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EXERCISES IN LOGIC.

EXERCISES IN LOGIC:

DESIGNED FOli THE

USE OF STUDENTS IN COLLEGES.

J. T. GRAY, Ph. D.

'Syllogismus assensum consinngit."—Bacou.

LONDON

TJKIVERSIT7J

TAYLOR AND WALT0N7

BOOKSELLERS AND PUBLISHERS TO UNIVERSITY COLLEGE,

28, UPPER GOWER STREET.
1845.

J^ ^ ^U U

PREFACE.

The following little work makes no preten-
sions to any other originality than that of plan.
It has been prepared under the conviction,
elsewhere expressed by the author, that a
practical skill in logic can only he attained hy a
practical acquaintance with its rules, and that
the means of a more progressive application of
these, than has yet been furnished in works on
the subject, was still a desideratum.

Of the examples given under the various
exercises, the author has supplied a consider-
able proportion himself; but for, perhaps, the
majority he is indebted to preceding writers.
His obligations to Archbishop Whateley in
particular, in this, as well as in other respects,
are of an extent to claim special acknowledg-
ment. From the views of this distinguished
logician, on one or two points, the student will

VI PREFACE.

perceive, as he proceeds, that dissent is freely
expressed. Occasional strictures on other
writers of celebrity, both ancient and modern,
will also be found interspersed in the notes.

The concluding chapters on the different
hinds of argument scarcely amount, the
author is aware, even to a sketch of a subject
inferior neither in interest nor utility to any
part of the science. Should the present pub-
lication be judged seasonable, he may here-
after expand these chapters into a separate
treatise. Next to the ever-recurring ambi-
guity of language, there is no more prolific
source, he is satisfied, of confusion in reason-
ing than indistinct conceptions on the topics
which they embrace.

It only remains to be noticed, that the
observations and examples which have a ^
prefixed to them, are designed for the especial
use of theological students.

10, South Crescent, Bedford Square,
July \6thy 1845.

CONTENTS.

CHAP. I. On Terms page 1

II. On the Predicables ....

III. On Genus and Species

IV. On Generalization ....

V. On Division

. 10

VI. On Definition

VII. On Propositions ....

. 16

viii. On Subject and Predicate

IX. Propositions classified and symbolized .

X. On Distribution

XI. On Opposition

XII. On Conversion

xiii. On the Copula

XIV. On Trifling Propositions

XV. On Compound Propositions

XVI. Recapitulatory Exercise ....

XVII. On Arguments

XVIII. On Syllogisms

XIX. On Categorical Syllogisms

XX. On the Canons of Syllogisms

XXI. On the Moods of Syllogisms

XXII. On Figures

XXIII. On Figures (continued J ....

XXIV, On Figures (continued)

CONTENTS.

CHAP XXV. On Compound Syllogisms

PAGE 62

XXVI. On Sorites

XXVII. Recapitulatory Exercise

. 72

XXVIII. On Hypothetical Syllogisms

XXIX. On Conjunctive Hypothetical

. 81

XXX. Hypotheticals Reduced

XXXI. On Disjunctives ....

. 87

XXXII. On Dilemmas ....

XXXIII. Recapitulatory Exercise .

. 93

XXXIV. On Probable Arguments.

XXXV. On Cumulative Arguments

. 99

XXXVI. On the ' A Fortiori' Argument .

102

XXXVII. On Subjects of Arguments

. 106

XXXVIII. On Fallacies ....

109

XXXIX. On Material Fallacies

. 113

xii. On Ambiguous Middle

118

xLi. On Kinds of Argument .

. 125

xiiii. On Kinds of Argument (Continued)

130

xLiii. On Kinds of Argument f Concluded J

. 134

Appendix — Logical Puzzles

141

Indices

. 147

fUHIVBESITT]
EXERCISES IN LOGIC.

CHAPTER I.

ON TERMS.

Whatever we can make an object of separate con-
templation is, when expressed in language, a Term.

Of such objects some are * Substances,' and some
^ Attributes,' the latter term being intended to include
what by some are made a third class, ^Relations.'
(The above division embraces three, of the ten* cate-
gories of Aristotle : the remaining seven may be
considered either as conditions of the existence of
substances, or as heads to which attributes may be
referred.) It is the peculiarity of substances that
they do not admit of degrees ; that they are sus-
ceptible of contrary states, but have themselves no
contraries. One main distinction of them is into
material and spiritual; iron and the other metals

* The names of these categories, as enumerated by Aristotle, are : —
Substance, Quantity, Quahty, Relation, Place, Time, Situation,
Habitude, Action, Passion. How unphilosophical this analysis is, it
is needless to remark ; ' action ' and ' passion, are plainly modes of ' re-
lation ' — and ' situation ' nothing but a mode of * place.' * ^

2 EXERCISES

hein^ instances of the one, and every human mind of
the* other. Attributes follow the same division, and
there is besides a class belonging to the common no-
tion of ^ Being/ under which both ^ Substance ' and
'Attribute' are comprehended, and which may be
termed ' metaphysicaV We may instance ^Dark' as
an attribute of the first class, ^Suspicious' of the
second, and ^Variable' of the third.

Another division of Substances and Attributes
(consequently of Terms) is into simple and complex;
butthe following distinctions will (to the logical stu-
dent) be of more frequent recurrence :

1 2 3

^^'^-^-^^'TCity I (U^fud Father ) ^--' J^ '^^ Wise . )
SC^^^^^MA. I London] I Son ) -^^^H Wisdom)

( Wise I I - Wise )

^ iFoohsh — Unwise] 1 Foolish — Wealthy )

1. Names* which stand for a class of things arej^^//
termed ^Common;' those which represent a single! £^
thing only ' Singular ; ' or they may be termed sub-
stantively, ' Individuals.'

* This division corresponds with that of the author of the categories
into primary and secondary substances, the * Singulars' being those which
he denominates primary ; it is only this class of substances, he justly
remarks, which have a real existence.

IN LOGIC. • O

2. Terms* expressive of objects, of which one
as ' Father/ implies the existence of the other, are
styled ^ Correlatives.'

3. Terms which represent qualities as they inhere
in some subjects, as ' Wise,' are denominated ' Con-
crete;' 'Abstract ' terms, such as 'Wisdom,' represent
the qualities as existing by themselves.

4. Of the terms here coupled together, the former
of those in the lower line, 'Foolish,' is styled the
' Contrary ' of that above ; the latter its ' Contradic-
tory;'! this is a direct negative of the upper term,

* Aristotle, in his %(f,Trf/mai^ ch. v., has some sentences to show
that this mutual implication is not invariable ; but his reasoning on the
subject is vitiated by a latent ambiguity. The instances, which he
alleges, in proof of his position, are l^idTYirlv and s'7rt(frr}fL7i ; the for-
mer of which may signify either an object of actual knowledge, or an
object of possible knowledge; and the latter accordingly. Now it seems
as certain as any metaphysical truth can be, that as an object of actual
knowledge implies actual knowledge, so does an object of possible
knowledge, possible ; and vice versa.

f In popular usage perhaps the term * Unwise ' has as much a positive
as a negative m6aning ; but we wish it to be taken in its etymological
import as Not-wise, as denoting, i. e. all to which the epithet ' Wise ' is
not applicable. Terms with the negative prefix thus before them
(whether expressly or virtually) are sometimes called ' Indefinite,'
(termina injinita) as not restricting the view to any class or individual,
but simply excluding one, and taken in connection with the correspon-
ding definite term, must be considered as exhausting the possibilities
of existence, in any given respect. Every thing whatever must be
either 'organized,' or * not-organized ' * corporeal,' or * incorporeal. '
On this account the following sentence from a writer usually luminous
and accurate seems open to objection : —

** The most considerable discovery of Mr. Grey was that all material
substances might be reduced, in reference to electrical phenomena, to

4 ' EXERCISES

and is applicable to objects not in the same class,
while the other simply denotes the most widely differ-
ent objects of any in the class.

5. The distinction here noticed is that of ^ Oppo-
site' and 'Compatible ' terms ; the same person cannot
be at the same time ' Wise ' and ' Foolish/ but may
be at the same time both ' Wise ' and ' Wealthy.

Exercise.

Explain the distinctions between the subjoined
pairs of Terms : —

(Mortal I (King | (Corj)oreal|

(Mortality) 1 Subject) I Spiritual )

(Corporeal | CKiver ) (Preceptor |

(Incorporeal) (Thames) (Pupil )

(Hard) (Hard) (Beauty ) (Giving )

(Soft ) (Cold ) (Beautiful) (Keceiving)

(Eight ) (Secure ) (Secure )

( Obligation ) ( Dangerous ) \ Insecure J

(Horse ) (Attract) (Ferocious)

(Bucephalus) (Repel ) I Ferocity )

two classes, electrics and non- electrics.'' — Lardnefs Electricity ^ Vol.
1, p. 7.

A division, which it was competent to any logical student acquainted
with the term * electrics' to make, could not be a * discovery.'

IN LOGIC.

CHAPTER II.

ON THE PREDICABLES.

Wine is a juice 1.

extracted from grapes 2.

inebriating 3.

sweet 4.

In the above lines is exhibited a succinct example
of what the Schools have termed the " Five Predica-
bles," i. e., of the five things, one or other of which
must be affirmed, whenever any thing is affirmed
concerning another thing.

1. 'Wine' and 'juice' are said to be related to
each other as 'Species' and 'Genus/ that is to say,,
'juice' is a 'Genus,' (or class) in which 'wine' is
included as a ' Species' (or subordinate class.)

2. The quality which distinguishes 'wine' from
all other 'species' of juice, is its being 'extracted
from grapes ;' the logical name for a quality of this
kind is the ' Difference.'

3. A quality which belongs universally to a species,
(as that of 'inebriating' to 'wine,') without being
its distinguishing quality is termed a ' Property' of it.

4. A quality which does not belong thus uni-
versally to a species, but is present only in some of the
individuals which compose it, is termed an 'Accident:'
thus some kinds of Avine only are ' sweet,' others not
so.

B 2

EXERCISES

Exercise.

Specify which of the above relations the lower
terms of the subjoined pairs sustain to the upper.

(Rose I (Gold ] (Bird |

1 Flower j I Heavy 3 1 Winged j

(Dictionary) [Dictionary ) (Winter)
(Book 3 I Alphabetical 3 {Cold 3

(Plough ) (Poetry) (Science )

I Implement 3 I Rhyme 3 (Geometry)

(Square ) (River) j Blood)

I Rectangular 3 1 Swift I i Red )

(Man I (House ) (Inspired writers)

I Civilized] 1 Cottage) 1 Apostles J

CHAPTER III.

ON GENUS AND SPECIES.

The most important of the distinctions noticed in
the preceding chapter is, beyond all comparison, that
of ^ Genus and Species;' it is a distinction which will
meet us continually in subsequent parts of these
exercises, and claims, therefore, a separate and fuller
consideration.

IN LOGIC. 7

We have seen that ^wlne' is a species of ^ juice/
which is said to be its genus; now ^wine' may be
regarded as itself a ^ genus' having under it the sub-
ordinate species, ^port,' ^claret/ ^champagne/ &c., and
similarly ^juice' may be itself referred to a higher
genus liquor.' In distinguishing the two kinds of
species from each other, we should call ^wine' the
proximate species of ^ juice/ and ^port/ &c., remote
species; and similarly with the genera.

A genus which is not itself a species of any thing,
is called its highest genus, a species which is not a
genus of anything, its lowest species ; in enumerations,*
it is improper to rank higher and lower species to-
gether ; thus e. g. to speak of flowers as being ^roses,'
lilies,' ^waterlilies,' ^violets,' &c., would be illogical,
the third article being manifestly included in the
second.

* It would be unreasonable to expect that this law of co-ordination
should be observed very strictly in animated composition, but where
we may assume that it has been observed, we shall sometimes be
enabled to decide between two meanings of a word, otherwise equally
eligible. Thus in Hebrews, xi, 37, where it is said of the ancient
worthies, that, " They were stoned, they were sawn asunder, they were
tempted, they were slain with the sword : " unless we may interpret the
third verb employed " seduced by promises of favour," we shall have
a genus mixed up in the enumeration with three of its species. A
similar observation will apply to a passage in the Corinthians, 1 Cor.
i, 30 : Who (i. e. Christ) of God is made unto us wisdom, righteous-
ness, sanctification and redemption. Redemption, in Scripture, is
sometimes put for the blessings of salvation generally, sometimes spe-
cifically for the resurrection of the human body. It is only on the
supposition that the latter is the kind of redemption intended here, that
the enumeration will be one of co-ordinate items.

:%^^:r:^:^^^ :^

y^^ OF THE

fnUIVEESITY)

mo; terms.

EXERCISES

Exercise 1

) intermediate species

between t^

Animal

MastifF

Instrument

Sword

Vessel

Frigate

Word

Adverb

Action

Perjury

Coin

Shilling

Eite

Baptism

Afflicted

Paralytic

Exercise 2

In the following enumeratipns specify the illogical
items.

Animals are Horses, Lions, Dogs, Spaniels,

Hares, &c.

Colours are White, Red, Crimson, Black,

Green, &c.

Compositions are Histories, Poems, Odes, Orations,

Essays, &c.

Subjects are Artisans, Manufacturers, Sea-

men, Sailors, Peasants, &c.

Virtues are Temperance, Integrity, Honesty,

Gratitude, &c.

Diseases are Consumptions, Nervous Fevers,

Fevers, Dropsies, &c.

IN LOGIC.

CHAPTER IV.

ON GENERALIZATION.

" When in contemplating several objects^ and find-
ing that they agree in certain points, we abstract the
circumstances of agreement, disregarding the differ-
ences, and give to all and each of these objects a
name applicable to them in respect of this agreement"
— when, in other words, to adopt the technical lan-
guage employed in the preceding chapters, we refer
two or more species to a common genus — we are said
to ^generalize.' The process of generalization is one
of the first importance in reasoning, and in every
branch of inquiry after truth. The power of employ-
ing it at pleasure has been regarded, and perhaps
with good reason, as the characteristic distinction of
the human mind. As examples of the process, we
may quote from the preceding chapter the reference
of the species ^port,' ^sherry,' ^claret,' &c., to the
genus ^wine,' or that of the species ^rose,' ^lily,'
^ violet,' &c., to genus ' flower.'

Exercise.
Refer the subjoined groups of terms to suitable

EXERCISES

/"Weaver "I
LCutler J

rSickness^
\Health J

r Diseases "I
\Accidentsj

{Kingdom"!
Republic j

/"Captain"!
tColonelJ

/"Adversity ^
I^Prosperityj

r Colours!
\ Odours J

/"Love "\
\ Hatred J

t TMiracles 1 rFaith"!
\PropheciesJ \Hopej

r Inflation* "1
"\_EdificationJ

/"Fencing"!
I^Dancingj

r Gluttony"!
\Ebriety J

r Tragedy"!
\ Comedy J

/"Acquittal 1
LCondemnationJ

r Knowledge* "!
\Love J

CHAPTER V.

ON DIVISION.

Logical division is the exact opposite of generali-
zation, consisting in the distribution of a ^ genus'

* See 1 Cor. viii, 2, As a further exercise the theological student
may set himself to generalize the particulars enumerated in Rom. ix,
3, 5 : viz. from the ' adoption ' to the ancestry of Christ. This will
be found sufficiently easy. A more perplexing group is that which
occurs in another epistle of the same writer, Heb. xii, 21 — 25. " We
are come to Mount Zion, &c." It is scarcely necessary to say that the
difficult items to a logician in this enumeration, are the last and the last
but three, the former on account of its apparent tautology, the latter
from its adaptation to excite solemn rather than cheerful emotion.

IN LOGIC. 11

into its several species: e. g., we divide the genus
^ flower' into the species ^ rose/ ^ lily,' ^ violet/ &c.

[* This kind of division must be carefully distin-
guished from physical division, which is the separation
of a whole into its component parts, thus —

Logically, ^ fruit' is divided into ^ orange,' ^ peach,'
^nectarine,' &c.]

Physically, ^ fruit' is divided into ^peel,' ^pulp,'
^ kernel;^ stalk,' &c.

There may be often two or more logical divisions
of the same genus, according to theprinciple on which
we proceed in dividing; e.g., a book would be di-
vided, according to its contents, into ^poetical,'
' historical,' &c. ; according to its size, into ' folio,'
^quarto,' &c. In enumerating the members of a
division, care must be taken that these different
species are not intermixed with each other, which
is styled ^ cross division.'! The rule by which
it is usually sought to obviate this error, is, that
the parts enumerated must be opposed to each other,
as ^ folio,' e.g. is to ^quarto,' not contained in each
other,

* A single consideration will suffice to show the importance of this
distinction :

What is true of a * logical whole' is true of each of its parts.
What is true of a * physical whole' by no means so.

f In the following sentence from Burke (Reflec. on Fr. R§v. p. 208,
ed. Dodsley, 1790) there seems, at least, an approach to an offence
against this rule.

"History," he says, "consists for the greater part of the miseries
brought upon the world by pride, ambition, avarice, revenge, lust,

12 EXERCISES

Exercise 1.

Explain whether the subjoined divisions are logical
or physical.

1. ^Oratory' may be divided into — ^deliberative/
' forensic', ' demonstrative.' — Aristotle,

2. ' Grammar' may be divided into — ' Orthography,
' Etymology,' ^ Syntax,' and ^ Prosody.'

3. ' Goodness of memory' may be divided into —
' susceptibility', ' retentiveness,' ' readiness.' — Dugald
Stewart,

4. ^Virtue' may be divided into — ^justice, ^tem-
perance,' ^fortitude,' and ^prudence.'

5. ' Repentance' may be divided into — ^ confession,'
^ contrition,' and ' amendment.'

6. ^ Consummate generalship' consists in ' military
skill,' ^valour,' ^authority,' and ^ good fortune.' —
Cicero,

7. Happiness consists in —

The exercise of the social affections :
The exercise of our faculties in the pursuit of some
engaging end :

sedition, hypocrisy, ungoverned zeal, and all the train of disorderly
appetites, &c."

Here the inclusion of * sedition' and * hypocrisy,' in an enumeration
of active principles of our nature, seems illogical, neither of them
being such a principle, but rather the effect of other principles, appear-
ing in the conduct.

ON Loaic. 13

The prudent constitution of the habits :
Health. — Foley,

Exercise 2.

Distinguish by* proper conjunctions the cross divi-
sions in the following enumerations.

1 . Men are — merchants, farmers, laAvy ers, negroes,
wliites, Pagans, Christians.

2. Substantives— are masculine, feminine, proper,
common, &c.

3. Triangles are — isosceles, scalene, right-, obtuse-,
acute-angled.

CHAPTER VI.

ON DEFINITION.
To prevent the confusion which arises in reason-
ino; from the indistinct or variable use of terms.

* [Sc. the conjunctions * either' and *or'] A slight attention to the
punctuation of a sentence will often remove the confusion occasioned
by an apparent cross division. So, in Romans viii, 38, 39 :

" For I am persuaded that neither death nor life ; neither angels, nor
principalities, nor powers ; neither things present, nor things to come ;
neither height, nor depth, nor any other creature shall be able," &c.

It is superfluous to inform the classical student that the substitution
which we have thrice made in the above version of * neither' for * nor,'
would not be necessary in the original text, qmtz being the term used in
each instance.

