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AUTHOR:

CLARKE, RICHARD
FREDERICK

TITLE:

LOGIC

PLACE:

NEW YORK

DATE:

1889

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Clarke, Richard Frederick. ###f#-^^:^>^

... . Logic, by Richard F. Clarke, S. J. Now iin|»F-etTtyie*i.
London, New York, [etc.], Longmans, Green, and Co.. ig^-lBSdm

xix, 497 p. diagrs. igi**". (,-/f/</<r</ /.-/.; Slonyhurst philosophical scries.)
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This book is due on the date indicated below or at th.
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MSO

MANUALS OF CATHOLIC PHILOSOPHY,

(STONYHURST SERIES.)

MANUALS OF CATHOLIC PHILOSOPHY;

*'^^r'

LOGIC.

KOEHAMPTON I
I'RINTBD BY JAMES STANLKY.

♦ «\l

ICHARD F. CLARKE, S.J

LONDON :

LONGMANS, GREEN & CO

1889.

PREFACE.

When Scholastic Philosophy ceased to be the
subject of systematic study in Protestant Univer-
sities, and was regarded as possessing an historical
rather than a scientific interest, there was one
branch of it that was treated with less dishonour
than the re',t. In Ethics and Metaphysics, in
Psychology and Natural Theology, the principles
handed down by a tradition unbroken for cen-
turies came to be looked upon as antique curio-
sities, or as merely illustrating the development
of human progress and human thought. These
sciences were either set aside as things of the
past, consisting of fine-spun subtleties of no
practical value, or else they were reconstructed
on an entirely new basis. But with Logic it was
different. Its underlying principles and its received
method were not so closely and obviously interlaced
with the discarded system of theology. It admitted

95869

Vlll

PREFACE.

of being more easily brought into apparent harmony
with the doctrines of the Reformation, because it
had not the same direct bearing on Catholic
dogma. It was, moreover, far less formidable to
the ordinary student. Those who had no stomach
for the Science of Being, were nevertheless quite
able to acquire a certain moderate acquaintance
with the Science and the Laws of Thought. Men
chopped Logic harmlessly, and the Logic they
chopped was the traditional Logic of the School-
men, with some slight modifications. The text-book
of Dean Aldrich, which has not yet disappeared
from Oxford, is mediaeval in its phraseology and
its method ; mediaeval, too, in its principles, except
where an occasional inconsistency has crept in
unawares from the new learning. It still talks of
** second intentions," and assumes the existence
of an Infima Species, and has throughout the
wholesome flavour of the moderate realism of
sound philosophy.

But this state of things could not last. Sir
W. Hamilton, the champion of conceptualism,
put forth in his Lectures on Logic a theory of
intellectual apprehension quite inconsistent with
the traditional doctrine which still lingered in the
meagre and obscure phraseology of Dean Aldrich.
Sir W. Hamilton's disciple. Dean Mansel, who

PREFACE.

carried on the work of philosophic scepticism which
his master had inaugurated, published an edition
of Aldrich, with explanatory notes and appendices,
which pointed out his supposed errors, while John
Stuart Mill, with far more ability and a wider
grasp than either of the two just named, substi-
tuted for the halting conceptualism of Hamilton
a nominalism which had but a thin veil of plausible
fallacies to hide from mankind the utter scepticism
which lay beneath it.

Since then, the Kantian principle of antinomies
which underlies the Logic of Mansel and Hamilton
has boldly come to the front in England under
the shadow of the great name of Hegel, and
English logicians have either ranged themselves
under the banner of one or other of these new
schools, or else have sought to cover the glaring
inconsistencies of some one of them with patches
borrowed from the others, until the modern student
has a bewildering choice among a series of guides,
each of whom follows a path of his own, leading
in the end to obscurity and confusion and self-
contradiction, but who are all united in this,
that they discard and misrepresent the traditional
teaching of Aristotle and of the mediaeval logicians.
Their facility in so doing is partly owing to the
fact that Aristotle has no methodical treatise cover-

PREFACE.

ing the ground of modern Logic, and St. Thomas
gives merely a rapid sketch of the technical part
of it in one of his Opuscula. But from the pages
of the great philosopher of Pagan times and of
the Angelic Doctor of the middle ages, can be
gathered by the careful student all the principles
necessary for the modern logician. Every Catholic
teacher of Logic follows of necessity closely in their
steps, and finds in them the solution of every diffi-
culty, and the treatment— at least the incidental
treatment — of almost every question that Logic
can propose.

The modern school of Logic departs from the
ancient from the very first, as the reader will see
as he studies the following pages. The very foun-
dations are different. The Principle of Contradic-
tion is in the Hamiltonian system subordinated to
that of Identity, while Stuart Mill goes still further
astray, and the Hegelians set it altogether aside.
The account given by these various schools of the
process of intellectual apprehension by which the
idea or general notion is arrived at, is one which
leads to an utter scepticism. The Doctrine of the
relativity of human knowledge is no less at variance
with all positive truth, while the modern theory of
Universals attempts to establish itself on the ruins
of the Scholastic Realism by a gross misrepre-

PREFACE.

sentation of what Scholastic Realism really

means.

It is the object of the present Manual of Logic
to lead back the English student into the safe
paths of the ancient wisdom, to point out where
it is that the speculations of modern philosophizers
have quitted the well-trodden high road of truth,
and to at least indicate the precipices of incon-
sistency and self-contradiction to which they
conduct the unhappy learner who allows himself
to be guided by them. It is, however, impossible,
in a compendious text-book like this, to discuss
at length the various ramifications of the errors
through which the different schools of to-day have
gone utterly astray. It has therefore been the aim
of the writer to select for attack, as far as possible,
the central and distinctive error of each, or the
one most likely to throw dust in the eyes of the
incautious reader from the very beginning.

This, however, is not the primary object aimed
at. The need of a Catholic text-book of Logic in
English, corresponding to those which are in general
use in Protestant schools and Universities, has been
long felt on both sides of the Atlantic. To the
more advanced students of our CathoHc Colleges
a thorough grounding in Logic is a most important
element in their intellectual cultivation. Yet there

Xll

PREFACE.

xiu

> I

has been hitherto no text-book which could be put
into their hands for the purposes of private study.
The Latin treatises which form the basis of the
lectures attended by the young ecclesiastic are
quite unsuited for them, apart from the mere
difficulties of the language. Their strange phrase-
ology, the technicalities of their style, the cut and
dried method they pursue in their advance from
principles to conclusions, their complete severance
from modern habits of thought and speech, render
them unintelligible to ordinary students without
an elaborate explanation on the part of the teacher.
He has to cover the dry bones with flesh, to
enlarge, illustrate, translate, and simplify, and often
entirely reconstruct, before he can reach the
average intelligence or rouse any interest in his
pupils.

The English text-books hitherto issued have
been little more than a literal translation from the
Latin, and though they have done a good work in
furnishing students unversed in Latin with text-
books in their own language, yet they have not
attempted the further task of translating scholastic
into nineteenth-century phraseology. It is hoped
that the present Manual may put before our Catholic
youth this most important branch of study in a
more simple and attractive form. The scholastic

terms have not been discarded, but they have
been carefully explained and rendered into words
which will convey to the man of average edu-
cation their real meaning. While the scholastic
system has been closely adhered to throughout,
the dress in which it is clothed is modern, and no
previous knowledge is necessary for the young
Catholic in whose hands it is placed.

There is another class to whom it is hoped that
the present text-book may prove useful. Many a
Protestant student, perplexed and bewildered by
the rival claims of half a dozen different systems,
each at variance with the rest, and often also at
variance with itself as well, is inclined to give up
the search for truth in despair and to fall back
on the Hamiltonian doctrine of the Relativity of
Knowledge, or in other words, on the non-existence
of truth at all. Such a one often craves in his
heart after some leader on whom he can rely, some
one who represents, not the newly-fangled inven-
tions of the individual, but the traditional authority
of centuries. He would fain know whether amid
Catholic philosophers there is the same discord
and the same contradiction as among Protestants,
and would eagerly drink in the teaching of one
who speaks, not in his own name or that of some
modern theorizer, but in the name of the men of

XIV

PREFACE.

genius, who gave themselves to the study of Logic
from the days of Aristotle till the unhappy period
when the old learning was discarded with con-
tempt by the ignorance of the Reformers. To
any such inquirer this text-book offers the ordinary
Catholic teaching grounded on Aristotle and set
forth by St. Thomas of Aquin, which flourishes as
vigorously as ever in every centre of higher
Catholic education. If there is any departure
from the doctrines of St. Thomas in these pages,
it is there without the knowledge of their writer,
whose object it has been to follow throughout in
the footsteps of the Angelic Doctor.

There is another class to whom such a text-book
as this will be a real boon, to whose existence the
writer can testify from personal experience. Con-
verts to the Catholic Church, trained in the English
Colleges and Universities, have unconsciously drunk
in a number of principles, some true, some false,
from their earliest years, and are often not a little
puzzled to discern the true from the false. Perhaps
in their early days Hamilton and Jevons, Mansel
or Veitch, had represented to them the orthodox
school, and Mill and Spencer and Hegel a more
consistent and at the same time more sceptical
system. On submission to the Church, they would
fain know how far these rival claimants possess any

fragments, large or small, of solid truth, and where
they each and all wander away into error. In the
following pages this need has been kept in view,
and the Author has sought to write what would
have been useful to himself twenty years ago, when
he made unsuccessful endeavours to master by
private study the principles of Catholic philosophy
from inscrutable Latin text-books.

Last of all we must remember that in these
days the old ideas respecting the limits of feminine
education have been not a little modified. This
is not the place to discuss the advantages and
disadvantages of a more enlarged intellectual train-
ing for women. It is enough to say that the
change which is being introduced is in many
respects only a re-assertion of what was common
enough in Catholic times. It is an undoubted gain
to the cause of Truth that women of cultivated
tastes should be trained to think correctly, and
should have such a knowledge of the principles of
Logic as may help them thereto. In Convent
schools and other Catholic institutions the higher
education is steadily making way, especially in the
United States, and the study of Logic is an im-
portant element in it. The present volume is
one which, even if it is not put into the hands
of the younger students, is well suited for the

I,
^1

dfr ^ -.Tlii^ -^ujuj

XVI

PREFACE.

Teacher's use in the instruction of her Catholic
pupils, as well as for those whose general training
may give them an interest in the subject and a
desire to investigate it for themselves.

One word to those who may desire to know
the best order in which to study the various parts
of CathoHc Philosophy. Ahhough this Text-book
of Logic has not been the first to appear in
order of time, it is the one which naturally
comes first in order of thought, and the Student
is recommended to pass from it to the Text-book
of First Principles, and so on to Ethics, Natural
Theology, Psychology, and the difficult though
important subject of General Metaphysics.

CONTENTS.

INTRODUCTION.

Chapter I.— The Province of Logic

II. The Definition of Logic

III. — The Foundations of Logic .
I. The Principle of Contradiction

II. The Principle of Identity

IV.— The Foundations of Logic (continued)
v.— The Foundations of Logic {continued)

III. The Principle of Causation .

IV. The Principle of Excluded Middle .

VI.— The Three Operations of Thought

PAGE

15
29

33
42

71
72
79
92

PART I.-OF SIMPLE APPREHENSION OR

CONCEPTION.

Simple Apprehension .

VII. Simple Apprehension {continued).

Errors respecting it
VIII.— The Doctrine of Universals
IX.— The Heads of Predicables .
X.— Definition
XI. — Division . • • •

Modern

121

140

163

193
225

CONTENTS.

PART II.— OF JUDGMENT OR ASSENT.

PAGE

Chapter I. — ^Judgment. ..... 245

Divisions of Judgment . . . .250

II —Propositions, their Nature and Divisions 261
Divisions of Propositions . . . 266

•I in. — Import of Propositions. Various kinds of

Propositions ..... 280

»i IV. — The Opposition and Conversion of Pro-
positions . . . . .293

PART III.— OF REASONING OR ARGUMENT.

Chapter I.
II.

-Reasoning

-The Syllogism and its Laws
Canons of the Syllogism .
Dictum de omni et nullo
General Rules of the Syllogism .

III—The Figures of the Syllogism
Rules of the First Figure
Rules of the Second Figure
Rules of the Third Figure
Rules of the Fourth Figure
Reduction

IV.— Various kinds of Syllogisms
Other Variations of the Syllogism

v.— Formal Induction

VI.— Material Induction . ,

Method of Agreement . ,

Method of Difference
Method of Concomitant Variations
Method of Residues

Reduction

305

313

315
316
316

324
332
333
334
335
339

348
356

364

376

389
390
393
395

VyV/l' •» x-x^ A w.

page

Chaptei

^ VII.— Example and Analogy

. 402

Example . . • • •
Analogy . . . . ■

. 402

. 407

VIII The Matter of the Syllogism .

. 412

I. Demonstrative Syllogisms
II. Probable Syllogisms .

. 419
. 424

IX. — Fallacies

. 432

I. Fallacies of Language
II. Fallacies outside Language .

. 434
. 445

X.— Method and its Laws
APPENDIX.

. 461

The Scholastic Method

475

LOGIC.

Part I.

CHAPTER I.

THE PROVINCE OF LOGIC.

Importance of Logic— Aim of Logic— Meaning of the word— Logic
and Grammar— Logic in its relation to Thought— Different
meanings of Thought— Logic and Psychology— Logic and Meta-
physics—Formal and Material Logic, and their respective
provinces— Formal Logic necessary to Material— Meaning of
Formal Logic— The Laws of Thought— Logic in its relation to
the Laws of Thought.

The importance of the study of Logic is derived
from its undeniable claim to an universal dominion
over the minds of men. No one can ever think
correctly unless he thinks logically. No one can
judge aright unless his judgment is one which Logic
can approve. No one can arrive at well-grounded
conclusions unless he argues in conformity with the
laws of Logic. He who professes a system of
Philosophy, or Theology, or Science which is in
any respect opposed to logical principles, thereby
declares his system to be false and irrational, and
himself an intellectual impostor. Logic must of
necessity control with its unerring laws every pro-
cess of thought, every act of judgment, every chain

THE PROVINCE OF LOGIC.

MEANING OF THE WORD.

of argument ; else the process of thought is faulty,
the act of judgment unwarrantable, the chain of
argument incorrect.

The ultimate end aimed at in the study of Logic
is to train the human mind to exactness of thought.
It is not to make a man ready in argument, nor to
add to the stock of human knowledge, but to teach
us to think correctly. As in a liberal education the
end aimed at is not to impart to the student a
vast number of accumulated facts, but to stimulate
the desire for acquiring information for himself, to
furnish him with the means of doing so, and to
enable him to make a good use of the information
when acquired, so the ultimate object of the study
of Logic is not so much to supply us with a detailed
analysis of our processes of thought, as to ensure
their correct performance. This is the end it has in
view in laying down the Laws of Thought which
are its foundation, and in analyzing the various
operations which fall within its province. This it
aims at still more directly in pointing out the mani-
fold dangers to which thinking is exposed, and the
fallacies by which the thinker is most liable to be
deceived. It seeks to arm the logical student
cap-a-pie, so that he may be able to detect at a
glance the incorrect judgment or unwarranted
assumption. It gives him the clue to the carefully
concealed fallacy, and enables him to expose its
weakness, to show where the inference is faulty, or
where the terms are used in an ambiguous sense, or
where statements are put forward as identical when
they are really different from each other.

But what is Logic ? Before we consider this
question, we will look at the origin of the word, as
an useful guide to its true meaning.

Logic is derived from the Greek Logos, which
has the double meaning of word and thought. It is
used in classic authors indiscriminately for the
internal word present in the mind, and the external
word uttered by the lips. It has, therefore, no exact
equivalent in English, although in theological lan-
guage word is sometimes used for that which is
hidden in the intellect without finding externa.1
•expression. I But such usage is exceptional, and in
ordinary English word implies some form of spoken
language.

The double use of the Greek word Logos corre-
sponds to the double nature of the subject-matter of
Logic. As Logos is primarily the internal thought,
and secondarily the external expression of the
thought, so Logic is primarily concerned with
thought, secondarily with language, as expressing
thought. The connection between correct thought
and correct language is so intimate, that any branch
of knowledge which treats of the one must to some
extent include the other. Logic, therefore, as being
concerned wdth thought, is necessarily concerned
also with language. Here we see its relation to
Grammar. Both Logic and Grammar have to do

^ Thus The Word is used to express the Second Person of the
Blessed Trinity, the Eternal Wisdom of God, hidden in the Intellect
of the Eternal Father before all ages ("The Word was made
Flesh "), and also the interior voice speaking with Divine authority
to the mind of the prophets ("The word of the Lord came to
Jonas," &c.).

THE PROVINCE OF LOGIC.

with thought and language, but Logic has to do
with thought primarily and essentially, and with
language secondarily, and only so far as it affects
thought, whereas Grammar, on the other hand,
treats of language primarily and essentially, and of
thought only secondarily, and so far as is necessary
for the due treatment of language.

Logic then is a branch of knowledge concerned
with Thought. But this is not sufficient for our
Definition. What do we mean by Thought ? Has
Logic to do with all our thoughts ? Does it include
an investigation into the origin of Thought, the
subject-matter of Thought, the various mental pro-
cesses which are connected with Thought ? Does it
treat of Thought in general, or is it limited to some
special province or department of Thought ?

In order to have an accurate knowledge of the
province of Logic, we must first of all have an
accurate knowledge of Thought. Thought is used
in two different senses.

I. It is sometimes used to include every mental
process, every activity of those faculties which
belong to the sphere of intelligent (as distinguished
from intellectual) life. Thus I say that my friend in
Australia is in my thoughts, and by this I mean that
he is present in my memory, and his image dwells
in my imaginative faculty. A child is said to be
thinking of its dinner, when we see it restless and
fidgetty in the school-room as the time of its mid-
day meal approaches, and we mean thereby that a
vague, half-conscious recollection of the expected
food, and a desire to partake of it, is present to its

LOGIC IN ITS RELATION TO THOUGHT.

mind. In this sense animals may be said to think.
The dog thinks of the rat when his master makes a
scratching noise in the corner of the room ; he
thinks of the pain of some recent castigation when
he sees the whip. Thinking, in this meaning of the
word, belongs to the material faculties of memory
and imagination, as well as to the immaterial faculty

of intellect.'

2. Thought is also used in the narrower and
stricter sense of the exercise of our intellectual
faculties properly so called, of that immaterial
faculty which brings within the range of our know-
ledge things above and beyond sense, which recog-
nizes in things sensible that which is suprasensible,
and contemplates under the external appearance
the underlying nature. It is the recognition m
things around of that which makes them to be what
they are, of the inner reality hidden under the shell
of the external and material object of sense, of that
which in scholastic language is termed the essence,
or quiddity, because it answers the question,^ What
is this ? Quid est hoc ? Thought is the grasping of
that common nature which is the foundation of all
classification, and binds together existing things

I When thought is used in this sense, it is true that in the case
of rational beings there is a real intellectual apprehension, since this
necessarily accompanies every act of their imagination. But it is
the sensitive act of which we are speaking when we use in reference
to such acts the word think, since we employ it in the same sense of
the acts of men and of the lower animals.

^ Quidditas is the somewhat barbarous, but very expressive
equivalent of the Aristotelian phrase. t6 rl fiv fivai. The essence
or quiddity of a thing consists in its corresponding to the pattern

THE PROVINCE OF LOGIC.

into what we call classes, or kinds, or species. It
is the apprehension of things immaterial and
spiritual, and of things material only after its own
immaterial fashion.

But it is more than this. It also includes those
processes by which the intellect compares together
the ideas which it has framed for itself from objects
about and around us, pronounces on their agreement
or disagreement, declares them to be compatible or
incompatible, identical or different from each other.
The decisions thus arrived at it places side by
side, and from them passes to further propositions
deducible from them, comparing these together in
their turn, and thus constructing arguments and
chains of argument with an activity of which the
only limit is the finite character of Thought. In
other words. Thought apprehends, judges, reasons,
not about individual objects, apprehended directly
and immediately as individuals, not about sensible
things in their capacity of objects of sense, but
about the inner nature which underlies all things,
whether sensible or suprasensible, material or
spiritual, and which intellect alone can grasp and
make its own.

Animals therefore are incapable of Thought in
this higher sense. Their knowledge is limited to
things sensible and material, and that which is
essentially dependent on sense and matter. They
have no capacity for apprehending the inner nature

after which it was fashioned. Hence ri ^»'=what is its nature?
what was it intended to be by its Creator ? And therefore rh ri ^v
thai = the being what it was intended to be by its Creator.

DIFFERENT MEANINGS OF THOUGHT.

of things. Animals can form a sort of judgment, it is
true, about things of sense, and act in consequence
of sensible impressions, as if they drew a conclusion
from such judgments, in a way that often strangely
counterfeits intellectual activity, but they never get
beyond the region of sense, and exercise their facul-
ties on objects which admit of being painted on the
Imagination, not on those which belong to the
special province of Intellect.

But is Logic concerned with all that concerns
Thought ? with the processes, for instance, by which
materials are supplied to the intellect for it to think
about ? or with the various phenomena of Thought
that observation and experience reveal to us ? Is it
concerned with the reliance to be placed on our
thoughts, and their correspondence with the things
about which we think ? Does an investigation into
the various faculties of the mind that think, and
of their mutual relation to each other, lie within
the scope of Logic? While we contend for all
reasonable liberty in defining the domain of Logic,
we must be careful not to encroach on kindred

sciences.

Logic is not concerned with an analysis of our
thinking faculties. This belongs to Psychology, or
the science of life, of intellectual life, as well as of
its lower manifestations. To Psychology, moreover,
belongs the study of the various phenomena of
thought, of the facts of intellect that we gain by
observation. To Psychology belongs the analysis
of the processes previous to Thought, by which
materials are furnished to the Intellect. To Psy-

THE PROVINCE OF LOGIC.

chology belongs the determination of the exact
distinction between the sensitive and the non-sensi-
tive faculties of the mind, and of their mutual
dependence on each other, and though the two
sciences have a certain amount of common ground,
yet we may say in general that Psychology is con-
cerned with all the operations of mind in its widest
sense, while Logic is concerned only with those
which contribute to correct thinking.

Nor is Logic concerned with the objects about
which we think, except in so far as they are repre-
sented in the thinking mind. Regarded in them-
selves they fall under the domain of Metaphysics,
which investigates the inner nature of things, and
regards them as in themselves they are. The
science of Metaphysics determines the nature of
various forms of beings of essence and substance, of
cause and effect, of goodness, unity, and truth. It
treats of that which lies outside the mind, and
contemplates it in its objective reality. Logic,
on the other hand, treats of that which is within
the mind only, and contemplates it in so far as it is
a part of the intellectual furniture.

But is it within the province of Logic to decide
on the reliance to be placed on our thoughts, or
their trustworthiness as representations of the
internal objects about which we think ? Here
we come on an important distinction between the
two parts of Logic.

I. Formal Logic has a limited, though a most
important province. Its jurisdiction- is confined to
those thoughts which already exist within the mind

FORMAL AND MATERIAL LOGIC.

and have passed the barrier between intellect
and sense. It has to take for granted that the
processes by which they have been received were
correctly performed. It accepts such thoughts as the
materials it has to employ, it pronounces on their
character as thus received, on their various rela-
tions to each other, whether of inclusion or exclu-
sion, compatibility or incompatibility, and from the
decisions passed it passes on to other decisions,
compares one with another and pronounces some
fresh decision as the result of the comparison. It
discusses the ideas which are the objects of thought,
and the judgments which express their mutual
relation, and the arguments which result from com-
bined judgments. Furthermore, as ideas ^ judgments,
arguments, must all be expressed in words, it treats
of terms as expressing ideas, propositions as expres-
sing jW^wj^w^s, syllogisms as expressing arguments,

2. Material or Applied Logic includes a much
wider province. It is not satisfied with taking
its materials for granted, but examines into the
processes by which those materials are brought
into the mind, so far as is necessary to their being
correctly performed. It includes the consideration
of the correspondence of the object of thought as it
exists in itself and as it exists in the thinking mind.
It pronounces on the nature of evidence, on the
various degrees of certitude from absolute ignorance
to the highest possible assurance of truth : on the
various grounds of certitude : on the distinctions of
doubt, opinion, knowledge, faith, on the necessity of
some kind of certitude if we are to think at all, and

THE PROVINCE OF LOGIC.

of the consequent folly of universal scepticism. It
acts the part of critic and investigator of truth, and
its investigations carry it outside the limits of the
thinking process properly so called, in order that it
may defend this process against the dangers to
which it is exposed from without.

In the present volume we shall confine ourselves,
though not with the rigour of too close an exactitude,
to Formal Logic. Material Logic is rather a part of
Fundamental Philosophy, and would lead us too far
afield. Yet we shall find it necessary to speak of
certain processes which strictly speaking lie outside
Formal Logic on account of the confusion that has
been introduced by the speculations of various
modern authors, who make it necessary for us from
time to time to make excursions outside our own
proper province in order to keep its limits intact,
and beat our opponents back when they seek to
bring confusion into the realm of Logic Pure.

Formal Logic is moreover the ally and the most
useful ally of Material Logic. Although it takes its
materials for granted, yet indirectly it detects error
admitted from without. For as we derive our
thoughts and our judgments from countless different
sources, any error existing in the mind is sure to
find itself sooner or later at variance with some
truth which is already settled there. Formal Logic
detects the inconsistency and declares that the
intruder must be driven forth. There cannot be
harmony in the soul as long as error remains there ;
and Formal Logic detects the jarring note. It
leaves indeed to Applied Logic the task of watching

MEANING OF FORMAL LOGIC.

at the gate and demanding the passport of propo-
sitions which demand admission into the mind, but
it exercises a vigilant surveillance over those already
within. Besides this, it has at its service a body of
efficient auxiliaries in the shape of necessary truths
which do not come from without at all (except so far
as external things are the occasion of their birth),
but are the citizens who are born within the thinking
mind. They are the ready instruments of Formal
Logic, and as they can never be driven out unless
absolute anarchy prevails, they are most useful in
' thrusting forth the stranger who is not furnished
with a passport, however plausible and fairspoken he
may be. There are, in truth, very few errors (and
those are errors of fact and not of principle) which
Formal Logic does not supply the means of detec-
ting and expelling from the mind.

But what is the meaning of Formal Logic " It
is that part of Logic which deals with the forms
according to which all correct thought proceeds
with the laws which regulate thought, the universal
and irrefragable rules which must govern every act
of thinking, if it is to be correct. Formal Logic
supposes its materials already received and trans-
formed into the intellectual pabulum suitable for its
own use. In using these materials the intellect,
from the necessity of its rational nature, has
certain fixed and unchangeable conditions under
which it thinks. It is from an analysis of these
conditions, from an investigation of its normal
method of procedure that the laws which govern
the intellect are ascertained, and it is the business of

THE PROVINCE OF LOGIC.

Formal Logic to enunciate these laws, to enforce their
observance on every thinker and to allow no sort of
deviaticn, even by a single hair's-breadth from their
enactments. It has to proclaim these laws eternal
and immutable as God Himself, and to pronounce
its anathema on all who declare that they admit of
any exception under any circumstances whatever.
From the beginning to the end of time, nay before
Time was and after Time shall be no more, in any
conceivable world which God has created or could
create, these laws are unchangeable and inviolable,
and God Himself cannot interfere with them in their
very smallest detail. For they are the foundation of
all Truth and are themselves founded upon the
nature of the God of Truth. God could not violate
them without ceasing to be God, and man cannot
violate them without violating that rational nature
which he possesses in virtue of his creation in the

Hkeness of God.

Logic, therefore, in the sense in which we are
using it, is concerned with the Laws of Thought.
But not with all the laws which may be termed
laws of thought. For the expression admits of two
different meanings. A Law of Thought may be a law
which regulates the relation of thought to the out-
side world, and ensures the correspondence of the
thought to the objects thought of. Such a law
would be a material Law of Thought. For instance,
after a certain amount of careful observation and
research, I feel myself justified in laying down the
proposition ; A II tortoises are slow in their movements,
and I apply to the logician to know whether I am

THE LAWS OF THOUGHT.

conforming to the laws of correct thinking in the
process which has led me to this conclusion. The
law about which I ask is a law which has to decide
the amount and the nature of the internal investiga-
tion which justifies me in uniting together in one
judgment the idea of tortoise and the idea of slow-
ness of movement. It is a law regulating the accep-
tance of the materials of thought. It involves
external research, and cannot be arrived at by a
mere comparison of the two ideas. It is therefore a
material law, and Formal Logic cannot pronounce
upon it. It is not a law of Thought itself as Thought.
It is not a law which may be known independently
of any reference to things outside. It belongs to
Material Logic to pronounce whether I have fulfilled
the conditions requisite to ensure certitude in the
assertion of the proposition in question.

But if I submit to the logician the proposi-
tion, ^// spirits are immaterial beings, and ask him
whether I am safe in asserting it, he as a formal
logician can answer me at once. The process
by which that proposition is arrived at needs
no outside investigation. It involves nothing more
than a comparison of the thought or idea of
spirit and the thought or idea of immaterial being.
Spirit implies immaterial, and the process of com-
parison which leads me to combine the two in my
judgment is a process of Formal Logic strictly so
called. The law which regulates the process is a
formal, not a material law, a law which is entirely
independent of external observation and research,
a law which follows from the nature of Thought
as Thought.

THE PROVINCE OF LOGIC.

Hence Logic is concerned with the Formal Laws
of Thought, with the Laws of Thought as Thought,
with the laws which concern Thought alone, in and
by itself.

Even when thus restricted the field of Logic is
sufficiently wide. Its sway extends over all our
thoughts. It has a word to say to us whenever
we think. It sits on its tribunal on every occasion
on which our intellect performs any intellectual
operation whatever. Even though Formal Logic
disclaim any interference with the introduction of
materials from outside into the thinking mind, or
with the faculties which supply those materials, or
with the nature of the mind itself which thinks, still
it is true to say that we cannot think a thought
without Logic having a control over it. This is why
we begin the study of Philosophy with Formal
Logic, for unless it stamp its approval on our
mind's work, that work all counts for nothing. If
Logic can show a flaw in our thinking process, if
it can point out a single idea inconsistent with
itself, or a judgment in which subject and predicate
are incompatible, or a conclusion at variance with
the premisses or which does not follow from them,
the whole argument has tn be put aside as valueless,
until it has conformed to the ruthless and inflexible
laws of Formal Logic.

CHAPTER 11.

THE DEFINITION OF LOGIC.

Summary of preceding Chapter— Is Logic an Art or Science?
—Distinction of Art and Science— Science learned by Study,
Art by practice— The Laws of Science immutable— Art
mutable— Science concerned with what already exists, Art
with production— Application of this to Logic— Logic primarily
a Science, secondarily an Art— Is the Science of Logic specula-
tive or practical ? — Distinctions between them — Logic both
speculative and practical — Various Definitions of Logic,
(i) Archbishop Whately, (2) Arnauld, (3) Port Royal, (4) J. S.
Mill, (5) Arabian Logicians— History of the Name of Logic.

Before we proceed with our Definition of Logic,
we must sum up the work done hitherto. The all-
important end at which Logic aims is exactness
of Thought. Logic is concerned with Thought, by
which we mean not every mental process, but the
operations of intellect and none other. These
operations fall under three heads, the consideration
of which furnishes the three divisions of a text-
book on Logic. Logic, however, is not concerned
with an analysis of our thinking faculties, or with
the mental processes which necessarily accompany
Thought, nor with the external objects about which
we think, but only with that which is immediately

THE DEFINITION OF LOGIC.

IS LOGIC AN ART OR SCIENCE?

necessary to correct thinking. It therefore has to
deal, (i) with those operations of the Human Intel-
lect which take for granted the correctness of the
materials supplied from without, and regulate the
disposal and development of those materials {Formal
Logic) ; (2) with those operations by which is en-
sured the correctness of the materials supplied, and
their correspondence with the external realities
which they represent (Material Logic). We are
going to occupy ourselves with Formal Logic, which
is so called because it defines the necessary /orms
or laws to which all correct Thought as such con-
forms itself, not with the laws regulating Thought
in its relation to things outside, but with those
only which regulate its internal operations in them-
selves. The scope of Logic, even under these restric-
tions, extends over the w^hole province of Human
Thought.

We have now arrived at the Definition of Logic
so far as this, that it is a branch of knowledge which
deals with the Formal Laws of Thought. We have
seen, moreover, that it has a practical end at which
it aims, that is, has fixed and immutable laws to
which all thinking must conform, that it is learned
by a careful study of our processes of thought. We
are now in a position to discuss the much disputed
question whether Logic is an Art or a Science^ or
both an Art and a Science ?

In order to answer this question satisfac-
torily, we must consider a few of the distinctions
generally regarded as separating the arts from the
sciences.

1. An art is learned chiefly by practice,^ a science
by study. Thus painting is an art, embroidery is an
art, rhetoric is an art. Each of these indeed, like
every art, has a scientific element in it, but its artistic
side is in the foreground, and the scientific element
is out of sight. None of these arts could be acquired
by years of patient study. It is by the labour of
continual practice that skill is attained in them, and
innate abihty rendered perfect. On the other hand,
geometry is a science, political economy is a science,
harmony is a science. Even where a certain amount
of experience is required, as in medicine , to complete
the results of the study and apply its principles, yet
this is quite a subordinate element. A man may
sit in his study with his books all his life long and
be learned in geometry, political economy, and in
harmony, and even in medicine, without any practice
whatever.

2. A science, again, is based on fixed and im-
mutable laws on which it depends for its very
existence, whereas an art is always ready to change
its method of procedure and to forsake the old
paths. Every true art must indeed have an intel-
lectual basis, and therefore certain underlying
principles that govern it, but in all matters which
are not of its essence as an art, it can adopt new
methods and new laws, often the very opposite of
those to which it has clung hitherto. It is far more
pliable than science, and varies almost indefinitely
with varying time and place. The laws of rhetoric

» Cf. Arist. Metaph. p. 981. (Berol. Ed.) al iroWal ^fiirdpiai
iroLOvffi T^v rex^V^'
C

^V*V.~™.- ■- 'V* '-"^*4if^*

THE DEFINITION OF LOGIC.

DISTINCTION OF ART AND SCIENCE.

vary with the character of a nation. The eloquence
which held a Roman audience spell-bound would
have little effect now in moving the minds of men,
and would be pronounced artificial and tedious, in
spite of the beauty of language and brilliancy of
expression. To the practical Spartan the florid
eloquence of other tribes of Greece was wearisome
in the extreme : the rule of Spartan rhetoric was :
Brevity above all things. The art of dyeing cloth
or of annealing iron, is always ready to adapt itself
indefinitely to new discoveries. The style of paint-
ing never remains the same for long. But a science
admits of no such variations. The fundamental
laws of political economy are the same now as in
the days of King Solomon, however great the change
that has been introduced into its practical working
by the changed conditions of society. Geometry
is not only the same in every age and every country,
but is unchangeable wherever space and quantity

are found.

3. Hence a science proceeds downwards from
first principles to the special and individual appli-
cations of them. It takes its laws ready made.
Even the inductive sciences use experiment and
observation as a means of discovering existing laws,
not of manufacturing them for themselves. But an
art has in general unbounded liberty to make its
own laws, so long as it violates no existing law of
nature. The art of painting, although it must
conform to a certain extent to the laws of perspec-
tive and colour, has the greatest possible freedom
in all other respects and can encroach even on

these. Anything is lawful which will produce a
really pleasing picture, even though it may violate
some conventional propriety and rules hitherto held
sacred. Poetry is equally free, and the purely
mechanical arts have more freedom still.

4. But we have not yet reached the central
distinction between Art and Science. Aristotle
more than once compares them with each other,
and gives us the key to their various points of
difference. Science, he tells us, is concerned with
that which exists already. Art with the production
of that which does not as yet exist. ' The end of
Science may be practical, but it is never productive,
or rather, as soon as it aims at production, it passes
into an art. For instance, the Science of Medicine
is essentially practical : it teaches the student what
are the conditions of perfect health, what means
are most serviceable to preserve it, what are the
effects upon the human body of this or that acid or
alkali, what is the nature and what are the causes of
this or that disease. But it is not an art until the
practical science is put into practice, with the view
of producing certain definite results hitherto non-
existent, of producing strength where before there
was weakness, health where before there was disease.
It then passes out of the character of the Science
of Medicine and becomes the Art of Healing. It
acquires new characteristics to quahfy it for its new
role as an Art. The scientific element is well-nigh
forgotten, experience becomes more important, and

* 'Eiri<rT^/iT7 irepl rb tiv, rix^r} 5c irtpl yfyfffip. Post. Anal. IV. 19,
p. 1008. (Edit. Berolin.)

.-■*«,- '«^ ■'-^-<;~-.'-.-^.i

THE DEFINITION OF LOGIC.

he who practises it adapts his treatment rather to
the results of his own experience than to the pre-
conceived theories of Schools of Medicine. He
begins to frame theories for himself, and throws to
the winds received principles if he finds that by
setting them at nought the health of his patients
is advantaged. The Art of Healing, productive of
health, acquired by practice, mounting up from
facts to principles founded on these facts, caring
little for theoretical laws, has taken the place of
the Science of Medicine which accepts health and
disease as already existing, is acquired by study,
investigates their various characteristics as facts to
be accounted for, argues downwards from general
principles to individual cases and follows fixed and
established rules.

Hence, art is science employed in production j^ or,
as Aristotle elsewhere defines it, a productive habit of
mind, acting in conjunction with reason,^ In every
case it is the production that makes the art :
painting, sculpture, rhetoric, music, poetry, are all
productive, and it is in virtue of their productive
or creative power that they have a claim to overleap
law, which is not granted to science.

To apply this to Logic. We may begin with
this central test, since all the rest are dependent
upon the question of productiveness. Is Logic
productive ? That it is practical no one can doubt ;
the study of it is of the greatest value in furthering
correctness of thought. But what does it produce

^ T«x»^ 7<^ ^-jno-T^/nTj xonfTiicf}. {Metaph. x. 9.)
* ?{is jU€T^ \6yov TTOi-nriKij. (Eth. vi. 3, 4.)

SCIENCE AND ART OF LOGIC.

to qualify it as an art ? We may answer the ques-
tion by the parallel of medicine. The science of
medicine deals with things as they are, studies
them, lays down the laws of sound health, and
describes the symptoms of disease. The art of
healing deals with the production of health, and
searches by every means of inquiry to find by
experience the means of restoring it.

In the same way the Science of Logic deals with
the existing Laws of Thought, clearly defines the
conditions of correct thinking and the characteristics
of correct Thought. But in the present condition
of human nature, Logic is also needed as medicine
to heal incorrect thought and produce truth and
consistency where error and inconsistency have
crept in. Hence we must have an Art of Logic
as well. The logician in his study is a man of
science, of practical, but not of productive sciepce.
But this is not enough if he is to fight the battle
of Truth. He must descend into the arena and
grapple with the prevalent fallacies of the day. He
must restore intellectual soundness where disease
had affected the faculty of thought ; he must produce
health where sickness had vitiated the intellectual
processes ; he must have at hand the appropriate
answer to the plausible objection ; he must watch
for the opportunity of providing a suitable remedy
for the poison which has weakened the keenness of
mental vision. All this needs experience — it needs
the power of ready a-gument and quick retort.
Success depends not merely on the soundness of
underlying principles, but also on the power of rapid

«a

THE DEFINITION OF LOGIC.

LOGIC PRIMARILY A SCIENCE.

and suitable production. Such a man is an expert in
the Art rather than in the Science of Logic. The
science he had acquired has passed into the pro-
ductive art. He derives his success from a skilful
application of Logica utens to the special matter
under discussion, but his skill necessarily implies
in the background a thorough acquaintance with
Logica docens,^

There is, then, an Art as well as a Science of
Logic. But the Art is an appendage to the Science,
and entirely secondary. The Science of Logic would
still exist if men, in point of fact, always thought
correctly ; but the Art of Logic would in this case
have no raison d'etre. If natural Logic always had
mastery over the thoughts of men, artificial or
acquired Logic would indeed remain as a body of
systematized rules for correct thinking (and there-
fore, as a practical science), but not as an art pro-
viding means of recovery from incorrect thinking.
The fact that natural Logic is violable by man is
the reason why acquired Logic partakes of the
nature of an art.^

» Logica docens is the theory of correct thinking, the statement
of the laws which always and everywhere are binding on the mental
processes of all rational beings. Logica utens is the application of
the general laws of Logic to this or that subject-matter ; it is the
practical employment of Logical laws in some special department
of knowledge. Logica utens, for instance, will aid us in examining
various theories of religious belief, and their accordance with right
reason. It will enable us to detect the fallacies underlying many
social and political, and even scientific arguments, by the use of
which brilliant hypothesis too often takes the place of well-estab-
lished principle.

= Natural or innate Logic consists of that body of unwritten law
which nature imposes on all rational beings, and which all correct

Hence Logic is primarily a Science, and in its
definition there is no need to introduce its subor-
dinate character and functions as an Art. Formal
Logic is the Science of the Formal Laws of Thought
or of the Laws of Thought as Thought. Material
Logic is the Science of those Laws of Thought
which arise not merely from the nature of Thought
itself, but from the nature of the objects about which
we think. Logic in general (including both Formal
and Material Logic) may be defined as The Science of
the Laws of Thought, or The Science which directs the
operations of the intellect in its knowledge of Truth, or
The Science which is concerned with the observance of due
order in our intellectual operations.

One other question must be briefly considered
•before we dismiss our Definition of Logic. Is it
a speculative or a practical Science ?

Let us see what is the distinction between
a speculative and a practical Science. We cannot
decide this by the mere examination of the matters
of which Logic treats, or of the manner in which
it treats of them. Its character as speculative or
practical depends on something extrinsic to itself.
It depends on the end whither it directs those who

thinking obeys. It is born in us, and we cannot run counter to it
without at the same time running counter to our reason. Artificial
or acquired Logic comprises all those systematized rules which are
drawn up to ensure correct thinking in those who are liable to thmk
incorrectly Its double object is to guard against error, and to act
as a remedy to inaccuracy of thought where it already exists. All
its rules must, of course, conform to the laws of natural Logic, but
it adds to it and goes beyond it, somewhat as medicme adds to and
goes beyond the ordinary food of man, though it must always con-
form to the laws of nutrition and digestion.

(iaaaMiiawfaB-jj^^A»,ij .■■j^-.^.^^aaE^tte;^

THE DEFINITION OF LOGIC.

LOGIC BOTH SPECULATIVE AND PRACTICAL. 25

devote themselves to the study of it. If this end
is merely the contemplation of some truth, the
science is a speculative one. Thus Natural Theology
is a speculative science, inasmuch as it aims at
teaching us certain verities respecting God and
His perfections. If, however, the end whither a
science tends is the contemplation of a truth with
a view to action, it is then a practical science.
Thus Political Philosophy is a practical science,
inasmuch as it inculcates certain truths with the
object of guiding the action of men as members
of society. Speculative and practical sciences alike
inquire into the nature of things and their proper-
ties, but the practical science goes on beyond this
inquiry, to apply the knowledge gained to human
action. Psychology and Moral Science both discuss
the obstacles to the exercise of the freedom of the
human will ; but the psychologist as such is satisfied
when he has laid down what they are, whereas the
moralist considers them with the object of laying
down certain rules for human action.

Is Logic merely speculative, or practical as well ?
Properly speaking it is neither one nor the other,
because it is introductory to all sciences, and the
foundation on which they rest.^ But it may be
classed under the speculative sciences inasmuch
as its object is to analyze certain intellectual
operations, while it is practical also, in so far as
it has for its object, according to the definition
just given, the guidance of the intellect in the

* " Logica non est proprie scientia speculativa sed tantum
reductive. Cf. St. Thos. la 2x, q. 57, art. 3, ad 3um.

pursuit of accurate knowledge. It is speculative in
so far as it teaches us truth ; it is practical in so
far as it teaches us how to follow after truth. It
is speculative in so far as it imparts information to
us ; it is practical in so far as it teaches us how to
gain information for ourselves. This distinction cor-
responds almost exactly to the distinction between
Logica docens and Logica utens given above.

We are now in a position to examine various
Definitions which have been given of Logic by
modern writers.

I. " Logic is the art and science of reasoning
(Archbishop Whately). It is an art so far as it
aims at the practical object of securing our minds
from error, a science in so far as it is an analysis
of our processes of thought."

This definition is at the same time too wide and
perhaps also too narrow. It is too wide because
it includes the subordinate element of the Art of
Logic, too narrow because it confines the province
of Logic to reasoning, omitting the other processes
of thought. It is true that these are processes
previous to reasoning, but they have their inde-
pendent value and laws of their own, and ought
not to be altogether discarded.

2. ** Logic is the Art of Thinking" (Arnauld).
Here the Science of Logic is entirely ignored,
and that which is the derivative and subordinate
aspect of Logic is put forward in usurped monopoly
of its whole domain. The Art of Thinking is, more-
over, an expression which is vague and meaningless.
Even if we put the best possible construction on it,

THE DEFINITION OF LOGIC.

VARIOUS DEFINITIONS OF LOGIC.

and explain it as the art of guiding our thoughts
aright, it would still be open to the objection that
it introduces considerations altogether foreign to
Logic, such as the avoidance of hasty conclusions,
preconceived notions, &c.

3. ** Logic is the Science of the operations of the
human understanding in the pursuit of Truth" (Port
Royal Logic).

This definition has an unnecessary appendage in
the last words. The human understanding is as
much ruled by Logic when it is in the possession
of Truth as when it is still pursuing it, when it
contemplates Truth already attained as much as
when it is still searching after it. Is Logic to
exercise no sway over our minds when we are
pondering over truth in re as well as when we are
hunting after Truth ui spe ? We may perhaps admit
the Definition if we omit these last words, though it
still fails clearly to mark off Logic from Psychology,
or to exclude from Logic ethical considerations
foreign to its scope and purpose.

4. ** Logic is the Science of the operations of the
understanding which are subservient to the estima-
tion of evidence" (J. S. Mill).

The objection that this on the one side extends
Logic beyond its proper limits, and on the other
limits it unduly, may be urged against this definition
no less than against the last mentioned. The ** esti-
mation of evidence " includes the weighing of the
character of the witnesses and the examination
whether their evidence is to be relied upon, and
with this Logic has nothing to do. It moreover

admits into the domain of Logic no truth based
on any source but external experience, since *' evi-
dence," in the sense in which Mr. Mill uses the
word, is something presented to the mind from
without. It thus involves the fundamental error
of the Empirical School.

5. ** Logic is the science of argumentation
(scientia argumentandi),'*

This is the definition of Albertus Magnus, as
well as of certain Arabian logicians. It is liable
to something of the same objection as the defi-
nition of Archbishop Whately, in that it tends to
limit the sphere of Logic to reasoning. At the
same time we must remember that, after all, the
chief function of Logic is to enable us to argue
correctly. This is its prominent characteristic, not
only in the popular conception of the science, but in
its practical application to the furthering of Truth.
At all events this definition must be classed as in-
complete rather than incorrect.

A few words must be added before we close this
chapter on the history of the name Logic. The
word itself (KoycKrj sciL Trpayfiareia) is not used by
Aristotle as the name of a separate branch of study.
The difficulty of defining its limits, or rather the
fact that its limits cannot be exactly defined,
sufficiently accounts for the omission. But he
speaks of logical arguments, logical difficulties,
logical demonstrations, and logical problems, much
in the sense in which we use the word to express
that which is concerned with thought. The term
Logic, as the name of a separate branch of know-

THE DEFINITION OF LOGIC.

ledge, came into use among the immediate followers
of Aristotle, and is found in extant works of the
third century.

The nearest approximation to a name for Logic
in Plato and Aristotle is Dialectic, But Plato used
the word in a wider sense, which included meta-
physics as well. It was the science of the mind
discussing with itself (BcaXefcrcKTf from SiaXeyofmc) the
inner nature of things. Aristotle, on the other
hand, restricted Dialectic to that branch of Logic
which deals with probable matter, and takes for
the principles from which it starts certain general
probabilities which a number of disputants are all
willing to accept as the basis of their discussion.
With him it was the art (or science) of discussion or
disputation, and thence it passed into the wider
meaning of that branch of knowledge which deals
with probable matter.

CHAPTER in.

THE FOUNDATIONS OF LOGIC.

Summary— Positive and Negative proof— Superiority of positive
proof— Direct and indirect proof— All proof must rest on one
common principle— Three conditions necessary to this principle
—First Principles of Logic. I. The Principle of Contradiction
necessarily the first of all— To deny this principle intellectual
suicide— Impugners of the principle of Contradiction— Four
conditions necessary to this principle, (i) Exactness of lan-
guage, (2) Identity of standard, (3) Reference to same part of
object, (4) Identity of time— Being and non-Being. II. The
Principle of Identity— Nature of the principle— False views
respecting it— Sir W. Hamilton's view, (i) Founded on false
theory of conception, (2) Untrue in itself. (3) Unnecessary and
useless.

In our last chapter we decided the difficult question
of the Definition of Logic, and after examining
the leading characteristics of Arts and Sciences
respectively, we came to the conclusion that Logic
is primarily a Science and secondarily an Art, and
that this is true both of Formal and Material Logic.
Its fixed and immutable laws, the necessity of study
rather than practice as a means of becoming a good
logician, the absence of any productive element as
an essential part of it, all point to its scientific
character. At the same time there is an art of

THE FOUNDATIONS OF LOGIC.

Logic which depends on practice and is far more
pHable in the laws on which it is based. Yet Logic
might perfectly well exist without it. We therefore
defined Logic as The Science of the Laws of Human
Thought, and we compared this definition with
several others given by modern logicians, and
stated our reasons for maintaining it.

Our investigation will therefore be into the
various laws or forms to which our thinking pro-
cesses are subject. But in building up our logical
structure we must first of all look to the Founda-
tions and make sure of the First Principles on
which all thinking rests, and of which the various
Laws of Thought are the detailed expression.
Whence are we to begin and what is to be the
solid basis, unassailable and impregnable, on which
all else shall rest secure ?

Every science has its primary laws or axioms. If
Logic is really the science of all sciences, we must
find in its First Principles that which is the founda-
tion, not of Logic alone, but of all other sciences
whatever. If Logic is to expound to us what correct
thinking is, it is of the greatest possible importance
that we should be able to place absolute confidence in
the axioms from which it starts, since they are to have
dominion over every thought we think, every judg-
ment we form, every conclusion we draw. What-
ever be the subject-matter, out of all things in
heaven and earth about which we think, those first
principles must be accepted as supreme, irrefrag-
able, universal, immutable, eternal.

Before we lay down what these First Principles

FOUNDATIONS AND FIRST PRINCIPLES.

are, there are one or two important points to be
noticed.

I. Without anticipating what we shall have to
say about proof we may lay down the existence of
a double method of proof. We may prove a thing
either directly, by showing from certain positive
principles respecting it that it is so, or indirectly, by
showing the impossibility of any other alternative.
I may prove, for instance, the proposition : The
exterior angle of a triangle is greater than either
of the interior and opposite angles : either directly
by a positive course of argument, or indirectly
by showing the absurdity which follows from the
supposition of its being equal to or less than either

of them.

2. It is clear that positive argument is better
than negative. Positive or direct proof teaches us
immediately what things are : negative or indirect
argument teaches us what they are, only by an
inference from what they are not. Positive proof,
moreover, not only teaches us what things are, but
gives us an insight into the reason why they are
so. Negative proof in its final result never gets
beyond the conclusion that something that was in
dispute is really true.

3. Direct and indirect proof starts in the first
instance from one and the same principle. But
direct proof has a secondary principle, which
depends upon and is immediately derived from their
common first principle, and is so closely allied to
it that some philosophers regard them as virtually
identical. This secondary principle of direct or

THE FOUNDATIONS OF LOGIC.

ostensive proof will be something positive, corres-
ponding to the nature of the proof which follows
from it.

4. The common principle on which direct and
indirect proof alike are based will be the ultimate
principle underlying all other principles, and by
means of which they can be demonstrated. It is
the principle to which they must all be brought
back and on which they depend for their validity.
By its supreme virtue they are established. If it
should fail, all other principles, nay, all reasoning
and all truth, disappears from the mind.

5. Three conditions are necessary for the first
principle on which all else are to depend :

(i) It must be such that it is evident in itself so
that no one can deny it, or set it aside.
Without this it could never obtain our con-
fidence, and all that followed from it would
be unreliable.

(2) It must be such that it does not depend on

any other principle going before it. It
must be absolute, not subject to any sort
of condition or qualification.

(3) It must be incapable of demonstration,

otherwise it would not be a first principle
but a conclusion from certain other prin-
ciples which it would suppose as going
before it.

6. It is clear from what we have said, our first
principle need not be our only principle. There
may be many primary laws known to us in them-
selves and not capable of direct demonstration.

THE PRINCIPLE OF CONTRADICTION.

But there must be one taking precedence of all the
rest on which all else in some way depend, by
means of which they can be directly or indirectly
proved to be true.

Having premised this, we may proceed to lay
down in order the Principles or primary laws of
Logic, and not of Logic only, but of all Science and
of all Truth. These are :

1. The Principle of Contradiction.

2. The Principle of Identity.

3. The Principle of Causation.

4. The Principle of Excluded Middle.

I. The Principle of Contradiction. — First
and foremost, implied in and underlying all other
principles is that which is commonly called the
Principle of Contradiction. It may be enunciated
thus : Nothing can at the same time exist and not exist ;
or. It is impossible at the same time to affirm and to
defiy ; or, Nothing can at the same time possess and be
without the same reality ; or. Contradictories are incom-
patible.

Why do we call this the First of all Principles ?
On a matter so important we have to justify our
assertion, more especially as we said that positive
proof is better than negative, and therefore we
should at first sight expect the foundation of all
the rest to be something positive also.

The one idea that underlies all others is the

idea of Being. Whatever we think of, we think

of as having some sort of Being ; else we could not

think of it. Being, therefore, is the idea which is

THE FOUNDATIONS OF LOGIC.

THE PRINCIPLE OF CONTRADICTION.

at the basis of every thought we think, the first and
most universal subject of Thought. Hence our
Ultimate, our Primary Principle will be that which
exhibits the primary relation of Being. But such
a relation cannot exist without something to be
related to it. Relation even in thought requires
two distinct terms. Hence the first Relation of
being must be to something distinct or different
from Being. But that which is different from Being
must necessarily be not-Being, and therefore our
ultimate and primary principle must enunciate the
relation between Being and not-Being. What is
this relation ? Obviously one of exclusion or con-
tradiction. ** Nothing can at the same time possess
Being and not-Being " — Nequit idem simtd esse et non
esse; or, in the words of St. Thomas: "We must
not affirm and deny simultaneously " — Non est simul
affirmare et negate.

On this Principle of Contradiction all proof is
based, direct and indirect. It enunciates the very
first Principle of Being, and therefore precedes in
the order of Reason any other possible statement.
It therefore underlies all thinking. It is implied in
every act of Thought, in every assertion we make.
It is a necessity of our reason. He who refuses
to acknowledge its universal supremacy, commits
thereby intellectual suicide. He puts himself out-
side the class of rational beings. His statements
have no meaning. For him truth and falsity are
mere words. According to him the very opposite
of what he says may be equally true. If a thing
can be true and false at the same time, to what

purpose is it to make any assertion respecting any
single object in the universe ? Fact ceases to be
fact, truth ceases to be truth, error ceases to be
error. We are all right and all wrong. What is
true is false and what is false is true. Statement
and counterstatement do not in the least exclude
one another. What one man denies another man
may assert with equal truth, or rather there is no
such thing as Truth at all. Logic is a science, yet
not a science. The Laws of Thought are universal,
yet not universal. Virtue is to be followed, yet not
to be followed. I exist, yet I do not exist. There
is a God, yet there is no God. Every statement is
false and not false, a lie yet not a lie. It is evident
that the outcome of all this can be nothing else
than the chaos of scepticism pure and simple, a
scepticism, too, which destroys itself by its own act.
If the Law of Contradiction can be set aside in a
single case, all religion, all philosophy, all truth, all
possibility of consequent thinking disappear for

ever.

Yet, strange to say, not a few of those who call
themselves Philosophers in modern days banish the
Law of Contradiction from a portion, or from the
whole field, of human knowledge. Kant has the
very questionable honour of having first initiated
the doctrine oi Antinomies, or contradictions exist-
ing side by side, but nevertheless both of them true
in point of fact, albeit to our reason irreconcilable.
Schelling and Hegel follow in his steps, and declare
that the Law of Contradiction has no application
to absolute Truth. Dean Mansel tells us, in his

THE FOUNDATIONS OF LOGIC.

Limits of Religious Thought, that the fundamental
conceptions of a rational Theology are self-contra-
dictory. Sir W. Hamilton assures us, in his Lectures
on Logic, that in our knowledge of the absolute
we must repudiate it.^ Archdeacon Farrar enume-
rates the antinomies of St. Paul, which he declares
to be irreconcilable to human reason.* Mr. Herbert
Spencer declares Theism and Atheism to be equally
untenable by the intellect of man. Many of the
Hegelian School go so far as to identify existence
with non-existence, and to declare that all contra-
dictions are but partial expressions of one all-
embracing Truth .3 What else is this but to deny
the existence of all Truth, to make all philosophy
impossible, to render all argument a mere childish
manipulation of unrealities, all investigation of
Truth a mere futile and fruitless search after the
Philosopher's stone ?

At the same time we must carefully guard our
definition of the Principle of Contradiction. It may
easily be misapplied unless we hedge it in with
certain conditions, which are all indeed implicitly
contained in it, but nevertheless may be overlooked
unless we state them explicitly.

I. When we say that contradictions cannot be
simultaneously true of the same object, we must
beware of any ambiguity in our language, and of
any consequent confusion in our thought. If there
is the faintest variation in the sense in which we use

' Lectures on Logic, Vol. III. p. 89.

2 Archdeacon Farrar's Life and Writings of St. Paul, II. 590-

3 Cf. Michelet, Esquisse de Logique, 3, 4, 12.

THE PRINCIPLE OF CONTRADICTION.

our terms, our law does not hold good. We may
admit that a man may be at the same time wise and
not wise, if we are alluding to two different kinds
of wisdom. If in the proposition: This man is
wise, we mean that he is a prudent, sensible, canny
man in business matters, and in the proposition :
This man is not wise, that he holds many foolish
opinions on speculative questions, the two propo-
sitions may be simultaneously true, in spite of their
being verbal contradictions. If I say of him that
he is a clever fellow, using the word in the American
sense of an amusing, witty, pleasant companion,
and afterwards assert that he is not a clever fellow,
using the word in the English meaning of a man of
good mental capacity, the two statements, notwith-
standing their apparent incompatibility, may both
be in accordance with fact. There are compara-
tively few common words which do not admit some
variation in meaning, and the fainter the variation
the more necessity for being keenly alive to it. An
event may be at the same time impossible and not
impossible, according as we used the word to signify
moral or absolute impossibility. A man may be at
the same time obsequious and not obsequious, if we
pass from the old-fashioned to the modern use of
the term. Our friend may be at home yet not at
home, on the occasion of our unwelcome visit ; a
dog may be intelligent, yet not intelligent ; prudence
may require that we should be simple, yet not simple,

and so on.

2. We must also take care that we use our
words in reference to the same standard, A man

THE FOUNDATIONS OF LOGIC.

is walking fast who completes five miles within the
hour, but a horse who takes the same time for the
same distance is not at all fast in his rate of motion,
so that we may say that the rate of five miles an
hour is both fast and not /as/— fast for a man, not
fast for a horse. In the same way, large, high,
broad y soft, wild, and many other adjectives are
modified by the word to which they are joined, and
have no absolute and fixed meaning in themselves,
but are referred to it as their standard. Wood is
esteemed soft when it is of a consistency which we
should not call soft if we were speaking of wool ;
a child of ten years old is tall, though it would be
the reverse of tall if its stature were the same eight

years later.

3. In speaking of composite objects, we must
be very exact in applying our terms to the same
part of the object. A child may be fair and yet
not fair, if in the one case we are speaking of eyes
and complexion and in the other of its hair. A
man may be cold and yet not cold, cold in reference
to his bodily temperature, not cold in respect of his
warm and generous heart : he may be strong and
yet not strong, strong in his muscles, not strong in
his general constitution.

4. Lastly, we must insist on the exact application
of the words at the same time. The same thing can-
not be true and false of the same object of thought
at the same point of time ; but we must remember
that in one instant that which was false may become
true and that which was true may become false.
It is for this reason that our comparison of two

THE PRINCIPLE OF CONTRADICTION.

external phenomena can never be perfectly exact.
We never can eliminate the element of a difference
of time between the two observations. While we
were observing the first, the second may have
changed its character, so that we are not com-
paring together P and Q as simultaneously existmg,
but P as it exists at the moment x and Q as it
exists at the moment x + dx. A complete reversal
of the conditions of being may take place m the
fraction of a second. There is no measurable
interval between the state of life and the state ot
non-life or death. An act of contrition flashmg
with the rapidity of lightning through the soul of a
dying man, may utterly and entirely change the
character of his soul and his relations to God so
that he who was before the enemy of God, a rebel,
loathsome and deserving of hatred, becomes at the
very next instant, by a sort of magic transformation
the friend of God, His loyal subject, beautiful and
worthy of His love. In such a case as this, good
and not good, obedient and not obedient, meet for Heaven
and not meet for Heaven, are true of the same object
within two seconds of fleeting time.

Or to take a very different illustration of the
necessity of thus guarding our law, and one of no
infrequent occurrence in practical hfe. A man is
being tried for robbery. The counsel for the
defence urges that the prisoner cannot be guilty
because the witnesses allow that the robber was a
bearded, a heavy whiskered man, whereas the
prisoner was on the very day of the murder closely
shaven. His argument is that bearded and not

THE FOUNDATIONS OF LOGIC.

THE PRINCIPLE OF CONTRADICTION.

bearded, shaven and not shaven, cannot be true of
the same man at the same time. But if the counsel
for the prosecution can show that the prisoner had
time enough between the moment when the robbery
was committed and the moment of his apprehension
to go home and shave off beard and whiskers aHke,
the defence obviously becomes worthless, because
the condition of simultaneity is not fulfilled.

These four conditions seem obvious enough, but a
large proportion of the error prevalent in the world
arises from a neglect of one or the other. When
men find contradictions in Rational Theology, it is
because they do not see that the attributes of God
are necessarily referred to a different standard from
the perfections of man, and exclude from them-
selves that which is a human perfection only in
virtue of man's finite and contingent nature. When
they attack the Christian religion as teaching that
which it is impossible to believe, they often do not
analyze exactly and distinguish from each other the
various meanings of the word impossible. They do
not distinguish between that which contradicts the
every-day evidence of sense, or the laws of pro-
bability, and that which contradicts the immutable
laws of Reason.

The Principle of Contradiction is therefore prior
to all other principles whatever. It is the ultimate
principle to which all others are reduced, and with-
out which they would have no force. It is the
principle which pre-eminently stands on its own
basis. ** In all human science," says Suarez,' "and

» Disp. Met. III. Hi. 8—10.

especially in the science of being, it is simply and
absolutely the first. From it all other principles
are proved. It is, as it were, the Universal Foun-
dation on whose virtue all proof depends, and by
means of which all other principles can be set forth
and established as truths known to men."

But an objection is sometimes raised to the
Principle of Contradiction as the ultimate principle,
on the ground that the positive is prior to the nega-
tive, and that therefore some positive Principle must
be anterior to it. This is no new difficulty, but is
met and answered by Suarez, who says that it is
quite true that in the constructive order and the
order of production {in ordine generationis et compo-
sitionis) the positive must precede the negative, but
not when we regard truths in the order in which
they are known to men (sub ratione veritatis humano
intellectui cognitce).

This distinction is worth a moment's considera-
tion. We may consider the growth of truth either
in itself, or as taking place in the mind of man.
The order of growth will not be the same under
these two aspects. '* Whatever is received, is re-
ceived according to the nature of the recipient,"
and human nature in receiving truth, must begin
by repudiating what is necessarily opposed to truth.
But it does not follow from this that Truth in itself
is built upon a negative foundation. In metaphysical
truth all is positive from the beginning to the end.
There is nothing to repudiate or reject. Being is
its foundation, and the attributes of being are its
superstructure. It does not recognize non-being at

THE FOUNDATIONS OF LOGIC,

all. Non-being from the very nature of things, has
no sort of existence.

But for us Non-being is but another name for
falsity, and we must begin by repudiating it.
Hence, for us it is the negative principle which
is above all self-evident and manifest, and there-
fore every branch of human knowledge must be
based upon it. In Logic we are not concerned
with realities as coming into existence outside of
us, but with realities as coming within the range
of mir intellects. We have not to consider the order
into which various truths fall in themselves, but the
order into which they fall as they take their place
in our mental furniture. In this latter character
the Principle of Contradiction has no rival. In the
order of truths, as known to us, it reigns supreme.

But this negative principle is only satisfactory as
preliminary to something farther. We need some
positive principle separate from it, depending indeed
upon it, but yet at the same time self-evident, if
once the Principle of Contradiction is previously
granted.

II. The Principle of Identity.— This second
principle may be termed the Principle of Identity.
It is enunciated in the formula : Every being is its
own nature, or. Every being is that which has an essence
of its own (onine ens est sua propria natura, or omne ens
est habens essentiam).

This principle is the foundation of all definition
and of all demonstration ; it is of all definitions
the most universal. In every definition that I lay

THE PRINCIPLE OF IDENTITY.

down, I am stating a particular instance of this
universal law. If, for instance, I lay down that. All
ink is a liquid used for purposes of writing or printing,
I am stating the proper nature or essence of ink,
and so merely a particular case of the proposition,
Every being is its own nature.

If I lay down that, A cygnet is a young swan, I
am again assigning to a special kind of being its
own special nature. Or if my proposition is, All
eicosahedrons are rectangular figures, I am acting on
this same principle, though here it is but a portion
of the complex nature of an eicosahedron that I am
assigning. Similarly, if I state that. All chimpanzees
are sensitive, my statement gives a part of the nature
of chimpanzeeism.

But while the Principle of Identity states that
every being is identical with its own nature or essence,
this does not mean merely its identity with itself.
It is not sufficiently expressed in the form, Omne
ens est ens. The principle of Identity goes further
than this. As the first relation of Being is to non-
Being, so its second relation is to its own charac-
teristics. Prius est esse quam tale esse. First comes
Being with its consequent relation to Non-being,
then comes that which characterizes Being— its
own nature, which is necessarily identical with it.
First comes the Principle of Contradiction, pre-
senting Being in its primary relation ; then comes
the Principle of Identity, stating the relation of
Being, not to itself (for such relation is no relation
at all, any more than a man could be called one of
his own relations), but to that which is comprised in it.

THE FOUNDATIONS OF LOGIC.

Thus A cygnet is a young swan, states the rela-
tion of cygnet not to itself, but to the combined
ideas of youth and swan-nature which are comprised
in it, and states this relation to be one of identity.
The notion of cygnet is resolvable into, but not the
same as, the notion of young swan. It may be true
objectively that the two things are identical, but we
are talking now of the foundation of mental truth.
The two ideas which are presented to our minds
are not the same. They are united in the act of
definition, and the definition given is coextensive
with, not identical with, the thing defined.

Here we have to be on our guard against a
modern error. The Principle of Identity, that Every
being is or contains its own nature or essence, has
been distorted by some modern logicians, and thrust
forward into the first place as the first and ultimate
basis of all Truth. It has been clothed in a garb
that was not its own. It has been stated in a formula
which has the plausible appearance of a guileless
simplicity, and it has then (or rather this perversion
of it) been put forward as the rival of the Principle
of Contradiction for the office of President of the
Court of Final Appeal for all Demonstration, and as
not only independent of it in its decisions, but its
superior and proper lord.

This new Principle, which is really no principle at
all, has usurped to itself the name of the Principle
of Identity, and enounces itself in the simplest of all
Propositions—^ is A , or. Every object of thought is
identical with itself It is indeed the most obvious
of all truisms, which the wildest sceptic would never

THE PRINCIPLE OF IDENTITY.

venture to deny. Even the man who questions his
own existence (if such an one exist) cannot deny
that A is A, Its upholders accordingly represent it
as the backbone of all thinking, the all-pervading
principle taken for granted of every mental act. It
is to be the underlying basis of every department of
knowledge. Art, Science, Philosophy, Theology, all
are to rest on A is A, and without it would cease

This is all very satisfactory if it is correct. We
must, however, examine into its claims before we
dethrone the Principle of Contradiction and set up
this new-comer in its place. We must subject it to
very careful scrutiny before we accept a law which
Aristotle and St. Thomas do not recognize.

What is the account given of this New Principle
by its great advocate, Sir W. Hamilton ?

**The principle of Identity (principium Identttatis)
expresses the relation of total sameness in which a
concept stands to all, and the relation of partial
sameness in which it stands to each, of its con-
stituent characters. In other words, it declares
the impossibility of thinking the concept and its
characters as reciprocally unlike. It is expressed in
the formula A is A, or A= A; and by ^ is denoted
every logical thing, every product of our thinking
faculty,— concept, judgment, reasoning, &c.

** The principle of Identity is an application ot
the principle of the absolute equivalence of a whole
and of all its parts taken together, to the thinking
of a thing by the attribution of constituent qualities
or characters. The concept of the thing is a whole,

4«

THE FOUNDATIONS OF LOGIC.

THE PRINCIPLE OF IDENTITY.

the characters are the parts of that whole. This
law may, therefore, be also thus enounced, — Every-
thing is equal to itself, — for in a logical relation the
thing and its concept coincide ; as, in Logic, we
abstract altogether from the reality of the thing
which the concept represents. It is, therefore, the
same whether we say that the concept is equal to
all its characters, or that the thing is equal to itself.

** The law has, likewise, been expressed by the
formula, — In the predicate, the whole is contained
explicitly, which in the subject is contained im-
plicitly."'

But this much-vaunted principle, which puts for-
ward such all-embracing demands and requires that
all else should be subservient to it, proves on careful
inspection to be a miserable impostor, usurping a
precedence to which it has no sort of claim. It has
its foundation in the false theory of Conception
which Sir W. Hamilton puts forward, and of which
we shall have occasion to speak in a future chapter.
Without anticipating what we shall there say, we
may state here that according to him our idea of an
object is nothing more than its various attributes
tied together in a bundle, combined together in a
sort of unity derived not from their co-existence in
the object as realities, but from the mind which has
power to invest them with it. Hence he regards
Definition as a sort of untying of this mental bundle
and declaration of its contents, not as an unfolding
of the nature of the thing defined. It is but a
reversal of the process that the mind has previously

' Logic, I. 79, 80.

performed, not an analysis of the object of thought.
Hence a Definition is the definition of a concept, a
summing up of the contents of the concept. All is
subjective. He talks of the constituent characters of
a concept, and asserts that " it is the same whether we
say that the concept is equal to all its characters, or
that the thing is equal to itself." Sir W. Hamilton
leads his readers astray by ignoring the distinction
between the identity of an object with its own
nature and the identity of a concept with its con-
stituent characters. The one, indeed, may be stated
in the formula, A is a + b + c+d + , &c. ; the other
ought to be stated A is A. He has no right to
treat these two propositions as the same. He
would not do so were it not that he supposes the
concept A to be simply a bundle of the attributes
of a, 6, c, d, &c., summed up under the name A.

This is our first objection to Sir W. Hamilton's
Principle of Identity. It is founded on a basis of
false analysis. It regards our ideas as a mere
bundle of qualities. It confuses the object outside
of us with the idea within us. It has in it the latent
venom of his doctrine of all concepts or ideas being
relative to the individual mind that forms them, and
not possessed of any sort of objective reality of

their own.

Hence, secondly, he states respecting the concept
what is true of his false notion of concept, but is not
true of concepts as they really are. If I say that
a parsnip is a non-sensitive substance, no one could say
that the idea of non-sensitive substance is identical
with that of parsnip, nor even that there is a partial

THE FOUNDATIONS OF LOGIC.

sameness. It is true that the external reahties are
identical, but it is not true that the ideas are iden-
tical, unless we regard ideas under the false light
under which he himself regards them. How can
A is A represent the proposition that parsnips
are non-sensitive substances, or that parsyiips are not
umbelliferous plants ? The two objects of thought
coincide in instances existing in the external world,
but not in the minds of men.

Thirdly, even if it were true that an idea is
identical with its constituent characters, this formula
A is A would apply to definitions only. If I say,
Men are substances, there is no identity between
the two concepts. What is meant by a partial same-
ness ? A is A supplies us with no support for a
proposition where subject and predicate are not
co-extensive. It does not even provide us with a
basis for a proposition in which they are co-extensive,
if their comprehension is different, e.g,. All men are
rational creatures, is not the same as A is A ; for
although the class of men is co-extensive with that
of rational creatures, yet man, besides the concept
rational and creature, is characterized by sensitive-
ness, life, &c., which must not be omitted if there
is to be real identity between the subject and

predicate.^

But all these defects in Sir W. Hamilton's Prin-
ciple of Identity are but the natural consequence of
its attempting to take the place of the axiom which
we have already proved to be the ultimate axiom to

» Cf. Rev. T. Harper, Metaphysics of the School, II. pp. 34. &C-' ^^
whom I am indebted for several of the arguments here adduced.

THE PRINCIPLE OF IDENTITY.

which all else ought to be referred. If what we
have said is true, that the Principle of Contradiction
represents the primary Relation of Being, that all
else must be referred to it, this Principle of Identity
must needs be an usurper. Instead of being the
fruitful tree that its advocates assert, it is but a
barren trunk whence nothing proceeds. The plau-
sible proposition A is A, with its sleek simplicity
and wonderful universality, turns out to be only
a foolish truism which never can get beyond itself.
If it had not presumed to usurp the first place,
and to arrogate to itself an universal and absolute
dominion to which it has no right, it might perhaps
have been tolerated under the unsatisfactory form
of the proposition A is A. But in seeking to
dethrone the Principle of Contradiction, it revealed
its true character, as the offspring of the false
theory of conception which underlies the whole of
the Hamiltonian Philosophy.

On the one hand then we have the true Principle
of Identity enunciated in the scholastic formula :
Every object is its own nature, and on the other, the
false Principle of Identity enunciated in the modern
formula A is A, or Every object is itself. The former
is the fruitful parent of all a priori propositions.
The latter is a purely tautological and unfruitful
formula which can produce nothing beyond itself,
which we may therefore dismiss as one of the many
mischievous impostures with which modern philo-
sophy abounds.

THE PRINCIPLE OF IDENTITY.

CHAPTER IV.

THE FOUNDATIONS OF LOGIC {continued).

Summary -The Principle of Identity-Propositions derived from
it-These Propositions not tautological or verbal Propositions
—Their limits-Distinction of a priori and a posteriori Propo-
sitions-Deductive and Inductive Sciences-Analytical and
Synthetical Propositions-Are all a priori Propositions ana-
Ivtical ?-Kanfs doctrine of a priori synthetical Propositions-
Its falsity-Implicit and explicit knowledge-Our advance
from truisms to Truth.

In our last chapter we laid down as the Primary
Law of the Human Mind, and therefore the ultmiate
foundation of Logic, the Principle of Contradiction.
We showed how the denial of this is mtellectual
suicide— a suicide of which many who call them-
selves philosophers are to be held guilty. We laid
down the conditions necessary for the validity of
this Law, and pointed out how almost all human
error arises from the neglect of one or other of
them. We then passed on to the Principle of
Identity, and distinguished it in its true form from
the false Principle which some modern philosophers
have thrust forward as the rival of the Law of
Contradiction. We must now discuss the Law of
Identity in its further character of the generative
source of further Truths.

We have already said that the true Principle of
Identity is the deductive basis of all positive reason-
ing, and we remarked at the end of the last chapter
that it is the parent of all a priori propositions.
Why do we draw this distinction between its
character as the basis of all positive reasoning and
the parent of a priori propositions ? What, moreover,
do we mean by a priori propositions, and to what
are they opposed ? Here we enter on an important
part of our subject, which is, indeed, in some
respects a digression, but which it is necessary to
explain here in order to show the true position of
the Principle of Identity.

The Principle of Identity is stated in general in
the formula we have already given. But when we
descend from the general to the particular, from
Being to some particular kind of Being, the form
that it assumes is a proposition which unfolds the
nature, or some portion of the nature, of the object
of which we speak.

Thus, when I apply the general principle. Every
object is its own nature, to that particular object called
a square, the form that it assumes, or rather, the
Proposition that it engenders, is an analysis of the
idea of a square. Viz,, Every square is a four-sided
figure with right angles and equal sides. But here we
must remember that these propositions are very
different from tautological or verbal propositions.

I. A proposition in which the predicate is an
analysis of the subject is not a tautological propo-
sition. It explains the nature of the subject, declares
its essence, and proclaims a fact of which we may

THE FOUNDATIONS OF LOGIC.

be entirely ignorant. A tautological proposition
never gets beyond the meaning of the words. It
is generally a mere translation from one language
to another, or a repetition of a set of words which
necessarily mean the same thing. It introduces no
ideas beyond those which can be extracted from the
word which forms the subject. If I say, A ringlet
is a little ring, my proposition is tautological. But
if I say, A ringlet is a lock of hair, twisted into
the form of a ring, my proposition is an assertion
of the identity of the object with its own nature.
Similarly the following propositions are tautological.
A quadrilateral is a four-sided figure. The Ursa Major
is King Charles' Wain, The periphery of an orb is the
circumference of a circle. Circumlocution is roundabout
talk, A Parliamentary orator is a man who delivers
orations in Parliament, &c. Here there is no analysis
of the object of which we are speaking or thinking ;
the statements made are merely verbal, and are
entirely independent of the nature of the thing.

2. The unfolding of the nature of the object
of thought does not mean a mere verbal explana-
tion. It is an analysis of the idea. Thus the
analysis of the object called a triangle is three^
sided figure, not three-angled. The etymological
signification of a word is often very misleading,
as in villain, hypocrite, silly, &c. Our analysis
must set forth the nature of the object as it is
in itself, and the object must be that which, in
the ordinary language of men, is represented by the

word. .

How far are we to extend the limits of pro-

A PRIORI AND A POSTERIORI PROPOSITIONS. 53

positions deducible from the principle of Identity ?
Is every affirmative proposition ultimately one of
its offspring? Are all the Truths in the world
derived from it ? Certainly not. There is a
wide distinction between two classes of Proposi-
tions. Those belonging to the one class claim this
Principle as their parent. Those belonging to the
other, though subject to its dominion, and in some
sense founded upon it, are nevertheless something
more than an application of it to some individual
•object, but are the product of observation or experi-
ment. They do not merely analyze the nature of
the subject and set it forth in the predicate, as a
particular instance of the identity of all Being with
its own nature, but add something which is not
contained in the idea which forms the subject of
the proposition.

This latter class of Propositions are called
a posteriori propositions as opposed to a priori proposi-
tions. They introduce an element which is derived
from outside. They are not necessitated by the very
nature of things. They are dependent on experience,
and with different experience they may be no longer
true. They are reversible in a different state of
things. They are true in the known Universe, but
there may be a Universe where they are not true.
It is possible that in some still undiscovered star,
the light of which has never reached us, they
may be false. They may be true at one time and
not at another. Even if they are in point of fact
always true, their truth is not a matter of absolute
necessity. They are called a posteriori because we

THE FOUNDATIONS OF LOGIC.

DEDUCTIVE AND INDUCTIVE SCIENCES. 55

argue up to them from particular facts which are
posterior to the laws which govern them.

All the Laws of the physical world are a postenort,
not a priori propositions. They cannot be evolved out
of our inner consciousness. No one could have dis-
covered the Law of Capillary attraction, or the Laws
of Light and Heat, by merely sitting in his study and
seeking to work out the problem from first pnnciples.
For all these careful observation and experiment
were needed. They are not necessary laws. They
are reversible, and sometimes are reversed or set
aside if their Divine Author intervenes by what is
called a miracle. Here it is that they differ from
necessary or a priori laws. No Divine power can set
aside the law that all the angles of a triangle are
equal to two right angles, or that the whole is greater
than its part. It is absolutely impossible that in
any portion of the Universe, actual or possible,
this could be the case. Necessary or a prion
laws are founded on the inner nature of things,
which cannot be otherwise than it is. They are
therefore eternal as God is eternal. They existed
before the world was, and will exist to all eternity.
They stand on quite a different footing from those
physical laws which are simply a positive enactment
of God, which He could at His good pleasure at any

moment annul.

Corresponding to these two sets of Laws are
two kinds of science. On the one hand there are
sciences which are based simply on these a prion
laws. As their First Principles are eternal, so they
are eternal. They all consist of a series of applica-

tions of the Law of Identity to the subjects with
which they deal. Mathematics is an a priori
science. Its axioms, postulates, and definitions are
all the direct offspring of the law of Identity. Ethics
is an a priori science, and therefore the whole
ethical system may be constructed out of a par-
ticular application of the fundamental laws of right
and wrong which are merely this same Law in
concrete form. Natural Theology is an a priori
science, and reason can attain to a knowledge of
God (so far as we can discover His nature by
our rational faculties) without any extrinsic aid,
starting from the Law of Identity as our point
d'appiii, and applying it to the various objects
around and about us.

