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INSTITUTES OF LOGIC
• ' •"'*.
INSTITUTES OF LOGIC
BY
JOHN VEITCH, LL.D.
PROFESSOR OF LOGIC AND RHETORIC IN THE
UNIVERSITY OF GLASGOW
M1CRGFORMED BY
PRESERVATION
S£RViCES
DATE. ,. P.?I.?.3;?J9i?
<x
WILLIAM BLACKWOOD AND SONS
EDINBURGH AND LONDON
MDCCCLXXXV
PEEFATOEY NOTE.
This volume is designed both for those who are com-
mencing the study of Logic, and for those who have
gone beyond the elements to the higher questions of
the science. The portion of the volume which is printed
in smaller type, as also the more strictly historical parts,
may, as a rule, be omitted in the first reading by those
who have not already mastered the main principles of
General Logic.
J. V.
The Loaning, Peebles,
October 24, 1885.
CONTENTS.
PART I.
LOGICAL PSYCHOLOGY. HISTORICAL NOTICES.
THE LAWS OF THOUGHT.
CHAP. PACK
I. INTRODUCTORY — LOGIC : ITS NATURE ; RELATION TO PSY-
CHOLOGY AND METAPHYSICS, 1
II. HISTORICAL NOTICES — ARISTOTLE — HIS VIEW OF LOGIC, . 9
III. HISTORICAL NOTICES — LOGIC SINCE ARISTOTLE, . . 14
IV. TRUTH, AND THE RELATIONS THERETO OF LOGIC — DEFINI-
TION OF LOGIC, ...... 29
V. OBJECTIONS TO LOGIC AS A FORMAL SCIENCE — THE VIEWS
OF KANT, HEGEL, AND UEBERWEG, . . .37
VI. LOGIC IS THE SCIENCE OF THOUGHT. SPEECH, THOUGHT,
THINGS. THE CATEGORIES OF ARISTOTLE AND KANT, . 48
VII. LOGIC — THE SCIENCE OF THOUGHT — WHAT THOUGHT IS —
INTUITION AND THOUGHT, ..... 57
VIII. LOGIC THE SCIENCE OF THOUGHT, AS THOUGHT, OR OF THE
FORMS OF THOUGHT — WHAT ARE THE FORMS OF THOUGHT, 68
IX. THE CONCEPT — HOW FORMED — THE GENERAL AND THE
ABSTRACT, .......
X. THE CONCEPT — ITS CHARACTERISTICS SPECIALLY CON-
SIDERED, .......
77
Vlll CONTENTS.
XI. THE CONCEPT — ITS CHARACTERISTICS SPECIALLY CONSID-
ERED— COMPREHENSION AND EXTENSION — RELATION TO
LANGUAGE — INTUITIVE AND SYMBOLICAL THINKING, . 100
XII. THE LAWS OF THOUGHT: IDENTITY — NON-CONTRADICTION
— EXCLUDED MIDDLE — DETERMINING REASON, . . 112
XIII. THE LAWS OF THOUGHT— HAMILTON AND MILL, . . 138
XIV. THE LAWS OF THOUGHT— THE DOCTRINE OF HEGEL —
STATEMENT AND CRITICISM, . . . .148
PART II.
CONCEPTS AND TERMS.
XV. CONCEPTS AS NAMED — TERMS— THEIR PRINCIPAL DISTINC-
TIONS, ....... 165
XVI. CONCEPTS: THEIR KINDS, ..... 182
XVII. CONCEPTS : THEIR EVOLUTION — DEFINITION AND DIVISION, 207
PART III.
JUDGMENT.
XVIII. THE NATURE OF JUDGMENT— COMPREHENSIVE AND EX-
TENSIVE, . . . . . . 220
XIX. JUDGMENTS — SIMPLE OR CATEGORICAL AND COMPOSITE —
THE CATEGORICAL — ITS ELEMENTS AND KINDS — AFFIR-
MATIVE AND NEGATIVE — UNIVERSAL, PARTICULAR,
SINGULAR, ...... 246
XX. MODALITY IN PROPOSITIONS, .... 261
XXI. COMPOSITE JUDGMENTS— HYPOTHETICAL OR CONDITIONAL,
DISJUNCTIVE, DILEMMATIC, .... 270
XXII. HEGEL'S THEORY OF JUDGMENT, .... 275
XXIII. THE POSTULATE OF LOGIC — THE QUANTIFICATION OF THE
PREDICATE— NEW PROPOSITIONAL FORMS, . . 288
XXIV. OBJECTIONS TO QUANTIFIED PROPOSITIONAL FORMS — GEN-
ERAL CONSEQUENCES OF QUANTIFICATION OF PREDI-
CATE, . . . . . . .311
XXV. QUANTIFIED PREDICATE — HISTORICAL NOTICES, . . 327
CONTENTS. ix
PART IV.
INFERENCE.
XXVI. INFERENCE— IMMEDIATE AND MEDIATE — IMMEDIATE (1)
TERMINAL EQUIPOLLENCE — (2) PROPOSITIONAL EQUI-
POLLENCE — SUBALTERNATION — CONVERSION, . . 337
XXVII. IMMEDIATE INFERENCE — OPPOSITION — CONTRARY AND
CONTRADICTORY, ..... 347
XXVIII. IMMEDIATE INFERENCE — OPPOSITION — CONTRARY — CON-
TRADICTORY—SUB-CONTRARIES— INTEGRATION, . 362
XXIX. MEDIATE INFERENCE — REASONING — ITS NATURE AND
LAWS — THE SYLLOGISM — ORDER OF ENUNCIATION, . 369
XXX. CATEGORICAL SYLLOGISMS — ON ARISTOTELIC PRINCIPLES
— MOOD AND FIGURE, .... 387
XXXI. CATEGORICAL SYLLOGISMS — ON HAMILTON'S PRINCIPLES
— FIGURED AND UNFIGURED SYLLOGISM — ULTRA-
TOTAL DISTRIBUTION, ..... 406
XXXII. CATEGORICAL SYLLOGISMS — COMPREHENSIVE REASONING
— THE FIVE SYLLOGISTIC FORMS, . . . 428
XXXIII. COMPLEX AND INCOMPLETE REASONINGS — DEDUCTIVE
— CHAIN-REASONING : EPICHEIREMA — SORITES — ORDI-
NARY ENTHYMEME, . . . . .443
XXXIV. INDUCTION — FORMAL AND MATERIAL — ANALOGY, . 449
XXXV. THE METHODS OF INDUCTION, .... 469
XXXVI. QUA SI-SYLLOGISMS— EXAMPLE — ARISTOTELIC ENTHYMEME, 484
XXXVII. HYPOTHETICAL, DISJUNCTIVE, HYPOTHETICO-DISJUNCTIVE,
FORMS OF REASONING, .... 492
XXXVIII. FALLACIES — FORMAL AND MATERIAL. (1) FORMAL FAL-
LACIES, . . .... 512
XXXIX. FALLACIES — (2) MATERIAL FALLACIES, . . . 534
INSTITUTES OF LOGIC.
PART I.
LOGICAL PSYCHOLOGY. HISTORICAL NOTICES.
THE LAWS OF THOUGHT.
CHAPTER I.
INTRODUCTORY — LOGIC : ITS NATURE ; RELATION TO PSYCHOLOGY
AND METAPHYSICS.
§ 1. The central conception of Intellectual Philosophy is
that implied in the term Truth. This, with the cognate term
Certainty, indicates the aim of intellectual effort as animated
by the natural desire of knowing. Knowing has various ends
or degrees. We may seek simply to know ordinary matters
of fact, to acquire science, to go back on the first principles
and laws of knowledge itself. We may rest in the individual
fact, we may generalise and classify, we may speculate on
what is ultimate in knowledge. In each case, however, what
we seek is Truth and Certainty.
§ 2. Speaking generally, Truth is the harmony or conformity
between fact or reality and our knowledge of it. Fact may
mean either an individual thing, quality, object, or a class
or law, generalised or necessary, of matter or mind. Con-
formity always implies a certain plurality or dualism, for of
A
2 INSTITUTES OF LOGIC.
the same to the same there is no conformity, only identity.
Certainty is the consciousness of truth, — conviction, as resting
on evidence, immediate or mediate.
§ 3. In ordinary knowledge, in history, in science, we aim at
truths rather than Truth. Each fact, event, each law of nature,
adequately known is in the mind a truth ; and a body of these
laws, co-ordinated, classified, systematised, is a science in a
more or less perfect form. We may ask the question, What
are the truths of history or of science, and seek to find them.
This would be historical or scientific knowledge. But we
may also ask the question, What is Truth? — truth itself —
the essence or inner being of it, so to speak. What have
truths in common that we call them truths ? Can we get the
mark, criterion, test of truth itself, or of this or that truth ?
How far can we go in assuring ourselves that what we
believe to be true is true ? And what is the meaning, or
what are the meanings, of saying that there is truth, or that a
given proposition is true? This is the question, or set of
questions, with which Intellectual Philosophy is concerned.
It occupies itself with the nature, conditions, criteria of truth.
§ 4. If we take this question of what is truth, or true know-
ledge, in its widest generality, it is obvious that we must
raise the questions as to the ultimate ground and nature of
knowledge and certainty. Supposing that we know at all,
or believe that we know, as a matter of fact, this knowledge
must have a ground or beginning, for us at least. " If it is
not possible," says Aristotle, u to know first things, neither can
we know, either absolutely or properly, things which result
from these, but by hypothesis, if these exist. All science is
not demonstrative, but the science of the immediate is inde-
monstrable. . . . Some time or other we must stop at immedi-
ate (propositions)." * And we thus are confronted with the
question as to the first principle or principles of knowledge.
And as true knowledge is real knowledge, or knowledge of
what is, we are met by the correlative question as to what we
know of the real, — what reality is, and what are its kinds. A
science of knowledge, therefore, in its widest scope would be
a science of first principles, and of being as it stands in know-
ledge. This would lead to the discussion of the difference
between phenomenal reality or knowledge, so called, and
l Aristotle, An. Post., 1. i. c. 3, 4.
PSYCHOLOGY AND LOGIC. 3
substantial reality, — what is the nature and what the limits,
if any, of our experience.
§ 5. These questions touching the nature of reality, the
nature of the various objects of our knowledge, have been
properly assigned to that branch of Philosophy known as
Metaphysics or Ontology. We may confine our inquiries
into the laws and conditions of our knowledge of the
contents of experience, without, for example, considering
whether these contents have a simply subjective reality, are
mere conscious impressions, or, as known, are something
more and other than this. We may further carry on this
inquiry without considering the question as to the nature
of ultimate or primary reality. It is sufficient for this end
that we know, and know what we call objects, whatever these
be in their essence or origin. That we are conscious, that we
have experience at all, is a sufficient basis for certain questions
regarding the conditions and possibility of this experience.
§ 6. The discussion even of these ultimate questions may
presuppose that there are certain laws or features of know-
ledge,— universal and essential in knowledge, — and thus
there may be a science which precedes even such discussion,
as regulating human intelligence and thought itself, or the
very conception of an object of knowledge itself. And if
there be such a science, it will have a place of its own, and
be so far independent of and above all other sciences. It
would profess to lay down the conditions of the knowable,
and especially of the thinkable, — that is, to state certain laws
or principles without which there is no object of knowledge
or thought for us at all. As such, it will be found to embrace
certain conditions of knowledge and thought, apart from the
fulfilment of which the ideal existence of an object, or an
object in knowledge, is not possible. This impossibility may
arise from two sides : first, from the side of knowledge. Here
there are certain conditions to be fulfilled ere an object can
be an object of knowledge or thought at all. These are the
conditions of Identity and Non-contradiction, and they are
inseparable from the nature of the act of knowing. Certain
conditions lie on the side of the object as existing, and these
are given in the object or with the object. They form the
essential elements or relations of the object. These are the
relations of Subject and Object, — Qualitative, as Substance
4 INSTITUTES OF LOGIC.
and Quality ; Quantitative, as Time, Space, &c. These are
properly metaphysical relations. They are part of the matter
of knowledge, — the given, yet essential, relations of things.
§ 7. The questions regarding the metaphysical laws of
knowledge are, first, as to their nature, number, genesis ;
secondly, as to their objective validity, or agreement with
the nature of things. The first question is obviously psycho-
logical. It is a question of mental genesis. The second
question may be regarded as coming under Logic, in as far
as this science is led to deal with Evidence, immediate or
mediate. This would form a special section of Logic rather
than be the adequate object of the science itself. But the
true relation of the metaphysical laws to Logic is simply that
of being part of the matter of thought, in this case necessary
matter to be legislated for in common with other matter.
Logic can only, consistently with its specific scientific char-
acter, treat such concepts as Cause, Substance, Unity, Iden-
tity, as Concepts.
§ 8. There may further be a question as to whether the
logical laws are independent, or are deducible from certain
corresponding metaphysical laws. But this is properly a
psychological question, — pertaining, it may be, to logical
science. It concerns Logic only indirectly, especially if it
be admitted that the logical laws are necessary and universal,
for the results of those laws would be the same whether
their necessity be primitive or derived from other necessary
laws. Meanwhile, it is sufficient to say that it will be found
that the logical laws are not derivable from any source higher
than themselves, but are in fact presupposed in every known
concept or law which can be in our consciousness — i.e., in
every process of analysis or reasoning, which might be ad-
duced to show their derivation.