14 EXERCISES

recourse is usually had to ^definition.' ^Logical
definition' (with which alone we are here concerned)
is effected by the specification of the ^ genus' and
^difference/ of a term, the former serving to mark
the points in which it agrees with other terms of the
same kind, the latter those in which it differs from
them. Thus, if ' logic' were defined to be ' The Art
of Reasoning,' we should explain this definition to
consist in the enunciation of its 'genus' as an ^art,'
and of its ^ different as the art ' of reasoning.' Simi-
larly, we might define the ^ scriptures' to be ^ The
Writings of the Old and New Testament,' that part
of the definition which is in italics being the 'genus'
of the term and the remaining part its ' difference,'"^

It is matter of indifference whether in a definition
we enunciate the 'genus' or the 'difference' first;
thus if ' virtue' were defined to be ' moral excellence,'^

* It follows from this account of the nature of logical definition, that
there are some terms which are incapable of being defined. Such are
alike those which have no * genus' (or none which is not purely meta-
physical) and those which have no single or no assignable ' difference. '
Under the first head will fall necessarily the *summa genera' in the
various departments of the objects of thought. Take, as an instance,
the genus * Motion.' To define this (as has been done) * the act of a
being in power, in so far as it is in power' is to resort for an explana-
tion of a term in Physics to the nomenclature of Ontology. Watts's
definition of it, * a change of place,' lies open to the same censure ;
for besides that such change is rather the result of motion than the
process itself, the term change is a 'metaphysical' (or ontological)
term, and therefore inapplicable to the elucidation of one which is
purely 'physical.'

Examples of the two cases of want of a * difference' in terms which
we have noticed may be derived from almost any of the simple sub-

IN LOGIC. 15

the genus to which it is here referred would be the
latter of the two terms.

In some cases, the mention of the ^ genus' is
omitted as being; too obvious to need enunciation.
Thus, when ^wisdom' has been defined to be ^the
adaptation of good means to good ends' we are to
consider the whole of this expression as constituting
the 'difference'' of the term, the ' genus ^^ which, if
the reference be to divine wisdom, is such a term as
' perfection' or ' attribute,' being understood.

Exercise 1.

Analyze into their respective ^genera' and ^differ-
ences ' the following definitions of terms.

A meadow is a field devoted to pasturage

A pension is an allowance for past services

Rhetoric is the art of speaking persuasively

Honesty is uprightness in pecuniary transactions

Slavery is compulsory subjection to a master

stances in nature, or of the sensible qualities which belong to them.
There is no single property which distinguishes ' gold' from other metals,
nor could any mere words convey an idea of the * difference ' which
distinguishes ' white ' from other colours. ( See Locke on the Under-
standing, book iii, ch. § 4. ) Little inconvenience, however, is sustained
from this, as it is precisely the terms which are unsusceptible of
definition which do not, in general, require it. Where any doubt could
exist as to the sense they might suggest, it may be sufficiently precluded
commonly, by mentioning their contraries, or by specifying some of
their concrete combinations; as, e. g., * white' might be explained to
be the opposite of ' black ' or the colour of * snow.'

16 EXERCISES

Poetry* is metrical composition

Bigotry is exclusive attachment to a party

Modesty is self-esteem not greater than what is

becoming
Bashfulness is self-esteem less than what is so
Conscience is the faculty by which we judge of

right and wrong
Sin is the transgression of the law

Exercise 2.

Define by ^ genus' and ^difference' the following
terms.

An island Patriotism Courage

A garden Prejudice Politeness

A chair Gratitude Pride

CHAPTER VII.

ON PROPOSITIONS.

When two terms are compared together, with a
view to judge of their agreement or disagreement,
the sentence expressing the decision arrived at, is
called a ^proposition.' Defined logically therefore,

* The accuracy of this definition will doubtless be questioned by
many, and exceptions will perhaps be taken against other of the
examples, (there being no fixed standard to which the terms are
referable) but their utility as exercises will remain.

IN LOGIC. 17

a proposition is ^a sentence assertive'* i. e. affirming
or denying, the term ' sentence' in this definition being
the genus, and ^assertive' the difference. In every
proposition there will be accordingly two (and only
two) terms, of which one will be always predicated,
i. e. affirmed or denied of the other. These terms
are named the ^Subject' and the ^Predicate,' the
Subject being that which is predicated or spoken of,
the Predicate that lohich is predicated of it. Thus,
in the sentence, ^ a stone is hard,' ' a stone' is the
subject, (being the thing spoken of) and 'hard' the
predicate (being the thing spoken of it;) the sub-
stantive verbf 'is' which expresses the predicability,
lis called the ' Copula.' It follows from this account of
a proposition, that sentences expressing a wish, or
conveying a command, or interrogative ones which
ask for information do not come under the name;
the subjoined may serve as further specimens of real
propositions.

1. Terms are [either abstract or concrete]

2. Who would be [insane enough without a hope

♦ Whateley says * indicative,' but it may be doubted whether this
epithet would now convey to any one the ideas of affirmation and
denial.

f According to some writers, (see Whateley, p. 62) the substantive
verb is the only one which Logic can recognize. This is too strong,
as the distinction of the copula is often one rather of convenience than
necessity. When we come to speak of arguments, we shall see that in
various clashes of propositions, the copula may be dispensed with.

C 2

18 EXERCISES

of future recompense to undertake constant labours?]
3. Gold [surpasses all metals in brilliancy]

[Note, the Predicates in each of these propositions are indicated by
brackets. ]

Observations.

1 is a specimen of a compound proposition, of which
more in a subsequent chapter.

[It is plain from this No. as also from 2 and 3, that a term may
consist of several words.]

2. Questions of appeal are implied propositions,
being plainly equivalent either to affirmative or
negative ones; thus the above question is evidently
tantamount to ^No one would be, &c.'

3. Propositions which do not explicitly contain
the Copula may be easily resolved into those which
do ; thus, we might state 3, ^ Gold is superior to all
metals in brilliancy.'

Exercise.

Express the following propositions in strict logical
form, making the Copula (where necessary) apparent,
and distinguishing the Subject and Predicate.

1. Are such abilities as the human made for no
rpose ?

2. Remorse follows disobedience.

purpose ?

m LOGIC. 19

3. Exercise promotes health.

4. A philosopher should understand geometry.

5. Friendship has no tendency to secure veracity.

6. Who is pleased to have his all neglected ?

CHAPTER VIII.

ON SUBJECT AND PREDICATE.

The following examples will illustrate some of the
varieties in the form or in the mutual relation of the
Subject and Predicate of a Proposition to which it is
desirable to attend.

1. [To tell all that we think] is inexpedient.
[Rising early] is healthful.

2. " Better [to reign in hell than serve in heaven."]
It is unlawful [to kill an innocent man.]

3. There is [no such thing as witchcraft.]

4. [The less] is blessed by the better = [He who
is blessed] is less than (i. e. is inferior in
dignity to) him who blesses.

[Note, the Subjects in the above propositions are bracketed.]
OBSERVATIONS.

1. As in Grammar, an infinitive-, participial-, or
other clause may be used instead of a noun, as the
Subject of a proposition.

20 EXERCISES

2. The Subject will sometimes succeed the Predi-
cate, though its common order is to precede it. In
this case it is often represented at the beginning
of the sentence by the pronoun 4t.'

3. Where the substantive verb is introduced by
the adverb there, it is itself both Copula and Predi-
cate, being equivalent to ' exist''

4. The apparent Subject and Predicate of a propo-
sition are not always the real ones.*

Exercise.

Distinguish the Subject and Predicate in the fol-
lowing propositions.

1. There can be no natural desire of artificial
good.

2. Men are governed by affection rather than by
reason.

3. Leading vanquished enemies in triumph is a
barbarous custom.

4. " The wise for cure on exercise depend."

5. Of good things even the signs are good.

6. Whatever is undertaken should be gone through
with.

7. " Sweet is the breath of morn."

8. H That the soul be without knowledge is not
good. (Prov. xix, 21.)

* No general rule will supersede the use of practical dexterity in
discovering the true analysis of a sentence. For another explained
example see Chap. 15, Note.

IN LOGIC. 21

9. Pure religion and undefiled is this — to visit
the fatherless, &c. (James i, 27.)

10. In the mouth of three witnesses shall every
word be established. (Matt, xviii, 16.)

11. God is not the God of the dead, but of the
living. (Matt, xxii, S2.)

CHAPTER IX.

PROPOSITIONS CLASSIFIED AND SYMBOLIZED.

Propositions may differ both as to their quantity
and quality. According to the former, they are
either universal or particular ; according to the latter,
either affirmative or negative. With any given sub-
ject and predicate then we may (leaving, for the
present, the truth or falsity of the predication out
of consideration) form four distinct propositions, viz :

1. A universal affirmative :

2. A universal negative :

3. A particular affirmative :

4. A particular negative : e.g.

1. All cowards are cruel.

2. No cowards are cruel.

3. Some cowards are cruel.

4. Some cowards are not cruel.

22 EXERCISES

The above kinds of propositions have^ for conve-
nience' sake, been denoted by logicians by the symbols
A, E, I, O, respectively, so that

A = Universal affirmative.
E=Universal negative.
I =Particular affirmative.
0=Particular negative -

CniU, Propositions are often met with which have no
7<'<rw^ sign of quantity before them ; as if, e. g., the first of
the propositions above had simply been ^Cowards are
cruel;' we must judge, in each such case, by the
import of the proposition, whether it be universal or
particular.

It is evident that in the last of the propositions
the sense would be the same, if the expression were

^ All cowards are not cruel ; ' the words ^ all ' ^ every '

: » therefore when prefixed to negative propositions are
^*^' not to be considered as si^ns of universality. ,

J^ ^ Singular' propositions i. e. those which hav^-a.^

singular subject e. g. ^ Dionysius was cruel,' belong
properly neither to universals nor particulars ; but as
the principal rules for imiversals will * apply to them^
they are, generally speaking, correctly denoted by
the symbols. A, E.

* The reason usually given for classing these propositions with
universals, viz. that their subjects are to be taken in their whole extent,
when, properly speaking, they have no extent, is little better than an
absurdity. The true ground of the arrangement is that, as with
universals, their application necessarily remains unchanged.

IN LOGIC. 23

It is sometimes necessary, in apparently negative
propositions, to observe whether the negation attaches
strictly to the copula or the predicate ; if the latter be
the case, as in the proposition, ' Sin is no-trifle,' * we
are to consider such propositions as really affirma-
tive.

Exercise.

Distinguish by their appropriate symbols the fol-
lowing propositions.

1. No one is gratuitously wicked.

2. Whoever is capable of deliberate crime is re-
sponsible.

3. All that glitters is not gold.

4. Cicero was no unskilful orator.

5. An enslaved people is not happy.
^, All the accused were not guilty.

7. Beasts have four feet.

8. Some blacks are'civihzed.

9. All philosophers are not wise.

* ^ We have a singular instance of this usage of the negative in
Isaiah x, i5. (See Lov/th's version.)

" Shall the axe boast itself against him that heweth therewith ?

Or shall the saw magnify itself against him that shaketh it ?

As if the rod should shake itself against him that lifteth it up.

Or as if the staff should lift up itself against no wood, i. e. as Lowth
explains it, * against its master.'"

24 EXERCISES

CHAPTER X.

ON DISTRIBUTION.

When a term is taken in its whole extent, so as to
stand for all which can be signified by it, it is said to
be ^ distributed.' In applying this to the parts of a
proposition, there are two rules which it will be
important to bear in mind.

^£ 1. All universal propositions distribute the subject
^ 0 2. All negative propositions distribute the predicate.

The necessity of the latter rule (respecting which
alone there can be any hesitation,) will appear, if we
consider that, if, in such a proposition as ^ No vice is
useful,' any kind of utility could be predicated of vice,
the proposition could not be affirmed.

[Note, some propositions, which are introduced by
the sign ^all,' are not universals, but collectives^ as
e. g., ^ all the rules of grammar overload the memory,'
where we could not substitute for ^ for all the rules,'
the distributive, ^ every rule;' and some propositions,
viz., exclusives, are really negatives though not appa-
rently so; e.g. ^the contented alone are happy' =
* none who are discontented are happy.

It is implied, of course, in the above rules, that
affirmative propositions do not distribute the predi-

IN LOGIC. 25

cate; and this will be obvious if, to take the first
example of the previous chapter, ^AU cowards are
cruel,' Ave reflect that the term ^ cruel' is applicable
to many besides cowards.

Exercise.

Explain in which of the propositions in the pre-
ceding exercise the subject is distributed, and in
which the predicate ; also in which of the following
propositions : —

1. All men are sinful.

2. All the angles of a triangle are equal to three
right angles.

3. No human government allows absolute liberty.

4. Only the experienced are wise.

CHAPTER XL

ON OPPOSITION.

We have seen (ch. ix) that, considered as to
quantity and quality, there are four principal kinds
of propositions, A, E, I, and O, of which the follow-
ing may be regarded as the respective forms : —

26 EXEKCISES

A 1. Every X is Y. * 1 3. Some X are Y.
E 2. No X is Y. 0 4. Some X are not Y.

Now as it regards the relations of such propositions
to each other, logicians have distinguished various
kinds of opposition, e. g.

The pairs which differ both in quantity and quality,
viz. A, O ; and E, I ; are termed f ' Contradictories/

* We here introduce for the first time symhok instead of terms,
which we shall continue at times to do in the explanatory examples of
succeeding chapters. The utility of the substitution will be abundantly
intelligible to all who are in any degree conversant with algebra.

t In subjects which admit of quantity this amounts to the same thing
as determining ' contradiction' by the presence or absence of the nega-
tive particle from the predicate, agreeably to the account given of
contradictory terms in chapter i. Thus, the proposition ' every X is Y,
would be fitly contradicted by the proposition * every X is not Y,' this
being equivalent (as we have seen in chapter ix,) to the proposition

* some X is not Y. ' The opposition therefore between the pairs A,
O ; E, I ; should be regarded solely as specific cases of contradiction,
(not as its exclusive forms. ) This is important to notice because by
those who derive their view of contradiction from the present cases, a
diflficulty has been supposed to lie in the contradiction of * singulars. '
But surely of the proposition

yj Brutus deserved well of his country,
both the logical and real ' contradictory ' must be,
£ ^ Brutus did wo< deserve well of his country,
and carrying out the explanation given in chap, i, of contraries, the

* contrary,' /iw^f- 1--^ p

yi Brutus deserved ill of his country, ci ^xu^UaJ oLuU^-cA. /K^qt-f^
Archbishop Whateley, in the remarks which he makes on the contra- ^^
diction of singulars, seems half inclined to give up their universality,
contending, (see Logic, p. 71.) that it is only by the insertion of some
modifying particle, such as 'occasionally' that their contradiction is

IN LOGIC. 27

Those which diiFer in quantity only, viz. A, I ; and
E, O ; ' Subalterns.'

The two universals, A, E ; are said to be ' Contra-
ries.'

The two particulars, I, O ; ^ Subcontraries.'

And it will be quite evident, on consideration, that
of the * contraries' on any subject both propositions
may be false, but both can never be true; of the
^subcontraries,' vice versa; that of the ^contradic-
tories' one will, of necessity, be always true and the
other false; that in ^subalterns' the truth of the
particular will follow from that of the universal, and
the falsity of the universal from that of the parti-
cular, &c.

Exercise.

Name the respective' contraries and contradictories
to the propositions in chapter ix.

CHAPTER XII.

ON CONVERSION.

It is sometimes convenient to transpose the terms
of a proposition, i. e. to make the predicate the subject

possible. It must surely be thought extraordinary that a formal defini-
tion of ' contradiction' given at the outset in the account of ' terms,
should afterwards be laid aside as altogether useless.

28 EXERCISES

and the subject the predicate ; such transposition is
.^ called* ^conversion/ which^ of course, is then only
' legitimate (or illative) when the truth of the propo-
sition remains unaltered. Now this can only be the
case when no term is distributed in the converse form
of the proposition^ which was not distributed in its
original form, and this proviso limits the species of
illative conversion to three, examples of which, with
the necessary explanatory observations, now follow : —

E .. If no X is Y, then No Y is X; ^lso..E ^/ijU,
I - If some X are Y, then some Y are X. .1

<i^^ A , , If every X is Y, then some Y are X. . . I ^ /^ta

If some X IS not Y=not-Y, men some j jl^-

X =(something) not-Y is X ; Jalso / '^

>f**^ * What is commonly called the * converse* of a proposition is simply

•f'^^the transposition of any two of its parts which are antithetically related

f I ► to each other, whether that relation be the one of subject and predicate

or not. Such a transposition can, of course, have no logical force

otherwise than by accident. The following illustrative anecdote is told

by Lambe : —

" ' I like Wrench,' a friend was saying to Elliston ono day, ' because
he is the same natural easy creature on the stage that he is off^ ' My
case exactly,' retorted Elliston, * I am the same person off the stage
that I am on.' The inference at first sight seems identical, but ex-
amine it a little and it confesses only that the one performer was never
and the other always acting.'' — Essays ofElia. — Ellistoniana,

IN LOGIC. 29

-A-^ If every X is Y, i. e. (if no X is not-Y,)
j|), , then^ no=(nothing) not-Y is X. ... A. /^jt^tzi

1. The first kind of conversion exhibited above is
termed ' simple,^ and may always be applied to propo-
sitions of the forms E and I.

2. This conversion is said to be, 'by limitations^ (per
accidens;) it is instanced in a proposition of the form
A, to which simple conversion would be inapplicable ;
for if we were to infer ^ every Y is X/ we should be
distributing a term Y, which had not been previously
distributed ; E may also be thus converted.

3. Neither of the above modes of conversion is
admissible in propositions of the form O ; but if we
consider the negative in these propositions as attached
to the predicate, we may then convert them as we do
those of the I form ; this latter conversion (which is
applicable to A as well as to O,) is said to be 'hy
negation,' (or ' contraposition.')

The following mnemonical lines may assist the
student in remembering the above rules.

SimpUdter fEcI, convertitur EvA, per accid: ^ lttti\...^<i
AstO per contra, sic Jit conversio totar

[Note, in the mnemonical words in these lines the consonants are
insignificant ]

Exercise.
Convert illatively the propositions giilai as exam-
ples in chapter 9, and also the following: —

D 2

30 EXERCISES

1. Some professors of religion are hypocrites.

2. Some sceptics are not vicious.

3. Nothing morally wrong can be politically right.

4. " Never rebel was to arts a friend." — Dryden.

5. Every poet is a man of genius, (by negation.)

IT 6. He that is not with me is against me. (Matt,
xii, 30.*)

CHAPTER Xni.

ON THE COPULA.

We have seen (chap, vii.) that the simple verb of exis-
tence (termed logically the 'copula') may be used to
connect the subject and predicate of any proposition
whatever. The kind of predicability which it most
properly expresses is that of ' comprehension ; ' when-
ever the relation of the predicate to the subject is

*• In this example we have an instance of the logical fact that con-
traries and contradictories are sometimes identical. We are accordingly
prepared for the converse aphorism which was uttered by the same divine
speaker on another occasion " He that is not against us is on our part,
( Mark ix, 40. ) It appears not an unfair generalization of the comparative
purport of the two sentences which Bacon somewhere makes, that the
former is the principle to guide our judgments in fundamental matters
of religion, the latter in indifferent ones.