But there are other sciences in which this is not
the case. What are called the Natural Sciences
are not exclusively based on the Principle of
Identity. They all are dependent on it indeed and
own its sway, but it is not sufficient of itself to
enable them to work up their materials without any
extrinsic aid. They have to appeal to other sources
for the means of working out their conclusions.
Chemistry could never have developed itself out of
chemical concepts and the fact of the identity of
every being with its own nature. Botany could not
have advanced a step unless it had been able to
call in other fellow-workers to produce its results.
Zoology would have no existence as a science unless
it could appeal to external aid in building up its
laws. The method of procedure of these sciences
is a different one altogether, and it is important to

THE FOUNDATIONS OF LOGIC.

the logician clearly to discern in what the difference

consists.

There are thus two main divisions of Science, as
there are two classes of Propositions. All Sciences are
either a priori and deductive sciences, or a posteriori and
inductive. It is very important to understand aright
the distinction between them. A Deductive science
is one which starts from certain first principles, and
from these it argues down to special applications of
them. It begins with the general and the universal,
and ends with the particular and the individual.
It starts from necessary and immutable laws, and
from them deduces the various consequences which
flow from them when they are applied to this or
that subject-matter. The external world furnishes
the materials with which Deductive Science deals,
but has nothing to say to the laws which control
those materials when once they are admitted into
the mind and have become objects of Thought.'
Mathematics is, for instance, a deductive or a priori
science. It starts from certain necessary and
immutable axioms. The world outside furnishes it
with its materials, lines, angles, figures, solid bodies,
&c. But these materials it manipulates without
any further reference to the external world (unless

« A distinction is sometimes made between those deductive
sciences which derive their materials from the external world, and
therefore require experience as a condition of their study, and those
which can be pursued altogether independently of the world out-
side when once the necessary ideas have been acquired and such
an understanding of the meaning of the terms employed as defi-
nition conveys. Mathematics belong to the former class : Logic and
■Metaphysics to the latter.

DEDUCTIVE AND INDUCTIVE SCIENCES.

by way of illustration); it imposes its own laws
on the materials received, and all its conclusions
are deduced from the laws as applied to the
materials.

Not so an Inductive Science, which starts, not
from necessary first principles, but from individual
facts. It begins with the particular and mounts up
to the universal. It does not start with its laws
ready made, but has to build them up for itself
gradually and step by step. It is true that it is
controlled by certain necessary and a priori prin-
ciples to which it must conform. It is subject to
the same general laws as the Deductive Sciences,
but besides this it has principles of its own which
it elaborates for itself and which after a time it is
able to establish as certain, though never certain
with the same irrefragable certainty that is pos-
sessed by the laws of the a priori sciences.

The absolute immutability of all the laws of
Deductive Science is based upon the fact that they
are one and all merely particular applications of
this Law of Identity. They are an elaborate and
developed expression of it, an application of it to
the materials supplied from outside. They are all
derived from it and capable of being finally resolved
into it again. When this fact is once grasped, it is
easy to understand the supreme and unassailable
position of the a priori sciences.

But there is another Division of Propositions
which we must examine in order to discover
whether what we have just said is true. Propo-
sitions, besides being divided into a priori and

!•

THE FOUNDATIONS OF LOGIC

a posteriori, are also divided into analytical and

synthetical,

I. An analytical proposition is one in which the
predicate is either contained in the subject or is
virtually identical with it, so that from a knowledge
of the meaning of words which stand as the subject
and predicate we are compelled to assent, and that
with infallible certainty, to the truth of the pro-
position. Thus, for instance, the proposition: All
planets are heavenly bodies, is an analytical proposi-
tion, since the predicate '* heavenly body" is already
contained in and a partial analysis of the idea of

planet.

For the same reason: All sycophants flatter the
great, All triangles have three sides and three angles,
are analytical propositions because sycophancy in-
cludes flattery, and triangle implies three angles and

three sides.

Hence, given the laws of thought and a complete
understanding of the terms employed, it is abso-
lutely possible to arrive at all the analytical propo-
sitions in the world. There is no reason why all the
truths of Pure Mathematics should not be thought
out by one who never reads a book or goes outside
his study-door. The only limit to the extent of our
knowledge of analytical propositions is the inactivity
and weakness of our feeble and finite intelligence.
We need the support of sensible images appealing
to eye and ear. Few men can work out an elaborate
proposition of Euclid without a figure before their
eyes to guide them. Yet none the less are all the
propositions analytical from beginning to end. The

ANALYTICAL AND SYNTHETICAL PROPOSITIONS. 59

figure adds nothing to the proposition ; it simply
facilitates our apprehension of it. , ^ •

2 A synthetical proposition, on the other hand, is
one in which the predicate is not contained m the
subject, but adds to it some fresh quality, or attri-
bute, which an analysis, however minute, could
never have discovered in it. Such propositions are
sometimes called ampliative, because they enlarge
our stock of knowledge. When, for instance, I say
that Canvas-backed ducks are found in Maryland, or
that Fools are known by the mtdtitude of their words,
I am adding to the ideas of canvas-backed ducks
and fools what no mere analysis could have revealed
in them. They convey into my mind fresh know-
ledge from outside, requiring experience and obser-
vation. These propositions are called synthetical,
because they synthesize, or put together the mde-
pendent ideas contained in the subject and predicate
respectively. They proceed from the simple to the
composite. They do not make use of materials
existing within our minds, but they mtroduce
fresh materials which no amount of thinking could
have thought out from the stock of knowledge
already possessed. They cannot be reduced to
the primary law given above, but are regulated by
another code of law belonging to material logic.
They may be universally true, but their universahty
does not depend on any primary law of thought.

Thus the proposition. All men are mortal, is a
synthetical proposition, because the idea of humanity
does not contain the idea of mortality. As a matter
of fact, all men are subject to death, but it is

HI'

THE FOUNDATIONS OF LOGIC.

quite conceivable that some healing remedy might
have been provided which would have averted death
until the time of their probation was over, and that
then they would have passed into a different state of
existence, where death is unknown and impossible.
As a matter of fact, Adam and Eve, at their first
creation, were exempt from the law of death, and
would never have died, had they not forfeited their
privileges.

In the same way the proposition. All men are
possessed of the faculty of speech, though an uni-
versal, is nevertheless a synthetical proposition. It
is quite possible that men might exist who had
no power of speech, but communicate their ideas
to one another by some sign or other external
expression. It is absolutely possible that men
might exist who would still be really and truly men,
though they had no power whatever of conveying
their ideas from one to the other, but lived in intel-
lectual isolation. The analysis of the idea of man
does not include the idea of speech-possessing, even
though we take the word speech in the widest
possible sense.

We have now seen that a synthetical proposition
is one in which the predicate is not contained in
the subject, but requires some further knowledge
beyond the meaning of the Terms and the Laws of
Thought in order to establish it. An analytical
proposition, on the other hand, presents in the
predicate merely a portion of that which is already
presented in the subject, and requires no further
knowledge beyond the meaning of Terms and the

ANALYTICAL AND SYNTHETICAL PROPOSITIONS. 61

Laws of Thought to make good its validity. If the
account we have given of them is correct, synthe-
tical and analytical Propositions differ in no way
from the Propositions we described above as a priori
and a posteriori. An a priori Proposition is identical
with an analytical Proposition, and means a Propo-
sition which is simply an application of the Principle
of Identity to some particular case. An a posteriori
Proposition is identical with a synthetical Proposi-
tion, and means one which adds something from
outside. The analytical or a priori Proposition
stands on its own basis, and that basis is the Law
of Identity. The synthetical or a posteriori Pro-
position is one which takes its stand on the basis
of external experience, though at the same time it
is referable to the Law of Identity as controlling
and regulating it.

But here we come into conflict with Kant and
a large number of modern logicians, who assert
that there are some synthetical propositions which
stand on their own basis, and are therefore a priori,
not a posteriori. They do not regard all a priori
propositions as ultimately reducible to an analysis
of the nature of the object, but assert that there are
some which, though universal, necessary, and immu-
table, nevertheless introduce in the predicate some-
thing which is not to be found in the subject. The
motive of this assertion is a good one, for it is
intended as a bulwark against the Experimental
School who refer all laws. Deductive and Inductive
alike, to experience, but it is a perilous bulwark if
it is not founded on Truth.

THE FOUNDATIONS OF LOGIC.

We will take the two instances given by Kant m
his Critique of the Pure Reasmi.' The first is the
geometrical axiom: A straight line is the shortest
possible line between any two points.

-We only require," he says, *'to represent
this statement intuitively, to see quite clearly that
it holds good in all cases, that its contradictory
is impossible, that to all eternity the straight hne
is the shortest way. No one will think of warnmg
us to be cautious about this statement, or of saymg
that we have not yet collected enough experience
to make the assertion for all possible cases, and
that a crooked line might possibly in some cases
turn out the shortest. The statement is valid,
independently of all experience. We know forth-
with that it will remain true throughout all experi-
ence. The statement is a cognition a priori. Is
it analytical or synthetical ? That is the important

question."

This important question Kant argues by the

following argument:

**In the concept of a straight line, however
accurately we may analyze it, the representation of
being the shortest way is not contained. Straight
and short are diverse representations . . . the
judgment is therefore synthetical and synthetical

a priori,'^

We will look into these two diverse concepts
short and straight, and examine whether the diversity
is a real or only a verbal one. If it is real, then we
must allow that the judgment is a synthetical one,

^ Kant's Critique of Pure Reasojt (English translation), I. 406.

KANT'S DOCTRINE.

and is not founded on the law of Identity. But
what is the meaning of the shortest possible line
between two points ?

When we come to analyze it we find that it is
only another name for the single word distance.
Distance means the shortest possible distance. If
a man asks me the distance from Fastnet Point to
Sandy Hook, and I answer 10,000 miles, and after-
wards defend myself against the charge of mis-
statement by explaining that I do not mean the
shortest distance across the Atlantic, but one which
would include a visit to Madeira and Demerara and
the West India Islands on my way, I should be
justly regarded as a lunatic. The two expressions,
shortest distance and distance simpliciter, are syno-
nymous.

But what do we mean by distance ? We mean
that amount of space which has to be traversed in
order to go straight from one point to the other.
And what is the measure of this space ? Nothing
else than a straight line drawn from one to the
other.

Hence we have in the shortest distance merely
another name for the distance simply, and distance
has for its definition a straight line drawn from one
to the other point. The one expression is an analysis
of the other. The distinction between straight line,
a shortest line, is merely a verbal one, and our axiom
turns out to be an analytical proposition reducible to
the identical proposition. A straight line is one which
goes directly from one point to another. It is therefore
an analytical, not a synthetical proposition.

THE FOUNDATIONS OF LOGIC.

Or again let us take Kant's other instance :
** Given the arithmetical statement 7 + 5 = ^2.
It is inconceivable that 7 + 5 could ever make any
sum but 12. It is an a priori judgment. Is this
judgment analytical or synthetical ? It would be
analytical if, in the representation 7 + 5» 12 were
contained as an attribute, so that the equation would
be self-evident. But it is not so. 7 + 5. the subject
of the proposition, says ' Add the quantities.' The
predicate 12 says that they have been added. The
subject is a problem, the predicate its solution.
The solution is not immediately contained in the
problem. The sum does not exist in the several
terms as an attribute in the representation. If this
were the case, counting would be unnecessary. In
order to form the judgment 7 + 5 = 12, I must add
something to the subject, viz., intuitive addition.
The judgment is then synthetical and synthetical

a priori.''
■ To this argument we reply that in the first place
it confuses together the equational symbol and the
logical copula. The proposition 7 + 5 =112 does
not mean that 12 is the predicate, so that if the
proposition were an analytical one, it would be con-
tained in the subject 7 -h 5- It is a proposition of
equivalence or virtual identity, not of inclusion. It
means that five units + seven units are equivalent
to or virtually identical with twelve units. But,
passing this by, is it true that there is anything
added to the predicate which is not already con-
tained in the subject ? ** The fact of intuitive addi-
tion," says Kant. But this intuitive addition does

KANT'S DOCTRINE FALSE.

not any more exist in the proposition 7 -f 5 = 12
than it does in the mere statement of the number
seven. Seven means a certain number of units
" intuitively added " together ; but when we speak
of seven we do not add anything to these seven
units. We merely used a system of abridged nota-
tion. Seven means i-f i-f i-f iH-i-f i + i. Counting
is unnecessary in an addition sum, not because
the proposition expressing it is a synthetical one,
but because, our finite and feeble imagination being
unable to picture at once more than a very limited
number of units, we use numbers to express units
added together, and we use higher numbers to
stand for these lower numbers added together, and
to express in condensed form a greater crowd of
units than before. When we say to a little child,
as we point to the cows standing around the
milking-pail, "There is one cow and another cow
and another cow : three cows in all," we do not
make any ** intuitive addition" when we sum them
up as three. We either explain the word three,
or seek to fix the number on the childish memory
by the symbol three.

When, therefore, I say twelve, I mean 1 +
i-fi-f-i-fi-fl + i-fi-fi-fi + i-fi; when I say
seven, I mean i-hi + i + i + i + i-fi; when I say
five, I mean iH-i-fi-fi-fi; and when I enunciate
the proposition 7-1-5 = 12, I merely analyze the
several concepts, and putting together these several
concepts, I recognize as the result of my analysis
that twelve is the symbol for a number of units
identical with the number of units for which seven

THE FOUNDATIONS OF LOGIC.

is the symbol, in conjunction with those for which

iive is the symbol.^

In the same way, The whole h greater than each
me of its parts, is an analytical proposition. If we
analyze whole we find that it means -that which
contains more parts than one," while greater means
^^ that which contains more parts," and the propo-
sition is therefore equivalent to an analysis of the
concept whole, and so is a particular application of
the Law, All Being is its own nature.

Mathematics, then, rest on analytical a prion
propositions. They add nothing to them save a

X I cannot refrain from quoting Mr. Mill's argument against the
a priori necessity of numerical propositions, as an '^^'^"^^f^l'^f
mustrious philosopher's method : "The expression ' two Pebbles and
one pebble • (he says. Logic, i. 289) and the expression 'three pebbles
stand indeed for the same aggregation of objects, but they by no
means stand for the same physical fact. . . . Three pebbles m two
separate parcels and three pebbles in one parcel, do not make the
same impression on our senses, and the assertion that the very same
pebbles may. by an alteration of place and arrangement, be made to
produce either one set of sensations or the other, though a very
familiar proposition, is not an identical one. It is a truth known to
us by early and constant experience; an inductive truth, and such
truths are the foundation of the science of number.

This paragraph is an excellent example of Mr. Mill s style of
argument In order to prove that 2 + 1 = 3 is a Proposition
learnt from experience, he turns his numbers into pebbles and
arranges his pebbles into separate parcels. Then he puts the two
parcels and the one parcel side by side and quietly says: "Don t
you see that the two parcels produce a different sensation from the
one oarcel ? " He quietly introduces external differences of place
and arrangement and then appeals to these very differences to prove
his point. Besides, it is not question of concrete and materia facts
present to sense, but of abstract truth present to the \ntellect. To
bring in sensation and that which appeals to sensation is to bring in
a confusing element which of itself renders the argument valueless.

KANT'S DOCTRINE FALSE.

system of abridged notation, which is only a special
use of technical language. All the propositions of
Pure Mathematics, even the most abstruse and
complicated, are the elaboration of these first pro-
positions, and are all ultimately reducible to the
principle whence they proceed and on which they
depend.

We have taken these instances from Mathematics
partly because it is here that the attack is chiefly
made, partly because mathematical truths come
more directly than those of other sciences from
the Law of Identity, without the intervention of the
other primary laws of Contradiction, Causation, and
Excluded Middle. But we desire to remind our
readers that the same is true of all Propositions
belonging to the strictly a priori sciences. In Theo-
logy, Ethics, Psychology, Metaphysics, there is no
single proposition which may not ultimately be re-
duced to the Proposition — Every Being is its own
nature. All a priori intuitions beyond this are
condemned by the Law of Parcimony, which forbids
unnecessary assumptions. Our conclusion therefore
is that we are right in identifying analytical and
a priori propositions on the one hand, and synthe-
tical and a posteriori on the other, and this though
there are some distinguished names opposed to us.
The foundation of the error is the failure to recog-
nize the universal parentage of the Law of Identity
in the case of all propositions to which we neces-
sarily assent as soon as the meaning of the terms is
made known to us.

One difficulty remains. If all the propositions

THE FOUNDATIONS OF LOGIC.

of a priori science are but an analysis of the ideas
we already possess, how is it that by reason of them
we acquire fresh knowledge, and become mformed
of that of which we were ignorant before ? It seems
that we should never advance by sciences which add
nothing from outside to our store of knowledge.

This objection is solved by the distinction
between implicit and explicit knowledge. Explicit
knowledge is that knowledge which we possess in
itself and of the possession of which we are fully
conscious. Implicit knowledge is that knowledge
which is contained in, or is deducible from, know-
ledge already possessed by us ; but which we do not
yet realize as existing in our minds. We have not
yet deduced it from its premisses, or become aware

of its reality.

To take a famihar instance. I have often
asserted the proposition, nay, I regard it almost as
a truism, that All animals are possessed of feeling.
My acquaintance with zoology has moreover taught
me that All jelly-fish are animals. These two pro-
positions exist side by side in my intelligence.
But I am staying at a watering-place facing the
broad Atlantic, and one day, after a morning
spent among my books, I go for a sail on the
deep blue waters of ocean. As we scud along
before the favouring breeze, we pass through a
perfect shoal of jelly-fish floating in lazy helpless-
ness on the surface of the water ; and in a moment
of mischief, I drive my iron-feruled stick right
through the body of an unfortunate jelly-fish. After
the performance of this feat, I remark half-inquir-

IMPLICIT AND EXPLICIT KNOWLEDGE.

ingly to my companion : *' I wonder if this jelly-fish
feels being run through ! " and I make the remark
in all the sincerity of unsatisfied doubt. Yet all the
time I was in full possession of the two premisses :
A II animals are possessed of feeling, A II jelly-fish are
animals. From which, by the simplest possible form
of syllogistic reasoning, there follows the conclu-
sion: Therefore all jelly-fish are possessed of feeling.
But in point of fact I had never drawn that con-
clusion. My knowledge respecting the feelings of
jelly-fish was implied in knowledge I already pos-
sessed, but was not unfolded or deduced from it as
consequent from antecedent. It was implicit, not
explicit knowledge, and as long as it remained in
this implicit condition, it was unavailable for prac-
tical purposes.

When, however, reflecting on the matter, I call
to mind the premisses above stated, and from these
premisses proceed to draw their legitimate conclu-
sion, when I have realized not only that all
animals are possessed of feeling, and that all jelly-
fish are animals, but also that all jelly-fish are
possessed of feeling, then my knowledge enters on
a new phase, it has become explicit instead of
implicit, I am in possession of a fact that I had
never made my own before. Every rational being
has therefore an almost unlimited range of implicit
knowledge. One who has mastered the axioms
and definitions of mathematics, knows implicitly
all Euclid, algebra, trigonometry, the differential
calculus, pure mathematics in general. But he may
not know a single proposition explicitly. They have

' I'

THE FOUNDATIONS OF LOGIC.

all to be unfolded, argued out step by step. By
the study of mathematics no fresh facts are added
to our intellectual stock-in-trade, but we learn to
make use of facts unused before, to develope that
which was previously undeveloped, to dig up stores
of knowledge hitherto buried in our mental store-
house This is one reason why mathematics are so
valuable for educational purposes. They teach us
how to avail ourselves of our existing knowledge, to
employ properly an unlimited treasure lying hid
within us, and useless to us before.

What is true of mathematics, is true of all the
deductive sciences, of logic, ethics, theology, all
branches of knowledge which start from general
a priori principles, and argue down to particular
facts All their propositions are analytical, and
therefore are truisms in disguise. But it is these
truisms in disguise which make up the sum of all
truth that is necessary, and immutable.

CHAPTER V.
THE FOUNDATIONS OF LOGIC (continued).

III. Principle of Causation — Various meanings of Principle —
Cause active and immediate — Cause not invariable, uncon-
ditional, antecedent — Meaning of Event — Law of Sufl5cient
Reason. IV. Principle of Excluded Middle— Mill on Laws of
Thought— Mill's Principle of Uniformity in Nature— Fallacy
of Mill's argument— Principle of Uniformity Derivative —
Involves a Petitio Principii — Bain's Principle of Consistency
— Its suicidal scepticism.

In our last chapter we discussed the Law of Identity
in its relation to various kinds of Propositions. We
saw that it necessarily regulates all thought and
has a controlling power over every branch of know-
ledge. But we distinguished between the guiding
influence that it exerts over Inductive or experi-
mental sciences and the all-important position it
occupies in the Deductive or a priori sciences, of
which it is the fruitful parent as well as the supreme
master. We pointed out the difference between
a priori and a posteriori science and also be-
tween analytical and synthetical propositions. We
then inquired into the truth of Kant's assertion,
that the axioms of mathematics are at the same
time a priori and synthetical propositions, and
arrived at the conclusion that no such propositions
exist, but that all the propositions of a priori science

THE FOUNDATIONS OF LOGIC.

are finally reducible by analysis to the principle
that Every object of thought is identical with its own
nature. Finally, in answer to the difficulty that if
analytical propositions are mere Truisms they do
not add to our knowledge, we examined into the
distinction between explicit and implicit knowledge,
and showed how useful a part is played by the
analytical propositions of a priori science, and by
the deduction of conclusions from their premisses,
in rendering explicit and available the hidden fund
of implicit knowledge which hitherto was practically

useless to us.

We now come to the third of the Fundamental

Laws of Thought.

III. Principle of Causation.— The Principle
of Causation may be stated as follows :

Every event must have a cause; or. Everything that is
of such a nature that it can begin to exist must have
some source whence it proceeds ; or. Every change implies
Causation; or. Every product must have a producer.
What do we mean by the word cause in the Law
that we have just enunciated? This is not the
place to explain the various kinds of causes which
exist in the world. But for the better understand-
ing of our Law we must have a clear notion of the
kind of cause the necessity of which it enunciates.

We are not speaking here of the material cause,
or that out of which the object is made, as the
marble of a statue ; nor of the formal cause, or that
which gives to the material its determinate character,
as the design present in the sculptor's mind and

i'^

PRINCIPLE OF CAUSE.

expressed in the material statue ; nor of the final
cause, or the end for which the object is made, as
the amusement or profit of the sculptor. We are
speaking here of the efficient cause alone, of that by
the agency of which the object is produced, the
sculptor using the chisel as the instrument of his
work.

When, therefore, we say that every event has a
cause, we mean that everything that comes into exist-
ence in the world must be the result of some active
agent whose agency has produced it. This notion of
cause we derive from our own activity. We are con-
scious of being able to bring into being that which
did not exist before, and thence we derive our general
notion of efficient cause. We transfer our experience
of that which takes place in ourselves to the agents
around us, and assign to them the same sort of
efficiency, whatever it may be, which enables us to
produce new results.

Moreover, in every event that takes place there is
always some one agency or set of agencies which by
common consent is regarded as the cause of the
event. When a surgeon gives a certificate of the
cause of death, he states, not all the predisposing
circumstances which ended in death, but that one
circumstance which directly and proximately
brought about the fatal result. He does not state
all the unfavourable circumstances antecedent to
death. He simply chooses one of them which
was the one most prominent in producing the result.
Death may have been the resultant of a number
of circumstances, the absence of any one of which

'•

THE FOUNDATIONS OF LOGIC.

MEANING OF CAUSE.

would have prevented its occurrence. The patient
may have inherited a weakly constitution from his
parents, he may have had an attack of rheumatic
fever some months previously, he may have been
for some time working at an unhealthy trade, but
the physician does not enumerate these when he
states the cause of death. He states only the
immediate cause. Beside this, at the time of death,
a number of unfavourable coincidences may have
concurred to the effect. The patient may have
been insufficiently protected against the cold, he
may have been in a violent perspiration when
suddenly exposed to it, he may have been weakened
by want of sufficient food, but of these the certificate
of death as a general rule says nothing. They
are predisposing circumstances, but they are not active
agents in producing the result. The one circum-
stance given as the cause of death is acute congestion
of the lungs, because this, according to the ordinary
use of terms, was at the same time the immediate
and the active cause of death.

Mr. Mill, in his chapter on Causation, attempts
to throw dust into the reader's eyes by keeping out
of sight these two characteristics of an efficient
cause, viz., immediate influence and active influence.
He tells us, for instance, that we speak of the absence
of the sentinel from his post as the cause of the
surprise of the army, and that this, though a true
cause according to common parlance, is no true
producing cause. But his instance is a most mis-
leading one. The surprise of the army is another
name for the unexpectedness of the enemy's arrival.

and this is a negative idea. But a negative idea
is no event which comes into being. It simply
states the absence of a certain event, which in the
instance brought forward, is the previous expec-
tation of the foe, and its absence is accounted for
by the absence of that which would otherwise have
produced the effect, viz., the presence of the
sentinel at his post, who would under ordinary
circumstances have given notice of the enemy's
approach. The sentinel would have been the effi-
cient cause of the iiotice, but the absence of the
sentinel cannot be called the efficient cause of the
absence of the notice.

Similarly, when we say that the cause of the
stone's fall is the stone's weight, we do not mean
that the weight of the stone was the agent which
produced its fall. What we really mean is that the
attraction exercised by the earth according to the
law of gravitation, was the cause of its fall. But
this idea is not sufficiently popularized to have as yet
passed into common parlance. Just as the motion
of the earth does not prevent us from following
appearances rather than realities, and saying that
the sun has risen, so the fact that the active agent
is the attraction of the earth rather than the stone,
does not prevent us from following appearances
rather than reahties, and saying, in common par-
lance, that the weight of the stone is the cause of

its fall.

Cause therefore does not mean invariable, uncon-
ditional antecedent, for this ignores altogether the
necessity of active influence in producing the effect*

\ «

THE FOUNDATIONS OF LOGIC.

i-i 1

It ignores the dependence implied in the very word
effect. To say that the effect is that which in-
variably and under all possible, as well as actual,
circumstances follows on the cause, and that they
are merely two detached facts which co-exist in the
order of succession, is to belie the common con-
sensus of mankind and the very meaning of words-
Cause implies an activity in working out the effect,
a positive energy exerted in its production. Those
who would reduce our conception of cause to the
sense assigned to it by Mr. Mill ought in con-
sistency to declare that all things which come into
existence come into existence of themselves, for, if
effect does not imply the activity of an efficient
cause, if that which is produced no longer needs a
producer, the only alternative open to us will be
that the effects achieved the task of being authors
of their own being, and that all things which are
produced are self-produced.

But we are not here treating the subject of
Causation ex professo. We are merely explaining
what we mean by cause in the Law of Causation.
Unless this is clearly understood, the source from
which our law arises will not be sufficiently

apparent.

The Law of Causation, when carefully examined,
turns out to be the application to a special case
of the Law that Every Being is its own nature.
The idea of efficient cause is contained in the idea
of what is called Inceptive Being, or Being which
is of such a nature that it can begin to exist.
It makes no diff"erence whether we call it event.

LAW OF SUFFICIENT REASON.

effect, or change. The simplest form of this Law is
the proposition: Every effect has a cause; which is
equivalent to the proposition: Every effect is some-
thing effected or brought into being by an efficient cause ;
and this is merely a particular application of the
proposition : Every being is identical with its own nature.
If for effect we substitute event, the nexus between the
subject and predicate is a little less apparent. Event
is a fact or circumstance which proceeds from certain
pre-existing fact or facts. The mere word event
no less than effect implies that it has not existed
from all eternity (or at all events need not have
existed from all eternity),' and that it is dependent
for its being on its antecedent (in time or at least
in nature), that it comes from it, owes its being to
it, is brought into existence by it. The antecedent
therefore from which it proceeds, of which it is the
event or result, is not merely its antecedent but its
cause, to whose agency its existence as an event is
due. Hence in the form. Every event has a cause,
it may be reduced to the above Law, no less than in
the forms previously stated.

This Law is sometimes stated in another form
and invested with another name. It is sometimes
called the Law of Sufficient Reason, and expressed
in the formula: Everything existing has a sufficient
reason, or. Nothing exists without a sufficient reason.
The Law as thus formulated has a wider range than
the Law of Causation. The Law of Causation is

« This qualification is necessary on account of the opinion of
St. Thomas, that we cannot say that the creation of the world from
all eternity is intrinsically impossible.

THE FOUNDATIONS OF LOGIC.

PRINCIPLE OF EXCLUDED MIDDLE.

applicable only to things which are created, the Law
of Sufficient Reason to God the Creator as well. He
alone of all things that exist is uncaused. The
existence of God, though it has no cause, has a
sufficient reason in Himself. But the existence of
God is not a primary fact of Reason, and the law
which professes to account for His existence is not
one of the primary Laws of Thought. We have
first to prove the existence of a First Cause by
independent arguments. Having done this, and
having previously proved that all things save the
First Cause have a cause or reason of their exist-
ence outside of themselves, we are able to extend
our Law to all things whatever. After proving
that all things save God have a sufficient reason in
the efficient cause outside of themselves, and that
God as the First Cause has a sufficient reason of
existence in Himself, we combine the Creator and
His creatures under the universal Proposition, All
things that exist have a sufficient reason. But this
Proposition is no axiom or First Principle. It is
a complex Proposition which unites in itself the
axiom. Every effect has a cause, with the derivative
Proposition, The First Cause is Its own effect.

The reader will observe that the Law of Causa-
tion does not state (as some modern writers most
unfairly would have us believe) that Everything that
exists has a cause. In this form it is quite untrue,
since God is uncreated and uncaused. If it were
worded thus, the objection, that we first formulate
our universal law and then exclude from it Him on
Whom all existence depends, would be perfectly

valid. But this is entirely to misrepresent our posi-
tion. It is one of the unworthy devices of the
enemies of a priori philosophy.

IV. Principle of Excluded Middle. — The
fourth and last of these primary Laws of Thought
is the Principle of Excluded Middle. Everything
that is not A is not- A ; or, Every object of Thought is
A or not- A ; or. Whatever is excluded from A is included
in the contradictory of A ; or. Any two contradictories
exhaust the whole field of thought; or, Between two
contradictories there is no third alternative ; or, Of two
contradictories one or the other must he true.

This law, in all its various forms, is but an imme-
diate application of the Principle that we have
described as the foundation of all demonstration.
If we analyze the meaning of contradictory, we shall
find that it means, in reference to any concept,
whatever is not included in it. If we analyze not-A,\\Q
find as the result of the analysis not A, Hence our
law will run : The contradictory of any object is that
which is not included in that object. This is but a
particular application of the general law: All Being is
identical with its own essence. The other forms of the
Law are but the same proposition couched in different
language, and hidden under more complex words.

But in whatever form it be announced, we must
be careful that our two alternatives are contra-
dictories strictly speaking, else they will not exhaust
the whole field of thought and the axiom will appear
to fail. Thus holy and unholy, faithful and unfaithful,
easy and wieasy, are not contradictories, but con-

I i

THE FOUNDATIONS OF LOGIC.

trades, and it is not true to say that Everything is
either holy or unholy. A table or an elephant or a
syllogism is neither holy nor unholy. But it is true
to say that : Everything is either holy or not holy,
since not holy means not possessed of the attribute of
holiness, and this holds good of a table or a syllogism
just as much as of a wicked man.

These four fundamental principles of all thought
are not accepted by the modern experimental school
of whom John Stuart Mill is the most prominent
representative among the English-speaking nations.
The philosophy of experience professes to start from
a different basis altogether. It asserts the Laws of
Identity, Contradiction, and Excluded Middle to be
not primary, but derivative. They are but con-
clusions arrived at from one universal axiom which
lies at the foundation of all thought, of all investiga-
tion of Truth, of every intellectual process whatever.
This new sovereign which is set up in the place of
the time-honoured monarchs of the past, is the so-
called Principle of the Uniformity of Nature's action.
"This universal fact (says Mill), which is our warrant
for all inferences from experience, has been described
by different philosophers in different forms of lan-
guage : that the course of nature is uniform : that
the universe is governed by general laws. By means
of it we infer from the known to the unknown : from
facts observed to facts unobserved : from what we
have perceived or been directly conscious of, to
what has not come within our experience.'*'

» Mill, Logic, I. 343, 344.

MILL'S PRINCIPLE OF UNIFORMITY,

But the Principle of the Uniformity of Nature,
in spite of its world-wide dominion, is not, in the
opinion of Mr. Mill and the school of experience, a
monarch ruling by any a priori right or inherited
claim to power. We will give the Theory of the
Experimental School in their own language, and will
try and state it with a fairness that we think none
can question.

* The Principle of the Uniformity of Nature,' they
say, * is not, like the old-fashioned axioms of Contra-
diction and Identity, supposed to be antecedent of
its own nature to all experience. On the contrary,
it has no authority whatever beyond that which it
derives from experience. It rules only in virtue of
its nomination to sovereignty by the voice of expe-
rience. It is the elect of the people, chosen by the
unanimous vote of all the particular instances which
exist on the face of the earth.

* Not that this vast constituency can ever be
marshalled to assert its sovereign will. The Law
of Uniformity appears in and through certain
selected representatives who have authority to speak
on its behalf, and who in their turn elect other
subordinate rulers entitled Laws of Nature, on
whose partial authority, limited to their own
sphere, rests the universal law which knows no
limits in the existing Universe. Among these sub-
ordinate Laws of Nature, the School of Experi-
mental Philosophy classes the Axioms of Contra-
diction, Identity, Causation, and Excluded Middle.
These are experimental Truths, generalizations from
experience, inductions from the evidence of our

ill

THE FOUNDATIONS OF LOGIC.

senses. They receive confirmation at almost every
instant of our lives. Experimental proof crowds
in upon us in endless profusion ; the testimony m
their favour is so overpowering, they become so
deeply engraved upon our minds, that after a time
we regard the contradictory of them as inconceiv-
able. They are so familiar to us that they become
almost part of ourselves, and we regard as primary
and a priori axioms what are merely the results
of our uniform experience.' ^

But these inductions do not stop short at any
Axioms of Laws of Nature save one which is the
foundation of the rest. The fundamental Principle
of Uniformity, which rules every Induction, is itself
an instance of Induction, not a mere explanation
of the Inductive process. It is a generalization
founded on prior generalizations. It expresses the
unprompted tendency of the mind to generalize its
experience, to expect that what has been found true
once or several times and never has been found false,
will be found true again. It is thus the basis of all
our knowledge, the necessary condition of all Truth.
But how is this all-important principle attained
to in the Experimental System of Philosophy ? It
cannot be an immediate truth, an instinct which
is born in us, but of which we cannot give any
rational account, a mere blind and unaccount-
able conviction which we must assume as true
without any attempt to prove it. Whatever Reid
and certain other philosophers of the last century
may have asserted respecting it, the modern experi-

» Mill. Logic, I. 260. seq.

MILL'S PRINCIPLE OF UNIFORMITY.

mental school eagerly and very rightly repudiate
any such groundless assumption ; on the contrary,
it is only arrived at gradually by a careful process
of observation and experiment. We begin with
observing that a certain consequent always follows
a certain antecedent in a certain limited sphere of
our experience. We cannot, however, on the ground
of this observed sequence, assert any invariable
dependence of the consequent on the antecedent.
The connexion between the two must be tested by
a series of processes known to us as the Methods of
Induction y and of which we shall have to speak
hereafter. By means of these processes we must
separate off those cases in which the consequent
depends on the antecedent, from those in which
the presence of both antecedent and consequent
follows from certain co-existing circumstances on
which both depend. By these means we are able
gradually to extend the sphere within which the
sequence holds good. By eliminating whatever fails
of satisfying the required conditions, we are able to
declare, with a continually increasing confidence,
that not only under the circumstances observed, but
under all circumstances actual and possible, the
consequent will make its appearance wherever the
antecedent is to be found. What was at first a mere
empirical law has now become a law of nature, a
well-established generalization, which declares the
dependence of the consequent on the antecedent to
be invariable and unconditional, and that the rela-
tion between the two is therefore one of the ante-
cedent Cause to consequent Effect.

THE FOUNDATIONS OF LOGIC.

It is from the studv of these generalized
uniformities, these Laws of Nature, that we ad-
vance to that one all-embracing Law, that genera-
lization founded on all previous generalizations,
which is called the Law of Causation, or more
properly speaking, the Law of Naturc^s Uniformity
of Action, ^^hich asserts that throughout the whole
of the known universe there is an unbroken uni-
formity in Nature by reason of which every event
has a cause, and the same cause is always
followed by the same effect. The Law of Cau-
sation is thus no a priori law, no instinctive
assumption incapable of proof. It is no con-
elusion arrived at from a mere enumeration ot
affirmative instances. It is based on a long and
careful induction. It is the major premiss of all
inductions, yet itself the widest of all inductions.
It is not the result of any mere formal inference,
but of an inference carefully tested by methods
which ensure its validity as a method of legitimate
proof It is arrived at by generalization from many
laws of inferior generality. We never should have
had a notion of Causation (in the philosophical
meaning of the term) as a condition of all pheno-
mena, unless many cases of causation had previously

been familiar to us.

Thus by a process of '' informal inference we
mount up step by step from our first observed
uniformities, limited and unreliable outside their
own sphere, to a firmly-grounded conviction of that
final and all-embracing uniformity which pervades
the whole world. The proposition that The course

FALLACIES OF THE EXPERIMENTAL SCHOOL. 85

of nature is uniform, while it is the fundamental
principle of all Inductions, is itself an instance of
Induction, and Induction of by no means the most
obvious kind. It is one of the last inductions we
make, or at all events, one of those which are latest
in attaining strict philosophical accuracy.'

Such is the account given by the experimental
philosophy of the all-pervading Principle of the
Uniformity of Nature, and of the means by which
it is arrived at. At first sight it appears plausible
enough, and when stated by Mr. Mill with that
power of clear exposition and apt illustration by
which he conceals from the reader the underlying
fallacies of his system, it is difficult not to be led
away by his well-chosen language and attractive
style. But when we look closely into the processes
by which instances are tested and laws deduced
from facts, we find that it is unhappily exposed to
the fatal objection, that it implies from the very
outset the existence of the very Law which it pro-
fesses to prove. It covertly assumes from the
beginning the truth of its final conclusion. Warily
indeed and stealthily does it impose upon us the
carefully disguised petitio principii that it involves —
nay, with ingenious but not ingenuous candour the
Coryphaeus of the school warns his readers* that
the process of his argument at first sight seems
to be liable to this very charge. He takes the
wise precaution of guarding himself against attack
by pointing out an apparent weakness on a sub-
ordinate point where in truth there is no weakness
» Mill's Logic, I. 343—401, and passim. ^ Mill, Logic, II. 95.

THE FOUNDATIONS OF LOGIC.

at all, and thus he seeks to divert the assailant from
the real weakness which is inherent in his whole
system. We must try and explain, in as few words
as possible, where lies the vulnerable point of this
carefully-guarded Achilles.

It is quite true, as Mr. Mill remarks, that there
is no petitio principii in the early assumption that
cases in which the general law is obscure really
come under it, and will on closer investigation make
it manifest as the principle underlying them. This
assumption is a necessary hypothesis to be after-
wards proved. Here the process is unassailable.
But it is in the course of the investigation, in the
proof by which the existence of the universal Law
is established, that the unwarranted assumption is
made. The test by which a true dependence of
consequent on antecedent is distinguished from one
which exists only in appearance, is one that assumes
that very dependence as an existing reality. When
the experimentalist asserts that he is going to lay
down certain tests to discover where the Law of
Causation is at work, he thereby implies the existence
of the Law. The distinction between sequences
which depend on the antecedent, and sequences
which depend on other co-existent circumstances,
has no meaning whatever unless we assume that
the Law of Causation prevails throughout the

Universe.

If I formulate a series of tests which are to
distinguish between inherited and acquired ten-
dencies, and to mark off real instances of inherit-
ance from those which are so only in appearance,

FALLACIES OF THE EXPERIMENTAL SCHOOL. 87

I thereby assume that there is the law of Heredity
prevalent in the world. If I explain in detail the
various characteristics which separate real gold
from ormolu ; if I propose a number of unfailing
signs of the genuine metal which are lacking in the
counterfeit : if I say that true gold is not affected by
hydrochloric acid, that it is of greater weight than
any of its imitations, and that it is malleable to an
extent unknown to any other metal ; I am all the time
taking it for granted that such a thing as real gold
exists. If, after the distinction is made in a number
of instances by means of the tests proposed, I go
on to argue that it is evident that true gold exists
because it fulfils the tests, I am obviously arguing in

a circle.

In just the same way, the methods which Mr.
Mill has rendered famous assume beforehand that
for every consequent there is a cause, or, as he
calls it, an invariable unconditional antecedent,
and that we have only to pursue with deliberate
care the methods proposed in order to recognize the
connection between antecedent and consequent in
each individual case. We are to begin by looking out
for "regularity" in particular instances as the test
by which we are to recognize them as coming under
the universal law and forming subordinate examples
of it, and when we have collected the instances and
formulated the law, we are expected to turn round
and say with all the joy of a hardly-won discovery
in the field of Thought: See how the Law of
Causation which establishes for us the Uniformity
of Nature is proved by our universal experience!

THE FOUNDATIONS OF LOGIC.

FALLACIES OF THE EXPERIMENTAL SCHOOL. 89

quite forgetting that the treasure which we profess
to have come upon thus unexpectedly and which is
to enrich all future ages, is but one which we
ourselves had brought and hidden there, taken out
of the very storehouse where we are now proposing
to lay it up in triumph.

The fallacy which thus underlies the First
Principle of the so-called Experimental Philosophy
naturally vitiates the whole system from first to last.
There is not a corner of the house that these
philosophers have built up where we can rest with
safety. They have put together their bricks and
rubble into a solid mass on which the super-
structure rests, but what is the basis on which
reposes the foundation of the edifice? It is the
workmanship and the excellency of the selected
bricks which is supposed to provide a secure foun-
dation. But however well chosen the bricks, they
cannot remain suspended in mid-air. They cannot
develope for themselves a basis out of their own
activity. Yet this is the aim of the experimentalist.
Given his methods of inquiry and he engages to
create or manufacture therefrom a First Principle
which shall be at the same time the foundation and
the culminating-point of all philosophical inquiry.

It was not to be expected that the other Primary
Axioms which underlie all processes of Thought
would fare any better at the hands of the Experi-
mentalists than the Law of Causation. Just as this
Law is to be built up by a process which takes it
for granted, so the Law of Contradiction is arrived
at by another process which in just the same way

has already assumed as true the very point that we
have to prove. We will quote Mr. Mill's account
of it in his own words. Speaking of the Law of
Contradiction, he says : '' I consider it to be like
other axioms, one of our first and most familiar
generalizations from experience. The original
foundation of it I take to be, that Bdief and
Disbelief are two different mental states, excluding
one another. This we know by the simplest observa-
tion of our own minds. And if we carry our observa-
tion outwards, we also find that light and darkness,
sound and silence, motion and acquiescence, equality
and inequality, preceding and following, succession
and simultaneousness, any positive phenomenon
whatever and its negative, are distinct phenomena,
pointedly contrasted, and the one always absent
where the other is present. I consider the maxim
in question to be a generalization from all these

facts." ^

Now, in the very statement of my conviction
that belief and disbelief are mental states excluding
one another ; in the mental assertion that light and
darkness, sound and silence, &c., are incompatible ;
I have already implicitly assumed the very principle
at which I am supposed to arrive by the observa-
tion of my own mind, or by an argument from my
own experience. If the Proposition Belief excludes
Disbelief, is to have any value whatever, I must
intend, at the same time, to deny the compatibility
of Belief and Disbelief, else my Proposition is
simple nonsense. If I declare that it is the result of

« Mill's Logic, Vol. I. pp. 309. 3io-

: I

THE FOUNDATIONS OF LOGIC.

my experience that light expels darkness, such a
declaration has no force if it may be equally true
that light does not dispel darkness. Unless contra-
dictions exclude one another, no statement that
we make is of any value whatever. As we have
seen above, the Law of Contradiction is already
implied in every possible statement made by any
rational being, and therefore to establish its validity
by means of certain propositions we are to derive
from experience is a still more obvious fallacy than
that by which the Empirical Philosopher seeks to
arrive at the Law of Causation and the Uniformity
of Nature.

We shall have to recur to the Experimentalist
Theory of Axioms when we come to discuss the
nature of Induction. We will close our present
chapter with a few words on another Universal
Axiom set up by one whose doctrines are closely
akin to those of Mr. Mill.

Mr. Bain includes under one head the three
Principles of Identity, Contradiction, and Excluded
Middle. They are all of them *' Principles of Con-
sistency," inadequate expressions of the general law
that is in our reasoning as well as in our speech,
that "What is affirmed in one form of words shall
be affirmed in another." This principle, he says,
and says with truth, requires no special instinct
to account for it; it is guaranteed by the broad
instinct of mental self-preservation. But when he
goes on to add that ''it has no foundation in the
nature of things, and that if we could go on as well
by maintaining an opinion in one form of words,

BAIN'S PRINCIPLE OF CONSISTENCY.

while denying it in another, there appears to be
nothing in our mental constitution that would
secure us against contradicting ourselves," he ex-
hibits in a still more undisguised and open form,
the scepticism which underlies the system of Mr.
Mill If the Axioms of Consistency are Axioms ot
Consistency alone, and not of Truth, if they express
merely the subjective tendencies of our own mmds,
and not any external reality. Truth disappears alto-
gether from the Philosophy which is based on such
foundations as these. We have already seen that
the new basis which both philosophers attempt to
substitute in the Uniformity of Nature's laws ascer-
tained by our own experience, involves the fallacy
of assuming by way of proof the very conclusion
which is finally arrived at. The Principle of Con-
sistency adds nothing new to the system enunciated
by Mr. Mill, save a novel and plausible method of
throwing dust into the eyes of the unwary.

CHAPTER VI.

THE THREE OPERATIONS OF THOUGHT. I. SIMPLE

APPREHENSION.

Recapitulation— The three operations of Thought— Simple Appre-
hension, Judgment, Reasoning— Three Parts of Logic— Terms,
Propositions, Syllogisms— Simple Apprehension— The steps
leading to it— Previous processes — Abstraction — Abstraction
and Simple Apprehension— The Concept an Intellectual image
—The Immaterial Phantasm and Concept— Phantasm and
Concept contrasted— Concept not pictured in the imagina-
tion—Concept ideal and spiritual— Concept accompanied by
Phantasm— Points of difference between the two — Common
Phantasms — Their individual character — Their origin —
Common Phantasm counterfeit of Universal idea.

We must recapitulate the substance of our last two
chapters before we proceed. We commenced by
laying down the Law of Contradiction and the
Law of Identity. The latter we described as the
basis of all positive reasoning and the parent of all
a priori Propositions. From these Primary Laws
we passed on to another fundamental Law, the
Law of Causation, defining carefully what sort of a
cause is alluded to in it. Last of all we laid down
the Fourth of this compact family of First Prin-
ciples, the law of Excluded Middle which, like the
Law of Causation, proceeds immediately from the
Law of Identity. We then examined the First

SIMPLE APPREHENSION.

Principle, which Mr. Mill and the Experimental
School propose to substitute for the Laws above
stated, and we detected in the process by which he
establishes it, the unfortunate fallacy of assuming
implicitly the very proposition which it professes to

prove.

Having thus laid our foundations, we must now
commence the building up of our Logical Edifice.

We have already seen that Logic is a science
which is concerned with the operations of Thought,
and the Laws that regulate them. In the begin-
ning of our inquiry,! we ascertained that every
exercise of thought, properly so-called, consists in
apprehending, judging, reasoning. We have now to
examine into the nature of these three operations,
since with them, and them alone, is Logic concerned.
The First of these operations of Thought is
called Simple Apprehension, or Conception (v6'n<rc<:).
The Second is called Judgment, or Enunciation

The Third is called Reasoning, or Deduction, pv
Discourse (avWojLcrfiof;).

I. Simple Apprehension is that operation of Thought
by which the object presented to us is perceived by
the intellectual faculty. It is called Apprehension,
because by means of it the mind, so to speak,
apprehends or takes to itself the object ; and Simple
Apprehension, because it is a mere grasping of the
object without any mental statement being recorded
respecting it. It also bears the name of Conception,
because the mind, while it apprehends the external

« P. 6.

SIMPLE APPREHENSION.

OPERATIONS OF THOUGHT.

object, at the same time conceives or begets within
itself the object as something internal to itself, in so
far as it is an object of Thought.'

2. Judgment is that operation of Thought by
which the identity or diversity of two objects of
Thought is asserted, by which one object of Thought
is affirmed or denied of another. It is called Judg-
menty because the intellect assumes a judicial atti-
tude, and lays down the law, or judges of the objects

before it.

3. Reasoning, or Deduction, or Inference, or
Argumentation (or as it is called in Old English
Discourse), is that operation of Thought by which
the mind infers one judgment from another, either
immediately, or mediately, by means of a third
judgment. It is called Reasoning, inasnmch as it
is the exercise of the faculty of human reason;
Deduction, inasmuch as it is a drawing {de ducere) of
one judgment from another; Inference, inasmuch as

» The word Conception is liable to mislead the unwary student,
especially if he has first encountered it in a non-Catholic text-book.
Almost all modern schools of philosophy outside the Church
describe conception as deriving its name from their own false
account of the process. They make it an act of the imagination,
not of the pure intellect, of a faculty which is dependent on matter,
not of one which is wholly immaterial. Hence they represent it
as a gathering together, a taking into one {con capcre) of the various
attributes, which we discover in a number of different objects, and
which, according to them, we unite together to form the intellectual
notion which stands for each and all of them, and represents their
common nature. We shall have to refute this error presently in
speaking of the process of Simple Apprehension, and of the nature
of Universals; at present we simply direct the attention of the
reader to the false theory which the word Conception is quoted to
confirm.

it brings in (infert) a judgment not made explicitly
before ; Discourse, inasmuch as it is a running hither
and thither of our minds {dis currere) in order to

arrive at truth.

Each of these operations of Thought has more-
over a certain result or product which it engenders
within the mind. This is the end or object to
which it tends, the child of which it is the intellec-

tual parent.

Si7nple Apprehension {evv6r}<TL<;, evvoia) engenders
the idea or concept {evv6r)^a) which is so called as
being the mental likeness, or aspect, or appearance
{IZea) of the external object which Thought conceives

within the mind.

Judgment (uTroc^ar/crt?) engenders the judgment
or declaration (\6yo^ d7ro</)ai/Tt/co9, or a'ir6(j)avaL^)
which derives its name from its being the declaration
or setting-forth of the agreement or disagreement
between two objects of Thought.

Reasoning (to XojL^eadaL, BLavoia) engenders the
argument {avWoyLO-fio^), or conclusion (avfiirepaafia),
or inference, the various names of which express
the fact that it proves {arguit) some point, that it
reckons together {avv Xoyl^erai) two judgments from
which it deduces or infers the conclusion following

from them.

The Science of Logic therefore naturally divides
itself into three parts, corresponding with the three
operations of Thought.

Part I. treats of Simple Apprehension, or Con-
ception, or Thought, apprehending its object,
and thus engendering the concept or idea.

SIMPLE APPREHENSION.

Part II. treats of Judgment, or Enunciation, or
Thought, pronouncing sentence, and thus
engendering the declaration.
Part III. treats of Reasoning, or Deduction,
or Inference, or Thought deducing one judg-
ment from another, or thus engendering the
argument.
But the task of Logic does not end here. Thought
must find expression in words. The very Greek
equivalent of Thought (X0709) stands equally for the
verbal expression of Thought. Without some sort
of Language Thought would be, if not impossible,
at least impeded and embarrassed to a degree which
it is difficult for us to estimate. We should lack a
most valuable instrument and auxiliary of Thought.
We should not be able to communicate our thoughts
to each other, or to correct our own mental ex-
periences by the experience of others. Thought
. and language are mutually dependent on each other.
A man who talks at random is sure also to think at
random, and he who thinks at random is on the
other hand sure to be random in his language. In
the same way accuracy of Thought is always ac-
companied by accuracy of language, and a careful
use of words is necessary to and promotive of a
careful and exact habit of thought.

Logic, then, is indirectly concerned with Lan-
guage; its subject-matter being the operations of
Thought which find their expression in language.
It has to deal with Language just so far as its inter-
ference is necessary to secure accuracy of Thought,
and to prevent any misuse of words as symbols of

SIMPLE APPREHENSION.

Thought. Just as one who is entrusted with the
training or care of the minds of the young, cannot
pass over or neglect the care of their bodily health,
if the mind is to be vigorous and healthy in its
action, so a science which has jurisdiction over
Thought, cannot afford to leave unnoticed the
external sign or symbol in which Thought finds
expression, and with which it stamps its various
products.

Hence the first part of Logic treats of the Concept
as expressed in the spoken or written Word or Term;
the second part, of the Judgment as expressed in the
Proposition; the third, of the Argument as expressed
in the Syllogism,

PART I.— OF SIMPLE APPREHENSION OR CONCEPTION.

Simple Apprehension or Conception is that opera-
tion of Thought by which the intellect apprehends
some object presented to us. It is the act
by which we attain to a general and undefined
knowledge of the nature of the object, and have
present to our mind in a general way that which
makes it to be what it is, leaving a more specific
knowledge, a knowledge of its essence in its details,
to be gained by subsequent reasoning and reflection.
It includes no sort of judgment respecting the
object thus apprehended, except, indeed, the impHcit
judgment that it contains no contradictory attri-
butes, since anything which contradicts itself is in-
conceivable, that is, cannot be grasped by the mind as
an actual or possible reality. It is the intellectual
H

SIMPLE APPREHENSION.

contemplation of the essential attributes of the object;
the perception of its substantial nature.

We are not concerned with any elaborate
analysis of the process itself, since this falls rather
under Psychology than under Logic ; but for clear-
ness' sake, we must briefly summarize the various
steps by which the concept is reached, and the mner
nature of the object apprehended by the human

intellect.

When any object is presented to us, and we
turn our minds to the consideration of it, the first
thing that comes before us is the sensible impression
made upon the inner sense or imagination. There
is painted upon the material faculty of the imagina-
tion an image, more or less distinct, of the object
to which we turn our attention. This image is
either transferred from our external senses to the
faculties within us, or else is reproduced by the
sensible memory recalling past impressions. If any
one says to me the word '' pheasant," and I hear
what he is saying, a vague general picture of a
pheasant, copied from the various pheasants I have
seen, is present to my imagination. So far, this
is no strictly intellectual process. Animals share
with man the faculty of imagination, and can call
up from their memories a vague image of familiar
objects. When I scratch unperceived the floor of
my room, and call out to my terrier, " Rat ! " there
rises up in his mind an incfistinct picture of the
little animal that he loves to destroy. When the
foxhound comes across the fresh scent on the path
which Reynard has but recently trodden, the con-

PROCESS OF APPREHENSION.

fused image of a fox comes up before him, and
suggests immediate pursuit. All this is a matter
of the interior sense ; for there is no intellectual
activity in the lower animals; they rest on the
mere sensible impression and cannot go beyond

it.

But an intellectual being does not stop here.
The higher faculties of his rational nature compel
him to proceed a step further. He directs his intel-
lectual faculties to the sensible image and expresses,
in his intellectual faculty, the object which caused the
image, but now in an immaterial way and under an
universal aspect. This character which the object
assumes in the intellect is the result of the nature
of the intellect. Quicquid recipitur, recipitur secundum
modum recipientis. Whatever we take into any faculty
has to accommodate itself to the nature of that
faculty. Whatever is received by the intellect must
be received as supra-sensible and universal. I mean
by supra-sensible something which it is beyond the
power of sense, outer or inner, to portray, something
which cannot be painted on the imagination ; some-
thing which belongs to the immaterial, not the
material world. I mean by universal something
which the intellect recognizes as capable of belong-
ing not to this or that object only, but to an
indefinite number of other objects, actual or possible,
which have the same inner nature, and therefore a
claim to the same general name. The individual
representation or phantasm which belongs to sense
and to sense alone, is exchanged for the universal
representation, or concept, or idea, which the intellect

100

SIMPLE APPREHENSION.

alone can form for itself by the first operation of
Thought properly so called.

We shall perhaps be able better to understand
the process of Simple Apprehension if we distinguish
it from certain other processes which either are
liable to be mistaken for it, or are preliminary steps
which necessarily precede it.

1. Sensation, the act by which we receive on
some one or more of the external organs of sense,
the impression of some external object presented to
it. The object producing the sensation may be alto-
gether outside of us, or it may be a part of our own
bodies, as when I see my hand or feel the beatings

of my pulse.

2. Co7isciousness, the act by which we become
aware of the impressions made upon our senses
and realize the fact of their presence. Every day
a thousand impressions are made upon our bodily
organs which escape our notice. We are not
conscious of their having been made. We have
heard the clock strike with our ears, but have
never been conscious of the sound. When our
mental powers are absorbed by some interesting
occupation, or by some strong excitement, almost
any sensation may pass unnoticed. In the mad
excitement of the battlefield men often receive
serious wounds and are not aware of the fact till
long afterwards.

3. Attention, by which the faculties are directed
specially to one object, or set of objects, to the
partial or complete exclusion of all others. The dog
following the fox has his attention directed almost

PREVIOUS PROCESSES.

101

exclusively to the fox he is pursuing and seems to
forget all else. The soldier in battle has his atten-
tion absorbed by the contest with the foe, and for
this reason his wound passes unobserved.

4. Sensible perception, the act by which the data
of the external senses are referred to an inner sense
which has the power of perceiving, comparing
together, and writing in one common image, all the
different impressions made on the various organs of
sense ; whence it obtains the name of the *' common
sense " (sensus communis). Sensible perception always
implies some sort of consciousness and memory.
A dog sees a piece of sugar ; this draws his atten-
tion to it and he becomes conscious of the impres-
sion (using the word in a wide sense) upon his
organs of sight. Next he smells it, and if not
perfectly satisfied as to its nature, applies his tongue
to it to discover its taste. He then compares together
the various impressions of sight, smell, and taste,
by an act of sensible perception, and the resulting
image is that of a piece of sugar good for food.

5. Memory (sensible), which recalls the past by
reason of the presence within us of certain sensa-
tions which recall other sensations formerly experi-
enced. A certain perfume recalls most vividly some
scene of our past lives; a familiar melody stirs
emotions long dormant; the fresh morning air
brings with it the remembrance of some exploit of
boyhood or of youth. The memory of animals is
exclusively a sensible memory dependent on sen-
sation.

6. Imagination, which paints upon the inner

102

SIMPLE APPREHENSION.

sense some picture, the scattered materials of
which already exist within us. It is the faculty
which reproduces the sensible impressions of the
past. It is able, however, to group them afresh,
and to arrange them differently. In this it differs
from the (sensible) memory which reproduces the
impressions of the past just as they were originally
made. In dreams the imagination is specially active.
Hitherto we have included in our list various
processes which belong to the faculties of sense
common to man and the lower animals. We now
come to those which belong to man alone, to the
processes of Thought strictly so called. We have
said that the first and simplest of these is that
of Simple Apprehension or Conception. But there
is a preliminary process which is not really dis-
tinguishable from Simple Apprehension, and differs
only in the aspect under which it presents itself

to us.

We have spoken of A ttention as a concentrating

of our faculties on some one object to the exclusion

of others. The object on which we concentrate

may be an object having an independent existence,

or it may be some quality or qualities out of the

many qualities belonging to something which is

present to our minds. In this latter sense it is

often called A bstraction, inasmuch as it is the draw-

ing away of our attention from some qualities in

order to fix it upon others. I may abstract from

the whiteness of a piece of sugar and fix my mind

upon its sweetness. I may abstract from whiteness

and sweetness and concentrate my attention on

ABSTRACTION.

103

its crystallization. I may abstract from whiteness
and sweetness and crystallization and mentally con-
template its wholesomeness for little children.

But Abstraction has a further meaning which
includes all this, and goes beyond it. In every
object there are certain qualities which may or may
not be there without any substantial difference being
made in its character. There are others, the absence
of any one of which would destroy its nature and
cause it to cease to be what it is. A man may be
tall or short, young or old, handsome or ugly, black
or white, virtuous or vicious, but none the less is he
a man. But he cannot be deprived of certain other
qualities without ceasing to be a man. He cannot
be either rational or irrational, living or dead, pos-
sessed of that form which we call human, or of
some other entirely different one. If he is not
rational, living, possessed of human form, he ceases
to be a man altogether, because these latter qualities
are part of his nature as man, constitute his essence,
and make him to be what he is, a man.

Now, Abstraction in this further sense is the
concentration of the intellect on these latter qualities
to the exclusion of the former. It is the withdrawal
of the mind from what is accidental to fix it upon
what is essential, or, to give the word a slightly
varying etymological meaning, it is the intellectual
act by which I draw forth (abstrahere) from the indi-
vidual object that determinate portion of its nature
which is essential to it and is said to constitute its
essence, while I neglect all the rest.

In this sense it is the same process as Simple

104

SIMPLE APPREHENSION.

Apprehension regarded from a different point of
view. It is called Apprehension inasmuch as the
intellect apprehends or grasps the nature of the
object. It is called Abstraction inasmuch as the
nature is abstracted or drawn out of the object
whose nature it is, and as it cannot be grasped
until the intellect has drawn it forth from the object,
Abstraction is, at least in thought, a previous process
to Simple Apprehension.

Thus, when a horse is presented to me, Abstrac-
tion enables me to withdraw my mind from the fact
of his being race-horse or dray-horse, chestnut or
grey, fast or slow trotter, healthy or diseased, and
to concentrate my attention on that which belongs
to him as a horse, and thus to draw out of him that
which constitutes his essence and which we may
call his equinity. In virtue of my rational nature
I fix my mental gaze on that mysterious entity
which makes him what he is, I grasp or
apprehend his equinity, I perceive intellectually
that hidden something which is the substratum of
all his qualities, the root whence the varying
characteristics which mark him out as a horse all
take their origin. It is in the assertion of this
faculty of Abstraction, as the power of drawing
out of the object something which is really there
independently of the mind that draws it forth, that
consists the whole distinction between scholastic
and the so-called modern philosophy. It is in the
definition of Simple Apprehension as not merely
the grasping into one certain qualities of the object
selected by the mind, but the grasping by the mind

RESULT OF THE PROCESS.

105

of an objective reality in the object, whence certain
qualities flow quite independently of the mind which
apprehends them, that consists the central doctrine
which gives to the philosophy of the Catholic Church
a bulwark against the inroads of scepticism, impos-
sible to any system which has lost its hold on this
central and vital truth. Modern error starts with
misconceiving the very first operation of Thought :
with such a foundation we cannot expect the super-
structure to be remarkable for solidity.

From the process of Simple Apprehension we
must now turn to the result of the process, from
the act to that which the act engenders, from con-
ception to the concept.

We have seen that whatever is received into
any faculty has to accommodate itself to the nature
of the faculty, and consequently that the image of
the external object received into the intellect must
be something supra-sensible and spiritual. It has
been grasped or apprehended by the intellect, and
transferred so to speak into it, and it has conse-
quently been purified of the materiality cHnging to
the image present to the imagination, and prepared
for its abode in the sphere of immaterial Thought.
It is thus no longer the representation of one single
object and no more; it is now applicable to each
and all of a whole class of objects ; it is no longer
a particular, it is an universal. It is not the sensible
image stripped of those attributes peculiar to the
individual as such and apphcable to a number of
objects by reason of its vagueness. It belongs to
quite a different sphere; it is raised above the

SIMPLE APPREHENSION.

io6

Thought properly so called.

This distinction between the two images--the

sensible image painted on the ^-^^^^f ;^."J"^.f;f
supra.sensible image dweUing m ^^e mtellect-is o^^
the greatest importance. The sensible image must
precede the supra-sensible ; we cannot form a con-
cept of any object unless there has been previously
Srinted on the imagination a material impression
of that object. The sensible image must, moreover
exist side by side with the supra-sensible : the one on
th imaginltion, the other in the intellect ; and as
ong as I am thinking of the intellectual concept, the
material phantasm must be present to my imagma-
tion TWs is the result of the union of soul and
body; in virtue of my animal nature the phantasm
is present to the material faculty, and m virtue of
my rational nature the concept is present to the
intellectual faculty. When I think of a tnangle my
intellect contemplates something which is above
sense, the idea of triangle, an ideal triangle if you
like, and at the same time my imagination has
present before it the material picture of a triangle.
The intellectual image is something clear, precise,
exact, sharply marked without any defects or
deficiencies. The material image is something
vague, indistinct, indefinite, and applicable to a
number of individuals only by reason of its indistinct-
ness and indefiniteness. The intellectual concept
I form of triangle is as precise as anything can be.
I know what I mean in every detail belonging to it.
I can define it and set forth all its characteristics

CONCEPT AND PHANTASM.

107

one by one with perfect correctness. The picture of
** triangle " present to my imagination is the reverse
of all this, it is dim, imperfect, undetermined. It
is neither isosceles, rectangular, or scalene, but a
sort of attempt to combine all these. If in order
to give it definiteness, I picture not only triangle,
but isosceles triangle, still I have to determine
whether the angle at the vertex shall be an obtuse
angle, a right angle, or an acute angle. Even if I
introduce a fresh limitation and decide on the acute
angle I am not much better off, my picture is still
quite indeterminate, for the sides must be of a
certain length, it must be drawn in a certain position,
and some colour must be chosen for the sides. But
however many limitations I introduce, I cannot be
perfectly determinate until I have thrown away
altogether every shred of generality belonging to
the triangle and am satisfied with some one indi-
vidual triangle with individual characteristics belong-
ing to itself and to no other triangle in the world.

But there is another important distinction
between the immaterial concept in the intellectual
faculty and the material phantasm in the imaginative
faculty. If I examine the latter I not only find that
it is vague and indistinct, but that it is not a true
representation of the object ; it is not what it pro-
fesses to be. The picture of triangle which is present
in my imagination is not, strictly speaking, a triangle
at all. For the sides of a triangle are lines, i.e,,
they have length but not breadth, whereas in the
picture of a triangle as imagined, or actually drawn,
the sides are not lines at all, but good thick bars of

io8

SIMI ; APPREHENSION.

appreciable breadth. If they were lines they would
be invisible, not only to the naked eye, but to the
most powerful microscope. Worse still, they are
not even straight ; they are wavy bars with rough
jagged edges. They have no sort of pretence to
be called straight lines, nor has the so-called triangle
any real claim to the name.

Not so the intellectual concept formed by the
process of Simple Apprehension. The image is
purged of its materiality when it is adopted by
the immaterial faculty ; it is also purged of all its
indefiniteness and incorrectness. It is an ideal
triangle; it is worthy of the noble faculty that
has conceived and brought it forth. It is not a
clumsy attempt at a triangle, with all the imperfec-
tions which cling to the figure depicted on the
imagination, or drawn on paper or on wood;
which for practical purposes serves the purpose
of a triangle, but has no true lines for its sides,
and is crooked and defective in every portion of it.
It is a true, perfect, genuine triangle, dwelling in
the spiritual sphere, the sphere of what philosophy
calls noume^m, things capable of being intellectually
discerned, as opposed to phenomena or mere appear-
ances. When I argue about the properties of a
triangle, it is about this ideal triangle that I argue,
else nothing that I said would be strictly true. I
argue about something which in point of fact, has
nothing corresponding to it in the world of pheno-
mena, only feeble attempts to imitate its inimitable
perfections. When I assert that an equilateral
triangle has all its sides and angles equal, I do

CONCEPT AND PHANTASM.

109

not assert this in reality of the triangle A B C, or
the triangle D E F, or any triangle that I have ever
seen with my bodily eyes, but of an ideal equilateral
triangle, which is not realized in the world of sense,
but is realized with the utmost precision in the
world of intellect. When I say that the radii of a
circle are all equal, I do not mean that any circle
has ever been drawn by the most skilful limner in
which any two radii were ever exactly equal, but
that in the ideal circle the ideal radii are actually
equal, and that in the attempts to draw a circle on
the blackboard, or on paper, or on the imagination,
the so-called radii are approximately equal, in pro-
portion as the circle approximates to an ideal circle,
and the radii to the ideal radii of that ideal circle.
It is true that the geometrician cannot pursue
his researches without palpable symbols to aid him.
This is the consequence of our intellect inhabiting
a tenement formed of the dust of the earth. We
cannot think of an ideal circle and its properties
without at the same time imagining in vague fashion
a circle which can be rendered visible to the eye.
It is because of this that intellectual activity so
soon fatigues. It is not the intellect which wearies
but the material faculty of the imagination which
works side by side with the intellect. Very fev.
men can argue out a single proposition of Euclid
by means of a triangle present only to the imagi-
nation, and they therefore draw a picture which
appeals to the external sense, in order to save their
imagination the impossible task of keeping before
the mind its own imaginary triangle. But whether

SIMPLE APPREHENSION.

CONCEPT AND PHANTASM.

Ill

the symbol be drawn on paper or on the imagina-
tion we must remember that it is not about the
symbol that we argue, but about the corresponding
image in the immaterial faculty, the ideal triangle
present to the intellect.

Before we discuss the strange aberrations of
modern philosophy on this subject we must clearly
mark the contrast between the two different images
that we form of every object of which we speak or

think.

I. There is the intellectual, immaterial image,
present in the intellectual faculty. It is something
ideal. It belongs to the spiritual world, not to the
world of sense. It is engendered in man as the
consequence of his being created in the Divine
image, with an intellect framed after the likeness
of the intellect of God. The intellectual image
which he forms by the process of Simple Appre-
hension is a pattern or exemplar of the object
which exists outside of him and corresponds
(though at the same time falling infinitely short of
its perfection) to the pattern or exemplar present
to the Divine Mind when the external object was
created. Man can idealize because he is a rational
being and possesses within him this gift of recog-
nizing the ideal of the object, such as we conceive
to be present in the mind of God. Brutes cannot
idealize because they are irrational and do not
possess this likeness to God. Their mental faculties
can apprehend only sensible phenomena as such ; they
cannot think of anything except so far as it can be
depicted on the imagination and is palpable to sense.

2 There is, moreover, the sensible, material
image present in the material faculty of the imagi-
nation. This necessarily accompanies the intel-
lectual image so long as the body is united to the
soul. We cannot think of any object whatever
without the material picture of it or something
resembling it being present to the fancy. This
picture is sometimes vivid and distinct, as when
I think of some individual object very familiar
to me. Sometimes it is utterly faint and indistinct,
as when I think of something which is applicable
to a number of varying external objects. In pro-
portion to the number and variety of these objects
is the faintness and indistinctness of the image
representing them. When I recall to my thoughts
my favourite little Skye terrier Die, whose wmning
ways and clever tricks have imprinted her image
on my grateful memory, the picture is clear and
vivid, as if I saw her before me begging for the
dainty morsel, or chasing the nimble rat just freed
from the cage, over the meadows that border on
the silver Isis or the sluggish Cam. But if I think
of Skye terriers in general, the image becomes
blurred; other Skye terriers, the associates and
predecessors of the much beloved Die, come up
vaguely before me. If I enlarge the circle and hx
my mind on terriers as a class, the image becomes
still more indistinct. Scotch terriers. Dandy Din-
mont terriers, black-and-tan terriers have all a claim
to be represented. The picture makes an attempt
to comprise them all : but as it is individual it can
only do so by abandoning its clearness of detail

fi^

CONCEPT AND PHANTASM,

112

SIMPLE APPREHENSION.

altogether. If I go still further afield and think of
dogs in general, the picture lapses into a still more
confused indefiniteness, and this again increases a
hundredfold when the subject of my thought is no
longer dog, but animal. In fact, we may say in
general that the vividness and brightness of the
material image varies in an inverse ratio to the
simplicity of the concept.

But all this time the concept has remained clear
and sharply marked. The intellectual image of
animal is no less distinct than the intellectual
image of Skye terrier, perhaps rather more so,
inasmuch as we can define in precise terms what
constitutes animal nature, but it is not so easy
to expound what are the special and essential
characteristics of a Skye terrier and constitute
his peculiar nature as distinguished from that of

other dogs. .

But whether the picture painted on the imagi-
nation be distinct or indistinct, vivid and life-like
or so faint and dim as to be scarcely perceptible ;
whether it be a real likeness of the object of thought,
or merely a feeble attempt to give a concrete and
sensible form to that which is abstract and spiritual,
still an image of some sort is always there. When
I think of ho7testy, or truth, or courage, some sort of
dim image having some sort of relation (generally
a very distant one) to the abstract quality present
to my intellect paints itself without fail on the
material faculty, just as certainly as when I think
of Skye terriers or ocean steamers, or balloons.
In the former case the resemblance of the image

to the object of thought is a very remote one,
in the latter it is clear enough.

We cannot too strongly insist on the necessary
and universal co-existence of the two images in the
spiritual and material faculty respectively, nor at the
same time can we too strongly insist on the points
of contrast between them. There is just enough
similarity to make the attempt to identify them a
plausible one. It is scarcely too much to say that,
as in the nobler animals there is something which
is a sort of shadow of reason, and so nearly
resembles reason that the a posteriori observer
cannot discern any wide distinction between the
intelligence of the dog and the intellect of the
savage ; in the same way the " common phantasm"
is so respectable an imitation of the concept, that
we can scarcely wonder that those who do not
start from the solid foundation of philosophic
truth have regarded the two images as identical.

We must first of all notice that they have this in
common, that they are both applicable to a number
of individuals ; the phantasm has thus a sort of
universality (counterfeit though it be) as well as
the concept. We also notice that one cannot be
present without the other, the intellectual image
is always accompanied by its material counterpart.
It is these two circumstances which have misled
so many modern schools of philosophy, and involved
them in the fatal mistake of confusing together the
immaterial and the material, conception and imagi-
nation, the region of intellect and the region of
sense. This unhappy confusion has in its turn

SIMPLE APPREHENSION.

114

^i^^^^^^^^dlhT^^^^^^^^^^^ and

has opened the door upon a boundless v.sta of
contradiction and scepticism.

The points of contrast between concept and
phantasm may be summed up under five heads
^ I The first difference between the concept and
the phantasm is that the cmtccpt is received into
the intellect, by the process of co,.eptton or ^nte^
lectual perccptron, and as the intellec is a jntu^^
and immaterial faculty, removed altogether above
sense, the concept too is a spiritual and immaterial
and supra-sensible image.

The phantasm, on the other hand, is received
into the imagination or fancy by the process J
sensible perception, and as the fancy or imaginat on
is a material and sensible faculty, the phantasm too
is material and sensible. . .

2 The intellect is, moreover, a faculty of perceiving
universals ; its special function is to see the uni-
v^rsal under the particular. It does not recognize
the individual object directly and immediately as an
individual, but only so far as it possesses a nature
capable of being multiplied. Hence the concept
is something universal, something which is found not
in one individual alone, but in many, either really
existing or at least possible. The imagmation on
the other hand, is a faculty of perceiving individuals.
All its pictures are pictures of individual objects as
such Hence the phantasm is also something indu
lidu'al and limited to the individual. It is a picture
of the individual object, or of a number of existing
individuals whose points of distinction are ignored

CONCEPT AND PHANTASM.

in order that they may be depicted in one and the
same individual image.

3. The concept, which is commjn to a number
of objects of thought, is something precise, definite,
distinct, capable of analysis. The phantasm which
represents a number of objects of thought is some-
thing vague, indefinite, indistinct, incapable of exact
analysis. It fades away before my attempt to
analyze or define it. I can explain and define my
concept or idea of triangle, but if I attempt to
explain and render definite my picture of triangle,
I find myself confronted with triangles of all sorts
and descriptions, dancing about before the eyes of
my imagination, some right-angled, some obtuse-
angled, some acute-angled, some equilateral, some
isosceles, some scalene. The picture is all and yet
none of these, utterly dim and uncertain, and
existing only in virtue of its dimness and un-
certainty. The larger the class of objects which
this picture painted on the imagination has to
represent, the fainter and more indistinct does it
become, until at length it fades away into space
altogether. Thus I can form a common general
outline picture of nian which, sketchy as it is,
has a sort of reality. But my picture of anijnal,
which is to represent at once men and brutes,
can scarcely be called a picture at all, while for
living thing, which is to combine together the
members of the animal and vegetable creation in
a common picture, I cannot produce any respect-

able phantasm at all.

4. The concept is not interfered with by minute-

ii6

SIMPLE APPREHENSION.

COMMON PHANTASMS.

117

ness of detail. I can form as distinct and accurate
an intellectual concept of an eicosahedron or dode^
cahedron as I can of a triangle or quadrilateral
figure. I can argue with no greater difficulty about
the number of degrees in the angles of the more
complicated figures or about any other of their dis^
tinguishing characteristics, than I can about the
number of degrees in the angles of an equilateral
triangle or a square. But the phantasm becomes-
gradually more difficult as it becomes more com-
plicated, until at last it becomes a thing impossible
I cannot imagine a dodecahedron with any sort of
exactness. I can picture it only in the vaguest
way. I cannot distinguish at all in my imagination
between an eicosahedron (or figure of twenty sides)
and an eicosimiahedron (or whatever the name for
a figure of twenty-one sides may be). When I
attempt to imagine a figure with a much larger
number of sides, say a muriahedron, or figure ot
ten thousand sides, I cannot for the life of me see
any difference between it and a circle, unless indeed
I have seen it drawn on an enormous scale.^

5 The concept is peculiar to man. No brutes
can form any ideas in the true meaning of the
word ; they cannot rise above the world of sensa-
tion • they have no appreciation of the spiritual and
the immaterial, and no faculties which can enable
them to apprehend them. If they possessed any
such faculties, they would in some way or other

I It may be well to remind the reader that the "symbolic con-
ceptions" of Mr. Herbert Spencer are. in spite of their name,
nothing else than pictures on the imagmation.

manifest them, whereas they show no trace what-
ever of any knowledge beyond a knowledge of
phenomena and of material things. They cannot
grasp anything beyond individual objects. They
have no power whatever of perceiving the universal
under the particular. They cannot idealize, they
cannot attain to any knowledge of the universal.

The phantasm, on the other hand, is common to
men and brutes. A dog can form a very vivid
mental picture of some individual, with whom it is
familiar. When, during my sister's absence from
home, I said to her little toy terrier Madge, "Where
is Alice ? " Madge would prick up her ears, look
in my face, search the drawing-room, and finally
run upstairs to my sister's room in anxious quest.
When, by a lengthened series of protracted sniffs
beneath the door, she had discovered that her
mistress was not there, she would come back to
the drawing-room and lie down on the scrap of
carpet provided for her with a half petulant air,
as much as to say: ** Why do you recall to me the
image of one who you know perfectly well is not
at home?" Every one who is familiar with the
ways of dogs has noticed how during sleep all
sorts of phantasms seem to pass through their
minds, often evolving outward expressions of sur-
prise or joy or fear.

But animals have also certain phantasms which,
individual though they always are, we may call by
reason of their indefiniteness common phantasms,
A dog is able to form a sort of mental picture,
not only of this or that rat, but of rat in general.

SIMPLE APPREHENSION.

COMMON PHANTASMS.

119

118

Zr~Z^^^^^^^^i:i^~^ a little terrier

T^LU .-a ,h.« is present ■" «"!■' ■X„ ^
a vame phantasm tepresentmg a sort of general

« :r There is a particular .ha^e-
or less definite, which is common to all rats
r particular mode of motion a Part-l- ^^^

a Ocular scent, ^ Z^^^^^^^^^'', ZT^^itl
particular noise caused by ^e -,ng o^^^^ ^^^^^^^^

Z ^ eat-indiXTrat. There are no two

rS in existence of exactly the same sue, or colour.

nr shape or who squeak in exactly the same note,

u Zvl exactly the same noise when they
or who make exactj. ^^^ ^^^^ ^j.^^^^

gnaw wood. But the^e ^^.^^. ^^^^^^^

S^^W;f totl^^^^^^^^^ be perceived even bythe
bThirte^rShr^^^^^^^

to all swans, or the -g corn^^^^^^^^^^
or the scent common to all roses, or

common to all ripe strawberries. A number of these
general impressions remain imprinted on his inner
sense, and thence arises in his imaginative memory
a picture ready to be evoked, in accordance with the
law of association, by any of them ; vague, indeed,
and not precise in particular points, but nevertheless
definite enough to suggest the eager pursuit of his con-
genital foe. If he does not distinguish between one
rat and another, but has a common picture which,
individual though it is, will, on account of a certain
vagueness of detail, directly suit any of them, he
does but follow the example of man, when not
directly exercising his intellectual faculties, but
those that he possesses in common with all other

animals.