§ 9. Logic Proper, — Pure or Formal Logic, — is the science
of the conditions of the knowable and thinkable, in so far as
these depend on the inherent constitution of the acts of
knowing and thinking; and these acts are regulated by strict
laws, called formal, inasmuch as their violation destroys the
form or ideal being of the act and object of thought, — as
known or thought. Formal Logic is the science of the laws
of possible, consistent, and necessarily connected thinking, or
of harmony and of necessary implication in thinking.
PSYCHOLOGY AND LOGIC. 5
§ 10. But knowledge, true knowledge, of experience has
what may be called a contingent side. Something is given,
presented ; and this something is very various, and not origin-
ally deducible or even predictable. There is the matter of
experience, of knowledge and thought. That something be
given to the knowing faculty, to sense, or intuition, is an
absolute condition of knowledge. Thought without intuition
is vain, empty. Here, too, we touch psychology, the analysis
of the intuition and its matter. But all that we need mean-
while to carry away is, that there is necessarily a given to
help to constitute knowledge. And this is variable, passing,
contingent. How much of it is subjective, how much ob-
jective, is a separate question. Metaphysics considers this.
As this given is essential to knowledge, it is essential to
true knowledge. And we have to inquire as to how we are
to secure the truth of our knowledge of the matter presented,
or of the intuition or presentation. How is knowledge accu-
rately to represent what is presented to us in the course of
experience ? How are we to get not only at the individual
or isolated fact, but at the law or laws which individual facts
embody? How are we to reach the classes, laws, causes,
which we suppose to be in experience ? How, in a word, are
we to acquire the truths of science ? There is a science
which has for its aim to investigate the rules or laws of the
processes by which we observe, generalise, and infer through
induction and analogy, and not less through deduction. This
is properly enough a part of Logic, in the wide sense of the
term. It is known narrowly as Inductive Logic. It makes
a part of what Hamilton calls Modified or Mixed Logic. By
some it is called Applied Logic ; but this should not be
understood as a special Logic, which is Logic in general
applied in this or that determinate matter or science. For
the rules of Applied Logic are generally, if not universally,
applicable to the sciences, and this Logic involves also the
universal use or application of the canons of Pure Logic.
§11. This problem of the conditions of truth thus presents
different aspects ; and, according as we regard one or other,
we have a different speculative science, different, yet converg-
ing in one great organic unity. Thus Psychology in dealing
with the Intelligence looks at the act of knowing as it exists
as a fact, or is spontaneously manifested in the consciousness,
6 INSTITUTES OF LOGIC.
at its nature, kinds, degrees. It cannot be denied that
we know, or believe we know. Even in such a denial there
would be an assertion of knowledge. Knowing is a fact or
phenomenon of experience. It is the inner fact of our being ;
it is our being, so far. We are, as we know. Logic, too,
looks at this act as fact. So far, it is identical with Psy-
chology. But Logic looks at the fact of knowing with a view
to ascertain its conditions, laws, if it have any, how it is car-
ried on, and what it is when it is finished. And Logic pro-
fesses to find that knowing is subject to certain conditions,
and to show that these conditions are of two different kinds at
least ; and, these being ascertained, to exhibit them in a sci-
entific way, to formulate them, make a body of knowledge of
them ; and, now indifferent to the actual fact whether know-
ing is going on or not in this or that matter or science, to show
ideally how it must go on, if it is to be successful in its aim,
or even to be at all. While Psychology is thus the science
of the facts of Intelligence, or of knowing, and also of its actual
laws as matter of experience, a science of facts or phenomena
of our conscious intelligence, as realities, Logic takes from it
the laws which it reveals, the laws of the acquisition, the
ordering, classification, and concatenation of knowledge, and
represents these as ideal abstractions universally applicable
in the processes of intelligence. Logic is thus wholly de-
pendent on Psychology for its principles. It is Psychology
carried up to its highest abstraction. And the moment it
loses hold of Psychology, Logic becomes arbitrary and un-
reliable, no longer applicable to the facts of experience. The
nominal difference between the two sciences is simply that
Psychology regards rather knowing in process, while Logic
regards knowing as completed, as a product, and the laws
which it has realised or fulfilled in becoming what it is, or in
reaching what it attains.
§ 12. Psychology thus, to a certain extent, and the method
of Psychology, observation of the actual procedure of the
understanding, are necessary to the knowledge of the nature
and laws of the understanding. The understanding is simply
the conscious mind acting and being conscious of its action
in a definite manner, and about a definite object. In thus
acting it realises the law of its action ; it thinks — i.e., con-
ceives, judges, or reasons coherently. Analysis and reflection
PSYCHOLOGY AND LOGIC. 7
bring out with a fuller consciousness the law or laws which
it naturally observes, and also reveal the necessity and uni-
versality of the law. In no sense whatever does this analysis
create the law ; in no sense whatever does it impose the law
on the understanding. The law is revealed in a definite
instance, and it is shown by reflection to be supreme in all
instances.
(a) Kant objects to the introduction of psychological principles into
Logic, or drawing the laws of thought from psychological observation.
The reason he gives is, that thus we should get only contingent, not
necessary laws ; and the question is not as to how we think, but as to
how we ought to think. The necessary use of the understanding is
discovered without any psychology. To this it is sufficient to say
that observation, followed by generalisation, would give us only con-
tingent principles ; but observation of the actual procedure of the
understanding, followed by reflection, or an experimental testing of
the procedure, may and does give us the necessary element in the pro-
cess. We can learn how we ought to think only through an analysis
of how we actually think, when we think consistently, i.e., think at
all. Indeed, Kant himself subsequently admits all that need be con-
tended for here, when he says "the necessary laws of thought can and
ought to be conceived a priori, independently of the natural and con-
crete exercise of the understanding and the reason, although they can
at first be found only by observation of this exercise." On this
point, as elsewhere, especially in the Critique, Kant shows that he had
no clear idea of the scope of Psychology, of its method, and only slight
acquaintance with the details of the science.
He further excludes Psychology from Logic on the ground that
Logic seeks' to know not the contingent but the necessary, not how
the understanding thinks, and has thought, but how it ought to
think, the accord of the understanding with itself. This assumes that
there can be no necessary exercise of the understanding in a given
instance, — for example, no absolutely necessary implication in a given
reasoning performed by the understanding, and consciously known to
be necessary ; whereas, this necessary relation is given and consciously
realised in a single instance of valid reasoning. Kant thus confuses
the particular or singular with the contingent.
It assumes, further, that the understanding may think in experi-
ence in a way different from that in which it must think, if it thinks
at all. This is not so. There is only one way of thinking by the
understanding, that is, the legitimate way. Any other is a mere
illusion, not a reality of thought at all. And there is no reason why
the understanding may not naturally perform its process of thinking
rightly rather than wrongly.
(b) One of the current Hegelian assertions, which is regarded as
new and important, is that " the knowledge of what knows cannot
precede the knowledge of reality." No one, I should think, ever
alleged, or at least required to allege, the converse of this. The
8 INSTITUTES OF LOGIC,
knowledge of what knows is and can only be found in the knowledge
of reality. We perceive, judge, and reason ; we get at, or think we
get at, reality in our intuitions and judgments. But the philosopher
says we get at more, — we get at a knowledge of what knows, if only
we will think of what a knowledge of reality is and means. For
therein are manifested the character and law of the knower as well. And
if we are ever to know the nature of the knower or knowing subject, we
are to do it by a reflection on the spontaneous acts of knowledge, — which
are conversant directly with the reality, and reflexly show the reality
in consciousness. But for this secondary or reflective knowledge, we
should be wholly unable to estimate the value and reach of our know-
ing, and only through this could we correct, if need be, our spontaneous
Or intuitive knowledge.
CHAPTEE II.
HISTORICAL NOTICES — ARISTOTLE — HIS VIEW OP LOGIC.
§ 13. The ultimate aim of Aristotle in his logical treatises,
especially those on the more advanced parts of the science, —
the Prior and Posterior Analytics, — is to show the nature and
laws of true Demonstration (diro8«£is). In the opening of the
Prior Analytics (1. i. c. 1) he tells us that the treatise con-
cerns demonstration, and is undertaken for the sake of demon-
strative science, and that consequently he has to define
proposition, term, and syllogism. This affords a certain
ground for a division of the parts of Logic, and the arrange-
ment of the Aristotelic treatises. (1) The theory. of the
elements of the proposition, that is, the term, given in the
Categories. (2) That of the proposition in the treatise On
Interpretation. (3) That of the syllogism in 'the Prior Ana-
lytics. (4) That of demonstration in the Posterior Analytics.
These may be regarded as exhausting the essential parts of
Logic, and as constituting Theoretical or Pure Logic. The
Topics and the Sophistical Elenchi may be taken as in Applied
Logic. In the Analytics and in the Topics, Aristotle treats of
definition and demonstration. But in the former .he seeks to
give the theory of true definition, and how it is to be con-
structed ; in the latter, what sort of definition can be im-
pugned. In the Analytics, demonstration is the best, which
is according to the true principles of its theory ; in the
Topics, that demonstration is to be preferred which is the
more difficult to assail. There is the difference in fact
between the scientific theory of truth, and the dialectical
interest of the appearance of truth and intellectual victory.1
i Cf. Waitz, An. Post., ii. 297.
10 INSTITUTES OF LOGIC.
§ 14. Aristotle tells us that he is to treat of syllogism pre-
viously to demonstration, since syllogism is more universal,
— demonstration being a certain kind of syllogism. The
differentia of demonstration is, that it is a syllogism from
necessary matter. " If there be a demonstration that a thing
cannot subsist otherwise, the (demonstrative) syllogism must
be from necessary (propositions). For it is possible, without
demonstration, to syllogise from what are true, but we cannot
do so from things necessary except by demonstration, for this
is now (the essence) of demonstration. . . . It is possible
to syllogise the necessary from things not necessary, just as
we may the true from things not true ; still when the medium
is from necessity, the conclusion is also of necessity, as the
true results from the true always."1
In the Posterior Analytics he expressly expounds the
theory of demonstration, with a view to show the use of
syllogistic in the constitution of true and certain science, — the
science of necessary principles and its consequences, includ-
ing the question of their guarantee. 'ETrurTrjfir) aTroSeiKTiKrj
has thus been translated the theory of knowledge, and re-
garded as part of Philosophy. On these grounds, it is held
by St Hilaire and others that Aristotle viewed demonstration
as the proper object of the books of the Organon, and of the
science afterwards named Logic.2
§ 15. The principles of science (dpyai), according to Aristotle,
are Koivat. and ZBiai : under the former are, d£iw//.a,Ta, the ori-
ginal premises from which demonstration proceeds ; under the
latter, assumptions, Oicrus, — that is, definitions, bpia-fiol, and
hypotheses (viroOecreis), assumptions of the existence of the
subjects.3
§ 16. The difference between a demonstrative and a dialec-
tical proposition is, that the former is assumed by the demon-
strator, the latter is accepted from another person. So far,
however, as syllogising from either proposition is concerned,
this difference, as Aristotle admits, is of no moment. All
that the syllogism supposes is, that something is or is not
present with something. We do not need to inquire why
one thing is predicated of another ; all that we require is that
it be predicated. A syllogistic proposition (7rpoTao-is) is an
1 Post. An.,i. 6.
2 Cf. St Hilaire, Organon, art. Logique, Dictionnaire de S. P.
8 Cf. An. Post., i. 2; Mansel, Prol. Log., App.
HISTORICAL NOTICES. 11
affirmation or negation ; it is demonstrative (a^oSei/m/^) if it
is true, and assumed on primitive data. By the phrase cu ig
apx^s vTroOeaeis is meant axioms (d|iw//,aTa) whose truth is in-
demonstrable and self-evident. The demonstrative proposi-
tion is thus of necessary matter. Thus X must be Y; but, so
far as the syllogistic act is concerned, this is not affected by
the necessity, — i.e, the modality, — of the proposition. The
consequence in syllogism is as necessary whether the major
proposition be apodeictic, — that is, of necessary matter or
relation between the terms ; or merely assertory, — that is,
of a simple categorical relation, X is Y. The difference is
purely extra-logical; the conclusion, as a proposition in the
case of necessary matter, is a necessary proposition ; it must
be true, or, as Aristotle puts it better, it must be thought in
one form, and as excluding its opposite. But this is a pecu-
liarity attaching to the matter of the proposition, not to the
sequence of it from the premises, or its form.
§ 17. It would be manifestly impossible to have a science of
reasoning or inference, if we were to ask the title of every
proposition to be regarded as necessary or as contingent, or
as more than assertory. We should require in each case to
go into Physical Science and Psychology to determine this
point, and the inquiry would be endless. Besides, if the
consequence of the inference depended on the modality of the
proposition, there could be no one science of inference : con-
clusions would be necessary or probable according to the
matter. Probability would have its ever-varying degrees,
and a science of pure inference would be impossible.