IN LOGIC. 31

either that of ^ genus/ MifFerence/ ^property,' or
^ accident/ the latter term may be said to comprehend
the former in its meaning, and this comprehension it is
which is expressed by the substantive word. In its
popular use, however, it is often the sign of a different
kind of relation e. g. * of ^ coexistence^^ ' resemblance,^
^ causation, and this variety in its import, it is neces-
sary to be aware of, to prevent mistakes in inferences.
The following three sentences will illustrate its appli-
cability to the expression of the ideas just enume-
rated, viz., those of ' coexistence,' &c. : —

1. Knowledge is power.

2. Society is a pyramid.

3. Intemperance is the death of thousands.

In each of these sentences the form of expression
may be said to be rhetorical, and, if translated into
logical language, would exhibit the three sorts of
relations between terms above noticed. The propo-
sition, e. g., ^ knowledge is power,' implies that power

* " Existence, Coexistence, Sequence, Causation, Resemblance :
one or other is asserted (or denied) in every proposition without ex-
ception. This fivefold division is an exhaustive classification of matters
of fact ; of all things that can be believed or tendered for belief, of all
questions that can be propounded, and all answers that can be returned
to them."— M7/s' Logic, Vol. 1, p. 139.

We have not included in our own enumeration the first of the items
above, because it is never expressed by the copula as copula ; it will
not be difficult to see that the third is resolvable into either the pre-
ceding or succeeding one.

^''ttHIVEESITY)

32 EXERCISES

invariably coexists with knowledge, and the others
similarly convey the notions of resemblance and
causation respectively.

Exercise.

State which of the relations above enumerated is
denoted by the copula in the following sentences : —

1. Union is strength.

2. Virtue is happiness.

3. Truth and justice are points.*

4. Seeing is believing.

5. Commodity (i. e. interest) is the bias of the
world. — Shakspere : King John.

6. Anger is short madness.

'^fe'^

f 7. All flesh is grass. (Isaiah xl. 6.)

8. I am the resurrection and the life. (John xl. 25.)

9. This is my body.f (Matthew xxvi. 26.)

10. Love is the fulfilling of the law. (Romxiii. 10.)

* " La justice et la verite sont deux pointes si subtiles, que nos
instruments sont trop emousses pour y toucher exactement. S'ils y
arrivent ils en ecachent la pointe et appuient tout autour, plus sur le
faux que sur le vrai." — Pascal, Pensees, Part 1, Art vi, sec. 16.

t It is felicitously remarked by Gibbon somewhere, in relation to
the Romish interpretation of this passage, that transubstantiation is
nothing but rhetoric turned into logic. The hypercalvinism of those
who so overstrain the scripture metaphor of a ransom for sin as to
make the forgiveness of the elect a debt vi^hich they may even claim
of divine justice is a similar perversion of language.

IN LOGIC. S3

CHAPTEE XIV.

ON TRIFLING PROPOSITIONS.

The junction of a Subject and Predicate by means of
Copula is not of itself sufficient to constitute a Pro-
position ; the nature of the connection between the
parts joined may be such as to render the proposition
a trifling one, if we should not rather say, a seeming
one only. Under the head of such propositions we
may class (1) all* identical propositions, those i. e.,
in which the predicate is the same as the subject,
(2) those in which it is a synonym of it, and (3) those
in which (without professing to define) it contains
only parts of the definition of the subject, whether^
the genus or ^ the difference. The propositions which
follow will be examples of these in order : —

1. A triangle is a triangle.

2. To pardon is to forgive.

3. Gold is a metal.

4. Gold is fusible.

* An exception ought to be made perhaps in favour of such in this
class as carry an emphasis in the copula. It is quite evident by such an ex-
ample, as the familiar proverb, ' Home is home,' i. e. * There is no
place like home,' that enunciations of forcible truth are often con-
veyed by preference in the form of identical propositions. Such a
course is sometimes pursued, when it is meant to insist on things being

34 EXERCISES

To this list some would be inclined to add such
propositions as ^ merit gains esteem' belonging to
the class usually denominated, ^ Truisms ;' * but as
that may not be a truism to one which is so to another
it would be scarcely correct to make this a fourth
instance.

EXERISE 1.

State on what grounds the following propositions
may be considered trifling.

1. Parsimony is frugality.

2. Poetry is metrical.

3. A palfrey is a horse.

4. There's ne'er a villain dwelling in all Denmark
But he's an arrant knave.

5. Man is rational.

Exercise 2.

Resolve the following seemingly identical proposi-
tions into others which are not so : —

called by their right names, it being a common artifice of the unprin-
cipled to gloss over their villany by specious phrases. Thus, in
Shakspere, we find one of the tribe saying.

Steal! a fico for the phrase ; convey the wise it call.

* Much damage has been done to the repute of Logic by a selection
of propositions of this class for the illustration of its rules. A whole
stock of such sentences may be found ready made in the papers usually
set before youths for writing copies.

IN LOGIC. 35

1.* Sensation is sensation.

2. What I have written I have written. (John
xix, 22.)
13. I am that which I am. (Exodus iii, 14.)

CHAPTER XV.

ON COMPOUND PROPOSITIONS.

Compound Propositions are those which are made
up of two or more subjects or predicates, or both;
they are either conjunctive or disjunctive, according as
the connection subsisting between these different
subjects or predicates is of a copulative or disjunctive
character, e. g.

1. ^For,' is both a preposition and an adverb [Cb/z-
junctiveJ\

* This is one of the many * dicta' of Johnson which BosweJl has pre-
served. The circumstances which occasioned it are thus related by him
in his * Tour to the Hebrides : *

" I was weary of the day, and began to think wishfully of being
again in motion. I fancied Dr. Johnson quite satisfied. But he owned
to me that he was fatigued and teased by Sir Alexander's doing too
much to entertain him. I said it was all kindness. — Johnson. — True,

Sir, but sensation is sensation Boswell. — It is so, we feel pain equally

from the surgeon's knife as from the sword of the foe.

t As a further exercise in the resolution of such propositions, we may
refer the theological student to Pro v. xiv, 24 ; Rom. vi, 16. The help
of biblical criticism will probably be thought necessary to the elucidation
of the former passage.

36 EXERCISES

2. Every action Is either good or bad \_Disju7ictive.']

We must carefully distinguish from compound proposition the fol-
lowing sorts,* which are so only in appearance :

1. Bodies, which are transparent, have pores.

2. Two and three make five.

3. A poet Is borji not made,'\

With regard to such propositions as these we may
observe that,

1 Is the kind of proposition called ^ Complex.' It
Is a proposition which includes an incidental or
subordinate proposition In Its structure ; but, although
in such propositions there Is more than one subject,
they are not subjects of the same assertion.

2. We have here a specimen of a ^ Collective' pro-
position. The copulative particle ^and' is evidently
equivalent to the mathematical sign + It scarcely
needs pointing out that the parts connected by this
copulative, form together but one subject, to which,
as a whole, the predicate is referred.

3. This species of proposition is sometimes called
^ DIscretive.' The predicate Is not really a double one

* We do not think it necessary to give instances of all the kinds of
propositions, viz., cavsals, relatives, &c., which are commonly noticed
by logicians in treating of compounds. What are called causal propo-
sitions, e. g., 'Logic is useful, since it helps us to reason,' are really
nothing but condensed arguments. In relatives, such as the scriptural
sentence, " Where your treasure is, there will your heart be also ;" that
there is but a single subject and predicate is evident; e.g., (* The
place) where your treasure is (is the place where) your heart will be.*

f In apparent contrast with this proposition, it is finely remarked by
Tertullian in his Apology, "Christianus^^ non nascitur.''

IN LOGIC. 37

but a single one, expressed in a double manner, i.e.,
by both a ^positive and a negative term.

Exercise.

Distinguish the really compound propositions among
those subjoined, from such as are compound in appear-
ance only ; state which of the former are conjunctive
and which disjunctive ; and point out the complex,

1. Friendship either finds or makes men equal.

2. He who voluntarily lives quite alone, must be
either more or less than a man.

3. The doctrine, which places the chief good in
pleasure, is unworthy of a philosopher.

4. It is not the cross, but the cause, which makes
the martyr.

5. Alike the subject and predicate are distributed
in universal negatives.

6. The sun, moon, and stars, cannot all be seen at
once.

7. " Syllogismus assensum constringit non rem."

8. " Rex est qui metuit nihil."

9. "Coelum non animum mutant qui trans mare
currunt."

1" 10. "Either this man has sinned or his parents."
(John ix, 2.)

11. Extreme riches and poverty are alike to be
deprecated. (Prov. xxx, 6.)

* See Note 1, chapter \i.

EXERCISES

CHAPTER XVI.

RECAPITULATORY EXERCISE.

Explain the relation of the subjoined pairs of terms
to each other.

r Repast"!
\ Dinner J

/Joy 1

\ Sorrow J

{Possible
Impossible

}

r Quadruped"!
\Lion J

/Debtor "I
\ Creditor J

r Condition!
(^Miserable J

{Sublime 1
Sublimity J

IF r Sower* ~1
l^Eater J

* See Isaiah Iv, 10. " For as the rain cometh down and the snow
from heaven and returneth not thither again, but watereth the earth, and
maketh it bring forth and bud, that it may give seed to the sower, and
bread to the eater.

The modern terms for the classes exhibited thus antithetically by the
the sacred writer are those of * producer' and 'consumer,* technical
terms in political economy. The occurrence of the distinction in the
prophet is not a solitary instance of the anticipation by Scripture of the
generalisations of modern science.

IN LOGIC. 39

Specify the illogical items in the following enume-
rations.

1. Words are — Nouns, Verbs, Prepositions, Par-
ticles, Pronouns.

2. Relatives are — Parents, Children, Brothers,
Sisters, Sons.

3. Figures are — Triangular, Square, Round, Cir-
cular.

4. Poems are — Dramatic, Epic, Tragic, Lyric,
Didactic.

Distinguish the ^ Genus' and ^Difference' in the
following Definitions.

1. A Mirror is — a surface so polished as to reflect
images.

2. Demonstration is — certain proof.

3. Punishment is — the infliction of suffering on an
offender for the sake of others.

4. Correction is — the infliction of suffering on an
offender for his own sake.

5. Shame is — the passion felt when reputation is
supposed to be lost. — Johnson,

Define by Genus and Difference the terms ' Envy,'
^Emulation,' ^Persecution,' ^ A Heretic'

40 EXERCISES

Point out the Subject and Predicate in the follow-
ing Propositions.

1. Whatever is expedient is right.* — Paley,

2. A mining speculation is no trifling business.

3. To gild refined gold, to paint the lily.
Is wasteful and ridiculous excess.

4. Where there is no property, there can be no
injustice.

5. " To be or not to be, that is the question."

^ 6. Without faith it is impossible to please God.
(Heb. xi, 6.)

State the respective ^Contraries' and ^Contradic-
tories' of Propositions 1 and 2 above, also of the
following.

1. Christianity is of divine origin.

2. It is impossible to overstate the evils of versa-
tility.

3. Where weariness begins, devotion ends.

* It has been justly observed by some one that this proposition, to be
worthy of a place in an ethical treatise should be converted, so.
*' Whatever is right is expedient." It would thus become an affirmation
of our faith in the wisdom and rectitude of God's moral administration ;
the sentiment which it expresses, with its present subject and predicate,
is alike pernicious and beggarly.

IN LOGIC. 41

7.
Convert by negation the first two of the following
propositions, by limitation the second two.

1. Whatever has had a beginning has had a cause.

2. Every human mind is fallible.

3. All squares are parallelograms.

4. Products, which arise from the multiplication of
negative quanties by negative, are themselves positive.

CHAPTER XVIL

ON ARGUMENTS.

An argument is an expression in which from some-
thing assumed or taken for granted, something else is
deduced or inferred. Thus the following are formulse
of argument leading respectively to affirmative and
negative conclusions.

1. 2.

Every X is Y:* No YisZ:

Therefore every X is Z. Therefore no X is Z.

* It will be desirable that the student should accustom himself
henceforward to the use of Symbols as representations of the terms in
argument ; should there be any who would be perplexed by the employ-
ment of them in this stage of the exercises they may consider in
Formula 1. Formula 2.

X= Human mind, X=A covetous person.

Y=Immaterial. Y= A person in habitual fear.

Z = Immortal. Z= Happy.

E 2

42 EXERCISES

In these formulae of argument it will be perceived
that *one of the terms of the lower proposition (or
conclusion) viz., either the subject or the predicate, is
in the upper proposition compared with another term
to which it also stands in the relation either of subject
or predicate. The new term thus introduced is, of
course, one the relation of which to each of the other
terms is supposed to be better known than their
relation to each other ; from its serving as a medium
of comparison, it is called by logicians the middle
term. The other two terms, which form sc. the
subject and predicate of the conclusion, have received
the technical designations of the minor and major
terms respectively ; e. g. in the conclusions above, X
is the minor ^ and Z the major term.

[Note, it is the proper order in an argument that
the conclusion should be the final proposition, as
above ; but this order is not essential to the argument,
for the proposition to be proved may be stated first,
and the proposition proving it follow, as it3 reason^
being introduced by some causal particle, such as
t^ because,' ^for.' Thus the aflSrmative formula of
argument above might have been expressed —

Every X is Z :

* In point of fact both are, there being still another proposition
implicitly assumed, as we shall see in the following chapter. Argu-
ments which are stated in the form above i, e. without the third propo-
sition, are styled Enthymemes.

f The modes of transition from one of the propositions to the other

IN LOGIC. 43

For every X is Y.]

EXEKCISE.

Point out the middle and major terms in each of
the following arguments.

An infant has no moral power :
Therefore it has no reponsibility.

Sheep are ruminant animals :
Therefore they are not predacious.

Religion is of a highly solemn character :
Therefore it is not suited to ■poetry.— Johnson.

4.
Kings have no friends :
For they have no equals.

5.
Yonder star twinkles :
Therefore it is fixed.

are indeed almost endless. The simple succession of one to the other
will sometimes have an illative force. Thus the observation or rather
observations of the Jews to our Lord, (John viii, 13,) are plainly equiva-
lent to an argument,

" Thou bearest witness of thyself:
[Therefore] thy witness is not true."
The student in logic will often be reminded of the fine remark of
Bacon. " Subtilitas naturae subtilitatem humani ingenii longe
exsuperat."

44 EXERCISES

6.
^ With many of them God was not well pleased :

For they were overthrown in the wilderness.
(1 Cor. X, 5.)

CHAPTER XVIII.

ON SYLLOGISMS.

In each of the arguments brought forward, whether
as explanatory examples or as exercises in the pre-
ceding chapter, a little reflection will shew that
another proposition besides the two exhibited was
really implied. Thus the argument (No. 1) that ^an
infant has no responsibility because it has no moral
power' could not be sustained unless we were at
liberty to assume that ^whoever is without moral
power is without responsibility.' Similarly, in the
symbolical formula of argument, it would not follow
that every X was Z because every X was Y unless
we could take it for granted that ^ every Y was
Z.' When this implied assertion is formally intro-
duced, the argument will be found to consist of
three propositions, and is styled a ' Syllogism.' As
may be inferred from the examples already com-
mented on, one, at least, of the propositions which
compose a Syllogism will be of a general nature (an

IN LOGIC. 45

exposition of the principle or law of the case ;) it is
commonly" this proposition which is suppressed when
the argument is enthymematic. According as the
general statement referred to is made in an absolute
or hypothetical manner the syllogism will be a
^Categorical' or ^Hypothetical' one; thus of the sub-
joined syllogisms, leading to the same conclusion, the
former is of the categorical^ the latter of the hypo^
thetical kind,

1. 2.

Every Y is Z : If X is Y, it is also Z :

Every X is Y: X is Y:

Therefore every X is Z. Therefore it is Z.

The difference between the two forms of statement
in the above syllogisms is sufficiently obvious of
itself. In the former it is explicitly asserted that Z
is universally predicable of Y; in the latter, im-
plicitly i. e. it is assumed. It is in the option of a
reasoner to put any argument which he may have
occasion to use in either of these forms.

Exercise.

Draw out the arguments given in the preceding
Exercise as regular Syllogisms.

As Categorical Syllogisms.

As Hypothetical Syllogisms.

46 EXERCISES

CHAPTER XIX.

ON CATEGORICAL SYLLOGISMS.

1. 2.

Every Y is Z: NoYisZ:

Every X is Y : Every X is Y :

Therefore every X is Z. Therefore no X is Z.

Taking the above formulse as specimens of
regular categorical syllogisms, each consisting, as
explained in the preceding chapter, of three propo-
sitions, we have next to notice the relations of these
propositions to each other. It has already been
remarked (see chap, xvii) that the final proposition
in every argument is termed the conclusion. Rela-
tively to it, the two preceding propositions in a
regular syllogism are designated, similarly, the
premises. Tliey are distinguished among themselves
as the major and the minor premiss. The major
premiss is that in which the middle term is compared
with the major term ; that in which the minor and mid-
dle are compared is the minor premiss. These denomi-
nation are given them irrespectively of the order in
which they may be ranged. Thus, in syllogism . 1 .
above, the premiss, ^ Every Y is Z' would not be
the less the major premiss^ though the order of the
propositions should be as follows.

IN LOGIC. 47

Every X is Y :
Every Y is Z :
Therefore every X is Z.

because it is the premiss in which the major term Z,
is compared with the middle Y. It is important that
the logical student should ground himself well in
these technicalities.

Exercise.

In the following Categorical Syllogisms point out
the major and minor premises.

1.
No predacious animals are ruminant :
The lion is a predacious animal :
Therefore the lion is not ruminant.

Some who are learned are much addicted to

prejudice:
None who are much addicted to prejudice

are of powerful mind :
Therefore some who are learned are not of

powerful mind.

Things which cannot be enumerated do not

exist:
Innate ideas cannot be enumerated :
Innate ideas do not exist. — Locke,

48 EXERCISES

4.
IT Those who are not subject to the law of
God cannot please him :
Those who are in the flesh are not subject

to the law of God :
Those therefore who are in the flesh cannot
please God. (Romans^ viii, 8.)

CHAPTER XX.

ON THE CANONS OF SYLLOGISMS.

Still considering the two symbolical syllogisms
which head the preceding chapter, as specimens of
regular categorical syllogisms, the former, i. e. of an
affirmative one, the latter of a negative, we may
explain the respective validity of each by the follow-
ing canons.

1.
Two terms, which agree with one and the same
third term, agree with one another.

Two terms of which one agrees and the other disa-
grees w^ith a third term, disagree with each other.

The practical violations of these canons into which
reasoners most commonly fall may be learnt from the
following (explained) examples of faulty syllogisms :

IN LOGIC.

Every X is Y:

NoXis Y:

Every Y is Z :

Every Z is Y:

NoZisY:

NoXis Y:

Every X* .-. is Z.

No X .'. is Z.

No X .-. is Z.

Every Y is Z:

Light f is contrary to darkness :

Every Y is X:

Feathers are light

Every X.-. is Z.

Feathers are contrary to darkness.

Of the preceding logical formulae, none are really
syllogistic, because,

1. The middle term is here undistributed; it is
r therefore possible that the major may have been

compared with one part of this term, and the minor
with another part; the two, consequently, not with
the same middle.