Thus I go into the cellar and surprise a big rat,

which scuttles off at my approach. The next day I

repeat my visit, and there is a big rat once more. My

first impression is to identify the big rat of yesterday

and the big rat of to-day. The phantasm I formed

yesterday and which still lingers in my imagination

is equally applicable to his fellow of to-day, if fellow

it be and not the same individual. I can perceive

no difference whatever between the two. A week

afterwards I go again into the cellar and there is

the rat again. It may be the same, it may be

another— at all events he is the same to me. Just

so in the mind of the terrier, a picture arises which,

though still an individual picture, is, by reason

of its vagueness, equally applicable to all rats,

and enables him to overlook the minute and

accidental difference between one rat and another

120

SIMPLE APPREHENSION.

in face of the more striking features which make
upon his senses a similar impression.

These comnmi phantasms may be compared to
the pictures of scenery familiar to every lover of
art, which, individual pictures though they are, are
nevertheless by reason of their generality equally
suitable to a dozen different localities. " Sunset on
the Coast " may be equally suggestive of the coast
of France, or North America, or Norway, or New
Zealand, or China, or the Leeward Islands.
" Mountain Stream in Early Summer " may recall
some well-known scene alike to the dwellers m
the Alps or the Pyrenees, in the Rocky Moun-
tains, or in Wales, or amid the Himalayas. The
want of preciseness of detail in the scene repre-
sented on the one hand and in our memories on
the other, gives to the individual picture a power of
adaptation something like that possessed by the

individual phantasm.

It is by such an apparent generality that the
whole of modern philosophy outside the Catholic
Church has been misled into the fatal error of mis-
taking the gross, material, individual phantasm
present in the imagination for the intellectual,
spiritual, universal concept present in the intellect.
There are, it is true, many excuses for the mistake,
and those who have never learnt to appreciate the
essential distinction between the material and the
immaterial, between imagination and intellect, can
hardly be expected to avoid it.

CHAPTER VII.

SIMPLE APPREHENSION (continued). MODERN
ERRORS RESPECTING IT.

Recapitulation-Modern Errors respecting Simple Apprehension-
Sir \V. Hamilton's, or Conceptualist account of it-Sceptical
consequences of his doctrine-The Confusion involved m it-
1 S Mill's, or Nominalist theory-More consistent in itselt—
Leads directly to Scepticism -Nominalism and Conceptuahsm
compared-Errors common to both-Aristotle's account of
Similarity ignored by them-The Common Phantasm agam-
False doctrine on Conception-The source of the aberrations
of Modern Philosophy.

IN our last chapter we enumerated the three opera-
tions of Thought, Simple Apprehension, Judgment,
and Reasoning-^nd divided Pure or Formal Logic
into three parts corresponding to these three opera-
tions of Thought.

To the first and simplest of all operations of
Thought we gave the name of Simple Apprehension.
We explained the various processes that lead up to
it Sensible Perception, Consciousness, Attention,
Sensible Memory, Imagination, which we may call
mental processes (if we use the word mental in the
wide sense in which it can be applied to the higher
faculties of animals), but which are not processes of
our intellectual faculty. These precede and sub-
serve, but are not a part of, Thought, in the strict and
proper sense of the word.

122

SIMPLE APPREHENSION.

Beyond these subsidiary processes we traced a
further process which conducts us from the sensible
to that which is above sense, from the material to
the immaterial, and which calls into exercise those
higher faculties which are peculiar to man. 1 his
process we called Abstraction, and we explained how
it is really identical with Simple Apprehension,
inasmuch as, when we apprehend the object, we
abstract the common nature which underlies the
individual attributes. We also found it necessary
to be on our guard against the fatal error of con-
fusing together the sensible image and the intellectual
idea, the phantasm and the concept. We drew out
four points of contrast existing between the two.

1 The phantasm is individual, and only becomes
a common phantasm by stripping off from it some
of its distinguishing characteristics : the idea is ot
its own nature universal.

2 The phantasm dwells in the imagination and
cannot pass beyond it : the idea dwells in the higher

region of the intellect.

3 The phantasm is something vague and obscure
and indistinct, the idea is precise and clear and

sharply defined.

4 The phantasm is estimated by our power ot
representing it. We cannot represent in fancy
a figure of three hundred sides. The idea has
no limits. A figure of three hundred sides
presents no more difficulties than a figure of three

sides. ,

5. The phantasm is common to brutes and men,

the idea is confined to rational beings.

MODERN ERRORS RESPECTING IT.

I2J

We now pass to the uncongenial but necessary
task of dealing with the aberration of modern philo-
sophers on this vital question, the importance of
which it is scarcely possible to overrate This error
however, is, I believe, universal in the Philosophy of

the Reformation. „ , r ^u •_

I ask my readers to keep continually before their
minds the essential difference between the common
phantasm of the imagination and the abstract idea
abiding in the intellect. This is the talisman to
keep the Catholic Philosopher unharmed by the
modern foe. It is the very touchstone of a philoso-
phical system. If the root is corrupt, the tree will
be unsound and the branches rotten " f .^ext-book
of Logic at its outset neglects this all- important
distinction, we shall find that it is infected with a
disease which will taint it from beginnmg to end and
render it unsound in almost every chapter.

We will take as our two representatives of the
modern teaching on Conception and Concepts two
men who in most respects stand widely apart-Sir
W. Hamilton and John Stuart Mi . The former
states the doctrine generally held outs.de the
Catholic Church with great clearness and at con-
siderable length. We will give for b^e-ty s^^f
only an abstract of his exposition of it, and w 11
refer our readers to the original if they desire to
obtain more detailed knowledge of it.

When a number of objects (he tells us) are pre-
sented to our sight our first perception of them is
something confused and imperfect. But as we dwel
more carefully upon them and compare their qualities

124

SIMPLE APPREHENSION.

together one with the other, we find that in them
there are some quahties that produce similar and
others dissimilar impressions. By the faculty of
attention we fix our minds on the former of these, and
by abstraction we turn away our thoughts from the
latter. When we come to examine these similar
impressions we find ourselves compelled to regard
them as not only similar but actually the same. To
use the words of Sir W. Hamilton, there are certain
qualities in the objects that ** determine in us
cognitive energies which we are unable to distinguish
and which we therefore consider as the same.'*
Having observed in succession a number of these
similar qualities, and one after another identified
them with each other on account of the indis-
tinguishable character of the impressions they make
upon us, we at length sum them up, bind them
together into a whole, grasp them in a unity of
thought, unite the simple attributes into the complex
notion or concept, and inasmuch as each and all of the
several qualities or attributes belongs to each and all
of the objects in which it has been observed, it
follows that this common notion or concept which
sums them up is the common notion or concept
formed in our mind as belonging to each and all of
these same objects. It is a notion, inasmuch as it
points to our minds, taking note of or remarking
the resembling qualities of the objects: it is a
concept inasmuch as it is a synthesis or grasping
together {con caper e) of the qualities.*

» Cf. Sir W. Hamilton. Lectum on Logic, iii. 131. whose words we
quote almost verbatim.

MODERN ERRORS RESPECTING IT.

125

We shall, however, make this process more intel-
ligible by a concrete example. I am standing in a room
in the Zoological Gardens, before a cage containing
a number of objects large and small, well-looking and
hideous, blue and grey and brown and black. As I
watch one of them, I observe in it movements which
indicate life, and I mentally apply to it the attribute
living. In a second I observe similar movements
indicating the possession of a similar endowment,
and in a third and fourth in like manner. Though
the life of the first is not identical with that of the
second, nor that of the second with that of the third,
yet the effects as observed by us are indistinguish-
able, and we feel ourselves compelled to regard all
these objects as sharing in a common quality of life,
and consequently to each of them I give the common
name of living. As I continue to watch them, one
of them seizes his neighbour by the tail and elicits a
cry of pain : this cry of pain indicates the possession
of what we call sensibility or feeling. A second
receives from a visitor some highly esteemed delicacy
and gives vent to a cry of joy, and this sign of
pleasure we attribute to a similar gift of sensibility.
A third and a fourth show corresponding signs of
pleasure or pain as the case may be, and though we
cannot say that the feeling of the one is the feeling
of the others, yet we cannot help identifying in all of
them the common quality of sensibility, and of each
we say that it is sensitive or possessed of feeling.
As my examination of the objects before me proceeds
I find in each of them other qualities, which I call
hairy, quadrnvianous, imitative, &c. ; each of the

126

SIMPLE APPREHENSION.

MODERN ERRORS RESPECTING IT.

127

females suckles its young, each of them has a certam
shape of body to which I give the name of apetkc
tlZoU. until at length, my detailed obser^^^^^^^^^^
over, I sum up its results m one comp x notion
which comprises in itself all the qualities I have
rbserved. I bind together into the common concept
tly the various attributes, ^^•-;^^-"f -;Xt^
rumanous. imitative, hairy, n^am.^al. &c^ ^J^^^^^^^^
these various objects as monkeys and ^^stow on
them the common name in recognition of their

'TuAtX';SSo, Simple Apprehension o,

conception according to a large class o moder

writers. I do not think that --y ^^^^.^^l^^^^^^^
have misrepresented their account of it. At first sight
it seems plausible enough. But the reader who has
borne'n mind the distinction between the sensible
and material phantasm existing in the mriagination
a^d the abstract and immaterial idea existing m the
intellect, will perceive how this theory labours und
the fatal defect of confusing them together, or rather
of ignoring the universal idea in favour of the
common phantasm. It tells us to stnp off from
a number of individual phantasms that which is
peculTar to them as individuals, and to retain only
?hat which is similar in all of them. But when the
process is complete and these similar qualities have
by the transforming power of the human mind been
regarded as ^dentual with each other, as not on y
similar but the same,-when, moreover these
^nti al qualities have been gathered together into
a ' unity of thought," into a concept comprismg them

all, into a composite whole of which they are the
components parts, this whole has its home in the
imagination just as much as the various attributes
originally observed in the individuals. The only differ-
ence between the individual objects and the common
concept is that the latter has lost the distinctive
characteristics of the individuals and by reason of
this dimness and indistinctness is capable of being
fitted on to all of them. It is not an independent
object of thought, it is essentially relative and imper-
fect ; it is not the essence of the various individuals,
that' inner something which is the substratum of
their qualities. We cannot even think it, until we sup-
plement it with the various qualities which charac-
terize it to us as an individual thing. We cannot
think of monkey as such, we must refer our concept
to some individual monkeys of which we form a
picture in our mind. Hence the modern theory of
the Relativity of all Human Knowledge.'

Hence, too, the philosophical scepticism to which
it necessarily leads if carried out to its ultimate
conclusions. If all knowledge is relative, absolute
truth disappears from the face of the earth. What

I •• But the moment we attempt to represent to ourselves any of
these concepts, any of these abstract generalities, as absolute
objects, by themselves, and out of relation to any concrete or indi-
vidual realities, their relative nature at once reappears ; for we find
it altogether impossible to represent any of the qualities expressed
bv a concept, except as attached to some individual and determinate
obiect • and their whole generality consists in this.-that though we
must realize them in thought under some singular of the class, we
may do it under any. Thus, for example, we cannot actually
represent the bundle of attributes contained in the concept man, as
an absolute object, by itself, and apart from all that reduces it from

SIMPLE APPREHENSION.

128

■;^^^^rir^^^^l^ is not true to another, The
identity of nature which we attribute to the var.ous
individuals comprised under the common concept
and calP 1 by a common name .s a Pleasant fict.on
of the human mind, and has no correspondmg like-
ness of nature in the individuals as they exist m
reality. There is nothing but a certam apparent
Lness which we consider as real because we
cannot distinguish between the effects produced
upon our cognitive energies by these apparently
Similar qualities.' Thought is no longer the exdus.e
nroperty of the intellect, but is a sensible faculty.
Picturing to itself the products of the imagination
af well It is true that a certain distinction is
drawn between Thotcght or Cognition on the one
hand and Representation or Imagination on the other :

•.-„„ .n an individual representation. We cannot
a general cognition to ^" '"^'^'^"^ ^ ^„ ^^,^ general notion or

figure in -;g'-"°" ^^ LC e tagteVlst ^ neither tall nor

term "-■/"/''^^^^'^^el^'^either black nor white, neither man nor
short, neither fat nor lean, neitne ^^ ^^^^

woman, neither young nor °'<1' '^"' *"/™„^„ ;" .^e contradiction

The relativity of our -"-P^V'^^'^ltsU " TsrW Hamilton's
and absurdity of the opposite hypothesis, (bir w. n

Lectures on Logic, i. pp. "8. 1^9 ) . ^j^^^m is

. The slovenly and naccurate use of the woro jn^s
The «'°^^"'>; of fundamental error in modern

from that of man.

MODERN ERRORS RESPECTING IT.

129

but this distinction is an utterly inadequate one. It
is explained as consisting in the manner of cognition,
in the way in which the objects are known. The
contrast between the immaterial faculty with which
we think, and the material faculty with which we
picture or imagine, is entirely ignored. The contrasts
between the objects of thought, which are essentially
abstract and universal, and the objects of imagina-
tion, which are concrete and singular, is in no way
recognized. Thought is made out to be a process
of the same faculty as imagination, and to be con-
cerned with exactly the same objects that we have
already pictured in our imagination, only in a
different sort of way. Thus the gulf which separates
the material from the immaterial is entirely ignored,
and the fundamental confusion, which is the neces-
sary result, extends itself to every part of the
systems which, outside the Church, have succeeded
to the clear and consistent teaching of scholastic

philosophy.

But as yet we have been considering only one
of the leading schools of English philosophy at the
present day, the one which, strange to say, represents
the more orthodox section of modern philosophers,
and this in spite of the utter scepticism which is
virtually contained in the fundamental doctrine
from which it starts. The weak points which it
presents are attacked, with great vigour and success,
by what we may call the rival school of John Stuart
Mill. We are not concerned with the dispute, but
simply with the counter-theory, which we may call
that of the modern school of Nominahsts, according

SIMPLE APPREHENSION.

130

t7^;;;;;r;i;r^^^^^^r7iir^ ^.^p'Sf tikes

rather of the formation of complex ideas, takes

^nX'tnT^ob^ect is presented to us we have
the power of fixing our minds on some of its aUn-
butes and neglecting the rest. To each of these
selected attributes we give a name for convenience
sake and when we have observed a certam number,
we give to the collection a name which combine
Them all and is regarded as the name of the object
n ^hth they are found united. Subsequent y
another object presents itself before us with another
set of attributes. Somehow or other this second
set of attributes recalls those observed in the former
object, and though there is really nothing common
Ser'tothe objects or to their attributes we give
them for convenience sake the same name that we
bestowed on those previously observed, on accoun
of a certain likeness between the one set and the
other. Each of these new attributes receives he
name bestowed on one of those belonging to the
former se, and so the second collection receives
he name given already to the former collection.
Between the two objects there is a likeness by reason
of the likeness between the attributes they severally
comprise, and this justifies their common name
Th?=ame process is repeated in the case of other
objects observed, until at length we have a number
^Mndividual attributes existing in a number of
individual objects, bearing the same name for con-
venience sake, and because they produce s.mila im-
pressions, but nevertheless having nothing whatever

MODERN ERRORS RESPECTING IT.

131

in common except the name. Similarly the indi-
vidual objects are called by the same name only as
a species of abridged notation necessary to the
working of the human mind, but not because they
have really a common nature.

Thus I suppose myself as before in the same
house in the Zoological Gardens. I fix my mind
on a certain group of attributes in one of the
objects before me and banish all the rest. Living,
sensitive, mammal, qiiadriimanous, hirsute, imitative,
pithecoid, &c., are the attributes which absorb my
attention. These I stereotype under the name
monkey, I am thus enabled to argue about them,
just as if there existed a corresponding entity which
had these attributes only, and was endowed with
none of the accidental characteristics of individual
monkeys. In another of the objects before me I
observe another group of attributes which makes
upon me a similar impression to those already enu-
merated, and I say to myself. This, too, is a monkey.
In a third and fourth case the same process is
repeated, and thus I form a class of monkeys,
including under it all those objects which possess
the attributes aforesaid. There is nothing really
common to the individuals that form the class save
only the name, and the upholders of this theory
point out with good reason the inconsistency of the
Conceptualist doctrine which makes concepts play
so prominent a part in the whole of Logic, though
all the time its upholders confess that a concept is
always something relative and has no existence apart
from the concrete image of which it forms a part.

SIMPLE APPREHENSION.

MODERN ERRORS RESPECTING IT.

133

132

""Tl^TN^ii^^^ must be confessed

more consistent than that of Conceptuahsm but at
The same time it is more directly and immed.atly
sceptical, and involves under its specious exterior
the same distinctive fallacy as its rival. It is
important that we should have this fallacy ve^.
clearly before us, lying as it does at the root of
the whole system and vitiating it from first to last.
Mill and Bain and the Nominalist school genera^^^^^
tell us that we are to select a group of at nbutes
from an individual and to bind them together by
meL of a common name. But what is to guide
"sL our selection of the Attributes ? Their answer
is that we are to choose those which ^re similar m
a number of individuals, and which therefore make
upon us the same impression. But what is the
origin of this similitude ? Why is it that we cannot
help recognizing in a number of objects what we
Sr common properties? I imagine that all would
admit that it has at least some foundation in the
objects themselves. If the impressions on our
senses, which we are compelled to regard as similar,
represent no corresponding qualities in the objects,
if the identity which we recognize is something
purely subjective, a mere delusion by which vve
deceive ourselves, without any counterpart in the
objects, then our senses can be in no way trust-
worthy, and we soon arrive at a self-contradictory
scepticism. Both Nominalist and Conceptualist
desire to avoid this conclusion from their premisses,
and therefore concede a certain likeness between
one and another of the objects around us which is

the cause of the impressions they make appearing
to us to be the same.

But in what does this likeness consist? To a
scholastic Logician the answer is simple enough.
The objects, he tells us, are alike inasmuch as
they share the same nature and are made after
the same ideal or pattern. There is the same
form in all of them. The common name of
monkey is given to a number of individuals because
they have one and all the common form or nature of
monkey. The common idea (or concept) of monkey
is not picked up from the mere observation of a
number of the class of monkeys. It represents some-
thing which has a real and true counterpart outside
the human mind, an intellectual entity which is not
simply dependent on the individuals. This entity
stamps its stamp, so to speak, on all the individuals,
and the human mind by a sort of rational instinct,
recognizes at once the common mark or type where-
ever it exists. The intellect claims it as its own,
transfers it into itself, abstracts it from the indi-
viduals, not by shaking off some of their attributes
and leaving others, but by the power it possesses
to extract the immaterial form from the material
object in which it is realized.

This external entity the Conceptualists deny.
They tell us that what we call a common idea or con-
cept has no reality apart from the human mind, that
it is the mind that creates it, and that it has no sort
of existence outside the creative mind of man. The
Nominalist goes still further, and says that there is
no such thing as a concept at all, but that the bundle

134

SIMPLE APPREHENSION.

of attributes common to a number of mdividuals
which the so-called concept is supposed to represen,
are but the selected attributes of a smgle mdividual,
on which we choose to fix our attention to the exclu^
sion of all other attributes. The attnbutes whi^^^^
form the bundle are in their first ongm, and always
emain, individual attributes. The ^f t^^^f ^^^^^^
similar are often found in other ^^ndividual does
not alter their character. All, therefore that i.
common about them and the concept mto which
they are combined is its name, which is applicable
to all the individuals to which we apply it as well
as to its original possessor.

Thus the Nominalist abolishes the very notion
of anything like universality in the concept or idea
that is the result of the process of Simple Appre-
hension. All that is universal is the name Here
it is that he breaks with the Conceptualist. Ihe
latter at least keeps up the theory of an universal
concept appHcable to a number of individuals, even
though the mere fact of its being relative to each of
them destroys any claim on its part to true Uni-
versality : he still asserts the existence of ens umnn
in nmltis, one and the same thing found in a number
of individuals, even though its unity is Purely a
factitious one, brought about by the action of the
faculty of Generalization, which enables us to
regard the sensibility of one ape as one and the
same with the sensibility of another, without there
being any real objective sameness on which this
mental identification of them is based The
Nominalist, more consistent and thorough-going.

MODERN ERRORS RESPECTING IT.

135

does not attempt to keep up the sham of the
Universal. Your concepts, he says to the Con-
ceptualist (and he says so very rightly), are but the
shadow of a shade, a convenient stalking-horse of
which, however, a closer examination shows the
utter unreality. Why not throw over the delusion
and frankly confess that universal names are but a
sort of abridged notation convenient for practical
purposes and as a means of classification, but having
really nothing corresponding to them in the objects

for which they stand ?

But Nominalists and Conceptualists alike leave
one question unsolved. What is it that guides us
in the process of Classification ? What is it that
enables us to regard as the same the different
attributes found in different individuals and to
give them a common name ? I imagine that the
answer of both Nominalist and Conceptualist
would be that these attributes, though different,
nevertheless so resemble one another that they
produce on our senses indistinguishable impres-
sions. But if we pursue the question and ask
whether similarity is possible without identity,
whether any two objects belonging to the same
order of things can be alike without having some-
thing in common, whether language does not cease
to have a meaning if resemblance does not imply
a certain unity of nature, Nominalist and Con-
ceptualist alike find it hard to make any satis-
factory answer.

We shall see as we proceed what the true doctrine
of Universals is. We are at present concerned with

SIMPLE APPREHENSION.

136

it only in ITfeT^r^T^cts the doctrine of Simple
Apprehension. We are considering Nvhat is the
underlying fallacy which vitiates the theory of Con-
^eptlon of Simple Apprehension as put forward by
Post-Reformation philosophers, and leads them to
the abyss of scepticism into which they are forced
bv the inexorable power of a pitiless Logic.

Their weak point, then, does not consist merely
in their confusion between the phantasjn of the
imagination and the idea of the inte lect. Th s is
rather the result than the cause of their errors.
Their radical and fundamental mistake consis s in
the supposition that it is possible for two objects to
resemble one another without having some fnnda-
Zuon in re, something truly and really common
to both of them, in which this resemblance has its

''" This error is very closely connected with other
errors that we have enumerated above as introduced
into the modern doctrine of Simple Apprehension
It is because Hamilton and Mill alike fail to
recognize identity of quality as the basis of resem-
blance that they fall into the blunder of confusing
together the material phantasm and the immaterial
idea. If Hamilton and his followers had clearly

. .,u,otle defines similarity as unity in some gualily. and dis-

"^"/•- ■>% "' :'? lience two hings tha't are alike must have
Metaphysus. IV. n ^> "^^^ ^ „^ ,/, ,,„, in both. It is not

"""' h Tharthev s^ou d have'-'- q-"ty or qualities, and that
rtnd llutd' h- the power of regarding the ..Uan.y as
identity.

MODERN ERRORS RESPECTING IT.

137

perceived that in each and all of the individual
objects which are classed together there must be,
in virtue of their mutual resemblance, some one or
more common qualities existing in each and all, and
the same in each and all, they would have seen how
the common phantasm, arrived at by stripping the
individual of its individual peculiarities, could never
furnish qualities common to the various individual
members of the class. In the same way if Mill and
his disciples had borne in mind that the group of
attributes on which they fix their attention in the
individual are, from first to last, individual attributes
inapplicable to other individuals, and incapable,
without some further process, of a name which is
really common, they would not have fallen into the
error of attempting to classify without any real
basis of classification.

The common phantasm, we once more repeat,
is not really common at all. It is simply an
individual phantasm rendered so vague and m-
distinct by the separation from it of its distin-
guishing characteristics that it will stand just as
well, or rather just as badly, for one individual as
another. It is like a man we see at a distance ; we
cannot see whether he is tall or short, fair or dark,
thin or stout, handsome or ugly, young or old ; he
will do for anybody— Brown, Jones, or Robinson,
simply because he is like the common phantasm,
stripped of the individual marks that divide him
off from other men. But he is an individual none
the less, and no amount of generalization will make
him really a type common to Brown, Jones, Robin-

SIMPLE APPREHENSION.

138

'^^;^^^r^^on\y because of the .^^f «"^^^^ °[
his outline and the uncertainty of his form that
our imperfect faculties can see m him, one or
the oth'er, and we know all the while that when
he approaches nearer we shall recognize his ind -
viduality. There is no sort of universality about
him, or nothing but that counterfeit universality
which consists in the vague indistinctness of im-
perfect perception. Modern philosophers and philo^
sophizers would never have mistaken two things
so different from each other if they had mastered
the principles, we do not say of Scholastic, but
of Aristotelian Logic. Nothing but ^Snor^^^oi
the very elements of the doctrine of the Staginte
could have led them into so fundamental an

"'Tust as in theology the central point of the
Reformation of the sixteenth century consisted
in the rejection of Papal Supremacy, so m Philo-
sophy the new order of things and the Ph>losophy
of the Reformation had their point d'appm in the
modern theory of the Concept and of Concep.
tion. It is not really new : like all modern errors
it dates from Pre-Reformation days, and is but
an old fallacy refurbished and dressed up in new
terms But it never took root in Europe until it
found a home under a congenial religious system
under which it grew and flourished, and to which it
afforded the most material assistance. Without this
new theory the confusion between intellect and
imagination, which serves Protestantism in such
good stead in its resistance to dogma, would never

MODERN ERRORS RESPECTING IT.

139

have gained a permanent footing. Without this the
philosophical scepticism, which is the offspring of
the Reformation, would have been checked at its
outset. It is this theory which, once adopted, is
fatal to the consistent acceptance of the Catholic
doctrine of the Blessed Eucharist, it is this which,
in its ultimate consequences, renders belief in God
impossible. It is an universal solvent : little by little
all rational belief, all religious dogma, becomes, under
its influence, faint and feeble, and at last altogether
disappears. All truth becomes subjective to the
individual, all knowledge becomes relative. If men
who number it among their philosophical opinions
still retain some positive belief, it is only because
the human mind so rarely follows out an opinion
to its final results, or because in contradiction
to all reason it holds opinions which are irre-
concileable with each other. This last alternative
we see realized in a most remarkable way in the
cynical philosophy of our modern " thinkers." The
antinomies of Kant, the contradictory propositions
which Hegel admits as simultaneously true, the
despairing agnosticism of Herbert Spencer, the open
infidelity of the MateriaUstic school, are all based
on one or other of the different phases of the modern
philosophical heresy respecting the Concept and
Conception.

RECAPITULATION.

141

CHAPTER VIII.

THE DOCTRINE OF UNIVERSALS.

Re statement of different doctrines of Conception-What is meant
"" ty u'versals-Various kinds of Unity-Errors of Modern
Conceptualism - Nominalist attack on ,t - Nommahsm-
Resutro Nominalism - Unity and Utuversahty - The
Scholastic Doctrine -Sir W.Hamilton's objection to it-
D rect and Reflex Cognition-The one and t^e --y-Wh^

is Essence ?-Two kinds of ^"'-"^^'-"^^Ti^^^Zs
t^vo Phases-Summary of the true Doctrme of Umversals.

We must now return from the digression of our
last chapter, in which we stated the modern
doctrine of Conception and Simple Apprehension
and pointed out its fundamental errors. But we
must first sum up the results at ^^ich we arrived^
Simple Apprehension is described by Sir W.
Hamilton as the grasping into one of a number of
Attributes observed in various individuals the result
being the common concept, or bundle of qualities,
which have made upon our minds indistinguishable
impressions, and which we therefore regard as the

'^"simple Apprehension, says Mill, is the exclusive
attention to one isolated group of attributes in an
obiect. apart from the rest, the attributes thus
isolated being those which are similar in a number

of individuals, to which we consequently give a
common name and describe as belonging to the

same class. ,

Each of these theories ignores the foundation ot
all resemblance which consists in the possession of
some quality, or set of qualities, which is the same
in all the individuals in which it is found, and con-
sequently of a real underlying similarity of nature
existing in the nature of things, and not a mere
mental fiction. It is this error which is the chief
source of all the confusion in modern philosophy :
of i^s inability to distinguish between the phantasm
and the concept, between the material and imma-
terial faculties, between mental processes of men
and animals. From this same error proceeds its
ever increasing scepticism, its elimination of all
absolute truth alike from Religion and Philosophy.
The rotten foundation renders each portion of the
edifice unsafe, and must necessarily end in gradual
decay and final destruction.

Our Catholic theory of Simple Apprehension or
Conception, on the other hand, is that it is the grasp-
ing by the intellect of that supra-sensible entity
which underlies the sensible and material qualities
of the things of sense. It is the apprehension of
that which makes the thing to be what it is. The
intellect pierces through the veil of sense to some-
thin- which lies beneath and beyond it. and which
is aUogether beyond the reach of the imagination,
or any other material faculty. It attains the true
nature of the object which constitutes its essence,
a nature which it shares with all other objects

142

THE DOCTRINE OF UN I VERS A LS.

belonging to the same class and called by the same
name : a nature which is perfectly alike m al and,
as conceived by us, is not only alike m all, but
the same in all; a nature which is the source of the
common qualities of the objects, causmg them to
resemble one another and to make upon us similar
impressions: a nature to which we never could
attain by the stripping off of some of the qualities
of a number of objects, or by any exclusive fixing
of the attention on one group of attributes to the
exclusion of the rest: a nature which can be
reached by the intellect, and by the intellect alone,
in virtue of its immaterial and supra-sensible

character. , •. i

But we now arrive at another of the most widely
discussed and disputed questions of Philosophy.
What are we to say respecting this common nature
found in many individuals ? How can it be really
one and the same in all ? It seems a contradiction
to say that a quality present in A is identical with
a quality present in B. There may be a certain
similarity between them, but are they not marked
off from each other by the fact that they belong to
different individuals ? If an apple-tree is to be found
in my neighbour's garden it cannot be the same tree
which is at the same time found in mine. If the
attribute of mischievous exists in one monkey, the
same attribute cannot also exist in another by its
side. So said the Nominalists and Conceptualists :
not only the modern teachers of error to whom we
have given these distinctive names, but their repre-
sentatives in mediaeval days. We have now to

DIFFERENT KINDS OF UNITY.

143

investigate a very important question, viz: What
is the true doctrine of Universals ?

In order to understand where lies the fallacy
into which all have fallen save those who have
followed in the steps of Aristotle and St. Thomas,
we have to try and gain a clear notion of what is

meant by «m(y.' , j- -j i

Unity is of two kinds, the unity of the Individual

and the unity of the Universal.

I. The unity of the Individual is a numerical
unity; we can count the individuals, one, two,
three. The unity of the Universal is a umty of
nature. The unity of the Individual enables us to
point to some object and say this is one and no
more. It is ens unum, non multa.

2 The unity of the Universal enables us to point
to a number of objects and say, " All these objects
have some common quality, one and the same m all.
It is ens unum in micltis.''

3. The unity of the Individual is a unity obvious
to sense and the sensitive faculties : it is the only sort
of unity that sense can appreciate : the unity of the
Universal is a unity above and beyond the capacity
of sense, one which it is possible only for intellectual

natures to grasp.

4. The unity of the Individual separates ott
that "in which it exists from all around. The unity
of the Universal binds together into one all those

■ Aristotle, Met. iv. 6, distinguishes four kinds of unity ; Con-
tinuity, totality, individuality, and universality-r!. ^u«x«, -rb
txoy, Ti ««• ««rTo., Ti KoeiKo.. The first two kinds of unity may
be passed over as irrelevant to our purpose.

144

THE DOCTRINE OF UNIVERSALS.

objects in which it is found, even though in all
other respects they may be separated from each

5. The unity of the Individual is that which the
mind first perceives in the order of time. The
unity of the Universal is that which comes first in
the order of nature, inasmuch as no mdividual
things could exist unless unity at least of Being
is previously supposed.

6 The unity of the Individual is but a secondary
and 'inferior unity. The unity of the Universal is
the primary and original unity.

7 The unity of the Individual is one of which we
can paint a picture, so to speak. Our imagination
can represent to itself one man, monkey, &c. The
unity of the Universal cannot be represented to our
imagination. We cannot put before ourselves a
picture of man in general, or of monkey in general.

But is the unity of the Universal a true unity?
Here it is that Nominalists and Conceptualists and
all the moderns fall away from the truth. They do
not recognize the true unity which is found in
various individuals who belong to the same class.
They do not recognize that there is a true unity in
that which we call by the name of htwiamty, and
which constitutes the nature of man ; that it is, as
represented in the human mind, one and the same
thing, whether found in John, Thomas, or Harry ;
in Jane, Mary, or Susan; in white or black; in
civilized or savage ; in the baby recently ushered
into the world and the patriarch of ninety summers ;
in go6d men or bad ; in antediluvian mortals and

CONCEPTUALISM.

145

those existing in the present day. Under its intel-
lectual aspect it is one and the same everywhere,
one and the same from all time, one and the same
to all eternity.

Here is the first principle that we must grasp in
order to understand the doctrine of Universals. We
must hold fast to the unity or oneness of Nature as
a true real unity, nay, a truer unity than the one-
ness of the Individual, a more permanent unity, a
unity derived from a higher source, a unity which
flows from the Divine Nature into the things God

has made.

Now what do the Conceptualists say about this
unity of Nature ? We have already seen that their
doctrine is that we observe in a number of objects
certain qualities in which they resemble each other,
and these similar qualities we consider as the same,
not because they correspond to a nature perfectly
alike in all the individuals, but because they
determine in us cognitive energies which we are
unable to distinguish. Observe, the qualities are
similar, but not the same. It is our minds which
identify them because they make on us impressions
which we cannot distinguish, not because our intel-
lect has the power to discern the nature common to
all of them. Their oneness is the creation of our
faculties, not the necessary aspect under which our
faculties regard the perfect objective likeness which
exists in all the individuals ; we do not, according
to the Conceptualists, recognize the oneness already
existing, but simply manufacture it for ourselves.
It is something factitious or fictitious. There is no

146

THE DOCTRINE OF UNIVERSALS.

true unity in existing things, and therefore no uni-
versality based upon this unity.'

The Conceptualists differ from the Nominahsts
in this, that the former, after noting the similarity in
the qualities observed, give to each of them and to
the concept they compose a factitious unity. One
and the same concept is assigned to all. After they
have noticed the mischievousness of the monkey,
his apelike-form, his quadrumanity, his mammality,
and noticed similar qualities in another, and in a
third, the Conceptualists say : " Why should we
not consider each of these qualities as identical in
all these different creatures? It will be very
convenient. O^ course it is not true, but for
practical purposes we will regard them as the
same, and we will regard, moreover, the nature
which they constitute as the same in all. We will
regard the mischievousness of the first of these
little animals as identical with the mischievousness
of the second and the third, and so on all their
other qualities, and we will, moreover (for the same
convenience sake, and because we cannot see any
difference of nature, however great it may really be),
think of them all by the common concept monkey.
We will identify them all in thought."

. Sir W Hamilton. Ledum on Logic. III. 125- I" hi^^ Lecluns
on MctapkyUcs. II. 3.5. he sums up the Concep.uaUst doctnne:
.. Generalization is notoriously a mere act of .^°"^P='"^^". ^^]f
compare objects ; we find them similar in certam respects, that is,
in certltn rispects they affect us in the same manner, we consider
hequ^ities i^them, that thus affect us in the same ma-er. as he
same ■ and to this common quality we g.ve a name .and as «e "n
prdiiate this name of all and each of the resembling effects, it
constitutes them into a class."

NOMINALISM.

147

"Not so," reply the Nominalists. "You have no
sort of right to regard these concepts as Universals.
As they are mental creations they are nothing but
what they are thought as being, and as they are
always thought or regarded by the mind as part of
an Individual object, they cannot be thought a
Universal. They can only be realized in thought
as enveloped in the miscellaneous attributes of the
Individual, and therefore Individual they must always

remain." • . <.

This is a just criticism. Conceptuahsm is but
Nominalism with an inconsistent attempt to be rid
of the scepticism it involves.

But what is the theory the Nominalists hold ?
All is Individual, they say, save only the name. Every
concept or attribute is different from every other
concept or attribute. In nature there is no unity-
only a certain similarity of nature which justifies us in
giving a common name to the various qualities and
groups of q^^alities observed. We fix our attention
on a certain group in a certain individual and sum
up this group in the name monkey, then we pass on to
a second individual and we are attracted by certain
qualities which by some law of association recall the
qualities of the former, and for convenience sake we
give the same name to the various individuals which
recall others which we have observed before. And
whenever we come across a quality or set of qualities
which recalls the group first observed, the name, too,
comes to our thoughts and is a very useful shorthand
expression for all of them alike. When I observe
certain actions which work destruction for destruc-

148

THE DOCTRINE OF UNIVERSALS.

lion's sake, I have recalled to my mind the monkey,
who thrust his paw outside the cage, and havmg
dragged within it the handkerchief held too near the
bars, tore it to pieces in triumph with malicious joy.
Whenever I observe similar aimless destruction,
whether in man or beast, the name mischievous
comes to my mind and I recur to the procedure now
dim and indistinct which I first characterized by the

term. .... ,

" We employ our conceptions," says Mr. Mill

(and he means by conceptions the group of qualities
which we observed in some individual), *' for the
colligation and methodization of facts, but this colli-
gation does not imply any connection between the
facts except in a merely metaphysical acceptation
of the term." The ideas may become connected,
but this connection is simply a connection of
thought, without any corresponding connection of
fact We are led to think of them together, but this
consequence is no more than may be produced by
any casual association. They are linked together
by the common name, but there is no corresponding
link in the objects themselves. Hence Umvcrsals
are mere words. This was the doctrine of the
mediaeval NominaHsts,who, according to St.Anselm,
taught that Universals were a mere empty sound.*

Now, what is the consequence of this doctrine ?
In the first place it utterly destroys the nature of
human language. Our words no longer express our

= " Univ^r^lia esse nonnisi flatum vocis docebant nominales."
(St. Anselm, De fide SS. Trinitatis contra blasphemias RosceUint, c. 2.)

RESULTS OF NOMINALISM.

149

ideas. If monkey is simply an abridged notation for
a group of external objects, who really have nothing
in common ; if when I say. Monkeys are mischievous,
I simply mean that whenever I see certain objects
of a certain shape and appearance I am thereby
reminded of the performance of a certain monkey
whom I once saw tearing a handkerchief to pieces,
and do not connect the name with any general idea
present in my mind, language ceases to have any
meaning. When I speak of honesty I do not have
present to my mind any characteristic common to
all men whom I call by the name honest, but I
simply allude to certain individual attributes in a
certain individual man which I choose for conveni-
ence sake arbitrarily to apply to other men whom I
include in the class honest. But as for honesty,
mischievousness, &c., that is no such thing— abstract
ideas are all nonsense. Nothing really exists except
those things which our senses can perceive. The
invisible world disappears altogether. All our
faculties are material. The imagination is the test
of truth. What we can realize with our imagi-
nation is true, what we fail thus to picture to our-
selves is either false or non-existent. In fact Nomi-
nalism is the necessary companion of the sceptical
philosophy of the school of *' Sensationalists," and
shares the contradictions and inconsistencies of
those who deny to man all his higher faculties.

If the Nominalists cling to their assertion that
there is a certain resemblance in the qualities of
objects outside of us, a certain uniformity of nature
that furnishes a basis for our classification, this is

150

THE DOCTRINE OF UNIVERSALS.

simply to give up their whole position. This is the
inconsistency of which John Stuart Mill is continu-
ally guilty. He allows that there must be an agree-
ment between the objects classified, that they must
produce upon us similar impressions of sense, that
they must resemble one another, that they must
have common properties. What else is all this but
to admit the existence of the very objective unity
that he denies ? He allows that the course of nature
is uniform, says this is a fact of experience. But
how can I recognize this uniformity unless it is
there to be recognized ? Clear instance of a vicious
circle 1 It begins by reading into things around us a
certain uniformity, and ends by drawing forth out of
them this same uniformity as the discovery of the
intellectual powers of man.

But we must not linger over these false theories.
We have not yet answered the difficulty with which
we started. How can the same thing be found in
two objects a thousand miles apart, except by a
miracle ? How can the same humanity be found in
John, who is young, fair, clever, virtuous, and lives
in Edinburgh, and in Sambo, who is old, ugly,
stupid, vicious, and lives in the Brazils? Is it
really the same identical thing which is found in
each of them ? No, it is not the same identical thing
which exists in each and all. It may seem a para-
dox to say it, but it is nevertheless true that the
Universal nature which the mind recognizes as the
same in all the individuals, is not really and objec-
tively the same, inasmuch as it is impossible that one
man's rationality can be objectively identical with

THE SCHOLASTIC DOCTRINE.

151

another man's rationality. But it is a perfect likeness
in the nature as it exists in the various individuals,
and the human intellect contemplating this perfect
likeness, regarding it under its intellectual aspect,
pronounces it as conceived by us to be an identity.
We know that the rationality of one man cannot be
in reality identical with the rationality of another,
but when by abstraction from all else we regard it
in one and another, we cannot perceive any sort of
difference between the rationality of the one and of
the other. The perfect objective likeness between
the two rationalities paves the way for their repre-
sentation in the mind by one common concept.

This one common concept, in virtue of which we
speak of rationality as ens unum in mtdtis, as the same
in all human beings, represents the rationality of each
inadequately not adequately. It is because of this in-
adequacy, which necessarily accompanies our mental
representatives, that we regard things perfectly alike
as the same. In scholastic language, the metaphysical
essence of all human things is the same : the physical
essence is not the same, but perfectly alike in all :
the metaphysical essence being nothing else than the
physical essence as inadequately conceived by us.

What is therefore perfectly alike as it exists in
nature, inasmuch as it is an exact though inadequate
copy of the edict or pattern which all things imitate,
is for us not not only perfectly alike but one and the
same, because our view of things is in its turn inade-
quate, and we cannot help regarding as the same
things which are necessarily conceived by us under
one and the same concept.

152

THE DOCTRINE OF UNIVERSALS.

Hence the common nature is for us the very
same identical thing as it exists in each. John has
the same human nature as Sambo. Humanity or
human nature is ens mum in mtcltis, one smgle thing
existing in many. It is mte, not with the umty of the
Individual, but with the unity of the Universal. That
which is one with individual unity cannot be mul-
tiplied. That which is one with universal unity
can be multiplied, because the mere fact of its bemg
universal implies that its unity is not an objective
unity, but yet it is a unity which we cannot regard
as anything else but one. It is a true unity, inasmuch
as there is no diversity, except such as is imphed
in its existing in different individuals-but never-
theless not an unity apart from its mental repre-
sentation, but rather a perfect likeness transformed
into unity by the mere fact of its being the object
of Human Thought.

But if the general idea of man is common to
John and Peter, how can it be realized in thought as
one and the same? Does it not contain contra-
dictory attributes according as it belongs to one and
the other ? Yes, says Sir W. Hamilton, and there-
fore to call up any notion or idea corresponding to
the universality of man is manifestly impossible.
The doctrine therefore of a common concept of man
must be rejected on account of these inherent
contradictions, in spite of its claiming the authority
of Locke.'

■ ■■ Locke maintains the doctrine (of Conceptualism) in its most
revolting absurdity, boldly admitting that the general "0"°" ""«
be realized, in spite of the Principle of Contradiction. Does .t

SIR IV. HAMILTON S OBJECTION TO IT.

»53

This line of argument, pervading as it does all
the Hamiltonian philosophy, shows his utter con-
fusion between the material phantasm and the
immaterial idea— between imagination and reason.
Because the imagination cannot conceive or re-
present to itself the phantasm of a man who is
neither white nor black, tall nor short, &c., this
school of Philosophers went on to the most inconse-
quent assertion that therefore the intellect cannot
conceive the universal idea of man without these
accidental attributes.

This strange blunder, for we can call it nothing
else, makes imagination, not reason, the test of truth.
What I am able to picture to my imagination, is or
may be true. What I cannot so picture is false.

But a further objection may be raised. It may
be urged that the intellect cannot recognize as
universal that which is found in the individual.
If I examine Peter and discover in him humanity,
how can I say that his humanity is something uni-
versal—e«s unum in multis. If so, it is not Peter's
humanity. If man is a Universal, do I mean when
I say that Peter is a man, that Peter is also a

Universal ?

The difficulty is solved by the distinction between

not require ' he says, • some pains and skill to form the general idea
0° a mangle ? (which is yePnone of the most abstract, compre-
hensive, and difficult) ; for it must be neither °''«<l"-°;j-'-f„^J
neither equilateral, equicrural. nor scalenan ; but all and none o
"h^ at once. In effect, it is something imperfect, that cannot
ex^^^ldea wherein some parts of several different and .neon-
"stent 'deas are put together." (Hamilton, Lectures on Metapky.cs,

300.301.)

154

THE DOCTRINE OF UNIVERSALS.

THE ONE AND THE MANY.

155

direct and reflex cognition, between direct and reflex
Universals. When an individual object is placed
before the intellect, the intellect has the power of
abstracting or educing from the sensible or accidental
qualities its underlying nature. Peter is presented
to it By its power of abstraction the intellect
draws out of him his humanity and recognizes h.m
as a man. It then has a direct cognition of Peter
and forms the direct concept man. It neglects all
the accidental peculiarities of Peter, his size colour
mental powers, nationality, age, character, &c., and
regards him simply as man. Man is the umvcrsal
term expressing the nature of Peter. This m poin
of fact, is a Universal, but I have no right as yet
to regard it as such, or to pronounce explicitly its
universality. It can at present claim only a poten-
tial universality. It may be called a direct Universal
in that it is directly known by the intellect m the
single object Peter, or ^fundamental Universal in that
the foundations of an explicit universality are laid, or
a metaphysical Universal, inasmuch as though in its
own proper nature it is such, yet it is not yet
acknowledged to be such by the mind that is con-
templating Peter. I have not yet gone on my
quest of other individuals, real or possible, in whom
it is found, or may be found. At present I am satis-
fied with Peter. I have put aside all the qualities
that individualize this nature in Peter, and look at
it in itself. I perceive the Universal in the particular
individual, but I do not as yet perceive it as a

Universal. ,.

But I now go a step further and say to myselt,

This concept of humanity belongs to other individuals
besides Peter. We must look at it not only as
something which I have abstracted from the indivi-
dual Peter, but in itself as common or communicable
to a number. We must regard it in its relation to
these various individuals to whom it communicates
itself and who share in its nature, and who, by
reason of their participation in it, acquire a unity of
their own. In other words, we must look at the
Universal as a Universal— zs a reflex Universal inas-
much as it is attained by the mind reflecting on
itself and exercising a reflex act of cognition— as a
logical Universal, inasmuch as it is found as a
Universal in thought and not in external fact.

But is the nature it expresses one or many ? It
must be one ; its very essence is that it is one nature
in many things. It must also be many; inasmuch as
it is multiplied so as to be found in John, Thomas,
Harry, Marjs Susan, &c., as well as in Peter. It is
then at the same time one and many : one in itself,
many in respect to the many individuals to whom it
stands in relation. Now, this logical Universal is not
found as such outside the mind. How can it exist
as one and the same in a number of individual things
without the mind coming to unite them into one
by its recognition of its identity in all ? It is indeed
the one nature in them all ; but Universality includes
more than this : it includes the conception of their
identity in each and all by the intellect exercising

itself upon them.

We have now another Scholastic mystery to
explain— a mystery, however, which, like all mys-

c\.

156

THE DOCTRINE OF UNIVERSALS.

TWO KINDS OF UNIVERSALS.

157

teries, has only to be examined to fade away inconti-
nently. What is that mysterious something called
essence, a word which mysteriously renders the
scarcely less mysterious language of Aristotle ? *

Let us ask ourselves what we mean by essence ?
In common language the essence of a thing is that
which comprises extracted qualities united together
in a small compass. It is that which constitutes it
what it is, that which contains its special charac-
teristics. Essence of peppermint comprises, or is
supposed to comprise, the virtues possessed by
the peppermint whence it is extracted. It is that
which makes peppermint what it is. So the essence
in philosophical language is that which makes an object
what it is, the inner nature whence springs all its
characteristic qualities. Humanity is the essence of
men inasmuch as it contains in itself all that makes
every individual member of the species really and
truly human. Hence essence is merely another
name for that which constitutes the nature of the
individual taken apart from the fact of his indivi-
duality. The direct Universal expresses that nature
so considered. It is the essence of John that he is a
man, and I directly take cognizance of his univer-
sality when I think of him as a man.

But the essence of John is also the essence of
Peter, Sambo, &c., and of all the individuals in whom
humanity is found, and the reflex Universal expresses
that common nature regarded as common. I reflect

* We have already explained (p. 5) the meaning of the Aristo-
telian expression rhrl^v thai, which is the equivalent of the Latin
essentia.

on the fact of its being common to them all, and man
becomes a reflex Universal as expressing the common
nature of them all. They lose their individuality, or
rather put it out of sight and appear before my
mind in their corporate capacity as a Universal
class.

Here we start a new question : Does the Uni-
versal contain the whole essence of each individual
or only part of it ? Does it ever express anything
which is not strictly the essence, but is yet always
joined to it ? We shall see that from this question
arise what are called in Logic the Heads of Pre-
dicables. These we must postpone to our next
chapter. In the present one we have still some-
thing further to say about Universals in order that
they may be clear to our readers.

We have seen that there are two kinds of Uni-
versals, the one which we have termed potential,
fundamental, metaphysical. The mind contemplates
the nature of Peter as found in Peter in a direct act
of cognition. The other is the logical Universal or
Universal regarded as a Universal, Here the mind
contemplates the nature of Peter in a reflex act of
cognition, not merely as found in Peter, but as
common to John, Thomas, Mary, Jane, &c. ; in
fact, to all existing members of the human race.

The mistake of the Conceptualists consists in
their confusion between these two kinds of Uni-
versals. Instead of keeping them separate, they
started the theory that the mind has the power
of transforming one into the other, or rather of
forming a logical Universal for itself out of the

158

THE DOCTRINE OF UN I VERS A LS.

similar qualities found in various individuals. They
did not distinguish between the act of the mind
contemplating the nature of Peter as human nature,
and so obtaining a knowledge of Peter through the
medium of the concept, and the act of the mind
putting aside all thought of Peter and reflecting on
the human nature found in him and in all other men
alike. They seemed to think that all knowledge was
reflex knowledge, and that we contemplate Peter's
nature, not as known to us through the concept,
but as a concept already formed by the process of
stripping off from him his individual peculiarities.
Hence they never rose above the picture of Peter
as painted on the imagination, and their error as to
Universals proves to be identical with their error
respecting the nature of Simple Apprehension.

The Nominalists, on the other hand, seeing the
weakness of the Conceptualist doctrine that the
mind can form for itself universal concepts out
of qualities not really identical, and can assert
the existence of unity where there is no true
unity, threw off all idea of Universals properly
so-called, except universal names. They asserted
everything to be individual and particular, though
at the same time they quietly assumed a certain
uniformity of nature which practically asserted what
they denied, and which was an assumption, uncon-
sciously introduced into their system in order to
give it some semblance of consistency.

But there is a third error respecting Universals
attributed by Aristotle to Plato, and found in a few
ancient and middle age Logicians, as a sort of

ULTRA-REALISM.

159

reaction against Nominalism and Conceptualism.
This was the error of the Ultra-Realists who
asserted that Universals as such have an existence
in external nature and apart from the mind. Their
doctrine assumed two different shapes. Some of
them asserted that there exist outside of us certain
universal forms, subsisting in themselves, eternal,
immutable, invisible. When we entertain any
universal idea, we really contemplate one of these
wonderful forms. They are the types or patterns
which are copied in existing things of which they
are the original archetypes. When I think of
Peter as a man, I am really contemplating an
archetypal humanity realized in Peter. When I
think of monkeys and their mischief, I am really
contemplating an archetypal and eternal monkey-
dom, and an archetypal and eternal mischievous-
ness, of which the objects before me are but an
imperfect copy.

Now this form of Ultra-Realism is not so ridiculous
as it at first sight appears ; in fact, under a kindly
interpretation, it is almost identical with the truth.
These archetypal ideas have a real existence in the
mind of God. They are contained in the Divine
Intellect as the patterns after which all things were
made, and man's power to recognize the universal
type under the peculiarities of the individual is the
result of his being made in the image of God, and
therefore being able to rise above the concrete
object to some sort of knowledge of the ideal type
of which it is the imperfect representation. This
was probably the meaning of Plato, and had Aristotle

THE DOCTRINE OF UNIVERSALS.

SUMMARY OF THE TRUE DOCTRINE.

i6i

1 60

teen .ore decided in "j- J""- ^ "S'Xt
doctrine ot Cteauon of '» "^ J^ p,,,„„ic

attribnting to ns a dmct sn"! ^^^

Mge of *« ;'*'^if,"o :.: beef t.ugb-.
mind of God (as seems

by some of the Platomsts), U - ^^^ J^^^
Our knowledge would be "» lo"S^[ ^i^^ j^eas

of objects -'f "^ J°:f,i3e%voul<^ be a direct
in the mind of God, or ^'^^^ j. ^^^^ ^rche-

-f:rrD-rinreu^^^^^^^

^'^ThtseldTrm of Ultra-Realism, s^d to have
heeltaught by WUUam oj Champed ^^^^^^^ ^

-'"tJ^STTL^^^^' that it exists
ruidrofXln^nd in the same -- . >t ex.s.
in the mind, that consequently here is
difference between the two aspects of the U.^^ .^

of which - j^-^,t:S -^^^^^^ -^''^

now exploded It ^^^^^^^^^^, ^^ ,„eh is found
on its refutation. » tne un ^^^

contemplates them, it ceases t .^ ^^

,U. on what ground ca^ that whch^i^^ ^^^,^^
individual object be termed a ^^^^ ^^^

ascribe to such a nature the character of Universality
in itself, is a contradiction in terms. How can the
same thing be Singular and Universal ?

We must now recapitulate the leading points of
the true doctrine on this subject.

1. The Universal nature at which the intellect
arrives by abstraction, exists in the Individual object
outside of us previously to and independently of
any operation of the human intellect by means of
which it is arrived at : it constitutes the essence
of the object : it is that which makes it to be
what it is — it is from this that all its essential
qualities proceed.

2. The Universal nature which the intellect
regards as the same is not the same in all the
individuals as it exists in them in its objective
reality. It is alike in all with a most perfect like-
ness. It copies the same pattern which is repro-
duced in each individual. But the copy is not
the original, nor is one copy, though perfectly like
all other copies, one and the same with them. *' In
three different subjects in which human nature is
found there are three humanities," says St. Thomas.
" The unity or community of human nature exists,
not according to the objective reality, but according
to our consideration of it." ^

3. The Universal nature is represented in the
human intellect as one and the same in all. All our

» •• In tribus suppositis humance naturae sunt tres humanitate
(St.Thos.,SKmwaTA^o/.,iaq. 39. art. ^.incorp.) " Unitasseu commu-
nitas humanae naturze non est secundum rem, sed solum secundum
considerationem." (lb. art 4. ad 3um.)

1 62

THE DOCTRINE OF UNIVERSALS.

conceptions are inadequate, and it is this very
inadequacy which identifies for us things which, as
they exist in their reality, are not identical.

4. The Universal nature exists as a universal in
the human intellect by virtue of its power to recog-
nize the common nature in the various members of
a class. Thus the Universal as a Universal is appre-
hended by the human intellect as existing in the
individuals, although it does not exist in them as
a Universal, or we may say that it is formed by
the human intellect, but exists fundamentally in the
various individuals in which it is found, a principle
which Scholastic Philosophy expresses by a phrase
which is of the greatest importance,^ furnishing the
key to the whole doctrine of Universals.

' "Universalia sunt formaliter in mente, fundamentaliter in
rebus ipsis."

CHAPTER IX.

ON THE HEADS OF PREDICABLES.

Recapitulation— Primary object of Thought— Direct and Reflex
Cognition — First and Second Intentions — Heads of Predicables
— Division of Heads of Predicables — Various kinds of Uni-
versals—Species— Genus— Differentia— Property— Accident—
Summum Genus and Infima Species — Double aspect of Uni-
versals—Subaltern Classes— Two meanings of Species— Abso-
lute Infima Species— Inseparable Accidents— False view of
Infima Species— Mill's Real Kinds— Categories orsPredicaments
— Predicaments or Predicables.

We have now had before us the vgynous doctrines
respecting Universals. We have seen that the
errors respecting them are closely allied to the errors
respecting Simple Apprehension or Conception.
They commence with confusion of thought and
they lead on to utter scepticism. These errors are
multiform, but may be summed up under three
heads :

I. The Ultra-Realists maintain that Universals
as such have a real existence outside the mind —
either as self-existent forms wandering about the
world, or as existing in the Divine Intellect — and
that when we form a general idea, the mind grasps
one of these forms, or contemplates some of the
ideas in the mind of God.

164

ON THE HEADS OF PREDICABLES.

2. The Nominalists hold on the other hand that
Universals as such have no sort of existence except
in general names, which are a useful shorthand
nomenclature under which classes may be summed
up. When we form a general idea we really think
of certain attributes which are individual, and which
we observed in an individual, but which we assign
to other individuals by reason of a supposed resem-
blance existing among them.

3. The Conceptualists assert that Universals
exist in the mind, and are the creation of the mind,
though based on certain similarities observed in a
number of individuals : that, consequently, they are
something relative, not absolute. In the act of
Simple Apprehension we identify these similar
attributes and give them a common name.

4. The Schoolmen, following Aristotle and
St. Thomas, who may be called Moderate Realists,
assert that Universals exist outside the mind but not
as Universals, that in the act of Simple Apprehension
the intellect abstracts from the individual appre-
hended the universal concept, and takes cognisance
of the individual through the concept.

The result of this act of Apprehension is the
concept or idea by means of which our intellect
grasps the thing apprehended or concerned. For
we must not forget that though Simple Appre-
hension consists in the formation of concepts, the
primary and immediate object of the intellectual act
is not the concept but the object of which it is the
concept. When I stand before the cage in the Zoo-
logical Gardens and form an idea of what a monkey

PRIMARY OBJECT OF THOUGHT.

165

is, when I say to myself respecting one of the
creatures before me, " Here is a monkey," the first
object of my thoughts is the individual monkey
who gives rise to my reflections. My idea of a
monkey is the means which I employ in order to
comprehend the individual before me. It requires
a further mental process to turn my thoughts away
from the concrete individual to the idea that I have
formed of it.

The fact that the first object of our thoughts is
not the concept, but the individual through the
concept, leads us to the difference between the two
kinds of cognition, direct and reflex. In Direct
Cognition we look directly and immediately to the
nature of the individual, without comparing it with
anything else. We look at it through the idea we form
in the intellectual act by which we take cognisance
of it, but we do not look at the idea itself. We
always begin in all exercise of our minds with a
direct cognition of the object which occupies them,
and for this reason direct cognition is sometimes
called an act of the first intention, because it is what
the mind from its very constitution first intends, or
turns its attention to, in the act it performs. When
for instance I stand before a cage in the Zoological
Gardens and contemplate one of the animals con-
tained in it, and say, " This is a monkey," the
primary object of my thoughts is the individual
before me. I consider it through the medium of the
idea monkey. My First Intention is to consider this
monkey. My idea of monkey is the means I employ
to comprehend this particular one of the class. I may

i66

ON THE HEADS OF PREDICABLES.

regard it under all kinds of aspects. I may turn my
attention to its thick black hair, or to its grinning
teeth, or to its fondness for nuts, or to the fact
that it is suckling a little monkey at its breast, or to
the malice with which it pinches another monkey
which has offended it, but I am in each case con-
sidering the various peculiarities of this individual
monkey. I am engaged in acts of the First Intention
inasmuch as my first intention naturally turns on
this particular monkey which has first attracted

my notice.

But it requires a further and subsequent process
to turn my mind from the contemplation of this
particular individual to the contemplation of the
nature of monkey in general, and the relation to
each other of the various ideas that have been
passing through my mind respecting it. I must
reflect in order to decide whether the term mottkey,
as I understand it, is applicable to other creatures
in the cage before me; whether not only this
monkey but all monkeys are mischievous ; whether
its mischievousness is the same as its malice
in pinching its unfortunate neighbour, or whether
there is only an accidental connection between
the two; whether in virtue of its monkeydom
it walks on all fours instead of on two feet;
whether there are monkeys who walk upright.
In all these considerations I am exercising a Reflex
Cognition in that the mind reflects or turns itself
back to the consideration of the various ideas
that are the result of its direct cognitions. I
am performing acts which are Second Intentions of

FIRST AND SECOND INTENTIONS.

167

the mind, in that the mind by a further and second
intellectual act considers, under a new aspect, the
various ideas formed in the acts of the first intention.
It marshals them in order, that it may take cog-
nisance of them, not as the media through which I
apprehend the nature of the poor beast before me,
but as separate entities having a certain relation to
each other, which I apprehend in themselves as
a part of my mental furniture. It contemplates
them now as forms of thought which I compare
together in order to discover their relations to each
other, and to other individual objects to which they
are applicable. I now put away the immediate and
direct thought of this individual monkey, and I
occupy myself immediately and directly with these
ideas in themselves.' I reflect and say to myself:
I have been looking at this object before me as a
monkey. Why do I call it a monkey ? What is the
connection between this individual and the idea of
monkey ? Why again do I think of it as, and call
it, an animal? What is the connection between
monkey and animal ? What again is the connection
between monkey and hirsute? Are all monkeys
hirsute ? — and so on.

These Second Intentions of our thoughts, the

' Cf. St. Thos. Opusc. 44 (Ed. Rom. 48). I. i ; " Sed quia intel-
lectus reflectitur supra se ipsum et supra ea quae in eo sunt, sive
subjective sive objective, considerat iterum hominem sic a se
intellectum sine conditionibus materiae : et videt quod talis natura
cum tali universalitate seu abstractione intellecta potest attribui
huic et illi individuo, et quod realiter est in hoc et illo individuo :
ideo format secundam intentionem de tali natura, et hanc vocat
universale seu praedicabile vel hujusmodi."

i68

ON THE HEADS OF PREDICABLES.

DIVISION OF HEADS OF PREDICABLES.

169

further aspect under which we contemplate the
objects and the ideas about which we think, intro-
duce us directly to what are called the five Heads
of Predicables. But we may arrive at them by a
different road. They are also the various divisions
under which all Universal ideas are comprised.

We have already spoken of Transcendental and
Non-transcendental as one of the divisions of ideas,
and we said that Transcendental ideas were certain
supreme and exhaustive notions which comprise,
under one or another aspect, all existing things.
Putting them aside, all other Universal ideas are
Hmited and partial, inasmuch as they comprise
only a certain limited number of individuals forming
separate and distinct classes. But classes may
be large or small, they may exclude or include
each other. The class living things includes under
it cauliflowers, sand-eels, porcupines, mosquitoes, apple-
trees, negroes, codfish, and members of the House of
Legislature; and these various classes mutually ex-
clude one another. One class, on the other hand,
may comprise a number of subordinate classes, each
of which has other classes subordinate to it, as
living things contains under it vegetables and animals,
vegetables contains trees, and herbs and shrubs, trees
contains cherry-trees, apple -trees, plum-trees, while
cherry-trees may be broken up at once into indivi-
duals— all the individual cherry-trees real or pos-
sible.

Corresponding to these classes are Universal
ideas or concepts, which express a part or the
whole of the essential nature of the various indi-

viduals in which it is found, and the part con-
tained will be large or small according as the
class is a restricted or a wide one. The wider
the class, the less of the nature contained in the
concept. Living thing tells me very little about the
individual monkey I am watching, or the plant I
have been studying in the Horticultural Gardens.
It is a concept which contains only a small portion
of the essence of the individual. The narrower the
class, the more I learn about the nature of the indi-
viduals, and the greater the amount of the essence
of the individual contained in the concept. If any
one says to me, **That object is a cherry-tree," I have
(accidental differences excluded) all the information
possible for man. I know its essential nature ; the
concept through which I regard it contains the
whole of the essence of the individual.

Hence, we have one division of Universals
according as the concept expresses the whole of the
essential nature of the individual or only part of it.
But it does not follow that the idea which we
form of any individual, expresses any part of its
essential nature, although it must be in some way
connected with it. It is not from every given class
that the individual is necessarily excluded or neces-
sarily included in it. There are many classes to
which the individual belongs, many formalities under
which he may be regarded, which are not a part of
his essence, and do not constitute him what he is
and what he always must remain. The Duke of Fitz-
battleaxe is necessarily included in the class man,
humanity is a part of his essence— but he is not

170

ON THE HEADS OF PREDICABLES.

necessarily as a Duke included in or excluded from the
class of good-looking, or richy or well-mannered. Nor
indeed is he of absolute necessity included in the
class of members of the Higher Court of Legislature,
or of creatures who cook their food, or who wear clothes.
There is nothing in the nature of things to prevent
him from eating his food raw, or of going about
unclad. Universals, therefore, may be, not a part of
the essence of the individual, but something joined
to it, either being present in some instances, but
not in others (as for instance riches or good manners
or virtue in the case of individual men) : or being
always present in point of fact, though the individual
might still retain his proper nature, even though this
particular quality were absent, as for instance cooking
food, or making exchanges, or using spoken language.

This gives us five different kinds of Universals,
according to the five possible relations of the
concept and the individual in whom it exists.

I. The concept may express the whole essence of
the individuals, in whom it is found, all else being
merely accidental to them ; that is to say, any
smaller class that we may form than that expressed
by the word standing for the concept, contains
additional pecuHarities which are not essential to
the nature of the individuals. Thus man is said to
contain the whole essence of the individuals con-
tained under it. It is not an essential characteristic
of John Smith that he is an European, or that he is a
gambler, or that he is given to too much whisky, or
that he is long-limbed, or that he has a white skin, or
that he trades with his neighbours, or that he has a

SPECIES.

171

slight squint, or that he uses very bad language, or that
he rarely, if ever, is seen inside a church. When I
have said that he is a man, I have set forth all
that is essential to his nature, without having to
include any of the amiable qualities aforesaid.

This furnishes the first of our Heads of Predi-
cables.

Species contains the whole essence of the indi-
vidual, and a concept which thus includes the
whole essence is said to be a species in reference to
each and all of the individuals contained under the
general term. Man in reference to John Smith (or
any other member of the human race) is said to be
the species to which John Smith belongs.

2. The concept may contain a part of the essence
of the individuals. It may not express the whole of
that which makes them to be what they are ; nor
the whole of their essential characteristics, but only
some of them. I may break up the concept man
into simpler concepts comprised in it. These
simpler concepts will not contain the whole of
the essence of John Smith, but they will contain
a part of his essence. If, for instance, I say that
he is an animal (not using the word in any uncompli-
mentary sense), I express only a part of his essential
nature. Or, again, if I say that he is a living being,
I express a still smaller part of that which is essential
to him. If again I speak of him as rational, or
possessed of the power of forming abstract ideas, I am
expressing only a portion of his essence, that,
namely, which distinguishes him as a man from all

172

ON THE HEADS OF PREDICABLES.

GENUS AND DIFFERENTIA.

173

Other animals. I am assigning to him the distinctive
or determining part of his essence.

Now in this last case the part of his essence
which we express is obviously different from that
which we express when we say that he is an animal
or living being. Animal or living being are the names
of wider classes, of more general concepts which
have to be restricted by some distinguishing mark.
They are called in scholastic language partes deter-
minabiles essentia, parts of the essence representing
classes which have to be limited in order that the
whole essence may be expressed in the class-name.
Rational, on the other hand, is the name of the
quality which restricts one of these wider classes :
it restricts animal to the species man. It is called
the pars determinans essentia, the part of the essence
which limits the wider concept in order that in the
two combined the whole essence may be contained.
The species man is thus composed of the concept
rational, added to and determining the concept

animal.

Thus we obtain two new Heads of Predicables
corresponding to these two parts of the essence.

Genus expresses the pars determinabilis essentia,
or as it is sometimes called, the material part, inas-
much as the matter of which anything is made
has to have its shape or essential characteristic
given to it by something that forms or informs it.
It represents the wider class which has somehow to
be limited, in order to reach the species or class
which is said to contain his whole essence.

Differentia expresses the pars determtnam
essentia;, or as it is sometimes called, the formal
part, inasmuch as it informs or gives the form to
the matter, and gives to what may be regarded
as an unformed mass its distinguishing form or
shape. It represents the limiting characteristic
which has to be added to the wider class in order
to limit the wider class as aforesaid.

3. The concept may contain something which
is foined to the essence, either flowing from it as
effect from cause, and so necessarily joined to it,
or not connected with it as effect with cause, but
holding such a relation to it that it might be there
or not. In the former case the Universal is said to
be peculiar to or a property of the individual. It
is found in all members of the species. It is
invariably and of necessity joined to their inner
nature, with which it is connected so intimately that
it is present wherever that nature is present and
absent where it is absent. Thus able to express hts
ideas by spoken or written language is a Property of
man It is found in all men ; it is invariably united
to human nature. Yet it might be absent without
encroaching on what is essential to humanity.
There is no contradiction in the idea of a man
who had a rational nature, yet could not convey
his ideas to other men.

In the latter case, that is, if the attribute be
not connected with the essential nature as effect
with cause, it is said to be accidental to the indi-
vidual. It may or may not be found in all members

174

ON THE HEADS OF PREDICABLES.

PROPERTY AND ACCIDENT.

175

of the class to which the individual belongs,
but it is of such a nature that it does not neces-
sarily accompany the inner nature of all the
members of a class. It may be present or it may be
absent. Thus white, European, teetotaller, Mahometan,
learned, virtuous, married, &c., are Accidents of
man. They are not in any way connected with
humanity as such. Even if they were present in
all men, still they would be Accidents. If every
living man upon the face of the earth were to take
the pledge (and keep it), or were to join the religion
of the Prophet, still teetotaller and Mussulman would
be Accidents of humanity. Hence an Accident is not
merely a quality found in some members of a class,
and not in others, but a quality found in some
members of a class (and perhaps in all), but un-
connected with the essential nature which constitutes
the individual members of the class, and which is
expressed in the idea or concept under which they
are contained. Accordingly we may distinguish
Accident into Separable and Inseparable : the former
are found in some members of a class, but not in
all; the latter are found in all the members of a
class, though unconnected with its essence.
This gives us two fresh divisions :

Property, which is not part of the essence, but
is necessarily joined to it by some law of causation,
so that it is invariably found in each and all indi-
viduals who belong to the species.

Accident, which is not part of the essence or
necessarily joined to it, but may or may not be

present in the individuals which belong to the

species.

Hence we have Five Heads of Predicables;
Species, Genus, Differentia, Property, Accident, They
are arrived at by the following process of division :

Every predicable expresses either

1. Whole essence of individuals . Species . (elSo?).

/Material part . Genus . (761/09).

2. Part of essence I p^^^^jp^^^ ^ Differentia (8ta(/)opc£).

3. Something (Necessarily . Property . {j^hiov),
joined to essence (Contingently. Accident (cri^/X/^eyST^/co?).

But why are they called Heads of Predicables?
Because they are predicated of, or proclaimed as
belonging to, a number of different individuals.
We can assert each of them as true, not of one
object alone, but of many. Moreover, they are the
various divisions or heads of all possible concepts
in their relation to each other and to the individuals
of which we think ; or, to put it another way, they
are the among the results of our acts of reflex or
indirect cognition.

There still remain several important considera-
tions respecting some of them.

I. For each individual there may be many
classes under which it falls from the highest of
all (which is the first breaking up of the Universal,
or rather the Transcendental concept of Being)
down to the lowest before we come to indivi-
duals, the concept which expresses the whole of
the essential nature of all the objects contained

176

ON THE HEADS OF PREDICABLES.

DOUBLE ASPECT OF UNIVERSALS.

177

under it. Between these there are a number of
classes greater or smaller according as they
approach more nearly to the concept of Being, or
to the concept which is broken up directly into
individuals and contains their whole essence.

This gives us a new division of Genus and
Species respectively. We have first of all a Genus
which can never be a Species ; last of all a Species
which can never be a Genus, and between the two
a number of classes accommodating enough to be
one or the other, as need shall require.

(a) The Simimum Genus is the highest and
largest class of all, the first breaking up of the
Transcendental and all-embracing concept of Being.

(6) The Infima Species is the lowest and smallest
class, the last Universal, the smallest collection of
individual objects.

(c) Subordinate^ or Subaltern, or Intermediate classes
are respectively genera or species, according as
we consider them in relation to the smaller classes
below them, or the larger classes above them. In
relation to the former they are genera ; in relation
to the latter they are species. Genera with regard
to those below them ; species with regard to those
above them. Thus animal is a genus as compared
with man, a species as compared with beings that live.
Mammals is a genus in regard to seals, a species as
compared with animals. Jewels is a genus with
regard to diamonds, a species with regard to stones^
or to things without life.

2. We have said that these universal concepts
may be looked at in a double aspect. They are at

the same time something contained in the individual,
and something under which the individual is con-
tained. They are both ideas comprising attributes,
and classes comprising individuals. Man as such
is either an idea which, expressed in the abstract, is
humanity, or a class belonging to the concrete order,
and which may be termed mankind. In the scho-
lastic language every Universal may be regarded as
a metaphysical or a logical whole ; ' as a metaphysical
whole it is a sort of bundle of attributes, as a logical
whole it is a sort of bundle of individuals, actual
and possible. Man as a metaphysical whole, as
an abstract idea, comprises the attributes rational,
sensitive, living, &c. Man, as a logical whole, as
a class, comprises all the individual men who have
existed, are in existence now, or who shall hereafter
exist. As a metaphysical whole it contains meta-
physical parts, the narrower concepts or attributes :
as a logical whole it contains logical parts, the
smaller classes or individual objects.

Now the contents of the concept under these
two aspects are in an inverse ratio to each other ;
the greater the extension the fewer the attributes.
This is the case throughout the series of classes

» There are other wholes which do not concern us as logicians,
except in so far as we must be on our guard against confusing them
with the logical and metaphysical whole. Thus there is the
Physical whole, containing physical parts, viz., matter and form, or
substance and accident; the Collective whole, where the parts are
simply a number of separate things accidentally united, as a
regiment of soldiers or a heap of stones; the mathematical whole,
composed of mathematical and integrating parts, as a tree, root,
stem, branches, leaves, &c.

178

ON THE HEADS OF PREDICABLES.

SUBALTERN CLASSES.

179

which proceed from the highest to the lowest, from
the Summiim Genus to the Infima Species.

3 The Siimmum Genus as being the largest class
next to the Transcendental concept of Being under
which all existing objects can be ranged, cannot be
subordinated to any higher Genus, therefore never
can be a Species. It is the colonel of the regiment
who can never be a subordinate officer, and is subject
only to the Transcendental concept, which is the
general in command of the whole army of existing
things. It is called by the Greek logicians 7^^^^
yevLKwrarov (the most generic of all genera). It
has the maximum of extension inasmuch as it is the
most extensive class under which the individual can
be ranged, and it contains a maximum of members
composing the class. It is, moreover, the nummum
of comprehension, inasmuch as it is the simplest ot
all concepts, and so has a minimum of attributes
contained in it. It is of all logical wholes the
greatest ; of all metaphysical wholes the smallest.

4 The Infima Species as being the last class we
come to previous to the individuals, is subordinate
to all the classes above it, and therefore never
can be a genus. It is the lance-corporal, the lowest
of non-commissioned officers, who never can have
any command, except over private soldiers. It is
called by the Greek logicians elho^ elhcKcoTarou,
the most specific of all species. It is the minimum
of extension, inasmuch as it is the least extensive
of all classes under which the individual can be
ranged It is, moreover, the maximum of compre-
hension, inasmuch as it is the most compre-

hensive of all ideas, and so has a maximum of
qualities or attributes contained in it. It is of all
logical wholes the smallest, of all metaphysical
wholes the greatest.

5. Between the Summum Genus and the Infima
Species there are a number of classes which are called
Subalterns, and which are subordinate to all the
classes above them, while the classes below them
are subordinate to them. They take the character
of genus or species, according as we compare them
with a class below, or with a class above them.
They are the various officers of the regiment, com-
missioned and non-commissioned, who are between
the colonel in command of the whole regiment and
the corporal, who commands nothing but private
soldiers. They are called by Greek logicians su,h-
altcrn genera (yii/rj avvdWrjXa). They contain under
them more individuals in proportion as they
approach to the Summum Genus, but fewer qualities.
They contain in them more qualities in proportion
as they approach the Infima Species, but fewer indi-
viduals. They are both logical and metaphysical
wholes: logical wholes in respect of the smaller
classes and individuals contained under them,
Metaphysical wholes in respect of the narrower
concepts or qualities contained in them.

We observe, therefore, that Species is used in two
rather different senses, i. Sometimes it means that
class which contains the whole essence of the indi-
viduals contained under it, and which, therefore, has
no species beneath it. This is the Infima Species,
and none other. 2. Sometimes it means that class

i8o

THE HEADS OF PREDICABLES.

which contains the whole essence common to the con-
cepts contained in it, and also the smaller classes
into which it is immediately broken up. Thus
animal is the species of men and brutes taken together,
as containing the nature common to both of them.
This is the Subaltern Species, which holds the same
relation to the species which immediately come
under it, when they are regarded in respect of what
is common to all of them, that the hifima Species
holds in relation to the individuals. It is, therefore,
called Species in relation to those immediately
subordinate species, in contrast to the classes
above it, which are called genera in relation to them.
Just as man contains the whole of the nature common
to John, Peter, Susan, Jane, &c., so does animal the
whole nature common to men, birds, beasts, fishes,

insects, &c.

We may now illustrate what we have been saying
by the familiar Porphyrian tree. At the root lies
the Summum Genus, Substance, while the leaves repre-
sent individual objects. We shall pursue only one
branch, that which is to lead to individual men.
We begin by breaking up the Summum Genus of
substance into material and immaterial, and as men
are material beings, we fix our attention on material
substances, or Bodies, We then break up Bodies
into Organic' and Inorganic, and as men have
organized bodies, we add Organic to body and thus
obtain the further class of Living things. But still

' It may be well to warn the reader that organic is not used here
in the sense which it has acquired in the vocabulary of modern
chemistry, but is simply equivalent to organized.

TWO MEANINGS OF SPECIES.

i8i

we are far from man. Some living things are sensitive
to pleasure, pain, &c., others are not. An apple-tree
does not, as far as we know, suffer from dyspepsia, or
a cabbage from headaches; and we select in our pro-

gress towards the human kind those bodies which can
feel pain. We thus obtain animals, and man begins
to dawn upon our view. But we have not reached

l82

ON THE HEADS OF PREDICABLES.

him yet, and we must therefore break up animals
We must narrow the class by the addition o( rational
and thus we reach at last the Infima species of rational
animal or man, Man we cannot break up, except
into individuals, Socrates, C^sar, St. Paul, Shake-

speare, &c. ,,,, •

But here a difficulty meets us. Why is man an
Infima Species ? Why should we not break him up
into white and coloured, virtuous and vicious, heathen
and Christian, European, Asiatic, American, African,
and Australasian? If we give as the reason that
man contains all the essence of individual men we
seem to be answering beside the point. For what
do we mean by essence ? That which makes them to
be what they are. But does not their education,
parentage, place of birth, &c., make them to be
what they are and contribute to their formation?
Why then should we not make lower classes based
on these considerations ? Now, if we examine these
various differentiating qualities by which it is pro-
posed to form classes narrower than that of man,
we shall find that many of them are eliminated by
the fact that they can be separated even from the
individual. A man who is vicious one day may be
virtuous the next : a heathen may become christian.
These therefore are separable accidents of the indi-
vidual and cannot belong to his inner nature.

But there are others which are not separable
from the individual. A blackamoor can never become
white 2.n Asiatic remains an Asiatic (in the proper
sense of being born in Asia of Asiatic parents) even
though he may have passed seventy years in Europe

INSEPARABLE ACCIDENTS.

183

or America. These then we may call inseparable
accidents of the individual, and the united sum of
them may be called his Differentia (in a wide sense of
the term) inasmuch as he is marked off from other
men by his height, colour, speech, intelligence, and
strength, together with all those other qualities
which, taken collectively, characterize him as an

individual.

But it is not enough that a quality should be
inseparable either from an individual or from a class,
in order to constitute it part of its essence or inner
nature. It must be not only inseparable mfad but
also inseparable in thought. It must be in such a
relation to the rest of his nature that it could not
be changed without introducing a contradiction into
his nature. Essences arc indivisible, say scholastic
logicians, as well as immutable. They cannot be
changed, and we cannot think of them as changed,
without an anomaly presenting itself in the nature,
an element of which has been thus reversed.

This then is the test in the case of indi-
viduals and of classes alike. In order to dis-
cover what is a part of their essence we must ask :
If I took away this or that quality, if I reversed
it, would their nature simply remain the same as
before, save only that this one attribute has disap-
peared ? If it would, then the attribute in question
is no part of the essence. But if there would be a
general disturbance, if there would be a general
change in the whole nature, then such a quality
belongs to the essence and is part of the inner
nature.

1 84

ON THE HEADS OF PREDICABLES.

FALSE VIEW OF INF IMA SPECIES.

185

Now, if we apply this test to all the various
qualities by which we proposed above to break up
man into lower classes, we shall find that every one
of them might be conceived as reversed without the
maiiy so to speak, losing his identity. If he is an
European, he will not have his nature changed if we
suppose him born in Asia ; if he is a man of talent,
he will still remain the same individual man if by
some strange transformation he becomes a dullard.
If he is a negrOy we can think of him as remaining
in all respects the same, though his skin should
become white. If he is cross-grained, his identity
will be the same, even though he overcomes himself
and becomes the sweetest-tempered man on the face

of the earth.

