  gall  is  either 
man,  or  horse,  or  mule,  etc. ;  therefore,  all  animal  void  of  gall  w  long-lived. 

This,  I  find,  was  an  old  opinion,  and  is  well  invalidated  by  the  commentators 
of  Louvain.* 

The  only  inducement  to  the  disjunctive  form  is,  that  the  predicate  is  ex- 
hausted without  the  predesignation  of  universality,  and  the  First  Figure 
attained.  But  as  these  crotchets  have  been  here  refuted,  therefore,  the  more 
natural,  etc. 

Some  logicians,  as  Oxford  Crakanthorpe  (Logica,  1.  iii.  c.  20,  published 
1622,  but  written  long  before),  hold  that  induction  can  only  be  recalled  to  a 
Hypothetical  syllogism.  As,  —  If  Sophocles  be  risible,  likeicise  Plato  and  all 
oilier  men,  then  all  man  is  risible ;  but  Socrates  is  risible,  likewise  Plato  and  all 
other  men;  therefore  all  man  is  risible.  Against  the  Categorical  syllogism  in 
one  or  other  figure  he  argues  :  —  "  This  is  not  a  universal  categorical,  because 
both  the  premises  are  singular ;  nor  a  singular  categorical,  because  the  conclu- 
sion is  universal."  It  is  sufficient  to  say,  that,  though  the  subjects  of  the  prem- 
ises be  singular  (Crakanthorpe  does  not  contemplate  their  being  particular), 
as  supposed  to  be  all  the  constituents  of  a  species  or  relatively  universal  whole, 
they  are  equivalent  to  that  species ;  their  universality  (though  contrarj-  to 
Aristotle's  canon)  is,  indeed,  overtly  declared,  in  one  of  the  premises,  by  the 
universal  predesignation  of  the  predicate.  Our  author  farther  adds,  that  In- 
duction cannot  be  a  categorical  syllogism,  because  it  contains  four  terms ;  this 


t  As  Ilcrbart,  Lehrbuch  iter  Logik,  i  69, 
Twesten,  Drobisch,  H.  Ritter. 

I "  I  am  nware  of  th»  opinion  of  many, 
that  the  singulars  in  the  Inductive  syUofnsm 
should  be  enumerated  by  a  disjunctive  con- 
junction, in  80  much  tliat  the  premises  of 
such  a  syllogism  are  commonly  wont  to  be 
thus  cast:  VVhalsoever  is  ,Tokn,  or  Peter,  or  Paul, 
etc.,  is  capable  of  instruction.  But  they  err, 
not  observing  that  the  previous  proposition 
is  manifestly  equivalent  to  the  following,  — 
John,  and  Peter,  and  Paul,  ttc,  are  capable  of 
instruction.^^  (Lovanienses,  Com.  In  An.  Pr., 
L  ii.  tr.  3,  c.  2,  p.  286,  ed.  1547;  1st  ed.,  1555.) 
This  here  said  of  the  major  is  true  of  Lam- 
bert's minor.  The  Louvain  masters  refer 
probably  [to  Versor.  etc.]  This  doctrine,  — 
that  the  Inductive  syllogism  should  be  drawn 
in  a  disjunctive  form,  —  was  commonly  held, 
especially  by  the  scholastic  commentators  on 
Tctrus  Hispanus.  Thus  Versor  (to  take  the 
books  at  hand),  whose  Exposition  first  ap- 
peared in  1487,  says  —  "  In  the  fourth  place. 
Induction  is  thus  reduced  to  syllogism,  seeing 
that,  in  the  conclusion  of  the  Induction,  there 
Are  two  terma  of  which  the  subject  forms  the 


minor,  and  the  predicate  the  major,  extreme 
in  the  syllogism;  whilst  the  singulars,  which 
have  no  place  in  the  conclusion,  constitute 
the  middle  term.  Thus  the  Induction  —  Soc- 
rates runs,  Ptato  runs  {and  so  of  other  men); 
there/ore,  all  man  runs,  —  is  thus  reduced  : 
All  that  is  Socrates,  or  Plato  [and  so  of  others), 
runs ;  but  all  man  is  Socrates,  or  Plato  [and  so 
of  others) ;  therefore,  all  man  runs.  And  these 
singulars  ought  to  be  taken  disjunctively,  and 
disjunctively,  not  computatively,  verified  of 
their  universal."  — {In  Hisp.  Summul.  Tr.  v.) 

The  same  doctrine  is  held  in  the  Repara- 
tiones  of  Arnoldus  de  Tungeri  and  the  Masters 
Regent  in  the  Burse  (or  College)  of  St.  Law- 
rence, in  Cologne,  1496.  (Tr.  iii.  c.  ii.,  Seo. 
Pri.) 

It  is  also  maintained  in  the  Copulnti  of 
Lambertus  de  Monte,  and  the  other  Regents 
in  the  Bursa  Montis  of  Cologne,  1490.  They 
give  their  reasons,  which  are,  however,  not 
worth  stating  and  refbting. 

But  Tartaretus,  neither  in  his  Commenta- 
ries on  Hispanus  nor  on  Aristotle,  mentioiw 
this  doctrine. 


APPENDIX.  69t 

quaternity  being  made  by  the  "aZZ  men"  (in  his  example)  of  the  premises 
being  considered  as  different  from  the  "  all  man "  of  the  conclusion.  This  is 
the  veriest  trifling.  The  difference  is  wholly  factitious  :  all  man,  all  men,  etc., 
are  virtually  the  same ;  and  we  may  indifferently  use  either  or  both,  in  prem- 
ises and  conclusion. 


n.  —  Material  Inddction. 

Material  or  Philosophical  Induction  is  not  so  simple  as  commonly  stated, 
but  consists  of  two  syllogisms,  and  two  deductive  syllogisms,  and  one  an  Epi- 
cheirema.     Thus : 

1-  —  What  is  found  true  of  some  constituents  of  a  natural  class,  is  to  be  pre- 
sumed true  of  the  whole  class  (for  nature  is  always  uniform) ;  a  a'  a"  are  some 
constituents  of  the  class  A  ;  therefore,  what  is  true  of  a  a'  a"  is  to  be  presumed 
true  of  A. 

II.  —  Wheit  is  true  of  a  a'  a,"  is  to  be  presumed  true  of  A ;  but  z  is  true  of  a 
a'  a ' ;  therefore,  z  is  true  of  A. 

It  will  be  observed,  that  all  that  is  here  inferred  is  only  a  presumption, 
founded,  1°,  Qn  the  supposed  uniformity  of  nature ;  2°,  That  A  is  a  natural 
class ;  3^,  On  the  truth  of  the  observation  that  a  a'  a"  are  really  constituents 
of  that  class  A ;  and,  4°,  That  z  is  an  essential  quality,  and  not  an  accidental. 
If  any  be  false,  the  reasoning  is  nought,  and,  in  regard  to  the  second,  a  a'  a" 
(some)  cannot  represent  A  (all)  if  in  any  instance  it  is  found  untrue.  '■'■Data 
instantia  cadit  inductio."  In  that  case  the  syllogism  has  an  undistributed 
middle. 


598 


APPENDIX. 


YIIL 

HTPOTHETICAL    AND    DISJUNCTIVE    RE ASONING  —  IMMEr- 
DIATE  INFERENCE. 

I.  —  Author's  Doctrink  —  Fraohbnts. 

(Seep.  231.) 

All  Mediate  inference  is  one;  that  incorrectly  called  Categorical j  for  tne 
Conjunctive  and  Disjunctive  forms  of  Hypothetical  reasoning  are  reducible  to 
immediate  inferences. 


B 


Immediate ; 

of  which  some 

kinds  are 


Recognized, 

as  Propositional. 

(Various.) 

Not  recognized, 
as  Syllogistic, 


/  Disjunctive, 


>  Hypothetical. 


\  Coi\junctive,> 


O  04 


Mediate; 

Syllogism  Proper,  < 

(Categorical.) 


A)  Analytic. 


B)  Synthetic. 


''a)  Unfignred. 

'b)  Figured, 
(Intensive 
or  Exten- 
sive) in 


F.  I. 


F.  II. 


.F.  m.. 


^1 


^ 


§  1.  Reasoning  is  the  showing  oat  explicitly  that  a  proposition,  not  granted 
or  supposed,  is  implicitly  contained  in  something  different,  which  is  granted  or 
supposed. 

§  2.  What  is  granted  or  snpposed  is  either  a  single  proposition,  or  more  than 
a  single  proposition.  The  Reasoning  in  the  former  case  is  Immediate,  in  the 
latter  Mediate. 

§  3.  The  proposition  implicitly  contaifted  may  be  stated  first  or  last.  The 
Reasoning  in  the  former  case  is  Analytic,  in  the  latter  Synthetic. 

Observations.  —  §  1.  "A  proposition,"  not  a  truth  ;  for  the  proposition  may 
not,  absolutely  considered,  be  true,  but,  relatively  to  what  is  supposed  its 
evolution,  is  and  must  be  necessary.  All  Reasoning  is  thus  hypothetical ; 
hypothetically  true,  though  absolutely  what  contains,  and,  consequently, 
what  is  contained,  may  be  false.* 


1  Reprinted  from  Discuaions,  p.  656.  —  Ed. 
*Tbat  all  logical  reasoning  is  hypotheti- 


cal, and  that  Categorical  Syllogism  is  really, 
and  in  a  higher  signification,  hypothetical, 
see  Maimon,  Yersueh  einer  neutn  Logik,  f  vi.  1., 


APPENDIX.  599 

Observations.  —  §  2.  Examples:  Immediate  —  If  \  is  B,  then  B  «  A;  Medi- 
ate —  If  ^  i^  B,  and  B  is  C,  then  A  is  C. 

Observations.  —  §  3.  Examples :  Analytic  —  B  is  A,  for  A  is  B  ;  A  is  C,for 
A  is  B,  and  B  is  C.  Synthetic  —  A  is  B ;  therefore,  B  is  A ;  A  is  B,  and 
B  is  C ;  therefore,  A  is  C. 


ON    THE   NATCKE   AND   DIVISIONS   OF    INFERENCE   OR   SYLLOGISM   IN   GENERAL. 

(November,  1848.) 

I.  Inference,  what 

II.  Inference  is  of  three  kinds;  what  I  would  call  the  —  1°,  Commutative; 
2°,  ExpUcative ;  and,  3°,  Comparative. 

1°,  In  the  first,  one  proposition  is  given;  and  required  what  are  its  formal 
commutations  ? 

2°,  In  the  second,  two  or  more  connected  propositions  are  given,  under  cer- 
tain conditions  (therefore,  all  its  species  are  conditionals) ;  and  required  what 
are  the  formal  results  Into  which  they  may  be  explicated.  Of  this  genus  there 
are  two  species,  —  the  one  the  Disjunctive  Conditional,  the  other  the  Conjunc- 
tive Conditional.  In  the  Disjunctive  (the  Disjunctive  also  of  the  Logicians), 
two  or  more  propositions,  with  identical  subjects  or  predicates,  are  given,  under- 
the  disjunctive  condition  of  a  counter  quality,  i.  e.,  that  one  only  shall  be  affir- 
mative; and  it  is  nquired  what  is  the  result  in  case  of  one  or  other  being 
affirmed,  or  one  or  more  denied.  (Excluded  Middle.)  In  the  Conjunctive 
(the  Hypotheticals  of  the  logicians),  two  or  more  propositions,  convertible  or 
contradictory,  with  undetermined  quality,  are  given,  under  the  conjunctive 
condition  of  a  correlative  quality,  i.  e.,  that  the  affirmation  or  negation  of  one 
being  determined,  determines  the  corresponding  affirmation  or  negation  of  the 
others ;  and  it  is  required  what  is  the  result  in  the  various  possible  cases. 
(Identity  and  Contradiction,  not  Sufficient  Reason,  which  in  Logic  is  null  as  a 
separate  law.) 

3°,  In  the  third,  three  terms  are  given,  two  or  one  of  which  are  positively 
related  to  the  third,  and  required  what  are  the  relations  of  these  two  terms  to 
each  other  ? ' 

III.  All  inference  is  hypothetical. 

IV.  It  has  been  a  matter  of  dispute  among  logicians  whether  the  class  which 

pp.  82,  88.    E.  Rejnhold,  Log-ii,  (  109,  p.  263  1  A  better  statement  of  the  tliree  different 

tt  xfq.    Smiglecius,  Logica,  Disp.  xiii.  q.  6,  processes  of  Reasoning, 

p.  496  (1st  ed.  1616).  I.  Given   a  proposition;    commutative^ — 

On  the  nature  of  the  Necessity  in  Syllogistic  what  are  the  inferences  which  its  commuta- 

Inference;  distinction  of  Formal  and  Mate-  tions  afford? 

ritLlJiecesmty,  or  of  necessitas  consequenticp  and  II    Given   two   or   more   propositions;  re- 

nteessitas  congequentif,  Me  Scotus",  Qitcpstiones,  lated  and  conditionally;  —  what  are  the  in- 

Super  Elenchos,  qu.  iv.,  227,  od  1639,  and  that  ferences    which    the    relative    propositions, 

all  inference  hypothetical,  In  An.  Prior,  L.  ii.  explicated  under  these  conditions,  afford? 

qu.  i.  p.  331.    Apuleius,  De  Hah.  Doct.  Plat.,  p.  III.  Given  three  notions;  two  related,  and 

34.    Aristotle,  An.  Prior,  i.  32,  i  5.  Smiglecius,  at  least  one  positively,  to  a  third ;  —  what  are 

Logica,  lot.  eit.    Balforeus',  In  Arist.  Org.,  An.  the  inferences  afforded  in  the  relations   to 

Prior,!,  t.  8,  p.  454,1616.     [See  also  Discus-  each  other,  which  this  comparison  of  the  tWO 

siotts,  p.  146,  note.  —  Ed.]  notions  to  the  third  determines? 


600  APPENDIX. 

I  call  Explicative  (viz.,  the  Hypothetical  and  Disjunctive  Syllogisms)  be  of 
Mediate  or  Immediate  inference.  The  immense  majority  hold  them  to  be  me- 
diate ;  a  small  minority,  of  which  I  recollect  only  the  names  of  Kant  [Fischer, 
Weiss,  Bouterwek,  Herbart],'  hold  them  to  be  immediate. 

The  dispute  is  solved  by  a  distinction.  Categorical  Inference  is  mediate,  the 
medium  of  conclusion  being  a  term;  the  Hypothetical  and  Disjunctive  syllo- 
gisms are  mediate,  the  medium  of  conclusion  being  a  proposition,  —  that  which 
I  call  the  Explication.  So  far  they  both  agree  in  being  mediate,  but  they  differ 
in  four  points.  The  first,  that  the  medium  of  the  Comparative  syllogism  is  a 
term ;  of  the  Explicative,  a  proposition.  The  second,  that  the  medium  of  the 
Comparative  is  one ;  of  the  Explicative,  more  than  one.  The  third,  that  in  the 
Comparative  the  medium  is  always  the  same ;  in  the  Explicative,  it  varies 
according  to  the  various  conclusion.  The  fourth,  that  in  the  Comparative  the 
medium  never  enters  the  conclusion  ;  whereas,  in  the  Explicative,  the  same 
proposition  is  reciprocally  medium  or  conclusion. 

V.  Logicians,  in  general,  h^ve  held  the  Explicative  class  to  be  composite 
syllogisms,  as  compared  with  the  Categoric ;  whilst  a  few  have  held  them  to  be 
more  simple.  This  dispute  arises  from  each  party  taking  a  partial  or  one-sided 
view  of  the  classes.  In  one  point  of  view,  the  Explicative  are  the  more  com- 
plex, the  Comparative  the  more  simple.  In  another  point  of  view,  the  reverse 
holds  good. 

Our  Hypothetical  and  Disjunctive  Syllogisms  may  be  reduced  to  the  class  of 
Explicative  or  Conditional.  The  Hypotheticals  should  be  called,  as  they  were 
by  Boethius  and  others,  Conjunctive,  in  contrast  to  the  coordinate  species  of 
Duy'unctive.     Hypothetical,  as  a  name  of  the  species,  ought  to  be  abandoned. 

The  Conjunctive  are  conditional,  inasmuch  as  negation  or  affirmation  is  not 
absolutely  asserted,  but  left  alternative,  and  the  quality  of  one  proposition  is 
made  dependent  on  another.  They  are,  however,  not  properly  stated.  The 
first  proposition,  —  that  containing  the  condition,  —  which  I  would  call  the 
Explicand,  should  be  thus  enounced :  ^s  B,  so  A ;  —  or.  As  B  is,  so  is  A  ;  or, 
Aa  C  is  B,  .vo  is  B  A.  Then  follows  the  proposition  containing  the  explication, 
which  I  would  call  the  Explicative ;  and,  finally,  flie  proposition  embodying  the 
result,  which  I  would  call  the  Explicate. 

They  are  called  Conjunctives  from  their  conjoining  two  convertible  proposi- 
tions in  a  mutual  dependence,  of  which  either  may  be  made  antecedent  or 
consequent  of  the  other. 

Disjunctive  syllogisms  are  conditional,  inasmuch  as  a  notion  is  not  absolutely 
asserted  as  subject  or  predicate  of  another  or  others,  but  alternatively  conjoined 
with  some  part,  but  only  with  some  part,  of  a  given  plurality  of  notions,  the 
affirmation  of  it  with  one  part  involving  the  negation  of  others.  Tlie  first 
proposition,  containing  the  condition,  I  would  call  the  Explicand,  and  so  forth 
as  in  the  Conjunctives.     They  are  properly  called  Disjunctives. 

(1  Kant,  Logik,  i  76.  Bouterwek,  Lehrbwh  187.  Weiss,  Logik,  n  210,  251.  IIerb«rt, 
der  philosophisehfn  Yorkenntnifse,  }  100,  p.  168,  Lehrbuck  zur  Einititung  in  die  Philosopkit,  i  (H, 
ad  ed.  1820.    Fischer,  Loffti;,  c.  v.  H  99, 100,  p.      p.  87, 1834.] 


APPENDIX.  601 

DISTRIBUTION    OF    REASONINGS. 

(Nov.  1848).  —  Inference  may  be  thus  distributed,  and  more  fully  and  accu- 
rately than  I  have  seen.  It  is  either  (I.)  Immediate,  that  is,  without  a  middle 
term  or  medium  of  comparison ;  or  (II.)  Mediate,  with  such  a  medium.* 

Both  the  Immediate  and  the  Mediate  are  subdivided,  inasmuch  as  the  reason- 
ing is  determined  (A)  to  one,  or  (B)  to  one  or  other,  conclusion.  (It  is  mani- 
fest that  this  latter  division  may  constitute  the  principal,  and  that  immediate 
and  mediate  may  constitute  subaltern  classes.) 

All  inference,  I  may  observe  in  the  outset,  is  hypothetic,  and  what  have  been 
called  Hypothetical  Syllogisms  are  not  more  hypothetic  than  others. 

LA  —  Immediate  Peremptory  Inference,  determined  one  conclusion,  con- 
tains under  it  the  following  species:*     

I.  B  —  Immediate  Alternative  Inference  contains  under  it  these  five  spe- 
cies, — 

1°,  Given  one  proposition,  the  alternative  of  affirmation  and  negation.  As 
—  A  either  is  or  is  not ;  but  A  is  ;  therefore,  A  is  not  not.  Or,  A  is  or  is  not  B ; 
but  A  is  B  ;  therefore,  A  is  not  nof-B. 

This  species  is  anonymous,  having  been  ignored  by  the  logicians;  but  it 
requires  to  be  taken  into  account  to  explain  the  various  steps  of  the  process. 

2°,  Given  one  proposition,  the  alternative  between  different  predicates.  This 
is  the  common  Disjunctive  Syllogism. 

3°,  The  previous  propositions  conjoined,  given  one  proposition,  etc.  As,  A 
either  is  or  'is  not  either  B  wr  C  or  D ;  hut  A  is  B ;  therefore,  it  is  not  nol-^,  it  is 
not  C,  it  is  not  D. 

Alias,  A  is  either  B  or  non-B,  or  C  or  non-C,  or  D  or  non-D ;  but  A  ts  B ; 
therefore  it  is  not  ?Jon-B,  and  it  ts  7ion-C,  and  it  is  non-D. 

4",  Given  two  propositions,  second  dependent  on  the  first,  and  in  the  first  the 
alternative  of  affirmation  and  negation.     This  is  the  Hypothetical  Syllogism  of 

1  [Cf.  Fonseca,  Instit.  Dial.,  L.  vi.  c.  1.,  1st  reinen   Lo^ik,  §   130,  p.  391.     Scheibler,    Op. 

ed.     1564.     Eustachius,    Surrnua     Philosopkim  Log.,  De  Proposit.  Consecutione,  p.  49*2  tl  sey.] 

Quo'tri partita,  Dialectica,  P.   jii.    tract,  i.,  p.  2  [Kinds  of  Immediate  Inference.     I.  Sub- 

112.    [•' Quoniam  argumentatio  est  quasdam  alternation.     II.    Conversion.    III.   Opposi- 

consequentia  (latius  enim  patet  consequentia  tion  —  (a)  of  Contradiction  —  (b)  of  Contra- 

quam  argumentatio),  prius  de  consequentia,  riety  —  (c)  of  Subcontrariety.    IV.  Equipol- 

quam    de    argumentatione     dicendura    est.  lence.     V.    Modality.     VI.    Contraposition. 

Consequentia  igitur,  sive  consecutio,  est  ora-  VII.  Correlation.    VIII.  Identity, 

tio  in  qua  ex  aliquo  aliquid  colligitur;  ut,  Fonseca  (IV),  (I),(II).    Eustachius  (I),  (IV), 

Omnis  homo  est  animal,  igitur  aliguis  homo  est  (II),  (VIII.)    Wolf,  (IV),  (VII),  (III),  a,  b,  c, 

animal."  — 'Ed.]    [Whether  Immediate  Infer-  (II).    Stattler,  (I),  (IV),  (II),  (III)     Kant,  (I), 

ence  really  immediate,  see,  on  the  affirmative,  (III),  a,  b,  c,  (II),  (VI).    E.  Reinhold,  (I),  (II), 

E.  Reinhold,  Logik,  f  106;  on  the  negative,  (VI),  (VII).    Rosling,  (I),  (IV),  (II),  (III),  a. 

Wolf,  Phil.  Rat.,  i  461.    Krug,  Logik,  §  94,  p.  b,  c,  (V).     Krug,  (IV),  (I),  (III),  a,  b.  c,  (II), 

287.    Schulze,  Log-iA:,  5§  85-90'(§  80,  5th  ed.).  (V).    G.  E.  Schiilze,  (IV),  (I),  (III),  (II).     S. 

(St.  MtLimon, Versuck  einerneuen  Logik,  Sect.  V.  Maimon,   (1),   (III),   (II),  (VI).      Bachmaiiii, 

i  2,  p.  U  et  seq.     F.  Fischer,  Log'i/t,  p.  104  er  (IV),    (I).    (Ill);     a,    b,    c,     (II),    (VI),    (V). 

sell.    Bachmann,  Logik,  f   105,  p.  154  e/  seq.  Plainer,  (I),  (II),  (III),  (IV).     F.  Fischer,  (V), 

Reimarus,  VemunfiUhre,  }   159  et  seq.  (1765).  (I),  (III),    (II),    (VI)       Reimarus,   (IV),   (I), 

Bolzano,    Wi.^stnsdiaftslthre,   Logik,  \o\.   M.  i,  (III),  a,  b,  (II).    Twesten.  (I),  (V),  (III),  (IV), 

255  ft  seq.    Twesten,    Logik,  insbeson'lere  die  (II),  (VI).     See  pp.  634,  535] 

Analytik,  j  77,  p.  66.     Rbsliug,  Die  Lrhnn  der  ' 

76 


602 


APPENDIX, 


the  logicians.  It  is,  however,  no  more  hypothetical  than  any  other  form  of 
reasoning  ;  the  so-called  hypothetical  conjunction  of  the  two  radical  propositions 
being  only  an  elliptical  form  of  stating  the  alternation  in  the  one,  and  the  de- 
pendence on  that  alternation  in  the  other.  For  example  :  If  A  is  B,B  is  C; 
this  merely  states  that  A  either  is  or  is  not  B,  and  that  B  is  or  is  not  C,  accord- 
ing as  A  is  or  is  not  B.     In  short  —  As  A  is  or  is  not  B,  so  B  is  or  is  not  C. 

(Errors,  —  1**,  This  is  not  a  mediate  inference. 

2°,  This  is  not  more  composite  than  the  categorical. 

3°,  The  second  proposition  is  not  more  dependent  upon  the  first  than  the 
first  upon  the  second.) 

5°,  Given  two  propositions,  one  alternative  of  affirmation  and  negation,  and 
another  of  various  predicates ;  the  Hypothetieo-disjunotive  or  Dilemmatic 
Syllogism  of  the  logicians. 

II.  A  —  Mediate  Peremptory  Inference.  This  is  the  common  Categorical 
Syllogism.  Three  propositions,  three  actual  terms,  one  primary  conclusion,  or 
two  convertible  equally  and  conjunctly  valid. 

II.  B  —  Mediate  Alternative  Syllogism.  Three  propositions,  three  possible 
terms,  and  conclusions  varying  according     .... 

2°,  The  Disjunctive  Categorical. 

4°,  The  Hypothetical  Categorical. 

5°,  Hypothetico-Disjunctive  CategoricaL 


HYPOTHETICAL   STLLOGISH.  —  CANON. 

(Oct.  1848.)  —  Canon  —  Two  or  more  propositions  thought  as  indetermined 
in  quality,  but  as  in  quality  mutually  dependent,  the  determination  of  quality  in 
the  one  infers  a  determination  of  the  corresponding  quality  in  the  other. 

This  canon  embodies  and  simplifies  the  whole  mystery  of  Hypothetical  Syl- 
logisms, which  have  been  strangely  imphcated,  mutilated,  and  confused  by  the 
logicians. 

1",  What  are  called  Hypothetical  Propositions  and  Syllogisms  are  no  more 
hypothetical  than  others.  They  are  only  hypothetical  as  elliptical.  When  we 
say,  If  A  is,  then  B  is,  we  mean  to  say  the  proposition,  A  is  or  is  not,  and  the 
proposition,  'B  is  or  is  not,  are  mutually  dependent,  —  that  as  the  one  so  the 
other.  If  here  only  means  taking  for  the  nonce  one  of  the  qualities  to  the 
exclusion  of  the  other ;  I,  therefore,  express  in  my  notation  the  connection  of 
the  antecedent  and  consequent  of  a  hypothetical  proposition,  thus  : 


(A 


-)  =  (Bx, 


2**,  The  interdependent  propositions  are  erroneously  called  Antecedent  and 
Consequent.  Either  is  antecedent,  either  is  consequent,  as  we  choose  to  make 
them.  Neither  Is  absolutely  so.  This  error  arose  from  not  expressing  overtly 
the  quantity  of  the  subject  of  the  second  {)roposItIon.  For  example  :  If  man  is, 
then  animal  is.    In  this  proposition,  as  thus  stated,  the  negatiod  of  the  first  does 


APPENDIX. 


603 


not  infer  the  negation  of  the  second.  For  man  not  existing,  animal  might  be 
realized  as  a  consequent  of  dog,  horse,  etc.  But  let  us  consider  what  we  mean  ; 
we  do  not  mean  all  animal,  but  some  only,  and  that  so7ne  determined  by  the 
attribute  of  rationality  or  such  other.  Now,  this  same  some  animal  depends  on 
man,  and  man  on  it ;  expressing,  therefore,  what  we  mean  in  the  proposition 
thus  :  — If  all  man  is,  then  some  animal  is,  —  we  then  see  the  mutual  dependence 
and  convertibility  of  the  two  propositions.*  For  to  say  that  no  animal  is,  is 
not  to  explicate  but  to  change  the  terms. 

3°,  The  interdependent  propositions  may  be  dependent  through  their  counter 
qualities,  and  not  merely  through  the  same.  For  example  :  .4s  our  hemisphere 
is  or  is  not  illuminated,  so  the  other  is  not  or  is  ;  but  the  other  is  not  illuminated ; 
therefore  ours  is.     Another :  If  A  is,  then  B  is  not;  but  B  is;  therefore  A  is  not. 

DISJCNCTIVB   AND   HYPOTHETICAL   SYLLOGISMS   PROPER. 

Aristotle  ignores  these  forms,  and  he  was  right*  His  followers,  Theophras- 
tus  and  Eudemus,  with  the  Stoics,  introduced  them  into  Logic  as  coordinate 
with  the  regular  syllogism  ;  and  their  views  have  been  followed,  with  the  addi- 
tion of  new  errors,  up  to  the  present  hour.  In  fact,  all  that  has  been  said  of 
them  has  been  wrong. 

1°,  These  arc  not  composite  by  contrast  to  the  regular  syllogism,  but  more 
simple. 

2°,  If  inferences  at  all,  these  are  immediate,  and  not  mediate. 

3°,  But  tliey  are  not  argumentations,  but  preparart;ions  (explications)  for 
argumentation.^   They  do  not  deal  with  the  quaesitum,  —  do  not  settle  it ;  they 


1  Cf.  Titius,  Ars  Cogitandi,  c.  xii.  §  26.  "  In 
specie  falsum  quoque  arbitror,  quod  Syllo- 
gismi  Conditionales  duas  habeant  figuras,  quae 
his  muniantur  regulis,  (1)  posito  antecedente, 
ponitur  consequens,  non  vero  remoto  antecedente, 
removetuT  consequens^  (2)  remoto  conseqtiente, 
removetur  antecedens,  non  autem  posito  conse- 
guente,  ponitur  uiUecedens,  ...  §  28.  Vide- 
amus  specialius ;  contra  primam  regulam  sic 
peccatur: 

Si  Chinenses  sunt  Mahometani,  sunt  infideles, 

At  non  sunt  Mahometani, 

Ergo  non  sunt  infideles, 
"nam  conclusio  hie  est  absurda!  Verum  si 
prasdicatum  conclusionis  sumatur  particular- 
iter,  nulla  est  absurditas,  si  autem  generaliter, 
turn  evadunt  quatuor  termini.  §  9.  Eodem 
exemplo  secunda  regula  etiam  illustratur,  sed 
assumemus  aliud  ex  Weisio,  d.  I. 

Si  miles  est  doctus,  novit  libros  (nempe  sicut 
eruditi  solent). 

Sed  novit  libros  (scil.  ut  alii  homines,  etiam 
indocti,  nosse  solent). 

Ergo  miles  est  doctus. 

"  Hsec  conclusio  itidem  pro  .falsa  habetur! 
8ed  jam  indicavimus  in  addita  parenthesi 
veram  causam,  r.empe  quatuor  terminos, 
quodsi  autem  mcdius  terminus  eodem  sensu 


tccipiatur,  ac  in  syllogismo  formaliter  pro- 
posito  queat  minor  probari,  turn  conclusio 
erit  verissima,  idque  virtute  prsemissarum. 
§  30.  Omnis  igitur  error  exinde  habet  origi- 
nem,  quod  quantitatem  prtedicati  vel  non 
intelligant,  vel  non  observent;  si  igitur  hunc 
lapsum  evites,  objecta  exempla  omnia,  qualia 
etiam  Weisius  d.  I.  commemorat,  facile  di- 
lues."  —  Ed. 

2  Cf.  Titius,  Ars  Cogitandi,  c.  xii.  $  7.  "  Syl- 
logismus  Disjunctivus  est  enthymema  sine 
majore,  bis,  oratione  disjuncta  et  positiva, 
propositum,  .  .  .  }  17.  Conditionalis  seu 
Hypotbeticus  nihil  aliud  est  quam  enthy- 
mema vel  sine  majore,  vel  minore,  bis,  prima 
scil.  vice,  conditionaliter,  secunda,  pure,  pro- 
positum. i  20.  Sequitur  nullum  peculiare 
concludendi  fundamentum  vel  formam  circa 
Syllogismos  Conditionales  occurrere,  nam 
argumentationes  imperfectas,  adeoque  mate- 
riam  syllogismorum  regularium  illi  conti- 
nent." —  Ed. 

3  This  I  say,  for,  notwithstanding  what  M. 
St.  Hilaire  so  ably  states  in  refutation  of  my 
paradox,  I  must  adhere  to  it  as  undisproved. 
—  See  his  Translation  of  the  Organon,  vol. 
iv.  p.  55. 


604  APPENDIX. 

only  put  tlie  question  in  the  state  required  for  the  syllogistic  process;  this, 
indeed,  they  are  frequently  used  to  supersede,  as  placing  the  matter  in  a  light 
which  makes  denial  or  doubt  impossible  ;  and  their  own  process  is  so  evident, 
that  they  might,  except  for  the  sake  of  a  logical,  an  articulate,  development  of 
iill  the  steps  of  thought,  be  safely  omitted,  as  is  the  case  with  the  quaesitum 
itself.     For  example  : 

1.  Hypothetical  (so  called)  Syllogism.  Let  the  quaesitum  or  problem  be,  to 
take  the  simplest  instance,  —  Does  animal  exist  f  This  question  is  thus  hypo- 
thetically  prepared  —  If  man  ts,  animal  is.  But  [as  is  conceded]  man  is;  there- 
fore, animal  is.  But  here  the  question,  though  prepared,  is  not  solved  ;  for  the 
opponent  may  deny  the  consequent,  admitting  the  antecedent.  It,  therefore, 
is  incumbent  to  show  that  the  existence  of  animal  follows  that  of  man,  which  is 
done  by  a  categorical  syllogism. 

Animal,  —i  :  Man  :  »'  ,  Existent. 


2.  Disjunctive  (so  called)  Syllogism.  Problem  —  Is  John  mortal  f  Dis- 
junctive syllogism  —  John  is  either  mortal  or  immortal:  but  he  is  not  immortal; 
ergo  [and  this,  consequently,  is  admitted  as  a  necessary  alternative]  he  is  mortal. 
But  the  [alternative  antecedent]  may  be  denied,  and  the  alternative  consequent 
falls  to  the  ground.  It  is,  therefore,  necessary  to  show  either  that  he  is  not  im- 
mortal, or  —  the  necessary  alternative  —  that  he  is  mortal,  which  is  done  by 
categorical  syllogism. 

John  urn  ,  Man  :  •— j :  Immortal, 

•    John  B^ ,  Man  :  ■■  ,  MortaL 


HTPOTHBTIOAL   INFERENCE. 


Inasmuch  as  a  notion  is  thought,  it  is  thought  either  as  existing  or  as  non-ex- 
isting ;  and  it  cannot  be  thought  as  existing  unless  it  be  thought  to  exist  in  this 
or  that  mode  of  being,  which,  consequently,  affords  it  a  ground,  condition,  or 
reason  of  existence.  This  is  merely  the  law  of  Reason  and  Conseijuent ;  and 
(he  hypothetical  inference  is  only  the  limitation  of  a  supposed  notion  to  a  cer- 
tain mode  of  being,  by  which,  if  posited,  its  existence  is  affirmed ;  if  sublated, 
its  existence  is  denied.     For  example  :  If  k  is,  it  is  B ;  hut  A  is,  etc. 

Again,  we  may  think  the  existence  of  B  (consequently  of  A  B)  as  depen- 
dent upon  C,  and  C  ns  dependent  upon  D,  and  so  forth.  We,  accordingly, 
may  reason :  If  -k  v<  B,  and  B  is  C,  and  C  is  D,  etc. 

DISJCNCTIVE   STLLOOI8M   PROPER. 

(October  1848.)  —  Inasmuch  as  a  notion  is  thought,  it  is  thought  as  deter- 
mined by  otu'  or  other,  and  only  by  one  or  other,  of  any  two  contradictory  at- 
tributes; and  inasmucli  as  two  notions  are  thought  as  contradictory,  the  one  or 


APPENDIX.  605 

the  other,  and  only  the  one  or  the  other,  is  thought  as  a  determining  attribute 
of  any  other  notion.  This  is  merely  the  law  of  Excluded  Middle.  The  dis- 
junctive inference  is  the  limitation  of  a  subject  notion  to  the  one  or  to  the  other 
of  two  predicates  thought  as  contradictories  ;  the  affirmation  of  the  one  infer- 
ring the  negation  of  the  other,  and  vice  versa.  As,  A  w  either  B  or  not  B,  etc. 
Though,  for  the  sake  of  brevity,  we  say  A  is  either  B  or  C  or  D,  each  of  these 
must  be  conceived  as  the  contradictory  of  every  other ;  as,  B  =  |  C  |  D,  and 
so  on  with  the  others. 


HTPOTHETICAL8    (COKJUNCTIVE    AND    DISJUNCTIVE    STLLOGISW). 

(April  30,  1849.)  —  These  syllogisms  appear  to  be  only  modifications  or  cor- 
ruptions of  certain  immediate  inferences ;  for  they  have  only  two  terms,  and 
obtain  a  third  proposition  only  by  placing  the  general  rule  of  inference  (stat- 
ing, of  course,  the  possible  alternatives),  disguised,  it  is  true,  as  the  major 
premise.  It  is  manifest  that  we  might  prefix  the  general  rule  to  every  mediate 
inference  ;  in  which  case  a  syllogism  would  have  four  propositions  ;  or,  at  least, 
both  premises  merged  in  one  complex  proposition,  thus  : 

If  k  and  C  be  either  subject  or  predicate  [of  the  same  termf],  they  are  both  subject  or  pred- 
icate of  each  other ; 
But  B  is  the  subject  of  A  and  predicate  of  B  [C?] ; 
.•.  A  is  the  predicate  ofCA 

Thus,  also,  a  common  hypothetical  should  have  only  tico  propositions.  Let  us 
take  the  immediate  inference,  prefixing  its  rule,  and  we  have,  in  all  essentials, 
the  cognate  hypothetical  syllogism. 

1.  — Conjunctive  Hypothetical. 

All  B  IS  {some  or  all)  A;  AU  men  are  {some)  animals; 

Some  or  all  B  exists ;  {AU  or  some)  men  exist ; 

Thei-efore,  some  A  exists.  Therefore,  some  animals  exist. 

Here  it  is  evident  that  the  first  proposition  merely  contains  the  general  rule 
upon  which  all  immediate  inference  of  inclusion  proceeds ;  to  wit,  that,  the  sub- 
jective part  being,  the  subjective  whole  is,  etc. 

Now,  what  is  this  but  the  Hypothetical  Conjunctive  ? 

If  B  is,  A  IS ;  If  man  is,  animal  is ; 

But  B  IS ;  But  man  is ; 

Therefore,  A  is.  Therefore,  animal  is. 

1  There  seems  to  be  an  error  here  in  the  C  is  B,  then  C  is  A;  but  B  ts  A,  andC  is  Bj 

author's  M.S.    It  is  obvious  that  a  mediate  therefore,  C  is  A.    This  is  apparently  what  the 

inference  may  be  expressed  in  the  form  of  a  author  means  to  express  in  a  somewhat  differ- 

hypothetical  syllogism.    Thus:  1/  K  is  A,  and  ent  form.  —  Ed. 


606  APPENDIX. 

2.  —  Hypothetical  Disjunctive. 

B  is  either  A  or  not  A;  Man  is  either  animal  or  non<uunidl ; 

Bitt  B  is  A ;  But  man  is  animal ; 

Therefore,  ^  is  not  not-A.  Therefore,  is  not  non-animoL 

Stating  this  hypothetically,  we  may,  of  course,  resolve  the  formal  contradic- 
tory into  the  material  contrary.     But  this  is  wholly  extralogicai. 

HYPOTHETICAL.  AKD   DISJUNCTIVE    SYLLOGISMS. 

(I848  or  1849.)  —  The  whole  antecedent  must  be  granted ;  and  there  can- 
not be  two  propositions  inferred.  In  Categorical  Syllogisms,  the  antecedent  is 
composed  of  the  major  and  minor  premises,  and  there  is  only  one  simple  con- 
clusion (though  this  may,  in  the  second  and  third  figures,  vary).  So  in  H\-po- 
thetical  and  Disjunctive  Syllogisms  the  whole  antecedent  is  the  two  clauses  of 
the  first  proposition ;  and  the  whole  inference  is  the  first  and  second  clauses  of 
the  second  proposition,  erroneously  divided  into  minor  proposition  and  conclu- 
sion. 

(January  1850.)  —  The  Medium  or  Explicative  may  be  indefinitely  various, 
according  to  the  complexity  of  the  Explicand  ;  and  so  may  the  Explicate.  The 
explicative  and  the  explicate  change  places  in  different  explications.  There 
is,  in  fact,  no  proper  medium-explicative  or  conclusion-explicate. 

(January  1850.)  —  In  Disjunctives  there  is  always  at  least  double  the  num- 
ber of  syllogisms  (positive  and  negative)  of  the  disjunct  members ;  and  in  all 
syllogisms  Avherc  the  disjunct  members  are  above  two,  as  there  is  thus  affonled 
the  possibility  of  disjunctive  explicates,  there  is  another  half  to  be  added.  Thus, 
if  there  be  two  disjunct  members,  as  A — x  B  C,  there  are  four  syllogisms,  but 
all  of  an  absolute  conclusion,  —  explicate.  But  if  there  be  three  disjunct 
members,  as  A — x  B  C  D,  in  that  case  there  are  six  absolute  explicates,  three 
positive  and  three  negative,  and,  moreover,  three  disjunctivo-positive  conclu- 
sions, —  explicates,  after  a  negative  explicative,  and  so  on. 

HTPOTHBTICAL   SYLLOGISM.  —  CANOKS. 

(February  1850.)  —  I.  For  Breadth,  —  The  extensive  whole  or  class  being 
universally  posited  or  sublated,  every  subjacent  part  is  posited  or  sublated  ;  or, 
for  Depth,  —  All  the  comprehensive  wholes  being  posited  or  sublated,  the  com' 
prehended  parts  are  universally  posited  or  sublated. 

n.  For  Breadth,  —  Any  subjacent  part  being  posited  or  sublated,  the  exten' 
sive  whole  or  class  is  partially  posited  or  sublated  ;  or,  for  Depth,  —  Any  com' 
prehensive  whole  being  posited  or  sublated,  the  comprehended  parts  (or  part) 
are,  pro  tanto,  posited  or  sublated,  —  Conversion  and  Restriction. 

in.  If  one  contradictory  be  posited  or  sublated,  the  other  is  sublated  or  posi- 
ted, —  Contradiction. 

IV.  If  some  or  a  part  only  of  a  notion  be  posited  or  sublated,  all  the  rest 
(all  other  some)  is  sublated  or  posited,  —  Integration. 

V.  If  the  same  under  one  correlation  be  posited  or  sublated,  so  under  the 
other, —  EquipoUence. 


APPENDIX.  607 

VI.  Law  of  Mediate  Inference,' —  Syllogism. 

Mem.  —  The  some  in  the  expllcand  is  (as  in  the  Conversion  of  propositions) 
to  be  taken  in  the  explicative  as  the  same  some.  There  is  thus  an  inference 
equally  from  consequent  to  antecedent,  as  from  antecedent  to  consequent.* 


HYPOTHETICALS,  OR  ALTERNATIVES. 

CONJUNCTIVE    (HYPOTHETICALS     EMPHATICALLY)    AND    DISJUNCTIVE     (ALTERNA- 
TIVES   EMPHATICALLY.) 

(August  1852.) 

Quantification,  —  Any. 

Affirmative,  —  Any  (Anytldng,  Aught)  contains  under  it  every  positive 
quantification,  —  All  or  Every,  —  Some  at  least,  —  Some  only,  —  This,  These. 
(Best.) 

Negative,  —  Not  any,  None,  No  (Nothing,  Naught),  is  equivalent  to  the  most 
exclusive  of  the  negations,  All  not :  All  or  every  not ;  Not  one,  and  goes  be- 
jond  the  following,  which  are  only  partial  negations,  —  Not  all ;  Not  some ; 
Some  not.     (Worst.) 

Affirmative,  —  Any,  a  highest  genus  and  best ;  not  so  Negative  —  Not  any,  — 
a  lowest  species,  and  worst.  Therefore  can  restrict,  —  subalternate  in  the 
former,  not  in  the  latter. 


—  Any  (all  or  every,  —  some).  Some  not,  or  not  some,  or  not  all — some  only  (def.). 

Pure  affirmative.  Mixed  affirmative  and  negative. 


All  or  every  not,  not  one,  not  any. 
Pure  negative. 

//"  any  (every)  M  be  an  (some)  A,  and  any  {every)  A  an  (some)  S,  then  is  any  (every)  M 
an  S ;  and,  v.  v.,  if  no  (not  any)  A  be  any  S,  and  any  M  some  A,  ihen  is  no  M  any  S. 
.".  (On  one  alternative),  some  M  beiny  some  A,  and  all  A  some  S,  some  M  is  some  S. 
(On  the  other),  no  A  being  any  S,  and  every  M  some  A,  no  M  is  any  S. 

J/" (on  any  possibility)  M  is,  some  A  is;  or,  v.  v.,  if  no  A  is,  no  M  is. 

.-.  (on  one  alternative)  (in  this  actuality),  some  M  being,  some  A  is;  (on  the  other),  no 

A  being,  no  JI  is. 
Possible  M : ,  i»- — ,  A  oj-  A :  ^        :  M.    Supposition  of  universal  Possibility.    In 

any  case. 
Actual  M  ,  ^         ,  A  or  A:^ — :A.    Assertion  of  particular  Actuality.    Jn  this 

case. 

From  Possible,  we  can  descend  to  Actual ;  from  Any^  to  Some  ;  but  Not  any 
being  lowest  or  Avorst,  we  can  go  [no]  lower. 

1  See  p.  636.  —  Ed.  2  See  p.  603.  —  Ed. 

/ 


608 


APPENDIX. 


The  Possible  indifferent  to  Affirmation  or  Negation,  it  contains  both  implicitlj. 
But  when  we  descend  to  the  Actual  (and  Potential?),  the  two  qualities  emerge. 
This  explains  much  in  both  kinds  of  Hypothetical  or  Alternatives,  —  the 
Conjunctives  and  Disjunctives. 

Higher  classes,  —  Possible,  Actual  —  Semper,  quandocunque,  tunc,  nunc  — 
Ubicunque,  ubiqite,  ibi,  hoc  —  Any,  all,  some — In  all,  every,  any  case,  in  this 
case —  Conceivable,  real. 

BULES   OF   HTPOTHETICAL   SYLLOGISMS. 

1.  Universal  Rule  of  Restriction.  —  What  is  thought  of  all  is  thought  of 
some,  —  what  is  thought  of  the  whole  higher  notion  (genus)  is  thought  of  all 
and  each  of  the  lower  notions  (special  or  individual). 

2.  General  Rule  of  both  Hypotheticals.  —  What  is  thought  (implicidy)  of 
all,  the  Possible  (genus),  is  thought  (explicitly)  of  all  and  each,  the  Actual 
(species). 

3.  Special  Rule  of  Conjunctives.  —  What  is  thought  as  consequent  on  every 
Possible,  is  thought  as  consequent  on  every  Actual,  antecedent 

4.  Special  Rule  of  Disjunctives.  —  What  is  thought  as  only  Possible  (alter- 
natively), is  thought  as  only  Actual  (alternatively). 

5.  Most  Special  Rule  of  Conjunctives. 

6.  Most  Special  Rule  of  Disjunctives. 


HYPOTHETICALS  —  EXAMPLES   DKQUAKTIFIED. 

(Higher  to  Lower.) 


Affirmative. 
If  the  genus  is,  tlie  specia  is. 
If  the  stronger  can,  the  voeaker  can. 


Negative. 
If  the  genus  is  not,  the  species  is  not. 
If  the  stronger  cannot,  the  uieaker  cannot. 


(Lower  to  Higher.) 
If  the  species  is,  the  genus  is.  If  the  species  is  not,  the  genus  is  not. 

If  the  weaker  can,  the  stronger  can.  If  ike  weaker  cannot,  the  stronger  castnoL 


(Equal  to  Equal.) 


If  triangle,  so  trilateral. 

Such  poet  Homer,  such  poet  Vtrgil. 

Where  {when)  the  carcass  is,  there  (then) 

are  the  flies. 
If  Socrates  be  the  son  of  Sophroniscus,  SopA- 

roniscus  is  the  father  of  Socrates. 
If  equals  be  added  to  equals,  the  wholes  are 

equal. 


If  A  be  father  of  H,  B  is  son  of  A; 
.•.  A  being  father  of  B,  Bis  son  of  A ; 
.'.  B  not  being  son  of  A,  A  is  not  father  of  B. 
If  the  angles  be  proportional  to  the  sides  of 

.'.  An  equiangular  will  be  an  equHateral  A. 
If  wheresoever  the  carcass  is,  there  will  the 

eagles    be   gathered   together    (Matt. 

xxiv.28); 
.'.If  here  the  carcass  is,  here,  etc. 


APPENDIX.  609 

A.)  —  CONJUNCTIVE  HYPOTHBTICAIA. 

«  .   ^/.  >  ,    -r^    ,   .  (A,  being  D,  is  A ; 

l.)IfAbeD,UisA;.-.<'       ,.'        .        ^ 
(A,  not  being  A,  is  )iotD; 

In  other  words  —  A  is  either  Dor  not  A  D. 

Identity  and  Contradiction. 


n  X  rr  r>  >.    A    •*  •       <         a  \  ^>  being  A,  is  not  nou-A'^ 

2.)  ff  Boe  A,ittsnotnon-A;  .■.   i„  ,   . 

(  B,  being  non-A,  is  not  A; 

In  other  loords  —  B  is  either  A  or  non-A. 
Excluded  Middle. 

»,  .   r^  T^  i^       .  .     ■.  ■  .  (  B,  )iot  being  A,  is  non-A; 

^.)IfJibenotA,ittsnon-A;.-.l'.  '        '        ' 

(  B,  bemg  non-A,  is  not  A; 

In  other  voords  —  B  is  either  not  A  or  not  non-A. 
Excluded  Middle. 


-..  ^  ,  ^    .    .  K'E,  not  being  T),  is  not  A: 

4.)  .ff  E  6c  not  D,  U  is  not  Ay  .-.   \  J  ,   .         ^ .   ' 

I  E,  being  A,  JsD; 

In  other  words —  E  is  either  not  D  A,  or  A  D. 

Contradiction  and  Identity. 


B.)  —  DI8JONCTIVE    HTPOTHETICALS. 

B  being  A,  is  not  non-A ; 
B  being ; 
Excluded  Middle. 


If  B  be  either  A  or  non-A;  .•.   ,„,.  .    . 

(  B  being  non-A,  is  not  A 


"  7)^  means  suppose  that,  —  in  case  that,  —  on  the  supposition  —  hypothesis, 

tinder  the  condition,  — under  the  thought  that,  —  it  being  supposed  possible  ; 

.-.  etc.,  means  then,  —  therefore,  —  in  that  case,  etc.,  etc.,  —  in  actuality  either^ 

Only,  properly,  in  both  Conjunctives  and  Disjunctives,  two  contradictory 
alternatives.  For  contrary  alternatives  only  material,  not  formal,  and,  in  point 
of  fact,  either  A  or  B  or  C  means  A  or  non-A,  B  or  non-B,  C  or  non-C 

The  minor  premise,  on  the  common  doctrine,  a  mere  materiality.  Formally, . 
—  logically,  it  is  a  mere  differencing  of  the  conclusion,  which  is  by  formal . 
aUternative  afforded. 

1.)  In  Hypothetieals  (Conjunctive  and  Disjunctive),  two  or  three  hypotheses. 
The  first  is  in  the  original  supposition  of  7)0.s.'ii&//<7?/.  (//^B  be  A,  it  i.<  7iot  non~ 
A  —  FfB  he  either  A  or  non-A.)  The  second  (and  third)  is  in  the  alternative 
suppositions  of  actualifj/  (.-.  either  if  B  be  A,  it  is  not  non-A,  or  if  B  be  non-A,,- 
U  is-  not  A.  — .-.  If  B  be  A,  it  is  not  non-A,  or  if  B  be  non-A,  it  is  not  A).  (Pos- 
sibly,  —  by  possible  supposition)  If  man  is,  animal  is;  .-.  (actually)  Man  being, 
animal  is  :  (or)'  animal  not  being,  man  is  not. 

1.)  Possibility'  —  a  genus  Indiflforent  to  negative  and  affirmative.  These  two- 
species  of  Possibility,  to  wit,  two  Actuals,  —  an  actual  yes,  and  an  actual  no. 
The  total  formal  conclusion  is,  therefore,  of  two  contradictories.     This  explain*. 

77 


610  APPENDIX. 

why,  in  Conjunctive  and  Disjunctive  Hj-potheticals,  there  are  two  alternative 
consequents,  and  only  one  antecedent. 

2.)  In  Hypotheticals  (Conjunctive  and  Disjunctive)  a  division  of  genus  in 
ihe  first  supposition  into  two  contradictories,  —  species.  The  inference,  there- 
fore, one  of  subalternation  or  restriction. 

3.)  In  Hypotheticals  (Conjunctive  and  Disjunctive),  two  alternative  contra- 
dictory conclusions  —  the  form  giving  no  preference  between  the  two,  the  mat- 
ter only  determining  (other  immediate  inferences  have  only  one  determinate 
conclusion,  and  all  mediate  syllogism  has  virtually  only  one).  Formally,  there- 
lore,  we  cannot  categorically,  determinately,  assert,  and  assert  exclusively, 
(!ither  alternative,  and  make  a  minor  separate  from  the  conclusion.  This  only 
materially  possible  ;  for  we  know  not,  by  the  laws  of  thought,  whether  a  cer- 
tain alternative  is,  knowing  only  that  one  of  two  alternatives  must  be.  For- 
mally, therefore,  only  an  immediate  inference,  and  that  alternative  double. 

4.)  Hypothetical  (Conjunctive  and  Disjunctive)  reasoning  more  marking 
out,  —  predetermining  how  a  thing  is  to  be  proved,  than  proving  it 

5.)  Thus,  three  classes  of  inference:  1°,  Simple  Immediate  Inference.  —  2**, 
Complex  Immediate  Inference  (Hypotheticals  Conjunctive  and  Disjunctive). — 
3°,  Syllogisms  Proper,  Mediate  Inference. 

6.)  If  we  quantify  the  terms,  even  the  formal  inference  breaks  down. 

7.)  The  only  difference  between  the  first  proposition  and  the  two  latter,  is 
the  restriction  or  subalternation.  These  last  should,  therefore,  be  reduced  to 
one,  and  made  a  conclusion  or  restriction.  The  genera  and  species  are  of  the 
most  common  and  notorious  kinds,  as  Possible  and  Actual,  —  Wherever,  Here, 
etc., —  Whenever,  Now, —  All  or  Everi/,  Some,  This,  etc.  The  commonness 
and  notoriety  of  this  subordination  is  the  cause  why  it  has  not  been  signalized  ; 
and  if  signalized,  and  overtly  expressed,  Hypotheticals  might  be  turned  into 
Categoricals.  It  is  better,  however,  to  leave  them  as  immediate  inferences. 
For  it  would  be  found  awkward  and  round-about  to  oppose,  for  example,  the 
Possible  to  the  Actual,  as  determining  a  difference  of  terms.  (See  Molinaeus, 
Elem.  Log.,  L.  i.  tr.  iii.  p.  95,  and  Pacius,  In  Org.,  De  Sgll.  Hyp.,  p.  533.)  The 
example  of  the  Cadaver  ther6  given  shows  the  approximation  to  the  ordinary 
Hypotheticals.  They  may  stand,  in  fact,  either  for  Categoricals  or  Hypotheti- 
cals. 

8.)  Disjunctives  —  (Possibly)  A  is  either  B  or  non-B ;  .•.  (Actually)  A  is 
either,  etc. 

9  )  The  doctrine  in  regard  to  the  Universal  Quantity,  and  the  Affirmative 
Quality  (see  Krug,  LogiL;  §§  57,  83,  86,  pp.  171,  264,  275),  of  the  supposition, 
proposition,  of  Conjunctive  (?)  and  Disjunctive  Hypotheticals,  is  solved  by  my 
theory  of  Possibility.  In  it  is  virtually  said  (whatever  quantity  and  quality  be 
the  clauses),  —  "  on  any  possible  supposition."  (On  the  Quality,  v.  Krug,  Logik, 
§  57,  p.  172.     Pacius,  In  Org.,  p.  533.     Molinajus,  Elem.  Log.,  I.  c.) 

10.)  Possibly, — problematically  includes  as  species  the  actual  affirmative  and 
the  actual  negative.  It  will  thus  be  superfluous  to  enounce  a  negative  in  op- 
position to  an  affirmative  alternative  ;  for  thus  the  possible  would  be  brought 
down  to  the  actual,  and  the  whole  syllogism  be  mere  tautological  repetition. 

11.)  The  quantified  terms,  if  introduced,  must  either  be  made  determinate, 
to  suit  the  Hypotheticals,  or  must  ruin  their  inference.     For  example  —  If  all 


APPENDIX.  611 

or  some  man  he  some  animal,  we  must  be  able  to  say,  Bicf  some  animal  is  not, 
therefore  7nan  (any  or  some)  is  not.  But  here  some  animal,  except  definitized 
into  the  same  some  animal,  would  not  warrant  the  required  inference.  And  so 
in  regard  to  other  quantifications,  which  the  logicians  have  found  it  necessary 
to  annul. 

12.)  The  minor  proposition  may  be  either  categorical  or  hypothetical.  (See 
Krug,  Lo(jik,  §  83,  p.  264.  Heerebord,  Instil.  Logicar.  Synopsis,  L.  ii.  c.  12,  pp. 
266,  267.)  In  my  way  of  stating  it:  —  If  man  is,  animal  is,  .^  If  man  is  (or 
mati  being),  animal  is. 

13.)  Of  notions  in  the  relation  of  sub-and-superordination  (as,  in  opposite 
ways  Depth  and  Breadth,. Containing  and  Contained),  absolutely  and  relatively, 
the  lower  being  affirmed,  the  higher  are  (partially)  affirmed;  and  the  higher 
being  (totally)  denied,  the  lower  are  (totally)  denied.  A,  E,  I,  O,  U,  Y  may 
represent  the  descending  series. 

The  first  proposition  is  conditional,  complex,  and  alternative ;  we  should 
expect  that  the  second  should  be  so  likewise.  But  this  is  only  satisfied  on  my 
plan  ;  whereas,  in  the  common,  there  is  a  second  and  a  third,  each  categorical, 
simple,  and  determinate. 

The  subaltern ation  is  frequently  double,  or  even  triple,  to  wit,  1°,  From  the 
Possible  to  the  Actual.  2°  (for  example).  From  Everyichere  to  here,  or  this 
place,  or  the  place  by  name.  3°,  From  all  to  some,  etc.  —  in  fact,  this  infer- 
ence meny  be  of  various  kinds. 

The  lueraATjif/is  of  Aristotle  may  mean  the  determination,  —  the  subalterna- 
tion  ;  the  Kara  TroiSr-nTa  may  refer  to  the  specification  of  a  particular  quality  or 
proportion  under  the  generic ;  and  the  irp<5<7A.7ji|/«  of  Theophrastus  (for  tlw 
reading  in  Aristotle  should  be  corrected)  may  correspond  to  the  kuto,  ■jroi6T7]ra. 

There  is  no  necessary  connection,  formally  considered,  between  the  antece- 
dent and  consequent  notions  of  the  Hypothetical  major.  There  is,  conse- 
quently, no  possibility  of  an  abstract  notation ;  their  dependence  is  merely 
supposed,  if  not  material.  Hence  the  logical  rule,  —  Propositio  conditlonalis 
nihil  ponit  in  esse.  (See  Krug,  Logil;  §  57,  p.  166.)  But  on  the  formal  sup- 
position,—  on  the  case  thought,  yvhat  are  the  rules  ? 

We  should  distinguish  in  Hypotheticals  between  a  propositional  antecedent 
and  consequent,  and  a  syllogistic  A  and  C  ;  and  each  of  the  latter  is  one 
proposition,  containing  an  A  and  C. 

The  antecedent  in  an  inference  should  be  that  which  enables  us  formally  to 
draw  the  conclusion.  Show  in  Categoricals  and  in  Immediate  Inferences.  On 
this  principle,  the  conclusion  in  a  Hypothetical  will  contain  what  is  commonly 
called  the  minor  proposition  with  the  conclusion  proper ;  but  it  will  not  be  one 
and  determinate,  but  alternative. 

If  there  were  no  alternation,  the  inference  would  follow  immediately  from 
the  fundamental  proposition  ;  and  there  being  an  alternative  only  makes  the 
conclusion  alternatively  double,  but  does  not  make  a  mediate  inference. 


il2  APPENDIX. 

To  make  one  alternative  determinate  is  extralogical ;  for  it  is  true  only  as 
■aaterially  proved.  1°,  The  splitting,  therefore,  of  the  conclusive  proposition 
iato  two  —  a  minor  and  a  conclusion  proper  —  is  wholly  material  and  extralogi- 
cal ;  so  also,  2°,  Is  the  multiplying  of  one  reasoning  into  two,  and  the  dividing 
between  them  of  the  alternative  conclusion. 

Errors  of  logicians,  touching  Hypothetical  and  Disjunctive  Reasonings : 

1°,  That  [they]  did  [not]  see  they  were  mere  immediate  inferences.  ^ 

2°,  Most  moderns  that  both  Hypothetical. 

S®,  That  both  alternative  reasonings  in  one  syllogism. 

4",  Mistook  a  part  of  the  alternative  conclusion  for  a  minor  premise. 

5°,  Made  this  a  distinct  part  (minor  premise),  by  introducing  material  conad- 
erations  into  a  theory  of  form. 

6°,  Did  not  see  what  was  the  nature  of  the  immediate  inference  in  botb,  — 
how  they  resembled  and  how  they  differed. 


n.  —  Historical  Notices. 

(COWJXmCTIVE    AND    DISJDJJCTIVE.) 
(a>  ARISTOTLK. 

(August  1852.) 

Aristotle  (Anal.  Pr.  L.  i.  c.  32,  §  5,  p.  262,  Pacii)  describes  the  process  of  the 
Hypothetic  Syllogism  (that  called  by  Alexander  8i'  oA«i/),  but  denies  it  to  be  a 
syllogism.  Therefore  his  syllogisms  from  Hypothesis  are  something  different. 
This  has  not  been  noticed  by  Mansel,  Waitz, 

Thus  literally:  —  "  Again,  if  7nan  existing,  it  be  necessary  that  animal  exist, 
and  if  animal,  that  substance :  man  existing,  it  is  necessary  that  substance  exist 
As.  yet,  there  is,  however,  no  syll(^istic  process ;  for  the  propositions  «Jo  not 
stand  in  the  relation  we  have  stated.  But,  in  such  like  cases,  we  are  deceived, 
by  reason  of  the  necessity  of  something  resulting  from  what  has  been  laid 
down ;  whilst,  at  the  same  time,  the  syllogism  is  of  things  necessary.  But  the 
Necessary  is  more  extensive  than  the  Syllogism;  for  though  all  syllogism  be 
indeed  necessary,  all  necessary  is  not  syllogism."  Why  not?  1**,  No  middle. 
i°.  No  quality,  —  affirmation  or  negation ;  problem,  also  not  assertory,  —  hypo- 
thetical not  syllogistic.     3°,  No  quantity.     Compare,  also.  An.  Pr.  L.  i.  c.  24. 

Aristotle  (Anal.  Post.,  L.  i.  c.  2,  §  15,  p.  418;  c.  10,  §§  8,  9,  p.  438)  maker, 
T/icsh  or  Position  the  genus  opposed  to  Axiom,  and  containing  under  it,  as 
spcL-ies,  1°,  Hifpothesis  or  Supposition  ;  and,  2°,  Definition.  Hyjwthesis  is  that 
thesis  which  assumes  one  or  other  alternative  of  a  contradiction.  Definition  is 
that  thesis  which  neither  affirms  nor  denies.  Hypothetical,  in  Aristotle's  sense, 
is  thus  that  which  affirms  or  denies  one  alternative  or  other,  —  which  is  not 
indifferent  to  yes  or  no,  —  which  is  not  possibly  either,  and,  consequeutlx» 


APPENDIX.  618 

iBckides  both.  Hypotheticals,  as  involving  a  positive  and  negative  aUemative, 
are  thus,  in  Aristotle's  sense,  rightly  named,  if  divided;  but,  in  Aristotle's 
sense,  as  complete,  they  are  neither  propositions  nor  syllogisms,  as  not  affirmiiKg 
one  alternative  to  the  exclusion  of  the  otfaer.^ 

(b)  AUUOmUS  HERSaM. 

I.  Ammonias  Hermiae,  on  Aristotle  Of  Enouncement,  Introduction,  f  3,  ed. 
Aid.  1546,  f.  1.  ed.  Aid.  1503.  After  distinguishing  the  five  species  of  Speech, 
according  to  the  Peripatetics,  —  the  Vocative,  the  Imperative,  the  InteiTogative, 
the  Optative,  and  the  Enunciative  or  Assertive,  —  having  further  stated  the 
corresponding  division  by  the  Stoics,  and  having  finally  shown  that  Aristotle, 
in  tliis  book,  limited  the  discussion  to  the  last  kind,  that  alone  being  recipient 
of  truth  and  falsehood,  he  thus  proceeds:  —  "  Again,  of  Assertive  speech  (oiro- 
4i«i/T<>for>  \6yov),  there  are  two  species ;  the  one  called  Categoric  [or  Predicative}, 
the  other  Hypothetic  [or  Suppositive}.  The  Categoric  denotes  that  something 
does  or  does  not  belong  to  something :  as  when  we  say,  Socrates  is  icalking,  Soc- 
rates is  tiot  walking ;  for  we  predicate  walking  of  Socrates,  sometimes  affirm- 
atively, sometimes  negatively.  The  Hypothetic  denotes  that  something  being, 
something  [else]  is  or  is  not,  or  something  not  being,  something  [else]  is  not  or  is  : 
As  when  we  say,  If  man  he,  animal  also  is,  —  If  he  he  man,  he  is  not  stone,  — ■ 
If  it  be  not  day,  it  is  night,  —  If  it  be  not  day,  the  sun  has  not  risen. 

"  The  Categoric  is  the  only  species  of  Assertive  speech  treated  of  by  Aris- 
totle as  that  alone  perfect  in  itself,  and  of  utility  in  demonstration ;  whereas 
Hypothetic  syllogisms,  usurping  [usually]  without  demonstration  the  [minorj 
proposition,  called  the  2'ransumplion,  or  Asstanplion,  and  sometimes  even  a 
[major  premise]  Conjunctive  or  Disjunctive,  requiring  proof,  draw  their  per- 
suasion from  hypotheses,  should  any  one  [I  read  il  res  for  ^ns]  concede  their 
primary  suppositions.  If,  then,  to  the  establishment  of  such  suppositions  we 
should  employ  a  second  hypothetic  syllogism,  —  in  that  case,  we  should  require 
a  further  establishment  for  confirmation  of  the  suppositions  involved  in  it ;  for 
this  third  a  fourth  would  again  be  necessary;  and  so  on  to  infinity,  should  we 
attempt  by  hypotheses  to  confirm  hypotheses.  But  to  render  the  demonstra- 
tion complete  and  final,  it  is  manifest  that  there  is  needed  a  categoric  syllogisnj 
to  prove  the  point  in  question,  without  any  foregone  supposition.  Hence  it  is 
that  Categoric  [reasonings]  are  styled  Syllogisms  absolutely;  whereas  Hypo- 
tlictic  [reasonings]  of  every  kind  are  always  denominated  Syllogisms  from 
hypothesis,  and  never  Syllogisms  simply.    Add  to  this,  that  Hypothetic  enounce- 

1  [Whether  the   SpUoghms  ex  hypothesi  of  Opera  Logiea  Tract.  Si/U.  P.  iv.  c.  x.  tit.  2,  p. 

■Aristotle  are  correspondeut  to  the  ordinary  548.    Bursgersdicius,  Instit.  Log.  L.  ii.  cc.  13, 

Hypothetical  Syllogism.  14,  pp.  263,  270,  275.     Ritter,  Gesh.  der  PhU. 

