71
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Southern Branch
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Los Angeles
Form I
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This book is DUE on the last date stamped below
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OCT 7 1925
AUG 121950
Form I. 9-5///-7,'23
LOGIC
OR THE
ANALYTIC OF EXPLICIT REASONING
BY
GEORGE H. SMITH
AUTHOR OK "ELEMENTS OF RIGHT AND OF THE LAW," "A CRITICAL
HISTORY OF MODERN ENGLISH JURISPRUDENCE," "THEORY
OF THE STATE," AND OTHER WORKS
i3331
'QtNAM'S S
G. P. PUTNAM'S SONS
NEW YORK AND LONDON
fnucfcerbocfcer prees
1901
COPYRIGHT, 1901
BY
GEORGE H. SMITH
Che Ytnicherbocfcer press, flew
v PREFACE
IT is well known to those conversant with
the current literature of Logic that recent
logical theories diverge widely from the old
Logic of Aristotle and the Schoolmen, and no
less widely from each other. From this it hap-
pens that, under the common name of Logic,
we have many doctrines essentially different
from each other ; and the student who desires
to enter upon the study of the subject is thus
confronted with the preliminary problem of
determining under what name the true Logic
is to be found. Nor in this case can he expect
much help from his instructors; who, like the
rest of the logicians, are hopelessly at a loss.
Whether he shall study Logic whatever may
be his wishes and his determination must
therefore be a matter for chance to determine.
And, even should he be so lucky as to light
on a place where something like Logic is
taught, it will probably be taught in so muti-
lated a form and so mingled with extraneous,
and even inconsistent matter, that it will be
IV PREFACE
impossible for him to understand it or to ap-
preciate its utility. Hence, if the plain truth
is to be told, Logic, in the true sense of the
term, is no longer taught or learned anywhere;
but has become a lost art.
But while the logicians of the day are thus
at variance among themselves, there is un-
fortunately one point in which they agree
with each other, and also with Whately and
others of the older logicians. This consists in
the opinion that Logic is a purely formal
science, and as such concerned only with the
forms, and not with the matter or content of
language or of thought; or, in other words,
that it does not deal with what is thought or
expressed, but with the forms of the thought
or expression only. From this it must follow
if the view be accepted that Logic, except
merely as an improving mental exercise, can
be of no practical utility; and this indeed is
commonly asserted and always implied in the
Logics of the day; which, though essentially
different in other respects, agree in this. And
from this again it must follow as on this view
was irresistibly argued by Locke, Stewart,
Reid, and others that the subject is unworthy
of the serious attention of rational men ; which,
on the premises assumed, has indeed come to
be the verdict of the common sense of man-
kind. Thus the student is discouraged from
PREFACE V
the study of the subject not only by the con-
fusion reigning over it and the almost insur-
mountable initial difficulty of recognizing the
true Logic among so many pretenders, but
by the conviction impressed upon him by an
irresistible argument and by the practically
unanimous teachings of logicians, that Logic
cannot be put to any practical use.
The view taken of Logic in this work is dif-
ferent. It is what I conceive to be the ancient
and orthodox view, that Logic has to deal with
the matter as with the forms of thought and its
expression ; that it embraces in its scope every-
thing that touches the right use of words, as
instruments of reasoning, or, in other words,
the whole subject of explicit reasoning or ratio-
cination ; that it is the science fundamental to
all others and essential to all who, in the search
after truth, would pass beyond the mere evi-
dence of their senses; that, in its educational
aspect, it is not only an essential part, but the
very foundation of rational education ; and
finally that, in use, it is indispensable to the
rectitude of thought and of life. Hence, of
all branches of learning, I believe it to be of
the largest practical utility to man, and that
all the learning of the day cannot compen-
sate for its loss; and also that its decadence
in modern times has been one of the great
calamities of mankind. All this I attempt to
vi PREFA CE
establish and to illustrate practically in the
following pages; to which I must refer for
the complete proofs; but perhaps something
towards this end may be effected in advance
by explaining briefly how the work came to be
written.
In the investigation of Jurisprudence, Poli-
tics, and Morality generally to which my
studies have been principally devoted two
important facts were forced on my attention,
that seem to establish my present thesis:
(i) The first of these was that the prevailing
errors in the theory of Politics, Sociology, and
Morality, and the Moral Sciences, or Science
of Human Nature, generally, have their
sources, almost always, in merely logical fal-
lacies, and may be readily refuted by the ap-
plication of familiar logical principles; all of
which will be practically illustrated in treating
of the fallacies. Here, then, I think, we have
a practical proof of the indispensable utility
of Logic, and the consequent refutation of the
error that it deals only with the forms of
thought or expression. For it is known to all
logicians that the most serious and pernicious
of the recognized fallacies are those that relate
to the matter expressed in language, and are
therefore called the material fallacies; which
by logicians generally are admitted into Logic,
but, as it were, on sufferance only.
PREFACE vii
(2) The second fact I learned was that,
though it is impracticable to refute such errors
otherwise than by the application of logical
principles, yet owing to the logical decadence
of the age, and the general disuse of Logic,
this mode of refutation is unavailable. Hence
under existing conditions, there is no practical
means of stemming the tide of moral and politi-
cal heresy with which, with increasing violence,
mankind is being afflicted; and from this it
follows, as a necessary inference, that the first
step towards reform of doctrine, or life, in any
direction, must be a revival of the study and
use of Logic. My work therefore is the result
of a profound realization of this practical neces-
sity, and of the imperative demand thus result-
ing. Nor however interesting the theory of
Logic may have been to me have I ever lost
sight of what I conceive to be the most import-
ant aspect of the subject, namely, its supreme
practical utility.
Generally, the object of the work is to vindi-
cate, as against modern innovations, the old or
traditional Logic. This constitutes a perfectly
definite body of doctrine, rivalling in accuracy
and in demonstrative force the Geometry of
Euclid. Nor are there wanting treatises in
which its theory and application are, on the
whole, well explained, as, e. g., notably
Whately's work; which, notwithstanding some
Vlil PREFACE
manifest defects, still remains, not only the
best, but the only elementary exposition of
Logic, in the English language, that can be
recommended to the student. But there are
many reasons why a mere reproduction of the
older works would be inadequate for our present
occasions, to some of which I will briefly ad-
vert.
The first of these relates to the error, already
considered, that prevailed with many of the
old logicians, as with the new, that Logic is
concerned only with the forms, and not with
the matter of thought, or its expression. For,
though this defect was supplied by the old
logicians, at the expense of their consistency,
by their admirable exposition of the doctrines
of Definition and of Classification and Division
and of the Term generally, and of the Material
or so-called Non-logical Fallacies, yet their
theory of Logic remained incomplete, and
Logic was thus mutilated of some of its most
vital parts.
Again, the searching investigation to which
the old Logic has been subjected by modern
logicians, though its general effect has been to
vindicate its substantial truth and to re-estab-
lish it on a broader and firmer basis, has yet
resulted in several additions to logical doctrine,
to which it is essential that the attention of the
student should be directed. Hence, while one
PREFACE ix
of the principal objects of this work is to vindi-
cate the truth and the supreme utility of Logic
as anciently conceived, it is also contemplated
to supply the radical defect I have alluded to,
and, at the same time, to incorporate with the
old Logic the approved results of modern re-
search ; some of which are of great importance.
It remains to add a few words as to the
method and style with which the subject of
the work is treated. Logic is admittedly a
demonstrative or apodictic doctrine, and should
therefore be treated by the method appropriate
to subjects of that nature. This consists in the
accurate formulation of our premises, and in
reasoning rigorously from them, as in geome-
try. But this method demands the use of
a style altogether different from that in com-
mon use; which may be called the popular or
rhetorical. For it is the peculiar characteristic
of the logical style that it must be accurate or
aphoristic, i. e., that it must express the exact
truth without any admixture of error. For
the same truth holds good in ratiocination, as
in nature generally, that hybrids are unprolific;
and hence the slightest admixture of error in
our premises will render them altogether use-
less for logical inference. Our method will
therefore demand the exact analysis of the
terms we use and the formal statement of our
propositions; which to the general reader is
X PREFACE
distasteful. For while the logical style ad-
mits, and even requires, great brevity of ex-
pression, so that, in general, volumes of
ordinary disquisition may, by means of it, be
compressed into a brief space, yet it demands
a degree of attention and independent thought
that only a few highly trained or exceptionally
gifted minds are willing to give, or perhaps
without great exertion are capable of giving.
But this is nevertheless essential to the fruitful
study of Logic, as of apodictic science gener-
ally. There is no royal road to Logic any
more than to Geometry.
The best type of this style is found in the
Mathematics, and especially in the writings of
Euclid and the geometers, whose style and
method I have sought to emulate, with what
success remains to be judged. I trust, how-
ever, I may, without vanity, say of the result,
with Hobbes, that while " there is nothing I
distrust more than my elocution, nevertheless
I am confident, excepting the mischances of
the press, it is not obscure."
GEORGE H. SMITH.
Los ANGELES, February 26, 1900.
CONTENTS
INTRODUCTION OF THE FUNCTION OF
LOGIC i
BOOK I
THE ANALYTIC OF RIGHT REASONING
CHAPTER I
RUDIMENTARY NOTIONS .... 23
CHAPTER II
DOCTRINE OF THE TERM
I OF THE NATURE OF THE TERM
II OF THE SEVERAL KINDS OF TERMS
III OF THE ANALYSIS OF TERMS
CHAPTER III
DOCTRINE OF THE PROPOSITION .
I RUDIMENTS OF THE DOCTRINE .
II SEVERAL THEORIES OF PREDICATION
III OF THE PREDICABLES
IV OF THE RELATIONS BETWEEN TERMS
33
33
40
44
5 1
55
61
64
xi
Xll CONTENTS
CHAPTER IV
PAGE
DOCTRINE OF THE SYLLOGISM ... 74
I RUDIMENTS OF THE DOCTRINE ... 74
II THE PRINCIPLE OF SUBSTITUTION . . 77
III OF MATHEMATICAL REASONING ... 85
CHAPTER V
SUMMARY OF THE TRADITIONAL LOGIC . 91
I OF THE TRADITIONAL LOGIC GENERALLY . 91
II THE TRADITIONAL DOCTRINE OF THE PROP-
OSITION ...... 92
III THE TRADITIONAL DOCTRINE OF THE SYL-
LOGISM > ... 104
BOOK II
APPLIED LOGIC
PART I
OF THE METHOD OF LOGIC
CHAPTER VI
OF THE LOGICAL PROCESSES . . . 123
CHAPTER VII
THE RULES OF LOGIC 137
I OF THE RULES OF LOGIC GENERALLY . 137
II RULES OF JUDGMENT .... 142
III RULES OF INFERENCE .... 145
CONTENTS Xlll
PART II
DOCTRINE OF THE FALLACIES
CHAPTER VIII
PAGE
DEFINITION AND CLASSIFICATION OF FAL-
LACIES ....... 149
CHAPTER IX
FALLACY OF NON-SIGNIFICANCE, OR NON-
SENSE 157
CHAPTER X
FALLACY OF FALSE DEFINITION . . . 168
CHAPTER XI
ILLICIT ASSUMPTION OF PREMISES (Petitio
Principii] . . . . . 175
CHAPTER XII
MISTAKING THE ISSUE AND IRRELEVANT
CONCLUSION (Ignoratio Elenchi} . .188
CHAPTER XIII
ILLICIT CONVERSIONS ..... 198
CHAPTER XIV
ILLICIT SUBSTITUTIONS OF TERMS . . 200
CHAPTER XV
EQUIVOCATION 203
CHAPTER XVI
THE TRADITIONAL DOCTRINE OF FALLACIES. 210
I ARISTOTLE'S CLASSIFICATION OF FALLACIES . 210
II FALLACIES in Dictione (EQUIVOCATION). . 214
III OF THE FALLACIES extra Dictionem . .219
LOGIC, OR THE ANALYTIC OF
EXPLICIT REASONING
INTRODUCTION
OF THE FUNCTION OF LOGIC
i. THE THEORY OF KNOWLEDGE, A DE-
PARTMENT OF THE THEORY OF OPINION.
The problem of the origin and nature of
knowledge has occupied the attention of the
philosophers for something over twenty-five
centuries without much progress toward solu-
tion. This perhaps results from the fact that
the problem itself is but part of a larger prob-
lem" that should be first considered; for know-
ledge is but a species of opinion, which may be
either true or false. Hence the inquiry as to
the origin and nature of opinion must be the
first in order of investigation. Nor until this
investigation has been made will we be pre-
pared to determine the specific characteristics
2 LOGIC
by which true knowledge is differentiated from
opinion in general.
2. KNOWLEDGE BUT VERIFIED OPINION.
Men generally confound this distinction, and
regard all their settled opinions or beliefs as
knowledge. This is not merely false, but ab-
surd ; for not only do the opinions of men
differ, but the opinions of the same man are
often inconsistent and contradictory ; and
some, it is clear, must be false. And this is
apparent also from the nature and generation
of our opinions. For, in general, these come
to us not from any conscious process, but
naturally and spontaneously and from many
sources, as, e. g., from testimony, from author-
ity, from inaccurate observation or careless
reasoning, and even largely from mere pre-
judice or bias. Hence, familiar to us as our
opinions are, their origin in general is as un-
known to us as were anciently the sources of
the Nile; nor have we any just notion of the
grounds on which they rest, or of the nature
and justice of their demands on our belief.
Hence, until some means of verifying our
opinions be found and applied, we can have
no assurance of their rectitude. The first step
in Science or Philosophy must, therefore, be
to distinguish between verified and unverified
opinions. The former constitutes true know-
ledge or science ; the latter though it is in
INTRODUCTION' 3
fact the stuff out of which most of the current
philosophy is woven has no just pretension
to the name.
3. THE SOURCES OF OPINION DISTIN-
GUISHED. With regard to the source of our
opinions, we must distinguish between those
derived from our own experience and those de-
rived from the experience of others; of which
those derived from the common experience of
mankind are the most extensive and important.
The last have come to us by means of lan-
guage, which may therefore be said to be
their source; nor could they otherwise have
been transmitted to us. The former constitute
comparatively speaking but a small and in-
significant part of the sources of the mass of
our opinions. For the greater part of what
we know, or think we know, is not original
with us, but has come to us from others by or
from language. The distinction, therefore, is,
not between opinions derived from experience
and opinions not so derived, for it may be
said all opinions that are true, or rather that we
know to be true, are derived ultimately from
experience, 1 but in the manner of their deri-
vation ; the one class being those opinions de-
rived by us, each from his own experience, the
other, those derived not directly from our own,
1 The distinction made in the text is of fundamental import-
ance. The necessity of a constant resort to experience as the
4 LOGIC
but from the experience of others from or
through language.
4, OF LANGUAGE AS A RECORD OF
HUMAN THOUGHT. Of the two classes of
opinions, the latter is infinitely the more ex-
tensive in scope and important in character;
for all that men have seen or thought or felt
has been expressed, and is thus preserved to
us in language; which thus constitutes, as it
were, the record of the results of all human
experience and reason. Here, therefore, is to
be found the principal source of our opinions,
verified and unverified that is to say, not
only of our opinions generally, but of our
knowledge or science. But, regarding lan-
guage as a record and source of opinion, we
must distinguish between the forms in which
opinion is embodied in it. These forms may
be described, with sufficient accuracy for our
purposes, as consisting in terms, propositions,
and syllogisms. But of these the syllogism in
its end and effect is but the reduction of two
ultimate source of our knowledge cannot be too strongly in-
sisted upon. But to construe this proposition as referring to
each man's individual experience is to fall into an error of the
kind called by Bacon " Idols of the Den" ; and thus to fall
under the reproach of Heraclitus " that men search for know-
ledge in lesser worlds, and not in the greater or common
world," i. e., the great world of the common notions of man-
kind, derived from the universal experience and embodied in
the common language. (Nov, Org., bk. i., aph. xliii.)
IN TROD UC TION 5
propositions to one, and, in this connection, is
of interest to us merely as exhibiting one of
the modes in which opinion is.formed. It will
be sufficient, therefore, to distinguish the term
and the proposition as the two forms in which
opinions, or the elements of opinions, are em-
bodied. But the proposition is itself of two
kinds, differing essentially in nature. In the
one if not an inference it is simply the state-
ment of a relation intuitively perceived to exist
between two terms or names, that is to say,
between the notions or concepts denoted by
them, as, e. g., where we say, " Bodies are
affected by gravity," or " Two islands cannot
be contiguous," or " Fishes live in the sea,"
or " Man is rational"; in the other, it is a
statement of a relation between terms, not in-
tuitively perceived or logically inferred but
assumed to be true from testimony or other-
wise, as, e. g., where we say, '' Brutus was
one of the murderers of Caesar," or " Hannibal
was conquered by the Romans." The former
- in accordance with the definitions used
throughout this work will be called a judg-
ment ; the latter, an assumption. In the former
case the truth of the proposition is involved in
the meanings of the terms, i. e., in the nature
of the concepts or notions denoted by them ;
and this is true also of all inferences, or propo-
sitions inferred from judgments. So that with
6 LOGIC
relation to all such propositions, whether in-
tuitively perceived or inferred, the original
sources of opinion are the notions or concepts
in which they are involved. We may therefore
distinguish, as the two sources of opinion af-
forded us by language, (i) the notions or con-
cepts expressed in terms, and (2) assumptions,
or assumed propositions.
With the truth of the latter, or the evidence
on which they rest for credence, Logic is not
concerned; nor is it concerned with them in
any way, except as premises from which to
argue ; or to reject them as such, if they can be
shown by logical processes to be false. But
where such propositions are justified by experi-
ence, and come thus to be generally received,
the result universally, or almost universally, is
the generation of a new notion, i. e., the
notion of the relation perceived between its
terms; which is either expressed in a new term
or added to the content or meaning of an exist-
ing term; and this, indeed, to the extent it is
attainable, is the end of science, and, in a per-
fect language, were such attainable, would
be the general result. Thus the general pro-
gress of human thought consists largely in the
conversion of propositions into terms or names
denoting the relations expressed in them ; and
hence, generally, in terms are contained many
propositions, as, e. g., in " gravity," ' justice,"
INTRODUCTION /
etc. in the former of which is contained a large
part of Physical Science, and in the latter nearly
the whole theory of the State. In this way the
stock of the common notions of mankind is
continuously accumulated, until it may be said
that the great part of all that has been achieved
in thought by men is expressed or implied in
terms or names. Here,' therefore, are to be
found the principal sources of opinion ; and,
compared with these, opinions embodied in
propositions that cannot be, or have not been,
reduced to single notions are limited in ex-
tent, and of secondary importance. And this
is especially true with regard to the Moral
Sciences; under which name I include all the
various branches of the science of human
nature; for in these sciences it is impossible
to conceive of any rudimentary notion or
thought that has not, in the long history of
man, been conceived by the human mind and
embodied in terms. With reference, therefore,
to all that has been achieved in science or in
popular thought, the sources of all our opin-
ions, verified and unverified, that is to say,
of all our knowledge or supposed knowledge,
are to be sought in language, and, prin-
cipally, in the notions expressed in terms or
or names ' ; and consequently, with reference to
1 If the reader will thoroughly apprehend this proposition,
he will find in it the key, not only to Logic, but to all Phil-
8 LOGIC
knowledge or supposed knowledge of this kind,
our method must consist in the study of lan-
guage.
5. RECEIVED OPINION DISTINGUISHED
FROMTRUE KNOWLEDGE. Our opinions, how-
ever, are derived from this source in two ways,
which must be distinguished : namely, by tradi-
tion, by which our opinions are delivered to
us ready made in the form of propositions,
and by reasoning upon the notions embodied
in terms. For the thought contained in lan-
guage is embodied in two ways, namely,
explicitly, in the form of propositions, and
implicitly, in terms;, and of propositions, as
we have seen, many are but explicit state-
ments of what is implied in the notions
osophy. The elements of knowledge, so far as already
achieved, we repeat, are the notions or concepts incarnate in
terms ; and these must always constitute the principal source
of our knowledge ; for, in comparison with the knowledge
thus expressed or implied, the original contributions of the
most gifted of men to the common stock must be inconsider-
able. Nor can any such contribution to the knowledge of
mankind be regarded as completely achieved until embodied
in definite terms ; and hence the formation of such terms, or,
what is the same, of the notions embodied in them, must be
regarded as the end of scientific discovery. There is, there-
fore, nothing paradoxical in the assertion of Condillac that
" Science is but language well made." Hence, to repeat what
has been said, it is to the common stock of notions thus gradu-
ally accumulated by mankind and permanently secured by ex-
pression in terms, that we must resort as the principal source
of all knowledge or science. See Appendix A.
INTRODUCTION 9
expressed in terms, as, e. g., in the prop-
osition, " All bodies are affected by grav-
ity," etc. With reference to these, though
they may be true, their mere reception cannot
be said to constitute knowledge; but in the
proper sense of the terms we can know them
only when we have reasoned them out for our-
selves from the primary notions in which they
are involved; as, e. g., in the Mathematics,
where we cannot be said to have mastered a
theorem until we are able to work it out from
the premises by the exertion of our own powers
unassisted by memory. With reference to all
that has been achieved in thought, therefore,
our method in the pursuit of knowledge must
begin with the apprehension of the notions
already formed by men and embodied in terms;
and this involves the testing of those notions
for ourselves by comparing them with the
realities to which they are supposed to corre-
spond.
$ 6. THE PHYSICAL AND MATHEMATICAL,
DISTINGUISHED FROM THE MORAL SCIENCES.
-These observations apply equally to the
Physical and Mathematical as to the Moral Sci-
ences ; but there are differences, partly essential
and partly accidental, between the two classes
of sciences, which must be adverted to ' :
(i) In the Physical Sciences and in the
1 See Appendix B.
IO LOGIC
Mathematics, technical terms expressing ac-
curately the concepts or notions involved are
exclusively used, but in the Moral Sciences it
is otherwise; for there the notions developed
by the experience and reasoning of mankind
which must always constitute the principal
source of our knowledge are in general loosely
and inaccurately expressed, and the same vocal
sign, or vocable, is commonly used to denote
many different notions more or less nearly re-
lated ; nor, with reference to these, does the
term in general express the notion accurately.
Hence the necessity of definition, which is at
once the fundamental and the most difficult
of the logical processes. But in the Physical
Sciences the notion is always accurately defined
by the thing itself; and so in the Mathematics,
though highly abstract, our notions are always
clearly defined. Thus in these sciences the
logical processes are so simple that it is impos-
sible to err, unless by inadvertence, and all
errors are quickly corrected ; and hence a tech-
nical knowledge of Logic is but little needed.'
But in the Moral Sciences it is different, for
here the difficulty of defining our terms is
1 Hence, from disuse of the more difficult of the logical
processes, a man in the former case, may be a competent
naturalist without being much of a reasoning creature ; and
in the latter, a great mathematician and yet a child in the
practical affairs of life, individual and social.
IN TROD UC TION 1 1
great, and often insuperable, and hence, in the
prosecution of these sciences, Logic must
always be an indispensable instrument.
(2) To a certain extent this difference be-
tween the two classes of sciences is an essential
one, and cannot be altogether removed. But
to a large degree the Moral Sciences are sus-
ceptible of apodictic treatment, and by such
treatment may be indefinitely assimilated in
nature to what are commonly called though
not exclusively entitled to the name the
Exact Sciences; for a large part of the Moral
Sciences, including nearly all the fundamental
principles upon which they rest, are purely
apodictic. For, though it is commonly sup-
posed there is an essential difference between
Mathematical and what is called Moral Reason-
ing, this is not true; all ratiocination (not fal-
lacious) is essentially of the same character and
equally conclusive. 1
(3) Hence it may be observed as a corollary,
1 This is much insisted upon by Locke : " Confident I
am," he says, "that if men would, in the same method, and
with the same indifferency, search after moral, as they do after
mathematical truths, they would find them to have a stronger
connection, one with another, and a more necessary conse-
quence from our clear and distinct ideas, and to come nearer
a perfect demonstration than is commonly supposed " (Essay,
bk. iv., chap, iii., 20). "By what steps we are to proceed
. . . is to be learned in the school of the mathematicians,
who, from very plain and easy beginnings, by gentle degrees,
12 LOGIC
the principal task before us, with reference to
the Moral Sciences, is to reduce them as far as
possible to apodictic or scientific form. This,
under present conditions, will still leave an im-
mense field of investigation in which we must
resort directly to experience, and especially to
experience as embodied in history and statis-
tics; but until all that is susceptible of being
so reduced is reduced to scientific form, no
progress can be made in dealing with matters
depending upon experience.
(4) With regard to the Physical Sciences
another difference is to be noted, namely,
between what has been achieved and the dis-
covery of new facts; with reference to which
the instrument of discovery is mainly experi-
ment and observation, or, as it is commonly
called, the Inductive Method. In this respect
these differ from the Moral Sciences, where,
though the same method must always be used,
its function is confined chiefly to the process of
definition. 1
and a continued chain of reasonings, proceed to the discovery
and demonstration of truths that appear at first sight beyond
human capacity " {Id., bk. iv., chap, xii., 7, 8). " This gave
me confidence to advance the conjecture which I suggest,
Chap, iii., viz., that Morality is capable of demonstration as
well as Mathematics."
1 The nature of Logic, and of the relation of the Inductive
Method to Logic, is thus precisely expressed by Bacon :
" The syllogism consists of propositions, propositions of
INTRODUC TION 1 3
7. OF THE MODES IN WHICH OPINION
is GENERATED. With reference to results
achieved and embodied in language, and to
our opinions generally, the process by which
our notions or concepts are derived is the re-
verse of what is commonly supposed. In the
discovery of new facts, or the formation of new
concepts, we commence with the conception of
the concrete, and, the concept being formed,
we find the name. But this, in the develop-
ment of thought at which we have arrived, can
occur only in the Physical Sciences. For, as
we have observed, it is hardly probable that
in the Moral Sciences any rudimentary thought
can ever occur that has not already occurred
to some one and been expressed in language.
Hence, with regard to all matters dealt with
in the Moral Sciences (as also in the Physi-
cal Sciences with regard to results already
achieved), the order of our cognitions is, first,
to learn the words, /. e., the word-signs or
words, words are the signs of notions. If, therefore, the
notions (which form the basis of the whole) be confused and
carelessly abstracted from things, there is no solidity in the
superstructure. Our only hope then is in genuine induction "
(Nov. Org., bk. i., aph. xiv).
The subject is more fully developed in aph. lix., and beauti-
fully illustrated in aph. xcv. See also his doctrine of Idols,
aph. xxxviii. et seq. It may be observed here, in passing, that
no student of Philosophy, and still less of Logic, can afford to
neglect the first book of the Novum Organum or the De
A ugmentis.
14 LOGIC
vocables, and afterwards, the concepts or
notions expressed in them.'
8. OUR SUPPOSED KNOWLEDGE OFTEN
NONSENSE. And as the latter function out-
side the Exact Sciences is in general very
lamely performed, the result is that the greater
portion of our supposed knowledge in abstract
matters consists of words without definite
notions attached to them, and is therefore
merely nonsense. For when we reason with
undefined or ill-defined terms we are dealing
with mere delusions or dreams like Ixion
embracing clouds and begetting monsters.
Thus, e. g. , when we assert, with Bentham and
Austin, that General Utility is the ultimate
test or principle by which the just and the un-
just and right and wrong generally are to be
determined, we are in fact talking nonsense;
for it cannot be determined from this expres-
sion whether we have in view the welfare of a
mere majority, or two thirds, or three fourths,
or other proportion of mankind, and hence
from this premise all sorts of extravagant
opinions are deduced. Hence the mass of us
1 The logicians, from and including Hamilton, have en-
tirely overlooked this distinction, and have thus substituted
for the old logical doctrine of Simple Apprehension, the psy-
chological doctrine of Conception, a doctrine necessary to be
understood, but which is concerned rather with the original
formation of language than with its use as an instrument of
reasoning.
INTRODUCTION 15
generally, and all of us in many matters, like
Moliere's hero, who was surprised to find that
he had been talking prose all his life, have all
our lives been talking nonsense. 1 And this is
true not only of opinions commonly regarded
as nonsensical, but of all opinions involving
either undefined notions or notions to which
there are no corresponding realities.
9. THE CRITICAL SPIRIT ESSENTIAL TO
WISDOM. Our wisdom is therefore to be
measured, not by the extent of our learning,
or by knowledge of detached facts, or by vivac-
ity of thought or expression, or by the confi-
dence of our belief, but chiefly by the capacity
to judge our supposed knowledge, and to de-
tect its falsity or non-significance. In this way
Socrates modestly explained the oracle of the
Delphic god, that he was " the wisest of man-
kind." For, he said, he alone had discovered
that all men were ignorant, including himself;
but others mistook their ignorance for know-
ledge. 2 We conclude, therefore, as we began,
that what we regard as our knowledge consists
mainly of unverified opinions or beliefs, and
that however firmly these may be established,
1 See Appendix C.
2 As explained by Grote (cited infra, 16, App. H), the thesis
of Socrates was that " the natural state of the human mind "
is "not simply ignorance, but ignorance mistaking itself for
knowledge."
l6 LOGIC
or however passionately they may be asserted
and believed, they do not necessarily, or even
generally, constitute true knowledge. Hence,
until we are enabled to distinguish the true
from the false, we can have no assurance of
their rectitude or truth.
10. LOGIC THE ULTIMATE TEST OR CRI-
TERION OF TRUTH. We must, therefore,
seek some tests or criterions if any there be
by which the truth or falsity of our beliefs
may be determined ; and of such two only can
be conceived ; namely, Experience and Reason-
ing, or Logic. Of these the former is more or
less efficiently used by men in general ; and in
concrete matters and in the ordinary familiar
affairs of life, its operation is moderately satis-
factory. For thus, by actual contact with the
hard facts of our experience, our opinions or
beliefs are, to a large extent effectually, and
often painfully, modified and corrected. But
the function of experience is simply to furnish
Reason with materials on which to work; and
of Reasoning, or Logic, as Hobbes says: " So
far are the mass of men from using it, that
they do not even know what it is."
1 " The most part of men, though they have the use of rea-
soning a little way, as in numbering to some degree, yet it
serves them to little use in common life ; in which they gov-
ern themselves, some better, some worse, according to their
differences of experience, quickness of memory, and inclina-
tion to several ends ; but especially according to good or evil
IN TROD UC TION 1 7
ii. THE DECADENCE OF THE AGE IN
LOGIC AND THE MORAL SCIENCES. And this
is true not only of the common people, but of
the educated, and even of the philosophers and
the professors; who in the last century, owing
to the disuse of Logic, have in fact lost the
very idea of it; so that in our schools and
universities, under the name of Logic, any-
thing but Logic itself is taught, and it has thus
become a lost art. 1 Yet, obviously, in all
abstract matters, and especially in Morality,
Politics, and all the different branches of the
Science of Human Nature, experience, while
useful to us, can go but a little way, and
therefore Logic must be an indispensable in-
strument. Hence it is to the disuse of Logic
that the existing incoherent and chaotic state
of the Moral Sciences is to be attributed." It
may therefore be confidently hoped that by the
renewed use of Logic a revival of these sciences
is to be anticipated, vying in extent with that
of the concrete sciences in modern times, and
fortune, and the errors of one another. For as for 'science,'
or certain rules of their actions, they are so far from it that
they know not what it is" (Lev., chap. v.).
1 " We live in an age," says De Morgan, " in which formal
logic has long been banished from education ; entirely we
may say from the education of the habits." The proposition
is even truer of the present day ; for in De Morgan's time
there still survived some of the old style of logicians.
* See Appendix D.
1 8 LOGIC
far surpassing them in practical utility to the
human race. 1
12. OF AUTHORITY AND PREJUDICE. I
would not, however, in thus explaining and
commenting upon the general dominance of
authority and prejudice over men, be under-
stood as altogether condemning it. Under
existing conditions, and perhaps under all con-
ditions, the opinions of the masses of mankind,
in Politics and other matters of common con-
cern, must be determined mainly by custom and
authority. Hence the distinction made by the
old philosophers between their esoteric and ex-
oteric doctrines; the latter consisting of those
that could be taught to the masses, the former,
of those that required the peculiar training of
the philosopher to comprehend a profound
distinction that has been lost in modern times.
But though it may not be possible, or perhaps
even desirable, to make all men philosophers,
yet it is possible to make the masses of them
logical in the matters with which they are con-
1 The argument of Demosthenes in the first Philippic may
be readily applied to the proposition asserted in the text :
" First I say, you must not despond, Athenians, under your
present circumstances, wretched as they are ; for that which is
worst in them as regards the past is best for the future.
What do I mean? That your affairs are amiss, men of
Athens, because you do nothing that is needful ; if, not-
withstanding you performed your duties, it were the same,
there would be no hope of amendment."
INTRODUCTION 19
versant ' ; and for those who aspire to be lead-
ers of opinion, Logic is essential. For these,
if worthy of the function to which they aspire,
cannot afford to be deficient in this respect;
they must either be logicians, or false prophets,
or blind leaders of the blind.
13. PLAN OF THE WORK. Though I re-
gard the study of Logic as essential to the cul-
tivation and the use of the reasoning powers,
and hence as indispensable to the Moral Sci-
ences, yet it is chiefly as a test or criterion of
fallacy that I propose to treat it. This use of it
will, of course, necessitate some consideration
of the elementary principles and rules of Logic
as necessary to the understanding of the Doc-
trine of the Fallacies. But this part of my essay
will be abbreviated to the utmost extent con-
sistent with this object ; that is to say, I will
try to include everything essential to the under-
standing of the rudiments of Logic, but noth-
ing more. If I should fail in this, and anything
necessary should be omitted, the defect may
be readily obviated by reference to the work
of Whately, who, among elementary writers,
may be regarded (in any true sense of the
word) as the last of the logicians.
The subject will be treated in two books, the
first entitled " The Analytic of Right Reason-
ing," the second, " Applied Logic " ; the latter
1 See Appendix E.
2O LOGIC
of which will include two subjects, namely:
' The Method of Logic " and " The Doctrine
of the Fallacies," or " The Analytic of Wrong
Reasoning." In treating of the last, the ex-
amples of the several fallacies will be taken
almost exclusively from current theories of
Politics and Morality. Our examples will
therefore consist, not of mere trivialities,
such as are so common in books on Logic,
but of fallacies that, in perverting moral and
political theory and in corrupting practice,
have dominated, and still continue to domi-
nate, the fortunes of mankind. They come
to us, therefore, as veterans of what Hobbes
calls the " Kingdom of Darkness," crowned
with the laurels of victory. 1
1 Lev., chap. xliv. : see Appendix F.
BOOK I
THE ANALYTIC OF RIGHT
REASONING
21
BOOK I
THE ANALYTIC OF RIGHT
REASONING
CHAPTER I
RUDIMENTARY NOTIONS
14. DEFINITION OF LOGIC AND OF IN-
VOLVED TERMS. Logic is defined by Whately
as the science and also the art of reasoning.
Reasoning may be defined as consisting in the
exercise of the comparative or discursive fac-
ulty of the mind that is to say, the faculty by
which our notions or concepts are compared
with each other, and with the realities to which
they are supposed to correspond, and their re-
lations with each other, and with such realities
are perceived. Or we may define reason as
the faculty, and reasoning as consisting in its
exercise. 1 But Logic by which I mean the
1 The terms reason and reasoning, though conjugate, have
unfortunately been divorced by logicians, and, following
23
24 LOGIC
traditional Logic is not to be regarded as
having to deal with reasoning in general, but
with explicit reasoning only, or ratiocination ;
which may be defined as reasoning expressed
in language, or, so far expressed that the miss-
ing parts are understood. Hence it is rightly
said by Whately that Logic is exclusively con-
versant with language; by which is meant, not
merely the signs of thought, but also the
thought signified. 1 This follows from the
definition, and also from considering the sev-
eral subjects of which it treats, which, by the
universal consensus of logicians, consist of the
Doctrines of the Term, of the Proposition, and
of the Syllogism. But all these are simply
parts or kinds of language.
15. RATIOCINATION DEFINED. But Ra-
tiocination, being a species of reasoning, must
consist in the comparison of concepts or
notions, and these, in order to fall within the
province of Logic, must, ex vi termini, be ex-
pressed in terms. Hence, Ratiocination must
be defined as consisting in the process of com-
them, by lexicographers generally ; and accordingly Locke
is blamed by Whately for confounding them. But in this
Locke is right, and the logicians wrong ; and the usage of the
latter has been the source of infinite confusion in Logic. As I
use the terms, Reason includes the faculties of Inference,
Judgment, and Simple Apprehension ; and Reasoning the
corresponding processes.
1 See Appendix G.
RUDIMENTARY NOTIONS 2$
paring terms, with the view of perceiving their
relations. And this necessarily implies, also,
the process of determining the meaning of the
terms compared, or, in other words, the process
of definition.
16. LOGIC DEFINED. Logic, regarded as
a theory, may, therefore, be defined as the
Analytic of Explicit Reasoning, or of Ratio-
cination meaning, by this expression, the
systematized results of an analysis of the pro-
cesses involved in ratiocination. 1 And its
practical end is to determine the meanings of
terms and the relations between the concepts
or notions denoted by them. 3
17. OF THE SEVERAL KINDS OF TERMINAL
RELATIONS. The relations between terms are
of two kinds, which may be called immediate
and inferred ; and the former, again, are of
two kinds, that, for lack of better names, may
be called intuitive and quasi-intuitive.