But if we take any of the attributes which
belong to man as sncJi, it is quite different. Take
away from man the faculty of sensation and he is a
different being at once. He can perceive none of
the things around him, cannot sustain his life,
cannot avoid dangers, cannot gather the materials
for general concepts, cannot exercise his reason.
This faculty is so interlaced with the other faculties
of man, that it cannot be separated even in thought
without destroying his nature. So it is with all
the other qualities which make up the concept man,
and we are therefore justified in saying that each
and all of these belong to the essence of the indivi-
dual and are not separable from him either in fact

or thought.

We may express this in other words by saying
that we have the power of discerning the essences of

things, of piercing through the characteristics of the
individual to the essential nature underlying it.
When we have any object presented to us we are
enabled by the reason that God has given us to see
what qualities belong to the individual (and this
whether they are in practice separable or insepar-
able from him) and what belong to the species to
which he appertains. This is what is meant by the
faculty of abstraction, by means of which we neglect
the individuating qualities, and fix our minds only
on those which constitute the specific concept under
which the individual is ranged by virtue of his inner
and essential nature.

The existence of an absolute Infima Species, which
is broken up at once into individuals and below
which no lower species can be framed, is of course
denied by modern logicians, who depart from the
doctrine of Aristotle and the Scholastics. '' In
point of fact," says Sir. W. Hamilton, **it is impos-
sible in theory to reach any lowest species ; for we
can always conceive some difference by which any
concept may be divided ad infinitum. This, however,
as it is only a speculative curiosity, like the infini-
tesimal divisibility of matter, may be thrown out
of view in practice." This '' speculative curiosity,"
which our modern conceptualist puts aside with
such jaunty ease, really involves the whole question
of the formation of Universals, and on our decision
respecting it depends the absolute character of
Truth. If essences are realities, not figments of
the human mind; if man possesses an intellect
capable of discerning the invisible under the visible.

1 86

ON THE HEADS OF PREDICABLES.

CATEGORIES OR PREDICAMENTS.

187

the inner nature under the external manifestation of
it ; if we have faculties which are different in kind
from those of the brutes, and which enable us to
take cognisance not only o{ phenomena but of noumena,
not only of things transitory and perishable but of
things immutable and eternal— this doctrme of an
absolute Infima Species, is a necessary element m our
philosophical convictions, the absence of which
would involve us in a number of serious contra-
dictions and would render the attainment of Truth
a thing impossible to the whole human race.

On the other hand, Mill and Bain,^ and those
to whom we have given the name of the Modern
Nominahsts, concede with a greater appreciation of
truth, but with very considerable inconsistency, the
existence of what they call real or natural kinds,
which are distinguished from those artificial kinds
which the mind fashions for itself. " A real kind,"
says Mill, ** is one which is distinguished from all
other classes by an indefinite multitude of properties
not derivable from each other." This is one of
several cases in which the school of Mill approxi-
mates to the Aristotelian philosophy, but in so doing
he does but thereby the more completely condemn
his own system. If kinds are real, if we do but
recognize the distinctions which already exist in
nature, the whole system of scholastic realism is
by such an acknowledgment virtually recognized
to be true. What constitutes the reality of those
kinds save that the same generic or specific nature
is found in all the individuals belonging to any one

» Mill, Logic, i. 137 ; Bain, Logic, i. 69..

of them ? The identity of what are called common
attributes is no longer a convenient fiction of our
intelligence, but is based on an objective fact, which
is true independently of the intelligence which takes

cognisance of it.

At the other end of the series to the Infima
species which breaks up into individuals, is the
Summum Genus, which cannot be broken up into
any classes beyond it. In our tree given above we
have substance as the Summum Genus. If we had
started from something which does not exist in
itself, but in something else, we should have had
accident as our Summum Genus. Everything must
either exist in itself or it must inhere in something
else If the former, it falls under the class of Sub-
stances, complete or incomplete ; if the latter, under
the class of Accidents : and therefore Substance and
Accidents are the two Summa Genera, the two al -
embracing classes, to one or other of which all
terrestrial things capable of being conceived in
thought belong, since everything has an existence
either in itself, and that may be called its own or
else in something else, on which it depends and in

which it inheres.

If the latter, i.e., if it inheres in some other
object it is an Accident, or mode of being of that
object The Accidents are nine in number, and
are arrived at as follows : Every mode of being
which can be ascribed to an object either ex-
presses something inherent in it, or something
outside of it, which, however, in some way affects
and characterizes it. In the former case the

1 88

ON THE HEADS OF PREDICABLES.

inherent mode of being either proceeds from
the material element in the object {quantity), or
from its formal or distinguishing element {quality),
or from the bearing of something within it to some-
thing without {relation). For instance, the fact
that a man weighs fifteen stone proceeds from his
material element and belongs to the category of
quantity; his wisdom or goodness from the character-
istics determining his nature, and therefore falls under
the category of quality ; his being older or younger
than his brother is clearly an instance of his relation
to something outside. If, however, the manner of
being ascribed to it is derived from something
external to it, it is derived from something which it
works outside of itself {action), or from something
which is worked in it (passion), or from something
which is regarded as its measure, viz., the time
when it exists, or the place where it exists, or its atti-
tude, that is, the position in space which its several
parts occupy. Or last of all that which is externally
related to it may be something which is not its
measure, but is attached to it, and so in some way
characterizes it as one of its surroundings or belong-
ings. For instance, the so-called Accidents of man
derived from things external to himself are that he is
killing, or comforting, or helping ; in which case we
have various forms of action; or else he is being
killed, or comforted, or helped, and then he is passive;
or if his position in space is described, he is charac-
terized as here or there, near or far. If in time, he
is one who belongs to the fourteenth century, or to
the present time, whereas his attitude is that he is

CATEGORIES OR PREDICAMENTS.

189

sitting down or standing up, cross-legged, or spraw-
ling, i&c. Finally his surroundings or belongings
(habitus) adjacent to him in space constitute his
dress or equipments. He is armed with a rifle or
has on a tall hat, or Wellington boots. We may put
this in tabular form.

Substance
exists in itself

Inherent in the
object

Accident
exists in something else

not inherent in the
object

Quantity, Quality, Relation existing as a merely adjacent

measure of the object to the object
I {habitus or be-

longings)

Time when
it exists

Place where Position
occupied

To recapitulate : If we say anything about some
object which has an existence of its own, we must
speak either of its quantity (quantitas) or its
qualities (qualitas) or its relation (relatio) the things
around it ; what it is doing (actio) or what is being
done to it (passio) ; of the place (ubi) or time (quando)
of its existence, or of its position (situs) or external
belongings (habitus). These form the nine different
classes under one or other of which every Accident
must fall, and these added to Substance form the ten
Categories, as they are called by Aristotle, under
which all ideas or concepts ultimately fall. In
scholastic logic they are called prce die anient a or
predicaments; and as when any idea gets into

igo

ON THE HEADS OF PREDICABLES.

one of them it can get no further, hence has
arisen, by a strange freak of language, the famihar
expression of ^'getting into a predicament," to
express the unpleasant situation of one who has
involved himself in circumstances from which he
would fain escape but cannot.'

But what is the difference between the Predica-
ments or Categories and the Heads of Predicables ?
The Categories are a classification of all existing
things as they are in themselves, regarded in their
own proper being, as the object of our mental
concepts or ideas, as capable of being introduced
into our minds and forming part of our mental
furniture. Thus, if we are asked under what cate-
gory tree falls, we answer at once : '' Tree is a sub-
stance, i.e., has an independent existence of its own."
Under what category does goodness fall ? " Under
the category of quality.'' In the same way son or
master falls under relation, to-morrow falls under the
category of time, ill-treated under the category of

passioy &c.

The Heads of Predicables are, on the other hand,
a classification of the forms of thought, that is to
say, of the various relations our ideas or concepts
bear to each other. They put our mental furniture

^ The Predicaments or Categories are enumerated in the follow-
ing distich :

Summa decern : Quantum, Substantia. Quale, Relatio.
Actio, Passio, ubi, Quando, situs, habitus.
The Greek equivalent, no less than the Latin, requires an
apology for the false quantity and other defects of versification.
EtVl KaT7j7(5piar iroToj/, ir6(TOV^ ovffla^ irpos ti,

PREDICABLES AND PREDICAMENTS.

191

in order and express the connection between the
ideas which constitute it. They express the kinship
of our mental conceptions— the connection between
the concepts or ideas present to our intellect under
their aspect of entia rationis (to use the scholastic
expression), that is, as things which derive their
being from human thought, which are manu-
factured by the mind, though the material conies
from outside. They are not the classes into
which external objects can be divided, but the
classes under which our ideas or concepts of
external objects fall in respect of each other. If I •
am asked under what predicable does tree fall ? 1
have to compare the concept of tree with other
concepts before I can answer the question. Tree, I
answer, is a genus in respect of oak, a species in
respect of living thing. Under what predicable
must good be classed ? I cannot answer the question
until you tell me with what other concept it is to be
compared. Goodness, if you mean moral goodness,
is an accident of man, but is a property of the
inhabitants of Heaven, inasmuch as it flows from
that confirmed sanctity, which is the essential mark
of the saints who have attained their reward.

There are, however, two classes of concepts
which can be classified at once without reference to
any other concept, if only a sufficient study of the
matter has made us acquainted with their essential
nature. Infima Species and Summum Genus are fixed
and absolute, as we have already seen. Under
what category does man fall? I can answer at
once : it is the species which expresses the whole

192

ON THE HEADS OF PREDICABLES.

essential nature of the individuals contained in it.
So again, tiger, oak, eagle. Under what category-
does Substance fall ? Here too the reply is ready.
*' Substance is a Summum Genus and can be nothing

else."

Hence the Categories are sometimes said to be an
enumeration of things as they come under the first
intentions of the mind, that is, under our direct acts
of cognition. As we explained above ^ the Predi-
cates are an enumeration of the second intentions
of the mind, of our indirect or reflex cognitions, in-
asmuch as they are a relative classification of the
concepts we form of things, viewed in their mutual
connection with each other.

' Pp. 165, seq

CHAPTER X.

ON DEFINITION.

Recapitulation— Importance of definite use of words— Dangers of
Indefiniteness— Definition and Definiteness— What is Defini-
tion ?— Real and Nominal Definition— Nominal Definition-
Real Definition— Various kinds of Real Definition— Description,
or Accidental Definition— Essential Definition— Physical Defi-
nition—Definition Proper— Usefulness of Definition— Various
meanings of the word " Impossible "—Value of Definition-
Theory of Definition— Definition in practice— First Rule of
Definition— Difficulty of Definition— Second Rule of Definition
—Defective Definitions — Definition by Synonym— Negative
Definition— Third Rule of Definition— Definition by Metaphor
bad— Ambiguities to be avoided— Far-fetched expressions un-
desirable.

In the last chapter we explained the difference
between Direct and Reflex Cognition, and the
meaning of those mysterious entities, First and
Second Intentions, and thus we passed to the
consideration of the Heads of Predicates. We
saw that they are five in number: Genus, Species,
Differentia, Property, and Accident, according as
they express (i) the material part of the essential
nature of any individual, or (2) the whole of it, or
(3) its distinguishing characteristic (or formal part),
or (4) something always joined to it of necessity,
or (5) something which may be joined to it or not.
We further explained the absolute nature of the
n

194

ON DEFINITION.

Summum Genus and the Infima Species against Sir
William Hamilton and other moderns, and remarked
on the inconsistency of Mill and Bain in conceding
the existence of real as distinguished from artificial
kinds, by which they offer to truth a tribute which
is subversive of their own modern inventions.
Finally, we said a word about the Categories or
Predicaments, the enumeration of all existing things
as they are the object of our direct as opposed to
our reflex cognitions. We now proceed to a different
but no less important portion of our subject.

One of the most fruitful sources of human error
is a misty, indistinct apprehension of the meaning
of the terms we use. A man often has a general
impression of the ideas conveyed by the words he
employs, without any precise and accurate realization
of their true sense. He has never analyzed the idea
in his own mind corresponding to the external ex-
pression of it. He has not asked himself what are
its precise limits, whether the word used has more
meanings than one, and what is the connection
between these varying significations. His know-
ledge of it is like our knowledge of some distant
object upon the horizon, seen through the haze of
early morn. We are not sure whether there is one
object or two ; whether it is on the earth or in the
heaven ; whether it is a horse, or a donkey, or a
cow, or a stunted tree; we judge of it rather from
our personal experiences of the past, than from any
well ascertained data respecting it in the present :
perhaps we hurry to an entirely false conclusion
regarding it and find ourselves entirely mistaken

DANGERS OF INDEFINITENESS.

as to its colour, shape, size, position, if at some
future time we have a better opportunity of studying
its nature.

So, too, it is with our use of words : we assign
to them qualities altogether absent from the concept
they express ; we have no definite grasp of the true
nature of their object ; we have a vague, hazy notion
in our minds that certain attributes, which observa-
tion has taught us to assign to many members of the
class of objects they represent, are really a part of
the essential nature of those objects, and therefore
included in the idea we have of them ; but we do
not feel at all certain whether it is so, or whether we
may not have been too hasty in regarding as neces-
sary to all what may be limited to some individuals
only, or at least not requisite to all, and therefore
only accidents, separable or inseparable, of the class
to which those individuals belong.

Every one must have encountered in his own
experience countless instances of error arising from
this source. If you tell an uneducated or half-
educated man that his soul is a substance, he will
think you are laughing at him. "A substance!'' he
will reply ; ** why a substance is something you can
touch or feel." In the same way the Agnostic objects
to a personal God on the ground that personality as
known to us is something Hmited: whereas there
can be nothing limited in God. In each case the
error arises from an inexact notion of the essential
qualities of substance and person. Because the sub-
stances of ordinary life are those which are per-
ceptible by the senses, the inference is wrongly

196

ON DEFINITION.

drawn that palpable is a necessary quality of sub-
stance : because the persons around us are limited
beings, the Atheist hurries on to the false proposi-
tion, All persons are finite beings. When the Pro-
testant talks about the unscriptural and untrue
doctrine of Intention taught by the Catholic Church,
the bugbear from which he shrinks is generally an
indefinite and undefined something, the true nature
of which he has never realized to himself.

It is the business of Logic in its capacity of a
mental medicine, to teach us to be exact in our
processes of thought, and so to avoid the errors
arising from inexactitude. It enables us to have a
well-defined view of what was ill-defined before. It
furnishes the glass that renders sharp in its outhne
what without it seemed to fade away into the objects
around. It puts into our hands the means of testmg
and trying the accuracy of our concepts, and of
ascertaining whether they are in accordance with

objective realities.

Among the various instruments employed by
Logic for this end, one of the most valuable is the
process of Definition. Its very name implies that
it has for its object to mark out or define the
boundaries of our notions, to see that they do not
intrude one upon the other and so generate con-
fusion in our thoughts. He who is in the habit of
defining to himself the terms he uses, of analyzmg
the contents of his ideas, has a ready test of the
presence of mental error. Error, mental or moral,
hates to be dragged to the light of day, and there
is no more powerful agent in performing this useful

WHAT IS DEFINITION?

197

service, than the mental process which demands of
us, with an authority which we cannot set aside, an
answer to the question : What is the exact nature
of the object of which you are thinking or speaking ?
We are thus brought face to face with our own
thoughts, and what we previously imagined we
thoroughly and perfectly understood we find to be
so confused and obscure as to expose us to the
danger of wandering far away from the truth

respecting it.

Definition is the unfolding of the nature of
an object. As conveyed by human speech it is
an expression by which we answer the question:
What is the object to be defined ? It is an analysis
of that which makes it to be what it is. It is the
breaking up of the concept into the simpler con-
cepts that are its constituent parts. It is a setting
forth of the essence of the thing defined.

But in defining any object we must distinguish
between the Definition which explains primarily the
nature of the object and that which explains primarily
the nature of the word, and the nature of the object
only in as far as it is explained in the meaning of the
word. The first of these is called the Real, the second
the Nominal Definition. In giving the Real Definition
we use a different expression from that which we
employ in Nominal Definition. In the former case
we say : such and such an object is, &c. ; in the
latter, such and such a word means, &c.

Thus the Real Definition of triangle is : Triangle
is a thrU'Sided figure, whereas the Nominal Definition
is : Triangle means a figure which contains three angles*

^t^.^

198

ON DEFINITION.

REAL AND NOMINAL DEFINITION.

igg

Real Definition analyzes the notion of triangle
present to the mind. When we think of a triangle
what is most prominent before us is the three
sides rather than the three angles ; it is its three-
sidedness which constitutes its essence. Nominal
Definition explains the word triangle. If we ask
ourselves, what does the word triangle mean ? We
naturally answer that it means a figure with three
angles. The word makes us think of the three
angles first, and the three-sidedness is a further
quality which results from its triangularity.
I. Nominal Definition is of various kinds:
I. Nominal Definition proper, which explains the
ordinary meaning of the word as current in the
mouths of men. Thus the Nominal Definition of
angel would be a messenger (ayyeXo^) ; the Nommal
Definition of laughing-gas would be a gas which
renders you so insensible to pain that you can laugh at
it, or a gas which incites to laughter. Such a defini-
tion generally is connected with etymology, but not
necessarily so. Thus centaur has for its Nominal
Definition, A monster half-horse half-man, but this
has nothing to do with the etymology of the word.
In this first kind of Nominal Definition we do not
lose sight of the existence of the object, the name
of which we are defining ; but we define the object
through its name.

2. Nominal Definition which simply explains the
word according to its derivation, e.£,y Sycophant
a shewer of figs ((tvkov <j>alva)) ; Lilliputian, an in-
habitant of the island of Lilli/nit ; Athlete, one who
contends for a prize; Blueberry, a shrub with blue

berries on it. In this case we lose sight altogether
of the object and simply think of the grammatical
meaning of the word before us. We break it up
into its constituent elements in the same or some

other language.

3. Nominal or Conventional Definition, which con-
sists in a meaning given to the word by the speaker,
or agreed upon by disputants. Thus if in discussing
the growth of a man's opinions it was arranged that
the word consistency should be used, not of the compa-
tibility of opinions held by the same person at the same
time, but of the identity of his opinions at different
periods of his life, we might call such a definition
nominal as opposed to real, inasmuch as it was a
meaning arbitrarily given to the word, rather than
an analysis of the idea expressed by it. In this
sense a man might say that political consistency is
a doubtful virtue, meaning that the opinions of wise
men are modified by time ; whereas if we use con-
sistency in its ordinary application to the opinions
held simultaneously, the absence of it would at once
condemn the doctrines which thus merited the accu-
sation of inconsistency. In the same way if some
writer or school of writers give their own meaning
to a word in general use, turning it aside somewhat
from its ordinary application, the definition of the
word thus used would be a nominal one, and would
fall under this third class of which we are speak-
ing. For instance, when moral theologians talk of
probability of opinions not as meaning they are
more likely to be true than false, but that there is
some solid ground for maintaining them, even

200

ON DEFINITION.

REAL DEFINITION.

201

though the ground for denying them be no less
solid, the definition of probability in this sense
would be a Nominal Definition, inasmuch as the
word is used not in the ordinary meaning which
the common sense of mankind attaches to the word,
but in another specially attached to it by the authors

in question.

II. Passing on to Real Definition, we observe in
general that its object is to unfold primarily the
nature of the thing defined, and that if it also
explains the meaning of the word, it is because the
word accurately represents in the minds of men
the nature of the object for which it stands. But
the nature of the object is a wide term, and may
be taken to include an almost unlimited territory if
it is used in its widest signification. A thorough
knowledge of the nature of any object includes a
knowledge of its history, of its first origin, of the
causes that produced it, of the end for which it
exists, of all that has influenced its development,
of all that it is capable of effecting, of the various
accidents that have befallen it, nay, of all that may
hereafter change or affect it in the future. The field
has no Hmits, and a thorough knowledge of the
nature of an object is possible only to a being of
an altogether higher order to ourselves. Take, for
example, the nature of man. What a miserably
imperfect knowledge of human nature is possessed
even by those who have the deepest insight into it !
What an infinitesimal portion of its ten thousand
possible variations is possessed by the wisest of
men ! If we are to sound it to the lowest depths

we must know the story of man's first creation, of
his days of early innocence and subsequent guilt.
We must be acquainted not merely with the great
events which affected the character of the whole
human race, but the history of every nation, every
tribe, nay, every family and individual from the
beginning of the world until now. We must not
only have studied the indefinite varieties of character
existing among men, but we must have watched the
causes which produced these various types, we must
have closely observed the effects of external circum-
stances, the handing down of physical and mental
excellences and defects from parent to child, the
moulding of the individual under the powerful
influence of early education, the results of obedience
to, or rebellion against, the internal voice of con-
science. All this, and much more, would be in-
cluded in a complete knowledge of human nature,
and we could not give an exhaustive account of man
as he is unless all this were comprised in what we

had to say of him.

But in any sort of definition, however wide be

our acceptation of the term, it is clear that all this

cannot be included. Even if our analysis of that

which has made man to be what he is, extend to

the past as the present, to what is accidental as

well as what is strictly necessary and essential, we

can but give the most prominent features of the

story of his development, and the most important

of the peculiarities which mark him off from all

things round. We may, however, put forward a

countless variety of circumstances respecting him,

202

ON DEFINITION.

DESCRIPTION OR ACCIDENTAL DEFINITION. 203

and these we find will fall naturally into three
different heads or classes, into which real definition

may be divided.

I. Description, or Accidental Definition, which
gives not the essential characteristics constituting
the nature of the object defined, but certain circum-
stances attaching to it which serve to mark it off
from all other objects. These circumstances may

be either :

(a) Properties, in which case the description
approaches nearly to Definition strictly so-called,
as: Man is a being composed of body and soul, and
possessed of the faculty of articulate speech ; or, Man
is a biped, who cooks his food, or, Man is an animal
capable of practising virtue or vice.

{b) Accidents, which, though separately common
to other objects beside the thing defined, yet
combined together, mark limits exactly co-extensive
with it, as : Man is a biped, resembling a monkey in
form, with a brain proportionately larger than that of
the class to which he belongs ; or. An Albatross is a bird
found between the joth and 4.0th degree of south latitude,
whose plumage is of glossy whiteness streaked with brown
or green, whose wings measure ten or eleven feet from
tip to tip, and familiar to the readers of Coleridge's
Ancient Mariner; or, A lion is one of the chief quad-
rupeds, fierce, brave, and roaring terribly, and used in
Holy Scripture to illustrate the savage malice of the
devil; or, Mangold-wurzel is a kind of beet-root,
commonly used as food for cattle ; or, A cricket is an
insect allied to the grasshopper, that makes a chirping
noise with the covers of its wings.

This kind of definition belongs to rhetoric, rather
than to philosophy. It is the only sort of definition
which can be given of individual objects, since they
are discerned from other members of the class to
which they belong only by these accidental marks, as
The Duke of Wellington was an English general, who
fought with great distinction in Spain and the Low
Countries against Napoleon, and finally crushed him in
a decisive battle at Waterloo ; or, Noah was the builder
of the Ark, who was saved with all his family from the
Deluge ; or, Marcus Curtius was a Roman of good
family, who jumped into the gulf at Rome at the com-
mand of the oracle.

The various circumstances which may combine
to mark off the object to be defined from all else
are almost unlimited in number. Sometimes they
consist in the catises which gave it its origin, as, for
instance, Man is a being created by Almighty God from
the slime of the ground, and endowed by Him with a
rational sow/— here God is the efficient cause of man,
the slime of the ground the material cause, the
rational soul the formal cause ; or, A bust is a figure
consisting of head and shoulders made after the likeness
of some human being by a sculptor or statuary— here
the sculptor is the efficient cause, and the human being
who is copied is the catisa exemplaris, or pattern after
which it is made ; or, A clock is a mechanical instru-
ment which is to indicate the time to eye or ear; or,
Man is a being created to praise, revere, and serve his
Creator, and so to attain eternal happiness, where the
marking of time and the service of God are the
final causes of clock and man respectively. Some-

204

ON DEFINITION.

PHYSICAL DEFINITION.

205

•'I

times it gives the manner in which it comes into
being, in which cases it is called a genetic Definition,
as, A cusp is a curve traced by some fixed point in a
circle as it travels along a straight line ; or, A circle is
a curve generated by the extremity of a straight line
revolving round a fixed centre.

2. Essential Definition gives the real nature of
the object, sets forth that which makes it what it is,
breaks it up into the various parts of which it is com-
posed. But these parts may either be those which
can be separated the one from the other, and can
actually exist apart, in which case they are called
the physical parts of the object, or they are insepar-
able in fact, and can only be separated in thought, in
which case they are called metaphysical parts. In
the former case it is the actual object which is
actually divided, as, for instance, if we divide man
into a rational soul and an organized body. In the
latter it is the idea of the object which is broken up
into the ideas which composed it, as, for instance,
if we divide man into rational and animal.

Corresponding to these physical and meta-
physical components we have two kinds of Defini-
tion, viz., Physical Definition, which breaks up the
thing defined into its physical parts, and Metaphysical
Definition, which breaks up the thing defined into
its metaphysical parts. Physical Definition does not
merit the name of Definition properly so-called,
since in Logic we have to deal with the external
object as presented to us in intellectual cognition,
and intellectual cognition as concerned with the
essential idea of the object, not with the object as

it exists in the external world and comes within the
range of sense. As a logician I have nothing to do
with the component parts of man in the physical
order. I have no claim to decide on the question
of the simpler elements which are united in his
composite nature. I am concerned only with the
component parts of man as he exists in the mind ;
primarily in the mind of his Creator, and secondarily
of all rational beings, who by their possession of
reason can form an idea or intellectual image of
man, corresponding to that which exists in the mind

of God.

Physical Definition is a description rather than a
definition proper-it gives characteristics which are
accidents or properties of the object under its logical
aspect, not those which make its nature to be what
it is. Sometimes it is not a real, but only a nominal
definition, inasmuch as it analyzes, not the object
to be defined so much as the word, as if I define
hydrochloric acid as an acid composed of hydrogen and

chlorine.

3. Last of all we come to Definition proper, or
Logical Definition. In a definition we do not attempt
to break up our idea of the object to be defined mto
its simplest constituent elements, for this would be
an endless task, but to give the higher class, (or
proximate genus as it is called), under which it comes,
and the distinguishing characteristic (or differentia)
which separates it from the other subordinate classes
coming under the genus. But we must explain a
little more at length what it is that Definition does
for us.

206

ON DEFINITION.

VARIOUS MEANINGS OF THE WORD IMPOSSIBLE. 207

All error respecting the nature of any object
consists in attributing to it qualities which it does
not possess, or in denying to it those that are really
to be found in it ; or, as we remarked at the com-
mencement of the present chapter, we may be
involved in a vague uncertainty whether this or that
quality belong to it or not. In this latter case our
knowledge is defective, rather than erroneous ; and
so long as we do not affirm or deny anything con-
cerning it of which we are not certain, but suspend
our judgment, we are ignorant rather than mistaken,
and only exercise a prudent reserve, if we do not
commit ourselves respecting any object which is
beyond our reach.

But error and ignorance alike are evils which
philosophy seeks to abolish, and though it is not
the business of logic ex professo to add to the
material of our knowledge, yet it plays a most
important part by laying down laws which regulate
all intellectual acts correctly performed. If it does
not add to our knowledge, it guides us in adding to
our knowledge, and furnishes us with varied means
of detecting the error which in our human frailty
we have unwittingly adopted as a part of our mental
furniture. It drags the impostor to the light, and
enables us to see that he is not clad in the wedding
garment of truth. It warns us that we must cast
him forth into the outer darkness of the realm of
falsehood. It clears away the mist which has so
long enabled him to lurk undisturbed in our in-
telligence, and shows him in his naked hideous-
ness, in contrast to the fair children of light. It

quickens that instinctive perception of truth which
is one of the privileges we enjoy as the children of
the God of truth, and which no amount of sin or
wilful blindness can ever wholly eradicate, though
it may deaden and impair its power and hinder or
thwart the exercise of it.

In this invaluable service rendered by Logic,
Definition plays a very important part. If men
would only define their terms they would escape
three-fourths of the fallacies that are prevalent in
the world. It is because their notions are misty
and undefined that they so often go astray. They
are misled by analogy of meaning and confuse it
with identity of meaning. We will illustrate our
meaning bv the various uses of the word Impossible.
When the Unbeliever objects to the doctrine of the
Real Presence in the Blessed Sacrament of the Altar
that it is impossible that our Lord's Body should
be at the same time in Heaven and in the Sacred
Host on earth, his objection is based on the want
of any clear perception of the various meanings of
the word impossible. He forgets that the term is
employed in different senses between which there is
a certain analogy, but which must be carefully dis-
tinguished from each other.

If I were to give the letters of the alphabet
all in a heap to a blind man and tell him to
lay them out on the floor, and, on looking
at them, were to find that they had arranged
themselves in their proper order, I should at once
gather that some one had guided his hand. If
he were to assert that they had so arranged them-

208

ON DEFINITION.

VALUE OF DEFINITION.

2CK>

selves by chance, I should refuse to believe it, and
say that it was quite impossible, I should mean by
this not that it was absolutely impossible, but that it
was so impossible as to be morally or practically
impossible. There is nothing to prevent the letters
from presenting themselves in the order a, b, c, d,
&c., any more than in the order they practically
do happen to assume, but nevertheless I should
say, and say rightly, that the thing was im-
possible, that is, that the chances are so over-
whelming against any one arrangement as to justify
the assertion that it could not have come about
without design.

But the sense of the word is very different when
I say that it is impossible that a man who has been
blind from his youth should be cured in an instant
by washing his eyes in a fountain of water. Here
I do not mean merely that it is highly improbable,
but that such a cure is altogether at variance with the
ascertained laws of nature. If I believe in a Personal
Author of these laws, I believe that it is possible that
He who made them can interrupt their operation^
and I shall not dismiss without investigation the
statement, that the occasion of this sudden cure,
which is irreconcileable with their ordinary working,
is the bathing the eyes that have never seen the
light, in some spring or fountain which has the
reputation of being miraculous. In this case I
mean by impossible not so utterly improbable under
ordinary circumstances as to be in a wide and loose
sense impossible, but actually in contradiction with
certain well-established laws which govern the natural

oi'der. Hence the impossibility is one that cannot
be removed unless we pass out of the natural into
the supernatural order. Then the impossibility
vanishes ; there is nothing in the order of things to
prevent the higher law superseding the lower. The
supernatural Providence of God acting in a super-
natural way makes that to be possible which in the
natural order is impossible.'

There is a third sense, and the only one in which
the word attains to its full and proper meaning.
When I say that it is impossible that two and two
could make five, or that there could be a triangle, in
which two of the sides were together less than the
third, I do not mean that it is so highly improbable
as to be practically impossible ; or that it is impos-
sible unless the Author of the laws of nature choose
personally to intervene and set them aside ; I mean
a great deal more than this. I mean that it is
impossible wider all possible circumstances, impossible
to the Author of the laws of nature as well as to
those who are subject to them. I mean that there
is something in the nature of things, and therefore
in the nature of God Himself, which forbids that
mathematical laws should be reversed. Any other
alternative would create a contradiction in God
Himself. The law is a part or parcel of absolute
Truth, and therefore is ultimately grounded on the
very essence of the God of Truth.

Now this important distinction which I introduce
here merely by way of illustration, escapes the
notice of ordinary men because they are not in the
habit of defining the words they use. Any one who

2IO

ON DEFINITION.

DEFINITION IN PRACTICE.

211

has realized the work of Definition and the impor-
tance of Definition, will at once ask himself: M hat
is the meaning of impossible ? He will break it up
into the elements of which it is composed : he wU
discover it to be an event opposed to some universal
law. Pondering within himself he will soon recog-
nize that the first meaning I have attached to it, as
indicating something so rare as in common parlance
to deserve the name, does not properly belong to it
at all; and that the second requires some expla-
nation, inasmuch as a universal law may be sus
pended or annulled by the Maker of the law, and
that it is only when it means something opposed to
the nature of things that it has its strict, proper,
and literal signification of that which cannot be.

But a definition, if it is to be of any use, must
be exact. When it breaks up any complex idea into
the simpler ideas that compose it, we must see that
it does so according to a fixed rule. We must see
that it consists of the genus or material part of the
complete idea, and the differentia or its/on»a/ and dis-
tinguishing element. Our definition must, at least as
far as this, make the idea of the object defined a
clear one. We cannot expect absolute perfection m
the clearness that is furnished by Definition. We
cannot be said to attain to an absolute or perfect
clearness unless we break up the complex idea into
each and all of the simple ideas that compose it.
We must not only be able to produce the proximate
genus and differentia, but also to analyze each of
these until we come to a 'genus that admits of no
further analysis. If I define a ligature as a bandage

used for tying up veins and arteries, I give a correct
definition. Bandage is the proximate genuSy and the
rest of the definition gives the distinguishing charac-
teristic which marks off a Hgature from all other
bandages. But this is but the beginning of the
process : the question that at once suggests itself
is : What is the definition of bandage ? I reflect a
little and say that Bandage is a strip of cloth or some
similar material used for the binding up of wounds. I
have now got a step further, but I am a long way
off from the complete analysis which is necessary to
absolute clearness. I must be able to give a correct
definition of cloth. After some little hesitation I
pronounce it to be a woven substance of which garments
are made. Now at last I am beginning to see day-
light. If my interlocutor asks me to define s«6-
stance, I have a right to send him about his
business, and tell him that substance is a summum
genus, and therefore incapable of definition. But
he may still, if he chooses to be captious, exact
of me an analysis of all the words that composed
the definition, i.e. of strip, wounds, and garments. It
is only when I have mounted up by a succession of
steps to the differentia and the summum genus (which
in each case will be substance) of each of these,
that I can be said to have furnished a definition of
ligature, which is perfectly clear and free from any
possibility of obscurity or confusion.

In practice, however, this ultimate analysis is
impossible, and to require it would be unnecessary
and vexatious. I have done my duty, I have defined
the object, when I have given the two constituents

212

ON DEFINITION.

DIFFICULTIES OF DEFINITION.

213

of its essence, the proximate genus and the differentia.
It may sometimes be necessary to go a step further,
and define this proximate genus. But this is no
part of my business as one called upon to define ; it
is a piece of superfluous generosity, for the sake of
enabling my reader to form a clear conception of
the meaning of the words I use. Thus if I define
a screw as a cylinder with a spiral groove on its outer
or timer surface, I must in pity go on to define a
cylinder, or else my listener will in all probability be
not one bit the wiser than before.

But we shall better understand the nature of Defi-
nition by laying down certain rules, the observance
of which is necessary to a good definition. They
are but an analysis of what Definition is : they do
but declare in other words that all Definition must give
the proximate genus of the thing defined, and the
differentia which separates it from all other species
coming under the genus. But at the same time they
are decidedly useful as practical guides ; and, more-
over, without them we should be liable to employ
words which should be excluded from a Definition.
They also show the correctness of some definitions
which we should at first sight be inclined to declare
inadmissible, and without them the beginner would
be exposed to errors in a process which is full of
difficulties, and at the same time most important to
correct thinking.

These rules are three in number.
Rule I. The Definition must be co-extensive with
the thing defined, that is, it must include neither
more nor less, else it would not be a definition of

that which it undertakes to define, but of something

else. This rule seems obvious enough, but like

many things that are obvious, it is very easy to

neglect it in practice and so fall into grave errors.

Thus if we take the common definition of wizard,

or witch, as a person who has or is supposed to have

dealings with the devil, such a definition would be

too wide, as there may be many persons who

have some communication with the enemy of souls

who are not in any sense wizards or witches.

Or, if we take another definition found in some

modern dictionaries, that a witch is a person who

has or is supposed to have supernatural or magical

powers, such a definition would again be far too

extensive as it would include all those who work

miracles by the power of God, or to whom such

miracles are attributed. If, on the other hand, we

define a witch as one who exercises magical powers to

the detriment of others, this definition would be too

narrow, as there may be persons possessed of such

powers who exercise them for gain, and not with any

sinister design on their fellow-creatures.

So, again, if I define Logic as the art and
science of reasoning, I am limiting Logic to only
one of the three operations of thought, I am ex-
cluding from it most unjustly all control over the
formation of ideas and of judgments, and my defi-
nition is altogether too narrow. If, on the contrary,
I define it as the science or art which guides the
mind to attain to a knowledge of truth, I extend it
altogether beyond its sphere. I make it include
all other sciences whatever, for what is the aim and

214

ON DEFINITION.

SECOND RULE OF DEFINITION.

215

object of every science save to lead man to the
attainment of truth ? Theology and mathematics,
botany and metaphysics, astronomy and ethics,
all set this end before themselves. Yet this defi-
nition, though so utterly incorrect, varies but a
hair's breadth from the true Definition : Logic is a
science (or art) which guides the mind in its attainment

of truth.

It is often exceedingly difficult, or even impos-
sible, to know whether our definition is co-extensive
with' the thing defined. The difficulty falls not [so
much on ascertaining the proximate genus, as on
making sure that the differentia really differentiates
this class from all others under the genus, and that
it does not shut out some of the individuals who
really belong to it. Take of all definitions the most
familiar : Man is a rational animal. Let us suppose
Gulliver's curious fiction to be true, and that in
some of the planets there is a true Laputa inhabited
by Houyhnhnms and Yahoos. What then becomes
of our definition? The Houyhnhnm is a rational
animal, but certainly not a man. We should have
to add to the definition some further distinguishing
mark to exclude the Houyhnhnm from our defi-
nition of man. Our justification of our present
definition is that on this earth, at all events, there
are not any other rational animals than man, and
that the possession of reason distinguishes man
from all around. Or to take a more practical case :
If we define the sun as a luminous body forming
the centre of the material universe, we cannot be
absolutely certain of the correctness of our differ-

entia. It may be that the whole of our solar system
is but a portion of some larger system, and that
the sun is but a planet revolving round some more
central body on which it is dependent. All then
that we can do is to define up to the limits of our
present knowledge and within the sphere familiar
to us. If I define the Pope as the Supreme Ruler
of the Catholic Church on earth, this would not
interfere with my recognition of our Lord's Supre-
macy if He were to return and rule over His people,
as the Millenarians believe He will, for a thousand

years on earth.

Rule 2. The Definition must be in itself clearer and

more familiar than the thing defined.

In this rule the words in itself are of great im-
portance, for many a definition is to ordinary mortals
more difficult and unintelligible than the thing defined
by reason of their ignorance and want of cultivation.
Man is the thing defined. Every child understands
the meaning of the word man, to whom rational
being conveys no sort of meaning. Most people
know what a screw is, but only an educated man
would have a clearer notion of its nature after
hearing the definition we have given above. Very
few of us, though we may fancy ourselves versed in
art and cognisant of its nature, will find ourselves
much enlightened when we are informed that it is
a productive habit, acting in accordance with reason.
Yet if we ourselves were asked to define art, we
should probably find ourselves utterly unable to do
so. Our knowledge of its character is an utterly
vague and indistinct one which we are unable to

: I

2l6

ON DEFINITION.

analyze. How many there are who, if they are asked
a question respecting the character of some object,
answer by an enumeration of the classes or indi-
viduals of which it forms the genus or the species.
If you ask a child what he means by an animal, he
will answer: Oh, dogs and horses, and that sort of thing.
Unable to break up the idea viewed as a meta-
physical whole into its metaphysical parts, he will
regard it as a logical whole and break it up into
some of its logical parts. Instead of splitting up
the idea into simpler ideas, he will separate the
wider class into some of the narrower classes. He
will regard it, not in its intension or comprehen-
sion, but in its extension; he will give you, not
what it contains, but the area over which it is
spread. He will look at it in the concrete, not in
the abstract, and the process is so much simpler
and easier that we cannot wonder at it.

But this will not do for the mental philosopher.
He aims at correct thinking, and no one can think
correctly without the habit of analysis, which is the
road to correct Definition. At the same time it is
enormously fostered by the effort which Definition
involves, and by the exactness of mind that it pro-
duces. If I am to have sound views about art, I
must know what is its object, and what are the
conditions of success. The true definition of art
here comes in to assist me wonderfully, and is
necessary to determine whether logic, for instance,
or political economy, is an art or a science, or both ;
and what is necessary to constitute the true artist ;
and a thousand other questions which mere vague

DEFECTIVE DEFINITIONS.

217

impressions will never enable me to answer cor-
rectly.

What, then, do we mean when we say that a
definition must be in itself clearer and more familiar
than the thing defined ? It does not mean that the
words employed are more familiar to us, but that
the ideas they express are more "simple than the
idea of which they are the analysis. Thus if I
define circle as a plane fignre, contained by a line,
every point of which is equidistant from a fixed
point within it, the general impression left upon
the ordinary mind by the definition is far more
perplexing than that which is left by the thing
defined. The words are more puzzling because less
familiar in ordinary life. Yet the definition is never-
theless a perfectly correct one. It is in itself simpler
and more familiar than the thing defined. Each of
the words used expresses an idea less complex than
the word circle. We cannot really fathom the
nature of a circle until we have fathomed those
various ideas of plane, figure, Hne, point, equi-
distant, &c. Without it our knowledge of a circle
is vague and indefinite. They are its component
parts, plane-figure is the genus, and contained by
a line, &c., the differentia. There is less to think
about in them— to each of them something has to
be superadded in order to complete the idea of a

circle.

Hence in framing a definition we must be very
careful that the thing defined does not come into
the definition concealed under some word or phrase
which cannot be understood without a previous

2l8

ON DEFINITION.

DEFINITION BY SYNONYM.

219

knowledge of the nature of the thing to be defined.
This rule would be broken if we were to define man
as a human being, since the idea of man is involved
in the idea of human, or if we defined sun as the
centre of the solar system. The definition of network
as a system of cordage, reticulated or decussated between
the points of intersection, sins against this law, as the
word reticulated includes the Latin equivalent for
the word net. An amusing definition, said to have
been given by Dr.Wilberforce, the Bishop of Oxford,
to a Committee of the House of Commons, sitting
on some Church question, is a good illustration of
this kind of fault in defining. He was asked to
define Archdeacon, and he wrote on a slip of paper
the following ingenious answer: An Archdeacon
is an ecclesiastical dignitary, whose business it is to
perform archidiaconal functions.

This kind of Defective Definition often takes the
form of what is called a vicious circle ; that is to say,
we first define one idea by a combination of other
ideas which is co-extensive with it, and then define
one of these by the idea which was in the first
instance to be defined. For instance, if we define
a sovereign as a gold coin equal in value to twenty
shillings, and when asked to define the value of a
shilling, answer that it is the twentieth part of a
sovereign, the circle is obvious enough. If we
desire to know which of the two definitions is the
faulty one, we have to ask ourselves what is the unit
of monetary value, or approaches most nearly to it
according to the ordinar>^ agreement of men, and
this will be the idea simpler and more familiar in

itself. Thus a penny is by common consent in small
sums our English unit, as we see by our using it
even in speaking of sums above a shilling, fifteen
pence, eighteen pence, &c. In America, on the
other hand, it is the dollar, and smaller sums are
reckoned as a half, a quarter, and a dime. So
again, if I define a day as a period of time consisting
of twenty-four hours, and then an hour as the
twenty-fourth part of a day, I commit the same
fault. Here again we have to ask a similar ques-
tion, and a little consideration will show us that
here the unit is the day, and that the hour is a
more complex and elaborate idea, that has to be
defined by the portion of time that is marked out
for us by the rising and the setting sun.

This rule is also transgressed if we define a term
by a Synonym. To define sin as iniquity or as
trespass, would be a violation of the law. Or to
define dyspepsia as indigestion, or oblivion as forget-
fulness, or forgiveness as remission, or banquet as
feast, or laundress as washerwoman. These are not
definitions, but translations for the most part of
some word borrowed from another language, and
often rather incorrect translations. It is rarely that
one language has a word exactly corresponding to
it in another. There is generally some delicate
shade of difference. True synonyms are very seldom
found, and to define by synonyms generally violates
also the first rule of good definition, since the defini-
tion and the thing defined are scarcely ever perfectly
co-extensive.

We also transgress this rule if we define by a

220

OS DEFINITION.

THIRD RULE OF DEFINITION.

221

Negative: for instance, if we define vice as the
absence of virtue, or sickness as the absence of health,
or a dii'arf as one who has not the ordinary stature of
a man. We can never learn the true nature of a
thing by any explanation of what it is not.

But what is to be done in the case of Negative
ideas ? Is not in this case Definition necessarily Nega-
tive ? It would be, if they were capable of a definition,
but a negative idea is not properly speaking an idea
at all, it is merely the negation of an idea. It is
a non-entity, something not existing, and therefore
incapable of definition. All that we can do is to
state that of which it is the negation, and thus we
describe it according to the test of our definition.
For instance, we explain darkness as the absence of
light, or weakness as the absence of strength. We do not
define in the strict and proper sense of the term,
we simply give a description of what is of its own
nature incapable of being defined.

A Negative Definition, however, is very useful in
clearing the ground and guarding against confusion.
When I am told in the pulpit that I should aim at
indifference respecting all the events of my life, I
am liable to mistake the preacher's meaning unless
he clearly guards himself against the negative signi-
fication of indifference, which is the obvious one. He
must explain what he does not mean before I can
grasp what he does mean, and can see that it is a
state of mind at which I am bound to aim. He
must make me understand that he does not mean
to recommend indifference in the sense of an
absence of interest in things around me, or a sort

of sceptical carelessness respecting truth and false-
hood, or a selfish disregard of the happiness of

others.

Rule 3. The Definition must be composed of words

used in their strict and proper sense.

This rule forbids the use of all metaphors,
equivocations, ambiguities, obscure or far-fetched
expressions in a definition.

(a) As we must avoid metaphors in a discussion,
so we must avoid them most carefully in a defi-
nition, and thic for the simple reason that exact
definitions are an essential part of an exact dis-
cussion. Very often an ingenious disputant, if he
finds that he is being worsted in an argument, will
throw in some plausible metaphor under colour of
making his meaning more evident. Thus a specious
objection to exactness of detail in some dispute may
be raised on the ground that such minute exactness
is like the work of the pre-Raphaelite painter, who
spoils the general effect of his picture by insisting
that every leaf and every flower shall be given with
the greatest precision. In the same way we hear
diversity of opinion in matters of religion defended
on the ground that in nature the diversities of shape
and size and tint among the flowers and foliage
combine into one harmonious whole, and are infi-
nitely preferable to a monotonous uniformity. We
shall have occasion when we come to speak of the
fallacies to give other instances of the danger of
treating metaphors as arguments. At present we
give it as a reason for laying great stress on exclud-
ing them from definitions.

222

ON DEFINITION.

But what is a metaphor ? It is the use of a
word in a transferred sense, the transference being
from the order to which it properly belongs to some
other order. Thus, if I define humility as the found a^
Hon of all virtue, I am transferring to the moral
order the word foundation which belongs to the
material order, and is primarily applicable to a
building. If I define a lion as the king of beasts, I
am transferring the notion of royalty from rational
to irrational creatures. The same sort of objection
would hold to the following definitions : The virtues
are the stepping-stones to Heaven amid the eddies of
passion and the whirlpools of temptation. Logic is the
medicine of the mind. Friendship is the link which
hinds together two hearts into one, A wiseacre is one
whose worst folly is a caricature of wisdom.

It is not always easy to say whether a defini-
tion includes a metaphor or not. The instance I
have just given is an illustration of this. The
word caricature, though it primarily belongs to the
material order and signifies a portrait in which the
defects are grossly exaggerated, has nevertheless
been adopted by common consent to express a cor-
responding meaning in the moral order.

(6) We must also avoid equivocations or ambi-
guities in a definition; that is, expressions which
admit of two meanings different from each other.
If I define a Conservative as a politician who upholds
the doubtful virtue of consistency, the double meaning
attaching to the word consistency— of which we
have already spoken— is an objection to my defini-
tion. If I define Liberality as the possession of the

AMBIGUITIES TO BE AVOIDED.

223

true Catholic spirit, the ambiguity of the word
Catholic is likely to mislead. So the definition of
an Oxford Professor or Tutor as a University trainer
would be liable to misconception on account of the
familiar use of trainer for one who regulates the diet
and exercise of those who take part in athletic

contests.

This is a flaw very easily overlooked in a defini-
tion where the two meanings of the word employed
are very closely akin to one another. If I define
Moral Theology as the Science of Casuistry, the defi-
nition would be misleading to those who include
in the idea of casuistry something of a tendency to
split hairs in questions of conscience. If I were
to define the human will as the faculty which is
necessarily influenced by motives, there would be a
double ambiguity ; first of all in the use of the word
motive, which means sometimes a cause of action
that compels, sometimes one that only suggests and
urges ; and also in the use of the words necessarily
influenced, which may mean that the influence is
always present or that it cannot be resisted when

it is present.

(c) We must also avoid obscure or far-fetched
expressions, as, for instance, the definition of fine
as a pecuniary mulct, or of a duck as a domesticated
mallard, or of Logic as the art of systematized ratioci-
nation, or of Philosophy as the science which renders
subjectivity objective, or of Eloquence as the essential
outcome of a combination of natural fluency and rheto-
rical cultivation.

We must, then, employ words in ordinary use

224

ON DEFINITION.

in our own day and in our own country, words the
meaning of which shall be generally intelligible to
average men, words that will not confuse or perplex
them, but simply make known to them the signifi-
cation of the word that we are defining.

This rule, like all the rest, is included in the
essential characteristics of a sound definition. If
we give the proximate genus and the ultimate
differentia, we cannot well give far-fetched or obscure
words, since we have seen that the words expressing
these are in themselves simpler and more familiar
than the word which expresses the thing to be
defined. So, again, it is impossible to define by
Synonym, or to give a definition which is not co-
extensive with the thing defined, as long as we
remember the true character which a definition
should bear. Yet these rules are always useful in
helping us to guard against the different perils to
which Definition is liable, and to put our finger at
once on any defect that has crept in unawares.

CHAPTER XI.

ON DIVISION.

Division— Various kinds of Totality— Actual and Potential Whole
—Definition and Division— Logical and Metaphysical Whole-
Physical Division— Metaphysical Division— Moral and Verbal
Division— Logical Division— Basis of Logical Division— First
Rule of Division— Dichotomy— Dangers of Dichotomy— Second
Rule of Division— Violations of this Rule— Third Rule of
Division— Cross Division— Choice of Principle of Division-
Fourth Rule of Division— Division per 5a//«m — Disparate
Division— Summary.

The importance of Definition, as we have seen, can
scarcely be exaggerated. It underlies all truth. It
is the starting-point of all our knowledge. It unfolds
the nature of the object of thought. It gives us in
spoken language an analysis of that of which we are
speaking. It is either nominal, which explains the
meaning of the words we use, or real, which opens
out the nature of the thing. Real Definition is of
various kinds, of which Logic only recognizes such
a definition as gives the gemis and differentia of the
thing to be defined. In order to define aright we
must observe certain rules : our definition must be
coextensive with the thing defined; it must be
stated in clear and familiar words, and must avoid
metaphors, ambiguities, archaisms, and far-fetched
expressions.

226

ON DIVISION.

From Definition we pass on to Division. Both
the one and the other process is a breaking up of
the whole into its parts, an analysis of the complex
into the more simple. This they have in common ;
yet they are at the same time, as processes, diame-
trically opposed to each other. That which Defini-
tion regards as a whole, Division regards as the
part; that which Division declares to be more
complex. Definition from its opposite point of view
declares to be more simple.

In order to understand this apparent anomaly,
we must remind ourselves of the various kinds of
totality, and the different senses in which we employ
the words whole and part.

What do we mean by a whole ? We mean that
which possesses some sort of unity, but is never-
theless capable of division. But unity may be
of various kinds : there is actual unity and pote7ttial
unity, and actual unity may either be physical unity
or metaphysical unity.

Unity is said to be actual when the whole is
made up of parts actually united to one another.
When they are things really joined together in the
physical universe, we have what is called physical
unity, and the whole so formed is said to be a
physical whole. Thus the human body is a physical
whole, of which the limbs are the physical parts.
But when the whole consists of things which are
distinct, not really, but only in the way in which we
conceive of them, then the whole is called a meta-
physical whole, and the parts are said to be meta-
physical parts. It is also sometimes called a whole

ACTUAL AND POTENTIAL WHOLES.

227

of comprehension. Thus animal nature, or animality,
is a metaphysical whole consisting of metaphysical
parts, viz., life and sensation. We think of these
as different from each other, but we cannot break
animality up into them, and put them apart one
from the other. They are not actually separable,
we cannot divide the life of an animal from its
capacity for sensation ; we can separate the two in
thought, but not in fact.

Unity is said to be potential when the parts of
the whole are not actually united together, either
in the physical world or in the world of thought,
but are capable of being classed together on account
of their being made after one pattern, realizations
of the same ideal which is common to all. Thus all
existing animals have nothing which really unites
them together, but nevertheless they are united in
so far as they copy one pattern and fulfil one and
the same idea. The various members of the class
do not, when all put together, constitute the Uni-
versal, but they are contained under it, inasmuch as
it can be applied to each and all of them. This is
why the Universal is called a potential whole : it is
because it has a certain power or capacity which
makes it applicable to each, and so comprises all
the individuals in its power to embrace them all.
The Universal is also sometimes called a logical
whole, because it belongs to the logical order, the
order of ideas, not of existing realities ; or a whole
oi extension, because it is extended over all the indi-
viduals that come under it. It does not consist of
the individuals as the parts that make it up, for it

228

OS DIVISION.

is capable of continually receiving fresh additions
without its nature being affected by them. It
comprises them in the sense that it is capable of
being applied to each and all of them, and to each
fresh instance that presents itself; it can accom-
modate them all within its unlimited and illimitable
circuit. Animal, as a logical whole, does not consist,
properly speaking, of men, horses, lions, tigers, &c.,
but it comprises them all ; it is in nowise affected
in itself by the discovery of some animal unknown
hitherto, and it can always find plenty of room for
it within its extension without being itself changed.

To return to Definition and Division. The whole
with which Definition deals is the actual whole, not
the physical, but the metaphysical. It breaks up man,
not into arms, legs, &c., for this would be Physical
separation, but into the various simpler ideas which
constitute the complex idea of man. It takes that
nature which constitutes him man, and analyzes it
into its constituent elements. It breaks up the
abstract idea of humanity into reason or rationality,
which is the distinguishing mark that separates him
off from all other beings, and animality, which is the
possession common to him and the brutes. It states
the results of its analysis when it says that man is

a rational animal.

The metaphysical whole is thus divided into its
metaphysical parts, the whole of comprehension
into the parts that are comprehended in it, the
complex idea with the simple ideas that make it up.
There is an actual separation, but not a physical
separation ; we cannot in fact separate man's reason

V{'

LOGICAL AND METAPHYSICAL WHOLES. 229

from his animal nature, but a separation of the two
ideas is possible. We can think of his reason away
from his animality ; we can conceive him just the
same in every respect save in the absence of reason
and all that flows from its possession. We can
conceive him also as just the same in all that
belongs to him as a rational being, and deprived
only of his animal characteristics. But neither the
one nor the other can exist apart. Take away man's
reason, and some other forms or specifying prin-
ciples must come in to determine his animality.
Take away his animal nature, and his reason
cannot stand alone, but requires some material
object which it can determine and inform.

On the other hand, the whole with which Divi-
sion deals in Logic is a potential whole. It breaks up
a class into the various smaller classes which it com-
prises. It separates the logical whole into logical
parts; it takes all the individuals that are ranged
under one head, and have one common name by
reason of their all copying the same pattern, and
analyzes them into a number of smaller groups which
contain fewer individuals, by reason of the pattern
copied by the members of these smaller groups being
of a more elaborate and more restricted character.

We are here speaking of Logical Division, and
must bear in mind that the word Division, like
Definition, admits of a number of different mean-
ings. Definition itself is a kind of Division. Perhaps
we shall clear up our notions on the subject if we
enumerate the various possible kinds of Division, and
so lead up to Logical Division properly so called.

230

ON DIVISION.

VARIOUS KINDS OF DIVISION.

231

I. Physical Division of a physical whole into its
physical parts, as of a man into soul and body, or of
water into oxygen and hydrogen, or of a tree into
root, trunk, branches, leaves, and flowers. But
these three instances reveal to us the fact that there
are various kinds of Physical Division :

(a) Into the essential parts of which the thing
divided is composed. What do we mean by the
essential parts? We mean those that are so
necessary to the whole that if one of them is taken
away the nature of the whole is destroyed. Take
away either man's soul or body, and he ceases at
once to be man. Take away the oxygen or hydro-
gen, and water ceases to be water.

(6) Into the integral parts of which the thing
divided is composed. What do we mean by the
integral parts ? Those which are a real portion of
the whole, but are not so absolutely necessary that
the nature of the whole is as a matter of course
destroyed by the absence of one of them. A tree
does not cease to be a tree because it has no flowers,
or a human body to be human because one of the
hands has been cut off.

But here we have another subdivision according
as the integral parts are homogeneotis or heterogeneous.
Homogeneous parts are those which are of the same
nature and are called by the same name, as the
various drops of which a body of water is composed.
Heterogeneous parts are those which are of a
different nature and are variously called, e,g., the
different limbs of the human body, eyes, ears, hands,
feet, &c.

2. Metaphysical Division or Definition. Of this
we have sufficiently spoken above. It is a true sort
of division, though it differs from Physical Division
or Logical Division. Yet inasmuch as it separates a
whole into parts it has a true right to the name,
even though those parts belong to the world of
thought and not of external realities.

3. Moral Division, or the division of a moral
whole into its moral parts. A moral whole is a
multitude of living beings connected together by
some relation to each other, as an army, or a family,
or a swarm of bees, or a pack of hounds.

The moral parts of such a whole are either the
individuals that compose it or certain smaller groups
possessing a somewhat similar relation to each
other. Thus in an army, the moral parts are either
the individual soldiers, or the various regiments of
which it is composed.

4. Verbal Division, or the division of an am-
biguous term into its various significations.

5. Logical Division, or Division properly so
called, in which the universal is broken up into the
various smaller classes or individuals which are
contained within its extent.

Physical Verbal

Division

L__

Moral

3hyj

I I ,

Into essential Into integral
parts. parts.

Division of a

genus into its

species.

logical Metaphysical
I or Definition.

Division per acciaens,
where the basis of
division is some acci-
dental point of diver-
gence.

232

ON DIVISION.

FIRST RULE OF DIVISION.

233

But we may break up the larger class into smaller
classes, either by following the hard and fast divi-
sions fixed by nature, or by framing principles of
division for ourselves. Every species is divided off
from all other species which come under the same
genus, not by any arbitrary distinction invented
by man for the purposes of his own convenience,
but by fixed and definite boundaries belonging to
the nature of things. The various species of animals,
for instance, are the realization of various distinct
types existing in the mind of God at the Creation.
Each of these has its own essence, the essential
characteristic without which it ceases to be what
it is. We have already explained this,' and it
is unnecessary to repeat our explanations here.
Now if we divide on the basis of the lines
of demarcation laid down by nature, we have
Logical Division in the strict and proper sense,
breaking up the genus into the various species
which compose it. In this sense we divide animals
into men, lions, tigers, bears, monkeys, and the
various species that come under the genus animal.
If, however, we select some arbitrary difference
for ourselves, then we have a sort of accidental
division useful for practical purposes, but not the
Division which is the converse of Definition, and
belongs itself to Logic as such. Such an accidental
division would be of animals into long-lived and
short-lived, carnivorous and graminivorous, hirsute
and smooth, &c., where the point of distinction
marks no radical difference of nature, but only in

« Pp. 183, 184.

one or two isolated characteristics. We must now
try and lay down the rules which constitute a
sound Division, not only in the more exact and
limited senses in which we are opposing the process
of Division and that of Definition, but in every sense
in which we employ the term.

Rule I. The dividing parts must together make up
the whole of the thing divided, neither more nor less.

This rule is one of those apparent truisms that
in practice is neglected every day and every hour.
To observe it faithfully is one of the most difficult
things in the world. How can we ever be sure
that we have exhausted every subordinate class that
comes under the larger class that we are dividing ?
If we are asked to give the various descriptions of
Church architecture prevalent in England before
the Reformation, we answer : ** Saxon, Norman,
Early English, Decorated, Perpendicular," and such
a division would be a fairly correct one. But there
are churches in England that could scarcely be
included under any of these divisions. The Flam-
boyant, that was imported from France in the
fifteenth century, is distinct from any of the above,
and our enumeration would not be complete without
it. If I divide politicians into Conservatives and
Liberals, I neglect the little knot of Anarchists. If I
divide lamps into candle-lamps, oil-lamps, gas-lamps,
and electric-lamps, I have still omitted spirit-lamps,
among the means of illuminating and heating which
I am reckoning up.

This danger can only be avoided by adopting a
kind of Division that is tedious but always safe.

234

ON DIVISION.

DICHOTOMY.

235

Dichotomy is a division by means of contradictories,
and as long as I cling to it, and am careful that the
positive dividing member is included under the class
to be divided, I cannot err in my division.

Thus I am always safe in dividing fruit into pears
and not-pears, or into ripe and not-ripe, or into edible
and not-edible. There is, however, often some diffi-
culty in discovering whether the dividing member is
included under the class. Unless I am sure of this,
my division will be a futile one. Moreover, Dicho-
tomy has another disadvantage, that it often escapes
the danger, only by covering our ignorance or uncer-
tainty at a certain stage by negative and indefinite
terms. I have to divide substances and I begin by
dichotomizing them, i.e,, I separate them into two
classes, material and non-material (or spiritual).
Then, again, I divide material substances into living
and not-living; by repeating the process I subdivide
living into sensitive and non-sensitive. Now if I
know that there are no non-sensitive material and
living substances, save vegetables, my division will
be a satisfactory one: but if I have to leave the
indefinite term non-sensitive, there remains a weak
point at the end of the process.

On the other hand a Division may easily err, in
that one of the parts includes more than the thing
divided. If I were to divide jewels into rubies,
sapphires, amethysts, emeralds, diamonds, topazes,
crystals, garnets, pearls, blood-stones, and agates,
my division would include too much, since crystals
is a name applicable to many stones that are not
jewels, and the same may be said of blood-stones

and agates. Or if I divide Africans into cannibals
and non-cannibals, either of these classes exceeds
the class to be divided, since there are both can-
nibals and non-cannibals in other parts of the world
besides Africa.

Yet in this last instance I might easily have
avoided the danger by making my division of
Africans, not into cannibals and non-cannibals, but
into cannibal Africans and non-cannibal Africans.
So again, if I divide Oxford men into Doctors,
Masters, Bachelors, and Undergraduates, my divi-
sion is a correct one if it is understood that I mean
by Doctors, Doctors of Oxford, by Masters, Masters
of Oxford, &c., and not of any other University.
But if any one were to meet a D.D., and conclude
from my division as giVen above that he must
therefore be an Oxford man, ignoring Cambridge,
Durham, London, &c., he would draw a very false
inference. Of course, in such a case as this, the
fact of Degrees being conferred by other Univer-
sities, is sufficiently obvious to render the mistake
an imaginary one. But this is not always the case.
If I divide quadrupeds into mammals and non-
mammals, I have to reflect a moment before it
occurs to me that there is a mammal biped, viz.,
man. If I accordingly re-cast my division, and
substitute for quadrupeds animals living on the
earth (as opposed to birds and fishes), and then out
of this new class form the two exhaustive classes
of mammal and non-mammal, I still am not quite
clear of the wood. Is there no animal living in the
water that gives suck to its young ? Yes, the whale.

\ .

236

ON DIVISION.

SECOND RULE OF DIVISION.

237

Hence I must change the terms of my division if I
desire to be accurate. I must divide quadrupeds
into mammal quadrupeds and non-mammal quad-
rupeds. But here a fresh difficulty arises. Are not
all quadrupeds mammals ? Are there any beasts of
the earth that do not give suck to their young ? If
not, then our division is a futile one. Once agam
I have to reflect, and perhaps to rummage a little
in natural history books as well, before I learn that
hares and rabbits are not mammals, and that there-
fore my new division is an unassailable one.

This last doubt respecting the existence of a class
of non-mammal quadrupeds, endangering, as it did,
our division, leads us to the second rule.

Rule 2. None of the dividing numbers must be
equal in extent to the divided whole.

When this rule is broken, the Division becomes
null and void, for one of the classes contains no
members. If I divide animals into sensitive and
non-sensitive, I have one of these futile divisions ;
there is no such thing as a non-sensitive animal, for
sensation is the distinguishing mark that separates
off animals from vegetables. The amount of feehng
may be so small as to be scarcely appreciable. The
poor jelly-fish commemorated above,' through which
my stick is barbarously thrust, suff^ers no tortures
by which my conscience need be disturbed. The
thousand animalculae which are said to exist in
every drop of river water that we drink, have no
prolonged agony before the warmth of the human
body or the action of the acids of the stomach put

■ Pp.68, 69.

an end to their feeble life. But, nevertheless, to the
class of sensitive beings they all belong.

This Division of animals suggests an objection.
It may be said that there are other sensitive beings
besides animals. How about the sensitive plant ?
Do we not say, moreover, that certain chemicals
used in photography are selected, because they
render paper soaked in them exceedingly sensitive
to the action of light ? Hence it appears that our
division would be assailable on another ground;
that one of the dividing classes extends beyond the

class divided.

The answer to this objection is clear enough, it
we collect our thoughts and fall back on the assist-
ance of Definition, which so often enables us to see
our way out of difficulties. We must define sensi-
tive and then we shall find that in its strict and
proper sense it is applicable to animals, and animals
alone. Sensitive means capable of sensation, or
susceptible of some sort of feeling. Our friend the
sensitive plant is not so called because we attribute
to it any kind of sensation, but because it presents
similar phenomena to those presented by things
capable of feeling ; by means of some mechanical
or organic process it simulates the appearance ot
sensation. Hence the word sensitive is in its case
used in a derived and improper sense. So too the
sensitive paper is so called because it is so delicate
in its appreciation of the influence of light, that it
resembles a living being whose senses or feelmgs
are very keenly appreciative of any impressions
made on them-another use of the word which

238

ON DIVISION.

departs not a little from the strict and proper
meaning.

This second rule is violated whenever we take
either the differentia or any property or inseparable
accident of the class to be divided as the principle
of Division. Nothing but a species of any class that
can be broken up into species, or an inseparable
accident of a class admitting merely of acci-
dental divisions, can be used for purposes of divi-
sion. If I were to divide Saints into holy and
not-holy, or into humble and not-humble, or into
those in the grace of God and those not, or into
those who have to suffer some trials and those who
have to suffer no trials, I should in each case break
this rule, for I should be trying to form a class
which would involve contradiction by attributing
to Saints properties directly or indirectly at variance
with their sanctity. A Saint who was not holy
would be a direct and immediate contradiction in
terms, for sanctity and holiness are but different
names for the same thing; a Saint who was not
humble would be no Saint at all, and a Saint who
was subject to no trials would lack an invariable
accompaniment of true sanctity. In order to break
up the class I must look for some quality sometimes
but not always belonging to the Saints. I may
divide Saints into Saints who have committed
mortal sin in the past, and Saints who never lost
their baptismal innocence, since the preservation of
baptismal innocence is not an invariable accompani-
ment of sanctity. Or I may divide Saints into
long-lived and short-lived ; or into Saints who led

THIRD RULE OF DIVISION.

239

an active life and Saints who did not lead an active
but a contemplative life ; or into Saints who were
Martyrs and Saints who were Confessors; or into
men Saints and women Saints; or into Saints
who worked miracles and Saints who worked no
miracles. Other instances of a breach of this rule
would be the division of dyspeptics into those who
suffer from indigestion and those who do not, or
philosophers into learned and unlearned.

Sometimes this rule appears to be broken when
it really is not. A hermit or eremite means a man
who lives in the desert, and if I divide hermits into
hermits who live in the desert and hermits who do
not live in the desert, I seem to be creating an
imaginary class. But common usage has lost sight
of the strict etymological meaning, and applies the
name to all who live by themselves apart from the
world. So a monk (/ioi/axo?) means a solitary, yet
I can rightly divide monks into solitaries and non-
solitaries, since custom has altered the original
meaning of the word. In the same way misers may
be divided into those who live happy lives (if any
such there be) and those who do not ; and pens into
those which are made of the feathers of birds and
those which are not, without any breach of this rule,
by reason of the change in the meaning of the word
that custom has introduced.

Rule 3. The various dividing classes must be ex-
clusive of each other ; no member of any class must be
found in any other class.

When this rule is broken, the Division is said to
be a Cross-Division, and a cross-division is always

240

ON DIVISION.

bad. Thus the division of newspapers into Catholic
papers, Church of England papers, Conservative
papers. Liberal papers, Radical papers. Democratic
papers. Home Rule papers, would be a cross-
division, for many a paper is to be found included
under more than one of these divisions. Or if we
divide monkeys into gorillas, apes, baboons, chim-
panzees, marmozets, orang-outangs, long-haired
monkeys, short-haired monkeys, Indian monkeys,
African monkeys, it is clear that as many a baboon
is also an African monkey, and some marmozets
are long-haired, the division is a faulty one.

The defect against which this rule guards us
may result either from one of the classes being
entirely included in another, as for instance in the
division of mankind into Europeans, Englishmen,
Frenchmen, Asiatics, Hindoos, Africans, Americans,
Australasians; or from one class overlapping the
other, so to speak, so that it is not entirely included
in it, yet it has some members in common with
it, as in the division of poems into lyric, epic,
heroic, elegiac, tragic and comic, sonnets, odes,

and hymns.

The secret of a good observance of this rule con-
sists in the choice of what is called a fixed Principle
of Division. I must form my different classes not
at hap-hazard, or looking first to one aspect, then
to another, of the nature of the individuals, but
to one and the same aspect of all. Almost every
class admits of being divided in several different
ways, according to the view taken of it. If a book-
collector has to break up the class of books, he will

CHOICE OF PRINCIPLE OF DIVISION.

241

do so on quite a different principle from the book-
seller. The ordinary reader, or the man who is
desirous to fill his shelves with handsome volumes,
or>he moral critic, will each of them naturally have
his own basis of division. The collector will divide
them into rare and common, and the rare books he
will divide according to the class of literature in
which he is interested. If he is a philosopher,
rare books will fall in his mind into the classes
philosophical and non-philosophical, for it is the
former alone that will interest him. If he is an
historian, they will be for him historical and non-
historical ; if a poet, or a classical scholar, or an
Orientalist, he will divide them according to his
own special taste and pursuit. The bookseller will
take an altogether different view ; for him books
will fall into the classes of books that can be sold
at a profit, and books that cannot be sold at a
profit. The man who has to fill his library with a
view to appearances, will divide them into books
with handsome backs and books which are not
well-looking, bound books and unbound books, into
folios, octavos, duodecimos, &c. The moral critic
will take quite a different Principle of Division ; to
him price, appearance, size, &c., are of no import,
his duty is to parcel all books off into those with
a wholesome, and those with an unwholesome moral
tendency, those that he can sanction and recom-
mend and those that he is bound to condemn.
Lastly, the general reader will regard books under
a general aspect, for him the important consider-
ation will be whether they interest him or not, or

242

ON DIVISION.

serve the purpose which he has in view, and his
Division will be into interesting and not-interesting,
or into useful and not-useful.

Rule 4 Wc should always divide a class into its
proximate or immediate classes, that is, into those which
on the Principle of Division which may be assumed Jollow
at once upon it without any intermediate classes.

This Rule is sometimes expressed by the phrase :
Divisio ne fiat per saltunu In dividing we ni^^t not
make jumps. It is not one the breach of w^hich
vitiates essentially a Division, it only impairs its
excellence and renders it less practically service-
able. For instance, I have to divide the menibers
of a regiment into smaller classes. If I begin
by dividing them into colonels, majors, captains,
lieutenants, ensigns, Serjeants, corporals, lance-
corporals, and private soldiers, I am somehow
conscious that I am going too far at once. I shall
do far more wisely if I first of all divide into
the immediate divisions of a regiment, viz., com-
missioned ofhcers, non-commissioned officers, and
privates, and then make a further subdivision, if
necessary, of commissioned officers into colonels
majors, captains, lieutenants, and ensigns, and ot
non-commissioned officers into Serjeants, corporals,

and lance-corporals.

This rule is more distinctly violated, it our
Division is a disparate one, i.e., if one of the classes
into which we divide is an immediate and proximate
class, while others are mediate and remote. The
division of triangles into spherical, right-angled,
acute-angled and obtuse-angled would be a breach

SUMMARY.

243

of this rule, since corresponding to the proximate
class of spherical the other member should be the
proximate class of rectangular, which ought by a
subsequent Division to be split up into the sub-
divisions determined by the character of its angles.
If we divide animals into birds, beasts, dog-fish,
fresh-water fish, and salt-water fish, we shall be
breaking this rule. If we divide inhabitants of the
United Kingdom into dwellers in England, Wales,
and Scotland, Ulster, Munster, Connaught, and
Leinster, such a Division, though it cannot be said
necessarily to involve any positive error, neverthe-
less leads to confusion of thought, and is likely to
mislead us altogether.

Our chapter on so important and practical a
subject as Division, must not be concluded without
summing up its contents. We began by explaining
that there are various kinds of Unity, actual unity
(subdivided into physical and metaphysical) and poten-
tial unity. Corresponding to these is the ^netU'
physical whole, or whole of comprehension, which
Definition breaks up into its metaphysical parts,
and the potential or logical whole, or whole of
extension, which Division breaks up into logical
parts. We are not in Logic concerned with the
physical whole any more than with the moral and
verbal, but simply with the metaphysical and logical.
Division as an analysis of the logical whole is
subject to four laws which control it :

I. The dividing parts must together make up
the divided whole, neither more nor less. This is
ensured by dichotomy.

244

ON DIVISION.

2. None of the dividing parts taken separately
must be equal to the divided whole.

3. There must be no cross-division, but the two
dividing parts must exclude one another.

4. We must descend to the proximate classes
when we divide, and not make jumps.

LOGIC.

Part II.

OF JUDGMENT OR ASSENT.

CHAPTER I.

JUDGMENTS.

Judgment— Meaning of the word— Definition of the word—Three
steps in Judgment— Various names of Judgment— Prudent and
Imprudent Judgments— Convictions and Opinions— Hypothesis
and Certainty— Immediate and Mediate Judgments—^ Priori
and A Posteriori Judgments— Test of A Priori Judgments—
Analytical and Synthetical Judgments.

The three parts of Logic correspond, as we have
already remarked,^ to the three operations of
Thought. In the first part we have been con-
sidering Simple Apprehension, which engenders the
Idea or concept, and expresses itself externally in
the Term. We now proceed to the consideration
of Judgment^ the second operation of Thought.

Judgment (judicium, airotfyavaL^) engenders the
mental declaration of judgment or declarative
expression (X0709 airo(^avriKosi) expressing itself

' P- 93.

246

JUDGMENTS.

externally in the Proposition (irporaai,^, enuntiatio, or
effaium). It derives its name from the fact that
in the second operation of thought the mind sits
like a judge upon its judgment-seat, and passes
sentence respecting the agreement or disagreement
of two objects of thought, affirming or denying one
or the other. We mentally place two things present
to our thoughts, one by the side of the other, and
after comparing them together, we pass sentence
respecting them. If we find them coincide one
with the other, or if our attention is fixed in some
point or points of agreement, we unite them together
in the sentence that we pass ; as. Tigers are savage
animals; Some negroes are thick-lipped. If we find
them at variance, or if our attention is fixed on
some point of disagreement, we separate them in
our judgments, as: Turtle-doves are not savage ; Some
negroes are not thick-lipped.
Here we notice :

1. That the word Judgment (like the Greek
a'jr6<l)avai^, and the Latin judicium) is a double word ;
(a) for the act of passing sentence; (6) for the
sentence passed. This is not a mere clumsiness
of language, but expresses an important fact of
psychology, which, however, it would be untimely
to discuss here.

2. That when we compare two objects of thought
together, it does not follow of necessity that we pass
sentence or form a judgment. We may suspend
our judgment, and if we are prudent men, we shall
invariably do so, unless we have good grounds for
arriving at a decision. Thus I compare together

DEFINITION OF JUDGMENT.

247

Kamschatkans and honest. I have never known
a Kamschatkan in my life, and cannot venture on
any assertion of their honesty, nor, on the other
hand, have I any reason to think they are dishonest.
Accordingly I suspend my judgment, and refuse to
make any statement at all respecting the coincidence
or dissidence of the two ideas.

3. That when we form a Judgment it may be
a tentative and uncertain and provisional judgment,
or it may be a firm and unwavering one. Thus
I compare together Dutchmen and intelligent. I
have. known half a dozen Dutchmen, and all of them
have been remarkably intelligent ; but at the same
time my half-dozen may have been exceptional in
their intelligence, and therefore when I lay down
the proposition, Dtitchmen arc intelligent, I do it
with some hesitation, and under the implied con-
dition that I will not maintain it, if further experience
reverses my belief in the intelligence of Dutchmen.

Judgment may be defined as a mental act in
which something is asserted and denied, or a mental
act in which one object of thought is pronounced
to be identical with or different from some other
object of thought. It includes three steps or stages.

First stage. The two objects of thought must
be separately apprehended. We cannot pass sen-
tence on things unknown to us. The first opera-
tion of thought must therefore invariably precede
the second. We do not mean that there need
be any interval between the Simple Apprehen-
sion and Judgment— one flash qi thought may
include them both— but there must at least be a

248

JUDGMENTS.

VARIOUS NAMES OF JUDGMENT.

249

precedence of order and of nature, if not of time.
Thus before I can form any judgment respecting the
agreement or disagreement of sophistry and philo-
sophy, before I can assert or deny that sophists are
philosophers, I must clearly apprehend what is the
meaning of the several terms that I am employing ;
what is the nature of the sophist and philosopher

respectively.

Second stage. The two objects of thought thus
apprehended must be compared together. We cannot
pass sentence without a trial ; the judge must examine
the parties to the suit before the decision is arrived
at. I must not only know what a sophist is, and
what a philosopher is, before I can assert or deny
that sophists are philosophers, but I must also put
them side by side and look at each in the light of the
other, just like a carpenter who puts his two pieces
of wood side by side before he unites them together.
Third stage. We are not arrived at the final
stage of our judgment. After examining the nature of
the two objects and comparing them together, we still
have something further to do ; our comparison must
eventuate in a perception of the agreement or dis-
agreement of the objects compared, before that
agreement or disagreement is laid down as a fact
by a positive act of the mind. The end we set
before ourselves in making the comparison was the
recognition of this relation between them, and must
precede in the order of nature any assertion res-
pecting their mutual attitude to one another.

Why do I say in the order of nature ? Because
in the order of time the recognition of agreement

and disagreement is simultaneous with the actual
judgment. Whether the two are one and the same
act, or whether they can be distinguished from each
other, is a point much disputed by philosophers.
It seems most likely that there is a distinction
between them : the recognition of the agreement or
disagreement has reference rather to the necessity
of the two objects of thought being united or dis-
united, the judgment passed to the fact that they
are united. But since any two objects of thought, the
union of which can be said to be necessary, always
are united, the question is one suited rather to
employ the subtle versatility of the practised dis-
putant than to occupy the mind of the student of
Logic. We may, therefore, pass it over without

further notice.

Judgment has various synonyms, representing its

different aspects. It is sometimes called Composi-

tion and Division ((rvvOetri^; koX huLip€<TL<;) because it

either puts together (componit) or separates from each

other (dividit) the ideas compared. If I place side

by side, as two objects of thought, chocolate-creams

and sweetmeats dear to the soul of youth, and after

due reflection perceive an agreement between these

two ideas, I compound or put together the delicacies in

question and the favourite confections of the young.

If after comparing together the moon and that

which is manufactured from green cheese, I pass

sentence that the moon is not made of green cheese,

I divide off the orb of night from all substances

which have green cheese for the basis of their

composition.

250

JUDGMENTS.

Sometimes it is called Assent {assensus or adhaesio)
inasmuch as the mind gives its adherence to the
verdict passed. I apprehend the idea of earwig and
the idea of nasty insect, and the result of my com-
parison is a strong assent, a firm adherence to
the objectionable character of that harmless, but
repulsive little creature.

Sometimes it has the name Assertion or Denial
{affirmatio or negatio), inasmuch as it asserts or
denies one thing of another. Thus if I am a
prudent man I shall assert the undesirable character
of roast pork for the ordinary supper of men of
average powers of digestion in the judgment : Roast
pork eaten at night is unwholesome; or I may put
the same assertion in the form of a denial by saying :
Roast pork eaten at night is not wholesome.

Divisions of Judgment. — Judgments are divided
either (i) according to the state of mind of the
person who frames the judgment, or (2) according
to the nature of the judgment in itself.