Fop  the  affirmative,  see  Pacins,  Com.  In  iii.  p.  96.    (Eng.  Tr.,  p.  80.)    Ramus,  Sehol» 

Org.  An.  Prior,  L.  i.  cc.  28,  29,  44,  pp.  153,  177,  Dial.  L.  vii.  CC.  12, 13,  pp.  492,  503.    Molinaeus, 

194.     St.  Hilaire,  Translation  of  Organon,  vol.  EUmenta  Logiea,  p.  95  et  seq.     Waitz,  Org.  i. 

ii  pp.  107, 139, 178.  pp.  427,  433.    Of.  Alexander,  In  An.  Prior,  If. 

For  the  negative,  see  Piccartus,  In  Org.  An.  88,  109.    Philoponus,  la  An.  Prior,  ff,  60»,  60*, 

Prior,  L.  i.  cc.  40,  41,  42,  p.  500.    Neldelius,  87^,  88.     Anonymus,    De   Syllogismo,   f.  4#. 

De  Usu  Org.  Arist.  P.  iiL  c.  2, pp.  38,  45  (1607).  Magentinus,  In  An.  Prior,  f.  17*.    Ammonias, 

Keckermann,  Qp<t«,  pp.  766,767.    Selieibler,  In  de  Interp.,2^.  Blemmidas,  .^rat.  Xof .  c. flS.] 


614  APPENDIX. 

ments  are  made  up  of  Categoric.  For  they  express  the  consetjuence  or  oppo- 
sition (o/coA.oM^ioj'  fi  iidarcurif)  of  One  Categoric  proposition  and  another,  uniting 
them  with  each  other  by  either  the  Conjunctive  or  Disjunctive  particle  (avft- 
irKeKTiK^  fl  Sia^evKriK^  &vvS4(t/jlw)  ,  in  order  to  show  that  they  constitute  together  a 
single  enouncement.  For  these  reasons,  therefore,  Aristotle  has  only  consid  • 
ered,  in  detail,  the  Categoric  species  of  Assertive  speech." 


(c;  ANomruovs  scholios} 

In  Hypothetic  Syllogisms,  the  first  [I]  are  those  of  two  terms  [a]),  Conjunc- 
tive, or  [b]  Disjunctive  (opoi  ol  awrifinfuoi  i)  SiaKekufitvoi)  ;  then  follow  [11]  the 
two  [classes  of]  syllogisms  with  three,  and  these  conjunctive  terms. 

[I.  a.]  "  There  are  four  syllogisms  through  the  Return  (^  ^xcw'oSos)  on  tlie 
prior  (i  wp6repos,  6  irpcoros')  [or  antecedent  clause  of  the  hypothetical  proposi- 
tion], and  four  through  it  on  the  posterior  (6  Seurepoi,  6  ^^x*'''''*)-  For  the 
terms  are  taken  either  both  affirmatively  or  both  negatively.  And  the  return 
upon  the  prior  is  ponent  (jcari  Afaiv'),  upon  the  posterior  tollent  (kot^  aycuptffw'). 
For  example  [the  return  upon  the  prior]  : 

(1.)  7/  A.is,B  is;  (Return)  but  A  i«;  (Conclusion,  av/iwtpairfta)  Aere/ore,  B  is. 

(2.)  J/  A  is,  B  is  not ;  bvt  Ais;  therefore,  B  is  not. 

(3.)  If  Ais  not.  Bis;  bvt  A  is  not;  therefore,  B  is. 

(4.)  If  X  is  not,  B  is  not :  but  Aisnot;  therefore,  B  is  not.  ■ 

"  The  return  upon  the  posterior: 

(1.)  If  A  is,  B  is ;  butB  is  not ;  therefore,  A  is  not. 

(2.)  If  A  is,  B  is  not ;  but  B  is ;  therefore,  A  is  not. 

(3.)  If  Ais  not,  B  is ;  but  B  is  not ;  therefore,  A  is. 

(4. )  If  A  is  not,  B  is  not ;  btU  B  is  ;  therefore,  A  too  it. 

[b.]  "  Following  those  of  conjunctive,  are  syllogisms  of  disjunctive  terms. 
In  these,  the  return  is  upon  either  [clause]  indifferently.  For  example  :  If  it 
must  be  that  either  A  is  or  B  ix  [in  the  one  case];  B  is  not,  therefore,  A  is  ;  or 
[in  the  other],  A  is  not,  therefore  B  is. 

[II.]  "  Of  three  conjunctive  terms,  there  are  [in  the  figures  taken  together] 
eight  syllogisms,  through  a  return  on  the  prior,  and  eight  [sixteen]*  through  a 
return  on  the  posterior  [clause].  For  the  three  terms  are  correlated  {vwri^fit- 
Tou),  either  all  affirmatively,  or  some ;  and  here  either  the  third  alone,  or  the 
third  and  second,  or  the  second  alone,  negatively.  Again,  either  all  are  neg- 
atively correlated,  or  some  ;  and  here  the  third  alone,  or  the  third  and  second, 
or  the  second  alone,  affirmatively.     In  this  manner  the  correlation  [in  each 


I  In  Waftz,  Org",  i.  pp.  9,  10.  premise  (the  minor  placed  first,  according  to 

»  It  would  seem  that  the  author  here,  and  the  common  practice  of  the  Greeks,  or  the 

in  the  last  sentence,  discount?  altogether  the  major  prior,  in  Aristotelic  theory)  he  should 

first   figure,  puzzled,  apparently,  to  which  accord  the  designation  of  first. 


APPENDIX.  615 

figure]  is  eightfold ;  taking  for  exemplification  only  a  single  mood  [in  the 
several  figures] : 

If  A  is,  B  is  ; 

If  B  is,  C  is ; 

If  A  is,  therefore,  C  is. 

This  is  of  the  first  figure.  For  the  middle  collative  term  (6  ffwdywv  ipos  fifaos) 
is  twice  taken,  being  the  consequent  (6  xirywv)  in  the  former  conjunctive 
[premise]  (t^  Trp6repov  avvmnfjLiuov) ,  the  antecedent  (6  riyov/xevos)  in  the  latter. 
Wherefore,  these  syllogisms  are  indemonstrable/  not  requiring  reduction 
{t]  avdxvffis)  for  demonstration.  The  other  moods  of  the  first  figure  are,  as  has 
been  said,  similarly  circumstanced. 

"  The  second  figure  is  that  in  which  the  collative  term  [or  middle]  {6  awiyuv) 
holds  the  same  relation  to  each  of  the  collated  [or  extreme]  terms,  inasmuch  as 
it  stands  the  antecedent  of  both  the  conjunctive  [premises],  except  that  in  the 
one  it  is  affirmative,  in  the  other  negative.  Wherefore,  when  reduced  to  the 
first  figure,  they  demonstrate,  as  is  seen,  through  the  instance  of  a  single  mood 
composed  of  affirmative  collated  terms.     As  — 

If  A  is,  B  is ; 

If  A  is  not,  C  is ; 

If  B  is  not,  tha'efore,  C  is. 

"  This  is  reduced  to  the  first  figure  in  the  following  manner  : — Whether  it 
has  the  collated  terms,  both  affirmative,  or  both  negative,  or  both  dissimilar  to 
the  reciprocally  placed  collative  term,  there  is  taken  m  the  reduction  the 
opposite  [and  converse]  of  the  prior  conjunctive  [premise]  ;  and  the  latter  is 
applied,  in  order  that  the  opposite  of  the  consequent  in  the  former  conjunctive 
[premise]  may  find  a  place  in  the  foresaid  mood.     As  — 

If  B  is  not,  A  is  not; 

If  A  is  not,  C  is ; 

If  B  is  not,  therefore,  C  is. 

"  This  it  behooved  to  show. 

*'  The  third  figure  is  that  in  which  the  collative  term  holds  the  same  relation 
to  each  of  the  collated  terms,  being  the  consequent  in  either  conjunctive  [pre- 
mise] affirmatively  and  negatively,  as  in  the  example  of  a  single  mood  again 
consisting  of  aflfirmative  collated  terms.     Thus  : 

If  A  is,  B  is ; 
»  If  C  is,  B  is  not ; 

If  A  is,  therefore,  C  is  not. 

"  The  reduction  of  this  to  the  first  figure  is  thus  effected.     The  opposite  [a 

1  Vide  Apuleius.     [De  Dogm.  Plat.  iii.  p.  37.  Elm.     Cf.  Discussions,  p.  836.  —  Ed.] 


616 


APPENDIX. 


converse  E]  of  the  second  conjunctive  [premise]  is  taken  along  with  tl»e 
first  conjunctive  [premise],  and  the  antecedent  of  the  former  is  apf^ied  to  iSw 
opposite  of  the  latter's  consequent ;  as  in  the  foresaid  mood.     Thus : 


I 


I  IfAis,B{s; 

If  B  is,  C  IS  tiot; 

If  A  is,  therefore,  C  is  tut. 

**  All  this  requires  to  be  shown  concretely.     As  in  the  first  figure  £fint 
mood]: 

If  day  is,  light  is ; 

If  light  is,  visible  objects  are  seen  ; 

If  day  is,  therefore,  visible  otijeeis  are  seen. 

*•  Second  figure,  first  mood : 

If  day  is,  light  is; 

If  day  is  not,  the  sun  is  under  the  earth ; 

If  light  is  not,  the  sun  is  [therefore]  under  ike  earth.  . 


"  Reduction : 


If  light  is  not,  day  ui  not ; 

If  day  is  not,  the  sun  is  under  the  earth  ; 

If  light,  therefore,  is  not,  the  sun  is  under  the  earth, 

••  Third  figure,  first  mood  : 

If  day  is,  light  is  ; 

If  things  visible  are  unseen,  light  is  not; 

If  day,  therefore,  is,  things  visible  are  not  unseen. 

'•  There  are  eight  moods  of  the  second  figure,  and  eight  of  the  third ;  two 
composed  of  athrmativcs,  two  of  negatives,  four  of  dissimilars,  with  a  similar 
or  dissimilar  coUative. 

**  End  of  Aristotle's  Analytics." 


Relative  to  the  translation  from  the  Greek  interpolator  on  Hypothetical 
Syllogisms,  in  Waitz   (Org.  i.  p.  9,  10);  and  in  particular  to  the  beginning 

of  [II]. 

Better  thus  :  —  In  all  the  Figures  :  —  the  quality  of  the  syllogism  is  either 
Pure,  —  and  here  two,  viz.,  ooe  affirmative  and  one  n^ative ;  or  Alixedf  — 
and  here  six,  viz.,  three  in  which  affirmation,  and  three  in  which  negation,  has 
the  preponderance. 


APPENDIX. 
The  ibllowing  are  thus  arranged  : 


617 


First  Figure. 

A]l     Jf  A  is,  B  is  ; 
A  If  B  it,  C  is; 

.:  J/Ais,  Cis. 


Second  Figure. 

^  B  is,  A  is ; 
If  Bis,  Cis; 
.'.  Jf  A  is,  C  is. 


Third  Figure. 

J/Ais,  B  is; 
Jf  G  is,  Bis; 
.*.  Jf  A  is,  Cis. 


1,2,    Jf  A  is,  B  is ; 
B  Jf  Bis,  Cis  not; 

.'.  J/Ais,Cisnot. 


Jf  B  is,  A  is  ; 
Jf  B  IS,  C  is  not ; 
.'.  Jf  A  is,  C  ie  not. 


If  A  is,  B  is; 
Jf  C  is  not,  B  is ; 
.'.  If  A  is,  C  is  noL 


1,3,     Jf  A  is,  B  isnot ; 
C  If  B  is  not,  C  is ; 

.-.  If  A  is,  Cis. 

2,  3,     If  A  is  not,  B  is  ; 
D  If  Bis,  Cis; 

.'.  If  A  isnot,  C  is. 


If  B  is  not,  A  is; 
If  B  is  not,  C  is ; 
.'.  If  A  is,  C  is. 

If  B  is,  A  is  not ; 

If  B  is,  C  is  ; 

.'.  If  A  is  not,  C  is. 


If  A  is,  B  is  not ; 
If  C  is,  B  is  not ; 
.'.  If  A  is,  C  is. 

If  A  is  not,  B  is; 
Jf  C  is,  B  is  ; 
.'.  If  A  is  not,  C  i 


All     If  A  is  not,  B  is  not. 
ElfBis  not,  C  isnot ; 
.'.  If  A  is  not,  C  is  not. 


//TO  is  not,  A  is  not ; 
If  Bis  notj  C  is  not ; 
.'.  If  B  is  not,  C  is  not. 


If  A  is  not,  B  is  not ; 
If  C  is  not,  B  is  not  ; 
.'.  If  A  is  not,  C  is  not. 


a.  M 


1,  2,     If  A  is  not,  B  is  not ; 
F  If  Bis  not,  Cis; 

.'.  If  A  is  not,  C  is. 


If  B  is  not,  A  is  not ; 
If  B  is  not,  C  is ; 
.'.  If  A  is  not,  C  is. 


1,3,     Jf  A  is  not,  B  is ;  If  B  is,  A  is  not ; 

G  IfB  is,  C  is  not ;  If  B  is,  C  is  not ; 

.'.  If  A  is  not,  C  is  not.     .•.  If  A  is  not,  C  is  not. 


If  A  is  not,  B  is  not ; 
If  C  is,  B  is  not  ; 
.'.  If  A  is  not,  C  is. 

If  A  is  not,  B  is ; 
If  C  is  not,  B  is  ; 
.•.  If  A  is  not,  C  is  not. 


2,  3,     JfA  is,  B  isnot; 
H  IfBis  not,  C  is  not ; 

,'.  If  Ais,C  is  not. 


If  B  is  not,  A  is ; 
If  B  is  not,  C  is  not  ; 
.'.  If  A  is,  C  is  not. 


If  A  is,  B  is  not  ; 
If  C  is  not,  B  is  not ; 
.•.  If  A  is,  C  is  not. 


These  eight  syllogisms  are  all  affirmative,  the  negation  not  being  attached 
to  the  principal  copula.^  If,  therefore,  the  negation  be  attached  to  one  or 
other  premise,  there  will  be  sixteen  negative  syllogisms,  in  all  twenty-four. 
The  negatives  are,  however,  awkward  and  useless.     (See  Lovanienses,  p.  3t)l.) 

But  each  of  these  twenty-four  syllogisms  can  receive  twelve  different  forms 
of  predesignation,  corresponding  to  the  twelve  moods  of  the  simple  categorical ; 
accoi'diiig  to  which  they  are  arranged  and  numbered.     It  is  hardly  necessary 

1  See  Lovanienses,  In  Arist.  Dial.,  Tract,  de  Hj/potheticis  Syllogisinis,  p.  299. 

78 


618 


APPENDIX. 


to  notice  that  the  order  of  the  premises  is  in  comprehension,  after  the  Greek 
fashion  of  the  scholiast. 


r  A 

MB 

c  c 

i. 

ii. 

» 

iii. 

1 

iv. 

V. 

vi. 
•  » 

TU. 

1    • 

1 

Tiii. 

ix. 

> 

X. 

> 

xi. 

» 

> 

xU. 

> 
•  » 

> 

This  is  exemplified  in  the  Syllogism  E  of  the  preceding  table,  thus : 


1.  If  all  K  is  not,  all  B  is  not;  if  all  B  is  not,  all  C  is  not;  .-.  if  all  A  is  not,  aH 

B  is  not. 

2.  If  some  A  is  not,  all  B  is  not;  if  all  B  is  not,  some  C  is  not;  .'.  if  some  A  is  not, 

some  C  is  not. 

3.  If  some  A  is  not,  all  B  is  not ;  if  all  B  is  not,  all  C  is  not ;  .'.  if  some  A  is  not, 

all  C  is  not. 
A.  If  all  A  is  not,  all  B  is  not  ;  if  all  B  is  not,  some  C  is  not;  .'.  if  aU  A  is  not,  some 
C  is  not ; 

5.  If  all  A  is  not,  some  "Qis  not;  if  all  BJs  not,  all  C  is  not ;  .'.  if  all  A  is  not,  all  C 

is  not. 

6.  If  some  A  is  not,  all  'D  is  not ;  if  some  B  is  not,  aUCisnot;  .'.  if  some  A  is  not, 

all  C  is  not. 
1.  If  aU  A  is  not,  some  B  is  not ;  if  all  B  is  not,  some  C  is  not ;  .'.  ifaUA  is  not,  some 
C  is  not. 

8.  If  some  A  is  not,  aU  B  is  iiot ;  if  some  B  is  not,  all  C  is  not;  .'.  if  some  A  is  not, 

all  C  is  not. 

9.  If  some  A  is  not,  some  B  is  not ;  if  all  B  is  not,  all  C  is  not;  .'.  if  some  A  is  not, 

all  C  is  not. 

10.  If  all  A  is  not,  all  B  is  not ;  if  some  B  is  not,  some  C  is  not;  .'.  if  all  A  is  not, 

some  C  IS  not. 

11.  If  some  A  is  not,  some  B  is  not ;  if  all  B  is  not,  some C  is  not;  .'.  if  some  A  is  not, 

sonte  C  is  not. 

12.  ^  some  A  is  not,  all  B  is  not ;  if  sotne  B  is  not,  someC  is  not;  .*.  \f  some  A  is  not, 

some  C  is  not. 


APPENDIX.  619 

IX. 

SORITES. 

(Sec  p.   274.) 
(Without  order.) 

All  logicians  have  overlooked  the  Sorites  of  Second  and  Third  Figures. 

In  Sorites  of  the;  Second  or  Third  Figures,  every  term  forms  a  syllogism 
with  eveiy  other,  through  the  one  niiddh'  term.  In  Sorites  of  the  First  Figure, 
every  Second  term  at  most  forms  a  syllogism  "witli  everv  other,  through  its 
relati\e  middle  term. 

No  subordination  in  Sorites  of  Second  or  Third  Figure,  i  lyjo  no  one  domi- 
nant coiK-hision. 

Alias —  In  First  Figu'-e.  tiiere  being  a  suboi-dination  of  notions,  there  may 
be  a  Sorites  with  diifcvi'iit  middles  (all.  however,  in  a  conmion  dependency). 
In  Second  and  Tliird  Figu'vs.  then'  being  no  sul)ordination  of  terms,  tlie  only 
Sorites  compettMit  is  that  by  repetition  of  the  same  middle.  In  First  Figure 
thei'e  is  a  new  middle  term  for  every  new  progress  of  the  Sorites;  in  Se(;ond 
and  Tliii'd,  oidy  one  nfiddle  term  for  an\"  nimiber  ot'  extremes. 

In  I'ii-st  Figure',  a  Ssllogisni  only  between  evi?ry  second  term  of  the  Sorites, 
the  intermediate  term  constituting  the  middle  term.  In  the  others,  everv  two 
propositions  of  the  I'ommon  middle  term  Ibrm  a  s_\  llogism. 

Alias  —  Thert'  being  no  subordination  in  Second  and  Tliird  Figures  between 
the  extremes,  there,  consecpiently,  arc  — 

l'^.  No  relations  between  extremes,  except  through  the  middle  term. 

'l"^.  Tliere  is  only  one  possible  middle  term  ;  any  number  of  othei's. 

.'!°.  Ever}-  two  of  the  terms,  with  the  middle  term,  may  form  a  syllogism. 

4^,  2s'o  order. 

Before  concluding  this  subject,  I  would  correct  and  amplify  the  doctrine  in 
regani  to  the  Sorites.^ 

1°,  I  would  state  that,  by  the  quantification  of  the  Predicate  (of  which  we 
are  hereafter  to  treat,  in  reference  to  reasoning  in  general),  there  are  two 
kinds  of  Sorites  ;  the  one  descending  from  whole  to  part,  —  or  ascending  from 
part  to  whole  ;  the  other  proceeding  from  whole  to  whole  :  of  wdiich  last  it  is 
now  alone  requisite  to  speak.  It  is  manifest,  that  if  we  can  find  two  notions 
wholly  equal  to  a  third  notion,  these  notions  will  be  wholly  equal  to  each  other. 
Thus,  if  all  trilateral  figure  be  identical  with  all  triangular  figure,  and  all  tri- 
angular figure  with  all  figure  the  sum  of  whose  internal  angles  is  equal  to  two 
right  angles,  then  all  figure,  the  sum  of  whose  internal  angles  is  equal  to  two 
right  angles,  and  all  trilateral  figure,  will  also  be  identical,  reciprocating,  or 
absolutely  convertible.  We  have  thus  a  simple  syllogism  of  absolute  equation. 
On  the  same  principle,  if  A  and  B.  B  and  C,  C  and  I),  are  absolutely  equiva- 
lent, so  also  will  be  A  and  D-     We  may  thus,  in   like  manner,  it  is  evident, 

1  IiiteriioIaliiJ-.i  in  Lertitres.     See  p.  27-1.  —  tu. 


mQ 


APPENDIX, 


have  a  Sorites  of  absolute  equivalents.  It  is  not,  indeed,  very  easy  always  to 
find  four  or  more  terms  or  notions  thus  simply  convertible.  In  geometry,  we 
maj'  carry  out  the  concrete  syllogism  just  stated,  by  adding  the  three  following 
propositions  : — All  fgure,  the  sum  of  whose  internal  angles  is  equal  to  two  right 
angles,  is  all  figure  which  can  he  bisected  through  only  one  angle  ;  — All  figure 
which  can  be  bisected  through  only  one  angle,  is  all  figure  which,  bisected  through 
an  angle  and  a  side,  gives  two  triangles ;  and  All  figure  tvhich,  thus  bisected, 
gives  two  triangles,  is  all  figure  which,  bisected  through  two  sides,  gives  a  triangle 
and  a  quadrangle  ;  and  so  forth.  In  theology,  perhaps,  however,  these  series  are 
more  frequently  to  be  found  than  in  the  other  sciences.  The  following;  twelve 
equivalent  concepts  constitute  at  once  a  good  example  of  such  a  Sorites,  and 
at  the  same  time  exhibit  a  c(Mnpendiou3  view  of  the  whole  Galvinistic  doctrine. 
These  are,— 1,  Elected;  2.  Redeemed;  3.  Called;  4.  Graced  with  true  repent- 
ance; 5.  With  true  faith ;  6.  With  true  personal  assurance;  7.  Pardoned;  8. 
Justified;  9.  Sanctified;  10.  Endotced  with  perseverance;  11.  Saved;  12.  Glorified. 
This  series  could  indeed  be  amplified ;  but  I  have  purposely  restricted  it  to 
twelve.  Now,  as  All  the  elect  are  all  the  redeemed,  all  the  redeemed  all  the  called, 
all  the  called  all  the  [^truly"]  penitent,  all  the  [/ru/y]  penitent  all  the  [^Iruly"]  believ- 
ing, all  the  [_(ruly2  believing  all  the  [/rz/Zy]  assured,  all  the  \truly'\iassured  all  the 
pardoned,  all  the  pardoned  all  the  justified,  all  the  justified  all  the  sanctified,  all 
the  sanctified  all  the  perseverant,  all  the  perseverant  all  the  saved,  all  the  saved 
all  the  glorified,  all  the  glorified  all  the  blest  with  life  eternal;  it  follows,  of  neces- 
sity, that  all  the  blest  with  life  eternal  are  all  the  elect.  To  turn  this  affiraaative 
into  anegaiivc  Sorites,  we  have  only  to  say,  either  at  the  beginning,  —  None 
of  the  reprobate  are  any  of  the  elect,  an<l,  consetjuently,  infer,  at  the  end,  that 
none  of  tfie  blessed  with  eternal  life  are  any  of  the  reprobate  ;  or,  at  the  end,  — 
None  of  the  hhM  icith  eternal  life  are  any  of  the  punished,  and,  consequently, 
infer  that  none  of  the  punished  are  any  of  the  elect.  Perhaps  the  best 
formula  lor  tiii^s  kind  of  Sorites  is  to  be  found  in  the  letters  a,  b,  c.  This  will 
afford  us  a  Sorites  of  six  terms,  viz.,  a,  b,  c — a,  b — b,  a,  c — b,  c,  a — c,  a,  b — c, 
b,  a, — which  are  all  virtually  identical  in  their  contents.  If  there  be  required 
a  formula  for  a  longer-  Sorites,  we  may  take  the  letters  a,  b,  c,  d,  which  will 
afford  us  twenty-four  terms.  Perhaps  the  best  formula  for  a  descending  or 
ascending  Sorites  is,  for  example,  a,  b,  c,  d,  e,  f— a,  b,  c,  d,  e, — a,  b,  c,  d, — a, 
b,  c, — a,  b, — a. 


J. COMPRKHENSIVK    SOKITES  —  PKOORESSITE    AKD   BEGRESSITE. 


E 

I.acephalus 


APPENDIX. 


921 


II.  —  EXTENMVB    SORITES. 

:  B,  ■   :  C  ,  ■   :  D  , 


:  E 


X. 


SYLLOGISM. 
L — Its  Enouncement  —  Analytic  and  Synthetic  —  Order  of  Premises. 

(See  p.  281.) 

(a)  BIfOV!TCEMENT    OF   SYLLOGISM. 

(Nov.  1848.)  —  There  are  two  orders  of  enouncing  the  Syllogism,  both 
natural,  and  the  neglect  of  these,  added  to  the  not  taking  into  account  tlic 
Problem,  or  Question,  has  been  the  ground  why  the  doctrine  of  syllogism  has 
been  attacked  as  involving  a  petitio  principii,  or  as  a  mere  tautology.  Thus, 
Buffier  cites  the  definition  the  art  of  confessing  in  the  conclusion  what  has  been 
already  avowed  in  the  premises}     This  objection  has  never  been  put  down. 

The  foundation  of  all  syllogism  is  the  Problem.  But  this  may  be  answered 
either  Analytically  or  Synthetically. 

L  Analytically  (which  has  been  wholly  overlooked)  thus,  —  Problem  or 
quaesitum.  Is  T  C  ?  Answer,  P  is  C ;  for  P  is  M,  and  M  is  C.  This  is  the 
reasoning  of  Depth.  More  explicitly  :  —  Does  P  contain  in  it  C^  T  contains 
in  it  C  ;  for  T  contains  in  it  M,  and  M  contains  in  it  C.  But  it  is  wholly  indif- 
ferent whether  we  cast  it  in  the  reasoning  of  Breadth.  For  example  :  —  Does 
C  contain  under  itT?  C  contains  under  it  P;  for  C  contains  under  it  M,  and 
M  contains  under  it  T? 

Here  all  is  natural ;  and  there  is  no  hitch,  no  transition,  in  the  order  of  pro- 
gressive statement.  The  wliole  reasoning  forms  an  organic  unity  :  all  the  parts 
of  it  being  present  tO'  the  mind  at  once,  there  is  no  before  and  no  after.  But  it 
is  the  condition  of  a  verbal  enouncement,  that  one  part  should  precede  and 
follow  another.  Here,  accordingly,  the  proposition  in  which  the  reasoning  is 
absolved  or  realized,  and  which,  from  the  ordinary  mode  of  enouncement,  has 


1  Seconde  Logique,  Art.  iii.  §  126.  —  Ed.  {that  good  mm  so  think),  lastly  the  major  [tlial 

2  Plato,  in  a  letter  to  Dionysius  (Epist.2),  the  presentiments  of  divine  men  are  of  highest 
reverses  the  common  order  cf  Syllogism,  authority).  Platonis  Of/era,  Bekker,  ix.  p.  74. 
placing  the  conclusion  first  {that  he  thinks  Cf.  Melanchthon,  Dinlectica,  L.  iii.,  De  Fig- 
there  is  some  stnse  in  the  dead))  then  the  minor  uratione,  p.  93,  ed  1542. 


622  >  APPENDIX. 

been  styled  the  Conclusion,  is  stated  first ;  and  the  grounds  or  reasons  on  which 
it  rests,  which,  from  the  same  circumstance,  ha\e  been  called  the  Premue  or 
Antecedent,  are  stated  last.  This  order  is  Analytic.  We  proceed  from  the 
effect  to  the  cause,  —  from  the  principiatum  to  the  principia.  And  it  is  evident 
that  this  may  be  done  indifferently  either  in  Depth  or  Breadth ;  the  only  dif- 
ference being  that  in  the  counter  quantities  the  grounds  or  premises  naturally 
change  their  order. 

II.  Synthetically,  —  the  only  order  contemplated  by  the  logicians  as  natural, 
but  on  erroneous  grounds.  On  the  contrary,  if  one  order  is  to  be  accounted 
natural  at  the  expense  of  the  other,  it  is  not  that  which  has  thus  been  exclu- 
sively considered.     For —  ' 

1°,  It  is  full  of  hitches.  There  is  one  great  hitch  in  the  separation  of  the 
conclusion  from  the  question  ;  though  this  latter  is  merely  the  former  proposi- 
tion in  an  assertive,  instead  of  an  interrogative,  form.  There  is  also  at  least 
one  subordinate  hitch  in  the  evolution  of  the  reasoning. 

2°,  The  exclusive  consideration  of  this  form  has  been  the  cause  or  the  occa- 
sion of  much  misconception,  idle  disputation,  and  groundless  objection. 

(On  the  two  Methods ;  tumultuary  observations,  to  be  better  arranged,  and 
corrected.) 

1°,  In  the  first  or  analytic  order,  what  is  principal  in  reality  and  in  interest 
is  placed  first,  that  is,  the  Answer  or  Assertion,  called  on  the  other  order  the 
Conclusion. 

2°,  In  this  order  all  is  natural ;  there  is  no  hitch,  no  saltus,  no  abrupt  transi- 
tion ;  all  slides  smoothly  from  first  to  last. 

a)  The  question  slides  into  its  answer,  interrogation  demands  and  receives 
assertion. 

b)  Assertion  requires  a  reason,  and  prepares  us  to  expect  it;  and  this  is 
given  immediately  in  what,  from  the  other  order,  has  been  called  the  Antecedent 
or  Premises. 

c)  Then  the  first  term,  either  in  Breadth  or  Depth,  is  taken  first  in  the 
ground  or  reason,  and  compared  with  M;  then  M  is  compared  with  the  other. 
As  in  Breadth  :  —  Does  C  contain  under  t7  F  ?  C  contains  T ;  for  C  contains 
under  it  M,  and  M  contains  under  it  T.  In  Depth  —  Does  T  contain  in  it  C  ? 
r  contains  in  it  C  ;  for  T  contains  in  it  M,  and  M  contains  in  it  C.  This  is  the 
first  Figure.  Second  Fijiurc,  usinjj  common  lanjjuase:  —  Is  F  C?  F  is  C 
(and  C  is  F)  ;  for  F  and  C  are  both  the  same  M.  Here  the  two  extremes  taken 
together  are  compared  with  M.  In  the  third  Figure  M  is  compared  with  both 
extremes  —  /sFC?     T  is  C  (and  M  is  F)  ;  for  the  same  M  w  both  F  and  C. 

8",  In  this  order  there  is  nothing  pleonastic,  nothing  anticipated. 

4°,  Nothing  begged. 

5°,  In  this  method  the  process  is  simple.  Thought  is  one ;  but  to  be  enounced 
it  must  be  analyzed  into  a  many.  This  order  gives  that  necessary  analj-sis, 
and  nothing  more. 

6°,  In  this  order,  wlu'u  assertive,  answer  is  limited  by  question  ;  goo<l  reason 
why,  in  S^'cniul  and  Third  Figures,  one  answer  should  be  given. 

7°,  Tliis  order  i.s  the  one  generally  used  by  the  mathematicians.  (See  Twea- 
ten,  Logik,  insltcsondere  die  Analytik^  §  117,  p.  105,  and  below,  p.  626.  Plato 
also). 


APPENDIX.  623 

8°,  If  the  Quaesitum  be  stated  as  It  ought  to  be,  this  order  follows  of  course; 
and  the  neglect  of  the  quaesitum  has  followed  from  the  prevalence  of  the  other. 
If  the  quaesitum  be  stated  in  using  the  common  form,  we  must  almost  of  course 
interpolate  a  yes  or  a  no  before  proceeding  to  the  premises  in  the  common 
method ;  and  in  that  case,  the  conclusion  is  only  a  superfluous  recapitulation. 

In  the  Synthetic,  or  common  order,  all  is  contrary.  (The  numbers  cor- 
respond.) 

1°,  In  this  order,  what  is  first  in  reality  and  interest,  and  in  and  for  the  sake 
of  which  the  whole  reasoning  exists,  comes  last ;  till  the  conclusion  is  given  we 
know  not  (at  least  we  ought  not  to  know)  how  the  question  is  answered. 

2°,  In  this  order  all  is  unnatural  and  contorted  by  hitches  and  abrupt  transi- 
tions, There  is  no  connection  between  the  question  and  what  prepares  the 
answer,  — the  premise.     (Show  in  detail.) 

3°,  In  this  order  all  is  pleonastic  and  anticipative.  The  premises  slated,  we 
already  know  the  conclusion.  This,  indeed,  in  books  of  Logic,  is  virtually 
admitted,  —  the  conclusion  being  commonly  expressed  by  a  therefore,  etc.  An- 
cient doctrine  of  Enthymeme  (Ulpian,  etc.),  unknown  to  our  modern  logicians; 
among  their  other  blunders  on  the  Enthymeme.  On  the  common  doctrine, 
iLogic  —  Syllogistic  —  is  too  truly  defined  the  art  of  confessing  in  the  conclusion 
Avhat  had  been  already  avowed  in  the  premises. 

4"^,  On  this  order  the  objection  of  petido  principii  stands  hitherto  unrefuted,  if 
not  unrefutable,  against  Logic' 

6°,  In  this  order  the  process  is  complex.  The  simple  thought  is  first  mentally 
analyzed,  if  it  proceed,  as  it  ought,  from  the  quaesitum;  but  this  analysis  is  not 
expressed.  Then  the  elements  are  recomposed,  and  this  recomposition  affords 
the  synthetic  announcement  of  the  syllogism,  —  the  syllogism  being  thus  the 
superfluous  regress  of  a  foregone  analysis.  Aristotle's  analytic  is  thus  truly 
a  synthetic ;  it  overtly  reconstructs  the  elements  which  had  been  attained  by  a 
covert  analysis.^ 

G°,  In  this  method,  the  problem  hanging  loose  from  the  syllogism,  and,  in 
fact,  being  usually  neglected,  it  does  not  determine  in  the  Second  and  Third 
Figures  one  of  the  two  alternative  conclusions  which,  ex  facie  syllogismi,  are 
competent  in  them.  The  premises  only  being,  there  is  no  reason  why  one  of 
the  conclusions  should  be  drawn  to  the  preference  of  the  other.  Mem.  Coun- 
ter-practice old  and  new.  The  logicians  ought  not,  however,  to  have  ignored 
this  double  conclusion. 

7°,  See  corresponding  number. 

8°,  See  corresponding  number.' 

1  [?,{eyc&Tt(Elemenis,  vol.  ii.  cli.  3,  §  2,  Works,  meaning  of  the  term  is  the  doctrine  showing 
vol.  iii.  p.  202,  et  alibi)  makes  this  objection,  how  to  analyze  or  reduce  reasonings  to  syl- 
Refuted  by  Galluppi,  Li?z.  di  Logica  e  di  Meta-  logisms;  syllogisms  to  figure;  figure  to  mood; 
/isicn,  Lez.  i.  p.  242,  f(  seq.]  second  and  third  figures  to  first;  syllogisms 

2  [Aristotle's  Anali/tics  are  in  synthetic  or-  to  propositions  and  terms;  propositions  to 
der;  they  proceed  from  the  simple  to  the  terms;  for  of  all  these  analysis  is  said.  See 
compound;  the  elements  they  commence'  Pacci  Organon,  An.  Prior,  i.  cc.  2,  32,  42,  44, 
with  are  gained  by  a  foregone  analysis,  which  45,  pp.  128,  261,  273,  275,  278,  280.] 

is  not  expressed.    They  are  as  synthetic  as  a 

grammar  commencing  with  the  letters.    The         3  Compare  Discussions,  p.  652.  —  Ed. 


624  ArrKNDix, 

(b)   ORDER  OF  PREMISES. 

Aristotle  places  the  middle  term  in  the  first  Figure  between  the  extremes^ 
and  the  major  extreme  first ;  —  iu  the  second  Figure  before  the  extremes,  an'! 
the  major  extreme  next  to  it ;  —  in  the  third  Figure,  after  the  extremes,  and 
the  minor  extreme  next  to  it. 

In  his  mode  of  enouncement  this  relative  order  is  naturally  kept ;  for  he 
expresses  the  predicate  first  and  the  subject  last,  thus  :  A  is  in  oi/  B,  or  A  u 
predicated  of  all  B,  instead  of  saying  All  B  is  A. 

But  when  logicians  came  to  enounce  propositions  and  syllogisms  in  conform- 
ity to  common  language,  the  subject  being  usually  first,  they  had  one  or  other 
of  two  difficulties  to  encounter,  and  submit  tliey  must  to  either ;  for  they  must 
either  displace  the  middle  term  from  its  intertoediate  position  in  the  first  Figure, 
to  say  nothing  of  reversing  its  order  in  the  second  and  third ;  or,  if  they  kept 
it  in  an  intermediate  position  in  the  first  Figure  (in  the  second  and  third  the 
Aristotelic  order  could  not  be  kept),  it  behooved  them  to  enounce  the  minor 
premise  first. 

And  this  alternative  actually  determined  two  opposite  procedures,  —  a  dif- 
ference which,  though  generally  distinguishing  the  logicians  of  different  ages 
and  countries  into  two  great  classes,  has  been  wholly  overlooked.  All,  it  must 
be  borne  in  mind,  regard  the  syllogism  in  Figure  exclusively,  and  as  figured 
only  in  Extension. 

The  former  difficulty  and  its  avoidance  determined  the  older  order  of 
enouncement,  that  is,  constrained  logicians  to  state  the  minor  premise  first  in 
the  first  Figure  ;  and,  to  avoid  the  discrepancy,  they  of  course  did  the  same  for 
uniformity  in  the  second  and  third.     Such  is  tlie  order. 

The  latter  difficulty  and  its  avoidance  determined  the  more  modem  order  of 
enouncement,  that  is,  constrained  logicians  to  surrender  the  position  of  tlie 
middle  term  as  middle,  in  following  the  order  of  the  major  premise  first  in  all 
the  Figures. 

Philoponus  on  the  First  Book  of  the  Prior  Analytics,  c.  iv.  §  4  (Pacian 
Division),  f.  xx.  ed.  Trincavelli. — "  This  definition  appears  to  be  of  the  extremes 
and  of  the  middle  term ;  but  is  not.  It  behooves,  in  addition,  to  interpolate  in 
thought  an  ^onli/;'  and  thus  will  it  be  rightly  enounced,  as  if  he  had  said:  — 
But  the  extremes  are  both  that  which  is  only  in  another,  and  that  in  which  another 
only  is.  For  if  A  is  [predicated]  of  all  B,  and  B  is  [predicated]  of  all  C,  it  is 
necessary  that  A  should  be  predicated  of  all  C.  This  is  the  first  syllogistic 
mood.  Two  universal  affirmatives,  inferring  a  universal  conclusion.  For  if 
B  is  in  all  C,  consequently  C  is  a  part  of  B ;  but  again  B  is  a  part  of  A ;  con- 
sequently, A  is  in  all  C,  inasmuch  as  C  is  a  part  of  B.  But  what  is  here  said 
will  appear  more  clearly  from  a  concrete  example  —  Substance  of  all  animal: 
(inimal  of  all  man;  (there  follows)  substance  of  all  man.  And  backwards 
(avanaMv^,  All  man  animal;  all  animxd  substance ;  all  man  therefore  substance. 
In  regard  to  this  figure,  it  is  plain  how  we  ought  to  take  the  terms  of  the  first 
mood.  The  first  [major]  is  most  generic ;  the  second  [middle]  is  a  subal- 
tern genus;  and  the  third  [minor]  is  a  species  more  special  than  the  middle. 
But  a  conclusion  is  here  always  necessary.  Thus,  following  the  synthetic 
order,  that  is,  if  we  start  from  the  major  term,  substance  begins,  beginning  also 


APPENDIX 


62{ 


tlie  conclusion.  Substance  of  all  animal  (^substance  stands  first);  animal  of  all 
man  ;  (finally  the  conclusion  commences  with  substance)  — substance  0/ all  man. 
But  if  [on  tlic  analytic  order]  we  depart  from  the  minor  term,  as  from  man,  in 
this  case  the  conclusion  will,  in  like  manner,  begin  therewith  :  All  man  animal ; 
all  animal  substance  ;  all  man  substance." 

This  is  the  only  philosophic  view  of  the  matter.  His  syllogisms  really  ana- 
lytic (  =  In  Depth). 

Analytic  and  Synthetic  ambiguous.     Better,  —  order  oi  Breadth  and  Depth.^ 


1  [Instances  and  authorities  for  the  enounce- 
ment  of  Syllogism,  with  the  Minor  Premise 
stilted  first: 

Ancients. 

Gr^'eks:  —  Gregory  of  Xyss-a,  Optra,  t.  ii.  p. 
612,  in  liis  12  (not  10)  Syllogisms  against  Slan- 
ieheans,  varies.  These  very  corrupt.  Joan- 
nes Damasceniis  (Diaieci/ca,  c.  G4,  Opera,  ed. 
Lequien,  Paris,  1712,  t.  i.  pp.  65,  66)  gives  two 
Syllogisms,  one  with  minor  first.  Alcinous, 
De  Doct.  Plat.  L.  i.  CC.  5  and  6.  Aristotle 
often  places  minor  first.  See  ZabareIla,0/icm 
Lo^ica.  De  Qiiarta  Figvra,  p.  124  Vallius, 
Logica,  t.  ii  ,  pp.  72,  76.  Aristotle  and  Alex- 
ander not  regular  in  stating  major  proposi- 
tions. See  in  First  Figure,  An.  Pr.  i.  c.  4. 
Aristotle  used  the  "  whole  ■'  only  of  the  predi- 
cate. See  Zabaiella,  Tabula-.  In  An.  Prior,  p. 
149.  (But  see  above,  p.  548.)  Boetliius,Opfm, 
pp.  502.  5S3  Aiistotle,  An  Pr.  i.  c.  \,suijfine, 
ubi  Alexander,  f.  9  a.  Philoponus,  f.  17  a.  f  11 
b.  Alexander  Aph.  In  An.  Pr.  i.  IT.  9  a,  15  b. 
I'hiloponus,  In  An.  Pr.  i.  flf.  11  b,  20  a,  explains 
tlie  practice  of  Greek  Peripatetics  in  this 
matter.  See  also  if.  17  a,  18  a;  and  11,  21  a 
—  these  in  i  Fig.  —  in  ii.  Fig.  23  b.  The  same 
In  Phystca,  i.  c  1,  f.  2.  Tliomistius,  In  An. 
Po.tt.  ii.  c.  4.  Anonymus,  De  Syllogismo,  f. 
43  a.  Gregorius  Ancponymus,  Coiw/ienrf.  Ph.il- 
oiophim  St/ntagmn,  L.  V  cc.  1,  6,  pp.  58,  70. 
Georgius  Diaconus  Pachymerius,  Epit.  Log. 
tit.  iv.  cc.  1 — 4.  Sextus  Empiricus,  Pyrrh.  Hy- 
potypos.,  L.  ii.  cc.  13, 14,  pp.  103, 110.  Clemens 
Alex.  Strom.  L.  viii.  Opera,  p.  784  (ed.  Syl- 
burgii).  liieraniidas,  E/iitome  Logica,  c.  31,  p. 
219.  Gregorius  Trapezuntius,  Dialeclica,  De 
Syll.  p.  30.  "  Prima  (Figura)  est  in  qua 
medius  terminus  subjicitur  in  majore,  et  in 
minore  prasdicatur:  qiuimcis  contrajieri et  soleal 
etpoasit.'''  A  Greek,  he  wrote  in  Italy  for  the 
Latins;  but  refers  here  to  the  practice  of  his 
countrymen. 

Latins:  —  Cicero,  De  Fin.  iii.  8;  iv.  18. 
Tiisc.  Disp.  iii.  7;  v.  15,  Opera  Phil.  pp.  885, 
903,  981, 1029,  ed.Verburgii.  3Iacrobius,  Opera, 
p.  181,  Zeunii.  Seneca,  Epist.  85,  p.  368.  Apu- 
leius,  De  Habit.  Doct.  Plat.  L.  iii.  p  36,  ed. 
Elmenhorst.  Isidorus  in  Gothofr.  Auctores,  p. 
873.      Cassiodorus,    DiaUctica,    Opera,   p.  556, 


Genev.  1650,  gives  alternative,  but  in  Psalm 
xxxi.  V.  16,  gives  a  syllogism  with  minor  first. 
Martianus  Capella,  De  Septem  Artibus  LiberaU- 
bus,  allows  both  forms  for  liist  Figure;  gener- 
ally makes  the  minor  first  (.'^ee  below,  p.  640). 
Boethius  (origo  mail),  v.   Opera,  p.  594  et  sec/. 

Orientals. 

Mohammedans: — Averroes  (enouncing  &a- 
we)  in  all  the  Figures,  has  minor  first.  (Sec 
below,  p.  640  ) 

Jeivs :  —  Kabbi  Simeon  [truly  MaimonidesJ," 
(in  Hebrew),  Logica,  per  S.  Munslerum,  cc.  G,. 
7,  Basil,  1527. 

Modern  anticipations  of  the  doctrine  that 
the  Minor  Premise  should  precede  the  Major, 
Valla,  Dialectica,  f  60  b,  etc.  Opera,  pp.  733,  , 
736.  Joannes  Neomagus,  In  Trnpezuntimn ,  f. 
38  b.  (only  adduces  examples).  Caramuel,, 
Rat.  et  Realis  Philosopkia,  Logica,  Disp.ix.  xvi. 
Aquinas,  Opusc.  47.  (Camerarius,  Difp.  Phil. 
P.  i.  qu.  13,  p.  117.)  Alstedius,  Encyclopadia, 
p.  437.  Gassendi,  Opera,  ii.  p.  413;  i.  p.  107. 
Camerarius,  Disp.  Phil.  P.  i.  qu.  13,  p.  117. 
Leibnitz,  Opera  ii.  Pars.  i.  p.  356,  Dissert,  de 
Arte  Combinatoria  (1666),  ed!  Dutens,  who  re- 
fers to  Ramus,  Gassendi,  Alcinous,  etc.  Cf. 
Nouveaux  Essais,  L.  iv.  §  8,  p.  454,  ed,  Raspo; 
and  Locke's  Essay,  ibid.  Puffier,  Logique,  § , 
68.  CKsarius,  Dialectica,  Tract,  v.  De  Syll. 
Cat.  p.  198  (first  ed.  1632).  J.  C.  E.  Nova  De- 
ucta  Veritas,  etc.,  see  Keusch,  Systema  Logicum,.. 
f  547,  p.  626.  Chauvin,  Lexicon  Philosophicum, 
V.  Figura.  Hobbes,  Computacio,  c.  iv.,  prefixes 
the  minor  (see  Hallam,  Lit.  of  Europe,  vol.  iii.  . 
c.  3,p  309,  ed.l839).  Lambert,  A'euM  Organon, 
i.  138,  §  225.  Bachmann,  Logik,  §  133,  pp.  202, 
226.  Hollmann,  Logica,  §  454.  Esser,  Logik,, 
§  107,  p.  210.  Krug,  Logik,  §  114,  p.  408.  Ben- 
eke,  Sy.-item  der  Logik,  c.  v.  p.  210  et  seg.  Stap- 
ulensis,  in  Sergeant's  Method  to  Science,  p.  127. 
Facciolati  (though  he  errs  himself),  Rudinunltt 
Logicce,  p.  86,  1',  iii.  c.  3,  note  4,  where  Boe- 
thius, Sextus  Empiricus,  Alcinous,  etc.  Ch. 
Mayne,  Essay  on  Natural  Notions,  p.  122  et  seq. 
Lamy,  Acta  Enid.,  1708,  p.  67. 

Who  have  erred  in  this  subject,  —  making 
our  order  of  enunciation  the  natural  and 
u:ual        Vives,   Censura    Veri.  Opera,  t.   i.   p. 


79 


626 


APPENDIX. 


n.  —  Figure.  —  Unfigured  and  Figured  Syllogism. 

(1853)    (a)   CONTRAST  AND  COMPARISON  OF  THE  VARIOUS  KINDS  OF  FORMAL  SYLLOGISM 
-DIFFERENCE  OF  FIGURE  ACCIDENTAL. 

A.)  Unfigured  Syllogism  —  One  form  of  syllogism :  for  here  there  is  abolished, 
1°,  The  difference  of  Breadth  and  Depth,  for  the  terms  are  both  Subject  or 
both  Predicate,  and  may  be  either  indifferently  ;  2°,  All  order  of  the  terms,  for 
these  maybe  enounced  from  first  or  second  indifferently  ;  3°,  All  difference  of 
major  or  minor  term  of  proposition,  all  duplicity  of  syllogism ;  4°,  All  difference 
of  direct  and  indirect  conclusion. 

B.)  Figured  Syllogism  —  Two  forms  of  syllogism  by  different  orders  of  terms : 

First  Figure.  —  Here  the  two  forms  of  syllogism  are  possible,  each  with  its 
major  and  minor  terms,  each  with  its  direct  or  immediate,  its  indirect  or 
mediate,  conclusion.  These  two  various  forms  of  syllogism  are  essentially  one 
and  the  same,  differing  only  accidentally  in  the  order  of  enouncement,  inasmuch 
as  they  severally  depart  from  one  or  from  the  other  of  the  counter,  but  correl- 
ative, quantities  of  Depth  and  Breadth,  as  from  the  containing  whole.  But,  in 
fact,  we  may  enounce  each  order  of  syllogism  [in]  either  quantity,  the  one  is 
the  more  natural 

Second  and  Third  Figures.  —  In  each  of  these  figures  there  are  possible  the 
two  varieties  of  syllogism ;  but  not,  as  in  the  first  figure,  are  these  different 
forms  variable  by  a  counter  quantity,  and  with  a  determinate  major  and  minor 
terai;  for  in  each  the  extremes  and  the  middle  term  (there  opposed)  are 
necessarily  in  ihe  same  quantity,  being  either  always  Subject  or  always  Preifi- 
cate  in  the  jugation.  They  differ  only  as  the  one  extreme,  or  the  other  (what 
is  indifferent),  is  arbitrarily  made  the  Subject  or  Predicate  in  the  conclusion. 
Indirect  or  Mediate  conclusions  in  these  figures  are  impossible  ;  for  the  indirect 
or  mediate  conclusion  of  the  one  syllogism  is  in  fact  the  direct  conclusion  of  the 
other. 

Thus  difference  of  Figure  accidental. 

If  rule  true,  it  will  follow  that  it  is  of  no  consequence  whether  — 

1°,  The  middle  one  or  any  other  of  the  three  terms  be,  in  any  proposition, 

subject  or  predicate,  if  only  either.     Hence  difference  of  Figure  of  no  account 

in  varjing  tlie  syllogism.    Thus  (retaining  the  subordination  of  terms),  convert 

major  proposition  in  Extension  of  first  Figure,  and  you  have  second  Figure ; 


G06.  J.  G.  Vossius,  De  Nat.  Art.  Liberal. ,  Log- 
lea,  c.  viii.  §  9.  J.  A.  Fabricius,  Ad.  Sext. 
Emp.  103.  Fncciolali,  Rudimenta  Logictr,  p. 
86.     Waitz,  In  Org.  Comm.,  pp.  380,  336. 

That  Reasoning  in  Comprehensive  Quantity 
most  natural.  Wolf,  Pkil.  Rat.  ^  399,  p.  327. 
Reiiscll,  Si/steina  Logicum,  ^  547.  Schuize, 
Logik,  i  77  of  old  (1817),  i  72  of  last  (1831) 
edition,  holds  that  dictum  de  omniy  etc., 
evolved  out  of  nota  notee,  for  mere  subordina- 
tion Ryllogisms.  Hauschius,  in  Acta  Erud. 
17'28,  p.  470  Lamy  (B.)  in  Acta  Erud.  1708,  p. 
67.  Oldfleld,  Ensay  on  Reason,  p.  246.  Valla, 
Dialectica,  L.  iii.  c.  45.  HofTbnuer,  Analytik 
der  UrUuile  t/nd  Sclililsse,  i  152,  p.  198.    llayne's 


Rational  Notiomt.  p.  123  et  seq.  Mariotte,  Lo- 
gique.  Part  ii ,  disc.  iii.  p.  161.  Paris,  1678. 
Chladenus,  Phil.  Def.  p.  18  (in  Wolf,  Phil. 
Rat.  §  551).  Castillon,  Mem.  de  Berlin,  1802. 
Hallam,  Lit.  of  Europe,  vol.  iii.  p.  309.  Thom- 
son ( W.),  Outlines  of  the  Laics  of  Thought,  p. 
39.  In  reference  to  the  above,  the  mathema- 
ticians usually  begin  with  what  is  commonly 
called  the  Minor  Premise  (as  A  =  B,  B  =  C, 
there/ore  A  =  C);  and  frequently  they  state 
theConclusion  first(as  A  =  h.  for  A  =  iS^and 
M  =  B),  or,  etc.,  see  Wolf,  PhU.  Rat.  i  561. 
and  Twesten,  Logik,  4  117,  p.  105;  and  Lam- 
bert, Neuti  Org.  i.  (  226-] 


APPENDIX.  62T 

convert  minor  proposition,  and  you  have  third  Figure ;  convert  both  premises, 
and  you  have  fourth  Figure. 

2°,  Whelher  one  of  the  extremes,  one  or  other  of  the  premises,  stand  first 
or  second,  be,  in  fact,  major  or  minor  term  of  a  proposition ;  all  that  is  required 
is,  that  the  terms  and  their  quantities  should  remain  the  same,  and  that  they 
should  always  bear  to  each  other  a  relation  of  subject  and  predicate.  Thus,  if 
[in]  any  of  the  Figures  the  major  and  minor  terms  and  propositions  inter- 
change relation  of  subordination ;  when,  in  the  first  Figure,  you  convert  and 
transpose;  and  when  [in]  the  other  three  Figures  (fourth?),  you  simply  trans- 
pose the  premises. 

Indifferent  (in  first  Figure)  which  premise  precedes  or  follows.  For  of  two 
one  not  before  the  other  in  nature.  But  not  indifferent  in  either  whole,  which 
term  should  be  subject  and  predicate  of  coinclusion.^ 

(b)   DOUBLE  CONCLUSION  IN  SECOND  AND  THIRD  FIGURES. 

My  doctrine  is  as  follows : 

In  the  Unjigured  Syllogism  there  is  no  contrast  of  terms,  the  notions  compared 
not  being  to  each  other  subject  and  predicate ;  consequently  the  conclusion  is 
here  necessarily  one  and  only  one. 

In  the  Figured  Syllogism  we  must  discriminate  the  Figures. 

In  the  First  Figure,  where  the  middle  term  is  subject  of  the  one  extreme  and 
predicate  of  the  other,  there  is  of  course  a  determinate  major  extreme  and 
premise,  and  a  determinate  minor  extreme  and  premise ;  consequently,  also, 
one  proximate  or  direct,  and  one  remote  or  indirect,  conclusion,  —  the  latter 
by  a  conversion  of  the  former. 

In  the  Second  and  Third  figures  all  this  is  reversed.  In  these  there  is  no 
major  and  minor  extreme  and  premise,  both  extremes  being  either  subjects  or 
predicates  of  the  middle ;  consequently,  in  the  inference,  as  either  extreme 
may  be  indifferently  subject  or  predicate  of  the  other,  there  are  two  indifferent 
conclusions,  that  is,  conclusions  neither  of  which  is  more  direct  or  indirect  than 
the  other. 

This  doctrine  is  opposed  to  that  of  Aristotle  and  the  logicians,  who  recognize 
in  the  Second  and  Third  Figures  a  major  and  minor  extreme  and  premise, 
with  one  determinate  conclusion. 

The  whole  question  with  regard  to  the  duplicity  or  simplicity  of  the  conclu- 
sion in  the  latter  figures  depends  upon  the  distinction  in  them  of  a  major  and  a 
minor  term  ;  and  it  must  be  peremptorily  decided  in  opposition  to  the  universal 
i  doctrine,  unless  it  cq,n  be  shown  that,  in  these  figures,  this  distinction  actually 

subsists.  This  was  felt  by  the  logicians;  accordingly  they  applied  themselves 
with  zeal  to  establish  this  distinction.  But  it  would  appear,  from  the  very 
multiplicity  of  their  opinions,  that  none  proved  satisfact(Try ;  and  this  general 
presumption  is  shown  to  be  correct  by  the  examination  of  these  opinions  in 
detail,  —  an  examination  which  evinces  that  of  these  opinions  there  is  no  one 
which  ought  to  satisfy  an  inquiring  mind. 

In  all,  there  are  five  or  six  different  grounds  on  which  it  has  been  attempted 

1  Compare  Discussions,  p.  653.  —  Ed. 


628  APPENDIX. 

to  establish  the  discrimination  of  a  major  and  minor  term  in  the  Second  and 
Third  Figures.  All  are  mutually  subversive  ;  each  is  incompetent.  Each 
following  the  first  is  in  fact  a  virtual  acknowledgment  that  the  reason  on  which 
Aristotle  proceeded  in  this  establishment  is  at  once  ambiguous  and  insuffi- 
cient. I  shall  enumerate  these  opinions  as  nearly  as  possible  in  chronological 
order. 

1.  That  the  major  is  the  extreme  which  lies  in  the  Second  Figure  nearer  to,  in 
the  Third  Figure  farther  from,  the  middle.  This  is  Aristotle's  definition  (^An. 
Pr.,  L.  i.  cc.  5,  6).  At  best  it  is  ambiguous,  and  has,  accordingly,  been  taken 
in  different  senses  by  following  logicians ;  and  in  treating  of  them  it  will  be 
seen  that  in  none,  except  an  arbitrary  sense,  can  the  one  extreme,  in  these 
figures,  be  considered  to  he  nearer  to  the  middle  term  than  the  other.  I 
exclude  the  supposition  that  Aristotle  spoke  in  reference  to  some  scheme  of 
mechanical  notation. 

2.  That  the  major  term  in  the  antecedent  is  that  which  is  predicate  in  the  con- 
clusion. This  doctrine  dates  from  a  remote  antiquity.  It  is  rejected  by 
Alexander;  but,  adopted  by  AmmOnius  and  Philoponus  (f  17  b,  18  a,  ed. 
Trine),  has  been  generally  recognized  by  subsequent  logicians.  Its  recognition 
is  now  almost  universal.  Yet,  critically  considered,  it  explains  nothing.  Educ- 
ing the  law  out  of  the  fact,  and  not  deducing  the  fact  from  the  law,  it  does  not 
even  attempt  to  show  why  one  being,  either  extreme  may  not  be,  predicate  of  the 
conclusion.  It  is  merely  an  empirical, — merely  an  arbitrary,  assertion.  The 
Aphrodisian,  after  refuting  the  doctrine,  when  the  terms  are  indefinite  (prein- 
designate),  justly  says :  "  Nor  is  the  case  different  when  the  terms  are  definite 
[predesignate].  For  the  conclusion  shows  as  predicate  the  term  given  as 
major  in  the  premises ;  so  that  the  conclusion  is  not  itself  demonstrative  of  the 
major ;  on  the  contrary,  the  being  taken  in  the  premises  as  major,  is  the  cause 
why  a  term  is  also  taken  as  predicate  in  the  conclusion." —  (^An.  Pr.  f  24  a, 
ed.  Aid.) 

8.  That  the  proximity  of  an  extreme  to  the  middle  term,  in  Logic,  is  to  he  decided 
hij  the  relative  proximily  in  nature  to  the  middle  notion  of  the  notions  compared. 
This,  which  is  the  interpretation  of  Aristotle  by  Herminus,  is  one  of  the  oldest 
upon  record,  being  detailed  and  refuted  at  great  length  by  the  Aphrodisian 
(f  23  b,  24  a).  To  determine  the  natural  proximity  required  is  often  difficult 
in  affirmative,  and  always  impossible  in  negative,  syllogism ;  and,  besides  the 
objections  of  Alexander,  it  is  wholly  material  and  extralogical.  It  is  needless 
to  dwell  on  tliis  opinion,  which,  obscure  in  itself,  seems  altogether  unknown  to 
our  modern  logicians. 

4.  That  the  major  term  in  the  Syllogism  is  the  predicate  of  the  problem  or 
question.  This  is  the  doctrine  maintained  by  Alexander  (f.  24  b)  ;  but  it  is 
doubtful  whether  at  first  or  second  hand.  It  has  been  adopted  by  Averrocs, 
Zabarella,  and  sundry  of  the  acuter  logicians  in  modern  times.  It  is  incompe- 
tent, however,  to  establish  the  discrimination.  Material,  it  presupposes  an 
intention  of  the  roasoncr;  does  not  appear  ex  facie  syllogismi ;  and,  at  best, 
only  shows  which  of  two  possible  qusesita  —  which  of  two  possible  conclusions 
— •  has  been  actually  carried  out.  For  it  assumes,  that  of  the  two  extremes 
either  might  have  been  major  in  the  antecedent,  and  predicate  in  the  conclu- 
sion.    If  Alexander  had  applied  the  same  subtlety  in  canvassing  his  own 


APPENDIX.  629 

opinion  which  he  did  in  criticizing  those  of  others,  he  would  not  have  given  the 
authority  of  his  name  to  so  untenable  doctrine. 

6.  That  the  inajor  exii-eme  is  that  contained  in  the  major  premise,  awl  the 
major  premise  .that  in  the  order  of  enouncement  Jirst.  This  doctrine  seems 
indicated  by  Scotus  {An.  Pr.,  L.  I.  qu.  xxiv.  §§  5,  6)  ;  and  is  held  explicitly 
by  certain  of  his  followers.  This  also  is  wholly  incompetent.  For  the  order  of 
the  premises,  as  the  subtle  doctor  him.<elf  observes  (/6.,qu.xxlii.  §6),  is  altogether 
indifferent  to  the  validity  of  the  consequence  ;  and  if  this  external  accident  be 
admitted,  we  should  have  Greek  majors  and  minors  turned,  presto,  into  Latin 
minors  and  majors. 

C.  Thai  the  major  extreme  is  that  contained  in  the  major  premise,  and  the 
major  premise  that  itself  most  general.  AH  opposite  practice  originates  In  abuse. 
This  opinion,  which  coincides  with  that  of  Herniinus  (No.  3),  In  making  the 
logical  relation  of  terms  dependent  on  the  natural  relation  of  notions,  I  find 
advanced  in  1614,  in  the  Disputationes  of  an  ingenious  and  independent  phi- 
losopher, the  Spanish  Jesuit  Petrus  Hurtado  de  Mendoza  (Disp.  Log.  et  Met.,  I., 
Disp.  X.  §§  50-55).  It  is,  however,  too  singular,  and  manifestly  too  untenable, 
to  require  refutation.  As  material,  it  is  illogical ;  as  formal,  if  allowed,  it 
would  jit  best  serve  only  for  the  discrimination  of  certain  moods ;  but  it  cannot 
be  allowed,  for  it  would  only  subvert  the  old  without  being  adequate  to  the 
establishment  of  aught  new.  It  shows,  however,  how  unsatisfactory  were  the 
previous  theories,  when  such  a  doctrine  could  be  proposed,  by  so  acute  a 
reasoner,  in  substitution.  This  opinion  has  remained  unnoticed  by  posterior 
If^icians. 

The  dominant  result  from  this  historical  enumeration  Is,  that,  in  the  Second 
and  Third  Figures,  there  Is  no  major  or  minor  term,  therefore  no  major  or 
minor  premise,  therefore  two  indifferent  conclusions. 

This  important  truth,  however  natural  and  even  manifest  it  may  seem  when 
fully  developed,  has  but  few  and  obscure  vaticinations  of  its  recognition  during 
the  progress  of  the  science.     Three  only  have  I  met  with. 

The  first  I  find  in  the  Aphrodisian  (f.  24  b)  ;  for  his  expressions  might  seem 
to  indicate  that  the  opinion  of  there  being  no  major  and  minor  term  in  the 
•  second  figure  (nor,  by  analogy,  in  the  third),  was  a  doctrine  actually  held  by 
jome  early  Greek  logicians.  It  would  be  curious  to  know  if  these  were  the 
"  ancients,"  assailed  by  Ammonius,  for  maintaining  an  overt  quantification  of 
the  i)redicate.  The  words  of  Alexander  are  :  — ''  Nor,  however,  can  It  be 
said  that  in  the  present  figure  there  is  no  major.  For  this  at  least  is  determi- 
nate, that  its  major  must  be  universal ;  and,  if  there  be  in  it  any  syllogistic 
combination,  that  premise  is  the  major  which  contains  the  major  term"  (f. 
24  a.).  Demurring  to  this  refutation,  it  is,  however,  evidence  sufficient  of  the 
opinion  to  which  it  is  opposed.  This,  as  it  is  the  oldest,  is,  indeed,  the  only 
authority  for  any  deliberate  doctrine  on  the  point. 

The  second  indication  dates  from  the  middle  of  the  fifteenth  centurj',  and  is 
contained  In  the  Dialectica  of  the  celebrated  Laurentius  Valla  (L.  ill.  c.  8 
[51]).  Valla  abolishes  the  third  figure,  and  his  opinion  on  the  question  is 
limited  to  his  observations  on  the  second.  In  treating  of  Cesare  and  Camestres, 
which,  after  a  host  of  previous  logicians,  he  considers  to  be  a  single  mood, 
there  is  nothing  remarkable  in  his  statement :  "  Neque  dlstinctae  sunt  pro- 


630  APPENDIX. 

positio  et  assumptio,  ut  altera  major  sit,  altera  minor,  sotl  quodammodo  pares ; 
ideoque  sicut  neutra  vindicat  sibi  primum  aut  secundum  locum,  ita  utraque 
jus  habet  in  utraque  conclusione.  Verum  istis  placuit,  ut  id  quod  secundo 
loco  poneretur,  vendicaret  sibi  conclusionem :  quod  verum  esset  nisi  semper 
gemina  esset  conclusio.  Sed  earum  dicamus  alteram  ad  id  quod  primo  loco, 
alteram  ad  id  quod  secundo  loco  positum  est  referri."  We,  therefore,  await 
the  development  of  his  doctrine  by  relation  to  the  other  moods,  Feslino 
and  Baroco,  which  thus  auspiciously  begins:  —  "Idem  contingit  in  reliquis 
duobus:  qui  tamen  sunt  magis  distincti."  We  are,  however,  condemned  to 
disappointment  For,  by  a  common  error,  excusable  enough  in  this  im- 
petuous writer,  he  has  confounded  singulars  (definites)  with  particula:-j 
(indefinites)  ;  and  thus  the  examples  which  he  adduces  of  these  moods  are, 
in  fact,  only  examples  of  Cesare  and  Camestres.  The  same  error  had  also 
been  previously  committed  (L.  iii.  c.  4).  The  whole,  therefore,  of  Valla's 
doctrine,  which  is  exclusively  founded  on  these  examples,  must  go  for  nothing ; 
for  we  cannot  presume,  on  such  a  ground,  that  he  admits  more  than  the  four 
common  moods,  identifying,  indeed,  the  two  first,  by  admitting  in  them  of 
a  double  conclusion.  We  cannot,  certainly,  infer  that  he  ever  thouglit  of 
recognizing  a  particular,  an  indefinite,  predicate  in  a  negative  proposition. 