18. THE INTUITIVE RELATIONS OF TERMS.
Of the former kind are all those relations
between terms that are intuitively perceived
upon comparing them together, as, e. g., the
1 See Appendix H.
2 " Knowledge [is] but the perception of the connection and
agreement or disagreement or repugnancy of any of our ideas "
(Locke, cited 110 n. g. App. N). " Knowledge is not so
much increased by a continued accession of new ideas as by
perceiving the relations of those ideas which we have already
acquired " (Eunomos, cited Chitty's Blackstone, introd. note).
26 LOGIC
relation of species and genus between the class
of beings denoted by the term man and the
class denoted by the term rational, or between
the classes denoted by the terms horse and
animal, or the relation of mutual exclusion
existing between the terms of the proposition,
No two islands can be contiguous."
19. JUDGMENT DEFINED. The perception
of a relation of signification between two terms
is called Judgment; which may be defined as
the intuitive perception of a significative rela-
tion between two terms. The result of the
process is called a judgment; which may be
defined simply, as a self-evident proposition.
20. THE QUASI-INTUITIVE RELATIONS
OF TERMS. Analogous to the intuitive rela-
tions of terms are the relations between the
terms of all assumed propositions, or assump-
tions; for these, though not intuitively true,
are assumed or supposed to be such for the
sake of the argument, and used as principles
from which to reason ; they may, therefore, be
regarded as quasi-intuitive^ Under this head
1 We borrow this form of expression from the lawyers, who
find it indispensable, as, e. g., in the expressions quasi-torts,
quasi-contracts" etc. As we are informed by Cicero, the
Epicureans held that the gods had not bodies, but quasi-
bodies only, i. e., something like bodies. An Indian com-
munity, I have read somewhere, were much annoyed by a
species of animal something like cows (nie/gkais, I believe
they called them) that destroyed their crops, and the question
RUDIMENTARY NOTIONS 2J
are included all the relations between the terms
of propositions assumed as premises, whether
upon authority, or from testimony, or other-
wise, i. e., between the terms of all proposi-
tions other than those that are intuitively
perceived to be true, or that are inferred from
other propositions.
21. THE INFERRED RELATIONS OF
TERMS. The inferred relations of terms in-
clude all relations that cannot be intuitively
perceived from an immediate comparison of
the terms, or that are not assumed, but that
can be inferred by comparing the given terms
respectively with a third or middle term, the re-
lations of which to the given terms are known.
Thus, e. g., we may not be able to perceive
from a mere comparison of the two terms, that
" Logic is a branch of the Science of Lan-
guage," but by comparing the two terms of
the proposition respectively with the middle
arose whether it was lawful to kill them. The pundits to
whom the question was referred were of the opinion that,
though not cows, the animals were quasi-cows, and therefore
not to be killed. The term will be found to be of equal
utility in Logic as in the Law. In fact, a very useful book
might be written on the subject that might be appropriately
termed Quasics. For, outside of concrete notions, all notions
denoted by terms are formed by analogy from sensible images,
and are quasi-things only, as, e.g., imagination, reflection,
perception, etc. We suggest the term Quasics not with a view
of seriously recommending it for common use, but simply for
the purpose of directing attention to a very important subject.
28 LOGIC
term, " The Science of the Term, the Proposi-
tion, and the Syllogism, ' ' the relation of species
and genus between the subject and the predi-
cate will be at once perceived. For" Logic is
the Science of the Term, the Proposition, and
the Syllogism," and " The Science of the
Term, etc.," is a species or kind of " the
Science of Language," and hence " Logic is
a species or kind (i. e., a branch) of the Science
of Language." And so we may not be able to
perceive from a mere comparison of the terms
that " the Thracians were barbarians, " but by
comparing these terms with the middle term,
" Not -Greeks," the conclusion is apparent ; for,
ex vi termini, all " Not-Grecks " were barba-
rians. So, generally, using the letters X, Y, Z,
etc., to represent the terms of any proposition,
we may not be able to perceive intuitively the
truth of the proposition that Z is X, yet, if it
be intuitively perceived or assumed that Z is
Y, and that Y is X, we may infer that Z is X.
22. PROPOSITIONS AND SYLLOGISMS. An
immediate relation of terms, whether intuitive
or assumed, can be expressed only in the form
of a proposition which may be defined simply
as the expression of such a relation ; and an
inferred relation, only in the form of three
propositions constituting what is called a syllo-
gism. The proposition may be expressed in
the formula: Y is X; and all syllogisms in the
RUDIMENTARY NOTIONS 29
formula: Z is Y, Y is X, . * . Z is X; or, Z is
Y, Y is not X . . Z is not X the letters
standing for terms or names, and the three
points (. * .) being the sign of illation, and
equivalent to the expression, " ergo," or
" therefore." '
23. OF APODICTIC AND DIALECTIC. Ra-
tiocination may consist wholly of judgments
and inferences, or partly of these and partly of
assumed propositions. In the former case it is
wholly illative, or demonstrative; in the latter,
1 To define a term (as indicated in the etymology of defini-
tion} is in effect to establish the boundaries by which the class
of significates denoted by it is separated from all other things ;
and these boundaries may be conveniently represented by
circles or other enclosed figures. These are known as Euler's
symbols, and are extremely convenient and universally used
by logicians. A universal affirmative proposition is expressed
by a circle contained in a circle, the former representing the
subject, the latter the predicate ; the universal negative by
two circles excluding each other ; and the syllogism, by thus
expressing its several propositions; as, c. g. , in the following
diagrams :
Affirm. Prop. Neg. Prop.
Neg. Syll.
3O LOGIC
only partially so, i. e., only so far as the valid-
ity of the inference is concerned. The prin-
ciples governing the former kind of ratiocination
constitute what is called Apodictic ; those gov-
erning the latter, Dialectic. It will be seen as
we progress that Apodictic is far more extensive
in its scope or use than is commonly supposed,
and that it includes, in fact, not only the
Mathematical Sciences, both pure and applied,
but also a large part of Morality, Politics, and
Jurisprudence generally. And especially, it is
important to observe, it includes the subject
of our present investigations. For Logic,
though not so treated by modern logicians, is
strictly a demonstrative science, and will be so
treated in this essay. 1
24. VALID RATIOCINATION ILLATIVE IN
NATURE. All ratiocination, or reasoning ex-
plicitly stated, discloses at once its validity or
invalidity that is to say, appears on its face
to be either conclusive in its effect, or fal-
lacious. Hence, all ratiocination, unless fal-
lacious, is illative or conclusive, or, we may
say, demonstrative in its nature. On the other
1 One of the most universal infirmities of the average mind
is an incapacity to distinguish (outside the mathematics) be-
tween mere opinion and apodictic, or demonstrated truth.
With regard to the latter, the man who is conscientious and
accurate in his Logic may realize the fine saying of Seneca :
" It is truly great to have in one the frailty of a man and the
security of a god " (cited Bacon, Essays, " Of Adversity ").
RUDIMENTARY NOTIONS 31
hand, unless explicitly stated, no reasoning,
however apparently convincing, can be re-
garded as of this. nature. Hence, from a logi-
cal point of view, reasoning in general may be
regarded as either valid (i. e., illative), or as
invalid; the latter of which may be either fal-
lacious or simply inconsequent. The former
may be appropriately called Logical Reason-
ing, the latter Non-logical or Rhetorical; by
which is meant not necessarily illogical or fal-
lacious, but either fallacious or simply inconse-
quent, i. e., non-illative.
25. RIGHT REASONING DEFINED. It is
with the former only that Logic is directly con-
cerned, and to it we may without impropriety
give the name of RigJit Reasoning. For the
logical quality of the reasoning does not de-
pend upon the truth or falsity of the conclusion,
but upon the rectitude of the definitions, judg-
ments, and inferences.
26. LOGIC THE ART OF RIGHT REASON-
ING. Logic, therefore, regarded as an art,
may be simply defined as the Art of Right
Reasoning; and it must therefore be regarded
as denoting the ultimate test or criterion of
truth or error. For until the reasoning is
made explicit, it cannot be determined whether
it is right or otherwise. It also includes the
doctrine of Fallacy, or Wrong Reasoning;
but as the latter has for its end simply the
32 LOGIC
avoidance of error, as a means of assuring the
rectitude of our reasoning, it may be regarded
simply as one of the practical aspects of the
doctrine of Right Reasoning.
27. LOGIC TO BE REGARDED AS INTEL-
LECTUAL MORALITY. Logic must, therefore,
be regarded as bearing to reasoning the same
relation as Morality to conduct. It may,
therefore, be appropriately called Intellectual
Morality*
1 Hence it is that Logic, like Morality, is not popular with
those who disregard its precepts ; among whom are to be in-
cluded the large majority of writers, and especially of phil-
osophers. The principle is as expressed in the adage :
" What thief e'er felt the halter draw
With good opinion of the Law ?"
CHAPTER II
DOCTRINE OF THE TERM
I
OF THE NATURE OF THE TERM
28. " TERM," " NAME," AND " WORD"
DISTINGUISHED AND DEFINED. These words
are often used as synonymous, but the distinc-
tion between them is material and important.
A word is a vocal sign, or vocable, express-
ing a thought, or a thought expressed by such
a sign. Under the name " word " is included
the substantive or noun, and also other parts of
speech, as, e. g., the article, the conjunction,
etc. A name (noun or substantive, which may
be either simple or complex'} is a word or set of
words used to signify an object of thought re-
garded as a thing, z. i\, as an existing substance
or entity. The knowledge or cognition of a
thing by the mind is called a notion or concept ;
hence a name may be otherwise denned as a
word, or set of words, expressing a notion, or
33
34 LOGIC
as a notion thus expressed. A notion or con-
cept is itself a thought, but it differs from
other thoughts as being the thought of a thing,
i. e,, of something as existing. A term is a
name used as a subject or predicate of a pro-
position. It is therefore to be regarded merely
as an element of the proposition ; and the pro-
position as the principal subject in Logic.
29. "THING" DEFINED. The term
thing is used in two different senses that
must be carefully distinguished. In its proper
sense the term denotes an actual thing or sub-
stance, whether material or spiritual, as, e. g.,
mineral, vegetable, animal, gas, man, soul,
God, etc. In this sense things constitute the
actual universe, and all notions or concepts
whatever, unless false or unreal, are ultimately
derived from them. But, in another sense,
the term is used to denote, not only actual
existences, or, as we may call them, real things,
but mere objects of thought, or things existing
only in contemplation of mind, and to which
there are, in fact, no real things directly cor-
responding. 1 These may be appropriately
1 All true or real notions must correspond to real or actual
things, but the correspondence may be either direct between
the notion and the real things signified by the term as in
the case of concrete terms, <?. g., " man," " horse," etc. ;
or indirect as in the case of abstract terms between the
notion and the things whose attributes are signified. Thus,
taking for example the term " redness ," there is apparently a
THE TERM 35
called <7?/rt.$7- things; and of this kind are the
concepts or notions denoted by all abstract
terms; which denote, not real things or in-
dividuals, but mere abstractions, as, c. g.,
such terms as " justice," " the state," the
names of the several colors, disease, death,
etc. ; where the things denoted are not actually
existing things, but mere concepts of qualities
or attributes of things objectified by the
mind.
30. " CONCEPT," " NOTION," AND
"THOUGHT" DEFINED. The term " con-
cept," or " notion," or " thought " (in this
connection we may use either indifferently) is
a relative term implying or connoting, in its
strict or proper sense, an individual thinking
mind of which it is the product; and hence
the term will have a different meaning accord-
ing to the correlative to which it refers. It
must therefore have many different senses; of
which two must be especially distinguished.
In its proper sense it denotes simply a certain
affection of the mind of the individual; and
in this sense, obviously, it is momentary and
evanescent, like the snow falling on the river,
described by the poet, as " ae moment white,
direct correspondence between the notion expressed and the
qttasi-\\\\ng signified, though in reality they are the same ; but
there is an indirect real correspondence between the notion of
redness and the red things of which it is a quality.
36 LOGIC
then gone forever." For though, it is said,
the thought recurs to us, it is not, nor can it
be, the same thought, but is merely a copy or
image of it. So, when a thought as it is said
recurs to us, it is always, or at least almost
always, suggested to us by the word in which
it is embodied ; and, as to us, so also to others.
But Logic does not have to deal with the mo-
mentary, fleeting thought of the individual,
but with the thought only that is continuously,
or we may say permanently reproduced, and
communicated by one to another; that has be-
come incarnate in words, and is thus, even
when lost from the mind, at once preserved,
and continuously suggested, or brought back
to the consciousness of each and all. Hence,
in Logic, the terms, notion, concept, and
thought, are to be regarded as used in a
secondary or derived sense, as denoting the
common notions, concepts, and thoughts of
mankind embodied in words. Hence the things
or significates denoted by abstract and other
universal terms have in fact a kind of exist-
ence outside of any and all individual minds;
which, as opposed to substantial, may be called
logical existence ; i. e., they exist in the word
(logos], and their existence is as real and of
precisely the same nature as that of the word
of which they are an essential part. Hence,
though we speak of abstractions as fictitious
THE TERM 37
(i. c. , feigned) or imaginary things, yet they
are real, and in some cases, as, e. g., in the
case of death, disease, misery, poverty, etc.,
terribly real facts. What is meant by the term
"fictitious tiling " is, not that the notion signi-
fied is false or unreal, but that, for logical pur-
poses, it is fictitiously regarded as a thing.
31. THE NORMAL LOGICAL TERM.
Every term legitimate for logical purposes,
or we may say every logical term, is therefore
to be regarded as involving or implying three
essential notions or elements, namely; (i) the
vocal sign, or vocable, (2) the notion denoted,
and (3) the actual tilings, or objective realities,
to which the notion and the vocal sign are sup-
posed to correspond. These are all to be re-
garded as, in one sense, essential elements of
the logical term. For though, where the last
is lacking, a term may exist, and it is, there-
fore, possible to have an absurd or nonsensical
term, yet such a term is not such as is contem-
plated when we regard the end of Logic ; which
is not to deal with absurdities or ingenious
puzzles, but to discover truth and avoid error.
Hence, an absurd or nonsensical term, or, in
other words, a term whose signification does
not correspond to reality, is not the normal or
true term, essential to legitimate ratiocination;
nor is Los[ic unless in illustrating some of its
o o
formal operations in any way concerned with
43331
38 LOGIC
it, except to detect and expose its inherent
vice and its essential insufficiency for logical
purposes.
32. THE DENOTATION AND CONNOTA-
TION OF TERMS. All terms are regarded in
Logic as denoting or signifying classes of in-
dividuals. 1 The individuals constituting the
class denoted by the term are marked or dis-
tinguished by certain common attributes, at
once common and peculiar to the class, as,
e. g., the class " man " by the mark ''rational,"
by which it is distinguished from other kinds
of animals. Accordingly a term is said to
denote the individuals designated by it, and to
connote the qualities or marks by which the
class is determined. Thus, e. g., the term
" man-" denotes the class of animals known by
that name, and connotes the quality or attribute
of rationality by which the class is distin-
guished.
33. THE MEANING AND SIGNIFICATION
OF TERMS. The individuals constituting the
class denoted by a term are said to be signified
by the term, and are called its significates,
Thus the term, man, denotes the class, man,
as a whole, but signifies each and all of the in-
dividual men composing it. The significates
of a term may be real, which is the case when
they are real individuals or things, existing in
1 See infra, 35.
THE TERM 39
nature; or they may be unreal, or fictitious,
i. e., existing only in contemplation of mind;
which is the case with all abstract terms, and
with concrete terms where the classes of indi-
viduals denoted are fictitiously regarded as in-
dividuals, as, e.g., when we speak of " man "
as one of the significates of "animal. " When
a term denotes a class of real individuals as,
t\ g.," man," regarded as denoting men gener-
ally its significates are real ; when it denotes a
class of lower classes as, e. g. , the several races,
Asiatics, Europeans, etc. they are unreal or
fictitious. In the former case the term is said
to denote an infima species ; which is to be de-
fined as a class made up of real individuals.
By the meaning of a term is meant both its
denotation, or signification, and its connotation
taken together; and the word " meaning"
may also be regarded as equivalent to notion
or concept.
34. THE EXTENSION AND INTENSION OF
TERMS. The extension of a term corresponds
to its denotation, or signification, and is deter-
mined by the extent of Ihe class denoted, or
by the number of significates signified by it.
The intension of a term is but another name
for its connotation, both words denoting
merely the qualities or attributes, or, in other
words, the marks by which the class is deter-
mined.
40 LOGIC
II
OF THE SEVERAL KINDS OF TERMS
35. SINGULAR, AND COMMON, OR UNI-
VERSAL, TERMS. Grammatically speaking,
terms are said to be either singular or common,
or, as otherwise expressed, singular or uni-
versal. A singular term is one that denotes
an individual or single thing, as, e. g. , any par-
ticular thing, animal, or man. A common or
universal term is one that denotes either a class
of individuals or a class made up of other
classes. But in the latter case, the subordinate
classes may be regarded as individuals consti-
tuting the superior class; and conversely the
individual may always be regarded as a class,
/. e., a class of one. 1 In this work, therefore,
the distinction between singular and common
or universal terms will be regarded as logically
immaterial ; all terms will be regarded as uni-
versals, or, in other words, as denoting classes
of significates.
36. ADJECTIVES. Hence also adjectives
used as terms will be regarded as nouns or sub-
1 " By a class is usually meant a collection of individuals
. ; but in this work the meaning of the term will be ex-
tended so as to include the case where but a single individual
exists, as well as cases denoted by the terms ' nothing' and
' universe' 1 ; which as 'classes' should be understood to com-
prise respectively 'no beings' and 'all beings.'" Boole,
Laws of Thought, p. 28.
THE TERM 41
stantives; that is to say, where a term is in
adjective form (which can occur only with the
predicate) it is either regarded as a substantive,
or converted into one by adding the substan-
tive understood. Thus, e.g., the proposition,
" Man is mortal," is to be read: " Man is a
mortal," or " a mortal being."
37. ABSTRACT AND CONCRETE NAMES.
A concrete name is one that denotes a class of
real individuals. An abstract name is one that
denotes qualities or attributes conceived as ex-
isting apart from the things in which they in-
here, or, in other words, fictitiously regarded as
things, as, e. g., whiteness, strength, goodness,
humanity, etc.' 2 Abstract names are commonly
singular in form, but in their essential nature
they are always universal. Thus, when we
speak of virtue, the name is to be regarded as
1 " If we attach to the adjective the universally understood
subject, ' being ' or ' thing,' it becomes virtually a substantive,
and may for all the essential purposes of reasoning be replaced
by the substantive. Whether or not in every particular of the
mental regard it is the same thing to say, ' water is a fluid
thing,' as to say, ' water is fluid,' it is at least equivalent in the
expression of the processes of reasoning." Boole, Laws of
Thought, p. 2J.
' 2 The distinction between concrete and abstract names cor-
responds precisely to the distinction made by old logicians
between names of first intention and names of second inten-
tion. The former are names that denote real significates ;
the latter, names that denote fictitious significates, or quasi-
things. See further on this point Appendix I.
42 LOGIC
denoting, not a quality existing in any par-
ticular man, or in itself, but the class of quali-
ties by which all virtuous men are distinguished.
So, though we may consider the color red, or
redness, in the abstract, dismissing from the
mind the individuals in which it is manifested,
yet, upon analyzing the concept, we cannot
fail to perceive that there are as many individ-
ual instances of red, or, we may say, as many
individual reds or rednesses, as there are indi-
vidual things in which the color is manifested;
and that red, or redness, is simply the denomi-
nation of the class of colors thus manifested.
Hence, abstract names, though grammatically
singular, are to be regarded as plural, and as
differing from concrete names only in this, that
the individuals constituting the class are quali-
ties, i. e., quasi- things, or fictitious, not actual
existences, and that among the marks by
which the class is distinguished are the actual
individuals in whom alone the qualities exist.
An abstract name is therefore to be regarded
as denoting a class of qualities ; and as connoting
the individuals in which they inhere.
38. THE DISTINCTION OF FUNDAMENTAL
IMPORTANCE. The distinction between con-
crete and abstract names, or names of first, and
of second intention, is one of fundamental im-
portance. In dealing with the former, the
things denoted by the names we use are ever
THE TERM 43
present to the mind, and we may therefore, as
is asserted by Mill, be said without violent
absurdity to deal with things, rather than
with notions or names. But where we deal
with abstract terms, the things present to the
mind are mere abstractions, fictitiously re-
garded as things; and we are, in fact, dealing
not with things, but with ^^.yz-things only. 1
39. POSITIVE AND NEGATIVE TERMS.
The distinction between positive and negative
terms is also one of fundamental importance
in Logic. By this division of terms the whole
universe of things, real and fictitious, is divided
into two classes, the one marked by having,
the other by not having, a certain quality or
qualities, as e. g., white things, and things
that are not white ; and it is obvious that to
each positive there must be a corresponding
negative term.
40. OF THE UNIVERSE OF THE PROPOSI-
TION. But ordinarily in speech we have in
view a more limited class, and must be under-
stood to refer, not to the universe of things,
but to some class less than the universe, but
superior to the classes denoted by the subject
and predicate; and this superior class is said
to constitute the universe of the proposition in
which the terms are used. Thus, when we
speak of " mortal" and " immortal," the class
1 See Appendix K.
44
LOGIC
of " living things" or " beings" is obviously
referred to as the superior class, and is, there-
fore, said to constitute the universe of the
proposition; and the division is to be under-
stood to be into " mortal" and " immortal"
beings. So, in the proposition, " Brutes are
irrational," the superior class we have in view
is that of animals, and this class is to be re-
garded as the universe of the proposition ; as
(denoting " no t " by the Greek privative, a]
may be illustrated by the following diagrams,
either of which may be used :
III
OF THE ANALYSIS OF TERMS
41. APPREHENSION. As it is the func-
tion of Logic to compare the notions de-
noted by terms, with the view of determining
their relations, a preliminary process is essen-
tial . namely, that of apprehending or under-
standing the significations of terms; which is
called by logicians, " Simple Apprehension."
1 The operations of the mind involved in reasoning are (i)
Simple Apprehension, (2) Judgment, and (3) Inference (see
THE TERM 45
This is effected by means of what may be
called the " Analytical Processes "; which will
next be considered.
42. ANALYTICAL PROCESSES. As pre-
liminary to apprehension, it is essential that
the sense in which the term is to be used shall
be identified, or, in other words, that of the
several senses usually denoted by a vocable,
one shall be selected. This is often called
nominal definition (i. e. , definition of the name),
but improperly; for until it is determined in
what sense a term is used, there is in fact no
name. Hence we call it, Vocal Definition, i. c.,
Definition of the Vocable. Next, it is necessary,
before the two terms can be compared, to ap-
prehend, in the case of each of them, the sig-
nificates of the term, or the class of significates
denoted by it ; for otherwise we will not be
able to compare their significations. This is
effected by the definition of the term ; which,
to distinguish it from vocal, is called nominal
or real definition 1 ; and this again involves the
process of classification or division.
Whately, Logic], I have altered the ordinary statement of
these operations by substituting for the third "Inference"
instead of "Discourse"; which is commonly defined as
"reasoning" or "ratiocination." But, as used in this work,
these words include both Apprehension and Judgment.
1 There is some confusion among logicians as to the use of
the terms, Nominal Definition and Real Definition. By some,
the former term is used as denoting what I have called vocal
46 LOGIC
43. VOCAL DEFINITION. A word, or vo-
cable, i. e. , the vocal sign, has usually many
significations; and commonly, in using it, we
do not, at first, distinguish between such of the
notions denoted by it as are nearly the same,
but, instead of regarding it (as we should) as
part of several names, use it as though it were
a single name. But in thus using a vocable
without distinguishing its several senses, it is
inevitable that, in the course of the ratiocina-
tion, it will be used in a shifting sense, or
rather, we should say, in several senses, as
suggested by the varying occasion ; and that
the coherency of our reasoning will thus be
destroyed. This fault in ratiocination is called
the fallacy of confusion or of ambiguity, and,
as will be seen in the sequel, is one of the most
common and most serious of fallacies. Hence
it is one of the most important and imperative
of logical rules that, in the case of every word
we have occasion to use in our reasoning, the
sense in which it is to be used shall be clearly
definition ; but this seems to be incorrect. According to the
better usage, a Nominal Definition is a definition of the
Notion expressed in a term ; and hence Whately says " that
Logic is concerned with nominal definitions only." To this
Mansel objects on the ground that " Logic is concerned with
real or notional definitions only ; its object being to produce
distinctness in concepts, which are the things of Logic " (Man-
sel's Aldrich, p. 39). But this is precisely what Whately
means ; and says.
THE TERM 47
distinguished and consistently observed. And
this indeed, ex vi termini, is essential even to
the beginning of ratiocination; for, until this
is effected, we have not even that essential
material of ratiocination, a name, with which
to deal. The vocal definition of a term may
be effected in various ways, as, e. g., by the
use of any other term, or phrase, or sentence
of equivalent signification ; or, negatively, by
rejecting those senses of the word that we do
not wish to use; or, often, by an imperfect
definition, as by simply specifying the genus of
the class denoted by the term ; or, in fine, by
any means that may serve to confine the term
to one sense only, and thus to prevent am-
biguity.
44. DIVISION AND CLASSIFICATION. -
Division consists in distributing the class of
significates denoted by a name into subordinate
classes, with appropriate names; classification
in the reverse process of assigning a class de-
noted by a name to a class denoted by another
name.
45. GENUS AND SPECIES. In the former
case, the class distributed is called the genus ;
the classes into which it is distributed, species,
In the latter, the class assigned is a species, the
class to which it is assigned, the genus. The
genus and species, however, as in the case of
synonyms, may be of equal extension.
48 LOGIC
46. DIVISION. Division is an act of Anal-
ysis ; Classification, of Synthesis. But the
same principles govern both, and the elucida-
tion of one will equally explain the other. In
Logic, the analysis of terms is the more im-
portant process, and we will therefore adopt,
as the subject of explanation, the process of
Division. The term to be divided, or, rather,
the class denoted by the term, is, as we have
said, called the genus; the subordinate classes
into which the genus is divided, species. The
species must, of course, be exclusive of each
other, i. e., they must not overlap; and taken
together they must exhaust the genus. Thus,
the term thing meaning thereby things and
quasi-things may be divided, and subordinate
classes subdivided, as follows:
Things
Real Things Ouasi-Things
Bodies Not Bodies
Organic Inorganic
Animal Not Animal
Rational Not Rational
etc.
47. DICHOTOMY. It will be observed
that the above division is, in each case, two-
THE TERM 49
fold, i. e.j into two classes, represented by
a term and its negative. This is called Dichot-
omy, and, as in using it we are less liable to
error than in other modes of division, it is
most commonly used. The genus may, how-
ever, be divided into three or more species, pro-
vided the species taken together exhaust the
genus, and be exclusive of each other, as, e.
g., in the division of Bodies into (i) Inorganic,
(2) Vegetable, and (3) Animal.
48. NOMINAL DEFINITION OF TERMS.
The definition (/. e., the real or nominal defini-
tion) of a term consists in assigning the class
denoted by it to an appropriate genus, and
giving its specific difference ; by which is meant
some mark or marks peculiar to it, by which it
may be distinguished from other species. It
is, therefore, a species of classification, i. e.,
it consists simply in classifying the given class,
or species, by assigning it to a genus, and in
adding also the appropriate marks, or specific
difference, by which it is distinguished from the
other species contained in the genus. The
definition of a term is, therefore, to be regarded
simply as a complete classification of it; and
the classification of it as an incomplete or im-
perfect definition. But the latter has the ad-
vantage that it can often be used where the
former would be inconvenient or impossible.
49. THE ESSENCE OF THE TERM. A
50 LOGIC
quality at once common and peculiar to the in-
dividuals denoted by a term is called a property
of the class denoted ; a quality common to the
class, but not peculiar to it, is called an acci-
dent* The definition of a term is made up by
selecting from the accidents of the term one to
serve as a mark for the purpose of determining
the genus, and from the properties one to serve
as specific difference. These together constitute
the essence of the term ; which will therefore
vary with the definition, and be determined by
it. Thus, e. g., if we define man as a rational
animal, "animal" will be the genus; ra-
tional" the specific difference; "talking',"'
laughing, " " cooking, ' ' etc. , properties ; ' ' mor-
tal," " carnivorous," " mammal," etc., acci-
dents. But we may, if we choose, define him
variously as a talking, laughing, or cooking,
mortal, carnivore, or mammal. The essence of
a term is therefore but another name for the
meaning of the term. Properties not used for
specific difference, and accidents not used for
genus, do not enter into the essence of the term.
1 There is much confusion among logicians in the use of the
term accident. The definition in the text is that of the best
authorities, including Aristotle ; and the term should be con-
sistently thus used.
CHAPTER III
DOCTRINE OF THE PROPOSITION
I
RUDIMENTS OF THE DOCTRINE
50. PROPOSITION DEFINED. A proposi-
tion may be defined as the expression of a rela-
tion of signification between two terms; which,
of course, implies the expression of the corre-
sponding relation between the notions ex-
pressed in the terms.
51. THE GRAMMATICAL PROPOSITION.
But here there is a difference between Logic
and Grammar, or, we may say, between the
logical and the grammatical proposition. In
the latter, any of the innumerable relations ex-
isting between terms, or, what is the same
thing, between the things denoted by them,
'whether past, present, or future, may be ex-
pressed as existing between the terms; and the
relation may be expressed by any copula or
connecting word, or the same word may be
51
52 LOGIC
used to express both copula and predicate, as,
e. g., " John struck William " ; " The sun will
rise at six o'clock to-morrow"; " It rains";
" The Carthaginians did not conquer Rome,"
etc. But in Logic the only copula used is the
present tense of the verb " to be" with or
without the negative particle ; and the only in-
terterminal relation considered is that of species
and genus; which may be either affirmed or
denied.
52. THE LOGICAL PROPOSITION. Ac-
cordingly the logical proposition is of two
forms, the affirmative and the negative. In
the former the relation of species and genus
between the terms is affirmed, as, e. g. , " Man
is mortal," ' Y is X," etc. ; in the latter it is
denied, as, e. g. , " Man is not perfect," ' Y
is not X," etc. The affirmative proposition
may be read, either, " Y is X," or " Every Y
is X," or " All Y's are X's " ; or, to take the
concrete example, ' Man is mortal," or
" Every man is mortal," or " All men are
mortal," these expressions being all equiva-
lent, and signifying equally that the subject
class or class denoted by the subject is a
species of the predicate class. The negative
proposition may be read either as above or as'
follows: " No man is perfect," ' No Y is X,"
etc. It is a cardinal postulate in Logic that all
propositions may, and indeed for purposes
THE PROPOSITION 53
of logical analysis must be converted into
logical form; as, e. g., the above examples
into the following : " John is the man who
struck William " ; " Six o'clock is the hour at
which the sun will rise to-morrow"; " Rain
is falling"; " The Carthaginians are not [or,
grammatically, we should say, " were not "]
the conquerors of Rome." '
53. INTERPRETATION OF THE LOGICAL
PROPOSITION. In all logical propositions the
copula is to be interpreted as meaning " is con-
tained in " or " is a species of," or the contrary,
as the case may be. 2 Hence in Logic the only
1 There are commonly recognized by logicians four forms of
the proposition, designated respectively by the letters, A, E,
I, and O, and called the " Universal Affirmative" the "Uni-
versal Negative" the "Particular Affirmative" and the
"Particular Negative" (see infra, 88). But if in I
and O we regard the expression "some Y" instead of
" Y " as the subject of the proposition, these forms will be-
come the same as A and E. Hence, propositions may, as in
the text, be regarded as of two kinds only, namely, affirma-
tive and negative ; the former affirming that the subject is
included in the predicate class ; the latter denying that it is so
included. This distinction agrees precisely with our defini-
tion, and will be sufficient for our present purposes, and,
indeed, for all practical purposes.
2 The affirmative proposition " Y is X " is to be construed as
asserting that the class Y is wholly included in the class X ; the
negative, " Y is not X," that it is wholly excluded. But the
class Y may denote a part of a class, as, e. g. , " Some A " ;
in which case the proposition " Y is X," or " Y is not X,"
would be equivalent to the ordinary forms, "Some A is X."
or " Some A is not X,"
54 LOGIC
significative relation recognized is the relation
of the inclusion or exclusion of the subject
class in or from the predicate: and accordingly
this may be called appropriately the logical
relation. Yet the logical proposition is not less
capacious of expression than the grammatical ;
for, as the latter may always be converted into
the former, it follows that all relations may be
expressed in the one as in the other. The
only difference is that in the grammatical prop-
osition the relations between the notions in-
volved may be expressed either in the copula,
or in the terms themselves ; while in the logical
proposition the only interterminal relation ex-
pressed (i. e. y affirmed or denied) by the copula
is that of species and genus, and all other re-
lations between notions are expressed in the
terms, i. e., in complex terms. 1
54. THE CONVERSION OF PROPOSITIONS.
By conversion is meant the transposition of
subject and predicate i. e., making the predi-
cate the subject, and the subject, predicate.
But, such conversion, to be legitimate, must be
illative, /. e., the force or conclusiveness of the
proposition must not be affected. Thus the
proposition, " Y is not X " (since the subject and
predicate classes are mutually exclusive), may
be converted into the proposition, " X is not
1 This is admirably illustrated by Mr. Boole's system of
signs, of which I append an epitome. See Appendix L.
THE PROPOSITION 55
Y," which is called simple conversion; and so
with all definitions, and other equational proo-
ositions; and also with the particular affirma-
.tive proposition, " Some Y is X." But the
affirmative proposition, " Y is X," cannot be
thus simply converted; for the subject class is
identical with only " some " of the predicate
class, and in conversion the predicate must be
qualified by that particle, thus substituting a
new term. Or, symbolically, the proposition,
' Y is X," can be converted only into the
proposition, " Some X is Y "; which is called
conversion per accidens.
II
SEVERAL THEORIES OF PREDICATION
55. THE COPULA. In the logical proposi-
tion, as we have seen, the copula is interpreted
as meaning "is contained in," or the contrary-
and this is the traditional, or, as it may be
called, orthodox, theory of predication. But
the copula may be otherwise interpreted ; and
from these several interpretations several theo-
ries of predication will result. Of these, two
may be distinguished as requiring some remark,
namely, the Equational Theory, in which the
copula is interpreted as meaning, " is equiva-
lent to," and is expressed by the sign of equiv-
alence (=) ; and the Intensive Theory, where it
56 LOGIC
is interpreted as meaning, " has the quality or
attribute" Thus, e. g. , the proposition, " Man
is rational," is interpreted according to the
Traditional Theory as meaning, " the class
man is contained in the class rational" ; ac-
cording to the Equational Theory, as meaning,
the class man is the same as the class
rational" ; and according to the Intensive, as
meaning, " the individuals constituting the
class man have the quality or attribute, rational,
or of rationality."
56. THE EQUATIONAL THEORY. In the
logical proposition, the classes denoted by the
subject and predicate may be equal ; for, where
this is the case, each may be said to be con-
tained in the other. Hence in such cases the
proposition is always convertible, as, e, g,, we
may say indifferently that " man is a rational
animal,' 1 or that "a rational animal is a man,"
or, generally, if Y = X, either that " Y is X "
or "X is Y." Such propositions are recog-
nized and used in the traditional Logic, as in
the case of definitions, and in other cases,
but it is not thought necessary to express the
equivalence of the terms. Hence in the affirm-
ative proposition " Y is X " it cannot be deter-
mined from the form of the proposition whether
X is of greater extension than Y, or of the
same extension.
57. QUANTIFICATION OF THE PREDICATE.
THE PROPOSITION . 57
The modern doctrine of " the quantification
of the predicate " has for its object to remedy
this supposed defect by expressing in every
proposition by an appropriate sign the quan-
tity of the predicate, or, in other words, by in-
dicating whether it is distributed or not ' ; and
this is effected by prefixing to the predicate a
sign indicating the relation of quantity between
it and the subject, and giving to the propo-
sition an equational form. Thus, e. g., the
proposition, " Y is X," may be expressed in
the form " Y = vX," which is the method of
Boole; or in the form Y = YX," which is
the form proposed by Jevons, and is read,
" Y = the part of X that is Y," or " the Y's
are the X's that are also Y's." Or, more sim-
ply, instead of the proposition, " Y is X," we
may say, " Y is a certain species of X " ; or,
to take a concrete example, instead of the
proposition, " Man is an animal," we may say,
' Man is a certain species or kind of animal."
Hence, whether an equational proposition shall
be expressed in the traditional or in the equa-
tional form is a matter of choice to be
determined by convenience. Generally the
1 A term is said to be " distributed" when it is taken uni-
versally, i. e., where the other term of the proposition is, or
may be, predicated of all the individuals denoted by it, as, e.g.,
the subject of a universal affirmative, or either subject or
predicate of a universal negative proposition (see ^ 87).
58 . LOGIC
traditional form is sufficient, as we can readily
determine from the matter of the proposition
whether it is to be regarded as equational or
otherwise. But in the mathematics the equa-
tional form is much the more efficient, and is
therefore always used.