The modality of necessity and contingency has no bearing
on the nature of the sequence, or on the conclusion as a con-
clusion. It is, therefore, wholly extra-logical. The quantity
and the quality of a proposition affect, not the sequence, but
the quantity and quality of the conclusion, as a conclusion
from* given premises ; and hence they are to be regarded in
the data as modifying the conclusion. Thus modality, as
quantity and quality, if the term be stretched so far, may be
regarded as of logical import ; but no other kind of modality
is of any relevancy.1
§ 18. Further, if it be true, as is alleged, that the canon of
demonstration is the principle that "two things compared
and found equal to a third, are equal to one another,"2
1 Cf. Mansel, Prol. Log., Appendix, Note H. 2 Post. An., i. 10.
12 INSTITUTES OF LOGIC.
it is clear that demonstration has no law independent of
ordinary syllogistic ; for this canon depends almost imme-
diately on the law of non-contradiction. This, as stated by
Aristotle, is — " It is impossible that the same attribute should
be and not be in the same subject, at the same instant and
under the same relation."1
§ 19. In truth, demonstration, according to Aristotle, does
not need to assume the common axiom in all its universality,
but only in so far as is required by the genus about which the
demonstration is concerned. The geometrician in demon-
strating assumes, not that every whole is greater than the
sum of its parts, but that every whole in the genus magni-
tude is ; and the arithmetician does the same in respect of
numbers. Demonstration is, in fact, not the whole of Logic,
or the theory of Pure Logic, but an Applied Logic, — logic
applied to necessary matter.
§ 20. It is held that while physical science is observational
and inductive, and therefore of contingent value, demonstration
may intervene and give absolute certainty. Thus a body is
known to fall to the ground. This is a fact of observation and
induction simply. But the fact may be connected with the
laws of motion, and thus demonstrated. Or the planetary move-
ments may be observed and described, and then led back to and
predicted from the law of universal gravity. But in neither
of those cases is there demonstration resulting in absolute
certainty. There is simply the reference of a fact or law to
a higher or wider law than itself. But this higher law is not
a truth of absolute necessity, any more than the narrower law
which is referred to it. It is a case simply of deduction ; and
the certainty may be complete, given the higher law. But it
is, after all, only a hypothetical necessity which subsists, be-
cause the universal, though to thought contingent, law, exists.
(a) Organon (opyavov) generally, and with Aristotle, means simply
instrument, or that which subserves the accomplishment of some end.
The soul is compared to the hand, which is the ftpyavov bpydvwv. — (De
Anima, ii. 8.) To discover the for and against of each question is a use-
ful instrument for science and reflection. — (Topica, viii. 14. Cf. i. 13.)
The term Organon, as subsequently applied to the six logical treatises
of Aristotle, was wholly unrecognised by their author. As a general
designation, it was equally unknown to the Greek interpreters, and,
down to the time of Psellus and Blemmides, the name for the treatises
1 Met., iii. c. 3.
HISTORICAL NOTICES. 13
of Aristotle afterwards comprised in the Organon was r) \oytKi], or
7] \oyiKT) eirurTTiiATi, or irpay/jLareia. Diogenes Laertius had said that
Aristotle made Logic opyavov npoo-riKpi^oofievov. It was, however,
through the Greek interpreters that the term Organon came ultimately
to be so generally applied. The doctrine of the Analytics, called by
them to airodfiKTiKa, was named by Alexander of Aphrodisias the
opyavov ; and the same designation was applied by Philoponus to
demonstration itself. These were the instruments for reaching true
and certain knowledge, — necessary truth. The term thus at first
applied to the Analytics came ultimately to designate the whole
logical treatises of Aristotle. In the fifth century, Ammonius and
Simplicius give, either originally or from tradition, going back to
Andronicus of Rhodes, or Adrastus of Aphrodisias, the logical works,
as a distinct class, as \oyata if dpyavmd. David the Armenian
emphasised this view. With him the Aristotelic works are divided
into theoretical and practical, with the supplementary branch of
the organic. The syllogism is a fan for winnowing the true from the
false, the good from the bad. From the commencement of the sixth
century certainly logic in the Peripatetic school was called to bpyavittbv
{ftepos) of the Aristotelic philosophy. Further, a passage of Ammonius
almost suggested the modern application to the logical treatises of the
term organon. He says, speaking of the Introduction of Porphyry,
that this work is comprised in the logical organon — virb to AoyiKbv
opyavov avdyeTai. It was not, however, until the fifteenth _ century
that the term Organon came to be habitually used as the common
name for the six logical treatises of Aristotle. This question of the
name is connected with the controversy as to the sphere of logic, —
whether it is. a part simply of philosophy, or the instrument. The
Stoics held the first opinion; the Peripatetics the second; the dis-
ciples of the Academy held logic to be at once science and instru-
ment. It was no doubt with the Greek commentators that the
exaggerated view of the Aristotelic logic as an instrument or method
for securing real truth originated. But it was only towards the
sixteenth century that some of the Peripatetics, in face of the energetic
protest of Vives, maintained the extreme view of logic as the method
of real truth, — a view which was not only erroneous, but incapable of
being put into practice. Hence arose the misconceptions of Bacon and
Locke regarding the real Aristotle, which were excusable only on the
part of the class of non-reading philosophers. No such view can fairly
be attributed to Aristotle himself, notwithstanding what he says about
demonstration. "It is not," says St Hilaire, "an organon which
Aristotle professes to give to philosophy; he has only intended to
treat in his logical works, in the fitdoSos tuv Aoyuv, of the instrument
of all philosophy, of the vovs, which, as he himself says, is the organon
of the soul, — 'to the body the hand, to the soul the intellect; for the
intellect is of those things naturally in us as the organon.'" — (Proble-
mata, 1. 30e, quest, v.) Taken in this sense, the term organon is per-
fectly correct. Logic is really occupied with the instrument of all
knowledge, since it is occupied with the science of thought and the
form under which thought is produced — viz., reasoning. — (St Hilaire,
De la Logique d'Aristote, t. i. Part I. c. 2. Cf. "Waitz, An. Post., i. 1.)
14
CHAPTEE III.
HISTORICAL NOTICES — LOGIC SINCE ARISTOTLE.
§ 21. Since Aristotle, logical investigation has been con-
fined to two principal lines. The one proceeds on the con-
ception and principles of the science as laid down by its
founder, in what may be regarded as their formal aspect, and
seeks to add to and modify certain of the doctrines, — to in-
troduce refinements and subtleties. The other has been the
questioning of the exaggerated pretensions made by some
regarding the science as a method of investigating and
reaching real truth, — truth of fact or science, — and the legiti-
mate attempt to found a method of truth and science which,
rising beyond the merely formal relations of thought, strives
to add to its content or matter, — to acquire, build up, arrange,
and classify science. The formal view of knowledge is so
exact and complete in itself, that men are led to rest in its
intellectual harmonies and adaptations, — its refinements and
subtleties. But the real needs of knowledge and of life have
ever and again led to a protest against the mere intellectual
sphere as narrow and insufficient, and compelled questions as
to the best rules and methods for conducting thought through
the broad field of experience, and guiding to a knowledge
of fact or reality as we may find it.
§ 22. This branch of Logic may be said to have two aims,
— the laws of Discovery and the conditions of Proof. In
Bacon, Herschel, and Whewell, the former aim is the pre-
dominant. In Mill, and in later writers on his lines, the
second aim is the main one, — his view of Logic being, that
it is the science of the intellectual operations which serve
for the estimate of evidence, — at once of the general procedure
HISTOEICAL NOTICES. 15
which goes from the known to the unknown, and of the
operations auxiliary to this fundamental operation.1
§ 23. This inquiry in either form is in no way against the
doctrine and spirit of Aristotle. The method of real science
is the complement, not the antagonist, of the Aristotelic logic.
Aristotle has even recognised, and, in a way, analysed in-
ductive method. Nor is he opposed to the method which
would analyse the speculative side of knowledge. He runs
Demonstration back to ultimate principles, first truths, them-
selves indemonstrable, and thus connects logic with the First
Philosophy, or theory of Ultimate Knowledge. " All demon-
strative science is related to three things — which are admitted
without demonstration, and these are the genus, the essen-
tial properties of which science considers ; and common
things called axioms, from which as primaries one demon-
strates ; and thirdly, the modifications of the genus, the signi-
fication of each of which the demonstrator assumes." — (Post.
An., i. 10, et passim.) It is on this side that the Aristotelic
logic touches the Method of Descartes, in not being satisfied
until it can connect the theory of science with the first
principles of knowledge. In fact, the need felt by Plato and
reflected in his Dialectic is not without an inspiring power
on the whole theory and development of human thinking, —
on the formal as well as the material side.
(a) Aristotle distinguishes Induction from Syllogism. — (Top. 12; An.
Pr. , ii. 23. ) There is a great difference, he tells us, between knowing
that a thing is, and why it is. We do not attain to the knowledge of
the why when the syllogism is not formed of immediate terms, for then
we have not remounted to the primary, which is cause. The middle
term here is not the primary and immediate cause. So in the case of
reciprocal terms — that is, where the effect is of the same extent as
the cause, and the one can be taken for the other, — the term which
is not the cause may be assumed as better known, and the why is not
demonstrated. Thus it is demonstrated that the planets are near the
earth, because they do not twinkle. Let C be the planets, B not
twinkling, A being near. We may say B of C, for the planets do not
twinkle. But we say also A of B, for when a body does not twinkle,
it is near. We may suppose further, that this last proposition is fur-
nished by induction or sensible experience (Si eirayuyrjs tf 81 al(r6r)<rews) ;
we conclude necessarily that A belongs to C, and in this way it has
been demonstrated that the planets are near. But under this form the
syllogism does not say why the thing is, it only says that it is ; for
1 Logic, Introd. , § 7.
16 INSTITUTES OF LOGIC.
the planets are not near the earth because they do not twinkle, but,
on the contrary, they do not twinkle because they are near. On the
other hand, we may still demonstrate inversely the effect by the
cause, and then the demonstration will give the why of the thing.
Thus, whatever is near (B) does not twinkle (A) : the planets (C) are
near (B), therefore the planets (C) do not twinkle (A). — (An. Post., i. 13.)
§ 24. The immediate successors of Aristotle seem to have
restricted themselves wholly to the formal side of Logic,
modifying details, and developing the theory of Hypothetical
Reasoning. This was done chiefly by Theophrastus (taught
from 322 to 286 b.c.) and Eudemus. The Stoics cultivated
logic, though the doctrines of the school are only preserved
in fragments. Chrysippus (280-208 b.c.) followed in the line
of Theophrastus and Eudemus ; but there was an attempt in
the Stoical school to widen the scope of the science, so as to
make it an instrument of real truth. Epicurus (d. 270 b.c)
regarded it as a canonic, and found the criterion of truth in
sensation. With the quickening of speculation in Alexandria,
attention was fixed on the logical writings of Aristotle. They
gave the only form of methodical thinking known, and thus
acquired great influence on the philosophical thought of
the time. From the latter part of the second century to the
beginning of the third, Alexander of Aphrodisias, so called
from a city of Caria, his birthplace, was the greatest power in
sustaining and spreading the influence of the logical treatises
of Aristotle. His commentaries and expositions are admira-
ble,— still unsurpassed ; and he was a man, besides, of orig-
inal faculty, as shown especially in his treatises on the Soul
and on the Fatalism of the Stoics. In the Schools he was
the Commentator, as Aristotle was the Philosopher. Alexan-
der seems to have taught both at Athens and Alexandria.
Galen, in the second century (131-200 a.d.) was not less
famous as an expositor of Aristotle than as a physician.
His logical writings have, however, perished, with the slight
exception of the 7rcpi 7w koto, ttjv Ae£iv a-o^Lo-^aTiov. The
Introduction to Dialectic, discovered at Mount Athos, and
published in Greek, 1844, is probably spurious. Plotinus
(205-270 a.d.) assailed the Categories ; and Porphyry (233-
304 a.d.), his disciple, expounded them in his Introduction,
so valuable as to have since been uniformly prefixed to the
Organon. Themistius, who taught at Constantinople in
HISTOEICAL NOTICES. 17
355, paraphrased the logical treatises. Ammonius Hermeiae
(after 485 a.d.), Simplicius, who was banished from the
School by the decree of Justinian (529), have left valuable
expositions of Aristotle. David the Armenian and John
Philoponus (about 533) in Egypt, are to be added to the
list of commentators.
§ 25. The contributions of the Latins to Logic are not of
much value. After the taking of Athens by Sylla (84 B.C.),
the writings of Aristotle were carried to Kome. There they
were arranged and edited by Andronicus of Rhodes. We
have notices of the doctrines in Cicero, and subsequently a
series of abbreviators, — Appuleius (160 a.d.), the Pseudo-
Augustine, and Marcianus Capella (c. 474 a.d.) Victorinus
(c. 350) translated the Elo-ayuyrj of Porphyry. Boethius
(470-524) was the only Eoman logician of consequence.
He translated a great part of the Organon, and contributed
commentaries and discussions of his own. The chief import-
ance of his writings arises from the circumstance that they
were for long, in the absence of a knowledge of Greek, the
means of making Aristotle known in the West.
§ 26. Even in the ages following the end of the Western
Empire (476 a.d.) and during the irruption of the barbarians
into Europe, the logical writings of Aristotle were never wholly
without study. We have Isidore of Seville (d. 636 a.d.),
Bede (673-735), John of Damascus (d. 754), Alcuin (736-804).
The last named introduced the study of Logic into the Court
of Charlemagne, and this and his other teaching determined
the line of thinking in Europe down to the time of Abelard
(1079-1142). In that period we have among the Greeks the
name of Michael Psellus (1020-1100 or later) ; and following
him Italus, Ephesius, Eustratius, and Leo Magentinus.
§ 27. With Abelard, the logic of Aristotle acquired a new
and powerful place in philosophy and theology. Though but
imperfectly acquainted even with the logical treatises of Aris-
totle, and ignorant of Greek, such was the force of his charac-
ter, that he sought on the one hand to widen logic so as to be a
method of real truth, and on the other to apply it to theology
as the regulator and even judge of its coherence and content.