The  third  and  last  indication  which  I  can  adduce  is  that  from  the  Melhofl  to 
Science  of  John  Sergeant,  who  has,  in  this,  as  in  his  other  books  (too  suc- 
cessfully), concealed  his  name  under  the  initials  "J.  S."  He  was  a  Catholic 
priest,  and,  from  1665,  an  active  religious  controversialist;  whilst,  as  a  philos- 
opher, in  his  Idea  Philonophice  Cartesiance,  a  criticrism  of  Descartes,  in  his  Solid 
PkUosophj,  a  criticism  of  Locke,'  in  his  Metaphysics,  and  in  the  present  work, 
he  manifests  remarkable  eloquence,  ingenuity,  and  independence,  mingled,  no 
doubt,  with  many  untenable,  not  to  say  ridiculous,  paracjoxes.  His  works, 
however,  contain  genius  more  than  enough  to  have  saved  them,  in  any  other 
country,  from  the  total  oblivion  into  which  they  have  fallen  in  this,  —  where, 
indeed,  they  probably  never  were  appreciated.  His  Method  to  Science  (a 
treatise  on  Logic)  was  published  in  1696,  with  a  "  Preface,  dedicatory  to  tlio 
learned  students  of  both  our  Universities,"  extending  to  si.xty-two  pages.  But, 
alas !  neither  tliis  nor  any  other  of  his  philosophical  books  is  to  be  found  in  the 
Bodleian. 

In  the  third  book  of  his  Method,  which  treats  of  Discourse,  after  speaking 
of  the  first,  or,  as  he  calls  it,  "only  right  figure  of  a  syllogism,"  we  lia\e  llio 
following  observations  on  the  second  and  thirtl :  —  "§  14.  Wherefore  the  other 
two  figures  [he  does  not  recognize  the  fourihj  are  tmnatura!  and  monstrous. 
For,  since  nature  has  shown  us,  that  M'hat  conjoins  two  notions  ought  to  be 
placed  in  the  middle  between  them  ;  it  is  against  nature  and  reason  to  place  it 
either  above  them  both,  as  is  done  in  that  they  call  the  second  Jiyure,  or  under 
them  both,  as  is  done  in  that  figure  they  call  the  third. 

"§  15.  Hence  no  determinate  conclusion  can  follow,  in  either  «f  the  last 

1  Sergeant  is  an  intelli;jent  antagonist  of  man  Undrrstamting.    In  certain  rjews  he  an- 

both  these  philosupherv,  and  I  have  elsewhere  ticipates  Kant :  and  Tope  lias  evidently  taken 

had   occasion  to  quote  him  as  the  first  and  from  his  brother  Catholic  the  hint  of  some  uf 

one  of  the  ablest  critics  of  the  Essay  on  Hu-  his  most  celebrated  thoughts. 


APPENDIX.  631 

figures,  from  the  disposal  of  the  parts  in  the  syllogisms.  For  since,  as  appears 
(§  13),  the  extreme  which  is  predicated  of  the  middle  term  in  the  major,  has 
thence  a  title  to  be  the  predicate  in  the  conclusion,  because  it  is  above  the 
middle  term,  which  is  the  predicate,  or  above  the  other  extreme  in  the  minor,  it 
follows,  that  if  the  middle  term  be  twice  above  or  twice  below  the  other  two 
terms  in  the  premises,  that  reason  ceases;  and  so  it  is  left  indifferent  which  of 
the  other  terms  is  to  be  subject  or  predicate  in  the  conclusion ;  and  the  inde- 
terminate conclusion  follows,  not  from  tlie  artificial  form  of  the  syllogism,  but 
merely  from  the  material  identity  of  all  the  three  terms ;  or  fi-om  this,  that 
tlieir  notions  are  found  in  the  same  Ens.  Wherefore,  from  these  premises  [in 
the  second  figure], 

Some  laudable  thing  is  [all]  virtue, 
[All]  courtesy  is  a  virtue ; 

or,  from  these  [in  the  third], 

[All]  virtue  is  [some]  laudable, 
Some  virtue  is  [all]  courtesy  ,• 

the  conclusion  might  either  be, 

Therefore,  [all]  courtesy  is  [some]  laudable, 
Or,  Some  laudable  thing  is  [all]  courtesy. 

So  that,  to  argue  on' that  fashion,  or  to  make  use  of  these  awkward  figures,  is 
not  to  know  certainly  the  end  or  conclusion  we  aim  at,  but  to  shoot  our  bolt 
at  no  determinate  mark,  since  no  determinate  conclusion  can  in  that  case  fol- 
low."    (P.  232.) 

Extremes,  it  is  said,  meet.  Sergeant  would  abolish  the  second  and  third 
figures,  as  petitory  and  unnatural,  as  merely  material  corruptions  of  the  one 
formal  fiist.  I,  on  the  contrary,  regard  all  the  figures  as  equally  necessary, 
natural,  and  formal.  But  we  agree  in  this  :  both  hold  that,  in  the  second  and 
third  figures,  there  is  a  twofold  and  indifferent  conclusion ;  howbeit,  the  one 
makes  this  a  monstrosity  of  the  syllogistic  matter,  the  other,  a  beauty  of  the 
syllogistic  form.  Therefore,  though  I  view  Sergeant  as  wrong  in  his  premises, 
and  "  shooting  his  bolt  at  no  determinate  mark,"  I  must  needs  allow  that  he 
has,  by  chance,  hit  the  bull's  eye.  I  have  inserted,  within  square  brackets,  the 
quantifications  required  to  restore  and  show  out  the  formality  of  his  examples. 
On  my  scheme  of  notation,  they  stand  as  follows : 


63^ 


APPENDIX. 


HL  —  HisTOsiCAL  Notices  Regakdixg  Figure  of  Stlu>gisk. 


(a)    ARISTOTLE. 

Aristotle ;  Figures  and  Terms  of  Syllogism,  Prior  Analytics,  B.  I.  ch.  iv. 

First  Figure,  ch.  iv.  —  §  2.  "  When  three  terms  [or  notions]  hold  this  mutual 
relation,  —  that  the  last  is  In  the  whole  middle,  whilst  the  middle  is  or  is  not 
in  the  whole  first,  —  of  these  extremes  there  results  of  necessity  a  perfect 
syllogism.^ 

§  3.  "  By  middle  term  [B  (B)]  I  mean  that  which  itself  is  in  another  and 
another  in  it ;  and  which  in  position  also  stands  intermediate.  I  call  extreme 
both  that  which  is  itself  in  another  [the  minor],  and  that  in  which  another  is 
[the  major].  For  if  A  be  predicated  of  all  B,  and  B  of  all  C,  A  will  neces- 
sarily be  predicated  of  all  C. 

§  10.  "I  call  that  the  major  extreme  [A  (A)]  in  which  the  middle  is;  the 
minor  [F  (C)]  that  which  lies  under  the  middle." 

Second  Figure,  ch.  v.  —  §  1.  "When  the  same  [predicate  notion]  inheres  in 
all  of  the  one  and  in  none  of  the  other,  or  in  all  or  in  none  of  both  [the  sub- 
ject notions],  —  this  I  denominate  the  Second  Figure. 

§  2.  "  The  middle  [M  (M)]  in  this  figure  I  call  that  which  is  predicated  of 
both  [notions]  ;  the  extremes,  the  [notions]  of  which  the  middle  is  said.  The 
major  extreme  [N  (N)]  is  that  towards  the  middle ;  the  minor  [H  (O)],  that 
from  the  middle  more  remote. 

§  3.  "  The  middle  is  placed  out  [from  between]  the  extremes,  the  first  in 
position" — 


lSo,M 

N 

H- 


M 

N 
O 


Third  Figure,  ch.  vi.  —  §  1.  "When  in  the  same  [subject  notion]  one 
[predicate  notion]  inheres  in  all,  another  in  none  of  it,  or  when  both  inhere  in 
all  or  in  none  of  it,  such  figure  I  call  the  Third. 

§  2.  "  In  this  [figure]  I  name  the  middle,  that  of  which  both  [the  other  terms] 
are  predicated ;  the  extremes,  the  predicates  themselves.  The  major  extreme 
[  n  (P)]  is  that  farther  from,  the  minor  [P  (Q)]  that  nearer  to,  the  middle. 


1  Ch.  iv.  s  2  —  This  definition  of  the  First 
Figure  (founded  on  the  rules  De  Omni  and  de 
Nullo)  applies  only  to  the  universal  moods, 
but,  of  these,  only  to  those  legitimate  and 
useful,  —  Barbara  and  Celareiit.  It,  there- 
fore, seems  inadequate,  but  not  superfluous. 

Aristotle  uses  the  phrase  "  to  be  in  all  or  in 
the  whole,"  both  with  reference  to  extension, 
—  for  the  lower  notion  B,  as  contained  under 


the  all  or  whole  of  the  higher  notion  A  ;  and 
with  reference  to  comprehension,  —  for  the 
higher  notion  A  as  contained  in  the  all  or 
whole  of  the  lower  notion  B.  In  the  former 
sense,  which  with  Aristotle  is  the  more  usual, 
and,  in  fact,  the  only  one  contemplated  by 
the  logicians,  there  is  also  to  be  observed  a 
distinction  between  the  inhesion  and  the  pre- 
dication of  the  attribute. 


APPENDIX.  633 

§  3.  "  The  middle  [2  (R)]  is  placed  out  ^[from  between]  the  extremes,  the 
last  in  position," 

[As,  n P  1 

P Q 

2  R 


Aristotle,  Prior  Analytics,  B.  i.  c.  23,  §  7. 

General  Theory  of  Figure.  —  "  If,  then,  it  be  necessary  [in  reasoning]  to 
take  some  [term]  common  [or  intermediate]  to  both  [extreme  terms]  ;  this  is 
possible  in  three  ways.  For  we  predicate  either  [the  extreme]  A  of  [the 
middle]  C,  and  [the  middle]  C  of  [the  extreme]  B  ;  or  [the  middle]  C  of  both 
[extremes]  ;  or  both  [extremes]  of  [the  middle]  C.  These  are  the  [three] 
Figures  of  which  we  have  spoken  ;  and  it  is  manifest,  that  through  one  or  other 
of  the  Figures  every  syllogism  must  be  realized."^ 

C)  and  (c)  -  ALEXANDER  AND  HERMINUS. 

Alexander,  In  An.  Pr.,  f.  23  b. 

Second  Figure,  c.  v.  Aristotle.  —  "  '  The  middle  extreme  is  that  which  lies 
towards  the  middle.' 

§  2.  "  But  it  is  a  question,  whether  in  the  Second  Figure  there  be  by  nature 
any  major  and  minor  extreme,  and  if  there  be,  by  what  criterion  it  may  be 
known.  For  if  we  can  indiiferently  connect  with  the  middle  term  whichsoever 
extreme  we  choose,  this  we  may  alwajs  call  the  major.  And  as  negative  con- 
clusions only  are  drawn  in  this  figure,  universal  negatives  being  also  mutually 
convertible,  it  follows,  that  in  universal  negatives  the  one  term  has  no  better 
title  to  be  styled  major  than  the  other,  seeing  that  the  major  term  is  what  is 
predicated,  whilst  both  are  here  indifferently  predicable  of  each  other.  In 
universal  affirmatives,  indeed,  the  predicate  is  major,  because  it  has  a  wider 
extent;  and  for  this  reason,  such  propositions  are  not  [simply]  convertible  ;  so 
that  here  there  is  by  nature  a  major  term  which  is  not  to  be  found  in  universal 
negatives. 

"  Herminus  is  of  opinion  that,  in  the  Second  Figure, 

[1°.]  "  If  both  the  extremes,  of  which  the  middle  is  predicated,  be  homoge- 
neous [or  of  the  same  genus],  the  major  term  is  that  most  proximate  to  the 
genus  common  to  the  two.  For  example :  If  the  extremes  be  Urd  and  man  ; 
bird  lying  nearer  to  the  common  genus  [^ani7nal']  than  man,  as  in  its  first 
division,  bird  is  thus  the  major  extreme ;  and,  in  general,  of  homogeneous 
terms,  that  holding  such  a  relation  to  the  common  genus  is  the  major. 

[2°.]  "  But  if  the  terms  be  equally  distant  from  the  common  genus,  as  Zto?\s-e 
and  man,  we  ought  to  regard  the  middle  predicated  of  them,  and  consider  of 

1  Ariptof  le  liere  varies  the  notation  by  let-  notation  mi^^ht  appear  to  indicate)  that  the 

ters  of  the  tliree  syllogistic  terms,  making  C  middle  term  was  a  notion  in  the  First  Figure, 

(!')  stand  for  the  middle  term,  A  and  15  for  necessarily  intermediate  between  tlie  two  ex- 

the  two  extremes.     This  he  did.  perhaps,  to  tremes,  in  the  Second  superior,  in  the  Third 

prevent  it  being  supposed  (what  his  previous  inferior,  to  them. 

80 


634 


APPENDIX. 


which  [term]  it  is  predicated  through  [that  term]  itself,  and  of  which  through 
some  other  predicate  ;  and  compare  that  through  which  it  is  predicated  of 
another  with  that  through  which  it  is  predicated  of  [the  term]  itself.  And  if 
that  through  which  [the  middle]  is  predicated  of  another  (viz.  the  one  extreme) 
be  nearer  [than  the  other  extreme]  to  the  common  genus,  that  [extreme]  of 
which  [for  tovjoiv  ov,  I  read  tovtov  ovJ  the  middle  is  [mediately]  predicated, 
from  its  closer  propinquity  to  the  common  genus,  rightly  obtains  the  title  of 
major.  For  example :  If  the  extremes  be  horse  and  7nan,  rational  being  predi- 
cated of  them,  —  negatively  of  horse,  affirmatively  of  man ;  seeing  that  rational 
is  not  of  itself  denied  of  horse,  but  because  horse  is  irrational,  whereas  rational 
is  of  itself  affirmed  of  man,  horse  is  nearer  than  7nan  to  their  common  genus 
animal ;  horse  will,  therefore,  be  the  major  extreme,  though  man  be  no  further 
removed  than  horse  from  its  proper  genus.  And  this,  because  that  through 
which  the  predicate  [i.  e.  the  middle]  is  predicated  of  this  last,  as  being 
irrational,  is  greater ;  for  rational  is  not  denied  of  horse  qua  horse,  whilst  it  is 
affirmed  of  man  qua  man. 

[3°.]  "  But  if  the  extremes  be  not  homogeneous,  but  under  diiferent  genera, 
that  is  to  be  considered  the  major  term,  which  of  the  two  holds  the  neai-er  of 
its  own  genus.  For  instance:  If  aught  be  predicated  of  color  and  man,  color 
is  the  major  extreme  ;  for  color  stands  closer  to  quality  than  man  to  substance : 
as  man  is  an  individual  [or  most  special]  species,  but  not  color. 

[4°.]  "  Finally,  if  each  be  equally  remote  from  its  proper  genus,  we  must 
consider  the  middle,  and  inquire  of  which  term  it  is  predicated  through  [that 
term]  itself,  and  of  which  through  something  else ;  and  if  that,  through  which 
the  middle  is  predicated  of  another  [/.  e.,  one  extreme],  be  nearer  to  its  proper 
genus,  and  if  through  that  the  middle  be  actually  predicated  of  this  term,  this 
term  is  to  be  deemed  the  major.  For  example:  If  the  terms  be  white  and 
man,  the  one  being  an  individual  species  in  quality,  the  other  in  substance ; 
and  if  rational  be  alfii'matively  predicated  of  man,  negatively  of  tchite ;  the 
affirmation  is  made  in  regard  to  man  as  man,  whereas  the  negation  is  made  of 
white,  not  as  white,  but  as  inanimate.  But  since  inanimate,  through  which 
rational  is  denied  of  white,  is  more  common,  more  universal,  and  more  proxi- 
mate to  substance  inanimate  than  man  to  \fubstance'\  animate,  on  that  account, 
white  is  the  major  term  in  preference  to  man."     [So  far  Herminus.] 

"  But  to  reason  thus,  and  to  endeavor  to  demonstrate  a  major  term  by  nature, 
in  the  Second  Figure,  is  a  speculation  which  may  be  curious,  but  is  not  true. 
[I  read  irpbs  tw.] 

[1°.]  "  For,  in  the  first  place,  if  we  consider  the  given  terms,  not  in  them- 
selves, but  in  relation  to  others,  in  which  the  predicated  term  docs  not  inhere ; 
the  major  term  will  be  always  found  in  the  negative  proposition.  For,  in  this 
case,  the  major  is  always  equal  to  the  middle  term  ;  since,  whether  it  be  thus  or 
thus  taken  froui  the  commencement,  or  be  so  made  by  him  who  denies  it,  'ho 
negative  major  will  still  stand  in  this  relation  to  the  middle  term.  For  the  mid- 
dle does  not  inhere,  where  it  is  not  supposed  to  inhere.  Wherefore,  its  repug- 
nant opposite  inheres  in  the  subject,  but  the  repugnant  opposite  of  the  middle 
IS  ecjual  to  the  middle.  And  this,  either  througii  the  middle  itself,  or  through 
another  notion  of  wider  extent ;  as  when  ralional  is  denied  of  something  through 
inanimate.     For  there  \s  here  an  equalization  through  irrational,  through  which 


APPENDIX.  635 

rational  is  negatively  predicated  of  horse.  For  either  the  middle  is  equal  to 
this  of  which  it  is  denied,  or  [I  read  tj  for  6]  it  is  less ;  as  when  through  inani- 
mate, rational  is  denied  of  aught.  For  inanimate  is  equal  to  animate,  under 
which  is  rational,  a  notion  greater  than  that  other  of  which  it  is  affirmed.  For 
since  the  affirmative  predicate  is  greater  than  its  subject,  of  which  the  middle  is 
denied  or  not  affirmed  ;  and  since  the  reason  why  the  middle  is  denied  is  equal 
to  or  greater  than  the  middle  itself,  which  middle,  again,  in  an  affirmative 
proposition,  is  greater  than  its  subject ;  —  on  these  accounts  a  negative  propo- 
sition is  always  greater  than  an  affirmative.  Nevertheless,  Aristotle  himself 
says  that  a  negation  is  to  be  placed  in  the  minor  [proposition]  ;  for  the  second 
syll(^sm  in  this  figure  [Camestres]  has  as  its  minor  premise  a  universal 
negative. 

[2°.]  "  Further,  why  in  the  case  of  negatives  alone  should  explanation  or 
inquiry  be  competent,  in  regard  to  the  reason  of  the  negative  predication, 
seeing  that  in  the  case  of  affirmatives  the  reason  is  equalK'  an  object  of  inquiry  ? 
For  rational  is  predicated  of  man,  of  itself,  indeed,  but  not  primarily,  that  is, 
not  inasmuch  as  he  is  man,  but  inasmuch  as  he  is  rational ;  so  that  if  rational 
[be  denied]  of  horse  through  irrational,  still  these  are  both  branches  of  the 
same  division.  By  this  method,  assuredly,  no  major  can  be  ever  found. 
Wherefore,  we  ought  not,  in  this  way,  to  attempt  a  discrimination  of  the  major 
of  affirmative  syllogisms  in  the  Second  Figure.  For  in  this  figure  affirmation 
and  negation  are  equally  compatible  with  the  major  term  ;  so  that  whatsoever 
term  has  by  the  foremeutioned  method  been  found  major,  the  same,  taken 
either  as  major  or  minor,  will  effectuate  a  syllogistic  jugation  ;  which  being 
competent,  there  is  no  longer  any  major  [or  minor]  in  this  figure.  For  the 
problem  is  to  find  not  a  major  term  absolutely,  but  one  of  this  figure."  [So 
much  touching  Herminus.] 

[3°.]  "  Nor,  on  the  other  hand,  as  is  thought  by  some,  is  that  unconditionally 
to  be  called  the  major  term  which  stands  predicate  in  the  conclusion.  For 
neither  is  this  manifest;  if  left  indefinite  [preindesignate],  the  same  term  will 
hold  a  different  relation,  though  a  conversion  of  the  universal  negative;  so 
that  what  is  now  tlie  major,  may  be  anon  the  minor.  We  may,  in  fact,  be 
said  to  constitute  the  same  term  both  major  and  minor.  Naturally  there  is  in 
negative  propositions  no  major  notion,  nor,  from  the  conclusion,  ought  we  to 
make  out  the  major  at  all.  Nor  is  the  case  different  when  the  term  is  defined 
[predesignate].  For  the  conclusion  shows,  as  predicate,  the  terfli  given  as 
major  in  the  premises  ;  so  that  the  conclusion  is  not  itself  demonstrative  of  the 
major;  on  the  contrary,  the  being  taken  in  the  premises  as  major  is  the  cause 
why  a  term  is  also  taken  as  predicate  in  the  conclusion. 

"  Nor,  however,  can  it  be  said  that  in  this  figure  there  is  no  major.  For  this 
at  least  is  determinate,  —  that  its  major  must  be  universal;  and,  if  there  be 
[in  it]  any  syllogistic  combination,  that  premise  is  the  major  which  contains  the 
major  term. 

[4°.]  "  But,  in  the  Second  Figure,  -which  of  the  terms  is  to  be  deemed  the 
major  ?  Tliat  is  to  be  deemed  the  major,  and  to  be  placed  first,  which  in  the 
problem  [question  or  quajsitum]  we  intend  to  demonstrate,  and  which  we 
regard  as  predii;ate.  For  every  one  who  reasons,  first  of  all  determines  with 
himself  what  it  is  he  Tvonid  prove ;  and  to  tliis  end  lie  applies  his  stock  of 


G36 


APPENDIX, 


suitable  propositions ;  for  no  one  stumbles  by  chance  on  ■»  conclusion.  The 
notion,  therefore,  proposed  as  predicate  in  the  problem  to  be  proved,  is  to  be 
constituted  the  major  term ;  for  although  the  proposition  be  converted,  and  the 
notion  thereby  become  the  subject,  still,  in  what  we  proposed  to  prove,  it 
[actually]  was,  and,  therefore  [virtually],  remains,  the  predicate.  Hence,  even 
if  there  be  drawn  another  conclusion,  we  convert  it ;  so  that,  to  us  who  prove 
and  syllogize  and  order  terras,  that  always  stands  as  the  major.  For  major  and 
minor  are  not,  in  negative  syllogisms,  regulated  by  their  own  nature,  but  by 
the  intention  [of  the  reasoner]  to  conclude.  Thus  it  is  manifest,  that  what  is 
the  predicate  in  the  problem,  is  also  the  predicate  in  the  conclusion." 

Alexander  on  Prior  Analytics,  L.  i.  c.  vi.  f.  30  a.  ed.  Aid. 

(Third  Figure.)  .  .  ,  This  is  the  Third  Figure,  and  holds  the  last  place 
because  nothing  universal  is  inferred  in  it,  and  because  sophistical  syllogisms 
chiefly  affect  this  figure  with  their  indefinite  and  particular  conclusions.  But 
the  sophistical  are  the  last  of  all  syllogisms.  .  •  .  Add  to  this,  that  while 
both  the  Second  and  Third  Figures  take  their  origin  from  the  Fii-st  of  the 
two,  the  Third  is  engendered  of  the  inferior  premise.  For  the  minor,  qua 
minor,  is  the  inferior  premise,  and  holds  reasonably  a  secondarj-  place  [the 
conversion  of  the  minor  jjroposition  of  the  first  figure  giving  the  second  figure]. 

F.  30  b.  (Darapti).  "  The  first  syzygy  in  this  figure  is  of  two  universal 
affirmatives  [Darapli].  But  it  may  be  asked  —  Why,  whilst  in  the  second 
figure  there  are  two  syllogistic  conjugations,  having  one  of  the  premises  a 
universal  aflHrmative,  the  other  a  universal  negative  (from  having,  now  their 
major,  now  their  minor,  as  a  universal  negative  proposition  converted^, —  why, 
in  the  third  figure,  there  is  not,  in  like  manner,  two  syllogistic  combinations  of 
two  universal  afliinnatives,  since  of  these  either  the  major  or  the  minor  propo- 
sition is  convertible  ^  Is  it  that  in  the  second  figure,  from  the  propositions 
being  of  diverse  form  [quality],  the  commutation  of  a  universal  negative  into 
^omctliiitg  else  by  conversion  is  necessary,  this  being  now  the  major,  iiow  the 
minor,  ami  it  not  being  in  our  power  to  convert  which  we  will?  In  the  thirtl 
figure,  on  the  other  hand,  there  being  two  universal  affirmatives,  the  position 
[relation]  of  the  propositions  (for  they  are  similar  in  character  and  position)  is 
not  tlie  cause  of  one  being  now  converted,  now  another;  the  cause  lying  in  us, 
not  the  jiigation.  Wherefore,  the  one  or  other  being  similarly  convertible, 
inasmuch  as  the  position  [relation]  of  the  two  propositions  is  the  same;  the 
one  which  affords  the  more  important  probation  is  selected,  and  hereby  is 
determined  the  syllogistic  jugation.  Moreover,  the  differences  of  syllogism 
[moods]  in  each  figure  are  effected  by  the  differences  among  their  jugations, 
not  by  those  among  their  probations.  Thus  that  the  combination  of  proposi- 
tions is  syllogistic  [or  valid],  is  proved  by  conversion  and  reductio  ad  impossibile, 
al.-o  by  exposition.  But  from  this  circumstance  there  does  not  emerge  a  plu- 
wlity  of  syllogij^ms  [moorls].  For  the  different  probations  [are  not  valid  from 
such  plurality,  but]  from  the  unity  of  the  jugation  from  which  they  are  inferred, 
so  that  one  jugation  of  two  universal  affirmatives  may  constitute,  in  the  third 
figure,  a  single  syllogism  [mood],  howbeit  the  probations  are  different ;  ina.<i- 
much  as  now  the  one,  now  the  other,  of  the  propositions  can  be  converted." 


APPENDIX.  637 

(d)  -  PHILOrOXUS. 

Philoponus  (or  rather  Ammonius)  on  Aristotle,  An.  Pr.,  i.  4,  §  i.  f.  17  a,  ed. 
Trincavelli,  1536. 

"  The  Predicate  is  always  better  than  the  subject,  because  the  predicate  is, 
for  the  most  part,  more  extensive  (^M  Trxiov)  than  the  subject,  and  because  the 
subject  is  analogous  to  the  matter,  the  predicate  to  the  form ;  for  the  matter  is 
the  subject  of  the  forms.  But  Avhen  the  middle  term  is  predicated  of  the  two 
extremes,  or  is  the  subject  of  both,  in  this  case  it  is  not  properly  intermediate. 
But,  howbeit,  though  in  position  external  to  the  middle,  it  is  still  preferable  to 
be  the  predicate  than  to  be  the  subject.  On  this  ground,  that  is  called  the 
first  figure,  the  middle  term  of  which  preserves  its  legitimate  oi-der,  being 
subject  of  the  one  extreme,  and  predicate  of  the  other.  The  second  figure  is 
that  in  which  the  middle  is  predicated  of  both  extremes,  and  in  which  it  occu- 
pies the  better  position  of  those  remaining.  Finally,  the  third  figure  is  that  in 
which  the  middle  term  is  subjected  to  the  two  extremes ;  here  obtaining  only 
the  lowest  position.  Wherefore,  in  the  first  figure  the  middle  term  is  delineated 
on  a  level  with  the  extremes ;  whereas  in  the  second  it  is  placed  above,  and  in 
the  third  beloio,  them."* 

Philoponus  (or  rather  Ammonius)  on  Aristotle,  An.  Pr.,  f  17  a,  ed.  Trinca- 
velli, 1536. 

Syllogistic  Figures  in  general.  — "  We  must  premise  what  is  the  Major 
Proposition  of  the  Syllogism,  and  what  the  Minor.  But  to  understand  this, 
we  must  previously  be  aware  what  are  the  Major  and  Minor  Terms.  And  it 
is  possible  to  define  these,  both,  in  common,  as  applicable  to  all  the  three 
figures,  and,  in  special,  with  reference  to  the  first  alone.  In  the  latter  relation, 
that  is,  regarding  specially  the  first  figure,  the  Major  Term  is  that  which  consti' 
lutes  the  Predicate,  the  Minor  that  tvhich  constitutes  the  Subject,  of  the  Middle,  so 
far  as  limited  to  the  first  figure.  But  since  in  neither  of  the  other  figures  do 
the  extremes  reciprocally  stand  in  any  definite  (?)  relation  to  the  middle  term, 
it  is  manilest  that  this  determination  is  inapplicable  to  them.  We  must,  there- 
fore, employ  a  rule  common  to  all  the  three  figures ;  to  wit,  that  the  major 
term  is  that  predicated,  the  minor  that  sid>jected,  in  the  conclusion.  Thus,  the 
Major  Proposition  is  the  one  containin;/  the  Major  Term  ;  the  Alinor  Proposition 
the  one  containing  the  Minor  Term.     Examples  :     Of  the  First  Figure,  —  Man 

[w]   animal ;   animal,  substance  :    therefore,  man,  sidistance Of  the 

Second,  —  Animal  [is  predicated]  of  all  man;  animal  of  no  stone;  man,  there- 

1  Ammonius,  or  Philoponus,  here  mani-  AVliether  these  diaptrams  ascend  higher  than 
lestiy  refei-s  to  the  diagrams  representing  the  Ammonius  does  iiot  appear;  for  tliey  are 
three  tigures,  and  accommodated  to  Aris-  probahly  not  the  constructions  referred  to  by 
totle's  tliree  sets  of  letters,  noting  tlie  thiee  Aristotle;  and  none  are  given  by  the  Aphro- 
terms  in  each  of  these;  thus:  disian  in  his  original  text,  though  liberally 

„  a  y         u         v  f>       supplied  by  his  J.atin  translator.    The  dia- 

grams of  Ammonius  were  long  generally  em- 
ployed. By  Neomagus,  1533  (In  Trnpe.zuntii 
Dialect.,  f.  35),  they  are  most  erroneously  re- 
ferred to  Faber  Stapuleusis.  [See  further. 
Discussions,  p.  C70.  —  Eo.  | 


638  APPENDIX. 

fore^  of  no  stone Of  the  Third,  —  Some  stone  i.<  tchite ;  all  stone  is 

inanimate  :  consequently,  some  while  is  inanimate." 

First  Figure. —  F.  19  b,  59;  Aristotle,  /.  c.  §  3.  '"But  I  call  that  the 
middle  term  which  itself  is  in  another,  and  another  in  it ;  and  which  in  position 
lies  intermediate.' 

"  This  definition  of  the  middle  term  is  not  common  to  the  three  figures,  but 

limited  to  the  middle  of  the  first  figure  only.     For,  etc But,  if  there 

be  a  certain  difference  in  ypecies  between  the  middle  terms  of  the  three 
figures,  they  have  likewise  something  in  common ;  ti>  wit,  that  the  middle  term 
is  found  twice  in  the  premises,  throughout  the  throe  figures ;  which  also  in 
position  is  middle.  For  Aristotle  wishes  in  the  Diagraph  (if  avrfj  rp  Karaypcuprj) 
lo  preserve  the  order  of  intermediacy,  so  that,  placing  the  three  terms  in  a 
straight  line,  we  assign  the  middle  place  to  the  middle  term.  ['?] 

Aristotle,  l.  c.  §  4.  "  '  But  [I  call]  the  extremes  both  that  which  is  in  another, 
and  that  in  which  another  is.  For  if  A  be  predicated  of  all  B,  and  B  of  all 
C,  it  is  necessary  that  A  should  also  be  predicated  of  all  C.  We  have  previ- 
ously said  what  we  mean  by  the  expression  [predicated]  of  all.' " 

"  It  may  seem,  perhaps,  that  this  is  a  [perfect]  definition  of  the  extremes  and 
of  the  middle  term.  But  it  is  not ;  for  it  behooves  us  to  sub-undei-stand,  in 
addition,  the  word  only ;  and  thus  the  definition  will  rightly  run,  —  But  [I  call] 
the  extremes,  both  that  which  is  in  another  [minor],  and  that  in  which  another 
is  [major].  For  if  A  be  predicated  of  all  B,  and  B  of  all  C,  it  is  necessary 
that  A  be  predicated  of  all  C. 

"  This  the  first  syllogistic  mood  is  of  two  aflirmative  universals,  collecting  an 
affirmative  conclusion.  For  if  B  inheres  in  all  C,  C  is,  consequently,  a  part  of 
B.  But  B  is  a  part  of  A  ;  A  therefore,  also,  inheres  in  all  C,  C  being  a  part 
of  B.  The  reasoning  will  be  plainer  in  material  examples  —  as  substance  [is 
predicated]  of  all  animal :  animal  of  all  man;  and  there  is  inferred  substance 
of  all  man:  and  conversely,  a//  man  [is]  animal;  all  animal  substance ;  there- 
fore, all  man  substance. 

"  But  it  is  manifest  how,  in  this  figure,  the  term  of  the  first  mood  [Barbara] 
ought  to  be  taken.  The  first  is  the  most  general,  and  the  second  the  subaltern, 
genus;  whilst  the  third  is  a  species  moi"e  special  than  the  middle.  The  con- 
clusion ought  always  to  be  drawn.  Thus,  if,  proceeding  synthetically,  we 
commence  by  the  major  term  [and  proposition],  substance  begins  ;  wherefore  it 
also  leads  the  way  in  the  conclusion.  [There  is  predicated]  substance  of  all 
animal  (here  .<iubstance  commences)  ;  animal  of  all  man ;  whilst  the  conclusion 
again  commences  with  substance,  —  substance  of  all  man.  But  if  we  start  from 
the  minor  term  [and  proposition],  as  from  man,  with  this  also  the  conclusion 
will  commence  ;  all  man  [is]  animal ;  all  animal  substance ;  all  man  substance. 

"  Aristotle  takes  the  terms  A,  B,  C ;  and,  from  the  relation  of  the  letters,  he 
manifests  to  us  the  order  of  the  first  figure.  The  major  term  he  calls  A, 
because  A  stands  first  in  order;  the  minor  term  C  ;  and  the  middle  terin  B;  as 
B,  in  its  order,  follows  A,  and  precedes  C. 

"  It  is  plain  that  the  terms  may  possibly  be  coadequate  [and  therefore  recip- 
i-ocating]  ;  as  receptice  of  science  —  risible  —  man;  for  all  man  is  risible;  all 
risible  is  receptive  of  science ;  therefore,  all  man  is  receptive  of  science." 


APPENDIX.  639 

F.  23  b.  Aristotle, ch.  5,  §  2,  Second  Figure.  " '  The  major  extreme  is  that 
which  lies  nearer  to  the  middle  ;  the  minor,  that  which  lies  farther  from  the 
middle.' 

"  In  place  of  more  akin  and  more  proximate  to  the  middle  ;  not  in  position, 
but  in  dignity.  For  since,  of  the  terms,  the  middle  is  twice  predicated,  while, 
in  the  conclusion,  the  major  is  once  predicated,  but  the  minor  not  even  once 
predicated ;  [consequently]  that  which  is  once  predicated  will  be  the  more 
proximate  to  that  which  is  twice  predicated,  that  is,  to  the  middle,  than  that 
which  is  not  even  once  predicated.  Wherefore,  we  shall  hear  him  [Aristotle], 
in  the  Third  Figure,  calling  the  minor  the  term  more  proximate  to  the  middle 
on  account  of  their  affinity,  for  they  are  both  subjects,  while  he  calls  the  major 
term  the  more  remote.  Perhaps,  also,  he  wishes  that  in  the  diagraph  (rp 
Karaypafij)  the  major  term  should  be  placed  closer  to  the  middle,  and  the  minor 
farther  off.  But  the  major  extreme  in  this  figure,  the  two  premises  being  uni- 
versal, exists  not  by  nature  but  by  position,  for  the  first  of  the  extremes  which 
you  meet  with  as  a  subject  in  the  second  figure,  —  this  is  the  minor  extreme, 
the  other  is  the  major.  So  in  the  example — All  man  an  animal;  no  plant 
animal ;  therefore,  no  man  plant.  In  like  manner,  if  we  take  the  commence- 
ment from  plant,  this  becomes  the  minor  term,  and  man  the  major ;  as,  no  plant 
animal;  all  man  animal :  no  plant,  therefore,  man.  Consequently  the  major 
and  minor  terms  exist  in  these  examples  only  by  position,  not  by  nature. 
If,  indeed,  one  or  other  of  the  propositions  be  particular,  the  major  and  the 
minor  terms  are  then  determined  ;  for  we  hold  that  in  this  figure  the  universal 
is  the  major." 

Aristotle.  —  §3.  "'The  middle  is  placed  external  to  [not  between]  the 
extremes,  and  first  in  ])osition.' 

"  The  middle  term  passes  out  of  what  is  properly  the  middle  position ;  it  is 
also  placed  out  of  or  external  to  the  extremes  ;  but  either  above  these  or  below. 
But  if  it  be  placed  above,  so  as  to  be  predicated  of  both,  it  is  called  first  in 
position  ;  if  below,  so  as  to  be  subjected,  it  is  called  second.  AVherefore,  here, 
as  predicate  of  both  premises,  he  styles  the  middle  term  the  first ;  for  if  it  be 
placed  above,  it  is  first  in  position,  and  in  being  apart  from  the  extremes,  it  is 
placed  without  them." 

Aristotle,  ch.  6,  §  2.  Third  Figure,  f  27  b.  "  '  The  major  extreme  is  that 
more  remote  from,  the  minor  is  that  more  proximate  to,  the  middle.' 

"  The  major  term  in  this  figure  is  twice  predicated  of  the  middle,  and  in  the 
conclusion  ;  but  the  minor  once  only,  and  that  of  the  middle,  for  it  is  subjected 
to  the  major  in  the  conclusion  ;  the  middle  alone  is  subjected,  never  predicated. 
When  he,  therefore,  says  that  the  major  term  is  more  remote  from  the  middle, 
he  means  the  term  always  predicate  is  in  affinity  more  remote  from  that  which 
is  never  predicate,  but  always  subject.  And  that  which  is  never  subject  is 
the  major  and  more  proximate  term ;  that  again,  which  is  now  subject,  now 
predicate,  is  the  minor." 

(e)    MARTTANUS  CAPELLA.l 

Martianus  Capella,  De  Sepiem  Artibus  TAberalibus,  L.  iv.  De  Dialectica,  in 
1  Flourished  A.  C.  457,  Passow ;  474,  Tennemann. 


640 


APPENDIX 


capite,  Quid  sit  Predicativus  Syllogismus,  p.  127,  ed.  Grotii;  p.  83,  ed.  Basil. 
1532. 

"  Hujus  generis  tres  form£E  [figuras]  sunt. 

"  Prima  est,  in  qua  declarativa  [praedicatum]  particula  superioris  sumpti, 
seqaentis  efficitur  subjectiva  [subjectum]  ;  aut  subjectiva  superioris,  declarativa 
sequentis.  Declarativa  superioris  fit  subjectiva  sequentis,  ut  Omnvi  voluptas 
bonum  est ;  omne  honum  utile  est ;  omnis  igilur  voluptas  utilis  est.  Subjectiva 
superioris  fit  declarativa  sequentis,  si  hoc  modo  velis  convertere :  Omne  bonum 
utile  est;  omnis  voluptas  honuin  est;  omnis  igitur  voluptas  utilis  est." 

In  First  Form  or  Figure,  notices  the  four  direct  and  five  indirect  moods,  — 
reflexion  ;  and,  in  the  second  and  third,  the  usual  number  of  moods.* 

In  Second  Figure  — "  Hie  reflexione  si  utaris,  alius  modus  non  efficitur, 
quoniam  de  utrisque  subjectivis  fit  illatio."  He  seems  to  hold  that  two  direct 
conclusions  are  competent  in  Second  and  Third  Figures. 

In  Second  Figure  he  enounces  generally  (four  times)  as  thus :  —  '■^Omne  jus^ 
turn  honestum  ;  nullum  turpe  honestum  ;  nullum  igitur  justu7n  turpe  ;  "  but  some- 
times (once)  thus,  —  "  Nullum  igilur  turpe  Justum." 

.  In  Third  Fonn  or  Figure  generally  (six  times)  thus,  as — ^'' Omne  justum 
honestum;  omne  justum  bonum;  quoddam  igitur  honestum  bonum;"  but  some- 
times (once)  as  —  ^'Quoddam  igitur  bonum  honestum." 

CO    ISWORUS. 

Isidorus,  Originum,  L.  i.  c.  28.  De  Sgllogismis  Dialecticis.  Opera,  p.  20 
(1617)  ;  in  Gothofred.  Auctores,  p.  878. 

"  Formulae  Categoricorum,  id  est,  Praedicativorum  Syllogismorum  sunt  tres. 
Primae  formulae  modi  sunt  novem. 

"  Primus  modus  est  qui  conducit,  id  est,  qui  colligit  ex  universalibus  dedica- 
tivis  dedicativum  universale  directim  :  ut,  Omne  justum  honestum ;  omne  hones- 
tum bonum  ;  ergo  omne  justum  bonum."  All  in  first  figure,  with  minor  first ;  in 
second  and  third  figures,  varies  ;  uses  per  reflexionem  et  reflexim  indifferently ; 
and  through  all  moods  of  all  figures  follows  Apuleius.  "  Has  formulas  Cate- 
goricorum Syllogismorum  qui  plene  nosse  desiderat,  librum  legat  qui  inscribitur 
PerHiermenias  Apulcii,  et  quae  subtilius  sunt  tractata  cognoscet." 

(»)    AVERItOES. 

Averroes,  In  Anal.  Prior,  L.  i.  c.  v.,  on  First  Figure.  —  "  If,  therefore,  the 
middle  term  be  so  ordered  between  the  two  extremes,  that  it  be  predicated  of 
the  minor  and  subjected  to  the  major  (as,  if  Ave  say  all  C  is  B,  and  all  B  ts  A)  ; 
it  is  plain  that  tliis  order  of  syllogism  is  natural  to  us;  and  it  is  called  by 
Aristotle  the  First  Figure."     And  tims  are  stated  all  the  examples  in  detail. 

C.  vi..  Figure  Second.  —  "And  the  proposition  whose  subject  is  the  subject 


1  Cassiodorus,  in  First  Figure,  gives  both 
forms,  "  vel  sic;"  in  Second  and  Third, 
though  he  gives  also  a  "vcl'sic,"  they  are 
examples,  both  in  converse,  of  Capella's  gen- 
eral mode  of  enunciation.  See  Dialect., Opera, 


pp.  538,  556,  Genev.  1650,  and  above,  p.  626 
(fl  520).  Cf.  Apuleius,  De  Si/Uogismo  Cntegor- 
ico.  Op.,  p.  35.  Elmen.  (A.  c.  160).  Isidorus, 
of  Seville  ( Got/io/r.  Auct.,  p.  878),  (A.  c.  600; 
died  636) 


APPENDIX.  641 

of  the  quaasitum  is  the  minor  proposition,  but  that  whose  subject  is  the  pred- 
icate of  the  (juaesitum  is  the  major.  Let  us  then  place  first  in  order  of  enun- 
ciation the  minor  extreme ;  let  the  middle  term  then  follow,  and  the  major 
come  last,  to  the  end  that  thus  the  major  maybe  distinguished  from  the  minor; 
for  in  this  figure  the  terms  are  not  distinguished,  unless  by  relation  to  the 
(jusesitum."     So  all  the  examples. 

C.  vii..  Third  Figure.  —  "  That  proposition  in  which  lies  the  subject  of  the 
quaesitum  is  called  the  minor  proposition,  since  the  subject  itself  is  called  the 
minor  term ;  that  proposition  which  contains  the  predicate  of  the  quaesitum  is 
named  the  major.  In  the  example,  let  the  minor  term  be  C,  the  middle  B,  and 
the  major  A,  and  their  order  be  that  we  first  enounce  the  middle,  then  the 
minor,  and  last  of  all  the  major."     And  so  the  examples. 

(h)    MELANCHTHON. 

Melanchthon,  Erotemata  DialecHcce,  L.  iii.  p.  1 75. 

"  Demonstration  why  there  are  necessarily  three  [and  only  three]  Figures. 

"  Every  argumentation  which  admits  the  syllogistic  form  (for  of  such  form  In- 
duction and  Example  are  not  recipient  [?])  proceeds  either  [1°],  From  genus, 
to  species  universally  with  a  universal  conclusion  ;  or  [2°],  From  species  to- 
^enus  with  a  particular  conclusion ;  or  [3°],  A  distraction  of  two  species  take.s 
place;  or  [4°],  There  is  a  concatenation  of  a  plurality  of  causes  and  effects. 
Nor  are  there  more  modes  of  argumentation,  if  we  judge  with  skill. 

"  The  process  from  genus  to  species  engenders  the  First  Figure.  And, the 
consequence  is  valid  from  the  genus  with  a  universal  sign  both  affirmatively  and 
negatively  to  the  species,  —  this 'is  naturally  manifest.  The  process  from 
.'species  to  genus  with  a  particular  conclusion  engenders  the  Third  Figure. 
And  it  is  evident  that,  the  species  posited,  the  genus  is  posited.    , 

"  The  distraction  of  species  engenders  the  Second  Figure.  And  the  reason 
of  the  consequence  is  clear,  because  disparate  species  are  necessarily  sundered. 
These  may  be  judged  of  by  common  sense,  without  any  lengthened  teaching 
Both  are  manifest,  —  that  the  figures  are  rightly  distributed,  and  th^t  the  con- 
sequences are  indubitably  valid." 

(i)    ARNAULD. 

Amauld,  EAirt  de  Penser   (Port  Royal  Logic),  P.   iii.  ch.  11,  p.  235. — 
General  principle  of  syllogisms  :  — "  That  one  of  the  premises^  should  contain 
the  conclusion,  and  the  other  show   that   it   does  so  contain  it." — [So  Purchot, 
Instil.  Phil,  Vol.  I.  P.  iii.  ch.  1.] 

Ch.  v.,  p.  215.  —"  Foundation  of  First  Figure." 

"  Principle  of  affirmative  moods  : — That  what  agrees  loitJt  a  notion  taken  uni- 
versally, agrees  also  with  all  of  which  this  notion  is  affirmed ;  in  other  words,  with 
all  that  vi  the  subject  of  this  notion,  or  is  composed  ivithin  its  sphere."  [Or,  more 
shortly  (says  Purchot,  c.  vi.).  Whatever  is  predicated  of  the  superior,  is  pred- 
icated of  the  inferior.'] 

"  Principle  of  the  negative  moods :  —  What  is  denied  of  a  notion  taken  uni- 
versally, is  denied  of  all  whereof  this  notion  is  affirmed."  [Purchot —  What  is 
repugnant  to  the  superior,  is  repugnant  also  to  the  inferior.    Ch.  vi.  p.  217.] 

81 


642  '  APPENDIX. 

•'  Foundation  of  the  Second  Figure.^  Principle  of  the  syllogisms  in  Cesare 
and  Festino: — That  what  is  denied  of  a  universal  notion,  is  denied  also  of 
whatever  this  notion  is  affirmed,  that  is  to  say,  of  all  its  subjects. 

"  Principle  of  the  syllogisms  of  Camestres,  Baroco :  —  All  that  is  contained 
under  the  extension  of  a  universal  notion,  agrees  with  none  of  the  subjects  whereof 
that  notion  has  been  denied,  seeing  that  the  attribute  of  a  negative  proposition  is 
taken  in  its  whole  extension." 

Ch.  vii.,  p.  220.     "  Foundation  of  the  Third  Figure. 

"  Principle  of  the  affirmative  moods :  —  When  two  terms  may  he  affirmed  of 
the  same  thing,  they  may  also  be  affirmed  of  each  other,  taken  particularly.  [So 
Purchot  nearly.] 

"Principle  of  the  negative  moods: — When  of  two  terms  the  one  may  be 
denied,  and  the  other  affirmed,  of  the  same  thing,  they  may  be  particularly  denied 
of  each  other."     [So  Purchot  nearly.] 

No  foundation  or  principle  given  for  the  Fourth  Figure. 

0)   GROSSES. 

Samuelis  Grosseri,  Pharus  Intellectus,  1697,  P.  iii.  S.  i.  Mem.  3,  c.  2  (prob- 
ably from  Weiss,  see  Pref ).  —  "  The  foundation  of  the  first  figure  is  the  Dic- 
tum de  Omni  et  Nullo ;  for  whatever  is  universally  aflirmed  or  denied  of  a 
universal  subject,  tliat  is  also  affirmed  or  denied  of  all  and  each  contained 
under  that  subject. 

"  The  foundation  of  the  second  figure  is  Contrariety ;  for  the  predicates  of 
contrary  things  are  contrary. 

"  The  foundation  of  the  third  figure  is  the  agreement  of  the  extremes  in  any 
third ;  for  what  agrees  with  any  third  agrees  with  each  other,  and  may  be 
joined  or  separated  in  the  same  proposition,  inasmuch  as  they  are  in  agree- 
ment or  confliction  in  relation  to  any  third  thing." 

Illustrates  the  three  figures  by  three  triangles,  p.  132.  In  the  first,  we  ascend 
to  the  apex  on  one  side,  and  descend  on  the  other ;  in  the  second,  we  ascend  at 
both  sides ;    in  the  third,  we  descend  on  both  sides. 

(t)  LAMBERT. 

Lambert,  Neues  Organon,  Vol.  I.  §  225.  (See  Melanchthon,  p.  641.) 
Relation  of  Figures.  —  "  We  further  remark,  that  the  first  discoverer  of  Syl- 
logisms and  their  Figures  was,  in  his  arrangement  of  their  propositions,  deter- 
mined by  some  arbitrary  circumstance ;  his  views  and  selections  at  least  were 
not  founded  on  aught  natural  and  necessarj'  (§  196).  He  places,  to  wit,  that 
premise  after  the  <>ther  which  contains  among  its  terms  the  subject  of  the  con- 
clusion, probably  in  order  to  introduce  into  all  the  figures  a  common  law.  To 
that  law,  however,  we  do  not  restrict  ourselves  either  in  speech  or  in  writing. 
The  mathematician,  who,  perhaps,  draws  the  greatest  number  of  formal  syllo- 
gisms with  the  fewest  paralogisms,  commences  to  take  the  first  figure,  for  exam- 

1  Purchot  says  this  Figure  rests  upon  a  sin-  but  something  agrees  with  the  one,  which  it  re- 
gie principle  —  Two  things  are  not  the  tame,     pugnaM  to  the  other. 


APPENDIX.  643 

pie,  not  ■nith  the  major,  but  with  the  minor  proposition,  because  not  only  in 
this  figure  is  such  premise  always  the  more  obtrusive,  but  also  because  its  sub- 
ject is  the  proper  matter  of  discourse.  Frequently  the  premise  Is  only  quoted, 
or  it  is  absolutely  omitted  whensoever  it  is  of  itself  obvious  to  the  reader,  or  is 
easily  discoverable  from  the  minor  and  conclusion.  The  conclusion  inferred  is 
then,  in  like  manner,  constituted  Into  the  minor  proposition  of  a  new  syllogism, 
wherewith  a  new  major  Is  connected.  This  natural  arrangement  of  the  syllo- 
gisms of  the  first  figure  rests,  consequently,  altogether  on  the  principle, — 2'Tiat 
we  can  assert  of  (he  subject  of  an  affirmatice  proposition  whatever  we  mai/  know 
of  its  predicate  ;  or  what  may  he  said  of  the  attribute  of  a  thing  is  valid  of  the 
thing  itself.  And  this  is  what  the  syllogisms  of  the  first  Figure  have  peculiar 
to  themselves.  It  Is  also  so  expressed :  —  What  is  true  of  the  genus,  is  true  also 
of  each  of  its  species. 

§  226.  "  On  the  other  hand.  In  the  second  and  third  Figures  there  is  no 
talk  of  species  and  genera.  The  second  Figure  denies  the  subjects  of  each 
other,  because  they  are  diverse  in  their  attributes ;  and  every  difference  of 
attribute  Is  here  effectual.  We,  consequently,  use  this  figure  principally  in  the 
case  where  two  things  ought  not  to  be  intercommuted  or  confounded.  This 
becomes  necessarily  Impossible,  so  soon  as  we  discover  in  the  thing  A  something 
which  does  not  exist  in  the  thing  B.  We  may,  consequently,  say  that  syllo- 
gisms of  the  second  figure  lead  us  to  distinguish  things,  and  prevent  us  from 
confounding  notions.  And  it  will  be  also  found  that  in  these  cases  we  always 
use  them. 

§  227.  "  The  third  Figure  affords  Examples  and  Exceptions  ;  and,  in  this 
Figure,  we  adduce  all  exempla  in  contrarium.     The  two  formula  are  as  follows : 

"  1.   There  are  B  which  are  C ;  for  M  is  B  and  C. 

"  2.   There  are  B  which  are  not  C  ;  for  M  is  B  and  not  C. 

"  In  this  manner  Ave  draw  syllogisms  of  the  Third  Figure,  for  the  most  part, 
in  the  form  of  copulative  propositions  (§  135)  ;  because  we  are  not  wont  twice 
to  repeat  the  subject,  or  to  make  thereof  two  propositions.  Sometimes  one 
proposition  is  wholly  omitted,  when,  to  wit.  It  is  self-manifest. 

"  In  the  Fourth  Figufe,  as  In  the  First,  species  and  genera  appear  only  with 
this  difference,  that  in  the  moods,  Baralip,  Dibatis,  Fesapo,  Fresison,  the  infer- 
ence is  from  the  species  to  the  genus ;  whereas,  in  Calentes,  there  is  denied  of 
the  species  what  was  denied  of  the  genus.  For  where  the  genus  is  not,  neither 
are  there  any  of  Its  species.  This  last  mood  we,  therefore,  use  when  we  con- 
clude negatively  a  niinori  ad  majus,  seeing  that  the  genus  precedes,  and  is  more 
frequently  presented  than  any  of  its  species. 

§  229.  "  The  syllogisms  of  the  four  Figures  are  thus  distinguished  In  relation 
to  their  employment,  in  the  following  respects  : 

"  1.  The  First  Figure  ascribes  to  the  thing  what  we  know  of  Its  attribute. 
It  concludes  from  the  genus  to  the  species. 

"  2.  The  Second  Figure  leads  to  the  discrimination  of  things,  and  relieves 
perplexity  in  our  notions. 

"  3.  The  Third  Figure  affords  examples  and  exceptions  in  propositions  which 
appear  general. 

"  4.  The  Fourth  Figure  finds  species  in  a  genus  in  Baralip  and  Dibatis ;  it 


644 


APPENDIX. 


shows  that  the  species  does  not  exhaust  the  genus  in  Feaapo,  Fresison  ;  and  -it 
denies  the  species  of  what  was  denied  of  the  genus  in  Calentes. 

§  230.  "  This  determination  of  the  difference  of  the  Four  Figures  is,  abso- 
lutely speaking,  only  manifested  when  we  employ  tht-m  after  natural  fashion, 
and  without  any  thought  of  a  selection.  For,  as  the  syllogisms  of  every  figure 
admit  of  being  transmuted  into  those  of  the  first,  and  partly  also  into  those  of 
any  other,  if  we  rightly  convert,  or  interchange,  or  turn  into  propositions  of 
equal  value,  their  premises  ;  consequently,  in  this  jjoint  of  view,  no  difference 
subsists  between  them  ;  but  whether  we  in  every  case  should  perform  such  vow- 
mutations,  in  order  to  bring  a  syllogism  under  a  different  figure,  or  to  assuru 
ourselves  of  its  correctness,  —  this  is  a  wholly  different  question.  The  latter 
.is  manifestly  futile.  For,  in  the  commutation,  we  must  always  undertake  a 
conversion  of  the  premises,  and  a  converted  proposition  is  assuredly  not  always 
of  equal  evidence  with  that  which  we  had  to  convert,  while,  at  the  same  time, 
we  are  not  so  well  accustomed  to  it;  for  example,  the  proposition,  Some  stones 
attract  iron,  every  one  will  admit,  because  The  mat/net  is  a  alone,  and  attracls 
iron.  This  syllogism  is  in  the  Third  Figure.  In  the  first,  by  conversion  of 
one  of  its  premises,  it  would  run  thus : 

Major,  —  AU  magnets  attract  iron ; 
Minor,  —  Some  stones  are  magnets  ; 
Conclu,sioii,  —  Some  xUmes  attract  iron. 

OHere  we  arc  unaccustomed  to  the  minor  proposition,  while  it  appears  as  if  wc 
4DUSt  pass  all  stones  under  review,  in  order  to  pick  out  magnets  from  among 
them.  On  the  other  hand,  that  the  magnet  is  a  stone,  is  a  proposition  which 
far  more  naturally  suggests  itself,  and  demands  no  consideration.  In  like  man- 
..ner,  A  circle  is  not  a  rquare  ;  for  Oie  circle  is  round,  the  square  not.  This  proof 
i[in  the  third  figure]  is  as  follows,  when  cast  in  the  first : 

What  is  not  round  is  no  circle  ; 

A  square  is  not  round ;  « 

Consequently,  etc. 


Here  the  major  proposition  is  converted  by  means  of  terminus  injinitus,  and  its 
truth  is  manifested  to  us  only  tlirough  the  consciousness  that  «//  circles  are 
round.  For,  indepeuviently  of  this  proposition,  should  we  not  hesitate  —  there 
being  innumerable  things  which  are  730/  round  —  whether  the  circle  were  one 
of  those  which  belonged  to  this  category?  We  thmk  not;  because  we  are 
aware. 

§  231.  "It  is  thus  apparent  that  we  use  every  syllogistic  figure  there,  where 
the  propositions,  as  each  figure  requires  them,  are  more  familiar  and  more  rur- 
rcnt.  The  difference  of  figures  rests,  therefore,  not  only  on  their  form,  but 
extends  itself,  by  relation  to  their  employment,  also  to  things  themselves,  so 
that  we  use  each  figure  where  its  use  is  more  natural :  The  first  for  finding  out 
9r  proving  the  Attributes  of  a  thing  ;  the  .second  for  finding  out  or  proving  the 
Difference  of  things  ;  the  third  for  finding  out  and  proving  Examples  and  Ex- 
ertions ;  the  fourth  for  finding  out  and  excluding  the  Species  of  a  Genus. 


APPEliFDIX.  645' 

§  232.  "  Further,  whether  the  three  last  5gures  are  less  evident  than  the 
first,  is  a  question  which  has  been  denied  [affirmed  (?)]  on  this  account,  that 
the  first  figure  only  rests  immediately  on  the  Dictum  <le  Omni  et  Nullo  [§  220] 
whilst  the  others  have  hitherto,  by  a  circuit,  been  educed  therefrom.  We  havfir 
already  remarked  [§  211]  that  this  circuit,  through  our  mode  of  notation,  is 
whblly  superseded.  We  need,  therefore,  only  translate  its  principle  into  the 
vernacular,  and  we  shall  find  that  the  Dictum  de  Omni  et  Nullo  is  on  that 
account  applicable  to  the  first  figure,  because  its  truth  is  based  on  the  nature 
of  the  proposition.  From  this  principle,  therefore,  the  first  figure  and  it* 
moods  admit  of  an  immediate  deduction  ;  it  is  thus  only  a  question  whether  the 
other  figures  are  incapable  [capable  (?)]  of  such  immediate  deduction,  or 
whether  it  is  necessary  previously  to  derive  them  through  the  first  figure.  Our 
mode  of  notation  shows  that  the  latter  is  an  [unnecessary]  circuit,  because 
every  variety  of  syllogism  admits  for  itself  a  various  notation,  and  because,  iri 
that  case,  the  premises  are  taken  for  what  they  actually  are.  Consequently, 
every  figure,  like  the  first,  has  its  own  probation,  —  a  probation  drawn  exclu- 
sively from  the  natures  of  the  propositions.  The  whole  matter  is  reduced  to 
this  :  —  Whether  a  notion,  wholly  or  in  part,  is,  or,  toholly  or  in  part,  is  not,  under 
a  second :  and  whether,  again,  this  second,  wholly  or  in  part,  is,  or,  wholly  or  in 
part,  is  not,  under  a  third.  All  else  proceeds  only  on  the  interchange  of  equiv^ 
alent  modes  of  expression,  —  the  figured,  namely,  and  those  which  are  not 
figured.  And  this  interchange  we  maj'  style  translating,  since  the  figurecf 
modes  of  expression  may  be  regarded  as  a  special  language,  serving  the  pur- 
pose of  a  notation.  We  have  above  (§  220),  after  all  the  syllogistic  mood's 
were  discovered  and  denoted,  adduced  the  Dictum  de  Omni  et  Nullo,  but  only 
historically,  since  our  manner  of  determining  the  syllogistic  moods  is  immedii- 
ately  founded  on  the  nature  of  the  propositions,  from  which  this  Dictum  is  only 
a  consequence.  Moreover,  this  eonseciuence  is  special,  resting,  as  it  does,  oni 
the  notions  of  Species  and  Genera.  Wherefore,  its  validity  only  extends  so  far 
as  propositions  can  be  recalled  to  these  notions;  as,  for  example,  in  the  First 
Fignre.  In  the  Second,  the  notion  of  Difference  emerges ;  and  in  the  Third, 
the  notion  of  Example.  If  we,  therefore,  would  have  special  dicta  for  the 
several  Figures,  in  that  case  it  would  follow,  and,  at  the  same  time,  become 
manifest  tliat  the  middle  term  of  a  syllogism,  considered  for  itself,  expresses,  in 
the  First  Figure,  a  principle  \of  Ascription  or  Procreation']  ;  in  the  Second, 
Difference ;  in  the  Third,  an  Example ;  and  in  the  Fourth,  the  principle  o( 
Reciprocity. 

'*  1.  For  the  First  Figure.  Dictum  de  Omni  et  Nullo.  What  is  true  of  all  A, 
is  true  of  every  A. 

'^  2.  For  the  Second  Figure.  Dictum  de  Diverse.  Things  which  are  different, 
are  not  attributes  of  each  other. 

"  S.  For  the  Third  Figure.  Dictum  de  Exemplo.  When  we  find  things  A 
which  are  B,  in  that  case  some  A  are  B. 

"  4.  For  the  Fourth  Figure.  Dictum  de  Reciproco.  I.  If  no  M  is  B,  then  no 
B  is  this  or  that  M.  IT.  If  C  is  [or  is  not]  this  or  that  B,  in  that  case  some  B 
are  [or  are  not]  C." 


646 


APPENDIX. 


(I)    PLATTER. 


Platner,  Philosophische  Aphorismen,  3d  ed.,  1 793.  —  Part  I.,  §  544,  conformed 
to  his  Lehrbuch  der  Logik  und  Metaphyslk,  1795,  §  227.  "  The  reason  why  the 
predicate  belongs  to  the  subject  is  in  all  possible  syllogisms  this,  —  because  the 
subject  stands  in  a  relation  of  subordination  with  [is  either  higher  or  lower 
than]  a  third  notion  to  which  the  predicate  belongs.  Consequently,  all  infer- 
ence proceeds  on  the  following  rule  :  If  the  subject  of  the  [concluding}  judg- 
ment stand  in  a  relation  of  subordination  with  a  third  notion,  to  which  a  certain 
predicate  pertains ;  in  that  case,  this  predicate  also  pertains  to  the  same  judg- 
ment, affirmatively  or  negatively." 

In  his  note  on  this  Aphorism,  Platner  (Lehrbuch)  admits  — "  My  funda- 
mental rule  is  only  at  fault  in  the  second  Aristotelic  figure,  which,  however,  is 
no  genuine  figure ;  because  here,  in  the  premises,  the  subject  and  predicate 
have  changed  places,"  etc.  In  the  2d  edition  of  his  Aphormns  (1784)  he  had 
adopted  the  principle  of  Identity  with  the  same  third,  as  he  has  it :  "  In  what 
exLen.sion  or  proportion  (Mousse)  two  notions  are  like  or  unlike  to  a  third,  in  the 
same  extension  or  proportion  are  they  like  or  unlike  each  other."     (§  G28.) 

Philosophische  Aphonsmen,  Part  I.,  third  edition,  1 793,  §  568,  compared  with 
second,  1 784,  §  672-676.  —  "  Nevertheless,  each  of  these  grammatical  figures  of 
syllogism  has  its  peculiar  adaptation  in  language  for  the  dialectical  application 
of  proofs ;  and  the  assertion  is  without  foundation  that  the  first  is  the  most 
natural.  Its  use  is  only  more  appropriate,  when  we  intend  to  show  —  that  a 
predicate  pertains  [or  does  not  pertainl^  to  a  subject  in  virtue  of  its  class.  More 
naturally  than  the  first  do  we  show,  in  the  second,  the  difference  of  things 
apparently  similar  :  and  in  the  third,  the  similarity  of  apparently  different  things. 
Tlie  fourth  figuie  [it  is  said  in  the  second  edition],  on  account  of  the  position 
of  its  terms,  is  always  unnatural  in  language." 

Philosophische  Aphorismen,  Part  I.,  last  edition,  1 793,  §  561.  —  "  The  principle 
of  the  first  figure  is  the  Dictum  de  Omni  et  Nullo." 

§  564. -^"  Touching  the  other  figure  [the  third,  for  in  this  edition  Platner 
abolishes,  in  a  logical  relation,  the  second],  its  special  principle  is  the  following 
rule  :  — What  belongs  to  the  subordinate,  thai,  since  the  subordinate  is  apart  of  the 
universal,  belongs  also  in  part  (particularly)  to  the  universal." 

In  the  second  edition,  1784,  the  second  figure  is  recognized,  and,  with  the 
third,  obtains  its  special  law. 

§  659.  —  "  The  principle  of  the  second  figure  is  :  —  If  two  notion.<t,  wholly  or 
in  part,  are  opposite  to  a  third,  so  are  they  also,  wholly  or  in  part,  opposite  to  each 
other." 

§  664.  —  "  The  principle  of  the  third  figure  is  :  — What  can  be  particularly 
affirmed  or  denied  of  a  sulxdtem  species,  that  also,  in  so  far  as  such  subaltern 
species  is  part  of  a  genus,  may  be  particularly  affirmed  or  denied  of  the  genus." 

Philosophische  Aphorismen.  Part  I.,  §  546.  Note.  —  "In  general,  logicians 
treat  the  subject  as  if  it  were  necessarily  subordinated  to  the  predicate.  It 
may,  however,  on  the  contrary,  be  the  higher  notion,  and  the  predicate  thus  be 
subordinated  to  it.  This  i.s  the  case  in  all  particular  propositions  where  the 
predicate  is  not  an  attribute  of  the  genus,  but  an  accident  of  the  subject.  For 
instance,  —  Some  creatures  are  animals  ;  here  the  subject  is  the  higher :    Some 


APPENDIX.  64T 

men  are  imperfect ;  here  the  higher  is  the  predicate.  We  must  not,  therefore, 
in  our  syllogistic,  thus  enounce  the  fundamental  rule  of  reasonings,  —  If  the 
suhject  he  subordinated  to  a  third  notion,  but  with  or  in  the  relation  of  subordina- 
tion with  a  third  notion." 

(m)  -  FRIES. 

Fries,  System,  der  Logik,  §  56.  —  "  The  species  of  categorical  syllogisms  are 
determined  by  the  variety  of  relations  in  which  three  notions  may  stand  to  each 
other,  so  that  a  syllogism  may  be  the  result. 

"  These  relations  may  be  thought  as  three. 

"  Case  I.  —  Three  notations  are  reciprocally  subordinated  in  gradation,  so 
that  the  second  is  subordinated  to  the  first,  but  superordinated  to  the  third. 

"  Case  II.  —  Two  notions  are  subordinated  to  a  third. 

"  Case  III.  —  Two  notions  are  superordinated  to  a  third.* 

"  When,  in  these  cases,  is  a  syllogism  possible  ? 

§  57.  —  "In  all  the  three  cases  the  syllogisms  are  equally  valid,  for  they  are 
founded  on  the  general  laws  of  the  connection  of  notions. 

"  They  all  follow,  to  wit,  from  the  relation  of  a  whole  sphere  to  its  parts, 
which  lies  in  the  Dictum  de  Omni  et  Nullo.  The  principles  for  the  three  men- 
tioned cases  are  thus : 

"  For  the  first,  —  The  part  (C)  of  the  part  (B)  lies  in  the  tvliole  (A),  and  what 
(A)  lies  out  of  the  whole  (B),  lies  also  out  of  its  parts  (C). 