2. Here, both premises being negative, the middle
term is not said to agree with either of the other
terms.

3. Here it will be perceived that the major term
is distributed in the conclusion, when it had not been

* This symbol, which is the known geometrical one for * therefore'
will be most conveniently employed henceforward in symbolical syllo-
gisms : in others, the sign of inference will be occasionally omitted.

f The reason of our recurring to verbal terms in this example will
be sufficiently evident from the nature of it.

50 EXERCISES.

previously in the major premiss. [This is called an
illicit process of the mqjor.^ The negation therefore
in the conclusion is more absolute than is warranted.

4. A fault the counterparty so to speak, of the last
is here committed i. e. the minor term in the conclu-
sion is taken distributively, without warrant from the
premises. [This is called an illicit process of the
minor.'] The only just inference would have been
' Some X is Z.'

5. Here the middle term is ambiguous ; and there-
fore, as in No. 1, the other two terms cannot be said
to be compared with one and the same third termJ^

Exercise.

Explain on which of the above grounds the follow-
ing (apparent) Syllogisms are faulty.

1.
j\_ . . Every rational agent is accountable :
E . - Brutes are not rational agents :
E.. Brutes are not accountable.

* It is an obvious corollary from the above observations that no con-
elusion can be logicalhj drawn from two particular premises, such pre-
mises either involving an undistributed middle or leading inevitably to
an illicit process.

It is further evident, on the same grounds, that if one of the
premises be particular, the conclusion must be particular; and if
negative^ negative.

IN LOGIC. 51

-^ The innocent should be protected from punish-
ment:
A, This person should be protected from punish-
ment:

A- This person therefore is innocent.

E . , A fish is not a quadruped :
E .. A bird is not a quadruped:
£ A fish is not a bird.

^ . No evil should be allowed that good may come of it :
J^ , . All punishment is an evil :

]g . . No punishment should be allowed that good may
come of it.

A . . All wise legislators suit their laws to the genius of

their nation :
A . . Solon did this:
A . - Solon was therefore a wise legislator.

A . , All who fight bravely deserve reward :

1 . . Some soldiers fight bravely :

/AI Soldiers therefore deserve reward.

[State what conclusion is deducible from the
premises in this last syllogism.]

52 EXERCISES

CHAPTER XXL

ON THE MOODS OF SYLLOGISMS.

Recurring to the notation of propositions explained
in chapter x, we shall perceive that the (apparent)
syllogisms given as an exercise in the preceding
chapter may be represented by the following ternary
forms; AEE, AAA, EEE, EAE, AAA, AIA,
where the order of the letters indicates the order in
which the respective propositions of the syllogisms
follow each other. Such varieties in the succession
of propositions in an argument are termed its Moods.
As far as the mere arithmetical law of variation is
concerned, the number of such moods which can be
obtained is * 64 : but of these the majority are in-
admissible from their violating some one or other of
the rules (already explained) to which syllogisms are
subject : and of the rest several are practically useless
from their being superfluous, i. e., virtually included
in others. Thus of the eleven legitimate moods, viz.,
AAA, AAI, AEE, AUO, All, AOO, EAE,

* " For there are four kinds of propositions, any one of which may
be the major premiss ; of these four majors each may have four different
minors, and of these sixteen pairs of premises, each may have four
different conclusions : 4 x 4 (^= 16) X 4 = 64."

IN LOGIC. 53

EAO^ EIO, lAI, OAO5 those which appear in
italics are really supernumerary, being contained in
the moods which respectively precede them.

Exercise 1.

Name the moods of the Syllogisms, both symbolical
and verbal, given in the preceding chapter.

Exercise 2.

Explain on what grounds the following Moods are
inadmissible.

lAA EEA OEO EI I

lAE EEE AIA IIA

OAA lEA AIO III

OAE lEE EIA AOA

AEA OEA EIE AOE

CHAPTER XXII.

ON FIGURES.

If we revert to the arguments given as examples
in the Exercises on chapters xix and xx, we shall

F 2

54 EXERCISES

perceive that the middle term does not stand in the
same position to the other two terms in each of these
arguments. For instance, in chapter xix, the middle
term, in the first of the examples given, is the subject
of the first premiss, and the predicate of the second ;
in the second, it is the subject of both premises. This
variation in the disposition of the middle term in a
syllogism, is called its Figure. There are usually
reckoned in Logic, * three Figures. In the first, as
in the first example noticed above, the middle term is

* The mere possibilities of position would give us still another
Figure; viz., one in which the middle term should be the predicate
of the major premiss, and the subject of the minor : but this figure is
not recognised by Aristotle, nor are its intrinsic merits such as to re-
commend its addition to the preceding three. Logicians v^^ho use it,
allow that it is awkward and unnatural : in the following specimen
of it by Whateley, it will be seen that the awkw^ardness consists in the
statement of the converse of a proposition instead of the proposition
itself.

What is expedient is conformable to nature :

What is conformable to nature is not hurtful to society :

W^hat is hurtful to society is not expedient ;

Here, it is evident, if we convert the conclusion, nothing will be want-
ing but an alteration of the order of the premises to make the syllogism
one of the first Figure, in which form its superior concinnity and force
must be readily apparent.

Lambert, a German author, attempts to show (Neues Organon) that
the fourth figure is speciall}' appropriate to the proof of a reciprocal
conclusion ; but he produces no example of reciprocity which would
not be better elicited by the ordinary laws of conversion. According
to this Figure, e. g., he says, it appears that * if no M is B,' then * no B
is this or that M ; ' butt his latter proposition is plainly only a subaltern
of the larger conclusion, which simple conversion would lead to., viz.,
that no ' B is M.' The employment therefore of a second proposition
in the proof is altogether superfluous.

IN LOGIC. 55

the subject of the major premiss, and predicate of the
minor; in the second, it is the predicate of both
premises; in the third, the subject of both. The
following formulae may serve as specimens of a nega-
tive syllogism in each Figure.

Fig. 1. Fig. 2. Fig. 3.

NoYisZ: NoZisY: NoYisZ:

Every X is Y : Every X is Y: Every Y is X :

iS"o X is Z. No X is Z. Some X is not Z.

Exercise.

State in what Figure the following Syllogisms
respectively are.

Every candid person will refrain from condemning
a book which he has not read :

Some reviewers do not refrain from this :

Some reviewers are therefore not candid.

No one who lives on terms of confidence with
another is justified in killing him :

Brutus lived on terms of confidence with Caesar:
Brutus was then not justified in killing Caesar.

The appointments of nature are invariable :
The principles of justice are variable :
The principles of justice are no appointments of
nature.

56 EXERCISES

Every true patriot is a friend to religion :

Some great statesmen are not friends to religion :

Some great statesmen are not true patriots.

A just governor will make a difference between
the good and the evil:

God is a just governor :

Grod will therefore make a difference between the
good and the evil.

CHAPTER XXIII.

ON FIGURES (CONTINUED.)

A VERY brief examination will suffice to show that all
the Moods spoken of in chapter xxi, as legitimate in
themselves, are not admissible in each figure. For
instance, lAI is an allowable mood in the third
Figure; but in the first, it would have an undis-
tributed middle. So AEE would in the first figure
have w[i illicit process of the Major ^ but is allowable in
the second; and AAA, which in the first figure is
allowable, would, in the third, have an illicit process of

IN LOGIC.

ihe Minor, as may be easily seen. The following are
' the Moods which alone are admissible in the respec-
tive Figures.

1. AAA, EAE, All, EIO:

2. EAE, AEE, EIO, AOO:

3. AAI, EAO, lAI, All, OAO & EIO.*

These results have been embodied in the subjoined
mnemonical lines, which^ it will be requisite to commit
to memory. It need scarcely be observed that the
vowels in the mnemonical words denote the moods ;
the selection of consonants has been made with a
view to other uses, some of which may be hereafter
noticed.

i * Barbara, Celarent, Darii, Ferioque / prioris :'

-t- . Cesare, Camestres, Festino, Baroko, /secundae:'

y f ^ Tertia'j Darapti '^ sibi vindicat atque'^Felapton :

"^' \ ^.' Adjungens',' Disamis, Datisi, Bocardo, Ferison.

* Similarly, the Moods of the fourth Figure are :— AAI, AEE,
lAI, E AO, EIO ; — the technical words embodying them.

-4 • • , . Bramantip, Camenes, Dimaris, Fesapo, Fresison.

According to Lambert, the respective uses of these moods are as
follows: of Bramantip and Dimaris to find spepies to a genus ; of
Fesapo and Fresison to show that the species does not exhaust the
genus ; and of Camenes to deny the species of that which is denied of
the genus. We forbear any comment on this distinction. The notice
of it would be, perhaps, more suitably inserted in the following chapter ;
but we were willing to prevent the necessity of a recurrence to the
Figure.

(See Lambert Neu. Org., Vol. I, p. 139.)

58 EXERCISES.

It will sufficiently illustrate the use of these lines
to remark that the first of the syllogisms in the pre-
ceding exercise is said to be in Baroco.

Exercise.

Distinguish by their appropriate mnemonical word
the Mood and Figure of the other syllogisms in the
above exercise, and also of the syllogisms which
follow.

The connection of soul and body can neither be
comprehended nor explained:

This connection must be believed :

Something then must be believed which can neither
be comprehended nor explained.

Matter cannot think :

Mind does think:

Mind then is not matter.

Ivory is hard :

Ivory is elastic :

Therefore some hard substances are elastic :

114.
Ordinary priests are made without an oath:
Jesus was not made priest without an oath :
Jesus is no ordinary priest. (Hebrews vii, 12.)

IN LOGIC. 59

CHAPTER XXIV.

ON FIGURES. (Continued,)

By a reinspectlon of the mnemonical lines which
exhibit the Moods admissible in each of the three
Figures it will be evident that universal affirmative
conclusions can be proved only in the first Figure, The
second Figure can he used only for negative conclusions,
but both universals and particulars of this sort can
be proved by it. The first Figure will also prove
any kind of negative ; in judging which of the two
Figures is the more eligible, in any given instance,
for such proof, it will be well to consider whether the
middle term to be employed is more naturally re-
garded as a genus or as a property. Particular con-
clusions only can be proved in the third Figure, and on
this account it is best appropriated to contingent mat-
ter ; — to reasonings, i. e. by which it is sought to
foreclose a universal statement. The following en-
thymeme, e. g., will be best exhibited in a Third
Figure syllogism.*

* It is not pretended that these observations will enable a reasoner to
determine infallibly in each case the most proper Figure for an argu-
ment ; but, like the rules in Greek respecting accents, they will be found
useful as far as they go.

■

60 EXERCISES

Universal belief of a doctrine does not prove its
truth, the sun having formerly been universally be-
lieved to move round the earth.

This naturally falls into Felapton ; e. g.

* The sun does not move round the earth:
The sun was once universally believed so to move :
What then is universally regarded as a fact may
yet not be so. t

Exercise.

Decide in what Figure the following Enthymemes
will be most appropriately drawn out as Syllogisms,
and draw them out.

The Epicureans cannot be regarded as true philo-
sophers ; for they did not reckon virtue a good in
itself.

As we may see in the case of Porson, great
scholars are not always virtuous men.

* In this and similar syllogisms, unless the two premises can be
regarded as universal propositions, the middle term will appear undis-
tributed. It was, in all probability, a perception of this difficulty which
led logical writers to refer singulars to the class of universals. But we
must in such cases ascend from the rule to the principle. The necessity
for the distribution of the middle arises from the necessity of preserving
the identity of the standard of comparison for the other terms. If then this
identity can be secured by other means, the question of distribution may
be disregarded. Now it is of the very nature of singular terms that
their reference cannot vary, and consequently the evil which would
follow the non-distribution of the middle cannot arise in their use, i e.,
as Whateley explains, the comparison of one extreme with one class of
objects, and the other with another.

IN LOGIC. 61

A B and C D are each of them equal to E F :
they are therefore equal to one another.

Dreams which appear to comprise the events of
hours may yet occupy no more than a minute; for
persons who have been asleep only a minute have
been known to have such dreams.* — Brougham.

(If)
5.

Predictions form no warrant for conduct ; for the
death of Christ was predicted as necessary while yet
it is imputed as criminal.

" How can ye believe who receive honour one of
another ? " — John v, 44.

* The accomplished author (in his " Natural Theology") attempts
to deduce from the above fact, an inference as to the actual length of
dreams; but the contingent conclusion drawn is evidently all which
the premises will justify.

62 EXERCISES

CHAPTEE XXV.

ON COMPOUND SYLLOGISMS.

1. 2.

As well C as D is B :^ Neither C nor D is B :

A is either C or D : A is either C or D :

A /. is B. A /. is not B.

3.
Either C or D is B :
A is as well C as D :
A /. is B.

In the above formulae are exhibited specimens of
compound syllogisms. The forms given are among the
most simple of the sort, the conclusion containing a
single subject and predicate only, and the composition
being therefore confined to the middle term. Three
kinds of such composition may be remarked, the mid-
dle term being of the form

As well C as D, or
Either C or D, or
Neither C nor D,

* Or " Both C and D are B." We have, for convenience sake, in
these examples made the composite terms himemhral only ; but it will
be understood that they may he plurimembral to any extent.

IN LOGIC. 63

corresponding to the universal affirmative^ particular
affirmative, and universal negative of simple syllogisms
respectively. It is to be observed that nat every
combination of two such propositions as the above will
constitute a compound syllogism. Two compound
conjunctive propositions, e. g.^ will not do so. The
symbolical syllogism, for example.

As well C as D is B :
A is as well C as D :
Therefore A is B :

will differ in no respect from a conjunction of two
simple syllogisms. It is evident that in either pre-
miss either of the symbols C or D may be omitted
without in the least damaging the conclusion. There
is therefore a cumbrous superfluity of proof. Again,
in the syllogism, •

B is as well C as D :
A is neither C nor D :
A .". is not B.

the same objection is applicable. The addition of the
symbol D contributes nothing to the force of the
argument. In every valid compound syllogism then
there must be, it will be found, one disjunctive pre-
miss. The principal valid combinations of compound
propositions which can be united in a syllogism on
this condition are six. They have received the
technical names

Caspida, Serpide, Dispaca71)iprepe, Perdipe, Diprese,

64 EXERCISES

in which the significance of the vowels is the same as
in the mnemonical lines of chapter xxiii substan-
tially, the consonants C, E, and D, correspond in
force with the respective first three vowels, and the
letters S and P stand for subject and predicate. The
symbolical syllogisms which head the chapter are
examples of the former three, viz., Caspida, Serpide,
and Dispaca respectively; we subjoin similar ex-
amples in order of the others.

1. 2.

B is either C or D : B is neither C nor D :

A is neither C nor D : A is either C or D :
A .*. is not B. A .*. is not B.

B is either C or D :
Neither C nor D is A:
A .'. is not B.

A single verbal exemplification of these moods may
suffice. Take then the following in Perdipe :

A problem is neither affirmative nor negative :
Every proposition is either affirmative or negative :
A problem is not a proposition.

Exercise.

Give the technical designation of each of the fol-
lowing compound Syllogisms.

IN LOGIC. 65

Mercury, Venus, the Earth, Mars, &c., move in
elKptical orbits :*

All planets are either Mercury, Venus, the Earth,
Mars, &c. :

All planets therefore move in elliptical orbits.

We ought to fret neither about evils which we can
help, nor about those which we cannot:

There are no evils which we either can or cannot
help:

There are no evils which we ought to fret about.

f Alike the heart, the blood, the brain, breath, fire,
will (though in different ways) perish :

The human soul is (according to vulgar philosophy)
either heart, blood, brain, breath, &c. :

* i.e., as Whateley well explains the diction, "All planets aie
adequately represented by Mercury, Venus, &c. The example is a speci-
men of the ancient mode of stating an argument from Induction; the
more eligible mode recommended by Whateley we shall have occasion
to notice in a subsequent chapter.

f See Tuscul. Disput. I, §. 10. In the following section the differ-
ent ways of possible destruction are enumerated ;

* Si cor aut sanguis aut cerebrum est animus ; certe quoniam est
corpus, interibit cum reliquo corpore ; si anima est, fortasse dissipa .
bitur ; si ignis, extinguetur ; [si est Aristoxeni harmonia, dissolvetur. ]

G 2

66 EXERCISES

The human soul (according to vulgar philosophy)
will perish.

There is neither divine nor human law against
goodness, faith, &c. :

Every law is either human or divine :

There is no law against goodness, faith, &c. — See
Galatians v, 22.

5.
Temptations to lie proceed ordinarily either from
shame or fear :

The Almighty is liable neither to shame nor to fear :
It is impossible for the Almighty to lie.

CHAPTER XXVI.

ON SORITES.

It will sometimes occur that the premises which es-
tablish a conclusion are not self-evident propositions,
but themselves conclusions deduced from preceding
premises, which are again perhaps dependent on pre-
mises still preceding. A series of arguments of this
description may be conveniently thrown into the form
of a Sorites. The following is a specimen of what

IN LOGIC. 67

we intend. We take two consecutive (symbolical)
syllogisms to prove, say, that A is D : e.g.

1. 2.

B is C: C is D:

A is B: A is C:

A is C. A is D.

Now we may represent this twofold argument in
an abbreviated form thus :

* A is B:
. B is C ;

C is D:

A .-. is D.

The conclusiveness of the process is as little liable
to dispute in the latter case as in the former, and it
may evidently be extended to any number of argu-
ments whatever.! If we now examine the nature of

* For the above symbols the student may, if he pleases, substitute
as follows :

The Epicurean deities are without action :
Without action there is no virtue :
Without virtue there is no happiness :
The Epicurean deities are without happiness.

f Care must be taken however, not needlessly to lengthen the chain
by introducing propositions which are not really links in progression.
This is a fault into which Cicero (with whom the Sorites seems to have
been a favourite mode of argument) not unfrequently falls : witness, e.g.,
the following specimens from the Tusculan Disputations :

68 EXERCISES

the abbreviation, it will be seen that only one minor
premiss, viz. the first, is expressed, with which the
Sorites commences;* that no conclusion also is
stated till the final one. The intermediate proposi-
tions are therefore all major premises. As the scheme
is in the first figure, it will also follow necessarily that
only one of the premises viz. the first, can be particu-
lar, and only one, viz. the last, negative ; [a negative

Necesse est, qui fortis sit, eandem esse magni animi :

Qui magni animi sit, invictum :

Qui invictus sit, eum res humanas despicere :

Despicere autem nemo potest eas res, propter quas segritudine aflfici

potest :
Efficitur .*. fortem virum cegritudine numquam affici, Tus. Dis.

iii. § 7.

Quicquid est, quod bonum sit, id expetendum est :

Quod autem expetendum, id certe approbandum :

Quod vero approbaris, id gratum, acceptumque habendum :

Ergo etiam dignitas ei tribuenda est :

Quod si ita est, laudabile sit necesse est :

Bonum .'. omne laudabile : Tus: Dis. § 15.

In the above two formulae of argument (to omit other objections) pot
either, it is plain, of the first couple of middle terms conduces any
thing to the progression. There is as little difficulty in admitting that
whatever is good is acceptable as in admitting that it should be pursued
or approved.

♦ The other Minor premises are assumed from the preceding con-
clusions.

IN LOGIC. 69

intermediate premiss would involve the consequence
of a negative minor^ which the first figure will not
admit,] each of the intermediate propositions must
therefore be universal affirmatives.*

Exercise.