58. THE INTENSIVE THEORY. The differ-
ence between the traditional and the intensive
theory of predication is that, in construing the
proposition, we have regard in the former to
the extension of the terms only ; but in the
latter, in construing the predicate, we have re-
gard to its intension. Thus, when we say " Man
is mortal," we mean, in the former case, that
the class man is contained in the class mortal ;
but in the latter, that man has the quality or
attribute of mortality. But the latter expres-
sion means nothing more than that " the qual-
ity of mortality is contained in, or among, the
qualities of man "; which is itself an extensive
proposition. Hence the intensive interpreta-
tion of the proposition simply results in an
extensive proposition in which the qualities
of the original terms are substituted for its
original significates, and the terms inverted.
Thus, e.g., if we denote by Y' the qualities of
Y, and by X' the qualities of X, the proposi-
tion, Y is X, may be converted into X' is Y';
which may be called Intensive Conversion, or
conversion by Intensive Interpretation.
THE PROPOSITION 59
59. TRADITIONAL THEORY OF PREDICA-
TION. Even under this theory the proposition
seems to be susceptible of several interpreta-
tions. Thus, e. g., we have interpreted the
copula as meaning " is contained in or " is a
species of " ; and again we may interpret it as
meaning that the significates constituting the
subject class may each and all be called by the
name constituting the predicate or, in other
words, that the name predicated belongs to
the significates of the subject term, or of any of
them ; which has been called interpreting the
judgment "in its denomination " (Thompson's
Laws of Thought, 195). But for all logical
purposes these interpretations are practically
the same, and it will make no difference whether
the proposition be interpreted in the one way
or the other. This is sufficiently obvious with
regard to the expressions, " is contained in,"
and " is a species of " ; and is equally true of
the interpretation suggested by Dr. Thompson.
For, taking as an example the proposition,
' Man is an animal," it is obviously indifferent
whether we construe it as meaning " the class
man is included in the class animal" or that
' it is a species of the class animal," or that
" the name animal is applicable to all signifi-
cates of the name man." These varieties of
interpretation will, therefore, not demand a
further consideration.
DO LOGIC
60. COLLECTIVE AND DISTRIBUTIVE IN-
TERPRETATION. There is, however, another
difference of interpretation it is important to
consider; and especially with reference to
mathematical reasoning, which is to be con-
sidered presently. Common terms, or terms
denoting classes of more than one, may be used
either collectively or distributively, i. e., the
class denoted by the term may be regarded
either as a whole made up of individuals, 1 or as
a number of individuals constituting a class, or
signified by the name. Thus, e. g., the term
" man " may be used to denote either the class
" man," as when we say, "Man is mortal";
or the individuals composing the class, as
when we say, " A man is a mortal," or " Men
are mortals." Whether a term is used collec-
tively or distributively may be indicated, as in
the above examples, by the expression, or may
be simply understood ; or the expression may be
such as not to indicate either expressly or im-
plicitly whether the term is used in the one way
or the other. With regard to the subject of the
proposition it is logically immaterial in which
way the term is used. Thus, in the proposi-
tion, " Y is X, " the subject is used collectively ;
and in the proposition, " All Y's are X's," or
1 When a concrete term is construed collectively, it becomes
abstract, and is to be regarded as denoting, not a number of
real individuals, but one quasi individual only.
THE PROPOSITION 6 1
' Every Y is an X," or "A Y is an X," distri-
butively ; but the forms are logically equivalent.
So with regard to the predicate, where the
terms are of equal extension, it is immaterial
whether it be construed collectively or distribu-
tively, provided, if the predicate be construed
collectively, that the subject also be thus con-
strued. For to construe a term collectively is
to regard the class denoted by it as an individ-
ual, and a term thus construed is therefore to
be regarded as a singular term. But a singular
term cannot be predicated of any but a singu-
lar term, with which it must exactly conform
in signification; or, in other words, a singular
term can be predicated of another singular term
only in the equational proposition. Thus,
e. g., in the proposition, " Y is X," it is im-
material whether we regard Y as denoting the
class Y, or as signifying the significates com-
posing the class. But the class X cannot be
construed collectively unless we also construe
the class Y in the same way, and unless also
the two classes are co-extensive, or, in other
words, unless the proposition can be put in the
form, Y = X.
Ill
OF THE PREDICABLES
61. DEFINITION AND DIVISION OF THE
PREDICABLES. A predicable may be defined
62 LOGIC
as a term that may be made the predicate of an
affirmative proposition. As explained above,
such propositions may be either equational or
non-equational. In the former case the predi-
cate is of the same extension as the subject ; in
the latter, of greater extension. All predi-
cables, therefore, may be divided into two
classes, namely, those that are equivalent to
the subject, and those that are not equivalent.
An equivalent predicable may be either defini-
tion or property ; for each of these is precisely
co-extensive with the subject ( 49). Non-
equivalent predicables must be either genera
or accidents ; either of which may always be
predicated of the subject (/#.). This is the
division of predicables used by Aristotle.
62. TWOFOLD DIVISION OF PREDICABLES.
But the distinction between " definition " and
" property " seems, with relation to the subject
of predicables, to be unimportant; for "prop-
erty" differs from "definition" only in the
use made of the former (/#.). And so with
reference to the distinction between genus and
accident (/#.). Hence it has been proposed
to abandon, as at least unnecessary for logical
purposes" (or rather, we should say, for pur-
poses of predication), "the distinctions between
property and definition, genus and accident,
and to form, as Aristotle has also done, two
classes of predicables ; one of predicables taken
THE PROPOSITION 63
distributively and capable of becoming subjects
in their respective judgments without limita-
tion ; the other of such as have a different ex-
tension. In the former the predicable has the
same objects [2. e. , significates] as the subjects,
but different marks, or a different way of rep-
resenting the marks. In the latter there is a
difference, both in the marks and the objects "
(Thompson's Laius of Thought, 69.)'
63. ONE KIND OF PREDICABLES ONLY.
But even the twofold division of predicables,
into equivalent and non-equivalent, is, from the
traditional standpoint, of minor importance;
for, as we have seen, the old Logic ordinarily
takes no account of equational propositions,
but these, like others, are regarded as import-
ing simply the inclusion of the subject in the
predicate; and in this mode of interpreting
the proposition, we have, in effect, a complete
doctrine of the predicables.
1 The division of predicables most commonly used is that of
Porphyry (Aristotle's Logical Treatises, Bohn's edition, Intro-
duction of Porphyry ; also Jevons's Lessons in Logic, p. 98).
According to this division, " Specific Difference" is substituted
for the " Definition " of Aristotle's division, and there is added
as a fifth predicable, " Species ," as being predicable of individ-
uals. But, as observed by Mansel (Aldrich's Logic, Preface),
"whether this classification is an improvement, or is consist-
ent with the Aristotelian doctrine, admits of considerable
question." The view taken in the text is in every respect
preferable (Thompson's Laws of Thought, pp. 136 et seq.).
64 LOGIC
IV
OF THE RELATIONS BETWEEN TERMS
64. OF THE RELATIONS OF TERMS GEN-
ERALLY. The end of Logic is to determine
the relations, and, as involved in this, the defi-
nitions, of terms, or (what is the same thing),
of the notions expressed in terms ( 16). Of
these notions, the most conspicuous are those
existing between what are called relative words
as, e. g., father and son, wife and husband,
higher and lower, etc., and also the active
and passive forms of the verb, and all in-
flections of verb or noun, or, in a word, all
paronyms, etc. But the term, relative, though
applicable, is not peculiar to this class of
words, and is, therefore, not altogether appro-
priate. Relations, more or less apparent, exist
between all terms, and in the development
of these consists the raison d'etre of Logic.
Hence, properly speaking, no term can be said
to be absolute, as opposed to relative. For
to consider only one of the most general of re-
lations any thing, or class of things (real or
fictitious), must always be assignable to one of
two classes, namely the class denoted by a
given term, or to the class denoted by its
negative ' ; and, in addition to this universal
1 This, of course, is true only on the assumption that we
reject Particular Propositions, as proposed ( 52, note).
THE PROPOSITION 65
relation, there are numerous others, either of a
general character, as e. g., the relation be-
tween numbers, or other expressions of quan-
tity, or such as are peculiar to certain words,
as, e.g., between hunger and animal, hunger
and edible, gravity and body, fish and water,
the sun and the planets, etc. In fine, the re-
lations between terms are innumerable, and,
when the significations of terms are appre-
hended, these relations may, in general, or, at
least, in innumerable cases, be either intui-
tively perceived, or demonstratively inferred.
65. OF THE SEVERAL KINDS OF INTER-
TERMINAL RELATIONS. The relations of
terms are, for various purposes, divided in so
many different ways that it would be impracti-
cable to enumerate them. But, of these divi-
sions, there are three that, either on account of
their intrinsic importance, or of the importance
attributed to them by logicians, will require
our attention. These consist in the distinction
made (i) between the Predicables and the Cate-
gories or Predicaments ; (2) between the formal
and the material relations of terms ; and (3) be-
tween the relations that are intuitively per-
ceived, and those that are not, or, more briefly,
between judgments and assumptions (19, 20).
66. (i) OF THE PREDICABLES AND OF THE
Otherwise we would fall into the same fallacy as Jevons and
Hobbes (v., infra, 90 and note).
5
66 LOGIC
CATEGORIES OR PREDICAMENTS. The dis-
tinction between these corresponds precisely to
the distinction we have made between the
logical and the grammatical forms of the prop-
osition. Etymologically both terms are of the
same import, denoting simply terms that may
be predicated of other terms, i. e. , that may be
made predicates of propositions; but, according
to inveterate use, the former term relates ex-
clusively to the logical proposition, the latter,
to the grammatical. There is, therefore, an
essential difference between the Doctrine of
the predicables and that of the Categories
or predicaments. The former which treats
simply of the relation of species and genus be-
tween the terms expressed in the logical prop-
osition has already been considered. The
latter treats of all the various relations that
may exist between the terms of the grammati-
cal proposition ; and, as these include all rela-
tions, whatever, that may exist between terms,
or between their significates, it follows that the
categories or predicaments are to be understood
as denoting the most general classes into which
such relations may be distributed. By such a
classification if it could be accomplished all
relations between terms and between things
would be developed, and thus a basis furnished
for a classification of all possible predicates.
But the subject is one of difficulty, and in the
THE PROPOSITION 6/
present state of philosophy, a satisfactory treat-
ment of it is impracticable. It would simply
serve, therefore, to confuse the student, if we
should enter upon it, and we will accordingly
omit it.
67. (2) OF THE FORMAL AND OF THE MA-
TERIAL RELATIONS OF TERMS. By informal
relations of terms are meant those relations that
are universal in their nature, i. e., that exist
generally with reference to all terms; as, e. g. ,
the relation between terms and their contra-
dictories, between a term used universally and
the same term used particularly, between the
subject and the predicate of the proposition,
etc. These are all apparent at once from the
mere expression, without taking note of the
matter of the term, except in so far as it is
universal or common to all terms. Thus, e. g.,
in the expression " not-man " we perceive at
once a formal relation between this term and
" man," and in this case the privative " not,"
though part of the matter of the term not-
man, is the ground of the relation; which is
formal because universal. And so, in the
terms " Y " and " some Y," a formal relation
is apparent, though the word " some " is in fact
part of the matter of the term " some Y."
Hence, the distinction between the formal
and the material relations of terms does not,
as is commonly supposed, rest upon the
68 LOGIC
distinction that, in the former case, the matter
of the term is not considered, and, in the latter,
that it is ; but on the distinction that the formal
relations are based upon such part of the mat-
ter or meaning of terms as is common to all or
to many terms, and with that regard to the
material relations this is not the case.
Hence, logically, there is, in fact, no essential
difference of nature between the two kinds of
relation. For the material relations between
terms are as apparent and as certain as the so-
called formal relations, as, c. g,, the relations
between relative terms, as " father " and " son,"
etc., or those between such terms as " island "
and "continent," "island" and "water,"
"body" and "weight," "five" and "seven,"
" nine " and " fifteen," etc. ; and they differ only
in this, that these subsist only in particular
cases, and not universally. Hence the notion
that would restrict the functions of Logic to the
merely formal relations of terms is based upon
an unessential difference of nature between
these and other relations, and therefore cannot
be sustained.
68. (3) OF JUDGMENTS AND ASSUMPTIONS.
Of the immediate relations between terms
some as we have seen are self-evident, or
may be intuitively perceived ; others are not
of this character. Where the relation between
the terms of a proposition is of the former
THE PROPOSITION 69
kind, it is called %. judgment ; where the rela-
tion expressed is of the latter kind (if not
an inference) it is called an assumption (
19 et seq,}. This division of propositions is
based upon an essential difference of nature,
and is one of fundamental importance. It
will therefore require our most attentive con-
sideration.
LOGICAL JUDGMENT DEFINED. In the logi-
cal proposition, the only relation between
the terms expressed is what we have called
the significative relation, i. e., the relation
of inclusion or exclusion of one of the terms
in or from the other. Hence judgment, in
the logical sense, may be defined as consist-
ing in the intuitive perception of a significative
relation between two terms, i. e. , in the in-
tuitive perception that the subject class is, or
is not, included in the predicate class, as,
c. g., where, from our knowledge of the signi-
fication of the terms, we affirm that " man is
an animal, ' ' or that ' ' fishes are denizens of the
water," or that " bodies are affected by grav-
ity," or that " fortitude is the only resource
against the inevitable," or, in the Latin,
" Quidquid crit super anda omnis fortuna ferendo
est."
69. OF THE DISTINCTION BETWEEN
JUDGMENT AND ASSUMPTION. The product
of this mental process as we have seen is
7<D LOGIC
called a judgment ; which may be defined as
a proposition at once self-evident, and not in-
ferred from another proposition or proposi-
tions. Hence, the opinion that " propositions
are judgments expressed in words" is a de-
parture from the logical definition of a judg-
ment. A judgment expressed in words is a
proposition, but the converse is not true. For
where a proposition is based not merely upon
a comparison of its terms, or upon an inference,
but upon extrinsic evidence, or authority, or
other grounds, the forming of an opinion is
not a logical process, and the proposition, from
a logical point of view, is to be regarded,
not as a judgment, but merely as an assump-
tion or hypothesis. Of this kind is the prop-
osition that Pompey's army was defeated at
Pharsalia; that Cicero was murdered by the
Triumvirate ; that a given policy as, e. g.,
protection to home industries, or the remon-
etization of silver, will be beneficial, etc.
70. OF THE DISTINCTION BETWEEN
APODICTIC AND DIALECTIC ( 23). Hence
it may be readily perceived how inadequate
is the conception of Logic that would re-
strict its functions to merely fornial infer-
ence to the exclusion of judgments; or the
conception of demonstrative or apodictic rea-
soning that would confine it to the mathe-
matics : or to the limited class of sciences that
THE PROPOSITION 71
rest upon intuitions, in the sense of the term
used by modern metaphysicians ; or that would
exclude from it all reasoning originating in
judgments involving empirical notions or con-
cepts. For, logically, a judgment as to a sig-
nificative relation between two terms denoting
notions or concepts, of which the apprehension
is empirical, as, e. g., the judgment that
bodies are affected by gravity," that " fish
live in water," that " food will assuage
hunger," etc., is quite as self-evident as the
judgment that " two and three are five," or
that" sixty-four is the square of eight." In
fact, the two classes of judgments are, logi-
cally, of precisely the same nature, each
being but an intuitive perception of a relation
between the significations of two terms; as
follows from our definition.
71. No DISTINCTION IN LOGIC BETWEEN
A PRIORI AND EMPIRICAL NOTIONS. Logic,
therefore, takes no account of the metaphysical
distinction between a priori and empirical no-
tions, but regards all judgments as intuitive.
Its function is simply to determine the relations
existing between the significations of terms;
and if the significations of the terms com-
pared be apprehended, and be of such nature
that the relation between them can be per-
ceived, either immediately i. e. intuitively,
or by intermediary comparison with other
72 LOGIC
terms, the conclusion reached which ex-
presses merely the relation between the signi-
fications of the terms is, so far, absolutely
true.
72. OF THE ERROR THAT RATIOCINATION
is ONLY HYPOTHETICALLY TRUE. Hence
it is an error to suppose that ratiocination is
only hypothetically true, or, in other words,
that Logic is not concerned \vith the truth of
premises. In many cases this is so; but it is
true in no case in which the ratiocination pro-
ceeds from judgments exclusively. For in all
such cases the premises which, as we have
said, merely express significative relations be-
tween their terms are not merely assumed,
but are intuitively known to be true, and the
conclusion is true, not hypothetically but ab-
solutely.
And this is essentially the case even where
the notions involved in the original judgments
or premises are themselves false or unreal; for
the ratiocination has for its direct object only
to determine correctly the relation between
the significations of the terms of the con-
clusion ; and all that is directly asserted in
the conclusion is that the signification of the
terms are related as expressed ; and hence,
when the ratiocinative functions have been
rightly performed, the conclusion must be
necessarily true. But as it is necessary for
THE PROPOSITION 73
purposes of ratiocination that grammatical
propositions be converted into logical, so also,
for practical use or application, all logical con-
clusions must be reconverted into grammatical
propositions, or, in other words, construed as
asserting not merely the significative relation
expressed, but also the truth or reality of the
notions or concepts denoted by the terms; and
when thus construed the conclusion cannot be
regarded as being absolutely true, unless the
terms express real notions. Hence, it may be
said that the conclusions reached in ratiocina-
tion proceeding exclusively from judgments
are, when construed grammatically, true only
upon the hypothesis that the notions involved
in the original judgments or premises are true
or real, and hence, that such conclusions are
true absolutely only as logically construed.
Thus, e. g., the judgment that " all bodies
are affected by gravity" is intuitive; but of
the truth or reality of the notions expressed
by these terms, respectively, we have no as-
surance but experience. And from these ob-
servations it may be perceived how, and in
what sense, it is that Politics, Morality, and
the Science of Human Nature generally are
all to a large extent susceptible of demonstra-
tion, and to that extent apodictic in their nature
( 23 et seq.\
CHAPTER IV
DOCTRINE OF THE SYLLOGISM
I
RUDIMENTS OF THE DOCTRINE
73. ELEMENTS OF THE SYLLOGISM. The
Syllogism consists of three propositions ( 22):
of which two are called the premises, and the
other the conclusion. It has also three terms.
Of. these, two appear as the subject and the
predicate of the conclusion, and are called,
respectively, the minor and the major term.
The other which is called the middle tenn-
is used in both premises: in the one with the
major, in the other with the minor term. The
premise containing the major term is called
the major, and that containing the minor, the
minor premise. Thus in the syllogism, Y is
X, Z is Y, .'. Z is X," Z is the minor, X the
major, and Y the middle term ; and the first
proposition the major, and the second the
minor premise.
74
THE SYLLOGISM 75
74. ANALYSIS OF THE SYLLOGISM. The
proposition is but the expression of a signifi-
cative relation between its terms. Hence the
premises of a syllogism are merely statements
of the significative relations of the terms of
the conclusion (the major and the minor) re-
spectively with the middle term ; and the
conclusion the significative relation thereby
inferred between its terms. The essential ele-
ments of the process consist, therefore, in the
comparison of the two terms of the conclusion
respectively with the third, or middle term,
and in inferring a direct relation between them.
75. DEFINITION OF THE SYLLOGISM.
Hence syllogistic inference may be more
specifically defined as consisting in the infer-
ence of a significative relation between two
terms from their known significative relations
to a third term with which they are respectively
compared. 1
76. THE PRINCIPLE OF THE SYLLOGISM.
The principle of the syllogism (by which is
meant the principle or axiom on which de-
pends the illative force or conclusiveness of
syllogistic inference) is expressed in the Dictum
of Aristotle, or, as it is technically called, the
1 The definition in the text is taken substantially from that
of De Morgan ; who defines the syllogism as "the inference
of the relation of two names from the relation of each of those
names to a third" (Formal Log., p. 176).
76 LOGIC
Dictum de Omni et Nullo. It is variously
stated by logicians, but the several forms are
all, in effect, identical. Its best expression is
as follows :
DICTUM DE OMNI ET NULLO. "Where
three terms (which we will call the middle
and the two extremes] so subsist with re-
lation to each other that the one extreme is
contained in the middle, and the middle is
contained in [or excluded froni\ the other ex-
treme, then [as the case may be] the extreme
included in the middle will be included in [or
excluded front} the other extreme." Where
the predication is affirmative the principle is
called the Dictum de Omni ; where negative,
the Dictum de Nullo.
Omitting in the form given above the words
in brackets, it becomes the Dictum de Omni ;
substituting the words in brackets, marked as
quoted, for the corresponding expressions, it
becomes the Dictum de Nullo.
The two forms of the Dictum (affirmative
and negative) correspond precisely to the two
forms of syllogisms called Barbara and Cela-
rent? viz. :
1 This is substantially the form given to the Dictum by
Aristotle, Prior Analytics, i., iv.
* Forms of the Syllogism. There are nineteen forms of
valid syllogisms recognized by logicians, which are explained
in the next chapter. But if we reject the use of particular
propositions ( 52 n.) all may be reduced to the two forms
THE SYLLOGISM 77
Y is X Y is not X
Z is Y Z is Y
.'. Z is X .'. Z is not X
II
THE PRINCIPLE OF SUBSTITUTION
77. RULES OF INFERENCE. The follow-
ing practical rules may be deduced from the
Dictum :
(1) In any affirmative proposition we may
always (without affecting its illative force or
conclusiveness) substitute for the subject any
other term denoting the same, or part of the
same, significates; and for the predicate any
term denoting the same significates, or a class
that contains them.
Or, more briefly, we may always in the sub-
ject substitute species for genus ; and in the
predicate, genus for species.
(2) So, in any negative proposition, we may,
without affecting its illative force, substitute
for either subject or predicate any term denot-
ing the same, or part of the same, significates.
Or, more briefly, we may always, in the
negative proposition, either in the subject or
the predicate, substitute species for genus.
above given, which are called Barbara and Celarent. In
these forms the several terms may be represented indifferently
by any letters ; and the order of the propositions is imma-
terial. In the traditional Logic the order of the propositions
is always as in the examples given in the text.
78 LOGIC
(3) To which may be added the following:
In any affirmative proposition we may always
substitute for the predicate any other term that
denotes the same significates as the subject, or
a class containing them. 1
78. EQUIVALENCE OF TERMS DEFINED.
In the above rules, it will be observed, the
term substituted is not necessarily equivalent
in signification to the term for which it is sub-
stituted ; but it is equivalent so far as the
force of the inference is concerned, or, as the
lawyers say, quoad the argument. It may be
said, therefore, briefly, that mediate, or syllo-
gistic inference consists simply in substituting
for the terms of propositions other terms equiv-
alent in ratiocinative value.
79. CONVERSIONS OF PROPOSITIONS.
The case of conversion of propositions seems
indeed, to be an exception ; for here the pro-
cess seems to consist, not in the substitution
of terms, but in the substitution of a new
1 The deduction of these rules from the Dictum is perhaps
sufficiently obvious, but as it may not be apparent to all, we
subjoin the demonstration :
In the first syllogism (Barbara) it will be perceived, as ex-
pressed in the minor premise, that Z is a species, and X the
genus, of Y, and that the conclusion is arrived at by substitu-
ting for Y, in the major premise, its species Z ; or, for Y in the
minor premise, its genus X.
In the latter syllogism (Celarent) the process consists in sub-
stituting for Y, in the major premise, its species Z ; and so it
is obvious we may substitute for X in the major premise any
THE SYLLOGISM
79
proposition containing the same terms as the
original with the order of terms transposed.
But the exception, in the case of negative and
equational propositions, is more apparent than
real ; for the two forms of the proposition (i. e.,
the converted and the original proposition) are
precisely the same in effect, and there is, in
fact, neither term nor proposition substituted.
For when we say " Y is not X," we equally
and as explicitly say " X is not Y " the mean-
ing of either proposition being simply that the
two classes denoted by X and Y are mutually
exclusive; and so in the equational proposition
(Y = X) we say, in the same breath, both that
Y is equal to X, and that X is equal to Y. So,
species of the genus X, as, e. g., A, B, or C, and thus con-
clude that " Z is not A, B, or C " (as the case may be) ; as may
be illustrated by appropriate diagrams :
So, in the major premise in Barbara, we may substitute for
X the expression YX, or any species of X containing Y, as,
e. g., A, and thus conclude that Z is YX, or Z is A, as the
case may be.
8O LOGIC
upon consideration, it will be found that the
conversion of the (universal) affirmative propo-
sition i. e., conversion per accidens is not an
exception to the rule, but an application of it;
for the process consists simply in substituting
for the predicate another term precisely equiv-
alent to the subject in signification, as, e. g.,
in the proposition Y is X," the expression
" some X" for " X," meaning, by the ex-
pression " some X," that part of X which co-
incides with Y; which is but an application of
Rule 3. And when this substitution is made,
the proposition becomes equational, and means
the same thing whether we convert it or
not.
80. OF IMMEDIATE INFERENCES GENER-
ALLY. Propositions derived from other propo-
sitions by conversion, and also those derived
by opposition (explained infra, 89), are re-
garded by recent logicians as inferences, and
to distinguish them from syllogistic inferences
are called immediate. This innovation we re-
gard as unfortunate, though of too general use
to be neglected, for, according to our view,
only one kind of inference is allowed, namely,
syllogistic. This, as we have shown, includes
the case of conversion per accidens ; and it also
includes other, and perhaps all, cases of so-
called immediate inference ; as may be readily
shown.
THE SYLLOGISM 8 1
(i) SUBSTITUTION OF CONTRADICTORY.
One of these is what is called by Bishop
Thompson, " Immediate Inference by Means
of Privative Conceptions" and by other logi-
cians, improperly, " Infinitation" It is, in fact,
identical with the process treated hereafter
under the head of " Conversion by Contrapo-
sition " ( 91). It consists in substituting for
the predicate its negative, or contradictory, and
in changing the quality of the proposition,
i. e., making the copula of the negative propo-
sition affirmative, or that of 'the affirmative
proposition negative. Thus, denoting the
terms by the capital letters Y and X, and their
negatives or contradictories by aY and aX,
the negative proposition " Y is not X " may be
converted into the affirmative proposition, " Y
is aX " ; and similarly the affirmative proposi-
tion, " Y is X," into the negative proposition,
" Y is not aX " (i. e., is not Not-X). The
validity of the process, as may be illustrated
by the following diagrams, rests upon the prin-
ciple that any negative proposition, as, e. g.,
" Y is not X," may always be regarded either
as denying that the class Y is included in the
class X, or as affirming that it is included in
the class aX, or "Not-X"; and conversely
the affirmative proposition, " Y is X," may
be regarded either as affirming that the
class Y is included in the class X, or as
82
LOGIC
denying that it is included in the class aX,
Not-X."
or
But when from the affirmative proposition
' Y is X " we conclude that " Y is not Not-
X," there is a syllogistic inference; which, de-
noting the negative or contradictory of X by
aX, may be thus expressed :
X is not aX (/. e., not Not-X)
Yis X
.*. Y is not aX.
The inference, therefore, rests upon the
judgment that the term " X " is equivalent to
the term " Not-aX," and consists in substi-
tuting the latter for the former. Hence the
principle of inference involved may be stated
generally by saying that a term is always
equivalent in signification to the contradictory
of its contradictory, or, as otherwise expressed,
the negative of its negative ; which is but a
different expression of the maxim that " two
negatives make an affirmative."
It is, indeed, said that the major terms in the
two propositions are the same the proposi-
tions differing only in quantity, and hence
THE SYLLOGISM 83
that no third term is introduced. But this is
incorrect ; for the major term in the former
proposition is X, and in the latter " not
Not-X " ; and it is a fundamental logical doc-
trine that no two terms are identical that differ,
.either in denotation or connotation, or vocal
sign ; and also that the very essence of ratio-
cination consists in the recognition of identity
of signification in terms having different con-
notations or vocal signs, and in the substitution
of the one for the other ( 77 et seg.}.
(2) IMMEDIATE INFERENCE BY ADDED DE-
TERMINANTS, AND (3) THE SAME BY COMPLEX
CONCEPTIONS. These kinds of supposed im-
mediate inference were introduced into Logic
by Leibnitz (Davis, Theory of Thought ; , p. 104).
The former is stated in the proposition that the
same mark may be added to both terms of a
judgment; the latter, in the proposition that
the two terms of a judgment may be added to
the same mark. Of the former, the example
given by Thompson is: "A negro is a fellow-
creature," therefore, " A negro in suffering is
a fellow-creature in suffering " ; of the latter:
" Oxygen is an element," and therefore, " The
decomposition of oxygen would be the decom-
position of an element." The two processes
seem to be in substance the same, and both
may be expressed symbolically by saying that
" If Y is X," then" ZY will be ZX," or (what
84 LOGIC
is the same) " YZ will be YX " ' ; as may be
thus symbolically illustrated:
This process is erroneously regarded by logi-
cians as an immediate inference; but it is, in
fact, mediate, and may be stated in syllogistic
form as follows :
Y is X
ZY is Y
.'. ZY is X
The conclusion " ZY is X," fully expressed,
is that ZY is that part of X with which it co-
incides ; or, in other words, that " ZY is ZYX."
But ZYX is ZX; and hence ZY is ZX.
In this case the observations made with
reference to infinitation (supra) will apply a
fortiori ; for here a new term, " ZY," is in-
troduced, differing from Y in denotation, in
connotation, and in verbal sign.
1 But the converse is not true, i. <*., from the proposition,
ZY is ZX, we cannot infer that Y is X ; as will appear from
the following diagram :
THE SYLLOGISM 8$
It may therefore be concluded, as already
asserted, that all inference consists in sub-
stituting, for terms of propositions, other terms
of equivalent ratiocinative value.
81. FORMAL AND MATERIAL SUBSTITU-
TIONS. Substitution of terms may be either
formal or material. The former includes all
cases where the substituted term is the original
term in a modified form, as, where the ele-
ments of a complex term are arranged in a dif-
ferent order, as, e.g., where YX is substituted
for XY ; or, as where the original term is
qualified by some other word or words express-
ing a formal relation existing between the sub-
stituted term and the original, as, e. g., where
in the proposition " Y is X," we substitute for
" Y " " some Y, " or for " X " " not Not-X ' ' ;
or, as in the example given above, where we
substitute for " negro " and " fellow-creature "
the terms " negro in suffering " and " fellow-
creature in suffering." Material substitutions
are those where a new term is substituted, as,
e.g., where we substitute for a term a syno-
nym, or species for genus, or genus for species.
Ill
OF MATHEMATICAL REASONING
82. MATHEMATICS THE TYPE OF ALL
RATIOCINATION. Hence it would seem that
86 LOGIC
the most perfect type of ratiocination is pre-
sented by the mathematical, and especially by
the algebraic methods of demonstration ; and
this is, in fact, the case, as may be illustrated
by two familiar examples:
ist Example. Thesis. The angles of a plain
triangle are together equal to two right angles;
or, referring to the figure, a -f- b -j- c = /K
(Euclid, Book I., Prop. XXXII.).
For
a + b' + c' = &. (/, Prop. XXIX.).
But
b' = b
c' = C.
Hence, substituting equivalents,
a-|-b' + c' = a-)-b-(-c= i\\. Q. E. D.
zd Example. T/iesis. The formula for com-
pound interest, i. e., S = p (1 -f- r) n , in which
p = principal, n = number of years, r = rate
of interest, and S = the amount.
At end of first year
S = p + pr = p (1 + r).
At end of second year
S = p(l + r)+pr(l + r) = p(l + r)-.
THE SYLLOGISM 8/
At end of third year
S = p (1 + r)' + pr (1 + r)' = p (1 + 0.
At the end of n years
S = p (1 + r) n .
83. A CURRENT ERROR ON THIS POINT.
It is indeed asserted by recent logicians that
there is an essential difference between ordinary
and mathematical, or, as it is otherwise ex-
pressed, between qualitative and quantitative
reasoning. But this opinion arises from the
failure to reflect that the comparison of magni-
tudes can be effected only by means of units of
measurement that can be applied equally to
the magnitudes compared, and that these con-
stitute the significates denoted by mathemati-
cal terms. Hence mathematical reasoning
consists not in directly comparing the magni-
tudes considered, but in comparing the units
that represent them ; and mathematical terms
must therefore be regarded as denoting like
other terms collections or classes of individ-
uals, /. e. , of the units expressed.
AN OPINION OF MR. BAIN. On this point
we have the following from Mr. Bain: " Logi-
cians are aware that the form ' A equals B, B
equals C, therefore A equals C ' is not reducible
to the syllogism. So with relation to ' greater
88 LOGIC
than' in the argument a fortiori ; yet to the
ordinary mind these inferences are as natural,
as forcible, and as prompt as the syllogistic
inference." But the first expression is a per-
fect syllogism differing from the ordinary form
only in the different interpretation given to the
copula; and this is true also of the argument
a fortiori, if we give it the form, " A < B,
B < C . *. A < C." It is strange this is not
recognized by the author; or, rather, would be
strange were not the error common. What
is meant, therefore, is that the mathematical
cannot be reduced to the ordinary form of the
syllogism. But this is not the case, for mathe-
matical reasoning can readily be expressed in
the ordinary logical forms, as, e. g., the equa-
tional syllogism in the two syllogisms follow-
ing:
a is b b is a
b is c c is b
.'. a is c .'. c is a;
and the argument a fortiori in the following:
" a is b, b is c, .'. a is c,"- meaning that the
class of units denoted by a is contained in the
class denoted by b, etc.
Or the inequalities may be converted into
equations, as, e . g. ," a < b " into " a -f- x = b, "
and the argument then be expressed in two
syllogisms as above.
THE SYLLOGISM 89
84. REDUCTION OF EUCLID'S FIFTH
PROPOSITION TO SYLLOGISMS. Recognizing
the mathematical form of the syllogism, there
is no need of the cumbersome method usually
adopted for the reduction of mathematical
reasoning to syllogistic form, as, e. g., in the
ancient example of the reduction of Euclid's
Fifth Proposition given by Mansel in his notes
to Aldrich ; or the reduction of the same prop-
osition by Mill (Logic, p. 142).
In fact, Euclid's demonstration is itself in
syllogistic form, and needs only a slight varia-
tion in the statement of it to make this ap-
parent, as, e. g., as follows:
Prop. V. The angles at the base of an
isosceles triangle are equal to one another.
Or, referring to the figure, in the isosceles
triangle ABC the angles a and c are equal.
The figure is constructed by
producing the equal sides A B
and A C to D and E, making
the lines A D and A E equal,
and by drawing the lines B E
and D C.
Demonstration
1ST SYLLOGISM
Major Premise. Prop. IV.
Minor Premise. The triangles ABE and
90 LOGIC
A C D are triangles having two sides of the one
equal to two sides of the other, each to each,
and the included angle equal.
Conclusion. They are therefore equal in all
their corresponding parts, and hence B E =
C D and the angle d = the angle e.
2D SYLLOGISM
Major Premise. Prop. IV.
Minor Premise. The triangles C B E and
BCD are triangles having two sides of the one
equal to two sides of the other, each to each,
and the included angle equal.
Conclusion. They are therefore equal in all
their corresponding parts, and hence the angle
f = the angle g.
3D SYLLOGISM
Major Premise, a d f. (Judgment, or
intuitive proposition.)
Minor Premise, d f = e g.
Conclusion, a = e g.
4TH SYLLOGISM
Major Premise, a = e g.
Minor Premise, e g = c.
Conclusion, a = c.
CHAPTER V
SUMMARY OF THE TRADITIONAL LOGIC
OF THE TRADITIONAL LOGIC GENERALLY
85. As explained in the preface, one of
the principal objects of this work is to vindi-
cate, as against modern innovations, the old or
traditional Logic; and accordingly, in all that
has been said with exceptions to be noted
presently I have kept close to the traditional
view, as expounded by Aristotle and the most
approved of the older logicians. I have, in-
deed, repudiated the doctrine advocated by
Whately, and by modern logicians generally,
that would distinguish between the formal and
the material relations of terms, and restrict the
scope of Logic to the former; but in this also
I follow Aristotle and the better authorities.
The only particulars, therefore, in which I
have departed from the traditional view of
Logic are: (i) that I reject the " Particular
Propositions " of the old Logic and those parts
of the old doctrine of the Proposition and of
91
92 LOGIC
the Syllogism that are founded on this view
of the proposition ; and (2) that I have adopted,
in place of the Dictum, the Principle of Sub-
stitution ; which is an obvious corollary from
the Dictum, and is more readily understood
and applied.
At the same time, it must be admitted, the
old doctrines of the Proposition and the Syl-
logism are remarkable for the accurate analysis
upon which they rest, and the wonderful ingen-
uity and acuteness with which they have been
developed. They have thus become part of
the accepted philosophy of the world ; and there
has thus been developed a technical language
that has come to be universally received and so
generally used that, without an understanding
of it, all the literature on the subject must be
a closed book to us. I now propose, therefore,
to give a brief exposition of these doctrines.
II
THE TRADITIONAL DOCTRINE OF THE PROPOSITION
86. QUALTITY OF PROPOSITIONS. Prop-
ositions are said to differ in quality accord-
ingly as they are affirmative or negative. Thus
the propositions " All Y is X and " Some
Y is X " are affirmative ; the propositions " No
Y is X " and " Some Y is not X," negative.
87. QUANTITY OF PROPOSITIONS. Again,
propositions, whether affirmative or negative,
TRADITIONAL LOGIC
93
are said to differ in quantity accordingly as the
predicate is asserted, or denied universally of
all individuals of the class denoted by the sub-
ject or only part of such individuals. In the
former case the subject is said to be distributed,
and the proposition is called universal ; in the
latter, the subject is undistributed, and the
proposition is said to be particular. Thus,
e. g., the propositions, " All Y is X" and
4 No Y is X " are both universal; and the
propositions, " Some Y is X " and " Some Y
is not X," both particular.
