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

... . Logic, by Richard F. Clarke, S. J. No w iin |»F-etTtyie*i. 
London, New York, [etc.], Longmans, Green, and Co.. ig^-lBSdm 

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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 




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 



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- 


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- 



sentation of what Scholastic Realism really 


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 





> 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 

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 





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 


dfr ^ -.Tlii^ -^ujuj 



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. 



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 









Simple Apprehension . 

VII. Simple Apprehension {continued). 

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










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 


Chapter I. 


-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 

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 











VyV/l' •» x-x^ A w. 



^ 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 

. 461 

The Scholastic Method 



Part I. 



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 





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 

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.). 


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 


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 


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. 


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 


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- 



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 


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 



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 



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 



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 



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. 


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. 



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 





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 

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 

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 

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^' 

^V*V.~™.- ■- 'V* '-"^*4if^* 






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 



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.) 



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 





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;^ 



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, 





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- 



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. 



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 

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 



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 



are, there are one or two important points to be 

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 



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. 



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- 

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 







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 


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 



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. 



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 



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 



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 





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 



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 

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 



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. 


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 



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, 





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 




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 


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. 



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. 





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 




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- 


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 




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 logician clearly to discern in what the difference 


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. 



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 

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 




a posteriori, are also divided into analytical and 


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 


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 


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 




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 

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 


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. 




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 


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. 



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- 

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 

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. 



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 



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 



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. 



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 

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 



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- 



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' 



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. 


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 






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 




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 

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 







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* 

\ « 



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 


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. 



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. 







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 



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. 



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 






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. 



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. 




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 


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. 






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 


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, 



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! 




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 



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, 




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. 





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 



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 


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. 






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 

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. 



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 
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 



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 

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, 


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 



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 


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- 



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 


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 




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 



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- 

6. Imagination, which paints upon the inner 



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 



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 



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 



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 



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 



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 



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 



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 





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 


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 






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 



^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 



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- 





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. 






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 

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 


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 



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. 



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. 



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. 



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 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 



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. 



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 





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 



■;^^^^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. 



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 


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 




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 



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. 





""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 




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. 



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 



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 



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- 



'^^;^^^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 



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 





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 



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 



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. 



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 



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 



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 a name .and as «e "n 
prdiiate this name of all and each of the resembling effects, it 
constitutes them into a class." 



"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- 



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.) 



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 



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 



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. 



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 



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, 







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- 






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 

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 

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 




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 



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 




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- 


^'^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 


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." 



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. 




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 





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 



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 




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." 





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- 

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 



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 



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- 

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 





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 


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 





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 


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 






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. 






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 




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. 



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 



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 



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 


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 

1 84 





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 




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 


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 



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. 

exists in itself 

Inherent in the 

exists in something else 

not inherent in the 

Quantity, Quality, Relation existing as a merely adjacent 

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


Time when 
it exists 

Place where Position 

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 



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, 



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 



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 


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 



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- 

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 



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 



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 



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 



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* 






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 





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, 





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- 






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 


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. 





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- 






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 






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 






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 





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 



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 



impressions will never enable me to answer cor- 

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 


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 





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 

We also transgress this rule if we define by a 






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 


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. 




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 



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 


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 




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. 



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 



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 



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 



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 



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. 






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 






I I , 

Into essential Into integral 
parts. parts. 

Division of a 

genus into its 


logical Metaphysical 
I or Definition. 

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





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. 







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. 

\ . 





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 



departs not a little from the strict and proper 

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 



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 



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 



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 




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 



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. 



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. 


Part II. 




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. 



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 



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 





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 


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 




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 


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 



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 

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 



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 




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 

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. 





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 

Hence there are three requisites for an a prion 


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- 




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 


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 


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 


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 



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." 



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 





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 


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 

» 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. 






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 


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 


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 




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 

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- 






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 





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 




1 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- 

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 


(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 

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. 




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 



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. 




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 



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 




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 



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 


» Asserit A, negat E, venim generaliter ambae. 
Asserit I, negat O. sed particulariter ambo. 


r I 



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- 



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- 




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 ' 


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^^^^^ 






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 


" 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, 



&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. 



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 


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 



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 


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. 