"  For  the  second,  —  What  (A  or  some  A)  lies  out  of  the  whole  (B),  lies  also 
out  of  its  parts  (C). 

"For  the  third,  —  Jf  a  part  (B)  lies  in  two  wholes  (A  and  C),  in  that  case 
these  have  a  pari  in  common  ;  and  if  a  part  (B)  lie  in  a  ivhole  (C),  but  out  of 
another  tchole  (A),  in  that  case  the  first  (C)  has  a  part  out  of  the  other  (A). 

"The  fiist  case  alone  coincides  immediately  with  the  perfect  declaration 
of  a  syllogism, — that  a  case  is  therein  determined  by  a  rule.  For  the  third 
case,  therefore,  our  two  declarations  of  a  major  premise  —  that  it  is  the  ride, 
and  that  it  contains  the  major  term  —  do  not  coincide,  seeing  that  here  the 
minor  term  may  be  forthcoming  in  the  rule.  On  this  account  the  arrangement 
of  the  first  case  is  said  to  be  the  only  regular,  and  the  others  are  reduced  to  it. 
That  this  reduction  is  easily  possible,  we  may  in  general  convince  ourselves,  by 
reflecting  that  every  syllogism  requires  a  general  rule  as  premise,  and  that  the 
other  cases  are  only  distinguished  from  the  first  by  a  converted  arrangement 
of  the  propositions.  But  as  all  propositions  may  be  either  purely  converted  or 
purely  counterposed,  consequently  the  two  last  cases  can  at  most  so  far  deviate 
from  the  first  that  they  are  connected  with  the  first  case  only  through  reversed 
((jegentheilige)  notions. 

§  57  b.  —  "  The  doctrine  of  the  several  species  of  categorical  syllogisms,  as 
regulated  by  the  forms  of  their  judgments,  is  at  bottom  an  empty  subtlety ; 
for  the  result  of  all  this  circuity  is^only  that,  in  every  categorical  syllogism, 
a  case  is  determined  by  a  rule,  and  this  is  already  given  in  the  law,  that 
in  every  reasoning  one  premise  must  be  universal.  The  scholastic  logic 
treats  of  this  doctrine  only  in  so  far  as  the  species  of  syllogism  are  determined 
by  the  forms  of  judgment,  and  thereby  only  involves  itself  in  long  grammati- 

1  [See  Jordano  Bruno  (in  Denzinger,  Logik,  t.  ii.  p.  269).    Stattler,  Logica,  J  237,  p.  163.] 


648  APPENDIX. 

cal  discussions.  Aristotle  has  been  falsely  reproached  for  overlooking  the 
fourth  figure,  he  only  having  admitted  three.  For  Aristotle  proceeds,  pre- 
cisely as  I  have  here  done,  only  on  the  relation  of  notions  in  a  syllogism,  of 
which  there  are  possibly  only  our  three  cases.  His  error  lies  in  this,  —  that 
he  did  not  lay  a  general  rule  at  the  root  of  fevery  figure,  but,  with  a  prolixity 
wholly  useless,  in  determining  the  moods  of  the  several  figures,  details  each, 
even  of  the  illegitimate,  and  demonstrates  its  illegitimacy.  This  prolixity  has 
been  too  often  imitated  by  other  logicians,  in  the  attempts  at  an  evolution 
of  the  moods.  Kant  goes  too  far  in  denouncing  this  whole  doctrine  as  a 
mere  grammatical  subtlety.  The  distinction  of  the  three  cases  is,  however, 
a  logical  distinction ;  and  his  assertion  that  the  force  of  inference  in  the  other 
two  is  wholly  derived  from  that  of  the  first  case,  is  likewise  not  correct.  I 
manifestly,  however,  conclude  as  easily  in  the  third  case,  — '  A  part  which  lies 
in  two  wholes  is  a  part  common  to  both,' —  as  in  the  first,  — '  The  part  of  the 
part  lies  in  the  whole.'  The  third  case  presents,  indeed,  the  readiest  arrange- 
ment for  reasonings  from  the  particular  to  the  general,  i.  e.,  for  syllogisms  in 
the  second  figure  according  to  our  terminologj'. 

"  The  scholastic  doctrine  of  the  four  syllogistic  figures  and  nineteen  moods 
of  categorical  syllogisms  requires  no  lengthened  illustration.  If  the  figures  are 
determined  by  the  arrangement  of  notions  in  the  premises,  then  the  following 

combination  is  exhaustive.     For  the  conclusion  in  all  cases  S P  [being 

supposed  the  same],  the  [terms  or]  notions  stand : 


1 )  According  to  our  first  case,  M P 

S M 

2)  With  converted  mi^or  premise,    P M 

S M 

3)  With  converted  minor  premise,   M P 

M S 

4)  Both  premises  converted,  P M 

M S 

"  Should  we  therefore  simply  convert  both  premises  in  a  syllogism  of  the 
first  figure,  we  are  able  to  express  it  in  all  the  figures.  Let  the  notions  given 
be  ^reproof,  lead,  metal,  there  then  follows  the  conclusion  —  Some  met(d  is  n(H 
^reproof —  from  the  premises  : 

In   the  First   Figure  —  No  lead  is  fireproof ; 

Some  metal  is  lead ; 
In  the  Second  Figure  —  Nothing  fireproof  is  lead  ; 

Some  metal  is  lead ; 
In  the  Third  Figure  —  No  iead  is  fireproof ; 

All  lead  is  metal ; 
In  the  Fourth  Figure  —  Nothing  fireproof  is  lead; 

All  lead  is  metal. 

"  It  is  here  apparent  that  the  first  three  figures  are  our  three  cases ;  but  the 


APPENDIX.  649 

fourfti  we  did  not  employ,  as  it  contains  no  peculiar  relations  or  notions,  but 
only  under  our  first  case  superordinates,  and  then  subordinates  a  middle  term. 
This  manner  of  enunciating  a  syllogism  is  thus  only  possible  where  we  are 
competent,  through  conversions,  to  transmute  the  arrangement  of  the  first 
figure  into  that  of  the  fourth.  Now  this  happens  :  1]  If  we  convert  the  conclu- 
sion S P  into  P— S,  since  then  the  major  arid  the  minor  terms,  as 

also  the  major  and  minor  premises,  change  names  ;  or,  2]  If  both  premises 
allow  of  an  immediate  conversion,  so  that  the  one  remains  universal ;  for  then 
the  converted  propositions  contain  the  same  thoughts  as  those  given,  and, 
consequently,  establish  the  same  conclusion." 

[Objections  to  Fries'  doctrine  of  figure  —  1°,  Only  applies  to  affirmatives; 
2°,  Only  the  arrangement  of  the  results  of  a  successful  comparison,  and  takes 
no  heed  of  the  comparison  that  may  have  been  fruitless  (the  illegitimate 
moods)  ;  3°,  Takes  account  of  only  one  subordination,  for,  in  the  second  and 
third  cases,  in  each  there  is  a  reciprocal  subordination  in  Extension  and  Coni- 
prehension.] 

Cnatido)    KRUG  ASD  BENEKE- THEIR  DOCTRIJfES  OF    SYLLOGISM  CRITICIZED. 

The  authority  of  the  two  following  philosophers,  who  conclude  this  series,  is 
rather  negative  than  positive ;  inasmuch  as  they  both  concur  in  proving  that 
the  last  attempts  at  a  reformation  of  the  Syllogistic  Theory  proceed  on  a 
wholly  different  ground  from  that  on  which,  I  think,  this  alone  can  be  accom- 
plished. These  two  philosophers  are  Krug  and  Beneke ;  for,  beside  them,  I 
am  aware  of  no  others  by  whom  this  has  been  attempted. 

Krug  was  a  disciple  of  the  Kantian  school,  Kant's  immediate  successor  in 
his  Chair  of  Logic  and  Metaphysics  at  Koenigsberg,  and,  subsequently,  Pro- 
fessor of  Philosophy  in  the  University  of  Leipsic.  He  is  distinguished  not 
only  as  a  voluminous  writer,  but  as  a  perspicuous  and  acute  thinker ;  and  his 
peculiar  modification  of  the  Kantian  system,  through  a  virtual  return  to  the 
principle  of  Common  Sense,  is  known  among  the  German  theories  by  the 
name  of  Sj/nthefism.  His  Logic  (the  first  part  of  his  System  of  Theoretical 
Philosophy)  was  published  in  1806,  and  is  one  of  the  best  among  the  many 
excellent  treatises  on  that  science  which  we  owe  to  the  learning  and  ability  of 
the  Germans.  (I  have  before  me  the  fourth  edition,  that  of  1833.)  Krug 
propounded  a  new  theory  of  S}-llogistic ;  but  the  novelty  of  his  scheme  is 
wholly  external,  and  adds  only  fresh  complication  to  the  old  confusion.  It  has, 
accoi'dingly,  found  no  favor  among  subsequent  logicians. 

Passing  over  the  perverse  ingenuity  of  the  principles  on  which  the  whole 
doctrine  is  founded,  it  is  enough  to  state  that  Krug  distributes  the  syllogistic 
moods  into  eight  classes.  Of  these,  the  first  (which,  with  some  other  logicians, 
he  considers  not  as  a  figure  at  all,  but  as  the  pure,  regular,  and  ordinary  form 
of  reasoning)  corresponds  to  the  First  Figurie  of  the  Aristotelico-Scholasti(^ 
distribution.  The  other  seven  classes,  as  so  many  impure,  irregular,  and  ex- 
traordinary forms,  constitute  (on  the  analogy  of  Rhetoric  and  Grammar)  so' 
many  figures.  Of  these,  the  new  is  only  the  old  First  Figure,  the  minor 
premise,  in  extension,  being  stated  before  the  major.  Krug,  like  our  other 
modern  logicians,  is  not  aware  that  this  was  the  order  in  which  the  syllogism 

82 


650  APPENDIX. 

was  regularly  cast,  in  common  language,  by  the  Greeks,  by  the  Arabians,  b/ 
the  Jews,  and  by  the  Latins  prior  to  Boethius.^  The  old  and  new  first  figures 
are  only  a  single  figure,  the  syllogism  being  drawn  in  the  counter  orders  of 
breadth  and  of  depth.  A  mood  in  these  orders,  though  externally  varying,  is 
intrinsically,  is  schematically,  the  same.  Krug's  distinction  of  his  new  first 
figure  is,  therefore,  null.  Thus,  Barama  is  Barbara ;  Caieme  is  Celarent ; 
Dirami  is  Darii ;  Firemo  is  Ferio.  Nor  is  his  discrimination  of  the  other  six 
better  founded.  His  new  (the  old)  Second  and  his  Fifth  Figures  are  also  one. 
The  latter  is  precisely  the  same  with  the  former ;  Fimeso  is  Festino,  and  Fomaco 
is  Baroco.  In  one  case  (under  Camestres),  Krug  adopts,  as  alone  right,  the 
conclusion  rejected  by  the  logicians.  In  this,  he  and  they  are,  in  fact,  both 
wrong,  though  in  opposite  ways.  Each  mood,  in  the  second  (as  in  the  third) 
figure,  has  two  indifferent  conclusions ;  and  the  special  one-sided  practice  of 
the  former  is  only  useful  as  gainsaying  the  general  one-sided  precept  of  the 
latter.  The  same  objection  applies  to  Krug's  new  (the  old)  Third,  in  connec- 
tion with  his  Sixth  Figure.  They  are  one ;  Daroco  is  Bocardo,  Fapimo  is 
Felapton,  and  Fisemo  is  Ferison.  In  two  cases  (under  Disamis  and  Bocardo) 
Krug  has  recognized  the  repudiated  conclusion.  Krug  (§  109)  has,  however, 
committed  an  error  in  regard  to  Bocardo.  He  gives,  as  its  example,  the 
following  syllogism,  in  which,  for  brevity,  I  have  filled  up  the  quantifications : 

"Swne  animals  are  not  [any]  viviparous ; 
AU  animals  are  [some]  organized  things ; 
Therefore,  some  organized  things  are  not  [any]  viviparous." 

In  a  note,  he  adds,  "  The  conclusion  should  here  be :  — '  Therefore,  some 
things  which  are  not  viviparous  are  (some)  organized.'  And  this  is  seen  also  by 
reduction.  We  have,  however,  followed  the  arbitrary  precept  of  the  logicians, 
that  the  extreme  in  the  second  proposition  should  stand  subject  in  the  conclu- 
sion ;  although  it  be  here  indifferent  which  extreme  becomes  the  subject.  The 
conclusion  is  only  changed  into  another  quality."  Only  changed  into  another 
quality !  Only  an  affirmative  conclusion  from  a  negative  premise !  The 
legitimate  inference  is : 

"  Therefore,  no  viviparous  is  some  organic  ;  "  or, 
"  Therefore,  any  viviparous  is  not  some  organic." 

Bachmann  (Logik,  §  135),  another  eminent  logician,  has  erred  with  Krug. 
A  particular  predicate  in  a  negative  proposition  seems  indeed  one  of  the  last 
difficulties  for  reformed  logic.  Krug's  new  (the  old)  Fourth  Figure  bears  a 
corresponding  relation  to  his  Seventh.  He  is  right,  certainly,  in  abolishing  all 
the  moods  of  the  fourth  figure  except  Fesapo  and  Fresiso ;  and,  from  his  point 
of  view,  he  is  hardly  to  be  blamed  for  not  abolishing  these  likewise,  along  with 
the  correlative  moods  Fapesmo  and  Frisesmo,  and,  with  them,  his  seventh 
figure.  Finally,  rejecting  the  scholastic  doctrine  of  Reduction,  he  adopts,  not 
without  sundry  p.^rverse  additions,  Kant's  plan  of  accomplishing  the  same  end; 
ao  that  Krug's  conversive  and  contrapositive  and  transpositive  interpolations, 

1  See  p.  625.  —  Ed. 


APPENDIX.  651 

by  which  he  brings  back  to  propriety  his  sevenfold  figured  aberrations,  are 
merely  the  substitution  of  one  "  false  subtlety "  for  another.  He,  and  Bach- 
mann  after  him,  renounce,  however,  "  the  crotchet  of  the  Aristotelians,"  in 
making  the  extreme  of  the  prior  premise  the  predicate,  always,  of  the  conclu- 
sion, in  the  first  and  second  figures ;  and,  though  both  do  this  partially  and 
from  an  erroneous  point  of  view,  their  enunciation,  such  as  it  is,  is  still 
something. 

Professor  Beneke,  of  Berlin,  is  the  last  to  whom  I  can  refer,  and  in  him  we 
have,  on  the  point  in  question,  the  final  result  of  modern  speculation.  This 
acute  and  very  original  metaphysician  stands  the  uncompromising  champion 
of  the  philosophy  of  experience,  against  the  counter  doctrine  of  transcenden- 
talism, in  all  its  forms,  now  prevalent  in  Germany ;  and,  among  the  other  de- 
partments of  mental  science,  he  has  cultivated  the  theory  of  reasoning  with 
great  ability  and  success.  In  1832  appeared  his  Lehrbuch  der  Logik,  etc.;  in 
1839,  his  Syllogismorum  Analyticorum  Origines  et  Ordo  Natnralis,  etc. ;  and  in 
1842,  his  System  der  Logik,  etc.,  in  two  volumes.  In  Logic,  Beneke  has  devoted 
an  especial  share  of  attention  to  the  theory  and  distribution  of  Syllogism ;  but 
it  is  precisely  on  this  point,  though  always  admiitng  the  ingenuity  of  his  reason- 
ings, that  I  am  compelled  overtly  to  dissent  from  his  conclusions. 

The  Syllogistic  of  Beneke  is  at  once  opposed,  and  correspondent,  to  that 
of  Krug;  there  is  an  external  difference,  but,  without  imitation,  an  internal 
similarity.  Instead  of  erroneously  multiplying  the  syllogistic  figures,  like  the 
Leipsic  philosopher,  the  philosopher  of  Berlin  ostensibly  supersedes  them 
altogether.  Yet,  when  considered  in  essence  and  result,  both  theories  agree 
in  being,  and  from  the  same  side,  severally,  the  one  an  amplification,  the  other 
an  express  doubling,  of  the  nineteen  scholastic  moods.  In  this,  both  logicians 
were  unaware  that  the  same  had  been  long  ago  virtually  accomplished  in  the 
progress  of  the  science  ;  neither  considered  that  the  amplification  he  proposed 
was  superficial,  not  to  say  mistaken  ;  and  that,  instead  of  simplicity,  it  only 
tended  to  introduce  an  additional  perplexity  into  the  study.  Beneke  has  the 
merit  of  more  openly  relieving  the  opposition  of  Breadth  and  Depth,  in  the 
construction  of  the  syllogism  ;  and  Krug,  though  on  erroneous  grounds,  that 
of  partially  renouncing  the  old  error  of  the  logicians  in  regard  to  the  one 
syllogistic  conclusion,  in  the  second  and  third  figures.  But,  in  his  doctrine  of 
moods,  Beneke  has,  I  think,  gone  wrong  in  two  opposite  ways  :  like  Krug,  in 
his  arbitrary  multiplication  of  these  forms ;  like  logicians  in  general,  in  their 
arbitrary  limitation. 

In  regard  to  the  former  —  the  counter  quantities  of  breadth  and  depth  do  not 
discriminate  two  moods,  but  merely  two  ways  of  stating  the  same  mood.  Ac- 
cordingly, we  do  not  multiply  the  moods  of  the  first  figure,  to  which  alone  the 
principle  apphes,  by  casting  them  in  the  one  dependency  and  in  the  other;  we 
only  show  that,  in  that  figure,  every  single  mood  may  be  enounced  in  a  two- 
fold order,  more  german,  the  one  to  the  quantity  of  extension,  the  other  to  the 
quantity  of  intension.  An  adequate  notation  ought,  equally  and  at  once,  to 
indicate  both.  But  in  reference  to  the  second  and  third  figures,  the  case  is 
worse.  For  in  them  we  have  no  such  dependency  at  all  between  the  ex- 
tremes ;  and  to  double  their  moods,  on  this  principle,  we  must  take,  divide,  and 


^^^  APfEJTD'rx. 

arbitrarily  appropriate,  one  of  the  two  indifferent  conclusions.  But,  as  evetj 
single  liibod  of  these  figures  has  a  double  conclusion,  this  division  cannot  be 
made  to  difference  their  plurality.  If  Professor  Bencke  would  look  (instar 
omnium)  into  Apuleius  or  Isidorus,  or,  better  than  either,  into  Blemmidas,  he 
will  find  all  his  new  moods  (not,  of  course,  those  in  the  fourth  figure)  stated  by 
these,  as  by  other  ancient  logicians;  who,  however,  dreamed  Aot  that  the  mere 
accidental  difference  of,  Avhat  they  called,  an  analrjtic  and  synthetic  enounce- 
ment,  determined  any  multiplication  of  the  moods  themselves. 

In  the  latter  respect.  Dr.  Beneke  has  only  followed  his  predecessors ;  I,  there- 
fore, make  no  comment  on  the  imperfection.  But,  in  accomplishing  what  he 
specially  proposes,  whilst  we  do  not  find  any  advancement  of  the  science,  we 
find  the  old  confusion  and  intricacy  replaced  by  another,  perhaps  worse.  To 
say  nothing  of  his  non-abolition  of  the  fourth  figure,  and  of  his  positive 
failures  in  doubling  its  moods,  the  whole  process  is  carried  on  by  a  series  of 
arbitrary  technical  operations,  to  supersede  which  must  be  the  aim  of  any  one 
who  would  reconcile  Logic  with  nature.  His  new  (but  which  in  reality  are 
old)  amplifications  are  brought  to  bear  (I  translate  his  titles)  through  "  Com- 
mutations of  the  Premises, — J)y  Subalternation,  —  by  Conversion,  —  by  Con- 
traposition ; "  and  "  of  the  Major,  —  of  the  Minor,"  —  in  fact,  of  both  premises 
(e.  g.,  Fesapo,  etc.).  And  so  diflicult  are  these  processes,  if  not  so  uncertain 
the  author's  language,  that,  after  considerable  study,  I  am  still  in  doubt  of  his 
meaning  on  more  points  than  one.  I  am  unable,  for  example,  to  reconcile  the 
following  statements :  —  Dr.  Beneke  repeatedly  denies,  in  conformity  with  the 
common  doctrine,  the  universal  quantification  of  the  predicate  in  aflSrmative 
propositions;  and  yet  founds  four  moods  upon  this  very  quantification,  in  the 
conversion'  of  a  universal  affirmative.  This  is  one  insolubility.  But  there 
arises  another  from  these  moods  themselves  (§  28-31).  For,  if  we  employ  this 
(juantific-ation,  we  have  moods  certainly,  but  not  of  the  same  figure  with  their 
nominal  correlatives;  whereas,  if  we  do  not,  simply  rejecting  the  permission, 
all  slides  smoothly,  —  we  have  the  right  moods  in  the  right  figure.  This,  again, 
I  am  unable  to  solve.  Dr.  Beneke's  duplication  of  the  moods  is  also  in  sundry 
cases  only  nominal ;  as  is  seen,  for  example,  in  Ferio  2,  Fesapo  2,  and  Fre- 
siso  2,  which  are  forms,  all,  and  in  all  respects,  identical.  I  must  protest  also 
against  his  violence  to  logical  language.  Thus,  he  employs  everywhere  "  non 
orane^"  "  non  omnia,"  "alle  sind  nicht,"  etc.,  which  is  only  a  particular  (being 
a  mere  denial  of  omnitude),  for  the  absolute  or  universal  negative,  "  nullum,** 
"  nulla,"  "  kein  ist,"  tio,  none,  not  any,  etc.,  in  opposition  both  to  principle  and 
to  tlie  practice  of  Aristotle  and  succeeding  logicians. 

(p)  TITJUS. 

Gottlieb  Gerhard  Titius,  Ars  Cogitandi,  sice  Scientia  Cogitationum  Cogitan- 
tiuni,  C'ofjifdtionibus  Necesaaris  tfistructa  et  a  Peregrinis  Liberata.  Leipsiae, 
r723  (first  edition,  1701). 

Titius  h.as  been  partially  referred  to,  by  Sir  W.  Hamihon,  &s'  having  main- 
tained the  doctrine  of  a  Quantified  Predicate.  See  above,  p.  555.  His  theory 
of  the  Figure  and  Mood  of  Syllogism  is  well  deserving  of  notice,  —  proceed- 
ing, as  it  does,  on  the  application  of  that  doctrine.     This  theory  is  principally 


APPENDIX.  668 

contained  in  the  following  extracts  from  his  Ars  Cogitandi,  which  show  how 
closely  he  has  approximated,  on  several  fundamental  points,  to  the  doctrines 
of  the  New  Analytic.^ 

Titius  gives  two  canons  of  syllogism : 

I.  AfBrmative.  "  Quaecunque  conveniunt  in  uno  tertio,  ilia  etiam,  juxta 
mensuram  illius  convenientiae,  inter  se  conveniunt." 

II.  Negative.  "  Quaecunque  pugnant  in  certo  aliquo  tertio,  ilia,  juxta  men- 
suram illius  disconvenientiae,  etiam  inter  se  pugnant."     C.  ix.  §§  30,  27. 

The  following  relates  to  his  doctrine  of  Figure  and  Mood,  and  to  the  special 
rules  6f  Syllogism,  as  commonly  accepted  : 

C.  X.  §  i.  "  Sic  igitur  omnium  Syllogismorum  formalis  ratio  in  genuina  medii 
termini  et  praedicati  ac  subjecti  Conelusionis  collatione  consistit ;  cam  si  dicere 
velis  formam  essentialem  aut  Jiguram  generalem,  vel  communem,  non  valde 
reluctabor. 

§  ii.  "  Praeter  earn  vero  Peripatetici  Figuras  ex  peculiari  medii  termini  situ 
adstruunt,  ea  ratione  ut  Primam  figuram  dicant,  in  qua  medius  terminus  in 
Majore  est  subjectum,  in  Minore  Praedicatum,  Secundam,  ubi  idem  bis  praedi- 
cati, et  Tertiam,  ubi  subjecti  locum  bis  subit.  Galenus  adjecit  Quarlam  primae 
contrariam,  in  qua  medius  terminus  in  majore  est  praedicatum,  In  minore  sub- 
jectum, quam  plurlbus  etiam  exposuit  Autor.  Ai't.  Cog.  p.  3,  c.  8. 

§  lil.  "  Caeterum  illae  figurae  tantum  sunt  accidentales,  ab  iisque  vis  conclu- 
dendi  non  dependet.  Qiiodsi  tamen  quis  diversum  medii  termini  situra  atten- 
dendum  esse  putet,  turn  noc  Quarta  figura  negligenda  esse  videtur,  licet  earn 
Peripatetici  nonnulli  haut  curandam  existiment,  vide  Ulman.  Synops.  Log.  1.  3, 
c  2,  p.  164. 

§  iv.  "  Interim  Prima  caeteris  magis  naturalls  ex  eo  vlderi  potest,  quod  Sub- 
jectum et  Praedicatum  Conelusionis  in  Praemlssis  suam  retineat  qualitatem,  cum 
in  secunda  et  terlia  alterum  qualitatem  suam  exuere,  in  quarta  vero  utrumque 
eam  deponere  debeat 

§  v.  "  Postea  in  unaquaque  figura,  pro  ratione  quantitatis  et  qualitatis  propo- 
sitlonum,  peculiares  Modi  adstruuntur,  ita  quidem  ut  Primae  figurae  Quatuor, 
totidem  Secundae,  Tertiae  sex  attribuantur,  ex  quibus  etiam  deblte  variatis 
Quarta  quinque  acclpiat,  prout  ilia  passim  cum  vocabulis  memorlalibus  recen- 
serl  solent,  ut  Ilia  quidem  hue  transcribere  opus  non  sit,  vide  Autor,  Art.  Cogit., 
p.  3,  c.  5,  6,  7,  8. 

§  vi.  "  Non  opus  esse  istis  figuris  et  modls  ad  dijudicandam  Syllogismorum 
bonitatem,  e.x  monito  §  3,  jam  Intelllgi  potest.  Quomodo  tamen  sine  iis  bonitas 
laudata  intelligi  queat,  Id  forte  non  adeo  lujuidum  est 

§  vll.  "  Non  diu  hie  quasrenda  sunt  remedia :  Observetur  forma  essentialis 
seu  figura  communis,  ac  de  verltate  Syllogismi  recte  judicabitur.  Applicatio 
autem  hujus  moniti  non  est  difficilis,  nam  primo  respiciendum  ad  conclusionem, 
deinde  ad  medium  terminum,  quo  facto  etiam  judicari  potest,  an  ejus  et  ter- 
minorum  conduslonis  collatio  in  praemlssis  recte  sit  instituta  nee  ne.     .     .     . 

§  ix.  "  De  caetero  uti  anxie  jam  non  inquiram,  an  omnis  bene  concludendi 

1  For  Titius"  doctrine  of  a  Quantified  Tred-  rropositions  and  to  the  Hypothetical  Syllo- 
icate,  its  application  to  the  Conversion  of     gism,  see  above,  pp.  555, 527,  603. — Ed. 


654 


APPENDIX. 


ratio  numero  modorum  denario  circumscribatur,  quod  quidera  juxta  htpi^^uof 
tnathematicam  detnonstrasse  videri  vult  Autor.  Ar(.  Coy.  p.  3,  c.  4,  ita  id  haut 
admiserim,  quod  illi  modL  quos  vulgo  laudant,- Primae,  Secundae  aut  Tertia; 
figurae  praecise  sint  assignandi,  licet  hoc  itidem  acucnine  mathematieo  se  demon- 
strasse  putet  dictus  Autor.  d.  I.  c.  5  seqq. 

§  X.  "  Cum  enim  quaevis  propositio  possit  converti,  modo  quantitas  praedicati 
probe  observetur,  hinc  necessario  sequitur,  quod  quivis  Syllogismus,  adhibita 
propositionum  conversione,  in  quavis  figura  possit  proponi,  ex  quo  non  potest 
non  fequalis  modorum  numerus  in  unaquaquc  figura  oriri,  licet  illi  non  ejusdem 
semper  sint  quantitatis.  ' 

§  xi.  "  Operae  pretium  non  est  prolixe  per  omnia  Syllogismorum  singulis 
figuris  adscriptorum  exempla  ire,  sufficiat  uno  assertionem  illustrasse,  v.  gr.  in 
prima  figura,  modo  Barbara  hie  occurrit  Syllogismus  apud  d.  Autor.  c.  6. 

0.  sapiens  tubjicitur  voluntati  Dei, 

0.  honestits  est  sapiens, 

E.  0.  konesbu  subjicUur  voluntati  Dei. 

§  xii.  "  Hunc  in  secunda  figura  ita  proponere  licet : 

Quidam,  qui  subjicitur  voluntati  Dei,  est  omnis  sapiens, 

Omnis  honestus  est  sapiens, 

E.  omnis  honestus  subjicitur  voluntati  Dei, 

ratio  concludendi  manet  eadem,  sapiens  enim  ct  is  qui  subjicitur  voluntati  Dei, 
uniuntur  in  Majore,  dein  sapiens  el  honestus  in  Minore,  ergo  in  conclusione  idea 
Mpientis  et  Ejus  qui  voluntati  Dei  subjicitur,  quoque  conveniunt 
§  xiii.  "  In  tertia  figura  ita  so  habebit : 

0.  sapiens  subjicitur  voluntati  Dei, 

Q.  sapiens  est  omnis  honestus, 

E.  0.  honestus  subjicitur  voluntati  Dei, 


nee  in  hac  concludendi  ratione  aliquid  desiderari  potest,  nam  medius  terminus 
univcrsaliter  unitur  cum  conclusionis  praedicato,  deinde,  quantum  sufficit,  con- 
jungitur  cum  ejusdem  subjecto,  seu  oinni  honesto,  ergo  subjectum  et  praedicatum 
se  quoque  mutuo  admittent. 

.  §  xiv.  "  Cajterorum  eadem  est  ratio,  quod  facile  ostendi  posset,  nisi  tricas  illas 
vel  scribere  vel  legere  tacdiosum  foret.  Ex  his  autem  sequitur,  quod  omnes 
regulcE  speciales,  quce  modis  vulgaribus  attemperaXcB  vulgo  circumferuntur,  falsce 
sint,  quod  speciatim  ostcndere  liceat. 

§  XV.  "  In  universum  triplici  modo  impingitur,  vel  enim  conclusio  creditur 
absurda,  quce  talis  non  est,  vel  vitiwn  est  in  materia,  ac  altera  pj-cemi^sarum  falsa, 
vel  aiisunt  quatuor  termini,  adeoquc  absurditas  conclusionis,  si  aliqua  subest, 
nunciuam  ab  ea  causa  dependct,  quam  refertint  rcgulae. 

§  xvi.  "  Sed  videamus  distinctius  (1)  major  in  prima  Jigura  semper  sit  univer^ 
salis 


APPENDIX.  655 

§  xvii.  "  Inflectam  hue  exemplum  minus  controversum,  quod  Autor,  Art.  Cog. 
p.  3,  c.  7,  in  modo  Dlsami^,  tertise  figurae,  proponit : 

Quidam  impii  in  honore  habentur  in  mundo, 

Quidam  vituperandi  sunt  omnes  impii, 

E.  quidam  vituperandi  in  honore  habentur  in  mundo. 

§  xviii.  "  Hie  habes  primam  figuram  cum  majore  partieularl,  optime  iterum 
concludentem,  nam  licet  medius  terminus  partieulariter  sumatur  in  majore, 
ejus  tamen  ille  est  capacitatis,  ut  in  eodcm  cbnvenientia  prsedicati  et  subject! 
ostendi  queat,  et  nisi  hoc  esset,  nee  in  tertia  figura  rite  concluderetur. 

§  xix.  "  Nee  valde  obsunt,  quae  vulgo  illustrandae  regulaj  adducuntur.  Ex 
sententia  Weis.  in  Log.  p.  1,  lib.  2,  c.  2,  §  4,  male  ita  concluditur: 

Q.  animal  volat, 
O.  leo  est  animal, 
E.  Q.  leo  volat. 

Verum  si  animal  sumitur  in  minore  sicut  in  majore,  turn  ilia  falsa  est,  si  vero 
alio  sensu,  tum  existunt  quatuor  termini ;  his  ergo  causis,  non  particularitati 
Majoris,  vitiosa  conclusio  tribuenda. 
§  XX.  "  Nam  alias  ita  bene  concluditur : 

Q.  animal  volat, 

O.  aids  est  animal  (illad  qnoddam), 

JE.  O.  avis  mlat, 

nam  licet  medius  terminus  particularis  sit,  tantas  tamen  est  latitudinis,  ut  cum 
utroque  Conclusionis  termino  possit  uniri. 

§  xxi.  "  Porro  (2)  Minor  semper  sit  affirmans.  Sed  quid  desiderari  potest 
in  hoc  Syllogismo : 

O.  homo  est  animal  rationale, 

Leo  non  est  homo, 

E.  non  est  animal  rationale? 

et  nonne  ilia  ratio  concludendi  manifeste  bona  est,  quae  subjectum  et  praedi- 
catum,  qu£e  in  certo  tertio  non  conveniunt,  inter  se  quoque  pugnare  contendit  ? 
§  xxii.  ''  Sed  ais,  mutemus  paululum  Syllogismum  et  absurditas  conclusionis 
erit  manifesta : 

O.  homo  est  animal, 

Leo  non  est  homo, 

E.  leo  non  est  animal ! 

Verum  si  terminus  animalis  in  Conclusione  perinde  sumitur,  sicut  suppositus 
fuit  in  majore,  nempe  partieulariter,  tum  conclusio  est  verissima ;  si  autem  aliter 
accipiatur,  tum  evadunt  quatuor  termini,  quibus  adeo,  non  negation!  Minoris, 


656  APPENDIX, 

absurditas  conclusionis  est  imputanda,  quse  observatio  in  omnibus  exemplls  quae 
hie  objici  possunt  et  solent,  locum  habet. 

§  xxvlil.  "  Sed  revertamur  ad  regulas  vulgares  !  Nimirum  (3)  In  secunda 
figura  major  sit  universalis.    Verum  cur  non  ita  liceat  concludere  : 

Quidam  dives  est  Saxo, 

Quidam  Germanus  est  omnis  Saxo, 

E.  quidam  Germanus  est  dives? 

quod  argumentum  Weis.  1.  2,  c.  4,  §  2,  intuitu  tertiaB  figurae  proponit. 

§  xxix.  "  Argumenta,  quaB  fallere  videntur,  v.  gr.  quod  Weisius  1.  2,  c.  3,  §  8, 
profert : 

Quidam  homo  est  sapiens, 

Nidlus  slultus  est  sapiens, 

E.  nullus  stidtus  est  homo, 

et  similia,  responsione,  §  22,  data  eliduntur;  nimirum  conclusio  vel  non  est 
absurda,  si  recte  intelligatur,  vel  adsunt  quatuor  termini,  quibus  adeo,  non 
pavticularitati  majoris,  vitium  est  imputandum. 

§  XXX.  "  Amplius  (4)  Ex  puris  affirmative^  in  secunda  Jigura  nihil  concludiiur, 
sed  mirum  foret,  si  ilia  concludendi  ratio  falleret,  quse  fundamentum  omnium 
Syllogismorum  affirmativorum  tam  evidenter  prae  se  fert !  Hoc  argumentum 
utique  formaliter  bonum  est : 

Omnis  sapiens  sua  sorte  est  contentus, 
Faulus  sria  sorte  est  contentus, 

E.  Faulus  est  sapiens. 

I 

§  xxxi.  "Sed  fallunt  multa  argumenta,  v.  gr.  Weisio  </.  c.  3,  §  3,  adductum: 

Omnis  lepus  vivit, 
Tu  vivis, 
E.  tu  et  lepus, 

verum  non  fallunt  ob  affimiationem  praemissarum,  sed  quia  vel  minor  falsa  est, 
si  scil.  praedicatum  accipiatur  eodem  sensu,  quo  in  Majore  sumtum  est,  vel 
quia  adsunt  quatuor  termini,  si  praedicatum  Minoris  particulariter  et  alio  eensu 
accipiatur. 

§  xxxii.  *' Non  possunt  etiam  vulgo  diffiteri,  quin  ex  puris  s^rmativis  ali- 
([uando  quid  sequatur,  verum  id  non  vi/orwice  sed  matericB  fieri  causantur,  vide 
Ulman.  Log.  1.  3,  c.  3,  §  4.  Haec  vero  est  petitio  prinoipii,  nam  quas  conveniunt 
in  uno  tertio,  ilia  etiam  inter  se  convenire  debent,  idque  non  fortuito,  sed 
virtute  unionis  laudats?,  seu  beneficio  formae. 

§  xxxiv.  "In  tertia  figura  (5)  Minor  semper  sit  affirmans.  Ego  tamen  sic 
jrecte  concludi  posse  arbitror  • 


^  APPENDIX.  657 

Quoddam  laudnndum  est  omm's  vhius, 
Nullum  laudandum  est  qwedain  magnificentia, 
E.  qucedam  magnificentia  non  est  virtus. 

§  XXXV.  "  Nee  valde  urgent  exempla  opposita  AVeisIus  d.  1.  2,  c.  4,  §  2,  hoc 
affert : 

Oinnis  homo  amhulat, 

Nullus  homo  est  parens, 

E.  quidam  porous  non  amhulat, 

nam  recurrit  responsio  §  22  data,  quae  vel  conclusionera  falsam  non  esse,  vel 
causam  falsitatis  a  quatuor  terminis  dependere  ostendit,  quse  etiam  locum  ha- 
beret,  licet  conclusionem  universalem,  Nidlus  porcus  amhulat,  assumas. 

§  xxxvi.  "  Tandem  (G)  In  tertia  Jigura  conclusio  semper  sit  particularis. 
Verum  Syllogismum  cum  conclusione  universali,jam  exhibui  §  13,  in  Exemplis 
autem  quae  vulgo  afferuntur,  v.  gr. 

Omnis  saiator  est  honoraius, 

Om.nis  senator  est  homo  (quidam  scil.), 

E.  omnis  homo  est  honoratus, 

vide  Weis.  d.  I.  2,  c.  4,  §  3,  occurrunt  quatuor  termini  (nam  homo,  in  minore- 
particulariter,  in  conclusione  universaliter  sumitur),  qui  adeo  veram  absurdae- 
conclusioiiis  causam,  ac  simul  regulae  vulgaris  falsitatem  ostendunt. 

§  xxxvii.  "  Ilia  autem  omnia,  quae  contra  vulgares  regulas  hactenus  dispiita- 
vimus,  non  oo  pertinent,  quasi  rationem  concludendi  rejiciendis  regulis  hinc 
inde  confectam  commendemus,  ita  ut  in  demonstrationibus  eadem  uti,  aut  valde 
delectari  debeamus.  Quin  omni  potius  eo  spectant,  ut  Peripateticos,  qui  for- 
mam  Syllogismorum  essentialem  vel  omnino  non  vel  nimis  frigide  exponunt,  in 
explicandis  etiam  eorum  figuris  accidentalibus,  falli  prpbarem. 


§  xxxix.  "  Atque  ex  hactenus  dictis  etiam  intelligi  potest,  quas  nostra  de- 
Reductione  sit  sententia.  Nimirum  ex  nostris  hypothesibus  ilia  nihil  aliud  est, 
quara  Syllogismorum  per  omnes  quatuor  Jiguras  accidentales,  salva  semper  con- 
clusione y  facta  variatio. 

§  xl.  '•  Pertinet  igitur  ilia  tantum  ad  Prcemissa,  Syllogismus  enim  semper  ut 
instrumentum  veritatis  inquirendae  considerari,  adeoque  quaestio  probanda,, 
(juae  semper  immobilis  sit,  nee,  prout  visum  est,  varietur,  przesupponi  debet. 

§  xli.  "  Rcductionis  unica  Lex  est,  ut  simpliciter,  juxta  figura;  indolem,  prop- 
ositiones  convertamus,  quod  sine  uUa  difficultate  procedit,  dummodo  quanti- 
tatem  subjecti  et  praedicati  debite  confideremus,  ceu  ex  iis  quae  de  Conversione 
diximus  satis  liquet. 

§  xlii.  "Finis  est,  ut  pe'r  ejusmodi  variationem,  terminorum  unionem  vel' 
separationem  eo  accuratius  intelligamus,  hinc  omnis  utilitas  reductioni  non  est 
abjudicanda,  si  enim  recte  instituatur,  ingenium  quantitati  propositionum 
observandae  magis  mj^Sque  assuescit,  ac  inde  etiam  in  penitiorem  formae  essen- 
tialis  intelligentiam  provehitur. 

83 


658 


APPEI^DIX. 


§  xHii.  "In  vulgari  Reductione,  quae  in  libelHs  logicis  passim  exponitur,  vide 
Aut.  Art.  Cog.  p.  3,  c.  9,  quaedem  exempla  reprehendi  non  debent,  quando 
V.  g.  Cesare  ad  Celarent  reducitur,  nam  ibi  simplici  conversione  alicujus  propo 
sitionis  defunguntur,  juxta  legem,  quam  §  41,  reductioni  dedimus. 

§  xliv>  "  Sed  si  ab  illis  exemplis  abeas,  parum  vel  nihil  est,  quod  in  eadem 
laudari  debeat,  dum  fere  ex  falsis  hypothesibus  omnis  reductio  oritur,  nam 
conversio  per  contraposhionem  priesupponitur,  quam  tamen  valde  dubiam  esse, 
.supra  ostendiraus,  prajterea  peculiares  modi  in  singulis  figuris  adstruuntur,  ao 
omnis  reductio  ad  primam  Jiguram  facienda  esse  existimatur,  cum  tamen  idem 
Syllogismus  per  omnes  figuras  variari  queat. 

§  xlv.  "  Ipsa  vero  reductio  nullis  legibus  adstricta  est,  oonvertitur  Con- 
c-lusio,  transponuntur  Praemissae,  propositiones  negativae  mutantur  in  affirma- 
livas,  atque  ita  quidvis  tentatur,  modo  figura  intenta  oblineatur.  Quo  ipso 
puerilis  error,  quo  Logica,  pro  arte  concinnandi  tres  lineas,  easque  in  varias 
formas  mutandi  habetur  satis  elucet.  Inepta  scientia  est,  quae  in  verbis  dispo- 
ncndis,  circumagendis  aut  torquendis  unice,  occupatur. 

§  xlvi.  "  Juxta  haec  igitur,  vulgari  modo  reducere,  maximam  partem  nihil 
aliud  est,  quam  errorem  errore  tegere,  ingenia  discentium  torquere,  ac  magno 
conatu  magnas  nugas  agere,  inscitiamque  professa  opera  ostendere." —  Ed.] 


IV.  —  Syllogistic  Moods. 

(p.  285.) 

I.  —  DIRECT    AND    INDIRECT    MOODS. 
(a)   TliEIR  PRmClPLE.- FIRST  AND  FOURTH  FIGURE. 

(Seep.  302.) 

Direct  and  Indirect  Moods  —  principle  of.  —  That  the  two  terms  should 
hold  the  same  relation  to  each  other  in  the  conclusion  that  they  generally  hold 
to  the  middle  term  in  the  premises.  This  determined  by  the  Question.  This 
constitutes  direct,  immediate,  natural,  orderly  inference.  When  reversed,  by- 
conversion, there  emerges  indirect,  mediate,  unnatural,  irregular  inference. 

In  the  two  last  Figures  (Second  and  Third),  the  two  terms  hold  the  same 
relation  to  the  middle  term  in  the  premises ;  ergo,  no  indirect  inference,  but 
always  two  direct  conclusions  possible. 

In  the  first  Figure,  as  the  two  terms  are  subordinated  to  each  other  in  the 
premises,  one  direct  conclusion  from  premises,  whether  read  in  Extension  or 
Comprehension,  and,  conseciuently,  an  indirect  one  also,  —  the  First  Figure 
being  first  fisrure  in  Extensive  quantity ;  the  Fourth  Figure  being  first  figure  in 
Comprehensive  quantity.     Direct  and  indirect  moods  in  each. 

1.  Blunder  about  definition  of  major  and  minor  terms  by  logicians  (for 
which  Aristotle  not  responsible),'  cause  of  fancy  of  a  Fourth  Figure,  consti- 
tuted by  indirect  moods  in  comprehension. 


I  See  Stahl  [NoUz  tt  Animadversionei  in 
Compendium  DiaUcticum  D.  Conradi  Horneii, 
nunc  primum  ex  Auetoris  AMograpko  editct  cura 


Caapari  Poaneri  Prof.  Pub.  Jena.    1666,  Ad.  h- 
iii.  c.  riii.]. 


APPENDIX.  659 

2.  That  predicate  could  have  no  prefinition,  and,  therefore,  though  thej 
allowed  its  converse,  the  direct  inference  was  not  suffered.  This  in  Fapesmo, 
Frisesmo  (these  alone,  by  some  logicians,  admitted  in  the  First  Figure),  and 
Fesapo  and  Fresison  in  Fourth,  or  Comprehensive  First.^ 

3.  That  major  proposition,  that  which  is  placed  first. 

Fourth  Figure.  —  The  First  Figure,  and  that  alone,  is  capable  of  being 
enounced  in  two  orders,  those  of  Breadth  and  of  Depth.  It  is  exactly  the 
same  syllogism  in  either  order ;  and,  while  the  order  of  Depth  was  usually 
employed  by  the  Greeks,  Orientals,  and  older  Latins,  that  of  Breadth  has  been 
the  common,  if  not  the  exclusive,  mode  of  enouncement  among  the  western 
logicians,  since  the  time  of  Boethius.  In  either  form  thece  are  thus  four  direct 
moods,  and  five  indirect  —  in  all  nine  moods ;  and  if  the  Figure  be  held  to 
comprise  the  moods  of  either  form,  it  will  have  eighteen  moods,  as  in  fact  is 
allowed  by  some  logicians,  and,  among  others,  by  INIendoza  (Disp.  Log.  et  Met. 
T.  I.  pp.  515,  516).  Martianus  Capella  {De  Septem  Ariihus  Liberalibuft,  L.  iv., 
De  Dialectica^  in  cap.  Quid  sit  Prcedicaticus  Sijllocjismus  —  see  p.  639)  states  and 
allows  either  form,  but,  like  his  contemporaries,  Greek  and  Latin,  he  employs 
in  his  examples  the  order  of  Depth. 

Now,  mark  the  caprice  of  the  logicians  of  the  West  subsequent  to  Boethius. 
Overlooking  entirely  the  four  direct  moods  in  the  order  of  Depth,  which  they 
did  not  employ,  as  the  conclusion  would,  in  these  cases,  have  been  opposed  to 
their  own  order;  they  seized  upon  the  five  indirect  moods  of  the  order  of 
Depth,  as  this  afforded  a  conclusion  corresponding  to  their  own,  and  consti- 
tuted it,  thus  limited,  into  a  Fourth  Figure. 

Did  not  make  two  forms  of  First  Figure. 

An  indirect  conclusion  is  in  subject  and  predicate  the  reverse  of  a  direct; 
opposed,  therefore,  to  the  order  of  predication  marked  out  by  the  premises 
which  the  direct  conclusion  exclusively  follows.  An  indirect  conclusion  (what 
the  logicians  have  not  observed)  ^  is  an  inference  from  the  direct  conclusion, 
and,  therefore,  one  mediate  from  the  premises. 

(5)  MOODS   OF  FOURTH  FIGURE  REDRESSED. 

(Early  paper  —  previous  to  1 844.    Later  signs  of  quantity  substituted. —  Ed.) 

I.  Bamalip,  —  only  Barbara  with  transposed  premises  and  converted  con- 
clusioa. 

(2)  All  irons  are  (some)  metals ; 
(1)  All  metals  are  {some)  minerals; 
All  irons  are  (some)  minerals. 

1  [That  fourth  Figure  difTers  from  first  only  Dialect.,  Lib.  ii.  c.  vi.  art.  xi.  p.  391,  and  art. 

by  transposition  of  Premises,  —  held  by  De-  iv.  p.  385  (1635).    Kidiger,  De   Sensu    Veri  et 

rodon,  Logica  Restltuta,  p.  606.     Camerarius,  Falsi,  ii.  6,  }  36.     Crusius,  Weg  Zvr  Gewisskeit, 

DLtputationes  Philosophical,  Disp.  i.  qu.  13,  p.  §  336,  p.  606.     Tlatner,  Philosophische  Aphoris- 

116.     Caramuel,  Rat.  ft  Jiedl.  Phil..  Disp.  xii.  men,  i.  {  554,  p.  267  ] 

p.  45.     Irenaeus,  Integ.  Phil.,  Elementa  Logir.es,  2  But    see   Contarenus,   De    Quarta  Figtira 

Sect.  ill.  §  3,  p.  29.     Campanella,  PAti.  iiat.  SyUog.,  Opera,  Tp.  1235.  — E.D. 


660 


APPENDIX. 


(By  conversion.) 
Some  minerals  are  {all)  irons. 


(Minerals) , 


a  -.{Metals), 
(Redressed) 


:  (Irons). 


II.  Calcmes,  —  only  Celarent  with  transposed  premise*  and  converted  con- 
cluaon. 

(2)  All  snails  are  (some)  mdUusca ; 
(1)  No  molhiscum  is  any  insect; 

No  snail  is  any  insect. 
(By  conversion.) 

No  insect  is  any  snail. 


{Insect) : 


IIL  Dimatis,  —  only  Darii  with  transposed  premises  and  converted  conclu- 
sion. 

(2)  Some  stars  are  {some  or  all)  planets; 

(1)  All  planets  are  some  things  moving  round  sun ; 

Some  stars  are  some  things  moving  round  sun ; 
(By  conversion.) 

Some  things  moving  round  sun  are  some  stars. 


(  Moving  round  Sun), 


;  (Planets) : ,  - 
(Redressed) 


I ,  (Stan) 


APPENDIX. 


66X 


IV.    Fesapo  [Felapos].* 

(2)  No  artery  is  any  vein ; 

(1)  AU  veins  are  (some)  bloodvessels ; 

No  artery  is  (some)  bloodvesseL 
(By  conversion.) 

Some  bloodvessel  is  no  artery. 


(^Bloodvessels) , 


s«:(Fem):- 
(Redregsed) 


'.{Artery) 


V.  Freslson  [Frelilosj. 


(2)  No  muscle  is  any  nerve; 

(1 )  Some  nerves  are  (some)  expansion  on  hand  j 

No  muscle  is  (some)  expansion  on  hand. 
(By  conversion.) 

Some  expansion  on  hand  is  no  muscle. 


{Expansion  on  hand), 


,  {Nerve) :  — 
(Redressed) 


:  {Muscle) 


+ 


(March  1846.)  —  My  universal  law  of  Figured  Syllogism  excludes  the 
Fourth  Figure.  —  What  worse  relation  of  subject  and  predicate  subsists  between 
either  of  two  terms  and  a  common  third  term  with  which  one,  at  least,  is  positively 
related ;  that  relation  subsists  between  the  two  terms  themselves.  What  relation, 
etc. ;  that  relation,  etc.  Now,  in  Fourth  Figure  this  is  violated  ;  for  the  predi- 
cate and  subject  notions,  relative  to  the  middle  term  in  the  premises,  are  in  the 
conclusion  turned  severally  into  their  opposites  by  relation  to  each  other.  This 
cannot,  however,  in  fact  be  ;  and,  in  reality,  there  is  a  silently  suppressed  con- 
clusion, from  which  there  is  only  given  the  converse,  but  the  conversion  itself 
ignored. 


1  Zabarella,  Optra  Logira  De  Quarta  Fig. 
SyU.  pp.  118,  119,  125.  Burgersdyk,  Instit. 
Log.,  L.  ii.  c.  7,  p.  167,  reverses  premises  and 


reduces  to  Fapesmo  an  indirect  mood  of 
First;  thus  violating  the  rule  of  tliftt  Fig- 
ure. 


6^2  APPENDIX- 

Fourth  Figure.     Reasons  against. 

1",  Could  never  directly,  naturally,  reach  (a)  Conclusion  from  premise, 
or  (b)  Premises  from  qusesitum. 

2°,  All  other  figures  conversion  of  premises  of  First,  but,  by  conversion  of 
conclusion  (as  it  is),  no  new  figure. 

3°,  All  other  figures  have  one  conclusion  Fourth  a  converted  one,  often 
different. 

(March  1850.)  —  Fourth  Figure.  The  logicians  who  attempt  to  show  the 
perversion  in  this  figure,  by  speaking  of  higher  and  lower  notions,  are  extra- 
logical.  Logic  knows  nothing  of  higher  and  lower  out  of  its  own  terms;  and 
any  notion  may  be  subject  or  predicate  of  any  other  by  the  restriction  of  its 
extension.  Logic  must  show  the  perversion  in  this  Figure  ex  facie  syUofjismi, 
or  it  must  stand  good.  On  true  reason,  why  no  Fourth  Figure,  see  Aristotle, 
Anal.  Pr.,  L.  i.  c.  2S,  §  8,  and  Pacius,  in  Commentate/. 

(March  1850.)  — Fesapo  and  Fresiso  (also  Fapesmo,  Frisesmo)  proceed  on 
the  immediate  inference,  unnoticed  by  logicians,  that  the  quantities,  apart  from 
the  terms,  may,  in  propositions  In  A  and  Anl,  be  converted. 

Averroes  on  Prior  Analytics^  B.  i.  Ch.  8. 

"  If  we  ask  whether  A  be  in  C,  and  say  that  A  is  in  C,  because  A  is  in  B, 
and  B  in  C  ;  in  this  case,  there  is  a  natural  syllogism  by  general  confession ; 
and  this  in  the  First  Figure. 

"  In  like  manner,  if  we  say  that  A  is  not  in  C,  becan.«c  B  is  in  C,  and  B  is 
not  in  A  ;  it  is  plain  that  we  collect  that  conclusion  by  natural  process  ;  and 
this  is  the  Second  Figure,  which  is  frequently  found  employed  by  men  in  their 
ordinary  discourse. 

"  In  like  manner,  also,  if  we  say  that  A  is  in  C,  because  A  and  C  are  in  B ; 
that  syllogism  is  also  natural  to  us,  and  is  the  Third  Figure.  But  if  we  say  A 
is  in  C,  because  C  is  in  B,  and  B  in  A ;  the  reasoning  is  one  which  no  one 
would  naturally  make,  for  the  reason  that  the  quaesitum  (that  is,  C  to  be  in 
A)  does  not  hence  follow  —  the  process  being  that  in  which  we  say  A  is  in  C, 
since  A  is  in  B,  and  B  in  C ;  and  this  is  something  which  thought  would  not 
perform,  unless  in  opposition  to  nature.  From  this  it  is  manifest  that  the 
Fourth  Figure,  of  which  Galen  makes  mention,  is  not  a  syllogism  on  which 
thought  would  naturally  light "  (etc.).  Thereafter  follows  a  digression  against 
this  figure.  See  also  the  same  book,  Ch.  23d,  and  the  Epitome^  by  Averroes, 
of  the  same,  Ch.  i. 

(c)  FOURTH  FiadRE,-  AUTHORITIES  FOR  AITD  AOAllTST. 

Admitted  by  — 

Ildefonsus  do  Penafiel,  Cursus  Philosophicus,  Disp.  Summul.  D.  iii.  p.  39. 
G.  Camerarius,  Dispul.  Philos.,  P.  i.  q.  xiii.  p.  116.  Port  Royal  Logic,  p.  iii. 
c  8,  and  c.  4.  Ridiger,  De  Sensu  Veri  et  FaLtif  L.  ii.  c.  6,  §  36.  Hauschius  ii» 
Acta  Erud.  ^.  470  et  serj.  Lips.  1728.  Noldius,  Logica  Recognita,  c.  xii.  ]y. 
377.  Crakanthorpe,  Zo(7<Va,  L.  iii.  c.  XV.  p.  194  (omitted,  but  defended).  Lam- 
hert,  Neues  Organon,!.  §237  et  seq.     Hoffh&UQr,  Analytik  der   Urtheile  und 


APPENDIX. 


663 


ScMusse,  §  138.  Twesten,  Logilc,  inshesondere  die  Anahjtik,  §  110.  Leibnitz, 
Opera,  ii.  357  ;  v.  405  ;  vi.  216,  217,  ed.  Dutens.  Oddus  de  Oddis  (v.  Con- 
tarenus.  Nun  Dari  Quart.  Fig.  SijlL,  Opera  Omnia,  p.  233,  ed.  Venet,  1589). 

Rejected  by  — 

Averroes,  In  An.  Pnor,  L.  i.  c.  8.  Zabarella,  Opera  Logica,  De  Qitarta 
Fig.  SglL,  p.  102  et  seq.  Purchot,  Instit.  Phil  T.  I.  Log.  P.  iii.  c.  iii.  p.  169. 
Molinaeus,  Elementa  Logica,  L.  i.  o.  viii.  Facciolati,  Rudimenla  Logica,  P.  iii. 
c.  iii.  p.  85.  Scaynus,  Paraphrasis  in  Organ.,  p.  574.  Timpler,  Logicce  Sys- 
tema,  L.  iv.  c.  i.  qu.  13,  p.  543.  Platner,  Philosophisclie  Aphorismen,  I.  p.  267. 
Burgersdicius,  Inatif.  Log.  L.  ii.  c.  vii.  p.  165.  Derodon,  Logica  Resiituta,  p. 
606.  Wolf,  Phil.  Rat.,  §  343  et  seq.  (Ignored.)  HoUmann,  Logica,  §  453,  p. 
569.  Goclenius,  Prohlemata  Logica,  P.  iv.  p.  119.  Keckermann,  Opera,  T.  L 
Syst.  Log.  Lib.  iii.  c.  4,  p.  745.  Arriaga,  Cursus  Philosophicus,  In  Summulas, 
D.  iii.  §  5,  p.  24.  Aristotle,  An.  Prior,  i.  c.  23,  §  8  ;  c.  30,  §  1  (omitted).  Jo. 
Picus  Mirandulanus,  Conclusiones,  Opera,  p.  88.  Melanchthon,  in  1st  edition 
of  Dialectic,  L.  iii.,  De  Figuratione  (1520),  afterwards  (1547)  restored  (Heu- 
.manni,  Acta,  iii.  753).  Cardinalis  Caspar  Contarenus,  Epistola  ad  Oddum  de 
Oddis,  De  Quart.  Fig.  Syll.,  Opera,  p.  233  (1st  ed.,  1571).  Trendelenburg, 
Elementa  Logica,  §  28,  etc.  Herbart,  Lehrbuch  der  Logik,  Einleit.  3,  §  71. 
Hegel,  Encyclopcedie,  §187.  Fries,  System  der  Logik,  %  57  h.  Griepenkerl, 
Lehrbuch  der  Logik,  §  29  et  seq.  Drobisch,  Logik,  §  77,  p.  70.  Wallis,  Institti- 
tio  Logicce,  L.  iii.  c.  ix.  p.  1 79.  , 


II. INDIRECT    MOODS    OF    SECOND    AND    THIRD    FIGURES.l 


ii. 


in. 


(II.  Fig.) 
''Cesare 
'  Camestres 


Festino 
iv.  j  Baroco 

j         (in.  Fig.) 

i.  {  Darapti 
ii.  I  Felapton 


iii.    /Disamis 
iv.  P-Datisi 


Bocardo 
vi.     Ferison 


Reflexim ;  (1,  2,  5,  8,  9.)2    Cesares. 

Beflexim;  (2,5,8,9.)    Camestre,  Camestres,  Faresmo 

(only  subaltern  of  Camestres) ;  rejected  (2),  admitted 

(3,  6.) 
Premises  reversed;    (2,  3,  4,  5,  6,  7,  8,  9.)    Firesmo, 

Frigeros. 
Premises  reversed;  (2,5,7,8,9.)    Bocardo,  Moracos, 

Forameno. 

Beflexim;  (1,  2,  3,  4,  10, 11.) 

Premises  transposed;    (4,  5,  6,7,  8,  9,  11.)    Fapemo, 

Fapelmos. 
JJe^xim;(4,  7,  10,  11.)  : 

i?e^«rwH.-(4,  7,  10,  11.)  ;■ 

Premises  transposed;  (4,  7,  9, 11.)    Baroco,  Macopos, 

Danorcoc. 
Premises  transposed;  (4,  5,  6,  7,  8,  9,  11.)    Frisemo, 

Fiseros. 


1  The  indirect  Moods  of  the  First  Figure         2  The  numbers  within  brackets  refer  to  the 
are  universally  admitted.  authorities  given  on  following  page.  —  Ed. 


664 


APPENDIX. 


(II.  Fis.) 

1. 

Mart.  Capella 

Cesare,  reflexim. 

2. 

Duns  Scotus 

Cesare  and  Camestres,  conclusions  simply  converted ; 
Festino  and  Baroco.  Rejects  (and  rightly)  what 
has  since  been  called  Faresnio,  as  a  mere  subaltern 
of  Camestres  {An.  Pr.  L.  i.  qu.  23.  See  also  Conim- 
bricenses,  In  Arist.  Dial.  II.  p.  362). 

3. 

Lovanienses,  (153.")) 

Faresmo,  Firesmo. 

4. 

Paciiis,  (1584) 

Firesmo  (on  An.  Pr.  L.  i.  c.  7,  and  relative  place  of  his 
Com.  AnaJ.). 

5. 

Gonirabricenses 

Record  that  indirect  moods  from  Cesare  and  Cames- 
tres; and  also  Friseso,  Bocardo  were  admitted  by 
some  "  recentiores"  (II.  p.  362). 

6. 

Burgersdicius,  (1626) 

Faresmo,  Firesmo. 

7. 

Caramuel,  (1642) 

Moracos,  Frigesos. 

8. 

Scheibler,  (1^53) 

Cosurcs,  Camestres,  Firesmo,  Bocardo. 

9. 

Noldius,  (1666) 

Cesares,  Camestre,  Firesmo,  Foramcno  (he  has  for 
the  direct  mood  Facrono,  in  place  of  Baroco). 

(HI.  Fig.) 

1. 

Apnleius 

Darapti,  reflexim. 

2. 

Cassiodorus 

Do. 

3. 

Isodoms 

Do. 

4. 

Duns  Scotos 

Darapti,  Disamis,  and  Datisi,  their  conclusions  simply 
converted;   Felapton,  Bocardo,  Ferison  (Sup.  An. 
Pr.  L.  i.  qu.  24). 

5. 

Lovanienses 

Fapemo,  Frisemo  (ib.). 

6. 

Pacius 

Fapemo,  Frisemo  (ib.). 

7. 

Conimbricenses 

Record  that  some  "  recentiores"  admit  indirect  moods 
from  Darapti,  Disamis,  Datisi;  also  Fapesmo,  Fri- 
sesmo,  and  Baroco. 

8. 

Burgersdicius 

Fapemo,  Frisemo. 

9. 

Caramuel 

Fapelnios,  Macopos,  Fiseros. 

10. 

Scheibler 

Admits  them  from  Disamis,  Datisi,  Darapti,  but  not 
from  those  which  conclude  particular  negations. 

11. 

Noldius 

Danorcoc  (ho  has  for  Bocardo  Docamroc),  Frisemo, 
Fapemo,  and  what  are  converted   ftom   Darapti, 
Disamis,  and  Datisi  without  names. 

Darapti  virtually  two  moods;  this  maintained  by  Theo- 
phrastns. 

Indirect  moods  are  impossible  in  the  Second  and  Third  Figures,  for  what  are 
called  indirect  conclusions  are  only  the  direct  conclusions.  Mem.,  that  in  the 
Second  Cesare  and  Camestres  are  virtually  one ;  while  in  the  Third  Figure 
Darapti  is  virtually  two,  as  Disamis  and  Datisi  are  one. 


APPENDIX 


665 


For  the  particular  quantification  of  the  Predicate,  useful  illustrations,  as  in 
the  First  from  Fapesmo,  Frisesmo,  or  (in  the  pseudo  Fourth)  from  Fesapo 
and  Fresiso ;  so  in  the  Second  Figure  of  what  have  been  called  the  indirect 
moods  of  Figure  II. 

Figure  U. 
1.  Bocardo. 


2.  Firesmo. 


1.  Baroco. 


2.  Fapemo. 


3.  Frisemo. 


(1853.)  Blunders  of  Logicians.  —  What  have  been  called  the  Indirect  Moods 
of  the  Second  and  Third  Figures,  arise  only  from  the  erroneously  supposed 
transposition  of  the  premises  ;  and  the  Fourth  Figure  is  made  up  of  the  really 
indirect  moods  of  the  First  Figure,  with  the  premises  transposed. 

III.  —  NEW  MOODS  —  NOTES  UPON  TABLE  OF  SYLLOGISMS.^ 

Fig.  I.  vi.  —  Corvinus  {Institutiones  PkilosopJdcE  Rationalls,  1 742,  §  540) 
says  :  —  "  There  sometimes  appears  to  be  an  inference  from  pure  particulars. 
For  example,  Some  learned  are  [some']  ambitious  men ;  some  men  are  [all  the] 
learned;  therefore,  some  men  are  ambitious.  But  the  minor  proposition, 
although  formally  particular,  involves,  however,  a  universal,  to  wit,  its  con- 
verse, —  All  the  learned  are  [some]  men,  —  which  Is  equipollent."  Why  not, 
then,  scientifically  enounce  (as  I  have  done),  without  conversion,  what  the 
thought  of  the  convertend  already  really  and  vulgarly  involved  ? 

In  all  Figures.  —  I  have  not  been  undoubtful  whether  the  syllogisms  of  the 
class  in  which  the  two  premises,  being  tlie  same,  arc  mutually  interchangeable, 
should  be  regarded  as  a  single  or  as  a  double  mood.  Abstractly  considered 
from  all  matter,  the  mood  Is  single;  for  the  two  premises,  however  arranged. 


1  See  Appendix  XI.  —  ED. 

84 


666  APPENDIX. 

afibrd  only  a  repetition  of  the  same  form.  But  so  soon  as  the  form  is  applied  to 
any  matter,  be  it  even  of  a  symbolical  abstraction,  the  distinction  of  a  double 
mood  emerges,  in  the  possible  interchange  of  the  now  two  distinguished 
premises.  To  the  logicians  this  question  was  only  presented  in  the  case  of 
Darapti  (III.  ii.)  ;  and  on  this  they  were  divided.  Aristotle  {An.  Pr.  i.  c.  6, 
§  6)  contemplates  only  one  mood ;  but  his  successor,  Theophrastus,  admitted 
two  (Apuleius,  De  Hah.  Doctr.  Platonis,  L.  iii.  Op.  p.  38,  Elm).  Aristotle's 
opinion  was  overtly  preferred  by  Alexander  (arf  locum,  f.  30,  ed.  Aid.  quoted 
above,  p.  63C),  and  by  Apuleius  (/.  c.)  ;  whilst  that  of  Theophrastus  was 
adopted  by  Porphyrj-,  in  his  lost  commentary  on  the  Prior  Analytics,  and, 
though  not  without  hesitation,  by  Boethius  (Z)e  Syll.  Categ.  L.  ii.,  Op.  pp.  694, 
598,  601,  604).  The  other  Greek  and  Roman  logicians  silently  follow  the 
master ;  from  whom,  in  more  modern  times,  Valla  (to  say  notliing  of  others) 
only  differs,  to  reduce,  on  the  counter-extreme,  Ccsare  and  Camestres  (II.  ix. 
a,  and  x.  b),  and,  he  might  have  added,  Disamis  and  Datisi  (III.  iv.  v.),  to  a 
single  mood  (De  Dial.,  L.  ii.  c.  51).  (For  the  observations  of  the  Apbrodisian, 
see  above,  p.  633  et  seq.) 

To  me  it  appears,  on  reflection,  right  to  allow  in  Darapti  only  a  single 
mood ;  because  a  second,  simply  arising  through  a  first,  and  through  a  transpo- 
sition, has,  therefore,  merely  a  secondary,  correlative,  and  dependent  existence. 
In  this  respect  all  is  different  with  Cesare  and  Camestres,  Disamis,  and  Datisi. 
The  principle  here  applies  in  my  doctrine  to  the  whole  class  of  syllogisms  with 
balanced  middle  and  extremes. 