88. TABLE OF PROPOSITIONS. Hence,
four forms of propositions are recognized by the
old logicians, viz. : (i) the Universal Affirma-
tive ; (2) the Universal Negative ; (3) the Par-
ticular Affirmative; and (4) the Particular
Negative ; which are designated respectively
by the letters A, E, I, and O; and, with their
expressions in Euler's Symbols, are as fol-
lows, viz. :
A: Y is X (/.<?., All Y is X)
E: Y is not X (/. e., No Y is X) ' (Y)
I: Some Y is X
O: Some Y is not X
1 The above differs somewhat from the ordinary notation ;
94 LOGIC
In the negative propositions, E and O, it
will be observed, the predicate is distributed or
taken universally ; in the affirmative proposi-
tions it is undistributed.
89. OPPOSITION OF PROPOSITIONS. Two
propositions are said to be opposed to each
other when, having the same subject and pred-
icate, they differ in quantity or quality, or both.
Propositions that differ both in quality and
quantity, as A and O, or E and I, are called
contradictories, as, e. g. , " Y is X," and " Some
Y is not X " ; or " Y is not X " and " Some
Y is X." Those that differ in quality only, if
according to which it is thought necessary in A and E to use
the signs " All " and " No," in order to indicate that the sub-
ject is distributed, as, e. g., "All Y is X," "No Y is X."
But, properly speaking, the signs "All" and " No" are un-
necessary and redundant. For when we say, e. g., "Man is
mortal," or " Man is not mortal" we mean, when we speak
properly, that in the former case the class "man" is wholly
included in, and in the latter that it is wholly excluded from,
the class " mortal " ; or, in other words, as the case may be,
that " All men are mortal" or that " No man is mortal"
( 53. n -)- The last expression is also objectionable on ac-
count of the liability to confound the expression " No man "
with the term " Not-man " in converting either of the above
propositions by contraposition (for which see infra, 91) ;
or (more generally) the negative proposition "No Y is X "
is liable to be confounded with the affirmative proposition,
"A T ot- Y is X." Hence it will be preferable to regard the
subject as always distributed, except where it is preceded by
the adjective " some " ; and, in place of the sign " no" before
the subject, to use the particle " not " after the copula.
TRADITIONAL LOGIC 95
universal, are called contraries, as, e. g., " Y is
X " and " Y is not X " ; and if particular, sub-
contraries, as, e. g., " Some Y is X " and
" Some Y is not X." Where propositions
differ in quantity only, as A and I, or E and
O, the particular propositions are called subal-
terns, as, e. g. , " Y is X " and " Some Y is
X "; and " Y is not X " and " Some Y is
not X."
There are, therefore, four kinds of opposition
recognized by logicians, viz. : (i) the opposi-
tion of contradictories ; (2) that of contraries ;
(3) that of subcontraries, and (4) that of subal-
terns to their corresponding universals; which,
with their relations to each other, are admi-
rably expressed in the following table, which
has come to us from ancient times:
!\ /\
I V I
5 <* "**>
V \\
-SUBCOMTRARY-
(i) CONTRADICTORIES. The most complete
kind of opposition is that of contradictories.
These cannot both be either true or false: i. e.,
if one is true, the other is false; or, if one is
96 LOGIC
false, the other is true. For if it be true that
" All men are sinners," it cannot be true that
" Some men are not sinners " ; and, conversely,
if it be true that " Some are not righteous," it
cannot be true that " All men are righteous."
In other words, between contradictories there
is no intermediate proposition conceivable ; one
must be true and the other false. This is
called the law of Excluded Middle.
(2) CONTRARIES. Contraries cannot both
be true; for if it be true that " Every man is
an animal," it must be false that " No man is
an animal." But both may be false, as, for
example, the propositions that " All men are
learned," and that " No men are learned";
which are both false, for some are learned and
some are not. In other words, contrary propo-
sitions do not exclude the truth of either of the
particular propositions between the same terms.
(3) SUBCONTRARIES. Subcontraries are con-
trasted with contraries by the principle that
they may be both true, but cannot both be
false. Thus it may be true that " Some men
are just," and also that " Some men are not
just " ; but if it be false that " Some men are
just," it must be true that " No man is just,"
which is the contradictory, and, a fortiori,
that "Some men are not just," which is the
subcontrary.
(4) SUBALTERNATE OPPOSITION. With re-
TRADITIONAL LOGIC 97
gard to subaltern propositions, their truth
follows from the corresponding universal pro-
positions; for if " all men are animals," " some
men are animals," and if " no man is an ape,"
" some men are not apes." But from the truth
of a subaltern proposition we cannot infer the
truth of the corresponding universal, as, e. g.,
from the proposition " Some men are false,"
the proposition " All men are false "; or from
the proposition " Some men are not false," the
proposition that " No man is false."
90. OBSERVATIONS UPON CONTRARY AND
CONTRADICTORY OPPOSITIONS. Accurately
speaking, these constitute the only kinds of
opposition. Subcontraries are, in fact, not op-
posites; and the same is true of subalterns and
their corresponding universals.
It will be observed it does not follow from
the principle of contrary opposition that of
two terms regarded as subject and predicate
as, e. g. , Y and X either the latter or its
negative may always be predicated of the
former, or, in other words, that Y must be
either X, or not X; for, in fact, some Y may
be X, and some Y not X, as will obviously
appear from the following diagrams:
98 LOGIC
Hence there arises, seemingly, a puzzling
contradiction between this principle and the
law of Excluded Middle as it is often stated.
Thus, it is said, " Rock must be either hard or
not hard" (Jevons, Lessons in Logic, p. 119),
or, generally, " Y is either X or not X." But
obviously this, unless accidentally, is not true;
for some rock may be hard and some soft ; or
some Y may be X, and some not X. And so
we cannot say of " men " either that they are
learned or that they are not learned ; for some
are the one and some the other. But the ap-
parent contradiction arises from the misstate-
ment of the law of Excluded Middle; which
is itself nothing more or less than the principle
governing contradictories, as expressed above.
We may, indeed, where a subject term (as,
e. g., Y) denotes an individual or single thing
(real or fictitious), affirm of it that it is either
X or not X; but if Y denotes a class of more
than one we cannot so affirm. 1
1 Even Hobbes falls into the error of Jevons on this point.
"Positive and negative terms," he says, "are contradictory
to one another, so that they cannot both be the name of the
same thing. Besides, of contradictory names, one is the name
of anything whatsoever (i. e., of any conceivable thing), for
whatsoever is, is either a man, or not a man, white, or not
white, and so of the rest." But, it may be asked, " Does the
name 'biped' denote (universally) either man, or not man?" or
" the name 'man', either white man, or man not white?"
The confusion results from the technical view that regards
TRADITIONAL LOGIC 99
91. CONVERSION OF PROPOSITIONS. A
proposition is said to be converted when its
terms are transposed, i. e., when the subject is
made the predicate and the predicate the sub-
ject ( 54). Such conversion is admissible
only when illative, i. e., where the truth of the
converse is implied in that of the original prop-
osition. When such conversion can be made
without otherwise changing the proposition it
is called a simple conversion; otherwise, it is
called a con version per accidens. Thus A (" Y
is X ") cannot be converted simply, because the
subject only is distributed; we therefore can-
not say that " All X is Y," but only that
" Some X is Y," which is called conversion per
accidens. But E (" Y is not X ") as both sub-
ject and predicate are distributed may be con-
verted simply ; or, in other words, we may say
the Particular Proposition as a form distinct from the Uni-
versal, and its source would be removed if, as elsewhere
suggested, this form of the proposition should be rejected
( 52, n.). We might then adopt, as equally accurate
and profound, the remaining observation of Hobbes, that
"the certainty of this axiom, namely, that of two contradic-
tory names one is the name of anything whatsoever, the other
not, is the original and foundation of all ratiocination, that
is, of all philosophy" (Logic, Sec. 8), which is in accord with
the view of Aristotle : " For the same thing to be present and
not to be present, at the same time, in the same subject, and
in the same sense, is impossible. . . . For by nature this
is the first principle of all the other axioms " (Metaphysics,
R. iii., chap. Hi.).
IOO LOGIC
that " No X is Y." So with I (" Some Y is
X "), as both subject and predicate are un-
distributed, the proposition may be simply
converted, i. e., if " Some Y is X," then it is
necessarily true that " Some X is Y."
By one or the other of these methods, i. e.,
either simply or per accidens, all propositions of
the forms A, E, and I may be converted. But O
(" Some Y is not X ") cannot be thus converted.
Thus, e. g., it cannot be inferred from the prop-
osition "Some Greeks are not Athenians"
that " Some Athenians are not Greeks." But
such conversion may be effected by simply re-
garding the negative particle (not) as part of
the predicate ; by which expedient O is changed
into I, and may be simply converted, as, e. g.,
"Some Greeks are Not-Athenians " ; which
may be converted into the proposition " Some
Not-Athenians are Greeks. ' ' So from the prop-
osition " Some men are not learned," though
we may not infer that " Some learned are not
men," we may infer that " Some unlearned
are men." This is called by the old logi-
cians "Conversion by Contraposition," and by
Whately, " Conversion by Negation."
This method of conversion is applicable to
A and E as well as O, and, as it is of very ex-
tensive use, we append a table of such conver-
sions, taken, with some alterations, from De
Morgan (Formal Logic, p. 67). In this table
TRADITIONAL LOGIC IOI
(altering De Morgan's notation) the original
terms of the proposition are denoted by the
capital letters Y and X, and their contraries
respectively by prefixing the Greek privative a.
We append also for illustration the symbolical
expressions for the several propositions:
A: " Y is X " ; " Y is not aX " ; " aX is not Y " ;
" aX is aY " :
The righteous are happy
The righteous are not unhappy /
The unhappy are not righteous '
The unhappy are unrighteous.
E: "YisnotX"; " Y is aX " ; " Some aX is Y " ;
" Some aX is not aY."
" X is not Y " ; " X is aY " ; " Some aY is X " ;
" Some aY is not aX " :
Perfect virtue is not human '' \j \
Perfect virtue is unhuman IS~\ /f~\\
Y Ca A I X I
Some unhuman virtue is perfect v^
Some unhuman virtue is imperfect. \ ,
^^ *s
Human virtue is not perfect
Human virtue is imperfect
Some imperfect virtue is human
Some imperfect virtue is not unhuman.
O: " Some Y is not X " ; " Some Y is aX " ; " Some
aX is Y " ; " Some aX is not aY " :
102 LOGIC
Some possible cases are. not probable
Some possible cases are not improb-
able
Some improbable cases are possible
Some improbable cases are not im-
possible.
It will be observed from the above table that
a universal affirmative proposition can always
be converted into another universal affirmative
between the contradictories of its original terms
by simply reversing the order of the terms and
substituting for them their contradictories.
92. OF MATERIAL CONVERSIONS. It will
be observed that the conversions of propositions
treated by logicians have regard to the dis-
tinction, heretofore explained, between the
formal and the material relations of terms
( 66 (2)), and are confined exclusively to what
may be called formal conversions, i. e., to cases
where the equivalence of the converted and
original propositions results from the formal or
general relations of terms. But conversions of
propositions based upon the material relations
of terms are of essentially the same nature, as,
e. g., where the proposition " John is the son
of William " is converted into the proposition
William is the father of John"; or the
proposition" Cain murdered Abel" into the
proposition " Abel was murdered by Cain," or
into the proposition " Cain is the man that
TRADITIONAL LOGIC 103
murdered Abel." These, having regard to
the received distinction between the formal
and the material relations of terms, may be
called material conversions ; and are infinitely
the more numerous class, and equally deserv-
ing of attention. But though conversions of
this kind are in constant use, and though, in-
deed, we cannot proceed a step in our logical
processes without them, yet the subject has
received but little attention, and remains as
yet a vast, unexplored domain. 1 It can only
be said, therefore, in the present condition of
logical doctrine, that as the distinction be-
tween the formal and the material relations of
terms has been found unessential, so must the
distinction between formal and material con-
versions be regarded. Both classes of conver-
1 To this domain belong such subjects as the "Categories"
"Intensive Propositions,'''' " Hypothetical Propositions" and,
in short, all forms of expression that differ from the ordinary
logical proposition. With these Logic is concerned only in
so far as is involved in their conversion into logical forms.
Otherwise, neither the Intensive nor the Hypothetical Logic
(if we may give either the name) can be regarded as part of
Logic as traditionally received ; which is based exclusively
upon the logical form of the proposition and its extensive
interpretation. With regard to the Hypothetical Logic, it
will be observed, it has no place in Aristotle's treatises ; and
Mansel is of the opinion in which I agree that in this he
showed a juster notion of the scope of Logic than his suc-
cessors. The subject is well treated in the current works on
Logic, and is worthy of some attention from the student.
104 LOGIC
sions rest equally for their validity simply
upon judgments as to the equivalence of ex-
pressions.
Ill
THE TRADITIONAL DOCTRINE OF THE SYLLOGISM
93. The following epitome of the doctrine
of the syllogism as traditionally received, brief
as it is, will with what has already been said
be found amply sufficient to expound it.
It will, indeed, require the same close attention
and thought as is usually given to mathemati-
cal demonstrations; but it may be said that
to those who are unwilling to give, or are in-
capable of giving, to it this kind of thought,
the study of Logic cannot be of much benefit.
I . Of the Moods and Figures of the Syllogism
94. MOODS OF THE SYLLOGISM. The syl-
logism is said to be in different moods, according
to the occurrence and arrangement in it of the
several forms of the proposition A, E, I, and
O; as, e. g., in the syllogism Y is X, Z is
Y, . *. Z is X, ' ' which consists of three universal
affirmative propositions, and is, therefore, said
to be in the mood A A A.
The four forms of the proposition, A, E, I,
O, may be arranged, in sets of three each, in
sixty-four different ways, but upon examina-
tion it is found that of these there are eleven
TRADITIONAL LOGIC 1 05
arrangements only that constitute valid syllo-
gisms; and hence the legitimate syllogism can
have but eleven moods, viz. :
Table of Moods
A A A, A A I, A E E, A E O, A I I,
A O O, E A E, E A O, E I O, I A I, O A O.
95. FIGURES OF THE SYLLOGISM. Again,
syllogisms are said to be of different figures,
according to the position of the middle term in
the syllogism with reference to the extremes;
and as there are said to be four different ways
in which the middle term may be thus placed,
syllogisms are said to have four figures, viz. :
the 1st figure, where the middle term is the
subject of the major and the predicate of the
minor premise ; the 2d, where it is fa& predicate
both of the major and of the minor premise ;
the 3d, where it is the subject of both the major
and the minor premise ; and the 4th, where it
is the predicate of the major and the subject of
the minor premise. Thus using the conven-
tional symbols the forms of the different
figures are usually expressed as follows :
Table of Figures
1st Fig. 2cl Fig. 3d Fig. 4th Fig.
Y X, X Y, Y X, X Y,
Z Y, Z Y, Y Z, Y Z,
Z X, Z X, Z X, Z X.
106 LOGIC
If the eleven moods of the syllogism were all
valid in each of the four figures, there would
result forty-four different kinds of syllogisms
differing in mood or figure. But none of the
moods are valid in all the figures; and it is
found on examination that there are in fact
only twenty-four kinds of syllogisms that are
valid ; and that of these five are useless. So
that the number of different kinds of legiti-
mate syllogisms recognized by logicians is
nineteen.
96. REDUCTION OF SYLLOGISMS. All
these forms may, however, be reduced or con-
verted without affecting their validity into
the form of the first figure ; which is accord-
ingly regarded by logicians as the principal, or
normal figure of the syllogism. The different
figures and moods of the syllogism, and the
methods of reduction or conversion from one
figure to another, are briefly expressed in the
following hexameter verses, constituting what
may be called
The Table of Syllogisms
Fig. i Barbara, Olar^nt, Dam, Ferioque, prioris
Fig. 2 Cesare, Canvstr^s, Festino, Fak^n?, secundae
Fig. 3 Tertia, Darapti, D/sam/s, Dat/sz', Fi?lapt<?n,
D0kam0, Feriso, habet, quarta insuper
addit
Fig. 4 Bramant/p, Camenes, D/man's, Fesapo,
Fresison.
TRADITIONAL LOGIC IO/
In these lines the words commencing with
capital letters (except " Tertia ") are the names
of the several syllogisms in each figure, and
the italicized vowels point out the moods of
the propositions constituting the several syl-
logisms. Thus, e. g., the vowels indicate that
Barbara consists of the three propositions, A,
A, A; Celarent of E, A, E; Darn of A, I, I ;
Feriso of E, I, O, etc.
The initial letter in the name of each syllo-
gism in the second, third, and fourth, or, as
they are called, the indirect figures, indicates
that the given syllogism is to be reduced to the
syllogism in the first figure commencing with
the same letter, as, e. g,, Cesare, Camestres,
Camenes into Celarent ; Bramantip into Bar-
bara ; Darapti y etc., and Dimaris, etc., into
Darii ; Festino, etc., Felapton, etc., and Fesapo,
etc., into Ferio.
The letters s, p, and k indicate that the pro-
position indicated by the vowel immediately
preceding is to be converted s indicating
simple conversion, / conversion per accidens,
and k conversion by contraposition, or nega-
tion. '
1 The use of conversion by contraposition as a means of
reduction is a late invention. It is, in general, used only in
the two forms, Fakoro and Dokamo, or, as they were origi-
nally called, Baroko and Bokardo, as all other forms can be
reduced without its aid, i. e., by the use of simple conversion
or conversion per accidens. Prior to the use of this method,
io8 LOGIC
The letter m indicates that the premises are
to be transposed.
The other letters are without significance.
TABLE OF SYLLOGISMS. By the use of the
' Table of Moods" and the " Table of Fig-
ures," all the syllogisms given in the " Table
of Syllogisms" may be readily constructed,
and the mode of reducing the syllogisms in the
second and third and fourth figures to the cor-
responding syllogisms in the first figure be
readily perceived. 1
Baroko and Bokardo could not be directly reduced to the first
figure, but indirectly only by a process called rednctio ad
impossible ; which consisted in substituting for one of the
premises the contradictory of the conclusion.
By this method Baroko is converted into a syllogism in Bar-
bara, having the contradictory of the original conclusion for a
minor premise, and the contradictory of the original minor
premise for a conclusion, which, as the minor premise is true
ex hypothese, is an absurdity, viz. :
(Original Syllogism) (Reduced Syllogism)
X is Y X is Y
Some Z is not Y Z is X
.'. Some Z is not X .'. Z is Y
By the same method Bokardo is converted into a syllogism
in Barbara, having the contradictory of the original conclusion
for a major premise, and the contradictory of the original
major for a conclusion, e. g. :
Some Y is not X Z is X
Y is Z Y is Z
. ' . Some Z is not X . ' . Y is X
1 A table of the several syllogisms, with their reductions,
illustrated by Euler's symbols, is appended (see Appendix M).
TRADITIONAL LOGIC 109
97. OBSERVATIONS UPON THE FORMS OF
SYLLOGISMS. It will be observed from what
has been said that the numerous forms of syl-
logisms recognized by the old logicians result
from two assumptions the one erroneous and
the other unnecessary.
The first is the erroneous assumption that
the symbols Y and X must always be taken as
denoting respectively the minor and the major
terms; from which results that there areyWr
figures of the syllogism, instead of three. But
if in the fourth figure we regard X as the minor
term and Y as the major, it becomes of the
first figure. Hence the fourth figure which
was not recognized by Aristotle, but is a late
invention is rightly rejected by the best
authorities.
The other assumption is that the particular
propositions (" Some Y is X " or " Some Y is
not X ") are to be regarded as involving the
same terms as the universal (" Y is X " or " Y
is not X "), and the expression " some " as a
mere sign of quantity; from which (and the
first assumption) there result the four forms of
the proposition, A, E, I, and O, and the nine-
teen forms of syllogism recognized by logicians,
Barbara, Celarent, etc. 1
1 The doctrine of the syllogism, and especially that of its
moods and figures, has been elaborated by the logicians per-
haps to an unnecessary extent, but as it stands must always
I IO LOGIC
98. PROPOSED SIMPLIFICATION OF
FORMS. But if in the particular propositions
(I and O) we regard the expression " some "
not as a sign of quantity, but as part of the
term, or, in other words, if we regard " Some
Y " instead of " Y " as the term, they be-
come the same as" A" and " E," i. e., Univer-
sal ( 52, n.). By this simple change the four
forms of the proposition are reduced to two (A
and E), and the nineteen forms of syllogism to
the two simple forms of Barbara and Celarent. 1
2. Of the Dictum de Omni et Nullo
99. OF THE SEVERAL FORMS OF THE
DICTUM. The principle of the syllogism, or
the Dictum de Omni et Nullo, has already been
considered at length, and what has been said is
sufficient to elucidate its nature. It is, how-
ever, variously stated by logicians, as indeed
by Aristotle himself, and it will be of interest
to consider some of its various forms.
constitute a necessary part of a liberal education. For prac-
tical use, however, it is unnecessarily complicated ; and it will
be found that when modified, as we have suggested (i. e., by
rejecting the particular proposition, and substituting for the
ordinary form of the dictum the Principle of Substitution),
the simplicity of its application will be largely increased.
1 More accurately, perhaps, it should be said to four forms,
namely, Barbara, Celarent, Cesare, and Camestres. But the
last two are essentially the same as the second, and there is no
advantage to be gained by distinguishing them.
TRADITIONAL LOGIC III
Of these, in addition to the form already
given, and which is on all accounts to be pre-
ferred, there are two others to which we will
refer.
These, as given by Whately, are as follows :
Whatever is predicated \i. e., affirmed or
denied] universally of any class of things, may
be predicated in like manner [viz., affirmed or
denied] of anything comprehended in that
class " (Logic, bk. i., iv.).
' Whatever is predicated of a term dis-
tributed, whether affirmatively or negatively,
may be predicated in like manner of everything
contained under it "(Id., bk. ii., chap, iii., 2).
In effect, these two statements may be taken
as types of all the other forms of the dictum.
But, as we have observed, ' ' thing " or " things
is an extremely vague and unsatisfactory term,
and it would be better to substitute for it the
expression " significate," or " significates."
These two forms of the dictum are in ef-
fect the same. For to say, as in the latter,
"Whatever is predicated of a term distributed,"
is in effect to say, " Whatever is predicated
universally of any class," etc. Bearing this
in mind, and substituting " significates " for
" t Jungs," both forms of the dictum may be
more briefly expressed by saying that " a term
predicated of a term may be predicated also of
any or all of its significates." Where the pred-
112 LOGIC
ication is affirmative the principle, as we have
seen, is called the Dictum de Omni ; where it
is negative, the Dictum de Nullo.
It is said by Whately that the dictum " can-
not be directly or immediately applied to all
even categorical syllogisms, but, as all syllo-
gisms may be reduced to the first figure, it may
be ultimately applied to all." Hence, " to
avoid the tediousness of reducing all syllogisms
to that form to which Aristotle's dictum is ap-
plicable, it has been deemed necessary to in-
vent separate rules or canons for the indirect
figures" (Whately, Logic, bk. ii., chap, iii., 2);
and in this logicians generally agree.
100. CANONS OF THE SEVERAL FIGURES.
These canons of the several figures omitting
the fourth figure, which is disallowed by the
best authorities as being a mere perversion of
the first are as follows :
First Figure : The Dictum de Omni et Nnllo,
as above.
Second Figure: Dictum de Diverse. If one
term is contained in and another excluded from
a third term, they are mutually excluded.
Third Figure: Dictum de Exemplo. Two
terms which contain a common part, partly
agree, or, if the one term contain a part which
the other does not, they partially differ (Devey's
Logic, pp. 109-111).
101. THE DICTUM, RIGHTLY EXPRESSED,
TRADITIONAL LOGIC 113
APPLICABLE TO ALL THE FIGURES. But if
the form of the dictum we have adopted, and
which is substantially as given by Aristotle
( 76), be taken, it will be found to apply to
all syllogisms universally. But as the form
given in the paragraph cited has reference to
the division of propositions there adopted into
two kinds only (namely, A and E, rejecting I
and O), it must now be stated somewhat differ-
ently, so as to apply to the ordinary division
of propositions into their four kinds, A, E, I,
and O:
' Where three terms (which we will call the
middle and two extremes) so subsist with rela-
tion to each other that the one extreme is in-
cluded (wholly or partly] in the middle, and
the middle is included in or excluded from the
other, then (as the case may be) the extreme
included in the middle will be (ivliolly or partly)
included in or excluded from the other ex-
treme."
Or dividing the proposition, and leaving the
terms " wholly " or "partly " to be supplied
as required, it may be stated thus:
Dictum de Omni: (a) If one extreme of a
syllogism be included in the middle and the
middle in the other extreme, then will the
former be included in the latter.
Dictum de Nullo : (b) If one extreme of a
syllogism be included in the middle, and the
1 14 LOGIC
middle be excluded from the other, then will the
former extreme be excluded from the latter.
In this form the dictum may be readily ap-
plied to each of the three figures.
With regard to the first this is sufficiently
obvious; for the syllogisms in this figure are
in fact but mere symbolical expressions of the
dictum that is to say, Barbara and Darii of
the Dictum de Omni, and Celarent and Fcrio
of the Dictum de Nullo.
With regard to the second figure, the Dictum
de Nullo is, in effect, identical with the Dictum
de Diverso. For to say, as is said in the former,
that " the middle term is excluded from the
last extreme," is in effect to say, " that ex-
treme is excluded from the middle"; and
hence the Dictum de Nullo agrees with the
Dictum de Diverso in asserting that two terms,
the one of which is included in and the other
excluded from a common middle term, are
mutually excluded.
So in the third figure the dictum is equally
applicable. For in the affirmative forms (Da-
rapt i, Disamis, and Datisi] it is asserted that
the middle is contained in, and in the negative
forms (Felapton, Dokamo, and Feriso] that it
is excluded from one of the extremes; and in
both it is asserted, in effect, that the other ex-
treme is partly included in the middle. Hence
the former come directly under the Dictum de
TRADITIONAL LOGIC 115
Omni, and the latter under the Dictum de
Nullo.
That the dictum agrees with the Dictum de
Exemplo, however, cannot be said ; for that, in
terms, merely asserts the truism that " two
terms which contain a common part " in that
respect agree, or, " if one contain a part
which the other does not," to that extent
differ. But it gives us no information as to
the principle by which it is determined
whether the two terms have or have not a
common part. Whereas the dictum of Aris-
totle explains that if one extreme be partly
included in the middle, and the middle be
either wholly included in or excluded from the
other extreme, then the two extremes will or
will not agree or have a common part, as the
case may be.
It is therefore obvious that the dictum of
Aristotle applies equally to all syllogisms, and
that to invent separate canons for the several fig-
ures is unnecessary and productive of confusion.
102. THE DICTUM APPLICABLE TO SING-
ULAR AND OTHER EQUATIOXAL PROPOSI-
TIONS. It has also been objected to the
dictum by several logicians that it is not ap-
plicable to syllogisms in which the terms are
singular, or to other syllogisms composed of
equational propositions; which, it is said, are
governed by a different regulating principle,
1 16 LOGIC
viz., that " notions equivalent to one and the
same third notion are equivalent to each
other" (McCosh, Logic, pp. 126, 127). But
this is obviously not so. For an individual
may, for logical purposes, be regarded as a
class (i. e., a class of one); and classes that are
equal to each other mutually include each
other. Hence the dictum applies directly to
syllogisms of this character; and we may al-
ways express such a syllogism, e. g. , Z = Y,
Y = X .'. Z = X, in the usual form: Z is Y,
Y is X .-. Z is X.
103. OF PROPOSED IMPROVEMENTS ox
THE DICTUM. Other objections are urged to
the dictum of Aristotle by modern logicians,
and, to remedy its supposed defects, numerous
new dicta or canons have been invented to take
its place. But these will be found on examina-
tion to be either erroneous or merely different
and less satisfactory statements of the old
dictum.
In at least this fundamental aspect of the
subject the opinion of Kant with reference to
the Old Logic must be accepted, viz., that
" Since Aristotle it has not had to retrace a
single step, and to the present day has not
been able to make one step in advance." '
1 In these views I find myself supported by the following
judicious observations of Professor Jevons :
"During the last two or three years," he observes, "the
TRADITIONAL LOGIC 1 1/
3. Rules of the Syllogism
104. STATEMENT OF THE RULES. The
following rules, with the fallacies resulting from
their violation, are given by logicians. They
are all obvious deductions either from the
definition of the syllogism or from the dictum
of Aristotle.
(1) Every syllogism has three, and only
three, terms, viz., the Major, the Minor, and
the Middle term.
The violation of this rule is called the Fal-
lacy of Four Terms (Quarternio Terminorum).
It generally results from the ambiguity of a
term, and indeed can hardly occur in any
other way.
(2) Every syllogism contains three, and only
three, propositions, viz., the Major and the
Minor premise and the Conclusion.
This rule can be violated only by violating
the first rule, and is therefore to be regarded
as superfluous.
(3) The Middle term must be distributed
once at least in the premises.
thought has constantly forced itself on my mind, that the
modern logicians have altered the form of Aristotle's proposi-
tion without making any corresponding alterations in the
dictum or self-evident principle, which formed the fundamen-
tal postulate of his system. Aristotle regarded the proposi-
tion as stating the inclusion of one term or class within
another ; and his axiom was perfectly adapted to this view
(Pure Logic, p. 86).
Il8 LOGIC
The violation of this rule is called the Fallacy
of Undistributed Middle, as, e.g., in the fol-
lowing pseudo-syllogism: X is Y, Z is Y .*. Z
is X.
(4) No term must be distributed in the con-
clusion that was not distributed in one of the
premises.
The violation of this rule is called the Fallacy
of the Illicit Process of the Major or of the
Minor term, as the case may be, as, e. g., in
the following syllogism : Y is not X, some
Z is Y . '. Z is not X, Nations capable
of self-government should not be despotically
governed; some nations are capable of self-
government; no nation should be despotically
governed, which is a case of illicit process of
the Minor term ; or as in the following syllo-
gism: Y is X, Z is not Y .*. Z is not X,
Anglo-Saxons love liberty, Frenchmen are
not Anglo-Saxons .'. Frenchmen do not love
liberty, which is an illicit process of the Major.
(5) From negative premises nothing can be
inferred.
The violation of this rule is called the Fallacy
of Negative Premises; e. g. , Y is not X, Z is
not Y .'. Z is X or Z is not X.
(6) If one premise be negative the conclusion
must be negative; and, vice versa, to prove a
negative conclusion one of the premises must
be negative.
TRADITIONAL LOGIC 1 19
The violation of this rule may be called the
Fallacy of Affirmative Conclusion, e.g., Y is
X, Z is not Y .'. Z is X.
And from the above rules may be deduced,
as corollaries, the following:
(7) From two particular premises no conclu-
sion can be drawn.
(8) If one premise be particular, the conclu-
sion must be particular.
4. Of Enthymemes and Sorites
105. OF ENTHYMEMES. An Enthymeme
is a syllogism incompletely stated, but in
which the omitted parts are understood or im-
plied. Most commonly the omitted part is the
major premise, which is then said to be sup-
pressed, as, e. g. , " Caesar was a tyrant, there-
fore he deserved death," where the suppressed
premise is the major, " All tyrants deserve
death." Or the suppressed premise may be
the minor, as, e. g., " Freemen are happy,
therefore the English are happy," where the
suppressed premise is the minor, " English-
men are freemen."
1 06. OF SORITES. The Sorites consists of
a string of syllogisms in the first figure, in
which the conclusion of each is made the
premise of the next, and so on, till finally in
the conclusion the predicate of the last premise
1 20 LOGIC
is predicated of the subject of the first, as,
e. g., A is B, B is C, C is D, D is E . \ A is E ;
or, to give a concrete example, " The English
are brave, the brave are free, the free are
happy, therefore the English are happy."
Obviously a Sorites may always be resolved
into as many separate syllogisms as it has
middle terms, as, e. g., in the above example,
the first into three and the last into two syllo-
gisms, as follows:
A is B A is C A is D
B is C C is D D is E
/. A is C .'. A is D .*. A is E
The English are brave The English are free
The brave are free The free are happy
.'. The English are free .'. The English are happy.
BOOK II
APPLIED LOGIC
121
BOOK II
APPLIED LOGIC
PART I
OF THE METHOD OF LOGIC
CHAPTER VI
OF THE LOGICAL PROCESSES
107. OF THE METHOD OF LOGIC. The
logical processes, as we have hitherto con-
sidered them, consist in three operations,
namely, Simple Apprehension, Judgment, and
Syllogism or Inference; of which the first is
an analytical process, the second and third
synthetical. Hence the logical processes may
be regarded as twofold, and as consisting in
Analysis and Synthesis. The first of these,
however, is not confined to Simple Apprehen-
123
124 LOGIC
sion or analysis of terms, but extends to the
analysis of propositions and syllogisms, and of
extended discourse ; of which the elements are
syllogisms. It also extends, as preparatory to
the expression in logical form of subjects to be
investigated, to the analysis of the general
facts involved and the determination of the
questions to be investigated. The logical
method consists in the use of these processes.
108. LOGICAL DISTINGUISHED FROM
PHYSICAL ANALYSIS AND SYNTHESIS. The
terms analysis and synthesis are used in differ-
ent senses, according to the subject-matter to
which they are applied. Of these, two princi-
pal kinds may be distinguished, which may be
called, respectively, physical and logical the
former dealing with physical substances, the
latter with notions or concepts. Of the former
kind, the most instructive illustration is pre-
sented by chemistry ; where these processes are
applied directly to matter, which is analyzed
by separating its elements, and synthesized by
rearranging those elements so as to form new
compound substances. These processes are
indeed essentially different in nature from the
processes with which we are now concerned,
yet the analogy between the two is almost
perfect; and hence, in chemical analysis and
synthesis, we find the best illustration of the
nature of analysis and synthesis of notions or
THE LOGICAL PROCESSES 12$
terms, by which in a way very similar to the
analysis and synthesis of material bodies
notions are analyzed into elementary notions,
and these again synthesized into compound.
109. OF THE WORLD OF THINGS AND
THE WORLD OF THOUGHT. The world of
things is made up of actual things or sub-
stances; the world of thought, of concepts or
notions. There is between the two a regular
correspondence, i. e., a correspondence deter-
mined by invariable law, and yet the two are
clearly distinct. For it is obvious that things
themselves cannot be in the mind but only,
notions or concepts of them. These, as we
have seen, if real or true, must correspond,
either directly or indirectly, with the things
which, or the attributes of which, they are
supposed to denote ( 29, n.). Where the
correspondence is indirect, the thing denoted
is a guast-thing only, and cannot be distin-
guished from the notion itself; but where the
correspondence is direct, there is a real thing
corresponding to the notion, and we may
either regard the notion or the thing as the
significate of the term ( 37, n.); though even
in this case it is really the notion, not the
thing, that we have in mind ( 38, n.). So
that it may be said that Logic, and science
generally, deal directly with concepts or no-
tions only that is to say, with the world of
126 LOGIC
thought only, and with the world of real things
only indirectly.
1 10. LOGIC AS THE DOCTRINE OF SIGNS
(SEMEIOTIKE). But the notions or thoughts
dealt with by Logic are not the evanescent
thoughts of the individual, but the common
notions of mankind embodied in language
( 30). Hence, as we have observed, Logic
is exclusively conversant with language, or
rather, more specifically, with terms and their
various ratiocinative combinations ( 14, 16)
that is to say, with the signs of the notions
or concepts and of their relations ; which
cannot be dealt with, at least to any con-
siderable extent, except by means of the
vocables by which they are signified. Hence
Logic must be regarded, in its direct scope, as
dealing with the signs by which notions and
their relations are expressed precisely as, in
the mathematics, the subject-matter dealt with
consists of the signs of numbers and of their
relations. In both cases, therefore, though
the ultimate object of Logic is to determine
the notions expressed in terms and their re-
lations, and ultimately the nature and the
relations of the things corresponding to the
notions, yet this is effected by means of signs,
which, therefore, constitute the immediate
subject dealt with. Hence Locke was quite
right in conceiving that a science of this char-
THE LOGICAL PROCESSES 12?
acter is indispensable, and in giving it the ap-
propriate name of " Semeiotike, or the Doctrine
of Signs," though quite wrong in supposing
that this would be a new kind of Logic. 1
in. THE METHOD OF LOGIC RESUMED.
By the method of Logic is meant the method
of its use in reasoning, or, in other words, the
method of ratiocination, or explicit reasoning.
This, as we have said, consists in two processes
or operations, namely, Analysis and Synthe-
sis, i. e., of language ( 107). By analysis is
meant the separation of a whole whether con-
sisting of a term, proposition, syllogism, or
larger discourse, or of the general problem
or subject to be investigated into its com-
ponent parts; by synthesis, the comparison (or
placing together) of any of the elements of
reasoning, with a view to determining their re-
lations; that is to say, in the comparison of
terms, in order to form a judgment of their
relations of propositions, in order to make an
inference; and of syllogisms, in order to make
an extended ratiocination or argument. An-
alysis and synthesis are, therefore, each the
converse of the other.
ii2. MODES OF APPLICATION OF THE
1 " The consideration then of ideas and words, as the great
instruments of knowledge. . . . Perhaps if they were
distinctly weighed and duly considered, they would afford us
another sort of Logic and critic than what we have hitherto
been acquainted with " (see Appendix N).