I. Draw out the two following Sorites into conse-
cutive regular Syllogisms.

Wilkes was a favourite with the populace :

He who is a favourite with the populace must

know how to manage them :
He who knows how to manage them must well

understand their character :
He who well understands their character must hold

them in contempt :
Wilkes therefore must have held the populace in

contempt.

* It may be thought at first that the verbal Sorites given in a former
note (see preceding page) is faulty on this ground ; but its validity may
easily be secured by attaching the negative (see chap xii) to the predi-
cate : e.g.

The Epicurean deities are inactive :

All who are inactive must be without virtue :

All who are without virtue must be without happiness :

The Epicurean deities must be, &c.

70 EXERCISES

Oneslmus^^ was a servant of Philemon:
Philemon was a hearer of Archippus :
Archippus was a minister at Colosse :
Onesimus was therefore a resident at Colosse .

Paley's Horse Paulinae.

11. Digest into the form of a Sorites the two fol-
lowing arguments.

He who inculcates benevolence^ humility, gentle-
ness, &c. is prescribing the sure preparatives for
friendship :

The Author of the gospel inculcated benevolence,
humility, &c. :

The Author of the gospel therefore prescribed the
sure preparatives for friendship.

He who prescribes the sure preparatives for friend-
ship virtually inculcates friendship itself :

* In the present form of this Sorites, a difficulty may be found in the
application of the rules above laid down; this will disappear if
in each proposition the implied truth is formally brought out and
stated ; e.g. in the first,

Onesimus resided where Philemon did.
The argument of the apostle (Heb. vii, 10) as far as it is meant to
be an argument, may be conveniently exhibited as a Sorites ; e.g.

What Abraham did (wg sVog g/Vs/i/) Isaac did :
What Isaac did, Jacob did :
What Jacob did, Levi did :
Abraham paid tithes to Melchisedek :
Levi paid tithes to Melchisedek.

IN LOGIC. 71

The Author of the gospel prescribed the sure
preparatives for friendship :

The Author of the gospel therefore virtually
inculcated friendship itself.*

III. Arrange the propositions of the following
Sorites in their regular order, and explain which of
them are logically faulty and why.

The Scriptures are confessedly agreeable to
truth :

The Church of England is conformable to the
Scriptures :

A. B. is a divine of the Church of England :

This opinion is in accordance with A. B's senti-
ments :

This opinion may be presumed to be true.

IV. Throw the Scriptural statement (Kom. viii,
30) into the form of a Sorites, making ^predes-
tinated' and ^glorified' respectively the minor and
major terms.

* ** Let it be admitted that our Lord did not formally prescribe the
cultivation of friendship and what then ? He prescribed the virtues
out of which it will naturally grow : he prescribed the cultivation of
benevolence in all its diversified modes of operation. In his per-
sonal ministry, and in that of his apostles he enjoined humility, forbear-
ance, gentleness, kindness, and the most tender sympathy with the
distresses and infirmities of our fellow creatures, and his whole life
was a perfect transcript of these virtues. But these, in the o^inary
course of events, and under the usual arrangements of provideno^, are
the best preparatives for friendship, as well as the surest guaSlntee
for the discharge of its duties and the observation of its rights." Hall's
Works, vol 1, p. 373.

72 EXERCISES

CHAPTER XXVII.

RECAPITULATORY EXERCISE,

Of the following Syllogisms, state which are
irregular in form only, and which are really faulty ;
of the latter class, explain for what reason each is so ;
reduce * the irregular ones to regular form, and name

* Reduction, in its more technical signification, is applied to the
conversion of a syllogism, in either of the two latter figures, into a
corresponding one of the first figure. The consonants which are found
in the mnemonical words, chap, xxiii, are intended to suggest rules for
this conversion. Thus, the initial consonant of a mnemonical word in
either of the last two figures, suggests the mood in the first figure into
which the conversion should take place : e. g., Cesare and Camestres
should be reduced to Celarent, Darapti to Darii, and so on. In the
process of reduction, a transposition of premises will sometimes be
necessary : the consonant employed to indicate this is *m.' The con-
sonants * s * and * p ' are meant to denote that the proposition indicated
by the vowel preceding should be converted, * s ' simply, * p ' by limita-
tion. Other uses belong to the remaining ones. We will exemplify
the manner of applying the rules by the reduction of the following
syllogism in Camestres to one in Celarent.

JL All true philosophers account virtue a good in itself :
g . . The advocates of pleasure do not thus account virtue : C ft /t" ^ Jr
g . . The advocates of pleasure are not true philosophers.

Here the 'm' in Camestres reminds us that the premises should be
transposed, and the former of the *s's,' that the second premiss should

IN LOGIC. 73

their Mood and Figure; also those of the regular
ones.

Some who are learned are much addicted to pre-
judice :

None who are much addicted to prejudice are men
of powerful minds :

Some who are learned are not men of powerful
minds.

An enslaved people is not happy :
The English are not enslaved :
The English are happy.

be converted. Let this be done, and we shall have at once the
following new syllogism : —
g .Those who account virtue a good in itself are not advocates of

pleasure: Cilfi

j^ ..AH true philosophers account virtue a good in itself:

Jrom which follows regularly the conclusion,
p • No true philosophers are advocates of pleasure.

And this is plainly the regular converse of the former conclusion which
the final ' s ' prepared us to expect. We have not thought it necessary
to devote a chapter to the explanation of this reduction, because the
conclusiveness of an argument is often as evident in one figure as it is
in another ; indeed, we have seen in chap, xxiv , that different figures
are appropriate to different arguments. The reduction called for in
the following exercise is simply such as has relation either to the present
order of the propositions in some of the examples, or to the present
form of some of the propositions.

74 EXERCISES

No irrational agent could produce a work which

manifests design:

The universe is a work which manifests design :
No irrational agent then could have produced the

universe.

A sensualist wishes to enjoy perpetual gratification
without satiety :

It is impossible to enjoy perpetual gratification
without satiety :

It is impossible for a sensualist to realize his
Welshes.

5.
No trifling business will enrich those engaged in it :
A mining speculation is no trifling business :
A mining speculation will enrich those engaged in it.

6.
All diamonds consist of carbon :
All carbon is combustible :
Some combustible substances are diamonds.

7.
A desire to gain by another's loss is a violation of
the tenth commandment :

Gaming implies a desire to gain by another's loss :
Gaming involves a breach of the tenth command-
ment.

IN LOGIC. 75

A man who deliberately devotes himself to a life of
sensuality is deserving of strong reprobation :

Those who are hurried into excess by the impulse
of passion do not thus devote themselves :

Those who are hurried into excess by the impulse
of passion are not deserving of strong reprobation.

9.
He* that is of God heareth my words :
Ye are not of God:
Ye therefore hear not my words: see John vlii,

47.

10
The less is blessed by the better : f
Abraham was blessed by Melchisedek :
Abraham was less than Melchisedek.

11.
Without faith it is impossible to please God:
Enoch did please God (for he had a testimony to
this effect: J)

Enoch therefore must have possessed faith.

* Before deciding on the validity of this syllogism, the student must
first suppose such a word as *only' to be understood before the major
premiss, that premiss being, in fact, a convertible proposition. The
convertibility of similar propositions in other parts of scripture is
express and manifest ; see, e.g., 1 John, iv, 6.

He that knoweth God heareth us :
He that is not of God heareth not us.
f See example viii, chap. 4.
^ A premiss of this nature, i. e., which carries with it its own

76 EXERCISES

11.

Convert the following Enthymemes into Syllogisms
of appropriate Mood and Figure.

" Possunt, quia posse videntur."

Shame is not a virtue ; for it is more a passion than
a habit.

These invalids cannot be suffering from fever ; for
they are not thirsty.

Not every species of resistance to law is to be
condemned; for no one condemns the resistance of
the clergy who refused to read the Book of Sports.

Jesus could not be an impostor ; for he warned his
followers to expect persecution.

evidence, and is itself expressed as a conclusion is sometimes termed,
an enthymematic sentence ; the use of such sentences as premises, it is
plain, detracts only from the symmetry of the argument.

IN LOGIC. 77

CHAPTER XXVIII.

ON HYPOTHETICAL SYLLOGISMS.

In chapter xviii, it was stated that the dependence of
one proposition on another might be exhibited in a
hypothetical, as well as in a categorical manner. A
specimen of a syllogism of the hypothetical kind was
there given. Where the terms of a syllogism are (as
they often are) entire propositions, this form is on
every account the preferable one; the appearance
e. g. of the two syllogisms subjoined in a categorical
form would evidently be cumbrous and inelegant.

1. 2.

If A is B, C is D: If A were B, C would be D:

A is B : C is not D :

C /. is D. A .'. is not B.

With regard to the parts of syllogisms such as the
above, we may remark that the member of the major
premiss which has the hypothetical particle is termed
the antecedent ;^ the other member, the consequent.

* This term must not be considered as implying that the proposition
so characterized is always stated first in order,

H 2

78 EXERCISES

The syllogisms themselves are either conjunctive^ or
disjunctive ; in the former, the coexistence of two (or
more) facts being asserted, in the latter, the certainty
of one of two (or more.) The following may serve as
specimens of the form of disjunctive hypotheticals, those
already given being of the conjunctive class.

1. 2.

If A is not B, C is D: Either A is B, or C is D:

A is not B : C is not D :

C then is not D. A then is B.

It is to be observed that a syllogism does not be-
come hypothetical by having a hypothetical premiss
in it, for this hypothesis may be transferred to the
conclusion, in which case it is to be regarded as part
of a term, and the reasoning becomes categorical.
For example, such a syllogism as the following must
be referred to the class of categoricals.

Every A is B :
If C is D, it is A:
If C .-. is D, it is B.

* We have purposely substituted this term for the term * conditional,
employed by Whateley, because disjunctives are really a species of
conditionals, as Whateley himself allows. (Logic, page 114.) To
oppose disjunctives to conditionals is, in fact, to be guilty of a cross
division.

IN LOGIC. 79

Exercise.

Explain which of the subjoined syllogisms are real
hypotheticals ; of these, state which are conjunctive
and which disjunctive, distinguishing in each the
consequent and antecedent.

If virtue is voluntary, vice is voluntary :
Virtue is voluntary :
Vice is voluntary.

If excommunication occasions no civil wrong, it
should incur no civil penalty :
It occasions no civil wrong :
It should then incur no civil penalty.

Logic deserves to be neglected, if it is useless :

It is not useless :

It does not deserve to be neglected.

4.
If the Pope is infallible, it must be from his being
inspired :

He is not inspired :

He * cannot then be infallible.

* Supposing the position here contended for to be the fallibility of
the Pope, we must regard the argument adduced as an indirect method

80 EXERCISES

The worshippers of images are idolaters :
If the Papists worship a crucifix, they worship an
image :

If the Papists worship a crucifix, they are ido-
laters.

of proving it. It is, in fact, the * reductio ad impossibile' or absurdum,*
stated in its most concise form. The * reductio ad absurdum' is a
mode of proof used, when it is proposed to show not that a given pro-
position is true, but (which is the same thing) that it cannot be false.
It is considered properly that this is done if some absurdity or impos-
sibility can be proved to follow from the denial of the proposition. For
example, let it be objected by a Romish controversialist to admit as
above that the Pope is fallible ; his Protestant antagonist would then
argue thus —

Whoever is infallible must be inspired :

The Pope (according to you) is infallible :

The Pope then (according to you) must be inspired.

It is presumed that the Romanist would not maintain this conclusion.
Unless then he is prepared to challenge the accuracy of the reasoning
which has led to it, he is of necessity driven from his original position,
i. e., from the present minor premiss, and the contradictory of that premiss
may be assumed as proved. We have not however given any exercises
on this reduction, as the hypothetical mode of stating the argument is
so obviously the more eligible one. In the following chapter it will be
seen that this hypothetical is always of the destructive kind, to use the
technical designation. Whateley, in his Logic, confines his account
of the argument to the case in which the disputed point is the conclu-
siveness of a syllogism in the second or third figure ; but this is a need-
lessly scholastic view of its use, and more befitting an exclusive advocate
of the first figure. For some valuable observations on the respective
advantages of the categorical and hypothetical forms of it, see the
Rhetoric of Whateley, pp. 140—146.

IN LOGIC. 81

6.
If penal laws against Papists were enforced, they
would be aggrieved :

Penal laws against them are not enforced :
They are therefore not aggrieved.

The adoration of images is forbidden to Christians,
if the Mosaic law was not designed for Israelites
alone :

The Mosaic law was designed for the Israelites
alone :

The adoration of images is not forbidden to Chris-
tians.

CHAPTER XXIX.

ON CONJUNCTIVE HYPOTHETICALS.

Conjunctive Hypotheticals are either constructive
or destructive, the former being those used when an
affirmative conclusion has to be proved, the latter
when a negative. We have given a specimen of each
sort towards the commencement of the preceding
chapter. The common rule respecting constructives
is, that the truth of the consequent is inferrible from

82 EXERCISES

the truth of the antecedent; in destructives, the
falsity of the antecedent is inferred from that of the
consequent. It is evident that the reverse inferences
to these would not be valid. For example, it would
not follow if A were not B, (to recur to the first of
the formulae already noticed,) that C was not D, there
being many other cases supposable in which it might
be so ; the falsity of the consequent therefore will
not follow from that of the antecedent, nor the truth
of the antecedent from that of the consequent.

A number of hypothetical syllogisms* may be
abridged into the form of a Sorites, as readily as of
categorical ones. It is easy to discover, e.g., the
simple conjunctive hypothetical of which the follow-
ing formula is made up :

If A is B, C isD; if C is D, E is F; if E is F,
G is H ; but A is B ; therefore G is H.

The laws which obtain with regard to such hypo-
thetical Sorites are similar to those which govern
categorical. All minors, e.g., but one are suppressed ;
and it is only in the last stage that we can introduce
a negative premiss. Thus it would be competent to

* Because of this possibility, Whateley would have the consideration
of Sorites postponed till hypothetical have been treated of ; but this
reason would equally call for the postponement of the consideration of
syllogisms altogether ; for we have seen chap, xviii, and Whateley him-
self allows, that every categorical syllogism maybe stated hypothetically.
The 'injudicious arrangement' therefore for which the distinguished
author censures Aldrich and others, is in this instance his own.

IN LOGIC. 83

US to make the above Sorites a destructive one, by
closing : " but G is not H, therefore A is not B."

Exercise 1.

Explain to which class the conjunctives in the
preceding exercise belongs, whether constructive or
destructive^ and in which of these the respective
rules are observed or neglected.

Exercise 2.

State which of the following Scriptural hypotheti-
cal are of the constructive and which of the
destructive kind.

IT
1.

If Jehovah had known any one greater than
himself, he would not have sworn by himself:

He did swear by himself:

Therefore he could not have known any one
greater than himself. (Heb. vi, 13.)

If Abraham had been justified by works, he would
have had whereof to glory before God :

Not any one can have whereof to glory before
God:

Abraham could not therefore have been justified
by works. (Eom. iv, 2.)

■

84 EXERCISES

If* you were blind (morally) you would have no
sin.

You are not blind (according to your own showing:)
You therefore have sin. (John ix, 41.)

If the Jews had known the hidden wisdom, they
would not have crucified the Lord of glory :

They did crucify him :

They could not have known the hidden wisdom.
(1 Cor. ii, 6.)

Exercise 3.

Decompose the following hypothetical Sorites into
their constituent syllogisms.

If the Scriptures are the word of God, they should
be well explained :

If they are to be well explained, they should be
diligently studied:

If they are to be diligently studied, an order of
men should be set apart to study them.

The Scriptures are the word of God :

An order of men should then be set apart to study
them.

* This proposition like the one numbered nine in chapter xxvii,
must be considered ex as well as in-clusive.

IN LOGIC. 85

If any are to be saved, they must first call on the
Saviour :

If they are to call on the Saviour, they must first
hear about him :

If* they are to hear about him, preachers must be
sent to tell them :

If any then are to be saved, preachers must be
sent, &c. (Rom. x. 13, 15.)

CHAPTER XXX.

HYPOTHETICALS REDUCED.

On an analysis of a conjunctive hypothetical syllogism,
it will be found, that two of the propositions com-
posing it, viz., the conclusion and preceding premiss,
are the same as would appear in an equivalent
categorical, the firfet proposition being simply an
expression of the connection subsisting between the

* In this proposition we have, as the biblical student will readily
perceive, condensed two of the original premises into one.

86 EXEKCISES

two others. To reduce* a hypothetical then to a
categorical form, nothing more is necessary than the
supplying an additional categorical premiss^ and, in
any given instance, it only needs to be considered
which is wanting. The premiss which is most com-
monly retained in Hypothetical syllogisms is the
Minor, but that this is not necessary will be evident
from the first example in chapter xxviii, in which
it is the Major that appears, the following being
the form which the example would take if reduced
to a categorical :

Virtue is voluntary :
t Vice is virtue :
Vice is voluntary.

In reducing a hypothetical, consider whether it is
the subject or predicate of the conclusion which occurs
twice as a term in the latter propositions ; if the
former, supply a Major premiss ; if the latter a Minor,

Exercise.
Reduce examples 2 and 3 in chapter xxvii to
categorical syllogisms; also examples 1, 2, and 4 in
preceding chapter.

* We here confine our attention to those hypotheticals of which the
first, i. e. the hypothetical premiss, has the iftibject of its antecedent and
consequent the same ; because as it is acknowledged on all hands, no
practical advantage attends the categorical reduction of the others.

f This sounds a little paradoxical ; but it is, of course, the meta-
physical properties of virtue alone which are here the subject of
predication. /

IN LOGIC. 87

CHAPTER XXXI.

ON DISJUNCTIVES.

A DISJUNCTIVE syllogism is one in which, of two or
more predicates assignable to a certain subject, the
present predicability of one may be assumed ; all the
other predicates then being negatived, the applicability
of the remaining one is inferred. To the validity of
this inference it is necessary, of course, that all the
predicates really supposable* should be comprehended;
otherwise, the omitted one may be the predicate
which should be assigned. Such a syllogism, e. g., as
the following : —

* On this ground the following disjunctive, taken from a modern
logical treatise, must be pronounced vicious:

The cause of the sufferings of infants must be either,

1. Sins before their birth, or

2. A want of power > • .1 • ^ .

o A * i? • i.- r in their Creator, or

3. A want of justice)

4. Original sin :

It cannot be either 1, 2, or 3 :
It must therefore be 4.

Here the two intermediate theories must be put ' out of court' at once
as, under the light of Christianity, not even supposable ; and that the
other two cases do not exhaust the conceivable alternatives, an attentive
consideration of the sufferings of many irrational creatures may evince.

88 EXERCISES

This proposition is either A^ E, or I :
It is not A or I :
It must then be E.

would be vicious, because in the enumeration in the
Major premiss, the class of propositions O was left
out. Where disjunctive syllogisms are defective, it
is chiefly from this incomplete enumeration at their
commencement; care must be taken then that such
enumeration be made exhaustive^ i. e. that all the sup-
posable cases be embraced.

It will be seen by a reference to chapter xxviii,
that such a disjunctive as the above may be stated in
a more directly hypothetical form : e. g.

If this proposition be not A or I, it must be E :
It is not A nor I :
It must then be E.

Exercise.

Reduce to hypotheticals of a similar form the fol-
lowing disjunctives, and vice versa,

This idea is derived either from sensation or re-
flection :

It is not derived from sensation :

It must then be derived from reflection.