A Conditional Proposition consists of two parts : 

1. The antecedent or condition : // trade is 


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 

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, 




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 



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. 



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. 




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 


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) 




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 



I Some schoolboys are not mischievous . (O) 

All schoolboys 
are mischievous. 


No schoolboys 
are mischievous. 

^^ ^ 










Some schoolboys 
are mischievous. 


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 


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 





(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 

2. Contradictories can neither be true together nor 
false together, but one must be false and the other 


{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- 

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- 


boys, and both my propositions may be perfectly 


(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 



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 
or, None but men of ability rise high in their profession. 

tf' w " i m i f-ite --*-* 





No animals that do not stickle their young are 

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 


(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- 

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 


Some not-polite beings are costermongers ; 
Some who are not polite arc costermongers. 


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 



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. 


Part III. 




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. 



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 



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 


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. 





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 



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. 



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 



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. 



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 



be. We shall at present speak only of the Simple 

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). 




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 


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. 




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 


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 



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 


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- 




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 


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- 


•. Some statesmen are tyrants ; 
but the fact that all tyrants as well as some states- 



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 

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 




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 



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. 



^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, 


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 



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. 


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 



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 : 






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 : 








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. 



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." 




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. 



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 

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 





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 


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 




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 •" 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 



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. 







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 

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 


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. 



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 



?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 









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. 



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. 



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- 

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 





--^-— — — 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 

rr:fXrr;r;Sucea to 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 





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 



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. 



W . 



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 

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 

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 






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 

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 

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. 






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 ; 






// / 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- 
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 ; 




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. 


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 



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 

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. 



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 





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 

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 

.\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 







of our second syllogism and the conclusion just 
drawn as its minor. 

All who appreciate the value of money make good 

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 

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. 





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 





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. 




(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- 
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. 



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 




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 



reason why the kings in question had remarkable 
gifts, or the flowers in question have one perianth 


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 

A II my friend's books are books of travel in China and 

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 — 





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 


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 







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^ ' 





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 

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. 




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 

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. 





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- 

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 




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 




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 






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 




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 



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 





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 : 


** 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 

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 




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 ; 


** 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 




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 



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 


Vegetus consueta ad munia surgo. 

Here I have the Method of Difference. At first the 



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 


*' 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." 



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 



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 : 


" 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 


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. 



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 


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 





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 






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. 






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 

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. 






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 






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 


A and B are both X ; 

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, 






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. 







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-:'^-- 





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 

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- 

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 

(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 : 





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 

» 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 


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 





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 


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 


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 







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 


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 






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 


ii t 




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 







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 

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 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 






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- 

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 




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 

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 





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.— 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 







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 

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 

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. 

// is impossible to be in two places at the same 

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 

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 






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 
.*. 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 
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- 

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 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^^^ ^ 



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. 



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^ 


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 


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 . 



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 

Every hasty induction involves the Fallacy of 

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. 



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 





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; 


,. 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 






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- 




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 



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, 



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- 



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)- 




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- 

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 

(i) Argumentum ad hominem, or appeal to the 



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 





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 





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 




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 

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 



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 



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. 



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 



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. 


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 





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 





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. 


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- 





vidual things, and by the diminution of the necessity 
of watching effects and judging from results, and 
from them ascending to axioms, principles, maxims, 


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 



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. 





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 






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 




■.'■S'-l. 'Hi Elll'iil* 




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 


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 





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 



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 





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- 






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. 






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- 







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- 

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 



Abstraction 102—105. 
Accent, fallacy of 443—445- 

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 

Amphibology, fallacy of 43° 

Analogy 407— 4^1- 
Analysis, when used 471 - 


idealization, incapable of 1 10, 

imagination of 98, 99, iw— 

thinking powers of 47-7. 
Anselm (St.) on Nommahsm 

ANTECEDENTS of propositions 

289, 307. ^ _ 

ANTINOMIES 35, 36, 139- 

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 

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— 

process of 98-100, 102— 

105 ; 
sensation, its relation to 100 ; 

sensible perception, its rela- 
tion to lOI.' . 