Fig.  II.  xii.  b.  —  David  Derodon  (Log.  Rest  De  Arg.,  c.  ii.  §  61),  in  canvass- 
ing the  special  rule  of  the  Second  Figure,  —  that  the  major  premise  should  be 
universal,  —  he  now  approbates,  he  now  reprobates  syllogisms  of  this  mood ; 
but  wrong  on  both  alternatives,  for  his  admissions  and  rejections  are  equally 
erroneous.  "  Hie  syllogismus  non  valet :  —  Aliquod  animal  est  [^aliquod]  ration- 
ale ;  sed  [ti//us]  acinus  non  est  [ullus'l  rationalis ;  ergo  [^ullus]  asintis  non  est 
[_aliquod^  animal."  (P.  635.)  The  syllogism  is  valid;  only  it  involves  a  prin- 
ciple which  Derodon,  with  the  logicians,  would  not  allow,  —  that  in  negatives 
the  predicate  could  be  particular. —  (See  Log.  Rest.  De  Argument,  c.  ii.  §  28,  p. 
628.)  Yet  almost  immediately  thereafter,  in  assailing  the  rule,  he  says  :  —  "At 
multi  dantur  syllogismi  constantes  majori  particulari,  qui  tamen  sunt  recti; 
ut,  —  Aliquod  animal  non  est  [Janus']  lapis;  sed  [^omni.s']  adamas  e.it  [^aliquis] 
lapis;  ergo,  [u//u.>}]  adamas  non  est  [aliquod']  animal."  (This  syllogism  is, 
indeed,  II.  iii.  a ;  but  he  goes  on :)  ''  Item :  Aliquod  animal  est  [aliquod] 
rationale;  sed  [idlus]  lapis  non  est  [ullus]  rationalis  ;  ergo  [u/Zits]  laj>is  non  est 
[aliquoiQ  animal."  Now,  tliese  two  syllogisms  are  both  bad,  as  inferring  what 
Derodon  thinks  they  do  infer,  —  a  negative  conclusion,  with,  of  course,  a 
distributed  predicate  (p.  623)  ;  are  both  goo<l,  as  inferring  what  I  suppose 
them  to  infer,  —  a  negative  conclusion  with  an  undistributed  predicate. 

Fig.  III.  viii.  b.  —  Derodon  (//>«</.  §  54),  in  considering  the  Special  Rule 
of  the  Third  Figure,  —  that  the  minor  premise  should  be  affirmative,  —  alleges 
the  following  syllogism  as  *^  cirious :" — ^'Omni.i  homo  est  [aliquod]  animal;  sed 
[ullus]  homo  non  est  [ullus]  asinus ;'  ergo,  [ullus]  a.s-mus   non  est  [aliquod] 


APPENDIX.  667 

animal"  (p.  638).  It  is  a  virtuous  syllogism,  —  with  a  particular  predicate 
(and  not  a  universal,  as  one  logician  imagines)  in  a  negative  conclusion. 
Again  (omitting  his  reasoning,  which  is  inept),  he  proceeds:  —  "Hie  vero 
syllogismus  uon  est  vitiosus,  sed  rectus:  —  l_Omnis']  homo  est  Iquidaml  rationalis, 
sed  \_uUusJ  homo  non  est  \ullus'\  asinus  [or  Dens']  ;  erfjo,  [u//us]  asinus  [or  Deus] 
nan  est  \_quidam2  rational^."  This  syllogism  is  indeed  correct ;  but  not  as 
Derodon  would  have  it,  with  a  distributed  predicate  in  the  conclusion.  That 
his  conclusion  is  only  true  of  the  asinus,  per  accidens,  is  shown  by  the  substitu- 
tion of  the  term  Deus  ;  this  showing  his  illation  to  be  fonnally  absurd. 

Fig.  III.  ii.  —  Derodon  (Ibid.)  says:  —  "Denique,  conclusionem  in  tertia 
figura  debere  esse  particularem,  non  universalem,  statuunt  communiter  Philos- 
ophi;  unde  hie  syllogismus  non  valet;  —  ^Omnis  homo  est  [^quidam]  rationalis; 
sed  omnis  homo  est  [^quoddam]  animal ;  ergo,  omne  \_quoddam~\  animal  est  \_quod~ 
dam]  rationale.'  Verum,  licet  conclusio  sit  universalis,  syllogismus  erit  bonus, 
modo,"  etc.  (p.  638).  The  syllogism  is,  and  must  remain,  vicious,  if  the  subject 
and  predicate  of  the  conclusion  be  taken  universally,  whilst  both  are  undis- 
tributed in  the  antecedent.  But  if  taken,  as  they  ought  to  be,  in  the  conclusion 
particularly,  the  syllogism  is  good.  Derodon,  in  his  remarks,  partly  overlooks, 
partly  mistakes,  the  vice. 

Derodon,  criticizing  the  Special  Rule  of  the  First  Figure,  —  that  the  major 
premise  should  be  universal,  —  says,  inter  alia :  —  "At  multi  dantur  syllogismi 
primae  figuraj  constantes  major!  particulari,  qui  tamen  sunt  recti:  ut,  —  '■Aliquod 
animal  est  [aliquod]  rationale  ;  sed  honm  est  [aliquod]  animal  ;  ergo,  [! !]  homo 
est  [aliquis]  rationalis':  item,"  etc.,  etc.  (p.  627).  This  syllogism  is  vicious ; 
the  middle  term,  animal,  being  particular  in  both  its  quantifications,  affords  no 
inference.' 


XL 

LOGICAL  NOTATION. 

(Seep.  215.) 
I.  —  Lambert's  Linear  Notation.^ 

This  very  defective,  —  indeed,  almost  as  bad  as  possible.  It  has  accordingly 
remained  unemployed  by  subsequent  logicians ;  and  although  I  think  linear 
diagrams  do  afford  the  best  geometrical  illustration  of  logical  forms,  I  have 
found  it  necessary  to  adopt  a  method  opposite  to  Lambert's,  in  all  that  is 
peculiar  to  him.     I  have  been  unable  to  adopt,  unable  to  improve,  anything. 

1°.  Indefinite  or  particular  notions  can  only  be  represented  by  the  relation 

1  Seep.  559. —Ed.  the  schemes  of  Lambert  and   Euler,  see    S. 

2  For  Lambert's  scheme  of  notation,  see  his  Maimon,  Vtrsuch  einer  neuni  Logik,  Sect,  iv., 
jVeuts  Organon,  L  §  21 ;  and  for  a  criticism  of     §  7,  p.  64  et  xeq.     Berlin,  1794.  —  Ed. 


068  APPENDIX. 

of  two  lines,  and  in  two  ways :  1°,  One  being  greater  than  the  other;  2*,  One 
being  partially  out  of  relation  to  the  other.  Instead  of  this,  Lambert  professes 
to  paint  particularity  by  a  dotted  line,  t.  e.,  a  line  different  by  an  accidental 
quality,  not  by  an  essential  relation.  But  not  even  to  this  can  he  adhere,  for 
the  same  notion,  the  same  line,  in  different  relations,  is  at  once  universal  and 
particular.  Accordingly,  in  Lambert's  notation,  the  relation  of  particular 
notions  is  represented  sometimes  by  a  continuous,  sometimes  by  a  dotted  line, 
or  not  represented  at  all.     (See  below,  1*,  1,  2,  3,  4,  5.) 

2°,  The  inconsistency  is  seen  at  all  climax  in  the  case  of  the  predicate  io 
affirmatives,  where  that  term  is  particular.  In  Lambert's  notation  it,  however, 
shows  in  general  as  distributed  or  univei'sal ;  but  in  this  he  has  no  constancy. 
(See  1*,  1,  2,  3,  4.)  But  the  case  is  even  more  absurd  in  negative  propositions, 
where  the  predicate  is  really  taken  in  its  whole  extent,  and  yet  is,  by  the  dot- 
ted line,  determinately  marked  as  particular.     (See  4.) 

3°,  The  relation  of  negativity,  or  exclusion,  is  professedly  represented  by 
Lambert  in  one  line  beyond,  or  at  the  side  of,  another.  This  requires 
room,  and  is  clumsy,  but  is  not  positively  erroneous  :  —  it  does  express  exclu- 
sion. But  his  affirmative  propositions  are  denoted  by  two  unconnected  Hnes, 
one  below  the  other.  This  is  positively  wrong ;  for  here  the  notions  are  equally 
out  of  the  other,  as  in  the  lateral  collocation.  But  even  in  this  he  is  inconsist- 
ent ;  for  he  as  often  expresses  the  relation  of  negativity  by  lines  in  the  relation 
of  higher  and  lower.     (See  below,  1,  4.) 

4°,  He  attempts  to  indicate  the  essential  relation  of  the  lines  by  the  fortuitous 
annexation  of  letters,  the  mystery  of  which  I  have  never  fathomed. 

5°,  He  has  no  order  in  the  relation  of  his  lines. 

The  middle  term  is  not  always  the  middle  line,  and  there  is  no  order  between 
the  extremes. 

This  could  not  indeed  be  from  his  method  of  notation ;  and  except  it  be  ex- 
plained by  the  affixed  letters,  no  one  could  discover  in  his  lines  the  three  com- 
paicil  notions  in  a  syllogism,  or  guess  at  the  conclusion  inferred.     (See  1 — 5.) 

6°,  P'rom  poverty  the  same  diagram  is  employed  to  denote  the  most  different 
moods  in  affirmative  and  negative.     (Compare  2  and  3  with  4.) 

7°,  No  order  in  the  terms  in  the  same  figure. 

8°,  Incomplete.  Lambert  can  represent  ultra-total,  etc.,  included  in  affirma- 
tive, but  not  ultra-total  excluded  in  negative.  Has  the  merit  of  noticing  this 
relation. 

9°,  Lambert  —  but  it  is  needless  to  proceed.  What  has  been  already  said, 
fihows  that  Lambert's  scheme  of  linear  notation  is,  in  its  parts,  a  failure,  being 
only  a  corruption  of  the  good,  and  a  blundering  and  incongruous  jumble  of 
the  natural  and  conventional.  The  only  marvel  is,  how  so  able  a  mathemati- 
cian should  have  pro[)Ounded  two  such  worthless  mathematical  methods.  But 
Lambert's  geometrical  is  worse  even  than  algebraic  notation. 

To  vindicate  what  I  have  said,  it  will  be  enough  to  quote  his  notation  of  the 
moods  of  the  Third  Figure  (I.  p.  133),  which  I  shall  number  for  the  previous 
references. 


APPENDIX.  669 

III.  Figure. 


I.*  Darapti.  .  .  .  .  C c  .  .  .  . 

M m 

.  .  .  .  B b  .  .  .  . 

1.  Felapton.  M mC c 

B b 

2.  Disamis.  B b 

M m 

.  .  .  C 


3.  Datisi.  C c 

M m 

.  .  B 

4.  Bocardo.  B b 

M m 

C 

5.  Ferison.  M m  C c 

.  .  B 


11.  —  NOTATIOX   BY   MaA88. 

Professor  Maass,  of  Halle,'  discontented,  not  unreasonably,  with  the  geomet- 
rical notations  of  Lambert  and  Euler,  has  himself  proposed  another,  compared 
with  which  those  of  his  predecessors  show  as  absolutely  perfect.  It  will  be 
sufficient  to  despatch  this  scheme  with  a  very  few  remarks.  To  use  it  is  wholly 
impossible ;  and  even  the  ingenious  author  himself  has  stated  it  towards  the 
conclusion  of  his  Logic  (§§  495 — 512),  in  the  course  of  which  it  is  not  (if  I  recol- 
lect aright)  honored  with  a  single  reference.  It  is,  however,  curious,  as  the  only 
attempt  made  to  illustrate  Logic,  not  by  the  relations  of  geometrical  quantities, 
but  by  the  relations  of  geometrical  relations  —  angles. 

1°,  It  is  fundamentally  wrong  in  principle.  For  example,  Maass  proposes 
to  represent  coinclusive  notions  — notions,  therefore,  to  be  thought  as  the  same 
—  by  the  angles  of  a  triangle,  which  cannot  possibly  be  imaged  as  united  ;  for 
surely  the  identity  of  the  concepts,  triangle,  trilateral,  and  figure  icith  angles 
equal  to  two  right  angles,  is  not  illumined  by  awarding  each  to  a  separate  corner 
of  the  figure.  On  the  contrary,  coexclusive  notions  he  represents  by  angles  in 
similar  triangles,  and  these  can  easily  be  conceived  as  superposed.  The  same 
may  be  said  of  coordinates.  But,  waiving  the  objection  that  the  different  angles 
of  a  figure,  as  necessarily  thought  out  of  each  other,  are  incapable  of  typifying, 
by  their  coincidence,  notions  to  be  thought  as  coinclusive,  —  it  is  further  evident 
that  the  angles  of  an  equilateral  triangle  cannot  naturally  denote  reciprocal  or 

1  Grundriss  der  Logik,  1793.  I  quote  from  do  of  Maass'  scheme  of  notation;  for  his 
the  fourth  edition,  1S23.  1  regret  the  neces-  Logic  is  one  of  the  best  compends  published 
8ity  imposed  on  me  of  speaking  in  the  way  I     even  in  Germany. 


670  APPENDIX. 

wholly  identical  notions,  in  contrast  to  others  partially  identical ;  for  every  angle 
of  every  triangle  Infers,  —  necessitates,  —  contains,  if  you  will,  —  the  whole  of 
everj'  other,  equally  as  do  the  several  angles  of  an  equilateral  triangle. 

2°,  But  Maass  is  not  consistent.  He  gives,  for  Instance,  a  triangle  (Fig.  12) 
to  illustrate  the  subordination  of  one  notion  to  another ;  and  yet  he  represents 
the  lower  or  contained  notion  by  an  obtuser,  the  higher  or  containing  notion 
by  an  acuter,  angle. 

3°,  The  scheme  Is  unmanifest,  —  In  fact,  nothing  can  be  less  obtrusive.  Il 
illustrates  the  obscure  by  the  obscure,  or,  rather,  it  obscures  the  clear.  Requir- 
ing itself  a  painful  study  to  comprehend  Its  Import  (if  comprehended  it  be), 
instead  of  informing  the  understanding  through  the  eye.  It  at  best  only  addresses 
the  eye  through  the  understanding.  Difficult ;  —  we  only  regret  that  it  had 
not  been  Impossible. 

4°,  It  is  clumsy,  operose,  complex,  and  superfluous.  For,  to  represent  a 
notion  denoted  by  a  single  angle,  it  is  compelled  to  give  the  redundance  of  a 
whole  triangle ;  and  three  repugnant  notions  demand  an  apparatus  of  three 
several  figures,  and  six  vacant  angles.  In  fact,  the  only  manifestation  to  which 
this  scheme  of  angles  can  pretend,  is  borrowed  from  the  scheme  of  figures 
which  it  proposes  to  supersede. 

5°,  It  Is  wholly  dependent  upon  the  accidents  of  foreign  aid.  To  let  it  work 
at  all,  it  calls  in  to  its  assistance  an  indefinite  plurality  of  figures,  a  Greek  and 
Latin  alphabet,  combinations  of  letters  straight  and  deflected,  and  an  assort, 
ment  of  lines,  thick  and  thin,  plain  and  dotted.  I  have  counted  one  diagram 
of  the  eighteen,  and  find  that  It  Is  brought  to  bear  through  three  varieties  of 
line,  four  triangles,  and  eleven  letters. 

It  is  needless  to  enumerate  its  other  faults,  Its  deficiencies,  excesses,  ambigu- 
ities, etc. ;  transeat  in  pace. 

in.  —  The  Author's  Notatioh. 

NO.  1.     LINEAR. 

The  notation  .previously  spoken  of  represents  every  various  syllogism  in  all 
the  accidents  of  Its  external  form.  But  as  the  number  of  Moods  in  Syllogisms 
Analytic  and  Synthetic,  Intensive  and  Extensive,  Unfigured  and  Figured  (and 
of  this  in  all  the  figures),  are  the  same  ;  and  as  a  reasoning,  essentially  identi- 
cal, may  be  carried  through  the  same  numerical  mood,  in  every  genus  and 
species  of  syllogism.  It  seems,  as  we  should  wish  it,  that  there  must  be  possible, 
also,  a  notation  precisely  manifesting  the  modal  process,  in  all  its  essential  dif- 
ferences, but,  at  the  same  time,  In  its  Internal  identity,  abstract  from  every  acci- 
dental variety  of  external  form.  The  anticipation  and  wish  arc  realized,  and 
realized  with  the  utmost  clearness  and  simplicity,  in  a  notation  which  fulfils,  and 
alone  fulfils,  these  conditions.  This  notation  I  have  long  employed ;  and  the  two 
following  are  specimens.  Herein,  four  common  lines  are  all  the  requisites  :  three 
(horizontal)  to  denote  the  terms  ;  one  (two  ?  —  perpendicular),  or  the  want  of  it, 
at  the  commencement  of  comparison,  to  express  the  rjualiti/  of  aflirniatlon  or 
of  negation ;  whilst  (juanlihj  is  marked  by  the  relative  length  of  a  terminal 

1  See  Tabular  Scheme  at  the  end  of  the  present  volume.  —  £d. 


APPENDIX.  671 

line  within,  and  its  indefinite  excurrence  before,  the  limit  of  comparison.  This 
notation  can  represent  equally  total  and  ultra-total  distribution,  in  simple  Syllo- 
gism and  in  Sorites  ;  it  shows  at  a  glance  the  competence  or  incompetence  of  any 
conclusion  ;  and  every  one  can  easily  evolve  it. 


Of  these,  the  former,  with  its  converse,  includes  Darii,  Dabitis,  Datisi,  Disa- 
mis,  Di maris,  etc. ;  whilst  the  latter,  with  its  converse,  includes  Celarent,  Cesare, 
Celanes,  Camestres,  Cameles,  etc.  But  of  these,  those  which  are  represented 
by  the  same  diagram  are,  though  in  different  figures,  formally  the  same  mood. 
For  in  this  scheme,  moods  of  the  thirty-six  each  has  its  peculiar  diagram ; 
whereas,  in  all  the  other  geometrical  schemes  hitherto  proposed  (whether  by 
lines,  angles,  triangles,  squares,  parallelograms,  or  circles),  the  same  (complex) 
diagram  is  necessarily  employed  to  represent  an  indefinite  plurality  of  moods. 
These  schemes  thus  tend  rather  to  complicate  than  to  explicate,  —  rather  to 
darken  than  to  clear  up.  The  principle  of  this  notation  may  be  realized  in 
various  forms.' 

The  problem,  in  general,  is  to  manifest,  by  the  differences  and  relations  of 
geometrical  quantities  (lines  or  figures),  the  differences  and  relations  of  logical 
forms.  The  comparative  excellence  of  any  scheme  in  solution  of  this  problem 
will  be  in  proportion  as  it  is,  1°,  Easy  ;  2°,  Simple ;  3°,  Compendious  ;  4°,  All- 
sufficient;  50,  Consistent;  6°,  Manifest;  7°,  Precise;  8°,  Complete. 

In  the  scheme  proposed  by  me, 

1°,  I  denote  terms  or  notions  by  straight  lines  ;  and,  as  a  syllogism  is  consti- 
tuted by  three  related  notions,  it  will,  of  course,  be  represented  by  three  re- 
lated lines. 

2°,  I  indicate  the  correlation  of  notions  by  the  order  and  parallel  coexten- 
sion  of  lines.  (The  perpendicular  order  and  horizontal  extension,  here 
adopted,  is  arbitrary.) 

3°,  Lines,  like  notions,  are  only  immediately  related  to  those  with  which 
they  stand  in  proximity.  Hence  the  intermediate  line  in  our  diagram,  repre- 
senting the  middle  term  of  a  syllogism,  is  in  direct  relation  with  the  lines 
representing  the  extremes,  whereas  the  latter  are  only  in  mutual  correlation 
through  it. 

4°,  The  relative  quantity  of  notions  is  expressed  by  the  comparative  length 
of  the  related  lines.  In  so  far  as  a  line  commences  (here  on  the  left)  before 
another,  it  is  out  of  relation  with  it,  —  is  indefinite  and  unknown.  Where  a 
line  terminates  under  relation  (here  towards  the  right),  it  ceases  absolutely  to 
be.  A  line  beginning  and  ending  in  relation  indicates  a  whole  notion.  A 
line  beoinninT  before  or  ending  after  its  correlative  indicates  a  part  of  a 


1  neprinted  from  Discussions,  p.  657.    For  a  further  explanation  of  the  relations  denoted 
by  the  diagrams,  Bee  p.  134.  —  Ed. 


672  APPENDIX. 

5",  The  kinds  of  correlation,  Affirmation  and  Negation,  arc  shown  by  tlio 
connection  or  non-connection  of  the  lines  (here  from  the  left).  The  connec- 
tion (here  a  perpendicular  line)  indicates  the  identity  or  coindusion  of  the 
connected  terms ;  the  absence  of  this  denotes  the  opposite.  The  lines  in  posi- 
tive or  affirmative  relation  are  supposed  capable  of  being  slid  into  each  other. 

This  geometric  scheme  seems  to  recommend  itself  by  all  the  virtues  of  such 
a  representation,  and  thus  stands  favorably  contrasted  with  any  other.  For  it 
is  Ccisy,  —  simple,  —  compendious,  —  all-suffiicient,  —  consistent,  —  manifest,  — 
precise,  —  complete. 

1°,  Easy.  —  Linear  diagrams  are  more  easily  and  rapidly  drawn  than  those 
of  figure ;  and  the  lines  in  this  scheme  require,  in  fact,  no  symbols  at  all  to 
mark  the  terminal  differences,  far  less  the  double  letterings  found  necessary  by 
Lambert. 

2°,  Simple.  —  Lines  denote  the  quantity  and  correlation  of  notions  far  more 
simply  than  do  any  geometric  figures.  In  those  there  is  nothing  redundant ; 
all  is  significant. 

3°,  Compendious.  —  In  this  respect  lines,  as  is  evident,  are  far  preferable  to 
figures  ;  but  Lambert's  linear  scheme  requires  more  than  double  the  space  suf- 
ficient for  that  here  proposed. 

4°,  All-sufficient.  —  Any  scheme  by  figures,  and  Lambert's  scheme  by  lines, 
is,  in  itself,  unintelligible,  and  depends  on  the  annexation  of  accidental  sym- 
bols to  enable  it  to  mark  out  the  differences  and  relations  of  terms.  Lambert, 
likewise,  endeavors  to  supply  this  exigency  by  another  means,  —  by  the  fortui- 
tous quality  (his  dottings)  of  certain  lines.  In  our  scheme  lines,  simple  lines, 
and  lines  alone,  are  sufficient. 

6°,  Consistent.  —  Lambert's  linear  scheme  is  a  mere  jumble  of  inconsisten- 
cies. Compared  with  his,  those  by  figures  are,  in  this  respect,  far  preferable. 
But  the  present  linear  scheme  is  at  once  thorough-going,  unambiguous,  and 
consistent. 

6°,  Manifest.  —  In  this  essential  condition^  all  other  geometrical  illustrations 
are  lamentably  defective.  In  those  by  figure,  each  threefold  diagram,  typifying 
an  indefinite  plurality  of  moods,  requires  a  painful  consideration  to  extract  out 
of  it  any  pertinent  elucidation ;  this  is,  in  fact,  only  brought  to  bear  by  the 
foreign  aid  of  contingent  symbols.  Nor  can  these  schemes  properly  represent 
to  the  eye  the  relation  of  the  toto-total  identity  of  a  plurality  of  terms ;  the 
intention  requires  to  be  intimated  by  the  external  accident  of  signs.  Lambert's 
lines  sink,  in  general,  even  below  the  figures,  in  this  respect.  But  as  lines 
are  here  applied,  the  sole  pertinent  Inference  leaps  at  once  to  sense  and  undei^ 
standing. 

7°,  Precise.  —  Ambiguity,  vagueness,  vacillation,  redundancy,  and,  withal, 
inadequacy,  prevail  in  the  other  schemes.  In  those  by  figure,  one  diagram  is 
illustrative  of  as  many  as  a  dozen  moods,  positive  and  negative ;  and  a  single 
mood  may  fall  to  be  represented  by  four  diagrams,  and  perhaps  in  six  several 
ways.  Lambert's  lines  are  even  worse.  In  our  scheme,  on  the  contrary,  every 
mood  has  a  diagram  applicable  to  itself,  and  to  itself  exclusively,  whilst  every 
possible  variety  of  its  import  has  a  corresponding  possible  variety  of  linear 
difference. 

8*^,  Complete.  —  In  this  last  and  all-important  condition,  every    scheme 


APPENDIX.  673 

hitherto  proposed  is  found  to  fail.  A  thorough-going,  adequate,  and  pliant 
geometric  method  ought  equally  and  at  once  to  represent  the  logical  moods  in 
the  Un figured  and  Figured  Syllogism,  in  the  Syllogism  Synthetic  and  Analytic, 
in  Extension  and  Intension,  —  this,  too,  in  all  their  mutual  convertibilities,  and 
in  all  their  individual  varieties.  This  our  scheme  performs,  but  exclusively.  So 
much  in  general.  Again,  in  particular :  —  Of  the  figures,  circles  and  triangles 
are  necessarily  inept  to  represent  the  ultra-total  inclusion  or  coexclusion  of 
terms,  —  in  a  word,  all  the  relations  of  proportion,  except  totality  and  indefinite 
partiality  ;  whilst  quadrilateral  figures  are,  if  not  wholly  incompetent  to  this, 
operose  and  clumsy.  Lambert's  linear  method  is  incompetent  to  it  in  nega- 
tives ;  and  such  inability  ought  to  have  opened  his  eyes  upon  the  defects  of  the 
whole  plan,  for  this  was  a  scheme  which  he  expressly  proposed  to  accomplisL 
The  present  scheme,  on  the  other  hand,  simply  and  easily  affirms  this,  ip 
affirmation  and  negation,  and  with  any  minuteness  of  detail. 


AUTHORS    SCHEME    OF    NOTATION UNFIGURED    AND    FIGURED    SYLLOGISM 

NO.    II. 

(1853.)     The  following  Diagram  (see  p.  674)  affords  a  condensed  view 
of  my  other  scheme  of  Syllogistic  Notation,  fragments  of  which,  in  detail,  will 
be  found  in  Mr.  Thomson's  Outline  of  the  Laws  of  Thought,  and  in  Mr.  Baynes*" 
Essay  on  the  Nciv  Analytic  of  Logical  Forms.     The  paragraphs  appended  will- 
supply  the  necessary  explanations. 

1.)  A  Proposition  (jStdarrifM,  intervallum,  irpSrcuns,  literally  protensio,  the- 
stretching  out  of  a  line  from  point  to  point)  is  a  mutual  relation  of  two  • 
terms  {ppoi)  or  extremes  (&KpoL).  This  is  therefore  well  represented, —  The- 
two  terms,  by  two  letters,  and  their  relation,  by  a  line  extended  between^ 
them. 

2.)  A  Syllogism  is  a  complexus  of  Three  Terms  in  Three  Propositions.  — It 
is,  therefore,  adequately  typified  by  a  Triangle,  —  by  a  Figure  of  three  lines  - 
or  sides. 

3.)  As  upwards  and  downwards  is  a  procedure  arbitrary  in  the  diagram,  the  ■ 
diagram  indicates  that  we  can,  indifferently,  either  proceed  from  the  Premises - 
(rationes)  to  the  Conclusion  (rationatum),  or  from  the  Conclusion  to  the  Prem- 
ises; the  process  being  only,  in  different  points  of  view,  either  Synthetic  or- 
Analytic.  (An  exclusive  and  one-sided  view,  be  it  remembered,  has  given  an, 
inadequate  name  to  what  are  called  Premises  and  Conclusion.) 

4.)  Rationally  and  historically,  there  is  no  ground  for  constituting  that 
Premise  into  Major  which  is  enounced  frst,  or  that  Premise  into  Minor  which 
is  enounced  last.  (See  after,  p.  697,  etc.)  The  moods  of  what  is  called  the 
Fourth  Figure,  and  the  Indirect  moods  of  the  First  Figure,  are  thus  identified. 
In  the  diagram,  accordingly,  it  is  shown,  that  as  right  or  left  in  the  order  of 
position  is  only  accidental,  so  is  first  or  last  in  the  order  of  expression. 

85 


eu 


APFEHriXlX. 


^ 


fro' 


© 


u 


ex. 

Co 


Unflgured  S. 
%      ^      ^ 


© 


Bzvadtk 


mm» 


Order 


Either  or  Neither. 


5.)  The  diagram  truly  represents,  by  its  various  concentric  triangles,  the 
Uh figured  Syllogism,  as  involving  the  Figured,  and,  of  tlie  latter,  the  First 
Figure  as  involving  the  two  others.  (In  fa<?t,  the  whole  differences  of  Figure 
and  Figures  are  accidental ;  Moods  alone  are  essential,  and  in  any  Figure  and 
in  none,  these  are  always  the  same  and  the  same  in  number.) 

6.)  Depth  and  Breadth,  Subject  and'  Predicate,  are  denoted  by  the  thick 
and  thin  ends  of  the  same  propositioual  line. 


7.)  Depth  and  Breadth  are  quantities  always  coexistent,  always  correlative, 
each  being  always  in  the  inverse  ratio  of  the  other.  This  is  well  shown  in  the 
connection  and  contrast  of  a  line  gradually  diminishing  or  increasing  in  thick* 
ness  from  end  to  end. 


XPPENDFX.  676 

8.y  But  though  always  coexistent,  and  consequently  always,  to  some  amount, 
potentially  inferring  each  other,  stitt  we  cannot,  without  the  intervention  of  an 
actual  inference,  at  once  jump  from  the  one  quantity  to  the  other,  —  change, 
per  saltum,  Predicate  into  Subject,  and  Subject  into  Predicate.  We  must 
proceed  gradatim.  We  cannot  arbitrarily  commute  the  quantities,  in  passing 
from  the  Qutesitum  to  the  Premises,  or  in  our  transition  from  the  Premises  to 
the  Conclusion.  When  this  is  apparently  done  (as  in  the  Indirect  moods  of 
the  First  Figure  and  in  all  the  moodc  of  the  Fourth),  the  procedure  is  not  only 
unnatural,  but  virtually  complex  and  mediate;  the  mediacy  being  concealed  by 
the  concealment  of  the  mental  inference  which  really  precedes.  Indicated  by  tlie 
line  and  broken  line  for  the  First  Figure. 

9.)  In  Syllogism,  Figure  and  the  varieties  of  Figure  are  determined  by  the 
counter  relations  of  Subject  and  Predicate  subsisting  between  the  syllogistic 
terms,  —  between  the  Middle  and  Extremes.     All  adequately  represented; 

10.)  Figure  and  the  differences  of  Figures  all  depending  upon  the  difference 
of  the  mutual  contrast  of  Subject  and  Predicate  between  the  syllogistic  terms  ; 
<onsequently,  if  this  relation  be  abolished, — if  these  terms  be  made  all  Sub- 
jects (or  it  may  be  all  Predicates),  the  distinction  of  Figure  will  be  abolished 
also.  (We  do  not  abolish,  be  it  noted,  the  Syllogism,  but  we  recall  it  to  one 
simple  form.)  —  And  this  Is  represented  In  the  diagram.  For  as  the  opposition 
of  Subject  and  Predicate,  of  Depth  and  Breadth,  is  shown  in  the  opposition 
of  the  thick  and  thin  ends  of  the  same  tapering  line ;  so  where  (as  in  the  out- 
most triangle)  the  proposltlonal  lines  are  of  uniform  breadth,  it  is  hereby 
shown  that  all  such  opposition  Is  sublated. 

11.)  It  is  manifest  that,  as  we  consider  the  Predicate  or  the  Subject,  the 
Breadth  or  the  Depth,  as  principal,  will  the  one  premise  of  the  Syllogism  or 
the  other  be  Major  or  Minor;  the  Major  Premise  in  the  one  quantity  being 
Minor  Premise  In  the  other.     Shown  out  in  the  diagram. 

1 2.)  But  as  the  First  Figure  Is  that  alone  in  which  there  Is  such  a  difference 
of  relation  between  the  Syllogistic  Terms, — between  the  Middle  and  Extreme, 
so  in  it  alone  is  such  a  distinction  between  the  Syllogistic  Propositions  realized. 
By  the  diagram  this  Is  made  apparent  to  the  eye. 

13.)  In  the  Unfigured  Syllogism,  and  in  the  Second  and  Third  Figures, 
there  Is  no  difference  between  the  Major  and  Minor  Terms,  and,  consequently, 
no  distinction  (more  than  one  arbitrary  and  accidental)  of  Major  and  Minor 
Propositions.     All  conspicuously  typified. 

14.)  All  Figured  Syllogisms  have  a  Double  Conclusion,  bat  in  the  different 
figares  in-  at  different  way.     Tbi*  is  well  represented. 

15.)  The  Double  Conclusions,  both  equally  direct,  in  the  Second  and  Third 
Figures,  are  shown  in  the  crossing  of  two  counter  and  corresponding  lines. 


676  APPENDIX. 

The  logicians  are  at  fault  in  allowing  Indirect  Conclusions  in  these  two  figures, 
—  nor  is  Aristotle  an  exception.     (See  Pr.  An.,  I.  vii.  §  4.) 

16.)  The  Direct  and  Indirect  Conclusions  in  the  .First  Figure  are  distinctly 
typified  by  a  common  and  by  a  broken  line ;  the  broken  line  is  placed  im- 
mediately under  the  other,  and  may  thus  indicate  that  it  represents  only  ia 
reflex  of,  —  a  consequence  through  the  other  (jcar'  kvdKXaaiv,  rejlexiin,  per 
rejlexionem).  The  diagram,  therefore,  can  show  that  the  Indirect  moods  of 
the  First  Figure,  as  well  as  all  the  moods  of  the  Fourth,  ought  to  be  reduced 
to  merely  mef/i'a^e  inferences;  that  is,  to  conclusions  from  conclusions  of  the 
conjugations  or  premises  of  the  First  Figure.* 


[The  following  Table  affords  a  view  in  detail  of  the  Author's  Scheme  of 
Syllogistic  Notation,  and  of  the  valid  Syllogistic  Moods  (in  Figure),  on  his 
doctrine  of  a  quantified  Predicate.  In  each  Figure  (tliree  only  being  allowed) 
there  are  12  Aflirmative  and  24  Negative  moods;  in  all  36  moods.  The 
Table  exhibits  in  detail  the  12  Affirmative  Moods  of  each  Figure,  and  the  24 
Negative  Moods  of  the  First  Figure,  with  the  appropriate  notation. 

The  letters  C,  T,  each  the  third  letter  in  its  respective  alphabet,  denote  the 
extremes;  the  letter  M  denotes  the  middle  term  of  the  syllogism.  Definite 
quantity  (all,  any)  is  indicated  by  the  sign  (:)  ;  indefinite  quantity  (some)  by 
the  sign  (,  or  ,).     The  horizontal  tapering  line  (■■  )  indicates  an  affirm- 

ative relation  between  the  subject  and  predicate  of  the  proposition.  Negation 
is  marked  by  a  perpendicular  line  crossing  the  horizontal  (■  [  ).  The 
negative  syllogisms,  in  all  the  Figures,  are  exactly  double  the  number  of  the 
affirmative;  for  every  affirmative  affords  a  double  negative,  as  each  of  its 
premises  may  be  marked  by  a  negative.  In  Extension,  the  broad  end  of  the 
line  denotes  the  subject,  the  pointed  end  the  predicate.  In  Comprehension 
this  is  reversed;  the  pointed  end  indicating  the  subject,  the  broad  end  tho 
predicate.  By  the  present  scheme  of  notation,  we  are  thus  able  to  read  a 
syllogism  both  in  Extension  and  in  Comprehension.  The  line  beneath  the 
three  terms  denotes  the  relation  of  the  extremes  of  the  conclusion.  Predesig- 
nation  of  the  conclusion  is  marked  only  when  its  terms  obtain -a  different 
quantity  from  what  they  hold  in  the  premises.  Accordingly,  when  not  marked, 
the  quantification  of  the  premises  is  held  repeated  in  the  conclusion.  In  tho 
Second  and  Third  Figures,  —  a  line  is  inserted  above  as  well  as  below  the 
terms  of  the  syllogism,  to  express  the  double  conclusion  in  those  figures.  The 
symbol  ^-'--r-^  shows  that  when  the  premises  are  converted,  the  syllogism 
remains  in  the  same  mood ;  ^!>-<d  shows  that  the  two  moods  between  whicli 
it  stands  are  convertible  into  each  other  by  conversion  of  their  premises.  The 
middle  term  is  said  to  be  Balanced,  when  it  is  taken  definitely  in  both  premises. 
The  extremes  are  balanced,  when  both  are  taken  definitely ;  unbalanced,  when 
the  one  is  definite,  and  the  other  is  not 

1  Reprinted  from  DiactuHom,  pp.  657—661.  —  Ed. 


APPENDIX.  677 

The  Table  here  given  exhibits  the  author's  final  arrangement  of  the  Syllo- 
gistic Moods.  The  Moods  are  either  A),  Balanced^  or  B),  Unbalanced.  In  the 
former  class  both  Terms  and  Propositions  are  Balanced,  and  it  contains  two 
moods,  —  i. ;  ii.  In  the  latter  class  there  are  two  subdivisions.  For  either,  a), 
the  Terms  are  Unbalanced,  —  iii.  iv. ;  or,  b),  both  the  Terms  and  Propositions 
are  Unbalanced,  —  v.  vi. ;  vii.  viii. ;  ix.  x. ;  xi.  xii. 

It  should  be  observed  that  the  arrangement  of  the  order  of  Moods  given  in 
the  present  Table  differs  from  that  of  the  earlier  scheme  printed  above,  p.  537 
et  seq.     The  following  is  the  correspondence  in  the  order  of  moods : 


Present  and 

Earlier 

Final  Table. 

Table. 

L 

corresponds 

to 

I. 

n. 

u 

u 

n. 

m. 

u 

It 

XI. 

IV. 

u 

ii 

xn. 

V. 

<i 

(( 

vn. 

VI 

(( 

u 

vm. 

VII. 

« 

(i 

HI. 

VIU. 

u 

it 

IV. 

IX. 

«( 

u 

V. 

X. 

« 

it 

VL 

XI. 

« 

(( 

IX. 

xn. 

u, 

u 

X. 

The  order  of  the  earlier  Table  is  that  given  by  Mr.  Baynes,  in  the  scheme  of 
notation  printed  at  p.  76  of  his  Essay  on  (he  New  Analytic.     The  order  of  the 
present  Table  corresponds  with  that  given  by  Dr.  Thomson  in  his  Laws  of  • 
Thought,  p.  244,  3d  edition,  1853.  — Ed.] 


AiPPJ^lJipiX. 


SCHEME    Oi<    i^OTATION-^ 

'.OABI.K   OF  SYLLO- 

A.    AFFIRMS Til^L  MOODS 

Fig.  I.  Fig.  il 


i.  C: .  ;  M  : :Y    C  r—^  :  M  :  ..r 


ii.  C,,, —  :M: ,r    C^i...^  :M: ^,r 


p  ' 


iii.  C. :M,    -    -:r    C,^^ :M,   :r 


iv.  C;~ ,  M  : >r    0:^^  ,  M  :    .,r 


V. c,-^ —  :M,  — ,r  OS- —  -M,  — ,r 


vi.  C. .  M  : ,r    '  \ ,  M  :  .,r 


Vii.  C: :  M  : ,£'    C:- —  :  M  :  — -,F 


viii.  C» :  M  :  ^l''    q»- :  M  ;  ^:p 


ix.  C: :  M. :r    0* •'  M  ,  :l 


v- 


X.  C: ,  M  :  <T    C: ,  M  : 


xi.  C: :  M, ^.r    C; :  M,    ^,r 


1^  xii.  C. ,  M  :  :r    C.—  »  M  :   —.-r 


'yth.  —A.  i.  and  ii.  mre  Balanced    B    ibe  other  moods  are  UnboUaiiced.   Of  these, 


APPENDIX. 


679 


FIGURED    SYLLOGISM. 

GiSTIO    MOODS. 
A.    AFFIRMATIVE  MOODS. 

Fig.  III. 


G:- 
C- 

C:- 


:  M 


-:r 


M 


:M, 


,M: 


C, — -   :M, 


-.T 


c,- 

C:- 

» ■ 
C:- 

»" 

C:- 
C:- 


,M 


:  M: 


:  M: 


:M, 


,M: 


M, 


,r 
>r 

:r 

T 

■> 

.r 

■» 


,  M: 


B.    NEGATIVE  MOODS. 

Fig.  I. 
aC:-4—   :M  :   -.T 


11. 


iii. 


IV. 


V. 


VI. 


vu. 


VIU. 


IX. 


X. 


XI. 


Xll. 


bC: 
aC- 


bC, 

aC,+r 
bC,^^^^ 


M 


M 


M 


M 


M 


■:r 
■,r 
■,r 
.:r 


\bC:— -^M|_4— ,r 

a  C  ,-4^  :  M  ,  — ,  r 

b  C  , :  M  , 

a  C  ,4—  ,  M 
bC, — -  ,M 
J  a  C  :±-  :  M 


bC: 
aC, 
bC, 
aC: 
bC: 
aOl 
bC: 


M 


M 


M 


M, 


M, 


,M: 


,M: 


aC:-f 
bC:- 


:M, 


M, 

+ 


,r 
,r 
,r 
,  r 
,r 
:r 
:r 
:r 
.:r 
:r 

,r 


aC,+-  >M:   :r 

b  c , —  ,  M :  -h- :  r 


lil  and  ir.  are  unbalanced  in  terms  only,  not  in  propositions;  th«  r«st  in  both. 


I  N^  D  E  X. 


Abstract  of  General  Logic,  see  Logic. 

Abstraction  or  Generalization,  what,  88, 
104-5 ;  its  synonyms,  16. 

Academical  Disputation,  493. 

AcciDEKTB,  or  Kxtiinsic  Denominations, 
wliat,  153. 

Acquisition  of  Knowledge,  Doctrine  of,  see 
Logic. 

Affections  or  Passions,  as  a  source  of  error, 
see  Error,  causes  of. 

ArRAMUS,  quoted  on  the  nature  of  experi- 
ence, 444. 

AonicoLA,  Rodolphus,  198. 

Albertus  Magnus,  referred  to  on  genus  of 
Logic,  7;  quoted  on  province  of  Logic, 
20;  quoted  on  quantification  of  predicate, 
553-4. 

Aldrich,  Dean,  his  Compendium,  21 ;  his 
abusive  employment  of  the  terms  hypofluti- 
cal  and  conditional,  167;  his  abuse  of  the 
phrase  propositio  exposita,  185,  249. 

Alexander  of  Aptirodisias,  the  oldest  com- 
mentator on  Aristotle,  4;  refierred  to  as  to 
his  use  of  the  term  \oyiK7\,  ib.;  has  the 
distinction  of  Abstract  or  General  and  Ap- 
plied or  Special  Logic,  38;  bis  illustration 
of  the  distinction,  38-9,  see  Logic;  198, 199; 
on  principle  of  name  of  major  and  minor 
terms,  207,  215, 240 ;  referred  to  on  quantity 
of  hypothetical  syllogisms,  247, 278,  296,  336, 
514;  quoted  on  quantification  of  predicate, 
649;  his  ground  of  the  discrimination  of 
major  and  minor  terms  in  the  second  and 
third  Figures,  628-9;  certain  early  Greek 
logicians  mentioned  by,  who  recognized  no 
major  or  minor  term  in  the  second  and 
third  Figures,  629-30;  (and  Herminus), 
quoted  on  figure  of  syllogism,  633-6. 

Alexander  de  Ales,  or  Alepsis,  held  the 
law  of  Contradiction  I0  be  the  primary 
principle  of  knowledge,  66;  but,  in  fact, 
identified  it  with  that  of  Excluded  Mid- 
dle, ib. 

86 


AlStkdius,  on  the  principle  of  Contradic- 
tion,63;  partially  anticipated  Lambert  in  the 
use  of  parallel  lines  as  logical  notation,  180. 

Alvarez,  326. 

Ammonius  Hermi.*,  referred  to  on  genus 
of  Logic,  7,  89;  on  the  principle  of  Contra- 
diction, 63,  135,  160,  172,  196,  240,  278;  re- 
ferred to  on  the  \6yos  btpi^tav,  or  reaper, 
331,  333,  336;  relerred  to  on  Division  and 
its  various  kinds,  350;  referred  to  on  Greek 
article,  531;  quoted  on  quantification  of 
predicate,  546, 549-51;  quoted  on  Hypothet- 
ical (Conjunctive)  and  Disjunctive  Syllo- 
gisms, 613-16;  (and  Philoponus),  their 
ground  of  the  discrimination  of  major 
and  minor  terms  in  the  second  and  third 
Figures,  628. 

Analogy,  what,  450-51,  453-4;  founded  on 
the  principle  of  Philosophical  Presumption, 
451 ;  its  agreement  with  and  distinction 
from  Induction,  ib.;  has  two  essential  con- 
ditions, 454-5;  summary  of  the  doctrine  of, 
455;  Induction  and  Analogy  compared 
together,  ib.;  these  do  not  atTord  absolute 
certainty,  455-6;  authors  referred  to  on, 
456. 

Analysis,  see  Method. 

Analytic,  name  employed  by  Aristotle  to 
denote  a  particular  part  of  Logic,  6. 

Anaximenes,  of  Lampsacus,  the  treatise 
Rhetoric  to  Alexander  attributed  to,  278. 

Ancillon,  Frederic,  refierred  to,  32. 

Andreas,  Antonius,  the  first  to  explicate 
the  law  of  Identity  as  a  coHrdinate  princi- 
ple, 65. 

Anschauunq,  expresses  what  is  common  to 
Perception  and  Imagination,  as  opposed  to 
Conception,  viz.,  the  individuality  and  im- 
mediacy of  their  objects,  90-1,  129;  can  bu 
translated  into  English  only  by  Intuition, 
but  ambiguously,  90-1- 

Antholwjia  Gr^ca,  280. 

'Atrapi^/jLtjcris,  its  character  and  meaning,  351. 


682 


INDPX. 


Apodeictic,  employed  by  Aristotle  to  denote 
a  particular  part  of  Logic,  6. 

Apophantic,  see  Judgments,  Doctrine  of. 

^Air6<pav(rts,  its  use  by  Aristotle,  159. 

Applied  Logic,  the  expression,  liow  employed 
by  Kant,  43;  can  only  with  propriety  be 
used  to  denote  Special  or  Concrete  Logic, 
and  is  improperly  employed  as  a  designa- 
tion of  Modified  Logic,  43,4^ 

APtTLEius,  296. 

Aquinas,  St.  Thomas,  42;  referred  to  on 
classification  of  the  Categories,  141;  his 
definition  of  truth  quoted,  378. 

Arabian  Schoolmen,  viewed  Logic  as  a 
science,  7. 

'Apxh  TVS  yydaeus,  distinguished  by  Aris- 
totle from  the  apxh  Tiys  ytyfiTfus,  66-7. 

Argument,  properly  denotes  the  middle  no- 
tion in  a  reasoning,  196;  Itow  defined  by  the 
Latin  Sfa^ericians,  ib. ;  oft«u  entployed  as 
coextensive  with  argumentation,  ib. 

Arjstotklic  questions,  ^n  iii,  etc.,  referred 
to,  445. 

Abibtotelians,  ancient  Greek,  denied  Logic 
to  be  either  science  or  art,  7 ;  their  views  on 
the  object-matter  of  Logic,  19,  20. 

Aristotelians,  modern,  many  of  them 
maintained  Logic  to  be  an  art,  7. 

Aristotle,  quoted,  4;  his  employment  of 
the  term  Dialectic,  6;  did  not  define  Logic, 
7;  his  relation  to  views  of  the  nature  and 
domain  of  Logic,  19;  by  far  the  greater 
number  of  his  logical  writings  lost,  19 ;  none 
of  his  treatises  affords  a  view  of  Logic  from 
a  central  point,  ib  ;  gave  no  general  defini- 
tion of  Logic,  ib.;  said  that  medicine  begins 
where  the  philosophy  of  nature  leaves 
ofi*,  26;  emphatically  enounced  tlte  law  of 
Contradiction,  62;  explicitly  enounced  the 
principle  of  Excluded  Middle,  65;  recog- 
nized the  law  of  Reason  and  Consequent, 
66;  distinguished  it  from  the  principle  of 
Production,  6C-7;  said  that  the  doctrine  of 
Syllogisms  deals  not  with  the  external  ex- 
pression, but  with  the  internal  reasoning 
of  the  mind  itself,  82;  see  aho  277;  used 
voiifiaTa  in  a  sense  equivalent  to  concepts. 
85;  his  first  anti-prsedicamental  ruleqiioted, 
103;  this  rule  translated  by  the  Nata  nota 
est  nota  rei  ipsius,  ib.;  hie  Categories,  what, 
189,  see  Categories;  noticed  the  dif1e.rer.ce 
of  Totential  and  Actual  Wholes,  14<i:  i-e- 
f'erred  to  on  inclusion  of  Copula  iu  prasdi- 
cate.  161;  called  subject  and  predicate, 
the  terms  or  extmnes  of  a  proposition,  ib. ; 
culled  a  proposition  on  IntTval,  SitLaTriixa, 
ih.;  allowed  only  four  kinds  of  modality, 
181 ;  described  Sub-contrary  opposition  as 
merely  in  liuiguiigc,  184;  se-'  aUo  632;  his 
conversion  iv  fxtpfi,  186;  noticed  Conver- 
sion per  Contrapositionem,  under  the  name 


of  the  inverse  consecution  from  contradictions, 
ib. ;  his  employment  of  the  term  fK^tats, 
exposition,  185;  his  expression  for  Simple 
Conversion,  186;  his  Jna/.v''"  are  Synthetic, 
195;  see  also  623;  his  definition  of  the  terms 
of  a  Syllogism,  210;  his  definition  of  the 
middle,  as  middle  by  position,  not  applica- 
ble to  the  mode  iu  which  subsequent  logi- 
cians enounce  the  syllogism,  ib. ;  but  appli- 
cable to  the  reasoning  in  comprehension, 
211 ;  did  not,  however,  necessarily  contem- 
plate the  reasoning  in  comprehension,  ib.; 
enounced  the  canons  both  of  Extensive 
and  Comprehensive  reasoning,  214,  243; 
his  law,  —  that  the  whole  is  necessarily 
conceived  as  prior  to  the  part,  —  criticized 
by  the  Author,  254-6;  only  once  vaguely 
alluded  to  the  process  of  what  was  after- 
wards called  Sorites, 267;  his  rule  translated 
■prtKtlicatum  pradicati,  etc., contains  tlje  prin- 
ciple of  Sorites,  268;  did  not  discriminate 
the  vulgar  Entbyroeme  as  a  distinct  species 
of  reasoning,  277;  his  Enthymeme  a  syllo- 
gism from  signs  and  likelihoods,  i6.  ,•  lihet- 
wic  to  Alexander  utiribuied  to,  278;  the  term 
axhf^j  Figure,  due  to,  285;  distinguished 
the  first  three  figiires,  286,  292,  296,  324,  333, 
839;  his  distinction  of  the  two  modes  of 
scientific  procedure  as  from,  and  to,  princi- 
ples, 340,  342;  his  argument  for  slavery  a 
petitio  principii,  371;  referred  to  and  quoted 
on  knowledge  and  belief,  383;  his  precept 
regarding  the  subjugation  of  self-love, 
406,  430,  479;  quoted  on  ability  to  teach  as 
a  mark  of  knowledge,  482;  first  systemati- 
cally developed  Logic  proper,  496;  referred 
to  on  postulates  of  Logic,  512-13;  quoted 
against  quantification  of  predicate,  546-49; 
the  true  meaning  of  his  esse  in  toio,  and  did 
de  omni,  547-8;  his  doctrine  of  predesig- 
uation,  548-9;  syllogisms  in  his  writings 
which  are  valid  only  through  quantifi- 
cation of  the  predicate,  549,  581 ;  his  doc- 
trine of  Induction  and  Example,  689-93; 
ignored  the  Disjunctive  and  Hypothetical 
syllogisms  of  the  logicians,  603;  quoted 
and  referred  to  on  Hypothetical  syllo- 
gism. 612-13;  his  syllogisms  ex  hypotkesi, 
—  wtiether  correspondent  to  tlie  oniinary 
hypothetical  syllogism,— nnthoi-s  referred 
to  on,  613;  his  doctrine  of  the  discrimina- 
tion of  major  and  minor  terms  in  the  second 
and  third  Figure,  627-8;  quoted  on  Figure 
and  Terms  of  syllogisms.  632-3. 

Arnaui.d,  along  with  Nicole,  author  of  the 
Port  Koyal  Logic  (VArtde  Penser),fiO;  re- 
ferred to  as  holding  that  men  arc  naturally 
envious,  408 ;  quoted  on  figure  of  Syllogism, 
641-2. 

Arnoldus  dk  Tdkqbci,  his  doctrine  of  In- 
duction, 696. 


INDEX. 


Arbiav,  referred  to  on  the  argiunent  ciUled 
Kiyoi  Kvpuivv,  33J. 

Arsenics,  334. 

Akt,  aucieiit  and  modern,  diverse  ebanu^ers 
of,  426. 

Association,  laws  of,  what,  419-20. 

Association  or  Suggestion,  as  a  sov^cce  oC 
ilirror,  set  Error,  «auseii  of 

Assumption,  name  for  Minor  Pitiemise,  201; 
but  not  a  suitable  term,  ib. 

Attbntion,  the  act  of,  how  constituted,  88; 
Prescision,  Abstraction,  and  Attention  cor- 
relative terms,  88. 
■  AugustiKj  St.,  his  answer  to  the  question 
what  time  is,  118. 

Acgustjn,  Pscudo,  referred  to  on  inapplica- 
bility of  the  categories  to  Deity,  140. 

AUftUSTINCS  NiPHUS  SUBSSANUS,  C3. 

AuLUS  Gkllius,  331-3. 

AVTHKNTiciry,  criticism  of,  see  Testimony. 

AvERiiOKS,  quoted  on  use  of  the  Arabic 
article  in  quantification.  631-2  ;  quoted  on 
quantification  of  predicate.  .553;  quoted  on 
figure  of  syllogism,  640-1 ;  quoted  on  fourth 
Figure,  662. 

AviCEKNA,  451,  454. 

Axio.MA,used  by  Stoics  and  Bamists  as  a 
synonym  for  proposition^  188. 

A^iujxa  t7js  ewTi<paff(a)s, —  name  applied  by 
Ammonius  and  Philoponus  to  principle  of 
Contradiction,  63  ;  see  Contradiction,  prin- 
ciple of. 

Axioms,  what,  188. 

Bachmann,  referred  to  on  the  analogy  be- 
tween Logic  and  Mathematics,  32, 68,  88, 149, 
162,  179,  183,  198,  215,  218,  219,  237,  243,  288 ; 
quoted,  with  brief  original  interpolations, 
on  the  figures  and  moods  of  Syllogism, 
28S-302;  his  reduction  of  Baroco,  314; 
quoted  on  character  of  ancient  Greek  Soph- 
isms, 323-4,  3'Jl;  quoted  on  the  prejudice 
of  learned  authority,  395-6,  414-17,  428,  440, 
45C. 

Bacon,  Lord,  wholly  misconceived  the  char- 
acter of  Logic  in  certain  respects,  20,  21 ;  at 
fault  in  his  criticism  of  Aristotle's  doctrine 
of  Induction,  230;  called  empirical  gen- 
eralizations axioms,  367  ;  his  classification 
of  the  .sources  of  error,  390;  quoted  on 
reading,  491 ;  the  aim  of  his  Or^anon,  496. 

Ualfour,  or  Balforeus,  referred  to  on  a 
spurious  passage  in  Aristotle's  Rkeioric,  6 ; 
quoted  on  illustration  by  the  Aphrodisian 
of  Abstract  and  Applied  or  Special  Logic, 
38;  on  Abstract  and  Applied  or  Special 
Logic,  44. 

3<^o$)  its  meaning  in  relation  to  concepts, 
100. 

Baumgabten,  a.  C,  the  Leibnitian,  the 
first  to  use  the  terra  principium  exclusi  medii. 


65;  caUed  the  principle  of  Id^itity,  prmeU 
pium  positionis  sive  identitatis,  66 ;  attempted 
to  demoojatrate  the  Jaw  of  Sufficient  Set- 
son  by  that  of  Contradiction,  68, 101 ;  quoted 
on  Canons  of  Syllogism,  564-S. 

Bavn£€(,  Tliomas  Spencer,  his  Essay  on  the 
jVew  Analytic  of  Logical  Forms  referred  to, 
31;  his  translation  of  the  Port  Koyal  Logic 
noticed,  60,  IW\  Itm  Essay  referred  to, 
558. 

Begrifp,  the  term  in  German  philosophy 
for  the  symbolical  notions  of  the  under- 
standing, 129. 

Belief,  see  Truth  and  Error,  doctrine  of. 

Ben  Gekson,  or  Gersonides,  Levi,  quoted «n 
quantification  of  predicate,  £54-5. 

Beneke,  68;  his  doctrine  of  syllogism,  651-2. 

B-ertids,  196,  268. 

Beza,  280. 

BiEL,  Gabriul,  his  use  of  conceptus,  SO. 

BiUNDE,  378. 

BI.EVMISA8,  Nicephorus,  85;  referred  to  on 
origin  of  distinction  of  propositions  jecimt^i 
and  tertii  adj(irentis,l(yi;  quoted  on  import 
of  the  tern*  <rvK\oyt(Tfi6s,  197,  274;  bis  Epit- 
ome for  many  centuries  tlie  text-book  of 
Logic  in  the  schools  of  the  Greek  Church, 
308  ;  mentioned  as  the  inventor  of  the 
Greek  mnemonic  verses  for  mood  and 
figure  of  syllogism,  ib.;  but,  according  to 
later  view,  these  verses  only  a  translation 
of  the  Latin,  ib.,  514;  quoted  on  Contingent 
Conversion,  521. 

BoETHirs,  referred  to  on  the  application  of 
the  term  logic,  4,101,110;  his  division  of 
Conversion,  186;  the  first  to  give  the  name 
Conversio  per  accidens,  ib. ;  nature  of  this 
process  as  employed  by,  186, 198 ;  quoted  for 
use  of  sumptum  and  assumptio,  201 ;  referred 
to  on  use  of  terms  ponnis  and  tolUns,  in 
connection  with  hypothetical  syllogism, 
240,  296,  344;  quoted  on  the  influence  of 
passion  on  the  mind,  400,  614;  quoted  on 
quantification  of  predicate,  551-3. 

Bolzano,  240,  244,  456. 

Boyle,  Hon.  Robert,  referred  to  for  dis- 
tinction of  reason  in  abstraeto,  and  reason 
in  eoncreto,  43. 

BuANDis,  Ch.  A.,  referred  to  on  the  title 
Organon  for  the  logical  treatises  of  Aris- 
totle, 24, 135. 

BuANiss,  Ch.  J.,  184,  320. 

Breadth  and  Depth,  names  for  the  exten- 
sion and  comprehension  of  concepts,  100, 
et  alibi, 

Buchanan,  George,  280. 

BuFFiER,  112,  S44 ;  quoted  on  canons  of  syl- 
logism, 574. 

Burgersdyk,  or  Burgersdicius,  referred  to 
on  genus  of  Logic,  7  ;  his  Institutionat 
LogiccB  noticed  and  recommended,  51,  493; 


684 


INDEX, 


referred  to  on  Whole  and  Part,  143;  quoted 

on  Potential  and  Actual  Whole,  146,  296. 
BUKIDANUS,  his  sopliism  of  the  Ass  referred 

to  the  head  of  Sophisma  Heterozeteseos,  333. 
r.URLEiGU,  Lord,  his  practice  in  reading,  487. 
UuTLKR,  Samuel,  quoted  as  to  the  principal 

utility  of  Rhetoric,  35. 

(.,'a.ietan,  Cardinal,  quoted  for  his  use  of  the 
terms  intensive  and  exUtisive  in  relation  to 
notions,  101. 

Calker,  101. 

Camerarius,  GuL,  referred  to  on  genus  of 
Logic,  7 ;  referred  to  for  scholastic  theories 
on  the  object-matter  of  Logic,  20. 

Campbell,  Puncipal,  quoted  on  indistinct- 
ness of  terms,  124. 

Capella,  Martianus,  quoted  on  figure  of 
eyllogism,  640- 

Caramdel,  see  Lobkowitz. 

Carleton,  Thomas  Compton,  referred  to  on 
the  metaphysical  character  of  the  Categories 
of  Aristotle,  141. 

Caro,  quoted,  407-8,  414,  435. 

Cartesiaks,  majority  of,  maintained  Logic 
to  be  an  art,  7. 

Cassiodorus,  279,  640. 

CATEaoRicAL  Proposition,  better  styled  Ab- 
solute or  Perfect,  165  ;  see  Judgments,  doc- 
trine of. 

Categorical,  the  term,  as  used  by  Aristotle, 
equivalent  to  o^rmati'ce,  1C5;  its  application 
by  Theoplirastus  and  Eudcmus,  in  opposi- 
tion to  conditional,  1G5  ;  this  difference  of 
signification  not  hitherto  observed,  160. 

Categories  or  I'rcdicameuts  of  Aristotle, 
what,  139;  original  meaning  of  the  term 
Category,  ib. ;  its  employment  by  Aristotle, 
130-40;  by  Plotinus,  140;  by  Kant,  ib.;  the 
Categories  of  Aristotle  metaphysical,  141  ; 
criticized  as  a  classiGcation  of  being,  ib.  ; 
object.s  not  included  under,  140;  diversity 
of  opinion  among  logicians  regarding  their 
number,  142  ;  various  authors  referred  to 
regarding,  i6. 

Certainty,  see  Truth  and  Error,  Doctrine 
of. 

Chacvin,  187. 

CiCEUo,  referred  to  on  the  use  of  Logica,  4; 
probably  borrowed  ijis  use  of  that  term 
from  the  Stoics,  ib. ;  quoted  on  the  province 
of  Logic,  26  ;  enounced  the  principle  of 
Excluded  Middle,  65;  recognized  the  prin- 
ciple of  Ilcasou  and  Consequent,  67;  bis 
definition  of  argumtntum  quoted,  196  ;  ap- 
plied the  term  Sorites  to  an  argument  like 
the  modern  Sorites,  but  which  could  also 
be  a  Chrysi/'pean,  268;  called  the  sophism 
Sorites  Acervalis,  ib.  ;  his  employment  of 
the  term  Enthymeme,  278 ;  his  statement  of 
the  Jgnava  Ratio,  S30,  332-3,  400,  480. 


ClECUI.US  m  demonstrando,  see  Probation. 

Classes,  names  for  the  different  steps  in  the 
series  of,  in  physical  s«ieuce,  142. 

Clearmebs  and  Obscurity,  Distinctness  and 
Indistinctness  of  Concepts,  see  Concepts, 
Quality  of. 

Clement  of  Alexandria,  quoted  on  teaching 
as  a  mean  of  self-improvement  in  knowl- 
edge, 482-3. 

Cleuc,  see  Le  Clerc. 

CoGiTATio  ( Thought),  its  use  by  Descartes,  9; 
see  Thought. 

Cognitive  Faculties,  Weakness  and  Dispro- 
portioned  Strength  of,  as  a  source  of  error, 
see  Error.  Causes  of. 

Coke,  Zachary,  his  use  of  the  t«rm  toneept, 
30. 

College  of  Alcale,  the,  see  Cursus  Complu- 
tensis. 

Commcmication  of  Knowledge,  Doctrine 
of,  see  Logic. 

CoMPAEisoic,  Faculty  of,  its  products  three- 
fold,—  Concepts,  Judgments,  and  Season- 
ings, 83;  its  offices,  87-8. 

Comprehension  and  Extension  of  Concepts, 
see  Concepts,  Quantity  of,  and  Reasonings. 

Concept,  should  be  used  to  denote  the  object 
conceived,  30;  its  derivation,  t6. ;  many 
words  in  English  formed  on  the  same  anal- 
ogy, as  precept,  digest,  etc.,  ib. ;  was  in  com- 
mon use  in  the  sense  proposed  among  the 
older  English  philosophical  writers,  ib. ; 
and  among  the  old  French  philosophers, 
31 ;  now  employed  in  French  in  translating 
the  German  Begriff,  ib. ;  see  also  ConcepCus  : 
what,  54  ;  its  synonyms,  55  ;  see  Concepts, 
Doctrine  of. 

Conceptio,  its  meaning,  85-6. 

Conception,  employment  of  the  term  by 
Stewart  to  denote  the  simple  representa- 
tion of  an  object  pre.sented  in  Perception, 
29;  vacillation  in  its  use  by  Reid,  i6. ,-  sense 
in  which  employed  by  the  author,  30  ;  its 
derivation,  30;  means  both  the  act  of  con- 
ceiving and  the  object  conceived,  to. ,-  should 
be  used  to  denote  exclusively  the  act  of  con- 
ceiving, and  concept  applied  to  the  object 
conceived,  t6. ,-  Reid  quoted  on,  78-80;  his 
mistakes  regarding,  80-1;  usually  called  by 
the  logicians  Simple  Apprehension,  85. 

Concepts,  Doctrine  of,  83-88 ;  of  Concepts  or 
Notions,  order  of  discussion,  —  A.  In  gen- 
eral, what  they  are,  and  how  produced,  84 
et  seq.,  93  et  seq.  ;  doctrine  of  Concepts 
omitted  by  Whately  in  his  Elements,  84  ; 
a.  Meaning  of  the  terms  Concept  or  Notion, 
85-6;  their  synonyms,  85;  Concept  denotes 
the  result  of  the  act  of  Conception,  that  is, 
of  comprehending  or  grasping  up  into 
unity  the  various  qualities  by  which  an  ob- 
ject is  characterized,  85-6;  Notion  denotes 


INDEX. 