I. In the former case the division is said to be
ex parte subjecti, on the side of the subject or party
whose mind undergoes the operation of forming a
judgment; in the latter ex parte ohjecti, on the side
of the object of thought, or that to which his
thoughts are directed. Under the first head they
are divided into prudent or well-advised when they
are the result of careful and deliberate thought, and
rash or imprudent or ill-advised when they are arrived
at after insufficient inquiry or under the impulse of
prejudice or passion. This division is not one

PRUDENT AND IMPRUDENT JUDGMENTS. 251

that comes, strictly speaking, under Formal Logic ;
but we have already said that we must from time
to time, in the cause of truth, stop outside our
proper domain, and watch for error that may creep
in unawares into the mind of man.

For instance, two men set to work to inquire
into the truth of miracles. One of them studies
theological treatises respecting their nature, con-
verses with those who uphold as well as those
who deny their reality, visits the spots which are
renowned for miracles, reads carefully the medical
testimonies respecting the sudden cures worked
there, studies the lives of the saints, inquires into
the moral and rehgious character of the most
celebrated thaumaturgi, weighs the evidence for
the Gospel miracles, and (we suppose him a theist)
begs God for light that he may arrive at a true con-
clusion. If such a man, after his careful inquiry,
arrives at the conclusion that miracles are undoubted
facts, no one can deny to his judgment the character
of prudence. The other man refuses to study the
details of alleged miracles, declares them before-
hand to be the result of a fervent imagination or
a deliberate imposture, challenges the believer in
miracles to show him one before his own eyes,
and if he sees one, or has evidence brought before
him which he cannot gainsay, attributes it to some
yet undiscovered power of nature. When he passes
sentence, as such a one certainly will, that miracles
are impossible and absurd, we shall be right in
calling this his judgment rash and wanting in
prudence.

252

JUDGMENTS.

What amount of investigation is necessary in
order that the judgment which results from it should
deserve the name of prudent, must depend on the
importance of the matter in question. Here it is
impossible to lay down any law ; the only rule that
can be laid down is that such an amount of inquiry
should be made as would be regarded as sufficient
by intelligent men conversant with the matter in
question. Nor is it possible to lay down any laws
for the elimination of antecedent prejudice, since
prejudice is, in a majority of cases, a disease of the
will rather than of the intellect, and, therefore, lies
altogether out of the scope of the logician.

Judgments may also be divided in regard of the
person who forms them into certain judgments or
convictions and uncertain judgments or opinions. The
former exclude all dread of the opposite being true,
and the state of mind that results from them is cer-
iitiide ; the latter do not exclude all dread of the
opposite being true, and the state of mind they
produce is hesitating assent or hypothesis, or supposi-
tion. To the former the mind clings absolutely, to
the latter only provisionally until further light is
obtained.

One of the chief sources of human error is the
tendency of mankind to exalt opinions into convic-
tions, to regard as certain what is still uncertain, to
jump at conclusions where there is no warranty for
doing so. A man obtains a partial knowledge of the
facts of the case, and from those facts constructs an
hypothesis ; additional facts come to his knowledge
which happen to fit in with his hypothesis ; under

HYPOTHESIS AND CERTAINTY.

253

the influence of these he unduly expresses his
hypothesis as an established law, manages to close
his eyes to all facts that militate against it, and pro-
claims to the world as axiomatic what is at best but
a brilliant guess, which may be true, and may also
be false.

In all scientific investigation this stage of hypothesis
must precede certainty, and these brilliant guesses
are often the precursors of most important and
valuable discoveries, but it is a fatal mistake to
regard as certain what is still uncertain, and to
assume the truth of an induction which has not been
sufficiently tested. Thus Evolution is still an hypo-
thesis, not a scientific law, and the man who calls
himself an Evolutionist should remember this when
his law comes into conflict with the statement of the
theologian. The conclusions arrived at by Lyell
and other geologists respecting the age of the w^orld
are but hypotheses, many of which have already been
overthrown by subsequent discovery. For a long
time the motion of the earth round the sun was in
the stage of hypothesis. It was a brilliant guess, a
scientific opinion which could not show sufficient
grounds for its acceptance, in opposition to what
were supposed to be the counter-statements of Holy
Scripture. In the time of Galileo it was not clearly
established, and though his genius, overleaping the
ordinary laws of investigation, may have instinctively
recognized its truth, and justified him in holding it
as a private opinion, yet the verdict of the Roman
Congregation was in accordance with the scientific
theories of the day. Galileo could bring forward no

254

JUDGMENTS.

A PRIORI AND A POSTERIORI JUDGMENTS. 255

proof sufficient to convince them that he was right
and they were wrong. If he had stated his discovery
with due modesty, merely as an hypothesis, and pro-
fessing all submission to lawful authority and readi-
ness to withdraw all that he could not prove, the
unfortunate conflict would never have arisen and
given the enemies of the Church a plausible ground
for their attacks on the alleged narrowness of the
theological mind.

2. Judgments are also divided in various ways
in regard of the objects of thought which are com-
pared together, without any reference to the state of
mind of the person comparing them. Under this
aspect they are divided into immediate judgments and
mediate judgments.

An immediate judgment is one in which the agree-
ment or disagreement of the objects compared may
be recognized at once from a knowledge of their
nature, or from experience. If from a knowledge of
their nature, we have an immediate analytic judgment,
if from experience, an immediate synthetic judgment.
A mediate judgment is one in which the agreement
or disagreement of the subject and predicate can
only be recognized by a process of reasoning.

Thus, if I compare together circle and round as
the two objects of my thought, I at once and imme-
diately perceive their agreement from the very nature
of the case, or if I compare together angel and in-
corporeal, and therefore the judgments, Circles
are round, and Angels have no bodies, are immediate
judgments.

But, if I compare together the human body and

mortal, I have to go through a process of reasoning
before I can ascertain whether these two objects of
thought agree or disagree. I have to say to myself:
The human body is material.
All material things are corruptible.
All corruptible things are liable to decay.
All things liable to decay are mortal,
.*. The human body is mortal.
Here I only ascertain the mortality of the human
body, through the medium of other objects of
thought, viz., material, corruptible, liable to decay;
and my judgment is therefore mediate.

Judgments are also divided into judgments a
priori, and judgments a posteriori. We have already
spoken of these incidentally, but we must again
discuss them here in their proper place.

An a priori judgment is one in which the pre-
dicate is included in or united to the very idea of
the subject, and is deducible from it, so that from
the very nature of things they agree together, and
any one who has a comprehensive knowledge of the
subject, perceives immediately that the predicate is
a part of it, or is necessarily connected with it, as
The whole is greater than a part ; God is omnipotent.
Similarly an a priori negative judgment is one in
which the predicate is excluded or disunited from
the very idea of the subject, so that from the very
nature of things they disagree from each other, and
any one who has a thorough knowledge of the subject,
perceives that the predicate is not a part of it, and
is necessarily disconnected with it, as Circles are not
square ; Honest men are not thieves.

256

JUDGMENTS.

TEST OF A PRIORI JUDGMENTS.

237

On the other hand, an a posteriori judgment is
one in which the predicate is not necessarily included
in or united to the idea of the subject, but may or
may not be connected with it, so that they do not
agree from the nature of things, but only because we
learn by experience and from the facts of the case
that they agree ; as. Houses are built of brick or stmie ;
Swans are white ; Foxes are cunning ; Gold is a precious
metal ; Telephones are a recent invention. Similarly an
a posteriori negative judgment is one in which the
predicate is not necessarily excluded or disunited
from the idea of the subject, but may or may not be
separated from it, so that they do not disagree from
the nature of things, but only because experience and
a knowledge of external facts teaches us that they
disagree, as Wolves are not found wild in England ;
Dyspepsia is not a pleasant malady,

A priori judgments are also called necessary,
because they declare the necessary agreement of
subject and predicate ; analytical because an analysis
of the subject at once shows that the predicate
belongs to it ; metaphysical because metaphysics deals
with the inner nature of things.

A posteriori judgments are also called contingent
because it may or may not happen (contingere) that
the subject or predicate agree ; synthetical because
they are not arrived at from an analysis of the
subject, but from putting together (orvvOelvaL) a
number of observed facts; empirical because they
are learned by experience (ifnreipU) ; physical be-
cause physics deals with the external nature of
things.

Hence there are three requisites for an a prion

judgment:

1. The predicate must be included in or

derivable from the idea of the subject.

2. It must have the character of necessity.

3. It must be universal.

The absence of any one of these conditions will
destroy its a priori or analytical character. We will
examine one or two judgments, and see to which of
these two classes they belong.

Let us take the Proposition of Euclid: All
triangles have the exterior angle greater than either of
the interior and opposite angles. In this judgment the
subject is triangles, iho. predicate having the exterior
angle greater than either of the interior and opposite
angles. Does an analysis of the notion of a triangle
contain all this long rigmarole ? Scarcely. I
might have a general knowledge of all the charac-
teristics of a triangle without recognizing this fact.
But from the notion of triangle it is derivable. I
am supposed already to understand the meaning of
terms, and that exterior angle means the angle
made by producing one of the sides with the side
adjacent to it. When I have produced the side, I
perceive that from the very idea of triangle there is
deducible this property of having an exterior angle
greater than either of the interior and opposite
angles. This judgment is necessary. Step by step I
prove it by irrefragable argument from first princi-
ples. It is universal; no triangle in the world can be
otherwise. Yet this necessity is not self-evident or
immediate. Probably many an intelligent school-

258

JUDGMENTS.

I {

n !

boy has covered his paper with triangles in which
he has vainly hoped that one may be found, in
which the exterior angle is equal to or less than
one of the interior and opposite angles. All in
vain ! The law admits of no exception. To all
eternity no such triangle will be found. Not in
the moon, not in Sirius, not in any of the stars
which make up the Milky Way. Not in the mind
of God Himself, to whom it would be impossible,
in spite of His omnipotence, to make a triangle
by the utmost exercise of His Divine power, in
which the exterior angle should be either equal
to or less than one of the interior and opposite

angles.

Let us take another proposition : Jews arc fond
of money. Is this an a priori proposition ? According
to some, the very word Jew implies the money-
loving temper, but this is not the proper meaning of
the word. Is the fondness for money universal ?
It may be so, but this would not of itself make the
proposition an a priori or analytical one. Does the
analysis of Jew furnish the idea of fond of money ?
Certainly not. What is there in the idea of being
descended from the chosen people of God that
involves the idea of a sordid desire for riches ? Is
it a necessary proposition ? Again we answer. No.
There is no necessity in the reason of things
why there should not be members of the race (and
such there are) who are absolutely indifferent to
sordid gain. The proposition is slti a posteriori and
empirical one, which may be true and may be false.
It is arrived at from experience; it may sometimes

ANALYTICAL AND SYNTHETICAL JUDGMENTS. 259

be the case and sometimes not ; it is essentially an
a posteriori proposition.

This distinction, clearly marked as it is, cannot
always be applied at first sight to particular cases.
We may sometimes find it very hard to discover
whether any given judgment is an a posteriori or an
a priori one. Take, for instance, the judgment. All
negroes are black. To which head is this to be
assigned ? On the one hand, it may be said that
blackness is of the essence of the negro race, and
that it is this which distinguishes them from white
men. On the other hand, what are we to say about
albinoes ?

The real test of this and similar propositions is
whether, in the notion of the subject as understood
by educated and well-informed men, there is in-
cluded the predicate. If so, the proposition is an
a priori or analytical one ; if not, it is a posteriori.
In the instance just given, there is no question that
the generally entertained idea of negro includes
blackness. Albinoes are a lusus natures. It is
doubtful whether they can be called negroes even
in an improper sense. The very expression, A
white negro y is just as much a contradiction in
terms as An irrational man. But just as madmen
or idiots are no bar to the a priori character of the
judgment that men are rational, so neither are
albinoes to that of the judgment: All negroes arc

black.

But if we examine by the common-sense test the
proposition : Lions are fierce animals, we shall find
it gives very different results. The judgment is

26o

JUDGMENTS.

generally true, but not necessarily, or indeed univer-
sally. The idea of a lion does not include that of
fierceness. If we found a race of lions gentle and
even cowardly (such a race is said to exist in Asia,
I know not where), we should regard them as lions
just the same. Cowardly lion does not jar upon our
intellect like white negro. We are well aware that
most lions are fierce and brave, but we are quite
ready to find that there are plenty of exceptions.

We have already discussed Kant's theory of
the existence of a priori propositions that are not
analytical, and we need not add anything here in
refutation of a priori synthetical propositions. His
theory arose from an imperfect analysis, and was
an easy way out of the difficulty of reducing them
in some cases to the laws by which all thouglit
is regulated. It is rejected by the best modern
logicians,' and is one of those fond inventions by
which men imagine that they have improved on
scholastic principles, not perceiving that they would
thus improve off the face of the earth the solid
foundations on which alone true philosophy can
rest unshaken.

« Cf. Zigliara, Logica, pp. 84. 85. who says: •' Impossibile igitur
est concedere universalitatem et necessitatem praedicati in aliquo
subjecto, et negare hujusmodi praedicatum includi in ipsa ratione
subjecti; consequenter judicia synthetica-a-priori. quae habent.
fatente Kantio, priores conditiones. habent a fortiori et alteram de
inclusione praedicati in notione subjecti ; ac proinde ilia judicia
revera sunt analytica absolute et a priori."

CHAPTER II.

ON PROPOSITIONS, THEIR NATURE AND DIVISIONS.

What is a Proposition— Parts of a Proposition— Ambiguity of word
Predicate— Analysis of Propositions— Divisions of Propositions
—Necessary and Contingent Propositions— Affirmative and
Negative Propositions— True and False Propositions— Truth
and Falsity in Logic— Logic as a test of Truth— Quantity of
Propositions— Singular Propositions— Indefinite Propositions-
Distribution of the Predicate— Rules of Distribution.

We have already said that Logic is concerned
primarily with thought, and with language in so far
as it is necessary for the expression of thought.
The first part of Logic dealt with Terms, inasmuch
as they are the external rendering of the ideas
which are the result of the first operation of thought.
In the same way the second part of Logic deals
with Propositions as being the external rendering
of the judgments which the mind forms in the
second operation of thought. Hence a Proposition
is nothing else than a judgment expressed in words
or other external signs. Not necessarily in words,
for we may state a proposition by a word or a shake
of the head. If a father asks his little girl whether
the cat has had her breakfast, and the child nods
her head by way of reply, she enunciates the affir-
mative proposition, '* The cat has breakfasted," just

262

ON PROPOSITIONS.

AMBIGUITY OF THE WORD PREDICATE, 263

as clearly as if she said yes, or repeated the words.
But in general we may say that language is the
natural expression of thought, and therefore in
general the Proposition is a Judgment expressed in

words.

We may now define a Proposition :
A Proposition {Trporaai^;, a'ir6(\>av(TL^, cnuniiatio,
propositio, predicatio, effatum) is an expression which
affirms or denies something of something else
{oraiio affirmans vel negans aliquid de aliquo), or a
form of words which states one thing of another
(oratio enuntiativa unins de alio),

A Proposition consists of three parts or elements:
the Subject y Predicate and Copula, The Subject (vTroKeL-
fievov, subjectum) of a Proposition is that of which
something else is stated.

The Predicate {KaTrf^opov^evov, praedicatuvi) of a
Proposition is that which is stated of something else.
The Copula (irpoaKarrjyopovfievov, appracdicatum)
of a Proposition is the link uniting (is, are) or sepa-
rating {is not, are not) the subject and the predicate.
Thus in the proposition: Rattlesnakes arc
poisonous, Rattlesnakes is the subject of which it
is stated that they are poisonous, poisonous is the
predicate which is stated of Rattlesnakes, and are
is the copula uniting them. In the proposition:
Sceptics are not true philosophers, sceptics is the
subject, true philosophers the predicate, and are not
the disuniting copula. The subject and predicate,
inasmuch as they occupy the extremities or the
beginning and end of the proposition, are called the
Terms (opoi, dxpa, termini) of the Proposition. Simi-

larly in the proposition. Old men are fond of talk-
ing, the subject is old men, and the predicate fond
of talking. In the proposition: The unparalleled
audacity of his conduct is sufficient to cause all honest
men to shun his company, the subject is the unparalleled
audacity of his conduct ; the predicate, sufficient to cause
all honest men to shun his company. Hence it is clear
that subject and predicate may consist of many
words so long as these words are expressive only of

one idea.

Here the reader must be warned of a certain
ambiguity in the word predicate. In grammar,
predicate is used in a different sense from that
which it bears in logic, and includes the copula as
well. In the proposition, Idleness demoralizes,
the grammarians would call demoralizes the predi-
cate ; in the proposition. Dogs bark, bark would be
the predicate in the grammarians' use of the word.
This terminology was also that of Aristotle and the
earlier logicians. They broke up the proposition
into the ovotia, or the subject, and the pripxi, or the
predicate. The change in the terminology of
logicians is post-Aristotelian, and is suggested by
a passage in his treatise De Interpretatione, 10. 4, in
which he says that the verb is sometimes added to
the subject and predicate as a third element in the
proposition.^

» tiray Sf rh rplrov tffri irpoffKarrjyoprirai, ^5tj 5tx«s Aryorrat oi
avTidcVtiJ. X€7« 5i, oh,^ rcrrt Si'/caios iydfrniros. From this expression
subsequent logicians drew the term irporiffas iK ^evrtpov TrpoffKarv
-/opovfifyov, or propositiones secundi adjacentis, where the copula forms
one word with the predicate, as Trees grow; and irpordtrus 4k rpirov
irpoffKarrrYopovfi^yov, or propositiones tertii adjacentis, as Trees are growing.

264

ON PROPOSITIONS.

ANALYSIS OF PROPOSITIONS.

265

A Proposition may consist of any number of
words from one to a thousand, but it must always
be capable of being resolved into three terms, viz.,
subject, predicate, and copula, e.g., loquitur, he
speaks, he is speaking, where he is the subject,
speaking the predicate, and is the copula. Troja
fuit—Troy is a city of the past ; Adversantur—They are

opponents.

In order to break up a Proposition we have
only to ask ourselves, i. What is it of which we
are speaking ? and the answer to this question will
give us the subject of the proposition. 2. What
is it that we affirm or deny of it ? and the answer
will be the predicate ; while the copula is always
some person singular or plural of the verb to be
with or without the negative. Thus in the pro-
position, Horses neigh, that of which we are speak-
ing is Horses : that which we say of them is that
they are creatures that neigh, and our proposition
in logical form will be, Horses are neighing creatures.
In the proposition. Misers are not generous. Misers
is the subject, generous the predicate, arc not the
separating copula.

It is not very easy in some cases to distinguish
the various elements in a complicated statement
into subject, copula, and predicate. The beginner
is prone to mistake the object of the verb for the
predicate, and if asked to give the predicate of
the sentence. Architects build houses, to imagme
that houses is the predicate, instead of builders of
houses. There is also the further difficulty of dis-
tinguishing the use of the present tense of to be

as copula from its use as indicating existence. In
the proposition, A million years ago the world was
not, was not means did not exist, and the predicate
will be, an object that had no existence. Besides
this we have to remember that the present tense of
to be is alone available as the copula. Thus, Casar
was a skilful general=CxsdiT is a man who was
skilful as a general. The sun will be burnt out so^ne
rfay=The sun is a fire that some day will be burnt

out.

A more serious difficulty arises from the frequent
transposition of sentences. Thus in the sentence.
Many are called but few are chosen, there are two pro-
positions of which the respective subjects are those
called, and those chosen, while the predicates are
many and few. In some cases it is impossible to
decide without the context, which is the subject
and which the predicate, as in the sentence: A
very young man was the judge in this importafit suit.
In such cases, we have to discover the predicate
by asking ourselves which is the emphatic word in
the sentence. If great stress is laid on the extreme
youth of the judge, then a very young man will be
the predicate ; but if the fact of his youth is men-
tioned as a fact only of secondary importance, then
iJie man who was judge in this important case is the
predicate. In the proposition, / read your letter with
very great sorrow indeed, the emphasis falls on the
concluding words. The logical order will be : The
feeling I experienced when I read your letter is a feeling
of very great sorrow. In the proposition. Most men
eat flesh meat, most is emphatic, and the logical

266

ON PROPOSITIONS.

NECESSARY AND CONTINGENT PROPOSITIONS. 267

I i

order will be : The eaters of flesh meat are a majority
of mankind.

Divisions of Propositions.— Every Proposition
has a material and a formal element. The material
element or matter of a Proposition is the subject and
predicate, for they are the material out of which the
Proposition is made.

The formal element of the Proposition is the
copula, since it gives it its form and shape, and
determines its quality, both its essential quality,
whether it is affirmative or negative, and its acci-
dental quality, whether it is true or false. Hence
we have three different Divisions of Propositions.

I. According to their matter (that is, according
to the relation existing in fact between the subject
and predicate), they are divided into four classes.

(a) When the subject and predicate are by the
very nature of the case united together, the proposi-
tion is said to be in necessary matter, as, A straight
line is the shortest distance between any two points, or,

God exists.

(6) When the subject and predicate are in point
of fact united together, but their union is not of the
nature of things, but is a fact that we could conceive
otherwise, they are said to be in contingent matter,
as. Cats have a strong attachment to the place in which
they live ; A red light is a signal of danger.

(c) When the subject and predicate in point of
fact are not united, but there is nothing in the nature
of things to prevent their union, the proposition is
said to be in possible matter, as, Horses are not long-

lived ; Omnibus drivers are not remarkable for excessive
smoothness of tongue.

(d) When the subject and predicate are of the
very nature of things disunited so that they never
are and never can be found together, the proposition
is said to be in impossible matter, as. The diameter
of a circle is not greater than the circumference ; What
is past cannot be undone.

These four different kinds of Propositions may be
reduced to two, viz., necessary and contingent. Pro-
positions in impossible matter simply mean those in
which the predicate is necessarily separated from the
subject. There is an element of uncertainty common
both to Propositions in contingent and to those in
possible matter. The fact that two ideas that may
or may not be united are always found together in
point of fact, does not give to their union a necessary
character.

II. This second Division is based on the tie or
link which binds together the subject and the pre-
dicate, and which is called the copula. It is of the
essence of a proposition to make some statement,
or to enounce something, and as such enouncement
either affirms or denies according to the character
of the copula, on the character of the copula depends
the essential quality of the proposition. Hence,
according to their form or essential quality, Propo-
sitions are divided into affirmative and negative, and
into true diud false.

An Affirmative Proposition {TrporaarL^ KarrjyopcKTf
or KaTa(t>aTLKrj), is one in which the copula unites
together the subject and the predicate, and pro-

268

ON PROPOSITIONS.

TRUE AND FALSE PROPOSITIONS.

269

It i

t :

claims their identity, as Novels arc works of fiction.
A Negative Proposition (irporaci^ awotjyarLKrj or
trrepvTCKv), is one in which the copula disunites the
subject and the predicate, and proclaims their
diversity, as Novels are not text-books of philosophy.

There are some cases in which the presence of a
negative in the proposition does not render it a
negative proposition, and affects not the copula but
the subject or predicate. Such propositions are
sometimes called in Latin Propositiones infimta, m
that their subject or predicate is indefinite in extent,
being limited only in its exclusion from some
definite class or idea: as, Not to advance ts to
recede, Rehellian is non-suhmission to lawful authority,
Heresy is not to acknowledge as true the teaching of
the Church, All the actimis of the lower animals are
non-voluntary. These propositions may be reduced
without difficulty to the ordinary form: He who
fails to advance recedes, Rebellion is a refusal to submit,
Heresy is a disavowal of the teaching of the Church, No
actions of the lower animals are voluntary.

We pointed out in a previous chapter the distinc-
tion between indefinite terms on the one hand, and
negative or privative terms on the other, between non-
voluntary and involuntary, non-religious and irre-
ligious. The one is a direct denial of the positive
term to which it is opposed, the other denies it in-
directly, by asserting something else. If I say that
a book is non-religious, I mean that there is nothing
about religion in it, and that the question of religion
does not come in; nay, there is something more
implied in the expression, I imply that there is no

room for religion in the book, or at all events there
is no need for bringing in religion. I imply that the
book itself lies outside the matter of religion, and
not merely that religion is absent from its pages.
This distinction is an important one in guarding
against fallacies, as we shall hereafter see.

But if the essential quality of propositions is to
affirm or deny, they have another quality which flows
from the fact of their making an affirmative statement
or negative. Such a statement must either be in
accordance with facts or not. If it agrees with the
external reality it is said to be true, if it does not, it

is said to be false.

This brings us back to a question we had occasion
to allude to in our first chapter. How far is Logic
concerned with the truth or falsity of propositions ?
We cannot attempt to discuss it at length, but it will
be useful to lay down one or two principles to guide
us in answering this question.

What do we mean by truth ? We are not speak-
ing of truthfulness or moral truth, but of logical
truth. Truth is by common consent allowed to be
a statement of things as they really are. If this
statement is an internal one, we have a true judgmejit ;
if it is an external one, a true proposition. If our
judgments are always true, our propositions will
always be true (supposing that our words correspond
to our thoughts). Hence, a true proposition is the
enunciation of a true judgment.

But what is a true judgment ? It is one in which
there is a conformity between that which the mind

LOGIC AS A TEST OF TRUTH.

271

270

ON PROPOSITIONS.

I I

? I

affirms of some object of thought and that which
the object is in itself. Logical truth is the corres-
pondence of the understanding to the thing under-
stood {adcsqttatio intelledus cum re intelleda). How far
can Logic secure this correspondence ?

We have seen that all Propositions are either a
priori or a posteriori. In the former the predicate is
contained in or necessarily united to the subject. In
the latter the connection between the subject and
predicate is not a necessary but a contingent one,
dependent on the evidence of external facts, not
simply on our own mental processes.

I. In all a priori propositions the logician can
as such at once determine whether a proposition is
true or false. He has only to analyze the subject,
and see whether the predicate is contained in it, or
united to it by some necessary law. If a friend were
to make a voyage to the moon, and inform me on his
return that he had found a circle of which the radii
were not all equal, and that in the moon whenever
you added together 5 and 7 it invariably made 14
instead of 12, I should opine that he had been so
struck with the moon as to be moonstruck.

2. In a posteriori propositions the logician, as
such, can determine that a proposition presented to
him is false, if it is in opposition to some a priori law.
If I were to be told, for instance, that of two roads
from New York to Chicago one was shorter than the
other, and on comparing them on a correct map to
find that the one said to be shorter went along the
two sides of a triangle, while the other travelled
straight along the base, I should at once resent the

assertion, as being opposed to an a priori mathe-
matical law.

3. Similarly, if a proposition presented to the
logician is in opposition to some other proposition
(of whatever kind) that he knows on other grounds
to be true, he can proceed at once to pass sentence
respecting the falsity of this new proposition. If
I know that all hawks are carnivorous, and a friend
tells me he has a hawk that will not touch meat, and
eats nothing but biscuits and preserved apricots, I
conclude that my friend is either joking with me, or
is mistaken in thinking that his bird is a hawk. My
knowledge of logical truth tells me that the proposi-
tion. This hawk is not carnivorous, is incompatible
with. All hawks arc carnivorous, and therefore is false.
4. But in the case of a posteriori propositions
which are opposed neither to any law of thought,
nor to any knowledge I already possess. Logic is
incompetent to deal with their truth or falsity. If
I am asked to accept the proposition. The moon is
made of green cheese, there is no means of saying
whether it is true or false, unless indeed I have
already made my own some proposition respecting
the composition of the moon, which is at variance
with the one now presented to me. If I am told
that in China there are blue flamingoes which sing
beautifully, I may smile incredulously, but I cannot
contradict the statement unless I have, either from a
knowledge of the internal nature of the flamingo, or
from the testimony of others, already accepted among
my convictions the propositions: All flamingoes are
red, No flamingoes are musical. In a word, Logic

272

ON PROPOSITIONS.

PARTICULAR AND SINGULAR PROPOSITIONS. 273

1 I

I i

i'i

can detect formal, but not material truth and falsity,
Le,, it can determine truth or falsity if it can be
decided by the formal laws of Thought, but not if
external investigation and experience are required
to verify the propositions in question.

III. The third Division of Propositions is based
upon their quantity ; that is, the number of indi-
viduals to whom they are applicable. In this division
the predicate is not concerned ; it is the extension
of the subject on which alone depends the quantity
of the proposition.

Propositions are divided according to their quan-
tity into Universal, Particular, Singular, and Inde-
finite,

I. A Universal Proposition is one in which the
predicate is asserted of each and all the individuals
comprised under the subject. The subject has the
sign all or nmie prefixed to it, and is said to be
distributed, or used distributively, as, All flatterers are
dayigerous companions, All material things are liable to
decay, No squares have five sides.

We must, however, distinguish three kinds of

Universality.

(a) Metaphysical or Perfect Universality, in which
the subject and predicate are so inseparably united,
that under no possible circumstances and in no
possible case can they be separated, as, All circles
are rotmd. No irrational animals can commit sin.

(b) Physical Universality ; when the subject and
predicate are invariably and inseparably united
according to the ordinary course of nature, but may
be separated by the power of God or by a miracle.

as, No man can be in two places at the same time, All
dead bodies decay.

(c) Moral Universality, where the subject and
predicate are in the opinion of man generally found
together, though the law admits of some exceptions,
as, A II bullies arc cowards at heart. No learned men are
noted athletes.

All three are true Universals. The first is
based on the nature of things, and, therefore,
never can be reversed. The second on the ordinary
laws which govern the universe, which the Author
of those laws can set aside at His good pleasure. The
third on the general characteristics of human nature,
which, however, the free will of man renders only
true within certain limits, and so far as men are
taken in the mass, and not necessarily in each par-
ticular case. Hence any deduction from the last
kind of Universal must be drawn with exceeding
caution, and must not be regarded as certainly
established.

2. A Partictdar Proposition is one in which the
predicate is asserted of a portion of the individuals
comprised under the subject, and which has the sign
some prefixed to it, and is said not to be distributed.
Some lawyers take snuff ; Some boys are not mis-
chievous. There are Particular Propositions to which
is prefixed a sign of universality, by which we must
be careful not to be misled. The proposition, All
men have not faith, is really a Particular, in spite
of the word all with which it commences, and is
equivalent to Not all men have faith or Some men have
not faith.

274

ON PROPOSITIONS.

3. A Singular Proposition is one in which the
predicate is asserted of one, and one only, of the
individuals comprised under the subject, as, Casar is
famous in history, This stone is valuable.

Under what head are we to class Singular Pro-
positions? Under Universals or under Particulars?
It may be said that in a Singular Proposition the
predicate is asserted of the whole of the subject,
and, therefore, that Singulars should be reckoned as
Universals. This is not the question, but whether,
when the predicate is asserted only of one member
of the class, it is asserted only of a portion, or of
all the class. Now if I say. This Hottentot is a
great rascal, my assertion has reference to a
smaller portion of the Hottentot nation than the
proposition Some Hottentots are great rascals. The
same is the case even if the subject be a proper
name. London is a large city, must necessarily be
a more restricted proposition than. Some cities are
large cities; and if the latter should be reckoned
under Particulars, much more the former. A Singular
term has no extension whatever, and a Singular
Proposition is to be reckoned as the most limited
possible form of which the Particular is capable.

4. An Indeterminate or Indefinite Proposition is
one in which the subject has no sign of quantity
going before it, as. Frenchmen are polite, Angels are
spiritual beings. How are we to deal with Indeter-
minate Propositions ? We must manage to decide
their quantity for them somehow. When I say
that Frenchmen are polite, do I mean some French-
men, or all Frenchmen? When I say that Angels

INDEFINITE PROPOSITIONS.

275

arc spiritual beings, do I mean some Angels, or all
Angels? In order to decide this question with
regard to any given Indefinite Proposition, we have
to refer to the Division of Judgments, given above.^^
We there said that all Judgments are either a /)non
or analytical, when the subject and predicate are
necessarily connected together, or a posteriori or syn-
thetical, when the union of subject and predicate is
based on experience, not on the inner nature of
things. In the latter case they are united, so far as
we know, in point of fact, but there is no absolute
necessity for their union, and a wider experience
might reveal them apart from one another. The
former are said to be drawn in necessary, and the
latter in contingent matter, because the subject and
predicate, the matter of the proposition, in the one
case must be united, and in the other may be united.
When an Indefinite Proposition is presented to
us, and we have to assign it a quantity, we have to
ask ourselves whether the subject and predicate are
of absolute necessity connected or not; whether
they must be found together, or whether they may
sometimes be found together, at another time be
found apart. If the former, the proposition in
question is a Universal ; if the latter, a Particular.
Thus, if I am asked to assign a quantity to the
proposition, Triangles have all their interior angles
equal to two right angles, I recognize at once the
necessity of the connection between the nature of
a triangle and the sum of its angles, and pronounce
it at once a Universal. If I have to decide re-

« Pp. 256, 257.

276

ON PROPOSITIONS.

specting the proposition, Dwellers in cities are weakly,
I ask myself whether a dweller in a city must
be weakly by the nature of things, and I perceive
that there is no necessary connection between city
life and feeble health, and I therefore pronounce the
proposition to be a Particular, viz.. Some dwellers m
cities are weakly. It is true that there are many
cases in which it is difficult to decide whether the
connection between subject and predicate is neces-
sary or not. Thus, if I am asked to assign a quantity
to the proposition. Bears are four-footed animals, I
consider whether there could by any kind of possi-
bility be a biped to whom we should give the name
of Bear on account of its similarity to the quadruped
familiar to us. If there should be discovered an
animal in all things like to Bruin, but walking
always on two legs, should the name of the Bear be
eiven to it? We leave our readers to settle the
question of fact. It is only the duty of the logician
to say that on the answer to it will depend the
quantity of the proposition ; whether we are to say
that Some bears are four-footed animals, or All bears
are four-footed animals.

But we have been speaking hitherto only of the
extension of the subject of the proposition. Is the
predicate never distributed, i.e., used of each and all
the members of the class? The extension of the
proposition does not depend on the extension of the
predicate, and when the predicate is used in all its
extension, there is, as a rule, no sign of universality
prefixed to it. Yet it is necessary to the due under-
standing of the nature of the proposition that we

RULES OF DISTRIBUTION.

277

should know when the predicate is distributed, i.e.,
used in all the fulness of its extension, so as to have
reference to all the members of the class, and when
it is not. We may lay down the following rules
respecting the Distribution of the Predicate.

I. In an Affirmative Proposition the predicate is
not distributed, at least as far as the form of the
proposition is concerned. If I say. All omnibuses are
public or private vehicles, I am not speaking of the
whole of the class of public or private vehicles, for
there are carts, cabs, coaches, broughams, &c., as
well. So if I say. Some books are very uninteresting, it
is equally clear that I do not exhaust the class of
uninteresting objects, or speak of the whole of them.
But we must observe here that we say that in an
Affirmative Proposition the predicate is not dis-
tributed so far as concerns the form of the proposi-
tion. But there are cases in which in virtue of the
matter, i.e., by reason of the particular objects
referred to, it may be distributed. This is the case
in all Definitions. When I say. All triangles are
three-sided figures, I am speaking of all three-sided
figures as well as of all triangles, and it is quite as
true that All three-sided figures are triangles, as that
All triangles are three-sided figures. This holds good,
not only of all Formal Definitions, but of every sort
of Definition and Description. If I describe the
cuckoo as a bird which is wont to lay its eggs in
the nest of another bird and utters a cry corre-
sponding to its name, my rather roundabout
description will, if put in the form of a Universal
Proposition, distribute its predicate in virtue of the

lilt

278

ON PROPOSITIONS.

fact that there are no other birds that imitate the
peculiarities of the cuckoo.

The same is true if I give a synonym, as, A
sycophant is an interested flatterer, A II giraffes are camel-
opards, and it applies also to all propositions in which
the predicate is the differentia or any other property
belonging exclusively to the class which forms the
subject as. All men cook their food. All spiders are web-
spinners, since there are no other beings in the
world save men who cook their food, no insects
which spin webs save spiders.

II. In a Negative Proposition the predicate is
always distributed, that is, every individual belonging
to the class is included in the assertion made. It
matters not whether the proposition is Universal or
Particular, or whether the subject of the proposition
is distributed or not. The presence of a negative
affecting the copula always involves the distribution
of the predicate. Thus in the proposition. No
savages are men of letters, the whole of the class of
literary men is excluded from the class of savages as
well as the whole of the class of savages from the
class of literary men. In the proposition, So7ne
kettles are not made of tin, the whole of the class of
articles made of tin is excluded from the particular
set of kettles referred to, and these in their turn are
excluded from the whole class of articles of tin.

Hence we arrived at the following rules for the
distribution of the terms of a proposition. Universal
Propositions distribute their subject. Negative Proposi-
tions distribute their predicate, or if we call the
Universal Affirmative by the letter A, the Universal

RULES OF DISTRIBUTION.

279

Negative by the letter E, the Particular Affirmative
by the letter I, the Particular Negative by the
letter O, our rules for distribution will be :

A distributes the subject only ;

E distributes both subject and predicate ;

I distributes neither subject nor predicate ;

O distributes the predicate only.

These letters are commemorated in the mnemonic

lines :

A asserts and E denies,

See, they each the whole comprise ;
I asserts and O denies,
Each to some alone applies.^

To these convenient letters we shall presently

recur.

» Asserit A, negat E, venim generaliter ambae.
Asserit I, negat O. sed particulariter ambo.

r I

CHAPTER III.

IMPORT OF PROPOSITIONS. VARIOUS KINDS
OF PROPOSITIONS.

Import of Propositions— Comprehension and Extension— Primary
Import of Propositions— The Predicate not quantified in
thought — Sir W. Hamilton's theory — Various kinds of
Propositions — Categoricals and Hypotheticals — Conditional
Propositions — Disjunctive Hypotheticals — Pure and Modal
Propositions — Nature of Modal Propositions.

We have seen that Propositions may be divided
according to their matter into Necessary and Con-
tingent ; according to their essential quality into
Affirmative and Negative ; according to their acci-
dental quality into True and False. According to
their quantity we have divided them into Universal,
Particular, Indefinite, and Singular; and we have
assigned Indefinite Propositions to the class of Uni-
versal or Particular according as they are a priori
or a posteriori propositions, while Singular Proposi-
tions we have relegated to the class of Particulars.
We must now pause for a moment to say a few
words on the Import of Propositions, and what it
is we mean by our assertion of the agreement or
disagreement of subject and predicate. This we
must discuss a little more at length, and in connec-

PRIMARY IMPORT OF PROPOSITIONS.

281

tion with this we must consider the proposal of a
modern teacher of Logic, which, if it were adopted,
would revolutionize Formal Logic.

We have already defined a Proposition as a
Judgment expressed in words, and a Judgment as
i mental act which unites or disunites two objects
of thought. But we may think of an object of
thought under two different aspects, either as an
idea, comprising a number of simpler ideas, or as a
class containing a number of smaller classes ; or. to
use ; nomenclature already familiar to our readers,
as a whole of comprehension, or a whole 0/ cxUnswn

This we have already explained at length What
we have now to decide is the aspect under which we
regard the subject and predicate of a proposition.
When I say that All chaffinches are birds, do I mean
that my idea of chaffinch comprises my idea of bird,
that in all the individuals in which are found reahzed
the idea of chaffinch will also be found realized the
idea of bird, or do I mean that the smaller class of
chaffinches is comprised in the larger c'^.^;;/ ^^f
Do I think of chaffinch and birds as ideas or as
classes ? Of the attributes they comprehend, or ot
individuals over which they extend ?

What is it that naturally occupies our mind
when we examine any sort of proposition? If we
Tsk ourselves this question, we shall find that we
turn instinctively to the inner nature of subject and
predicate, to the simple ideas which make up the
more complex idea, and look to these in order to
discover whether our proposition is true or false. If
any one asks me respecting the meaning of the pro-

il-

282

IMPORT OF PROPOSITIONS.

position, All garnets are precious stones, I unconsciously
begin to analyze my idea of a garnet and my idea of
a precious stone to see if they coincide. I think of
all that is contained in the idea of garnet and the
idea of precious stone ; of all the marks of a precious
stone that divide it off from all other stones, and I
examine whether these marks are all found in the
idea of a garnet. If again I should assert that No
shopkeepers are learned men, I must first analyze my
notion of a shopkeeper and all that is compre-
hended under the term, and I must also analyze my
idea of learned men ; and then compare together the
contents of each, to see if there is any contradiction
between the attributes which belong to the shop-
keeper as such, and those which belong to learned
men as such. I shall not be justified in laying
down the proposition unless such contradiction can
be shown to exist.

Do I at the same time think of the subject and
predicate as classes ? It is true that when I say all
garnets are precious stones, the word all impHes
that if all the garnets existing in the world were
brought together into a big heap, this heap would be
found to be a small portion of a larger heap com-
prising all the precious stones of the universe. But
this is not what is present to my mind primarily
and as the Import of the proposition. I am not
thinking of garnets as a class.' I do not cast my

» This is excellently expressed by Mill. " When I judge that
All oxen ruminate, what do I mean by all oxen ? I have no image in
my mind of all oxen. I do not, nor ever shall, know all of them,
and I am not thinking even of all those I do know. • All oxen '

THE PREDICATE NOT QUANTIFIED IN THOUGHT. 283

mental eye over a collection of garnets to see
whether there may not be among them one which
is not a precious stone, but I pierce by my PO^er of
mental sight the nature of the garnet to see whether
there may be among the characteristics of a precious
stone one which is not found in it. In technical
terms I look not to the extensioit, but to the compre-
hension of the stcbjcd. I regard it as an idea, not as

a class. , . .. .1 ^

If this is so with the subject, much more is it the
case with the predicate. When I say All garnets are
precious stones, there may be some excuse for the
notion that I am speaking of the class of garnets^
as the word all gives a certain colour to it But
there is no sort of ground for asserting that I am
thinking of precious stones as a class, or considering
whether all or some of them are comprised in the
class of garnets. All that I am thinking of is that
the idea of precious stone is invariably united to
the idea of garnet. What I have i" ^ny nimd is
the two ideas and their co-existence. It is true that
by a further process I may turn my mind to the
consideration of the question whether there are
other precious stones besides garnets; whether
garnets constitute the whole class of precious stones

in rny thoughts does not z'\^^-^:\::'::^:^L":;':::^

obiects,wha.ever.heymay I. tha ha^e theatt^r^^^ J ^^ ^^^

oxen are recognized, and «*> f V=°"^P _. i :„dge, the

wherever these attributes '^aUbefo-d^ Theresas ,J^^^^^

284

IMPORT OF PROPOSITIONS.

SIR W. HAMILTON'S THEORY.

285

II '

or only a part of it. But in the original proposi-
tion I took no notice of this question, and when I
consider it now, I do not by considering it elicit any
fresh information as to whether I have been speak-
ing of all precious stones, or only of some. My
statement has been an indefinite one, and indefinite
it must remain, as far as the force of the terms is
concerned. If I say. All men arc rational animals, it
may be quite true that the whole of the class of
rational animals is exhausted by the class of men,
but as far as the proposition is concerned this is not
the case. When I turn from the natural meaning
of the proposition which asserts the co-existence of
the two ideas, to the question of the respective ex-
tension of the two classes, I have no data for
deciding whether I am alluding to the whole of the
class of rational animals or only to some of them.
I can learn this fact only by external inquiry. I
must search all through the universe before A
can decide the question whether there are other
rational animals besides men, whether there are
Houyhnhnms in Sirius or in the moon. As a
logician, with nothing before me but the propo-
sition. All men arc rational animals, I know nothing
about it.

What does all this amount to? That in a
proposition I speak neither of the subject or the
predicate as classes, but as ideas. I have before
me their comprehension, not their extension. In
the case of the subject, when the proposition is a
Universal, I have before me, in the sign of quantity
attached to it, the means of knowing that the whole

of the class is included, but I have no such source
of information with respect to the predicate. In
other words, wc do not in thought quantify the predicate
of propositions.

It is strange in face of these facts to find a man
of the ability of Sir W. Hamilton proposing to
quantify the predicate of all propositions. He
makes this proposal on the ground that we ought to
state in language what is already understood in
thought. This principle is a perfectly sound one,
but unhappily for his argument, we do not, as I
have shown above, quantify the predicate in our
thoughts. Let us hear what he has to say on the

subject.

" In a proposition, the two terms, the Subject
and Predicate, have each their quantity in thought.
This quantity is not always expressed in language,
for language always tends to abbreviation ; but it is
always understood. For example, in the proposition.
Men are animals, what do we mean ? We do not
mean that some men, to the exclusion of others, are
animals, but we use the abbreviated expression men
for the thought all men. Logic, therefore, in virtue
of its postulate, warrants, nay requires, us to state
this explicitly. Let us, therefore, overtly quantify
the subject, and say. All men are animals. So far
we have dealt with the proposition,— we have quan-
tified in language the subject, as it was quantified in
thought. But the predicate still remains. We have
said— ^// men are animals. But what do we mean
by animals ? Do we mean all animals, or some
animals ? Not the former ; for dogs, horses, oxen,

286

IMPORT OF PROPOSITIONS.

&c. are animals as well as men, and dogs, horses,
oxen, &c., are not men. Men, therefore, are animals
but exclusively of dogs, horses, oxen, &c. AU
men, therefore; are not equivalent to all ammals ;
that is, we cannot say, as we cannot thmk, that
all men are all animals. But we can say, for
in thought we do affirm, that all men are some

animals,'''^ . ,

All this goes on a false assumption as to the
import of propositions. It assumes that the exten-
sion of the terms of a proposition is present to our
mind when we lay down the proposition ; that when
I say All men are animals, I am not merely explicitly
stating the coincidence of two ideas, but am also
explicitly stating the inclusion of one class in a
larger one. It also implies, that when I assert this
proposition, I am in thought affirming either All men
are all animals, or, All men are some ammals, whereas
in point of fact I do nothing of the sort ; I am not
thinking of animals as a class at all, but simply as
an idea coincident with my idea of man. When
Sir W. Hamilton goes on to say that a proposition
is simply an equation between two notions in
respect of their extension, he shows so complete a
misconception of what the meaning of a proposition
is that we are not surprised at the wild proposals
into which he is drawn by his untrue theory. It is
not true that a proposition states the inclusion of
the class in a larger one, or the co-extension of two
classes of the same extension. It is not true that a
proposition is an equation between the subject and

X Sir W. Hamilton's Lectures, Vol. IV. pp. 270. 271.

VARIOUS KINDS OF PROPOSITIONS.

287

the predicate. It is not true that when we say All
men are animals we in any way admit the question
whether there are other animals besides men; and
therefore to advert to it in language would be a mis-
representation of our thoughts. Instead of being an
improvement in Logic, it would divorce Logic from
ordinary language and introduce into it a phrase-
ology not only clumsy and mischievous in practice,
but founded on a false assumption. Hence his
whole doctrine respecting the quantification of the
predicate, as based on a false theory, falls to the

ground.

It is true that it has certain conveniences in that
it would simplify certain logical processes and that
there are certain propositions which appear to be
(but are not really) an equation between the subject
and predicate. But it is strange that a man of Sir
W. Hamilton's ability could be led astray by so wild
a theory, and should venture to condemn Aristotle
and all philosophers who follow in his steps as guilty
of a cardinal error because they did not recognize
in Propositions a meaning rejected by mankind
generally, or force them into an unnatural shape
which no one would adopt outside the pages of a
logical manual.

We now proceed to distinguish various kinds of
Propositions. Our examples hitherto have been only
of the simplest form of Proposition, in which the
agreement or disagreement of the subject and the
predicate is asserted in the most plain and straight-
forward way. Such propositions are termed in

288

IMPORT OF PROPOSITIONS.

Logic Categorical Propositions, as making a simple
statement. But they are opposed to Hypothetical
Propositions, which state only the dependence of one
statement on another.^ Hence :

I. Propositions are divided into Categorical and

Hypothetical.

A Categorical Proposition asserts the agreement
or disagreement of the subject and predicate without
any sort of condition or alternative. Categorical
Propositions are either si^nple, when there is a smgle
subject and a single predicate, as The inhabitants
of all wine-producing countries are temperate; or
compound, when several subjects and predicates are
united by connecting particles in a single sentence,
as No man or angel can create a grain of dust ; This
boy is both headstrong, idle, and quarrelsome. Where
your treasure is, there will your heart be also. Such
compound propositions can always be broken up
into two or more simple propositions.

A Hypothetical Proposition asserts the dependence
of one proposition on another as, // men grumble they
are miserable. Hypothetical Propositions admit of

three subdivisions.

I. A Conditional Proposition contains two cate-
gorical propositions united together in such a way
that the one is the condition on which the other
depends, as // trade is bad, the poor suffer for it. If a
novel is dull, the sale will not be large.

« The use of the word categorical (KarnyopiKhs) in this sense,
is not Aristotelian, but was introduced by later logicians. As
we have stated above, categorical, in Aristotle, has the meaning
of affirmative as opposed to negative.

DISJUNCTIVE HYPOTHETICALS.

2S9

A Conditional Proposition consists of two parts :

1. The antecedent or condition : // trade is

bad.

2. The consequent or thing conditioned : The

poor suffer for it.

A Conditional Proposition may be either affirma-
tive or negative. In an affirmative conditional it is
asserted that the fulfilment of the condition involves
the truth of the consequent. In a negative con-
ditional it is denied that the fulfilment of the
condition involves the truth of the consequent, as
// this man is unfortunate he is not therefore to be
despised.

We must notice that the presence of a negative
in either or both parts of a conditional proposition
does not render it a negative proposition, unless the
negative affects the copula, so as to render the
whole proposition a denial of the existence of any
dependence of the consequent on the antecedent,
e.g., If this man is not guilty, he will not be condemned
to death, is an affirmative proposition, though both
the antecedent and consequent are negatives.

2. A Disjunctive Hypothetical Proposition is
made up of two or more Categorical Propositions
united by a disjunctive particle, as Either Socrates
was an enemy of religion, or the Athenians were unjust
in putting him to death. A man who asserts his own
freedom from defects is either a liar or a fool. In
Disjunctive Hypothetical Propositions the following
Rules must be observed :

Rule I. The different members of the propcsitions
must exhaust every possible alternative,

290

IMPORT OF PROPOSITIONS.

Thus if I laid down the proposition. Every one
r,ho becomes rich acquires his money either by trade or
I speculation, my proposition would be false becau e
I omit other methods of acquiring money such as
by some profession, inheritance, &c. Similarly,
if a man is found drowned, and I lay down the
proposition, Either this man was murdered or he
committed suicide, my proposition is faulty in that ,t
omits the third alternative, that he may have fallen
into the water by accident.

Rule 2 All the members must net be true together.
If they are, there is no true disjunction between
them, e.g.. Either a triangle has three sides, or tt has

three angles. . , , . ^i

Rule 3 All the members must not be false together.

For if they are all false, every alternative is not
exhausted and Rule i is broken: for example Etj^*^
Charles I. was a just King, or his subjects were
justified in putting him to death.

.. A Conjunctive Hypothetical Proposition is one
which consists of simple propositions which are
incompatible, joined together by an f ^f ^^ P^^'
tide, as JVo one can have his cake and eattt. Or it
may be described as a proposition which denies
that the two simple propositions it contains can be
at the same time true. It is necessarily always
negative in form.

II. Propositions are also divided into Pure and

Modal. , , . . ^^ .

A Pure Proposition (propositto de tnesse) is one in

MODAL PROPOSITIONS.

2gi

which the assertion of the agreement or disagree-
ment of the subject and predicate is made simply
and without any qualification, as Equilateral triangles
are equiangular,

A Modal Proposition is one in which the pre-
dicate is said to agree or disagree with the subject
in a particular mode or manner, as Equilateral
triangles are necessarily equiangular.

The mode does not affect the subject only, nor
the predicate only, but the connection existing
between them. The distinction between Modals
properly so called, and other propositions which
are sometimes called Modals, is to be found in this,
that in Modals properly so called the mode affects
the copula, as TJie ex-Cathedra definitions of a Pope
are necessarily true; The sentence passed by any of the
English judges is possibly a false one. In all other
Modals it affects the predicate, as Hares run swiftly,
when the adverb swiftly affects not the copula but
the predicate, and the proposition is equivalent to
the simple proposition. Hares are swift of foot, and
therefore not a true Modal.

There are four Modes : the Necessary, the Con-
tingent, the Possible, and the Impossible. All other
modes are variations of these : the Certain is but
another form of the Necessary, the Uncertain of
the Contingent, the Probable of the Possible joined
to a certain approbation on our part and a certain
leaning to its truth.

How are we to deal with Modals ? They are
really only simple Categorical Propositions of which
the word expressing the mode is the predicate.

292

IMPORT OF PROPOSITIONS.

Thus, The statements of informers are possibly false is
equivalent to The falseness of an informer's statements
is possible ; or, It is possible that an informer's state-
ments should be false. Many of the cures at Lourdes
are certainly miraculous is equivalent to That many
of the cures at Lourdes arc miraculous is certain.
This is the only true way of dealing with Modals.
In some cases a Modal is equivalent to a Universal
Proposition, and an Indefinite Modal may often by
reason of its mode be resolved into a simple propo-
sition ; Universal, if the mode is the Necessary or
the Impossible ; Particular, if it is Contingent or
Possible. Thus : Men are necessarily mortal is equi-
valent to ^// men are mortal. Street beggars are probably
tmdeserving is equivalent to Some street beggars arc
undeservi7ig. But in each case some portion of the
meaning and force of the proposition is lost if it
is thus transformed.

CHAPTER IV.

ON THE OPPOSITION AND CONVERSION OF

PROPOSITIONS.

Opposition of Propositions— Various kinds of Opposition— Law
of Opposition— Contraries and Subcontraries- Conversion-
Various kinds of Conversion— Laws of Conversion— Conver-
sion per fon/m— Value of Conversion per contra.

We discussed in our last chapter the Import of Pro-
positions, and condemned the quantification of the
predicate proposed by Sir. W. Hamilton as false in
theory and unworkable in practice. We further
distinguished various kinds of Propositions from
each other, Categorical from Hypothetical, and Con-
ditional from Disjunctive ; and we laid down certain
rules which govern each. We divided Propositions,
moreover, into Pure and Modal, and pointed out
what constitutes modality properly so called, and
how Modals are to be dealt with.

We now come to the relation to each other of
Propositions having the same subject and predicate.
If they have the same subject and predicate and yet
are not identical, there must be some diversity
between them, and this diversity must consist either
in a difference of quality, in that one of them is

294 OPPOSITION AND CONVERSION OF PROPOSITIONS.

affirmative and the other negative, or of quantity,
in that one is universal and the other particular, or
in difference both of quantity and quality, one
being universal and affirmative, the other particular
and negative, or else the one being universal and
negative, and the other particular and affirmative.

Such propositions are said to be opposed to each
other, although, as we shall see, the opposition is
in some cases verbal rather than real. And as
there are four kinds of propositions. Universal
Affirmative, Universal Negative, Particular Affirma-
tive, and Particular Negative, which we called
respectively by the letters A, E, I, O, there will be
four kinds of opposition, according as the opposi-
tion is between two Universals or between two
Particulars, or between a Universal and a Par-
ticular of the same quality, or between a Universal
and a Particular of a different quality.

1. Contrary Opposition (eVain-tWt?) is between
two Universal Propositions, A and E, one of which
is affirmative and the other negative, as between

A II schoolboys are mischievous . . (A)
No schoolboys are mischievous . . (E)

2. Contradictory Opposition (avTi<f>a(ri<;) is be-
tween a Universal Proposition and a Particular
differing from it in quality ; i.e,, between A and O,
or between E and I, as between

(All schoolboys are mischievous . . (A)
\ Some schoolboys are not mischievous (O)

or between

(■ No schoolboys are mischievous . . (E)
\ Some schoolboys are mischievous . (I)

{

VARIOUS KINDS OF OPPOSITION.

295

3. Subcontrary Opposition is between two par-
ticulars, one of which is affirmative and the other
negative, e,g,,

j" Some schoolboys are mischievous . . ( I )
I Some schoolboys are not mischievous . (O)

4. Subaltern Opposition is between a Universal
and the corresponding particular, e,g., between A
and I, and between E and O, as,

{All schoolboys are mischievous .
Some schoolboys are mischievotis
or between

r No schoolboys are mischievous

(A)
(I)

(E)

I Some schoolboys are not mischievous . (O)

All schoolboys
are mischievous.

Contraries,

No schoolboys
are mischievous.

^^ ^

c
cr

►1

$^^
^<^

Some schoolboys
are mischievous.

Contraries,

Some schoolboys
are not mischievous.

These last two kinds of opposition are not really
deserving of the name ; there is no real opposition
between Subcontraries and Subalterns. In the in-
stance we have given the two Subcontraries are both
true at the same time ; while if the Universal is true

296 OPPOSITION AND CONVERSION OF PROPOSITIONS.

the Particular is always true. There may, however,
be a real opposition between the Universal and the
Particular, if the latter is intended as a correction
of the Universal. If a nervous old bachelor declares
testily that All schoolboys are mischievous, and there-
fore he will not have his little nephew home for the
holidays, and I in opposition to him say : No, sir,
you are wrong, some schoolboys are mischievous, but
your nephew Charlie is a most well-behaved lad, quite
the reverse of mischievous, it is true that there is an
opposition between the Universal asserted by the
old gentleman and the Particular which I substi-
tute for it. But this only arises from the special
matter in question. The mere emphasis that I
throw on the word some shows that my assertion
gives my friend to understand that if some school-
boys are mischievous, some are not.

Between the two Particulars there never can be
any opposition, since the objects of which they
speak are altogether different. The section of
schoolboys of whom I assert that they are not mis-
chievous, in the proposition, Some schoolboys are not
mischievous, is altogether apart from the section
of which some one else may justly affirm that they
are mischievous in the proposition, Some schoolboys
are mischievous.

We may now give the Laws of Opposition.

I. Contraries cannot be true together, but can be

false together,

(a) They cannot be true together, for if it is true
that the predicate (mischievousness) is to be assigned
to every member of the class that forms the subject

CONTRARIES AND SUBCONTRARIES.

297

(schoolboys), it must be false that the same predi-
cate is to be assigned to no member of the class.

(b) They may be false together, for it may
happen that the predicate is to be assigned to some
members of the class and not to others. Hence
from the truth of any proposition may be inferred
the falsity of the contrary, but from the falsity of
any proposition the truth of the contrary cannot be
inferred.

2. Contradictories can neither be true together nor
false together, but one must be false and the other

true.

{a) They cannot be true together, for if the pre-
dicate is applicable to every member of the class
that forms the subject, it must be false that it is not
applicable to some members of the same class. If
schoolboys each and all are mischievous, it must
be false that some of them are not mischievous.

(6) They cannot be false together, for if it is
applicable to all the members of the subject, it
follows that it is true that there are some to whom
it is not applicable.

Hence from the truth or falsity of any proposi-
tion can be inferred the truth or falsity of its con-
tradictory.

3. Subcontraries may be true together, but cannot
be false together,

{a) They may be true together since the
predicate may refer to different portions of the
same class which forms the subject. If I say,
Some schoolboys are mischievous and some are not,
I am speaking of different subdivisions of school-

293 OPPOSITION AND CONVERSION OF PROPOSITIONS,

boys, and both my propositions may be perfectly

correct.

(b) But they cannot be false together, for if a
Particular is false the contradictory of it is true, and
if the Universal is true the Particular coming under
it is also true. If it is false that some schoolboys are
not mischievous, it must be true that all schoolboys
are mischievous, and much more that some school-
boys are mischievous.

Hence, if one of two subcontraries is true, the
other may be true and may be false, but if one of
them is false the other must be true.

4. Subaltern Propositions may be true together, or

false together.

This is because the Particular is included m
the Universal. But the truth of the Universal
implies the truth of the Particular, and the falsity of
the Particular implies the falsity of the Universal.

If it is true that all schoolboys are mischievous
much more is it true that some schoolboys are
mischievous ; if it is false that some schoolboys are
mischievous much more is it false that all schoolboys
are mischievous. But the truth of the Particular
does not imply the truth of the Universal, and the
falsity of the Universal does not imply the truth of
the Particular, as is sufficiently obvious.

Opposition in the case of Compound and Modal
Propositions follows exactly the same laws as that
of those that are simple and pure.

On the Conversion of Propositions.— By the
Conversion of a Proposition we mean the transposition

VARIOUS KINDS OF CONVERSION.

299

of its terms so that the predicate becomes the
subject and the subject the predicate. The new pro-
position thus formed must either be equivalent with
the original, or at least must be included under it, as
we shall see. There are three kinds of Conversion.

1. Simple Conversion takes place when, after
the transposition of the terms, the quantity of the
proposition, and also the quality remain the same.
If the subject and predicate were Universal before.
Universal they must remain ; if Negative, Negative ;
if Affirmative, Affirmative they must remain ; if
Particular, Particular; as

Some old men are talkative,
Some talkative creatures are old men.
No good Christians are cannibals.
No cannibals are good Christians,

2. Conversion per accidens takes place when the
Universal Proposition after conversion becomes a
Particular, as

All Catholics regard the Pope as infallible.

Some who regard the Pope as infallible are Catholics,

No good Christians are cannibals,
Some good Christians are not cannibals,

3. Conversion per contra takes place when an
Affirmative Proposition after conversion becomes
Negative, or a Negative becomes Affirmative, as

All men who rise high in their profession are men

of ability.
No men who are not men of ability rise high in their
profession,
or, None but men of ability rise high in their profession.

tf'w "i mif-ite--*-*

300 OPPOSITION AND CONVERSION OF PROPOSITIONS.

CONVERSION PER CONTRA.

301

No animals that do not stickle their young are

mammals,
All mammals suckle their young.
The Laws of Conversion are as follows:

1. The Universal Negative and the Particidar Affir-
mative are capable of Simple conversion,

{a) The Universal Negative, for since the subject
is wholly excluded from the predicate, it follows
that the predicate is wholly excluded from the
subject. If triangle is excluded from quadrilateral,
quadrilateral is excluded from triangle.

(6) The Particular Affirmative, for it asserts the
partial agreement of the subject with the predicate,
whence it follows also that the predicate partially
agrees with the subject.

2. The Universal Affirmative and Universal Nega-
tive are capable of conversion per accidens.

{a) The Universal Affirmative, for if the Universal
Affirmative, All rogues are liars, is true, the Particular
Affirmative, Some rogues are liars is also true, and
therefore its converse. Some liars are rogties, is likewise

true.

(b) The Universal Negative, for if the Universal

which is the simple converse is true, the Particular

will also be true. If it is true that, No thieves are

honest, the simple converse. No honest men are thieves,

is also true, and therefore, Some holiest men are not

thieves, is also true.

3. The Universal Affirmative and the Particular
Nef^ative are capable of conversion by contraposition.

Conversion by contraposition is based on the
fact that to assert an agreement of two objects of

thought, is to deny the agreement of either of them
with the contradictory of the other. To assert
the agreement between gentleness and the nature
of the turtle-dove is to deny the agreement
between the nature of the turtle-dove and non-
gentleness.

We desire to convert the Universal Affirmative,
All turtle-doves are gentle. This proposition is equi-
valent to the Negative Proposition : No turtle-doves
are not gentle. Now the Universal Negative can be
converted simply, and the result will be a proposition
which is the converse of the Universal Proposition
with which we started, viz. :

No not-gentle birds are turtle-doves ;
or. None but gentle birds are turtle-doves ;
or, Only gentle birds are turtle-doves.

On the other hand, to assert the disagreement of
two objects of thought, is to assert the agreement of
each of them with the contradictory of the other.
To assert the disagreement of the idea of politeness
in some cases from that of costermonger, is to assert
the agreement in those cases of costermonger with
that of non-politeness.

Some costermongers are not polite . . (O)
Some costermongers are not-polite , , (I)

The Particular Negative has become a Particular
Affirmative, and we are now able to convert it simply

to,

Some not-polite beings are costermongers ;
Some who are not polite arc costermongers.

302 OPPOSITION AND CONVERSION OF PROPOSITIONS.

This sort of conversion is called Conversion by
contraposition (avTL<TTpo<f)rj avv avriOea-eL), because
we make use of the laws of opposition by putting
one against the other, or contraposing the object of
thought (gentle, polite), and its contradictory (not-
gentle, not-polite), and argue from the truth or
falsity of the one to the falsity or truth of the other.

This sort of Conversion is the only means of con-
verting O. By it E may sometimes be converted,
but only when there is a double negative, e.g.

No circles are not round figures,
.*. No figures that are not round arc circles.

What are we to say about this Conversion by con-
traposition ? We find no trace of it in Aristotle or
St. Thomas. How is this if it is perfectly legitimate ?

The answer seems to be that strictly speaking it
is not Conversion at all. In Conversion the subject
becomes the predicate, and the predicate the subject,
while the copula remains unaltered. In this sort of
Conversion it is true that the old subject becomes
the new predicate, but the new subject, instead of
becoming the same as the old predicate becomes its
contradictory, while the copula which before was a
negative separating the terms asunder, now becomes
affirmative and unites them together, or if previously
affirmative, now it appears as negative.

It can therefore be called Conversion only by
courtesy and by reason of that laxer use of terms
which distinguishes modern from ancient days.
What we really have is not the converse of the
convertend, but of a proposition which is equipollent

VALUE OF CONVERSION PER CONTRA.

303

with the convertend. We restate the original pro-
position in an altogether different form. It is no
longer O but I, no longer A but E. Having done
so, we now have not the original proposition but the
equivalent that we substituted for it.

These various kinds of Conversion are summed
up in the following Latin mnemonic lines,' which
inform us that E and I may be converted simply ,
E and A per accidens, A and O per contra, and beside
these there is no other kind of conversion.

J FEcI simpliciter convertitur, EvA per acci,
AstO per contra, sit fit conversio iota.

LOGIC.

Part III.

ON REASONING OR ARGUMENT.

CHAPTER I.

ON REASONING.

Reasoning — Analysis of its meaning — Foundations of Reasoning —
Deductive and Inductive Reasoning — Argument — Canons of
Reasoning — Premisses unduly assumed.

A KNOWLEDGE of the truth, says St. Thomas,' con-
stitutes the perfection of every spiritual nature.
Some natures there are that at once comprehend
and accept the truth without any reasoning process,
as is the case with the angels. Others have to
arrive at truth by a slow process of reasoning from
the known to the unknown, as is the case with men.
Hence angels are called intellectual, as distinguished
from men who are rational beings. The angelic
grasp of truth is something immediate, simple, and
absolute, whereas man attains to it only mediately

• De Veritate, q. 15, art. i.
U

3o6

ON REASONING.

and gradually, advancing with toil through the
medium of reasoning or argument.

It is with reasoning that the Third Part of Logic
is concerned. How are we to define it, and what
are the various forms under which we reason ?

Reasoning is the third operation of the human
mind. As the first, Simple Apprehension, consists
in apprehending ideas, and the second. Judgment, in
comparing ideas together and pronouncing on their
agreement or difference, so the third consists in com-
paring together judgments and deducing from them
a further judgment, wherever the laws of thought
permit of our so doing.

But Reasoning may be looked at in another light.
In order that we may reason, the two judgments
compared together must have one idea common to
both of them either as subject or predicate. Reason-
ing consists in the comparing together of the other
two ideas contained in these two judgments through
the medium of that which is common to both of
them, and pronouncing on the agreement or difference
of these two ideas according to their respective
relations to it. For instance, in the judgments, All
smoky cities are comparatively free from zymotic diseases;
Cincinnati is a smoky city; I compare together the two
ideas of Cincinnati and freedom from zymotic diseases
through the medium of smoky city, and by reason of
the agreement of both of these with the same common
idea, I am able to arrive at the conclusion, Cincinnati
is comparatively free from zymotic diseases.

Reasoning then in its widest sense is an act of the
mind by which one judgment is inferred from some other

FOUNDATIONS OF REASONING.

307

judgment or judgments previously known. The judg-
ment or judgments that precede are called the
antecedent, that which is inferred the consequent. Or
if we look at Reasoning under the other aspect, we
may define it as an act of the mind by which two ideas
are compared with a third, and their agreement or
difference thus ascertained.

A judgment thus inferred from an antecedent
judgment or judgments is called mediate, as opposed
to immediate judgments, which are known at once
and without needing the support of any previous
knowledge. Immediate judgments fall into two

classes.

1. First principles, universals, axioms, analytical
or a priori propositions, the truth of which is known
to us from the very nature of things, e.g.. Nothing can
be at the same time true and false; The whole is greater
than its part ; All effects have a cause.

2. Truths of fact, particulars, and individual or
empirical propositions ; truths of experience, which
depend on no general principle and can only be
arrived at by observation or experiment, e.g., Saul
was the first king of Israel ; This ostrich is a long-lived
animal ; Chicago is a flourishing city ; Bees lay up honey
for their winter food.

These two kinds of immediate judgments furnish
us with our stock-in-trade when we reason: every
conclusion at which we arrive, must be capable of
being verified by its having been logically inferred in
its ultimate origin from truths of fact or from first
principles, or, as is generally the case, from a com-
bination of the two.

308

ON REASONING.

DEDUCTIVE AND INDUCTIVE REASONING. 3'->9

But in most cases we do not go back to ultimate
first principles. Sometimes we begin from some
mediate principles agreed upon by mankind as true,
and by combining these with other mediate principles
similarly agreed upon, or with individual facts, arrive
at our conclusion. For instance, I have deduced
from ultimate first principles by a previous chain of
argument, or I have received from the oral teaching
of my instructors in my youth, the mediate principle.
All violation of the law of God entails misery, I have
also made my own the farther principle that, Theft is
a violation of the law of God ; and I thus arrive at the
conclusion, that Thieving never prospers. Or I may
go farther and apply my principle to the case of some
one (A. B.) who has acquired money dishonestly,
and I thus deduce the further conclusion that A. B.
will never prosper.

Sometimes, again, we begin with individual facts,
and from them infer some mediate universal, and
then combine this with some other partial or mediate
universal, and so arrive at some more widely
extended principle. For instance, I may have
observed the wonderful sagacity displayed by dogs
belonging to myself and several of my friends, and
from those observations I arrive at the conclusion :
Dogs are sagacious animals, I hear or read stories of
the sagacity displayed by horses, of their fertility of
resource, their ingenious devices for gaining their
ends, and I sum up my experience in another
proposition : Horses are sagacious animals. My friends
tell me similar anecdotes of cats. From books on
animals I find the same cleverness common in

monkeys, in trained elephants, &c. I further reflect
upon the fact that dogs, cats, horses, monkeys, &c.,
are the ani..als mostly chosen by man for his
companions, and putting this and that together I
arrive from my observation of things familiar to me
at a general principle which was not familiar to me
before, viz., that in animals sagacity and the
companionship of man generally go together. Or,
to put in a logical form my process of argument,
Dogs, horses, cats, &c., are sagacious animals; Dogs,
horses, cats, &c,, are the chosen companions of man;
therefore, The chosen companions of man amongst the
animals are remarkable for their sagacity.

These two instances furnish us with examples of
the two kinds of reasoning which exhaust every
possible kind of argument, viz. :

1. Reasoning from the Universal to the Particular,
a priori reasoning, reasoning from first principles

2. Reasoning from Particulars to the Universal,
a posteriori reasoning, reasoning to first principles

Of these two kinds of reasoning the former is
termed deductive or syllogistic ; the latter inductive or
experimental. Yet we must bear in mind that all
inductive reasoning must be reducible to syllogistic
form in order to be valid. Of this we shall have
to speak when we come to treat of Induction. For
the present it is enough to say that it is identified
with the Syllogism in as far as it argues from a
general principle (the uniformity of nature's laws),
but differs from it in that it employs that general

310

ON REASONING.

principle to ascend from the observation of particular
facts to a mediate principle based on them, instead
of descending from some mediate or universal
principle to the individual facts.

When Reasoning is expressed in words it is
called Argument or argument aiim. As the Syllogism
is the natural type of all reasoning, every argument
can be stated in the form of a Syllogism. In practice
we do not generally state our syllogisms at full
length, but omit one or other of the three proposi-
tions of which they consist, and often condense the
two remaining into a single sentence.

For instance, the schoolmaster does not say
elaborately to the unfortunate boy who is to be

flogged :

All boys who play truant must be flogged,
You, Ishmael Jones, are a boy who plays truant,
.*. You, Ishmael Jones, must be flogged,
but he simply says : All boys who play truant must be
flogged, and therefore you, Ishmael Jones, must be flogged;
or, You, Ishmael Jones, have played truant and must be
flogged ; or. You must be flogged for playing truant,
Ishmael Jones.

There are certain general canons common to all
reasoning which we must notice before we pass on
to the consideration of the Syllogism.

I. When the antecedent propositions or pre-
misses of an argument are true, a false conclusion
cannot be logically drawn from them. If falsehood
seems to follow from truth, we shall always detect
some flaw in the reasoning process if we examine it
more closely. This needs no illustration or proof.

PREMISSES UNDULY ASSUMED.

311

2. When the conclusion is true, it does not at all
follow that the premisses are true. One or both of
the premisses may be false and yet the conclusion
perfectly correct in itself, and also correctly drawn
from the premisses, e.g.,

All the Roman Emperors were cruel tyrants;
Nero was one of the Roman Emperors;
/. Nero was a cruel tyrant.
Here one premiss is true, the other false, and yet
the conclusion is true.

All the Roman Emperors were cruel tyrants;
But Dionysius of Syracuse was not a cruel tyrant ;
/. Dionysius of Syracuse was not a Roman Emperor.
Here both premTsses"are false and the conclusion
logically drawn from them, but nevertheless the
conclusion is true.

This principle is an important one on account ot
the tendency of mankind to judge of a line of argu-
ment by its final results. Some hypothesis is started
from which there follows a conclusion which is
confessedly in accordance with known facts, and
men accept the hypothesis as an established truth
merely because it is apparently founded upon the
facts and accounts for their existence. Thus the
corpuscular theory of light seemed so successfully to
account for all the facts of the case that it was
maintained by no less an authority than Newton.
He held that light is caused by certain minute
particles which pass from the luminous body and
sticking on the eye, cause the sensation of light. In
the present day the undulatory theory has ousted it

312

ON REASONING.

from the field, but there are still some of the
phenomena which are more easily explained by the
older hypothesis.

It is a neglect of this principle that has led to
the premature acceptance of many scientific hypo-
theses, a great proportion of which have afterwards
proved incorrect. The arguments of some geologists
proving the extreme antiquity of man, because the
"kitchen-middens" and the finding of flint instru-
ments deep down in the earth were explained
thereby. Mr. Darwin's theory that coral reefs were
formed by subsidence, and his whole system of
evolution and development in its relation to the
formation of species and the development of man,
are instances of premisses assumed as certainly
established, because they accounted for a vast array
of facts which had never before been subject to so
imposing a process of generalization. But the truth
of the conclusion, and its logical deduction from the
assumed premiss, do not prove that premiss to be
true, even where they justify its character as a
valuable working hypothesis, which may be allowed
to pass current, until some facts hitherto unobserved
put an end to its claim to truth.

CHAPTER II.

THE SYLLOGISM AND ITS LAWS.

SvUorism the type of Reasoning-Terms and Premisses-Order of
'p^r misses-Principles of Syllogism-Dictum de omm et nullo-
General Laws of the Syllogism-Illicit Process-Undistnbuted
Middle-One Premiss affirmative-One Premiss universal.

The Syllogism is the principal type of reasoning to
which all others may be reduced. It may be defined
as a form of reasoning or argument m which two
ideas are compared together through the medium of
a third, and their mutual agreement or difference
deduced therefrom. Or it may be defined as a form
of reasoning or argument consisting of three propo-
sitions so related to one another that two of them
being laid down, the third necessarily follows from
it The first of these definitions refers to the Syllo-
gism primarily as a mental act, the latter to the
external expression of that act.

Hence we have in every syllogism three terms
and three propositions.

When the three terms of a syllogism are all ot
them categorical propositions, the syllogism is said
to be a categorical simple one. If any of them are
hypothetical or complex, the syllogism is said to be
a hypothetical or compound syllogism as the case may

3^4

THE SYLLOGISM AND ITS LAIVS.

be. We shall at present speak only of the Simple
Syllogism.

The three terms {termini, aKpa) are called the
major, middle, and minor. The major term {aKpov
TO ^lel^ou) is that which forms the predicate of the
conclusion. The minor term {aKpov to eXarrov) is
that which forms the subject of the conclusion. The
idea expressed in the major term is compared with
the idea expressed in the minor term through the
medium of the middle term.

Every Syllogism also contains three popositions,
called respectively the major premiss, the minor pre-
miss, and the conclusion. The major premiss {propo-
sitio, or sumptio major, Tr/aorao-t? rj fiel^cov) is that
premiss in which the major term is compared with
the middle term. The minor premiss {propositio or
sumptio minor, or altera, irpoTacTL^ rj iXdrrwv) is that
premiss in which the minor term is compared
with the middle. The conclusion {conclusio, illatio,
a-vfiiripaa-fUL) is the final proposition which declares
the relation between the major and the minor term
resulting from their several comparison with the
middle term. It is introduced by the word There-
fore, or Ergo, and announces the inference drawn
from the premisses.

The two premisses combined are called the
antecedent. The conclusion is the consequent therefrom.

Middle term. Major term.

All jewels are mineral substances (major premiss).

Minor term. Middle term.

All diamonds are jewels . . (minor premiss).
/.All diaynonds are mineral substances (conclusion).

PRINCIPLES OF SYLLOGISM.

315

The reader must be careful to notice that the
major premiss is not necessarily the premiss which
comes first. The order is very often mverted m an
argument, and the minor premiss placed first. The
major premiss is invariably the premiss in which the
major term is to be found ; the minor premiss that
in which the minor term is to be found. Thus in the
syllogism :

All ostriches have good digestion.
All animals with good digestion livelong lives,
/. All ostriches live long lives,
the minor premiss comes first, since it contains the

minor term ostriches. u- u ^u

What are the common principles on which tne

Syllogism is based ?

Canons of the SvLLOCisM.-If we look at the
material structure of the Syllogism as composed of
three terms, we shall find that it is based on two

principles.

1 Things which are identical with one and the same
thinrr are identical with one another. This is the prin-
ciple of all Affirmative Syllogisms. The major and
minor term are identical with the middle, and
therefore are identical with each other.

2 When of two things one is identical with and tlic
other different from some one and the same third thtng,
these two things are different from each other. This
is the principle of all Negative Syllogisms. Of the
major and minor terms one is identical with, the
other different from, the middle term, and therefore
they arc different from each other.

3i6

THE SYLLOGISM AND ITS LAWS.

GENERAL LAWS OF THE SYLLOGISM. 31?

But we may regard the Syllogism under another
light, viz., as an argument that descends from the
universal to the particular, from a wider to a
narrower object of thought. Looked at under this
aspect it is based on a principle known to ancient
logicians as the Dictum de omni et nullo,^

Dictum de omni et nullo. — Whatever is
necessarily affirmed or denied of a universal subject
may be affirmed or denied of each of the particulars
contained under that subjuct.

The Dictum de omni et nullo is applicable to
deductive reasoning only. The two principles pre-
viously given include inductive reasoning as well,
when expressed in syllogistic form.

Some moderns have attacked the Dictum de
omni et nidlo as a high-sounding truism. This is
no ground for assailing it. A principle underlying
all a priori reasoning must be one which is familiar
to all beings who reason. The more universal a
truth, the more it partakes of the nature of a truism.
There is no principle more familiar than that which
asserts the incompatibility of contradictories; yet
this is the foundation of all possible thought. To
call a familiar truth a truism is to disparage it with
an ill-sounding title. It deserves the name only
when it is announced as some wonderful discovery
or recondite principle, which is to shed fresh light
on human knowledge.

General Rules of the Syllogism. — The
Rules of the Syllogism arise from its very nature as

» This dictum is derived from Aristotle^ Anal. Pr., I. 4.

laid down in the canons or principles which we
have stated as the foundation on which it is

based.

Rule I. There must be three terms, and three only.

In the Syllogism the two extremes (the major
and minor term) are compared with the middle
term, in order that their mutual identity or diver-
sity may be thus affirmed or denied. If there were
no third term there would be nothing to act as a
medium or middle term, by means of which the
extremes might be compared together. If there
were more than three terms there would be not one
middle term, but several, and consequently no
common chain to bind together or sever asunder
the major and minor.

Here we must bear in mind, that when we say
that there must be one middle term, we mean one m
meaning, not in words only, as when we say :

All pages wear the livery of their masters.
The component parts of a book are pages ;
.', The component parts of a book wear the livery of
their masters.
Rule 2. No term must have greater extension in the
conclusion than it has in the premisses.

If any term is used in its full extension in the
conclusion without being used in its full extension
in the premiss, the inference would be one that the
premisses would not justify, for we cannot argue
from a part of the extension to the whole. The
breach of this rule is called an illicit process or

3i8

THE SYLLOGISM AND ITS LAWS.

unlawful proceeding of the major or minor term,
as the case may be. For instance, if I argue :

All sheep are graminivorotiSy

But horses are not sheep,
,\ Horses are not graminivorous,

my argument is faulty in that in the conclusion I
speak of the whole of the class of graminivorous, and
exclude horses from it ; whereas in the major pre-
miss I am speaking of only a portion of the class.
In Logical language the predicate of the negative
conclusion is distributed, the predicate of the affirma-
tive major is undistributed, and we therefore have an
illicit process of the major. Or again, if the rigorous
moralist argues.