His teaching at Paris was the most powerful factor in the
European thought of the age. It marked the commencement
of the spirit of modern inquiry, the piercing through the
B
18 INSTITUTES OF LOGIC.
forms of words and facing the reality of things. The ques-
tions of Nominalism and Realism are in another form chiefly
the modern metaphysical questions. John of Salisbury (d.
1180), the disciple of Abelard, defended logic in his Meta-
logicos, and showed a knowledge of the whole of the logical
treatises of Aristotle. Up to this period only certain of those
treatises were known in Western Europe. Hence we have
the designations of the Old and the New Logics. The result
of the most recent investigations on this point seems to be,
that, until nearly the middle of the twelfth century, the only
logical writings of the ancients known in the middle ages were
the Categories and Interpretation of Aristotle, as translated by
Boethius ; Porphyry's Isagoge, in the translation and com-
mentary of Victorinus and Boethius, the works of Marcianus
Capella, the Principia Dialectical of Augustine, the Pseudo-
Augustine on the Ten Categories, and Cassiodorus, and cer-
tain of the writings of Boethius (cf. Ueberweg, Logic, § 21 Hist,
of Phil.) The Categories and Interpretation, with the Isagoge
of Porphyry, formed the Logica Vetus. The Analytics, Topics,
and Sophistical Elenchi were as yet unknown, and when intro-
duced about the middle of the twelfth century, constituted the
Logica Nova.1 These were known only in translations. It
was not until after the taking of Constantinople by the Cru-
saders, in 1204, that the Greek texts were obtained. The
Logica Nova must not, however, be confounded with the Logica
Moderna or Tractatus Modernorum. This arose from the Sum-
mulce Logicales of Petrus Hispanus, who died as Pope John
XXI. in 1277. The SummuUz consist of seven Tractatus. The
seventh is entitled De Terminorum Proprietatibus, called also
Parva Logicalia, and is mainly grammatical, developing,
among other things, the doctrine of Suppositio. This was
the specific doctrine of the Moderns and of Modern Logic. In
this work of Hispanus appear for the first time the well-known
mnemonic lines Barbara, Celarent, &c. That they are original
to Hispanus, or at least were first given in the Summula,
there can be now no doubt. For it is now certain that the
Synopsis Organi attributed by Ehinger to Michael Psellus (the
younger) was not by him at all, but was simply a translation
into Greek of the work of Hispanus (see Hamilton, Discussions,
i See Questiones Magistri Johannis Versoris in Totam Novam Logicam.
Cologne, 1497.
HISTOEICAL NOTICES. 19
p. 128 and 671; cf. Ueberweg, Logic, § 22; Hist, of Philosophy,
i. p. 404 ; Saint Hilaire, De La Logique d'Aristote, ii. p. 160,
on the other side). The rough version of the mnemonic lines,
given on the margin of the Epitome Logicce of Blemmides, is
obviously a copy of the Latin of Hispanus.
§ 28. It was not until towards the end of the twelfth
century that the other works of Aristotle were introduced into
Western Europe. This was due to intercourse with the
Arabians, mainly through the Crusades. The Arabians had
been for centuries diligent students of Aristotle. Alkendi
(fl. 800), Alfarabi (d. 954), Avicenna (980-1036), Alghazel
(1072-1109), Averroes (d. 1206 or 1217), were all distin-
guished names in this line. Averroes translated and com-
mented on the whole logic of Aristotle, and divided with
Alexander Aphrodisiensis the title of the Commentator.
In the reign and by order of the Caliph Abdallah alMamon,
about 819 a.d., the works of Aristotle were for the first time
translated into Syriac by Joannah Mesnach, Christian of the
sect of the Nestorians. They were translated a second time
into the same language by Honain and his son Isaac, who also
professed the doctrines of the Nestorians, and lived at Bagdad
in the beginning of the tenth century. After them came the
Arabian translators and commentators, — a school of Dialectic,
frequently mentioned by Moses Maimonides and the other
Spanish rabbis under the name of Medabrim, speakers, dialec-
ticians. The matter of their teaching was the Organon, with
the Introduction of Porphyry. The Jews translated into
Hebrew the lessons of their Arabian masters. Maimonides
wrote an abridgment of the Organon in Hebrew, very precise
and clear, under the title of Vocabulary of Logic. This was
translated in 1527 into Latin by Sebastian Munster. Another
Hebrew translation of the Organon is — Hebraica editio universal
rei logical Aristotelis ex compendiis Averrois, Rivm de Trento,
anno MDLX. — (Cf. Franck, Logique, p. 248, and Jourdain,
Sur Aristote, c. iii.)
The Arabians brought their learning, with the Aristotelic
works and commentaries, into Spain ; and their doctrine
flourished in the Universities of Cordova, Seville, and
Grenada. Amid the differences of religious belief, there
was thus formed between Mohammedan and Christian the
bond of a common philosophic culture and faith.
20 INSTITUTES OF LOGIC.
§ 29. It was from this importation into Western Europe of
the Aristotelic books that Scholasticism took its rise and im-
pulse ; and henceforward, with the temporary check of the
burning of the non-logical works of Aristotle in Paris in 1210,
in accordance with the demand of the Papal Envoy, Aristotle
reigned supreme in Europe, as logician and philosopher, the
Master of Human Thought, — his works " The Evangel of In-
telligence,"— until the gradual decay of his empire through
the Renaissance, the foundation of Modern Method by Bacon
and Descartes, and the Reformation. Albertus Magnus
(1193 or 1205-1280), in full possession of the Aristotelic
works, and with a thorough mastery of them, as shown in
his commentaries, was the man who, by his writings and
teachings in the University of Paris, then the centre of
intellectual influence in Europe, laid the foundations of the
Aristotelic empire, which, lasting for four centuries, moulded
the European mind and languages, united the nations of
Europe in common intellectual conceptions, — formed, in
fact, modern intelligence on its side of clearness, distinct-
ness, and connectedness. For true it is that the moulds
even of that science and of that thought which repudiate
Aristotle are his creation. " The dialectic," says St Hilaire,
" which presided over the infancy of the European sciences,
has permeated our entire civilisation. The logic of Aristotle,
though dead in the schools, lives in the general thought
which it has so greatly contributed to form and to instruct."
§ 30. The scholastic study of logic, and, in most cases,
the application of logic to theology, were carried on through
Thomas Aquinas (1224-1274), Nicephorus Blemmides (fl.
1254), Duns Scotus (1275-1308), Walter Burleigh (1275-
1337), Petrus Hispanus (Pope John XXL, d. 1277), Georgius
Pachymeres (d. about 1310), William of Occam (d. 1343 or
1347), John Buridanus (alive in 1358), Cardinal Bessarion
(1395-1472), George of Trebisonde (1395-1486), Laurentius
Valla (1408-1457), Rodolf Agricola (1443-1485). In the
critical period of the Renaissance we have Ludovicus Vives
(1492-1540), Peter Ramus (1515-1572), James Zabarella
(1532-1589).
§ 31. The criticism of the Renaissance was the prelude
to a period of violent, and not particularly discriminate,
attack on Aristotle. The new philosophic spirit, and the
HISTORICAL NOTICES. 21
Keformation movement, were hostile to his authority ; the
mystics of the time were likewise opposed to his definite-
ness of form ; he was attacked by Vives, Ramus, Gassendi,
Gerson, Nizzoli, Patrizzi, and Luther ; then by Bacon, and
virtually by Descartes. But in the end, and very shortly,
it was found that the method and discipline of the logical
treatises could not be dispensed with by any school or sect,
philosophical or theological ; and all the essentials of the
logical theory were readopted by the followers of those who
had assailed it.
§ 32. There were two things which led to the passionate
revolt against the Aristotelic logic in the sixteenth and seven-
teenth centuries. The one was the misapplication of its laws,
to some extent at least, as if aiming at positive truth or science ;
the other was the speculative misapprehension of its nature
on the part of several reformers, not excluding even Bacon
and Locke, as a method of real truth, whereas it but showed
the forms. The methods of Bacon and Descartes had totally
different aims from those of the Aristotelic logic ; yet these are
complementary, not opposed. The necessity of recurring to
the school logic was shown very shortly after the first im-
pulse of Bacon and Descartes had spent itself. Hobbes gave
us a logic ; the school of Descartes did the same in the Port
Koyal Logic of Arnauld ; the Reformation gave us the logics
of Melanchthon, Derodon, and Goveanus, — all essentially
Aristotelian. Kant himself only touched logic to recognise
that Aristotle had created a science which, in his view, had
neither advanced nor receded for twenty-two centuries. All
this clearly shows what is apparent, from the nature of the
case itself, that a logic of form and formal method is an in-
dispensable need of intelligence, and that the attempted sub-
stitution by Bacon of Induction for Syllogism proceeded on
a misconception of the province of the latter and its place in
the sphere of human knowledge. It might further be very
readily shown that Aristotle had a sufficiently accurate con-
ception of Induction as a real method.
The exception of the logical treatises of Aristotle from the
flames in Paris in 1210 is, as has been remarked, charac-
teristic of the history of those books themselves. While his
other writings have been repudiated or partly superseded,
the logical treatises cannot reasonably be either cast aside
22 INSTITUTES OF LOGIC.
or neglected. They are of universal truth and application.
They are indispensable to different nationalities and to varying
faiths. The Induction of Bacon and the Analytic Keflection
of Descartes alike need them. Modern science, in the person
of certain of its followers, is supercilious enough about them.
This only shows that these people do not know their own
origin, or appreciate their own needs. They act as scientifi-
cally in this as if they were to contemn the study of gram-
mar, because certain people have accidentally learned to
speak grammatically without it. Empirical accomplishment
is not a thing which modern science can consistently, with
its character or pretensions, afford to applaud or exalt above
methodical culture.
§ 33. In the seventeenth century, the logic of Burgersdyk
(Institutionum Logicarum Libri Duo, 1626), especially with
Heereboord's annotations (d. 1659), is very valuable (Er-
meneia Logica, 1666). The influence of Descartes is recog-
nised in the logics of Clauberg (1625-1665), the Port Boyal
(of Antony Arnauld, d. 1694). We find Leibnitz (1646-1716)
returning to precise views of the nature and laws of formal
Logic, and these were systematically developed by Christian
Wolf (b. 1679).
The logicians of the eighteenth century on the Continent
worthy of note are Leclerc (d. 1735), after Locke ; Crousaz
(d. 1748), after Leclerc ; Ploucquet (d. 1790) ; Wyttenbach
(d. 1820).
The short treatise of Kant on Logik first laid down pre-
cisely the lines of the science, as a body of formal doctrine,
in the terms since accepted in modern philosophy.
§ 34. The logicians of the Kantian school, more imme-
diately related to Kant himself, are Jacob, Kiesewetter, Hoff-
bauer, Maass, Krug, E. Eeinhold, Twesten, Bachmann, F.
Fischer. Fries and Herbart follow the same line, with im-
portant independent investigations and contributions to the
science ; and connected with Herbart are Drobisch, Harten-
stein, Waitz, Allihn. — (See Ueberweg, § 29, p. 60.)
§ 35. Since the time of Kant, in Germany, Fichte and
Schelling have done nothing in formal logic. Hegel recog-
nised the value of the Aristotelic treatises, and gave a certain
impulse to the study of them. But, as has been said of
his own Logic, it has nothing in common with Aristotle but
HISTOEICAL NOTICES. 23
the name. It is an ontology, to be criticised on its own
assumptions and method. Hegel has discussed Logic in the
Wissenschaft der Logik, 1812-16, 2d ed. 1833-34, and in the
Encyclopadie der philosophischen Wissenschaften im Grundrisse,
1817, Part I., §§ 19-244. There are three main points in
Hegel's view, as Ueberweg has thus succinctly put them : —
" 1°. He identifies the form and the most general content of
thought — i.e., what is regarded as logical with what is held
to be metaphysical. But even supposing these to be essen-
tially connected, they cannot be identified ; and, besides, their
proper scientific treatment demands two distinct sciences or
departments of philosophy. The discussions on Being and
Essence have no proper place in Logic.
" 2°. Hegel identifies the forms of thought with the forms
of existence, and regards the Notion, Judgment, and Inference
as of metaphysical or objective significance. ' The notion is
immanent in things, things judge and infer, the planetary
system, the state, everything in accordance with reason is
an inference.' There is in this simply an absence alike of
scientific and philosophical precision. The mind conceives,
judges, infers. Things do not, — they only show analogies and
correlations with these processes. They are like but not the
same." To be trained to think in a rut of this sort is, as
Fechner justly puts it, " to unlearn thinking."
" 3°. The dialectic method sets before it a false problem, and
solves it only apparently, (a) Pure thinking, — thinking that
does not depend on and relate to experience, to the matter of
outer and inner perception, — thinking in itself, — cannot pro-
duce human knowledge. This arises from the action of
thinking on the material of outer and inner perception. It
is this knowledge which Logic considers, not the (so-called)
working of thought in vacuo, (b) Further, the more ab-
stract and extensive notion cannot produce in the thinking
subject the more concrete and comprehensive. 'The pro-
duct,' says Beneke, ' cannot contain more than what the fac-
tors have given.' (c) The logical categories, as transferred
to reality, are hypostatised and treated as independent essences,
which are capable of a peculiar development, and of passing
over the one into the other. The outgoing in the objective
reality from Being to Nothing, and then to Becoming, and so
on to the Absolute Idea, is given as a timeless prim in the
24 INSTITUTES OF LOGIC.
development of nature and spirit. But such an outgoing is
utterly unthinkable." — (Ueberweg, § 31, p. 68.)