685 


either  the  act  of  apprehending  the  notes  or 
marks  of  an  object,  or  tlie  result  of  that 
act,  86  ;  employment  of  the  terms  animo 
vel  mente  concipere,  and  animi  eonceptus,  ib.  ; 
of  concipere,  conceptus  and  conceptio,  without 
adjunct,  ib.;  the  term  Notion,  liow  employed 
by  the  author,  t6.;  b.  Nature  of  the  thing 
expressed,  87  et  seq. ;  a  concept  equivalent 
to  the  mediate  and  relative  knowledge  we 
have  of  an  object,  as  comprising  qualities 
or  characters  common  to  it  with  other  ob- 
jects, 87;  nature  and  production  of  concepts 
illustrated  by  reference  to  the  history  of 
our  knowledge,  87  et  seq. ;  the  results  of 
comparison  and  abstraction  or  attention,  as 
operating  on  objects  originally  presented  in 
confused  and  imperfect  perceptions,  and 
reducing  multitude  to  unity,  87-8;  the  je- 
duction  of  multitude  to  unity  involved  in 
conception  explained  and  illustrated,  89  et 
seq. ;  thought  one  and  the  same,  while  its 
contents  are  identical,  ib. ;  objects  are  to  us 
the  same  when  we  are  unable  to  distinguish 
their  cognitions,  whether  as  wholes,  or  in 
their  partial  characters,  89;  concepts  or 
notions  are  constituted  by  the  points  of 
similarity  discovered  in  objects,  and  identi- 
fied in  the  unity  of  consciousness,  90;  con- 
cepts may  themselves  become  the  objects  of 
comparison  and  abstraction,  90;  concepts 
or  notions  superfluously  styled  general,  ib.; 
general  characters  of  concepts,  91  et  seq.,  96 
et  seq. ;  a.  A  concept  alTords  only  an  inade- 
quate knowledge  of  the  thing  thought  under 
it,  91  et  seq. ;  b.  Affords  no  absolute  object 
of  knowledge,  but  can  be  realized  only  by 
being  applied  as  a  term  of  relation  to  one 
or  more  of  the  objects  which  agree  in  the 
point  or  points  of  resemblance  which  it 
expresses,  (6. ;  this  doctrine  explains  the 
whole  mystery  of  generalization  and  gen- 
eral terms,  ib.;  the  generality  of  a  concept 
is  potential,  not  actual,  92-6;  concepts  are 
not,  on  that  account,  mere  words,  97;  c. 
Their  dependence  on  language,  97  et  seq. ; 
language  necessary  to  the  perfection  of 
concepts,  99;  B.  Of  concepts  or  notions  in 
special,  99  et  seq.;  quantity  of  concepts,  100 
et  .leq.;  what  is  meant  by  saying  that  a 
concept  is  a  quantity,  102;  tin's  quantity  of 
two  opposite  kinds,  —  Intensive  or  Com- 
prehensive and  Extensive,  102-10,  see  Con- 
cepts, Quantity  of;  quality  of  Concepts, 
111-31,  s'e  Concepts,  Quality  of;  Recipro- 
cal Relations  of,  132  et  seq.,  see  Concepts, 
Reciprocal  Relations  of. 
Concepts,  Quantity  of,  or  Comprehension 
and  Extension  of  Concepts,  wliat,  100-3; 
how  respectively  designated,  100;  these 
quantities  opposed  to  each  other,  103;  law 
regulating  the  mutual    relations  of,  104; 


this  illustrated,  t6. ;  processes  by  which 
amplified  and  resolved,  —  Determination  or 
Concretion,  Abstraction  or  Generalization, 
Definition,  and  Division,  102-4;  opposed 
in  an  inverse  ratio,  105-6;  Definition  and 
Division  the  processes  by  which  the  Com- 
prehension and  Extension  of  concepts  are 
respectively  resolved,  106-7;  diagram  repre- 
senting, with  relative  illustration,  108-10. 

Concepts.  Quality  of.  111  et  seq. ;  this  deter- 
mined by  their  relation  to  their  subject, 
111 ;  consists  in  their  logical  perfection  or 
imperfection,  111-12 ;  this  of  two  degrees,  — 
Clearness  and  Distinctness,  and  Obscurity 
and  Indistinctness,  112;  these  degrees  dis- 
tinguished, ib.;  original  application  of  the 
expressions,  clearness,  obscurity,  etc.,  ib.; 
illustrated  by  reference  to  vision  and  rep- 
resentation, 112-13,  115-16;  clearness  and 
obscurity  as  in  concepts,  113  et  seq. ;  the 
absolutely  clear  aind  the  absolutely  obscure, 
114;  distinctness  and  indistinctness  of,  ib.  ; 
liistorical  notices  of  this  distinction,  ib.  et 
seq.;  due  to  Leibnitz,  115;  notice  of  Lock© 
in  connection  with  it,  114-15;  difference 
between  a  clear  and  distinct  knowledge 
illustrated,  115  et  seq. ;  the  judicial  deter- 
mination of  life  and  death  supposes  the 
difference  betv»een  a  clear  and  distinct 
knowledge,  116;  further  illustration  from 
the  human  countenance,  ib. ;  special  condi- 
tions of  the  distinctness  of  a  concept,  and 
of  its  degrees,  116-17;  the  distinction  be- 
tween clear  and  distinct  knowledge  illus- 
trated by  examples,  118 ;  how  the  distinct- 
ness of  a  concept  is  affected  by  the  two 
quantities  of  a  concept,  118  et  seq. ;  distinct- 
ness is  internal  and  external,  119;  relations 
of  Definition  and  Division  to  internal  and 
external  distinctness,  ib. ;  simple  notions 
admit  of  an  extensive,  individual  notions 
of  an  intensive,  distinctness,  ib.;  the  high- 
est point  of  the  distinctness  of  a  concept, 
120;  imperfection  to  which  concepts  are 
liable,  in  respect  of  the  thought  of  which 
they,  are  the  expression,  121;  this  imper- 
fection illustrated,  l'-2  et  seq.;  noticed  by 
British  philosophers,  123;  Stewart  quoted 
on  the  subject,  123-5;  Locke  anticipated 
Hume  in  remarking  the  employment  of 
terms  without  distinct  meaning,  125;  Locke 
quoted  on  this  point,  12&-6;  the  distinction 
of  Intuitive  and  Symbolical  knowledge 
first  taken  by  Leibnitz,  126;  this  distinction 
superseded  the  controversy  of  Nominalism 
and  Conceptualism  in  Ccrmany,  126-9;  dis- 
cussed by  him  in  De  Cognitimie,  Veritnte,  ft 
IiJei.t,  127;  the  passage  quoted,  128-9;  the 
distinction  apjjreciated  by  the  disciples  of 
Leibnitz,  129;  Wolfquotcd  on.  129-31. 

Concepts,  Reciprocal  Relations  of,  132-58; 


fN&EX. 


relation  proper  of,  whsrt,  132;  can  be  com- 
pared together  with  reference  only  eiti)er, 
1°,  To  their  Extension,  or,  2°,  To  their 
Comprehension,  ib.;  considered,  A.  As  de- 
pendent on  extension,  132-49;  a« dependent 
on  extension,  concepts  stand  to  each*otl>er 
in  the  five  mutual  relations  of  Exclusion, 
Cbextension,  Subordination,  Coordination, 
and  Intersection,  132;  examples  of  the  five 
mutual  relations  of  concepts,  133-3;  dia- 
grams illustrative  of,  134-;  of  tliese  rela- 
tions, subordination  and  coilrdination  of 
principal  importance,  138;  subordination 
considered,  133-48;  terms  expressive  of  the 
diflerent  modes  of  the  relation  of  subor- 
dination^ 133  et  seq. ;  Superior,  Inferior, 
Broader,  Narrower  Notions,  135;  Univer- 
sal, Particular,  ib.;  General  Notion,  Genus, 
Special  Notion,  Sijecies.  135-6,  ««  Genus 
and  Specie*-;  Co<frdiuatiou,  what,  14S;  the 
tM'o  general  laws  by  which  subordination 
and  coordination  under  extension  arc  regu- 
lated, viz.,  of  Homojreneity  and  Heteroge- 
neity, ib  ;  their  import,  ib  ;  law  of  Hetero- 
geneity, true  only  in  theory,  ib. ;  additional 
law  of  Logical  Affinity  promulgated  by 
Kant;  but  to  be  rejected,  149;  B.  As  de- 
pendent on  comprehension,  but  not  in  the 
relations  of  involution  and  coordination, 
150-8;  notions,  in  relation  to  each  other, 
*re  Identical  and  Different,  150;  identical, 
divided  into  absolutely  and  relatively  iden- 
tical, ib.;  absolutely  identical  notions  im- 
possible, ib: ;  relatively  identical,  called  also 
Similar  and  Reciprocating  or  Cun\<ertiblc, 
ib  ;  notions  are  Congruent  or  Agreeing, 
and  Conflictive,  151;  Congruent  and  Iden- 
tical notions,  and  Diverse  and  Contictive, 
distinguished,  i6.,  see  Concepts,  Opposition 
of;  Intrinsic  and  Extrinsic,  153;  Involution 
and  CoUrdination  in  comprehension.  15S, 
155;  these  relations  of  notions  neglected  by 
logicians,  and  hence  also  neglected  rcasan- 
ing  in  comprehension,  153  et  .vtj. ;  the  rela- 
tion of  the  containing  and  the  contained  in 
comprehension  properly  called  involittion, 
155;  this  illustrated,  156;  the  involving  no- 
tion the  more  complex,  the  involved  the 
more  simple,  157;  coordination  in  compre- 
hension, 157-8;  notions  coordinated  in  com- 
]>rehension  called  Disparate,  in  extension 
Disjunct  or  Discrete,  158. 

Concepts,  Opposition  of,  arises  under  Com- 
prehension, 151  ;  constituted  by  conflic- 
tion,  or  the  impossibility  of  being  con- 
nected in  thought,  i6. ;  twofold,  1=",  Imme- 
diate or  Contradictory ;  2°,  Mediate  orCon- 
trary,  (*. ;  these  distinguished  and  illus- 
trated, 152;  their  logical  significance,  15'J-3; 
.v«  Opposition,  of,  Propositions. 

CoNCBrTUALis.\t  and  Nominalism,  the  whole 


controversy  originated  in  the  amfoignitj'  of 
w-ords,  111.97;  how  to  be  reconciled,  92;  this 
question  not  agitated  in- Germany,  97. 

CoxcKPTUP  i'.s  use  by  IJiel,  Occam,  30;  Con- 
e€f/ius.  and  corufpttrs  animi,  its  meaning,  86- 

CoNCiPKiiK,  its  meaning,  8ft. 

Conclusion,  of  a  syllogism,  \Hiat,  198;  its 
synonyms,  ib. ;  is  the  problem  stated  as  a 
decision,  ib. 

CoscKETK  or  Special  Logic,  !^e  Logic. 

CoxDiLLAC  quoted  on  influence  of  Associa- 
tion, 42;i.  454. 

CoxDiTiONAL  Jirdgment  or  Proposition,  »c 
JudfrniL-ntb-.  Doctrine  of. 

CosoiTiONAL  and  HypotheticnlyXKrintivaKin 
regard  to  the  application  of  the  terms, 
166-7-;  Boethius,  used  conditionnlis  {coni/iUon- 
ai)  and  hypot/uticvt  (/n/pni^iftit^)i\s  convert- 
ible,  167;  ronilitional  to  be  applied  to  the 
genus  as  including  h^poihetical  and  tthjunc- 
tire,  ib. 

CoKFKREKCB,  see  Knowled)^,  DoctrliM'  of 
the  Acquisition  and  Perfecting"  of. 

CONFUCIDS,  his  remedy  for  precipitntiori,  4D3. 

CoNtMBBiCENSES,  184;  their  error  regarding 
the  opposition  of  Boethius  and  Averroes  to 
Aristotle  on  quantification-  of  pr<edieate, 
£53. 

C0N8PECIH8,  what,  148;  in  so  far  as  they  are 
considered  different,  but  not  contradictor}-, 
called  Discrete  or  Dif\)unct  Notions,  ib. 

CoNTiNOKNT  Conversion,  of  the  Lower 
Greeks,  what,  521;  Blemnidas  cited  on,  i6. 

Contra  DICTION,  or  Non-Contradiction,  prin- 
ciple of,  a-  fuudaraentat  law  of  thongtit,  57; 
what,  58;  properly  the  law  of  Non-Contra- 
diction, 59 ;  how  enounced,  ib. ;  the  princi- 
ple of  all  logical  negation  and  distinction, 
t6. ;  differs  IVom  the  law  of  Identity  only 
by  a  negative  expression,  69;  its  historj-, 
62  et  seq. ;  can  be  traced  back  to  Plato,  62; 
emphatically  enounced  by  Aristotle.  62-3; 
with  the  Peripatetics  and  Schoolmen  the 
highest  principle  of  knowledge,  ib. :  ob- 
tained its  name  from  the  Greek  Aristoteli- 
ans, tit.,-  said  by  Ammonins  and  Philopo- 
nus  to  be  the  criterion  which  divides  truth 
from  falsehood  throughout  the  universe  of 
existence,  ib.;  said  by  Suarez  to  hold  the 
same  supremacy  among  the  principles  of 
knowledge  which  the  Deity  does  among  the 
principles  of  existence,  ib. ;  controversies 
touching  its  truth  and  axiomatic  charac- 
ter, 6.3-4;  its  truth  denied  by  modern  abso- 
lutists, 64;  how  viewed  by  Schelling  and 
Hegel,  ib. ;  along  with  that  of  Identity, 
regulateslhe categorical  syllogism, 207,251 ; 
authors  referred  to  on,  508;  conditions  of, 
ib. ;  proof  of.  attempted  by  Clauberg^  *.  ; 
see  Puiidamentnl  Laws  of  Thougbti 

CoNTDS,  Sebastianus,  553. 


nSTBEX. 


687 


Conversion, peritetid»n»,-what,  186;  Conver- 
sion if  fifpfi,  not  the  mere  synonym  of, 

525;  differently  defined  by  different  logi- 
cians, 526;  by  Boethius,  ib. ;  by  logicians  in 
general,  ih. ;  as  ampliative,  not  logical,  520; 
as  restrictive,  fortuitous,  or  not  a  conver- 
Kion,  ib. 
CosVEKSiDN,  of  Judgments  or  Propositions. 
185-8;  what,  185;  ste  oiso  514-15 ;  terms  em- 
ployed to  denote  the  original  and  converted 
proposition,  185;  the  original  proposition 
ought  to  be  called  the  Convertend  or  Con- 
vertible.  the  product  of  the  conversion  the 
Converte.il  or  Converse,  184-6;  ste  also  514-15, 
521-2;  species  of  conversion  distinguished 
by  logicians,  186;  (1),  Simple  or  Pure,  ift.  ,• 
(2),  Conversio  per  Accidens,  ib. ;  this  name 
first  given  by  Boethius,  ib. ;  (3);  Conversio 
per  Conti-apositionem,  j6.  ;  divisions  of,  by 
Boethius,  ib  ;  mnemonic  -vei-ses  for  con- 
version, 186-7;  definitions  of,  in  general, 
514-15;  a  case  of  immediate  inference,  ib.; 
names  for  the  proposition  given  in,  and  its 
product,  515;  best  names  lor  these  together, 
Convertent  or  Converiitif^,  and  for  each  apart, 
ConvfrlentI  and  Converse,  ib.,  522;  errors  of 
the  common  logical  doctrine  of,  two  —  first. 
That  the  quantities  are  not  converted- with 
the  quantified  tenns,515-16,  529  ;  this  wrong 
shown,  1°,  Because  the  terms  of  a  proposi- 
tion are  only  terras  of  relation,  515;  2°, 
Only  compared  as  quantities,  ib. ;  3^,  Quan- 
tity of  proposition  in  conversion  remains 
always  the  same,  515-16,  525;  4°,  Of  no  con- 
sequence logically  whether  subject  or  pred- 
icate placed  first,  516;  second  error  — The 
not  considering  that  the  predicate  has  al- 
ways a  quantity  in  thought  as  well  as  the 
subject,  516-20;  see  also  525-7,  529;  only  one 
species  of,  and  that  thorough-going  and 
self-suflicient,  520  ;  conversio  per  nccidtns,  as 
ampliative,  not  logical,  and  as  restrictive, 
merely  fortuitous,  ib. ;  see  also  526-6,  see 
Conversion  per  accidens;  Conversio  per  con- 
trapositionem  only  holds  through  contradic- 
tion, and  is  independent  of  conversion,  520, 
see  Conversion  per  conUapositionem ;  the 
Contingent  Conversion  of  the  lower  Greeks, 
not  a  con\"ersion,  521,  see  Contingent  Con- 
version ;  advantages  of  the  author's  own 
method  over  those  of  the  logicians,  521-2; 
the  character  of,  as  given  by  Greek  logicians 
subsequent  to  Aristotle  correct,  521;  errors 
of  Aristotle  and  the  logicians  regarding, 
522,  528-9  :  authorities  referred  to  on,  527-«.  j 
CONVKIJSION  per  conlraposilionem,  only  holds 
through  contradiction,  and  is  not  properly 
a  conversion,  620-21,  528;  held  by  some  to 
be  mediate,  520;  this  erroneous,  ib.  ;  rules 
for,  520-1;  historical  notices  of^  and  au- 
thors referred  to  on,  id. 


CoNVERsroN  ^v  fiepfi,  its  meaning  in  Aris- 
totle, 525-6. 

Coordination  of  concepts,  see  Cotcepts, 
Relations  of.- 

COPUI.A,  the  logical,  what,  K31-2 ;  included 
in  the  predicate  by  Aristotle;  ib. ;  styled 
the  Appredieate,  irpotTKaTTiyopoufifvov,  161; 
that  negation  does  not  belong  to,  held  by 
some  logicians,  177;  the  opposite  doctrine 
maintained  by  the  author,  ib. ;  true  import 
of,  177-8;  origin  of  the  controversy  jegard- 
ing  tlie  place  of  negation,  178;  its  msaning 
in  Comprehensive  and-  Extensive:  proposi- 
tions, 193. 

CouAx  and  Tisias,  case  of,  referred  to,  334. 

Corollaries,  what,  188. 

CoRViNUS,  quoted  on  inference  from  pure 
particulars,  665. 

CocsiN,  Victor,  his  contradictions  on  the 
cognition  of  tJie  Absolute,  61. 

Crakanthorpb,162;  referred  to  on  names 
of  propositions  in  conversion,  186j  229,  261; 
his  doctrine  of  Induction,  596. 

Crellius,  38,  230,  243,  342. 

Crenius,  402,  483i 

Criticism,  Art  of,  see  Testimony. 

Crousaz,  399^  quoted  in  illustration  of  pre- 
cipitancy, 402-3;  quoted  on  sloth  as  a  source 
of  error,  404,  430,  435. 

Crpsius,  Christi&n  August,  411  ;  quoted  on 
canons  of  syllogism,  561-3. 

Cv R8US'  Complutensis,  referred  to  on  induction 
of  Aristotle,  594. 

CuSTOjr,  power  of,  as  a  source  of  error,  see 
Error,  Causes  of. 

D'Abra  de  Raconis,  referred  to  for  scholas- 
tic theories  of  the  object-matter  of  Logic, 
20. 

Damascenus,  Joannes,  5  ;  referred  to  on 
method  in  Logic,  341. 

Damiron,  his  Logique,  50. 

David,  the  Armenian,  referred  to  on  thecat- 
egoriesi  142. 

Darjks,  or  Daries,  25;  referred  to  on  prin- 
ciple of  SuflScient  Reason,  68. 

De  Morgan,  A.,  Letter  of  Sir  "W.  Hamilton 
to,  587. 

Definite  and  Indefinite  Propositions,  as  un- 
derstood by  the  author,  171-2, 175,  see  Judg- 
ments, Propositions. 

Definition,  or  Declaration,  the  analysis  of 
the  comprehension  of  a  concept,  104-6;  doc- 
tHne  of,  341-2;  what,  ib.:  the  terms  declaration 
and  definition  express  the  same  process  in 
different' aspects,  ib. ,-  definition  in  its  strict- 
er sense,  342;  this  explicated,  ib  ft  seq.;  va- 
rious names  of —  Declaration,  Explication, 
Exposition,  Description,  Definition  Proper, 
ib. ;  Nominal,  Real,  and  Genetic,  what, 
342-3;  rules  of,  341;  these  explained,  ib.  et 


688 


INDEX, 


seq.;  first  rule,  844-6;  second  rale,  345-6; 
third  rule,  346;  circular  definition,  346-9; 
fourth  rule,  346-7;  fifth  rule,  347-8;  Defini- 
tion, in  its  looser  sense,  348-;  Dilucidations 
or  Explications,  ib. ;  Descriptions,  348-9. 

Deoerando,  Baron,  68,  123,  366. 

Delariviere,  his  Logigue,  50;  referred  to 
on  definite  article  in  relation  to  quantifica- 
tion, 531. 

Dexzinger,  Ignatius,  referred  to  on  Catego- 
ries, 142,  184,  187;  quoted  on  modes  of 
faUacia  sejvius  compositi  tt  dU'isi,  326-7,  333. 

Deuodon,  David,  referred  to  on  Whole  and 
I'art,  143,215;  quoted  on  quantity  of  dis- 
junctive and  hypothetical  propositions,  237, 
244,  247;  held  syllogism  and  enthymeme  to 
be  the  same  species  of  reasoning,  276,  289, 
291.  311;  his  method  of  reducing  Camestres 
to  Barbara, 314;  notice  of,  559;  his  polemic 
against  the  special  rules  of  syllogism,  560; 
quoted  on  Induction,  594;  his  criticism  of 
the  special  rules  of  the  figures  reviewed, 
636-7. 

Desca  RTE8,  quoted  regarding  the  extension 
of  the  terra  Thought  {cogitatio),  9;  quoted  on 
the  means  of  avoiding  error,  388;  his 
doubt,  393;  his  precept  to  doubt  all,  898-9; 
conditions  which  modify  its  application, 
399. 

Determination,  or  Concretion,  what,  lOi-6; 
its  synonyms,  ib. 

Dialectic,  ancient  name  (with  certain  limi- 
tations) for  Logic,  5;  its  use  by  Plato,  ib.; 
its  origin,  ib. ;  its  use  by  Hegel,  6;  by  Aris- 
totle,—  the  logic  of  probable  matter,  6; 
mistakes  regarding  the  use  of  the  term  by 
Aristotle,  t6. ,-  employed  in  a  vacillating 
mnnner  by  the  Stoics,  6. 

AtoAcKTifrf;  X'^P^^  irpayfidroty,  equal  to  Ab- 
stract or  General  Logic,  38,  see  Logic. 

AtaKtKTiKij  iv  xPV<^fi  foi  yvfivoffltf  trpcey- 
IxJltwv,  equal  to  Special  or  Applied  Logic, 
38,  see  Logic. 

Dicta  de  Omni  tt  de  NuUo,  the  canons  of 
deductive  categorical  syllogisms  in  exten- 
.sion,  214;  how  expressed,  ib. ;  logicians 
who  confound  the  Dictum  de  Omni  with 
the  Nota  Kota;,  etc.,  575;  who  make  the 
Dictum  the  fundamental  rule  of  syllogism 
in  general,  575-6,  J*e  Syllogism;  who  con- 
found or  mnkc  coordinate  the  law  of  Pro- 
portion or  Analogy  with,  576;  who  restrict 
the  Dictum  to  the  first  figure  (immediately), 
»/>.  ,•  who  make  the  Dicta  the  supreme  can- 
ons for  universal  syllogisms,  i6. ;  who 
erroneously  suppose  Aristotle  to  employ, 
besides  the  Dictum,  the  rule  of  Proportion 
as  a  fundamental  law  of  syllogism,  ifc.  ;  how 
enounced  by  Noldius,  577;  by  Keu.«ch,  i6.  ; 
by  Aristotle,  ib  ;  by  Jac.  Tbomasius,  ib.; 
otijeotions  to,  678. 


Diderot,  quoted  on  memory,  418. 

Dilemma,  see  Uypotbetico-disjunctire  sjrllO' 
gism. 

Dilemmatic  judgment  or  proposition,  tee 
Judgments. 

Diogenes  Laertius,  referred  to  on  genus  of 
Logic,  7;  attributed  the  invention  of  Soph- 
ism Sorites  to  Eubulides,  268,  324,  331-3; 
referred  to  on  the  Platonic  definition  of 
man,  347,  3G9. 

Diagrams  of  Ammonius.  637;  erroneously 
referred  to  Faber  Stapulcnsis,  it. 

Dialogue,  492,  see  Knowledge,  Doctrine  of 
the  Acquisition  and  Perfecting  of. 

DiOKVsins  of  Ualicarnassus,  bis  employment 
of  the  term  enthymeme,  278. 

DiONYSics  Cato,  on  teaching  as  a  means  of 
self-improvement  in  knowledge,  483. 

DiscussioKS  on  Philosophy,  Author's,  referred 
to  for  scholastic  theories  on  object-matter 
of  Logic,  £0;  on  the  character  of  Dr. 
Whately's  Elements,  21,  22;  referred  to  fer 
a  later  development  of  the  author's  doc- 
trine on  the  Logical  Laws,  70,  75, 196, 2907; 
referred  to  on  history  of  Latin  and  Greek 
mnemonic  verses  for  Mood  and  Figure  of 
Syllogism,  308. 

Disjunctive  Reasoning  or  Syllogism,  first 
class  of  Conditional  Syllogisms,  and  second 
class  afiiorded  by  Internal  Form  of  Syllo- 
gism, 231 ;  a  reasoning  whose  form  is  deter- 
mined by  the  law  of  Excluded  Middle,  and 
whose  sumption  is  accordingly  a  disjunctive 
proposition,  either  of  Contradiction  or  of 
Contrariety,  ib. ;  either  affirmative,  consti- 
tuting the  Modus  Ponens.  or  Modus  ponendo 
toUens,  or  negative,  constituting  the  Modus 
ToUenSfOT  Modus  tollendo  ponens,  ib.;  mne- 
monic verses  for  these  modes  of,  ib. ;  its 
definition  explicated,  ib.  etseq  ;  a  syllogism 
with  disjunctive  major  premise  is  not  neces- 
sarily a  dii'junctive  reasoning,  231-2;  gen- 
eral view  of,  232  et  seg. ;  formula  for  a  syllo- 
gism, a.  With  two  disjunct  members,  ib.; 
b.  With  more  than  two  disjunct  members, 
233-4;  the  principle  of,  234;  the  several 
parts  of,  235;  the  rules  of,  235-6;  these 
explicated,  236  et  seg. ;  first  rule  of,  236; 
second  rule  of,  237;  third  rule  of,  237-8; 
the  disjunctive  syllogism  of  comprehension 
and  extension,  t6. ;  though  specially  regu- 
lated by  the  law  of  Excluded  Middle,  still 
the  other  logical  laws  /operative  in,  252; 
may  be  drawn  in  all  the  four  figures,  319; 
this  illustrated, 319-20;  its  character  accord- 
ing to  author's  latest  view.  604-5,  612-13, 
614,  see  Hypothetical  Reasoning  or  Syllo- 
gism. 

Disputation,  see  Knowledge,  Doctrine  of 
the  Acquisition  and  Perfecting  of 

Division,  the  analysis  of  the  Extension  of  a 


INDEX. 


689 


concept,  105-7;  doctrine  of,  350-9;  division 
ill  general,  wliat,  300-1;  of  two  specifs, 
Partition  and  Logical  Division,  351;  parti- 
tion eitlier  Keal  or  Ideal,  351-2;  examples 
of  these  two  liinds  of.  351;  logical  division, 
what,  352-3;  its  rules,  353;  its  cliaracter 
and  rules  explicated,  ib.  tt  seij. ;  the  end  of, 
is  Distinctness,  which  involves  Complete- 
ness of  thinking.  354;  as  many  kinds  of 
possible  as  there  are  characters  affording 
a  principle  of  division,  iO.;  a  universal 
noiion  tlie  only  object  of,  ib.;  general  prob- 
lem of,  354-5;  rules  of,  353  et  seq.;  these 
classified,  356;  those  spiingiiig,  i.),  from 
the  principle  of  division,  —  first,  second, 
and  third  rules,  35f!-7;  ii.),  from  the  rela- 
tions of  the  diviiling  members  to  the  divided 
wholes,  —  fourth  and  fifth  rules,  358;  iii), 
from  the  relations  of  the  several  dividing 
members  to  each  other,  —  sixth  rule,  ?6.; 
iv.),  from  the  relations  of  tlie  divisions  to 
the  subdivision. —  seventh  rule,  859. 

Doubt  or  doubting,  the  art  of  doubting  well 
difficult  to  teach  and  to  learn,  303,  <■  e  Error, 
Causes  of,  Descartes. 

DowxAJi,  330;  referred  to  on  Aristotle  and 
Plato's  views  of  method,  SIC'. 

Drobiscit,SS;  referred  to  on  opposition  of 
concei)ts,  151 ;  on  coordination  of  notions 
iu  comprehension,  155,  15S,  179,  219,  320, 
351. 

DUXCAN,  William,  of  Aberdeen,  his  Logic, 
50. 

DUNCAX,  Mark,  240,  244,  261,  311;  reduced 
Camestres  to  Celarent,  and  Baroco  to  Ferio 
by  counterposition,  314. 

ExcYCLOPvEDiA  Britannica,  81  et  nlibi. 

Enxoematic.  see  Concepts,  Doctrine  of. 

"Ej/i/oia,  ivv6i]fjia.  v6ri,ua,  umbijiuous,  85. 

K.NTUYMEMK.  a  syilo;;ism  detective  in  exter- 
nal form,  275;  the  common  doctrine  of 
logicians  regarding,  ib. ;  this  doctrine  fu- 
tile, and  erroneously  attributed  to  Aristotle, 

276  et  seq. ;  1°,  Not  a  special  form  of  rea- 
soning, 276;  2^,  Distinction  of,  as  a  special 
form  of  reasonirhg,  not  made  by  Aristotle, 

277  et  seq.;  the  enthymeme  of  Aristotle, 
what,  ib. ;  various  applications  of  the  term, 
by  Dionysius  of  Halicarnassus,  author  of 
Rhetoric  to  Alexander,  Sopater  Apameensis, 
Aulus  Gellius,  Cicero,  Quintilian,  278; 
denoted,  with  some  of  the  ancients,  a  syllo- 
gism with  some  suppres.sed  part,  as  the 
Aphrodisian,  Ammonius,  Philoponus,  Pa- 
chymcres,  Quintilian,  Ulpian,  Scholiast  on 
Ilermogenes,  it. ,-  3°,  Admitting  the  validity 
of  the  discrimination  of  the  Enthymeme, 
it  cannot  be  restricted  to  a  .syllogism  of  one 
suppressed  premise,  279;  examples  of,  of 
the  first,  second,  and  third  order,  ib. ;  epi- 

87 


grammr.tic  examples  of,   with  suppressed 
conclusion,  280-1. 

Epicheiuk.ma  or  Eeason-Keudering  Syllo- 
gism, the  first  variety  of  complex  syllogism, 
what,  259;  authors  referred  to  on  varia- 
tions ill  the  application  of  the  name,  220; 
in  Aristotle  the  term  is  used  for  a  dialectic 
syllogism,  ib. :  as  a  polysvllogism  compara- 
tively simple,  274;  may  be  drawn  in  any 
figure,  320. 

Epictetu.'?,  332;  fallacies  mentioned  by,  i7;. 

Erasmus,  his  advice  to  a  young  man  on  the 
conduct  of  his  studies^402. 

Enizzo,  Sebastiano,  25. 

EuNESTi,  435. 

Eitr.OR,  .■iee  Truth  and  Error,  Doctrine  of. 

Enaon,  Causes,  Occasions,  and  Komedies  of, 
390 ;  Uacon's  classification  of  the  sources  of, 
390;  its  causes  and  occasions  comprehended 
in  one  or  other  of  four  classes,  —  1'^,  In  the 
general  circumstances  which  modify  the 
intellectual  character  of  the  Individual;  2^, 
In  the  Constitution,  Habits,  and  llelationsof ' 
his  powers  of  Cognition,  Feeling,  and  De- 
sire; 3^,  In  Language  as  an  Instrument  of 
Thought  and  Medium  of  Communication; 
or,  4°,  In  the  nature  of  the  objects  about 
which  his  knowledge  is  conversant,  393-1; 
these  considered  in  detail,  £91  et  .^eq. ;  I. 
General  circumstances  which  modify  the 
intellectual  character  of  the  individual,  ib. 
et  seq.;  these  of  two  kinds, —  1^,  The  par- 
ticular degrees  of  cultivation  to  which  his 
nation  lias  attained  ;  2°,  The  stricter  associ- 
ations, as  schools,  sects,  etc.,  391 ;  these  illus- 
trated, 391-400;  man  by  nature  social,  and 
influenced  by  the  opinion  of  his  fellows, 
391-2;  I'ascal  quoted  on  the  power  of  Cus- 
tom, 392;  an  ingenious  philosopher  quoted 
on  the  same  subject,  392-0;  the  art  of 
doubling  well  difficult  to  learn  and  to 
teach,  393-4;  two  general  forms  of  the 
influence  of  example,  394,  —  (1)  I'rejudice 
in  favor  of  the  Old,  394-5;  (2)  Prejudice 
in  favor  of  the  Kew,  895;  Prejudice  of 
Learned  Authority,  395-6;  means  by  which 
the  influence  of  Society  as  a  source  of  Error 
may  be  counteracted,  398  (t  seq. ;  necessary 
to  institute  a  critical  examination  of  the 
contents  of  our  knowledge,  ib. :  the  pre- 
cept of  Descartes  on  this  point,  ib.  et  seq.; 
conditions  which  modify  its  application, 
399;  a  gradual  and  progressive  abrogation 
of  prejudices  all  that  can  be  required  of 
the  student  of  philosophy,  ib.  II.  The 
Constitution,  Habits,  and  Reciprocal  Rela- 
tions of  the  Powers  of  Cognition,  Feeling, 
and  Desire,  400;  of  two  kinds,  —  i.  The 
undue  preponderance  of  the  Affective  Ele- 
ments of  Mind,  400  et  seq.;  influence  of  pas- 
sion on  the  mind,  ib  ;  Boetbius  quoted  oni 


690 


INDEX. 


this  influence,  ib.  ;  the  possibility  of  error 
limited  to  Probable  Keasoning,  401;  the 
PuEsions  as  sources  of  error  reduced  to  four, 
401-2;  1  Precipitancy,  402  et  seq.  ;  Seneca 
quoted  on,  ib.  ;  Erasmus  quoted  on,  ib. ;  il- 
lustrations of,  from  Seneca,  Montaigne, 
402-3;  precipitate  dogmatism  and  Fkepti- 
cism  phases  of  the  same  disposition,  403; 
remedy  for  precipitation,  ib.;  2.  Sloth,  ib.  ; 
Seneca  quoted  on,  404;  its  remedy,  ?6. ;  3. 
Hope  and  Kcar,  ib. ;  how  these  passions 
operate  unfavorably  on  the  Understand- 
ing, 405;  4.  Self-love,  including  Vanity, 
Piide,  etc.,  406  (t  seq.;  Aristotle's  precept 
regarding  this  passion,  ib. ;  illustrations 
of  the  ii.fluence  of  Self-Love  on  our  opin- 
ions, 406-7  i  Self-Love  leads  us  to  regard 
with  favor  the  opinions  of  those  to  whom 
we  aie  in  any  way  attached,  406;  ilale- 
branche  adduced  to  this  effect,  406-7;  this 
shown  especially  when  the  passion  changes, 
408;  Arnauld  holds  that  man  is  naturally 
envious,  ib. ;  the  love  of  Disputation,  ib. ; 
the  affections  now  mentioned  the  immedi- 
ate causes  of  all  error,  409;  preliminary  con- 
ditions requisite  for  the  efliciency  of  pre- 
cepts against  the  sources  of  error,  409-10; 
rules  against  errors  from  the  Affections,  410. 
Weakness  and  Disproportioned  Strength 
of  the  Faculties  of  Knowledge,  411-31; 
neglect  of  the  limited  nature  of  the  Human 
Intellect  a  source  of  error,  411  tt  srq.;  (1) 
Philosophy  of  the  Absolute,  411-12;  (2)  A 
one-sided  view  of  the  linilude  of  the  mind, 
412  tisfq.;  this  illustrated  by  reference  to 
the  two  contradictories,  —  the  absolute  com-  i 
mencement  and  the  infinite  nou-com- 
moncement  of  time,  412;  the  same  priHci- 
l)lc  exemplified  in  the  case  of  the  necessita- 
rian argument  against  the  freedom  of  the 
human  will,  413;  and  in  the  case  of  the 
libertarian  argument  in  behalf  of  free-will, 
ib. ;  weakness  and  disproportioned  strength 
of  the  several  Cognitive  Faculties,  as  a 
source  of  error,  414  et  seq. ;  these  faculties 
of  two  classes  —  a  Lower  and  a  Higher,  ib. ; 
A.  The  Lower  Class,  i6.  et  seq.;  (1)  The 
Prcsentative  Faculty,  of  two  kinds,  t6.  ,•  a. 
External  Perception,  as  a  source  of  error, 
ib.  et  seq.;  conditions  of  its  adequate  activ- 
ity, 415;  precautions  with  a  view  to  detect- 
ing illusions  of  the  Senses,  and  obviating 
the  errors  to  which  they  lead,  415-16;  b. 
Self-Consciousness,  as  a  source  of  error. 
416  ft  «ei?.;  this  power  varies  in  intensity  ac- 
cording to  time,  state  of  health,  and  object, 
i6. ;  (2)  Jlemory,  as  a  source  of  error,  417 
tt  feq. ;  as  feeble,  417;  as  too  strong,  417-18; 
remedies  for  these  opposite  extremes,  418; 
(3)  The  Ueproductive  Faculty,  of  two  kinds, 
419;  a.  Uemiuiscence,  as  a  source  of  error. 


ib. ;  its  undue  activity,  ib  ;  its  inactivity, 
ib.;  b.  Suggestion  or  Association,  as  a 
source  of  error.  419  et  seq. ;  influence  of  As- 
sociation in  matters  of  Taste,  421;  Stewart 
quoted  on  this  influence,  421-3;  Condillac 
quoted  on  the  same,  423:  'S  (Jravesandc, 
Herodotus,  and  Justin,  referred  to  on  the 
same,  423-4;  only  remedy  for  the  influence 
of  Association  is  the  Philosophy  of  tlie 
Human  Mind,  424-5;  (4)  Imagination,  as  a 
source  of  error,  426  et  seq  ;  its  necessity  in 
scientific  pursuits,  420;  defect  in  the  art  of 
modern  times  as  compared  with  that  of 
ancient,  arising  from  imperfect  culture  of 
imagination,  426-7;  errors  arising  from  the 
disproportion  between  imagination  and 
judgment,  427  ft  seq. ;  those  arising  from  the 
weakness  of  imagination,  427;  from  its  dis- 
proportionate vivacity,  ib.;  remedies  for 
these  defects, /A.  ,•  IJ.  Higher  faculties,  428 
etseq.;  (5)  Elaborative  Faculty  as  a  source 
of  Error,  ib.  et  seq  ;  error  does  not  lie  iu 
the  conditions  of  our  higher  faculties,  but 
is  possible  in  the  a])plication  of  the  laws  of 
those  faculties  to  determinate  eases,  428-9, 
defective  action  of  the  understanding  may 
arise  from  one  of  three  causes;  a.  Natural 
feebleness,  b.  Want  of  necessary  experi- 
ence, c.  Incompetency  of  attention,  429; 
(6)  Regulative  Faculty  not  properly  a 
source  of  error,  430;  remote  sources  of  er. 
ror  in  the  different  habits  determined  by 
sex,  age.  bodily  constitution,  education, 
etc.,  ib  ;  (elected  examples  of  these,  —  a 
one  sided  cultivation  of  the  intellectual 
powers,  i6. ;  this  exemplified  in  three  differ- 
ent phases,  —  in  exclusive  cultivation,  1. 
Of  the  powers  of  observation,  2.  Of  meta- 
physics, 3.  Of  mathematics,  431;  Stewart 
referred  to  on  the  two  latter  errors,  ib. ; 
III.  Language  as  a  source  of  error,  432-9; 
its  general  character  considered  with  a  view 
to  show  how  it  becomes  the  occasion  of 
error,  432-4;  in  what  sense  language  is 
natural  to  man,  432-3;  difiiculty  as  to  the 
origin  of  language,  433;  language  has  a 
general  and  a  special  character,  434 ;  no  lan- 
guage is  a  perfect  instrument  of  thought, 
ib.;  languages,  from  their  multitude,  difii- 
culty of  tlieir  acquisition,  inadequacy,  am- 
biguity of  words,  are  sources  of  error,  ib.; 
this  illustrated,  4;i5  et  .^eq. ;  signs  nece.«- 
sary  for  the  internal  o|K'ration  of  thought. 
435;  and  for  itscomnuiijic:;tioi),  ih. .-  intona- 
tions of  the  voice  the  only  adequate  sen- 
sible symbols  of  thought  and  its  commu- 
nication, ib  ;  these  inarticulate  and  artlc- 
Blate,  438;  the  latter  constitute  Langnng* 
Proper,  ib.;  how  this  is  a  source  of  enor. 
ib. :  the  ambiguity  of  words  the  prlnri> rl 
source  of  error  originating  in.  ih. ;  two  cii- 


INDEX. 


691 


cumstanccs  under  this  head  which  mutually 
p.fTect  encli  other,  43")-";  the  vocabulary  of 
every  laiigunge  necessarily  finite,  and  tlie 
conscquer.ces  of  this;.  437 ;  words  are  merely 
hints  to  the  mind,  437-8;  remedy  for  error 
.  arising  from  language,  438-9;  IV.  The  Ob- 
jects of  our  knowledge  a  source  of  error, 
439;  rules  touching  the  causes  and  reme- 
dies of  our  false  judgments,  439-40. 

r.ssExcE,  Ksseutials,  or  Internal  Deuomiua- 
tioi'.s,  what,  153. 

I-lSPL-R,  quoted  ou  the  distinction  of  the  mat- 
ter aiid  form  of  thought,  11;  on  tlie  latter 
as  the  object  of  Logic  to  the  exclusion  of 
the  former,  11-12;  on  the  laws  of  thought 
an  thought  as  strictly  the  object  of  Logic, 
12-13;  quoted  on  the  distinction  of  logical 
and  metaphysical  truth.  75-7;  referred  to 
on  relation  of  concepts  to  their  origin  as 
direct  or  indirect,  100-1;  quoted  on  the 
clearness  and  obscurity  of  concepts,  113-14; 
quoted  on  the  special  cor.ditions  of  the  dis- 
tinctness of  a  concept,  117-18,  119;  quoted 
on  the  highest  point  of  the  distinctness  of  a 
concept,  120;  quoted  on  the  impossibility 
of  notions  absolutely  identical,  151 ;  quoted 
on  the  agreement  and  difference  of  con- 
cepts and  judgments,  162-3, 174;  quoted  on 
certain  ultra-logical  distinctions  of  propo- 
sitions, 187-8;  quoted  on  the  act  of  reason- 
ing, 189-90;  quoted  on  the  general  condi- 
tions of  syllogism,  197;  quoted  on  the  form 
of  syllogism  as  a  ground  of  its  division 
into  sp.ecies,  203-4 ;  on  the  laws  regulating 
tlie  various  kinds  of  syllogisms,  204,  215; 
quoted  ou  positive  and  contrary  opposition 
in  a  di.«junctive  reasoning,  233;  on  the 
principle  of  the  disjunctivesyliogism,  234-5; 
on  the  several  parts  of  the  di.>^junctive  syl- 
logism, 234-5;  quoted  on  the  peculiar  prin- 
ciple of  the  hypothetical  syllogism,  241-2; 
quoted  on  the  first  rule  of  hypothetical  syl- 
logisms, 215-6;  on  the  ground  on  which  the 
hypothetical  syllogism  has  been  regarded 
as  having  only  two  terras  and  two  propoti- 
tions,  246-7;  quoted  on  relation  of  syllo- 
gisms to  each  other,  2.58;  quoted  on  Epi- 
cheirema  and  Sorites,  258-9,  323;  quoted  ou 
division  in  general,  350-2;  ou  logical  divi- 
sion, 354-5  ;  quoted  ou  the  rules  of  division, 
351-9;  quoted  on  rules  of  division  spring- 
ing from  relations  of  dividing  members  to 
the  divided  wholes,  358;  on  the  relation  of 
the  several  dividing  members  to  each  other, 
359;  on  the  rule  of  division,  —  Divisio  ne. 
Jiat  persaUum,Sb9-G0;  quoted  on  the  difier- 
ences  of  probations,  364-0;  on  pure  and 
empirical  probations,  366;  quoted  on  dis- 
tinctions of  probations  from  tlieir  internal 
form,  367-8 ;  on  probations,  under  the  in- 
ternal   form,  as   synthetic    aud    analytic, 


369-70,  380,  385,  442;  quoted  on  experience 
and  observation,  444-9;  quoted  on  induc- 
tion aud  analogy,  451,  452,  453;  quoted  on 
sum  of  doctrine  of  induction,  453  ;  quoted 
on  induction  aud  analogy  as  not  airordiiig 
absolute  certainty,  465-6;  quoted  on  testi- 
mony, 456-9,  460;  quoted  on  credibility  of 
testimony  in  general,  460-4;  on  testimony 
in  special,  461-7;  quoted  on  criticism  and 
interpretiitiofi,  469-75;  quoted  on  specula- 
tion as  a  means  of  knowledge,  476-7. 

EcDEMUS,  referred  to  on  use  of  the  term  cate- 
gorical,165;  his  nomenclature  of  the  parts 
of  the  hypothetical  syllogism,  241. 

EuGENios,  or  Eugenius,  85, 101, 142;  referred 
to  on  the  distinction  of  Potential  and 
Actual  in  relation  to  notions,  14,5-0;  quoted 
on  import  of  the  term  crvWoyiaixhs,  197, 
198,  230. 

EuLEU,  employed  circular  diagrams  as  logi- 
cal Botatiou,  180  ;  but  not  the  first,  ib. 

EuSTACHiCS,  referred  to  ou  Method  in  Logic, 
3il. 

EUSTRATIUS,  336. 

Example,  Aristotle  quoted  on,  591. 

Excluded  Middle,  or  Third,  principle  of,  a 
fundamental  law  of  thought,  57;  what,  59; 
its  logical  significance,  59-60;  the  principle 
of  disjunctive  judgments,  60 ;  its  history, 
62  et  seq. ;  can  be  traced  back  to  Plato,  62, 
65;  explicitly  enounced  by  Aristotle,  65; 
enounced  by  Cicero,  ib. :  received  tlie  ap- 
pellation by  which  it  is  now  known  at  a 
comparatively  modern  date,  probably  from 
Baumgarten,  65;  regulates  in  conjunction 
with  that  of  Reason  and  Consequent  Hypo- 
thetico-disjusictive  Syllogisms,  204-5;  deter- 
mines the  form  of  the  Disjunctive  Syllo- 
gism, 231,  252;  authors  referred  to  on,  508; 
whether  identical  with  law  of  Contradic- 
tion, ib. ;  whether  a  valid  and  legitimate 
law,  50S-9;  see  Fundamental  Laws  of 
Thought. 

Exclusive  and  Exceptive  Particles,  what, 
and  their  effect  as  indirectly  predesignating 
the  predicate,  517;  authorities  referred  to 
on,  518;  .ife  Propositiones  Exponibiles. 

ExPEKiEKCE,  Sfe  Knowledge,  Doctrine  of  the 
Acquisition  and  Perfecting  of. 

Experiential  or  Experimental  Proposi- 
tions, what,  188. 

Facciolati.  135, 139;  quoted  on  the  mean- 
ing and  distinction  of  categoricum,  vagum, 
and  trnnacenilens,  140;  referred  to  on  Cate- 
gories, 142 ;  referred  to  on  Whole  and  Part, 
143, 160,  193,  219,  260,  261,  268,  330,  331,  369; 
quoted  on  Induction,  595. 

Fallacies,  what,  321;  of  two  kinds, —  Pa- 
ralogisms and  Sophisms,  ib. ;  this  distfno- 
tion  not  of  strictly  logical  import,  223;  but 


692 


INDEX, 


not  without  logical  value,  ib. ;  divided  into 
Formal,  Material,  and  those  at  once  Formal 
and  Material,  ib. ;  Material,  lie  beyond  the 
Jurisdiction  of  Logic,  ib. ;  Ancient  Greek 
Sophisms,  their  character,  323-4;  consid- 
ered in  detail  in  as  far  as  they  lie  within  a 
single  syllogism,  325  ft  seg. ;  I.  Formal  Fal- 
lacies. Categorical,  325-7;  first  subordinate 
Class, — those  consisting  in  quattrnione  Ur- 
tninorum,  325;  under  this  genus  are  com- 
prised three  species,  1^,  Fallacia  sensus 
eompositi  et  divisi,  325-6;  modes  of  this 
fallacy,  32G;  2°,  FuUacio  a  dido  secundum 
quid  ad  dictum  simpltciter,  ib.  ;  3^,  Fnllaeia 
figurer,  diciionii,  327;  II.  Material,  327-34; 
of  two  kinds,  —  1.)  Of  an  Unreal  Universal- 
ity, 327-8;  2.)  Of  Unreal  3Iiddle  or  Reason, 
828;  these  kinds  of,  coincide,  328-9;  this 
fiillacy  as  dangerous  in  its  negative  as  5n  its 
positive  form,  329 ;  species  of  this  fallacy,  — 
1°,  Sophisma  cum  hoc,  vel  post  hoc,  ergo  propter 
hoc,  329-30;  2°,  Ignava  Ratio,  330-1;  the 
history  of  this  fallacy,  831;  its  vice,  331-2; 
8°,  Sdp/iisma  pol'jzeteseos,  332;  its  various  I 
designations,  ib. ;  4"^,  Sophistna  hcterozeteseos,  j 
i6. ,- it-i  various  narmes,  333 ;  its  character,  i6.,-  | 
the  Litlgiosiis,  ib. ;  illustrated  in  the  case  of  i 
Protagoras  and  Euathlus,  333-i ;  and  in  the 
parallel  case  of  Corax  and  Tisias,  SSi; -ue 
Probation,  Doctrine  of. 

Fear,  see  Error,  Causes  of. 

Feueklin,  referred  to  on  principle  of  Suffi- 
cient Reason,  68. 

FtcnTE,  placed  the  law  of  Identity  as  the 
primary  principle  of  all  knowledge,  66. 

Figure,  of  Syllogism,  constituted  by  the 
place  which  the  middle  term  holds  in  prem- 
ises, 281-2,  285;  the  Four  Figures  ari.se 
from  the  relative  positiui:s  of  the  middle 
term,  282;  formulic  of  the  Figui-os  in  Com- 
prehension and  Extension,  ib. :  mnemonic 
verses  for  these  in  Comprehension  and 
Extension,  ib. ;  the  name  trxvt'M,  fs«re, 
given  by  Aristotle,  285;  the  first,  on  the 
prevalent  doctrine,  not  properly  a  figure, 
t6. ,-  three  figures  distinguished  by  Aristotle, 
ib.;  fourth  uftributod  to  Ciulen,  but  on 
slender  authority,  285,  423;  first  notice  of 
Fourth  Figure  by  Averroes,  285;  complex 
modification  of  Figure  by  the  Quantity  and 
Quality  of  the  propositions,  or  the  Mood, 
of  a  reasoning,  286,  see  Mood  of  Syllogism; 
doctrine  of  the  Figures  according  to  the 
logicians,  and  in  Extension  alone,  288-302; 
symbol  by  letters  of  the  First  Figure,  288; 
rules  of  First  Figure,  28S-9;  legitimate 
moods  of  First  Figure,  with  circular  dia- 
grams illustrative  of,  289-90;  Second  Fig- 
ure, its  symbols,  291:  its  rules,  291-2;  its 
legitimate  moods,  with  diagrams,  292-3; 
Third  Figure, — its  symbol,  294;  its  rules, 


294-5;  its  legitimate  moods,  with  diagrams, 
295-8;    Fourth  Figure,— its  symbol,  299; 
its    rules,  299-300;    its    legitimate  moods, 
with  diagrams,  300-2;    whatever  figure  is 
valid  and  regular  in  Extension  is  also  valid 
and  regular  in  Comprehension,  302;  criti- 
cism of  the  foregoing  doctrine  of  Figure, 
ib  ft  seq  ;  the  Fourth  Figure, —  repudiated 
by  the  great  majority  of  the  rigid  Ariiitotel- 
ians,  3f)2;  logicians  not  in  possession  of  the 
grounds  on  which  this  figure  may  be  set 
aside,  303;  grounds  on  which  tl-.e  Fourth 
Figure  ought  to  be  disallowed,  ib.  et  seq.; 
a  cross  inference  possible  from  Extension 
to  Comprehcr.sion,  and  vice  versa,  303;  this 
the  nature  of  the  inference  in  the  Fourth 
Figure,  304;   this  proved  and  illustrated, 
804-5;   this  hybrid  inference  is,  —  1°.  Un- 
natural; 2",  Useless;  3',  Logically  invalid, 
305;  general  character  of  the  Second,  Third, 
and  Fourth  Figures,  307;   the  last   three 
figures  only  the  mutilated  expressions  of  a 
comjjlex  mental  proce.es,  and  virtually  iden- 
tical with  the  first,  308-9  et  seq. ;  this  shown 
in  detail,  310-11.  but  «;<  Mood  of  Syllogism; 
Figure  in   i-elatiou   to  Hypothetical,  Dis- 
junctive, and  llypothetico-Disjunctive  Syl- 
logisms, 318-20;  of  no  account  in  varying 
the  S)  llogism,  620-7;  double  conclusion,  in 
Second  and  Third  Figures,  627-31;  grounds 
on  which  it  has  been  attempted  to  establisli 
the  discrimination  of  a  major  and  minor 
term    in  the  Second  and    Third    Figures, 
627  et  seq.:  Aristotle,  628;  Ammonius  and 
I'hiloponus,  ib  ;  llcrminus,  ib.;  Alexander 
Aphrodisicnsis,  628-9;    Scotus,  629;    Men- 
dozu,  ib.:  anticipatory  recognitions  of  the 
truth  that  there  is  no  major  or  minor  term 
in  the  second  and  third    figures,  629-Sl; 
by  certain  early  Greek  logicians,  629;  by 
Valla,  629-30;    by  John  Sergeant,  C30-S1 ; 
historical  notices  regarding  figure  of  sylio- 
gi<m.  632:  Ari.stotle,  632-3;  Alexander  and 
Herniinus,  033-0;    IMiiloponus  (or  Ammo- 
nius). 037-9;  MartianusCapclla,  639-40;  Isi- 
dorus,640;  Averroes,  040-1 ;  Melanchthon, 
641;  Arnauld, 641-2;  Gro.«ser.642;  Lambert, 
643;  Platner.  646-7;  Fries,  647-9;  Iv rug  and 
lieneke,  649-52;   Tithis,  662-8;    direct  and 
indirect  moods  in  lirst  and  fourth  figure, 
658;  but  not  in  second  and  third,  (4.  ,•  fourth 
figure,  —  its    character,   659;    authors    by 
whom  held  that  fourth  figure  diifors  from 
fii-st  only  by  transposition  of  preni.jcs,  ib  ; 
moods  of  fourth  figure  redressed,  659-61; 
criticism  of  fourth  figure,  062;  authorities 
for  and  against  this  figure,  662-3. 

First  Figure,  see  Figure. 

Fischer,  186;  referred  to  on  coBrdination  of 
notions  in  Comprcliensiou,  155-8. 

FlSCHABEU,  486. 


INDEX. 


693 


Fontaine,  La,  quoted,  390. 

FONSECA,  r..  184,  207,  21G,  289,  292,  325;  re- 
ferred to  as  against  the  doctrine  of  a  mate- 
rial quantification  of  the  predicate  in  recip- 
rocating propositions,  543. 

Formal  Induction,  see  Induction. 

Foii-MAL  Trutli,  see  Truth  and  Error,  Doc- 
trine of. 

FoH.MAL  and  Material,  their  distinction,  539- 
42. 

FoDRTH  Figure.  .<;'e  Figure. 

Fkies,  43;  on  principle  of  Double  Negation, 
68,  149,  203.  215,  243,  249,  2G1,  364,  380,  385, 
428,435,  450;  quoted  on  Canons  of  Syllo- 
gism, 570-2;  quoted  on  Figure  of  Syllogism, 
647-9. 

Fundamental  Laws  of  Thought,  order  of 
their  consideration,  57;  these  tour  in  num- 
ber,—  1.  Identity,  2.  Contradiction  or  Non- 
Contradiction,  3.  Excluded  Middle,  4.  Rea- 
son and  Consequent,  or  Sufficient  Keason, 
57  ft  set},  (but  see  61);  their  history,  62-8, 
iw  these  Laws  ;  general  observations  in 
relation  to,  09  et  set/.;  these  fall  into  two 
cla.«ses,  the  first  class  consisting  of  the  three 
principles  of  Identity,  Contradiction,  and 
Excluded  Middle,  the  second  of  the  princi- 
ple of  Reason  and  Consequent  alone,  ih.  : 
this  classification  founded,  1°,  On  the  differ- 
ence of  connection  Ijetween  the  laws  tliem- 
eelves,  70;  2°,  On  the  diflerence  of  the  ends 
which  the  two  classes  severally  accomplish, 
ib. ;  two  counter  opinions  regarding  the 
limits  of  objective  possibility,  71;  the  re- 
fpeotive  spheres  of  the  two  classes  of  the'' 
laws  of  thought  defined  and  illusi rated,  71 
ft  se(j. ;  to  deny  the  universal  application 
of  the  fiist  three  laws  is  to  subvert  the 
reality  of  thought,  71;  but  this  is  not  in- 
volved in  the  denial  of  the  universal  appli 
cation  of  the  law  of  Reason  and  Ccn-sequent, 
72  et  seg.:  this  law  shown  in  general  not  to 
be  the  measure  of  objective  possibility ,  72-5; 
by  reference  to  Extension,  P,  As  a  whole, 
72-3;  distinction  of  positive  and  negative 
thought,  73;  this  law  not  the  criterion  "of 
objective  possibility  shown  by  reference  to 
Extension;  2°,  As  a  part,  74 1  3^,  I5y  reference 
to  the  law  of  Reason  and  Consequent  itself, 
74-5;  this  law  reducible  to  a  higher  princi- 
ple, 75;  summary  statement  of  the  spheres 
of  these  laws,  75;  the  general  influence 
which  the  foregoing  laws  exert  on  the 
operations  of  thinking,  7.5-7;  the  highest 
criterion  of  non-reality,  but  no  criterion  of 
reality,  76;  erroneously  held  to  be  the  posi- 
tive standard  of  truth,  ib.;  the  absolutists 
proceed  on  their  subversion,  77;  the  whole 
of  these  laws  operative  in  each  form  of 
syllogism,  although  certain  of  them  more 
prominently  regulate  each  various  form, 


251-2;  their  relations,  506;  authors  on,  in 
general,  ib. ;  of  two  kinds,  —  the  laws  of  the 
Thinkable,  and  the  laws  of  Thinking,  507; 
that  they  belong  to  Logic,  ib. ;  on  order  and 
mutual  relation  of,  ib. ;  by  whom  intro- 
duced into  Logic,  ib. ;  in  particular,  authors 
on,  507;  see  Identity,  Contradiction,  Ex- 
cluded Middle. 

Gale,  Theophilus,  326. 

Galex,  the  fourth  figure  of  syllogism  attrib- 
uted to,  but  on  slender  authority,  285,  302; 
new  logical  treatise  of,  285. 

Galileo,  his  rebuke  of  the  Professor  of 
Fadua.  406. 

Galluppi,  quoted  on  canon  of  syllogism, 
574. 

Gassendi,  330,  332,  338;  referred  to,  on 
Method  in  Logic,  .341. 

Gellius,  see  Aulus  Gellius. 

General  or  Abstract  Logic,  see  Logic. 

Generalization,  what,  90;  its  whole  mys- 
tery explained,  91,  see  Concepts,  Doctrine  of. 

Generic  and  Specific  Difference,  see  Genus 
and  Species. 

Gknerification  and  Specification,  limited 
exjjressions  for  the  processes  of  Abstraction 
and  Determination,  considered  in  a  partic- 
ular relation,  135-8;  depend  on  the  two 
laws  of  Homogeneity  and  Heterogentjity, 
148;  see  Genus  and  Species. 

Genetic  Definition,  see  Definition. 

Ge\ovesi.  or  Genuensis,  referred  to  on  one 
science  being  the  instrument  of  another.  25; 
his  Latin  Logic  noticed,  51,  474. 

Gknue.nsis,  .<iee  Genovesi. 

Genus  and  Species,  or  General  and  Special 
notion,  what  and  how  designated,  1.35-6; 
the  distinction  of,  merely  relative,  138-7; 
the  ab.straction  which  carries  up  species 
into  genera,  called  Generification  or  Gener- 
alization, 136-7;  the  determination  which 
divides  a  genus  into  its  species,  called  Speci- 
fication, 137-8;  gradations  of  genera  and 
species,  and  their  designations,138;  Supreme 
.  or  Most  General  genus,  what,  ib. ;  Subal- 
tern or  Intermediate  genus,  what,  ih.  ; 
Lowest  or  Most  Special  species,  what,  ib.  ; 
Subaltern  or  Intermediate  species,  what, 
ib.  ;  these  distinctions  taken  from  Porphy- 
ry's Introduction  to  the  Categories,  139;  a 
genus  as  containing  under  it  species,  or  a 
species  as  containing  under  it  individuals, 
is  called  a  Logical,  Universal,  Subject, 
Subjective,  or  Potential  whole,  142;  an 
individual  as  containing  in  it  species,  or  a 
species  as  containing  in  it  genera,  is  called 
a  Metaphysical,  Formal,  or  Actual  whole, 
142-3;  these  distinctions  illustrated,  143  et 
seq.,  see  Whole;  Generic  and  Specific  Dif- 
ference, 146-7 ;  as  contradistinguished  from 


694 


INDEX. 


Individual  Difference,  147 ;  Conspecies, 
what,  148;  the  classification  of  tilings  by 
genera  and  species  governed  by  two  laws 
—  viz.,  of  Homogeneity  and  of  Heteroge- 
neity, 148;  a  third  law  alleged  by  Kant  — 
Tiz.,  of  Logical  Affinity  or  continuity,  but 
rejected,  149  ;  Gcnns  and  Difference,  the 
elements  of  Definition  Proper,  342-3. 

Georgk  of  Trebisoud,  or  Oeorgius  Trape- 
zuntiu.s,  described  the  process  of  Sorites, 
but  gave  it  no  appropriate  name,  269. 

Gerlach,  58. 

Gibbon,  his  practice  in  reading,  489-90. 

Gleio,  Dr.,  mistook  Keid's  view  of  Concep- 
tion, 81. 

GocLEXius,  Rodolphn.o,  discovered  and  sig- 
nalized the  Kegressive  Compreliensive 
Sorites.  273;  but  before  him  tbia  given  by 
I'acius,  344. 

Godwin,  quoted  on  composition  as  a  means 
of  intellectual  improvement,  482. 

Goethe,  liis  estimate  of  mathematics,  425. 

Great  Britain,  the  country  in  which  Logic 
has  been  most  generally  and  completely 
misunderstood,  20. 

Greek  Sophisms,  ancient,  their  character, 
823-4. 

Grosser,  or  Groesenu,  26;  quoted  on  fignre 
of  syllogism,  642. 

GUMDLINO,  25. 
GUNKER,  ib. 

Harvey,  Gideon,  his  use  of  Concpt,  30. 

Hekuebord,  his  Praxis  Logica  ix-fcrrcd  to, 
4U3. 

Heokl,  his  employment  of  the  term  Dialectic, 
6;  repudiated  the  principles  of  Contradic- 
tion and  Excluded  Middle  in  relation  to  the 
absolute,  64;  rejected  the  principle  of  Iden- 
tity as  applicable  only  to  the  finite,  66;  a 
dying  deliverance  of,  281 

Hbraclitus,  quoted,  481. 

Herbart,  referred  to  for  a  complicated  the- 
ory of  Sorites  in  different  figures,  320. 

Heudkr,  quoted  on  tendency  of  the  age  to 
Over-reading,  487. 

Hermakn,  Gottfried,  280. 

Herminus,  his  ground  of  the  discrimination 
of  major  and  minor  terms  in  the  second 
and  third  figures,  628;  quoted  on  figure  of 
syllogism,  533-4 

Her-mooenes,  833,  351. 

Herodotus,  case  cited  from,  illustrating  the 
power  of  Association,  424. 

IIeteuooeneity.  Law  of,  what,  148-9,  see 
Genus  and  Species. 

HiBKisMCUS,  Thomas,  484. 

HiLAiRE,  St.,  603. 

Hinds,  Dr.,  his  encomium  of  the  Elements  of 
Logic  of  Dr.  Wlmtely.21. 

UiBFANUS,  Petrus,  Pope  John  xx.,  or  xxi., 


or  xxii.,'187;  author  of  the  Latin  mne- 
monic verses  for  Mood  and  Fignre  of  Syl- 
logism, 308;  notice  of,  ib- ;  his  Summulct, 
for  many  centuries  the  text-book  of  Logic 
in  the  .•schools  of  the  Latin  Church,  ib. 

HoBBES,  maintaiued  all  thought  to  l)c  at  bot- 
tom a  calculation,  197;  quoted  on  the  influ- 
ence of  authority  on  opinion,  401. 

HOCKER.  85. 

UoEFBAUKR,  43,  59, 174,  215,  338;  quoted  oii 
canons  of  syllogism,  456. 

IlOLLMAKN,  289,  291,  294,  456. 

Uomooeneitv,  law  of.  what.  148,  see  Genus. 

Hope  and  Fear,  .«e  Krror,  Causes  of. 

HospiMAN,  John,  erroneously  attributed  llie 
invention  of  the  Fourth  Figure  to  Scotua, 
303. 

Human  Mind,  limited  nature  of,  as  a  source 
of  error,  iee  Error,  Causes  of. 

Hu.ME,  David,  84;  quoted  on  indistinctncits 
of  terms,  123-4;  quoted  on  belief  as  the 
root  of  knowledge,  3S4. 

HcTCiiESON,  Francis,  quoted  ou  canons  of 
syllogism,  5C3-4. 

Hypolemma,  name  for  minor  premise  or 
subsumption  of  a  syllogism,  199. 

UvpoTHtsis,  what,  188, 449-60;  its  place  and 
end  in  scitiico,  450. 

Hypothetical  Judgment,  or  Proposition, 
see  Judgments,  Doctrine  of. 

Hypothktical  Iteasoning  or  Syllogism,  the 
second  class  of  Conditional  Syllogisms,  and 
third  class  afforded  by  Internal  Form  of 
Syllogi.sm,  239;  its  general  character  —  a 
rca.soning  whose  form  is  determined  by  the 
Law  of  Iteason  and  Consequent,  and  whose 
sumption  is  thus  necessarily  an  hypu:l.etic:il 
proposition,  239-40;  of  two  forms,  Ailirm- 
■tive  or  Constructive  —  modus  portent, nnd 
Negative  or  Destructive  —  modns  tolUttx, 
239;  authors  referred  to  on  use  of  terms 
ponens  and  toUrns,  240;  mnemonic  verses  for 
these  forms,  ib.;  authors  on,  in  general, 
referred  to,  i6. ,-  its  general  character  expli- 
cated, 240  tt  seq. ;  contains  three  pioposi- 
tions,  i6. ;  the  modus  puitins  and  ntnlus 
tolUns  illustrated,  241;  nomenclature  of 
Theophrastus,  Eudomus,  etc.,  regarding, 
ib  ;  its  |)eculiar  principle  —  the  Law  of 
Reason  and  Consequent,  241  et  seq  ;  this 
principle,  how  variously  enounced,  242 ; 
why  we  cannot  conclude  from  the  tnith  of 
the  consequent  to  tlje  truth  of  the  antece- 
dent, and  from  the  falsehood  of  the  ante- 
cedent to  the  falsehood  of  the  consequent, 
ib. ;  conversion  of  to  categorical  sylIogi.»mH 
is,  1°,  Unnecessary,  243;  2°,  Not  always 
possible,  248-4 ;  authors  on  the  conversion 
of,  referred  to,  243 ;  those  of  one  form  easily 
convertible  into  another,  244;  siiecinl  rulou 
of,  245  i  these  explicated  —  tirst  rule,  246  «t 


INDEX. 