views on, . r 1 

Aristotle's reduction of syl- 
logisms 339 «• ; . . 
certainty, degrees of 407, 

468 ; 





contradiction, principle of 

enthymemes, 356, 357 ; 

eternity of creation, 77 n. ; 
experiment, minute 365 ; 
fallacy, 449 ; 
figure, first 33^ «• ; 
induction 378 ; 
intentions, second 167 ;/. ; 
knowledge perfecting nature 

logic as a science 24 n ; 

universals 164 ; 

unityof human nature 161 ;/. 


a non causa pro causa 453, 

ad hominevt 450 — 452 ; 

ad populum 452 ; 

a non tali pro tali 455 ; 

a non vera pro vera 454, 

adverecundiam^ 452, 453 ; 

conclusion, synonym for 95 ; 

logic treats of 9 ; 

reasoning expressed by, 95, 

Aristotle on 325 ; 

synonym for reasoning 90 — 
Aristotle, his views on 

Argumentation 325 ; 

art 17 «•, I9> 20; 
categorical, meaning of word 

categories, the 189 ; 
certitude, degrees of 467 ; 
conversio per contra 342 ; 
deduction 400 ; 
dialectic, meaning of word 

dictum de omni^ the 316 «. ; 
enthymeme, the 356 — 358 ; 
epichirem, 359 ; 
example, definition of 402 n. ; 
experiment, minute 365, 386; 

induction, complete 366 

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 


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. 

idea of, underlies all ideas 

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»- 


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»- 


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. 

fallacy of 439; 44© ; 

synonym for judgment 249. 

of subject and predicate 282 

-287 ; 

whole of 281. 
Conception, see apprehen 

sion. , 

Concept, see idea. 


Locke's theory of modern 

1 52 w. ; 
refutation of modern I2j— 

129,132—139; - ^ 
universals, doctrine of 144— 
147, 157-158; see also 
Conclusion, ^ 

argument, synonym tor 95 , 

truth of 3ic>-3i2- . -. r 

Condition (special), fallacy ot 

446 — 448. 
Consciousness 100. 


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. 
as judgments 252 ; 
confused with opinions 252 





definition of 262 ; 

its relation to propositions 
Creation, eternity of 77 n. 

induction, its relation to 370, 

moderns' estimate of 364, 

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. 

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, 

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, 

moderns' neglect of 316, 365. 

Difference, Mill's method of 

Differentia Specifica 172, 

i73» 183. 
Dilemma, 353—356. 

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. 




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, 

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. 


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. 

of subject ^f! predicate, 2»i 

whole o) Si. 


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, 

(c) a dicto simpliciter 

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— 

(13) plurium interrogantium 

Falsity 42. 
Figures of Speech, fallacy 

of 444 ; 
of syllogism 324—339- 
Formalism 412. 

Galen, inventor of fourth figure 

Galileo, his condemnation 

253, 400. 
Genius, how it reaches con- 
clusions 406. 

definition of 171 ; 






subaltemate 176 — 179; 
suitunum 176^ 178, 187. 
GOUDIN on the fourth figure 

Grammar, its relation to logic 

Habitus a predicament 188 

— 9- 
Hamilton (Sir W.), his ideas 

apprehension or conception 

123— 129, 132— 139, 146 «.; 
concepts 46 — 48, 123 — 129 ; 
contradiction (principle of) 

definition 46, 47 ; 
identity (principle of) 45— 


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. 

certitude confused with 253, 

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, 

Mill's nominalistic view of 

phantasms differ from 105 


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, 

truth, its relation to, 53. 
Ignorance, definition of 418. 
IgnoratioElenchi 448—459. 
Image, intellectual, see ideas ; 

sensible, see phantasms. 
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. 
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 


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, 


Kant, his doctrine on, 
antinomies 35, ^39; 
contradiction (principle ot) 

synthetical propositions 61 — 
70, 260. 
Kinds 186, 187. 

explicit and implicit 68—70; 

perfecting nature 305 ; 

relativity of 127, 128. 

Language, relation to thought 

and logic 3, 4,96, 97- 

of Association 469, 470 ; 
a posteriori and a prion 54, 

384, 385 ; . ^.. 

physical, certainty of :,85, 

see also principle. 
Liberators on, 

incomplete induction, 379 '•> 
on genius and its conclusions 

LOCKE a conceptualist 152 n. 