The chief logicians of the Hegelian school are Erdmann,
Kosenkrantz, Kuno Fischer. The chief critics of the Hegelian
logic are I. H. Fichte, Schelling, Trendelenburg, Kym, Lotze,
Chalybaus, George, Ulrici, Von Hartmann, Herbart and his
school.— (Cf. Ueberweg, § 31, 32.)
§ 36. Schleiermacher (DialeJctik, 1839) adopts the concep-
tion which makes the forms of thinking and knowing parallel,
while not identical, with the forms of real existence. The
notion and judgment correspond respectively to substantial
forms and to actions. He denies Hegel's doctrine that " pure
thinking " has a character or beginning distinct from all other
thinking, ordinary or reflective, and can arise specially for
itself. He properly makes human thought dependent on per-
ception. There can be no act of knowledge apart from two
functions, — the " intellectual " and the u organic." H. Eitter,
Vorlander, Beneke, Dressier, Trendelenburg, Hoffmann, Lotze,
Braniss, are all more or less related to Schleiermacher. — (Cf.
Ueberweg, § 33.)
Occupying a position intermediate between the Kantian
and Hegelian views of Logic are I. H. Fichte, Balzano,
Chalybaus, H. Ulrici, Katzenberger, Sengler, Friedrich, Von
Kirchmann, Seydel, and others.
In the Aristotelian line, yet with modern reference, are
Hagemann, Babus, Hoppe (Ueberweg, § 34, p. 72 et seq.)
§ 37. In France, during the eighteenth century, formal
logic was neglected, even despised. In the present century,
Cousin drew attention to it and its place in philosophy ; and
to his influence we may attribute the valuable and learned
works of B. St Hilaire on the Organon of Aristotle, — De la
Logique cFAristote, 2 tomes (1838), and his Logique cTAris-
tote traduite en Francais (1844), 4 tomes, and also Franck's
Esquisse ctune Histoire de la Logique (1838). Vacherot, Tissot,
Duhamel, Waddington, Duval-Jouve, Pellissier, Delbceuf, are
the chief recent French logicians.1
§ 38. From the middle of last century down to a date well
past the first quarter of the present, the important branches
of Logic, Deductive and Inductive, especially the former,
1 See especially Keiffenberg, Principes de Logique (Bruxelles, 1833), p. 289,
for a Precis de V Histoire de la Logique, and p. 350, for Bibliotheqite Logique.
HISTORICAL NOTICES. 25
were imperfectly treated in the Scottish Universities, and
hence in Scotland itself. The Experimental Method of in-
quiry, as it was called, which, through the precept of Bacon
and the practice of Newton, had become dominant in Britain,
powerfully affected the habits of thought in last century in
Scotland. Its results were so great and brilliant, and its
promise so high, that there was an unreasoning reaction
against Deductive Logic, whereas all that really deserved
censure was its wearisome and fruitless application in books
to abstract terms and definitions. From 1453 up to the end
of the seventeenth century there had been a tolerably con-
tinuous course of instruction in the Aristotelic logic in the
University of Glasgow. What John Major had taught, even
Andrew Melville resumed and continued. The lingering
influence of this is seen in the teaching, but especially in the
text-books on Logic, of Gershom Carmichael (1672-1729),
and Francis Hutcheson (1694-1746). Carmichael's treatise
is entitled Breviuseula Introductio ad Logicam (1722); that of
his successor Hutcheson, Logical Compendium. Praejixa est
Dissertatio de Philosophies Origine, ejusque inventoribus aut
excultoribus prcecipuis (ed. 1759-1764).
Both treatises show an acquaintance with the Aristotelic
writings, accuracy and precision in the definition of terms,
and both bear traces of the advance of new doctrines on the
older stereotyped formulae, probably mainly suggested by
the Port Koyalists. We have in them distinctions set forth
which were subsequently lost sight of, and only revived and
scientifically applied in our own time, — such as the discrimi-
nation of Extension and Comprehension in notions, of Imme-
diate and Mediate Judgment involving Beasoning, and of
Immediate Judgments as abstract and concrete. Hutcheson
distinguishes with precision Sensation, Imagination, and Pure
Intellection (Pars I. c. 1.) Both treatises contain valuable
rules of Deductive Logic. The Elements of Logic of William
Duncan of Aberdeen are of but slight relevancy and value.
Even Dr Thomas Keid could speak of the syllogistic art u as
a mechanical mode of reasoning, by which in all cases truth
and falsehood might be accurately distinguished," * though
he has left us a very intelligent abridgment of the Organon ;2
1 Statistical Account of the University of Glasgow, Works, p. 735.
2 Works, p. 763.
26 INSTITUTES OF LOGIC.
and there is now evidence that in his teaching at Aberdeen
he gave considerable importance to Logic.
(a) In a MS. volume in my possession there is a short compend of
101 pages, entitled 'A System of Logic taught at Aberdeen, 1763, by
Dr Thomas Reid, now Professor of Moral Philosophy at Glasgow.' This
is obviously made up of notes of lectures given by Reid. It is full
and clear, and gives a very good view of Reid's opinions on Logic.
Reid refers under Simple Apprehension to the Predicaments and Predi-
cables, criticises Locke and Hume, deals with Judgment, Belief,
Evidence, Induction, and Method. (The part on Reasoning is not
given by the transcriber, on the ground that it contained nothing new.)
These lectures, in fact, contain the germ of the most important of the
new views of Reid, afterwards more fully developed in the Essays on
the Intellectual Potvers.
§ 39. Dugald Stewart echoes the crudities of Locke on the
subject of Deductive Logic, and seldom loses an opportunity
of speaking disparagingly of " the logic of the Schools."
Owing to a current of opinion of this sort, Logic as a science
and organic branch of Mental Philosophy ceased to be studied
in the Universities of Scotland. It was treated in a cursory
manner as an intellectual curiosity which had enjoyed the
attention of men in " the dark ages," but which must give
way to new and fresh studies conducted by the advanced
intellects of the time.1 The increase of the material of know-
ledge was regarded as all-important. It was forgot that the
science of method and form, — of the processes of the acqui-
sition and concatenation of knowledge, — cannot be set aside
without a disregard of the completeness and symmetry of
knowledge itself; that the assumptions of the scientific pro-
cesses need vindication ; that the processes and their results
need rules of purification, testing, and verification ; and that
Logic which deals with those points is not rendered super-
fluous, but only widened by the opening up of new spheres
of inquiry and science.
§ 40. It was not until Hamilton fully and lucidly set forth
the true character and place of Formal Logic as a depart-
ment of Mental Philosophy, in a contribution to the Edin-
burgh Review of 1833, that the study recovered its true posi-
tion in Scotland and in the Scottish Universities. Of the
influence of this remarkable essay, we could not have a better
1 There is a very meagre compend by Professor Jardine, Quwdam ex Logicce
Comjpoidiis Selectee.
HISTORICAL NOTICES. 27
illustration and evidence than in the Elements of Logic of
the late Professor Spalding of St Andrews (1857), one of the
ablest of our modern logics, and one which shows the high
tone of teaching in that ancient though small University
from 1845 to 1860, the recovery in fact of its mediseval
prestige. From 1836 to 1856, the period during which
Hamilton occupied the chair of Logic in the University of
Edinburgh, he developed in his lectures the science of formal
logic with a fulness, precision, and learning wholly new to
Scotland, -even to Britain. These lectures, published, after
his death, in 1860, represent the Aristotelio doctrines, the
Kantian point of view and some of its subsequent modifica-
tions, and, in part, the author's own new logical development.
§ 41. One of the earliest treatises which aimed at extend-
ing a knowledge of Hamilton's logical system beyond the
class-room, was an Essay on the new Analytic of Logical
Forms, by Thomas Spencer Baynes (1850), now Professor of
Logic in St Andrews. Mr Baynes is also the author of an
excellent Translation of the Logic of Port Royal (1850).
§ 42. The same influence which acted in Scotland ex-
tended to Oxford, and freshened the faded dialectic of that
University, as represented by the meagre and inaccurate com-
pend of Aldrich ; for the Outline of the Necessary Laws of
Thought, by William Thomson of Queen's (1842), now Arch-
bishop of York, and the able, learned, and valuable logical
writings of the late Dean Mansel are, with much that is
distinctively original, especially in the latter, the almost
direct inspiration of Hamilton. We have to thank Oxford
for Whately's Elements of Logic (1826), as one of the most
useful and practical books on the subject which we yet have ;
but Oxford has had to look to Scotland, rather than to its
own Oriel, for a systematic development of the science, and
for the learning needed to correct errors in its nomenclature
and history.
The most recent additions to the literature of Logic in
Scotland are by Professor Bain of Aberdeen, who has given
us two important treatises on Inductive and on Deductive
Logic. His Deductive Logic is marked by Mr Mill's peculiar
view of the syllogism, which need not at present be dis-
cussed. It is curious and interesting to find that one who
may be regarded as the most eminent of the school of Locke
28 INSTITUTES OF LOGIC.
in Scotland in our time, has written valuable works on that
department of philosophy which Locke himself so greatly
misunderstood and contemned.
Since the date of Hamilton's essay in 1833, and with it
the rise of an accurate view of the province of formal logic,
the revival in Britain of logical studies, deductive as well
as inductive, has been very remarkable. In Deductive Logic,
we have had the treatises of De Morgan, Boole, and Jevons.
Other writers in the department are Maccosh, Kidd, Morell,
Karslake, Milnes, Swinbourne, Abbott, Monck, W. G. Davies,
Alfred Sidgwick, Fowler, Stebbing, Hughlings, Poste, Venn,
Lindsay, and Bradley. The abridgment of Hamilton by
Bowen of Harvard is well worthy of notice and study.
One important function of this branch of literature is that
it serves to preserve the balance and the symmetry of human
knowledge, aids reflective thought, gives us a width of vision
over the realm of science, otherwise unattainable, and thus
helps to save us in a measure from the besetting sin of
modern intellectual habit, blinding specialism.
29
CHAPTEE IV.
TRUTH, AND THE RELATIONS THERETO OP LOGIC — DEFINITION
OP LOGIC.
§ 43. While Truth in general may be regarded as a har-
mony or conformity between thought and reality, or more
precisely, between thought as representative and fact as
given in intuition or presented, it is to be observed that the
consciousness of truth as a mental act implies a synthesis,
or composition of notions or terms as one, or better as in
one.1
So long as notions or terms are in the mind apart
from this synthesis, we have not properly either truth or
error. And this applies equally to nouns and verbs, — for the
verb, apart from its relation to time or assertion, is essen-
tially an attribute or noun. Notions out of combination, and
combination as one, are merely representations devoid of
truth or error. The notion, for example, of goat-stag [rpay-
e'Aa^os) may be in the mind, but it is neither true nor the
reverse, until it is added that it is, or is not, either absolutely
or in some determinate time.2
A sentence even may be significant without being prop-
erly either true or false, as in the case of the expression
of a prayer or wish. The sentence which admits of truth
or error must be enunciative (d7ro<£avTiKos), — represent two
notions or terms as in or not in one and the same subject,
— in other words, affirm or deny.3 There is the assertion
of a relation of identity or congruity, or the denial of this,
between the notion or term spoken of, and that which is
1 SvVOeo-is tis 7)5»? vorj)jia.T<ov Sxrnep i'v oitwj'. 2 Cf . Aristotle, De Int. , c. i.
3 De Int., c. iv.
30 INSTITUTES OF LOGIC.
spoken of it. This synthesis of thought is expressed in that
form of words into which the verb enters, as Water cleanses —
man is organised.
§ 44. It may be a question as to whether, and in what
sense, concepts by themselves are true or erroneous. If con-
cepts be regarded as representative of reality or things, —
and such is their essential character, — then they may be
correct or incorrect representations. Man, animal, organised,
are concepts ; each contains a series of attributes, and they
have a relation to objects considered as possessing those
attributes. So all scientific concepts, — chemical affinity,
gravitation, &c. If they represent the attributes in the
objects of the class correctly, they are true ; if incor-
rectly or imperfectly, they are false or inadequate. This,
however, may be regarded as a potential truth or error.
Until the concept is declared adequate to the object of
the class, or until the attributes of a concept are actually
referred to the subject, they have but an ideal reality,
and cannot be said to be actually true or the reverse. Syn-
thesis, composition, the regarding as one of a plurality, —
the object and concept, the subject and attribute, — is essen-
tial to truth, — in other words, there is need of actual predi-
cation. The point to be kept in view regarding the concept
is, that it is not a mere work of framing or fiction at the
arbitrary pleasure of the mind, but determined and consti-
tuted by and in accordance with the nature of things. As
Aristotle well puts it, referring, however, actually to enunci-
ation, expressions are similarly true as things — '0//,ouos ol
Xoyoi aX.rj0€L's iocnrep to. Trpayfiara. — {T)e Int., C. ix.)