All occasions of sin are to be avoided ;

Card-playing is an occasion of sin,
,\ Card-playing is to be avoided,
I remind him that he is using in the conclusion the
word card-playing in its full extension, whereas the
minor is only true of some card-playing, of card-play-
' ing when the stakes are high, of card-playing that
occupies time that ought to be spent in serious
pursuits, of card-playing in dangerous company, &c.,
and that he is therefore violating this second rule of
a good syllogism, and is guilty of an illicit process of

the minor.

Rule 3. The middle term must not be found in the

conclusion.

The business of the middle term is to be the
medium through which the major and middle terms
are compared with the other. This office is per-

UNDISTRIBUTED MIDDLE.

319

formed in the premisses ; after which its work is
done, and it gracefully retires. If I were to argue
as follows :

All great orators are men of genius ;
Cicero and Demosthenes were great orators,
,\ The genius of Cicero and Demosthenes consisted in
their powers of oratory,
the middle term great orators would thrust itself
unbidden into the conclusion and render the whole
syllogism futile.

Rule 4. The middle term must be distributed {i.e.,
used to the full extent of its significance), at least
once in the premisses.

The reason of this rule is the fact that the major
and minor terms are compared together through
the medium of the middle term. Now if in each of
the premisses we spoke only of a part of the subject
that forms the middle term, the two parts might be
entirely different, and there would then be no
common term with which the extremes are com-
pared, e.g.,

Some learned men are unbelievers ;
But the Doctors of the Church are learned men,
.'. The Doctors of the Church are unbelievers,
where it is evident that the section of learned men
who are unbelievers is entirely different from the
section who are Doctors of the Church.

This rule should teach us to look very carefully
to the universality of the middle term when it stands
as the subject of the major premiss, else from a
statement generally, but not universally true, we

THE SYLLOGISM AND ITS LAWS.

320 ^

^^^^lil^^^^ is at variance

with facts, e,g,y ri ' t

The Rulers of the Jews were enemies of Jesus Llmst,
But Nicodemus was a Ruler of the Jews,
• Nicodemus was an enemy of Jesus Christ,

These first four rules affect the terms of the
Syllogism, the next four affect the premisses or the
propositions that compose it.

Rule 5. From two negative premisses no conclusion

can be drawn. .

Unless one of the premisses be affirmative,
neither of the extremes agrees with the middle
term, but they both of them are at variance wi h it.
But from the fact that two things are both of them
different from a third, we gain no information as to
their mutual relations to one another. For instance,
from the premisses.

No shoemakers are astronomers,
But some astrofiomers are not classical scholars,
we learn nothing as to the connection between
shoemakers and classical scholarship. As far as
the above premisses are concerned, all classical
scholars may be shoemakers, or none may be ; or
some may be and others not. Sometimes syllogisms
with this defect seem to justify an inference, e,g,,
No tyrants are friends to liberty,
But some statesmen are not friends to liberty.
At first sight it looks as if we could draw the con-

elusion,

•. Some statesmen are tyrants ;
but the fact that all tyrants as well as some states-

RULES OF THE SYLLOGISM.

321

men are excluded from the class of friends of liberty
really proves nothing as to their mutual relation to
one another.

Rule 6. From two affirmative premisses a negative
conclusion cannot be drawn.

For if both of the premisses are affirmative, each
of them declares one of the extremes to be in agree-
ment with the middle term, and therefore by the
first of the principles given above they will neces-^
sarily agree with each other, and the conclusion
must be affirmative. If for instance I were to argue
that

A II lemons are sour,

Some ripe fruits are lemons,

and were to draw the conclusion that

Some ripe fruits arc not sour,

it is clear that, however true the statement, it is one
which is not justified by the premisses.

Rule 7. No conclusion can be drawn from two-
particular premisses,

1. Let us suppose that both premisses are
affirmative ; then the middle term is not distributed
in either premiss. This is in contradiction to-
Rule 4.

For instance, from the premisses :

Some cab-drivers are deficient in politeness.
Some gentlemen are cab-drivers,

it would be very injust to infer anything disparaging
the politeness of gentlemen.

2. Let us suppose one of the premisses to be
negative and the other affirmative. In this case

THE SYLLOGISM AND ITS LAWS.

322

ii^^^^^Ta^^TihTii^i^^^^ distributed

it must be the predicate of the negative premiss, for
this is the only term distributed in the premisses.
But as one of the premisses is negative the condu^
sion must be negative, and its predicate, ue the
major term, will be distributed. But the major term
was not distributed in the major premiss and ve
have therefore here an illicit process of the major
in opposition to Rule 2, eg..

Some buffaloes are fierce,
Some tigers are not buffaloes,
/. Some tigers are not fierce,
where the major term fierce is distributed in the
conclusion and not in the major premiss.

Rules The conclusion must follow the weaker
premiss, i.e., it must be particular if either of the
premisses is particular, negative if either of the

premisses is negative.

(a) It must be particular if either of the premisses
is particular, for the particular premiss asserts the
agreement or disagreement of the middle term with
one of the terms taken in a restricted and not in a
universal sense, taken in part and not as a wholcw
Thus in the syllogism :

All swans are said to sing before they die,
Some waterfowl are swans,
:.All waterfowl are said to sing before they die,
this" rule is clearly violated, and we have an illicit
process of the minor. .

(6) It must be negative if either premiss is
negative, because the negative premiss states the

RULES CF THE SYLLOGISM.

323

disagreement of one of the extremes from the middle
term, while the affirmative premiss states the agree-
ment of the other extreme with it, Kence the
conclusion must assert the disagreement of the two
extremes from each other. If for instance I argue,

No private persons wear uniform,

A II Policemen wear uniform,
.'. All Policemen are private persons^
the violation of right reason is patent.

CHAPTER III.

THE FIGURES OF THE SYLLOGISM. REDUCTION.

^X^.cS^o( the various Figures-First Figure type
o relSning-Rules of the Figures-Fourth Figure anomalous
Rules ofFourth Figure-Principle of Reduction-Importance
of FTrsfFfgure-Mefhod of Reduction-Reduction pnmposs.b.U
lulciL pn „„..«-aumsiness of Reduction per contra-
Singular Propositions in the Syllogism.

IN discussing the Syllogism, we explained that it
consists of three terms and three propositions, and
that it is governed by certain Laws or Rules the
observance of which is necessary to its validity.
Every Syllogism, moreover, is subject to special
rules according to its Form or Figure.

The Figure of a Syllogism is determined by the
position of the middle term with respect to the
extremes. Its normal place, as the middle term, is
between the two extremes, since it is less in extent
than the major term, but greater than the minor.
This will place it as the subject of the major premiss
in which it is compared with the major term, and
the predicate of the minor premiss, in which it is
compared with the minor term. For instance :
All courteous men are gentle in words ;
All well-bred men are courteous;
.-.All well-bred men are gentle in words,

PRINCIPLE OF THE FIRST FIGURE. 325

where the middle term, courteous, comes in point of
extension between the major gentle in words and the

minor well-bred. . . e ^r ♦!,»

This is the normal and most perfect form of the
SvUogism. It is the only one which gives a scientihc
knowledge of the nature of things. It is the type
and model of all reasoning, the shape into which
it naturally and easily falls. It is the only figure
bv which Demonstration properly so called can
be carried on : the only one which carries out
the Aristotelian method of argument from a prion

^" When'the middle occupies this position, we have
what is called the First Figure. Hence the First
Figure is the ideal form of reasoning, the pattern
of all argument ; it is the scientific figure, the only
figure that leads up to a conclusion at the same
time universal and affirmative.

I The First Figure, then, is that form of the
syllogism in which the middle term is the subject
of the major premiss and the predicate of the minor.
It may be depicted as follows :

when Ma=major term, M=middle, Mi=:minor.
II. But the middle term may fail of this relation

326

THE FIGURES OF THE SYLLOGISM.

in point of extension to the major and minor, and yet
may truly remain the middle term. For if one of the
premisses is negative, thus excluding the middle term
from one of the extremes, it is not necessary that it
should occupy this middle position between the ex-
tremes. In the affirmative premiss the middle term
must occupy its proper place as less extended than
the major or more extended than the minor term ;
but in the negative premiss which asserts the
mutual exclusion of the middle and one of the
extremes, it is not necessary that we should take into
account the relation, in point of extension, of the
middle term and the extreme from which it is thus
excluded. For instance,

No gouty men arc centenarians j
All the Patriarchs before the Flood were centenarians,
.\ None of the Patriarchs before the Flood were gouty men,

where the middle term {centenarians) in the affirma-
tive minor is more extended than the minor term
{patriarchs) but it is not necessarily less extended
than the major term {gonty men) in the negative
major premiss.

Hence it is not always necessary to look to the
extension of the middle term with regard to both
the extremes, and we may have other figures different
from the first and in which the middle premiss may
occupy a position other than that of the subject of
the major premiss and predicate of the minor. In
the instance just given it is the predicate of both
premisses, and the syllogism is said to be in the
Second Figure.

ORIGIN OF THE SECOND, THIRD, &- FOURTH FIGURE. 327

The Second Figure may be thus represented :

®-

III. Beside the case of one of the premisses
being negative, there is another in which without
anomaly the middle term need not be placed between
the extremes. If in one of the premisses we speak
only of apart of the extension of the middle term,
and in the other of the whole of it, the middle
term may in its partial signification be less than
either of the extremes without violating syllogistic
principles. This always leaves the possibility that m
its universal meaning and as a whole it is greater
than the minor term ; for instance,

A II men are prone to err.
Some men are Doctors of Divinity,
.-. Some Doctors of Divinity are prone to err,

where the middle term men, though greater in its
full extension than the minor term Doctors ofDtvtntty,
is not necessarily so when restricted by the limiting
word some, and therefore can take its place as the
subject of the minor premiss.

Even if in point of fact the middle term, taken
as a whole, is less than the minor in extension, yet
as we cannot, in the case we are considering, know
this from the form of the syllogism, it does not

328

THE FIGURES OF THE SYLLOGISM,

violate the principle we have laid down respecting
its position, e.g., if instead of the above we had,

All men are prone to err ;
Some men are animals of a savage nature ;
^\ Some animals who have a savage nature are prone to err.

It is clear that there are more savage animals
than there are men, yet this does not appear from
the form of the syllogism, and therefore there is no
real anomaly in the minor premiss.

But we may go beyond this. Even though in the
minor premiss the middle term is in the entirety of
its extension put under the minor, yet if in the
conclusion we speak only of a portion of the exten-
sion of the minor term, our syllogism may still pass
current, because the portion of the minor term
spoken of in the conclusion may be less in extension
than the middle term taken in its entirety in the
minor premiss, as for instance :

All civilized men wear clothes,
All civilized men cook their foody
,'. Some who cook their food wear clothes,

where we speak in the conclusion of only a portion
of those who cook their food, and as far as the form
of the syllogism is concerned, the general class of
civilized men may come between the class of food-
cookers and the class of clothes-wearers in point of
•extension. In these instances the middle term is
the subject of both premisses, and the syllogism is
said to be in the Third Figure, of which our diagram
will be :

PRINCIPLE OF THE VARIOUS FIGURES.

329

■®

IV. Can we go further still, and suppose a case
in which in the major premiss the middle can occupy
the anomalous position of predicate, and therefore
appear as greater than the major term, and the
minor premiss the anomalous position of subject
appearing therefore as less than the minor term ?
This can be done if in the conclusion we reverse
the natural order of things, and subordinate the
subject which possesses the larger extension to the
subject which possesses the lesser extension, e.g..

All Frenchmen are civilized,
A II civilized men are courteous,
.*. Some courteous beings are Frenchmen.

Here the largest class is the minor term, the
smallest the major term, and the middle is larger
than the major, smaller than the minor. The
anomaly is only explicable by the fact that we
speak in the conclusion only of such a portion of
the class of largest extension as can come under
the class of smallest extension. This anomalous
arrangement gives us the Fourth Figure. Its
symbol will be :

330

THE FIGURES OF THE SYLLOGISM.

G>-

®-

We now turn from theory to practice. We have
seen that though the middle term, normally and in
the scientific form of the Syllogism, is a class which
should in its entirety be greater in extension than
the minor term taken in its entirety, and less than
the major term taken in its entirety, yet that when
we exclude one class from another we need take no
notice of their mutual relation in point of extension.
The same is the case when we speak of a portion
and not of the whole of the minor term in the con-
clusion. In other words, provided that our conclu-
sion is either negative or particular, we can depart
from the first figure and may place our middle term
in the various possible positions that any term which
comes twice in the premisses can occupy. By this
method we shall thus arrive at four figures.

I. First Figure.— Middle term the subject of
the major premiss, predicate of the minor.

II. Second Figure.— Middle term the predicate

of both premisses.

III. Third Figure.— Middle term the subject

of both premisses.

IV. Fourth Figure.— Middle term the predi-
cate of the major premiss, subject of the minor.

PRINCIPLE OF THE VARIOUS FIGURES.

331

We have already spoken of the First Figure as
the type and model of all reasoning. This is so much
the case that arguments in the other figures are
valid only so far as they are reducible to sound argu-
ments in the first figure. It is moreover the shape
into which every argument naturally falls, and if we
depart from it and employ other figures in its place,
it is more because there is a certain convenience in
their adoption than because they are a necessity.
The author of the work on the Logic of Aristotle
found among the Opuscula of St. Thomas,^ remarks
that the First Figure is the most perfect because in
it alone the middle term is really the middle, and
partakes of the nature of the two extremes, inasmuch
as it is the subject of the major term, the predicate
of the minor. If however, continues this author,
the middle term is the predicate of both premisses,
the middle term, though it departs from its proper
place, holds as predicate of both premisses a
more dignified position than if it were the subject
of both; if however it is the subject of both,

* De Totius Logicce Aristotelis Summa, Tractat. de Syllogismo, c. 4,
p. 128. " Si enim medium in una propositione subjicitur et in altera
praedicatur, dicitur esse prima figura ; et merito, quia tunc medium
vere est medium, quia sapit naturam utri usque extremi, scilicet
subjecti et praedicati : praedicatur enim et subjicitur, ut dictum est.
Si vero medium in utraque propositione praedicatur, dicitur esse
secunda figura ; quia licet medium non sit vere medium sapiens
naturam subjectionis et praedicationis, tamen quia dignius est prae-
dicari quam subjici, ideo hac figura secundum locum tenet. Si
vero medium in utraque propositione subjicitur, dicitur tertia
figura et ultima, quia in ea medium non stat in medio sicut in
prima et subjicitur semper, quod est indignius. Plures figurae non
possunt esse, quia tres termini in duabus propositionibus non
possunt pluries variari."

332

THE FIGURES OF THE SYLLOGISM.

it neither holds its proper position nor the digni-
fied place of predicate, but is subject in each, and
therefore this figure is the third and last. The
Fourth Figure this author does not recognize at all.
We shall presently see the reason of the omission.
It is enough to say here that the poor middle term
is in it thrust into an utterly false position, inas-
much as it is subject in the premiss where properly
speaking it ought to be predicate, and predicate
where it ought to be subject.

Rules of the First Figure.— The very nature
of the First Figure is to apply a general law to a
particular case. From this it follows :

1. That the major premiss which states the law

should be universal.

2. That the minor premiss which applies the

law should be affirmative.

These two conditions exclude from the first figure
a number of combinations of various kinds of
propositions. The major premiss must be A or E,
the minor A or I. The conclusion must be nega-
tive if there be a negative premiss, and parti-
cular if one of the premisses be particular. This
reduces the various moods or combinations pos-
sible under Fig. i to 7, viz., AAA, EAE, All,
EIO, AAI, EAO, of which the last two are only
weakened forms of the first two. These four moods
are summed up in the mnemonic line,

BArbArA, CEUrEnt, DArii, FErioque, prions.^

I The capitals in this line indicate the nature of the propositions
in the various moods. The small letters in Figure i have no
special meaning.

RULES OF THE SECOND FIGURE.

333

If we violate either of the above rules, or attempt
any other combination in the first figure, our argu-
ment will be faulty, and will sin against one or other
of the general rules given above. For instance, let
us try a syllogism with a particular major premiss.
Some Africans have woolly heads ;
All Egyptians are Africans ;
.', All Egyptians have woolly heads.
Here the middle term is not distributed in either
premiss.

Or suppose we attempt a negative minor.
All great talkers arc wearisome to their friends ;
No silent men are great talkers ;
.-. No silent men are wearisome to their friends.
Here wearisome is distributed in the conclusion, but
not in the major premiss (illicit major).
Lastly we will take both faults together.
Some sweetmeats are unwholesome ;
No beverages are sweetmeats ;
,\ No beverages are unwholesome.
Here unwholesome is distributed in the conclusion,
but not in the major premiss (illicit major).

Rules of the Second Figure.— The Second
Figure, as we have seen, arises from the fact that when
the middle term is the predicate of a negative pro-
position, we need not take into account its exten-
sion as compared with the major and minor. The
Second Figure always has one of its premisses nega-
tive, either deriving from a law of universal exclu-
sion, the exclusion of some subordinate class (major
negative), or, arguing from a positive law^ universally

334

THE FIGURES OF THE SYLLOGISM.

RULES OF THE FOURTH FIGURE.

335

applied to some class, the exclusion of a subordinate
class from the larger class by reason of its exclusion
from the jurisdiction of the universal law (minor
negative). Hence follow the Rules of Figure 2.

1. The major must be universal.

2. One premiss must be negative.

3. The conclusion must be negative.

This limits the possible moods of this figure to
four, viz., EAE, AEE, EIO, AOO, which are
commemorated in the mnemonic line,

CESArE, CAmEstrEs, pEstmo, BAroko, secundae.

Break either of the above rules and you will find
yourself with some syllogistic defect, eg,,

Sotne pagans are virtuous ;
No housebreakers are virtuous ;
^\ Some housebreakers are not pagans (illicit major).

All sparrows are impudent;
Some schoolboys are impudent ;
-.*. Some schoolboys are sparrows (undistributed middle).

Rules of the Third Figure. — The Third
Figure is based on the consideration that when in the
conclusion we speak only of a portion of the minor
term, it does not follow that the middle term should
be greater in extension than the whole of the minor
term, as is required if the whole of the minor term
occupies the subject of the conclusion. In this
Figure therefore the rules will be,

1. The conclusion must be particular.

2. The minor premiss must be affirmative,

else we shall find ourselves involved in
an illicit major.

This reduces our possible moods to six: A A I,
lAI, All, EAO, OAO, EIO, or rhythmically.

Tertia DArApti, DisAmis, DAtisi, FElApton,

BokArdo, FErison, habet.

Here, too, any attempt to construct syllogisms
other than these will be fatal to right reason-
ing, e,g.,

All oysters are nutritious;
No oysters are in season in July ;
.'. Nothing in season in July is nutritious (illicit major).

or. No mosquitoes are pleasant companions ;

All mosquitoes buzz;
/. No buzzing things are pleasant companions (illicit

minor).

Rules of the Fourth Figure.— We now come
to that niauvais sujet of syllogistic reasoning, the
Fourth Figure, in which, contrary to all symmetry
and to the very nature of things, the middle term
occupies the doubly anomalous position of being
the predicate of the major term where it ought to
be subject, and subject of the minor where it ought
to be predicate.

Is it based on any principle ? Can any excuse
"be found for it ? We have already mentioned that all
that can be said in its favour is that, whereas in the
legitimate syllogism the class smallest in extension
is in the conclusion included in the largest, because
included in the one which occupies the middle term
between them, in this bastard offspring of syllo-
gistic reasoning a bit of the largest class is included

1 J

THE FIGURES OF THE SYLLOGISM.

336

r;^;^;^;^^^[^^^^:^^s included in that bit of
the middle which is included in the smallest

It has its origin in what are called the indirect
moods of the First Figure, viz., those •" -h.ch the
conclusion is inverted, the subject ^-ng taken from
the major premiss and the predicate from the

minor, e.g.y

Some fishes fly . • • ' '

No birds are fishes . . • • ^
:, Some creatures that fly are not birds . o

There are five of these moods, viz: AAI, EAE,
MI, AEO, lEO, given in the line,
BArAlip, CElAntEs, DAbitis, FApEsmo, FrisEsmo.
They are anomalous but perfectly valid as argu-
ments. The Fourth Figure is an attempt to arrange
Them under some principle, and to make a home or
them. Is this necessary? No. It is much better
that these anomalous moods should return to their
allegiance and be retained as syllogistic curiosities.
TheTare one and all reducible to the ordinary moods
of Figure i ; to provide them with a dwelling-place
of their ow^ is to encourage the grossest syllogistic

''TlheTourth Figure of any practical use ? Not
a bit Does syllogistic reasoning ever fall naturally
L^it? Never. What is it then? Nothing else
than the First Figure turned upside down. It is a
mere mechanical invention of those who arrange he
figures according to the possible position of th
middle term in the premisses, without having any
regard to its due relation to the major and minor in

RULES OF THE FOURTH FIGURE.

337

extension. '* Its conclusions," saysGoudin, ''are true ;
but it arrives at them in an inordinate and violent
fashion (violente admodum et inordinate), upsetting the
arrangement of the terms of the conclusion.''

Ought we to retain it ? If we do, it should be
as a sort of syllogistic Helot, to show how low the
syllogism can fall when it neglects the laws on which
all true reasoning is founded, and to exhibit it in the
most degraded form which it can assume without
being positively vicious.

Is it capable of reformation? Not of reformation,
but of extinction. It is absolutely unnecessary, and
the best thing it can do is to transfer whatever rights
or privileges it may possess to the First Figure,
which does all the work that it can do in far better

fashion than itself.

What then is the Fourth Figure ? Simply the First
with the major and minor premisses inverted and the
conclusion weakened by conversion. Where the same
premisses in the First Figure would prove a universal
affirmative, this feeble caricature of it is content with
a particular ; where the First Figure draws its conclu-
sion naturally and in accordance with the forms into
which human thought instinctively shapes itself, this
perverted abortion forces the mind to an awkward
and clumsy process which rightly deserves to be
called *' inordinate and violent." For instance, in
the First Figure I have the following syllogism :

A II birds can fly ;
A II ostriches are birds ;
/, All ostriches can fly.
W

■•*

338

THE FIGURES OF THE SYLLOGISM.

PRINCIPLE OF REDUCTION.

339

In Figure 4 this syllogism will be as follows :

A II ostriches arc birds ;
A II birds can fly ;
.-. Some things that can fly are ostriches.
Or again :

No good men are unmerciful to the poor ;
Some police magistrates are good men ;
.'. Some police magistrates are not unmerciful to the poor.

When this is stated in Figure 4 it will run thus:

Some police magistrates are good men ;
No good men are unmerciful to the poor ;
,\ Some who are not unmerciful to the poor are police
magistrates.

But we must turn to the Rules of this poor
mis-shapen figure ; they are three in number.

1. If the major is affirmative, the minor must be
universal, else the middle term will not be distributed
in either premiss.

2. If the minor is affirmative the conclusion must
be particular, else illicit minor.

3. If one premiss is negative the major must be
universal, because the negative conclusion which is
the result of a negative premiss will distribute the

major term.

Hence the legitimate moods of the Fourth Figure
will be AAI, AEE, lAI, EAO, EIO, comme-
morated in the line —

BrAmAntip CAmEnES, DimAris, FESApo

FrEsison.

We need not linger over instances of this figure.

It is not worthy of our consideration It is not
rlcognized by Aristotle or by the scholastic log.
cianf It is the invention of Galen, the physician,
who lived towards the end of the second century
Ind was termed by his contemporaries Parado.^
logos or the wonder-talker. Hence it is sometimes
called the Galenian figure-

REDUCTION.-If the First Figure is the type
and pattern of all reasoning, it will be necessary
Z at' least desirable, that all the various forms
of lawful argument should be reduc.bk to it U
the Dictum dc omni ci nulla is the bas.s of he
Syllogism, it must be the test of all good Syllo-
giLs, that we should be able to arrange them
under that figure to which alone the Dictum
is applicable. Nay more, it is only to those
moods of the First Figure which have a universal
conclusion that this dictum is strictly and property
applicable, and Aristotle' is not satisfied until he
has reduced, in the way that we shall presently
describe, all other syllogisms whatever to a form
which enables them to come, directly or indirectly,
under this fundamental principle of all reasoning.
Modern philosophers, impatient of the elabora e
process required for this universal reduction, would

. C( St Thos , Opusc.. XLIV. (Ed. Rom. xlviii ), Di Totius
CI. bt. 1 nos^, yjv • ^^ sciendum quod licet isti duo

Toxica AristoUUs Summa, c. 4. Bcienuum 4

eorum et hoc faciemus in fine omnium.

340

REDUCTION.

have each figure to stand on its own basis, and each
mood to be proveable by the two principles which
we have given above.

At the same time they do not deny the fact
that any vaHd argument may be stated in some
way or other under the First Figure, and each
proved indirectly, if not directly, by Barbara or
Celarent; to the exclusion of all other forms of
reasoning. We will first give the laws of Reduction
as generally laid down by modern logicians, and will
afterwards compare the ancient and modern methods
of Reduction, and see whether it is desirable or not
to improve upon Aristotle and St. Thomas.

We have given certain mnemonic words for the
various moods of the different figures. We will
combine them here into a convenient little stave
which it is well to commit to memory,

BArbArA, CEUrEnt, DArii, FErioque, prioris.
CESArE, CAmEstrEs, FEstino, BAroko, secundae.
Tertia, DArApti, DisAmis, DAtisi, FEUpton,
BokArdo, FErison, habet ; Quarta insuper addit,
BrAmAntip, CAmnnEs, DimAris, FESApo, FrEsison.

Here it will be noticed that all the various
forms begin with one of the four letters, B, C, D, F,
corresponding to the various moods of Figure i.
This indicates the mood in Figure i, to which
the moods of the other figures are reducible;
Baroko, for instance, to Barbara, Cesare to Celarent.
We also observe certain letters recurring which
point out the changes necessary Iqt effecting this
reduction. The letter m directs that the premisses

METHOD OF REDUCTION.

341

?1 .heT^ewa, indicates that the p.opos.fon

Sets; ;;:sr;rrc.«io„ J. .„,,

converted (s). For instance,

All fishes breathe by gills • • • '
No porpoises breathe by gtlls.

.'. No porpoises are fishes

becomes when reduced

No creatures breathing by gills arc porpoises

All fishes breathe by gills •

• No fishes are porpoises • • '

* * • • r:•rrr^^ri^ 1 \\\\\c\\ ouW coutams

converted per acctdens, e.g.,

All lobsters turn red when boiled . ■ ■ ^^^
All lobsters arc good for food . • "

... Some creatures good for food turn red when boded, ti

becomes ^^

All lobsters turn red when boiled . • •

Some creatures good for food are lobsters .
... Some creatures good for food turn red when boded i

cAm

trES

rEnt

342

REDUCTION.

But what is the meaning of k ? According to
the old logicians it indicated that the reduction
employed must be of an indirect kind called per
impossibtle ; according to moderns it indicates that
the proposition indicated by the preceding letter is
to be converted by contraposition or per contra.

We have already remarked ' that conversion per
contra is not really conversion at all, but the con-
version of some proposition equivalent to the pro-
position to be converted. For this reason it is
ignored by Aristotle and scholastic logicians. Hence
in Reduction they make no use of any such pro-
cess, but adopt the more strictly scientific, though
perhaps rather cumbersome process which is termed
Reductio per impossibtle. The reader is requested to
recall the system of proof occasionally adopted in
Euclid of assuming the contradictory of the conclu-
sion which is to be proved, and showing how this
contradictory is false, and therefore the original
conclusion true. The process of the logician is
almost exactly similar ; it is as follows :

If we suppose that the conclusion of our syllo-
gism is false, its contradictory must be true. We
will therefore assume this contradictory for a new
premiss to be combined with one of the original
premisses, and see what new conclusion we thence
deduce. For instance, I take a syllogism in Baroko
(Fig. 2).

A II angels are perfectly happy . . b A
Some intellectual beings are not happy . rok
.-. Some intellectual beings are not angels . o

» P. 302.

REDUCTION PER CONTRA

343

If the conclusion is false, its contradictory will

be true, viz.,

All intellectual beings arc angels.
We will therefore assume this as our new premiss

Retaining our old major P---^;-^-;, f^^^^^^
as our new minor : our argument will then be as

follows :

All angels arc perfectly happy • • ^^
All intellectual beings arc angels . ■ rbA
.-. All intellectual beings arc perfectly happy t\

But this new conclusion contradicts our former
minor premiss, and must therefore be false. Hence
o Hf our new premisses --t be false ; .tcanno
be our new major premiss, which remams the same
as before. Hence our new mmor premiss, viz..

All intellectual beings are angels,
is false, and therefore its contradictory.

Some intellectual beings are not angels,

cT our orieinal conclusion, is true.

So far the ancient method. We v.ill now turn
to the light and airy method which -->^^^-^^l^'^;
tute for the system of Aristotle and St. Thomas.
Instead of reducing Baroko and Bokardo ^.. "k^o.^
iSL. they make use of conversion per contra or b>
contraposition, and reduce these n^°«f /^ Jf J
and Darii respectively. If conversion per c^tra ^
no conversion at all. Reduction per coiUra is of all
methods of Reduction the clumsiest. We will take
the instance of Baroko already cited.

344

REDUCTION.

All angels are happy . . . ba

Some intellectual beings are not happy rok
.-. Some intellectual beings are not angels o

The modern plan is to attach the negative to
the predicate in the minor premiss and in the con-
clusion.

All angels are happy .... a

Some intellectual beings are not-happy . i

.-. Some intellectual beings are not-angels . i

This, however, involves us in a fresh difficulty,
which we must remedy before we go further. We
have altered one of our terms from a definite term
(happy) to its contradictory (not-happy). We must
therefore manage to foist a similar term into the
major premiss, and for this purpose we must intro-
duce a double negative, and for our old major, All
angels are happy ^ we must substitute a new negative
major. No angels are not happy. Our new syllogism
will now be,

No angels are not-happy . • • ^
Some intellectual beings are not-happy . i
.-. Some intellectual beings are not angels . O

But in order to reduce it to Figure i we must con-
vert the major premiss,

No not-happy beings are angels . . FE
Some intellectual beings are not-happy . ri
/. Some intellectual beings are not angels . O

Whether this process is a satisfactory one we
leave our readers to judge. Suffice it to remark
that it does not deserve the name of Reduction at

BOk

REDUCTION PER CONTRA

--^-— — — manipu-

„.„« and ,s ™- '., ^'^„:: , co„(»sio„ ot

Shf J..1 ctU >"" co-"^-'^ """'•

between ../.^^^^^^^^^^^^ ^^^ ^anipu-

transposition of the premisse^ Thus .
Some philpsiphers are not poli^^ ■
All philosophers are rational Veings
■•y ,., Some rational beings are no^oltte .

Uk^ becomes -^ _ p^

. Some heings .-ho are not.polite are rat,onal i

-HenceBaroUoandBoUar^^^^^^^^^^^^^^^
rr:fXrr;r;Sucea to ..no ana

""iHrmodrorReduction, if Reduction it can be
This mode oi ^^^^^j gymnastic

^^"f' r tttn y and skill of learners. As a
to tiy t;^^. 7;™„ess of the original argument
proof of he ^^M ^^.^^^ .^ ^^, ^he

it is valueless, f ^ .^'""^f/,^'' ^n 5^3 point and force

only end of ^^^-^'J'^^^^^^^Sing he'validity of the
as an instrument for ^^^ Jf ^;\if i3„,3 ,vith Nvhich it
reasoning employed in the syiiog

deals.

346

REDUCTION.

Before we close the subject of Reduction there is
one question to which it is necessary briefly to recur.
We laid down above that Singular Propositions are
to be treated as Particulars, that the proposition.
This parrot is a good talker, is a still more restricted
form of the proposition, Some parrots are good talkers.
But when we come to deal with certain Singular
Propositions in the Syllogism, we are met by the
fact that in some cases we may treat them as Uni-
versal without endangering the legitimacy of our
inference, e,g,,

Jtdius Casar was a skilftd general ;
Jtditis CcBsar was a Roman Emperor ;
.*. One of the Roman Emperors was a skilful general.

We shall not have any difficulty in solving this
difficulty when we recall what was said on pp. 282,
seqq., respecting the Import of propositions. We
advert primarily not to the extension, but the com-
prehension of the subject of a proposition, to the
nature it expresses, not the class over which it is
spread. The name of an individual, like every other
name, stands for a certain nature endowed with
certain attributes and gifts, essential and accidental.
It is perfectly true that in respect of the quantity of
the proposition in which it stands, the individual
proper name, as more restricted than any portion
of the class containing more individuals than one,
should be treated as a Particular. But by reason of
its expressing a nature which cannot be communi-
cated to any one save to him who possesses it, it
shares the nature of the Universal, in that it stands

SINGULAR PROPOSITIONS.

347

for the whole of that to which the name is apph-
,.He. even though th ^ ^^^

^,!^^^^rLr. in point of extension
more restricted than any portion of a class cons.s -
TnA more than one, but it is be-se he . a s.g e
individual, and has his own '"d'^-'dual na ure a 1 to
himself, that he shares the P-'leges o the Un. ersal
When we speak of som members of a class n one
c\u ^r.mU<;es and of some members also in the
: her i'tsSw is possible that I niay be speaking
otner, K ii> «^*^ j ^ ^,. p^^not be so

c ,*^rM,nc qUo^ether different, inis caiiuut
ITT sp ak'tf one individual, and only on.
As all men exhaust the nature found m man so
Juliu c" sar has all to himself the nature wh.h^
lame suggests^ It is^st the same .n^a^Sm.ular

roTsretrrtslTwh^^^^^^^^^^ subject to a

f/iis, or some e y ^^^^^^^^ ^^,,^5 .

single -ndividual, as, TJ. to J ^^^^^ ^^^

:tir:^: sil trfS a n'ature which in point
of fact admits of no repetition by reason of the md-

a Univ rS and from two smgular Propos. -
a legitimate conclusion may be deduced, ^^hereas
Lm two particular Propositions no mference can

be made.

COSDITIONAL HYPOTHETIC A L5.

349

W .

CHAPTER IV.

VARIOUS KINDS OF SYLLOGISMS.

Hypothetical Syllogisms— i. Conditional Hypotheticals— 2. Dis-
junctive Hypotheticals — 3. Conjunctive Hypotheticals —
4. The Dilemma— Rules of the Dilemma— The Enthymeme—
True nature of the Enthymeme— The Epichirem— Sorites —
Rules of Sorites — The Polysyllogism.

In our last chapter we discussed the various Figures
of the Syllogism, and the rules that govern them.
We said that the Fourth Figure is but a clumsy and
useless distortion of the First, and not recognized
by ancient logicians. We then explained the pre-
eminence of the First Figure, and the consequent
necessity of reducing the mood of the other Figures
to it. We now come to the various kinds of
Syllogisms.

All Syllogisms are either simple or compound,
categorical or hypothetical. They are, as we have
already remarked, Categorical or simple when they
consist of three simple categorical propositions. It
is of these we have been hitherto speaking. We
must now proceed to treat of Compound or complex
Syllogisms, to which St. Thomas and the scholastic
logicians give the name of Hypothetical.^

* This name has been objected to as the Greek equivalent of
conditional, but this is not the case. In Greek v-iroeiais has a far wider
meaning.

Hypothetical Syllogisms fall into three different

^^"rconditional Syllogisms, ir. .-hich the ^ajor
preLss is a conditional p^oposU-onwhU^^^^^^ m-r
Lher affirms the condmon den -^ th ^ ^^^^^

quent dependmg on it (or, as u accordingly

L conmo.aU.n), the conclusion bemg ac o d ^,^

an assertion of the condiUonaUm, or a dem
conditio, e.g.f

,/,», ..W .■«,» tt. ~"McondMo) ««.■».*<' "

... The weather is cold (assertio conditionati),
or But the weather is not cold (negatio conditionati)
. The mnd is not m the north (negat.o condUion.s).

// the sUk man's disease is typho.d fever (conditio) /..
« in danser of death (conditionatum),
tstnaan^cT J . , , _„ /.gcertio conditioms),

0,, Bui I,, h «,! i« *»«"• »/ ''"'"' '"'S'"" ""■"'

B», it we deny .he condition, it does no. Mow
.ha. we n,.,. also deny '^^'"^'^^ 'Z^^^Z

350

VARIOUS KINDS OF SYLLOGISMS.

DISJUNCTIVE HYPOTHETICALS.

351

■\n

typhoid fever it does not follow that he is not in
danger of death, for he may be suffering from some ,
other fatal malady.

So again the truth of the antecedent does not
follow from the truth of the consequent, cold weather
does not prove a northerly wind ; or danger of death
the presence of the typhoid fever.

When the antecedent or consequent of a Hypo-
thetical Syllogism is a Negative Proposition, its
denial will consist in the omission of the negative,
and will take the form of an Affirmative Proposition.
Thus I argue as follows,

// sceptics are right, Holy Scripture is not

inspired of God;
But Holy Scripture is inspired of God;
.'. Sceptics are not right.

Here the minor premiss, though an affirmative pro-
position, is a denial of the consequent, from which
we rightly infer that the antecedent was false.

Hence the rules of Conditional Syllogisms are : '
(i) If we affirm the antecedent we may affirm
the consequent. (2) If we deny the consequent we
may deny the antecedent. (3) From the affirmation
of the consequent or the denial of the antecedent no
conclusion can be drawn.

II. Disjunctive Hypothetical Syllogisms are those

1 These rules are summed up in Latin thus :

Posita antecedente, ponitur consequens,

Sublata consequente, tollitur antecedens,

Sublata antecedente vel posita consequente, nihil probatufy

in which the major is a Disjunctive Proposition, and
the minor either asserts or denies the truth of one of
the alternatives, the conclusion accordingly denying
or asserting the truth of the other alternative, as

Either the sun moves round the earth or the earth

moves round the sun ;
But the sun does not move round the earth;
,-. The earth moves round the sim.

Either God created the world or it came into existence of

itself;
But God did create the world ;
,-. The world did not come into existence of itself ,

Disjunctive Syllogisms may have more than two
alternatives in the major premiss, in which case if
the minor asserts one of the alternatives, the conclu-
sion will deny the rest.

Either I am older than you, or the same age, or
younger ;

But I am older than you ;
/. I am neither the same age nor younger.

If the minor denies one of them the conclusion
will affirm the truth of one or other of those that
remain.

Either I am older than you, or the same age, or
younger ;

But I am not older than you ;
/. / am either younger or of the same age.

If the minor denies all except one, that one will
be affirmed in the conclusion.

■IHl

352

VARIOUS KINDS OF SYLLOGISMS.

CONJUNCTIVE HYPOTHETIC ALS.

353;

Either I am older than yon, or the same age, or

younger ;

But I am not older, nor am I younger ;
.'. I am of the same age.

The laws laid down for the legitimacy of Disjunc-
tive Propositions^ must be carefully attended to in
order that these syllogisms may be valid. If for
instance, a student should say (as students have
often said before now),

Either I failed in my examination through illness, or
through ill-luck, or through the spite of the examiner

against me ;
But it was not through illness, for I was quite well on
the day of the examination, nor through ill-luck, for
I was asked the questions I knew best ; -x,

.-. It must have been through the spite of the examiner;
the unfortunate reasoner forgets the further alter- •
native of ignorance or stupidity, and the major^ \
premiss is therefore not exhaustive. < C

So again if I argue,
This man lives either in Australia, or New South ^

Wales, or Victoria ;
But he lives in Australia ;
.-. He docs not live in New South Wales, nor in Victoria.

The conclusion is false, inasmuch as Rule 2 of
Disjunctive Propositions is neglected, there being no
opposition between the various propositions which
compose the major premiss.

In the same way the alternatives of the dis-

' Pp. 289. 290.

junctive premiss must be opposed to one another,
else there is no real opposition. The American
hunter neglected this rule when he proposed to his
Indian companion the following division of their

spoils :

Either I will take the lion and you the jackal, or you
shall take the jackal and I will take the lion.
To which the redskin mournfully rejoined,

You no say lion for poor Indian once,

III. A Conjunctive Hypothetical Syllogism is one
in which the major premiss is a Conjunctive Hypo-
thetical proposition, and the minor denies one of
the alternatives given in the major, e.g.,

No man can be at the same time a Freemason and a

good Catholic ;
But this man is a Freemason ;
.-. He is not a good Catholic.

IV. The Dilemma is a syllogism with a disjunctive
major while the minor takes each of the alterna-
tives and shows how they establish the statement of
him who employs it against a real or imaginary
opponent, e.g.,

Herod after his promise to Herodias cither had to put
St, John the Baptist to death or to spare his life ;

If he put him to death he was a murderer, if he spared
his life he was a perjured liar;
/, He had the alternative of murder or perjury.

Either I shall pass my preliminary examination or I
shall fail ;

354

VARIOUS KINDS OF SYLLOGISMS.

VARIOUS KINDS OF DILEMMAS.

355

// / pass, I shall have the pleasure of succeeding ; if I
fail, I shall he free of the nuisance of any further
examinations ;
,-. I shall have reason to he satisfied in either alterna-
tive.
The rules of the Dilemma are three in number.

1. The disjunctive premiss must exhaust every
possible alternative, e.g.,

Either I must devote myself to the interests of my soul

or to my worldly interests ;
If I do the latter I shall lose my soul, if the former I
shall ruin the interests of my family ;
.*. I am therefore a most miserable man ;

where the major premiss omits the third alter-
native of attending to the interests of both.

2. The consequences which are shown to follow
from the alternatives of the disjunctive premiss must
be indisputable.

I must either give up wine altogether or I shall

continue to take wine ;
If the former, I shall lower my general tone, if the

latter, I shall gradually become a drunkard ;
Hence, whether I drink wine or not, my health will he

ruined ;

where in the disjunctive premiss the consequences
do not necessarily follow. I may preserve my tone
by tonics, or I may drink only in moderation.

3. It must not admit of a telling retort.

A man is offered a more lucrative situation eke-
where and argues thus :

Either I shall have to give up a comfortable and
remunerative post or I shall miss a better one
which has been offered me;

To ^ive up my post will be a serious sacrifice, to miss
a better one will be very prejudicial to my prospects ;

Hence I am very much to be pitied;
where the argument is open to the obvious retort :

If you keep your present post, you will continue in one
which you say is comfortable and remunerative; if
you resign it, you will have a better one ;

Hence you are not to be pitied at all.

There are three different forms of the Dilemma.
I. Simple Constructive where the same result
follows from each of the alternatives in the disjunc-
tive major.

If this cancer be allowed to take its course, the result

will probably be fatal, and if the patient submits to

an operation, he will probably succumb to its effects;

But either he must allow it to take its course, or submit

to an operation ;

.-. In either case he will die.

2. Complex Constructive, where different results
follow from each of the alternatives in the disjunctive
premiss, and the supposed opponent is offered the
•choice of the results in the conclusion.

If Sir Thomas More were to have acknowledged
Henry VI I L to be the Supreme Head of the Church,
he would have forfeited the grace of God; if he refused
to acknowledge it, he forfeited the favour of the
King ;

356

VARIOUS KINDS OF SYLLOGISMS.

But he was compelled either to ackftowledge it or to

refuse to do so ;
,\ It was necessary for him either to forfeit the grace of

God or the King's favour,
3. Complex Destructive, where different results
follow from the various alternatives of the disjunc-
tive premiss, and from the denial of all the different
results follows a denial of one or other of the alter-
natives presented, as

If this man has £100,000 in the bank he is a rich

man, but if his word is to be trusted he has no

money invested anywhere ;
But either he is not a rich man, or he must have money

invested somewhere ;
.*. Either he has not £100,000 in the bank or his word is

not to be trusted.

Other Variations of the Syllogism.

The Enthymeme is a form of the syllogism in
which some mediaeval logicians have strangely de-
parted from their master, Aristotle. According to
Aristotle, the Enthymeme is a syllogism drawn from
probabilities, and signs of the conclusion {av\\oyLo-fio<;
ef ecKOTcov Kal crrj^ieicov). It differs from the syllo-
gism proper in its matter; the form may be the
same, though it is not always so.

A probability (et/co?) is a premiss that is generally
esteemed true, and a thing is said to be probable
which men know to be so for the most part, though
perhaps not always: as, Fat men are good naturcd ;
Love begets love; Suffering improves the character;
Swafis are white ; Children resemble their parents.

TRUE NATURE OF THE ENTHYMEME. 357

A sign {ar)iielov) is a demonstrative premiss which
invariably, or for the most part, coexists with some-
thing else ; or has taken place previously or subse-
quently to some other event, and is an indication
of its existence ^or of its having happened. Thus a
certain unsteadiness of gait is a sign of too much
intoxicating liquor having been drunk ; remorse is
a sign of guilt ; pallor a sign of indifferent health.
The premiss which contains the sign being, Men of
unsteady gait are intoxicated; Those who feel remorse
have a sense of guilt; The pale are in indifferent health,
Enthymemes then have a premiss which is either
a general probability or a sign, e.g,y
Fat men are good naturcd (et/co?) ;
Horace was a fat man ;
/, Horace was good natured.

Children resemble their parents (et/co?) ;
Charles is the son of John and Mary;
.', He will resemble them.

Men who roll in their gait are intoxicated {a'niiuov) ;
This man rolls in his gait;
,', This man is intoxicated.

The same thing can be under different aspects
both a general probability and a sign of the conclu-
sion. Thus Obesity is a sign of good nature, and
a tendency to become fat points probably, though
not certainly, to a good-natured disposition.

This is the true account of the Enthymeme as
-iven by Aristotle and St. Thomas, but some logicians
of the middle ages, mistaking the derivation of the
word, described it as syllogism with one of its premisses

35S

VARIOUS KINDS OF SYLLOGISMS.

suppressed, and existing not in outward expres-
sion but in the mind (eV Ov^iu))^ This meaning
has however some basis in classical authors.
Quintilian^ tells us that Enthymeme means some-
times that which is conceived by the mind ; some-
times an expressed opinion with the reason attached ;
or the conclusion of an argument either from conse-
quences or from contradictories. Hence, he says,
some call it a rhetorical, others an imperfect
syllogism because its premisses are not distinct or
complete.

The Enthymeme is almost identical with the
Rhetorical Syllogism. It is the same thing looked
at from a different point of view. It is an Enthymeme
in so far as it has for one of its premisses something
which we discover by reflection (ivOvfirjacf;) to be a
general probability or a sign of the conclusion. It is a
Rhetorical Syllogism inasmuch as orators argue as a
rule from premisses of this kind. It is this coincidence
between the two which has given rise to the false
definition and the modern idea of the Enthymeme.
The rhetorician naturally suppresses one of his
premisses. To take Aristotle's instance.^ When the
orator declares that Darius is to be crowned because
he has been victorious in the Olympic games, he
would sadly w^eary his audience if he were to insert
the major premiss and to argue thus :

1 The real derivation is from ivBvufladaiy the verbal substantive
ivBvu^fxa being that which is laid to heart or reflected upon, or
conceived or discovered by reflection.

2 Inst. Or. V. ii.

3 Rhet. I. 2, p. 1357, a. 16, Bekker.

THE E RICH I REM.

359

All who are victorious in the Olympic games are to be

crowned ;
Darius has been victorious ;
Therefore he is to be crowned.
The Enthymeme borrows this peculiarity from the
Rhetorical Syllogism.

A sign may be either a certain sign or proot
positive {reKMP^ov), or a probable sign. The posses-
sion of sensation is a certain sign of animal lite.
The equality of all straight lines drawn from some
point within the figure to various points of the
circumference is a certain sign that a figure is a
circle. In this case the Enthymeme is a vahd
Deductive Syllogism, e,g.,

All creatures possessing sensation are animals;
Glowworms are creatures possessing sensation ;
/. Glowworms are animals.

The Epichirem (eTnxelpVf^a) or Dialectical Syllo-
gism, like the Enthymeme, is used in modern books
of Logic in a very different sense from that which it
bears in Aristotle. Aristotle defines it as a Dtalecttcal
Svllogism, ...., a syllogism such as is employed in
discussions where the debaters do not profess to be
in possession of truth, but to be in search of it ; or
where the speaker or writer leads up gradually, by
means of careful examination of various considera-
tions and by discussion of difficulties, to the con-
clusion at which he ultimately arrives. The name
Epichirem thus signified that he who employs it takes
the matter in hand, attacks his opponents and
endeavours to arrive at a conclusion ; all which

36o

VARIOUS KINDS OF SYLLOGISMS.

SORITES.

361

ideas are included in the verb {i-mxeipeco) whence
epichirem is derived.

But in the time of Quintilian the meaning had
changed, and an Epichirem signified a process of
argument already taken in hand and accomplished ;
a perfect proof which adds to one of the premisses
•the reason of its truth, as

All rational beings arc to be treated with respect^ inas-
much as they are made in the image of God;

Slaves arc rational beings ;
^\ Therefore slaves should be treated with respect.

This is the modern sense in which the word
•epichirem is used. Hence we define the Epichirem
as a syllogism in which one of the premisses contains the
reason for its truth. It can always be broken up
into two valid syllogisms if it is itself valid.

Sorites (from aoopof;, a heap) is a heap or string
of propositions in which the predicate of each is the
subject of the following, the final conclusion being
composed of the subject of the first proposition and
the predicate of the last, as

All the children of Jacob are Jews,

All Jews appreciate the value of money,

All who appreciate the value of money make good

bargains,
All who make good bargains become rich,
A II who become rich are able to help the poor,
A II who are able to help the poor are bound to do so,
^'.All the children of Jacob are bound to help the poor.

There is always a certain accidental weakness or
chance of weakness in a Sorites, on account of the

possibility of some error creeping in unobserved in
the course of the series, and as no chain is stronger
than its weakest link, the value of the conclusion is
vitiated if a single one of the propositions is untrue.
Similarly we must watch carefully to see that there
is an exact identity throughout of the sense in
which the terms are used.

The following is an instance in which lurk both
these sources of weakness :

All consumptive patients arc ordered by their physician

to eat meat on a Friday,
All who arc ordered by the doctor to eat meat on a

Friday are bound to do so.
All who are bound to eat meat on a Friday are bound

to break the laws of the Church,
All who break the laws of the Church give grave

scandal to others.
All who give grave scandal to others commit a serious

sin,
.\All consumptive patients commit a serious sin.

The Sorites may be broken up into the same
number of syllogisms in the First Figure as there
are propositions between the first and last. We
must begin with the second proposition as our first
major premiss, and take our first proposition as the
minor. From these two premisses we shall draw
our first conclusion, e.g,,

All Jews appreciate the value of money,

A II the children of Jacob were Jews,
,',All the children of Jacob appreciate the value of money.
We then take our third proposition as the major

362

VARIOUS KINDS OF SYLLOGISMS.

THE POLYSYLLOGISM.

363

of our second syllogism and the conclusion just
drawn as its minor.

All who appreciate the value of money make good

bargains,
All the children of Jacob appreciate the value of money,
.'.All the children of Jacob make good bargains.

Our fourth proposition will be the major and our
new conclusion the minor of our third syllogism, and
so on until we come to our last syllogism, in which
the major premiss will be the last but one of our
string of propositions, and the minor the conclusion
drawn in the preceding syllogism.

All who are able to help the poor arc bound to help

them,
A II children of Jacob are able to help the poor,
/.All children of Jacob are botmd to help the poor.

As the Sorites is broken up into syllogisms of
Figure i, it must obey the rules of that figure.
No major premiss must be particular in any of
the syllogisms, no minor must be negative. For if
any of the premisses from the first to the last but
one inclusive, be negative, we shall have a negative
conclusion for our first syllogism, and therefore
negative minors for those following it. Hence the
rules of Sorites are :

1. Only the first premiss can be particular.

2. Only the last premiss can be negative.

For every premiss except the first is the major,
and every premiss except the last is the minor, of
one of the syllogisms into which it is resolved.

The Polysyllogism is a sort of variation of Sorites..
It is a series of syllogisms, in which the conclusions
are not repeated, but are left to be supplied as the
minor of the syllogism following next, e.g.,

All American citizens are proud of their country.
President Lincoln was an American citizen,
/.President Lincoln was proud of his country.

All who are proud of their country are anxious to

serve it,
.'. President Lincoln was anxious to serve his country.

All anxious to serve their country arc willing to
sacrifice themselves on its behalf,
.'. President Lincoln was willing to sacrifice himself for
his country.
All who are willing to sacrifice themselves for their
country are true patriots,
.'.President Lincoln was a true patriot.

GROWTH OF THE INDUCTIVE SPIRIT.

365

CHAPTER V.

ON FORMAL INDUCTION.

Summary — Growth of the Inductive Spirit — Influence of the
Inductive Spirit — Ancient Induction — Aristotle's account of
Induction — Induction Proper — Induction and Deduction —
Value of Formal Induction — Weakness of Formal Induction —
Contrast between the Ancient and Modern Spirit.

In our last chapter we discussed different forms of
simple and complex syllogisms which have some
variation from the normal type. Such are the
Hypothetical Syllogism, the Dilemma, the Enthy-
meme, Epichirem, Sorites, and the Polysyllogism.
We now enter on a more important chapter, one
which discusses a matter where first principles are
at stake.

The growth of the Inductive Sciences is one of
the notes of modern research. The very word Science,
once appropriated to Deductive or a priori know-
ledge, is now claimed as the exclusive property of
Inductive or a posteriori knowledge. Some of our
modern treatises on Logic give far more space to
Inductive than to Deductive Logic, and regard it
as far more important. Observation and experi-
ment take in modern systems a prominence that
was quite unknown to the ancients. The laws of

right observation and trustworthy experiment are
examined and sifted with a carefulness of detail
and a minuteness of inquiry to which Aristotle
and St. Thomas were wholly strangers. Laws and
canons are laid down for their employment, the
methods that are to regulate them are represented
as the very groundwork of Philosophy; and the once
cherished principles of the Dictum dc omni et nulla
and the a priori laws of thought are relegated to an
unhonoured obscurity.

This change dates from Bacon and Locke.
It does not concern us to trace its origin or the
cause of its development. It is enough to say
that as men turned their thoughts from laws re-
ceived upon authority to those which were framed
as the result of human experience— or rather as all
authority began to be regarded as built up from
below rather than coming down from above, it
was but natural that the new process of construction
should assume an importance it had never enjoyed
before, and that instinctive obedience to prevail-
ing laws should be exchanged for a very critical
inquiry into the validity and source of those laws.
And when the school of reform in philosophy had
decided that they came from below rather than
from above, that they were true, because every-
where of force, not everywhere of force because
true, it was but right and proper that they should
be challenged by the scientific inquirer, and that
their authority should be made subject to the most
approved principles of impartial and unbiassed
research.

366

ON FORMAL INDUCTION.

ANCIENT INDUCTION.

367

We have first to consider the relation of the
ancient and modern Induction, and how far we
ought to give in to the claims of the latter to be the
dominant method of modern Logic. We must see
if there is in our two great authorities, Aristotle
and St. Thomas, any recognition of modern Induc-
tion, and of the methods by which it is safe-
guarded. We must then examine the distinction
between the Induction of ancient and modern
times, and see what laws and canons regulate the
one and the other. This portion of our inquiry is
certainly no unimportant one, and one too beset
with difficulties. We have to steer our course
between the Scylla of a narrow and blind indifference
to the value of the new discovery, and the Charybdis
of a too great devotion to a hungry monster that
seeks to swallow up all truth in its rapid and all-
devouring vortex.

Induction in its widest sense is, according to
Aristotle, a process by which we mount up from
particulars to the universal. ' This may be done in
three different ways :

I. The particulars may be the occasion which
enables us to recognize a universal a priori law.
They put before us in concrete form two ideas, the
identity of which we might not have been able to
recognize in the abstract. Owing to our composite
nature, we cannot see universal principles, except as
embodied in concrete representations. We cannot
exercise an act of thought respecting triangles

* Eiraycoyrj rj airh ruv Ka6* (Kaarov iirl ra Ka66\ov l</)o5os. (Ar.,
Top., I. 12).

without having some sort of triangle present to our
imagination. The intellect cannot work without
the phantasy. We must have some sort of picture
before our bodily or mental sight. If I tell a man
ignorant of Euclid that the exterior angle of every
plane triangle is exactly equal to the two interior
and opposite angles, he does not intuitively recog-
nize the truth of my statement. But if I draw first
one triangle and then another, and prove it to him
in the separate cases, he is able to mount up to the
universal law. Even a single instance is sufficient to
make it plain to him, when once he sees that the
proof is independent of the kind of triangle of which
there is question, and that it holds good whether
the triangle be equiangular, isosceles, or scalene,
obtuse -angled, or right-angled, or acute-angled.
This, however, is scarcely Induction in the strict
meaning of the word, for the argument is rather
through than from the particular instance or in-
stances to the universal.

2. Induction in its strict sense is based upon
the particulars and argues from them, not through
them. It is any process by which we are enabled
to affirm or deny respecting the universal subject
something that we have already affirmed or denied
of the several particulars contained under it. It is
naturally divided into two different kinds which
furnish us with the second and third of the various
meanings of the word.

(a) Complete Induction, in which all the
particulars are enumerated.

•I

368

ON FORMAL INDUCTION.

(b) Incomplete Induction, in which only a
portion of the particulars are enume-
rated, but from this portion a conclusion
is drawn which covers those not enu-
merated.
Complete Induction is the exact reverse of the
Deductive process. As in the latter we argue from
the universal subject to each and all of the par-
ticulars contained under it, so in the former we
argue from each and all of the particulars to the
universal subject. Aristotle defines it'^ as proving the
major term of the middle by means of the minor. It is
thus opposed to deductive inference which proves
the major of the minor by means of the middle.
For instance.

Said, Davidy and Solomon were men of remarkable

achievements ;
But Saul, David, and Solomon were all the Kings

of the whole of Palestine ;
.-. All the Kings of the whole of Palestine were men of

remarkable achievements,

or, Nettles, pellitories, figs, mulberries have flowers with

a single perianth ;
But nettles, pellitories, figs, mulberries are all the

plants belonging to the order Urticece ;
,', All the plants belonging to the order Urticece have

flowers with a single perianth.

» Prior Anal. \l. 2^. 'Eira7cc7T? tikv olv itrrX koX 6 4^ 4iray(ayiis
<ruAAo7tor/ii>s rh did rov kripov Bartpov 6xpov T<fi iifffCf ffvWoyiffaffdai,
olov ft rwv A r fifffoy rh B, 8<i rod T Sd^ai rh A r^ B urapx*"'
oStw 70^ iroiOUjueSa reks ^ira7a>7ay.

INDUCTION AND DEDUCTION.

369

In these syllogisms the names of the individuals
or the lowest species are the miiior term, inasmuch
as they come under the class to which they belong,
and though collectively they are identical with it in
extension, yet they have a certain inferiority to it
because it is always possible that some fresh histo-
rical or botanical or other discoveries might add
another, whether to the list of kings who ruled over
the whole of Palestine, or to the urticeous plants, or
to any other enumeration of particulars coming under
ail niversal. Hence in an Inductive argument the
middle and minor change places, or rather that
which is minor in point of possible extension, stands
as the middle term, because in actual extension it is
its equal. In this kind of argument the true middle
humbly resigns its rights, and takes the place of the
minor term of the syllogism.

Is the Inductive Syllogism a legitimate one ?
We must look back at the Import of Propositions.
We have seen above that it states the existence of
such a connection between two objects of thought
that in whatever individuals you find the one you
will also find the other. When I apply this test to
the major premiss, I find it to be a true proposition;
wherever Saul, &c., are found as objects of thought,
there we shall also find remarkable achievements.
But it is not similarly applicable to the minor. It is
not true that wherever I find possible kings of all
Israel there I shall find Saul, &c. ; it is only true in
the case of the actual kings as known to us. This
weak point comes out when we fix our attention on
the copula. Saul, David, Solomon, are all the kings of

370

ON FORMAL INDUCTION.

the whole of Palestine, means not that the ideas of
Saul, &c., are present whenever the idea of king
of the whole of Palestine is present as an object of
thought, but merely that in point of fact the class of
all the kings is made up of these individuals. This is
not the logical meaning of the copula, and at once
creates the opposition between the syllogism and
the induction of which Aristotle speaks, and the
anomaly which he mentions respecting the middle
term. This, moreover, accounts for the further
anomaly of a universal conclusion in Figure 3,
though this anomaly may be avoided by transpos-
ing the terms of the minor premiss.

Is Complete Induction of any practical useful-
ness ? Yes, it has the same function as Deduc-
tion; it renders implicit knowledge explicit. We are
enabled to realize what we had not realized before,
to trace a universal law where we had not previously
suspected one. It brings out some universal charac-
teristic of a class, teaches us to recognize in those
who are bound together as members of that class
the possession of a common peculiarity which before
we had only recognized as belonging to them as
individuals. It is true that this sort of Induction,
per enumerationem simplicem, does not establish any
connection by way of cause and effect between the
common property and the common class. It may be
a matter of chance that all the kings who ruled the
whole of Palestine were distinguished men, or that
all the i^rticecB have a single perianth. But it is at all
events a suggestive fact, and leads us to question
ourselves whether there must not have been some

VALUE OF FORMAL INDUCTION.

371

reason why the kings in question had remarkable
gifts, or the flowers in question have one perianth

only.

For instance, if I go into the room of a friend and
find his library consists of ten books, and ten only,
and on examining them find that they are one and
all books describing travels in China or Japan, a
complete induction enables me to lay down the
proposition,

A II my friend's books are books of travel in China and
Japan,

This suggests to me a train of thought that
would never have arisen had I confined myself to
the isolated fact respecting the nature of each book.
Looking at them one by one, my thoughts are
directed merely to the character of each, and the
individual facts narrated in it. Looking at them
together, I begin to think that my friend must either
have been travelling in China or Japan, or that he
is intending to go there, or that he must have friends
in one or other of these countries, or that he is pro-
posing to write an article on the subject, or that for
some reason or other he must have a special interest
in China and in Japan.

Or to take an historical instance. I am studying
Roman history, and as I read the history of the
early Emperors who ruled the Empire, I am dis-
gusted at the low standard of morality prevalent
among them, the cruelty, the ambition, the lust that
attaches to their name. I find Julius Caesar en-
grossed by an insatiate and unscrupulous ambition —

372

ON FORMAL INDUCTION.

VALUE OF FORMAL INDUCTION.

373

Augustus a man of pleasure — while the rest were
among the vilest of men. I observe, moreover,
that when the Empire had passed out of the hands
of the Caesars there was a decided improvement,
I also notice that the evil tendencies of the Caesars
increased, and that the first two Emperors were
superior to. the four who succeeded them.

I embody my reflections in an inductive syllogism :

Julms Ccesar, Augustus, Tiberius, Caligula,

Domitian, Nero, were men whose lives were

marked by selfishness or crime ;
All the Ccesars who ruled the Roman Empire were

Julius CcEsar, AiigustuSy Tiberius, Caligida,

Domitian, Nero ;
.', All the CcBsars who rided the Roman Empire were

men whose lives were marked by selfishness or

crime.

The conclusion of this syllogism naturally leads
me to ask whether there must not be some influence
tending to deteriorate the character in the position
of Emperor of Rome, and further whether that
influence is a universal one, or is limited to this
family whose members appear to have been spe-
cially affected. This gives occasion to an interesting
train of thought which would never have been
suggested had I not mentally gone through the
process of Complete Induction.

The weak point of a Complete Induction is that
in so many cases we are not perfectly sure that it is
Complete. We fancy that we have not overlooked
any one of the particulars whence we argue to the

universal law, while all the time there is one that for
some reason has escaped our notice, and perhaps
this very one is fatal to the universality of our law.
In the case of the Roman Emperors, it is always
possible that there might have intervened between
the reign of one Emperor and the next recorded, a
short space of time during which there reigned some
Emperor whom historians never knew of, or for
some reason passed over in silence. We may prac-
tically feel certain that this is not the case, but we
never can have that absolute certainty that leaves no
room for any possible doubt. To take a more
practical case : let us suppose a chemist arguing a
century ago about the known metals :

Iron, copper, silver, gold, lead, tin, mercury, anti-
mony, bismuth, nickel, platinum, and aluminium,
all are heavier than water ;

Iron, copper, silver, gold, lead, tin, mercury, anti-
mony, bismuth, nickel, platinum, and aluminium
are all the metals ;
,-. All the metals are heavier than water.

Here would be a Complete Induction of the metals
then known, but nevertheless the conclusion would
be false ; since that time potassium, sodium, lithium,
&c., have been pronounced to be metals, and all
these are lighter than water.

Of course there are some cases where an enu-
meration is perfectly secure of completeness, e.g., if
I argue that January, February, &c., all have twenty-
eight days or more, I cannot be wrong in concluding
that all the months of the year have twenty-eight

i
i

374

ON FORMAL INDUCTION.

THE ANCIENT AND MODERN SPIRIT.

375

days or more. From the fact that Sunday, Monday^
Tuesday, &c., are all named after some heathen
deity, that all the days of the week derive their
names from heathen deities. But this is merely acci-
dental and comparatively rare, and for this reason
we cannot draw any clear line of demarcation
between Complete and Incomplete Induction.

The real contrast is between the Induction
mentioned above, in which the instance or instances
given merely sicggest the a priori law, and inductions
in which the instances given are the foundation on
which the a posteriori law is based, whether they
are a complete or an incomplete enumeration. The
modern spirit, ever since the time of the Refor-
mation, has been doing its best to obliterate this
contrast, to degrade the law which has its reason
in itself, and which looks to examples merely as
the means of enabling us to realize its binding force,
to the level of the law which depends upon the
examples for the existence of its power to bind.
Under pretence of questioning nature, it ignores
the God of nature, and is willing to accept as laws
only those which are gathered together by human
industry, and will not allow a higher kind of law
which is based on the inner essence of things, and
ultimately upon the nature of God Himself. It
recognizes only those which can be secured by a
plebiscite, and allows no superiority to any of those
having the direct sanction of the Supreme Ruler of
the Universe, and binding as soon as a single
concrete instance presents itself to us. In other
words, the Inductive spirit thrusts out of sight

a priori laws, and makes a posteriori investigation
to be all in all. While it certainly fosters com-
mercial activity and progress in all that pertains
to things material and sensible, it tends to make
men forget things immaterial and spiritual, and
destroys their realization of, and their belief in, those
inner realities, compared with which the visible
world is but a shadow and a thing of nought.

SS5S3IS^^^^«*^^^^irtt««itei^ '

ARISTOTLE ON MATERIAL INDUCTION.

377

CHAPTER VI.

MATERIAL INDUCTION.

Material Induction recognized by Aristotle— Opinion of Catholic
Philosophers— Induction and the Syllogism— Incomplete In-
duction— Material Induction and Formal Logic— The Province
of Material Logic— The certainty of Physical Laws— Hypo-
thetical Certainty — The Inductive Methods — Method of
Agreement— Methods of Difference— Instances of the various
Methods— Method of Concomitant Variations — Method of
Residues— Combination of Inductive Methods— Fallacy of
Mill's Theory of Causation— Value of Inductive Methods-
Dangers of rapid Induction.

We now come to Incomplete or Material Induction.
Incomplete Induction as such is recognized by Aris-
totle, though he does not say very much respecting
it. It comes under his definition of Induction as a
process from Particulars to Universals, and the very
inf,tance he gives is an instance of Material and
Incomplete Induction.

Pilots, charioteers, &c., who know their business are
most skilful,

.*. Generally all who know their business are most
skilful.

Further, he describes it as more persuasive, and
clearer, and more capable of being arrived at by per-
ception, and more within the reach of the masses,
while the syllogism is more forcible and clearer as an

answer to gainsayers.^ Here it is evident that he is
speaking of an argument from a limited number of
instances to the whole class. He describes the object
of Induction as being to persuade rather than to con-
vince, as being clearer in the eyes of ordinary men,
inasmuch as it appeals to their sensible experience ;
as more within their reach, as being an argument
that all can appreciate, whereas the argument that
starts from first principles implies a grasp of such
principles, and this is comparatively rare among the
mass of men. Yet it has not (he says) the com-
pelling force of deductive reasoning, inasmuch as
it can always be evaded. It is not in itself so
clear as the Syllogism, it does not hit home
with the same irresistible force as the argument
that makes its unbroken way from the first
principles that none can deny to the conclusion
which we seek to establish. And this is exactly
applicable to Material Induction, and would have
little or no force if we were speaking of Formal
and Complete Induction. The example, moreover,
that he gives is so incomplete as scarcely to deserve
the name of Induction at all. He merely takes two
instances of the arts, and from them at once draws
the conclusion that in the arts skill and success
are inseparable. Possibly he chooses this extreme
instance to show how very imperfect an induction

* Cf. Arist. Top. I. 12: 'Ewayury^ ^ a-wh rwv naff <tKa<nov iiri to.
Kad6\ov ^<^o5os, oTov d tffri Kvfi(pvi]rr\s 6 4vi<TTafi€Vos KpdTiffTOS Kcd
7}vloxos<, Kol SAws ^<rr\y & iiri<rr<in(vos irepl fKaffrov &pi<rTos. (<tti 5* ^
fify i-Kaywy^ iriQavwrfpov koX aatpfffrtpov kolL Kara r^v aX<TB-r]<nv yvwpi-
^uintpov KoX rois TroWots K0iv6vy 6 5^ crvWoyifffihs fiiaffriKwrfpov koI
-Kphs Tovs ityriKoyiKovs ^vepytcrfpov.

378

MATERIAL INDUCTION.

CATHOLIC PHILOSOPHERS ON INDUCTION. 379

may be sufficient to establish a general law, where
that law has the constant and universal testimony of
mankind in its favour, and that men need only to be
reminded of the law by the instances adduced rather
than to be taught any fresh truth from an examina-
tion of the invariable co-existence of the two objects
of thought, which the instances exhibit as invariably
united.

Aristotle's brief reference to Induction is a re-
markable contrast to the elaborate treatment of it by
some modern writers on Logic. St. Thomas and the
scholastic logicians generally are equally meagre in
their discussion of it. Even the Catholic logicians
of the present day pass it over in a few paragraphs
or a few pages, which are devoted in part to an attack
on Baconian Induction, and to an assertion that
Induction has no force unless it can be reduced to
syllogistic form. Sir W. Hamilton, Mansel, and the
Scottish school of philosophers are at one with the
schoolmen and modern Catholic writers in their
jealousy of the intrusion of Induction, and, although
they do not agree with them in advocating the neces-
sity of reducing it to the form of the syllogism, yet
they would assign it a very subordinate place in a
treatise on Logic.

It is the modern school of experimentalists, of
which Mr. John Stuart Mill is the illustrious leader,
who put forward Induction as ** the main question
of the science of Logic, the question that includes
all others." This suggests to us three questions :

1. How far does Induction come into Logic at all ?

2. Is it true that all Induction must be capable

of being reduced to a syllogistic form in order to be

valid ?

3. Is the neglect of Induction by modern Catholic

logicians to be praised or blamed ?

We are speaking here of Material or Incomplete
Induction, and unless we warn our readers to the
contrary, we shall continue to use it in this sense to
the end of our present chapter.

"Induction," says Cardinal Zigliara, "has no
force whatever apart from the Syllogism." " Incom-
plete Induction," says Tongiorgi, "is not a form
of argument different from the Syllogism." ** In-
duction," says Mendive, " is a true form of reason-
ing, and it pertains to the essence of reasoning that
it should be a true Syllogism." " Induction," says
Liberatore, "does not diifer from the Syllogism
in its essence, but only in the form it takes."
Yet we have seen that when reduced to syllogistic
form, it breaks the rules of the Syllogism and uses
the copula in an altogether different meaning. How
then are we to solve the difficulty ?

As usual we have to examine carefully into our
use of terms. 5y//o^/sm is an ambiguous term. There
is the Deductive Syllogism with its figures and moods,
such as we have described them above, and which
is subject to and based upon the Dictum de omni et
millo, viz., "Whatever may be affirmed or denied
of a universal subject may be affirmed or denied of
each and all the individuals who are included under
that subject." In this sense Induction is outside the
Syllogism, and any attempt to reduce it to syllogistic
form at once exhibits a violation of syllogistic laws.

38o

MATERIAL INDUCTION.

MATERIAL INDUCTION AND FORMAL LOGIC. 381

But beside the Deductive Syllogism the word
Syllogism is used in a wider sense for any process of
reasoning based on the more general principle,
** Whenever two objects of thought are identical
with a third they are also identical with each other."
This principle includes not merely the Deductive
Syllogism, but the Inductive Syllogism also.

Induction therefore comes into Logic as reducible
to syllogistic form, but not to the form of the Deduc-
tive Syllogism. This is true of both Complete and
Incomplete Induction. When I argue :

James I. and IL, Charles L and II. zcere head-
strong monarchsy

James I, and II., Charles I. and II. were all the
monarchs of the Stuart dynasty,
,'. All the monarchs of the Stuart dynasty were head-
strong,

I violate one of the rules of the Third Figure by my
universal conclusion. I use the copula not for the
necessary co-existence of true objects of thought,
since it is not inconceivable that future Stuarts might
arise and falsify my minor, but for the fact which
is true in the concrete. My argument, moreover,
refuses to obey the authority of the Dictum de omni et
mdlo, and is therefore no true form of the Deductive
Syllogism. But my argument is a perfectly valid
syllogism in that it is in accordance with the principle
of identity I have just given : it is in accordance
with the laws of thought, it is perfectly logical.

But is this true of Incomplete Induction ? For
instance, I argue from the fact that I have observed

on a number of separate days in the year that all the
days when there has been a gradual fall in the baro-
meter have been followed by rain ; and I state the
result of my observation in the following premiss :

January iSth, March 4th, April yth, October igth
were succeeded by rainy weather ;

January iSth, March 4th, April yth, October igth
were days on which there was a fall of the baro-
meter ;
.', All the days on which there is a fall of the barometer
are days followed by rainy weather.

In order that the conclusion may hold true in
strict logic, I must be able to assert that January
i8th, March 4th, April 7th, October 19th were all the
days when there was a fall in the barometer, and
this is obviously ridiculous. But may I not put my
minor in another form, and say : What is true of
January iSth, &c., is true of all days when there was a
fall in the barometer? If I can, the conclusion
certainly follows, and I can re-arrange my syllogism
in a convenient form in the First Figure, and argue
thus :

What is true of January iSth, March 4th, April yth,
October igth, is true of all days when the barometer

falls ;
Rain near at hand is true of January iSth, March 4th,
April yth, October igth ;
.-. Rain near at hand is true of all days on which the
barometer falls.
Everything therefore depends on the representa-
tive character of the days in question. If they have

382

MATERIAL INDUCTION.

nothing in common save this one common feature of
the fall of the barometer which can be connected
with the coming change in the weather, then no
one can deny that there must be some sort of
connection between a fall in the barometer and
rainy weather near at hand, which will justify us
in predicting of all days on which the barometer
falls, that they will be succeeded by rain.

We have then to find out by some means or
other whether the major premiss of our syllogism is
true. But before we enter on an investigation of this
point, there is a previous question. Does it concern
us as logicians to investigate it at all ? Is it within
our scope to examine into the various instances in
order to sift their value as evidence ? Has not the
logician to assume his premisses as true, suppos-
ing always that they contain nothing which violates
the laws of the human mind and of right reason ?
Or is he to employ, in order to discover their truth,
the various methods of observation and experience
by which the truth of all a posteriori and Synthetical
Propositions have to be tested ? If these lie outside
the province of Logic, the moderns are not only
one-sided and unfair in giving so large a space to
Induction, but are all wrong in their very conception
of the task that they have to perform.

This question can only be satisfactorily answered
by reminding the reader of the distinction between
Formal and Material (or Applied) Logic. Formal
Logic simply takes its premisses for granted so long
as they do not sin against any law of thought or
contradict any proposition of the truth of which we

^^1

ON MATERIAL INDUCTION.

383

are absolutely certain. Applied Logic steps outside
the comparatively narrow field, and asks what the
terms are which regulate our admission into the
mind of any proposition as a part of our mental
furniture. Formal Logic in its strict sense, therefore,
has nothing to do with the conditions under which
we can arrive at Universal Propositions other than
those to which we are compelled by the nature of the
mind itself. It has nothing to do with those Propo-
sitions which we are led to regard as true, by reason
of what we witness in the external world, and which
depend upon laws learned by observation and not
rooted in us as a priori conditions of thought. It
has nothing to do with the methods of arriving at
those a posteriori truths.

But the hard and fast line between Formal and
Applied Logic is one of theory rather than one that
can be practically observed. We have already con-
sidered the Foundations of Logic, though here we
were stepping outside the strict boundary of Formal
Logic. Similarly we shall do well in a question so
important to look to the matter of our syllogism in
order to discover whether modern Induction can
furnish us with a solid basis for a universal premiss.

But there is now the further question whether
observation and experiment have any claim to
consideration under the head of Applied Logic;
whether as means of adding to the propositions
that we regard as certain and adopt as such, they
should be examined into, and the results to which
they lead tested as to their qualifications for
admission into the mind. Can they give us the

^':J

384

MATERIAL INDUCTION.

THE CERTAINTY OF PHYSICAL LAWS.

385

certainty we require as logicians ? Probably no one
in his senses would deny that external observation
can give us some sort of certainty. That the sun
will rise to-morrow morning, that a stone thrown
into the air will fall to earth again, are as certain
as anything can be that does not depend upon the
inner laws that regulate all being.

But such a certainty is, strictly speaking, always
a practical or hypothetical^ never an essential or
absolute certainty. It is within the bounds of
possibility that some unknown comet might inter-
vene between the earth and the sun during the
coming night, or that some undiscovered and mys-
terious influence might whisk away our stone to the
moon, not to mention the further possibiHty of
Divine interference by what we call a miracle.

Here it is that a posteriori laws, which are based
on observation and experiment, differ (as we have
already remarked more than once) from a priori
laws. In the case of the latter, no miracle can
intervene, no possible hypothesis can set them aside.
God Himself cannot make five out of two and two,
or prevent things equal to the same from being
equal to one another, or cause the exterior angle of
any plane triangle to be less than either of the
interior or opposite angles. It is beyond the utmost
limit of Divine Omnipotence to bring about any of
these results, simply because they are in themselves
contradictory and would if they were realized make
God deny Himself. These a priori laws are not only
laws of thought and of human reason, but of Being
and of the Divine Nature. They are based upon the

nature of God Himself, and thus on eternal and im-
mutable Truth.

Not so the physical laws at which we arrive by
observation and experiment. God could reverse
them all to-morrow if He chose. He does from time
to time intervene and hinder their efficacy. They
are not founded on the Divine nature, but in the
Divine enactment. They are, therefore, liable to
exceptions, and this is why we say that they are
only an hypothetical or conditio7ial certainty.

But they have another source of weakness. Not
only can God set them aside at any moment if He
pleases, but we are not absolutely certain whether they
exist at all. All that we call physical laws are but
hypotheses which have gradually won their way to
the stage of certainty. They are never metaphysi-
cally certain. We have not the means of arriving at
any metaphysical certainty, when we depart from
those laws which are stamped on all being, and
therefore on the human intellect, which are the very
conditions under which we think, because the condi-
tions under which all things, and even God Himself,
necessarily exist. When we come to laws which are
partly a posteriori, we never can say more than that
they are generalizations from experience ; that they
explain all the facts known to us ; and that they
satisfy every test applied to them.

Such are the law of gravity, the undulatory theory
of light, the laws of attraction and distance, &c. All
this gives us physical certainty respecting them, but
this is utterly inferior to absolute certainty. We not
only have to accept them as conditionally true, but

386

MATERIAL INDUCTION.

our acceptance of them, as such, has in it an element
of weakness.

It is the attainment of this kind of certainty
which is regulated by the various methods that have
come in since the time of Bacon, and which have
been elaborated by Mill under the name of the
Methods of Induction. It cannot be denied that these
methods were an object of comparative indifference
and neglect to the Scholastic and Aristotelian philo-
sophy. The pre-reformation world did not recog-
nize the importance of those modern discoveries and
inventions which have revolutionized the world since
the days of Bacon. With the Aristotelian philo-
sophy dominant, the steam-engine, gas, the electric
light, the steam-loom, sewing-machines, and all the
mechanical substitutes for human labour, would, in
all probability, either not have existed at all, or
never arrived at their present perfection. The
a priori method had no fondness for hypotheses,
and hypothesis is the fertile mother of physical
research and discovery. Whether all these have
really fostered human progress, whether they have
made men stronger, healthier, more honest, virtuous,
and happy, is a point which does not concern us.
We have already wandered too far away from the
question before us, which is this : Are we to admit
into Logic in its wider sense what are called the
Inductive Methods, and which are elaborated with
wonderful skill and ability by John Stuart Mill ?

If we look at the matter with the strictness and
accuracy of the philosophic logician, who knows no
certainty save absolute certainty, no universal laws

HYPOTHETICAL CERTAINTY,

387

save those which are founded on the inner nature of
things, we must answer this question in the negative.
To give the Inductive methods a place in a strictly
logical treatise, seems to exalt the laws which
are based on them to a sort of equality with the a
priori laws. It seems to exalt hypothesis into law,
to confuse practical with absolute certainty, to obli-
terate the distinctions between the eternal, the
necessary, the immutable, and the transitory, the
contingent, the mutable.