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 ; 





formal and applied 8 — 14, 23, 

382, 3^3 ; 
importance of i, 2, 14 ; 
induction, its relation to 380 

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 

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, 

Utens et Docens Logica 22 ; 

word, meanings of the 3, 27, 

Mansel (Dean) on induction 
on principle of contradiction 


on theology 35. 
Memory, sensible, loi. 
Metaphor, 22 i, 222, 409 — 41 1. 

being, foundation of 41, 42 ; 

logic, its relation to 8 ; 

province of 8. 

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 — 

a priori and a posteriori 475 

scholastic 475 — 483 ; 

synthetic and analytic 462, 
Mendive on incomplete in- 
duction 379. 

principle of excluded 79, 80 ; 

of syllogisms 314, 315. 
Mill (J. S.), his doctrine of, 

causation and causes 74 — 76, 

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 — 

principles (fundamental) 80 — 


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 — 

Anselm (St.) on 148 ; 
apprehension according to 

modern 129 — 139 ; 
kinds according to modem 

mediaeval and modern 148 ; 

refutation of modern 129— 

^39; , ,. „ 

sensationalism, its relation 

universals according to 140 

—150, 158; 
see also Mill. 


definition of ^\l, 418 ; 
exalted into convictions 252 

Opposition of propositions 293 


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- 

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, 


account of (detailed) 171— 

account in general 168— 171 ; 
predicaments contrasted with 

190 — 192. 

account of 187—190;^ . . 
predicables contrasted with 

190 — 192. 
definition of 262 ; 
distribution of 276—279 ; 
propositions, its relation to 

266, 267 ; 
quantification of 283 — 287 ; 
word, its ambiguity 263. 
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. 
description of 425— 43' *» 
in a premiss 359- 





foundation of all 32 — 35 ; 

direct or positive 31, 32 ; 

indirect or negative 31. 
Property, a predicable 174, 


affirmative and negative 267 

analytical and synthetical 58 

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 — 

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 — 


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 

Quality, a predicament 188, 

Quantification of pro- 
positions 272—279, 283 

Question, fallacy of 459, 460. 

Quiddity, definition of 5. 

QuiNTiLiAN on Enthymeme 

Realists, 158—160. 
Reason, law of sufficient 77 — 

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, 

a posteriori and a prion 309, 




Reduction of syllogisms, 
per contra and per impos- 

sibile 342—345 •» 
methods of 339—347 ; 
particular propositions 346, 

Relation, a predicament 188, 

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— 


analytic and synthetic 463— 

.■\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- 

causes according to 396, 397 ; 

Nominalism, its relation to 

Similarity 136 n. 

Socrates, on induction 404- 

Sophism 414, 415, 433- 
Sorites 360—363. 

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' 

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. 

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, 

dilemma 353—356 ; 
disjunctive 35^>— 353 ; 
enthymeme 356—359 ; 
epichirem 359, 360; 
figures of 324—339 ; 
foundation of 316, 339i 379» 

inductive 368-371, 379- 

I matter of 4 1 2— 431; 





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 — 


Tautology, in propositions 

Sh 52. 


apparent contradictions of, 
explained 40 ; 

Mansel's idea of 35, 36 ; 

unchangeable 481 — 483. 

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, 

operations of 93 ; 

psychology, its relation to 7, 

relativity of 113, 114, 127— 

uses of the word 4—7. 
Time, a predicament 188, 189. 

Tongiorgi on incomplete in- 
duction 379. 
Transcendentals 168. 
Truisms 316. 

formal and material 272 ; 

Hegel on 479 ; 

in itself and as known to us 

identity (principle of), its re- 
lation to 53 ; 
inductive spirit, its influence 

on 365, 477—482 ; 
known to us and in itself 41, 

logic, its relation to 9— 14»- 
204, 205, 269—272, 382, 

logical 270 ; 

material and formal 272 ; 
metaphysical 41, 42 ; 
necessary 1 1. 

Uniformity of nature's action 

80—87, 91- 

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. 

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^ 

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. 

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 






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