(a) The name of truth has been improperly given " to the mere
reality of existence, altogether abstracted from any conception or
judgment relative to it, in any intelligence human or divine. In this
sense physical truth has been used to denote the actual existence of a
thing. Some have given the name of metaphysical truth to the con-
gruence of the thing with its idea in the mind of the Creator. Others
again have bestowed the name of metaphysical truth on the mere logical
possibility of being thought ; while they have denominated by logical
truth the metaphysical or physical correspondence of thought with its
objects. Finally, the term moral or ethical truth has been given to
veracity, or the correspondence of thought with its expression." —
(Hamilton, Logic, L. xxvii. )
(b) He judges truly who thinks that what is divided is divided,
and what is combined is combined ; but falsely who thinks contrarily
DEFINITION OF LOGIC. 31
to things as they are. — (Met. ix. 10.) In other words, truth is not the
mere licence of thought, but lies in the act of thought, which is con-
formed to the nature or reality of things. Truth in modern language
is denned as the harmony of thought with the thing itself, or of the
subjective with the objective. — (Cf. Trendelenburg in loco.)
A true sentence is by no means the cause of a thing's existence, but
in some way the thing appears the cause of the sentence being true,
for in consequence of a thing existing, or not existing, is a sentence
said to be true or false. — (Cat. xii.)
It is the combination of our thoughts which gives us truth or error,
but the reality which serves as their basis is absolutely independent
of human thought. — (Be Anima, iii. 8, 432a, 11. Cf. Ibid. 6, 4306, 1.)
As Bacon puts it : " Scientia nihil aliud est quam veritatis
imago ; nam Veritas essendi et Veritas cognoscendi idem sunt, nee plus
a se invicem differunt, quam radius directus et radius reflexus." —
(N. 0., I. Aph. xiii.)
§ 45. Formal Logic, though concerned with truth, does not
consider all the laws, conditions, and methods through which
we are to reach the harmony of thought and reality, — the
principles, in particular, of observation, classification, general-
isation, induction of causes. At the same time, it is not to
be regarded as divorced from the conditions of our knowledge
of the real. The laws with which it deals relate to the form
and very possibility of our knowledge, and essentially to the
connection and development of our knowledge. They are
laws of the ideal possibility of an object of thought, of the
consistency of our objects of thought, and of the necessary
connections of the matter of our thought. Logic, as it has
been defined, is "the science of the laws of thought as
thought." * Other equivalent expressions are " the science
of the formal laws of thought," " of the laws of the form of
thought," 2 " of the necessary form of thought." 3
These expressions, when fully explicated, bring out the
essential character of Formal or Deductive Logic. For they
can be shown to contain the points (1) of the ideal possibility
of any object of thought, (2) the consistency of attributes in
an object, (3) the necessary implication of one judgment in
another, whether as in immediate inference or as in reasoning.
(a) By some writers Logic is denned simply as the Science of
Reasoning. This is inaccurate. It is the Science of Thought in its
three forms of Conception, Judgment, and Reasoning. These are all
equally forms of the same fundamental power, — that of Comparison.
1 Hamilton, Logic, L. i. par. 1. 2 Ibid., L. i. 8 Ibid., L. iii.
32 INSTITUTES OF LOGIC.
They are essentially related ; no adequate theory of reasoning can be
given without a previous consideration of conception and judgment.
Farther, the laws which regulate reasoning are already exemplified in
conception and judgment. This mistake of limiting Logic to the
theory of Reasoning was long ago corrected by intelligent logicians,
as Smiglecius, who maintains that neither Argumentation, as held by
Albertus, nor Syllogism, as by Sextus, nor Demonstration, as by the
Greeks, is the adequate object of Logic, but that this is found in the
three operations of the mind in as far as they are dirigible — qua dirigi-
biles, or capable of direction to an end. Dirigibility belongs to the
operation as such ; and through this quality only, through the abstract
laws and forms of the operations, can Logic be said to embrace all
things. — (Smiglecius, Logical Disp., ii. 9. 1.)
(b) This definition of Hamilton is related to the view of Kant as to
the sphere of Logic : Kant's view of General Formal Logic is that
it is the rational science of the necessary laws of thought, as these
refer to all objects generally, or all objects whatever. It is the science
of the pure form of thought. This science is divided into Pure and
Applied. Pure considers the Understanding in itself ; Applied deals
with the Understanding in its conjunction with the other faculties.
Pure General Logic is divided into the Doctrine of Elements and the
Doctrine of Method. Special Logic treats of the special methods of
the particular sciences. — (Cf. Logik, and Ueberweg, § 28.)
Kant's full conception of Logic is as follows : —
" Logic is a rational science, not only in respect of mere form, but
also of matter ; a science a priori of the necessary laws of thought,
not by relation to particular objects, but by relation to all objects in
general : it is, consequently, the science of the legitimate use of the
Understanding and the Reason in general ; science not subjective,
that is to say, executed not according to empirical principles (psycho-
logical), but science objective, that is to say, made after principles
a priori determining the manner in which the understanding ought to
think.
" If we make abstraction of all knowledge which we can acquire
only on occasion of objects, and reflect only on the use of the under-
standing in general, then we shall discover those rules which are
absolutely necessary under all relations, and without any regard to the
particular objects of thought, because that without them there would
be no thought. These rules may thus be considered a priori, that is,
independently of all experience, because they contain simply, without
distinction of objects, the conditions of the exercise of the understand-
ing in general, whether it be pure or experimental. Whence it follows
at the same time that the general and necessary rules of thought can
concern only the form, and not the matter. The science of these
necessary and universal rules is therefore simply the science of the
form of our intellectual knowledge or thought. We can thus frame
the idea of the possibility of such a science, in the same way as we
form the idea of a General Grammar. This contains but the simple
form of language in general, and not the words which constitute the
matter of languages.
LOGIC FOKMAL. 33
" This science of the necessary laws of the Understanding and of
Reason in general, or which is the same thing, of the simple form of
thought in general, is that which we call Logic." — (Logik, Introd., § 1.)
§ 46. Esser's argument, adopted by Hamilton, for the formal
character of Logic is in substance that, if the science were
to take account of the matter or objects regarded as realities,
it must either consider all cogitable objects, or some only. If
the former, it would be the one universal science, an impos-
sible science. If the latter — -if it were to take cognisance of
certain objects only on their real side, — it would do so arbi-
trarily, or without ground of selection. This would not be a
scientific procedure. Logic has thus no immediate concern
with that which is thought about. It is thus a science of the
form of thought.1
(a) No one has put this more clearly than Occam. Logic, he says, is
a rational science, dealing with those objects which cannot be without
reason, — not real, which refers to things existing apart from the mind.
Whether man be species, rational difference, white an accident, cannot be
determined by logic, because these points cannot be known apart from
a perfect knowledge of the nature of the thing signified by the subject.
There would thus be no perfect science of logic, unless the logician
knew the nature of all things — nay, unless he knew all the conclusions
and all the principles of all the sciences. Such propositions are only
pertinent to logic as a science, in the way of examples. — (Expos, sur
Procem. and Summa totius Logiccz, iii. 2, 22, f. 53. Prantl., Ges. d. Logik,
iii. 744. ) He also tells us that Logic is practical, inasmuch as it directs
the intentions of the mind, which are our own acts, such as judging
and reasoning, and not external things, unless in a secondary way,
which are beyond our power. — {Expos, sur Procem. Prantl., iii. 742.)
The part of logic which deals with the categories is speculative,
inasmuch as their objects are not our operations. — {Prced. Procem.
Prantl., iii. 743.)
Whether terms, propositions, syllogisms, which we make, exist
only subjectively in the mind, or in some other manner, belongs not
to logic to consider, but to metaphysics. — (Occam, Expos. Am.
Procem. Prantl., iii. 756.)
Again : It is incorrect to allege that some definition of man is
logical, some natural, some metaphysical, because the logician, since
he does not treat of things which are not signs, does not treat of man
nor has to define man, but has to teach in what mode other sciences
treating of man have to define him. The logician, therefore, ought
to assign no definition of man, except by way of example. — [Log.,
i. 26.)
(6) It was a question with the earlier schoolmen whether logic was
of things, or concepts, or words (de rebus aut de conceptibus out de
1 Logic, L. i.
C
34 INSTITUTES OF LOGIC.
vocibus). On this point, the more intelligent followed Avicenna
(980-1037), who held that the object of logic was concepts, but
concepts of the second intention applied to first (intentiones intellects
secundo, qua apponuntur intentionibus primo intellectis. — (In Metaph., i.
2, f. 70, v. A. Prantl., ii. xvi. 74).
Intentio, or intentio animce, is equivalent to ens in anima, conceptus
animce, passio animce, similitudo rei. Out of intentions is formed the
mental proposition (propositio mentalis). In the widest sense of the
term, it is that in the mind which is a sign naturally signifying some-
thing for which it can stand, or be substituted. — (Occam, Log. , i.
c. 12.)
In the stricter sense of the term, the first intention, or a concept of
the first intention, is a concept immediately abstracted from things ;
a concept of the second intention is a concept abstracted from the first
concept, or from first concepts. For the names of things existing
beyond the mind are of the first intention, as man; but concepts ab-
stracted from these are signified by names of the second intention, as
genus, species, subject, predicate, or, as Occam elsewhere puts it, strictly
speaking, the first intention is the mental name produced to stand for
its significate ; the second intention is the sign of such first intention.
As man, a first intention, is predicable of all men, so one common
intention, as genus, is predicable of several first intentions, animal,
stone, colour (Log., i. 12). Logic is of things of the second intention as
they are of the second intention, because in logic nothing is determined
concerning things or words unless by relation to second intentions {per
habitudinem ad intentiones secundas). Ens rationis is identical with
second intention. — (Expositio, s., Act. Vet., f. i. v. A. Prantl., iii. 579.)
The definition here given of Logic, as de rebus secundm intentionis, tit
sunt secundai intentiones, is even in its terms equivalent to the definition
as " the science of thought as thought," or the science of the form of
thought. Intentionalk, intentionalitas, may be translated by formal and
formality.
Intention, says another schoolman, is the same as concept. The
concept of the first order or intention is that which the intellect forms
about things while not reflecting upon its own concepts ; second inten-
tions are concepts of the second order, which the intellect forms by
reflecting and returning upon its first concepts. All those intentions
of this sort are in the category of relation. Universality is a universal
relation to the particular, and particularity is similarly to the universal,
and affirmation and negation are relations, relations of extremes, —
(Petrus Aureolus, Sent. L, Dist. 23, art. 2, p. 539 A. Prantl., iii. 322.)
Syllogism always indicates relation, and it may be alleged that the
syllogism is expressed relatively to the conclusion. — (P. 541 A.)
(c) The older logicians came very near the definition of the text, even
in words. Thus Smiglecius (Log. Disp., xii. p. 451, ed. Oxon. 1658)
tells us that the term, both subject and predicate, is the matter of the
proposition (materia propositionis), but the formal mode (ratio) of predi-
cation is in the verb. The term is the material predicate, the verb
the formal, because it is predication itself.
Albertus Magnus says that because he speaks of the simple syllogism,
LOGIC FORMAL. 35
which is only formally syllogism, and holds in every matter, and is
peculiar to no matter, he uses transcendent terms signifying nothing
and all.— (Anal. Pr., i. 9, p. 298 A. Prantl., iii. xix. p. 106.)
§ 47. The actual inseparability of the form and matter is no
argument against the abstract consideration of the former
by Logic. In this, Logic demands nothing which must not
be conceded to science in general. Extension and Colour are
actually inseparable ; yet Mathematics considers the former
apart from any regard to the latter. Each diagram drawn
and imagined must be coloured, and this in no way affects
the mathematical process or proof. So it is with the logi-
cal consideration of form apart from matter.1
§ 48. It follows from the formal character of Logic that it
is not an organon of science, — that is, an instrument for the
discovery by observation, generalisation, induction, of facts
and general laws. Logic can but form part of a science ;
it cannot anticipate its matter — i.e., any fact in it. It does
not extend knowledge, but seeks merely to put what we
know in accord with the forms of the understanding.2 Its
main functions in relation to knowledge are to preserve self-
consistency, and to secure necessary evolution. We can thus
determine precisely in what sense Logic is an organon or
instrument of science. Formally, one science is the organon
of another, when it determines the scientific form of another.
As it appertains to Logic to consider the general doctrine
of Method and of systematic construction, Logic is to the
sciences an instrument, but only a formal instrument.3 An
extension of any science through Logic is absolutely impos-
sible. By conforming to logical canons we acquire no know-
ledge, but are enabled to render what is already obtained
more intelligible, by analysis and arrangement. The logical
laws do not amplify science more than the grammatical laws
of a language discover to us what is written in the language,
without a perusal of the several writings themselves.4
§ 49. But while not an instrument of science, it is a canonic of
thought and science.5 As containing the necessary and uni-
versal laws, the violation of which renders the proper exercise
of the understanding impossible — that is, when thoroughly
1 Hamilton, Logic, L. ii. 2 Cf. Kant, Logik, Int.
3 Logic, L. ii. 4 Ibid., L. iii.
6 So called by Epicurus, and adopted by Kant.
36 INSTITUTES OF LOGIC.
analysed, the exercise of the understanding at all, — it is a
legislative science in the highest sense. Any so-called
thought, — be it a concept, a judgment, or a reasoning, —
which violates the form of the Understanding, ceases to be, —
becomes, in a word, nonsensical and merely verbal.
This is shown in detail, with the strictness of demonstration,
by the application of the rules of logical science to the various
products of the understanding — Notion, Judgment, Seasoning.
These special rules strictly form the fundamental laws of
thinking, and partake of a demonstrative character. The
special rules of Seasoning, for example, are but tests of
validity which, resting ultimately on the character and num-
ber of the primary laws of thinking, are deducible from them.