ON LOGIC. 89

The earth is either eternal, or the effect of chance,
or the work of an intelligent being :

It is neither eternal nor the effect of chance :
It must then be the work of an intelligent being.

If this conjunctive hypothetical be not a construc-
tive, it must be a destructive :
It is not a constructive :
It must then be a destructive.

4.
A tumult is either peace or war :
It is not peace :
It must then be war. — Cicero^ Philipp. vii.

The side A B must be either equal to, less, or

greater than A C :

It is neither equal to nor less than it :

It must then be greater than it. — Euclid^ book 1,

Prop. xix.

I 2

90 EXERCISES

CHAPTER XXXII.

ON DILEMMAS.

A Dilemma properly signifies a double antecedent.
If we have two (or more) antecedents with either
the same or several consequents: then if, in the
minor premiss, we disjunctively grant the antece-
dents, we may either absolutely or disjunctively infer
the consequents; also, if we have two (or more)
consequents with either the same or several antece-
dents, then if we disjunctively deny the consequents
we may either absolutely or disjunctively deny the
antecedents. The former is a case of the constructive^
the latter of the destructive Dilemma ; what is common
to both, and characteristic of the Dilemma, is the dis-
junctive minor premiss. The following are symbolical
representations of "a Dilemma of each description.

1.
If A is B, C is D: and if E is F, G is H:
Either A is B, or E is F :
Therefore either C is D, or G is H.

IN LOGIC. 91

2.
If AisB, CisD: andif EisF, G is H :
Either C is not D, or G is not^H :
Therefore either A is not B, or E is not F.

It should be .observed that the minor premiss,
although (as in categorical syllogisms) properly placed
after the major, does not always stand in that
order; this is immaterial to the validity of the Di-
lemma.

Exercise 1.
Supply the requisite conclusion to the premises of
the subjoined Dilemmas.

1.
If (Eschines joined in the public rejoicings, he is
inconsistent : if he did not, he is unpatriotic :
Either he did join or did not :
Therefore

2.
If the taking of OczakofF was an adequate motive
for hostilities, the war ought to be continued ; if not,
it ought not to have been commenced:

Either it was an adequate motive or it was not :
Therefore

If this man were wise, he would not speak irrever-
ently of the Scriptures in jest ; if good, he would not
do so in earnest :

He does so either in jest or in earnest:

Therefore

92 EXERCISES

If the blest in heaven have no desires, they will be
perfectly content; they will be equally so, if their
desires are fally gratified :

Either they will have no desires, or their desires
will be fully gratified :

Therefore

If Jepthah included rational beings in the intention
of his vow, he was wantonly inhuman in the forma-
tion of it ; if he did not, he was needlessly scrupulous
as to its execution :

Either he must or must not have so included
rational beings :

Therefore

Exercise 2.

Interpose the ^premiss requisite to the complete-
ness of the following Dilemmas : —

* The most common fault of Dilemmas, as of Disjunctives, is found
in the precipitate, not to say arbitrary, assumption of this premiss. It
is seldom, in actual life, that the different cases of possibility are
either so few or so precisely definable as this part of Logic would per-
suade us. " Our business is at present rather with the sequence than the
truth of arguments ; or we might fairly impeach the validity of some of
the examples given above on this ground. A great part of the well-
known classical dilemmas have no farther value than as indifferent jests.
Let the following specimen suffice, in illustration : —
Si uxor ducenda formosa sit, zelotypiam inducet ; si deformis, fastidium :
Nulla ergo ducenda est.

The assumption which is here contained in the omitted premiss, viz. ,
that every * uxor* will be either formosa or deformis is obviously as
little consonant to truth as it is to gallantry.

IN LOGIC. 93

A person who is able to endure pain, will be likely
to utter falsehood under torture ; he will be equally
so, who is not able :

A person therefore under torture will be likely to
utter falsehood. — Quintilian.

For those who are bent on cultivating their minds
by diligent study, the incitement of academical hon-
ours is unnecessary; for the idle and such as are
indifferent to mental improvement, it is ineffectual :

The incitement of academical honours therefore is
either unnecessary or ineffectual.

(H)

If we shall say that the baptism of John was from
heaven, he will reproach us for not believing him;
if from men, we shall be in danger from the people :

Either therefore we shall be reproached by him,
or be in danger from the people.

CHAPTER XXXIII.

RECAPITULATORY EXERCISE.
State the nature of the following Hypotheticals,
whether conjunctive or disjunctive, whether construc-
tive or destructive, &c. ; explain also which are
logically faulty and why : —

("aiflVERSITT)

'^4^^^

94 EXERCISES

If the earth had a beginning, it had a cause :

It had a beginning :

It had therefore a cause.

Government is either a property or a trust :

It is not a property :

It must therefore be a trust.

If the fourth commandment is obligatory, we are
bound to set apart one day in seven for religious
purposes :

We are bound to set apart one day in seven :
The fourth commandment is therefore obligatory.

If a king of Spain has a right to alter the law of
succession, Carlos has no claim ; equally, if a king of
Spain has not that right, Carlos has no claim :

A king of Spain either has or has not the right :

Carlos therefore has no claim.

If there were no divine providence, no human
governments could long subsist :

Various human governments have subsisted long :
There must then be a divine providence. — Grotius,

IN LOGIC. 95

If the British constitution were perfect^ we should
enjoy liberty :

We do enjoy liberty :

The British constitution is therefore perfect.

Divine favour will be bestowed hereafter with res-
pect either to men's persons or to their conduct :

It will not be bestowed with respect to their per-
sons: (for see Bomans ii, 11.)

It will be then with respect to their conduct.

Justification must be either of debt or of grace :

It cannot be of debt :

It must then be of grace : (Bomans iv.)

If expiatory sacrifices were appointed before the
Mosaic law, they must have been expiatory, not of
ceremonial, but of moral guilt :

If so, the Levitical sacrifices must have had like
efficacy :

If so, these sacrifices ^\5mild have been able to
make the offerers ' perfect : '^^*k^

They were not able to make the offerers perfect :

No expiatory sacrifices therefore were appointed
before the Mosaic law. — Davison.

■

96 EXERCISES

CHAPTER XXXIV.

ON PROBABLE ARGUMENTS.

The syllogisms which we have hitherto given as
examples have consisted almost entirely of one or
other of the four propositions which fall under the
especial cognizance of logic, viz. A, E, I , O ; the
majority of them of the universals A, E. But it is
not always that conclusions of this absolute univer-
sality can be established. In truth which, like
political and moral truth, has relation to human in-
terests and passions, a high probability, is, for the most
part, all which can belong to propositions — the sole
universality* that of general rules. According to the
probability of the premises, in each such case, will,
of course, be the probability of the conclusion. A

^ * It is especially this sort of universality which must be attributed
to maxims^ proverbs, and observations on character. The Psalmist
accordingly, (Psalm cxvi, 11,) acknowledged himself to have spoken
in haste when he censured all men as liars. Surprise has been some-
times expressed at the occasional failure of efforts of religious training,
as if the divine declaration (Prov. xxii, 6) was thereby discredited.
The true light, we need scarcely say, in which this declaration should
be considered and interpreted is rather as a maxim than a promise.

IN LOGIC. 97

syllogism of this nature may^ e. g., have one only of
its premises probable, or it may have both; in the
latter case, the aid of arithmetic must be called
in to estimate the probability of the conclusion. We
subjoin an example of each kind, with the explanatory
comment requisite.

Most Y's are Z :

Every X is Y :

Most X's are Z.

[If we suppose the proportion of the cases in which Y is Z, as predi-
cated in the first premiss, to be 4 out of 5, the same proportion will be
the measure of the probability with which we may predicate, in the
conclusion, that X is Z, i. e. out of every 5 X's, we may conclude that
4 are Z.]

Most Y's are Z :
Most X's are Y :

[Suppose that § is the measure of the preponderance in the first
premiss, and ^ in the second, then, compounding these fractions, we
shall have § X -| =-|4 =-x^ as the degree in which we may conclude
that -

Most X's are Z:

i. e. out of every 15 X's, we may infer with safety that 8 are Z.]

Exercise.

Determine the probability of the respective con-
clusions deducible from the following premises,
supplying those conclusions.

■

98 EXERCISES

The reports which this author heard are probably
true :

[Suppose 5 out of 7 of the reports to be so.]

This which he records is probably a report which
he heard :

[Suppose his accounts of reports in 2 cases out of 3 to be accurate.]

A theory will, if false, be probably soon exploded,
which appeals to the evidence of observation and
experiment :

[Suppose the probability here stated to be -X.]

Phrenology appeals to the evidence of observation
and experiment :

A person infected with the plague will probably
die:

[ Suppose 3 in 5 of the infected die. ]

This person is probably infected with the plague :

[Suppose it an even chance.]

m LOGIC. 99

CHAPTER XXXV.

ON CUMULATIVE ARGUMENTS.

In probable* reasoning there will often be a variety
of arguments all tending to the same point, i. e. to
establish the same conclusion. In this case, although
the logical force of each separate argument may be
inadequate to conviction, their collective strength may
amount to the fullest certainty. The estimation of
the probability of each item in such a cumulation
must belong, of course, to the particular science from
which it is derived ; the computation of their collec-
tive probability is the business of arithmetic. For
example, let there be the two subjoined arguments
to prove that X is Z :

* There may be a similar plurality of arguments in demonstrative
reasoning, the united force of which will, of course, amount to more
than certainty. Thus, in astronomy, the rotundity of the earth's figure
is proved alike from the voyages of navigators around it ; from the ap-
pearance invariably presented by the visible horizon, when seen from
any considerable elevation ; from the phenomena of vessels approaching
or receding from a shore ; from the shadow of the earth in eclipses, &c.
We have, however, thought it the less necessary to dwell on this kind of
aggregation, as it is common for reasoners, when they have an argu-

100 EXERCISES

1. 2.

Most Y's are Z : Most Ws are Z:

Every X is Y: Every X is W:

Most X's are Z. Most X's are Z.

Here let us suppose the probability of the first
conclusion to be f and of the second ^ ; then, by the
common rule for the addition of fractions, the com-
bined probability will be if +it=fQ^ i. e. that X is
Z may be considered as more than estabhshed.

In many instances it will happen that there will be
items on the debtor side, so to speak, as well as on the
creditor, i. e. there will be arguments tending to
disprove a given conclusion, as well as arguments
to prove it. When this is the case, a balance must,
of course, be struck. Suppose, for example, to recur
to the above specimen of cumulation, that there
were considerations which went to show that X was
not Z ; an argument, e.g. which exhibited the proba-
bility of this being the case, as no more than ^y 5 i^
would then be requisite to deduct this fraction ^\ from
the proportion previously obtained: thus f§— 2t =
ft J""if§=ff^? or less than a unit, making the whole
result to be now below absolute certainty.

ment confessedly convincing to bring forward, voluntarily to waive the
production of others. The anecdote is well known of the parliamen-
tary orator, who had proposed to assign several reasons for the absence
of a fellow member, but was excused by the Speaker from proceeding
after he had given the first, viz., that the member in question had died
a week ago.

IN LOGIC. 101

Exercise 1.

Compute the ^cumulative force of the following
arguments.

From identity of features may be inferred identity

of person:
This person's features are those of A. B :
We may conclude therefore that he is A. B.

From identity of gait may be inferred identity of

person :
This person's gait is that of A. B :
We may conclude therefore that he is A. B.

* The argument called ' Sorites' is etymologicaUy a cumulative one,
but its nature and effect are very different from those of the cumulatives
noticed in the present chapter. In a Sorites, except in absolutely de-
monstrative reasoning, the more links or premisses there are, the less is
the probability of the conclusion, and, as in a material chain the whole
is not stronger than its weakest part, if there be a single proposition in
the series which is less probable than the contrary, the whole argument
is vitiated. It would be an amusing problem, to calculate the degree of
probability belonging to some of the chains of arguments by w^hich so-
called medical discoveries are commended to the public. The follow-
ing is the Morisonian (pills) Sorites :

All diseases proceed from one source :

All must be cured by one medicine :

This medicine must be a vegetable cathartic :

This cathartic is found only in Morison's pills.

[Given, for argument's sake, the probability of each proposition in
this series |^ ; what is the probability of the conclusion ?]

K 2

102 EXERCISES

From identity of dress may be inferred identity of

person :
This person's dress is that of A. B :
We may conclude therefore that he is A. B :

[Let the probability of the first conclusion be 4., of the second
|., of the third |^.]

Exercise 2.

Express the series of interrogations (2 Cor. vi, 15)
as so many cumulative arguments.

CHAPTETt XXXVI.

ON THE 'A FORTIORI' ARGUMENT.

1.
YisZ:

X is more than Y :

X is therefore more than Z.

Y is greater than Z :
X is greater than Y :
Much more then is X greater than Z.

The above are specimens of the forms into which

IN LOGIC. 103

arguments designed to prove that a given predicate
belongs in a greater degree to one subject than
another may be conveniently thrown. The technical
name by which such arguments are known is a
fortiori. It is not necessary to subject them to the
tests of ordinary syllogisms, as their conclusiveness is
* self-evident. Formulae of the kind will be familiar
to the mathematical student; but, except in form,
the reasoning is as common to other descriptions of
subjects as to mathematics ; it abounds in the Scrip-

♦ Professor de Morgan ( First Notions of Logic, pp. 24, 25, &c. )
has devoted two or three pages to the discussion of eligible formulae
for exhibiting such arguments in the regular syllogistic form. The
following, e.g., are representations which he would propose to give of
premises like those in No. 2 above :

Every Y is Z, and there are Z's which are not Y :
Every X is Y, and there are Y's which are not X :

or
The Y's contain all the Z's and more :
The X's contain all the Y's and more :

or
All the Z's make up part (and part only) of the Y's :
All the Y's make up part (and part only) of the X's :

from which he would draw, as conclusions, in the first instance.
*' Every X is Z, and there are X's which are not Z," and so on. Such
experiments as these appear, we confess, to our own minds very much
like attempts to ^smooth the ice.* Nothing would be gained, we
apprehend, to the elucidation of Euclid's second axiom by an endeavour
to evolve it from the 'idea' of the firsts and we can discern as little
utility in the proposed application to the present argument of the dictum
of Aristotle. The particular case of the argument where individuals
rather than classes are compared together, the Professor takes no
account of.

104 EXEKCISES

tures. We may illustrate by the two following ex-
tracts^ the first from a well-known passage in Virgil,
the mode of its occurrence.

Pallas exurere classem
Argivum at que ipsas potuit submergere ponti :
Ast ego, quae Divum incedo regina, Jovisque
Et soror et conjux, una cum gente tot annos
Bella gero ; et quisquam numen Junonis adoret :
Prseterea, aut supplex aris imponat honorem !

We may represent the reasoning of this passage in
an d fortiori form, as follows :

Minerva was able to avenge her w^rongs :
I (Juno) am greater than Minerva :
Much more then ought I to be able to avenge my
wrongs.

"Had we assurance that after a very limited,
though uncertain period, we should be called to
migrate into a distant land, whence we were never

to return much of our attention would be

occupied in preparing for our departure . . . How
strange is it then that with the certainty we all
possess of shortly entering into another world, we
avert our eyes as much as possible from the prospect,
&c., &c."— Hall's Works, Vol. i, pp. 346, 347.

(In this passage, the following a fortiori argument
is also evidently contained.)

IN LOGIC. 105

A journey from one country to another demands
suitable preparation :

The journey we take at death is far greater than
that from one country to another :

Much more then does this journey demand suitable
preparation.

* Exercise.

Draw out, with regular premises and conclusion,
the following d fortiori arguments from ^ Scripture.

"Behold the fowls of the air; for they sow not,
neither do they reap nor gather into barns : yet your
heavenly Father feedeth them: are ye not much
better than they?" (Matthew vi, 26.)

We have had fathers of our flesh who corrected us,
and we gave them reverence; shall we not much
rather be in subjection unto the Father of spirits and
live ? (Hebrews xii, 9.)

If thou hast run with the footmen and they have
wearied thee, then how canst thou contend with
horses ? f Jeremiah xii, 5.)

* The general student will find an example of this argument among
those given as an exercise in the following chapter.

106 EXERCISES

*If the righteous scarcely be saved^ where shall
the ungodly and the sinner appear? (1 Peter, iv, 18.)

CHAPTER XXXVII.

ON SUBJECTS OF ARGUMENTS.

It can scarcely have escaped notice that the
specimens of syllogisms which we have given in pre-
ceding chapters have embraced all varieties of subject
matter. The syllogism is, in fact, a form of argument
applicable to all subjects, and the like may be said of
the k fortiori argument just noticed. Were it not
that .many have distinguished between syllogistic and
mathematical, &c., arguments, it might suffice to state
this as a self-evident truth. To remove such mis-
apprehensions of this kind as may remain in any
minds, we propose, in this chapter, to adduce a few
syllogisms on a selected diversity of subjects. The
student, who is already satisfied of the universal
applicability of the syllogism, will find his account in
determining the Figure, &c., in which each example
is.

* That this (and by consequence, the preceding) is but an a fortiori
argument disguised, the student may easily satisfy himself by an exami-
tion of the parallel passage. (Proverbs xi, 31.)

IN LOGIC. 107

Exercise.

Distinguish by their appropriate mnemonical name
the various categorical syllogisms following.

Whatever is associated with pain in the contem-
plation of it is a source of the sublime :

Objects of great height are associated with pain in
the contemplation:

Objects of great height are a source of the sublime.

The three angles of every triangle are equal to

two adjacent angles :

Two adjacent angles are equal to two right angles :
The three angles of every triangle are equal to

two right angles.

^Except' is a preposition :

^Except' was originally an imperative verb:

Some prepositions were originally verbs.

Lias lies above Red Sandstone :
Red Sandstone lies above Coal :
Lias lies above Coal.

■

108 EXERCISES

ISTo person can serve both God and Mammon:

(Matt, vi, 24.)
The covetous person serves Mammon :
He cannot therefore serve God.

Trade, to be properly advantageous, should seek
frequent returns and a near market :

The colonial trade does not offer either frequent
returns or a near market :

The colonial trade is not properly advantageous.

Revenge, Robbery, Adultery, Infanticide, &c.,
have been countenanced by public opinion in various
countries :

All crimes are made up of Revenge, Robbery,
Adultery, Infanticide, &c. :

All crimes have been countenanced by public
opinion in various countries.

IN LOGIC. 109

CHAPTER XXXVIII.

ON FALLACIES.

Fallacies have been defined to be "^deceptive or
apparent arguments by which a man is himself con-
vinced, or endeavours to convince others, of something
which is not really proved." The most common divi-
sion of fallacies is into * verbal and material fallacies ;

* Under the former of these heads are placed by Aristotle, who is
the original author of the distinction, six varieties, and under the latter,
seven. They ^re respectively as follows : —

Fallacies in the diction. Fallacies not in the diction.

^quivocationis.

Accidentis.

Amphiboliag.

A dicto simpliciter ad dictum secundum

Compositionis.

quid.

Divisionis.

Ignorationis elenchi.

Prosodise,

A non causa ut causa.

Figurae dictionis.

Consequentis.

Petitionis principii.