In spite of this, these methods cannot be passed
over in the present day. They are too important a
factor in the present condition of human society
to admit of our neglecting them. They are weapons
which have been forged by what is called the march
of human intellect, and it would be suicidal to deny
their value and their efficacity. As science has
now a new meaning, so we must admit under
the category of scientific laws those which the
scholastic philosophy with all good reason repu-
diated. Besides, we must understand and appre-
ciate them in order to protest against their abuse.
We must give them their due in order that they
may not usurp the whole field of human science.
Mill and his followers drag down all the a priori
laws to the level of the a posteriori, or rather
deny the existence of a priori laws at all. This
is the fatal result of the rejection of scholastic
methods which began at the Reformation, and has
been carried further day by day. But fas est et ah hoste
doceri, and the various methods set forth in detail
by Mill have, in their own proper limits, a most

THE INDUCTIVE METHODS.

389

388

MATERIAL INDUCTION.

important function to perform, and are of constant
application to our every-day life.

We have now to return to our consideration of
the premiss which asserts the representative nature
of the instances on which we are going to base our
law. Our methods are to give us the means of
ascertaining this ; they are to decide for us whether
what is true of the instances under our consideration
is true of all instances real or possible, or at least
they are to settle the question for us, so far as it is
possible in the nature of things to arrive at any
certainty respecting it.

Our premiss then asserted that what was true of
January i8th, &c., is true of all days on which the
barometer falls, and the value of our argument
depends upon our being able to establish this propo-
sition. What is necessary in order to prove it satis-
factorily is to show, that these days had nothing in
common which could possibly be connected with the
approach of rainy weather save a certain heaviness
in the air indicated by the fall in the barometer. If
this could be ascertained beyond a doubt, then we
should have a perfect physical certainty that there
was a connection of cause and effect between the
heaviness in the air and the subsequent rain. But
in point of fact we never can be sure that there are
not other characteristics common to these days
which might be the source of the phenomenon of
rain. To be absolutely certain of this would require
a knowledge of the inner nature of things which
even the greatest of scientists does not possess. All
that we can say is that we are unable to detect any

common characteristic in the days in question which
would account for the subsequent rain, save only the
heaviness in the air and the consequent fall in the
barometer, and therefore the connection between
the rain and the heaviness in the air is at most but
a strong probability.

Here we have a case of the first of Mr. MilFs
experimental methods — the Method of Agreement.
We cannot do better than formulate it in his own
words :

METHOD OF AGREEMENT.

** If two or more instances of the phenomenon
under investigation have only one circumstance in
common, the circumstance in which alone all the
instances agree is the cause (or eifect) of the given
phenomenon."

Our readers will observe that in this law Mr. Mill
goes beyond the requirements we have given above,
and exacts not only the presence of no common
circumstance which would account for the result
save one, but absolutely the presence of no common
circumstance at all save one alone. In the case
before us we can never find two rainy days, devoid
of any common circumstance save that on one the
barometer falls and on the other it does not ; and
the same is true of all possible instances of pheno-
mena to be investigated. Until we have this impos-
sible condition fulfilled, the law can never be applied,
and therefore we can never derive from this method
more than a strong probability.

But there is another method which comes in to

390

MATERIAL INDUCTION.

supplement the former. Let us suppose that we
find a day exactly corresponding to one of the days
afore-named in every circumstance save one, viz.,
the weight of the air. In all else they are exactly
alike. When we examine the rain record of the year
we find that on the day when the air was heavy
rain followed, and on the day when it was light
fine weather came after it. Here we should have
perfect physical certainty if only we could find two
days corresponding exactly in every possible circum-
stance save one ; there would be no doubt whatever
as to the connection of this circumstance with the
result that was present where the circumstance in
question was present, absent where the circumstance
was absent. But here, too, it is impossible to find
any two such days ; there must of necessity be a
thousand points of difference between the two. All
that we can have is a certain amount of correspon-
dence, and the absence of any points of difference
which seem likely to be connected with the result
save the single circumstance which is conspicuous
for its presence in the one case and its absence in the
other. Here, therefore, again we are limited to a
probable connection, and can get no farther.

In this case we have an instance of the Method
of Difference. Again we will give it in Mr. Mill's
words ;

METHOD OF DIFFERENCE.

** If an instance in which the phenomenon under
investigation occurs and another in which it does
not occur have every circumstance in common save
one, that one occurring only in the former, the

♦,i

METHOD OF DIFFERENCE.

391

circumstance in which alone the two instances differ,
is the effect, or the cause, or an indispensable part
of the cause of the phenomenon."

But this second method, as Mr. Mill very per-
tinently remarks, is applicable rather to experiment
than to observation, that is to cases where we can
artificially vary the antecedents instead of having to
receive them ready-made. We will, therefore, take
another instance, which will, moreover, have the
advantage of illustrating other methods of Inductive
Research which cannot be so easily applied to the
case of the weather.

We will take a familiar and very practical case.
I have of late, from time to time, risen with a head-
ache in the morning for which I cannot account.
Somehow I fancy it must be connected with some
sort of digestive disarrangement, and that this dis-
arrangement is the result of some food which I have
taken and which does not suit my stomach. One
day it occurs to me that my headache always follows
a special diet, and that possibly this may be its
cause. I therefore take note of what I have for
dinner, and after a little experience I discover that
in most cases when I have eaten jugged hare for
dinner I have a headache the next morning. I set
to work to test the connection by means of the
methods of Agreement and Difference. First of all
I take a number of days when my dinner has been as
varied as possible. On one day I have taken soup, on
another day none. On one day I have had beef for
the chief dish, on another mutton, on another veal, on

392

MATERIAL INDUCTION.

another pork. On one day I have drunk port wine,
on another sherry, on another champagne, on another
hock, on another claret, on another nothing but
water. On one day I have taken pastry, on another
not, on one day cheese, on another none, and so on
ad infinitum, varying my dinner in every possible way
on the days of trial. But on all these days there has
been the common element of jugged hare, and on
each of them there has been a headache following.
Here we have a good instance of the Method of
Agreement, The various days on which I suffer
from headache agree, as far as I can tell, in no
common circumstance of diet, save only in this one
special dish.

But I cannot be certain that there may not
have been any other cause for my headache which
happened to coincide with the jugged hare. I may
have been rather tired on the evenings in question,
or perhaps a little more thirsty than usual, and
the wine may have been more attractive than on
other days. So I proceed to a further experiment.
On two given days I take the same amount of exer-
cise and order exactly the same dinner, drink exactly
the same amount of wine, and go to bed at the same
hour. The only difference between these two days
is that on the former I make jugged hare an item in
my bill of fare, and on the other omit it. The result
is that the former day is followed by a severe head-
ache, whereas on the latter I rise fresh and ready for

business.

Vegetus consueta ad munia surgo.

Here I have the Method of Difference. At first the

INSTANCE OF THE VARIOUS METHODS.

393

experiment seems decisive. But it is not really so.
It may be the mere difference of quantity involved in
the presence of the jugged hare that is the cause of
the headache ; or perchance on the day I ate of it
the wind was in the east, or my stomach was already
out of order, or some unwonted worry had befallen
me. I therefore am;still in the region of probabilities.
Can I ever escape from them ? I can do a good
deal towards it by means of a third method which is
often extremely useful.

I resolve on a new experiment. I determine that
I will try the effect of eating on one day a very small
portion of jugged hare at my dinner, on another a
good deal more, on another of making it the chief
part of my dinner, and on another of having no other
meat dish at all. The result is that I find the
severity of my headache is exactly or almost exactly
proportioned to the amount of jugged hare that I
have eaten on the previous evening. A small quantity
produced a very slight headache, a larger quantity a
more serious one, while, on the morning following
the day when I ate nothing else than hare I was so
wretchedly ill that I was unable to attend to my
ordinary business. Here is what is generally known
as the

METHOD OF CONCOMITANT VARIATIONS.

*' Whatever phenomenon varies in any manner
whenever another phenomenon varies in some par-
ticular manner, is either a cause or an effect of that
phenomenon, or is connected with it through some
fact of causation."

394

MATERIAL INDUCTION.

I am now approaching certainty, but there is
nevertheless a possible element of uncertainty arising
from the chance of the varying headache having
been owing to circumstances which by a curious
coincidence happened to produce it in a severity
which quite by accident was in proportion to the
amount of jugged hare eaten for dinner. I am after
all still in the region of probabilities, and I look
around for a final method to try and assure the
truth of my inference.

I have for years been studying the effect of various
sorts of food and drink, as well as of walking, hard
study, riding, boating, &c., on my constitution.
Long experience has taught me the effect of each of
those. Beef and mutton make me rather heavy the
next morning, so does port wine ; champagne makes
me rise well contented with myself. Plum-pudding
produces indigestion ; walking, riding, &c., various
different kinds of bodily fatigue ; severe mental
labour a curious feeling of oppression on the top of
my head, and so on. On some particular morning
I take stock of my bodily condition and its various
constituent symptoms ; I am able to trace each and
all of them to some familiar antecedent, all except
the headache. I can trace in the present state of
my body the result of most of the circumstances of
the previous day, the mental and bodily labour, the
various kinds of food, the amount of sleep, each has
its familiar result, all save the jugged hare. Hence
I subduct from the various results all those I can
trace to known causes, and (neglecting minor details)
I have left on the one hand the headache and on

METHOD OF RESIDUES.

395

the other the jugged hare. Surely then this result
unaccounted for must spring from the cause not yet
taken into consideration. This method, which can
often be employed with much advantage, is called
the Method of Residues, Mr. Mill formulates it in
the following law :

METHOD OF RESIDUES.

" Subduct from any phenomenon such part as is
known by previous induction to be the effect of
certain antecedents, and the residue of the pheno-
menon is the effect of the remaining antecedent."

Does this give us perfect physical certainty?
Most decidedly not, if we take it by itself. My attri-
bution of effect a to cause ^ , of 6 to B, is at best only
a probable argument, and even if it is all correct, I
cannot be sure that I have exhausted either con-
sequents or possible antecedents. I am not abso-
lutely certain that the oppression in the head is due
to study or the heaviness of the port wine. At most
this method only contributes its share to the ever-
increasing stream of probability which is gradually
developing itself into the resistless river of practical

certainty.

But when all these Methods are united together,
surely then we have certainty. Surely we can go
beyond the mere tentative assertion of an hypothesis
to the firm conviction of a well-grounded law, a law
which certainly connects together the circumstances
we are considering as cause and effect ; or at least
as in someway connected together by a fixed and
stable law of causation.

396

MATERIAL INDUCTION.

Here we enter upon a wider topic which we have
already discussed in this volume. To those who
still hold to a priori truths, to the school of Aristotle
and St. Thomas, there opens out an endless vista of
causes and effects descending from God, the First
Cause, to every detail of His works. These causes
and effects are twofold, metaphysical causes, con-
nected with their effects with an absolute certainty
which is inviolable, and physical causes, connected
with their effects with physical or conditional certainty.
With metaphysical causation these methods are not
concerned ; it needs no series of experiments or of
observation to detect the a priori law. It is with
physical causation and physical laws that they are
alone concerned. They have to detect the a
posteriori laws which depend on the free action of
the Creator. All things that God has made are
connected together by physical laws which He has
decreed, but from the action of which He may at
any time except certain cases at His good pleasure,
and which He does except from time to time by
what we call a miracle.

But to the modern school of sensationalists, to
Mill and Bain, cause and effect are words which
have no meaning. Cause is but invariable uncon-
ditional antecedent, and effect invariable, uncon-
ditional consequent. The cause need not contain
its effect : there is nothing in the nature of things
that links them together : there may be portions of the
universe where there is no such thing as invariable
unconditional sequence. The belief in the connec-
tion between cause and effect is to the sensationalist

COMBINATION OF INDUCTIVE METHODS. 397

merely the result of long experience in the past, and
how do we know that this experience may not here-
after vary? If sensationalists were logical there
would be for them no certainty about the future, for
what possible reason is there why it should resemble
the past? Because it has always done so? The very
supposition is a contradiction in terms ; for the future
is still unborn. All that experience has taught them is
that one portion of the past has hitherto resembled
another, that there has always been an unbroken
uniformity of succession in the series of antecedents
and consequents. But of the future as such we never
have had and never can have any experience, and
our conjectures respecting it are, if we logically
follow to their conclusions the theory of Mr. Mill
and his school, the merest guess-work, an arrow
shot into the air without any sort of reason for
believing that it will hit the mark.

Our conclusion, therefore, is that these Methods are
a most valuable contribution, if not to Logic strictly
so called yet to the course of human discovery and
scientific research. The Catholic philosopher learns
from Aristotle and St. Thomas the a prion law, one
of the first principles of all knowledge, that '* every
effect must have a cause." He knows that this law
extends not merely to effects following as particular
applications of some a priori law, which becomes
known to us as soon as a single instance of it is
presented before us and grasped by the intelligence,
as in the case of the deductions of mathematics, but to
others also. It extends to effects following from what
is rightly called a /flic-, inasmuch as it is a general

398

MATERIAL INDUCTION.

VALUE OF INDUCTIVE METHODS.

399

principle under which a vast number of particulars
are ranged, but is nevertheless arrived at by
generalization from a vast number of particular
instances. In the one case as in the other the uni-
versal law of causation holds. In the one case cause
is joined to effect in virtue of the inner nature of
things ; in the other, simply because the will of God
has so disposed the arrangements of the universe
that He has created. In the one case, experience
makes known to us a law which is already imprinted
on our intelligence ; in the other, experience makes
known to us a law which is stamped upon the world
outside, but which only becomes a part of our mental
furniture when we have carefully weighed and sifted
a number of individual instances of its operation.
In the one case the Methods of Induction are rarely,
if ever, of any practical use ; in the other they are
simply invaluable.

We are now in a position to assign their true
place to the Inductive methods of which Bacon was
the harbinger, and Mr. John Stuart Mill and his
school the prophets and apostles.

I. They certainly claim a place in Material Logic
if not in Formal. To ignore them and pass over
Material Induction with a passing remark that it
must be virtually complete, i,c., must include a
number of instances sufficient to afford a reasonable

' At the same time we have absolute certainty as to the per-
manence of physical laws as long as the universe remains in existence,
since this is demanded by the wisdom of God. But we have not
absolute certainty as to the application of the law in a particular
case, nor have we absolute certainty that the universe will continue
to exist.

basis of certitude, is to omit a subject which
is of the greatest importance in every branch
of modern investigation. A just appreciation of it
is necessary if we are to keep pace with the
development of scientific research. We should not
be so easily taken in by the hasty generalizations
of the modern scientist, if we had the use of these
methods and the kind of certainty that may be
derived from them at our fingers' ends. It is of
no use to allege the authority of Aristotle and St.
Thomas. If they had lived in the present day they
would have taken the lead in regulating the methods
of modern research, just as in their own day they laid
down the principles of deductive argument. The
eager questioning of nature was in their day a thing
conducted in a very different fashion from that which
experience has gradually perfected, and mechanical
discovery advanced. Any elaborate setting forth of
the methods to be pursued would then have been
superfluous and unnecessary and premature, whereas
now it is not only of the greatest value in itself, but
necessary to one who would successfully encounter
the inroads of hasty generalization, and the preten-
sions of hypothesis to take its place among estab-
lished laws.
I 2. These Inductive Methods can never give us abso-
I lute certainty, but they can give us physical certainty.
They cannot give us absolute certainty, because the
laws they reveal to us are reversible at the will of
their Maker. They can give us physical certainty,
for the simple reason that the human mind is so
constructed as to be able to judge without any

400

MATERIAL INDUCTION.

DANGER OF RAPID INDUCTION.

40X

reasonable doubt, from a combination of arguments
of which it may be that no single and individual
one is sufficient to carry conviction to the mind.
But the number of them combined is enough,
and more than enough, to make us perfectly sure
of the conclusion to which they one and all con-
currently point.

3. We must always be on our guard against
allowing ourselves to be persuaded into a conviction
of the truth of some general hypothesis when the
concurrent evidence is not sufficient of itself to
establish it. We must remember Aristotle's admir-
able distinctions between Deduction and Induction,
that the one is more forcible and clear {fiLaa-riKo^Tepov
Koi cra(j)6(TT€pov) ^ the other more persuasive {TTiOavw'
repov), and within the reach of the masses. We
have too often seen the intellectual convictions
of scientific men shaken by the brilliant guesses
which Induction suggests, and which they regarded
as justifying them in discarding the beliefs that they
previously held to be true. Very slow and cautious
should we be in allowing any law arrived at by a
process of Pure Induction to set aside any conviction
based upon a higher and more certain mode of
argument. Of course there are occasional instances,
as the so-often quoted case of Galileo,^ but for one

* The condemnation of Galileo has been so often explained by
Catholic writers that it is scarcely necessary to point out that it
does not in any way affect the question of Papal Infallibility.
Galileo was condemned by the Congregation of the Index, not by
the Pope ex cathedra, and the Pope cannot delegate his Infallibility.
Whether Galileo's brilliant guess had sufficient data at that stage
of astronomical science to justify him in asserting it as a fact, it is
not easy to decide.

such instance there have been hundreds in which
some premature hypothesis has been allowed to
weaken the grasp on a priori truth, to be in its turn
discarded for some equally premature successor
sitting in its turn for a brief period in the usurped
throne of truth.

SOCRATIC INDUCTION.

403

CHAPTER VII.

EXAMPLE AND ANALOGY.

Example — Socratic Induction — Dangers of Socratic Induction-
Value of Example— Analogy— Weakness of Analogies— Analogy
and Metaphor.

We have somewhat outstepped the strict limits of
Formal Logic in our last chapter, but it was
necessary to do so, in order that we might do
justice to the services rendered by Material Induc-
tion and point out its true place in philosophy. We
now return to forms of argument recognized by all
logical text-books and which are closely akin to
Induction.

I. Example. — Example (irapdBeiyfiay cxcmplum,
argumentum ex paritate), is a form of argument that
proceeds from one or more individual instances to
a general law, and then applies the general law to
some further individual instance. It is the most
limited possible form of material induction, with a
syllogism appended applying the result of the in-
duction to a particular case.^

* It is defined by Aristotle as proving the major of the middle by a
term resembling the minor, a definition which it is not very easy to
understand, but which appears to have been worded with a view to
contrast it with Induction. The meaning of Aristotle's definition
is explained in Mansel's Aldrich, Appendix, note H, " On Example
and Analogy," to which we would refer our readers.

For instance, I happen to be staying in an
hotel in Paris where I make the acquaintance of
a Russian gentleman. I find him not only most
courteous and kind, but full of information and an
excellent linguist. His talents in this respect make
such an impression on me that I unconsciously
argue as follows :

M. Nicolaieff is a good scholar and linguist ;
M. Nicolaieff is a Russian gentleman ;
/. All Russian gentlemen are good scholars and linguists.
But I do not stop here. Some little time after-
wards I encounter at Berlin another Russian
gentleman, and at once I jump instinctively to
the conclusion, or at all events to the expectation,
that he too is a man of wide knowledge, and well
versed in modern languages. If I put my argument
into syllogistic form it will run thus :

A II Russian gentlemen are good scholars and linguists;
M. Smolenski is a Russian gentleman;
.-. M. Smolenski is a good scholar and linguist.
If my first acquaintance at Paris has not been
limited to M. Nicolaieff only, but has extended to a
number of his friends, cultivated and scholarly
gentlemen like himself, then my first argument by
which I ascend to the universal will not be the same
rapid leap from a single instance. It will have a
degree of probability higher in proportion to the
number of instances from which I am able to argue,
and I shall have a more reasonable ground for my
conclusion respecting the further instance or in-
stances that I may encounter.

■JMjM

404

EXAMPLE AND ANALOGY.

VALUE OF EXAMPLE.

405

When the argument thus proceeds from a
number of instances it is called a Socratic Induction,
It was the method which Socrates continually em-
ployed to prove all kinds of conclusions true or
false. Nothing can give a better notion of the
extreme danger of arguing from a few plausible
instances than the ingenious employment of it by
the Athenian philosopher. We will take an instance
from the First Book of the Republic' He is seeking
to disparage justice as defined by his opponents,
and argues as follows :

" Is not he who can best strike any kind of blow,
whether fighting or boxing, best able to ward any
kind of blow.

** Certainly.

** And he who can prevent or elude a disease is
best able to create one ?

'' True.

" And he is the best guard of a position who is
best able to steal a march upon the enemy ?

** Certainly.

" Then he who is a good keeper of anything is
also a good thief? "

** That, I suppose, is to be inferred."

" Then if the just man is good at keeping, he is
good at stealing money ? "

** So the argument declares."

'* Then, the just man has turned out to be a thief."

Example is a method of argument that we all of us
are constantly employing, and are too often misled by

» Plat. Rep., Bk. I. (Jowett's translation, Vol. III. p. 201.)

it. Of all fallacies the commonest is that of hurrying
to an unfounded conclusion from one or more
instances, or of arguing from the existence of some
circumstance in one instance of a phenomenon to
the existence of the same circumstance in another
instance presented to us. The infant who looks
out of the window and on seeing a man pass by
in a black coat and hat cries out, Dadda ! ; the
too credulous invalid, who, because he has swallowed
a box of patent pills and afterwards recovered,
attributes his recovery to the pills ; the cynic who
condemns all ministers of religion as insincere,
because he has on one or two occasions met with
a clergyman who did not live up to his profession ;
the traveller who denounces the dishonesty of a
country, because he has once been cheated during a
passing visit there ; the superstitious of all kinds,
who attribute good luck to horseshoes nailed over
their door, or ill-luck to their having seen a magpie
or walked beneath a ladder; all these and ten
I thousand more are fallacies of Example or Imperfect
I Induction. They leap from a single instance, or a
handful of instances, to a universal conclusion,
often forgetting or leaving out of sight the cases
that are fatal to their too hasty generalization.

But are there never cases in which we can follow
this convenient and rapid process which satisfies
itself respecting a universal law from one or two
instances casually encountered? Must we always
pursue the painful and laborious process of Induc-
tion and its elaborate methods before we can assert
even the probability of the universal law ? We shall

4o6

EXAMPLE AND ANALOGY.

ANALOGY.

407

have a word to say on this subject when we come
to the question of hypothesis. The rapid generali-
zation, so dangerous to all, is nevertheless within
its own proper limits a most invaluable instrument
of scientific research and discovery. To make such
discoveries is one of the prerogatives of genius;
there are some who possess a sort of natural
instinct, an inborn power of detecting the general
laws under the single instance, or under a number
of instances so small that they would reveal nothing
to the ordinary observer. Such men obtain their
results by what Father Liberatore calls a sort of
keen scent that enables reason to track its prey, and
that is not acquired by teaching, but given by nature
as a gift.' But the mass of men have to follow the
steady and safe path of observation and experiment,
employing as their guides the methods that Mr. Mill
sets forth so clearly.

But has Example no logical force, no power to
compel an opponent ? Yes ; it at least proves this,
that the two qualities in question, the two circum-
stances common to each of the cases are not incom-
patible. When I argue that A and B are both X,
A is Y, .'. B is Y, I show that X and Y are at least
compatible, and I am justified in drawing as my
conclusion not B is Y, but B may be Y. Thus
if I meet a Londoner and find him a vulgar,
impudent fellow, I very much overstep the laws of
reasoning if I conclude that all Londoners are vulgar

^ " Obtinetur (haec notitia) olfactu quasi venaticae rationis, qui
praeceptis non acquiritur sed dono traditur a natura." (Liberatore.
Inst. Phil., 1.91.)

and impudent. The only inference I can draw from
my observation is that cockneydom and vulgarity
are not incompatible.

2. Analogy.— Analogy is clearly akin to Example,
and indeed it is not always possible to distinguish
between them. But properly speaking. Example
[ argues from one instance to another similar instance
in the same order: Analogy from one instance to
another similar instance in a different order. If I
argue from the fact that one man's body is liable to
disease to the fact that the body of some other man
is exposed to the same malady, I am arguing from
Example. But if I argue from the liability of the
body to disease to a similar liability on the part of
the mind, I am arguing from Analogy ; or to put the
difference in another way. Example argues from an
absolute identity in some particular, Analogy from

an identity of ratios.

Example may be stated mathematically as

follows:

A and B are both X ;

MsY;
Therefore B isY.

Analogy will have a different formula :

A : M :: B : N

A is Y ;

Therefore B is Y.

Angels and men, for instance, have an absolute
identity in this, that they are creatures of Almighty
God. If from this characteristic common to both I
argue that because men are dependent upon God,

j|o8

EXAMPLE AND ANALOGY.

WEAKNESS OF ANALOGIES.

409

SO are angels also, I am arguing from Example,
and my argument may be stated thus :

Men and angels are alike creatures of God ;
Men are dependent on their Creator ;
.*. Angels also are dependent on their Creator,

But angels and men have also a proportional
identity, in that angels have in the spiritual world a
subordination to the archangels, which corresponds
to and has a certain proportion to the subordination
of priests to their bishops. If I therefore argue
that because a priest is bound to obey his bishop in
matters pertaining to his office, so is one of the
lower angels bound to obey an archangel, I am
arguing from Analogy, because I am not arguing
from a common fact but a common relation or pro-
portion, and my argument will be :

Priests : Bishops :: Angels : Archangels ;
Priests are bound to obey their Bishops;
Therefore Angels are bound to obey Archangels.

If Example is prone to mislead, much more is
Analogy. It adds to the weakness of Example the
further weakness of a transference to another order
of things, which may be governed by altogether
different laws. If a man points out that in the
physical world beauty implies variety, and that a
monotonous uniformity is destructive of all true
grace and loveliness; and then goes on to deduce
from this premiss the beauty of a divergence in
religious beliefs, representing the countless varieties
of Protestantism as more attractive than the uni-
formity of belief in the Catholic Church, we answer

him that to argue from the sphere of sense to the
sphere of intellect is always untrustworthy, and that
you might as well argue that because in the physical
world of sense we test the reality of physical objects
by their resistance to our bodily senses, therefore
some such resistance is necessary to test reality in
the world of intellect.

When we argue from Example we are said to
illustrate our thesis: when we argue from Analogy
it is not illustration but metaphor that we employ.
A preacher is urging on his audience the advantage
of imitating the saints. He enforces his counsel
both by illustration and by metaphor. He illustrates
his advice by cases of those who have imitated the
saints with the most happy results ; of St. Augustine
reading of all that the heroes of the early days of
Christianity had done and suffered for God, and
saying to himself: '* If they could do all this, why
not I ? " ; of the sentinel, who watching the holy
Martyrs of Sebaste frozen to death in the icy lake
for the love of Christ, was moved by grace to strip
off his uniform and plunge into the water to take
part with them ; of St. Louis of France, trained up
to be a saint by the example of his holy mother.
Queen Blanche.

All these are arguments from Example, and put

in logical form would be :

St. Augustine, the sentinel at Sebaste, St. Louis, &c.,

became great saints ;
But St. Augustine, the sentinel at Sebaste, St. Louis,
&c., imitated the saints ;
.'. All who desire to become saints must imitate the saints.

rir

410

EXAMPLE AND ANALOGY.

ANALOGY AND METAPHOR.

411

Or the preacher may employ metaphor and say:
"We sometimes see a herd of deer at a river's
brink, longing to cross to the rich pastures which
lie beyond it, but fearing to plunge into the stream.
But when at length one larger and nobler than the
rest shakes his branching antlers, as if in defiance
of the danger, and fearlessly leads the way, the
timid herd take confidence and boldly follow their
monarch and their leader, so we see some great Saint
who boldly encounters the trials and dangers that
frighten ordinary men, and emboldened by his
example, others venture into the painful waters of
hardship and self-sacrifice which without it they
would never have dared to enter, and thus reach
the rich pastures of a holiness reserved for those
who are willing to suffer and to labour for God,'*
&c. Here we have an argument from Analogy :

Deer and men are both prone to follow a leader ;
Deer attain to richer material pastures by following a

leader superior to themselves ;
.*. Men may reach richer spiritual pastures by imitating

the noble example of men who are spiritually

superior to themselves.

If the object of Induction is to persuade and make
things clear to the mass of men rather than to con-
vince or enforce an argument, much more is this
the case with both Example and Analogy. Sometimes
an apposite illustration or judicious metaphor will
have a greater influence than the most logical of
deductive arguments, and will convince the intel-

lect through the medium of the will. But here we
are encroaching on the field of Rhetoric.

Has Analogy any strictly logical force ? As an
answer to an objector, it sometimes has a real
value such as the strict Laws of Thought recognize

and approve. .

If a non-Catholic urges the indifferent or nnmoral
lives of some Prelates or Popes as an argument
against the truth of the Catholic Church, the obvious
answer is to point to the evil life of Judas Iscariot,
and to remind the objector that this was no argu-
ment against the truth of the doctrine of our Lord,
or the authority of the Apostolic College. The
argument would take the following shape drawn out
in syllogistic form :

The contrast between the belief and the practice of
Judas Iscariot did not prove the doctrine he pro-
fessed to be false ;
But Judas Iscariot had the same relation to the
Apostles of Christ that any Prelate or Pope, whose
practice should be at variance with his belief
would have to the followers of the Apostles ;
/. The contrast between the belief and the practice of any
Prelate or Pope is no argument against the
teaching of the Catholic Church.
In this case the logical force of the argu-
ment depends on the admission that the posi-
tion of Judas amongst the Apostles was similar to
that of a Prelate or Pope of evil life amongst the
followers of the Apostles, and this granted, the con-
elusion that follows from it will be granted also.

I - ' ? ;

-S'^-s-U'Sei^iV' ^,if-:'^--

DEMOS STRATIOW

413

CHAPTER VIII.

ON THE MATTER OF THE SYLLOGISM.

Matter of the Syllogism— Demonstrative Syllogisms— Probable
Syllogisms — Sophisms — Metaphysical, Physical, and Moral
Certitude — Opinion, Doubt, and Error — Science and Demon-
stration— Physical Science — Various kinds of Demonstration —
Probability, Certainty, and Certitude— Converging Probabilities
— Weakness of Probable Arguments - Cumulative and Chain
Evidence.

We have already said that our present treatise is
one of Formal Logic, and that if we limit Formal
Logic to what the word strictly means, we shall be
obliged to admit that the matter of the Syllogism lies
completely outside its sphere. But such a restric-
tion is one that cannot be adhered to without con-
siderable inconvenience, and the name of Formalism
in its most uncomplimentary sense rightly belongs
to any attempt to exclude from our treatise all
possible considerations of the matter of our argu-
ments.

Thus we cannot grasp the difference between
Ancient and Modern Induction without at least a
short consideration of the material side of Reason-
ing. If it is the function of Logic to direct the
mind in taking cognizance of Truth, we cannot pass
over the difference between various kinds of syllo-
gisms, which vary not in the legitimacy of their
inference but in the character of their premisses.

Among forms of argument in which the conclusion
follows logically from their premisses, some we can
accept with firm and unhesitating confidence, while
to others we can only yield a qualified assent, or
perhaps no assent at all. This is not owing to any
variation in their form, all may be alike syllogisms
in Barbara or any other legitimate form. It simply
results from the nature of the premisses.

When the premisses are certain, we have the
king of reasoning called Demonstration, and the
syllogism is called the Demonstrative Syllogism;
of this there are two kinds :

I. Demonstrative Syllogisms.— (a) A priori:
When the premisses are absolutely certain and are
necessitated by the very nature of things, we have
Demonstration a priori, and the syllogism expressing
it is said to be absolutely demonstrative, e.g.,

A II equiangular triangles are isosceles ;
All isosceles triangles have the angles at the base equal;
,\ All equiangular triangles have the angles at the base
equal,

(6) A posteriori : When the premisses are physically
or morally certain, and are necessarily true as long
as the present order of nature goes on undisturbed,
and the nature of man remains the same, we have
Demonstration a posteriori, and such a syllogism is
said to be only conditionally not absolutely demon-
strative, e.g,

(i) Major premiss physically certain :

414

MATTER OF THE SYLLOGISM.

CERTITUDE.

415

All fruit-trees flower ;
The banana is a fruit-tree ;
,\ The banana flowers,

(2) Major premiss morally certain :

What is vouched for by all travellers to China is a

geographical fact ;
The existence of Pckin is vouched for by all travellers to

China ;
/. The existence of Pckin is a geographical fact.

II. Probable Syllogisms.— When the premisses
are not certain but only more or less probable, then
we have only a probable argument, and the syllo-
gism is said to be a Probable Syllogism, as

Wicked men are unhappy ;
Nero was a wicked man ;
.*. Nero was unhappy.
All the phenomena of light are explained by the

undulatory theory ;
The colouring of the woods on the Hudson River is a
phenomenon of light ;
.*. The colouring of the woods on the Hudson River is
explained by the undulatory theory of light.

III. Sophisms.— When the premisses are such
that from them a false conclusion is drawn, without
however violating the rules of the Syllogism, such
a defect in our reasoning is called a Fallacy or
Sophism.^

» This strict meaning of the words is not always adhered to.
Fallacy is often used to include both sophism and paralogism.

All sophisms are based on the matter not on the
form. When the defect lies in the form we are said
to have what is called a Paralogism, an argument
false in form, a syllogism which is only apparent
and not real.

Before we consider these various kinds of Syllo-
gisms we must briefly explain the various states of
mind which they severally produce, leaving the fuller
consideration of these to the volume of our present
series which deals with the First Principles of Human

Knowledge.

I. When an argument is rightly drawn from
premisses which are certain, the state of mind
produced is Certitude, which may be defined as a
firm assent to some object of knowledge without any fear

of going wrong.

But as the premisses can be certain with absolute
(or metaphysical), physical, or moral Certainty, so
the certitude they produce will be absolute (or meta-
physical), physical or moral. We are certain with
absolute certainty that two and two make four. We
are certain with physical certainty that the stone
which I throw upwards will fall again to earth. We
are certain with moral certainty that Julius Caesar
was the first Roman Emperor.

In all the three cases there is a complete
exclusion of the possibility of the opposite being
true, but metaphysical certainty is nevertheless
on a different level from the other two. It is so
bound up with the Divine Nature that God Himself
could not interfere with it. No exercise of the

4i6

MATTER OF THE SYLLOGISM.

METAPHYSICAL, PHYSICAL, &- MORAL CERTITUDE. 417

Divine Omnipotence could make five out of two and
two, or cause the exterior angle of any triangle to be
less than the interior or opposite angle. God could
not create a world in which the theory of Hegel
respecting contradictions would be true, or Kant's
doctrine of antinomies, or Mill's denial of the neces-
sary universality of the laws of the a priori sciences.
But it is very different with physical or moral
certainty. A doctor is physically certain that an
ulcerated sore cannot be healed in a day, or an
ovarian tumour disappear, or sight be restored on a
sudden to eyes that have received an organic lesion
of the retina. Yet all these wonders have been
worked at Lourdes, and the evidence is so indispu-
table that no man in his senses who carefully
investigates it can deny the facts. Hence Physical
Certitude is, as we have said, only conditional, not
absolute. The Author of Nature's laws can at any
time set them aside or suspend their operation if
He pleases, and He does from time to time and
will continue to do so as long as the world lasts.

There is, moreover, another reason why our
certitude about the laws of nature is only conditional.
(They are not like the inner laws of Being, stamped
jpon our intelligence so that they have only to be
3nce brought before us to be recognized at once as
universally and unconditionally true. They are
arrived at by a long process of observation and
experiment, and are (as we have already remarked)
nothing more than hypotheses which long expe-
rience justifies us in regarding as universally true.
The law of gravity, certain as it is, certain with all

the certainty of which any a posteriori law is capable,,
is only an hypothesis verified by the universal expe-
rience of mankind for seven thousand years, and by
every sort of experiment of which scientific men are

capable.

In the same way moral certainty depends on the
character and dispositions of mankind, such as they
are known to us by experience. We know for
instance that lying for lying's sake is against nature.
Men in their sound senses, whether good or bad, will
not deceive their fellows, as long as there is no
advantage to be gained by doing so. It is a law of
human nature that word and thought correspond.
It is again a law of nature that habit enables us to
do easily what is difficult at first, or that education
refines the character, or that men naturally seek after
happiness ; and in our actions we are perfectly safe
in acting on these laws as certain. Nevertheless
there is nothing contradictory in the supposition
that a tribe might exist who lied for lying's sake
without any view to gain ; or a race of men with
whom frequent repetition of an act did not lead
to the foundation of a habit, and so on. Hence
they are not true absolutely and a priori, but only
conditionally and a posteriori, the condition being,
as long as human nature remains what it is at

present.

2. When an argument is rightly drawn fromt

probable premisses, the state of mind induced is-

called Opinion, which may be defined as adherence

\or assent to one of two opposite statements with Or

certain fear lest the other alternative be true. Thus it

4i8

MATTER OF THE SYLLOGISM.

DEMONSTRATIVE SYLLOGISMS.

419

i!l

is my opinion that Socrates was a good and con-
scientious man, although I am not altogether free
from a fear of the opposite, especially when I read
certain Dialogues of Plato. It is my opinion that
Romulus was the first King of Rome, though the
treatment of him as a mythical personage by some
learned historians prevents me from being certain
of his existence. It is my opinion that earthquakes
are caused by the upheavings of the igneous contents
of the earth, but I am not sure about it, and am
ready to accept any other explanation of them if it
shall be established by scientific men.

When I have such a dread of the opposite that I
do not venture to express myself either one way or
the other, then my state of mind is no longer
opinion, but Doubt, For instance, I doubt whether
the use of gas in the place of candles and lamps has
been a real advantage to mankind or not ; whether
it is desirable that the civil government should
interfere in education; whether Savonarola was
justly put to death, &c. In these cases I recognize
a great deal to be said on both sides of the question,
and cannot give my assent to either.

When I have no sufficient data to form an
opinion at all, then my state of mind is not Doubt,
but Ignorance, For instance, I am ignorant of the
state of education in China, of the state of politics
in New Mexico, of the causes of the various
changes in the weather, and of a million questions

more.

3. When an argument is drawn from false
premisses, or is wrongly drawn from true principles,

then the state of mind of him who accepts it is
f Error, which may be defined as a discrepancy between
ihe judgment formed by the mind and the object
respecting which it is formed. Error is very different
from ignorance, though it implies the presence of
ignorance and arises from it. For ignorance is some-
thing negative, it expresses the absence of know-
ledge, but does not imply the formation of a judgment
respecting the matter of which we are ignorant;
r whereas error implies the further step of forming a
judgment, and that judgment a mistaken one.

Hence we have three states of mind : Certitude,
the offspring of what we have called the Demon-
strative Syllogism, Opinion of the Probable Syllogism,
and Error of the Sophistical Syllogism.

We must now return to our consideration of
these various kinds of Syllogisms.

I. Demonstrative Syllogisms.— A Syllogism
which produces Certitude proceeds by way of
Demonstration, We are all familiar with the phrase :
^'I can prove this to demonstration," which means,
I can prove this from premisses which are certain,
and which no man can reasonably doubt.

Demonstration therefore may be defined as an
argument in which the conclusion is logically drawn from
premisses known to be certain. It does not differ in its
form from all other modes of argument, but in its
matter. Moreover it always proceeds either imme-
diately or mediately from premisses incapable of
demonstration, from self-evident propositions of
which no proof is possible, whether it proceeds

420

MATTER OF THE SYLLOGISM.

PHYSICAL SCIENCE.

421

downwards from First Principles, or upwards fron>
individual facts.

The end of demonstration is Science, which may
be defined as a certain knowledge of the truths arrived
at by demonstration. It deals with conclusions, not
with the principles from which those conclusions
are ultimately derived, since we are said to appre-
hend First Principles rather than to have a scientific
knowledge of them. Science does not teach us that
things equal to the same thing are equal to one
another, or that every effect must have a cause.
First Principles are more certain and better known
to the human intellect than the conclusions drawn
from them, since our knowledge of them is immediate,
our knowledge of conclusions only mediate.

Science, properly speaking, is in its highest
sense a knowledge of things that are metaphysi-
cally certain by reason of their inner nature, of
things that are necessary and cannot possibly be
otherwise. But in a wider sense science is used of
a knowledge of things that are only physically or
morally certain, the truth of which knowledge
depends, not on the inner nature of things, but on
the physical or moral laws that govern the world,
laws which might be reversed by Almighty God
at His good pleasure. Thus, the knowledge that
all the angles of a triangle are together equal to
two right angles, is scientific knowledge in the strict
and accurate sense, but the knowledge that the
flame of the candle will burn me if I thrust my
hand into it, is scientific knowledge in the wider and
less accurate sense of the term.

Each of these propositions is the conclusion
from a general proposition. In the former case the
conclusion is deduced from a mathematical axiom,
viz., '' Things which are equal to one and the same
thing are equal to one another," in the latter case
from an a posteriori proposition based upon observa-
tion and experiment, and only physically certam.
To reverse the former law and the consequence
flowing from it is beyond the power of God Himself
in the present order of things. To prevent the
action of the latter law and the consequence flowmg
from it, is not only within the power of God, but it
has repeatedly been done by Him in favour of His
servants, or to manifest His power.

This suggests a passing remark respecting the
strange perversion of language by which science is
confined by modern usage to physical science, and
scientific to that which is concerned with what only
deserves the name in a secondary and inferior sense.
We do not refuse the word science to that branch of
human knowledge which deals with nature's laws,
but to regard this as the only, or even as the primary
meaning of the word, is one of those degradations
of human speech which bears unconscious testimony
to the degradation of the minds that frame the
speech. Science is, with our modern scientists, no
longer the knowledge of Divine things, no longer the
acquaintance with the immortal and immaterial part
of human nature, no longer the search after the
eternal and immutable. It is the knowledge of
things corruptible, the acquaintance with the brute
matter doomed to perish, the research mto the

|i'

ii t

422

MATTER OF THE SYLLOGISM.

VARIOUS KINDS OF DEMONSTRATION. m

various phenomena of which the dirt and dust of
earth is capable.

Science being the end arrived at by demon-
stration and the demonstrative syllogism, we have
divisions of Demonstration corresponding to the
various uses of the word Science.

I. Demonstration a priori proceeds from universals
to particulars, from first principles to the conclusions
following from them, from causes to effects.

Demonstration a posteriori proceeds from parti-
culars to the universal, from the results of principles
to the principles themselves, from effects to causes.

Thus, if I argue from the immutability of God
to His eternity, I argue a priori ^ and my syllogism
is as follows :

All immuiahle things are eternal ^
God is immutable J
.'. God is eternal.

But if I argue from the dependent and contin-
gent character of things created, to the existence
of an independent and necessary Being, who is their
Creator, I am arguing a posteriori, and my syllogism
will be :

All things dependent and contingent imply the
existence of a Being on whom they depend.

All created things are dependent and contingent,
,', All created things imply the existence of a Being on
whom they depend,

where my argument proceeds from the effects to
their efficient cause.

2. Demonstration is also pure, empirical, and

mixed, . i 4.u f

Pure Demonstration is from premisses, both ot

which are a priori, as in Mathematics.

Empirical Demonstration is from premisses, both
of which are a posteriori, as in Chemistry and the

physical sciences.

Demonstration is said to be mixed when the

Minor premiss applies to the real

order what the major premiss

asserts of the ideal, c,g,,

All plane triangles have straight
lines for their sides,

ABC is a plane triangle, A

.-. ABC has straight lines for its sides,
where in point of fact AB, AC, BC, are none of
them either straight or lines, however carefully the
triangle be drawn. Nevertheless the mind forming
to itself the idea of a plane triangle and the idea
of a straight line from the imperfect representa-
tions of them, rightly judges respecting A B C
what is, strictly speaking, only true of the ideal

it copies. , • J- ^

3 Demonstration is also direct and indirect.
In Direct Demonstration we show our conclusions
to be true by positive arguments.

In Indirect Demonstration we show our con-
clusions to be true by showing the absurdity of
every other alternative. This latter is also called

reductio ad abstirdum.

We have an instance of the former in the large

424

MATTER OF THE SYLLOGISM.

PROBABILITY.

425

majority of propositions of Euclid ; of the latter in
those propositions in which he begins, " If it be
possible, let," &c.

Indirect Demonstration is always inferior to
-direct. It does not lead the mind straight to its
mark or leave it so fully satisfied, but takes it by a
roundabout way. There is always a latent fear lest
there may be some weak point in the conditional
premisses which give the various alternatives ; and
we suspect either that there is some further possi-
bility beside those enumerated, or else that one
or other of those adduced does not lead to the
absurdity attributed to it, or that they may not be
•exclusive of one another.

4. Demonstration is also divided into absolute
and relative.

Absolute Demonstration proceeds from premisses
that are true in themselves.

Relative Demonstration proceeds from premisses
which are agreed upon between myself and my
adversary, without taking into consideration whether
they are true or not ; as when I prove the sceptic to
be wrong by assuming his own premisses, and
showing him from them how he is at variance with
himself.

II. Probable Syllogisms. — As the Demonstra-
tive Syllogism leads to certainty, so the Probable
Syllogism leads to opinion. St. Thomas^ remarks
that the operations of human reason have their
counterpart in the processes of nature. There are

' Lect. i. in Post. Anal.

some things in which nature acts as of necessity,
and which invariably produce the same results.
There are others in which she generally, but not
always, pursues the same course. Thus, if we sow
a seed in the ground, we generally see it under
normal circumstances grow up to a perfect plant,
but this is not always the case. Our seed may
never come up at all, or may never attain maturity.
In the same way our mind sometimes draws a con-
clusion as of necessity and without any hesitation.
At other times it draws a conclusion which is true
in a majority of cases, but is not necessarily true.
In the former case the mind proceeds by means
of the Demonstrative Syllogism and attains to
scientific certitude ; in the latter the mind proceeds
by means of the Probable Syllogism and attains to

probability.

Probability may be described as an approach to
I truth. Truth is, as we have seen above, a conformity
I of the mind with the object known. Probability,
then, is an approach to this conformity. In Proba-
bility, then, are countless different degrees, varying
from the highest to the lowest, from a very near
approach to certainty to the greatest improbability.
Just as in natural things (we borrow again from
St. Thomas) nature may be stronger or weaker, and
according to her degree of strength is her success in
attaining to the end aimed at, so in all processes
of argument that fall short of certainty, the mind
approaches near to or withdraws further from the
condition of certitude, according as it attains to
propositions which appear to have a larger or smaller

426

MATTER OF THE SYLLOGISM.

CERTITUDE AND CERTAINTY.

427

conformity to truth. But however high the degree
of probability attained to, the mind cannot be
said to have scientific knowledge so long as it
does not pass beyond the probable, since in all pro-
bability there is a certain dread of the alternative
opposite to that towards which we ourselves incline.
Truth does not consist in the combination of a
number of probabilities, or certainty of a number of
probable opinions all tending to the same point.

Nevertheless we must be on our guard here lest
we confuse together certitude and certainty. It is
true that certainty can never consist of probabilities
united together, but certitude may be produced in
the mind by the effect of such a union of proba-
bilities. Certainty is something objective, and is
concerned with the nature of the proposition in
itself. Certitude is subjective, and is concerned with
the state of mind of one before whom the propo-
sition is placed. Now when any proposition has
in its favour a large number of converging proba-
bilities, the effect upon the mind of any reasonable
man is to produce a real kind of certitude. He is
morally certain that the proposition is true, using
the phrase ** morally certain " in its proper and true
sense, as meaning that he has no dread lest the
contradictory be true, as long as the nature of
man remains what it is.

An example will make my meaning clearer. I
see in a New Zealand paper the announcement of
the death of a man whose name is that of an old
University friend and companion of my own. The
name is a common one, it is true, but I know that

my friend emigrated, though I never heard where he
went. I begin to wonder whether it is really my
friend who is dead. A few days afterwards I meet
a mutual acquaintance of both of us, who tells me
that he has just received a letter stating that so-and-
so (mentioning my friend) died suddenly abroad.
Not long afterwards I pass a brother of the man
reported to be dead and observe (I have no oppor-
tunity of speaking to him) that he has a mourning-
band round his hat, such as would be worn for a
brother or sister. Now each of these sources of
information does not give anything more than
probability. It is very possible that there may
have been in New Zealand another man of the same
name as my friend, not to mention the chance of a
mistake in the newspaper. The report that reached
our mutual acquaintance may be a mistaken one,
and my friend's brother may be in mourning for
some other relative. Yet I feel certain that my
friend is dead, and I think that under such cir-
cumstances any ordinary man would feel sufficiently
certain to take practical action, if such action de-
pended on the report being true. The combination
of probabilities produces certitude, not the highest
certitude, not absolute certitude, but moral certitude.
It does not merely produce a high degree of proba-
bility.

In the same way, I suppose every one would
allow that a jury ought not to declare a prisoner
guilty, unless they are quite certain of his guilt.
Yet in nine cases out of ten the evidence consists of
probabilities, and that even where it is not only

428

MATTER OF THE SYLLOGISM.

WEAKNESS OF PROBABLE ARGUMENTS. 429

circumstantial but direct. A man is tried for
robbery and violence. The prosecutor swears to his
identity, he is found with purse and money in his
possession, and he is a man with several convictions
recorded against him. Under those circumstances
what jury would not convict, and rightly so ? Yet
the prosecutor may have made a mistake, the thief
may have picked up the purse in the street, or may
have had a similar purse of his own, and as to his
character, this affords a very feeble presumption of
his guilt on this particular occasion. Yet the com-
bination of probabilities produces, on the mind of
jury and judge alike, a sufficient certitude to make
them perfectly certain of the prisoner's guilt, suffi-
ciently certain to pronounce him guilty without any
need of deliberation.

What should we say to a juror who, after the trial
was over and the man condemned, were to feel
scruples as to the verdict passed, or worse still,
who were to starve out the other eleven on the
ground that it is still possible that the prisoner is
innocent, and he ought to have the benefit of the
doubt ? We should answer him that his doubt was
what is called an imprudent doubt ; that it is
absolutely possible that the whole matter was a
mistake, but that it is not morally possible, when
we take into account the credibility of ordinary
witnesses, the tendency of a man once convicted to
commit some other crime, and the general reliance
that can be placed on a man's identification of his
own property ; so that we can have no reasonable
doubt, and are morally certain of the prisoner's guilt.

To return to the Probable Syllogism. It is one
in which one or other of the premisses is a general
probability, not a certain fact. The orator argues
for the most part from Probable Syllogisms, and the
Probable Syllogism is almost identical with the
Rhetorical Syllogism, which is drawn, as Aristotle
tells us, from probabilities and things which are an
indication of the conclusion (ef eUoT^v koI (rrjfieLcov),
We have already spoken under the head of
Enthymeme of the general coincidence of the
Rhetorical Syllogism and the Enthymeme, and of
the frequent coincidence of the Probable Syllogism
and the Enthymeme. The three in fact form a sort
of happy trio who are rarely separated, and, though
each has a separate pied-a-tcrre of his own, yet they
are usually found united into one.

The degree of probability of the conclusion is
exactly the same as that of the probable premiss.
But when both premisses are probable, it represents
the combined weakness of both. Thus in the
syllogism,

Most Hindoos are courteous.
This man is probably a Hindoo,
,\ This man is probably courteous,

the probability of his displaying the courtesy of the
Hindoo is comparatively small. If, for instance,
Hindoos are polite in three cases out of four, and
the chance of this man being a Hindoo is three
to two, nevertheless it is more unlikely than likely
that we shall find in him the politeness we desire.
Few dangers are more fatal to sound reasoning

430

MATTER OF THE SYLLOGISM.

CHAIN EVIDENCE.

431

than the assumption of probable premisses as certain.
A few probable premisses in the course of an argu-
ment may render the final conclusion very improbable
indeed. If in a long argument I take for granted
six times over a premiss that has two to one in its
favour, the weight of evidence against my final con-
clusion will be nearly ten to one.

Sometimes we have a number of premisses thus
depending on one another. In this case the con-
clusion represents the combined weakness of all of
them. For instance, a man is accused of murder.
There is very strong evidence that a man just like
the prisoner was in the company of the murdered
man on the night when the murder was committed.
It is also almost certain that the man who was known
to be in his company did the deed. There is, more-
over, a strong presumption against the theory urged
by the counsel for the defence, that the deceased
made an unprovoked attack on his companion on
the night in question and met his death from him
in self-defence. But it does not follow that the
accused should be convicted of murder. For if the
probability of each of the three circumstances point-
ing to guilt is three to one, the balance of pro-
bability is nevertheless rather against than in favour
of their being all of them true, and this means that
it is more likely that the accused was innocent than
that he was guilty.

This kind of argument is sometimes called Chain
evidence. It has two laws which govern it.

I. The chain is never stronger than its weakest
link, i.e., the conclusion is never stronger than

the weakest of the premisses. All the pro-
positions in the series save one may be
absolutely certain, but nevertheless the final
conclusion is not a whit stronger than the
one which has in it signs of weakness.
2. The conclusion represents the combined
weakness of all the premisses. Even though
each of the probable premisses may have a
moral probability approaching to certainty,
nevertheless, if they are many, the conclusion
may be very improbable indeed.
Chain evidence must be carefully distinguished
from circumstantial evidence, of which we gave two
instances above. In the latter, the conclusion
represents the combined strength, not the com-
bined weakness of the premisses. Each of them
strengthens the rest, and their combined strength
may be such as to justify moral certitude. They
may when taken separately have even a low degreee
of probability, but when united together may afford
an incontrovertible proof of the conclusion to which
they point.

FORMAL AND MATERIAL FALLACIES. 433^

CHAPTER IX.

ON FALLACIES.

Formal and Material Fallacies.— L Fallacies of Language— Equivo
cation — Amphibology — Fallacies of Metaphor — Composition
and Division — Fallacies of Scepticism — Fallacy of Accent.
IL Fallacies outside Language — Fallacy of Accident — Its
Frequency — Fallacy of Special Conditions — Evading the Ques-
tion— Instances of Evasion — Argumentiim ad hominem — Argu-
mentum ad populum — Argumentiim ad verecundiam — Fallacies of
Causation— Faulty Inference — Begging the Question — Arguing
in a Circle — Fallacy of Questions.

We are now approaching the end of our task. In
our last chapter we stepped a Httle outside of the
sphere of Formal Logic to speak of the matter of
the Syllogism, and we discussed Demonstrative and
Probable Syllogisms. We glanced at the various
kinds of Certitude, explained the strict meaning of
Opinion and Doubt, and Error. We then explained
the various kinds of Demonstration, and how we
can only arrive at scientific knowledge through the
medium of Demonstration.

We have to discuss in our present chapter some
of the more common sources of Error.

Whenever we neglect any of the Laws of Thought,
or of the principles which ought to be observed in our
reasoning processes, the defect is called a Fallacy.
The term is generally applied to such a flaw in

reasoning as is not at once patent to the ordmary
observer, but in some ingenious manner counter-
feits the appearance of truth, and for this reason is
liable to mislead the incautious.

A Fallacy then is any incorrect argument which
imitates in some way or other the appearance of

truth. . -

As we distinguish in every syllogism the form
and matter, so the incorrectness of a fallacy may be
either /onnaZ or material. When it is formal, that is,
when it is in the form or shape of the argument, the
syllogism is no syllogism at all, but a paralogism, or
a false or apparent syllogism. Thus if I argue :

All comets have a fiery tail,
No peacocks are comets,
.-. No peacocks have a fiery tail,

the premisses are true and the conclusion is true, but
the argument is an incorrect one in form, and the
conclusion does not follow from the premisses.

When the incorrectness of the argument is to be
found not in the form but in the matter of the syllo-
gism, the fallacy is a Sophism, and the syllogism called
a Sophistical Syllogism, If we take a purely mecha-
nical view of such a syllogism, examining it by the
rules given above, and using the terms merely as
counters, we shall find no flaw in it, whereas in the
paralogism the object will appear at once quite
independently of the meaning of the premisses or

force of the terms.

Material fallacies lie either in the words used or
form of expression, the same words or expressions

434

ON FALLACIES.

EQUIVOCATION.

435

being used in a different sense in the two premisses,
or in one of the premisses and conclusion respec-
tively, or in the things spoken of, points of differ-
ence being overlooked or points of agreement ignored.
Where the fallacy lies in the words, it is said to be
in the diction (in dictione) ; when it lies in the things
spoken of, it is said to be outside the diction (extra
dictionem).

I. Fallacies of Language. — Fallacies in die-
tione or in the language are divided into six classes :

I. Fallacies oi Equivocation, when the same word
is used in a different sense in different parts of the
argument, which, however, proceeds as if these
senses were the same, as,

He who is outside the Church of Christ cannot be

savedy
All who hold any heretical doctrine are outside the

Church of Christ,
.-. None who hold any heretical doctrine can be saved,

where I am using Church in the major premiss
for the sotd of the Church, which consists of all who
are united to Jesus Christ by faith and charity, and
in the minor premiss for the body of the Church,
i,e,, the external body consisting of those who are
united by one Faith under the Vicar of Jesus Christ
upon earth.
Again,

// is impossible to be in two places at the same
time,

There is a story of St. Philip that he was in two
blaccs at the same time,
.-. There is a story of St. Philip that he did wivat was

impossible.
This argument is well enough as far as it goes,
but if in the conclusion 1 use impossible in the sense of
what cannot possibly happen, and therefore disbe-
lieve the story, I am liable to the charge of eqtavo-
catimv, in that I have used the word >niposs.ble m
the major premiss for physically impossible wh ch
impossibility does not exclude a miracle, and in the
conclusion for absolute impossibility, which no

miracle can set aside.

We must give one or two more instances ot this

frequently occurring fallacy, e.g.,

hidifference is a high degree of virtue.
He who says all religions arc equally good exhibits
a complete indifference,
.-. He who says all religions arc equally good exhibits

a high degree of virtue,
where indifference of the will or that conformity
with the will of God which implies a total absence
of self is treated as identical with the indiffer-
ence of the intellect, or a suspension of judgment
where there is an obligation to come to a decision.
He who calls any man on earth Father sins against

Christ's command,
A child speaking to his parent calls him Father
,-. A child speaking to his parent sins against Christ s
command.

AMPHIBOLOGY.

437

436

ON FALLACIES.

Here the command of Christ, ** Call no man
Father upon earth," is treated as if it forbade
children to acknowledge their parents.

All able men are consistent with themselves^
He who changes his opinions is not consistent with
himself,
.*. He who changes his opinions is not an able man,

where consistent in the major premiss refers to
opinions held together and at the same time, while
in the minor premiss it refers to opinions held at

different times.

2. Amphibology , where the ambiguity lies not in a
word, but in the sentence, the grammatical construc-
tion being doubtful, or the expression used admitting
of different explanations.

If there is no possible difficulty which justifies absence
at Mass, the law enjoining attendance is cruel and
severe,
But to-day there is no possible difficidty which justifies
our absence from Mass,
.'. The law of the Church is cruel and severe,

where the words no possible difficulty, &c., are am-
biguous.

This instance is an obvious catch, but there are
dozens of cases occurring every day in which we
are taken in by the sophism of Amphibology-. When
the duty of Bible-reading is established on the words
of Our Lord, " Search the Scriptures," the well-
meaning argument is weakened by the fact that the
words in the original are Epewdre ra^ 'ypa<\>a<; —

.. Scrutamini Scripturas," and that the cont-t^ m
the opinion of many scholars, m favour of thxs bemg
the indicative mood. When the words of St. Jade
resoecting the Cities of the Plam that they were
Srrn%xample. suffering (the) pumshm^^^^^^^^^
eternal fire," are used as showmg that the wora
eter^a is u ed in the Bible for a mere Passmg con-
flagratn, they forget that the -eamng probably
ijthat they were n^ade^ an e^-P^^ o^ type)jf
eternal punishment m the penaiiy

" %Tio turn from sacred to profane. Shakespeare's

^°'^^ '' The Duke yet lives that Henry shall subdue,
are a good instance of constructional ambiguity H
a man'were to be branded as a parnc.de because ■
A ^f \^\rx^ ** This man his father kiuea, we
loddtve firTt' to^nquire whether the ambiguous
nhrase did not mean that he was slam by has
father The student of .Eschylus and Thucyd.des
S ,1 remember instances, not a few o amph.bolo^.
The oracles of old often resorted to it and the
modern fortune-teller finds it a convenient resource^
The atheist who justified his ^0^-^^- ^^ ^
attacks on God by quoting ^^e words that ^he fool
said in his heart that there is no God, as mean mg
Sal ;L philosopher proclaims it ^^1^^;^^^!-

''''fJ:f^^lZl^^TS^ faCwhich is the
re:s:;; tuVo^ the imperfections of human

language. , g^ j^^^ ^

438

ON FALLACIES.

There is no form of this more common than the
confusion between the literal and the metaphorical
meanings of language, between the straightforward
sense of the words and some derived meaning which
may be discerned behind them. It is very easy indeed
for any one who takes detached passages of a
speech or a letter to distort their meaning. When
Our Lord says to His Apostles, ** Salute no man by
the way,"^ such a command might by itself be
accused of extreme discourtesy, until we learn from
the word translated " salute " (ao-Trda-rjaOe) that what
was to be avoided was the making of acquaintances,
and that the whole phrase is a hebraism, and
indicates a rapid journey.* Many conventional
phrases are instances of amphibology. " Not at
home," for instance, as a softened form of refusal ;
or, " I do not know," as an equivalent for I have no
knowledge that I can communicate to you.

Metaphor is the natural resort of all who desire
to be obscure, or to veil their meaning from some
of those who listen to them. Our Lord's teaching
to the multitude was, as He Himself tells His
disciples, couched in the form of parables, because
they had a meaning for His friends which He
desired to hide from His enemies. The symbolic
teaching of the early Church concealed, under
figures which the heathen could not interpret, the
Divine Mysteries. Those who had the key to one
or the other, understood them in the sense in which
they were meant, but the stranger to the Faith
gave them a false meaning, or no meaning at all.

I St. Luke X. 5. 2 Cf. 4 Kings iv. 29.

COMPOSITION AND DIVISION.

439

ProDhecy good or bad. often veils its meaning.
The UuT'prophet knows what ^e means ; the false
J.U a^- - employing w.ds wh.h he^^c^n

"P^tV <"Ho:i%e so s^f B^^^^^^^ the lily shall
r;r S land^f fts captivity, and the |r- river
shall run down to the sea red with blood, may be
a true prediction, but it is suspiciously vague and
almost any great battle would furnish a respectable
e.planaUon of jt. ^^ ^^^^^^^,^^^^

J,^^ what ought ^o^^-^^lJ^

LiiSfit;:^^^^^^^^^^^^^^

from lome German -"-^f ^.-J^fX •
of a State lo- or lottery o wH.hte^^^^^^^ pn.e ^^

200,000 marks, or i 10,000. 1 1

£4^00, the third £2,000, and a number of others

ba^rifs^/s^n^^ES

J„, a -t ;nordin- ^^ ^-

many prizes one at least ot > ^^^^ ^^ ^^^

'° ttTcSSy. ? should find that the total

rSrSTaSls xoo,ooo,and the total n^^b^r

of prizes (even counting the lowest, which are only

r.1 is 200 and therefore my chance of a prize is

fust I oo^'to I against each of my shares, or 250.

To I iainst the four combined. In other words,

I invested £x every year of my life in the lo tery

he chance would be 5 to i against -y f J^^f ^

penny of my money back in the course of 50 jears .

440

ON FALLACIES.

The source of this delusion is the Fallacy of
Composition. I look at the money given in prizes
in its collective character as a lump sum, instead
of dividing it as I ought to do amongst the total of
shares. The big sum dazzles me, the crowd of
hungry investors is kept well out of my sight ; I do
not reckon up the enormous mass of those who
invest and invest again, and all to no purpose.
Perhaps, even after I have failed once and again,
I go on clinging to the fond hope that it cannot be
long before Fortune's wheel turns in my favour, and
bestows on me the dangerous boon of sudden
riches.

Every hasty induction involves the Fallacy of
composition.

4. The opposite Fallacy of Division consists in
taking separately what ought to be taken collectively.
A man is being tried for murder. There is a cumulus
of evidence against him quite sufficient to hang half
a dozen men. The principal witnesses are four in
number. One of them was present at the murder,
and swore to the identity of the accused. Another
had heard him vow vengeance. He was, moreover,
apprehended with the pistol still smoking from
which the fatal shot had been fired. Already more
than once he had attempted the life of the deceased.
Suppose one of the jurors were to urge that a
verdict of ** not guilty " should be returned, and
ivere to give as his reason that the testimony of
•each of the witnesses admitted of an explanation
compatible with the innocence of the accused, and
that he ought to have the benefit of the doubt.

FALLACIES OF SCEPTICISM.

441

The first might be mistaken in asserting the identity
of the accused; the second, who testified to his
threats, did not prove that they were carried out
for such vows are rarely kept ; while as to the
smoking pistol, he might have fired it off by accident,
or not known that it was loaded. The previous
unsuccessful attempts on the life of the deceased
would be rather an argument for his innocence,
because no one likes repeated failures. No one can
deny the possibility, at least the remote possibility
of each of these explanations being true, and each of
the facts alleged without corroborative evidence
would be quite consistent with the innocence of the
culprit Yet when taken collectively, they could
leave no possible doubt in the mind of any reason-
able man. He who takes them separately, one by
one, dividing instead of combining, is guilty of the
sophistical argument called the Fallacy of Division.
Or to take another practical instance. A certain
number of miracles are reported to have taken place
at a well-known sanctuary. Medical men of high
repute attest their reality; other unimpeachable
witnesses bear testimony to the suddenness of the
cure Those who bade the sick man farewell when
he left his home, thinking that it was impossible
that he should survive the journey, cannot believe
their own eyes when he returns in perfect health
The case stands the test of time, and no attenipt
is made to set aside or invalidate the printed
account which is submitted to the world for general
criticism. Now, what is the manner of proceeding
on the part of the sceptic when brought face to face

442

ON FALLACIES.

FALLACY OF ACCENT.

443

with a String of such miracles ? He argues as
follows : Of the seven miracles adduced, it seems
to me that the first (a case of paralysis) may be
explained by hysteria. It is not at all rare for an
hysterical patient to fancy himself paralyzed, and
anyhow the affection is one of the nerves, and any
sudden shock or powerful influence may recall the
nervous power that had been lost. In the second
case, in which a tumour suddenly disappeared, it
may be that the plunge into the cold water caused
an almost instantaneous contraction of the parts
affected. The third, in which cancer had been
cured, our sceptic explains by saying that there
may have been a false diagnosis on the part of the
medical man attending the patient. The fourth, in
which a needle that had been buried in the fleshy
part of the thumb, and had defied the attempts of
surgeons to reach it, suddenly appeared on the
surface, and was easily drawn out with the hand,
is explained as a curious coincidence. The needle,
which had been gradually working its way towards
the surface, had happened to show itself for the first
time on the occasion of the visit to the fountain.
In the fifth case our incredulous friend remarks that
the medical witness is a Catholic, and that probably
his faith obscured his scientific impartiality. The
sixth he pronounces to be possibly due to some
chemical influence in the water ; while the seventh,
which consists in the perfect restoration to sound-
ness of a gangrened sore, our philosopher, driven
to his last resource, allows indeed to be beyond
any power of nature known to medical science in

the present day, but he declares it to be probably
due « mysterious and hidden forces of nature
thichupto th'e present time ha^. been -needed
from our eyes, though we may hope that further
nvTst^gation may hereafter make them known to
us^and so he despatches to his sat.sfaction all the

'%";t the good man forgets that his argument
r>ui III-; b T7„iurv of Division. He

contains a very signal Fallacy o^ ^J

looks at these instances singly, and ^^^^^J"'^
down or thinks that he does so one after another
ne'er considering that those single sticks which he
Ja'cie he manages to break singly are -ally united
into a sturdy staff which is unbroken and un-

'" wf may put his fallacy into syllogistic form as
follows :

The first miracle cited admits of a possible cxplam-
£ also the second and the third, up to the seventh;

ButZAsec..d,third,&c.,areallthenuracles

,. All Tmiracles cited admit of a possible explanation'.
5. The Fallacy of accent or prosody is one of
which logicians remark that if any one is foo
rn^ugh to be taken in by it, it --/-^J
(quibls qui falli potest, debet). It consists '"jnis aking
one word for another which is pronounced like it
b" wrTtten differently, as of a herald ordered o
insert n the arms of some nouveau riche a «'/''«'«(^ J'
we to represent a tenant threatening h.s land! d
Or if a narrator were to declare that a battle was

444

ON FALLACIES.

FALLACIES OUTSIDE LANGUAGE.

445

fought in a district of France abounding in vine-
yards because it took place in a champaign country.
Or else it confuses together two words written in
the same way, but pronounced differently, as for
instance, if I were to understand an author who said
that some one traversed the character of the King
as meaning that he went over it in detail ; or if I
accused a man of practising unlawful arts because
he conjured his judges to have pity on him, and
so on in an indefinite number of instances, which,
however, for the most part, involve too obvious a
fallacy to have any serious power to deceive.

6. The Fallacy of figure of speech consists in
assigning to a word which has a certain gram-
matical form, characteristics which belong to it in
virtue, not of its form, but of its meaning. This
fallacy is one that is more liable to deceive those
who are not conversant with more than one or
two languages. Translation and re-translation, the
habit of speaking and thinking in different languages,
tends to obviate it. Still it is not altogether obsolete
in the present day, at all events among schoolboys.
The boy who argues that tribus must be masculine
because words of the fourth declension are mas-
culine, or that the a in dare must be long because
all words of the first conjugation have a before re
and ris, falls into this fallacy. So, too, does he who
says that all active verbs imply action, and therefore
there must be some activity on the part of him who
sleeps, since sleep is an active verb, else how could
we sleep a sleep ? A student of logic would fall
into this fallacy if he in one of the premisses

employed a word in its ordinary sense, and in the
other in what we call its second intention, as

Animal is a genus ;
This giraffe is an animal ;
.-. This giraffe is a genus.

II Fallacies outside LANGUAGE.-Fallacies
extra 'dictionem, or outside language, are those m
which the fallacy lies, not in the form of expression,
but in the idea of the objects about which we argue ;
when things which differ are regarded as the same,
; the same things as different. They like the
fallacies of diction, fall under seven several heads_

I. Fallacia acadentis, where we confuse together
the essential and the accidental charactens ics of the
object of our thoughts, whether it be a class or an

"' Thuf my acquaintance with swans has taught me
to regard them as always (except in the early stages
of their growth) as birds of snowy plumage. But one
dariseeabird in the Zoological Gardens jus like
1' ler friends except that is is of a swarthy black,
and my first impulse is to argue as follows :

All swans are white ;
This bird is not white ;
.-. This bird is not a swan.
If I commit myself to this syllogism I fall into
a notable instance of the Fallacia accidenUs. I have
put down the accidental whiteness of the swans I
hkve seen as their universal and essential character-

istic.

446

ON FALLACIES.

This Fallacy of accident is a very common one in
ordinary life. If I were to argue against a man in Cali-
fornia being identical with one whom I had formerly
known in Dublin, because my acquaintance was a
Protestant, whereas the dweller in California is a
good Catholic, I should fall into this fallacy. So
too, if I allow myself to attribute to all Freemasons
a hatred of the Catholic Church, or if I assert that
all men who have had a University training are
good scholars, or if I am so unfair as to be prejudiced
against a man because in his youth he was guilty of
some act of folly proceeding from generous impulse
or passion, and not from any serious fault. Of
this fallacy Nathanael was guilty when he asked :
*' Can any good thing come out of Nazareth ? "
The idea prevalent in England that all Americans
speak with a nasal twang, and say ** I guess," or ** I
reckon," in every sentence, and the corresponding
American impression of an Englishman that he
is burly, insolent, and rather wanting in intel-
ligence, are other instances among many. In fact,
almost every prejudice and misconception falls under
or may be reduced to this wide-embracing fallacy.

2. The second Fallacy of those extra dictionem
is called a dicto secundum quid ad dictum simpliciter ;
from a word used of some particular part of anything
or with some other qualification, to the same used
generally and without such qualification. The
common instance given : He has white teeth, therefore
he is a white man, is a very obvious instance, which
could deceive none. But if we were to apply to
a naturalist the epithet learned because he was

FALLACY OF SPECIAL CONDITIONS.

447

acquainted with the history, nature, appearance,
and habits of every butterfly and moth on the face
of the earth, we should run into this fallacy. We
argue from the fact that a man is learned secundum
quid (t..., in butterflies), to the further fact that he is
learned when we use the word in a general sense
for one possessed of all learning, or at any rate ot
all the learning we should expect in a learned natu-
ralist. Of this fallacy all are guilty who judge
that because a man is skilful in the material and
physical sciences, therefore his words ought to carry
weight when he lays down the law about things
immaterial and spiritual, and that the lay sermons
and addresses of one who has attained a just repu-
tation by his careful observation of the irrational
and mechanical creation, are worthy of being
listened to when he deals with metaphysics and
theology, and other subjects of which he is pro-
foundly ignorant. He who concludes that school
fights are to be encouraged because sometimes
a bully may be suppressed by a challenge from one
of his victims, would be justly condemned as a
sophist, or he who should argue that all servants
may help themselves to their master's goods because
such action is justified in one who is deprived of the
wages due to him, or he who should defend the
position that a son may disobey his parents when-
ever he thinks proper, because under certain special
circumstances disobedience is justifiable.

The opposite form of the fallacy, which argues
from something generally true and undeniable to
the same when some special condition is introduced,

448

ON FALLACIES.

is also a very frequent and often a very perni-
cious one. The teetotaller who refuses to give wine
to the sick, even when the doctor orders it, on the
ground that it is dangerous to take stimulants — or
the parent who will not correct his pilfering child
on the plea that it is cruel to beat children, or
the theologian who condemns Abraham's intention
to sacrifice Isaac, on the ground that murder is
always unjustifiable — are all guilty of arguing a
dido simplicitcr ad diciwn secundum quid. The whole
class of narrow-minded people who get some idea or
principle into their heads and apply it, irrespective
of circumstances, are all sophists, though they
know it not.

3. Not less universal is the kind of Fallacy
which goes by the name of Ignoratio Elenchiy or
setting aside the question to be proved for some
other like it, but nevertheless different from it. It
may be translated by evading the question, or more
literally, ignoring the disproof, since elenchus
(eX,€7;^09) is an argument which is used to confute
or disprove the arguments of an opponent. He
therefore who, instead of disproving his opponent's
statement, disproves something which merely
resembles it, ignores the real point at issue, and
does not refute his opponent in reality, though he
may seem to do so. The skilful barrister will often
seek to draw off the attention of the jury from the
real point at issue, viz., the guilt or innocence of the
prisoner, by a pathetic description of the havoc that
will be wrought in his home if he is convicted, or by
seeking to create an unfair prejudice against prose-

IN STANCES OF EVASION.

449-

cutor or witnesses. The host who seeks to enhance
his guests' appreciation of his wine by letting him
know what it cost him, really ignores the point at
issue, which is, not whether the wine is expensive but
whether it is good. His argument is vahd only so
far as price and excellence go hand in hand. The
Protestant who seeks to discredit the Catholic
religion by adducing the immoral life of some
meLval priest or bishop, or even Pope equally
argues beside the point, which is, whether the
Catholic religion is true, not whether there are
not men whose unholy lives disgrace the holy

religion they profess.

St. Thomas remarks in the Opusculum on the
Fallacies,' which bears his name, that every fallacy
may be reduced to this as to a general principle,
and gives as his reason that in every fallacy there
is a deficiency of one of the elements necessary ta
elenchus or disproof of the opposite. In every
fallacy either the reasoning itself is bad or if it
is good, it fails to meet the arguments of the
opponent. Whichever is the case, there is a failure
in what is necessary to disproof, there is an evading
of the question, there is an ignoring of the point

^* 'sTfar as this fallacy has a special character of its
own, it consists in the veiled attempt to set aside the
assertions of an opponent by a counter-sta ement
which does not really contradict it It is a fdkcy.
moreover, which has this peculiarity, that it some

Opusc. 35- (Ed. Rom. 79)-

450

ON FALLACIES.

times serves the purposes of truth, by affording one
who is stronger in the truth of his position than in
the argument by which he can support it, an oppor-
tunity to turn the laugh against a sceptical opponent
by some telling retort or personal accusation. A
man accuses me of superstition because I believe in
modern miracles, and instead of attempting to argue
in favour of my convictions I turn round to him and
say : " You talk of superstition ! Why you refused
only yesterday to sit down to table because there
were thirteen in company ! " This may turn the
laugh against him, but it is no real argument, it is at
most a refusal to discuss the question with him.
A story is told of O'Connell that on one occasion
when he had to defend a man who was clearly in the
wrong, the counsel for the prosecution was a certain
Mr. Keefe, who had come in for some money in
rather a questionable way, and had taken the name
of O' Keefe. O'Connell commenced his defence by
addressing his opponent :

Mr. Keefe O' Keefe

I see by your brief o'brief

That you are a thief o'thief,

which so disconcerted Mr. O'Keefe and so tickled
the jury that a verdict was returned for the defen-
dant.

These two last examples come under the first of
three subdivisions of this fallacy which are so
common in every-day life that we cannot pass them
unnoticed.

(i) Argumentum ad hominem, or appeal to the

ARGUMESTUM AD HOMINEM.

451

individual ; when we do not defend our position m
itself, but merely show that our opponent is not the
Ln to attack it. This is a perfectly legitimate
argument on many occasions. If a man of noto-
riously immoral life puts himself forward as the
champion of morality, or if a man is zealous in some
cause which brings him in a large income, or
strongly denounces a measure which, though good
L itself, will act to his personal disadvantage, we
have a right to urge the suspicious -rc^-^tan^^
against his right to speak on the subject. When
Dr. Newman answered the calumnies of the apostate
AchiUi against the Church by enumerating a few of
his crimes, he was doing a service to truth as wel
as to religion. If a home manufacturer argues
warmly for protective duties, it is quite fair to
answer him by reminding him that he is an in er-
ested party. If a publican opposes Local Opt on.
we are justified in replying that his arguments lose
their weight from the fact of his fearing for h.s

1 ipense

But if we seek to divert the minds of our hearers
from the force of a solid argument by an irrelevant
attack on the character of the man using it, we
incur the charge of offending at once against Logic
and against common fairness. If a preacher de-
nounces self-love, and shows how it is opposed to
the spirit of Christianity, it is no answer to him
to remind him that he often manifests this defect
n his own conduct. All that it justifies the listener
in answering to him, is that the denunciation of
self-love loses a great deal of its force m coming

452

ON FALLACIES.

ARGUMENTUM AD VERECUNDIAM.

453

from the lips of one who is chargeable with it, but
it does not justify the rejection of the arguments
he employs. ** Physician, heal thyself," is a telling
response to one who is unable to cure in himself
the disease he professes to heal in others. But if
the remedies he proposes are in themselves effica-
cious, and fail in his case only because he will not
fulfil the necessary conditions under which alone
they will act, then we have no right to reject his
remedies on account of his unwillingness to avail
himself of them.

(2) Argumenttim ad populum, or appeal to the
people, when an orator or demagogue, instead of
employing solid argument, appeals to the passions
or prejudices of the mob. " Are you, freeborn
citizens, going to allow your liberties to be
trampled upon by the minions of the oppressor?
Are you going to permit those who have robbed
you of the land that is your own, to go on to
rob you of the very bread that is to feed your
poor hungry children ? Are you going to put
up with the selfish exactions of the rich, who, not
content with all their own unjustly-gotten gains,
want to rob you of the little that still remains to
you ? " All this is ignoring the point at issue, and
an appeal to the unenlightened ignorance and pre-
judices of the people. The No-Popery cry of 185 1
was an argumentum ad populum, and so is the talk
about Englishmen not submitting to the yoke of a
foreign despot, and other similar fallacies of pious
orators who denounce the Pope.

(3) Argicmentum ad verectindiam, an appeal to a

man's sense of shame or natural modesty m esti-
mating his own powers. A man ventures to differ
from the Theory of Evolution, and he is accused of
impertinence and presumption in setting up his
own opinion against that of a man of genius like
Darwin, who had devoted his life to the study of
it In the Convocation of Oxford it was once
proposed to set aside the recommendation of a
committee of the Hebdomadal Council on some
University question. One of the -e-Jers of the
committee indignantly protested against the rejec-
tio" of a measure to which he and other learned
seniors had devoted a considerable portion of time
and seemed to think this a decisive argument for
accepting it. A man intends to become a Catholic
Before doing so, he has an interview with a Protes
tant clergyman. " In your presumptuous ignorance,
you are "proposing to forsake the Church of your
Baptism vou find fault with the teaching that
fatS the saintly Keble and the learned Pusey,
anrthousands of holy men besides. Who are >^u
that in your pride you should think you know better

'^VheC'der will have no difficulty in thinking out
for himself plenty of similar arguments that we meet
^ith almost every day. It is not alw^y^ ^ J^/;^
distinguish between a legitimate use of these three
forms of ignoraiio elenchi and an erroneous one As
a rde, it is better to avoid them, unless we feel very
sure that we are treading on the sohd ground of

4." The .Argument a non causa pro causa is under

454

ON FALLACIES.