(a) On this head, Kant says that, as canon of the understanding,
Logic can borrow nothing from another science, or from experience. It
must contain only the pure a priori laws, which are necessary, and
which are the heritage of the understanding in general. This language
is misleading and exaggerated. Along with other expressions of the
same sort, it has led to the delusion that there is "a rational science,"
or science of abstractions ; and this has been employed to supersede
— even abolish — the reality from which the abstraction was taken, and
which alone gave it meaning. Logic is, in a sense, an abstraction from
experience, and can be nothing else. It is the science of what is neces-
sary in experience, and, therefore, universal. Our means of knowing
and testing the necessity of its laws are found in experimenting on
particular instances. The strength of the particular thought which
embodies truly a law is as great as the strength of the abstract law
itself ; it is only not so extensive as the law.
(b) " Ratio de suo actu rationari potest . . . et hsec est ars logica,
id est rationalis scientia, quse non solum rationalis est ex hoc quod est
secundum rationem, quod est omnibus artibus commune, sed etiam in
hoc quod est circa ipsam artem rationis sicut circa propriam materiam."
— (St Thomas, quoted by St Hilaire, i. p. 24.)
" Logica enim est omnium artium aptissimum instrumentum, sine
qua nulla scientia perfecte haberi potest ; quse non more materialium
instrumentorum usu crebro consumitur, sed per cujuslibet alterius artis
vel scientise studiosum exercitium continuum recipit incrementum. " —
(Occam, Procem. Sum t. Log.)
37
CHAPTEE V.
OBJECTIONS TO LOGIC AS A FORMAL SCIENCE — THE VIEWS OF
KANT, HEGEL, AND UEBERWEG.
§ 50. If Logic be, as Kant puts it, the rational science of
the necessary laws of thought, and as these have to do not
with particular objects, but with all objects generally, this
science cannot be said to be subjectively formal, or to be
divorced from any relation to objects, even real objects.
On the contrary, it embraces the most general aspects of
objects as these are actually and possibly cognised and cog-
nisable by us. These aspects, no doubt, are named forms
of thought, — our notions, judgments, and reasonings. But
they are also, in relation to intuition or perception, forms of
the realities, — the objects therein given. They are the ways
in which we may, nay, must, mediately represent to ourselves
what is given in the course of experience, through intuition.
If the forms apply to all objects generally, and to every object
indifferently, they ought not to be represented as having no
application to any object.
§ 51. Further, as it is very distinctly the doctrine of Kant and
of others on whom this exaggerated formal view is charged,
that the contradictory is necessarily non-existent, — unreal as it
is nonsensical, — it can hardly be fairly maintained that the
logic they teach is abstracted from any relation to objective
existence. Kant's vital mistake lay in regarding the laws of
thought as of a wholly subjective character, and in restricting
in the Logic as elsewhere what is necessary in thought to
a purely subjective function, — a function of constitution,—
whereas they represent but one side of a coincidence between
human thought and divine thought as embodied in things.
38 INSTITUTES OF LOGIC.
The true conciliation of the Kantian and the realistic view is
to be found in the principle that the understanding is appre-
hensive as the intuition, — apprehensive, to wit, of relations,
as the latter is of the terms of the relations.
§ 52. We may go quite beyond saying that we have only to
do with the consistency of our thoughts. We may quite well
hold that this consistency is essential, negatively, to truth of
fact, — and we may even vindicate the many connections of
Identity and Non - Contradiction as correspondences to the
actual connections of things. For these may be denied, and
spoken of as " not absolute," — that is, the actual oppositions
of experience may be denied to be such, because it is assumed
that behind this experience there is some one thing, or force,
or entity which, being one, manifests itself in all. This, even
if it could be proved, could not be shown to abolish the defer-
ences in time or as we actually perceive things.
§ 53. There is the view of Hegel, which, assuming the identity
of thought and existence, identifies the laws of thought with
the laws of being, or the forms of thought, as he interprets
them, with the forms of being ; then describes a certain pro-
cess of so-called self-development of pure thought as also the
process of the self-production of existence ; identifies (or con-
fuses) the form and the matter of thought, professing to
evolve the latter out of the former as a pure evolution, apart
from intuition or experience. This may be called the meta-
physico-logical theory. But, in point of fact, there is nothing
in its method in the least analogous to any recognised logical
law ; in fact, there is, from first to last, an absolute, even
proclaimed, reversal of logical law, and thus of definite intel-
ligibility, even rationality.1
§ 54. This is not the place to enter into a full discussion of
the Logic of Hegel, what may be called Speculative Logic.
This would involve a discussion of the whole principles of his
philosophy. But I may indicate generally the nature of his
logical theory, and its relation to the Aristotelian. In Aris-
totle throughout truth is regarded as a relation, — a harmony
between thought or judgment, our judgment and reality.
The spirit of realism or dualism permeates the whole think-
ing of Aristotle, and no where is it more felt and seen than
in the Organon. The logical conceptions, forms, terms,
1 On this see Descartes, Introd., §§ xi. xii.
VIEW OF HEGEL. 39
laws, are taken directly from experience, and they are tested
by reference to experience. Aristotle is the most concrete
of logicians, in some respects the healthiest. His practical
sense is as outstanding as his unmatched subtlety. His con-
ception of truth as a relation or harmony between thought
and reality, it is the principal end of Hegel to break down.
With him there is no such distinction. There is no dualism,
either of man and nature, of subject and object, of spirit and
matter, of finite and infinite, of the real and the ideal, of man
and God. So that logic in his conception need not seek to
lay down criteria or rules for testing the true or real har-
mony of thought and things. There is no difference or dis-
tinction. And how does he proceed to show this ? Of
course, his process is that of Eeason, — the pure reason, —
pure thought. The idea in its total development. And
what is this ? In plain words, throw away man, nature, God,
— go back to the stage of thought in itself — pure thought,
objectless, indeterminate ; or as it is identical with being, go
back to qualityless being, without mark, feature, or discrimen
of any sort, and you will get what will develop necessarily
into all truth or reality, for these are but names for the
same thing. This is thought in itself; the bare form of
thought without object is your starting-point, — Eeason in its
first expression, Being in its primary reality. The develop-
ment of this prius of all is the dialectic process, — the march
of the speculative reason, the ongoing of the speculative
logic. It makes, it is, in its course, man, nature, God, —
all being ; it is in its course all truth. " What is rational is
real; what is real is rational." And this is the rational ; this
is the real. In the march — the wonderful march of the Idea
— from in selfness, which is not yet even conscious, and is
objectless, — from Being, which has not quality to distin-
guish it from nothingness, — the Aristotelic Logic is com-
prised. It is a stage, an early stage of the course, which
is trampled out and yet absorbed. Aristotle represents the ab-
stract point of view, — the point of view of the understanding,
which still holds by difference and distinction and the laws
of Identity and Non-contradiction. Speculative truth, how-
ever, lies in the fusion of contradictories and the march of
universal identity. Yes is only yes as it is also no, and no is
only no as it is also yes ; and the truth lies in the yes which
40 INSTITUTES OF LOGIC.
is no, and the no which is yes. And we must not speak of
contradiction as "absolute"; it is only temporary; in the
real nature or truth of things opposites are one, and are only
as they are one. What, in this case, we may ask, comes
of moral distinctions? What, for example, of veracity and
unveracity? Are these simply temporal distinctions, to be
fused in a higher medium, since contradiction is not absolute
but perishable ? And what of man the worshipper, and God
the object of worship? When man worships does he wor-
ship only himself in another form ? And is this God ? Are
there two orders of truth? One in which there is difference
and distinction, another in which all this is abolished ? Then,
which is the true ? and who is to decide this question ? It
will be meanwhile more reasonable for us intellectually, and
better for us morally, to keep by the knowledge we have
than trust in the " Speculative Logic."
§ 55. The Idea is developed, or rather develops itself, from
stage to stage in virtue of its inherent power, — its being all
potentially, — though it is at the same time a perfectly quali-
tyless conception, — in three great lines, — Being, Essence, No-
tion, which of course come in the end to be the same. The
treatment of these makes up the Philosophy or Logic of
Hegel. And under the first two heads Hegel borrows the
Aristotelic and Kantian categories, and seeks to show how
they arise, move, and are transmuted. Under the third, —
Notion, — we have the Aristotelic forms, — Notion, Judgment,
and Eeasoning, taken up and dealt with according to Hegel's
conceptions. These forms are not in his view to be taken as
modes of our knowing merely or as representing reality.
They are " the living spirit itself of the reality, and nothing
in the reality is true except what is by those forms and in
those forms " (En., p. 161, 162). The notion is an abstraction,
but in its true concrete totality it is all that is. Judgment is
the identity of the general and the particular. Attribute is
only the general. The subject is the particular. The cop-
ula is their identity, — and so on. The outcome of the whole
matter is that there is but one reality, and that is the Idea
or Keason ever developing itself, absorbing its developments,
and so becoming enriched, and rising, we cannot say finally,
for there is no limit anywhere, but somehow and somewhere,
to the consciousness of itself, as God who manifests all and
VIEW OF UEBERWEG. 41
is all. This system here concerns us principally under the
third head of Notion, and the theory of contradiction, to
which reference will be made below. Meanwhile it is enough
to say that a system which alleges the law of non-contradic-
tion in reference to a definite concept or judgment not to be
absolute, i.e., that the statement is simply other than it is,
even not what it is, must imply that this very statement
is impossible ; for it cannot be made except in terms of a
definite proposition, and therefore, as at once alleging and
denying the very same point, cannot be made at all.
§ 56. Another view which professes to follow Aristotle in
substance is that of Ueberweg, who makes Logic " the science
of the regulative laws of human knowledge." He explains
his position thus. It is opposed to that of Kant " in the
thoroughgoing proof of the way by which scientific insight
is obtained, which is not brought about by a priori forms
of purely subjective origin, finding application only to phge-
nomenal objects present in the consciousness of the subject,
but is reached by the combination of the facts of experience
according to the logical rules which are conditioned by the
objective order of things and whose observance secures an
objective validity for our knowledge." x Ueberweg in this
view follows in the line at least of Schleiermacher (Dialektik
1839), Bitter, Vorlander, George, Trendelenburg, Lotze,
Beneke.
Ueberweg's view may be summarily stated thus : That
Logic is the science of the forms of knowledge in general,
of perception as well as of thought proper — mediate or repre-
sentative knowledge ; that the logical forms, or the forms of
knowledge — Intuition, Notion, Judgment, Inference, System
— correspond to, and are derived from the forms of real
existence, the metaphysical laws ; and that through the
harmony of the forms of knowledge with those of reality,
we obtain truth, material truth, or the correspondence of
knowledge with what actually exists, at least as a presen-
tation. This view approaches that of Aristotle. Aristotle
" finds the standard of truth in the agreement of thought
with what actually exists, which is the limit of science.
The notion rightly formed, corresponds, according to Aris-
totle, to the essence of the thing (ova-ia, or to ti r/v eTvai) ; the
1 Logic, Preface.
42 INSTITUTES OF LOGIC.
judgment is an assertion about an existence or a non-exist-
ence ; affirmation and negation correspond to union and
separation in things ; the different forms which the notions
take in the judgment (or the kinds of denotation of existences,
axvH-aTa r>7s Karrjyopca<s twv ovtwj/) determine themselves accord-
ing to the forms of existence ; the middle term in a syllogism,
correctly constructed, corresponds to the cause in the con-
nected series of real events ; the principles of scientific know-
ledge correspond to what is actually first in the nature of
things." (Cf. Met., iv. 7 ; ix. 10 ; x. 6. ; Categ., 12, 14 B, 21.)
Ueberweg develops his view more completely in § 36 et seq.
Those who, like Ueberweg, hold that there is a correspond-
ence between the logical laws and forms and the order of
things, do not dispute the psychological fact of the necessary
character in consciousness of these laws and forms. When
it is said that there is this correspondence between the law
in the consciousness of the subject, and the fact in the con-
stitution of the object, a reference is made to the origin of
the law as conditioned by the objective reality, and also as
expressing and representing that reality. These are no
doubt very important points ; but they are rather of meta-
physical import and significance than of logical. It is pos-
sible at least fully and scientifically to consider the nature
and number of the logical laws as in consciousness, the forms
of thought which flow from them, and their mutual relations,
without considering especially the origin of the laws, or their
representative character in relation to reality. Logic would
thus be a complete though an abstract science ; but not more
abstract, or less capable of concrete application than arith-
metic, which deals with numbers, their laws and relations,
apart altogether in the first instance from any conception of
their application, and apart also from the question as to the
origin of number, in, for example, the successive units of
time. We may thus deal abstractly with the laws of Logic
and their evolutions, without at all, as Kant is supposed to
have done, committing ourselves to the view of their purely
subjective character, or a purely subjectivo-formal logic.
§ 57. Besides, the question of the origin of the laws and their
precise metaphysical import may give rise to much doubtful
disputation, and must necessarily involve both psychological
and metaphysical theories, which, if kept up, as they need to
VIEW OF UEBEKWEG. 43
be, through a whole treatise of logic, may hamper greatly the
systematic development of the science. To confine Logic as
a science to what is common and universal in all human
thinking, whatever be. the particular psychological, meta-
physical, or moral opinion we hold, is to give it a good,
useful, and legitimate sphere. And so to treat it, does not
imply or demand a greater abstraction than is common in
kindred sciences. Besides, nothing could be of greater im-
portance than that varying thinkers should agree as to a
general science or canonic of thought for all actual and
possible matter of thought.