128 LOGIC
LOGICAL PROCESSES. In each stage of ratio-
cination analysis and synthesis are used con-
jointly, and each is equally indispensable. The
order in which their applications occur, how-
ever, differs according to the purpose we have
principally in view, which may be either In-
vention or Criticism; that is to say, either (i)
the Discovery of Truth, or (2) the Criticism or
Judgment of what is supposed or alleged to be
true; or, in other words, the verification of
truth and the detection of fallacy. Of these
two aspects of Logic, the latter is commonly,
and perhaps rightly, regarded as the more im-
portant, or, at least, as of the greater practical
utility. But the former, though commonly
undervalued, is hardly of less utility or less
fruitful of practical results.
113 (i) INVENTION. The operations of
Logic, regarded as an Instrument or Organon
of Invention, consist in the analysis and conse-
quent apprehension of terms (Simple Appre-
hension), and in the discovery or invention of
judgments and of syllogisms, and of argu-
ments which are composed of syllogisms;
which is effected by synthesis; and the process
of ratiocination proceeds in this order, i. e. ,
from the term to the proposition, from the
proposition to the single syllogism, and from
that to the extended discourse or argument.
114. OF THE DISTINCTION BETWEEN
THE LOGICAL PROCESSES 12$
ORIGINAL AND COMMONPLACE THOUGHT.
Where the notions expressed in terms are dis-
tinctly apprehended, and, with reference to all
terms, to the extent they are apprehended, the
relations between them are readily perceived,
and indeed spontaneously present themselves.
Hence with such notions men reason with
facility and accuracy; and thus originate the
numerous opinions that are common to man-
kind, or common at least to men generally
under the same conditions of environment;
and also those that are common to large classes
of men. Of such opinions which may be ap-
propriately named Commonplace the current
literature and thought of the day largely, or,
we may say almost exclusively, consist. Hence
the effect of current thought and discourse
is simply to disseminate such opinion more
widely, and thus gradually to develop and
consolidate Common Opinion, or Conscience,
which has been called by the Greeks Nomos,
and by some philosophers Common Sense.
This, indeed, is a useful and essentially neces-
sary function; for it is recognized by political
writers generally that opinion is the ultimately
controlling force in politics, and that when it
becomes universal and inveterate, it is supreme.
But current thought is marked by an essential
characteristic, or, we may say, defect namely,
that it is incompatible with originality, either
130 LOGIC
in the acquisition of new truths or in the ap-
preciation of original thought in others. Hence
it has happened, throughout the history of
mankind, that the results of original thought
meet with almost insuperable obstacles to their
reception ; and that, even where they have es-
tablished their footing, they pass into the
hands of commonplace thinkers, who treat
them after their own methods. Hence the
original works of great thinkers, with their
methods of thought and expression, and the
vivifying effect of actual example, are sub-
merged by the newer and inferior literature.
On the other hand, where the Analytical
Method is rigorously applied to all forms of
discourse, and especially when it is applied to
the notions or concepts embodied in terms,
numerous delicate and important but unsus-
pected relations between the notions thus de-
termined suggest themselves. For in this also
logical is like chemical analysis, where,
by the resolution of compound substances,
thousands of relations between them and
between the elements of which they are
composed are developed and disclosed. The
perception of these unsuspected relations con-
stitutes originality, which is but another name
for logical power. Nor is this originality any-
where more conspicuously displayed than
where men of original genius, as, e. g., Bacon
THE LOGICAL PROCESSES 131
in \\isEssays, deal with commonplace subjects. 1
Hence the use of Logic as an Instrument of
Invention cannot be too highly appreciated,
for in the capacity to use Logic in this way,
or, in other words, in the capacity to apprehend
the whole significance of terms by resolving
them into their elements, lies the essential dif-
ference between the Original and the Common-
place Thinker. 1
115 (2) CRITICISM. In this aspect Logic
may be likened to the touch of Ithuriel's spear. 2
1 Where terms are clearly defined and analyzed into their
constituent elements, that is to say, thoroughly apprehended,
innumerable relations between them are intuitively per-
ceived ; and thus, by the use of this method, we are led on,
as Locke says in a passage cited (supra 6, n.), " f rom
very plain and easy beginnings, by gentle degrees and a con-
tinued chain of reasonings, ... to the discovery and
demonstration of truths that appear, at first sight, beyond
human capacity." This it was, probably, that inspired the
beautiful hymn of Newman :
" Lead on, Heavenly Light ; amid the encircling gloom,
Lead Thou me on " ;
which may be very properly regarded as in reality an ode to
the divine gift of Intuition the only source of perfect
knowledge.
2 "Him there they found
Squat like a toad at the ear of Eve.
Him thus intent Ithuriel with his spear
Touched lightly ; for no falsehood can endure
Touch of celestial spear, but returns
Of force to its own likeness ;
So started up in his own shape the fiend,"
132 LOGIC
Commonly the reasoning processes operate
unconsciously and automatically, and the rea-
soning is more or less inaccurate, and hardly
ever consecutive or logically coherent. As
observed in the Introduction, proposition fol-
lows proposition in our minds, suggested by
various principles of association, such, e. g., as
experience, habit, authority, inclination, etc. ;
and thus the great mass of our opinions and
beliefs which we very erroneously call our
knowledge comes to us we know not how.
Nor, however firmly we may be convinced of
them, or however passionately we may assert
them, have we any just assurance of their
truth; nay, it is matter of familiar knowledge
that they are all mingled with error. Hence,
we concluded, the necessity is apparent for
some test or criterion by which to judge them ;
and this, except the sometimes painful test of
experience, can be nothing else than Logic.
In its critical aspect, therefore, Logic is indis-
pensable, not only to save us from errors and
absurdities, but to distinguish real from unreal
knowledge, and to give us assurance of the
former ( 7 et seq.\ Without it, except in
concrete matters, no man can know whether
he is right or wrong; and while some, happily
born, learn by practice the application and
use of the logical processes, the great mass of
mankind, for the lack of Logic, go through life
THE LOGICAL PROCESSES 133
mistaking falsehood and even nonsense for
knowledge, and yet firmly convinced of their
wisdom and of the folly of those who differ
from them. Hence, in the critical aspect of
Logic, the order of applying the logical pro-
cesses is the reverse of what it is in the use of
Logic as an organon or instrument of inven-
tion. There the order is to commence with
the analysis of the term, and then to proceed
to the synthesis of terms in propositions,
syllogisms, and extended discourse; here we
commence with the complex result, and by
analysis resolve it into its elements.
116. OF THE USE OF ANALYSIS GENER-
ALLY. In the use of Logic, whether for in-
vention or for criticism, analysis and synthesis
are equally indispensable; but the latter, after
the former has been effected, is largely a
natural and spontaneous process, and presents
but little difficulty in its performance. On the
other hand, analysis, while to a certain extent
also spontaneous, requires, for its efficient per-
formance, the most vigorous and protracted
exertion of the mental faculties, as, e. g., in
the mathematics, and hence is at once the
most important and the most difficult of the
logical processes. It will therefore require
our special attention.
We have distinguished between the inven-
tional and the critical functions of Logic, and
134 LOGIC
also with reference to the use of the logical
processes as applied in the performance of the
one or the other function ; and with reference
to invention, we have regarded the function of
analysis as limited to the analysis of terms,
with a view to an apprehension of the notions
expressed by them. In practice, however, it
is difficult to distinguish between the uses of
analysis for invention and for criticism. For,
as we have observed, the human mind is so
constituted that the synthetical process is
performed spontaneously and involuntarily.
Hence there is no subject that can present
itself for our investigation which we can ap-
proach unembarrassed by opinions already
formed; and, indeed, until such opinions or
theories are formed, the process of investiga-
tion cannot commence. Hence, as is generally
recognized, the method of scientific investiga-
tion must consist largely in the forming of
theories and their subsequent investigation.
We may distinguish, however, between our
own theories, either accidentally formed or
formed for the purpose of the investigation of a
proposed subject, and the theories formally pro-
pounded by others, either in writing or speech ;
and we may conveniently regard the former as
belonging to the function of invention, and the
latter to that of criticism. The latter, as being
the simpler subject, will be first considered.
THE LOGICAL PROCESSES 135
117. (i) OF THE USE OF ANALYSIS IN
CRITICISM. In this case the function of
analysis extends to the analysis of all forms
of language, from the term to the extended
discourse or argument; and, as we have ob-
served, it commences with the latter, which is
in fact the most difficult task. For here it is
necessary to determine from the loose and in-
accurate expressions of ordinary disquisition
the precise nature of the conclusions asserted
and of the arguments used to establish them ;
and this task is always difficult, and sometimes
impossible. When these matters have been
determined it will be necessary also to analyze
carefully every syllogism, proposition, or term
involved in the course of the reasoning. But
this in general, to the trained logician, presents
but little difficulty.
118. (2) OF THE USE OF ANALYSIS IN IN-
VENTION. Strictly speaking, this perhaps ex-
tends only to the analysis of the term with a
view to simple apprehension, and in a previous
passage we have so regarded it. But before
this task can be approached, it is necessary for
us to determine the nature of the precise ques-
tions to be investigated ; and this will require an
analysis of the facts involved in the investiga-
tion, and also of the opinions or theories with
regard to those facts casually existing in the
mind. For, as will be explained more fully in
136 LOGIC
the next chapter, the questions demanding in-
vestigation are in general determined by the
nature and the conditions of the problems
involved ; and it is essential to a rational in-
vestigation that the issues thus involved be
clearly ascertained. When the issues or ques-
tions are thus determined and logically ex-
pressed, our investigation is then narrowed to
the determination of the truth of one of two
alternative propositions, which are called the
thesis and the anti-thesis, and of which one or
the other must be true; and thus our task is
in general greatly facilitated. The use of this
sort of analysis finds its best illustration in the
practice of the lawyers, with whom it is an im-
perative rule that the first step in the investi-
gation of a case must consist in settling the
issues. In ordinary discourse this task is
almost always neglected, and, as will be seen
as we proceed, this is one of the most fruitful
sources of fallacy.
119. OF ANALYSIS AND SYNTHESIS GEN-
ERALLY. This subject is one of extreme im-
portance, and to the advanced student should
constitute one of the principal subjects for his
meditations; but for the purposes we have in
view it may be sufficiently developed by a
statement of the practical rules by which the
reasoner should be governed, which will be
given at length in the next chapter.
CHAPTER VII
THE RULES OF LOGIC
I
OF THE RULES OF LOGIC GENERALLY
120. SCOPE OF THE RULES OF LOGIC.
According to the view we have taken in this
essay, inference is only one of the processes of
ratiocination. Judgment is also a ratiocinative
process, and, like inference, must have its rules
by which false or pretended judgments may be
distinguished from the real. Moreover, where
our reasoning is not apodictic, we have to use
assumed propositions, or assumptions, as prem-
ises ; and though it is said that Logic is not
concerned with the truth or falsity of these, yet
this is true only in a qualified sense. For
where the falsity of such propositions can be
detected by logical processes, i. e., by defini-
tion, judgment, and inference, it is the func-
tion of Logic to condemn and reject them ;
precisely as in the case of self-contradictory
138 LOGIC
propositions or propositions otherwise absurd
on their face. And in all cases it is its func-
tion to determine the logical character of an
assumed premise, as being an assumption or
hypothesis, and not a judgment.
121. TWOFOLD DIVISION OF THE RULES
OF LOGIC. We propose, therefore, to regard
the rules of Logic as legitimately extending to
all the processes of ratiocination ; and hence as
including all rules necessary to direct us in the
right use of terms as instruments of ratiocina-
tion. They will include, therefore, not only
the rules directly governing the process of in-
ference, but also those governing the statement
of the premises. The latter which will first
be considered will be called the " Rules of
Judgment,'" the former, the " Rules of In-
ference."
122. RULES OF JUDGMENT. The rules of
judgment have for their object, not the form-
ing of right, but the prevention of wrong judg-
ments. Judging is a natural and involuntary
operation of the mind. But in the ordinary
processes of the mind we are apt to go astray
in our judgments; and the object of the rules
of judgment is to guard against this infirmity
by preventing false judgments, or, where they
occur, by detecting them.
123. RULES OF INFERENCE. The rules
of the syllogism given in a previous chapter
THE RULES OF LOGIC 139
cover all cases of inference except conversion
per accidens. But these rules are needlessly
complex, and may be advantageously replaced
by the rules of substitution, which include
all inferences whatever, and are simpler both in
their expression and application than the old
rules, of which they are but another expres-
sion. The rules of the syllogism, however,
are of such familiar use by logicians, and are so
wrought into the terminology and literature of
Logic, that a familiar acquaintance with them
is essential to the logical student; for whom
also it will be necessary to recognize clearly
the substantial identity of the two processes.
124. FALLACIES OF THE SYLLOGISM, ALL
RESOLVABLE INTO FALLACIES OF SUBSTITU-
TION. This is especially important with refer-
ence to the violations of the rules of the
syllogism, or, as they are called, the fallacies
of the syllogism (104 ct scq.\ These are
of frequent occurrence, and are familiarly
known by technical names; and as these have
become firmly established in logical termi-
nology by a use of many centuries, they must,
of course, be retained. It will be of advantage
to the student, therefore, to have pointed out
to him that all these fallacies are simply cases
of illicit substitution ; which can be readily
shown.
Thus, e. g<, the fallacy of an ambiguous
I4O LOGIC
middle term (Quarternio Terminorutri) consists
simply in the substitution of a new term, hav-
ing the same verbal sign as in the original, but
a different meaning as in the examples given.
The case of undistributed middle as, e. g. ,
" X is Y, Z is Y .-. Z is X " - consists in the
illicit substitution of species for genus in the
predicate of an affirmative proposition (i. e., X
for Y in the minor premise).
In the case of illicit process of the minor term,
as, e. g., " Y is not X, some Z is Y .'. Z is
notX," genus is illicitly substituted for species
in the subject of an affirmative proposition
(i. e,, Z for " Some Z " in the minor premise).
In the case of illicit process of the major, as,
e. g., " Y is X, Z is not Y .-. Z is not X,"
genus is illicitly substituted for species in the
predicate of a negative proposition (i. e., X for
Y in the minor premise).
In the case of negative premise, if the con-
clusion be affirmative, as, e. g. , " Y is not X, Z
is not Y .'. Z is X," genus is substituted for
species in the predicate of a negative proposi-
tion (i. e., Not-X for Y in the minor pre-
mise). If the conclusion be negative, as, e.g.,
" Y is not X, Z is not Y . . Z is not X," the
fallacy will consist in the illicit substitution of
one for another of two unrelated terms (i. e.,
X for Y); and the same will be true of the
other cases, if any there be.
THE RULES OF LOGIC 141
125. THE LAWS OF THOUGHT. The
rules of Logic are founded upon what are
called the primary Laws of Thought, viz. :
(i) the Law of Identity (or rather the Law of
Equivalence); (2) the Law of Contradiction;
and (3) the Law of Excluded Middle; the first
of which governs the process of Inference, the
last two, that of the Judgment. The corre-
sponding fallacies consist in their violation.
These laws may be enunciated in a form to
make them of practical utility, as follows:
(i) THE LAW OF IDENTITY.
Significates (i. e., things or quasi-things) re-
main the same though denoted by different
terms.
Hence terms denoting the same significates
may, to the extent of their equivalence, be
used interchangeably, i. e., the one substituted
for the other.
The mathematical axiom that " things equal
to the same thing are equal to each other " is
merely a special application of this principle,
its meaning being simply that terms denoting
the same class of significates are equivalent to
each other.
It is obvious, therefore, that this law is not
adequately stated (as is sometimes said) by the
equation, A = A, but rather by the equation,
A = B; both terms being supposed to denote
the same class of significates, and the term B
142 LOGIC
to be either A, or any other vocable or sign
denoting the same significates.
(2) THE LAW OF CONTRADICTION, OR
RATHER THE LAW OF NON-CONTRADICTION.
A term, and its negative, or contradictory,
cannot be predicated universally of any term.
This law and the next are often misstated.
(3) THE LAW OF EXCLUDED MIDDLE.
Of two contradictory propositions, one must be
true ; or symbolically : ' ' Either A is It," or
' ' Some A is not B. " l
II
RULES OF JUDGMENT
126. Rule I. TERMS TO BE SIGNIFICANT.
In every logical proposition by which is meant
every proposition to be used in ratiocination the
terms must be significant, i. e., must have defi-
nite signification.
This rule follows from the definition of the
term and of the proposition ; for unless the
word or vocable has such definite signification
there is no name, and consequently no term or
proposition, or valid ratiocination. The viola-
tion of this rule may be called the Fallacy of
Non-significance or Nonsense.
Rule II. TERMS TO BE RIGHTLY DEFINED.
Terms used in ratiocination must not only have
1 V., supra, 90.
THE RULES OF LOGIC 143
a definite signification, but the signification
must be legitimate, i. e., they must not be falsely
defined. This implies (i) that a term shall not
be used in an improper sense, i. e. , in a sense not
permitted by the usage of the language ' / and
(2) that the term shall be so defined as to signify
a real concept ; or, at least, that the contrary
shall not affirmatively appear.
The violation of this rule will be called the
Fallacy of False Definition.
Rule III. PREMISES NOT TO BE ILLICITLY
ASSUMED.
A proposition that is obviously untrue, or that
can, on logical principles, be affirmatively shown
to be untrue, cannot be legitimately used as a
premise.
The violation of this rule is called the fallacy
of " Begging the Question," or Petitio Prin-
cipii ; and this and the fallacies resulting from
the violation of Rules I. and II. may be
classed together under the general head of
Illicit Premises.
Rule IV. PREMISES TO CORRESPOND TO
THE THESIS OR ISSUE.
In all ratiocination if designed to be fruitful
1 The unnecessary use of a term in a sense not justified by
usage is commonly indicative either of mental incapacity or
fallacious intent ; and should therefore be forbidden, as to
children \ve forbid the use of deadly weapons, or to all the
possession of counterfeiters' tools.
144 LOGIC
the premises, and, consequently, also the con-
clusion, must correspond to the Thesis or Issue,
^whether that be expressed or understood, or
merely determined by the conditions of the
problem.
By the thesis is meant the proposition to be
demonstrated ; by the issue t the thesis and the
anti-thesis, or contradictory, considered to-
gether with a view of determining whether the
one or the other is true.
With regard to nearly all subjects presented
to us for investigation the material question at
issue is more or less definitely determined by
the conditions of the problem ; and hence it is
said, " A prudent questioning is a kind of half
knowledge ' ' (Prudens interrogatio est dimidium
sapientice}. Where the issue is thus determined,
it constitutes the real issue, or thesis and anti-
thesis of the problem. In other cases it must
be determined by agreement, or by actual in-
tention, either expressed or understood. In
many cases it is not formally stated, but we
ascertain it, for the first time, from the use
made of the conclusion.
The fallacy resulting from a violation of this
rule if we assume there is no fallacy in the
inference will necessarily involve a departure
from the thesis or issue, both in the premises
and in the conclusion. With regard to the
premises, it is called the fallacy of Mistaking
THE RULES OF LOGIC 145
the Issue ; with regard to the conclusion, that
of Irrelevant Conclusion; and in either case,
Ignoratio Elenchi.
Ill
RULES OF INFERENCE
127. All inference, as we have observed,
may be resolved into the process of substituting
for terms other terms of equivalent ratiocina-
tive value. There is an apparent exception in
the case of conversions of propositions, but the
exception is only apparent ( 79). To conform
to usage, however, the rule for conversion will
be given, though in fact, as explained, the illicit
conversion of a proposition is simply a case of
illicit substitution of terms.
Rule V. CONVERSIONS TO BE ILLATIVE.
A conversion, to be legitimate, must be illative,
i. e, , the truth of tlie converted must be implied
in the original proposition.
The violation of this rule may be called the
Fallacy of Conversion, or simply Illicit Conver-
sion. It can occur only in the simple conver-
sion of a universal affirmative or a particular
negative proposition (e. g., " Y is X," " Some
Y is not X "). In the former case the fallacy
will consist in the substitution of genus for
species (X for Y) in the subject, and of species for
genus (Y for X) in the predicate of a universal
146 LOGIC
affirmative proposition, thus doubly violating
the first rule of substitution. In the lat-
ter (" Some Y is not X ") X is substituted for
Y in the subject, and Y for X in the predi-
cate, though neither is necessarily, and one at
least cannot be, a species of the other; which
is a violation of the next rule.
Rule VI. EQUIVALENCE OF TERMS TO BE
OBSERVED.
In all substitutions the substituted term must
be equivalent in signification i. e., equivalent in
ratiocinative value to the term for which it is
substituted.
The violation of this rule by the substitution
of a new term is called the Fallacy of Illicit
Substitution.
The rule will cover all cases of legitimate
substitution of terms whatever ; but it is ob-
vious, where an ambiguous term is used in a
different sense from that originally adopted,
that a new term is in fact illicitly substituted.
We must add, therefore, as a corollary the
following:
Rule VII. THE SENSE OF TERMS TO RE-
MAIN UNALTERED.
Every verbal expression, ivJietJier a term or
proposition, shall, throughout the ratiocination,
be used in the sense originally given to it.
The violation of this rule constitutes what is
called the Fallacy of Equivocation, which is to
THE RULES OF LOGIC 147
be regarded as a species of Illicit Substitution ;
and of this there are two kinds: the first con-
sisting in shifting the sense of an ambiguous
term, which is called the Fallacy of Ambiguity ;
the second, in shifting the meaning of what is
called an amphibolous sentence, which is a sen-
tence equivocal by reason of its grammatical
construction, as, e. g., the sentence, " The
Duke yet lives that Henry shall depose";
which may mean either that the Duke shall de-
pose Henry, or Henry the Duke. If construed
in the former sense, the subject of the proposi-
tion is, " The Duke that shall depose Henry " ;
for which under the latter construction is sub-
stituted, " The Duke that shall be deposed
by Henry." This is called the Fallacy of
Amphibology, or, perhaps better, of Amphiboly.
But these fallacies are of essentially the same
nature, and will be classed together under the
one head of Equivocation.
PART II
THE DOCTRINE OF FALLACIES
CHAPTER VIII
DEFINITION AND CLASSIFICATION OF FAL-
LACIES
128. DEFINITION OF FALLACIES. A fal-
lacy may be defined as a false semblance of
valid ratiocination ; to which it bears the same
relation as hypocrisy, conscious or unconscious,
to virtue. Fallacy is therefore a species of
error, whose specific difference consists in its
semblance of right reasoning and its conse-
quent liability to be mistaken for it. 1 It may
1 Hobbes, with his usual acuteness, thus clearly explains the
distinction between error a.\\<\ fallacy :
" When we reason with words of general signification (uni-
versalibus} and fall upon a general conclusion (conclusionem
universalum) which is false, though it be commonly called
error, it is indeed an absurdity or senseless speech (pratio
insignificans)" Lev., chap. v. According to this view, all
fallacies are absurdities, i. e., they necessarily involve either a
contradiction, or the use of non-significant or senseless words.
149
1 50 LOGIC
consist either in a false judgment or a false in-
ference. But, it will be remembered, the terms
judgment and inference in the logical sense de-
note, the one intuitive judgment, and the
other illative inference. Hence, when we
speak of a false judgment or inference, we do
not mean a real judgment or inference that is
untrue (which would involve a contradiction
of terms), but as when we speak of a false
prophet a pretended or simulated judgment
or inference that is not really such.
129. CLASSIFICATION OF FALLACIES.
All fallacies must consist in the violation of
some one or more of the rules of Logic, and
hence may be correspondingly classified. Such
a classification has, indeed, already been sub-
stantially effected in our statement of the
logical rules; where, under each rule, the cor-
responding fallacies have been named. It
remains, therefore, only to arrange them in
convenient order, which is done in the table
that follows:
Table of Fallacies
130. FALLACIES OF JUDGMENT.
I. Illicit Premises.
(1) Fallacies in Definition.
Nonsense (or Non-Significance).
False Definition.
(2) Illicit Assumption of Premise (Petitio
Principii ).
CLASSIFICATION OF FALLACIES 151
II. Mistaking the Issue, or Irrelevant Conclusion
(fgnoratio Elenchi}.
131. FALLACIES OF INFERENCE, OR IL-
LICIT SUBSTITUTIONS.
I. Illicit Conversions of Propositions.
II. Illicit Substitutions of Terms ; Scil.
1 i ) Of Vocal Signs, or Vocables.
Formal.
Material.
(2) Of Notions, /. e., of Senses of Terms
{Equivocation, Homonymia et Amphi-
bolia) .
132. OBSERVATIONS ON THE FALLACIES.
Of the two principal kinds of fallacies con-
tained in the above table, the first excepting
the Fallacy of Irrelevant Conclusion consist in
the illicit assumption of the propositions to
be used as the premises of ratiocination. But
false or nonsensical propositions do not of
themselves constitute fallacies, but only by
reason of their use as judgments; for, accord-
ing to our definition, a fallacy is a false sem-
blance of ratiocination, and therefore cannot
exist except as part of ratiocination. Hence
we are not concerned with the truth or falsity
or the absurdity of any proposition that may
be asserted by any one, unless it be used as an
independent judgment or as the premise of an
152 LOGIC
argument, in which case its pretensions may
be examined, and, if found to be baseless, it
may be challenged as illicit.
Where such an assumed premise is either
non-significant or involves a false definition, it
is in itself a fallacy, and therefore entitled to
an independent rank as such. But such fal-
lacies are innocuous if the sense of the terms
be preserved unaltered throughout the ratio-
cination. For all conclusions in which they
are involved must necessarily be without sig-
nificance, or, in other words, nonsensical, and
hence unsusceptible of use. But, as will be
seen at large as we proceed, the conclusions
from such premises, being in themselves un-
susceptible of use, are invariably used as
equivalent to other and significant proposi-
tions, and thus inevitably result in the Fallacy
of Irrelevant Conclusion, or Ignoratio Elenclii,
which consists in substituting for the conclu-
sion another proposition (i. e., the true thesis);
and which, though for convenience treated
separately, may itself always be resolved into
the Fallacy of Illicit Substitution, i. e., into an
illicit conversion, or an illicit substitution of a
term. And the same observation is true gen-
erally, though not universally, of illicit assump-
tions of false premises. These, if regarded as
mere hypotheses, and if no misuse be made of
the conclusion, are not illegitimate ; but, it will
CLASSIFICATION OF FALLACIES 153
be seen, a conclusion deduced from such pre-
mises almost invariably either comes in conflict
with some inconsistent fact, or otherwise fails
to be sufficient for the purposes the reasoner
has in view; and thus, almost inevitably, it is
treated as equivalent to some other proposi-
tion, thus again presenting a case of Ignoratio
Elenchi. Hence if, as we conveniently may,
we regard all assumed propositions as mere
hypotheses, and therefore as not illegitimate,
unless an ill use be made of the conclusion
all illicit assumptions of premises must neces-
sarily result in an Ignoratio ElencJii ; which, as
we have observed, must necessarily consist
either in an illicit conversion or the illicit
substitution of a term. Hence, as all valid
ratiocination consists in the substitution of
equivalent ( 78), so all fallacy must consist in
the substitution of non-equivalent terms.
Hence the simplest and most scientific classi-
fication of fallacies would be to regard them
all as species of illicit substitution that is to
say, as cases, either of illicit conversion of pro-
positions or illicit substitution of terms; and
that we have adopted a different mode of classi-
fication is due simply to the consideration that
we may thus more conveniently exhibit the
different sources of fallacy. Hence, as we
proceed, it will be found that the several fal-
lacies all have a tendency, as it were, to run
J54 LOGIC
into each other; which mainly results from the
fact that they are all in their essential nature
the same, differing only in the peculiar sources
in which they originate; though partly also
from the fact that, in general, fallacious argu-
ments are not explicit, and the fallacy may
vary according to the manner in which we may
express them.
In our classification of the fallacies we have
distinguished as a class the fallacy of " Mis-
taking the Issue, or Irrelevant Conclusion,"
thus apparently including two separate fal-
lacies. But this is only apparently so. For
unless there be some fault in the inference
which would constitute another kind of fallacy
the conclusion and the premises must neces-
sarily correspond, and we may therefore regard
either the illicit assumption or the illicit con-
clusion as constituting the fallacy. If we re-
gard the latter as the fallacy, it necessarily
resolves itself into a case of illicit substitution.
But, for convenience, we regard it as relating
to the premises, and thus regarded, it consists
in the illicit assumption of one proposition in
place of another i. e., of the actual premise
for some other proposition more or less resem-
bling it which is admitted.
In concluding these introductory observa-
tions I would refer the student to what is said
in the conclusion of the Introduction, and
CLASSIFICATION OF FALLACIES 155
which, for convenience of reference, is here
repeated :
" In our treatment of the subject, the several
fallacies will be illustrated almost exclusively
by examples taken from current theories of
Politics and Morality. Our examples will
therefore consist, not of mere trivialities, such
as are so commonly used in works on Logic,
but of fallacies that, in perverting moral and
political theory and in corrupting practice,
have dominated, and still continue to dominate,
the fortunes of the world. They come to us,
therefore, as veterans in the army of what
Hobbes calls the ' Kingdom of Darkness,'
crowned with the laurels of victory " ( 13).
Among these theories there are two fruitful,
above all others, in examples of logical fallacy
namely, the modern doctrine of Absolute
Sovereignty, and the Utilitarian Theory of
Morality; the former of which may be ex-
pressed in the proposition that " Sovereignty
is, in its essential nature, an absolute poiver,
and, as such, unsusceptible either of limitation
or division"; the latter, in the proposition
that " General Utility is the trite and only
standard of justice and injustice, and of right
and wrong generally." Most of our examples
will be taken from these theories; and these,
and other current theories used for the same
purpose, will be found not only to serve as the
1 56
LOGIC
most effective means of illustrating the nature
of the several fallacies involved, but also to
enable us to perceive the frequent use and
formidable influence of fallacy upon political
and moral speculation, and to realize how dis-
astrously and commonly the most vital affairs
of mankind are thus affected.
CHAPTER IX
NON-SIGNIFICANCE, OR NONSENSE FALLACY
OF
133. The nature of this fallacy is explained
under Rule I. of the Rules of Logic. The fal-
lacy is of two kinds; namely, (i) where a term
is used that has an impossible or absurd mean-
ing or no meaning at all which constitutes the
Fallacy of Nonsense in the narrower sense of
the term ; and (2) where an ambiguous term is
used without definition which is called the
Fallacy of Confusion. But, logically, the two
kinds are of essentially the same nature, and
hence are classed together under the general
head of Non-significance or Nonsense. For
the purpose of illustrating their nature, they
will, however, be considered separately.
i . The Fallacy of Nonsense '
134. In dealing with concrete matters, it
is difficult to use nonsensical speech without
1 According to Ilobbes (cited supra, 128, n.), all fal-
lacies, in their ultimate analysis, may be reduced to this head.
157
158 LOGIC
discovering it; and hence the kind of nonsense
to which the term is colloquially applied is gen-
erally of an obvious and transparent character.
But when we come to deal with abstract terms,
or terms of second intention, such as are con-
stantly used in Morality, Politics, and Meta-
physics, the case is quite different. For here
not only are we liable constantly to use non-
sensical or non-significant terms, but it often
requires the most searching and difficult analy-
sis to discover that we have done so. Hence,
the nonsense of which we are to discourse is
something very different from the nonsense of
colloquial speech ; which is generally so obvious
that only foolish people can fall into it, or, at
least, persist in it. It is a kind of nonsense
that constantly imposes itself upon the most
eminent statesmen, jurists and philosophers,
and even upon the most acute logicians. To
escape it altogether a. man must be endowed
with more than mortal sagacity, and hence the
fallacy may be illustrated by examples from
the writings of the most eminent men.
Examples
135. SOVEREIGNTY. The most striking
example of this fallacy is presented by the
modern doctrine of Absolute Sovereignty (
132), a doctrine almost universally received by
modern political writers, and which (with an
FALLACY OF NON-SIGNIFICANCE 159
exception, to be touched upon under the next
head) has contributed more than any other
cause to the corruption of political philosophy
and practice. This will require some explana-
tion.
The term Sovereign, in its original and proper
sense, denoted merely a single ruler or monarch,
and Sovereignty, the power of this monarch.
But in modern times the application of these
terms has been much extended, and the latter
term is now used in many different ways; of
which four may be distinguished, namely : (i)
Personal Sovereignty, or the power of an abso-
lute monarch otherwise known as "the
Divine Right of Kings"; (2) Corporate Sover-
eignty, or the Sovereignty of the government,
whether monarchic, aristocratic, democratic,
or mixed; (3) Popular Sovereignty, or the Sov-
ereignty of the state or people ; and (4) The
Sovereignty of Right or the Lazu. 1 To which
may be added as many other senses as abstrac-
tions can be imagined for the purpose as, e. g. ,
the Sovereignty of Reason, or, in a theocracy,
the Sovereignty of God. All these different
1 This expression originated with Aristotle : " Moreover, he
who bids the law to be supreme, makes God supreme ; but he
who trusts man with supreme power gives it to a wild beast,
for such his appetites often make him ; passion, too, influences
those who are in power, even the very best of men ; for which
reason the law is intellect free from passion." Politics, iii.,
xvi.
l6o LOGIC
senses of the term are inconsistent with each
other; and all except the first (now happily ob-
solete) are in their direct sense without
definite signification, or, in other words, non-
sensical. For the government or state, and
likewise right or law and reason, are purely
imaginary or fictitious persons, existing only
in contemplation of mind /. e. , they are quasi-
persons only; and the power of such fictitious
or imaginary beings must be as imaginary as
themselves. For the government or state or a
corporation cannot, properly speaking, be said
to have rights, or will, or power, or conscience,
or other human attribute; and when, other-
wise than as a mere figure of speech, we speak
of such <5w<7.$7-persons as having such attributes,
we talk pure nonsense. And so with reference
to the sovereignty of God, though the same
observation is not literally true, yet practically,
as we can know but little of His will, or the
exertions of His power, the term, as generally
used, carries with it no meaning.
The following examples are in effect identical
with the above :
(i) The doctrine of Kant, Rousseau, and
others, that the will of the government or the
state is to be regarded as " the united will of
the people" ; which is obviously a mere fiction,
and, construed literally, not only false, but
impossible.
FALLACY OF NON-SIGNIFICANCE l6l
(2) The proposition of Hobbes, that the
effect of the institution of government was to
create not merely " a consent or concord " of
the people, but " a real unity of them all in one
and the same person"
(3) The equivalent proposition of Bluntschli
and others, that the state is an " organized be-
ing " or "organism," having a soul and a body,
a conscience and active powers, and also a will
different from the wills of the individuals com-
posing it.
(4) And finally the celebrated theory of the
Social Compact or Contract, which served
Hobbes, Locke, Rousseau, and others as the
foundation of their respective reasonings; and
from which, as a premise, their several essen-
tially different and antagonistic theories are,
with equal felicity, deduced.
136. OF LEGAL FICTIONS. These are all
examples of what lawyers call legal fictions ;
which are at least as common with the philoso-
phers as with the lawyers. 1 In all of them
except the last the government or state is re-
garded as a body politic or corporation ; which
1 The difference between the lawyers and the philosophers
in this respect is that by the former the fiction is always recog-
nized as such, and used merely as a convenient mnemotechnic
device. It is also used, not as a universal, but as a particular
proposition its use being restricted by the maxim, " In fic-
tione juris semper tequilas." But the use of it by philosophers
is often the reverse.
I 62 LOGIC
is defined as a fictitious or imaginary person,
existing only in contemplation of mind, i.e., as
a guasi-person, and the definition is, in fact,
but a bold metaphor. Hence, as we have said,
the power of this fictitious or imaginary being is
as imaginary as itself. For human power can
exist only in actual human beings; and though
for convenience we may speak of the power of
the government as of that of any other corpora-
tion, yet the expression is always to be under-
stood as really denoting the concurrent powers
of certain individuals in the government.
Hence, when we attribute to the state or gov-
ernment, or any other corporation or fictitious
entity, will, conscience, soul, body, sex, or other
human faculty, feeling, or quality, we speak
figuratively, and, as in all cases of figurative
language, if literally, absurdly. The examples
cited may therefore be more specifically as-
signed to the class of fallacies called by the old
logicians the Fallacy of Figure of Speech (Fal-
lacia Figures Dictionis), (infra, 203).
With regard to the doctrine of a social
compact, it has not the excuse of being even
figuratively true. Like the fiction of the Eng-
lish law that husband and wife are one, it is
simply an undisguised, recognized absurdity,
assumed as a first principle. That it should
ever be asserted would, were it not for experi-
ence to the contrary, be simply incredible.
FALLACY OF NON-SIGNIFICANCE 163
137. THE DARTMOUTH COLLEGE CASE.
A similar example of this fallacy is presented
by the decision of Chief Justice Marshall in the,
Dartmouth College case (4 Wheat., 518), where
it was held that an act of the Legislature re-
organizing a collegiate corporation was in con-
flict with the provision of the Constitution of
the United States forbidding enactment by a
State of any law " impairing the obligation of
contracts." It was not perceived that a corpo-
ration, being a fictitious person, is not capable
of having any rights, except as representing
real persons, and that its so-called rights are in
fact merely the rights of its stockholders or
other parties interested in it. But in eleemosy-
nary corporations there are no private parties
interested, and hence the supposed rights of
the corporation are in fact those of the State,
and consequently subject to its disposition.