7. Secundum plures interrogate ones ut unam.

We shall not think it necessary to take up each of these particulars
for illustration. Some of the species enumerated are resolvable into
what would now be termed puns, and others such as none but a pro-
fessed sophist would condescend to. Bishop Sanderson, from whom
we have borrowed the Latin designations of the species, speaks of the
enumeration as ' non incommoda;' but in this epithet, qualified as it is,
more of the compiler, we cannot but think, than of the independent
thinker, appears.

110 EXERCISES

— to use the language of the schools — fallacies in die-
Uone and fallacies extra dictionem. This division^
which is sufficiently intelligible and convenient^ we
shall adopt. Of the former class of fallacies, viz.,
those which are faulty in the diction we have already
had occasion to speak in the chapter on the canons of
syllogisms; they are chiefly undistributed middle and
illicit process either of the major or minor term,
(see chapter xx.) Fallacies of this sort are alike
capable of detection, whether the reasoning be con-
ducted by words or symbols. In the exhibition of
material fallacies, on the contrary, symbols are less
applicable ; — consideration must be generally had of
the nature of the subject-matter ; of the truth or fal-
sity of the propositions used as premises. The fol-
lowing argument, e. g. is fallacious, because the major
premiss is unduly assumed — is, in fact, as a universal,
false : —

Events recorded in the Chinese annals have really
happened :

Such an eclipse is recorded in the Chinese annals :
Such an eclipse really happened.

The most frequent fallacy in practice is, perhaps,
one which may be said to belong indifferently to each
of the classes above distinguished, sc. that which is
founded on the ambiguity of language in reasoning
and termed 'Equivocation' — a principal term being
used in one sense in one part of the argument and in
quite a different sense in another. This fallacy has
been sometimes characterised as semi-logical ; it will

IN LOGIC. HI

demand a separate consideration. In the following
exercises it is to be assumed that the conclusion is
unwarranted and it will be required of the student to
determine to which of the two classes of fallacies
the argument is referable.

Exercise 1.

Determine whether the subjoined categorical syllo-
gisms are Verbal or Material Fallacies.

None but Whites are civilized :
The ancient Germans were Whites :
The ancient Germans were civilized.

Every change is agreeable :

Death is a change :

Death therefore is agreeable.

Warm countries alone produce wine :
Spain is a warm country :
Spain produces wine.

§ " One symptom of the plague is a fever :

§ The examples with this mark before them are taken from Chilling-
worth's " Religion of Protestants."

112 EXERCISES

Such a man has a fever :
Therefore he has the plague."

§ " He that obeys God in all things is innocent :
Titius obeys God in some things :
Therefore he is innocent."

6.
Whoever is visited with severe affliction is to be
presumed wicked :

Thou (Job) art visited with severe affliction :
Thou art therefore to be presumed wicked.

Exercise 2.

Determine whether the subjoined hypothetical
syllogisms are Verbal or Material Fallacies.

If all testimony to miracles is to be admitted, the
popish legends are to be believed :

The popish legends are not to be believed :

No testimony to miracles is then to be admitted.

§ "Either the Roman Church was the true visible
church, or Protestants can name and prove some
other that was, or they must say that there was no
visible church :

IN LOGIC. 113

They will not say that there was no church and
they can name or prove no other :

The Roman Church must therefore have been the
true visible church."

If I denied the being of a God, I should be
impious :

I do not deny the being of a God :
I am not therefore impious.

If any objection that could be urged would justify
a change of established laws, no laws could reasonably
be maintained :

Some laws can reasonably be maintained :
No objection therefore that can be urged will justify
a change of established laws.

CHAPTER XXXIX.

ON MATERIAL FALLACIES.

The two principal material fallacies which require
notice are those which are termed by Aristotle (see

L 2

1 14 EXERCISES

note, chap, xxxvili) ^ignoratlo elenclii/ and ^petitio
principii.' The former has been happily *generaUsed
by Whately into the fallacy of irrelevant conclusion^
and is committed, whenever the premises adduced
prove not the point in dispute, but one resembling it,
and likely to be mistaken for it. In illustration of
this, it has been well remarked, that a reasoner,t
"instead of proving ^that a prisoner has committed
an atrocious fraud,' will prove ' that the fraud he is
accused of is atrocious;' instead of proving ^that a
man has not the right to educate his children in the
way he thinks best;' will show ^that the way in
which he educates them is not the best;' instead of

* Elenclms properly signifies the contradictory of an opponent's
position, which is, of course, in disputation the thing to be proved ; but
the supposition of an opponent and a disputation is needlessly circui-
tous and savours a little too much of the times when Logic was
considered as an *art of wrangling.' It is every way preferable to
examine the conclusiveness of an argument in itself. The fallacy now
before us is of very frequent occurrence, being the one which is com-
plained of whenever the remark (so often heard in conversation) is
made, 'that is not the question.' It is evident, however, that this
fallacy can only be exemplified by a previous stating, in each instance,
what the question is ; and for this reason no separate exercises on it
have been given in the present chapter. One very common case of it>
that, sc. in which a universal conclusion is substituted for a particular,
and a contradiction faulty in quantity thus made, belongs rather to the
class of verbal fallacies ;» many instances of it have been inserted,
without remark, in previous exercises.

v^He

' J^SOI

f This and the follow^Blentence are taken, in substance, from a
little work entitled * Easy ^Rsons in Reasoning,' (pp. 138, 139,) which,
though anonymous, is commonly attributed, not without good apparent
reason, to the eminent writer already named.

IN LOGIC. 115

proving ' that the poor ought to be relieved in this
way rather than in that/ will prove ^that the poor
ought to be relieved^ &c. &c."' The reasoner then
proceeds to assume as premises, conclusions different
from those which have really been established.

The fallacy ^petitio principii' answers very much
to what is popularly called in English ^ begging the
question.' It is the fallacy which is committed when-
ever either of the premises on which a conclusion
rests is unduly assumed. This undue assumption
may take place in several ways. Sometimes the pre-
miss which is employed is substantially identical with
the conclusion, the terms in which it is expressed
being only so varied as to conceal the sameness.
Great facility is afforded to this disguise in English,
by the mixed derivation of the language, and the num-
ber of interchangeable terms which it consequently
affords. Thus it is assigned as a reason by a writer
of some merit why reputation is desirable that it pro-
cures us esteem. Sometimes the only difference
between the conclusion and premiss will be, that a
truth is expressed in popular phraseology in the one,
and in philosophical in the other. A fact has in this
manner often been assigned as a *cause for itself, as

* Taken in this view, the present fallacy will be seen evidently to
include that of ' non causa pro causa,' the intermediate one in Aristotle's
list of material fallacies, as exhibited in the previous chapter. The
fallacy of * non causa' is sometimes subdl^ded into the two species of
* non vera pro vera* and * non talis pro ta^' the former being equivalent
to the falsity of a major premiss, the latter of a nftinor ; but the truth
and falsity of propositions being matters of opinion, it is plain that no
exercises on this branch of the subject could be usefully given.

116 EXERCISES

when, e.g, the magnet's drawing iron to itself has
been ascribed to its attractive properties. Sometimes
the premiss used will be absolutely unauthorised and
without evidence, not to say false, as in the instance
quoted in a previous chapter of the authenticity of
the Chinese annals. Lastly, a premiss, is sometimes
made dependent for its evidence on the conclusion,
and the conclusion and premiss are thus proved alter-
nately from each other. This is technically called
arguing in a circle, and the larger the circle, the more
difficult is it of detection. We may exhibit this
fallacy by means of symbols. A reasoner will per-
haps prove that A is B, because C is D, and that C
is D, because E is F, and so on, — finally proving the
last premiss, say, that M is N, because A is B. The
most notable instance of this procedure is that of the
Romanists who first prove the Scripture to be the
Word of God, by the infallible testimony of their
church, and then, when evidence is called for of the
infallible authority of their church, proceed to prove
it by the Scripture. * This absurdity is the same, as
if, of two correlative terms, we should make each in
turn the other.

* The absurdity of a circle is not confined to argument; it may
attach equally to definition; in short, it is committed whenever two
correlates are made alternately to represent each other. It is accord-
ingly justly remarked by Mackintosh (Ethical Philosophy, page 212)
that the moralist who should first explain the criterion of right actions
to be that they are approved and commanded by conscience, and after-
wards define conscience to be the faculty which approves and commands
right actions would be treading a vicious circle. In the following

IN LOGIC. 117

Exercise 1.

Show which of the fallacies given in the preceding
chapter belong respectively to the two classes ex-
plained in this chapter.

Exercise 2.

Explain on what grounds the enthymemes subjoined
involve the fallacy ^ petitionis principii.'

This country is distressed; therefore it is mis-
governed.

Pleasure is not the chief good :
The philosophers therefore who held it to be so
were mistaken.

anecdote given from Campbell, (Eccles. History, p. 384, ed. 1824,) an
explanation and thing explained will be seen thus to reciprocate.

'* Implicit faith has been sometimes ludicrously styled ^ fides carbo-
narid' from the noted story of one who, examinining an ignorant collier
on his religious principles, asked him what it was that he believed. He
answered ' I believe what the church believes.' The other rejoined
' What then does the church believe.' He replied readily, ' The
church believes what I believe. ' The other, desirous, if possible, to
bring him to particulars, once more resumed his inquiry, * Tell me then
I pray you, what it is that you and the church both believe.' The only
answer the collier could give was, * Why, truly, Sir, the church and I
both believe the same thing.'"

118 EXERCISES

Popples have a soporific tendency ; therefore they
induce drowsiness.

A negro is a man; he therefore who murders a
negro murders a man.

The soul has a contrariety to death ; therefore it is
immortal.

6.
I think ; therefore I am,

7.
Nature abhors a vacuum ; therefore water rises in a
pump.

CHAPTER XL.

ON AMBIGUOUS MIDDLE.

By far the most frequent class of fallacies is that
which is constituted by the unavoidable ambiguity

IN LOGIC. 119

attending the use of terms In argument ; no less than
eight of the thirteen kinds enumerated by Aristotle
being referrible to this class. We have already re-
marked that such fallacies may be regarded as of a
mixed character, attention to the sense of the terms
employed being necessary to discover the ambiguity,
but, this once ascertained, the invalidity of the argu-
ment being evident from logical rules. One Instance,
accordingly, of such fallacy was given In the classifi-
cation of vicious syllogisms, chapter xxi, (as also one
in the exercise appended,) but the Importance of the
subject is such as to call for a more extended Illus-
tration. 'Ambiguous middle' has been divided by
logical writers Into various species; the names and
nature of the principal of these will be best understood
by a succession of examples, which we now subjoin
with the necessary comments.
•

Communications conveying a double sense are in-
consistent with moral uprightness :

The Scripture contains communications (viz. pre-
dictions) conveying a double sense :

The Scripture contains communications Inconsistent
with moral uprightness.

The heart (In the animal body) may be too large :
A metropolis Is the heart of a country :

120 EXERCISES

A metropolis may be too large.

Copleston, as quoted by Whateley, Rhetoric, p. 435.

The testimony of this witness is insufficient to
prove the fact alleged — so is the testimony of that
witness — and so of the other:

We believe the fact on the testimony of this, that,
and the other witness :

We believe the fact therefore on insufficient testi-
mony.

We are forbidden to kill :

Using capital punishment is killing :

We are forbidden to use capital punishment.

Observations.

1. We have, in this example, an instance of the
fallacy of ^ Equivocation,' the principal term, 'double,'
being used equivocally. The duplicity remarked on
in the major premiss intends undoubtedly two mu-
tually inconsistent senses; but no other duplicity is
ascribed by Christian expositor, to passages in pro-
phetical Scripture, than that of two senses perfectly '^
accordant with each other.

* We may illustrate this accordancy by that of two concentric circles,
of which, though one is necessarily larger than, and indeed embraces
the other, there is yet a parallelism of relation extending throughout.

IN LOGIC. 121

2. This example may illustrate the fallacious use of
' Analogy' and ^Metaphor.' It is a common expression
that metaphors do not run on all fours ; i.e., the re-
semblance which they indicate seldom obtains in more
than a single point. In the above apparent-argu-
ment, the point of similitude in the two things com-
pared is that of a ^ centre of communication ; no
warrant is found in this analogy for the inference,
that every aiFection of the one will be an affection of
the other.

3. We have here a specimen of what is termed by
Aristotle, the fallacy of * ^Division' and ^Composition.'
The insufficiency predicated in the major premiss of the
testimonies noticed, can only be understood of them,
separately taken; in the conclusion, however, it is
stated as belonging to their collective force.

The secondary sense of a passage may thus be contained in, and (so to
speak) enveloped by the primary and more obvious sense. Whether
a twofold significance of this kind be allowed to Scripture predictions
or not, it must be manifest that it has nothing in common with that
other kind of double sense by which a speaker may palter with his
hearers :

May keep a word of promise to the ear.

But break it to the hope.

* The mention of division leads us to notice a fallacy which fre-
quently results from a non-observation of the laws of division; the
fallacy, sc. of omission. It will be recollected that in an early chapter
(see chap, v) we noticed the difference between logical and physical
division, remarking that in the former only, that which was true of the
7vhole was true also of the parts. Now, it is not uncommon in actual
argument, where a term entering into a conclusion is a complex one,
to apply a predication which might be made of the term as a whole, to

■

122 EXERCISES

4. From this example we may take occasion to
explain the nature of the fallacies which, in the Aris-
totelian list, bear the designation of ' Accidentis/ and
of 'a dicto secundum quid ad dictum simpliciter.'
The cases which these technical descriptions con-
template are, (1,) when that which is true of a thing
absolutely is assumed to be true of it under certain
circumstances; or, (2,) vice versa, when that which
may be predicated of it under certain circumstances, is
predicated of it absolutely ; or, (3,) when that which
is true, and may be predicated of it under some cir-
cumstances, is assumed to be true of it, under other
(perhaps quite different,) circumstances, A little re-
flection will shew, in the above example, that the
violence against human life, which the divine com-
mand prohibits, is private (not public and judicial)
violence ; yet is the inference drawn from one to the
other.

It is sometimes a matter of option to what class we

an incomplete combination of its parts. As if, to recur to example 6,
exercise 1 in the above chapter, any one should claim the praise of

* consummate generalship,' for an individual, on the grounds of his

* valour,' * authority', and ' good fortune' alone. The absence, it is
evident, alike of one or more ingredients necessary to the integrity of
a composition, will preclude all predication respecting it. Such
omission, it is only candid to believe, is in most instances undesigned,
being the effect rather of a partial view of the subject, than of any
mental dishonesty ; it is, however, the flaw in most fallacious trains of
argument. For a fine instance (in parvo) of the recognition and suc-
cessive proof of the several parts of an argument, the theological student
is referred to a discourse by the late R. Hall, (See Works, Vol 1,
pp. 487—524.) on ' Substitution.'

IN LOGIC. 123

will refer any particular fallacy; thus the one last
noticed might, without impropriety, be considered as
exemplifying the ^ equivocation^ of the first class. The
classification of ambiguities is only of use as it may
assist in their detection.

EXEKCISE.

Point out the ambiguity latent in the following
(apparent) syllogisms, referring each to its proper
head.

Testimony is a kind of evidence very likely to be
false :

The evidence on which pyramids are believed to
exist in Egypt, is testimony :

The evidence on which pyramids are believed to
exist, in Egypt, is very likely to be false.

A monopoly of the sugar refining business, is
beneficial to sugar refiners ; of the corn trade, to corn
growers; of the silk manufacture, to silk weavers,
&c., &c. :

All these classes of men make up the community :
A system of restrictions is therefore beneficial to
the community.

Children owe subordination to their parents :

■

124 EXERCISES

Colonies are the children of the original countries
to which they belonged :

Colonies owe subordination to their original coun-
tries.

A miracle is an impossibility :

No one can possess power to perform impossibilities :

No one can possess power to perform a miracle.

No man ought to withhold his property from
another :

A sword may be the property of a madman :
No one ought to withhold his sword from a mad-
man.

What is possible of one miracle of Scripture is
possible of others :

The miracle now in question may have been the
effect of legerdemain :

All the miracles of Scripture may have been the
effect of legerdemain.

7.
We are forbidden to commit murder :
Suicide is (self) murder :
We are forbidden to commit suicide.

8.
He who has received a full ransom for any one has
no further claim on him :

IN LOGIC. 125

The Almighty (through Jesus) has received a full
ransom for the elect :

The Almighty has no further claim on the elect.

CHAPTER XLI.

ON KINDS OF ARGUMENT.

The preceding chapters have been devoted chiefly to
the exhibition of different forms of argument, irre-
spectively of the relation which, in any case, the
subject-matter of the premises may bear to that of the
conclusion. A brief notice of this latter topic must
not be omitted. A very important distinction of
arguments, considered apart from their form, is into
those which simply exiince the truth or probability of
a conclusion, and those which also explain it. While
the latter class may be said to furnish us with a
reason for the conclusion itself the former affords one
solely for our belief of it. Into one or other of these
classes the examples of arguments given in previous
chapters may be readily distributed. Thus, to recur
to the instances of enthymemes (chap xvii), when we
infer the absence of responsibility in infants from their
want of moral power^ it is felt at once that we have

M 2

126 EXERCISES

not only proved the fact in question, but accounted
for it : when, on the contrary, we argue the divine
displeasure against the Israelites from their overthrow
in the wilderness, no information, it is evident, is
given us as to the reason of the displeasure, but simply
the /«c^ ascertained. Such an argument may be con-
veniently designated by the term ' Sign ;' the former
would be spoken of as an argument from ^ Cause,'*
[where however by ^ cause' we are not to understand
solely or chiefly physical cause, but often what in moral
reasoning is commonly denominated principle^ Thus
understood, the one class of arguments will be, in its
nature, from cause to consequence ; the other from
consequence to cause.'f A little reflection will easily
show that the one class is more applicable in matters
of opinion, the other in matters of fact.

* Whateley (Rhetoric p, 48) would denominate the former class of
arguments * a priori,' but without sufficient authority, as it appears to
us, either from etymology ox philosophical usage. The literal meaning
of the phrase 'a priori' is undoubtedly, as explained by himself farther on,
(seepage 53,) /rom an antecedent ; it is therefore properly applicable
to argument Jrom antecedent probability t which, whether it has neces-
sarily any explanatory or illustrative force, a glance at the third of the
subjoined examples may show. In the ordinary use of writers, * a
priori' evidence is opposed to that of observation and experiment ; and
this, we think, is the correct view to take of it. P'or some acute remarks
on its distinctive nature and value, see Wardlaw's Christian Ethics, Note
N, p. 428, ed. iii.

t According to Whateley, from consequent to condition^ it not
being necessary that the antecedent proved should be strictly a cause ;
but as a condition of a phenomenon may be regarded as, so to speak,
a negative cause of it, we have preferred retaining the more symmetri-
cal term.

IN LOGIC. 127

Exercise 1.

Of the following enthymematic sentences state in
which the proof from ' cause,' and in which the other
proof is employed.

1. Sensuality is destructive to health: therefore it
is to be shunned.

2. The clothes of this person are bloody; he is
therefore probably the murderer.

3. The influences of light, heat, &c. decrease as
the square of the distance increases; therefore
probably that of electricity does.

4. ' Lac habet ; ergo parturivit.'

5. The volumes of Nature and Providence have
each their inexplicable mysteries ; therefore (not
incredibly,) that of Revelation has.

6. It thundered just now; it must therefore have
lightened.

Exercise 2.