FAULTY INFERENCE.

455

its various forms one of the most universal of the
fallacies. How common to assign effects to an
imaginary cause ! Every rash judgment is an
instance of it. Heli judging the emotion of the
mother of Samuel to be due to too much wine,
argued a non causa pro causa. All superstition is fond
of employing it. I walk under a ladder and lose
the train just afterwards. Foolishly I attribute my
misfortune, not to my unpunctuality, but to the
ill-luck resulting from going under a ladder. A
ship sails on a Friday and is shipwrecked, and
one of the passengers blames his folly in starting
on an unlucky day. An habitual drunkard accounts
for his shattered nerves to the fact that he studied
hard for the army in his youth. A preacher obtains
a great success, and attributes the number of con-
versions to the eloquence wherewith he has preached
the word of God, whereas all the while what obtained
from God the grace that moved the hearts of men
was the prayers and sufferings of some good old
dame saying her beads in a corner of the church.
As it is one of the marks of genius to discern the
underlying causes of events,

Felix qui potuit rerum cognoscere causas,

so it is one of the marks of a weak and narrow
intellect to seize without reflection on some imaginary
cause and cling to it even though the evidence is all
the other way.

Under this fallacy come others resembling it.
A non vera pro vera, where we assume as true some-

thing which we think admirably suited to explain a
faS though it is a pure fiction of our own. Many
an Lnchadtable word hinted rather than spoken is

a fallacy of a non --^- -"' -^^d wt did
against the moral law. Some one is asked, Why did
A dve up his partnership in the firm of A B, C. and
Co and'by some significant gesture implies though
he does nol actually assert, that A's money transac-
tions were not creditable. Such a reply is a fallacy,
as well as a sin against justice. All false suspicion
and unkind judgments come under this fallacy, as
wdl as posit'ive'mistakes owing to inadvertence or

'° TZ^^ipro iali is but a variation of the a non
.era pro vera. It arises from a mistaken >dea respect
ine the nature of some person or thing. We argue
hat the book we have just published is sure to suc-
ceed because of the ability with which it ,s written
The old-fashioned thorough-going P-testant ha e
the Catholic Church simply because he imagines it
to be utterly different from (nay, the very opposite of)

what it really is. . ,

I The Fallacy of cmm'^"^^ ^^^'^ ^" }^^°'
thetical syllogisms, where the antecedent and con-
equ-t are c'onfused together, and we over oo^ e
difference between the condition and that which
;iws from it. For instance, I have learned by
experience the truth of the proposition : If I drink
oo' much champagne I shall have a headache w^en
I wake One morning I wake with a headache, if 1
n7er hat the headache from which I am suffering
results from my indulgence in "Veuve Chquot

456

ON FALLACIES.

or Perrier and Jouet's best over night, I am guilty
of this fallacy ; my inference may be true, but it
is not justified by my premiss. I have inverted
the consequent and the antecedent, and argued
as if consequent were antecedent and antecedent
•consequent.

This fallacy is one we very frequently encounter.
^' If the wind changes, it will rain," may be a
true proposition, but from the descending showers
we cannot argue that the wind has changed. "If
you do not take my advice you will not succeed
in your enterprise," is a warning often uttered
by those who love to give advice to others.
The failure comes, and the adviser at once lays
it down to the neglect of his wise counsel, even
though a thousand other causes may have produced
it. ** I told you so," is the irritating and fallacious
remark with which he meets his poor disappointed
friend, forgetting that the failure, though following
•on the neglect of his advice, is not necessarily a
•consequence of it.

This fallacy is in many cases only a veiled
form of the formal fallacy of faulty inference. The
difference, however, lies in this, that here the error
results, not from the fact of the inference being
unjustifiable, but from the confusion existing in the
mind of the reasoner between antecedent or conse-
quent in the major premiss. He simply identifies
the two propositions which are united together,
instead of regarding the consequent merely as
dependent on the antecedent.

6. The fallacy of Petitio ^rijtcipii, or Begging the

BEGGING THE QUESTION.

457

Question, consists in assuming our conclusion m
some way or other in our premisses. Petitio prin-
cipii, is a not very exact translation of the name given
to this fallacy by Aristotle {to ef apxh^ alrelcrOaL), or
the assumption of the question originally proposed
for proof; but practically the meaning of the two
phrases is identical.

We beg the question whenever we veil the pro-
position we profess to prove, under other words
which are more likely to be acceptable to our mter-
locutor, or which throw dust in his eyes by reason
of his not being able to understand them. If I
account for morphia producing sleep by saying that
it is endowed with a certain soporific virtue, or for
headache caused by too much wine by saying that
the patient is suffering from alcoholic cephalalgia,
or for his having been suffocated, by saying there
has been an interruption of the respiratory move-
ments, culminating in acute asphyxia and apnoea I
am not really proving anything, but only saymg the
same thing in different words. This is, however,
rather a repetition of the same proposition than
an argument properly so-called.

But where the propositions are not really identical,
but dependent one on the other, we have a more
real and true Petitio Principii. If, for instance, 1
first assume the Infallibility of the Church, and from
its infallible definitions prove the inspiration of the
Bible, and afterwards, when asked how I know the
Church to be infallible, argue that it is so from the
Bible as the inspired word of God, and therefore
decisive of the question, I am obviously guilty of

458

ON FALLACIES.

this fallacy.^ If I attempt to prove the truth of my
religious tenets from the fact that I find them very
comforting to my soul, and at the latter stage of
the argument account for their comforting properties
from the fact of their being a part of the revelation
of Almighty God, I am clearly arguing in a circle,
and begging the question at issue.

The skilful sophist will ingeniously slip his
conclusion unawares into one of his premisses in
which he thinks it will not be detected. For instance,
I am arguing in favour of protective duties on corn
in an over-crowded country. I point out the hard-
ships to the farmer that result from foreign com-
petition and the injury that is done to the agricultural
labourer. I bring forward instances of trades that
have flourished when they were protected, and have
declined and disappeared when cheaper goods could
be imported from elsewhere. I urge that the advan-
tage resulting to the foreign grower should not be
weighed against the misery caused at home, and I
appeal eloquently to the patriotism of my audience
not to declare themselves in favour of free trade
when it is so injurious to the country where it
prevails. But in this appeal I am assuming the
very point to be proved, which is that a tax on corn
is beneficial to the inhabitants of the country im-

* It is scarcely necessary to inform the reader that nothing but
gross ignorance can excuse those who accuse Catholics of this sort
of fallacy. The real process of the argument respecting inspiration
is this. We first prove by reason from the Bible received as an
ordinary historical record, that our Lord pronounced words which
confer Infallibility on the Church. The inspiration of Scripture is
subsequently proved from the decrees of the Infallible Church.

FALLACY OF QUESTIONS.

459

posing it ; under the veil of my patriotism I most
unjustifiably beg the whole question.

Or I am advocating compulsor>- secular educa-
tion. I draw a picture of the debasing effects of
ignorance, of the increased intelligence and moral
superiority of those who have been trained m letters
over those left in ignorance ; and I protest against
the narrow bigotry that allows benefit done to the
poor children to be frustrated by religious prejudice.
In doing this I am assuming the very point to be
proved, that compulsory education without God is
more beneficial than voluntary education joined to

a love and fear of Him. ,, . . n j

7. The last on our list of Fallacies is called
Fallacia Plurium Interrogation urn, where several ques-
tions are asked as if they were one or could al be
answered together, or when one questionis asked
which involves a previous assumption which may or
may not be true. I demand, for instance, a Cate-
gorical answer Yes or No to the question : Were
not St. Paul, Socrates, Savonarola, Martin Luther,
noble and devoted men ? or I ask a man when he
left off drinking to excess? The child who was
asked whether it loved its father or mother best
judiciously recognized the latent fallacy when it
answered: I love both best. This fallacy often
takes the form of demanding the reason for some-
thing that is not really the case. ^^ How can Jesuits
defend their maxim that you may do evil that good
may come of it?" is a question which assumes
as granted what is simply false. This fallacy of
Questions is a common resource of all who attack

46o

OS FALLACIES.

the cause of Truth. How do you account for the
contradiction between the infalhble utterances of
earlier and later Popes? is one of those insidious
questions which contains a lie impossible to refute
by reason of its dishonest vagueness. How is it
that the Church is always in the wrong in her con-
tests with men of science ? How is it that she
suppresses the spirit of research and honest inquiry ?
Such foolish assumptions of what is false as true
are of every-day occurrence ; in fact the prejudice
existing among Protestants is in great measure due
to the dark hints thrown out by those who seek to
discredit Catholicity, and do not venture to do so
by open statement.

Before we quit the subject of Fallacies, we
must remind the reader that it is impossible to
draw a hard and fast line between their various
divisions. Various attempts have been made to
classify them in modern times. We have preferred
to follow in the steps of Aristotle and St. Thomas,
rather than to adopt the improvements, or the
fancied improvements, that have been introduced
with liberal hand by all who have set themselves
to the task of recasting the Logic of their more
distinguished predecessors.

CHAPTER X.

ON METHOD AND ITS LAWS.
Tf DttTnctions-Method and the end to be attained by it.

WE have now considered reasoning as an advance
from certain given premisses to a -"f ;-"' ^"*^
have examined the form or shape mto which it must
be thrown, in order to ensure correctness in he
process. We have also touched briefly on the
character of the premisses from which we start
and have said that they are the maiUr of our
arguments, the material on which we have to work
by means of the reasoning process. But matter
and form may both be excellent : our premisses
corre t and the conclusion rightly deduced from
them, without our being able thereby to do very
Ich towards the attainment of T-th, unless we
can make sure of choosing the right method to be
pursued. A man might have an excellent pair of
horses and drive them in the most approved form
bu he would not do much towards the attainment
orthe end of his journey, if he chose a road over

462

ON METHOD AND ITS LAWS.

METHOD OF VARIOUS SCIENCES.

463

the blue waters of ocean, or even over the soft sands
of the desert. His method of proceeding would be
faulty, and this would stop his advance.
I Method is therefore a very important consider-
ation, and we mean by Method, a system of right
procedure for the attainment of Truth,

Method in general may be divided into synthetic
and analytic. Synthetic Method is that which starts
from the simple and proceeds to the compound,
starts from the universal and proceeds to the parti-
cular. It is the method of composition {avvOeai^),
inasmuch as it puts together {crwOelvai, componcre)
the simple elements which form the complex or
composite whole. Thus Geometry is synthetic inas-
much as it begins from axioms, postulates, and defi-
nitions, and from them builds up the most intricate
and complex problems and theorems. The method
of Logic is synthetic inasmuch as it starts from
ideas or concepts, unites ideas together in a judg-
ment, or judgments into a syllogism. Ethics is
synthetic in method, inasmuch as it starts from the
simple data of the moral law, and advances from
them to frame more elaborate rules of conduct and
laws of human action.

Analytic Method, on the other hand, starts from
the complex and thence proceeds to the simple,
from the particular and proceeds to the universal.
It is the mode of analysis or resolution (avaXvaLf;)^
inasmuch as it resolves {avaXveiVy resolvere) the com-
posite whole into its component elements. When
a theorem is proposed to the geometrician for
solution, and he separates off the various portions

of the figure, assigning to each its own laws, and
thus arriving at a proof of the proposition laid
before him, he pursues a method of analysis When
the logician argues from the individuals to the whole
of the class composed of them, he is proceeding
from a greater to a less complexity, and is pursu-
ing the analytic method. When a theologian has
placed before him some difficult case of conscience,
and discerns the principles which are to be his guide
in arriving at a solution of it, his method ,s clear y
one of analysis. All sciences are partly analyic
and partly synthetic in their method. The analy-
tical chemist pursues the method of analysis when
he has submitted to him the stagnant water or
adulterated food, and gives in detail the various
ingredients of which it is composed. On the other
hand he pursues the synthetic method when the
prescription is made up for the sick man, or some
delicate perfume composed of elements perhaps not
very attractive in detail.

But there are some sciences which are primari y
synthetic in their method, and use analysis only
as subsidiary to their primary and natural system
of proceeding. Others, again, are primarily analytic
Jd for them synthesis is subsidiary. The method
of Logic, Geometry, Ethics, is primarily synthe c,
that of Chemistry or Botany, primarily analytic.
How are we to account for this difference ?

We have here to fall back on a distinction we

have more than once laid stress upon in the course

,of our investigation. Some sciences are a pr^

lor dednclivc sciences, inasmuch as they start from

464

ON METHOD AND ITS LAWS.

LAWS OF METHOD.

465

principles which are based on the inner nature
of things and on the laws of reason. These prin-
ciples are discernible underlying the concrete case
as soon as it is presented to us. Such sciences are
Logic, Ethics, Algebra, Politics, Geometry.

Other sciences are a posteriori or inductive sciences,
inasmuch as they start from principles which are
learned from observation and experiment and from
a study of the external world, and are based, not on
the inner nature of things or on the laws of reason,
but on the laws of external nature. These laws can-
not be at once discerned, but can only be arrived at
gradually and by questioning nature and searching
into the material universe around us. Such sciences
are Acoustics, Optics, Hydrostatics, Mechanics,
Chemistry, Botany, &c.

Other sciences, again, are mixedy in that they
depend partly on a priori principles, partly on a
posteriori laws. In these it is necessary to employ in
due proportions the data of some a priori science,
and the laws that are learned by experiment and
observation. Such a science is Astronomy, which
is based partly on geometrical principles, partly on
physical laws. Such a science again is Political
Economy, which depends partly on the moral law,
partly on the physical conditions of individual
countries. Each science is primarily synthetic or
analytic in method according as it is chiefly de-
ductive or inductive in its character, according as
its laws are for the most part a priori or a
posteriori laws.

But as we shall see, the Laws of Method admit of

certain variations according to the end which is pro-
posed to be attained. The rule we have laid down
has reference to the Method which belongs to this or
that science, apart from the special end in view.

ON THE LAWS OF METHOD.

Method is governed by certain fixed laws which
furnish us with the principles on which we are to-
act in selecting our mode of procedure, and alsa
by certain practical rules which must be carefully
observed if we hope for success in our investigations.
I. We must always begin from that which is near
at hand, and thence make our way to that which is-
remote, from that with which we are familiar, and
thence proceed to that with which we are unfamiliar,
from that which is more easy, and thence attain to-
that which is more difficult. What is more at hand
and familiar will not be the same to one who is
arguing synthetically and to another who is pursumg
the analytic method ; nay, what is most familiar ta
one will be most unfamiliar to the other. The
former starts from axioms and first principles ; these
are his stock in trade, and the first step in his
apprenticeship is to make himself completely familiar
with them. The latter starts from concrete facts
and individual instances ; it is with these that he is
furnished, and from these he has to mount up to the
universal. By this we are able at once to discern a
Deductive from an Inductive Science, and the pro-
gress from the Inductive to the Deductive stage is
marked by an ever-increasing possession of the
principles which determine the character of indi-

466

ON METHOD AND ITS LAWS.

vidual things, and by the diminution of the necessity
of watching effects and judging from results, and
from them ascending to axioms, principles, maxims,

laws.

This law seems to be too obvious to be worth
stating, but it is one that in practice is often sadly
neglected. The student who, with a foolish ambition,
aims at that which is beyond his reach ; the teacher
who thrusts into his unhappy pupils laws and
principles without any attempt to render them in-
telligible by concrete instances; the metaphysician
who assumes as innate, principles to which we can
only rise from the data of sense interpreted by
reason, all transgress this primary and simple law.

Here we must recall the distinction we drew
between things in themselves more simple and better
known, and things more simple to us, better known
to us. To the child the proposition that two and
two make four is simpler than the primary Law of
Identity on which it is based ; to ordinary men the
coming change of weather is better known from a
gathering together of a hundred familiar signs, than
from the application of a few elementary laws. The
simplicity which we require in method must be the
simplicity which is relative to the individual. What
avails it to us that an idea or a proposition should
be more simple in itself, if it is not more simple

io us ?

I 2. All method to be sound must be gradual. The
great rule for attaining true knowledge is pedctentim
procedere. Slow and sure must be our motto. It is
true that genius will sometimes by a brilliant guess

CERTITUDE OF VARIOUS KINDS.

467

or an instinctive appreciation of truth overleap the
steps that are necessary to ordinary men. But even
a man of genius will, if he is wise, test and try, it
may be for long years, his wide hypothesis, before he
ventures to stamp it with the honoured name of law.
Besides, legislation is for ordinary mortals, not for
men of genius, and for them to hurry to a conclusion
is an unfailing course of error.

3. The same certainty cannot be attained in all
the sciences. This is Aristotle's sage remark at the
beginning of the Ethics. We must expect only that
degree of certitude which our subject-matter admits
of. You might as well, he says, expect persuasive
oratory from a mathematician as demonstration from
an orator. He might have added that you might
as well expect a mathematician to illustrate meta-
physics by a series of tableaux vivants, as expect a
teacher of physical science, or one who pursues its
method of argument, to attain to the certitude of the
metaphysician. We need not repeat here what we
have already said under the head of certitude, and
in speaking of the inductive methods. It is enough
to quote a few words from St. Thomas.^ Speaking
of two contrary rules which lead men to be sceptical
and to doubt, ^* There are some," he says, "who
will not receive anything that is told them unless
it is mathematically proved. This is common
with those who have had a mathematical training,
because custom is second nature. Others there are
who will not receive anything unless there is put
before them some instance of it that their senses

1 Lect. 5, in Metaph, 2.

468

ON METHOD AND ITS LAWS.

A NECESSARY CAUTION.

469

can perceive. This results either from habit, or
from the predominance in them of the influence
of their senses, and a want of intellectual power.
Others, however, there are who desire that every-
thing stated to them should be based on certitude,
that it should be founded on a diligent and rational
inquiry. This is the result of the exercise of a sound
understanding in judging and reason in inquiry,
supposing always that it is not sought in matters
where it cannot exist."

This golden advice has a practical value for every
intellect that inquires. The fatal habit of accepting
unproved conclusions and treating them as if they
were mathematically established, is a vice no less
common than that of an obstinate refusal to accept
unpalatable results for which there exists evidence
enough and to spare. To start some magnificent
hypothesis is always a strong temptation to men of
intellectual ambition, and to receive on authority
general principles the proof of which they cannot
follow step by step, is a serious, and too often fatal
trial to their intellectual humility.

We must add to these laws a number of practical
rules applicable to all scientific investigation, whether
it proceed from universals to particulars, or from
particulars to universals.
I (i) Never employ any term unless it be under-
l stood. There is no need to repeat what we have
already said in speaking of definition. Indistinct-
ness of perception, vague and ill-defined ideas, an
inaccurate confusion of things really different, an

assignment of imaginary differences to thmgs really
the same, all go hand in hand with the neglect of
a careful definition of terms used. Most of the
common objections to the worship of our Lady, to
the doctrines of the Immaculate Conception, of
Transubstantiation, and of Indulgences ; to the
Infallibihty of the Roman Pontiff, to the system
of Casuistry, to the doctrine of Intention, &c., are
due to either inexact or erroneous notions respect-
ing the meaning of the terms employed. •

(2) Distinguish clearly between the essential
and accidental elements in the matter discussed.
The law of Association, which is liable to a very
perilous abuse, and unless carefully watched is a
constant source of error, exhibits to us in union
with one another, things the union of which is but
accidental. The invariable antecedent is mistaken
for the cause; the phenomenon which, as far as our
own observation goes, has never been separated from
some other phenomenon, is regarded as inseparably
united with it. An Englishman resident in some
city of South America sees united in the inhabitants
a profession of the Catholic religion, a great laxity
of morals, and an absence of all energy, fortitude or
perseverance. Neglecting our rule, he comes to the
conclusion that there is a necessary connection
between Catholicism and the vices around him. Or
to take a very different example, a man given to field
sports observes that a day's shooting is invariably
followed by a headache on the following morning.
When experience has taught him that the ts^^ in-
variably go together, he begins to connect the

470

ON METHOD AND ITS LAWS.

IMPORTANCE OF DISTINCTIONS.

471

exercise taken on the previous day with the head-
ache from which he is suffering, but fails to observe
that the day's shooting induces an exhaustion at
dinner-time, which he seeks to remedy by several
extra glasses of bottled stout or port wine. He
mistakes the accidental for the essential, the ante-
cedent for the cause, till one day, when he observes
his usual moderation, he finds to his surprise that
he may walk all day over a heavy country under a
burning sun, without any inconvenience following
thereupon, as long as he keeps to his pint of stout
and two glasses of wine. Or again, we may have
observed in the newspapers that a larger number of
persons lose their lives by drowning on a Sunday
than on any other day. On this fact the Scotch
Presbyterian makes the remark that it can only be
explained by the anger of God with all who take
their pleasure on His holy day ; quite overlooking
the circumstance that it is on Sunday that a great
number of excursionists of the middle and lower
classes, who are unskilled in the use of boats and
rarely can swim, take their pleasure on the water.

1(3) We must very carefully separate off the
various parts of the question to be discussed one
from the other, and follow them up in detail until
we have mastered the several parts of which the
whole is composed. It is only by this means that
we are able to separate the accidental from the
essential, and thus to clear our ground. If, for
instance, a man who was investigating the truth
of Christianity were considering the cause of the
vice in some South American State, he would

take in detail the evils that exist, and the circum-
stanc s that seem to foster them. He would examme
he condition of neighbouring -""t"- -'?'^%" ;
cumstances very much resemble those o the State
unde discussion in everything save rehgion and
havfng thus isolated one element in the question
toTd' see what was the result ^^o^l^^l^yj^^
absence. He would, moreover, examme the mora
and soc al condition of countries diffenng m most
:tcts from the South AmeHca^^^^^^^^^^^ w h
which we are concerned, but resemoimg
wnicnwe rhrUtianitv But here, as our

Srer;°:ill hav??br;ei we are recurring to
he Methods of Agreement and Difference not.ced
above, and for the clear exposition of which ve are
tndeUed to the labours of Mr. John Stuart ilL

(4) Lastly, we must remember that >t makes
a great difference whether we are making investi-
LSn for ourselves with a view to the attainment
5 scientific knowledge, or seeking to communicate
toothers knowledge already in our P^^^^^f «"• J^^
I the former case. Analysis is the natural method
to be pursued, inasmuch as we have before u
complex' knowledge, and results which ar^ the
combined results of a number of ^^^^^^ , ^^J ^
' have broken up our phenomena and formed an
hypothesis as to its component parts, we shall have
S 'test this hypothesis by the opposUe process o

Synthesis. We shall have to ^^^/^^f f ^ ^^^^ "T"
which are supposed to have produced it have really
I^e so, and with this object we combine them
tgether to see what the result will be. An analytical

^'1

■.'■S'-l. 'Hi Elll'iil*

472

ON METHOD AND ITS LAWS.

chemist has some water sent him from a mineral
spring which works such cures that it is generally
esteemed to be miraculous. He has been asked
whether, so far as he can tell, its health-giving effects
can be due to the effect of the combination of certain
minerals which are held in solution in it. He
accordingly begins by applying certain tests by
which he can ascertain the nature and quantity of
the various ingredients it contains. After he has
satisfied himself on this point, he has recourse to
the experience of himself and others with regard to
the results produced on the system by these various
minerals when administered together in the propor-
tions in which they exist in the spring, and from
those two processes, first analysis and then synthesis,
he draws his conclusion respecting the question
asked of him.

But suppose this same chemist has to lecture
on the subject to an intelligent audience : to explain
to them why it is possible or impossible (as the case
may be) that the spring could produce naturally the
effects ascribed to it. Here he reverses the process.
He appears on the platform with a series of phials
containing the different mineral salts which he has
discovered in the spring. He explains to his audience
the results of each on the human body, and the
probable effect of the whole. He begins with
synthesis, in that he combines together the simple
elements in his lecture, and exhibits in his descrip-
tion the complex result they would produce together.
He then goes on to analyze the various cures, to
explain in their separate details the changes wrought

METHOD ASD THE END TO BE ATTAINED BY IT. 473

by the wonder-working water, and to e^^P'^ss his
scientific opinion as to the possibility of th's or that
effect having been produced by this or that ing e^
dient, working either by itself or in umon with
some other ingredient which furthers its effect

In each of these opposite processes, the rule
given above of commencing with what is more
familiar, and thence proceeding to what is more
remote and unfamiliar, is observed by th« ch-^ist^
In his investigation he commences with hat which
is more familiar to ordinary mortals (nobis notwra)
the water of the spring where thousands have drunk
or bathed, and thence proceeds to the various
chemical agents it contains which are to us a
mystery, though in themselves they may be so
Zple as to admit of no further analysis. n
imparting to others the results of his experiments.
h7beg.n's from what is simpler in itself and there^
fore more famiUar to nature (natum noHora), and
thence proceeds to the complex results with wh^ch
ordinary men are familiar, however complex they

may in themselves be. , • * ^

I This distinction between discovery and instruc-
tion holds good alike in deductive and inductive
IsSnces. The skilled mathematician has submitted
to him the equation to some curve His first step
is invariably in the direction of analysis. He gives
various values to . and y in the equation finds out
the separate value of each when the other disappears,
or when it has this or that positive or negative value,
breaks up the equation, if possible, into >ts facto s
seeks by every means in his power to reduce its

474

ON METHOD AND ITS LAWS.

complexity to simplicity. Having thus discovered
the nature of his curve, he draws it in detail, putting
together by synthesis the results of his analysis, and
thus constructing the geometrical curve, the equation
of which constituted his original data. But if it is
a question of imparting knowledge to a learner, of
teaching the formula which expresses, in mathe-
matical language, hyperbola, or parabola, or cusp,
the whole process is reversed. First of all there is
given, in the form of a definition, the simplest notion
of the curve or figure in question. This definition,
in combination with other algebraic and geometric
principles already acquired, enables the learner to
perform, under the guidance of his teacher, an
elaborate process of synthesis which proceeds step
by step from the more simple to the more complex,
until at length he arrives at the equation of the
curve in question. This done, he tests his know-
ledge by a subsequent analysis. He gives to the
various symbols different values, and so verifies his
synthesis, thus ending with a process exactly corre-
sponding to that by which the skilled mathematician
commenced.

APPENDIX.

ON THE SCHOLASTIC METHOD.

IT is a common charge against Scholastic Philo.
sophy that instead of pursuing the safe method of
interrogating nature, it assumed certam prmciples
unproved, and employed them as a means of solvmg
all the various questions that presented themselves.
The modern Experimental School, who date from
Bacon, prides itself on setting aside the a prion
method for that of a careful and elaborate mquiry
into facts with a subsequent generalization based
upon the facts examined. It does not fall within our
province to give a history of this great change, which
Ls given so strong an impulse to physical discovery
and to the advance of the physical sciences. \Ve
have already alluded to it elsewhere.^ But the accu-
sation against the Scholastics cannot be passed over
unnoticed, and as it has a certain foundation in tact,
it may be well to point out how far there was any-
thing deserving censure in the Scholastic Method.

We have pointed out that the a posteriori, or ana-
lytic method, is the method of discovery, the a prrort
or synthetic, that oUnstruction. The Schoolmen are

1 Pp. 82, seqq., 379. seqq

476

APPENDIX.

THE SCHOLASTIC METHOD.

477

accused of neglecting to cultivate the former, and of
consequently making no progress in the way of
enlarging the field of human knowledge, and of devo-
ting themselves entirely to the latter, and of being
satisfied with a traditional system of dogmas borrowed
one from the other, without any serious attempt to
verify them by an appeal to experience. They are
accused of starting on philosophical investigation
with certain dogmatic prejudices, instead of taking
the facts, and by the a posteriori method building up,
from a careful examination of them, the principles
which when once firmly established were for all future
time the landmarks to guide the onward march of
human knowledge. Instead of setting out on their
investigation with a fair field and no favour, with no
fixed ideas on the subject of Ethics or Logic or
Psychology, they are supposed to have blindly taken
for granted that what was taught to them was true,
instead of searching the book of nature and their
own intelligence to see whether those things were so.
Of the physical sciences it is perfectly true that
in mediaeval times they did not make any very
rapid progress. Since the Reformation, physical
science has advanced with giant strides. Material
civilization has been developed to an extent that
would have been scarcely possible if the Church had
not lost her dominion over a large part of modern
Europe. Victories have been won over Nature of
which the Schoolmen never dreamed, and the spirit
of enterprise, unchecked by fear of authority, has
fought its way with astonishing success in all the
natural arts and sciences.

I But is the same true of the sciences that deal
\not with the material but the immaterial ? not with
khe visible but with the invisible ? not with brute
tiatter but with mind, thought, conscience, God ?
•it is on the answer to this question that must de-
pend our approval or disapproval of the Scholastic

Method. , , . ^^^

No one will, I imagine, deny that the sciences
which deal with the invisible and immaterial are of
far greater importance than those which are con-
cerned with the visible and the material, that Theo-
logy has a greater influence for good or evil than
Chemistry, and Psychology than Botany. If to the
a pnori sciences as they are called, the « posUnon
method has been successfully applied, the folly of
the Schoolmen in neglecting it must be conceded.
But if not. if it has proved a failure when once the
consideration of the corruptible things around us is
exchanged for the study of the incorruptible and
eternal, then we shall rejoice i" the conservative
maintenance of the a priori .method by Scholastic
Philosophers, even though they forfeited thereby the
superior acquaintance with Heat and Light, with
Physiology and Botany and Chemistry, which is
the boast of the present day.

Now in all the mental sciences the acceptance of
fixed principles as universally true has become year
by year a rarer phenomenon among those w-ho have
apphed to them the a posteriori methods that have
been so successfully pursued in the physical sciences
m the latter, the brilliant hypothesis cannot hold
the ground unless it is true, and there is a con-

478

APPENDIX.

THE SCHOLASTIC METHOD.

479

tinually increasing consensus on all physical ques-
tions. In the former, the hypothesis, whether
brilliant or not, holds its ground in spite of its
falsity. There is no means of testing it and detect-
ing its true character if it is an imposture.

The consequence of this is that there is no sort
of convergence of opinion on moral and religious
questions, but on the contrary an ever increasing
divergence. New forms of religion with new dogmas
continually appear and are eagerly accepted. On
questions of morality the disagreement even on
matters that concern the natural law increases day by
day. Psychology is in a state of the wildest confusion.
All the fundamental Laws of Thought are called
in question, and the logician, who is supposed to
be the champion of Truth, professes with suicidal
scepticism that a proposition may be at the same
time true and false, and that contradictories in no
way exclude each other from simultaneous accept-
ance. These are the results of the departure from
the a priori method of the Schoolmen : judged even
by the a posteriori method they certainly cannot be
regarded as happy. An army fighting within itself
is not marching to victory; there is no increasing
grasp of Truth w^here the discordant questioning as
to what is Truth is continually increasing.

But is it possible to shake off entirely the a priori
method and the acceptance of certain principles as
true prior to all reasoning ? We saw in discussing
the philosophy of Mr. MilP that he assumes uncon-
sciously a First Principle which he professes to prove,

' Cf. pp. 80—91.

The same petitio principii runs through the whole of
the Experimental School. The Scottish metaphy-
sicians, on the other hand, by their assertion of the
conditional and of the relative character of our
concepts, practically declare Truth to be somethmg
subjective to the individual, and destroy the reality
of Objective Truth at all ; while the German Hege-
lians, carrying out the antinomies of I^^nt, and
declaring that contradictories are true together,
shut themselves out of the field entirely : for who
can argue with a man who practically asserts that
what he says is at the same time true and false, or
that the opponent who contradicts him is equally in
possession of Truth with himself?

When Aristotle at the begining of his Ethia lays
down that we must begin from things familiar to us
rather than first principles, he does not mean that
we are to imitate the method of the moderns and to
assume no principles for granted. He is advocating
the procedure from the concrete fact to the universa
law, inasmuch as the latter is more difficult for
ordinary men to grasp in abstract form. The
"rLiple, he tells us will, in the case of those who
are well-trained in morals, be clear to them as under-
lying the fact, and for this reason he urges the
importance of a careful education for those who are
to study moral questions. They will be able at
once to grasp the innate principle when its particular
applicatfon is put before them, just as a man by
reason of his mental constitution at once grasps the
fact that things equal to the same thing are equal to
each other.

THE SCHOLASTIC METHOD.

481

480

APPENDIX

This it is which is the true a posteriori method of
Scholastic Philosophy in what are called the Deduc-
tive sciences as opposed to the false method of the
moderns. With the former it is the recognition of
the universal law under one single instance ; with
the latter it is the building up of the universal law
by an observance of results to be carefully tested by
the Experimental methods. On physical questions
we are ready to admit that the Schoolmen were far
behind, and that they had not thrown their energy
into the investigation of the properties of steam and
electricity and light and heat and sound. This was
because they regarded as the true objects of human
interest, questions which are now practically subor-
dinate in the minds of men. Their interests w^ere
in the science of sciences, in Theolog>', the science
of God, and in all the other sciences in propor-
tion as they ministered thereto. Hence their
method was the method of Theology and of the
sciences that were its immediate handmaids, and as
all these were Deductive and a priori sciences, not
Inductive and a posteriori, their method was naturally
the Deductive and not the Inductive method.

Did this hinder their advance in the acquisition
of knowledge ? Perhaps so, in what in modern
parlance bears the name of Science, but not in
Philosophy or Theology, or Pure Mathematics.
For in Philosophy all discovery is but an applica-
tion of a priori principles to fresh facts. There are
no fresh principles to discover. The laws of the
human mind may be elaborated or re-stated, but
from the beginning they have been the guides of

human intelligence and from the days of Aristotle
they have been familiar to all sound Philosophers.
The Aristotelian Logic, the Aristotelian Metaphysics,
the Aristotelian Psychology have never been im-
proved upon, allowing for certain necessary modifica-
Tions introduced by Christianity, as regards the
substance of the doctrine taught. If we cannot say
the same of the Aristotelian Theology or Ethics, it
is partly because Christianity reconstructed even
Natural Theology, partly because it opened out
indefinitely the field of Theology by the introduction
of the Christian Revelation. But for Theology,
revealed as well as natural, there was no fresh
discovery from the days when the deposit of
V Revealed Truth was completed. Henceforward
progress was by way of development, not of dis-
covery ; from within, not from without. When men
accuse the Scholastics of inventing no fresh system
of Philosophy and contrast them with modern
philosophers since the days of Bacon they are
perfectly right. Since the days of St. Thomas .there
is no fresh foundation of philosophical truth to be
laid, no fresh system to invent, save by mventmg
falsity in the place of Truth. If this is the invention
which is recommended, God save us from it !

One philosophy after another rises up in modern
days and proclaims itself to be the voice of a
teacher sent from God. For a time its prophet
feathers round himself a number of enthusiastic dis-
ciples, and promises great things to an unenlightened
world. But soon a rival appears, and denounces his
predecessor as inconsistent with himself and incon-

482

APPENDIX.

THE SCHOLASTIC METHOD.

483

sistent with Truth, and engages to remedy the evil
by fresh discoveries of its own. But alas! the
promise is but ill fulfilled ; he, too, is slain in his
turn by one who follows close upon his heels, and
who denounces him with no less vigour than he
had himself displayed against his discarded pre-
decessor.

Sometimes, indeed, some bolder spirit, perceiving
the inconsistencies of his own system of philosophy,
defies criticism by announcing the necessity of
antinomies and by asserting that contradictories
can be true together. Thus indeed, he escapes his
enemies, but it is to fall by his own sword, for what
becomes of Truth if a proposition and its contra-
dictory are allowed to be equally in accordance with

Truth ?

Thus it is that the battle goes on contmually
outside the Catholic Church, and the internecine
warfare is mistaken for a healthy sign of life. The
multiformity of error is misnamed the many-sided-
ness Qf truth, and even when one hypothesis after
another proves to be utterly untenable, men are
content to invent yet another, that it too may be
rejected in its turn. But within the fold of Truth a
system at variance with Truth cannot long flourish.
It may for a time gain adherents, advocated if it be
by the force of genius and the plausibility of an
active intelligence. But it will soon find itself in
conflict with Truth, and sooner or later will be con-
demned by the infallible voice of the Vicar of Him
who came to bear witness to the Truth. For within
her the perfect Truth dwells, and, dwelling there.

must soon expel the subtlest form of error that the
mind of man can devise.

This is why in the philosophy of the Church there
can be no new discoveries, but only developments of
Truth already possessed. For fresh discovery means
a setting aside of what exists already, and if what
exists already is the perfect Truth, to set it aside is
but to introduce the destructive poison of error.

We cannot, therefore, be surprised if the
Method of Discovery did not flourish among the
Scholastic philosophers. Nor can it ever be the
adopted method of the Catholic Church. She
will ever look on, from her throne upon the
Rock and will watch unmoved the discoveries of
modern science, knowing that they will contribute
sooner or later, one and all, to illustrate the truth of
her philosophy. She will watch the rise and fall ot
one system of philosophy after another, knowing
that amid their dismantled ruins she will remain
in her unshaken supremacy the true Queen of all
Science and the Mistress of all Philosophy. For to
her all arts and all sciences minister, but none more
than the Art and Science of Logic, since the Catholic
Church alone can challenge the world to point out
a single inconsistency in her teaching, or a single
weak point in the perfect system of Divine philo-
sophy which God through her has given to the
world.

THE END.

INDEX.

Abstraction 102—105.
Accent, fallacy of 443—445-
Accidents,

definition of i73> '74;

fallacy of 44 5» 446;

inseparable i82-~i85 ;

predicamental 187—192;

separable 182—185.
ACTiON,a predicament i8M»9-
Agreement, Mill's method of

389,390,392,393.
Amphibology, fallacy of 43°

—439-
Analogy 407— 4^1-
Analysis, when used 471 -

474-
Animals,

idealization, incapable of 1 10,

116,117;
imagination of 98, 99, iw—

thinking powers of 47-7.
Anselm (St.) on Nommahsm

ANTECEDENTS of propositions

289, 307. ^ _

ANTINOMIES 35, 36, 139-

APPREHENSION (SIMPLE),
Abstraction, its relation to
102—105 ; . _

attention, its relation to 100,

Id ;

conceptualist's account of

123—129, 132— 139,140;!. ;

consciousness, its relation to

100;
definition of 93, 97, 98 ; ^
false notions of, generate

scepticism 113, i' 4, 127

129, 138, 139; . ^^,
Hamilton's view ot 123—

129, 132—139, u6 «. ;

ideas, engendered by 95 ;
imagination, its relation to

101, 102 ; .

judgment, its relation to 247r

248 ;
memor>% its relation to loi ;

Mill, on 129—139;
moderns' error on 105, 121 —

139 ;

nominalistic view of 129—

139;
process of 98-100, 102—

105 ;
sensation, its relation to 100 ;

sensible perception, its rela-
tion to lOI.' .
AQUINAS (ST. THOMAS), his

views on, . r 1

Aristotle's reduction of syl-
logisms 339 «• ; . .
certainty, degrees of 407,

468 ;

INDEX.

487

486

INDEX.

contradiction, principle of

34;
enthymemes, 356, 357 ;

eternity of creation, 77 n. ;
experiment, minute 365 ;
fallacy, 449 ;
figure, first 33^ «• ;
induction 378 ;
intentions, second 167 ;/. ;
knowledge perfecting nature

305;
logic as a science 24 n ;

universals 164 ;

unityof human nature 161 ;/.

Argument,

a non causa pro causa 453,

4S4;
ad hominevt 450 — 452 ;

ad populum 452 ;

a non tali pro tali 455 ;

a non vera pro vera 454,

455;
adverecundiam^ 452, 453 ;

conclusion, synonym for 95 ;

logic treats of 9 ;

reasoning expressed by, 95,
310.
Argumentation,

Aristotle on 325 ;

synonym for reasoning 90 —
94.
Aristotle, his views on

Argumentation 325 ;

art 17 «•, I9> 20;
categorical, meaning of word

288;
categories, the 189 ;
certitude, degrees of 467 ;
conversio per contra 342 ;
deduction 400 ;
dialectic, meaning of word

28;
dictum de omni^ the 316 «. ;
enthymeme, the 356 — 358 ;
epichirem, 359 ;
example, definition of 402 n. ;
experiment, minute 365, 386;

induction, complete 366

368;
induction incomplete 376 —

378, 386, 400 ;
logic, use of word 27, 28 ;
petitio principii^ name for

457 ;
Plato's idea of universals

158 — 160 ;
predicate, use of word 263 ;
a priori reasoning 479, 480 ;
science 17 «., 19, 20 ;
similarity, definition of 136

n. ;
subject, use of word 263 ;
syllogisms, reduction of 339;
t6 rl ^v flvai, meaning of 5 n. ;
unity, kinds of 143 n.;
universals 164.
Arnauld, definition of logic

25-

Art, Aristotle's views of 1 7 —
20 ; nature of 1 7 — 20.

Assent, synonym for judg-
ment 250.

Assertion, synonym for judg-
ment 250.

Association, errors arising
from law of 469, 470.

Attention 100—102.

Bain, his views on
causation 396, 397 ;
consistency, principle of 90,

91 ;

kinds 186.
Being,

idea of, underlies all ideas

33,34;
metaphysics, its relation to

8, 41, 42 ;
non-being, its relation to 34 ;
non-being and falsity 42.

Categories, jr^ predicaments.
Causation, principle of,
Bain's view on 396, 397 ;

enunciation of 72 ;

explanation of 73—79 *»

falsification of 78, 79 ;

identity (law of) its connec-
tion with 76, 77 '»

Mill's idea of 80-88 ;

sufficient reason (law of) its
connection with 77»7»-

Causes,

efficient 73— 7o ;

final 73 ;
formal 72 ;
immediate 74, 75 *,
material 72 ;
metaphysical 390 ;
nature of 72—76 ;
physical 396 ; . ,

sensationalist's view of 39^,

Certainty 426— 42»-

Certitude,

absolute 384-386, 4 1 5-41 7,

certainty, relation to 420—

428 ;
definition of 415 ;
degrees of 467, 4o8 ', . , ^^,
hypothesis confused with 25j,

hypmhetical, see physical ;
induction, generates 399-

meTaphys^cal, see absolute ;

moral 415— 4>7 j

physical 384-386, 415-417

Circle (vicious) 218.
cognition, direct and reflex

154, 165—167.
Composition,

synonym for judgment 249.
comprehension,

of subject and predicate 282

-287 ;

whole of 281.
Conception, see apprehen

sion. ,

Concept, see idea.

Conceptualism,

Locke's theory of modern

1 52 w. ;
refutation of modern I2j—

129,132—139; - ^
universals, doctrine of 144—
147, 157-158; see also
Hamilton.
Conclusion, ^

argument, synonym tor 95 ,

truth of 3ic>-3i2- . -. r

Condition (special), fallacy ot

446 — 448.
Consciousness 100.

Consequent,

fallacy of 45 5;
of propositions 307.
Consistency, principle ot 90,

Contradiction, principle of,
Aquinas' (St. Thomas) idea ^

of 34;.
enunciation of 33 ,

errors from abuse of 40 ;

first of all principles 33—35,

40-42 ;
Hamilton on 30 ;

Hegel on 35 ;

identity (principle of), its re-
lation to 43—49 ;

Kant on 35 ;

logic, founded on 42 ;

Mansel on 35 ;

Mill's idea 0(89,90;

moderns reject It 3 5» 36;

rules for its application 36—

40 ;
Schelling on 35 ;
Suarez on 40, 4i ; . . ,
thinking, its connection with

34—36, 40—42-
Conversion of propositions

298—303, 341, 342.
Convictions,
as judgments 252 ;
confused with opinions 252

—254.

488

INDEX.

Copula,

definition of 262 ;

its relation to propositions
266—268.
Creation, eternity of 77 n.

Deduction,
induction, its relation to 370,

400;
moderns' estimate of 364,

365;
reasoning, synonym for 94 ;
sciences of, 56, 57, 463, 464 ;
syllogisms of 379 ;
value of 474—483.
Definition 474—438 ;
accidental 202 — 204 ;
defective 218 ;
descriptive 202 — 204 ;
division, its relation to 226,

231 ;

essential 204, 205 ;

Hamilton on 46, 47 ;

identity (principle of), foun-
dation of 42, 43 ;

logical 205 ;

metaphor, by means of 221,
222 ;

metaphysical 204, 205 ;

nature of 197 ;

negative 220, 221 ;

nominal 197 — 200;

practical 211, 212 ;

physical 204, 205 ;

proper 205 ;

real 197, 200 — 202 ;

rules for 212 — 224 ;

synonym, by means of 219 ;

theoretical 210, 211 ;

value of Z96, 197, 206—210 ;

wholes, treated by 228, 229.
Demonstration,

absolute 424 ;

direct 423, 424 ;

empirical 423 ;

identity (principal of), foun-
dation of 42, 43 ;

indirect 423, 424 ;

mixed 423 ;

nature of 419, 420, 422 — 424;

a priori and a posteriori 422,

423;
pure 423 ;

relative 424.
Denial, synonym for judg-
ment 250.
Dialectic 28.
Dichotomy 234.
Dictum de Omni et Nullo^

Aristotle author of 316 «.;

basis of syllogisms 316, 339,

379;
moderns' neglect of 316, 365.

Difference, Mill's method of

390—393-
Differentia Specifica 172,

i73» 183.
Dilemma, 353—356.
Division,

accidental 232, 233 ;

cross-division 239 ;

definition, relation to 226^

231 ;
dichotomy, method of 234 ;
disparate 242 ;
divisions of 230, 231 ;
fallacy of 440—443 ;
judgment synonym for 249 ;
logical 229, 231 ;
metaphysical 231 ;
moral 231 ;

principles of 240 — 242 ;
physical 231 ;
rules for 233 — 244 ;
per saltum 242 ;
verbal 231 ;

wholes treated by 228, 229.
Doubt, definition of 418.

Effect, physical and meta-

physical 397, 398.
Enthymeme 356—359, 429.
Epichirem 359, 360.
Equivocation 434—436.

INDEX.

489

Error,

definition of 4^9 »

detected by logic 2, 10, 14,

21,196,206-210; ,

springing from confusion

about association (law ot)

469, 470 ; , . .

convictions and opinions,

252-254;
idea and phantasm II3»

120 -I ">9 '.
meaning of words 194--
196; 206 — 210, 460,

469; J. ,•

principle of contradiction

truth* of conclusion and
premisses 311, 3^2.

Essence,

definition of 5, 1 56 ; .
indivisibility and immuta-
bility of 183;
knowable by man 164, 105 ;
metaphysical 151 ;
pars determinans et pars
determinabilis 172—174 ;

physical 151 :
species gi\e the 171 ;
universals contain the 1 57-

Evasion 449-

Evidence, . .

chain, cumulative, and cir-
cumstantial 430, 431;

material lo^ic treats of 9.
Exactness aimed at in Logic

Example 40: 407-
Experiment mmute) not

used b> St. Thomas or

Aristotle. 65, 386.
EXPERIMKM'AL SCHOOL, see

Mill.
Extension.
of subject ^f! predicate, 2»i

—287
whole o) Si.

Fallacy,

Aquinas (St.Thomas) on 449 ;
formal and material 433, 434 ;
nature of 432, 433 ;
species of (i) accent 443>

444, .

(2) accident 445? 44o,

(3) amphibology 436—439*

(4) Argumentum

(a) a non causa 453,

(b) a dido secundum
quid 446, 447,

447. 448,

(d) ad hominem 45°—

452, ,

(e) adpopuhnn 452,

(f) a non tali pro tali

(g) ad verecundiarn 452,
(h) a non vera 454, 45 5>

(5) condition 446—8,

(6) composition 439, 44°,

(7) consequent 455, 456,

(8) division 440— 443»

(9) equivocation 434—436,

(10) figure of speech 444,

(11) Ignorantia Eknchi 448—

y| C '2

(12) pditio principii 456—
459,

(13) plurium interrogantium

459-
Falsity 42.
Figures of Speech, fallacy

of 444 ;
of syllogism 324—339-
Formalism 412.

Galen, inventor of fourth figure

339.
Galileo, his condemnation

253, 400.
Genius, how it reaches con-
clusions 406.
Genus,

definition of 171 ;

490

INDEX.

491

subaltemate 176 — 179;
suitunum 176^ 178, 187.
GOUDIN on the fourth figure

337.
Grammar, its relation to logic

Habitus a predicament 188

— 9-
Hamilton (Sir W.), his ideas

on,
apprehension or conception

123— 129, 132— 139, 146 «.;
concepts 46 — 48, 123 — 129 ;
contradiction (principle of)

36;
definition 46, 47 ;
identity (principle of) 45—

.49;.

induction (incomplete) 378 ;

phantasms 46 — 48,123 — 129 ;

quantification of predicate
285—287 ;

species infima 185, 186;

thought 123 — 129 ;

universals 146 «., 152, 153.
Harper (Fr.). quoted 48.
Hegel, on contradictories 35 ;

on truth 479.
Hypothesis,

certitude confused with 253,

254;
origin of 252, 253.

Ideas for concepts),
description of 95, 98, 99, 105

— 107 ;
errors from false notions of

113, 120—139;
logic treats of 9 ;
Hamilton's error on 46 — 48,

123—129;
Mill's nominalistic view of

129—139;
phantasms differ from 105

—117;

Platonic 1 58 — 60 ;

transcendental 168.
Identity, principle of:

causation (principle of) its
relation to 76, 77 ;

contradiction (principle of),
relation to 43—49 ;

definitions and demonstra-
tions founded on 42, 43 ;

Hamilton's error on 45 — 49 ;

moderns' error on 44 ;

propositions founded on 49,
52, 53, 67—70 ;

statement of 42, 43 ;

tautology not a note of 51,

52;
truth, its relation to, 53.
Ignorance, definition of 418.
IgnoratioElenchi 448—459.
Image, intellectual, see ideas ;

sensible, see phantasms.
Imagination,
animals possess 98, 99, 1 1 7 —

120 ;
characteristics of loi, 102 ;
definition of loi, 102 ;
impression on 98, 99 ;
phantasms engendered by
107, 108.
Impossible, different uses of

word 40.
Individual, unity of 143, 144.
Inference, synonym for rea-
soning 94.
Induction,
Aristotle's idea of 366 ;
complete or formal 368 — 374;
deduction, how related to

370—400 ;
incomplete or material, Aqui-
nas (St. Thomas) on 378 ;
Aristotle's idea of 376—-

379, 386—400;
certainty attainable by 399

—401 ;
Catholic philosophers' neg-
lect of 379 — 386 ;

estimate to have of 397—

401, 475—483;
Hamilton on 378 ; .

logic and syllogism, their

relation to 379—382, 386,

387, 398, 399 ;
Mansel on 378 ;
Mill's exaggeration of 378,

480—483 ;
Mill's methods of agree-
ment 389, 390 ;
of difference 390— 393 5
of residue 395 *»
variation 393—395 5
rapid 400, 401 ;
Socratic 404 ; , .

spirit of, its growth and in-
fluence 364, 365, 374,375,
475—483 ;
uses of the word 366, 367.
Intentions, first and second
165—168.

Judgment,

apprehension, its connection

with 247, 248 ;

analytical, see a priori, cer-
tain 247 ;

convictions and 252—254 ;

contingent, see a posteriori ;

definition of 94, 247 ;

description of 95, 246—248 ;

division of 250—260;

expression of 245, 246, 261 ;

immediate 254, 255 ;

imprudent and prudent 250

—252 ;
logic treats of 9 ;
mediate 254, 255 ;
necessary, see a prion;
opinions and 252—254 ;
a prion and a posteriori 255

— 260 ;
prudent and imprudent 250

—252 ; . ,

relation of terms perceived

before 248, 249 ;

stages in formation of 247,

249 ; , ^

suspension of 240, 247 ;
synonyms for 249, 250 ;
synthetical, see a posteriori;
uncertain 247 ;
word, double meaning of 240,

247.

Kant, his doctrine on,
antinomies 35, ^39;
contradiction (principle ot)

synthetical propositions 61 —
70, 260.
Kinds 186, 187.
Knowledge,

explicit and implicit 68—70;

perfecting nature 305 ;

relativity of 127, 128.

Language, relation to thought

and logic 3, 4,96, 97-

Laws,
of Association 469, 470 ;
a posteriori and a prion 54,

384, 385 ; . ^..

physical, certainty of :,85,

386.
see also principle.
Liberators on,

incomplete induction, 379 '•>
on genius and its conclusions

406.
LOCKE a conceptualist 152 n.

Logic,
applied and formal 8— 14>

23 382,383;
art or science? 16, 20—25 ;
artificial 22 ; aspect of treated

in present volume 10 ;
definitions of 23, 25—27 ;
divisions of 95, 96 *,
Docens Logica 22, 25 ;

end of 2 ;

errors combated by 2, 10,
14, 21, 196, 206 — 210 ;

492

INDEX.

493>

formal and applied 8 — 14, 23,

382, 3^3 ;
importance of i, 2, 14 ;
induction, its relation to 380

-388;
grammar and language, its
connection with 3, 4, 96,

97, 194—197 ;

innate 22 ;

language and grammar, its

connection with 3, 4, 96,

194—197 ;
material, see applied ;
metaphysics, its relation to

8;
natural 22 ;
principles of 30 — 33 ;
psychology, its relation to 7

science or art ? 16, 20 — 25 ;
science of 95, 96 ;
thought, its relation to 3, 14;
truth, its relation to 9 — 14,
204, 205, 269—272, 382,

383;
Utens et Docens Logica 22 ;

word, meanings of the 3, 27,
28.

Mansel (Dean) on induction
378;
on principle of contradiction

35;

on theology 35.
Memory, sensible, loi.
Metaphor, 22 i, 222, 409 — 41 1.
Metaphysics,

being, foundation of 41, 42 ;

logic, its relation to 8 ;

province of 8.
Method,

analytic and synthetic 462,

463, 471—483 ;

certitude to be got by 467 ;
definition and division of 462;
importance of 461 ;
laws of 465 — 474 ;

moderns' errors on 481 —

483;
a priori and a posteriori 475

-483;
scholastic 475 — 483 ;

synthetic and analytic 462,
463,471—483.
Mendive on incomplete in-
duction 379.
Middle,

principle of excluded 79, 80 ;

of syllogisms 314, 315.
Mill (J. S.), his doctrine of,

causation and causes 74 — 76,
80—87;

contradiction (principle of) 89
—91 ;

ideas 129 — 139 ;

induction 378, 480 — 483 ;

kinds 186, 187 ;

logic, definition of 26 ;

nominalism 129 — 139 ;

numerical propositions 66
n. ;

a posteriori methods 475 —

483;
principles (fundamental) 80 —

91;

subject and predicate, mean-
ing of 282 n. ;

uniformity (principle of) 80 —
^^\

universals 148 — 150;

his inconsistency 149, 150.
Minor of syllogism 314, 315.
MODALS 290 — 292.
Modes of propositions 291.
Moods of syllogisms 332 —

Nominalism,
Anselm (St.) on 148 ;
apprehension according to

modern 129 — 139 ;
kinds according to modem

186;
mediaeval and modern 148 ;

refutation of modern 129—

^39; , ,. „

sensationalism, its relation

universals according to 140

—150, 158;
see also Mill.

Opinion,

definition of ^\l, 418 ;
exalted into convictions 252

—254.
Opposition of propositions 293

—298.

Paralogism 4M «•» 4i5» 433-
Parcimony, law of 67.

Part, , ,

essential, integral, homoge-
neous and heterogeneous

230 ; ,

metaphysical 204, 226—231 ;
moral 231 ;

physical 204, 226—230.
Passion, one of the predica-
ments 188, 189.
Perception, sensible loi.
Petitio Principii 456—459-
Phantasms,

characteristics of 98, 99> i^S

— 120;
common 117— 120, I37, I3» '»
Hamilton's doctrine on 40—

48,123—129; .^
ideas, contrasted with 105—

"7; . ,. . • ^„ i
Mill's nominahstic view on

129—139 ;

reproduction of 102.
Philosophy, no change in

doctrines of 48 1 —483-
Place, a predicament 188, 189.

Plato, , , . o
his name for logic 28 ;
on universal ideas 158—160.

Plurium interrogantium,
fallacy of 4 59» 460.

Porphyrian tree 180—182.

Port Royal logic, its defini-
tion of logic 26.
Position, a predicament 188,

189.
Predicables,

account of (detailed) 171—

186;
account in general 168— 171 ;
predicaments contrasted with

190 — 192.
Predicaments,

account of 187—190;^ . .
predicables contrasted with

190 — 192.
Predicate,
definition of 262 ;
distribution of 276—279 ;
propositions, its relation to

266, 267 ;
quantification of 283 — 287 ;
word, its ambiguity 263.
Premisses,
assumed unduly 311, 3^2 ;
conclusion, its relation to 310

— 312 ;
major, minor, and middle 313

probability and signs, kinds

of 356— 359; „ . .
{see also rules for syllogisms).

Principles, • , .q

analytical and synthetical 5»

of causation 72— 79t 80—88 ;.
of consistency 90, 91;
of contradiction 33—42, 89 ;•
first30— 33. 80— 91,307;

of identity 42— 53;
of middle, excluded 79» 80 ;
a posteriori 53, 54, 58—70 ;
a priori 49, 53, 54, 58—70 ;-
synthetical 58—70 ;
tautological 51, 52 ;
of uniformity 80—87.
Probability,
description of 425— 43' *»
in a premiss 359-

494

INDEX.

Proof,

foundation of all 32 — 35 ;

direct or positive 31, 32 ;

indirect or negative 31.
Property, a predicable 174,

175.
Proposition,

affirmative and negative 267

—269;
analytical and synthetical 58

—70;
antecedents of 289, 307 ;
categorical 288 ;
conditional 288, 289 ;
conjunctive 290 ;
consequent of 307 ;
contingent and necessary

266, 267 ;
contrary and contradictory

294 — 298 ;
conversion of 298 — 303, 341 ;
copula of 266, 267 ;
definition of 261 — 263 ;
disjunctive 289, 290 ;
divisions of 266 — 279, 288 —

292;
elements of 264 — 266 ;
false 269 — 272 ;
hypothetical 288—290 ;
import of 281 — 287 ;
impossible matter of 267 ;
identity (principle of) its re-
lation to 49 ;
indeterminate 274 — 276 ;
judgments expressed by 246,

261 ;
modal and pure 290 — 292 ;
negative 267 — 269;
numerical 66 n. ;
opposition of 293 — 298 ;
particular 273, 275, 346, 347 ;
parts of 262, 263 ;
a posteriori and a priori 53,

54, 61—70, 270—272 ;
predicate of 262, 263, 276 —

279, 281 — 287 ;
possible matter of 266, 267 ;

pure 290 — 292 ;
quality of 266 ;
quantification of 272 — 279,

283—287 ;
singular 274 ;
subcontrary and subaltern

295—298 ;
subject of 272—279, 281 —

287;

synthetical 58 — 70, 260 ;

tautological 51 52 ;

terms of 262, 263 ;

true 269 — 272 ;

universal 272—279, 346, 347.
Prosody, fallacy of 443, 444.
Psychology 7, 8.

Quality of propositions
266.

Quality, a predicament 188,
189.

Quantification of pro-
positions 272—279, 283
—287.

Question, fallacy of 459, 460.

Quiddity, definition of 5.

QuiNTiLiAN on Enthymeme
358.

Realists, 158—160.
Reason, law of sufficient 77 —

79-
Reasoning,
deductive, see a priori ;
deduction, synonym for 94 ;
definition of 94, 306 ;
description of 305 — 307 ;
expression of 310, 313 ;
foundation of 307 — 309 ;
inductive, see a posteriori ;
laws of 310 — 312 ;
syllogism, its relation to 310,

313;
a posteriori and a prion 309,

475—483.

INDEX.

495

Reduction of syllogisms,
per contra and per impos-

sibile 342—345 •»
methods of 339—347 ;
particular propositions 346,

Relation, a predicament 188,

189.
Residues, Mill'smethodof 395.

■Scepticism, arising from
errors on apprehension 113,

114, 127—129, 138, 139.;
exaggeration of induction
374, 375, 477-482.
Scholastics, method ol 474—

483.
Science,

analytic and synthetic 463—

465;
.■\ristotle on 17 «•, I9» 20;
art contrasted with 17—20 ;
deductive and inductive 56,

57, 463, 464, 475—483 ;

definition of 420 ;
demonstration, its relation to

420; , , . ,

inductive and deductive 50,

57,463, 464, 475-483;
laws of 30, 33 ;

natural 55> 56; ^ . .,,

a posteriori and a prion 54

—57,462—465, 475-483; '
practical and speculative 23,

24 ;
synthetic and analytic 463—

465, 474—483 ; ^

term, limited use of 421, 422.

iSENSATlON 100.

Sense 99, Joo-
Sensationalism,

causes according to 396, 397 ;

Nominalism, its relation to

149-
Similarity 136 n.

Socrates, on induction 404-

Sophism 414, 415, 433-
Sorites 360—363.
Species,

definitionof 171, '75;

injima 176, 179, 180, 185, 186,

^91 ; o

subalternate 176, 179» 180.
Spencer (Herbert),
agnosticism of 139;
rejects principle of contradic-
tion 36 ;
symbolic conceptions of 11 0«.

SUAREZ, on the principle of

contradiction 40, 4i'
SUBALTERNS 295.
SUBJECT OF PROPOSITIONS,

definition of 262 ;
distribution of 278, 279 ;
extension of 274—276, 283 ;
as the matter of propositions

266 ;
meaning of 282—287 ;
quantity of propositions de-
termined by 272.
Syllogism,

categorical and simple 3^3 ;
hypothetical and compound

313, 348, seq. ;
conditional 349, 35° ;
conjunctive 353 ;
deductive 379, 380 ;
definition of 313 ;
demonstrative 4^3, 4 '4, 4^9

i —424 ;

I descriptive 314, 3^5 ;

dialectic or epichirem 359,

360;
dilemma 353—356 ;
disjunctive 35^>— 353 ;
enthymeme 356—359 ;
epichirem 359, 360;
figures of 324—339 ;
foundation of 316, 339i 379»

380;
inductive 368-371, 379-

382;
I matter of 4 1 2— 431;

496

INDEX.

497

major, minor, and middle of

314, 315;
moods of 332—336 ;

polysyllogism 363 ;

principles of 315, 316;

probable 414, 424—431 ;

reasoning, its relation to 310,

313 ;

reduction of 339 — 347 ;

rhetorical 358 ;

rules of 316 — 323 ;

sophistical 433 ;

Sorites 360 — 362 ;

terms of 314, 315.
Synonym 219.
Synthesis, when used 471 —

474-

Tautology, in propositions

Sh 52.

Theology,

apparent contradictions of,
explained 40 ;

Mansel's idea of 35, 36 ;

unchangeable 481 — 483.
Thought,

animals without power of 5 —

contradiction (principle of) a
foundation of 34, 35, 40,

41 ;

exactness of 2, 3 ;
Hamilton's error on 123 —

129 ;
laws of II — 14 ;
language, its relation to 96 ;
logic, its relation to 3 — 14 ;
moderns' ideas on 365, 374,

375;
operations of 93 ;

psychology, its relation to 7,

8;
relativity of 113, 114, 127—

129;
uses of the word 4—7.
Time, a predicament 188, 189.

Tongiorgi on incomplete in-
duction 379.
Transcendentals 168.
Truisms 316.
Truth,

formal and material 272 ;

Hegel on 479 ;

in itself and as known to us

41,42;
identity (principle of), its re-
lation to 53 ;
inductive spirit, its influence

on 365, 477—482 ;
known to us and in itself 41,

42;
logic, its relation to 9— 14»-
204, 205, 269—272, 382,

383;
logical 270 ;

material and formal 272 ;
metaphysical 41, 42 ;
necessary 1 1.

Uniformity of nature's action

80—87, 91-
Unity,

actual 226 ;

Aristotle on 143 rt. ;

comprehensive 227 ;

extensive 227, 228 ;

individual 143, 144 ;

logical 227 — 229 ;

metaphysical 226 — 231 ;

moral 231 ;

nature's 145, seq. ;

potential 227—229;

physical 226 — 230;

ofuniversals 143 — 162.
Universals,

Aquinas (St. Thomas) on 164 ;

Aristotle on 164 ;

Champeaux (William of) on.
160 ;

conceptualists on 145— I47r

157, 158;
direct and reflex 1 53— 1 57 ;

divisions of 169, seq. ;
essences, their relation to 1 5^

157 {see also genus and

species) ;
Hamilton on 146 «•» o^

158;
Locke'stheory of iS2«. ;

logical, J^^ reflex ;

metaphysical, see direct ;

Mill on 148;

nominahsts on i47-i5o»

158; ^. ,

potential, see direct ;
propositions as 272, 273 ;
Platoon 158— 160;
realists (ultra) on i5» —

160 ;
reflex and direct i53— ^57;

scholastics on 150—153, 102,

1 77 '

true doctrine on 142— 145>

161, 162;
unity of 143—162 ;
as wholes 177,227.
Universality 272, 273-

Variation (concomitant),
Mill's method of 393—395-

Whately, his definition of

logic 25.
Wholes,

actual 228 ;

characteristics of 226 ;

comprehensive and extensive

227, 281 ;
definition treats of 228, 229 ;

kinds of 177;

logical 227-229; .

metaphysical 226, 228—231 ,

moral 231 ;
physical 226 ;
potential 227—229-.
Words, error from ignorance
about 194-196, 207-210;

meaning of 3.

Zigliara, .

on incomplete induction 379 ,
Kant's a priori propositions
260.

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Gwilt's Encyclopaedia of Architecture. 8vo. 62 j. Gd.

Keith Johnston's Dictionary of Geography, or General Gaietteer.

ICCulloch's Dictionary of Commerce and Commercial Navigation.

Maunder'B Biographical Treasury. Pep. 8vo. 6s.

— Historical Treasury. Fcp. 8vo. 6s.

— Scientific and Literary Treasurj-. Fcp. 8vo. 6s.

— Treasury of Bible Knowledge, edited by Ayre. Pep. 8vo. 6s.

— Ti«asary of Botany, edited by Lindley & Moore. Two Parta, IJi.

— Treagury of Geography. Fcp. 8vo. 6s « „ -

— Treasury of Knowledge and Library of Reference. Pep. 8vo. 8j.

— Treasury of Natural History. Fcp 8vo. 6s.
Quain's Dictionary of Medicine. Medium 8vo. 31«. 6d., or in 2 vols. 34i.
Reeve's Cookery and ITousekeeping. Crown 8vo. 5«. o ^ a^
Rich's Dictionary of Roman and Greek Antiquities. Crown 8vo. 7*. 6<f.
Roget's Thesaurus of English Words and Phrases. Crown 8vo. 10<. 6d,
WilUch's Popular Tables, by Marriott. Crown 8vo. lOi. 6<i.

WORKS BY MRS. DE SALIS.

Savouries k la Mode. Fcp. 8vo. U.
Entries a la Mode. Fcp. 8vo. !». 6d.
Soups and Dressed Fish i la Mode.
Pep. 8vo. Is. 6d.

Sweets and Supper Dishes, & la Mode.

Fcp. 8vo. If, 6d.
Ovsters 4 la Mode. Fcp. 8vo. 1*. 6d.
Vegetables H la Mode. Fcp. 8vo. Is. 6<J.

LONGMANS, GKEEN, & CO., London and New York.

A SELECTION

EDUCATIONAL WORKS.

-•o*-

TEXT-BOOKS OF SCIENCE.

FtJLLY ILLUSTRATED.

Abney's Treatise on Photography. Fcp. 8vo. 3i. 6d.
Anderson's Strength of Materials. 8*. 6d.
Armstrong's Organic Chenmtry. 3<. 6d.
Ball's Blementi of Astronomy. 6s.
Barry's Railway Appliances. 3*. 6<i.
Bauerman's Systematic Mineralogy. 6s.

— Descriptive Mineralogy. 6j.
Bloxam and Huntington's Metals, bs.
Glazebrook'i Physical Optics. 6s.
Qlaaebrook and Shaw's Practical Physics. 6s.

Gore's Art of Electro-Metallurgy. 6*. „ , .. , „^

Griflln's Algebra and Trigonometry. 3i. 6d. Notes and Solutions, 3j. 6(1.

Holmes's The Steam Engine. 6s.

Jenkin's Electricity and Magnetism. 8i. 6(1.

Maxwell's Theory of Heat. 3«. 6d.

Merrifleld's Technical Arithmetic and Mensuration.

Miller's Inorganic Chemistry, ^s.6d.

Preece and Sivewright's Telegraphy. 6*.

BuUey's Study of Rocks, a Text-Book of Petrology.

Shelley's Workshop AppUances. ^3.6d.

Thom6'8 Structural and Physiological Botany. 6^.

Thorpe's Quantitative Chemical Analysis, is. 6d.

Thome and Muir's Qualitative Analysis. Zs.6d.

TM^s Chemical Philosophy. ds.6d. With Answer, to Problems, is. 6d.

TJnvein's Blemente of Machine Design. 6*.

Watflon's Plane and SoUd Geometry. 3*. 6d,

THE GREEK LANGUAGE.

Bloomfield's College and School Greek Testament. Fcp 8vo. 64.
Bolland & Lang's PoUtics of Aristotle. Post 8vo. 7s. 6d.
Collis'B Chief Tenses of the Greek Irregular Verbs. 8vo. Is

— Pontes Grseci, Stepping-Stone to Greek Grammar. 12mo. is. W.

— Praxis Grseca, Etymology. 12mo. 2j. 6<i.
I — Greek Verse-Book, Praxis lambica. 12mo.is.6d.

Farrar'8 Brief Greek Syntax and Accidence. 12mo. 4*. 6J.

_ Greek Grammar Rules for Harrow School. 12mo. Is. 6d,
Gcare'8 Notes on Thucydides. Book L Fcp. 8vo. 2i. 6cf.

Zs. 6d. Key, Si. 64.

U.6d.

LONGMANS, GREEN, & CO.. London and New York.

A Selection of Educational Works.

Hewitt's Greek Examlnation-Papew. 12ino. 1*. 6d.

Isbister's Xenophon's Anabasis, Books I. to III. with Notes. IJmo. 34. Bd,

Kennedy's Greek Grammar. 12mo. is. 6d.

Liddell & Scott's English-Greek Lexicon. 4to. 86*. ; Square 12mo. It. 6d.

Mahafly's Classical Greek Literature. Crown 8vo. Poets, 7i.6d. Prose Writers,

It. 6d.
Morris's Greek Lessons. Square 18mo. Part I. 2.t. 6<i. ; Part IL It,
Parry's Elementary Greek Grammar. 12mo. 3*. 6d.

Plato's Republic, Book I. Greek Text, English Notes by Hardy. Crown 8vo. 3*.
Sheppard and Evans's Notes on Thucydides. Crown 8vo. 7*. 6d.
Thucydides, Book 17. with Notes by Barton and Chavasse. Crown Svo. 6t.
Valpy's Greek Delectus, improved by White. 12mo, 2t. ed. Key, 2t. 6d,
White's Xenophon's Expedition of Cyrus, with English Notes. 12mo. 7t. td,
WilMns's Mannal of Greek Prose Composition. Crown 8v( . 6«. Key, 5t,

— Exercises in Greek Prose Composition. Crown 8vo. At. M. Key, 2i. 6d.

— New Greek Delectus. Crown Svo. Zs. 6d. Key, 2*. 6d.

— Progressive Greek Delectus. 12mo. 4*. Key, 2t. 6d,

— Progressive Greek Anthology. 12mo. 5*.

— Scriptores Attici, Excerpts with English Notes. Crown 8to. It. 64.

— Speeches from Thucydides translated. Post Svo. 6*.
Yonge's English-Greek Lexicon, 4to. 21i. ; Square 12mo. 8*. 6d,

THE LATIN LANGUAGE.

Bradley's Latin Prose Exercises. 12mo. 3*. Gd. Key, 6*.

— Continuous Lessons in Latin Prose. 12mo. 6*. Key, it. 6d.

— Cornelius Nepos, improved by White. 12mo. 3*. 6<i,

— Eutropius, improved by White. 12mo. 2«. 6d.

— Ovid's Metamorphoses, improved by White. ISmo. it. W.

— Select Fables of Phaedrus, improved by White. 12mo. 3*. 6d.
Collis's Chief Tenses of Latin Irregular Verbs. Svo. 1*.

— Pontes Latini, Stepping-Stone to Latin Grammar. I3mo. 3*. Sd,
Hewitt's Latin Examination-Papers. 12mo. 1*. 6d.
Isbister's Caesar, Books I.-VII. 12mo. is. ; or with Reading Lessons, it. M.

— Caesar's Commentaries, Books I.-V. 12mo. 3*. 6d.

— First Book of Caesar's Gallic, War. 12mo. 1*. 6d.
Jerram'i Latin6 Reddenda. Crown Svo. It. Gd.

Kennedy's Child's Latin Primer, or First Latin Lessons. 12mo. 2t,

— Child's Latin Accidence. 12mo. 1*.

Elementary Latin Grammar. 12mo. Zs. Gd.

— Elementary Latin Reading Book, or Tirocinium TAtinnm. 13ino. 3i.

— Latin Prose, Palaestra Still Latini. 12mo, St.

— Latin Vocabulary. 12mo. 2«. 6J.

— Subaidia Primaria, Exercise Books to the Public School Latin Primer,

I. Accidence and Simple Construction, 2t. Gd. II. Syntax, Zt. Gd.
•— Key to the Exercises in Subsidia Primaria, Parts I. and'II. price 5#.

— Subsidia Primaria, III. the Latin Compound Sentence. 12mo. It,

LONGMANS, GREEN, & CO., London and New York.

A Selection of Educational Works.

Kennedy's Curriculum Still Latini. l2mo. 4*. Gd. Key, Is. Gd.

— Palaestra Latina, or Second Latin Reading Book. 12mo. St.

Moody's Eton Latin Grammar. 12mo. 2s. Gd. The Accidence separately, 1*,
Morris's Elementa Latina. Fcp. Svo. 1*. Gd. Key, 2s. Gd.
Parry's Origines Romanae, from Livy, with English Notes. Crown Svo. it.
The Public School Latin Primer. ISmo. 2s. Gd.

— — — — Grammar, by Rev. Dr. Kennedy. Post Svo. 7s. Gd,
Prendergast's Mastery Series, Manual of Latin. 12mo. 2s. Gd.
Rapier's Introduction to Composition of Latin Verse. 12mo. 3*. Gd. Key, 2s. Gd,
Sheppard and Turner's Aids to Classical Study. 12mo. 5*. Key, Gs.
Valpy's Latin Delectus, improved by White. 12mo. 2*. 6d. Key, 3*. Gd.
Virgil's .Sneid, translated into English Verse by Conington. Crown Svo. 9*.

— Works, edited by Kennedy. Crown Svo. 10s. Gd.

— — translated into English Prose by Conington. Crown Svo. 9*.
Walford's Progressive Exercises in Latin Elegiac Verse. 12mo. 2s. Gd. Key, 5*.
White and Riddle's Large Latin-English Dictionary. 1 vol. 4to. 21*.

White's Concise Latin-Eng. Dictionary for University Students. Royal Svo. 12j.

— Junior Students' Eng.-Lat, k Lat.-Eng. Dictionary. Square 12mo. 5«.

Separatelv I '^^^ Latin-English Dictionary, price 3s.
^ ' I The English-Latin Dictionary, price it.
Yonge's Latin Gradua. Post Svo. ds. ; or with Appendix, 12«.

WHITE'S GRAMMAR SCHOOL GREEK TEXTS.

iEsop (Fables) & Palaephatus (Mvths).

32mo. 1*.
Euripides, Hecuba. 2t.
Homer, Iliad, Book I. Is.

— Odyssey, Book I. 1*.
Lucian, Select Dialogues, It.
Xenophon, Anabiisis, Books I. III. IV.

V. <fc VI. 1*. Gd. each ; Book U. It. ;

Book VII. 2t.

Xenophon, Book I. without Vocabu-
lary. 3d.

St. Matthew's and St. Luke's Gospels.
2s. Gd. each.

St. Mark's and St. John's Gtwpels.
Is. Gd. each.

The Acts of the Apostles. 2s. Gd.

St. Paul's Epistle to the Romans. I*. Gd.

The Four Gospels in Greek, with Greek-English Lexicon. Edited by John T,
White, D.D. Oxou. Square 32mo. price 5s.

WHITE'S GRAMMAR SCHOOL LATIN TEXTS.

Cassar. Gallic War, Books I. & II. V.

ds VI. 1*. each. Book I. without

Vocabulary, 3d.
Csesar, Gallic War, Books III. <fe IV.

9d. each.
Caesar, Gallic War, Book VII. 1*. Gd.
Cicero, Cuto Major (Old Age). 1*. Gd.
Cicero, La^lius (Friendship). 1*. ed.
Eutropius, Roman Hiptorv, Books I.

& II. 1*. Books III. & IV. 1*.
Horace.Odes, Books I.II.& IV. lj.each.
Horace, Odes, Book II L Is.Gd.
Horace, Epodes and Carmen Seculare.

It.

Nepos, Miltiades, Sim,on, Pausanias,

Aristides. 9d.
Ovid. Selections from Epistles and

Fasti. Is.
Ovid, Select Myths from Metamor

phoses. 9d.
Phaedrus, Select Easy Fables,
Phaedrus, Fables, Books I. & II. It.
Sallust, Bellum Catilinarium. 1*. Gd.
Virgil, Georgics, Book IV. Is.
Virgil, ^neid, Books I. to VI. Is. each.

Book I. witliout Vocabulary, 3d.
Virgil, ^neid, Books VU. to XU,

Is. Gd. each.

LONGMANS, GREEN, & CO., London and New York.

fart L 34. 6i.

THE FRENCH LANGUAGE.

Albit&'s How to Speak French. Fcp. 8vo. 5s. 6d.

— Instantaneous French Exercises. Fcp. 2j. Key, 2j.
Caasal's French Genders. Crown 8vo. 3j. 6d.
Oassal & Karcher'a Graduated French Translation Book.
Part II. 5j. Key to Part I. by Professor Cassal, price it.
Contanseau'8 Practical French and English Dictionary. Poet 8vo. Si. 64,

— Pocket French and English Dictionary. Square 18mo. 1*. 64,

— Premiftres Lectures. 12mo. 2j. Qd.

— First Step in French. 12mo. 2». 6<i. Key, It,
_ French Accidence. 12mo. 2*. 64.

Grammar. 12mo. 4j. Key, 8«.

Contanseau'a Middle-Class French Course. Fcp. 8vo. :—

Accidence, 84.
Syntax, 84.

French Conversation-Book, 84.
First French Exercise-Book, 84.
Second French Exercise- Book, 84
Contanseau's Guide to French Translation.
— Proaateurs et Pontes Fran^ais.

French Translation-Book, 84.
Easy French Delectus, 84.
First French Reader, 84.
Second French Reader, 84.
French and English Dialogues, 84.

12mo. Is. 64. Key 3*. 64.

12mo. is.

_ Precis de la litt^rature Fran9alse. 12mo. Zs. 64.

— Abr6g6 de VHistoire de France. 12mo. Is. 64.

F6val's Chouana et Bleus, with Notes by C. Sankey, MA. Fcp. Svo. Ji. M.
Jerram's Sentences for Translation into French. Cr. Svo. U. Key, 2i. 64.
Prendergast's Mastery Series, French. 12mo. 2s. 64.
Souvestre's PhUosophe sous lea Toits, by StiSvenard. Square 18mo. U. 64.
Btepping-Stone to French Pronunciation. 18mo. Is.
SU6venard'B Lectures FranQaises from Modern Authors, 12mo. 4i. 64 .

— Rules and Exercises on the French Language. 12mo. 3*. 64.

Tarver'a Eton French Grammar. 12mo. 6a. 64.

THE GERMAN LANGUAGE.
Blackley'B Practical German and EngU«h Dictionary. Post 8to. 8«. 64.
Buchheim'g German Poetry, for Repetition. 18mo. 1*. 64.
CoUis's Card of German Irregular Verbs. 8vo. 2s.
Fischer-Fischart'8 Elementary German Grammar. Fcp. 8vo. 2*. 64.
Just's German Grammar. 12mo. U. 64.

_ German RWing Book. 12mo. 3i. 64.
Longman's Pocket German and English Dictionary. Square 18mo. 2*. 64.
Kaftel's Elementary German Courae for PubUc Schools. Fcp. 8vo.

German Proae Composition Book.
First German Reader. 94.
Second German Reader. 94.

12mo. 2j. 64.

German Accidence. 94.

German Syntax. 94.

First German Exercise-Book. 94.

Second German Exerciae-Book. 94,
Prendergast's Mastery Series, German.
Quick's Essentials of German. Crown 8vo. 3i. 64.
Belas's School Edition of Goethe's Faust. Crown 8vo. It.
— Outline of German Literature. Crown 8vo. ■U. 64.
Wirth'a German Chit-Chat. Crown 8vo. 2j. 64.

LONGMANS, GREEN, & CO., London and New York.

94.

Spottistcoode <t Co. Prinfert, yrv-ttrert Square, London,

V ■

COLUMBIA UNIVERSITY

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