For it is absurd to speak of rights that have no
real owners; and to such rights the Constitu-
tion which was designed to protect the rights
of real persons can have no application. The
decision was therefore simply a case of the Fal-
lacy of Nonsense, of the kind called F. Figures
Dictionis.
138. OBSERVATIONS ON THE FALLACY OF
NONSENSE. It may be observed here by the
reader, who is somewhat familiar with Logical
Doctrine, that the Fallacy of Nonsense is ap-
1 64 LOGIC
parently a new kind of fallacy, not to be found
in the books ; but this is very readily explained.
; For, as we have observed, a conclusion involv-
ing a nonsensical term, being itself nonsensi-
cal, can in its proper sense, or rather nonsense,
be of no use for any purpose, and hence is
always used as equivalent to some significant
proposition, and thus becomes an Ignoratio
Elenchi. Thus the doctrine of Absolute Sov-
ereignty, like other nonsensical theories, is in
itself innocuous, and becomes otherwise only
by illicit use. There can be no harm in saying
that Leviathan, the creature of our imagina-
tion, is vested with unlimited power, or even
to say with Hobbes that he is a " mortal
god," and therefore omnipotent. For his
power, if left to himself, is no more formidable
than that of the wooden or brazen gods of the
heathen. But as in the latter case the power
of the god is, in practice, the power of the
priest, so the imaginary power of Leviathan is
but a word used to cover the actual power of
some officer or officers of the government; and
to them the meaning of the doctrine is: " You
must not resist us." Hence, invariably, a non-
sensical term is used only in the argument, and
the conclusion is always used as equivalent to
some other and significant proposition, thus
making a case of Irrelevant Conclusion, or
Ignoratio Elenchi; under which head it is
FALLACY OF NON-SIGNIFrCANCE 165
commonly treated. Of this numerous exam-
ples will be given in the sequel.
2. 77^ Fallacy of Confusion
139. This fallacy is recognized in the books
as one of the most common and pernicious;
and, indeed, it is a commonplace in philosophy
that the use of undefined terms is one of the
most fruitful sources of error. The nature of
the fallacy is explained under Rule I. of the
Rules of Logic. A few examples will be suffi-
cient to illustrate its nature.
Examples
140. UTILITARIANISM. The most serious
example of this fallacy is presented by the
theory of Utilitarianism ( 132 ad fin.), which
for the greater part of a century has exercised
a predominating and pernicious influence over
English thought. The theory, briefly stated,
is that general utility is the paramount and
sole standard of right and wrong and of the
just and unjust. But the term " general util-
ity " has no definite meaning; because it is im-
possible to determine from it who are the people
whose utility or welfare is to be considered
whether a mere majority or less, or two thirds,
or three fourths, or other proportion ; and
1 66 LOGIC
hence the proposition must be regarded as non-
significant or nonsensical.
141. EDUCATION. So he who asserts the
benefit of education is, in general, talking non-
sense. For education is but the development
of character, mental, moral, and physical,
and may be either good or bad. For there is
an education of the thief, of the bully, of the
tramp, as well as of the honest man, of the
hero, of the efficient man, or of the scholar,
or statesman, or philosopher. And so, even
among legitimate kinds of education, there is
an education of the mechanic, of the farmer, of
the laborer, of the lawyer, of the doctor, and
many other kinds. Consequently, when one
asserts the benefit of education generally,
without defining the term, the proposition is
nonsensical.
142. PROTECTION. So the man that as-
serts that he is in favor of the protection of
American industries is, in general, talking pure
nonsense. For there are many kinds of pro-
tection, as, e. g., (i) The prohibition of all
foreign imports that compete with our own in-
dustries; (2) the equalization of the cost of
production; and (3) the encouragement of in-
fant industries; and until we are told which of
these various kinds of protection is intended
the proposition conveys no definite meaning.
143. EXPANSION. So when an American
FALLACY OF NON-SIGNIFICANCE 167
announces himself as an advocate of territorial
expansion he is, generally, talking nonsense;
for there are many kinds of expansion, among
which three may be especially distinguished,
namely: (i) The acquisition of contiguous
homogeneous territory essential to the safety
of the government, as, e. g., in the case of the
purchase of Louisiana; (2) the acquisition of
contiguous and homogeneous territory desir-
able as giving room for the expansion of popu-
lation, but not essential to the safety of the
government, as, e. g., the acquisition of Cali-
fornia, New Mexico, etc. ; and (3) the acquisi-
tion of territory far removed from our own, of
a climate unsuited to our people, and inhabited
by an alien and non-assimilable race. Such a
country must be governed by despotic power,
and its acquisition must therefore be distin-
guished from other kinds of expansion by the
name of Imperialism.
CHAPTER X
FALLACY OF FALSE DEFINITION
144. The nature of this fallacy is explained
under Rule II. of the Rules of Logic. As
there explained, the fallacy is of two kinds
consisting, the one in the use of a term in an
improper sense, i. e., in a sense not permitted
by the usage of the language the other, in
using a term in an unreal sense, /. e. , as denot-
ing a notion to which there is no corresponding
reality.
The former kind of the fallacy is not admitted
by logicians generally ; for it is an unfortunate
delusion of philosophers that they are at liberty
to define a term as they please. But whether
this claim be admitted or otherwise, it has been
the source of infinite error; so that the viola-
tion of the rule, if not regarded as a fallacy,
must at least be regarded as a most prolific
mother of fallacy. For where a term is used
in a novel sense, though clearly defined, it is
hardly within the power of the human intellect
168
FALLACY OF FALSE DEFINITION 169
to emancipate itself from the influence of its
usual and proper signification. Hence, inevi-
tably, the use of improper terms will result in
the fallacy of Ignoratio Elenchi.
Examples
145. WHATELY'S DEFINITION OF LOGIC.
Whately's definition of Logic as " the science
and art of reasoning," and of Reasoning as
consisting solely in syllogistic inference, pre-
sents an instructive example of the Fallacy of
False Definition. This definition excludes from
the province of Logic the doctrine of Judgment,
and, as involved in this, the doctrine of the
Term, and also that of the fallacies called Non-
logical or Material, thus mutilating it of its
most vital parts. But these subjects are in-
variably treated of by the logicians, including
himself, arid as is now generally admitted
belong to logical doctrine ; which is an effective
reductio ad absurduin of the definition.
146. STEWART'S DEFINITION OF REASON-
ING. From the same false definition of Logic,
and of reasoning, Dugald Stewart deduces the
paradoxical conclusion that not only Logic, but
reasoning itself, is but of little utility; which
constitutes a still more effective reductio ad
absurdum of the falseness of the definition. 1
1 "Of the different elements which enter into the composi-
tion of reason, in the most enlarged acceptation of the word,
1 70 LOGIC
147. LOCKE'S ATTACKS ON LOGIC.
Locke's diatribes against Logic had their
source in the same false definition of Logic as
being merely the doctrine of syllogism. But,
strangely enough, at the end of his work he
gives a correct definition of it; which, as we
have seen, he takes for an invention of his own
( no).
148. MILL'S DEFINITION or LOGIC.
According to Mill's definition, " Logic is not
the science of belief, but is the science of proof
or evidence," or, as otherwise expressed, " the
science of the operations of the understanding
which are subservient to the estimation of evi-
dence." But bearing in mind the essential
difference between judgments and assumptions
it will be observed if we leave out of view
axioms, which are to be regarded merely as
laws or conditions, to which the mind operating
intelligently must conform that the former
constitute the first principles of all demonstra-
tive or apodictic reasoning, and therefore ne-
cessarily fall within the province of Logic ; but,
with regard to assumptions, that Logic is not
concerned with the evidence of their truth.
But the term, evidence, in its proper sense, re-
lates exclusively to assumptions or propositions
the power of carrying on long processes of reasoning or deduc-
tion is, in point of importance, one of the least." Phil, of
the Mind, v. ii, p. 154.
FALLACY OF FALSE DEFINITION l?l
in which the significative relations of the term
are not intuitively perceived; and hence, with
regard to such propositions, the respective pro-
vinces of Logic and of the other sciences are
clearly defined. The latter deal with the evi-
dence of the propositions assumed ; the former,
exclusively with inferences from them, upon
the assumption or hypothesis that they are true.
Hence the definition of Mill precisely reverses
the several functions of Logic and of the other
sciences that furnish it with assumed proposi-
tions as premises.
149. HAMILTON'S DEFINITION OF LOGIC.
The definition of Logic as " the science of
the laws or forms of thought " may be cited
as another example. Logic is concerned, not
with all thought, but with a particular kind of
thought only namely, reasoning; and it is
concerned, not only with \\\z forms, but with
the matter of reasoning. The definition is
therefore at once too wide and too narrow; it
would include, e.g., rhetoric and grammar,
and would exclude the best part of Logic.
150. DEFINITION OF THE LAW. A most
striking example of the Fallacy of False Defini-
tion is presented by the definition of the Law,
invented by Blackstone and adopted as the first
principle of jurisprudence by Bentham and
Austin. According to this definition, the law
is merely an expression of the will of the
1^2 LOGIC
government an obviously false and illegiti-
mate definition. Yet the theory of Bentham
and Austin, based on this definition, has abso-
lutely dominated jurisprudence in England and
this country for nearly a century; and, as the
result, English and American jurists and publi-
cists have lost mental touch with the jurists of
other countries and ages; and have thus, with
reference to scientific jurisprudence, been ren-
dered incapable of dealing with this great and
important subject. And indeed the effect of
the theory on the practical administration of
justice has been scarcely less deleterious.
151. THE THEORY OF PRIVATE UTILITY.
Another conspicuous example of this fallacy
is furnished by the theory of individual utility
assumed by Hobbes, Bentham, and Austin as
the first principle of Morality and Politics; in
which self-interest is regarded as the sole pos-
sible motive of human conduct, and right and
wrong, just and unjust, and good and evil are
defined as consisting in conformity or noncon-
formity to that interest.
152. THE GREATEST GOOD OF THE
GREATEST NUMBER. Bentham also incon-
sistently held the theory that " the greatest
good of the greatest number" is the true stand-
ard of Morality ; which must either be regarded,
like the theory of General Utility, as simply
nonsensical, or as holding that the standard of
FALLACY OF FALSE DEFINITION' 173
right and wrong and of the just and unjust is
the good of the majority. An execrable doc-
trine; for it cannot be asserted that the life or
faculties or property of an innocent man can
be converted to the use of another or of others,
except in the case of a clearly defined right in
the one and an obligation to submit to it in
the other.
153. MAINE'S DEFINITION OF THE LAW
OF NATURE. Another example is presented
by the peculiar and curious view taken by Sir
Henry Maine of the term Jus Nat ur ale as
used by the Roman lawyers, and its equiva-
lent, the Law of Nature, or Natural Law, as
used by modern jurists and philosophers. This
notion, he erroneously assumes, had its origin
in the supposed state of nature ; which doctrine,
he says, the Roman jurisconsults borrowed
from the Greek philosophers. But the term
Jus Naturale, or Law of Nature, is one of the
comparatively small class of terms whose mean-
ing is perfectly definite and settled. As used by
jurists, it is but another name for Natural Jus-
tice, 1 or Right Reason applied to the jural
1 Hobbes's Lev., chap. xxvi. "It is not used among them
that be learned in the laws of England to reason what thing
is commanded or prohibited by the law of nature." But,
" when anything is grounded on the law of nature, they say
that reason will that such a thing be done ; and if it be pro-
hibited by the law of nature, they say it is against reason "
(Doctor and Student, chap. v.). "True law is right reason
174
LOGIC
relations of men ; which, as universally held by
them, " is part of the law of every common-
wealth in the world."
conformable to nature" (Cicero, De Rep.). " Right reason is
what we call law" (id., De Leg.). "Natural law is the
rule and dictate of right reason " (Taylor, Elements of Civil
Law). ' ' The law is intellect free from passion " (Arist. , supra,
135 n.).
CHAPTER XI
ILLICIT ASSUMPTION OF PREMISES (PETITIO
PRINCIPII}
I. Of the Nature and Several Forms of this
Fallacy
1 54. This fallacy may occur in various ways,
and it would therefore be an "endless task to
enumerate or classify all its different forms;
nor would there be any advantage in doing so.
There are, however, several forms of the fallacy
that, on account of their frequent occurrence
and their powerful influence over the minds of
men, demand a particular consideration, and
to these our attention will be directed.
155 (i). ILLICIT GENERALIZATION. The
most important of these, which may be called
the Fallacy of Illicit Generalization, consists in
the use of a universal proposition in cases where
the corresponding particular proposition is
alone admissible. This fallacy is one of the
most common and formidable, not only in
popular discourses, but in more pretentious
12
175
1/6 LOGIC
works on Politics and Morality; for almost all
the wisdom of common sense is embodied in
this sort of propositions, i. e., particular propo-
sitions assumed to be universal. Such propo-
sitions may, indeed, be used with profit by
men of sense in practical affairs; as, in general,
when a question presents itself it is easy to
perceive whether the principle should be ap-
plied or not; or, if a mistake be made, it is
corrected by experience; but the masses of
men are easily misled by them. Hence they
serve well for rhetorical purposes; for the
hearer, unless of a critical mind, will in general
accept them without hesitation.
Examples
156. COMMONPLACES. The most impor-
tant cases of this fallacy occur in the use of
Commonplaces ; by which is meant, opinions
current among men generally, or particular
classes of men, and used as premises for reason-
ing. 1 These are commonly founded upon some
truth which they purport to express, and to
which they more or less nearly approximate;
1 Hence Bacon, as a useful rhetorical device, recommends
the preparation of tables of Commonplaces, of which he gives
an example in his De Augmentis ; wherein should be arranged,
for the use of speakers and writers, in parallel columns, argu-
ments pro and con, or theses and anti-theses, on all questions
of general interest.
ILLICIT ASSUMPTION OF PREMISES 1 77
so that there is here, as " in all things evil, a
soul of truth." But they are hardly ever uni-
versally true; and therefore to assume them as
universals is illicit.
157. POPULAR PROVERBS. Of these com-
monplaces, the most striking examples are
furnished by popular proverbs; and of these,
as illustrating precisely the nature of such
maxims, two may be cited that, in their literal
expression, are contradictory, but, as maxims
go, may both be said to be true, i. e., they are
each true in certain cases, but neither univer-
sally. They are the old adages, " Never put
off till to-morrow what you can as well do to-
day " and " Never do to-day what you can as
well put off till to-morrow " ; the first of which
points out the danger of procrastination, the
latter, the danger of committing ourselves be-
fore necessity requires. It may be readily seen
that, according to circumstances, either of
these may serve as a useful hint for conduct ;
but, in using it, the caution of the nautical
philosopher is to be observed, that " the bear-
ing of the observation lies in the application
of it."
158. LEGAL MAXIMS. Another striking
illustration of the same class of propositions is
furnished by what are called the maxims of the
law ; which, in general, are true only as particu-
lar propositions, /. e., only in particular cases,
178 LOGIC
but are habitually spoken of by legal writers as
" first principles," analogous to the maxims of
science; though every competent lawyer is
familiar with the fact that they admit of numer-
ous exceptions. A very large proportion of the
so-called principles of the law, and of the rules
founded upon them, are of precisely this nature,
z. e., admit of exceptions, and are, therefore,
true only as particular propositions. And it is
also a fact that many of these principles and
rules are opposed by others, equally approved,
that are contradictory to them. Hence, if we
regard bulk only, the greater part of the law
might be readily and advantageously arranged
in a table of contradictory commonplaces, i. e.,
a collection of theses and anti-theses, as sug-
gested by Bacon in the De A ugmentis; wherein,
under each topic, one column should represent
the one side and the other, the other, of the
various questions that may arise in litigation.
The cases might also be arranged in the same
way.
The above examples are all cases of illicit
generalization, and will serve to show how wide-
spread is the use of this particular form of illicit
assumption of premise. And, it may be added,
such is the lack of critical acumen in the gener-
ality of mankind, that the fallacy is seldom
detected, and consequently it constitutes the
most powerful of rhetorical devices.
ILLICIT ASSUMPTION OF PREMISES 1/9
159(2). OF THE FALLACY OF NON CAUSA
PRO CAUSA. Another form of the Fallacy of
Illicit Assumption of Premise is presented by
the fallacy called " Non causa pro causa" ;
which is also called the fallacy of " Post hoc
ergo propter hoc." It consists in the illicit as-
sumption that an event preceding another
event is the cause of the latter, as, e. g., that
a change in the moon is the cause of a change in
the weather ; or that the fact of thirteen dining
together is the cause of any accident that may
happen to any one of them ; or that the Dog
Star is the cause of heat. This is, indeed, one
of the most familiar of fallacies in political
arguments, where it is common to argue that
the condition of the country, whether good or
bad, is caused by some particular policy, as,
e. g., where it is argued alternately, according
to vicissitudes of events, by the one party that
a prosperous, by the other that a depressed,
condition of affairs is caused by the tariff or
other political measure. 1
1 It will be observed that there are some differences of
opinion among logicians as to this fallacy. A distinction is
made between what is called the causa essendi and the causa
cognoscendi ; or between the cause of an event and the cause
of our knowing it. These may coincide, as, e. g., when from
the fact of its raining in the night we infer that the ground
will be wet in the morning ; where the rain is both the causa
essendi and the causa cognoscendi. But, when, from finding
the ground wet in the morning, we infer that it rained during
l8o LOGIC
160(3). ARGUING IN A CIRCLE. Another
common form of the Fallacy of Illicit Assump-
tion is presented by the fallacy called arguing in
a circle ; which consists in assuming for a prem-
ise the very proposition to be proved, or one
obviously equivalent to it, or one that is form-
ally involved in it. 1 When the argument does
not extend beyond a single syllogism it is
called a Hysteron Proteron (the First-last). 2
161 (4). QUESTION-BEGGING TERMS.
Another very common and very dangerous
the night, the causa cognoscendi is the wet ground, from which
we infer the causa essendi, i. e., the rain. Logic is, however,
concerned with the causa essendi only so far as it constitutes
the causa cognoscendi ; and hence logically the distinction may
be regarded as immaterial.
1 This occurs most frequently in the use of synonyms, and,
as observed by Whately, is peculiarly favored by the composite
character of our language. It can occur only where the prop-
osition assumed is so obviously equivalent to the conclusion
as to be evidently the result of a trick or inadvertence. In
general the premises assumed are equivalent to, or imply, the
conclusion ; and the conclusion is arrived at by the substitu-
tion of an equivalent term ; which is the very essence of ratio-
cination. Such assumptions are not only admissible, but
inevitable. Otherwise all syllogisms would be fallacious, as
involving a pctitio principii ; and inference, inconceivable.
2 The following is a striking example of this fallacy :
" Since every unjust act is inexpedient, then no unjust act is
expedient ; then no expedient act is unjust ; then every expe-
dient act is just." This has been given as a valid argument.
But the premise is obviously but an inference from the conclu-
sion, which is the principle of the reasoning ; and for it the
thesis has been illicitly substituted as the premise.
ILLICIT ASSUMPTION OF PREMISES l8l
form of this fallacy is that of using question-
begging terms (which is also a case of the Fal-
lacy of False Definition). It consists either in
including in the formal definition of a term
some unproved assumption, as being of the es-
sence of the conception denoted, or in using
the term without formal definition, as though
such assumption were included in its meaning.
By this method, the propositions from which
our conclusions are to be deduced, instead of
being proved as they ought to be, are uncon-
sciously imbibed by the mind, with the defini-
tion, or with our conception of the term, and
the conclusion thus in effect assumed. The
power of this method of persuasion is well un-
derstood by many, and unscrupulously used
as, for example, by Hobbes and other support-
ers of governmental absolutism ; who realize
the truth of Rousseau's observation that " the
strongest is not strong enough to continue al-
ways master, unless he transforms his power
into a right, and obedience into a duty." But
with the mass of writers the fallacious process,
though none the less efficacious, is entirely
unconscious. A notable example of this fallacy
is usually given by political writers in their
definitions of " the State"; which is simply
an independent society of men," but is
usually defined so as to include in its essence
absolute power, or some other theory of the
I 82 LOGIC
writer. Any recent work on Politics will serve
to illustrate the fallacy.
2. Of tlie Tests of Illicit Assumption
162. ENUMERATION OF THE TESTS.
There are numerous tests by which the legiti-
macy of assumed premises may be determined,
of which the most important and familiar are:
(1) the ''Instance,'' 1 or " Extreme Case";
(2) the " Burden of Proof," or Onus Probandi ;
and (3) the Reductio ad Absurdum. These will
next be considered.
163. THE INSTANCE, OR EXTREME CASE.
This test applies most appropriately to the
Fallacy of Illicit Generalization, and is most
efficacious in its operation ; though, as is ob-
served by De Morgan, it is commonly regarded
as not only inadmissible, but impertinent. It
consists simply in adducing an exception to the
proposition assumed. The subject is admi-
rably treated by the author cited. 2
164. THE ONUS PROBANDI. An ex-
tremely effective means of testing the truth of
1 The term ' ' instance " is commonly used as synonymous with
'' example," but it is said by De Morgan that by the mediaeval
logicians it was always used to denote an inconsistent example,
or, in other words, to denote what we would call an instance
to the contrary, an expression that would have been regarded
by them as tautological.
2 "The application of the extreme case is very often the
only test by which an ambiguous assumption can be dealt
ILLICIT ASSUMPTION OF PREMISES 183
a proposition, and of thus exposing an Illicit
Assumption, is often afforded by considering
what is the presumption in the case ; or, con-
trariwise, on which side of the question lies the
burden of proof , or onus probandi. In general,
this is on the party affirming the proposition,
and, in the absence of other presumptions, we
are always entitled to demand his proofs. This
simple test will be sufficient to dispose of all
propositions for which proofs cannot be found,
but which have been inadvertently assumed ;
and this test we should always apply to our
own reasoning, remembering that " Slowness
of belief and distrust are the very sinews of
wisdom." But in certain cases, and especially
in Moral and Political Science, the test will
often have a conclusive efficacy. For in
Morality, Public and Private, or in Jurispru-
dence or Right, the questions presented are
generally questions, not of fact, but of right
and wrong ; and among these there are certain
fundamental principles, as, e.g., touching the
right of personal liberty or security or self-
ownership, with reference to which the pre-
sumption is clearly defined, and its contradictory
obviously absurd. Of this kind is the general
presumption in favor of liberty; which, of
with ; no wonder that the assumer should dread and protest
against a process which is as powerful as the sign of the cross
was once believed to be against evil spirits." Formal Logic.
1 84 LOGIC
itself, is sufficient to dispose of numerous and
important political theories that, from a neglect
to consider the onus probandi, have been care-
lessly or dishonestly assumed.
165. OF THE REDUCTIO AD ABSURDUM.
This consists in reasoning from the conclu-
sion deduced from the premises assumed to
some absurd, or admittedly untrue, conclusion ;
and this method of refutation will apply not
only to the fallacy of illicit generalization, but
to all forms of petitio principii whatever. It
is, indeed, one of the most efficacious means
that Logic has at its command for the detection
of fallacy, and will therefore repay an attentive
consideration.
Strictly speaking, the phrase would seem to
indicate that it applies only to the establish-
ment of the contradictory of the proposition
under consideration '; but the method has, in
fact, a much wider application, and the term,
in common use, a corresponding extension.
For it is the essential characteristic of all true
1 In the narrower sense, the term reductio ad absurdiim is
equivalent to the reductio ad impossibile ; of which examples
are given supra ( 96, n.). But more generally it is used
as including all cases where, from the conclusion of an
argument, the contradictory of some admitted proposition
or, in other words, a conclusion contrary to the hypothesis
can be deduced. Hence it is called by Aristotle the "Argu-
ment from Hypothesis." (Mansel's Aldrich, App., note I,
p. 228.)
ILLICIT ASSUMPTION OF PREMISES 18$
propositions that they will be consistent with
each other; and it is an almost equally univer-
sal characteristic of untrue propositions that
they will be inconsistent with other proposi-
tions known to be true.
This is particularly the case in all the
different branches of the Science of Human
Nature ; all of whose parts and particular prin-
ciples are so connected by numerous relations
that it is almost impossible to assert an untrue
principle without coming in conflict with others
that are self-evident, or readily demonstrable,
and which have thus come to be universally
admitted. Hence it may be said that in
Morality or Politics we may set out from al-
most any principles, provided we hold them
with indifference and are capable of abandon-
ing them when shown to be inconsistent with
settled principles and known facts. From
which it may be inferred that the reductio ad
absurdum in fact constitutes not only an effi-
cient, but almost an all-sufficient, instrument
for the detection of fallacy in Moral and Politi-
cal Science.
General Examples
166. LOCKE'S THEORY OF SIMPLE IDEAS.
A most instructive example of Illicit As-
sumption of Premise occurs in the fundamental
assumption of Locke's theory of knowledge;
1 86 LOGIC
which is, that the original notions received in
the mind from sensible objects are notions of
the qualities of substances, such as color, hard-
ness, etc., which he calls simple ideas ; and out
of which, he holds, all our notions are com-
pounded. But on reflection it will be perceived
that the original or primordial notions of the
mind are the composite notions of substances
or things ; and what Locke calls " simple no-
tions " are the result of subsequent analysis.
167. THE OBLIGATION OF CONTRACTS.
It is one of the so-called maxims of the law
that contracts are obligatory and ought to be
enforced (Pacta quczlibet servanda sunf); and
this is commonly assumed as a universal prop-
osition, as, e. g., by Bentham and Spencer in
the examples given below ( 180, 181). But
there are innumerable cases in which it is
obviously not right that contracts should be
enforced, and in which, in fact, the law does
not enforce them ; which is an effectual refuta-
tion of the principle. The true principle is
that in case of breach of contract the injured
party is entitled to compensation as in the
case of torts for the detriment suffered by
him by the acts of the wrongdoer (i. e., by the
making of the contract and its breach).
168. FALSE ASSUMPTION OF FACT. This
includes innumerable cases, which it would be
impossible to classify. One of the most in-
ILLICIT ASSUMPTION OF PREMISES 1 87
teresting is furnished by Tacitus in his account
of the mutiny of the Pannonian legions on the
accession of Tiberius, in the address of the
soldier, Vibulenus, to the general, Bloesus.
His brother, he said, coming as a delegate
from the German army, had been butchered
by the commands of Bloesus. " Answer,
Blcesus," he said; " where hast thou thrown
away his corpse ? " By which, says Tacitus,
he raised such a spirit of frenzy and ven-
geance that had it not been quickly manifested
that there was no corpse to be found
and that Vibulenus never had any brother,
they had gone nigh to sacrifice the general."
The example, so far as Vibulenus is concerned,
was simply a lie, but, in the soldiers, a fallacy
that would have been readily refuted by apply-
ing the test of the onus probandi.
CHAPTER XII
MISTAKING THE ISSUE, AND IRRELEVANT
CONCLUSION (IGNORATIO ELENCHI)
169. The nature of this fallacy, which is
explained under Rule IV. of the Rules of
Logic, is precisely expressed by the first of
the names we have given it, which is a techni-
cal term taken from the law. This differs from
the equally appropriate term Irrelevant Conclu-
sion only in this, that the former has regard to
the origin, the latter to the outcome of the fal-
lacy. Or, in other words, when we regard the
beginning of the fallacy, we call it Mistaking
the Issue; when the end, Irrelevant Conclu-
sion; and, in either case, Ignoratio ElencJii.
The two names, i. e., Mistaking the Issue and
Irrelevant Conclusion, present, therefore, two
different aspects of the same fallacy, under
each of which it will be convenient to consider
it.
170. MISTAKING THE ISSUE. This, as is
well appreciated by the lawyers, is one of the
most formidable and most common of all fal-
188
MISTAKING THE ISSUE 189
lacies. For the most fruitful of all sources of
fallacy is bias or logical dishonesty, of which the
expedient of mistaking or misstating the ques-
tion at issue is one of the most obvious and
most potent instrumentalities. And as logical
honesty is, in fact, one of the rarest of intel-
lectual virtues, it can be readily understood
that the fallacy must be common.
171. FALLACY OF SEVERAL QUESTIONS
OR ISSUES. One form of this fallacy may be
identified with the technical Fallacia plurium
interrogationum ( 197), which consists in mix-
ing in one several questions or issues. As
defined by Aristotle, it results " from making
two questions one, when it escapes notice that
there are many, and one answer is given, as if
there was one question only."
The following examples are taken from a
recent work :
Did you steal anything when you broke
into my house last night ? ' ' Are you the only
rogue in your family ? ' ' Have you quit drink-
ing ? ' ' Have you cast your horns ? ' (Hence
sometimes called Cornutus.}" (Davis, Theory
of Thought, 294.)
The fallacy is readily solved by separating
the compound question into its several compo-
nents, as, e. g. , in the following: Menedemus,
Alexino rogante, Numquid, pair em verberare
desiisset ? inquit, Nee verberavi, ncc desii ; or,
190 LOGIC
as in the answers of the two thieves to the
question: " Did you steal the sheep you have
in your possession ?"; to which the one an-
swered, " He did n't steal the sheep"; the
other, that " He did n't have it."
172. It is added by the author, " All this
seems quite frivolous." And another, gener-
ally accurate, logician says: " The so-called
' Fallacia plurium interrogatiomim ' has not
been noticed in the text, because it is a rhe-
torical artifice rather than a logical fallacy."
(Fowler, Deductive Logic, 150.) But it cannot
be doubted that the fallacy, as described by
Aristotle, consists simply in mixing several
questions or issues in one, and therefore comes
under the head of mistaking' the issue; or that
it is at once a very common and a very for-
midable fallacy. And especially, it is to be
observed, it is the hard fortune of the citizen,
in all ages and countries, that, in general,
whether by accident or design, no question in
practical politics is presented to him that does
not involve this fallacy.
Thus, in American politics, for some time
after the war, several questions (plures intcr-
rogationes) were presented at each federal
election, namely: (i) as to the expediency of
the protective policy; (2) as to that of the re-
construction policy; (3) as to that of the con-
traction of the currency; and thus practically
MISTAKING THE ISSUE 19!
the questions presented to each voter were:
" Are you in favor of all these policies ? " or
" Are you against them all ?" So in the last
election, the issues presented were equally
numerous namely : (i) as to the policy of
protection ; (2) as to the relative advantages of
the single gold or a bimetallic standard ; and
(3) assuming the desirability of bimetallism
as to the practicability of adopting it in this
country alone, without the concurrence of
other nations.
In the case put, and in fact in almost all
political contests, each question involved is dis-
cussed separately, and the conclusion pro-
fessedly drawn is simply the affirmative or the
negative of the particular question, as the case
may be; but the conclusion intended is, not
the affirmative or negative of the particular
question, but that of all of them taken to-
gether thus presenting a case of irrelevant
conclusion.
Hence, generally, in political contests the
actual issue presented is simply as to the as-
cendancy of one of two parties; while the
voters are persuaded, or persuade themselves,
that they are deciding some other issue. Hence
it results as a general though not as a uni-
versal proposition that politics becomes a
mere struggle for political supremacy.
173. IRRELEVANT CONCLUSION. All fal-
IQ2 LOGIC
lacies of judgment must, as we have observed,
take the form of irrelevant conclusion ( 132);
which, in turn, becomes a fallacy only when
used as an equivalent to some other proposi-
tion. Hence the examples of fallacy already
given, and many of those to be given hereafter,
will equally serve our present occasion.
Examples
174. THE DOCTRINE OF ABSOLUTE SOV-
EREIGNTY. The use made of this doctrine by
its advocates presents a conspicuous example
of this fallacy. The doctrine, like all other
nonsensical theories, is in itself innocuous, and
becomes otherwise only by illicit use. But it
is invariably used in some different and signifi-
cant sense, as, e. g., Rousseau's theory of the
" Sovereignty of the People," which gave rise
to the various political doctrines rife in the
French Revolution, and to which historians
have ascribed the terrible scenes of the Reign
of Terror ; from which they draw the infer-
ence that it is dangerous to apply Logic to
practical politics. But this also is a case of
Irrelevant Conclusion. For the conclusion
should be only that Fallacy is dangerous, i. e.,
not Logic, but the want of Logic.
175. SOVEREIGNTY OF THE LAW. Of the
various forms of the doctrine of Sovereignty,
that of the Sovereignty of Right, or the Law,
MISTAKING THE ISSUE 193
as it metaphorically expresses a doctrine at
once true and fundamentally important, might
seem to be unobjectionable were it not that, in
the direct effect of its language, it is merely
nonsensical, and therefore liable to be used as
equivalent to some other form of the doctrine,
as, e. g., in the use made of it by Von Hoist in
his Constitutional History of the United States ;
where his expressed conclusion is that " Sover-
eignty is One and Indivisible the Sovereignty
of the Law" ' But his real doctrine to the
establishment of which all his arguments are
marshalled is that sovereignty is indivisible,
and therefore vested exclusively, not in the
law, but in the Federal Government, and not
to any extent in the States.
176. AUSTIN'S USE OF THE DOCTRINE OF
SOVEREIGNTY. An example of this fallacy is
furnished by Austin and his followers in the
use made by them of their conclusion, that
' ' Sovereign poiver is incapable of legal limita-
tion "/ which, accepting his definition of the law
as being merely an expression of the will of the
sovereign, is quite true, and altogether inno-
cent; for obviously one's power cannot be said
1 This though, if the sense of the term be observed, a
harmless proposition is not a very consistent one ; for, as in
the United States, each State, as well as the Federal Govern-
ment, has its own independent system of law, it would seem
to follow that there are several sovereignties.
13
194 LOGIC
to be limited by his own will ; but the proposi-
tion is habitually used in the ordinary sense of
the terms.
177. USE OF THE DOCTRINE BY HOBBES.
Another example, precisely similar, is fur-
nished by Hobbes, who logically deduces from
his premises the conclusion that " the right or
just power " of the sovereign over the life and
fortunes of the subject is unlimited; and the
corresponding duty of the subject, absolute;
which, according to his definition of the terms,
right, justice, and duty, means simply that the
so-called right of the sovereign is an unbridled
or lawless power, to which prudence demands
of the subject that he should submit for fear of
worse consequences. The conclusion, in the
sense of the terms defined, is, therefore, quite
true; but it is habitually used by him and by
modern English jurists as though the terms,
right, justice, and duty were defined in their
ordinary and proper sense.
178. BENTHAM'S MISUSE OF THE THEORY
OF PRIVATE UTILITY. But the most flagrant
example of this fallacy is that of Bentham, who,
having established, or professed to have estab-
lished, the doctrine of Private Utility, or Utility
to the Individual, which asserts that the sole
possible motive of human conduct and the
only standard of right and wrong is self-inter-
est, afterwards assumes as equivalent to it the
MISTAKING THE ISSUE 195
principle of General Utility, and systematically
uses the latter as the premise established.
179. MISUSE OF THE THEORY OF GEN-
ERAL UTILITY. This theory, in the use
habitually made of it by Bentham and by
utilitarians generally, also presents a most in-
structive example of this fallacy. The theory,
being non-significant, is in itself innocuous ; but
it is commonly used as equivalent to the pro-
position that the interest of the majority is the
sole test of right, or, as expressed by Bentham,
as equivalent to the sacred truth that the
greatest good of the greatest number is the
foundation of morals and legislation." Thus
we have the apparently innocuous principle of
General Utility converted into the execrable
maxim that the good of the majority is alone
to be consulted.
180. BENTHAM'S DEFENCE OF USURY.
Bentham's celebrated defence of usury has
been commonly regarded ever since its publica-
tion as finally settling the question involved ;
but in fact it presents a striking example of the
fallacy of Ignoratio ElencJii.
His thesis, as proposed, is to establish " the
liberty of making one 's own terms in money bar-
gains "/ and his conclusion, which is entirely
legitimate, is that no man, not under disability,
ought to be hindered, with a viciu to his own
advantage, from making such bargains in the
196 LOGIC
way of obtaining money as he sees fit." But
obviously this is to mistake the issue ; for the
question is, not whether one should have the
liberty of making usurious contracts, but
whether he should be compelled to perform
them ( 167), and hence his conclusion is
obviously irrelevant. He fails, therefore
(though the world has thought differently), to
establish his proposition. 1
181. SPENCER'S ARGUMENT. Spencer's
argument in Social Statics and Justice for
liberty of contract is also an example of the
same fallacy. His first principle is his well-
known law of equal liberty, namely, " that
every man is free to do that which he ivills, pro-
vided that he infringes not the equal freedom of
any other man." From this principle he de-
duces, with admirable logic, the several per-
sonal rights that may be summed up in the
general right of self-ownership, and also the
right of property, and, as a corollary to the last,
the right of free exchange, and from that (illog-
ically, 189) the right of free contract ; but
he illicitly assumes, with Bentham, that the
1 In these observations it will be understood we are con-
sidering, not the moral or political question as to the propriety
of enforcing contracts for the payment of interest (on which
we have nothing to say), but simply the logical question as to
the validity of an argument in favor of usury that has served
to convince mankind of its righteousness, and that is univers-
ally regarded by an unlogical world as conclusive,
MISTAKING THE ISSUE 197
question is one touching the liberty of contract,
and not as to the righteousness of coercing the
parties ( 167), which was his thesis. Hence
his conclusion is essentially distinct from the
real conclusion intended, which is, that men
should be compelled to perform contracts.