In the following combinations* of argument to prove
the same conclusion, explain which of the arguments
are referable to the class ^ Cause,' and which to the
opposite class.

* When more than one argument of either of these sorts is used in
reasoning, together with other arguments, it is important that the
two classes of proofs should be ranged by themselves, and not
mixed up promiscuously. In the essay of Channing, from which our

128 EXERCISES

Position. That a man cannot lawfully be held as
property.

1. We have a plain recognition of this principle in
the universal indignation excited towards a man
who has made another his property.

2. A man cannot be seized and held as property
because he is a rational, moral, immortal being.

Channing,

Position. That a luxurious nation is likely to
lose its liberties.

1. A luxurious nation cannot resist temptations to
barter away its liberties.

2. A luxurious nation wants the hardihood to
defend its liberties.

3. The Romans, soon after their becoming luxuri-
ous, lost their liberties.

Position. It is absurd to choose a general by lot*

first example is taken, the argument from 'sign' against slavery
is very illogically alike preceded and followed by one from 'cause.'
^ This is the chief defect, it strikes the writer, in a work otherwise not
undeservedly praised, " Fuller's Calvmism and Socinianism compared."
While in some of the chapters both kinds of proof are employed to
establish the position laid down, in others one kind only, and that from
* sign' or * consequent' is resorted to. This virtually amounts to a con-
fession that evidence of the other kind is not to be had, and where it is
not less accessible than in other branches of the subject is peculiarly
unfortunate.

IN LOGIC. 129

1. No one chooses a pilot, or a musician, or an
architect, or a physician by lot.

2. It is absurd to choose by lot an officer in whom
skill is needed.

4.
Position. Affliction is morally beneficial.

1. The Scriptures frequently assert the moral
benefit of affliction.

2. Affliction disposes to serious reflection, checks
pride, &c.

5.
Position. Sin is offensive to the divine nature.

1. Sin is a ^transgression of the divine law.'

2. The destruction of the world by water was the
expression of the divine displeasure against sin.

3. The death of Christ was occasioned by the
necessity of expiating sin.

6.
Position. The baptism of John was a different
institute from Christian baptism.

1. Christian baptism involved an explicit profession
of faith in Jesus as the Messiah : that of John
did not.

2. Various disciples (some at Ephesus particularly,
see Acts xix, 1 — 5) who had received John's
baptism were afterwards rebaptized.

130 EXERCISES

CHAPTER XLII.

ON KINDS OF ARGUMENTS. (Continued.)

Another division of arguments important to be
noticed is into Deductive and Inductive; into argu-
ments, i. e. in which the reasoning is from generals to
particulars, and in which from particulars to generals,
A third sort nearly allied to the latter, viz., from
particulars to particulars is commonly denominated
^ Example.'

We may conveniently illustrate the respective
peculiarities of these three arguments, by a recurrence
to the third of the examples given in the preceding
exercise. According as we vary in the following
methods the premises and conclusion of that No.
we shall have a specimen of ' Deductive' reasoning,
of ^ Inductive,' and of reasoning from ^ Example.'

I. Deductive.
It is absurd to choose by lot an officer in whom
skill is needed :

It is therefore absurd to choose a general by lot.

IL Inductive.

It is absurd to choose by lot a musician, architect,
pilot, or physician :

It is therefore absurd to choose by lot an officer in
whom skill is needed.

IN LOGIC. 131

III. Example.
It is absurd to choose a pilot by lot :
It is therefore absurd to choose a general by lot.

When we compare* the last of these arguments
with the two preceding ones, it may seem to be a
compounded f expression of their joint force, and
there can be no doubt that its conclusiveness does
depend on the sub-intellection of the general principle
found in the other arguments. The first of Aristo-
tle's instances is the following :

Pisistratus, when he requested a body guard, con^*
templated a tyranny :

Dionysius therefore, in requesting a body guard,
contemplates a tyranny.

* In the relation of the two former enthymemes to each other, (as it
would be obviously competent in the conclusion of the first to substi-
tute ' musician,' or ' pilot,' for * general,') some have discovered a falla-
cious circle ; but we must consider the propriety and validity of the
two arguments relatively to diiFerent classes of minds. The difficulty,
it is clear, with some might be to apprehend or admit the general prin-
ciple ; with others, the referribility to the principle of the particular
case. The inductive enthymeme would then be the argument applica-
ble to the one state of mind ; the deductive to the other.

f This composition is represented in an ingenious mode by Whate-
ley. (Rhetoric, page 75.) e. g.
It is absurd to choose a pilot by lot | It is absurd to choose a general by lot

It it absurd to choose by lot an officer in whom skill is required.
An argument like the above may be styled doubly -enthymematic.

132 EXERCISES

Here every one must see at a glance that the illa-
tion would be nugatory, unless the general principle
were inferrible, that whoever requested a body guard
contemplated tyranny.

There is then a general premiss to be understood
in every ^Example' argument, and there is no less
one in every ^Inductive;' the two arguments agree
with one another, (and with the argument from Testi-
mony,*) in this, that the suppressed premiss may be
represented in a form applicable to every particular
instance. In an instance of the former argument,
e. g., the general premiss to be assumed will be much
of the following nature :

Whatf is predicable of one individual (of a class)
is predicable of another :

In the latter, somewhat as follows :

What is predicable of this, that, and the other indi-
vidual of a class is predicable of the whole class :

The reasoning in the first case being from one
individual to another individual, in the second from
several individuals to a class. Of course, the nature
of the predication will be determined in each case by
the scope of the argument ; in most instances ^ predi-
cable,' will be equivalent to ^true;' in others, the
epithets ^good,' ^fit,' ^just,' &c. will be convenient {
synonyms for it.

* For a further account of the nature of this argument see following
chapter.

f For some acute remarks on this topic, see " Eclectic Review,"
September 1844, page 273.

\ The argument from ' example' will generally be most satisfactory
when simple possibility or credibility is the idea predicated, i. e. when it

IN LOGIC. 133

Exercise 1.

Decide which of the following arguments are res-
pectively ^Deductive,' ^Inductive/ orfrom ^Example/
drawing out each in a syllogistic form; of those of
the former class give the mnemonical name, stating
the latter also in a doubly-enthymematic form.

1.
Astronomy was decried at its first introduction as
adverse to religion :

Geology is therefore likely to be so decried.

Philip, Alexander, Julius Caesar, Napoleon, were
all reckless of human life :

All great conquerors will be found reckless of hu-
man life.

Agriculture might have been invented by man
without a superhuman instructor; so might the
working of metals; so might medicine; so might
navigation, &c., &c. :

There is no art therefore which might not have
been invented without a superhuman instructor.

4.
A diamond is carbon :
A diamond is therefore combustible.

is used for contingent conclusions, E xcept in physical inquiries, it is
seldom that a single instance will suffice to establish a general prin-
ciple.

PfWP

134 EXERCISES

5.
The Athenian^ the Spartan, and the Roman con-
stitutions degenerated :

The British constitution will therefore (probably)
degenerate.

No ruler is infalhble :

No ruler therefore should persecute.

Wherefore approached ye so nigh to the city when
ye did fight; knew ye not that they would shoot
from the wall? Who smote Abimelech the son
of Jerubbesheth ; did not a woman cast a piece of
a millstone upon him from the wall? 2 Samuel
xi, 20, 21.

CHAPTER XLIII.

ON KINDS OF ARGUMENTS (CONCLUDED.)

" * The objections which may be brought against
a conclusion are fourfold; they are derived either

* A/ hcTd^iig (ps^ovTa/ rsr^a^Ofg' ri jol^ sE, sccvtov, rj Ix toj
ApiffTOTiXovg VriroDizT}, B. Ks^. ?c<^.

IN LOGIC. 135

from the subject itself, or from a similar subject, or
from an opposite subject, or from decisions upon it."

In the above extract from the Rhetoric of Aris-
totle, we have a fair specimen of the looseness of
classification in which that eminent writer sometimes
allows himself. It is evident from the examples
which he adduces, that the second and third members
of his enumeration are identical, the illustration given
of the second presenting only a similarity of relation^
but imih opposition of subjects, which is precisely and
solely the kind of opposition by which he illustrates
the third. Making this exception, however, we may
find in the account he gives of objections another
division of arguments suggested not unimportant.
The technical name for the intermediate class of
proofs which he notices, is plainly that of ' Analogy ' ;
the term ^Authority' expresses the last.

^Authority,' in matters of opinion, may be con-
sidered as coincident with ' Testimony' in matters of
fact. We have an instance of it in No. 5 of the
examples given in chap. xH. As intimated in the
preceding chapter, there is in every such argument
an understood premiss to be supplied. Its general
form will be

Whatever is asserted by is true

where the blank must, of course, be filled up variously
according to the* author cited. ^Analogy' may be

* If the authority be human only, this argument will answer pretty
nearly to what has been termed * argumentum ad verecundiam.* Simi-
lar designations of other kinds of reasoning are * argumentum ad homi-

136 EXERCISES

regarded as a branch of the ^a priori' argument. It
is otherwise known by the designations ^Parity of
reasoning,' reasoning from ^Parallel cases/ &c. We
may regard the ^ example' argument in the preceding
chapter from the case of a ^ pilot' to that of a ^ general,'
as Analogical reasoning.

It scarcely requires to be remarked, that arguments
from ^ Analogy' and ^ Authority' may be sophistical as
well as other arguments. The former kind of fallacy
is what is intended when we object that the case is
not parallel^ the objection being to the soundness of
the minor premiss. We may cite the alleged paral-
lellism between ^colonies' and ^children,' as an illustra-
tion of such fallacy. The obligation of children to
obey their parents rests, it is obvious, on the ground,
mainly, of the dependence of the former on the latter ;
this dependence may or may not obtain in the case of
colonies.

In regard to objections, we may advert further to
an expression which we often hear applied to an
argument, viz., that it proves too much. This objec-
tion will be commonly found, in distinction from the
preceding, to lie against the major premiss. Thus, if
it should be attempted, (as has frequently been done,)
to account for the greatness of the gospel salvation
(see Hebrews ii, 3) by alleging the greatness of its

nem or ex concessis,^ * argumentum ad ignorantiam,' &c. Of the first
of these, which sufficiently explains itself to be * an argument addressed
to the professed principles of an opponent, various instances have been
inserted incidentally in preceding chapters. See, e.g., chap, xxv,
example 3.

IN LOGIC. 137

author, this consideration would clearly prove the
meanest insect to be a great production, its author-
ship being equally divine.

Exercise 1.

Explain which of the subjoined examples are
^Analogical' arguments, and which arguments from
'Authority.'

Lord Bacon contends against stocking a colony
with the refuse of jails :

Such colonisation is therefore doubtless improper.

For crimes committed in intoxication Pittacus
imposed severer penalties :

Such crimes should therefore be punished more
severely.

The dependence of a husbandman on the influ-
ences of heaven does not supersede his own
efforts :

The dependence of a Christian therefore on divine
influences does not supersede his own efforts.

N 2

138 EXERCISES

5.
The insensibility of a chrysalis is only temporary :
The insensibility therefore of a human body (at
death) may be only temporary.

Those who have received benefits do not always
love:

Those who have received injuries do not therefore
always hate.

David describeth the blessedness of the man to
whom God imputeth righteousness without works,
saying, ^ Blessed is the man, &c. :' Kom. iv, 67.

Exercise 2.
Of the following fallacies, state in which the cases
are not parallel and in which the argument proves too
much,

1.
Human bodies as they grow old decay :
Political bodies therefore as they grow old will
decay.

The reading of the Scriptures is liable to abuse :
The reading of the Scriptures should therefore be
discouraojed.

IN LOGIC. 139

In every (first figure) Syllogism there is an as-
sumption of the conclusion :

A (first figure) Syllogism is therefore useless for
proving a conclusion.

Stones cannot hew themselves :
Christians therefore (who are spiritual stones, see
1 Peter ii, 5.) cannot renew themselves.

APPENDIX.

LOGICAL PUZZLES.

We have purposely abstained from introducing into
the exercises given in past chapters any arguments
which would be seen at first inspection to be futile or
fallacious. It has been the employment of logical
formulae for the (apparent) proof of manifest absurdities,
which has been very much the cause of bringing the
science into that disrepute in which it is at present
held by many. Not a few of the examples given
even by good writers in their discussion of fallacies
fall under the merited censure thus conveyed. The
following is a common instance, e.g. usually adduced
under the head of ' Fallacies of composition and divi-
sion,'^

Three and two are even and odd :

Three and two are five :

Five is therefore even and odd.

Our own chapters on 'Fallacies' have been the
shorter, from our unwillingness to occupy space in unra-
velling equivocations thus gross. There can, however,
be no objection, when this part of logic has been
treated in a serious manner, to put together a few of
the more amusing sophisms of the kind, as an exer-

APPENDIX. 141

cise for the student's acumen. A brief collection of
such we, accordingly, here subjoin. In going through
them we need scarcely say, that the student's business
will be not to decide on the fact of their absurdity,
but to analyse its nature,

EXEKCISE.

Explain what are the logical rules violated by the
following Sophisms.

Methodists are Christians :
Quakers are Christians :
Quakers are Methodists.

Hector slew Patroclus :
Achilles slew Hector :
Achilles slew Patroclus.

Meat and drink are necessaries of life :

The revenues of Vitellius were spent on meat

and drink :

The revenues of Vitellius were spent on the

necessaries of life.

He who calls you a man speaks truly :
He who calls you a fool calls you a man :
He who calls you a fool speaks truly.

142 APPENDIX.

•>.

Opium is a poison :

Physicians advise some of their patients to take
opium :

Physicians advise some of their patients to take
poison.

The musical instruments in the Jewish temple
made a noble concert :

The harp was a musical instrument in the
Jewish temple :

The harp made a noble concert.

What I am you are not :

I am a man :

You are not a man.

Notliing is heavier than Platina :
Feathers are heavier than nothing :
Feathers are heavier than Platina.

Those who work hard deserve reward :
Those who work on the treadmill work hard :
Those who work on the treadmill deserve reward.

10.
Whatever body is in motion must move either
in the place where it is, or in the place where
it is not :

APPENDIX. 143

Neither of these is possible :

No such thing as motion is possible.

11.

He who is most hungry eats most :
He who eats least is most hungry :
He who eats least eats most.

12.

Animal food may be entirely dispensed with, (as
is shown by the practice of the Brahmins,)
and vegetable food may be, (as is plain from
the example of the Esquimaux:)

All food consists of animal and vegetable food :

All food may be dispensed with.

13.

The child of Themistocles governed his mother:

The mother governed Themistocles :

Themistocles governed Athens :

Athens governed Greece :

Greece governed the world :

The child of Themistocles governed the world.

14.
* If the hour hand of a clock be any distance, (sup-

* Not quite consistently, we think, with his repeated statement that
all arguments are but varieties of the syllogism, Archbishop Whateley
denies the possibility of exhibiting the above apparent-argument in a
syllogistic form. To us it appears plainly a condensed syllogism in

144 APPENDIX.

pose a foot) before the minute hand, this last,
though moving twelve times faster, can never
overtake the other ; for while the minute hand is
moving over those twelve inches, the hour hand
will have moved over one inch : so that they will
then be an inch apart; and while the minute
hand is moving over that one inch, the hour hand
will have moved over -^^ inch, so that it will be
still ahead ; and again, while the minute hand is
passing over that space of -^-^ inch, the hour
hand will pass over y^^ inch ; so that it will be
still ahead : and this, it is plain, may go on for
ever:
The minute hand can therefore never overtake
the hour hand.

* Barbara,' the major and minor premiss of which will run in somewhat,
the following manner :

" Of any two moving bodies, having different velocities, if the slower
body shall be any distance in advance of the more rapid one, it will be
impossible for the latter to overtake the former : for &c. &c.

The hour and minute hand of a clock are two such bodies :

Therefore, &c."

J. S. Mill (System of Logic, Vol. ii,) refers the fallacy to the class
of those which are occasioned by ambiguous language, conceiving the
difficulty to lie in the words 'for ever.' He accordingly dilates on the
difference between ' any length of time' and * any number of subdivisions
of time' between what is ' infinite' and what is * infinitely divisible'
fortifying his solution with the authority of Hobbes. But this refine-
ment seems to us beside the mark. In the reasoning of the example
there is a plain * petitio principii,' viz. that the unit of movement of the
quicker body may become an infinitesimal quantity, whereas it is
clearly di fixed one. The fallacy is therefore of the 'extra dictionem'
or material kind.

APPENDIX. 145

15.

The divine law bids us obey secular magistrates :

Bishops are not secular magistrates :

The divine law does not bid us obey bishops.

16.

jSTo man can serve God and Mammon :
The spendthrift does not serve Mammon :
He therefore serves God.

17.

All the miracles of Jesus would fill more books
than the world could contain :

The things related by the evangelists are the
miracles of Jesus :

The things related by the evangelists would fill
more books than the world could contain.

18.

We ought to believe Scripture :

Tradition is not Scripture :

We ought not to believe tradition.

19.
If Judas was not rightly made an apostle, he
deserved rejection :

He was rightly made an apostle :
He did not deserve rejection.

146 APPENDIX.

20.

If Abraham was justified, it must have been either
by faith or by works :

He was not justified by faith (according to James,)
nor by works (according to Paul:)

Abraham therefore was not justified.

^INDICES.

TOPICS.

PAGE. PAGE ,

* A priori* argument 126 Elenchus, what 114

Argumentum ad hominem ... 136 Enthymemes 42

ad verecundiam 1 35 double 131

Categories, the 1 Indefinable terms 14,15

Circle, logical 116 Indefinite terms 3

Conditional syllogisms 78 Induction 65, 130

Converse of propositions ... 28

Contradiction of do 26, 30 Reduction of syllogisms ... 72

Co-ordination 7 Reductio ad absurdum 80

Correlatives 3

Singular propositions 60

II.
AUTHORS.

Aristotle 1,3,109,134 Lambe, Charles 28

Lambert, Neues Organon of 54

Bacon, Lord 30, 43 Lardner, Dr. D 4

Brougham, Lord 61 Locke, John 15

Burke, Edmund 11

Mackintosh, Sir J 116

Campbell, Dr, George 117 Mill, J. S 31, 145

Channing, Dr 128

Chillingworth, W Ill Paley, Archdeacon, 40,70

Cicero 65,67 Pascal, Blaise 32

De Morgan, Professor 193 Sanderson, Bishop 109

Shakspere, W 34,121

TertuUian 36

Fuller, Andrew 128

Gibbon, E 32

Wardlaw, Dr 126

Hall, R. 71,122 Whateley, Archbishop, 17, 26,

Johnson, Dr. S 53

78, 80,82, 114, 126,145

* The references of these indices, it should be stated, extend no farther than
to the notes ; it is presumed that the table of contents at the commencement
will be found a sufficient guide to the main points in the text.

148 INDICES.

Ill

TEXTS.

PAGE. PAGE.

Psalm cxvi, 11 96 John ix, 41 84

Proverbs xi, 31 106 Romans vi, 16 35

xiv, 24 35 viii, 38, 39 13

xxii, 6 96

1 Corinthians i, 30 7

Isaiah X, 15 23 viii, 2 10

Iv, 10 38

Hebrews vii, 10 70

Mark ix, 40 30 xi, 37 ,.. 7

xii,21,25 10

John viii, 13 43

—47 75 1 John iv, 6 75

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