695 


»eq  ;  regulates  the  general  form  of,  245: 
ground  on  which  it  has  been  regarded  as 
Jiaving  only  two  terms  ui:d  two  proposi- 
tions. 243;  this  view  erroi.eotis,  (6.  .•  —  sec- 
ond rule,  247;  that  t)ie  fumption  is  always 
delinito,  to  be  understood  in  a  qualified 
sen£C,  lb.;  that  the  sumption  is  always  af- 
firmative, ib.;  the  subsumption  of,  248;  — 
third  rule, /A.,  «e  602-6;  though  prominently 
regulated  by  the  law  of  Reason  and  Conse- 
quent, still  the  other  logical  laws  operative 
in,  252;  difficulty  in  connection  with,  in 
regard  to  the  doctrine  that  all  reasoning  is 
either  from  whole  to  part  or  from  the  parts 
to  the  whole,  stated  and  obviated,  i6.  ft 
seq. ;  antecedent  and  consequent  of,  equal 
to  condition  ai.d  conditioned,  252-3;  hence 
the  reason  or  condition  must  contain  the 
consequeut,  253;  whole  and  parts  respect- 
ively may  be  viewed  in  thought  either  as 
the  conditioning  or  as  tlio  conditioned,  '254 ; 
application  of  this  doctrine  to  the  solution 
of  the  previous  dilliculty,  255;  not  liable 
to  the  affection  of  li;,'ure,  318;  author's  later 
doctrine  of  Hypothetical  (or  (.'onjunctive 
and  Disjunctive)  Reasonings,  598-618;  these 
reducible  to  immediate  inferences,  698-9, 
599-600,  eOl-2,  603-4,  605;  referred  to  the 
class  of  Explicafivcs  or  Conditionals,  599- 
600;  not  composite  by  contrast  to  the  regu- 
lar syllogism,  but  more  simple,  603;  only 
preparations  for  argumentation,  603-4,  609- 
10;  canons  of  Hyjiotlietical  syllogism,  602, 
606 ;  theory  of,  regarded  as  alternatives, 
607-12;  errors  of  logicians  regarding,  612; 
historical  notices  of,  012-18;  Aristotle, 
612-13  ;  Ammonius  llermije,  013-14;  Anony- 
mous Scholion,  and  matter  relative  to, 
611-18. 

IlYPOTHKTicAL  Proposition,  application  of 
the  doctrine  of  a  quantified  predicate  to, 
and  its  result,  512,  see  Hypothetical  Syllo- 
gism. 

llYPOTHETico-DiSJU>'CTivE  or  Dilemmatic 
Judgment,  see  Judgments,  Doctrine  of. 

Hypothetico-Dis.juxctivk  Syllogism,  Di- 
lemmatic or  Dilemma,  third  class  of  Con- 
ditional Syllogism  and  fourth  class  afforded 
by  Internal  Form  of  Syllogism,  205,  249  ; 
regulated  by  the  laws  of  Excluded  Middle 
and  of  Reason  and  Consequent  in  conjunc- 
tion, 205;  what,  248-9;  held  by  Wallis  to 
be  a  negative  induction,  249;  its  character 
explicated,  ib.  ;  designations  of — ceracinus, 
eornuttm,  sc,  syilogixmus,  etc.,  249-50;  rules 
for  sifting  a  proposed  dilemma,  250. 

Idea,  the  term,  reason  why  not  regularly 
employed,  and  sense  in  which  it  is  occa- 
sionly  used  by  the  author,  90. 

IDKMTITY,  principle  of,  a  fundamental  law  of 


thought,  57;  what,  ib. ;  variously  enounced^ 
ib.  ;  its  logical  importance  —  the  principle 
of  all  logical  afhrniation  and  definition, 
58;  its  history.  62  ft  f>-q. ;  developed  last  in 
the  order  of  time,  62,  65;  first  explicated  as 
a  Cfjordinate  principle,  by  Antonius  An. 
dreas,  at  the  end  of  the  13ili  century,  65; 
maintained  by  Andreas  against  Aristotle 
to  be  the  one  absolutely  first  principle,  65, 
66;  controversy  regarding  the  relative  pri- 
ority of  the  laws  of  Identify  and  Contra- 
diction, 66;  called  by  Wolf  principium  cer- 
titi/rjinis,  ib. ;  by  Baumgarteu  jirincipiuni 
po.iitionis  sive  identitatis,  ib.  :  placed  by 
Fichte  and  Schelling  as  the  primary  prin- 
ciple of  all  knowledge,  ib  ;  rejected  by 
Hegel,  i6.;  along  with  that  of  Contradic- 
tion, regulates  the  categorical  syllogism, 
207,  251 ;  formally  the  same  with  that  of 
Reason  and  Consequent,  251;  authors  re- 
ferred to  on,  507-8;  see  Fundamental  Laws 
of  Thought,  I'roportion,  law  of 

Imagination,  what,  425-6;  its  necessity  in 
scientific  pursuits,  426;  as  a  source  of  error, 
»6.,  see  Error,  Causes  of 

Immediate  Inference,  what,  514;  cases  of, 
recognized  by  logicians.  514  ft  seq. ;  1.  Con. 
version,  ift-.-t*?  Conversion,  515  ;  2.  Equipol- 
lence,  or,  better.  Double  Kegation,  —  merely 
grammatical,  522;  3.  Subalterr.ation,  better 
Restriction,/*.;  this  Bilateral  and  Unilat- 
eral. 523;  not  noticed  by  logicians  that  in 
suballernation  the  .•■ome  means  some  at  lensi^ 
ib. ;  the  two  propositions  in  subalternation 
should  be  called  Restringent  or  Beslrictive, 
the  given  proposition  the  JiestringentJ,  and 
the  product  the  Rf strict  or  Re.'itnrlet/.  513; 
logicians  have  overlooked  the  immcdiatf 
inference  of  Subcontrariety,  523-4,  53-i; 
this  called  by  the  author  Inlegmiion,  f;24, 
534;  the  two  propositions  in  integration 
called  the  Integral  or  Litegrnnt,  the  given 
proposition  the  Integmml.  and  the  product 
the  Integrate,  ib. ;  tabular  scheme  of,  535; 
Eustachius  quoted  on,  601;  authors  referred 
to  on,  ib.:  kinds  of,  ib.;  authors  by  whom 
adojjted,  ib. ;  Immediate  I'eremjjtory,  and 
Immediate  Alternative  Inference,  601-2 ; 
the  latter  contains  five  species,  embracing 
among  these  the  Disjunctive,  Hypotheticai, 
and  Uypothetico-Disjunctive  syllogisms  of 
the  logicians,  i!>. ;  logicians  who  refer  Hy- 
pothetical and  Disjunctive  Syllogisms  to, 
600. 

Impkdiments  to  thinking.  Doctrine  of,  tee 
Logic. 

Indefinable,  the,  what,  105,  107. 

Indefinite,  the,  how  distinguished  ft-om  the 
Infinite,  74. 

Indefinite  Propositions,  171,  iee  Judgments, 
Propositions. 


696 


INDEX. 


iHDETERMniED,  the,  what,  55,  56. 

iMDiviDUAL  or  Singular  Difference,  what, 
146-7,  see  Genus  and  Species. 

Individdal  Propositions,  171,  see  Judg- 
ments, Propositions. 

Individuum  sii^natum  and  Individuum  va- 
gttm,  547. 

Indivisible,  the,  what,  105-7. 

Induction,  of  two  kinds,  —  Logical  or  For- 
mal, and  Philosophical,  Real,  or  Material, 
22G,  5S9-90,  C97;  the  views  of  logicians  re- 
garding the  nature  of  Logical  Induction 
erroneous,  22.0;  the  characlers  of  Logical 
and  uf  Real  Induction,  226-7;  canon  of 
Inductive  Syllogism,  227;  this  equally  for- 
mal with  that  of  Deductive  Syllogism,  t6. / 
a  material  induction,  how  expres.scd  as  a 
formal,  ib. :  ohjection  obviated,  228;  for- 
mula: for  Inductive  Syllogisms  in  Compre- 
hension and  E.vtension,  228-9:  Whately 
and  others  erroneously  make  the  inductive 
syllogism  deductive,  229;  this  done  before 
Whately  by  Schramm  and  Wolf,  ib. ;  doc- 
trine of  the  older  logicians  regjirding, 
correct  as  far  as  it  goes,  229-30;  doctrine  of 
Imperfect  Induction,  230;  Bacon  at  fault 
in  his  criticism  of  Aristotle's  doctrine  of, 
i6.  ,•  authore  referred  to  on,  in  general,  ti.,- 
Keal  or  Material,  founded  on  the  principle 
of  Philosojihical  Presumption,  450;  its  agree- 
ment with  and  distinction  from  Analogy, 
450-1;  of  two  kinds,  —  Individual  and 
Special,  452;  but  in  the  last  result  all  In- 
duction is  individual,  452;  two  conditions 
of  legitimate,  452-3;  summary  of  the  doc- 
trine of,  453;  Induction  and  Analogy  com- 
pared together,  455;  these  do  not  afford 
absolute  certainty,  46.5-6;  authors  referred 
to  on,  4-56;  authors  quoted  and  referred  to 
on,  589-97;  Aristotle,  589-93;  example  of, 
given  in  the  Ors;finnn  of  Aristotle,  probably 
not  that  proposed  by  the  author  himself, 
690;  Aristotle's  doctrine  of  the  correct, 
692-3;  Pachy  meres,  593;  Ramus,  593-4;  De- 
rodon,  594;  the  college  of  Alcala  —  their 
error  noticed.  594;  certain  vulgar  errors 
on,  releircfl  to.  59t-5;  Facciolafi,  .595;  Lam- 
bert, ilj.:  strictures  on  Lambert's  doctrine, 
595;  his  doctrine  adopted  by  certain  subse- 
quent German  logicians,  596;  his  doctrine 
old,  and  well  invalidated  by  the  commen- 
tators of  Louvain,  ib.  ;  a  similar  doctrine 
to  that  of  Lambert  held  by  Versor,  Ar- 
iioldus  de  Tungeri,  and  Lambertus  de 
Monte,  i6.  ;  Crakanthorpe  held  that  Induc- 
tion can  only  be  recalled  to  a  hypothetical 
syllogism,  693-7;  Material,  its  character. 
687. 

IMPKRENCE,  meaning  of  the  term,  196:  dis- 
tribution of,  69S-600:  its  two  grand  classes, 
—  Mediate  and  Immediate,  588;   all  infer- 


ence hypothetic,  598-9 ;  authors  by  whom 
this  maintained,  59S-9;  the  distinction  of 
as  Commutative,  £.\plicative,  and  Conipar- 
otive,  599-600;  Mediate  I'eremptory,  and 
Mediate  Alternative  Inference,  602. 

Ikpinite,  its  name  and  notion,  73-4;  ex- 
pressed by  negative  terms,  74;  how  distin- 
gubihed  from  the  Indelinite,  ib. 

lusTRUCTios,  its  end,  1;  methods  of  writ- 
ten and  oral  instruction  different,  ib.,  sex 
Knowledge.  Dictrine  of  the  Acquisition 
and  Perfecting  of. 

IsTEORiTV,  Criticism  of,  see  Testimony. 

IsTERPRETATiox,  or  Exegcsis,  Art  of.  «e 
Testimony. 

Intuition,  the  term,  its  meaning,  90;  ambig- 
uously translates  the  Ge:'nian  Anschauung. 
ib. :  what,  386,  .ve  Truth  and  Error,  Doctrine 
of. 

Iktuitive  and  Symbolical  Knowledge,  see 
Concepts,  Quality  of. 

Intuitive,  the  term,  sense  in  which  used  by 
Leibnitz  and  the  continental  philosophers, 
121. 

Involution  of  Concepts,  see  Concepts,  Belm- 
tions  of. 

ISENDOORN,  Gisbert  ab,  37-8,  230. 

IsiDORUS,  quoted  on  Figure  of  Syllogism, 
640. 

Jakob,  456. 

Jerome,  St.,  quoted  on  the  snperior  effect  of 
the  living  voice,  484. 

Judoments,  Doctrine  of,  159-88;  a  Judg- 
ment, what,  159-60;  how  distinguished  from 
a  Proposition,  t&. ;  what  is  implied  in  judg- 
ment, 160;  condition  under  which  notions 
are  judged  congruent,  160-1;  a  judgment 
must  contain  three  notions  —  viz,  of  Sub- 
ject, Predicate,  Copula,  161;  these  con- 
stituents illustrated,  162;  propositions  of 
the  Third  Adjacent,  and  of  the  Second 
Adjacent,  ib. ;  concepts  and  judgments,  bow 
far  they  coincide  and  differ,  162-3;  judg- 
ments, how  divided,  163:  I.  From  the  rela- 
tion ol  subject  and  predicate  as  reciprocally 
whole  and  part,  judgments  are  divided  into 
Comprehensive  and  Extensive,  »6.,-  this  dis- 
tinction founded  on  the  comprehension  and 
extension  of  concepts,  1G3-4 ;  II.  From  the 
difference  in  the  relation  of  determination 
between  subject  and  predicate,  divided  into 
Categorical,  and  Conditional,  including 
Hypothetical,  Disjunclive,  and  Dilemmatic, 
166;  categorical  judgment  explained,  ib.  et 
teq.;  the  term  categorical  used  by  Aristotle 
in  the  sense  of  affirmative,  ib. ;  in  its  second 
signification,  as  opposed  to  conditional, 
probably  first  applied  by  Theophrastus,  ib.  ; 
in  this  employment  the  terms  absolute  and 
perftct  t>etter  expressions,  166;   natura  of 


INDEX. 


697 


a  categorical  judgment,  166;  conditional 
judgments,  166-71;  these  comprise  three 
species,  163;  1.  Hypothetical,  ib.  et  seq.; 
variations  iu  regard  to  the  application  of 
the  terms  conditional  and  hypothetical,  166-7; 
a  hypothetical  judgment,  what,  167;  appel- 
lations of  its  constituent  elements,  168;  not 
composite,  JO. ;  not  convertible  into  a  cate- 
gorical, ib. ;  2.  Disjunctive,  169  et  seq. ;  not  iu 
reality  composite,  and  not  convertible  into 
a  categorical,  169-70;  3.  Dilemmatic,  or 
Hypothetico-Disjunctive,  170  et  seq. ;  indi- 
visible, and  not  reducible  to  a  plurality  of 
categorical  judgments,  170;  these  various 
kinds  of  judgments  may  be  considered  in 
reference  to  Quantity,  Quality,  and  Rela- 
tion, 171 ;  a.  In  relation  to  Quantity,  ib.  et 
seq. ;  the  Common  doctrine  of  the  division 
of  judgments  according  to  their  quantity, 
171;  the  doctrine  of  tlie  author  on  this 
point,  171-2;  all  judgments  are,  according 
to  the  author,  either  Definite  or  Indefinite, 
171;  Definite  includes  Universal  and  Indi- 
vidual judgments,  171-2 ;  Indefinite  includes 
Particular  judgments,  172;  projjositions  are 
either  Fredesignate  or  Treindesignate,  ib. ; 
common  doctrine  errs  by  taking  into  ac- 
count only  the  quantity  of  the  subject, 
ib.;  these  doctrines  explicated,  173  et  seq.; 
Universal  judgments,  what,  ib  ;  Singular 
or  Individual  judgments,  what,  ib. ;  Par- 
ticular judgments,  what,  ib. ;  words  which 
serve  to  mark  out  quantity  iu  universal, 
individual,  and  particular  propositions,  ib. ; 
distinction  of  universal  and  individual 
from  particular  judgments,  173-4  ;  cate- 
gorical judgments  alone,  according  to  the 
logicians,  admit  of  all  the  forms  of  quan- 
tity, 174;  this  doctrine  erroneous,  ib.;  b. 
In  relation  to  Quality,  judgments  are  di- 
vided into  Affirmative  and  Negative.  176; 
generality  of  the  definition  of  predication 
and  of  affirmation  and  negation,  as  given 
by  the  author,  176;  affirmative  and  negative 
propositions,  176-7;  that  negation  does  not 
beloug  to  the  copula  held  by  some  logi- 
cians, 177;  the  opposite  doctrine  maintained 
by  the  author,  177-8;  origin  of  the  contro- 
versy regarding  the  place  of  negation,  178; 
the  possibility  of  enunciating  negative  prop- 
ositions in  an  affirmative,  and  affirmative 
propositions  in  a  negative,  form,  the  occa- 
sion of  much  perverse  reflilement  among 
logicians,  178-9;  negative  terms,  how  desig- 
nated by  Aristotle,  178;  by  Boethius,  ib.; 
by  the  Schoolmen,  ib.;  propositiones  infinitcp. 
of  the  Schoolmen,  ib  ;  Kanfs  division  of 
judgments  into  Affirmative,  Negative,  and 
Limitative  unfounded,  179;  judgments 
divided  according  to  their  quantity  and 
quality    taken    together,     into    Universal 

8b 


Affirmative,  Universal  Negative,  Particular 
Affirmative,  Particular  Negative,  ib.;  these, 
how  symbolized,  ib. ;  circular  diagrams 
illustrative  of,  180;  division  of  propositions 
into  I'ure  and  Modal,  180-81;  this  distinc- 
tion futile,  181;  division  of  Modal  propo- 
sitions by  logicians  as  Necessary,  Impossi- 
ble, Contingent,  and  Possible,  extralogical, 
181-2;  Whately  quoted  on  this  distinction, 
and  criticized,  182-3;  the  terms  Assertory, 
Problematic,  Apo'teictic,  or  Demonstratice  in 
relation  to  propositions,  explained,  183; 
c.  By  Eelation  to  each  other,  judgments 
divided  into  Identical,  Different,  Relatively 
Identical,  Disparate,  Di.'junct,  Subalter- 
nant,  Subalternate,  183-4;  out  of  Relation 
arises  the  Opposition  of  judgments,  181; 
opposition  either  of  contradiction  or  of 
contrariety,  ib. ;  Congruent  Judgments, 
ib. ;  Sub-contrary  opposition,  what,  ib.  ; 
not  a  real  opposition,  ib.,  see  Opposition; 
conversion  of,  185-6,  see  Conversion ;  cer- 
tain distinctions  of,  not  strictly  logical, 
explained  — viz.,  Theoretical  and  Practi- 
cal, Indemonstrable  and  Demonstrable, 
Axioms  and  Postulates,  Theorems  and 
Problems,  Corollaries,  Experimental  Prop- 
ositions, Hypotheses,  Lemmata,  Scholia, 
187-8;  .^ee  Propositions. 
Justin,  case  cited  from,  illustrating  the 
power  of  Association,  424. 

KaKov  KopaKos  icaKhf  io6v,  the  proverb,  its 
origin,  334 

Kant,  42;  his  Applied  Logic  identical  with 
the  Author's  Modified  Logic,  43;  his  em- 
ployment of  the  phrase  censured,  44,  58,  -59, 
88,  112;  his  employment  of  the  term  caie- 
gory,  140,  170;  his  threefold  division  of 
propositions  as  Affirmative,  Negative,  and 
Limitative,  groundless,  179-83  ;  rejected 
Sub-contrariety  as  a  species  of  opposition, 
184, 242 ;  his  doctrine  of  Figure  borrowed  by 
the  Author,  307;  his  speculation  founded 
on  the  general  relations  of  distance  between 
the  planets,  367 ;  his  argument  from  the  law 
of  duty  for  human  liberty,  and  the  exist- 
ence of  a  Moral  Governor,  valid,  372,456; 
quoted  on  Crusius's  supreme  canon  of  Syl- 
logism, 561;  quoted  on  Canons  of  Syllo- 
gism, 568-9. 

Keckermann,  216,  230.  243,  250,  342. 351, 527. 

KlESEWETTER,  174,  243,  469;  quoted  on  can- , 
ons  of  syll  jgism,  572 

KlRWATU,  Dr.  IJichard.  435. 

Knowledge,  Doctiine  of  the  Acquisition 
and  Perfecting  of,  441,  493;  the  means  of 
perfecting  knowledge  are,  in  general,  two, 
—  the  Acquisition  and  the  Communication 
of  knowledge,  441;  tlic  first  mean,  — the 
Acquisition    of    knowledge,  —  considered, 


698 


INDEX. 


441  et  seq. ;  this  must  be  viewed  in  relation 
to  the  different  kind^j  of  knowledge,  which 
are  two,  as  of  contingent  and  of  necessary 
matter,  441-2 ;  consists  of  two  parts  —  acqui- 
sition through  Experience,  and  through  In- 
telligence, 442;  in  what  sense  all  knowledge 
may  he  called  acquired,  ib.;  I.  The  doctrine 
of  Experience,  442  et  seq. ;  experience  of 
two  kinds,  442;  1.  Personal,  442-3;  this  in 
general,  what,  443;  explicated,  ib.  et  seq.; 
common  and  scieutilic,  444;  Observation, 
what,  li.  /*  of  two  kinds  —  Observation 
proper  and  Experiment,  ib. ;  pra'Cognita 
of,  445  et  seq  ;  First,  The  object  of  observa- 
tion, 445-7;  this  fourfold,  445;  1°,  What 
the  phxnomeua  are  in  their  individual  pe- 
culiarities and  contrasts,  and  as  under 
determinate  genera  and  species,  ib. ;  2^, 
What  the  conditions  of  their  reality,  446; 
3'^,  What  their  causes,  44G-7;  i°.  What  the 
order  of  their  consecution;  Second,  The 
manner  of  observation,  447-8;  1°,  Proper 
state  of  the  observing  mind,  447;  2°,  Con- 
ditions of  the  question  to  be  determined  by 
observation,  447-8;  Third,  The  means  by 
which  the  data  of  observation  are  to  be  re- 
duced to  system  —  viz.,  Hypothesis,  Induc- 
tion, and  Analogy,  449-56,  see  those  words; 
2.  Foreign  experience,  457  tt  seq.;  this  re- 
alized through  testimony,  ib.;  testimony, 
what,  ib. ;  oral  and  recorded,  457-75,  ."ee  Tes- 
timony ;  II.  Speculation  —  the  second  means 
of  acquiring  and  iwrfecting  knowledge, 
475-6;  principal  distinctions  of  empirical 
and  noetic  cognitions,  476;  III.  Communi- 
cation —  the  Inst  mean  of  acquiring  and 
perfecting  knowledge,  478  93;  this  an  im- 
portant mean  of  perfecting  knowledge  in 
the  mind  of  the  communicator,  479;  man 
naturally  determined  to  communication, 
and  his  knowledge  of  the  object  of  his 
thought  is  thereby  rendei-ed  clearer,  76.  ,• 
this  fact  noticed  by  Plato,  16. ;  by  Ari.«tollc, 
Themistius,  Lucilius,  Persius,  Cicero,  Sen- 
eca, 479-80;  the  modes  in  which  communi- 
cation is  conducive  to  the  perfecting  of 
knowledge  are  two,  480;  1.  By  reciprocally 
determining  a  higher  energy  of  the  facul- 
ties, a.  Tlirough  sympathy,  b.  Through  op- 
pasition,  480-81 ;  Plutarch,  and  J.  C.  Scal- 
iger,  quoted  on  the  benefits  of  opposition 
and  dispute,  481 ;  2.  Uy  imposing  tlie  neces- 
sity of  obtaining  a  fuller  conscionsness  of 
knowledge  for  ourselves,  481;  influence  of 
composition  and  instruction  in  perfecting 
our  knowledge,  481-2;  Godwin  quoted  to 
this  effect,  482  ;  and  Aristotle,  Plato,  Sen- 
eca, Clement  of  Alexandria,  Dionysius, 
Cato,  Scho!!i.«tic  .Maxims,  Vives,  Sai.der- 
Hon,  482-3;  influence  of  the  communication 
of  knowledge  on  those  to  whom  it  is  ad- 


dressed, 483  c(  seq.;  A.  Unilateral  Commu 
uicatiou  or  Instruction  Oral  and  Written, 
483-92;  Oral,  its  advantages,  484-6;  a, 
Slore  natural,  therefore  more  impressive, 
484;  Theophrastus,  the  younger  Pliny,  Vale- 
rius Maximus  ( ?),  St.  Jerome,  cited  to  this 
effect,  ib. ;  b.  Eess  permanent,  therefol-e 
more  attended  to,  ib. ;  c.  Hearing  a  social 
act,  484-5 ;  testimony  of  Menage  and  Varil- 
las  to  tlie  advantages  of  conversation,  485; 
reading,  a  substitute  for  oral  instruction, 
its  advantages,  a.  More  easily  accessible,  b. 
More  comprehensive,  c.  More  permani-nt, 
485;  itsdisadvantagesasan  exclusive  means 
of  acquiring  knowledge,  485-C;  Written 
Instruction,  and  its  employment  as  a  means 
of  perfecting  knowledge,  rules  for,  486;  1. 
Quantity  to  be  read  —  rule,  Kend  much,  but 
not  many  works,  487 ;  testimonies  to  this 
rule  by  Solomon,  Quintilian,  the  younger 
Pliny,  Seneca,  Luther,  Sanderson,  Lord 
Burleigh,  Herder,  ib. ,  end  of  reading,  488; 
2.  Quality  of  what  is  to  be  read  —  lirst  rule, 
Reud  by  selection,  16.  ,•  —  second  rule.  Begin 
with  the  general,  489;  Gibbon  quoted  to 
effect  of  second  rule,^  ib. ;  —third  rule.  Study 
a  science  as  it  is,  before  proceeding  to  its 
chronological  development,  490;  —  fourth 
rule.  Read  different  works  on  the  same  sub- 
ject, ib.;  —  fifth  rule.  Study  works  which 
cultivate  the  understanding,  and  also  those 
which  cultivate  the  taste,  490;  3.  Manner 
of  reading,  491  et  seq. ;  —  first  rule.  Read 
that  you  may  remember,  but  especially  that 
you  may  understand,  491; — second  rule, 
Seek  to  compass  the  general  tenor  of  a 
work,  before  judging  of  it  in  detail,  ib. ;  — 
third  rule,  Accommodate  the  intensity  of 
the  reading  to  the  importance  of  the  work, 
ib. ;  Lectio  cursoria,  and  Lectio  stainria,  ih.  ' 
Bacon  quoted  on  this  distinction,  ib., 
Johaun  Von  MUller  quoted  on  the  same, 
492;  —  fourth  rule.  Regulate,  on  the  same 
principle,  tl^p  extracts  from  the  works  you 
read,  ib.;  B.  Mutual  communication,  or 
conference,  492-3;  of  two  kinds  —  Dialogue 
and  Formal  Dispute,  492;  (1),  Dialogue, 
16. ,-  (2),  Disputation  —  oral  and  written, 
492-3;  Academical.  493. 

KopPEN,  262. 

Kpiffis  and  Kplueiy,  rarely  used  by  the 
Greek.-i,  and  never  by  Aristotle,  as  techiiiciil 
terms  of  Logic  or  of  i'sychology,  159. 

KiiUG,  W.  T.,  referred  to  on  the  form  of 
thought  as  the  e.xclusive  object  of  Logic, 
12;  on  the  laws  of  thought  as  thought,  13; 
referred  to  for  definitions  of  Logic,  25;  re- 
terred  to  and  quoted  us  to  Logic  being 
merely  a  foimal  instrunici.t  of  the  sciences, 
26-7;  quoted  as  to  the  sense  in  which  Logic 
can  be  St  vied  the  Medici  He  0/ the  iVimi/,  26, 


INDEX. 


699 


32-3;  quoted  on  the  utility  of  Logic  as 
serving  to  guard  against  error,  34,  36,38; 
not  aware  of  the  original  distinction  of 
Logica  doctns  and  Lo^ica  vtens,  42,  43,  56, 
67,  59,  60  ;  quoted  on  the  distinction  of 
Keason  and  Consequent,  and  Cause  and 
Effect,  61-2 ;  referred  to  as  to  Conception 
and  Reasoning,  involving  Judgment,  84, 
88, 101,  104,  112,  118, 119,  120,  132,  135, 136, 
147;  quoted  on  Individual  and  Singular 
Difference,  147, 149, 151 ;  quoted  on  tlie  Op- 
position of  Concepts,  152-3,  160 ;  quoted  on 
the  Copula,  162;  quoted  on  Hypothetical 
Judgments,  168-9;  quoted  on  Disjunctive 
Judgments,  169-70;  quoted  on  quantity  of 
Hypothetical  and  Disjunctive  Judgments, 
174,  179,  184,  188,  203,214,  215;  quoted  on 
the  first  rule  of  Deductive  Extensive  Cate- 
gorical Syllogism,  216;  quoted  on  Quaternio 
terminorum ,  216-17, 218, 219 ;  quoted  on  third 
rule  of  Deductive  Extensive  Categorical 
syllogisms,  219-20,  227;  quoted  on  the  first 
rule  of  the  Disjunctive  Syllogism,  236  ; 
quoted  on  Hypothetical  Syllogism  in  gen- 
eral, 241,  242;  quoted  on  the  application  of 
the  principle  of  Reason  and  Consequent  to 
tlie  Hypothetical  Syllogism,  242;  quoted  on 
Ueductiou  of  Hypotheticals,  243-4;  on  Con- 
version of  Hypotheticals  from  one  form  to 
another,  244-5;  quoted  on  the  third  rule  of 
Hypothetical  Syllogisms,  248:  quoted  on 
the  designations  of  the  Hyjjothetico-dis- 
junctive  Syllogism,  249-50;  on  the  rules  for 
sifting  a  proposed  dilemma,  250;  quoted  on 
classes  and  desiguations  of  related  syllo- 
gisms, 258,284,  311,  320,  321;  quoted  on  a 
categorical  syllogism  with  four  capital  no- 
tions, 326,  327;  quoted  on  fallacies  of  an 
Unreal  Universality,  327-8;  quoted  on  the 
Janata  Ratio,  330;  quoted  on  vice  oi  Ignava 
Ratio,  331;  quoted  on  Sophisiria  polyzeteseos, 
332;  quoted  on  character  of  the  Sophisma 
lieterozeteseos,  333,  338,  341;  quoted  on  the 
constituents  of  Logical  Methodology,  341, 
'MS;  quoted  on  Nominal,  Real,  and  Genetic 
deliuitions,  343,  344,  345;  quoted  on  tauto- 
logical definition,  346-7;  quoted  on  the  rule 
of  definition  which  requires  it  to  be  pre- 
cise, 347 ;  quoted  on  the  necessity  for  a  defi- 
nition being  perspicuous,  347-8 ;  on  defini- 
tion in  the  looser  sense,  348-9,  351 ;  quoted 
against  complexity  of  division,  357-8,  864, 
366,  370;  quoted  on  the  circle  in  probation, 
372,  373;  quoted  on  the  Mulatto  Elenchi,  374, 
375;  quoted  on  conditions  of  the  adequate 
activity  of  External  Perception,  414-15;  on 
precautions  against  errors  of  the  Senses, 
415-16,  417, 418;  quoted  on  the  Laws  of  As- 
sociation, 420,  427,  428;  quoted  on  error  as 
lying  not  in  the  conditions  themselves  of 
the  higher  faculties,  but  in  their  applica- 


tions, 428-30,  436;  quoted  on  remedy  for 
error  arising  from  language,  438-9,  440, 
451,  452,  454,  455;  quoted  on  Induction  and 
Analogy,  455,  458,  459, 469,  478,  486,  493;  his 
doctrine  of  Syllogism,  649-51. 

La5ibeut,43;  employed  parallel  lines  as  logi- 
cal notation,  180,  230,456;  his  doctrine  of 
the  ultra-total  quantification  of  the  middle 
term,  5S4-6;  quoted  on  Induction,  595; 
strictures  on  his  doctrine  of,  ib. ;  quoted  on 
Figure  of  Syllogism,  642-5. 

Lambertus  dk  Montx,  bis  doctrine  of  In- 
duction, 596. 

Lange,  25. 

Lasgius,  484. 

Li^KGUAGE,  its  relation  to  thought,  and  the 
influence  which  it  exerts  on  our  mental 
operatioi  s.  98  etseq.;  nni:ecessary  in  cer- 
tain mental  operations,  ib. ;  indispensable 
in  certain  other  mental  operations,  and  its 
relation  to  these,  98-9 ;  has  man  invented 
it?  —  ambiguity  of  the  question,  432;  in 
what  sense  natural  to  man,  432-3;  was  the 
first  language  actually  spoken  the  inven- 
tion of  man,  or  the  inspiration  of  the 
Deity  ?  433;  the  latter  hypothesis  consid- 
ered, ib.;  difiBculty  of  the  question,  ib. ; 
Rousse:;u  cited  on,  ib. ;  language  has  a  gen- 
eral and  a  special  character,  434;  no  lan- 
guage is  a  perfect  instrument  of  thought, 
434;  signs  necessary  for  the  internal  opera- 
tion of  thought,  435  ;  and  for  its  commu- 
nication, ib. ;  intonations  of  the  voice,  the 
only  adequate  symbols  of  thought  and  of 
its  communication,  ib. ;  these  inarticulate 
and  articulate,  436;  the  latter  constitute 
Language  Proper,  ib. ;  the  vocabulary  of 
any  language  necessarily  finite,  437;  words 
are  merely  hints  to  the  mind,  437-8;  Lan- 
guage as  a  source  of  Error,  436,  see  Error, 
Causes  of. 

Larroque,  quoted  on  canons  of  syllogism, 
572-4. 

L'Art  DE  Penseb  {Port- Royal  Logic},  25; 
its  study  recommended,  50,  408;  authors  of 
very  nearly  took  the  distinction  between 
notions  as  Clear  and  Obscure,  Distinct  and 
Indistinct,  114. 

Latin  Schoolmen,  viewed  Logic  as  a  science, 
7;  their  views  as  to  the  object-matter  of 
Logic,  19-20. 

Laurembergius,  p.,  26. 

Laws  of  Thought,  see  Fundamental  Laws  of 
Thought. 

Le  Clerc,  71. 

Lectio  Cuksoria  and  Lectio  Stataria,  491, 
see  Knowledge,  Doctrine  of  the  Acquisition 
and  Perfecting  of. 

Leibnitz,  on  the  principles  of  Identity  and 
Contradiction,  64;  did  not  always  distin- 


00 


INDEX. 


guisb  the  principles  of  Identity  and  Con- 
tradiction, 66;  called  attention  to  law  of 
Sufficient  Reason,  C7;  founded  bis  philoso- 
phy on  the  principles  of  Sufficient  Reason 
and  Contradiction  (including  Identity),  »6.; 
did  not  sufficiently  discriminate  the  law  of 
Causality  from  tlie  law  of  Sufficient  Reason, 
xb. :  gave  various  names  to  the  principle  of 
Sufficient  Reason,  ib.  ;  controversy  between 
and  Clarke,  on  province  of  Sufficient  Rea- 
son, ib.;  his  distinction  of  Intuitive  and 
Symbolical  Knowledge,  noticed,  87;  to 
him  is  owing  the  distinction  of  Concepts 
into  Clear  and  Distinct,  112-14;  the  first  to 
take  the  distinction  of  Intuitive  and  Sym- 
bolical knowledge,  126;  unacquaintance  of 
the  philosophers  of  this  country  with  the 
doctrines  of,  127;  manner  in  which  he  gave 
his  writings  to  the  world,  ib. :  his  paper 
De  Cognitione,  Verilatf,  ct  LJeis,  quoted  from 
on  Intuitive  and  Symbolical  Knowledge, 
121,  456;  quoted  on  canon  of  Syllogism, 
56(^-1;  referred  to  on  simplicity  of  sorites, 
274. 

Leidenprost,  maintained  all  thought  to  be 
at  bottom  a  culculution,  197. 

IjaMMA,  name  for  the  major  Premise  or 
Sumption  of  a  Syllogism,  200. 

L.EM.\iATA,  what,  188. 

liEXCoutra'/icloriarum,  principiiim  Contradieen- 
limn,  it.s  exlen^:ion  in  the  schools,  65. 

hoBicowiT^,  JoannesCaramuel,  184;  referred 
to  on  various  kinds  of  wholes,  351. 

LoCKK,  John,  totally  misapprehended  the 
nature  of  l.osic,  21;  on  the  principle  of 
Contradiction,  64;  liis  real  merits  in  rela- 
tion to  the  dit-'.iiictions  of  Ideas,  the  doc 
trine  of  Uefinition,  etc.,  115;  anticipated 
iiume  in  remarking  the  employment  of 
terms  without  distinct  meaning,  125;  quoted 

.  on  this  point.  125-6. 

Looic,  the  first  .>^even  lectures  of  the  Author's 
Metaphysical  Course  delivered  as  a  general 
introduction  to  the  course  of,  1;  mode  In 
which  its  consideration  ought  to  be  con- 
ducted, i6.  ,•  system  of,  consists  of  two  parts, 
viz. :  —  Introduction  to  the  Science,  and 
Body  of  Doctrine  constituting  the  science 
itiiclf,  3;  questions  to  be  answered  in  the 
Introduction  to  Lopfic,  3  et  srq.;  I.  Defini- 
tion of,  3-24,  .?(•(?  ai<()  496-7 ;  the  Science  of 
the  Laws  of  Thought  as  Thought,  3  tt  seq.  ; 
this  definition  explained  in  detail,  i6.;  (I) 
The  word  Losic,  a.  Its  history,  3  ft  .vq.;  the 
term  (\oytKrj)  as  marking  a  particular 
science  not  so  old  as  the  science  it.self,  i6.  ; 
not  used  in  this  sense  by  Aristotle.  3,  4; 
according  to  Boethius.  first  applied  to  the 
science  by  the  ancient  I'eiipatetics,  4;  used 
in  the  wide  sense  by  Alexander  of  Aphro- 
dieias,  ib.;  but  previously  to  Alexander  a 


common  designation  of  the  science,  as  ap. 
pears  from  Cicero,  4;  b.  Its  derivation 
and  meaning,  from  Ao-yoj,  signifying  both 
thought  and  its  expression,  4;  this  ambigu- 
ity favored  the  rise  of  two  counter-opinions 
regarding  the  object-matter  of,  5,  23;  this 
twofold  meaning,  how  contradistinguished 
in  expression  by  Aristotle,  5 ;  by  others,  ib. ; 
appellations  of  the  science  afterwards  called 
Logic,  ib. ;  vacillation  in  the  application  of 
the  term  by  the  Stoics,  Epicureans,and  other 
ancient  schools  of  philosophy,  6;  (2)  The  Ge- 
nus of  Logic, —  whether  science  or  art,  7  et 
seq.,  see  also  498-501;  a  science  according  to 
Plato  and  the  Platonists,  but  Dialectic  with 
them  equivalent  to  the  Logic  and  Metaphys- 
ics of  the  Peripatetics,  7;  denied  to  be  either 
science  or  art  by  the  Greek  Aristotelians 
and  many  philosophers  since  the  revival 
of  letters,  ib. ;  a  science  according  to  the 
Stoics,  i6.  ,•  and  according  to  the  Arabian 
and  Latin  schoolmen,  ib.;  maintained  to 
be  au  art  in  more  modern  times  by  many 
Aristotelians,  the  Rami^ts,  and  a  majority 
of  the  Cartesians,  ib. ;  both  science  and  art, 
according  to  others,  t6. ;  in  Germany,  since 
Leibnitz,  regarded  as  a  science,  ib. :  the 
question  futile,  7;  errors  of  Whately  on 
this  point,  7,  8;  what  is  implied  in  defining 
Logic  as  a  science,  8,  9;  held  by  some  to 
be  a  science,  498;  and  either  Speculative 
science,  ib  ;  or  Practical,  t6. ;  or  both 
Speculative  and  Practical,  ib.;  an  art,  449; 
science  and  art,  ib. ;  neither  science  nor 
art,  but  instrument,  organ,  habit,  or  instru- 
ment:tl  discipline,  (6.  ;  that,  loosely  taking 
the  terms,  is  either  art,  or  science,  or  both. 
600;  that  at  once  science  (part  «(  philoso- 
phy) and  instrument  of  philosophy,  ib. ; 
that  question,  whether  part  of  philosophy 
or  not,  an  idle  question,  ib. ;  that  question, 
whether  art,  science,  etc.,  only  verbal. 
500-1;  Eugeuius  quoted  to  this  efiect,  ib.  ; 
(3)  Its  Obji-cf-matter,  9  et  .leq. ;  a.  Thought, 
what,  ib.  ft  seq.;  in  its  wider  meaning, 
thought  denotes  every  Cognitive  act,  and 
even  every  mental  modification  of  which 
we  are  conscious,  ib.  ;  in  the  more  limited 
meaning.  Thought  (Thought  proper)  denotes 
only  the  acts  of  the  understanding,  Faculty 
of  Comparison,  Elaborative,  or  Discursive 
Faculty,  9-10;  in  the  more  limited  mean- 
ing, Thought  is  .the  object-matter  of  Logic, 
9;  objects  that  lie  beyond  the  sphere  of 
Logic,  i6. ,-  b.  Thought  as  thought,  what, 
10  et  seq. ;  Matter  and  Form  of  Thought, 
distinguished.  11;  Logic  properly  conver- 
sant only  with  the  Form  of  Thought,  11  et 
seq. ;  this  shown  by  a  consideration  of  the 
nature  and  conditions  of  the  thing  itself, 
11-12;  c.  Laws  of  Thought  as  Thought,  12 


INDEX. 


701 


tt  seq. ;  these  the  proper  object  of  Logic, 
12-13,  see  also  14-17;  how  distinguished  from 
Empirical  or  Uistorical  Psychology,  17;  as 
the  science  of  the  Laws  of  Thought  as 
Thought,  is  the  science  of  the  necessary 
Forms  of  Thought,  17,  1S2-3;  necessary 
form  of  thought  implies  four  conditions  — 

I.  Determined  by  the  nature  of  the  think- 
ing subject  itself;  2.  Original ;  3.  Universal ; 
4.  A  Law,  17-18;  hence  the  object-matter  of 
Logic  explicitly  enounced,  in  saying  that 
Logic  is  the  science  of  the  Laws  of  Thought 
as  Thought,  or  of  the  Formal  Laws  of 
Thought,  or  of  the  Laws  of  the  Form  of 
Thought,  18,  see  also  28-9;  hence  analogy 
between  and  Mathematics  as  both  formal 
sciences,  31-2:  general  historical  retrospect 
of  views  in  regard  to  the  object  and  domain 
of,  18  et  seq. ;  merit  of  the  author's  view  of, 
ib.;  Aristotle's  relation  to  views  of  the 
nature  and  domain  of.  19;  views  of  Greek 
Aristotelians  and  Latin  schoolmen  regard- 
ing, in  general  correct,  19-20;  views  of  the 
object-matter  of,  in  the  Leibnitio-Wolf- 
ian  and  Kantian  schools,  20;  its  nature 
most  completely  and  generally  misunder- 
stood in  Great  Britain,  ib. ;  in  certain  re- 
spects wholly  misconceived  by  Bacon,  20-21; 
totally  misapprehended  by  Locke,  21;  gen- 
eral character  of  Whately'.^  EUments  nf,  ib.  ; 
his  view  of  the  object-matter  and  domain 
of.  stated  and  criticized,  21-23,  see  Whately ; 

II.  Utility  of,  24  et  seq.;  Utilities  falsely 
attributed  to,  ib.  et  seq. ;  supposed  to  be  an 
instrument  of  scientific  discovery,  24;  hence 
called  an  Instrument,  or  Instrumental  Philos- 
ophy, etc.,  24-5;  supposed  to  be  the  infallible 
corrector  of  our  intellectual  vices,  25;  its 
designations  on  this  supposition,  ib.,  348; 
in  what  respect  an  instrument  of  the  sci- 
ences, 25-6,  32;  not  properly  an  art  of 
discovery,  26,  32;  in  what  sense  to  be  styled 
the  medicine  of  the  mimi,  26,  32;  the  laws  of, 
the  negative  condition  of  truth,  ib. ;  its 
utility  that  of  a  formal  instrument,  or  mean 
by  which  knowledge,  already  acquired, 
may  be  methodized  into  the  form  nccom- 
modated  to  the  conditions  of  the  under- 
standing, 33;  useful  as  giving  us,  to  a  cer- 
tain extent,  dominion  over  our  thoughts, 
33-4;  as  supplying,  in  part,  the  criterion  of 
Truth  from  Error,  34;  as  invigorating  the 
understanding,  ib. ;  as  affording  a  scientific 
nomenclature  of  the  laws  by  which  think- 
ing is  governed,  and  of  the  violation  of 
those  laws,  35-6  —III.  Its  Divisions,  37  e« 
seq.,  see  also  49')-7;  division  of  into  Natural 
and  Artificial  inept,  33;  its  Kinds,  or  Spe- 
cies, and  Parts,  ib.  et  .':eq. ;  1°,  By  relation 
to  the  mind,  is  ObJE'Ctive  and  Subjective, 
—  Systematica  and  Habitualts,  37;  both  of 


these  to  be  proposed  as  the  end  of  instruc- 
tion in,  ib.;  2°,  By  relation  to  objects,  is 
Abstract  or  General,  and  Concrete  or  Spe- 
cial, 38,  see  also  497;  these  kinds  of,  how 
designated  by  the  Greek  Aristotelians,  and 
by  the  Arabian  and  Latin  schoolmen,  38; 
this  division  of  remounts  to  Alexander  the 
Aphrodisian,  ib. ;  his  illustration  of  the  dis- 
tinction, ib. ;  other  illustrations  of  this 
division  of,  39;  General  Logic  is  alone  one. 
Special  Logic  is  manifold,  and  part  of  the 
science  in  which  it  is  applied,  39-40;  the 
distinction  of  Logica  docens  and  Logica 
utens  mistaken  by  some  modern  authors, 
42;  3^,  By  reference  to  the  circumstances 
under  which  it  can  come  into  exercise  by 
us,  is  divided  into  Pure  and  Modified,  42 
et  seq.;  I'ure  Logic,  what,  43;  Modified 
Logic,  what,  ib.;  nomenclature  of  Modified 
Logic,  43-4;  this  identical  with  the  Applied 
Logic  of  Kant  and  others,  43;  not  properly 
an  essential  part  of,  44-5;  Conspectus  of 
the  present  course  of,  45;  Formal  and  Ma- 
terial Logic  contrasted,  497;  division,  va- 
rieties, and  contents  of,  in  detail,  501-6. — 
IV.  History  of,  postponed,  48. —  V.  Bibli- 
ography of,  ib. ;  this  shortly  noticed,  49-51; 
first  great  division  of,  —  Pure  Logic,  — 
considered,  52-375;  Part  I.,  Stoicheiology, 
52-334;  Section  I.,  Noetic,  or  of  the  Funda- 
mental Laws  of  Thougiit,  52-82;  in  what 
aspect  Thought  is  viewed  by,  52-3;  the  true 
relations  of  Logic  overlooked  on  two  sides, 
76  et  seq.  —  1.  Erroneously  held  to  afford 
the  positive  standard  of  truth,  76 — 2.  Re- 
pudiated as  affording  no  criterion  of  truth 
in  relation  to  the  absolute  by  some  philoso- 
phers, 77;  its  Postulates,  81,  see  also  512-13; 
of  these  only  one  signalized, — To  be  al- 
lowed to  state  explicitly  in  language  all 
that  is  implicitly  contained  lin  thought,  81, 
see  also  510;  this  cannot  be  refused,  81;  is 
implied  in  what  Aristotle  states  of  the  doc- 
trine of  Syllogism,  82;  Section  IL  — Ofthe 
Products  of  Thought,  83-334;  i.  Ennoe- 
matic, —  Of  Concepts  or  Notions,  8.3-1-58, 
.see  Concepts,  Doctrine  of;  ii.  Apopliantie, 
or  the  Doctrine  of  Judgments,  159-88,  5e^ 
Judgments,  Doctrine  of;  on  t'.ie  supposition 
that  Logic  takes  cognizance  ofthe  modality 
of  objects,  the  science  can  have  no  exist- 
ence, 1S2:  iii.  Doctrine  of  Reasonings,  189- 
334,  see  Rer.Fonings,  Doctrine  of;  Part  II. 
Methodology,  Section  i.  Method  in  general, 
Section  ii.  Logical  Metliodology,  33')-375; 
Logical  Methodology,  what,  335-'J,  340-41: 
consists  of  three  parts,  —  1°,  The  Doctrine 
of  Definition,  2^,  Of  Division,  3^,  Of  Pro- 
bation, .341;  historical  notices  of  Logical 
Methodology,  tft.,-  1^,  Doctrine  of  Definition, 
341-9,  see  Definition,  Doctrine  of;    2°,  Of 


702 


INDEX. 


Doctrine  of  Division,  350-69,  see  Division, 
Doctrine  of;  3^,  Doctrine  of  Trobation, 
360-75,  see  Probation,  Doctrine  of ;  second 
great  division  of,  —  Modified  Logic,  376- 
493;  its  object, — the  conditions  to  which 
thought  is  subject,  arising  from  tlie  empiri- 
cal circumstances,  external  and  internal, 
under  which  man's  faculty  of  thinking  is 
manifested,  376;  its  problems  three,  1^, 
Wliat  is  Truth,  and  its  contradictory  oppo- 
site, Krror?  2^,  Wliat  r.re  (he  causes  of 
Error  and  the  impediments  to  Truth,  and 
what  are  the  means  of  their  Removal?  3^, 
What  are  the  Subsidiaries  by  which  Human 
Thought  may  be  strengther.ed  and  guided 
in  the  exercise  of  its  functions  ?  ib. ;  the 
first  two  questions  belong  to  the  Stoicheiol- 
o.:;y  of  Modified  Logic,  the  third  to  its 
Methodology,  377;  I'art  L  Modified  Stoi- 
cheiology,  376-440;  Section  i.  Doctrine  of 
Truth  and  Error,  376-96;  Section  ii.  Error, 
its  Causes  and  Remedie.x,  397-440, «'«  Truth 
nnd  Error,  Doctrine  of;  Modified  Method- 
ology, Section  i.  Of  the  Moans  by  which 
oiir  Knowledge  obtains  the  character  of 
I'erfcction, — the  Acquisition  and  Commu- 
nication of  Knowledge,  441-93,  see  Knowl- 
edge, Doctrine  of  the  Acquisition  and  Per- 
fecting of. 

LoGicA  Doctns,  equal  to  Abstract  or  General 
Logic,  see  Logic. 

LooiCA  Uabitualis,  see  Logic. 

LoGiCA  Systematica,  see  Logic. 

LoGicA  Utfns,  equal  to  Concrete  or  Special 
Logic,  see  Logic. 

Logical  Division,  see  Division. 

i^ooiCAL  Induction,  see  Induction. 

Logical  Laws,  see  Fundamental  Laws  of 
Thought. 

Logical  Methodology,  *e<  Logic. 

Logical  Perfection  and  Imperfection  of 
Concepts,  see  Concepts,  Quality  of.  . 

Logical  Truth,  see  Truth  and  Error,  Doc- 
trine of. 

Logical  Affinity  or  Continuity,  Law  of, 
alleged  by  Kant,  but  rejected  by  the  Author, 
149. 

Logical  Notation,  that  by  circular  diagrams 
us  illustrating  propositions,  180;  the  first 
employment  of  these  improperly  ascribed 
to  Euler,  ib.;  to  be  found  in  Weise,  i6.  ; 
that  by  parallel  lines  of  ditferent  lengths 
(Lambert's),  partially  anticipated  by  AI- 
stedius,  j6.  ,•  circular  diagrams  illustrative 
of  reasoning,  191;  circular  and  linear,  for 
Syllogisms  in  E.vtension  and  Comprehen- 
fion,  214-15;  objection  to  notation  by  cir- 
cles, 214;  diagrams,  circular  and  linear,  il- 
lustrative of  the  Sorites,  261,  the  Author's, 
for  propositions,  529;  circular  for  the  same, 
ib. ;  Lamberfs  linear  scheme  of,  criticized, 


C67-9;  Maass"«  scheme  of,  criticized,  669-70; 
the  Author's  scheme  of, — Ko.  I.  Linear, 
070-3;  Author's  Fclien»e  of,  —  No.  II.  Un- 
(igured  and  Figured  syllogisip,  673;  No. 
III.  Figuied  yyllogitm,  —  table  of  Syllo- 
gistic Moods,  in  ciicli  figure  12  affirmative 
and  24  negative,  in  all  33,  678-9. 

Logical  (and  Dialectical)  Beasoning,  its 
meaning  in  Aristotle,  4. 

Logical  terms,cliiefly  borrowed  from  Mathe- 
matics, 196,  209  10. 

Ao-yi/cis  \oyix-fi,  how  employed  by  Aristotle, 
3,  4;  by  Alexander  of  Aphrodisias,  4;  by 
the  subsequent  Aristotelians,  ib. 

A6yos,  its  twofold  meaning,  —  thought  and 
its  e.xpression,  equivalent  to  the  ratio  and 
oratio  of  the  Latins,  4,  5;  the?c  meoniflgs 
how  contradistinguished  by  Aristotle.  5; 
by  others,  ib. ;  K6yos  irpocpopiKhs,  and 
X6yos  dy^ieLdf-Tos,  probably  originated  with 
the  Stoics,  ib. 

LovANiKNSES,  or  Masters  of  Louvain,  289, 
291,  294;  quoted  on  quantification  of  pi-ed- 
icate,  555;  quoted  on  error  regarding  In- 
duction, 590,  617. 

LcciAN,  331,  333. 

LuciLius,  479. 

Luther,  quoted  on  Knowledge  and  Belief, 
883 ;  quoted  on  reading,  487. 

Maass,  Professor,  of  Halle,  his  edition  of 
tlie  Prcecepta  of  Wyttenbach  noticed  and 
censured,  CO;  in  his  edition  of  the  Prcecepta 
of  WytteuLach  rever.>;ed  tlie  aathor's  mean- 
ing on  analysis  and  synthesis,  338. 

Magentinus,  240,  514;  variation  of  histori- 
ans as  to  the  age  in  which  he  lived,  590. 

Magirus,  486. 

Maimon,  S.,  referred  to  on  schemes  of  logi- 
cal notation,  667. 

Ma.iok  proposition,  see  Premise. 

Mako  vii  Kerek-Gede,  Paulus,  42. 

Malebkakche,  quoted  on  the  influence  of 
Self-Love,  407-8. 

3IANILIU8,  quoted,  389,428;  quoted  on  the 
nature  of  experience,  443-4. 

Mariotte,  referred  to  for  correct  doctrine  of 
the  Aristotelic  enthymeme.  278. 

Masters  of  Louvain,  the,  see  Lovanienses. 

Masters  Regent  in  the  College  of  St.  Lau- 
rence in  Cologne,  their  doctrine  of  Induc- 
tion, 596. 

Material  Induction,  see  Induction. 

MATHEMATicALTruth,««  Truth  and  Error, 
Doctrine  of 

Mauritius,  refers  to  St.  Augustin  as  author- 
ity for  quotation  as  to  Logic  being  the 
Arx  artium  and  Scientin  fcifntinruni,  25. 

Mazuuk,  quoted  on  the  office  of  the  natural 
sciences,  390. 

MkimlRS,  392. 


INDEX. 


703 


Melakchthon,  261 ;  his  doctrine  that  there 
is  a  greater  force  in  the  negative  particle 
none,  not  any,  than  in  the  affirmative  a//, 
627  ;  this  doctrine  shown  to  be  erroneous, 
/6.,  621 ;  quoted  on  Figure  of  Syllogism,  641. 

Menage,  330, 332,333;  quoted  on  the  benefit  of 
Conversation  as  a  mean  of  Knowledge,  485. 

JlKNDOZA,  Hurtado  de,  quoted  on  proximate 
and  remote  matter  of  Syllogism,  202,  207; 
his  ground  of  the  discrimination  of  major 
and  minor  terms  in  the  Second  and  Third 
Figures,  629. 

MfToAij(j/«s,  of  Aristotle,  its  probable  mean- 
ing, 611. 

Metaphysics,  the  Author's  Course  of  Lec- 
tures on,  the  fii-st  seven  were  delivered  by 
the  author  as  a  General  Introduction  to  the 
course  of  Logic  proper,  1 ;  relerred  to,  88 
et  alibi. 

Metaphysical  Truth,  ««  Truth  and  Error, 
Doctrine  of. 

Method,  in  general,  what,  335-6  ;  authors  re- 
ferred to  on,  336;  in  reference  to  science, 
what,  336-7 ;  considered  in  its  integrity  is 
twofold  —  Analytic  and  Synthetic,  what, 
33G-7;  the  Analytic,  what,  337;  the  Syn- 
thetic, what,  ib. ;  confusion  in  regard  to 
the  application  of  the  terms  Analysis  and 
Synthesis,  337-8;  authors  referred  to  on  this 
confusion,  338 ;  these  counter  processes  as 
applied  to  the  counter  wholes  of  compre- 
hension and  extension  correspond  with  each 
other,  338^  the  Synthetic  method  has  been 
called  the  Trogiefsive,  and  the  Analytic 
the  Regressive,  331) ;  these  designations 
wholly  arbitrary  and  of  various  application, 
339-40;  in  general.  Synthesis  has  been  des- 
ignated the  Progressive,  and  Analysis  the 
Regressive,  process,  340. 

Methodology,  see  Logic,  Method. 

Metz,  456. 

MlCR^LlUS,  85. 

Minor  I'roposition,  see  Premise. 

MlP.ANDULANUS,  Jo.  Picus,  142. 

MiuANUULANUS,  J.  F.  Picus,  230. 

Mne.monic  Verses,  those  embracing  the  dif- 
ferent kinds  of  propositions  in  reference  to 
quantity  and  quality  combined,  "Asserit 
A,"  etc.,  179,  287;  author's  English  metri- 
cal version  of  these,  287;  previous  English 
metrical  versions  of  the  same,  ib.,  see  also 
589;  for  Conversion,  186-7;  for  Di.«juncfive 
Syllogisms,  231;  for  Hypothetical  Syllo- 
gisms, 240;  for  Figure  of  Syllogism,  282. 

MoDiFiKD  Logic,  see  Logic. 

MoLlN^US,  quoted  on  meaning  of  the  Lex 
ContraiJictorianim,  65.  230,  243,  336,  338. 

MoNBODUo,  Lord,  quoted  en  the  distinction 
of  potential  and  actual  in  relation  to  no- 
tions, 145-6;  his  error  on  this  point,  146. 

Montaigne,  quoted  on  illustration  of  Pre- 


cipitancy, 402-3;  quoted  on  precipitate 
dogmatism  and  skepticism  as  phases  of  the 
same  disposition,  403. 

Mood  of  Syllogism,  doctrine  of,  according 
to  logicians,  286  ft  seq. ;  name  for  the  ar- 
rangement of  the  three  propositions  of  a 
syllogism,  with  designation  of  quantity  and 
quality  of  each,  286;  the  Greek  logicians, 
looking  merely  to  the  two  premises  in  com- 
bination, called  these  Syzygies,  ib. ;  in  all 
sixty-four  moods,  287-8:  but  only  eleven 
valid,  288;  of  the  six  in  each  tigure,  in  all 
twenty-four,  only  nineteen  useful,  ib.  ; 
these,  according  to  doctrine  of  author,  may 
be  still  further  simplitled,  ib. ;  the  doctrine 
of,  explicated,  287  ft  seq.  ;  the  possible  com- 
binations of  premises  tested  as  to  their 
validity  by  the  general  laws  of  tlie  Cate- 
gorical Syllogism,  287-8;  these  laws  give 
eight  possible  moods  of  a  legitimate  syllo- 
gism, 288;  these  eight  moods  being  further 
tested  by  the  special  rules  of  the  First  Fig- 
ure, leave  only  four  legitimate  moods  in 
that  tigure  —  viz.,  Barbara,  Celarent,  Darii, 
Ferio,  288-9 ;  examples  with  diagrams  of 
the  legitimate  moods  of  the  First  Figure, 
290-91;  in  the  Second  Figure  there  are  four 
legitimate  moods  —  viz.,  Cesare,  Camestres, 
Festino,  Baroco,  291-3;  examples  of  these 
vi'ith  diagrams,  292-3;  in  the  Third  Figure 
there  are  six  legitimate  moods— viz.,  Da- 
rapti,  Felapton,  Disamis,  Datisi,  Bocardo, 
Ferison,  294-5;  examples  of  these  with  dia- 
grams, 295-8;  some  ancient  logicians  made 
two  moods  of  Darapti,  295-6;  in  the  Fourth 
Figure  there  are  tive  legitimate  moods  — 
viz.,  Bramantip,  Camenes,  Dimaris,  Fesapo, 

■  Fresison,  299-300;  examples  of  these  with 
diagrams,  300-1;  what  is  true  of  mood  in 
Extension  holds  also  of  it  in  Comprehen- 
sion, 302;  Latin  and  Greek  mnemonic 
verses  for  moods  —  historical  notice  of, 
307-8 ;  the  Latin  due  to  Petrus  Hispanus, 
308;  the  Greek  less  ingenious  than  the 
Latin,  and,  according  to  author's  latest 
view,  probably  copied  from  the  latter,  ib. ; 
reduction  of  the  moods  of  the  Second, 
Third,  and  Fourth  Figures  to  those  of  the 
First, 309-18;  direct  and  indirect  moods,— 
their  principle,  658-9;  direct  and  indirect 
moods  in  First  and  Fourth  Figures,  658; 
indirect  moods  of  logicians  of  Second  and 
Third  Figures,  663-4;  these  impo.'sible,  664  ; 
new  moods,  665-7;  Author's  table  of  moods, 
678-9. 

More,  most,  etc,  the  predesignations,  vari- 
ously referred  to  universal,  particular,  or 
to  neither  quantity,  586;  authors  relerred 
to  on,  ib. ;  Corviuus,  ib. 

MuLLER,  Johaun  von,  his  practice  in  read- 
ing, 492. 


704 


INDEX 


MuRETtrs,  referred  to  on  a  spurious  passage 
of  Aristotle's  lihetoric,  6. 

MtJBMELLitJS,  mnemonic  verses  of,  compris- 
ing the  Ten  Categories,  139;  bis  mnemonic 
verses,  quoted  of  objects  not  included  under 
the  Ten  Categories,  140. 

MuTATio  Elexchi,  see  Probation. 

Necdssitas  Consequentiae  et  Kecessitos  Con- 
sequeutis,  authors  referred  to  on  distinction 
of,  599. 

Xeqatiox,  controversy  regarding  the  place 
of.  178;  negjitive  terms,  how  designated  by 
Aristotle,  Boethius,  the  Schoolmen,  ib.  ; 
particula  injinitans,  what,  ib. ;  propositioms 
infinitee,  what,  ib. 

New  Analytic  of  Logical  Forms,  proposed 
Essay  by  the  author  on,  509;  extract  from 
Prospectus  of,  509-12. 

Noetic,  set  Logic. 

NOLDius,  185;  referred  to,  on  History  of 
Fourth  Figure,  303;  his  reduction  of  Ba- 
roco,  314-17;  called  the  mood  Bocardo 
Dociimroc. 

NoMENCLATCRE,  Scientific,  importance  of, 
35. 

Nominal  Definition,  see  Definition. 

?«ON-CoNTRADiCTiON,  principle  of,  see  Con- 
tradiction. 

NON  ens  logicum,  what,  55. 

XoTiON.  see  Concept. 

NUNNESIL'8,  3.36,  451. 

Objective  Logic,  see  Logic. 

OnsERVATiox.  see  Knowledge,  Doctrine  of 
the  Acquisition  and  Perfecting  of 

Occam,  William,  his  use  of  Concepius,  30. 

Olberb,  his  speculation  founded  on  the 
general  relations  of  distance  between  the 
planets,  367. 

Opision,  see  Truth  and  Error,  Doctrine  of. 

Oppositiojn,  or  Incom]K)Ssibility,  of  Judg- 
ments or  Propositions,  what,  184 ;  either  of 
Contradiction  or  of  Contrariety,  ib.;  Sub- 
contrary  opposition,  what,  ib.;  not  a  real 
opposition,  ib. ;  this  described  by  Aristotle 
as  an  opposition  in  language,  not  in  real- 
ity, ib. ;  distinction  between  Indefinitude 
and  Semi-definitudc  or  Definite  indefini- 
tude, 533;  the  author's  doctrine  of,  evolved 
out  of  this  distinction,  (6.;  Subalternation 
and  Subcontniriety  as  forms  of,  rejected, 
ib  ;  Inconsistency  introduced,  lA. ;  Contra- 
dictory and  Contrary  opposition  among 
propositions  of  diflTerfnt  quality, what,  53-3-4; 
Inconsistency  among  propositions  of  the 
same  quality,  533;  subdivisions  of  Contra- 
diction, Contrariety,  and  Inconsistency, 
533-4;  diffV'ri'nces  in  Compossibility  of  the 
two  schemes  of  Indefinite  and  Definite  Par- 
ticularity, 534 ;  tabular  scheme  of,  535. 


ORGAUoif,  name  bestowed  on  the  collection 
we  possess  of  the  logical  treatises  of  Aris- 
totle, 24;  but  not  by  Aristotle  himself,  lA.  ,■ 
as  thus  applied,  contributed  to  the  errone- 
ous supposition  that  Logic  is  an  instrument 
of  discovery,  lA. 

Ovid,  quoted,  482. 

Fachvmebes,  or  Pacbymerins,  Georgius, 
278;  quoted  on  Induction,  593. 

Pacius,  Julius,  37,  196,  243,  268;  gave  the 
Regressive  Comprehensive  Sorites  before 
Goclenius,  273;  referred  to,  on  Figure,  285; 
quoted  on  error  of  phrase  petitio  principii, 
369. 

Paralogism,  see  Fallacies. 

Part,  see  Whole. 

Particclau  Propositions,  171,  see  Judg- 
ments, Propositions. 

Partition,  see  Division. 

Pascal,  quoted  on  the  dignity  of  man  as 
consisting  in  thought,  34;  quoted  on  the 
power  of  custom,  392. 

Passion,  as  a  source  of  Error,  see  Error, 
Causes  of. 

Paul,  St.,  quoted,  399. 

TlfpioxV)  not  used  by  Aristotle,  but  the  verb 
iTfpifXf'i  in  relation  to  notions,  100. 

Peripatetics,  their  nomenclature  of  the 
parts  of  the  Hypothetical  Syllogism,  241. 

Persius,  quoted  on  Chrysippus,  as  inventor 
of  the  Sophism  Sorites,  268;  quoted,  272, 
479. 

Petersen,  referred  to  on  history  of  Catego- 
ries in  antiquity,  142. 

Petitio  Principii,  what,  369;  error  of  the 
phrase,  >A.,  see  Probation. 

Petrcs  a  Cornibus,  satirized  by  Buchanan, 
Beza,  and  Rabelais,  280. 

Philo,  5. 

Piiiloposus,  or  Grammaticus,  Joannes,  89; 
on  the  principle  of  Contradiction,  63, 196, 
207,  240,  241,  278,  i:96,  336;  referred  to  on 
analysis  of  Geometry,  339;  (or  Ammonius), 
his  definition  of  conversion,  514;  quoted, 
on  order  of  Premises,  624-5;  quoted  on 
Figure  of  Syllogism.  637-9. 

Philosophical  or  Logical  Presumption, 
principle  of,  450;  the  foundation  of  Induc- 
tion and  Analogy,  lA. 

Philosophy  of  Common  Sense,  the,  what, 
383;  well  stated  by  Aristotle,  lA. 

PiiocYLiDES.  Greek  epigram  by,  280. 

Piccartcs,  196. 

Platina,  referred  toon  death  of  Petrus  Hia- 
panus,  308. 

Platner,  Ernst,  referred  lo,  on  Logic  being 
a  formal  instrument  of  the  sciences,  26,249, 
456;  quoted  on  Figure  of  Syllogism,  646-7. 

Plato,  his  use  of  the  term  Dialectic,  5,  6;  (and 
the  Platonists)  considered  Dialectic  (>■  «.| 


INDEX. 


705 


Logic  and  Metaphysics)  as  a  science,  7; 
frequently  employed  tlie  laws  of  Excluded 
Middie  and  of  Contradiction,  62-5;  his 
(alleged)  Second  Atcibiades  spurious,  65;  rec- 
ognized the  law  of  lleason  and  Consequent 
or  Suihcient  Reason,  66;  employed,  in  ref- 
erence to  this  principle,  the  ambiguous  term 
otTia,  66,  340;  guilty  of  the  vice  of  circidus 
in  flemonurando,  in  his  proof  of  the  immor- 
tality of  the  soul,  372;  quoted  to  the  effect 
that  man  is  naturally  determined  to  com- 
munication, 479. 
Plato,  I'seudo,  quoted  on  teaching  as  a  mean 

of  self-improvement,  482. 
Platonists,  the,  referred  to  o:i  knowledge 

and  belief,  384. 
TlKaros,  its  meaning  in  relation  to  concepts, 

100. 
Plautus,  quoted  on  the  superiority  of  im- 
mediate to  mediate  testimony,  459. 
Pliny,  the  younger,  quoted  on  the  greater 
tendency  of  hearing  to  rouse  the  attention, 
484;  his  maxim  regarding  quantity  to  be 
read,  487. 
Plotinus,  his  employment  of  the  term  cntf- 
gory,  140:  referred  to  on  Categories,  142; 
referred  to  on  analysis  of  Geometry,  339. 
Ploucqukt,  Godfrey, 43;  referred  to  on  Pos- 
tulate of  Logic,  512;  quoted  on  Conversion, 
628;  referred  to  on  quantification  of  predi- 
eate,  558;  his  general  canon  of  Syllogism, 
658. 
PLUTAncH,  5,  331;  cited  on  the  benefits  of 

opposition,  481. 
PoNCius,  referred  to  for  scholastic  theories 

of  the  object-matter  of  Logic,  20. 
Pope,  Alexander,  has  borrowed  from  Ser- 
geant, G30. 
PoRPUYUY,  101,104;  quoted  on  the  relation 
between  the  Breadth  and  Depth  of  notions, 
104,  139;  made  two  moods  of  Darapti,  296. 
PonsoN,  Itichard,  his  imitation  of  an  e\n- 
gram  of  I'hocydides  as  applied  to  Hermann, 
280. 
Port  Royal  Logic,  see  L'Art  de  Penser. 
Postulates  of  Logic,  set  Logic. 
Postulates,  what,  188. 