182. BERKELEY'S THEORY AS TO THE
NON-EXISTENCE OF MATTER. This furnishes
another example. His argument is that, if
matter exists, it is impossible for us to know
the fact, or to know anything about it. But
this conclusion he habitually uses as equivalent
to the proposition that " matter, in fact, does
not exist," i. e., he substitutes the " non-
existence of matter" for " ignorance of its
existence."
CHAPTER XIII
ILLICIT CONVERSIONS
183. SIMPLE CONVERSION OF UNIVERSAL
AFFIRMATIVE PROPOSITION. The most usual
form of this fallacy occurs in the simple con-
version of a universal affirmative proposition,
as, e. g., where from the proposition Y is
X " we illicitly infer that " X is Y " ; and to
this form all other cases may be reduced. The
fallacy is so obvious that it might be supposed
it could not often occur, but it is in fact very
common.
Examples
184. CONFUSION OF PROPOSITION WITH
JUDGMENT. An example of it seems to be
presented by the commonly received doctrine
that " a proposition is a judgment expressed in
words "; which seems to result from an illicit
conversion of the proposition that a " judg-
ment expressed in words is a proposition."
185. ILLICIT CONVERSION BY NEGATION.
198
ILLICIT CONVERSIONS 199
The fallacy frequently occurs in the conver-
sion of a proposition by negation or contra-
position. Thus, c. g., the proposition " Y is
not X " becomes by negation " Y is not-X " ;
from which converting per accidens we may
infer that " Some not-X is Y " ; but not as is
often inferred that " All not-X is Y."
By this method any universal affirmative
proposition (" Y is X ") may be converted into
a proposition between the negatives of its terms
(i. e., Not X is not Y) ; but not, as is often
done, without converting the terms, i. e.,
from the proposition " Y is X " we may infer
that " Not X is not Y," but not that " Not
Y is not X " ( 91).
1 86. AN ARGUMENT OF HOBBES. A
striking example of this fallacy is presented by
Hobbes, that prince of logicians. Justice he
defines as the keeping of covenants, and injus-
tice as the failure to keep them. But, accord-
ing to his theory, covenants become valid only
upon the institution of government, from which
they derive their validity. Hence in a state of
nature there is neither justice nor injustice.
But he says also: " Whatever is not unjust is
just," and this conclusion which is contra-
dictory to his main position is obviously
arrived at by an illicit conversion of the univer-
sal affirmative proposition, " Whatever is just
is not-unjust."
CHAPTER XIV
ILLICIT SUBSTITUTIONS OF TERMS
187. Substitutions of terms may consist
either in the substitution of a new vocable or
vocal sign, or in the substitution of a new
sense to the same vocable. The latter is always
illicit, and constitutes the Fallacy of Equivoca-
tion. The former will be considered in this,
the latter in our next chapter.
The substitution of new terms of equivalent
signification for terms originally occurring is
the most common and extensive in application
of all the processes involved in ratiocination;
and the corresponding illicit processes if we
include equivocation may be regarded as in-
cluding all fallacies whatever. Hence the
examples already given, and especially those
given under the head of Irrelevant Conclusion,
will serve equally well to illustrate the fallacy
now under consideration.
Examples
188. AUSTIN'S ARGUMENT. Many ex-
amples of this fallacy are furnished by Austin,
ILLICIT SUBSTITUTION 2OI
as, e. g., in substituting for the predicate of the
proposition that " The sovereign power is in-
capable of legal limitation ," the term " legally
despotic," and thus inferring from the former
proposition that government is vested by law
with despotic power; which is not only untrue,
but upon his own theory impossible. For, if
law is but an expression of the will of the
sovereign, it is equally absurd to say either
that the sovereign power " is limited" or that
" it is conferred" by law.
189. SPENCER'S ARGUMENT. Another
example is furnished by Spencer in inferring
from the " right of free exchange " the " right
of free contract," which is in effect to substitute
genus for species in the subject of a universal
affirmative proposition. For exchange is only
a species of contract (v. supra, 181). It is true
that the right of free contract cannot be
doubted, but the substitution is none the less
a logical fallacy.
190. FLETCHER vs. PECK. Still another
example of this fallacy is furnished by Chief-
Justice Marshall (the greatest and most logical
of American jurists) in Fletcher vs. Peck, 6
Cranch, 135 ; where it was decided that an act
of the Legislature of Georgia revoking a grant
of land was in contravention of the provision of
the Constitution of the United States forbid-
ding the States to pass any act " impairing
202
LOGIC
the obligation of contracts.'" The argument in
effect was that a grant is a contract, and that
this was impaired by the act ; which was in
effect to substitute " Contract" for " Obliga-
tion of Contract."' The fallacy is the more
glaring from the fact that a grant is an exe-
cuted contract, which carries with it no obliga-
tion. Hence the constitutional provision must
be held to refer only to executory or obligatory
contracts.
CHAPTER XV
EQUIVOCATION
191. The ambiguity of terms and sentences
(Homonymia et AmpJiibolid) is undoubtedly the
most prolific of all sources of fallacy. This is
recognized by all logicians, and, indeed, by
philosophers generally ; but we doubt that
many appreciate the extent of the evil or the
universality of the danger to which men are
exposed by reason of it, or (especially) their
own infirmity in this respect.
' Instances of this fallacy," says Mr. Mill,
" are to be found in most all the argumentary
discourses of imprecise thinkers"; a proposi-
tion true in its literal statement but false in its
obvious implications; for it implies that the
proposition is not true of precise thinkers, and
also (though with becoming modesty) that it is
not true of the author. But in fact the most
precise, or, as we would prefer to say, the
most logical thinkers are liable to fallacy, and
especially to this kind of fallacy ; and none
203
204 LOGIC
more so than Mr. Milh 1 In this respect, if
fallacies be regarded as intellectual sins, we
may say: " There are none righteous. No,
not one." For it is with logicians as with
generals: the best that can be said of them is,
that the greatest are those who commit the
fewest blunders. Hence the only difference,
other than degree, between the more precise or
logical thinker and the unprecise is, that the
fallacies of the latter are difficult, those of the
former easy to expose. Hence it may be said
that, while it is the greatest achievement to be
right, it is no mean achievement to be clearly
and unequivocally wrong, i. e., perspicuous in
our errors. Hence the value of the political
theories of Hobbes and Austin, the most logi-
cal of modern writers; which, though false,
and even pernicious, are yet full of instruction.
Nor is the proportion of men of great logical
genius so large as is generally supposed. They
are in fact as scarce as great generals, or great
statesmen, or great poets. Nor is it to be as-
sumed that philosophical writers are less liable
to this and other fallacies than the less preten-
tious classes. ' For it is most true, as Cicero
saith of them somewhere, that there can be
nothing so absurd but may be found in the
books of the Philosophers" (Hobbes,
1 This is very fully shown by Mr. Jevons (Pure Logic and
Minor Works, p. 201).
EQUIVOCATION
v.). So, as observed by the author cited, the
educated classes generally are inferior to the
vulgar in this respect. For " those men that
take their instruction from the authority of
books, and not from their own meditations,
[are] as much below the condition of ignorant
men as men endued with true science are above
it. For between true science and erroneous
doctrines, ignorance is in the middle " (/</.,
chap. iv.). Hence no one should imagine him-
self free from this general infirmity of mankind ;
and he who most thoroughly realizes his weak-
ness in this respect may, like Socrates, be justly
pronounced the wisest of mankind. All are
liable to it; and he who supposes he is not is
simply unaware of his infirmity.
The nature of the Fallacy of Equivocation is
obvious, and has been sufficiently explained.
It remains, therefore, only to illustrate it by
appropriate examples, and for this purpose the
examples already given under other heads will
with one or two others be sufficient to serve
our purposes.
Examples
192. EQUIVOCAL USE OF NONSENSICAL
TERMS. Some of the most important cases of
this fallacy occur from the use of nonsensical
terms. The very nature of these is that they
2O6 LOGIC
cannot be used for any practical purpose, ex-
cept by changing their meaning and thus
giving them a definite sense; and hence, for
the propositions in which they occur, significant
propositions are always substituted. Thus, as
we have seen, the term Sovereignty varies es-
sentially in meaning, as used in the several
doctrines of Personal Sovereignty, Corporate
Sovereignty, the Sovereignty of the People or
State, and the Sovereignty of Right or the Law ;
all of which different senses of the term are in-
consistent with each other, and all, except the
first, in their direct sense, without definite
signification, or, in other words, nonsensical.
Yet the term is habitually used by political
writers without distinguishing the sense in
which it is used, or without attempting to give
it any definite signification. But in the prac-
tical application of the doctrine of Sovereignty
the term is invariably used as equivalent to
such definite conclusions as the occasions of
the writer may require, or as a premise from
which such conclusions may be deduced; and
thus the most extravagant doctrines are ap-
parently established. Of which, as we have
seen, a striking example is furnished by Prof.
Von Hoist ( 175); and others equally ap-
propriate may be easily collected from almost
any work touching the subject.
The same observation will apply to the
EQUIVO CA TION 2O/
theory of general utility, or Utilitarianism,
and also to the notions that the will of the
government is the united will of the people ;
that the State is an Organism ; that it is
founded on compact, etc. ; all of which are, in
their direct sense, in themselves nonsensical,
and therefore innocuous, but are habitually
used as premises to establish all sorts of ex-
travagant conclusions.
193. OF EQUIVOCATION GENERALLY.
The above will suffice for examples of equiv-
ocations consisting in giving significance to
nonsensical terms. In illustrating other equiv-
ocations, the only embarrassment consists in
the number of examples that crowd upon
our attention ; but the following may be
sufficient.
194. ARGUMENT OF AUSTIN. One of the
most striking of these is furnished us by the
argument of Austin in support of his famous
position that judicial decisions are in their
essential nature laws or statutes, and the judges,
in fact, legislators; and another by his equally
remarkable position that " Custom does not con-
stitute part of the law" ; both of which rest
upon the equivocal use of the ambiguous term
" Law " ; which may denote either a law or
statute (lex], or the Law (Jus).
195. AN ARGUMENT OF BAIN. An ex-
tremely effective example of this fallacy is also
208 LOGIC
furnished by Mr. Bain in his statement of the
doctrine of Utility. It consists in using the
term "party " in the double sense of a natural
and of a corporate person. Utility, he says, is
" the tendency of actions to promote the happi-
ness and prevent the misery of the party under
consideration; which party is usually the com-
munity in which one's lot is cast." '
196. AN ARGUMENT ATTRIBUTED TO
PROFESSOR HUXLEY. Still another example
is presented by an argument attributed to Pro-
fessor Huxley. It consists in the equivocal use
of the term "power,'" which is commonly used
in two senses, namely, as denoting actual power,
or might, and as denoting rightful, or jural,
power, or right. The argument is as follows:
' The power of the State may be defined as
the resultant of all the social forces within a
definite area. It follows, says Professor Hux-
ley, with characteristic logical thoroughness, that
no limit is or can be set to State interference "
(A Plea for Liberty, Donisthorpe).
This fallacy is common to all the Austinian
school of jurists, and, indeed, constitutes the
common fundamental infirmity of all their dis-
quisitions. These jurists, according to their
theory, have, indeed, no right to use the term
in any but the former sense; but, as we have
1 Bentham is guilty of the same fallacy (Principles of Legis-
lation).
EQUIVOCATION
209
seen, after establishing their conclusions they
habitually use it as though equivalent to right,
in the proper sense a notion that can properly
have no place in their system.
CHAPTER XVI
THE TRADITIONAL DOCTRINE OF FALLACIES
I
ARISTOTLE'S CLASSIFICATION OF FALLACIES
197. The received classification of fallacies,
adopted by the schoolmen from Aristotle,
though remarkable for its profound insight, has
but few pretensions to scientific accuracy; and
it is to be suspected that much of the obscurity
and confusion that surround the subject results
from the undue authority given to it by logi-
cians. It has, however, so profoundly affected
logical doctrine and nomenclature that, apart
from its intrinsic value, it must always remain
one of the principal subjects for the student's
attention.
198. TABLE OF FALLACIES. According
to this scheme, fallacies are divided into two
classes, called by the schoolmen and by later
logicians, Fallacies in Dictione, or in Voce (i. e.,
in diction or speech), and Fallacies extra Dic-
tionem, or in Re (i. e., not in diction, but in
210
DOCTRINE OF FALLACIES 211
matter). Of the former class six forms or
examples are given, and of the latter, seven,
which are as follows:
Aristotle ' s Division of Fallacies
I. FALLACIES IN DICTIONE :
(i) Homonymia (Ambiguity of Terms).
(*) Amphibolia (Ambiguity of Sentence).
(3) F. Compositions (F. of Composition).
(4) F. Divisionis (F. of Division).
(5) F. Accentus (F. of Accent).
(6) F. Figures Dictionis (F. of Figure of
Speech).
II. FALLACIES EXTRA DICTIONEM :
(1) F. Accidentis (F. of Accident).
(2) F. a Dicto Secundum Quid ad Dictum Sim-
pliciter (Illicit Substitution of Unquali-
fied for Qualified Terms).
(3) Ignoratio Elenchi (Irrelevant Conclusion).
(4) F. Consequents (Non-Sequitur).
(5) Petitio Principii (F. of Illicit Premise).
(6) Non-Causa pro Causa (Mistaking Cause).
(7) F. Plurium Interrogationum (F. of Several
Issues in One).
199. OBSERVATIONS UPON THIS CLASSI-
FICATION. As will be seen presently, all the
fallacies In Dictione are simply cases of Equivo-
cation, and of the fallacies Extra Dictionem all
except the 4th (F. Consequentis) are Fallacies
of Judgment ; under which head most of them
have already been considered at large. The
212 LOGIC
excepted fallacy (the F. Consequentis) includes
all the Fallacies of Inference, except Equivoca-
tion. It is obvious, therefore, that the current
expressions (In Dictione and Extra Dictionetn)
whether from being a mistranslation of Aris-
totle's language or otherwise do not truly ex-
press the nature of the distinction between the
two kinds of fallacies, and are, therefore, cal-
culated to mislead us as they have Whately
and others with regard to it.
200. The true scheme of division is as fol-
lows:
Table of Fallacies
I. FALLACIES IN DICTIONE (EQUIVOCA-
TION).
(Including the six forms specified in the
first table.)
II. FALLACIES EXTRA DICTIONEM.
(i) Fallacies of Judgment.
(Including all fallacies Extra Dictionem
given in the table, except F. Conse-
(2) F. Consequentis (JVon-Sequitur).
(Including all Fallacies of Inference ex-
cept Equivocation.)
(a) Formal Fallacies (/. e., of Inference).
(Including Undistributed Middle, Il-
licit Process.)
(b) Material Fallacies.
(Including Illicit Substitutions of New
Terms.)
DOCTRINE OF FALLACIES 213
The terms "Formal" and " Material Fal-
lacies" correspond to the "Logical" and
" Material Fallacies " of Whately, whose
" Semi-logical Fallacies " correspond precisely
to the fallacies In Dictione of Aristotle, or, in
other words, to the Fallacy of Equivocation.
This division of Whately's has, since his time,
been very generally adopted ; but, as is re-
marked by Mansel, it " is not the ancient prin-
ciple of distinction which is stated with more
or less clearness by several logicians," as, e. g.,
in the following definitions of Sanderson:
Every fallacy In Dictione arises from some
ambiguity (mnltiplicitate} of expression."
' Fallacies Extra Dictionem are those in which
the deception happens, not so much from some
ambiguity latent in the words themselves, as
from ignoring things " (i. e., the notions ex-
pressed). ' The former arise," says Mansel,
"from defects in the arbitrary signs of thought,
and hence are generally confined to a single lan-
guage, and disappear on being translated into
another. The latter are in the thought itself,
whether materially, in the false application of
notions to things, or formally, in the violation
of the laws by which the operations of the
reason should be governed ; and thus adhere
to the thought in whatever language it may be
expressed. Under this head are thus included
both false judgments and illogical reasonings"
214 LOGIC
(i. e., both Fallacies of Judgment and Fal-
lacies of Inference) (Mansel's Aldrich, p. 132).
II
FALLACIES IN DICTIONS (EQUIVOCATION)
2OI (l) (2). HOMONYMY AND AMPHI-
BOLY. These are both cases of the Fallacy of
Equivocation, the former consisting in the
illicit use of ambiguous terms, the latter in the
illicit use of ambiguous sentences. They are
essentially of the same nature; and we, there-
fore, as is most in accord with the usage of our
language, class them together under the com-
mon name of Equivocations. This fallacy
has already been fully considered.
202 (3) (4). COMPOSITION AND DIVISION.
These fallacies are essentially of the same
nature. They consist in using a term succes-
sively in a distributive and in a collective sense,
or, in other words, in substituting for a term
used distributively the same term used collect-
ively, or vice versa. The former constitutes the
Fallacy of Composition, the latter the Fallacy
of Division.
The following are examples of the Fallacy
of Composition :
3 and 2 (distributively] are two numbers ;
5 is 3 and 2 (collectively)-,
.'. 5 is two numbers.
He who necessarily ^tv-y or stays (i. e., either
DOCTRINE OF FALLACIES 21$
necessarily goes, or necessarily stays) is not a
free agent ;
But every one either necessarily ^w.? or stays
(i. e., necessarily does one or the other);
. . No one is a free agent.
The following are examples of the Fallacy of
Division :
5 is one number;
3 and 2 (collectively) are 5 ;
. *. 3 and 2 (distributively) are one number.
The angles of a triangle are equal to two
right angles ;
A B C is an angle of a triangle ;
. . A B C is equal to two right angles.
All the black and white horses of the de-
ceased (/. e. , all the black, and all the white
horses) are the property of the legatee ;
The piebald horses are black and white
(/. e. , each is black and white);
. . The piebald horses are the property of
the legatee. 1
Obviously these fallacies (Composition and
Division) constitute merely a species of equivo-
cation, i. e., of either Homonymy or Amphiboly.
1 The last example is suggested by the celebrated Moot case
of the legacy of "all the testator's black and white horses."
The question was, whether the legatee was to have the black
and the white horses, or the piebald horses, i. e., the horses
that were each black and white. The legatee claimed that he
was entitled to both classes ; and, hence, in the one or the
other of his claims, was guilty of this fallacy.
2l6 LOGIC
203 (5). THE FALLACY OF ACCENT OR
PROSODY (F. ACCENTUS F. PKOSODI^E}.
This fallacy is also a species of equivocation,
i. e., either Homonymy or Amphiboly. It con-
sists in varying the meaning of a term or
proposition by change of accent, tone, or
punctuation.
The most extreme case of this is that of
irony, by which the sense is precisely reversed,
as, e. g., in the speech of Job to his friends:
" No doubt but you are the people, and wis-
dom shall die with you." In this way, i. e.,
by ironical use afterwards forgotten, the name
of the subtle doctor, Duns Scotus, has come
to be the peculiar name of a fool (i. e., dunce).
The fallacy resulting from changing the sense
of an ironical expression is too obvious to be
dangerous, but if it should occur would be a
case of F. Figures Dictionis.
204 (6). FIGURE OF SPEECH (F. FIGURE
DICTIONIS}. This fallacy (which is also
merely a species of equivocation) consists in
the illicit use of figures of speech, or, in other
words, in substituting for the indirect or fig-
urative, the direct or literal sense, as in the
following example:
" Herod is a fox ;
A fox is a quadruped ;
.'. Herod is a quadruped."
DOCTRINE OF FALLACIES 21J
Or as in the following example, which was
given by a student called on for a syllogism.
The logical Professor, it may be explained,
was of corpulent habit, and known as " Old
Boll."
" All flesh is grass, the Scriptures say,
And grass when cut is turned to hay ;
Now if Death's Scythe Old Boll should take,
Golly ! What a haystack he would make ! "
But more serious examples may be found
among those already given, as, e. g., the
equivocal use of the term poivcr in the argu-
ment attributed to Professor Huxley, and also
in the misuse of the propositions that " the
State is a person," that "it is an organism,"
that " its ivill is the united will of the people,"
that " it has an interest or ivelfare distinct
from that of the people," etc., as heretofore ex-
plained. A striking example of this fallacy is
also presented in the famous case of Dart-
mouth College vs. Woodward ( 137). The
fallacy consisted in regarding the college as
a person ; which was only figuratively true.
For a corporation is a qua ^z'-person only, i. c.,
is regarded as a person for certain purposes
only.
205. Hamilton strangely speaks of this as
" a contemptible fallacy," and as though to
furnish an example at once of confusion of
2l8 LOGIC
things essentially different and of misappre-
hension of the nature and scope of Logic he
couples with the Fallacy of Figure of Speech
that of Equivocation, as being, the latter, a
species of the former, instead of vice versa, as
is in fact the case. ' These fallacies," he says,
(" ' sophismata equivocationis, anipliibolia, et ac-
centus) may easily be reduced to sophismata
figures dictionis ; they are only contemptible
modifications of this contemptible fallacy."
But, as is in effect observed by the author to
whom we are indebted for the above quota-
tion, when we reflect that nearly all words
denoting mental or moral qualities or acts
which is but to say nearly all terms used in the
different branches of the science of human
nature are in their origin metaphors, derived
from sensible objects or events as, e. g,, intui-
tion, perception, appreJiension, inference, induc-
tion, deduction, reflection, education, justice,
right, wrong, straight, power, organic, etc.,
and that these terms still carry with them, to
a large extent, their material associations, by
which, as the history of philosophy shows, we
are continually being misled, we can hardly
fail to agree " that the sophism Figure Dic-
tionis, so far from being contemptible, is
worthy of our closest and most watchful
consideration" (Theory of Thought, Davis, p.
27).
DOCTRINE OF FALLACIES 21$
III
OF THE FALLACIES EXTRA DICTIONEM
206. OBSERVATIONS. Of these fallacies,
all except the fourth are Fallacies of Judgment ;
and four of them, namely, Ignoratio Elenchi,
Petitio Principii, Non Causa pro Causa, and F.
Plurium Interrogationum, have already been
considered in detail under that head. The
others, namely, the Fallacies of Accident, of
Secundum Quid, and of the Consequent of
which the first two are also Fallacies of Judg-
ment remain to be considered.
Logicians are widely at variance with refer-
ence to the nature of these fallacies; and, if
we may judge from the translations and from
the confusion reigning over the subject, Aris-
totle's own explanation of them must be re-
garded, in some particulars, as hopelessly
obscure. Hence, though I have attempted to
interpret his meaning correctly, I am by no
means sure that I have succeeded in this better
than others. It may, however, be claimed for
the exposition of the subject here given that it
is at least intelligible and consistent, and that,
in connection with the rest of Aristotle's
scheme, it renders his classification of the fal-
lacies complete. And, it may be added, it is
in accord with the best authorities.
22O LOGIC
207. THE FALLACY OF ACCIDENT CF. Ac-
CIDENTis}.T:\\\s fallacy has its source in the
assumption that an accident of some of the
significates of a term, or of all its significates
for a certain time, is an accident of the term,
and therefore predicable of it without qualifi-
cation (v. supra, 49.) This assumption in
the case of an inseparable accident of all the
significates of the term is, indeed, legitimate;
for obviously such an accident may always be
predicated of all the significates of the term,
and hence of the term. But with separable ac-
cidents of the significates of a term, it is other-
wise; for, though these are commonly spoken
of as accidents of the term, they are not such
in fact, for their relation to the term is tem-
porary or transient. 1 Hence such an accident
can be predicated of the term only for so long
as it continues to be an accident of it, or, in
other words, only with relation to some par-
ticular time expressed or understood. For in
the logical proposition the copula has no rela-
tion to time, but expresses simply a permanent
significative relation between the terms, and
1 The terms separable and inseparable accidents can apply
only to real individuals, and hence only to concrete terms or
terms of first intention. With relation to these the distinc-
tion is sufficiently obvious. Thus, e. g., with reference to
Socrates, " Stagyrite" is an inseparable accident ; "standing,"
"sleeping," etc., separable the last being predicable of him
only at times.
DOCTRINE OF FALLACIES 221
hence a separable accident cannot be predi-
cated generally of a term. For, as is said by
Aristotle, " it is uncertain when [i. e., at what
times] an assertion can be made of a thing
present from accident"; or, in other words,
whether at any given time the accident con-
tinues to exist (Soph. Elenc/i, chap. xxiv.).
Thus, e. g,, an attacking party might be rightly
informed at a given time that the enemy was
sleeping, and hence conclude that it would be
safe to attack him; but it might be a fatal
error to assume the truth of the premise as
continuing to exist an hour later.
208. DEFINITION OF THE FALLACY. The
fallacy may therefore be defined as consisting
in predicating of a term a separable accident of
its significates without qualifying it by refer-
ring to the time at or during which it is inher-
ent ; or, in other words, in assuming, in place of
a proposition of which the predicate is an ac-
cident thus qualified, another proposition of
which the predicate is the accident unqualified ;
as if, e. g., from knowing a man is lame we
should assume that he is permanently lame.
Or the subject may be more generally illus-
trated as follows: Let Y denote the subject
(" John "), A the accidental predicate (" tem-
porarily lame," i. e., "lame for the time being"),
and X the general predicate (^'permanently
lame "); then we may be entitled to say " Y
222 LOGIC
is A " ; but to assume, in place of this, that
Y is X would be to substitute for A the term
X, i. e., species tor gemis in the predicate of a
universal affirmative proposition. For the
class of " temporarily lame" will include all
the "permanently lame," and many others.
It will be noted here that there is necessarily
a significative relation between the accidental
and the general predicate, namely, that of
partial coincidence. Hence, to substitute X
for A is, in effect, to substitute AX (i. e.,
" Some A ") for A, which presents a case of
illicit substitution of species for genus in the
predicate of an affirmative proposition.
It will also be observed that the Fallacy of
Accident is defined as consisting in the illicit
assumption of a premise. But, where the same
fallacy occurs in a formal inference, it con-
stitutes the Fallacy of Undistributed Middle,
which is a case of Non-sequitur or F. Consequen-
tis, as may be thus illustrated :
Some A is X
Y is A
.'. Y is X
The stock example of this fallacy, which I
have taken from Aldrich, is as follows:
' What you have bought you have eaten ;
you have bought raw meat; therefore you
DOCTRINE OF FALLACIES 22 3
have eaten raw meat " (Quod emisti comedisti ;
crudum emisti ; ergo crudum comedisti); which
may be expressed in the following syllogism,
which, in form, is unobjectionable:
The meat you buy is raw ;
The meat you eat is the meat you buy ;
.'. The meat you eat is raw.
The fallacy here may be regarded as a case
of equivocation, consisting in the use of the
term " raw " in the major premise in the sense
of " raw when bought," and in the conclusion
in the sense of " raw when eaten." But if the
term " raiv " be construed simply in both
cases (/. e., as used without qualification), the
fallacy must be regarded as a case of F. Acci-
dentis, consisting in the illicit assumption of
the major premise. For all that can be right-
fully affirmed is that the meat bought is raw at
the time of purchase; instead of which it is
assumed that it is permanently raw. For,
as we have observed, in the logical prop-
osition the copula includes both the future
and the past, and the significative relation be-
tween the terms is asserted, not as true only
at the moment of assertion, but before and
afterwards; and hence a universal proposition
may always be negatived by showing an in-
stance to the contrary, either in the past or in
the future.
224 LOGIC
The following examples are furnished us by
Aristotle, and are given as paraphrased in the
notes of Mr. Owen's translation :
" Do you know what I am about to ask ?
No. But I am about to ask whether virtue is
good. Therefore, you know not whether virtue
is good."
" Do you know who approaches ? No.
But Socrates approaches. Therefore, you do
not know Socrates."
Here in each case the most obvious source
of the fallacy is in the use of the equivocal
terms, " What I am about to ask " (in the
first case), and " Who approaches " (in the
second). But this ambiguity may be removed
and the arguments expressed syllogistically in
unobjectionable form as follows:
1 i ) The question, I am about to ask, is unknown to
you.
The question whether virtue is good is the question
I am about to ask.
.'. The question whether virtue is good is unknown
to you.
(2) The man approaching is unknown to you.
Coriscus is the man approaching.
.'. Coriscus is unknown to you.
Indeed, even as thus expressed, the most
obvious solution of both these fallacies is still
to regard them as cases of equivocation, con-
DOCTRINE OF FALLACIES 22$
sisting in using the term " unknown to you " in
a double sense, i. e., in the major premise in
the sense of " unknown to you before you are
told," and in the conclusion in the sense of
" unknown to you after you are told," But if
the term be regarded as used in the same sense
in both places, the case is evidently one of F.
Accidenlis, consisting in the illicit assumption
of the major premise, or, in other words, in
the illicit substitution of the unqualified term,
" unknown to you," for the qualified term,
" unknown to you before you are told," which
alone was admissible as a predicate.
209. THE FALLACY OF SECUNDUM QUID
(F. A DIC TO SECUNDUM QUID AD DICTUM
SIMPLICITEK], This fallacy consists in as-
suming an unqualified in place of a qualified
proposition. But as the copula has but one
meaning, a proposition can be qualified in no
other way than by qualifying one or both of
its terms. Hence the fallacy must consist in
substituting for an unqualified a qualified term.
But a term can be qualified (i. e., its signifi-
cation or extension altered) only by coupling
with it another term that partly, but not
wholly, includes it, thus making a new term of
less extension, as, e. g., men by white, which
gives us for the new term, white men; or,
more generally, Z, Y, or X, by A, which
gives us, for new terms, AZ, AY, and AX, all
15
226 LOGIC
included in, but of less extension, than the
originals; or, in other words, the class denoted
by a qualified term will always be a species
of the class denoted by the unqualified term.
Hence the Fallacy of Secundum Quid is simply
a particular case of the illicit substitution of
genus for species in the subject of an affirmative,
or in either the subject m predicate of a negative
proposition.
Where the illicit substitution occurs in the
inference, the fallacy belongs to the general
class of fallacies that go by the name of F.
Consequentis or Non-scquitur ; but if in one
of the premises, it constitutes the Fallacy of
Secundum Qiiid, now under consideration;
which must, therefore, like the F. Accidentis,
be regarded as a case of Illicit Assumption of
Premise, or of Petitio Principii. The Fallacy
of Secundum Quid may therefore be defined as
consisting in the illicit assumption of a premise
in which there is an unqualified term in place
of another in which the same term is qualified ;
or, as expressed by Aristotle, is assuming that
" what is predicated in part is spoken simply "
(Soph. Blench., chap. v. , 2).
210. OF THE RELATION BETWEEN THE
FALLACIES OF ACCIDENT AND SECUNDUM
QUID. The Fallacy of Secundum Quid will
therefore include the Fallacy of Accident, which
is but a particular case of it. Or, in other
DOCTRINE OF FALLACIES
words, the latter is a species of the former, its
specific difference being that the qualification
omitted relates exclusively to time ; whereas,
in the case of Secundum Quid generally, the
omitted qualification may relate either to time
or to place, quantity, or any other quality or
attribute.
The following examples of the F. Secundum
Quid are taken from various sources :
(1) Pernicious things are things to be forbidden;
The use of wine is pernicious ;
Therefore the use of wine is a thing to be for-
bidden.
(2) Things productive of bad effects are unfit for
use ;
Antimony is a thing productive of bad effects ;
.'. Antimony is unfit for use.
(3) Things productive of bad effects are to be dis-
couraged ;
Eloquence is a thing that produces bad effects ;
.'. Eloquence is to be discouraged.
(4) Things destructive to human life are to be
avoided ;
Medicine is a thing destructive to human life ;
.'. Medicine is to be avoided.
(5) Y is X
Z is Y
/. Z is X.
228 LOGIC
In each of these arguments all of which are
regular in form the fallacy consists in the
illicit assumption of the minor premise, consist-
ing in substituting in the subject an unqualified
in the place of a qualified term, viz., in the
first, the term " use " for " excessive use"; in
the second, " antimony" for " antimony when
misapplied" ; in the third, "eloquence" for "elo-
quence when abused" ; in the fourth, " medi-
cine" for " medicine when used by ignorant
doctors" ; and in the fifth, denoting by A any
term qualifying Z, Z, for AZ. The fallacy,
therefore, in each case consists in the substitu-
tion of genus for species in the subject of an
affirmative proposition, and hence differs from
the corresponding fallacy of inference simply
in being an illicit assumption instead of a
formal inference.
211. ERRONEOUS VIEWS OF LOGICIANS
AS TO THESE FALLACIES. The F. Accidentis
was defined by Aldrich, and probably by the
old logicians generally, as in the text. But
Whately, who is followed by most of the later
logicians, defines it as the converse of the
Fallacy of Secundum Quid ; and since then the
subject has been involved in the greatest con-
fusion. The prevailing view is thus expressed
by De Morgan :
" (i) The Fallacia Accidentis and (2) that
a dicto sccundum quid ad dictum simplicitcr.
DOCTRINE OF FALLACIES 229
The first of these ought to be called that of
a dicto simpliciter ad dictum sccundum quid, for
the two are correlative in the manner described
in the two phrases. The first consist in infer-
ring of the subject with an accident that which
was premised of the subject only, the second in
inferring of the subject only that which was
premised of the subject with an accident " (For-
mal Logic, p. 250).
The latter process is undoubtedly fallacious,
but the former/, e., inferring of the subject
^vitJl an accident that which was premised of
the subject only ; or, in other words, of infer-
ring that what is predicated of a term generally
may be predicated of the term as qualified by
an accident is entirely legitimate. For to
qualify a term, either by an accident or other-
wise, is simply to diminish its extension, and
thus to create a subclass or species of the class
denoted by the unqualified term; and accord-
ing to the dictum whatever may be predicated
of the unqualified term or genus may be predi-
cated of the qualified term or species; or, in
other words, in any universal proposition of
which the unqualified term is the subject, the
same term qualified by an accident may be legiti-
mately substituted for it; that is to say, sym-
bolically, denoting by AY, Y as thus qualified,
if Y is X, then AY is also X; as may be thus
illustrated :
230 LOGIC
In illustration of the supposed fallacy (F. a
dicto simpliciter ad dictum secundum quid] De
Morgan and others give us the story of the
stork, from Boccaccio, which, as quoted by
Professor Davis, is as follows :
A servant who was roasting a stork for his
master was prevailed upon by his sweetheart
to cut off a leg for her to eat. When the bird
came upon the table the master desired to
know what was become of the other leg. The
man answered that ' the stork never had but
one leg.' The master, very angry, but deter-
mined to strike his servant dumb before he
punished him, took him the next day into the
fields, where they saw storks standing each on
one leg, as storks do. The servant turned
triumphantly to his master, upon which the lat-
ter shouted, and the birds put down their other
leg and flew away. 'Ah, sir,' said the servant,
but you did not shout to the stork at dinner
yesterday ; if you had done so, he would have
showed his other leg too.'
The gist of which, the author says, " is the
assumption that what can be predicated of
storks in general can be predicated of roasted
DOCTRINE OF FALLACIES 2$ I
storks, a dicto simpliciter ad dictum secundum
quid" But undoubtedly (assuming for the
sake of the argument that dead and roasted
one-legged storks belong to the genus stork)
whatever may be universally predicated of
storks may, unless the dictum be a delusion, be
predicated of roasted and one-legged storks as
well as of others. The error, therefore, con-
sists, not in an incorrect inference of the
particular proposition from the universal prop-
osition including it, but in the illicit assump-
tion of the universal proposition that whenever
you shout at a stork it will put down a second
leg, though it may have only one leg, and be
dead and roasted.
212. F. Consequentis. There is much dis-
pute as to the nature of the fallacy intended by
Aristotle under this name. De Morgan and
other logicians following Aldrich regard it
as consisting in the " affirmation of a conclu-
sion " which does not follow from the premises,
or, in other words, as but another name fora
Non-scquitur, which is at least the most con-
venient view.
213. CLASSIFICATION OF FALLACIES OF
THIS KIND. According to this view, the F.
Consequentis will include (i) the merely formal
fallacies, commonly known as fallacies of the
syllogism ; and (2) all the material fallacies of
inference except Equivocation. The former
232
LOGIC
have been sufficiently treated in considering
the rules of the syllogism ; the latter, under
the head of Substitution. The former as well
as the latter, and also the fallacies of Equivoca-
tion (or In Dictione), are also, it will be remem-
bered, fallacies of Substitution.
APPENDIX OF NOTES
A- 4
Perhaps, when men understand that the main
sources of Philosophy are to be found in the
study of words, we may hope to escape the dreary
treadmill on which philosophers have hitherto been
exercising themselves. All progress in Philosophy
that has been made has been the result of the un-
conscious observation of this method as, e. g., the
work of Locke, which, though weak in its meta-
physics, constitutes the greatest contribution to
philosophy made in modern times; and which, as
shown by Home Tooke, is merely an essay on lan-
guage. " Perhaps," he says, " it was for mankind
a lucky mistake (for mistake it was) which Mr.
Locke made when he called his book an Essay on
the Human Understanding. For some part of the
inestimable benefit of that book has, merely on ac-
count of its title, reached to many thousands more
than, I fear, it would have done had he called it
"A Grammatical Essay," or "A Treatise on
Words or Language " {Diversions of Pur ley).
B 6
Comparing the physical sciences and the mathe-
233
234 LOGIC
matics with the moral sciences, the latter are infi-
nitely the more difficult of achievement; and also
infinitely more important to the welfare of man-
kind. For under the name of the moral sciences
are included all the several branches of the
Science of Human Nature; which is obviously the
principal concern of mankind, and as such the sci-
ence to which all others are to be regarded as sub-
sidiary. This was the distinguishing characteristic
of Socrates' philosophy. It was expressed in the
injunction written over the portals of the Delphic
god: " Know thyself! " and in modern times has
been finely rendered: " The proper study of man-
kind is man." It is also embodied in the fine old
term, the Humanities, which signifies those parts of
education that have for their end the development
of our manhood or humanity, and which must
therefore constitute the essential elements of a
rational general education.
This was the great discovery of Socrates; to the
preaching of which, as the gospel most needed by
men, his life was devoted. Nor have there been
wanting, in succeeding ages, philosophers and
those the greatest to continue his mission. But so
averse are men to being convinced of their errors
that nothing is more odious to them than the at-
tempt. Hence, generally, all means of defence are
regarded as legitimate, that is to say, not only fal-
lacies, but falsehoods and slanders, and, at times,
APPENDIX OF NOTES 235
the prison, or the rack, or death. Thus Socrates
was poisoned for this offence only; which, though
otherwise atrocious, was creditable to the Athen-
ians, as at least proving an uncomfortable mental
susceptibility to the power of reasoning or Logic.
For in modern times we have invented a better
method of dealing with such fellows, and have
developed a mental integument as impervious to
the weapons of reason as that of the elephant or
rhinoceros to the weapons of the primitive hunter;
and against which the Socratic wit would batter
in vain. Thus we are enabled to dispose of those
who would disturb our mental peace and compla-
cency, by simply refusing to listen to them, and by
extolling our own idols, like the Ephesians; who,
in answer to the preaching of the apostles, "all
with one voice, about the space of two hours, cried
out: Great is Diana of the Ephesians." By these
two means which have been aptly called "the
conspiracy of silence," and " the society of
mutual admiration " our opinions are now im-
pregnably buttressed. Thus we live in a sort of
Fools' Paradise ; though, as Bacon says, " the
apotheosis of error is the greatest evil of all, and
when folly is worshipped, it is, as it were, a plague-
spot upon the understanding " (Nov. Org., bk. i.,
aph. Ixv.).
D it
The disuse of Logic must necessarily affect the
teaching of Moral and Political Science, Metaphys-
ics, and the Science of Human Nature generally;
236 LOGIC
for the investigation of which it is indispensable.
Hence, as the proper study of mankind is man, it
may be said that the universities of the day have
fallen behind their predecessors in efficient perform-
ance of their most essential function. It should
not be forgotten that the task of reorganizing Euro-
pean society as it emerged from the chaos of the
dark ages was mainly effected by such men as
Lanfranco, Suger, Anselm, and other churchmen
graduates of the mediaeval schools and universi-
ties, and consequently educated in Logic and Law;
studies the art of teaching which has been lost by
our modern universities, and which yet surpass all
others as means of a rational education. That this
is the case with Logic, it is the aim of this woik to
show; with regard to the Law, the opinion of Burke,
by those competent to judge, has been generally
accepted, that it " is one of the first and noblest
of human sciences a science which does more to
quicken and invigorate the understanding than all
other kinds of learning put together." Though,
he adds, "it is not apt, except in persons happily
born, to open and liberalize the mind exactly in
the same proportion."
E 12
The peculiar merit of Logic, as one of the Hu-
manities, is its perfect cognoscibility, and the
consequent facility with which it can be taught.
Arnauld in the preface to the Port Royal Logic
tells us that he undertook to teach a young noble-
APPENDIX OF NOTES 237
man all that was useful in Logic in four days, and
successfully performed the task. The claim is
seemingly extravagant, but as his notion of Logic
was confined mainly to the doctrine of the syllo-
gism, and to so much only of the doctrines of the
term and of the proposition as was incidentally
necessary, and as the student was a young gentle-
man of remarkable ability, it may very well be
credited. Nor will a more complete and compre-
hensive study of the subject add much to the labor
of mastering it ; if indeed it will not facilitate the
task. The general diffusion of logical culture can-
not be regarded, therefore, as a vain aspiration.
The subject requires no preliminary culture other
than the studies usually taught in the common
schools, and may be readily mastered by almost
any young man of average ability and the proper
age say sixteen or seventeen. And this will espe-
cially be the case with one who has thoroughly
mastered the elements of algebra and geometry.
Thus it is quite possible to devise a very brief
course of study sufficiently thorough to train the
student as a reasoning creature, and to make him
equally competent with the graduates of our great
universities to grapple with all the great problems
of Politics and Morality; and, indeed, until our
modern university education be reformed, even
more so. This was illustrated by the mediaeval
universities, to whose graduates, as we have ob-
served, the reorganization of society at the close of
the dark ages was entrusted, and by whom the
task was successfully accomplished; nor do I think
238 LOGIC
it extravagant to say that alongside of them in prac-
tical politics our modern graduates would be but
children. Of the subjects taught outside of The-
ology the principal, as we have said, were Logic and
Law, and these must be regarded as the most essen-
tial parts of a rational education. The latter will
require long and persevering study, but a thorough
logical training will render the student competent
to master it; and without such training either
systematically taught to him at the outset, or grad-
ually acquired in the study of the law itself its
mastery is impracticable ; and the same observation
is true with reference to Political Science generally.
I have been admonished by a friend that the use
of examples of this kind in an elementary work
may be hazardous; and this, I understand, on the
double ground that the younger student may find
it difficult to understand them and the older, regard
them as disputable; and that thus they must prove
to the one a stumbling-block, and to the other fool-
ishness. With regard to the last objection, it is to
be admitted that if any of the examples are in fact
disputable, the objection is well taken. But I am
persuaded that, if they appear so to any one, it is
only because of the universal bias of men in these
unlogical times in favor of their opinions, and that
any one who will provisionally reject all prejudice
will see at once that the argument is in every case
demonstrative. Or if in any case I am deceived,
APPENDIX OF NOTES 239
then my own reasoning will serve for example.
With regard to the younger student, the opinion
seems to be that it would be better to illustrate
the nature of the fallacies by the more familiar
examples of the character commonly used in the
current logics. But this, I think, to be a great
mistake. The fallacies are themselves sufficiently
simple to be readily understood, and trivial
examples merely serve to lead the student to
suppose that he is in no danger of falling into
them. I have therefore thought it far better to
take my examples from theories that have played
and are now playing a great part on the stage of
history. Nor are these, when treated logically, at
all difficult, with a little reflection, to understand;
and indeed it is to be assumed that, if a young man
has arrived at the age at which he can study Logic
profitably without some familiarity with these ques-
tions, his education has been much neglected.
Neither this nor any part of my work can, indeed,
be understood without the independent thought of
the reader; but this also I consider not only a great
advantage, but an essential condition to the right
exposition of the subject. For though the princi-
ples of Logic are extremely definite, and therefore
readily cognoscible, yet, as already observed, they
require for their mastery the same kind and degree
of study as is required by the mathematics; and
there is no royal road to Logic any more than to
geometry. If the student, therefore, will take the
trouble to work out thoroughly these examples, and
others of the same character (of which many will
240 LOGIC
suggest themselves), he will achieve not only a
mastery of the principles involved in them, and of
the practical use of Logic, that cannot be otherwise
attained, but also an accurate, though limited,
knowledge of all the great political, social, and
moral questions involving the welfare of mankind;
which, better than anything else, will serve as
an introduction to those studies. I have also,
in the use of these examples, another point in
view, which is, that, by means of the application
of logical principles, these apparently difficult
problems are readily solved, and the most im-
portant heresies in Politics and Morality that
afflict mankind exposed; and thus are proved, by
practical illustration, the theses with which I com-
menced, that in all the moral sciences the use of
Logic is essential, and that the confused and un-
satisfactory condition of the literature of these
subjects is due to the decay of Logic.
In conclusion, however, I would say that while
regarding the current examples used in the logics
as inadequate for the illustration of the subject, I
have not neglected them, but, in the chapter on
the Traditional Doctrine of Fallacies, have con-
fined myself mainly to them.
G 14
This is strenuously objected to by Hamilton.
" Dr. Whately, " he says, " is contradictory. . . .
In some places he makes the operation of reasoning
not only the principal, but the adequate object of
APPENDIX OF NOTES 241
Logic. ... In others, he makes this total or
adequate object to be the language. But as there
cannot be two adequate objects, and as language
and the operation of reasoning are not the same,
there is therefore a contradiction " (Logic, u).
But though language and reasoning are not the
same, yet they are the same so far forth as Logic
is concerned with either; for, as Logic has to deal
only with reasoning expressed in language, it is
necessarily concerned with both to the same extent;
and we may say, with equal propriety, that the
subject-matter of Logic is either language or
reasoning.
The error of Hamilton lies in the illicit assump-
tion that the term " language " is equivalent to the
external logos, i. e., the expression, as opposed to
the inward thought. But if language be construed
as denoting both the thought and the expression, as
it should be, the only objection disappears; and
when thus construed, the proposition that Logic is
concerned wholly with language is too clear to be
disputed.
H 1 6
The name given to the subject by Aristotle was
the " Analytics." The name Logic seems to
have been first applied to it in the time of Zeno,
the Stoic. Many names have been invented to sig-
nify the scope of Logic, as, e. g., the Architectonic
Art; the Organon, or Instrument; the Ars Artium,
or Disciplina Disciplinarum; Heuristic, or the Art
of Discovering Truth; the Medicina Mentis, or the
16
242 LOGIC
Cathartic of the Mind, etc. (Thompson, Laws of
Thought, 35); and to these should be added the
name given by Socrates to his own doctrine (which,
though the fact is commonly overlooked, was noth-
ing else than Logic), namely, the Obstetrics of the
Mind (Maieusis),
Of these, the last two names express precisely
the two main functions of Logic, that is to say,
ist, to serve as a cathartic of the mind to rid it of
the false persuasion of knowledge; for, as has been
well said, " the natural state of the human mind "
is " not simply ignorance, but ignorance mistaking
itself for knowledge " (Grote's Plato, i., p. 373) ;
and, 2d, to bring forth from the mind " answers of
which it is pregnant" (Id., p. 367); or, in plain
language, to develop and formulate the unformed
ideas in our minds, whether innate or acquired
from without. See Socrates' own account of this
function, as given in the Thesetetus (Id., iii., p.
112).
I-37
There is much confusion with modern logicians
with regard to the nature of first and second inten-
tions or notions, but the above definition seems to
accord with the best authorities and expresses a
distinction of fundamental importance. According
to this definition, Notions of Second Intention
will include all abstract notions, and also notions of
classes of real individuals construed collectively;
in which case they become abstract.
The following is the definition of Aquinas (Opus-
APPENDIX OF NOTES 243
cula, cited Krauth, Voc. of Phil. Art., " Intention,
First and Second "):
" Nouns of first intention are those which are
imposed upon things as such, that conception alone
intervening by which the mind is carried imme-
diately to the thing itself. Such are man and
stone. But nouns of the second intention are those
which are imposed upon things not in virtue of
what they are in themselves, but by virtue of their
being subject to the intention which the mind
makes concerning them, as when we say that man
is a species and animal a genus." Which seems to
accord with our definition : that is to say, if we
speak of man as denoting the class of individual
men, the name is of the first intention, but if we
regard man collectively as a significate of the class
animal, the name is of second intention; and so
with reference to all other abstract names. Names
of second intention are precisely denoted by the
term " univer sales a parte ret," /. e., universal
notions considered apart from things, or, in other
words, abstract notions, and also by the term
" beings of reason," as quoted infra.
The division of names into names of first and of
second intention was obviously intended to com-
prehend all names; and hence, if names of first
intention are identical with concrete names, as they
evidently are, names of second intention must in-
clude all abstract names; and it is not admissible
to confine them (as Mansel does) to some of that
class only. Accordingly a universal (ens unum
in multis] is defined by Aldrich simply as a
244 LOGIC
predicable, /. e. , as "Nomen Commune, Univocum,
Secundce Intentionis, uno verbo, Predicabilis, Sive
Vox apta prcedicare, i. e. , Univoce did de multis ' '
(Aid. Log., p. 23).
It is singular that in the Port Royal Logic this
distinction should be regarded as unimportant, and
even made the subject of ridicule. " No one,
thank God! " it is said, " now takes any interest in
' the universal a parte rei,' or ' beings of reason,' or
in ' second intentions.' Thus, there is no ground
to apprehend that any one will be offended at our
having said nothing about them." But it may be
safely said that no one can have an adequate con-
ception, either of the nature or use of Logic, until
the notion expressed in the term " second inten-
tions," and the other phrases cited (which are
similar in meaning), are thoroughly grasped.
K- 3 8
Even where we use concrete terms, it is not the
thing itself, but the notion of the thing that is pres-
ent to the mind. For, as is said by Hobbes,
" seeing names ordered in speech (as is defined)
are signs of our conceptions, it is manifest they are
not the signs of the things themselves." Hence,
as Mansel says, " concepts (or notions] are the things
of Logic." On this point Max Miiller's Laws of
Thought (the opening chapters) may be read with
profit. For without acceding altogether to his the-
ory, that thought is impossible without language,
this is certainly true (ex vi termini), as to ratioci-
nation, or explicit reasoning, and may therefore be
accepted without error, and much to his profit, by
APPENDIX OF NOTES 245
the logician. According to Home Tooke " thing "
and " think " are but the same word spelt differ-
ently; and hence, he says, " the vulgar pronuncia-
tion of ' nothink ' instead of ' nothing ' is not so
very absurd."
L-53
BOOLE'S LOGIC
" All the operations of language, as an instru-
ment of reasoning, may," it is claimed by Mr.
Boole, " be conducted by a system of signs com-
posed of the following elements," viz. :
ist. " Literal symbols, as x, y," etc., represent-
ing names or terms.
2d. " Signs, as -|-, , X," representing relations
to each other of the substantive elements of com-
plex terms.
3d. " The sign of identity ( = )," or, as I should
call it, the sign of equivalence, /. e., of significative
equivalence, or equivalence of denotation.
The names signified by signs of the first class
may be either single names denoting classes, as,
e. g., man, horse, good, white, etc., or they may
be composed of several names, denoting classes
that partially coincide as, e. g., good men, black
sheep, etc. In the latter case the signs may be
combined together precisely as the words denoting
the terms. Thus, if we represent the class men
by x, and the class good by y, " good men " will
be denoted by the expression yx. So if x stands
for sheep, y for black things, and z for horned things,
zyx will denote " horned black sheep." But it is
obvious that in the expression " black sheep," the
246 LOGIC
order in which the component terms are placed
makes no difference ; or, in other words, that it is
the same thing whether we say " black sheep" as in
English, or " sheep black" as in Spanish and other
languages. Consequently, the class " black sheep "
may be written either yx or xy, which may be ex-
pressed by the following equation:
(i)yx = xy.
In which the complex term yx or xy denotes a
class of individuals that is at once included in the
class 7 and the class x. On the same principle, if
we represent by z the adjective " horned," zyx will
stand for the term "horned black sheep" and we
will have the following equations:
(2) zxy = xyz = yxz.
If, in the equation xy = yx, we suppose y to be
wholly included in x, as, e. g., if it denote the
black sheep in the flock x, then we will have the
equation :
(3) xy = y.
Again, if x = y, then xy =x a . But a class is not
APPENDIX NOTES 247
enlarged or diminished by repeating the term de-
noting it. Thus, " white white " or "sheep sheep "
mean nothing more than "white" or "sheep."
Hence we have the equation:
(4) x' = x.
If the class denoted by a term is composed of
two classes, denoted respectively by x and y, as,
e.g., " men and women," it may be expressed by
the complex term x + y. But obviously, the ex-
pressions, " men and women," and " women and
men," are equivalent in meaning. Hence the
equation:
(5) x + y = y + x.
Again, if we qualify the term ' ' men and women ' '
by the adjective "Asiatic," we have the expres-
sion "Asiatic men and women "; but this is equiv-
alent in meaning to the expression " Asiatic men
and Asiatic women." Hence, denoting men by x,
women by y, and Asiatic by z, we have the equation :
(6) z(x + y) = zx + zy.
If we denote the adult population of a city by x,
and the women by y, then x y will denote the
men. But it is indifferent whether we express the
excepted class first or last, provided it be distinctly
represented as the exception. Thus the expres-
sion, " the adult population less the women," and
the expression, "excepting the women, the adult
248 LOGIC
population," are equivalent in meaning to each
other, and botli to the expression " the men."
Hence we have the equation:
(7) x - y = - y + x.
But the expression, " the white population, less
the women," is equivalent in meaning to the ex-
pression, " the white population, less the white
women."
Hence, representing " while " by z, we have the
equation:
(8) z (x y) = zx zy.
If, in the proposition, " The stars are the suns
and the planets," we denote stars by x, suns by y,
and planets by z, we shall have the equation :
(9) x = y + z.
But, if the stars are the suns and the planets, the
stars, except the planets, are suns. Hence we have
the equation:
(10) x z = y.
If the terms x and y are equivalent, it is obvious
that those of the class x, or, as we may say, the x's,
that possess a given quality, must be identical with
the y's that possess it. Hence, if x = y, we have
the equation:
(n) zx = zy.
APPENDIX NOTES 249
But, per contra, it cannot be inferred from the
equation, zx = zy, that x = y. ( 82 (2) n.)
For, " suppose it true that those members of a
class x which possess a certain quality, z, are iden-
tical with those members of a class y, which possess
the same quality, z, it does not follow that the
members of the class x universally are identical
with the members of the class y." Thus, return-
ing to our sheep, let x denote one portion of a
flock of sheep, and y another, and let z denote
"horned" ; then zx will denote the horned sheep
in one portion of the flock, and zy the horned sheep
in the other; and, if we suppose these to be equal,
we shall have the equation:
zx = zy.
But it will not follow that the two portions of the
flock are equal in number, and we therefore can-
not say x y ; as may be thus illustrated :
Adverting to the above equations, it will be per-
ceived that the laws governing the convertibility of
the different forms of expression are, to a certain
extent, identical with those obtaining in mathe-
matics. Thus, in the equations (i) and (2), the
symbols are commutative like the symbols of algebra.
The logical process here involved is, therefore,
expressed in the same manner as in the correspond-
250 LOGIC
ing algebraic expression ; and this expression,
whether regarded as logical or algebraic, will be
subject to the same law. There is, therefore, in
the process involved in these equations, (i) and (2),
a certain resemblance or analogy to the process of
multiplication; and this is also true of equation
(").
In equations (6) and (8) a process is exhibited
closely resembling that of factoring in algebra.
In equations (5), (7), (9), and (10), we have
illustrated a principle of conversion of symbols
apparently identical with the corresponding process
in algebra. Hence we may affirm as logical axioms:
ist, that if equals be added to equals the wholes
will be equal; and, 2d, that if equals be taken from
equals, the remainders will be equals.
Hence, with regard to the equations specified
(i, 2, u, 6, 8, 5, 7, 9, and 10), we may affirm gen-
erally that the logical symbols may be transposed
or converted precisely in the same way as in the
operations of addition, subtraction, and multiplica-
tion in algebra. But with regard to the analogy
between multiplication and the corresponding
logical operation, it will be observed that in one
respect it fails, namely, in equation (4), x 2 = x;
which is good in Logic, but not generally true in
algebra. Also, it will be observed, there is appa-
rently no logical process corresponding to the alge-
braic operation of division. Thus, as we have
seen, we cannot infer from equation (n), " zx =
zy, " that x = y, as we may in algebra.
But if we conceive of an algebra or arithmetic
APPENDIX NOTES 251
that deals only with the two numbers, i and o, this
discrepancy will altogether disappear. For on such
hypothesis, equation (4), x 2 = x, will be true, both
in Logic and in mathematics. And in equation
(u), zx = zy, if z = i, the proposition, x = y,
may be inferred, both in Logic and in mathe-
matics. But if z be equal to zero, it cannot be
thus inferred, either in Logic or algebra. Hence,
if we conceive of an algebra in which the symbols
x, y, z, etc., " admit indifferently of the values of
i and o and of those values alone," then " the laws,
the axioms, and the processes of such an algebra
will be identical in their whole extent with the laws,
axioms, and process of an algebra of Logic."
Accordingly, Mr. Boole's system is founded on
this hypothesis, and " the logical value and signifi-
cance " of the terms dealt with (i and o) are thus
explained. In algebra, the equation oy = o is true,
whatever the value of y. So, in Logic, if o be re-
garded as a class, whatever class may be denoted
by y, the equation oy = o will be true; for, as we
have seen, oy denotes the class of individuals that
are at the same time included in the two classes,
/'. e., o and y. But none are included in the class
o, and therefore, oy = o.
So in algebra, the equation ly = y is true, what-
ever the value of y may be, and this is true in Logic
also, if i be regarded as including y. For as we have
seen (equation 3), if one of the two terms making a
combined term is included in the other, the com-
bined term is equal to the term of least extension.
But this condition may be satisfied by regarding i
252 LOGIC
as denoting the Universe. " Hence, the respective
interpretations of the symbols, o and i, in the sys-
tem of Logic, are Nothing and Universe. ' ' Denoting
the Universe by i, and men by x, the expression
i x denotes the class " not-men," /. e., all
animals that are not men.
The equation x 2 = x may be put in the form,
x" x = o, and this again in the form, x (i x)
= o; of which the interpretation is obvious; for,
if x denotes " men," and i x " not-men," it is
clear that there can be no individuals belonging at
once to the two classes, x and i x, or, men and
not-men. So if we denote by x any class charac-
terized by the possession of any quality whatever
the same result will follow.
It is observed by Mr. Boole that the principle of
analysis and classification involved in his system is
" division into pairs of opposites, or, as it is techni-
cally said, Dichotomy " ( 47), and this is in fact the
fundamental process in Logic. And this, it will
be observed, agrees with the opinion of Hobbes
and of Aristotle ( 90 n.).
In equation (5), it will be observed, there is a
certain ambiguity in the expression x -)- y. In
common speech the classes denoted by the sym-
bols x and y may either be exclusive of each
other, or they may overlap, as, for instance, in the
proposition, " Scholars and men of the world de-
sire happiness," or, " Useful things are those that
either produce pleasure, or prevent pain." In
Mr. Boole's system this ambiguity is removed.
If the two classes are intended to include each
APPENDIX NOTES 253
other, the expression to denote the aggregate class
will bex(i y) + y( I x ); which is to be read
x's that are not y's,- and y's that are not x's.
If we intend two classes that overlap, then the
full expression should be, xy + x (i y) -j- y (i x).
" The result of these investigations may be em-
bodied in the following rule of expression:
" RULE. Express simple names or qualities by
the symbols x, y, z, etc., their contraries by i x,
i z, etc. ; classes of things defined by common
names or qualities, by connecting the correspond-
ing symbols as in multiplication; collections of
things consisting of portions different from each
other, by connecting the expressions of those por-
tions by the sign +. In particular, let the expres-
sion, ' Either x's or y's ' be expressed by x
(i y) + y (i x) when the classes denoted by
x and y are exclusive; by x -[- y (i x) when they
are not exclusive. Similarly let the expression,
' Either x 's or y's or z's ' be expressed by x
(i - y) (i - z) + y (i - x) (i - z) + z (i - x)
(i y), when the classes denoted by x, y, and
z are designed to be mutually exclusive; and by
x + y (i z )+ z (i x) (i y), when they are
not meant to be exclusive, and so on."
For illustration, " let us assume
x hard, y = elastic, z = metals;
and we shall have the following results:
" ' Non-elastic metals ' will be expressed by
zO - y);
254 LOGIC
' Elastic substances with non-elastic metals ' by
y + z(i - y);
' Hard substances, except metals,' by x y;
" ' Metallic substances, except those which are
neither hard nor elastic,' by z z (i x) (i y),
or by z[i - (i - x) (i -y)]."
The above brief account of the elements of Mr.
Boole's system is given for the purpose of illus-
trating the laws that govern the convertibility of
terms, and of substantive elements of terms; or, in
other words, that govern the formal substitution of
equivalent expressions, ( 67 (2)) a purpose for
which it admirably serves. It will require some
attention to understand it, but with such attention,
no difficulty will present itself.
It may be readily perceived that by the use of
fhe above data a very extensive calculus may be
developed, and such a one has in fact been devel-
oped by Mr. Boole; but with regard to its utility,
opinions may widely differ.
' The idea of a logical calculus," says Lotze,
"has been often taken up and often abandoned;
but the Englishman Boole has recently made an
elaborate and careful attempt to carry it out, which
is beginning to attract attention in Germany, as
well as in his own country. Though I freely
admit that the author's ingenuity makes his able
work very charming, I am unable to convince my-
self that this calculus will help us to solve problems
which defy the ordinary methods of Logic."
(Logic, vol. ii., 277.)
APPENDIX NOTES
M 96
TABLE OF SYLLOGISMS
255
rYX
ist Figure < ZY
( ZX
A:
Barbara
V is X S^i
v\
A:
z is Y nf^
A:
.'.ZisX V_
JJ
E:
Celarent
Y is not X /
Is
\' \
A:
Z is Y (( z
E:
Y""
.'. Z is not X >
-S
Darii
Ferio
A:
I:
Y is X /
Some Z is Y I t
^~X**\ E: Y is not X ^_^^
^T\l I: Some Z is Y \_//v\ * J
I:
\
.'. Some Z is X
V.5/ O: .'. Some Z is not X ^ *
rXY
^</ Ft git re < ZY
(ZX
Cesare
Cif/iS^M/
E:
A:
E:
X is not Y
Z is Y
.'. Z is not X
x ^ E: Y is not X
(0 Y )
V*' J E: .'. Z is not X
256
LOGIC
Came sir es
Celarcnt
A:
X is Y
E:
Y is not Z
E:
E: .
Z is not Y
'. Z is not X
A:
E:
X is Y
.'. X is not Z
or Z is not X
Festino
E: XisnotY
I: Some Z is Y
O: .'. Some Z is not X
Fakoro
A: X is Y
O: Some Z is not Y
O: .'. Some Z is not X
Ferio
E: YisnotX
I: Some Z is Y
O: .'. Some Z is not X
Ferio
E: Not-Y is not X
I: Some Z is not Y
O: .'. Some Z is not X
rYX
jd Figure -j YZ
(zx
Darapti
Darii
A:
YisX /^~~/*\^\
A:
Y
isX
A:
YisZ (z /(7)J x J
I:
Some Z
isY
I:
.'.SomeZisX Vj^Lx
I:
.'. Some Z
isX
Disamis
Darii
I:
Some Y is X / ^N,
A:
Y
is Z
A:
Y is Z /f> /jX
I:
Some X
is Y
I:
.-. SomeZisX \S-K / X )
I:
.'. Some X
is Z
^V y
or Some Z
isX
APPENDIX NOTES
257
Datisi
Darii
A:
Y isX /^S^^rx
A: Y is X
/( Y /) \2\
I:
Some Y is Z ( V_J()/
I: Some Z is Y
\ X y'
I:
.'. Some Z is X ^~-^*/
I: .'. Some Z is X
Felapton
Ferio
E:
Y is not X /^~^>< ~x K:
Y is not X
A:
Yis Z O( ) X] I:
Some Z is Y
O:
. '. Some Z is not X ^~_3<^ >/ O:
.'. Some Z is not X
Dokamo
Darii
O:
Some Y is not X / ^^ A:
YisZ
A:
Yis Z [C y Q)x\ ^
Some not X is Y
Some not X is Z
O:
.'. Some Z is not X \^2^^ or
Some Z is not X
Ferison
Ferio
E:
Y is not X /'TN / \ E:
Y is not X
( * JL-L x i
I:
Some Yis Z V^Vy I:
Some Z is Y
O:
.'. Some Z is not X ^ / O:
.'. Some Z is not X
/XY
4th Figure -| YZ
(zx
Bramantip
Barbara
A:
Xis Y /""""X
A: Y is Z
A:
Y is z /fer\ \
A: X is Y
I:
.'. Some Z is X \&jj
A: .'. X is Z
v^_/
or Some Z is X
Camenes
Celarent
A:
X is Y /TX
E: Y is net Z
E:
O:
Y is not Z /V" X \ x"~x
.-. z is not x \v x y / ( z y
A: X is Y
E: .'. X is not Z
or Z is not X
258
LOGIC
Dimaris
I : Some X is Y
A: Y is Z
I: .'. Some Z is X
Fesapo
E: XisnotY
A: Y is Z
I: .'. Some Z is not X
Fresison
X is not Y
Some Y is Z
O: .'. Some Z is not X
Darii
A: Y is Z
I: Some X is Y
I: .'. Some X is Z
or Some Z is X
Ferio
Y is not X
Some Z is Y
O: .'. Some Z is not X
Ferio
E: Y is not X
I: Some Z is Y
O: .'. Some Z is not X
N no
The opinion of Locke cited, which occurs at the
end of his essay, may be taken as the consumma-
tion and final generalization of his theory of knowl-
edge. In the body of the work the conclusion
reached by him is, that the elements of all knowl-
edge are ideas (by which is meant what are now
commonly called notions or concepts), and that
" knowledge [is] but the perception of the connec-
tion and agreement, or disagreement, or repugnancy
of any of our ideas " (Essay, b. 4, c. i).
This definition, it will be observed, is too nar-
row, as it excludes the knowledge derived directly
from the perception of concrete objects. But al-
lowing for this defect it is accurate and profound
and must be taken as the foundation of all science.
In the beginning it seems that Locke had no
APPENDIX NOTES 259
conception, or at least a very inadequate conception
of the intimate connection between language and
thought, and of the indispensability of the former
as an instrument of thought. But as he proceeded
he seems gradually to have realized this great truth,
which is treated of in his third book; and upon
the conclusions thus reached is based his theory of
knowledge and his general philosophy as developed
in his fourth book, and as generalized in the conclu-
ding chapter, to which we have referred. His theory
of knowledge, therefore, is to be regarded as based
to a great extent expressly, and otherwise implicitly,
upon the notion that all knowledge beyond that
coming from experience consists in the perception
of the agreement, or disagreement, of our ideas, or
notions; and hence that all reasoning must consist
in the comparison of notions or concepts; that
practically this can be effected only by means of
the names of the concepts or notions; and hence
that Logic must consist in Analysis and Synthesis
of names or terms; which is the theory of this
work. (See observation of Home Tooke, Appen-
dix A.)
INDEX
Abstract and concrete terms, 37
Accent, fallacy of, 203
Accident and genus distinguished, 49
Accident and secunJum quid, relation between, 2IO
Accident, fallacy of, 207, 208
Adjectives regarded as substantives, 36
Amphiboly, 201
Analysis and synthesis, logical and physical, distinguished, 108
Analysis, use of, 116
Analytical processes, 42
Apodictic, 23, 70
Apprehension, 41
A priori, and empirical notions, 71
Arguing in circle, 160
Aristotle, his dictum, 76 ; his classification of fallacies, 197
Bain, an opinion of, 83
Burden of proof, 164
Canons of the several figures of syllogism, 100
Categories and predicables distinguished, 66
Classification, division and, 44
Collective and distributive interpretation, 60
Commonplace and original thought distinguished, 112
Commonplaces, 156
The numbers refer to sections.
26l
262 INDEX
Common terms, singular and, 35
Composition and division, fallacy of, 202
Concept defined, 30
Concrete terms, abstract and, 37
Confusion, fallacy of, 139
Connotation and denotation of terms, 32
Consequent, fallacy of the, 212
Consequentis, F., 212
Contradiction, the law of, 125
Contradictory, substitution of, 80
Contraposition, conversion by, So
Conversion by intension, 58
Conversion of propositions, 54, 70, 91
Conversions, material and formal, distinguished, 92
Copula, the, 55
Criticism, 115
Definition, vocal, 43 ; nominal or real, 48
Denotation and connotation of terms, 32
Dialectic, 23, 70
Dichotomy, 47
Dictum, Aristotle's, 76 ; forms of, 99 ; applicable to all fig-
ures, 100, 101 ; and to singular and other equational
propositions, 102 ; proposed amendments of, 103
Division, 46
Division and classification, 44
Enthymemes, 105
Equational theory of predication, 56
Equivalence of terms, 78
Equivocation, fallacy of, 127, 191, 201
Essence of term, 49
Euclid, his fifth proposition reduced to syllogisms, 84
Excluded middle, the law of, 125
Extension and intension of terms, 34
The numbers refer to sections.
INDEX 263
Fallacies, classification of, 129 ; definition of, 128 ; observa-
tions on, 132 ; extra dictionein, 206 ; in dictione (equivo-
cation), 201 ; of inference, 131; of judgment, 130; of
the syllogism, 104, 124
False definition, fallacy of, 126, 144
Figiirce dictio nis, F., 204
Figure of speech, fallacy of, 204
Figures of the syllogism, 95
Formal and material conversions, 92
Formal and material relations of terms, 67
Formal fallacies, 104
Genus and accident, 49
Genus and species, 45
Genus of term, 49
Ilomonymy, 201
Hypothesis, argument from, 165
Hysteron proteron, 160
Identity, the law of, 125
Ignoratio elenchi, fallacy of, 126, 169
Illicit assumption of premises (petitio principit), 154 ; tests
of, 162
Illicit conversions, 127, 183
Illicit generalization, 155
Illicit substitution, fallacy of, 127, 187
Immediate inferences, 80
Inference, rules of, 77, 123, 127
Inferences, immediate, 80
Infinitation, 80
Instance, or extreme case, 163
Intension and extension of terms, 34
Intensive conversion, 58
Intensive theory of predication, 58
Intuitive propositions or judgments, 18, 19
The numbers refer to sections.
264 INDEX
Invention, 113
Irrelevant conclusion, fallacy of, 126, 169, 173
Judgment, defined, 19 ; rules of, 126
Judgments and assumptions distinguished, 68
Knowledge defined, i, 2, 5
Language, as record of human thought, 4 ; as source of
opinion, 3
Laws of thought, the, 125 : the law of identity, 125 ; the
law of contradiction, 125 ; the law of excluded middle,
125
Legal maxims, 158
Logic, definition of, 14, 16 ; the traditional, 85 ; decadence
of the age in, n ; method of, in ; the morality of in-
tellect, 27 ; the art of right reasoning, 26 ; the ultimate
criterion of truth, 10 ; as the doctrine of signs, no
Logical processes, 107, 112
Logical term, elements of the, 31
Material and formal conversions, 92
Material and formal relations of terms, 67
Mathematical reasoning, 82
Meaning and signification of terms, 33
Method of logic, in
Mistaking the issue, 169, 170
Moods of the syllogism, 94
Moral sciences, distinguished, 6 ; decadence of the age in the,
ii
Name defined, 28
Negative terms, positive and, 39
Nominal or real definition, 48
Non causa pro causa, fallacy of, 159
Nonsense, fallacy of, 126, 134, 138
Notion defined, 30
The numbers refer to sections.
INDEX 265
Onus probandi, 164
Opinion, its modes of generation, 7 ; language as source of, 3
Opposition of propositions, 89
Original and commonplace thought distinguished, 112
Petltio prin fipii, fallacy of, 126
Plurium inter rogationum, F., 171
Popular proverbs, 157
Positive and negative terms, 39
Post hoc ergo propter hoc, 159
Predicahles, definition and division of, 61 ; and categories dis-
tinguished, 66
Predication, theories of, 55, 60
Property and specific difference distinguished, 49
Proposition, defined, 22, 50 ; the grammatical, 51 ; the logi-
cal, 52 ; interpretation of the logical, 53 ; the traditional
doctrine of the, 86
Propositions, conversions of, 54, 91 ; kinds of : intuitive, 18,
20 ; quasi-intuitive, 20 ; inferred, 21
Proverbs, popular, 157
Quality of propositions, 86
Quantification of the predicate, 57
Quantity of propositions, 87
Quasi-thing defined, 29
Question-begging terms, 161
Ratiocination, defined, 14, 15 ; not merely hypothetical, 72
Real things defined, 29
Reasoning, defined, 14 ; supposed distinction between quali-
tative and quantitative, 82
Rcductio, ad absurdum, 165 ; ad impossibile, 165
Reduction of syllogisms, 96
Relations of terms, immediate ; intuitive relations or judg-
ments, 18, 19 ; quasi-intuitive, or assumptions, 20 ; in-
ferred relations or syllogisms, 21
The numbers refer to sections.
266 INDEX
Right reasoning defined, 25
Rules, of logic, twofold division of, 121 ; of inference, 77,
123, 127 ; of judgment, 122, 126 ; of the syllogism, 104
Secundum quid, fallacy of, 209
Semeidtike, or the doctrine of signs, no
Several questions, fallacy of, 171
Significates of terms, 33
Signification and meaning of terms, 33
Simple apprehension, 41
Singular and common terms, 35
Sorites, 106
Species, genus and, 45
Specific difference, 49
Substitution, the principle of, 77 ; formal and material, Si ;
of contradictory, 80
Syllogism, analysis of, 74 ; definition of, 22, 75 ; elements of,
73 ; moods and figures of, 94, 95 ; principle of, 76 ; re-
duction of, 96 ; rules of, 104 ; the traditional doctrine of,
93
Term, defined, 28 ; kinds of, 35
Terminal relations, generally, 64 ; kinds of, 17, 65
Tests of illicit assumption, 162
Thing defined, 29
Thought defined, 30
Traditional doctrine of fallacies, 197
Traditional theory of predication, 59
Universe of the proposition, 40
Vocal definition, 43
Word defined, 28
The numbers refer to sections.
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