Pn.a!DICATUM  pra-dicati  e.^t  etiam  prmdicatum 
subjecti,  the  canon  of  Deductive  Categorical 
Syllogisms  in    Comprehension,  214;    how 
otherwise  expressed,  ib. 
Precipitancy,  see  Error,  Causes  of. 
Predesionate  and  Preindesignate  Proposi- 
tions, what,  172,  see  Judgments,  Proposi- 
tions. 
Predicate,  of  a  judgment,  what,  161 ;  in  Aris- 
totle tlie  predicate  includes  the  copula,  ib.  ; 
called  the  trrm  or  extreme  of  a  proposition, 
ib. :  Quantification  of,  date  of  its  discovery 
by  author,  510;  its  results  specified,  510-11, 
624-7;  considered  in  detail,  516-20;  estab- 

89 


lished,  1°,  That  the  predicate  is  as  extensive 
as  the  subject,  516-17;  2°,  That  ordinary 
language  quantifies  the  predicate  so  often 
as  this  determination  is  of  importance,  517; 
this  done  either  directly,  or  by  Limitation 
or  Exception,  517-19;  3°,  The  doctrine  of 
the  non-quantification  of,  only  an  example 
of  the  passive  sequacity  of  the  logicians, 
519;  4°,  The  non-quautitication  of,  given 
up  by  logicians  themselves,  in  certain  casi-s, 
519-20;  logicians  {but  not  Aristotle)  rs- 
serted  that  in  aflSrmative  propositions  in 
which  subject  and  predicate  are  quantified 
to  their  full  extent,  the  predicate  is  distrib- 
uted in  virtue  of  its  matter.  526;  logicians 
wrong  in  their  doctrine  that  in  negative 
propositions  the  predicate  is  always  dis- 
tributed, ib. ;  objections  to  the  doctrine  of 
the  quantification  of,  considered,  539  ft 
seq  ;  I.  General,  —  objections  founded  on 
the  distinction  of  Formal  and  Material 
considered,  539-43;  .II.  Special,  — 1*^,  That 
it  is  false,  543-5;  2°.  Useless,  545-6;  histori- 
cal notices  regarding  quantification  of, 
546-559;  Aristotle,  545-9;  Alexander  Aph- 
rodisiensis,  549;  Ammonius  Hermia?,  545, 
549-51;  Boethius,  551-3;  Averroe.s  5.53;  Al- 
bertus  Magnus.  553-4;  Levi  Ben  Gerson, 
554-5;  Masters  of  Lou  vain,  555;  Titiua 
and  Kidiger,  ib. ;  Godfrey  I'loucqUL-t,  558; 
Ulrich,  559;  authors  referred  to  on  the 
doctrine  that  the  extension  of  predicate  is 
always  reduced  to  extension  of  su.bject, 
559;  authors  referred  to  on  the  doctrine  that 
predicate  has  quantity  as  well  as  subject, 
ib.;  references  to  Aristotle  for  use  of  dis- 
tributed predicate,  ib. 

Prejudice,  authors  referred  to  on,  894,  see 

Prelection,  Author's  Method  of,  2;  same 
as  that  prevalent  in  Germany  and  Holland, 
ib. 

Premise,  Premises,  of  Syllogism,  what.  198, 
199,  207;  Major  and  Minor  Premise  or 
Proposition,  i6.  ,•  objections  to  these  terms 
as  denominations  of  the  propo.sitions  of  a 
syllogism,  200;  their  designations,  ib. ;  best 
names  for  are  Sumption  and  Subsuniption,.,. 
199-201;  order  of  624;  Philoponus  quoted 
on,  624-5;  instances  and  authorities  for  the 
enouncement  of  syllogism  with  the  minor- 
premise  stated  first,  625-6. 

Prescision,  wliat,  88. 

Presentative  Faculty,  as  a  source  of  Error, 
see  Error,  Causes  of. 

Prevost,  456. 

I'rijxary  Laws  of  Thought, .««  Fundamental : 
Laws  of  Thought. 

Pri.vum  Cognitum,  controversy  regarding, 
156. 

Principi^m  Contradicentium,  sec  Lex  Contra-- 
dictoriarum 


roe 


INDEX. 


PnoBATiox.  Doetrine  of,  360-75;  its  diame- 
ter and  elements,  360;  these  explicated,  3C1 
et  seq.;  terms  employed  for  Probation, — 
Ari^umnntatioti,  Argument,  Demonstration, 
l^adint;  of  Proof,  361 ;  in  general,  what,t6.  ; 
how  distinguished  from  Syllogism,  t6.; 
whereon  depends  the  logical  value  of, 
861-2;  ground  of  Proof  either  tibsolute  or 
relative,  362;  distinctions  of  propositions 
in  respect  of  the  general  form  of  a  system 
of,  361-5;  divisions  of  Probations,  365  ;  the 
differences  of  probations  depend  partly 
on  their  matter  and  partly  on  their  form, 
>6. ;  (1)  In  respect  of  their  Matter,  they  are 
Pure  and  Kmpirical,  364-6;  this  distinction 
of  Probutions  not  taken  into  account  by 
Logic,  337;  (2)  In  respect  of  their  Form  this 
is  Internal  and  External,  365-6 ;  Probations 
are,  in  respect  of  Internal  Form,  a.  Direct 
and  Indirect,  366-7;  principle  of  indirect 
proof,  367-8;  differences  ot  Indirect  or 
Apagogical  Probations,  368;  b.  Deductive 
and  Inductive,  365-8;  c.  Synthetic  and 
Analytic,  365,  369;  in  respect  of  External 
form,  they  are,  1°,  Simple  and  Composite, 
2°,  Perfect  and  Imperfect,  3^,  Regular  and 
Irregular,  365-6;  (3)  In  respect  of  their 
Degree  of  Cogency,  they  are,  1°,  Apodeictic 
or  Demonstrative  and  Probable,  366;  2^, 
Universally  and  I'articularly  Valid,  ib. ;  the 
formal  legitimacy  of,  determined  accord- 
ing to  the  logicians  by  live  rules,  369-70; 
these  rules  reduced  to  two,  370;  the  five 
rules  explicated,  370  H  serj. ;  first  rule.  Noth- 
ing is  to  be  begged,  borrowed,  or  stolen, 
869-71 ;  its  violation  affords  the  Pttitio  Prin- 
cipi't,  339;  limitation  under  which  this  rule 
is  to  be  understood,  371;  second  rule,  That 
no  proposition  is  to  be  employed  as  a  prin- 
ciple of  proof,  the  truth  of  which  is  only 
to  be  evinced  as  a  consequence  of  the  prop- 
osition which  it  is  employed  to  prove,  3'j9- 
72;  its  violation  affords  the  vice  of  vtrrtpov 
itp6T(povy  339;  third  rule.  That  no  circular 
probation  is  to  be  made,  369-72;  its  violation 
affords  the  vice  of  Cimdus  in  demonstramlo, 
369;  regressive  and  progressive  proofs  not 
to  be  confounded  with  the  tautological  cir- 
cle, 373;  fourth  rule.  That  no  leap,  no  hia- 
tus must  be  made,  370-73;  its  violation  af- 
fords the  vice  of  Snltus  in  demonstrnmlo, 
370,373;  fifth  rule,  The  scope  of  the  proba- 
tion is  not  to  be  changed,  370-4;  this  rule 
admits  of  three  degrees,  374;  (1)  Mutatio 
EUnehi,  374;  (2)  Proving  too  little,  t6. ;  (3) 
Proving  too  much,  375. 

Problem,  the,  what,  198. 

Problemb,  what,  188. 

PnocLua,  referred  to  on  Knowledge  and  Be- 
lief, 384. 

Pbooressive  Method,  see  Method. 


Proof,  sre  Probation. 

Proportion,  Analogy  or  Identity,  law  of, 
as  a  fundamental  rule  of  syllogisms,  575; 
made  by  some  logicians  the  one  supreme 
canon  of  syllogism,  i6.;  logicians  by  whom 
this  law  is  confounded,  or  made  coordinate 
with  the  Dictum  de  Omni,  ib. ;  names 
given  by  logicians  to,  ib. ;  erroneously 
supposed  to  be  employed  by  Aristotle  as  a 
fundamental  rule  of  syllogism,  676;  terms 
under  which  enounced,  575-8 ;  Syrbius 
thought  that  this  law,  unless  limited,  is 
false,  577,  see  Syllogism. 

Propositio  Conrfitionnlis  nihil  ponit  in  esse, 
the  rule,  its  origin,  169. 

Proposition.  The,  name  for  major  premise, 
200;  but  ambiguous,  200-1. 

Proposition,  what,  159;  ius  synonyms,  159- 
60;  called  by  Aristotle  an  interval,  Sida-rv/JM, 
l''l ;  how  divided  by  the  logicians,  in  resp)ect 
of  quantity,  171;  propositions  distinguished 
by  the  author  into  Predesignate  (Defi- 
nite), and  Prcindesignate  (Indefinite),  ac- 
cording as  their  quantity  is  or  is  not  marked 
out  by  a  verbal  sign,  172,  see  Judgment^ 
distinctions  of,  in  respect  of  the  generaV 
form  of  a  system  of  proof,  362-3,  see  also  187 
et  seq.  ;  terms  of,  only  terms  as  terms  of  a 
relation,  615;  these  only  compared  as  quan- 
tities, ib. ;  of  no  consequence  logically 
whether  subject  or  predicate  of  be  placed 
first,  516,  527;  in  common  language  predi- 
cate often  placed  first,  516;  simply  an  equa- 
tion of  two  notions  in  respect  of  their 
extension,  525,  526-7,  528-9;  new  preposi- 
tional forms  resulting  from  the  doctrine  of 
a  quantified  predicate,  529  et  uq.,  see  also 
637;  these,  with  the  old,  in  all  eight,  529- 
30,  534-6;  their  literal  symbols,  629-30; 
their  notation,  ib. ;  quantity  of,  530  et  seq.; 
Indefinite  propositions  (of  the  logicians), 
better  Indesignate  or  Preinrlesignate,  ib.;  va- 
rious opinions  as  to  their  cla.'sification,  ib. ; 
authors  referred  to  on  this  subject,  530-31; 
prevalent  uncertainty  in  regard  to  Particu- 
larity and  its  signs,  531 ;  two  meanings  of 
some,  either  Semi-definite,  and  equivalent 
to  liome  only,  or  Indefinite,  and  equivalent 
to  some  at  least,  ib. ;  how  these  may  be  sym- 
bolized, 632;  Aristotle  and  logicians  recog- 
nized only  the  latter  of  these  meanings, 
631-2;  reasons  of  this,  532-3;  Dcfinitudeor 
Non-particularity  of  three  kinds,  531-2; 
how  these  forms  maybe  symbolized,  i6. ; 
effect  of  the  definite  article  ond  its  absence 
in  different  languages  in  reducing  the  defi- 
nite to  the  indefinite,  531;  to  what  the  In- 
definites of  Aristotle  correspond,  632;  logi- 
cians who  have  marked  the  quantities  by 
definite  and  indefinite,  532  ;  the  three  pos- 
sible relations  of  the  terms  of,  1.  Toto-total 


INDEX, 


•  707 


covnclusion,  2.  Toto-total  coiixclusion,  3. 
Iiicoinjjietc  coinclusion,  involving  Incom- 
plete coixclusion,  633;  the  whole  order  of 
best  and  uort-t  quantification  of  the  terms 
of,  throu^liout  the  two  qualities  of  Affirma- 
tion and  Kegatiou,  537-39,  see  Judgments, 
Doctrine  of. 

I'ROPOSITIOXES  tertii  arljactntis,  or  tfrtii  ad- 
jecti,  what,  102;  liow  designated  by  the 
Greeks  after  Aristotle,  161-2  ;  secundi  atlja- 
centis,  what,  1G2. 

ruoposiTiONES  Exponibiles,  the  doctrine  of, 
iis  given  by  logicians,  018-10,  see  Exclusive 
and  Excejjtive  Particles. 

ripoffATji^ts,  of  Theophrastus,  its  probable 
meaning,  611. 

l\p6Taais,  its  use  by  Aristotle,  159. 

I'RUTAOOUAS  and  Euathlus,  the  case  of, 
quoted,  334. 

ruovERBS,  The  Book  of,  cited,  480. 

I'SKLLUS,  Michael,  the  Synopsis  of  the  Orga- 
non  atti'ibuted  to,  in  all  probability  a  trans- 
lation from  llispanus,  308. 

I'SYCHOLOGY,  Empirical  or  Historical,  how 
distinguished  from  Logic,  17,  22. 

ruKCUOT,  rel'erred  to  on  Categories,  142) 
mnemonic  verse  for  Disjunctive  Syllogism, 
from,  231 ;  his  formula  for  the  Figure  of 
Syllogism  (in  Extension),  282;  referred  to 
on  the  predesignation  of  the  predicate  by 
nil  collectively,  559. 

I'UKE  and  Applied^  as  usually  employed  in 
opposition  in  Olerman  philosophy,  not 
proiK-'rly  relative  and  correlative  to  each 
other,  44;  pure  and  mixed,  applied  and  un- 
applied,  properly  correlative,  (6. 

Pure  and  Modal  Propositions,  180-81,  see 
Judgments. 

PuilE  Logic,  see  Logic. 

Qualities,  or  Modes,  what,  55;  their  syno- 
nyms, 55. 

QuiNTiLiAN,  260;  his  employment  of  the 
term  Eiuiii/meme,  278,  332;  his  maxim  re- 
garding quantity  to  be  read,  487. 

Rabelais,  280. 

Hamists,  maintain  logic  to  be  an  art,  7. 

Kamus,  referred  to  on  genus  of  Logic,  7, 142; 
his  illustration  of  the  distinction  between 
Abstract  or  General,  and  Concrete  or 
Special  Logic,  39;  referred  to  on  Method  in 
Logic,  341;  relierred  to  on  postulate  of 
Logic,  512;  quoted  on  Induction  of  Aris- 
totle, 593-4. 

Rapix,  referred  to  on  canon  of  syllogism, 
500. 

Reading,  see  Knowledge,  Doctrine  of  the 
Acquisition  and  Perfecting  of. 

Real  Definition,  see  Definition. 

Rbal  Induction,  see  Induction. 


Real  Truth,  see  Truth  and  Error,  Doctrine  of 

Reason  and  Consequent,  Law  of,  ste  Suffi- 
cient Reason. 

Reasoning,  see  Reasonings,  Doctrine  of, 
Syllogism. 

Reasonings,  Doctrine  of,  189-334;  the  act  of 
Reasoning,  what,  189-90;  this  illustrated  by 
an  example,  190;  the  example  given  is  a 
reasoning  in  the  whole  of  Extension,  and 
may  be  represented  by  three  circles,  191; 
the  reasoning  of  E.xtension  may  be  exhib- 
ited in  Comprehension,  191-3;  the  copula 
in  extension  and  comprehension  of  a 
counter  meaning,  193  ;  definition  of  the 
process  of  Reasoning  with  the  principal 
denominations  of  process  and  product, 
193-4;  these  explicated  and  illustrated,  194 
ft  set/. ;  1.  The  Act  of  Reasoning,  —  a  rea- 
soning is  one  organic  whole,  ib. ;  errors  of 
logicians  ou  this  point,  195;  utility  of  the 
process  of  reasoning,  ib. ;  2.  Terras  by 
which  the  process  of  reasoning  is  denom- 
inated, —  Heasoning,  Ratiocination,  Dis- 
course, Argu7nentation,  Argument,  Inference^ 
To  conclude.  Conclusion,  To  syltogizf,  CoUee- 
tio,  Colligere,  195-7;  general  conditions  of 
Rea.soning  or  Syllogism,  197,  see  Syllogism; 
reasoning  may  proceed  in  the  quantity  of 
Extension,  and  in  that  of  Comprehension, 
207  et  seq.  ;  reasonings  in  these  opposite 
quantities  explicitly  compared  and  con- 
trasted, 209  et  seq. ;  logicians  have  over- 
looked reasoning  in  Comprehension,  and 
have  thus  given  narrow  and  erroneous  defi- 
nitions of  the  major,  middle,  and  minor 
terms,  209-10,  «e  also  153  et  seq. ;  difficulty 
in  legai-d  to  the  doctrine  that  all  reasoning 
is  either  from  the  whole  to  the  part,  or 
from  the  parts  to  the  whole,  stated  and  ob- 
viated, 252,  see  Inference,  Syllogism. 

Reciprocating  Propositions,  common  doc- 
trine of  logicians  that  predicate  in  these 
quantified  vi  »nn«eri«,  526,  542,  544;  this  in- 
correct, 544  ;  authors  referred  to  who  hold 
that  they  may  be  simply  converted,  528; 
Pacius,  Alexander  Aphrodisiensis  referred 
to  on,  ib. ;  Fonseca  cited  against  their 
quantification  vi  mattritr.,  543. 

Rkui,  his  anecdotes  of  two  Peripatetics,  407. 

Reduction  of  Syllogisms,  the  whole  of  the 
rules  given  by  logicians  for,  unphilosoph- 
ical,308;  these  superseded,  809-18;  reductio 
ad  impossibile  applied  to  Baroco  and  Uocar- 
do.  but  awkward  and  perplexing,  312,  314. 

REGRESSn'E  Method,  see  Method. 

Reid  quoted  on  Conception,  78-80;  his  mis- 
takes regarding,  80,  81;  not,  however,  opc« 
to  Dr.  Gleig's  censure  on  this  point,  81. 

Reimaiius,  U.  S-,  anecdotes  cited  from,  of 
the  intlucnce  of  passion  on  opinion,  407; 
quoted  ou  canons  of  Syllogism,  565. 


t08- 


INDEX. 


^EixnoLD,  370. 

■IKeminisckncb,  as  a  source  of  Error,  see  Er- 
ror, Causes  of. 

■Eep RESENT ATION  {repreientatio),  the  term, 
sense  in  wliicli  it  lias  been  used  on  the 
'•Continent  since  the  time  of  Leibnitz,  90; 
want  in  English  of  a  term  to  express  what 
Is  thus  (improperly)  denoted  by  represen- 
'lation,  ib.;  Sense  in  which  used  by  the 
autlior,  i6. 

Eepugnajjce,  of  Notions,  equivalent  to  Con- 
••tradictory  Oj)position.  152. 

'Bedscu,  or  Keu.schius,  101,  243,  259,  311;  his 
'reduction  of  Baroco,  314,  315.  317,  313,  451, 
456;  quoted  on  canons  of  Syllogism,  501. 

■RHKTor.ic  to  Aleximder,  author  of,  his  employ- 
ment of  the  term  tnthymeme,  278. 

EiciiTKii,  ileinricli,  referred  to,  as  to  Logic 
not  being  properly  nn  art  of  Discovery,  20; 
quoted  on  the  dominion  which  Logic  gives 
us  over  our  thoughts.  33^,  45, 183,  312,  3S0. 

^ItlDiOER.  186;  noticed  the  error  of  those  who 
make  Sorites  only  of  comprehensive  whole. 
♦270;  erroneously  attributed  introduction  of 
Fourth  Figure  to  Galen  and  Scotus,  303: 
quoted  and  criticized  on  quautitication  of 
predicate,  555-8;  syllogistic  forms  pro- 
pounded by,  557-8. 

ROMAONOSI,  51. 
•■K()9LINO,  66. 

Kous-SEAU,  cited  on  the  difficulty  as  to  the 

origin  of  Language,  433. 
'Buiz,  Didacus,  referred  to,  on  history  of  dis- 
•tinction  of  Sensus  Compositi  et  Divisi,  326, 
«7S,  337. 

■SALTua  in  fiemimstrando,  what,  370-3;  only  a 
'  special  ou.sc  of  tlic  Petitio  Frincipii,  873,  see 
Probation. 

Samdeiison,  lUshop,  quoted  on  objects  not 
included  under  the  ten  categories,  140;  re- 
ferred to  on  mimes  of  propo.«itions  in  con- 
version, 185,227;  quoted  on  importance  of 
teacliing  as  a  mean  of  self-improvement, 
4*^3:  his  jiractice  in  reading,  487. 

Bauteii,  42;  quoted  on  canons  of  Syllogism, 
666. 

Savonarola,  quoted  on  canon  of  Syllogism, 

ScALioER,  J.  C.,  quoted  on  the  benefits  of 

»dijCussion,  431. 
ScuEjHLER,  131,  210,  210;    quotetl  on  what 
constitutes  a   Di.xjunctive   Koasoning,  232, 
240;    referred  to  on   Aristotle  and  Plato's 
vii;\vs    of    Method,    340;     rcferre<l     to    on 
Method  in   Logic,  311,342.458;  quoted  on 
I'ropositioncs  Exponibiles,  518-19;  referred 
to  on  opposition  of  Subalternation  «nd  of 
■fiubcontrariety,  532. 
8CI1EIDI.EU,  426,  48;;,  490,  492,  493- 
SouKLLiNO,  repudiated  tbc  principles  of  Oon- 


tradiction  and  Excluded  Middle  in  relation 
to  the  Absolute,  C4;  respect  in  which  his 
treatment  of  the  principle  of  Contradiction 
differed  from  that  of  Hegel,  ib. ;  placed  the 
law  of  Identity  as  the  primary  principle  of 
all  knowledge.  60. 

SCUMOLDERS,  451.  454. 

ScuoLiA,  what,  188. 

Scholiast  on  llermogenci,  his  doctrine  of 
the  Enthymomo,  279,  334. 

SciiOTTUS,  Andreas,  334. 

ScHRAM.M,  made  the  Inductive  Syllogisln 
deductive,  229. 

SciiULER,  referred  to  for  scholastic  theories 
of  tlie  object-matter  of  Logic,  20. 

SciiULZE,  G.  E  ,  56,  57,  69,  60,  88, 104, 162, 174, 
179, 183, 196,  215.  219. 

ScHWEinii.<EaBER,  200;  referred  to  on  true 
reading  of  Epictetus,  3.32. 

Science,  definition  of,  335-6;  its  perfection 
of  two  kinds —Formal  and  Material,  337; 
distinguished  as  Keul  and  Formal.  380; 
under  the  Keal  Sciences  are  included  the 
3Iental  and  Material,  3S0-81;  divided  into 
two  great  branches,  according  as  it  is  con- 
versant, P,  About  objects  known,  or,  2P, 
About  the  manner  of  ki. owing  them,  495-6; 
these  branches  called  respectively  Direct 
Science  or  Science  Simply,  and  Keflex  Sci- 
ence, the  Science  of  Science,  the  Method  of 
SciLMice.  495;  the  latter  falls  into  two  great 
bninches  as  it  is  conversant,  1°,  About  the 
laws  under  which  the  human  mind  can 
know,  or,  2^,  The  laws  under  which  what 
is  propo.<ed  by  the  human  mind  to  know, 
can  be  known,  493;  the  former  is  Logic 
proiHJrly  so  called,  the  latter  not  named,  ib.  ; 
but  in  its  parts,  called  Hetirflic,  Areltitec- 
tonie,  ib. ;  these  sciences,  res|K'ctively  devel- 
oiied  by  Aristotle,  and  by  Bacon,  ib.  ;  not 
inconsistent,  but  correlative  and  dependent, 
ib. 

Scotus,  John  Duns,  referred  to  as  to  genus 
of  Logic,  7;  referred  to  for  scholastic  theo- 
ries on  the  object-matter  of  Logic,  20;  (or 
St.  Augnstin)  quoted  as  to  Logic  being  the 
Ar.t  artimn  and  Sci'titia  .<c(>ii«iVirim7.  25,  42, 
227,291;  alleged  as  defending  the  Fourth 
Figure,  303;  this  erroneous,  i6,-  held  Feri- 
son,  Bocardo,  and  Felapton  as  useless,  be- 
cause concluding  indirectly, 318;  his  ground 
of  the  discrimination  of  major  and  miimr 
terms  in  tlic  Second  and  Third  Figures, 
629. 

Second  P'igure,  .ve  Figure. 

Seouy.  quoted  on  canons  of  Syllogism,  567. 

Selp-Ix)VE,  srf  Error,  Causes  of 

Seneca,  example  of  Sorites  from,  272,  .*»;; 
quoted  on  Division,  357;  quoteil  on  evil 
intiuence  of  precipitancy,  402;  quoted  on 
the  hope  of  dying  old,  as  an  illustration«f 


INDEX. 


TO^ 


precipitate  judgment,  402 ;  quoted  on  sloth 
as  a  source  of  error,  404,  480;  quoted  on 
teaching  as  a  mean  of  sell-improvement  in 
Uuowledge,  482;  Iiis  maxim  regarding  the 
quantity  to  be  read,  487. 

Seegeant,  John,  notice  of,  630;  bis  doctrine 
of  the  Second  and  Third  Figures,  630-31. 

Skxtus  Emi'iuicus,  5, 198,  339. 

'S  G  iiAVESANWE,  cited  ou  influence  of  Asso- 
ciation, 424. 

SiGWAUT,  referred  to  on  what  truly  consti- 
tutes a  Disjunctive  Keasoning,  234,  334,  344, 
375,  390. 

SiMPLicius,5;  referred  to  on  genus  of  Logic, 
7,65.      . 

Sloth,  $fe.  Error,  Causes  of. 

Smiolecius,  referred  to  ou  genus  of  Logic, 
7 ;  referred  to  for  8chola.stic  tlieories  of  the 
object-matter  of  Logic,  20,  42. 

Smith,  Adam,  quoted  on  influence  of  Asso- 
ciation. 422-3. 

Smkll,  469,  475. 

SooiETY,  influence  of,  as  a  source  of  Error, 
set  Error,  Cairecs  of. 

SoeBATi;9,  bis  saying  regarding  the  extent  of 
his  knowledge,  393-4. 

Solomon,  487.     ^ 

SQI'ATER  APAMEENSie,  211. 

SoPUls.'tf,  &te  Fallucies. 

SOKITES,  or  Chain  Syllogism,  257-74;  the 
second  variety  of  Complex  Syllogism,  280; 
what,  ib.;  its  form.uhc  in  Comprehension  and 
Extension,  ib. ;  Piogressive  and  Regressive, 
260-1;  authors  on,  in  general,  referred  to, 
261;  diagrams,  circular  and  linear,  illustra- 
tive of,  ib.;  concrete  examples  of,  261-3; 
the  formal  inference  equally  necessary  in, 
as  in  simple  syllogism,  263;  resolvable  into 
simple  syllogisms,  ib.;  tliis.illustrated,  263-4; 
equally  naturaJ  as  simple  syllogism,  204; 
may  be  either  Categorical  or  Hypothetical, 
ib.;  law8ofthe.se  forraus  of,  2t)4-5;  tbrmula 
of  Hypothetical  Sorites,  265;  resolution  of 
Hypothetical  Sorites,  progressive  and  re- 
gressive, into  simple  syllogismf*,  265-G ;  a  Dis- 
junctive Sorites  possitile  after  a  sort.  266-7; 
but  complex  and  unserviceable,  267;  his- 
torical notice  of  the  logical  doctrine  of,  ib. 
et  seq. ;  neither  name  nor  doctrine  found  in 
Aristotle,  ib. ;  but  the  principle  of  given  in 
Aristotle's  first  antipredieamental  rule,  268; 
the  term  sorites  never  applied  by  any  an- 
cient writer  to  designate  a  certain  form  of 
reasoning,  (6. ,-  with  them  denoted  a  par- 
ticular kind  of  sophism,  ib. ;  first  used  in  its 
present  acceptation  by  Laurentius  Valla, 
'.69';  the  process  of,  described  in  the  Dialec- 
tic of  George  of  Trebisond,  the  contempo- 
rary of  Valla,  ib. ;  the  doctrine  of  logicians 
regarding,  illustrates  their  one-sided  view 
of  the  nature  of  reasoning  in  general,  ib. ; 


the  Sorites  of  extension  overlooked,  and; 
that  of  comprehension,  the  progressive^ 
alone  contemplated  by  logicians,  270;  dif- 
lerence  between  the  two  forms  of,  ib. ;  probr. 
able  reiison  why  logicians  overlooked,  ia 
the  case  of  Sorites,  tJie  reasoning  in  extent- 
sion,  271-2;  examples  of,  in  comprehension 
and  extension,  272-3;  the  Goclenian,  or 
Kegressive  Comprehensive  Sorites,  273; 
names  given  to,  273-4;  before  Valla,  called 
vaguely  complex  syllogism,  274;  as  a  poly- 
syllogism,  comparatively  simple,  ib. ;  may 
bedrawm  in  any  figure,  320;  observations 
on,  619;  correction  and  amplification  of 
the  common  doctrine  of,  619-21;  diagrams 
illustrative  of,  620-21. 

SouiTES,  the  sophism,  its  derivation  and 
meaning,  268;  its  nature,  ib.;  said  to  have 
been  invented  by  the  Stoic  Chrysippus,  ib.  ; 
by  Eubulides,  ib. ;  called  (paXaKphs,  calvus, 
ib. ;  called  acervalis  by  Cicero,  ib. ;  its  char- 
acter, 332;  itfi  various  designations,  ib.; 
well  defined  by  Ulpian,  ib. ;  exemplified, 
332-3. 

Space,  or  Extension,  as  absolutely  bounded, 
unthinkable,  73;  as  unlimited,  inconceiva- 
ble, because  contradictory,  ib. ;  as  an  abso- 
lute minimum,  or  as  infinitely  divided, 
inconceivable,  74. 

Special  Logic,  see  Logic. 

Special  or  Concrete  Logic,  see  Logic. 

Species,  sff  Genus. 

Speculation  as  a  means  of  knowledge,  «« 
Knowledge,  Doctrine  of  the  Acquisition 
and  Perfecting  oL 

Stattleii,  42;  quoted  on  canons  of  syllo- 
gism, 566. 

Stepiianus,  H.,  85;  his  imitation  of  an  epi- 
gram of  Phocylides,  280. 

Stewart,  Dugald,  quoted  on  the  liability  of 
notions  to  vagueness  and  ambiguity,  123-5; 
■  refers  to  Hume  and  Campbell,  ib. ;  his  un- 
favorable strictures  on  the  alleged  modern, 
origin  of  certain  teehnicallogical  language, 
groundless,  146,  197,  418;  quoted  ou  influ- 
ence of  association,  421-3,  430,  431. 

Stoicheiology,  or  doctrine  of  Elements, .««« 
Logic. 

Stoics,  viewed  Logic  as  a  science,  7 ;  thei» 
nomenclature  of  the  parts  of  the  Hypothetfe 
ical  Syllogism,  241;  the  excogitation  of  the 
sophism  Ign/ima  Ratio  attributed  to,  33Q; 
but  this  doubtful,  331. 

Stbabo,  280. 

Stp.igelius,  526. 

SuABEZ,  on  the  principle  of  Contradiction, 
63,66;  referred  to  on  classification  of  the 
categories,  141. 

Subject,  of  a  Judgment  or  Proposition, 
what,  161;  called  term  or  txtretne,  ib.,  u* 
Judgments,  Propositiou. 


no 


INDEX. 


Subjective  Logic,  »ee  Logic. 

Subsidiaries  or  Aids  of  thinking,  Doctrine 
of,  ut  Logic. 

Subordination  of  Concepts,  ttt  Concepts, 
Relations  of. 

Sufficient  Reason,  or  Reason  and  Conse- 
quent, principle  of,  a  fundamental  law  of 
thought,  57  (frtit  we  61);  what  and  how  ex- 
pressed, 60;  relations  between  Reason  and 
Consequent,  60-1;  logical  significance  of, 
61 ;  discriminated  from  the  principle  of 
Cause  and  Effect,  ib.  ;  logiccU  and  metaphysi- 
cal reason  and  consequent,  ib. ;  these  both  in- 
cluded under  the  terms  condition  and  condi- 
tioned, ib.;  this  law  should  be  excluded 
from  Logic,  i6.  ,•  recognized  by  I'lato,  66; 
by  Aristotle,  ib.;  by  both  under  the  ambig- 
uous term  atria,  aXrtoy  (cause),  ib. ;  but  the 
principle  of  Knowledge  discriminated  by 
Aristotle  from  the  principle  of  Production, 
66-7 ;  comprehended  by  Cicero,  and  by  the 
schoolmen,  under  the  formula  nihil  sine 
tausa,  67 ;  but  under  that  discriminated,  ib. ; 
in  modern  times  attention  called  to  it  by 
Leibnitz,  ib. ;  but  not  adequately  discrim- 
inated by  him,  ib. ;  controversy  between 
Leibnitz  and  Dr.  Samuel  Clarke  on  this 
law,  among  other  points,  t6. ,-  assumed  by 
Leibnitz  as  the  foundation  of  Natural 
Philosophy,  ib. ;  the  form  of  the  Hypothet- 
ical Syllogism  determined  by,  239;  how- 
enounced  by  Wolf,  67;  discussion  regard- 
ing the  Leibnitian  principle  of,  63;  law  of, 
regulates,  in  conjmnction  with  that  of  ex- 
cluded middle,  Hypothetico-disjunctivesyl- 
logisnos,  204-5;  only  another  expression  of 
Aristotle's  law,  that  the  whole  is  neceasarily 
conceived  as  prior  to  the  part,  253-4;  au- 
thors referred  to  on,  509;  that  can  be  de- 
duced from  law  of  Contradiction,  ib.  ;  that 
cannot  be  so  deduced,  ib.,  set  Fundamental 
Laws  of  Thought. 

SuiDAS,  334. 

SuumoN  and  Subeumption,  best  names  for 
the  premises  of  a  syllogism,  199;  their  em- 
ployment vindicated,  199-200;  not  consti- 
tuted by  the  mere  order  of  enunciation, 
218;  what  truly  constitutes  these,  219. 

SuTEii,  quoted  on  canon  of  Syllogism,  567. 

Syllogism,  original  meaning  of  the  term, 
196;  borrowed  from  Mathematics,  ib. ;  Eu- 
genios,  Ulemmida.«,  and  Zabarella  quoted 
on  Import  of,  197, 198,  tt  seq. ;  general  con- 
ditions of,  197;  the  parts  of  which  com- 
po!<ed,  and  their  denominations,  197-8; 
these  explicated,  198,  et  seq.  ;  Tremises,  ma- 
jor and  minor,  190;  Sumption,  Subsump- 
tion,  Conclusion,  best  mimes  for  the  three 
propositions  of,  ifr. ;  Lemma,  Ilypolemma, 
t6. ,-  Assumption,  200;  objections  to  the 
denomiuations  of  the  propositions  of,  in 


ordinary  nse,  ib. ;  the  nse  of  Sumption  and 
Subsumption  sanctioned  by  precedent,  201 ; 
Divisions  of,  ib.  et  seq. ;  first  division  of 
Syllogisms,  comprehending  all  the  others, 
into  Extensive  and  Comprehensive,  201-2; 
matter  and  form  of,  202-3;  proximate  and 
remote  matter  of,  202  ;  the  form  affords  the 
next  grand  distinction  of,  203;  the  form  of, 
twofold  —  Internal  and  External,  ib.;  I. 
According  to  Internal  or  Essential  Form, 
Syllogisms  are  divided  into  four  classes,  as 
regulated  by  the  laws  —  1^,  Of  Identity  and 
Contradiction,  2^,  Of  Excluded  Middle,  2P, 
Of  Reason  and  Consequent,  and,  4°,  Of 
Excluded  Middle  and  of  Reason  .and  Con- 
sequent, viz.,  Categorical,  Disjunctive,  Hy- 
I>othetical,  and  Uypothetico-di-juuctive,  or 
Dilemmatic,  205-6  (but  see  598-600,  and  Infer- 
ence); these  four  classes  comprised  in  two 
genera.  Simple  and  Conditional,  206,  see 
Categorical,  Hypothetical,  Disjunctive  and 
Hypothetico-disjuuctive  Syllogism;  Cate- 
gorical Syllogism,  the  one  class  under  the 
genus  Simple  Syllogism,  206;  its  general 
I  nature,  206-7;  may  proceed  in  the  quantity 
j  of  Extension,  and  in  that  of  Comprehen- 
sion, 207-8;  examples  of  tMb  Extensive,  and 
of  the  Intensive  or  Comprehensive  Cate- 
gorical Syllogism,  203;  these  reasonings  or 
syllogisms  explicitly  compared  and  con- 
trasted, 209  et  seq. ;  logicians  looking  only 
to  the  reasoning  in  Extension  have  given 
narrow  and  erroneous  definitions  of  the 
Major,  Middle,  and  3Iinor  terms,  209-10; 
Aristotle's  definition  of  these  will  apply  to 
both  quantities,  210-11,  see  aUo  154-5.  ste 
Terms  of  Syllogism  ;  most  convenient  node 
of  stating  a  syllogism  in  an  abstract  form 
by  the  letters  S,  V,  M,  211-12  (hut  see  674. 
676,  678);  divided  into  special  classes  accord- 
ing to  the  application  of  the  laws  of  Iden- 
tity and  Contradiction,  under  the  relation 
of  whole  and  part,  212  tt  seq  ;  this  rela- 
tion may  be  regarded  in  two  points  of 
view,  and  thus  affords  two  classes  of  Rea- 
sonings, viz..  Deductive  and  Inductive, 
212-13;  I.  I>eductive  Categorical  Syllogism, 
character  of  the  process  in,  213  tt  seq. ;  its 
canons,  in  Intension  and  in  Extension, 
213-14;  connection  of  the  propositions  and 
terms  of,  illustrated  by  sensible  symbols, 
214-15;  proximate  rules  of,  1  Extensive  — 
Three  Rules,  215;  tirst  rule  of,  illustrated, 
216-17;  second  rule  of,  illustrated.  217-19; 
misconception  in  regard  to  definition  of 
Sumption  in  second  rule  obviated,  218-19; 
third  rule,  219-20;  2.  Intensive,  three  rules. 
222  tt  seq  ;  first  rule  illustrated,  223;  second 
rule  illustrated.  223-4;  grounds  of  the  rules 
regarding  Sumption  and  Sul>sumption  in 
Extensive  and  Comprehensive  Syllogisms. 


INDEX, 


711 


224;  third  rule  illustrated,  224-5;  II.  In- 
ductive Categorical  Syllogism,  what,  225; 
views  of  logicians  regarding  the  nature  of 
this  reasoning  erroneous,  225  et  seq.,  see  In- 
duction ;  canons  of  the  Deductive  and  Induc- 
tive Syllogisms  equally  formal,  227;  these 
reasonings  illustrated,  227-8;  objection  obvi- 
ated, 228;  formula)  for  Inductive  Syllogisms 
in  Compreljension  and  Extension,  228-9; 
Whately  and  others  erroneously  make  the 
inductive  syllogism  deductive,  229;  doctrine 
of  the  older  logicians  different,  and  correct 
as  far  as  it  goes,  229-30 ;  though  the  Cate- 
gorical Syllogism  is  specially  regulated  by 
the  laws  of  Identity  and  Contradiction, 
still  the  other  logical  laws  also  operative  in, 
261;  Divisions  of  according  —  II.  To  E.xter- 
nal  Form,  257-320  ;  A.  Complex,  —  Epi- 
cheirema,  and  Sorites,  257-74 ;  relation  of 
syllogisms  to  each  other,  258;  classes  and 
designations  of  related  syllogisms,  ib.  ; 
Monosyllogism,  what,  i6.;  Polysyllogism, 
what,  ib.;  this  Analytic  and  Synthetic,  i6.  ; 
Prosyllogism,  ib. ;  Episyllogism,  ib  ,  see 
Epicheirema,  Sorites;  probable  reason  why 
logicians,  in  the  case  of  simple  syllogisms, 
overlooked  the  reasoning  of  Comprehen- 
sion, 270-71;  divisions  of,  according  to 
External  Form,  B.  Defective,  —  Enthy- 
meme,  275-81,  iee  Euthymcme;  C.  Regular 
and  Irregular,  281-320,  .<ee  Figure,  Mood, 
Reduction  of  Syllogisms;  irregular  by  re- 
lation, 1°,  To  the  transposed  order  of  its 
Propositions;  2°,  Of  its  Terms;  3^  Of  both 
its  Propositions  and  Terms, 281-2;  doctrine 
of  logicians  regarding  the  regularity  and 
irregularity  of,  in  respect  of  the  order  of 
its  propositions,  281;  this  one-sided  and 
erroneous,  282;  in  respect  of  its  Terms,  a 
syllogism  is  regular  or  irregular,  according 
to  the  place  which  the  Middle  Term  holds 
in  the  premises,  ib. ;  regular  and  irregular 
order  of,  in  Comprehension  and  Extension, 
282;  the  relative  position  of  the  Middle 
Term  in  a  syllogism  constitutes  its  Figure, 
i6. ;  the  Four  Figures  of,  ib. ;  mnemonic 
verses  for  Figures,  ib.,see  Figure  of  Syllo- 
gism; regularity  and  irregularitj^f,  expli- 
cated, 283  et  seq. ;  irregularity  in  external 
form  of,  arising  from  transposition  of  the 
I'ropositions,  283-5;  can  be  perspicuously 
expressed  by  any  of  the  five  irregular  con- 
secutions of  its  propositions,  283-4;  true 
doctrine  of  consecution  of  syllogism,  which 
is  either  Synthetic,  the  premises  being 
placed  first,  the  conclusion  last,  or  Ana- 
lytic, the  conclusion  preceding,  the  prem- 
ises following,  284-5;  second  ground  of 
regularity  and  irregularity  of,  —  the  natu- 
ral and  transpo.sed  order  of  the  Syllogistic 
Terms,  285  et  seq.,  set  Figure  of  Syllogism; 


all  the  varieties  of,  divided  into  classes,  ac- 
cording to  their  Validity,  viz.,  into  Correct 
or  True,  and  Incorrect  or  False,  321;  the 
meaning  of  these  terms  as  applied  to  syllo- 
gisms determined,  322;  incorrect,  divided 
into  Paralogisms  and  Sophisms,  321-3  ;  this 
distinction  not  of  directly  logical  imi;oit, 
323;  but  not  altogether  without  logical 
value,  ib.;  incorrect,  vicious,  either  in  re- 
spect of  their  form,  or  of  their  matter,  or 
in  respect  of  both  form  atid  matter,  322-3; 
syllogisms  incorrect  in  respect  of  their  mat- 
ter lie  beyond  the  jurisdiction  of  Logic, 
323;  syllogisms  formally  incorrect,  to  bo 
judged  by  an  application  of  the  rules  of 
syllogism,  ib.,  .^ee  Fallacies;  how  distin- 
guislied  from  Probation,  361;  on  the  mu- 
tual relations  of  the  terms  of,  in  quantity 
and  quality,  through  the  ai)plicatJon  of  the 
doctrine  of  a  quantified  predicate.  536-9; 
general  canon  of,  53i5;  the"  three  possible 
relations  of  terms,  —  1.  Toto-total  Coinclu- 
sion;  2.  Toto-total  Coijxclusion ;  3.  Incom- 
plete Coinclusion,  involving  Incomplete 
Cocxclusion,  ib. ;  the  fiist  is  the  best,  the 
second  the  worst,  the  third  intermediate, 
ib. ;  the  whole  order  of  best  and  worst 
quantification  throughout  the  two  qualities, 
537;  application  of  this  doctrine  in  special 
cases  of  the  general  canon  of,  in  the  12  af- 
firmative and  24  ne;;ative  moods.  537-9 ; 
Canons  of,  general  historical  notices  re- 
garding, 559-79;  quotations  from  various 
logicians  on,  559-75;  Derodon  referred  to 
in,  559-60;  Kapin,  560;  Leibnitz,  560-61; 
Reusch,  561;  Crusius,  561-3;  iiutchoson, 
663-4;  Savonarola,  564;  Alex.  G.  Baum- 
garten,  564-5;  Reimarus,  565;  Waldin, 
565-6;  Stattler,  566;  Sauter,  j6.  ;  Suter,  567; 
Seguy,  567;  Hoflbauer. 567-8;  Kant,  568-9; 
Christian  Weiss,  569;  Fries.  570-2;  Kiese- 
wetter,  572;  Larroque,  572-4;  Galluppi,  574; 
Buffler,  ib. ;  Vietoi  in,  575;  references  to  au- 
thors on  fundamental  laws  of,  575-6;  enun- 
ciations of,  576-8;  Dictum  de  omni  et  nullo, 
criticized,  578;  general  Ipws  of,  in  verse, 
578-9 ;  criticism  by  the  author  of  the  spe- 
cial laws  of,  579-83;  the  author's  supreme 
canons  of,  583-4;  doctrine  of.  attacked,  as 
involving  a  petitio  principii,  621;  how  this 
objection  is  to  be  met,  621.  0-3  ;  this  objec- 
tion made  by  Stewart  and  refuted  by  Gal- 
luppi, 623;  its  enouncement—  Analytic  and 
Synthetic,  621-2;  these  met  hods  of  enounce- 
ment compared,  622,  623;  Unflgured  and 
Figured,  626;  difference  of  Figure  of,  of  no 
account,  626-7. 

Symbolical  and  Intuitive  Knowledge,  m« 
Concepts,  Quality  of. 

Synthesis,  338,  see  Method. 


712 


INDEX.. 


Tacitits,  quoted,  427. 

Tartauetus,  I'etrug,  commentator  on  His- 
imiius,  1.S7,  MB. 

Tk-nnkmanx,  142. 

'i  LUMftofa  riopofition,  sfe  Proposition. 

■|  liij.MS  of  Syllogism,  Major,  Minor,  and 
Jlifklle,  what,  207;  borrowed  from  Matlie- 
iiiatic!--,  210;  their  synonyms,  j6.;  in  Exten- 
sion the  predicate  of  the  conclusion  the 
greatest  whole,  and,  therefore,  the  major 
term,  the  subject  the  smallest  part,  and, 
therefore,  the  mir.or  term.  20";  incompre- 
hension, the  subject  of  Die  conciusiou  is 
the  greatest  whole,  and,  therefore,  the  ma- 
j6r  term,  the  predicate  the  smallest  part, 
and,  therefore,  the  minor  terra,  ib. ;  narrow 
and  erroneous  dclinitions  by  logicians  of, 
209-10:  Aristotle's  definition  of,  210;  his 
definition  of  the  middle  term  as  middle 
by  i)osilion  not  applicable  to  the  mode  in 
wliich  subsequent  logicians  enounce  the 
syllogism,  ih.;  but  applicable  to  the  rea- 
soniag  in  Compreher.sion,  211;  poss-ible  to 
state  a  reasoning  in  E.\ttMision  in  which  the 
major  term  shall  stand  first,  the  middle 
second,  and  the  minor  lat-t,  i6.  ,•  what  is 
projKjrly  to  be  regarded  as  a  term  of  syllo- 
gism, 216. 

Testimoxv,  what,  457;  explicated,  458  ft  aeq  ; 
its  picpcr  object,  45S-9;  the  object  of,  called 
tl'.c  Fact,  451);  the  validity  of.  called  Hix- 
torical  Cr-rlibilittj,  ib. ;  cither  immediate  or 
mediate,  ib.  ;  an  immediate  witness  styled 
au  ei/e-icitne.\x,  ib  ;  n  mediate  an  enr-witne^^, 
ib. ;  the  f^iiamiiifr,  wl;a:,  ib. ;  testimony  may 
be  I'artial,  Comp'etc.  (onsisfent,  Contrn- 
dictorv,  ih.:  divi.-ion  of  the  subject:  — I. 
(.'redibilily  of  Testimony  in  general,  ib.  et 
.*<■</  ;  1'^,  The  olject  of  the  testimony  —  its 
absolute  possibility,  400;  physical  and  tnet- 
aphrsiCHl  possibility,  460-61:  its  relative 
l)<)s.>-ibilit.y,  451 ;  '2P.  The  subject  of,  or  per- 
K)iial  trustworthiness  of  tJie  witness,  ib.; 
this  consists  of  two  elements,  a.  Honesty  or 
veracity,  461-2;  the  presumption  of  the 
honesty  of  a  witness  enhanced  by  certain 
circumstances,  462;  b.  Compcttnicy  of  a 
witness,  ib. ;  circumstances  by  which  the 
pivsumpfion  of  competency  is  enhanced, 
(6.  ,■  the  credibility  of  Testimony  not  invali- 
dated because  the  fhct  testified  is  one  out 
of  the  ordinary  course  of  experience,  463; 
summary  regarding  the  credibility  of  testi- 
mony in  general.  4(i3-i;  II.  Testimony  in 
special,  as  immediate  and  m-idiate,  464  et 
Sfq. ;  1^,  Immediate,  ib. ;  conditions  of  its 
credibility,  il>. ;  whether  all  these  condi- 
tions are  fulfilled  in  the  case  of  any  imme- 
<liate  testimony,  cannot  be  directly  ascer- 
tained, 461-5;  when  testimony  attains  the 
taigliest  degree  of  probability,  465;  iiegativ" 


and,  positive  discrepancy^  46%ff;  2°,  Sledi- 
ate,  4GG  ft.seq. ;  mediate  wJine.-ises  are  eitiier 
proximate  or  remote,  and  either  indepen- 
dent or  dependent,  468-7;  liumor,  Tiadi- 
tion,  ib.;  Recorded  Testimony,  468  ft  seq. ; 
Criticism  and  luterpretutiou,  what.  468-9; 
these  explicated,  ^)9  n  seg. ;  the  examina- 
tion of  a  testimony  twofold — of  ita  Au- 
thenticity and  Integrity,  and  of  its  Meaning, 
ib.;  the  former  the  problem  of  Criticism 
(Criticn),  the  latter  of  Interpretation  or 
exposition  (H-rjnemutica,  Eregetica),  470; 
I.  Criticism  considered  in  detail.  470-74;  its 
problems,  470;  Universal  and  Special  Criti- 
cism, ib. ;  Universal  Criticism  alone  within 
the  sphere  of  Logic,  ib  ;  this  divided  into 
Higlier  and  Lower  Criticism,  or  the  Criti- 
cism of  Authenticity  and  the  Criticism  of 
Integrity,  ib.;  (1)  Criticism  of  Autlienticity, 
470-71;  a.  Internal  Grounds,  these  of  them- 
selves not  suiBcieut  to  establish  the  authen- 
ticity of  a  writing,  471;  but  omnipotent  to 
disprove  an  alleged  authenticity,  ib.;  b. 
External  Grounds,  ib. ;  (2)  Criticism  of  In- 
tegrity, 472-4;  emendation  of  the  text  of 
two  kinds —  viz..  Historical  and  Conjectu- 
ral, 472;  historical,  of  two  kinds.  External 
and  Internal,  473;  Conjectural,  t6.,-  II.  In- 
terpretation, 474-5:  Generjil  and  Special, 
474;  sources  of  interpretation,  475. 

Text-Book,  its  use  in  a  systematic  course  of 
Lectured.  2. 

TuEMiSTiL'S,  referred  to  on  genus  of  Logic, 
7,  479. 

Thegphkastcs,  referred  to  on  use  of  the 
term  rates;oTicnl,  K5, 172:  his  nomenclature 
of  the  parts  of  the  Hypothetical  Syllogism, 
241;  quoted  on  hearing,  484;  made  two 
moods  of  Daiapti,  686;  this  opinion  adopted 
by  Porphyry,  ib. ;  and  by  Boethius,  ib. ;  but 
opposed  by  the  author,  i&. 

Tbeouems,  what,  18H. 

Third  Figure,  ser  Figure. 

TuoMAfsius,  Jacobus,  holds  that  simple  ap- 
prebensiou  is  impossible  without  judgment, 
84. 

Thought,  the  Products,  of,  ate  Concepts, 
Judgm?iit8,  Keaiiouiug. 

Thought,  what,  9  ft  seq. ;  in  its  wider  mean- 
ing, equivalent  to  every  cognitive  act,  or 
even  to  every  conscious  mental  modifica- 
tion,9;  in  its  narrower  meaning  as  thought 
proper,  denotes  the  acts  of  the  Understand- 
ing proper,  9-10;  in  the  hitter  sense,  the 
object-matter  of  Logic,  9:  Matter  and  Form 
of,  disthiguished,  11;  phenomena  of  for- 
mal, of  two  kinds,  contingent  and  neces- 
sary. 17;  necessary  form  of,  implies  four 
conditions, —  (1)  Determined  by  the  nature 
of  the  thinking  subject  itself,  (2)  Original, 
(8> Universal,  (4)  A  Law,  17,  18;  its  Mii^^ 


INDEX. 


713 


form,  iiiul  matter  disciiminatccl,  £3;  as  the 
■object  respectively  of  Psychology  and  of 
Logic,  »Va  ,-  a  mcdinte  and  complex  cogni- 
tion, 54-5;  the  various  terms  by  wliich  the 
modes  'of  thought,  or  cogitable  existence, 
are  designated,  55-G;  what  is  involved  in 
thinking  an  object,  55;  the  attribution  im- 
plied in,  regulated  by  laws,  56,  see  Funda- 
mental Laws  of  Thought;  distinction  of 
Positive  and  Negative,  73;  its  products  are 
of  three  kinds,  —  Concepts,  Judgmer.ts,  and 
Heasouings,  83  ft  alibi;  these  arc  all  prod- 
ucts of  comparison  and  all  moditications  of 
Judgment,  S3-4,  see  Concepts,  Judgments, 
Reasonings;  its  formal  or  logical  perfec- 
tion consists  of  three  virtues, —  Clearness, 
Distinctness,  and  Harmony,  335,  340. 

TiMPLER.  37,  13S;  referred  to  on  whole  and 
part,  143,  140. 333,  339. 

TiTiDS,  Gottlieb  Gerhard,  referred  to  on  ap- 
plication of  quantification  of  predicate  to 
the  Hypothetical  Proposition,  512;  his  doc- 
trine of  Conversion  proceeds  on  the  doc- 
trine of  a  quantitied  predicate,  627;  quoted 
on  quantification  of  predicate,  556;  his 
doctrine  of  Hypothetical  Syllogism  as  pro- 
ceeding on  the  application  of  the  principle 
of  a  quantified  predicate,  603;  his  doctrine 
of  Disjunctive  Syllogism,  ib.;  held  both 
forms  merely  to  be  the  matter  of  regular 
syllogism,  ib. ;  his  doctrine  of  the  Figure 
and  Mood  of  Syllogism,  652-8. 

TiTTKL,  435. 

Topic,  employed  by  Aristotle  to  denote  a 
particular  part  of  Logic,  6. 

ToussAiNT,  435. 

Transuexdent  and  Transcendental,  their 
original  application,  and  use  by  Kant,  140. 

TuENDELENnuRO,  F.  A.,  referred  to  on  the 
title  Orifaiion  for  the  logical  treatises  of 
Aristotle,  24;  referred  to  for  the  doctrines 
of  tlie  Platonists  and  Stoics  on  the  Catego- 
ries, 142, 188,  260.  333. 

Troxler.  33,  249,  333. 

Truth,  its  division  into  Logical  and  Metg- 
physical,  criticized,  76;  what,  ib. ;  logical 
discriminated  from  absolute,  322,  see  Truth 
and  Error,  Doctrine  of. 

Truth  and  Error,  Doctrine  of,  376-90;  Truth 
and  Certainty,  what,  377;  Truth  is  defined 
the  correspondence  or  agreement  of  a  cog- 
nition with  its  object.  377,  378;  this  defini- 
tion due  to  tlie  schoolmen,  378;  Aquinas 
quoted  to  this  eflect,  ib  ;  philosophers 
agreed  as  to  the  definition  of  truth,  ib  ; 
questions  in  debate  regarding,  —  whether 
truth  be  attaliial)Ic,  and  wlwther  we  possess 
any  criterion  by  AVincli  we  can  be  assured 
of  its  attainmenf,  Jh  ;  lor  niiin  only  two 
kinds  of, —Formal  and  Heal,  .37'J;  I.  For- 
mal Truth,  the  harm<>ny  of  Thouglit  with 

90 


the  form  of  Thought,  ib. ;  Formal  Truth  of 
two  kinds. —  Logical  and  JIathematical, 
379-80;  II.  Keal  Truth,—  the  harmony  be- 
tween a  thought  and  its  matter,  3S0;  Ileal 
and  Fcrmal  Sciences,  380-81 ;  How  can  wo 
know  that  tliere  is  a  correspondence  be- 
tween our  thought  and  its  object?  381;  fub- 
divis^ions  of  Real  Truth,  —  Jletaphysic.Tl, 
Psychological,  Physical,  381-2;  various  a]  - 
plications  of  the  term  truth,  SSI;  tlie  cri;e- 
rion  of.  —  the  necessity  determined  by  the 
laws  wliich  govern  our  faculties  of  knowl- 
edge, 377-82;  Certainty,  the  consciousness 
of  this  necessity,  382;  truth  considered  in 
relation  to  the  degree  and  kind  of  certainty 
is  distinguished  as  Knowledge,  Belief,  and 
Opinion,  377-83;  Knowledge  and  Belief,  ~ 
their  dilTurence,  383;  that  the  certainty  of 
all  knowledge  is  ultimately  resolvable  into 
a  certainty  of  belief  maintained  by  Luther, 
ib.;  by  Aristotle,  383-4;  by  the  Platoni.sts, 
384;  by  David  Hume,  ib. ;  the  manifestation 
of  Belief  involves  knowledge,  3S5;  Intui- 
tion, what,  ib.;  the  question  as  to  the  rela- 
tion of  belief  and  knowledge  properly  met- 
aphysical, »6. ;  Pure  and  Empirical  Truth, 
distinguished,  385-6;  Error,  its  character 
and  sources,  3S7;  this  explicated,  ib.  et  seq. ; 
as  the  opposite  of  truth,  consists  in  a  want 
of  agreement  between  a  thought  and  its 
object,  387;  distinguished  as  Slaterial.  38-: 
as  Formal,  ih.;  when  closely  scrutinized  is 
found  to  arise  from  the  want  of  adequate 
activity  of  the  cognitive  faculties,  ib.;  dis- 
criminated from  Ignorance,  389;  from  Illu- 
sion, lb.,  ste  Error,  Causes  of. 

TSCHIRXHAUSliN.  25. 

TwEPTEN.  237,  377,  387;  quoted  on  the  nature 
of  Error.  387-9;  quoted  on  ignorance,  Illu- 
sion, €tc.,  389-90. 

Ulpia>',  his  doctrine  of  the  Enthymeme,  279; 

his  definition  of  the  Sorites,  3.32. 
ULniCH,  184, 2S9;  quoted  on  quantitication  of 

predicate,  559. 
Ultua-total  Quantification  of  SliddleTerm, 

Lambert's  doctrine  of,  384-0;  this  doctrine 

criticized,    6S4-5;     author's    doctrine    of, 

586-8. 
Universal  Propositions,  171.  see  Judgments. 
"TcTTepoy  TrpArtpov,  see  Probation. 

Vali-a,  Laurentius,  142,  261;  first  to  use  the 
term  Sorites  m  its  present  application.  269; 
quoted  on  Conversion.  527;  his  doctrine  of 
the  Second  and  Third  Figures,  €29-30. 

Valerius  Maximus  (?)  quoted,  4-4. 

VALLiU8,Paulus,  quoted  on  Conversion,  628, 
553 

VA  KILL  AS,  485. 

Versok,  liis  doctrine  of  IiKlucfion,  596. 


714 


INDEX. 


Victoria,  338,  344;  quoted  on  canons  of 
Sj'Ilogism,  575. 

Vi^jTORixus,  liis  doctrine  of  Enthymeme,  279. 

VlTlDM  Subreptionis,  what,  427. 

ViVES,  Liulovicus,  198;  his  opinion  regard- 
ing silent  meditation  as  a  means  of  intel- 
lectual improvement  combated  by  Scal- 
iger,4Sl;  quoted  on  importance  of  teaching 
as  a  mean  of  .self-improvement.  483. 

VOET,  or  Voetius,  Gisbert,  liis  conduct  cited 
as  an  instance  of  the  influence  of  passion 
on  opinion,  406. 

Vossius,  Gerard  John,  referred  to  on  genus 
of  Logic,  7;  referred  to  for  scholastic  theo- 
ries of  the  object-matter  of  Logic,  20,  37. 

Waitz,  quoted  regarding  \oyiK)i  avopia,  4, 
85.  160, 186,  193,  240. 

•VValcii,  261. 

Waldin,  quoted  on  canons  of  Syllogism, 
565-6. 

Wallis,  Dr.  John,  his  Institutio  Logictr,  21; 
referred  to  on  names  of  propositions  in 
Conversion,  185;  referred  to  on  character 
of  Hvpotlietico-Disjunctive  Syllogism,  249; 
his  English  version  of  the  Latin  mnemon- 
ics for  the  four  kinds  of  propositions,  287. 

AValz,  333. 

Watt8,  Dr.  Isaac,  25;  his  Logic,  50. 

Weoelin,  514,  547. 

Weise,  Christian,  e\pployed  (before  Euler) 
circular  diagrams  as  logical  notation,  ISO. 

Weiss,  Christian,  1C9;  quoted  on  canons  of 
Syllogism.  569. 

Wkrenkelsius,  his  De  Lngomarhiis  Erudilo- 
Tinn  referred  to,  433. 

WiiATELY,  Dr..  his  definition  of  Logicquoted 
and  criticized,  7-9;  general  character  of 
his  Elements  of  I^gir,  21 ;  his  view  of  the 
object-matter  and  domain  of  Logic,  stated 
and  criticized,  21-3;  propo.«es  to  Logic 
diflereiit  and  contradictory  object-matter, 
22  ft  se(/. ;  the  ojieration  of  Ueasoning  not 
tlie  object-matter  of  Logic,  us  affirmed  by, 
ib.;  erroneously  and  contradictorily  makes 
Language  the  object-matter  of  Logic,  22-3; 
the  true  nature  of  Logic  more  correctly  un- 
derstood by  the  scholastic  logicians  than  by, 
23;  his  EUmnUs  nf  Logic,  50;  omits  the  doc- 
trine of  Concepts  from  his  Elements  of 
Logic,  84;  abusively  employs  the  terms  Ex- 
tension and  Comprehension  as  convertible, 
85, 184;  follows  Aldrich  in  his  abusive  em- 
ployment of  the  phrase  propofitio  erposiln, 
185-6;  his  abusive  employmentof  the  terms 
hypothetical  and  conditional,  167;  quoted  ou 
the  modality  of  propositions,  182;  his  doc- 
trine criticized,  ib. ;  his  reduction  of  the 
rules  of  Categorical  Syllogism  to  six,  215, 
454. 

Wholk  aad  Fart,  what,  143;  whole  per  se, 


and  whole  per  aecidens,  ib. ;  whole  per  te 
dividud  into,  1°,  Logical  or  Potential,  2°, 
Metaphy-icrJ  or  Actual,  3^,  Physical,  4^, 
Mathematical,  5°,  Collective,  143-4;  the 
terms  subjfrt  and  subjective  as  applied  to  the 
Logical  Whole  and  Parts  144;  the  term. 
potential  as  applied  to  denote  the  Logical 
Whole,  145;  Lord  Monboddo  quoted  on 
potential,  libS;  Stewarfs  strictures  on  the 
pai=sage  from  Monboddo  rebutted,  146; 
Monboddo  wrong  in  ascribing  the  author- 
ship and  application  of  the  term  potential 
to  Eugenius,  146;  both  term  and  applica- 
tion to  be  found,  with  few  exceptions,  in 
all  the  older  systems  of  Logic,  ib. ;  Burg- 
ersdyk  quoted  as  an  example,  i6.  ;the  dif- 
ference of  the  Potential  and  Actual  Whole 
noticed  by  Aristotle,  ib. ;  all  reasoning 
under  the  relation  of,  191,212;  this  relation 
may  be  regarded  in  two  points  of  view,  and 
thus  affords  two  classes  of  Reasonings,  — ' 
Deductive  and  Inductive,  212-13;  diflSculty 
in  connection  with  Hypothetical  Syllo- 
gisms in  regard  to  the  doctrine  that  all  rea- 
soning is  either  from  the  whole  to  part  or 
from  the  parts  to  the  whole,  —  considered 
and  obviated,  262  tt  seq.;  Antecedent  and 
Consequent  in  Hypotheticals  equal  to  Con- 
dition and  Conditioned,  253;  hence  the 
reason  or  condition  must  contain  the  con- 
sequent, ift.  ,•  the  law  of  Reason  and  Con- 
sequent only  another  cxpres.«ion  of  Aris- 
totle's law,  That  the  whole  is  necessarily 
conceived  as  prior  to  the  part,  253-4;  Aris- 
totle's law  criticized,  254;  Whole  and  Parts 
respectively  may  be  viewed  in  thought 
either  as  the  conditioning  or  as  the  condi- 
tioned, 254;  application  of  this  doctrine  to 
the  solution  of  the  difficulty  previously 
stated,  255. 

Wilson,  his  English  metrical  version  of  the 
Latin  mnemonics  for  the  four  kinds  of 
Propositions,  287. 

AVoLF,  Christian,  misapplied  the  terms  Logica 
docens  and  Logica  vtens,  42  ;  his  division  of 
Logic  into  Theoretical  and  I'ractical,  ib .  ; 
used  the  phrase  excliisio  medii  inttr  eontradic- 
toria,  65;  called  the  principle  of  Identity 
principivm  certiliidinis,  66;  did  not  sufB- 
ciently  discriminate  the  principles  of  Ident- 
ity and  Contradiction,  ib. ;  his  formula  for 
the  law  of  Sufficient  Reason,  67;  blamed  the 
schoolmen  for  not  distinguishing  reason 
{ratio)  and  cause  {causa),  ib.;  attempted  to 
demonstrate  the  law  of  Sufficient  Reason 
by  that  of  Contradiction,  68  ;  quoted  on 
Intuitive  and  Symbolical  Knowledge,  129- 
31,178,227;  made  the  inductive  syllogism 
deductive,  229,  240,  24S,  261;  his  reduction 
of  Baroco,  341,  343, 451,  456. 

WoLFiA>'S,  some,  distinguished  judgments  as 


INDEX. 


715—731 


Limitative,  1T9;  followed  by  Kant,  178;  the 
distinction  groundless,  179- 

Words,  n'e  Language. 

"Wyttenbach,  Daniel,  5;  his  Logic  recom- 
mended, 50,  332;  referred  to  on  Analysis 
and  Synthesis,  435. 

ZAit.\iiELLA,  Jacobus,  referred  to  on  genus 
of  Logic,  7;  referred  to  for  scholastic  theo- 
ries  of   the   object-matter  of   Logic,  20 ; 


quoted  on  import  of  the  term  crv\Koytafi6s, 
197,  230,296;  held  Cesare  and  Camestres  to 
be  the  same  syllogism,  310,  sef  aUo  296,  336, 
838,  451. 

Zedlke,  456. 

Zeko,  the  Stoic,  said  by  Laertius  to  have 
purchased  the  knowledge  of  seven  fpeciei* 
of  the  argument  Koyos  bepi^uy  for  two 
hundred  raiu%,  331. 


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