§ 58. It seems to me that the whole of Ueberweg's reason-
ing on this point is really guided by extra-logical considera-
tions. He holds a certain metaphysical doctrine of the truth
or agreement of intuition, inner and outer, with reality. He
holds distinctly that our internal intuition, or apprehension
of the states of consciousness and of Self, is identical with
the reality, that there is nothing in itself, self in itself or
phenomenon in itself, above and beyond the actual self and
phenomenon of conscious intuition, to which the latter have
to conform, in order to be real or true. He discards all this
superfine transcendentalism or verbalism. And very properly
so. He further maintains the reality of space and time, as
objects perceived, and not merely imposed on the matter of
perception, as actual precepts as well as the matter, or ele-
ments in the matter, and as objective, conditioning our
particular perceptions. He further maintains, on the ground
of analogy, the reality of minds similar to our own in this
world of experience, and on the same ground of analogy
he holds that individual intuitions in general arise out of the
original blur of perception, when man first begins to recognise
himself as an individual essence in opposition to the outward
world.
§ 59. The logical correctness of the application of this
form of knowledge is to be tested by the same criteria as the
truth of all those elements of knowledge which originate
in our internal, and go to complete our sense perception.1
The whole of this doctrine really is based on an unverifiable
trust in our faculties of intuition, a certain psychological
analysis of their declarations, and a certain metaphysical
i Logic, § 46.
44 INSTITUTES OF LOGIC.
theory founded partly on this analysis and partly on analo-
gical inference from it. But there is nothing here specially
logical, except the principle of analogy, the laws of which it
is the function of logic to investigate. There is also, of course,
the special application of the principles of reasoning in general
to certain psychological data. But to suppose that this par-
ticular realistic theory of inner and outer Intuition is the
essential basis of Logic, is to peril the whole character of the
science as a body of assured universal principles. We have
a much wider, and, I think, a truer conception of Logic as
a science when we leave those problems to psychology and
metaphysics, and restrict, really widen, Logic by regarding
it as the science of those principles which regulate our con-
ceptions of any sort, negatively by the law of non-contradic-
tion, and positively by the laws of necessary inference, and
which, while not assuming any special psychological or meta-
physical theory to be the true one, can yet, to a certain extent,
regulate all. Even Material or Inductive Logic, on which the
doctrine has the closest bearing, is independent of metaphys-
ical theories regarding the nature of reality, and the corre-
spondence therewith of human thought. All that it does or
needs to do is to seek causes and laws or uniformities. The
principles which regulate these, the tests of them, are very
much independent of our views as to the exact contents of the
notions and their relation to reality.
It is clear at least that on such a view of the sphere of
Logic, " the regulative laws " of which it is called upon to
treat must be of the most varied sorts. It must deal with
matter of fact in intuition, and its general laws of cognition,
with the necessary conditions, space and time ; it must deal
not only with the nature of conception, but with its relations
to actual existence, not only with the nature of judgment
as a process or product of cognition, but with the question of
its relation to things. These are the questions of Psychology
and Metaphysics. The theories, for example, of Descartes,
Locke, Berkeley, Hume, Condillac, Kant, regarding the ob-
ject of perception, and the process of perception, would all,
on such a hypothesis, fall to be reviewed and the true theory
given. The question of the origin of knowledge, the validity
of our primal beliefs, the nature of causality and substance as
forms of existence to which our knowledge ought to conform,
► VIEW OF UEBERWEG. 45
— these would be treated, as well as the laws of Inductive
and Deductive Inference. This is true even though we dis-
tinguish the several contents of thinking from the contents
of thought in general. This method can only lead to delay-
in the decision of the logical questions, to the confusion of
what may be truly dealt with on any theory of the universe,
real or ideal, with what is now, and may ultimately remain
doubtful and unsolved. Surely we may treat of what is
common in Concept, Judgment, and Inference, as we find
these in actual and necessary exercise, without waiting for
or even seeking for a settlement of all the possible ques-
tions, which may be raised regarding their origin, nature,
and relations to their materials or contents, considered as
objects of actual reality.
§ 60. The value of Ueberweg's doctrine lies in drawing
attention to the genesis or grounds of logical forms and
processes — viz., Conception, Judgment, Eeasoning. Why, it
may be asked, does thought take the forms of conception,
judgment, and reasoning? This is no doubt a question
preliminary to a study of the essential features and neces-
sary laws of those processes. To answer this question of
ground and origin^ we need to go back to psychology and
even to metaphysics ; for we first spontaneously conceive,
judge, and reason about the matter of intuition or experience.
In other words, we exercise definite acts of consciousness, in
the face of objects and upon objects. We affirm existence,
we distinguish the permanent from the passing ; we divide
or conjoin existences, and we connect these causally or uni-
formly with the other. Still these acts have what may be
called a logical side ; they have a community of character
subject to certain essential and necessary laws ; and these
we may study without specially considering whether the ob-
ject apprehended, conceived, and judged is real or ideal, and
what are the differences in the metaphysical characters of
the objects which form the matter of our knowledge. This
is truly all the formality which Logic need claim.
§ 61. But it may be asked, What precisely is the meaning
of the reference or relation in these cases ? How are they
related — the logical and metaphysical judgments — for ex-
ample ? Animal has organisation. This is Substance and
Inherence. This corresponds closely to the Comprehensive
46 INSTITUTES OF LOGIC.
Judgment. It is the logical relation of subject and attri-
bute. Again, fire burns. This is the relation of causality.
But the advantage of the logical expression is that it is more
general than either, and embraces both, and can be legislated
for as such. In fact, the logical relation means that there
are laws, possible laws, for predication whatever be the
ground of predication, or whatever be its specific relation
to the forms of reality.
§ 62. Further, this relation of Substance and Inherence,
or Substance and Attribute, is not the only possible form
of enunciation. We refer the subject to a class. We have
judgments in extension. This represents quite a different
relation in reason, or logically. The real relation here
symbolised is that of Kind and Species, or Species and
Individual in nature. Any given judgment is to be tested
as true or false by reference to the actual matter which it
embodies, the subject and class as these really are. But
logic, as the universal science of thinking, finds points in
common which can be legislated for in all class references,
just as it does in all references of inherence. And these are
dependent on the essential in the act of judging, and, there-
fore, indifferent to the matter judged. And what is more,
logic finds, in its higher universality, points in common
between the judgment of inherence and the judgment of
classification, and these, too, dependent on the nature of the
judging act, and is thus able to reach scientific precision,
necessity, and universality, and to lay down the laws or
conditions so far vof a valid act of judging. Logic has in
its proper or scientific character only remotely to do with
even the abstract metaphysical forms, — the Predicaments of
Aristotle, or the Categories of Kant.
§ 63. With regard to the Conditional Judgment — if A is, B
is — this may refer to the relation of Cause and Effect. But
in that case it would not be a strictly necessary inference, —
not properly logical. For we can only know the terms of
any causal relation by experience. It is, then, for us wholly
contingent. The relation itself of causality, — if an event be,
it has a cause, — is strictly necessary, but it can never warrant
us in determining a similar necessity regarding any special
instance of cause and effect, — regarding, in a word, actual
effects and causes.
VIEW OF UEBERWEG. 47
§ 64. When formal truth is represented as simply the
absence of contradiction — i.e., the agreement of thought with
thought — as consequent with antecedent, a question may be
raised as to whether we have in this agreement any ground
for holding it to represent material or real truth. We think
the consequent as dependent on the antecedent — e.g., the
motion of the tide on the position of the moon ; or the
responsibility of man on his possessing free-intelligence, or the
predicate of every one, as likewise the predicate of this or that
one of the class. The general answer to this is, that where
the antecedent is already found to be real — i.e., real as a
matter of fact, — the consequent as necessarily involved in it is
real also as a matter of fact. This holds in inference from
whole to part. If the whole, of which something is predi-
cated is, the part as involved in the existence of the whole
is justly credited as really possessing a similar predicate.
Valid or correct thought guarantees the connection between
the antecedent and the consequent ; and if the antecedent is,
the consequent justly drawn from it is also.
48
CHAPTEE VI.
LOGIC IS THE SCIENCE OF THOUGHT. SPEECH, THOUGHT, THINGS.
THE CATEGORIES OF ARISTOTLE AND KANT.
§ 65. Logic is the science of thought, not of speech. Logic
is from Xdyos, and this means thought and word equally, —
ratio et oratio. The thought indicated may be taken as mean-
ing intelligence or reason generally, or this or that intel-
lectual act, be it concept, judgment, or reasoning, as con-
trasted with its expression in words. Etymologically, Logic
may mean the science of the mental or inward thought, or
of the outward expression ; it may thus be the science of
thought, or of language, — Grammar. Omitting meanwhile
special consideration of the relations of thought and language,
Logic is not the science of language. It only indirectly
affords the main principles of Universal Grammar.
(a) Plato defined thought as the internal word, the communion or
dialogue of the soul with itself, — ivrbs rrjs tyvxys irpbs kavr^v SidXoyos
&vev (pwvrjs yiyi>6fievos.
A6yos, or discourse, with Aristotle is made up of the noun and
verb, and has its meaning through convention ; but each part has sig-
nificance, at least has simple expression. — (Z>e Int. c. 4.) A6yos and
other similar expressions in Aristotle appear with a clear grounded
reference to the mental acts, — the waG-hnara, — ultimately, in fact, to
the essence (t6 rl ?jv ehai). — (Cf. Met., ii. 4, 1029, b. 19.)
(b) The Stoics distinguished the \6yos ivtiidderos, and the \6yos irpo<po-
Pik6s. In later logicians this appears as the inward and outward word,
— as Discursus M entails and Discursus Vocalis. — (Wallis, Logica, P. I.
c.i.)
"Ita quamvis \6yos sua signification tam sermonem quam rationem
complectatur, tamen non a sermone sermocinalem, ut nonnulli autum-
nant, sed a ratione rationalem et Logicam appellandam existimo."
(Brevia et dUucida qucedam Proeludia de Divmone, Definitione, et Argu-
mentatione. — Auctore Joanne Hamiltonio Scoto-Parisiis. 1580.)
Logic was not applied by Aristotle as a name for the science which
LOGIC AND GRAMMAR. 49
he founded and nearly perfected. He had, indeed, no one name for it.
Analytic, as applied to the principal parts of it, is the widest term to
be found in Aristotle himself.
Cicero (De Fin., i. 7, 22) uses the term logica for the science. It is
in common use in this application with Alexander of Aphrodisias, and
even with Galen. It was probably due to the earliest Aristotelic com-
mentators, who employed it in opposition to the Dialectic of the Stoics.
— (See Boethius ad Cic, Top., p. 766. Cf. Prantl, G. d. Logik, i. 9,
p. 535.)
A late commentator on Hermogenes divided Logic into Dialectic and
Rhetoric. — (Cf. Prantl, ibid.)
(c) Aristotle speaks of those who contemplate logically (\oyiKws ^tv
Bewpowiv,~An. Post., c. 21, 88 b. 35). On this Waitz, following Philo-
ponus, remarks that rb avaKvriKuis is opposed t<£ XoyiKcis. The former
is an accurate demonstration, which depends on the true principles of
the thing itself, as opposed to that which is contained in a certain
probable ratiocination. Biese translates \oyiKws ' ' out of general
grounds," ava\vTiKa>s "out of the essential determinations of proof."
The logical is thus almost the same as the dialectical, or that which does
not belong to the truth itself, but to the art of discussion, by which we
defend an opinion either as true or false. Hence is clear the sense in
which the logical syllogism (Xoyiubs <rv\Aoyio-fj.6s) is opposed to true
demonstration (an6Sfi^is), although in some passages the logical, in
opposition to the rhetorical syllogism (enthymeme), may seem to
signify true demonstration. The logical is also opposed to the physi-
cal point of view, as the abstract to the concrete. Logical doubt
arises not from the contemplation of physical or singular things, but
from ratiocination. Hence, after Aristotle, Cicero opposes logic to
physical science, and calls logic that part of philosophy ' ' quae sit qua3r-
endi ac disserendi." — (De Finibus, i. 7. See Waitz, An. Post., 82 b. 35.)
§ 66. Logic is essential to Grammar, while Grammar is not
essential to Logic.
Grammar is the science of Speech, and Speech proper is
reached in the combination of words called the sentence.
That with which grammar begins is properly the sentence.
The sentence is speech completed or perfected ; it is the
oratio perfecta of the older logicians as opposed to the mere
term or oratio imperfecta. The analysis of the sentence by
grammar yields us the parts of speech. The phrase, parts of
speech, has no meaning except in relation to a whole of which
there are parts. The whole is the sentence, that is, com-
pleted speech.
Logic is not the science of speech or of the parts of
speech. It is not in any proper sense the science of ex-
pression. It is the science, within certain limits, of that of
which speech is the expression. It is in fact the science of
D
50 INSTITUTES OF LOGIC.
thought, — of that indicated by the Term, the Proposition, the
Keasoning. As the sentence is the unit of speech, that with
which grammar begins, the Concept or Notion is the unit of
Logic, that with which Logic begins, but with which it does
not terminate.
§ 67. It is true that the principles of Logic are ordinarily-
proceeded upon in all thinking, in all reasoning, and they are
embodied in every civilised language. But they are not ex-
plicit in the consciousness of the individual, and they lie
scattered in language. Language testifies to their reality and
their use, but no mere study of language could give us a
scientific Logic. This can be reached only by a study of that
consciousness which underlies all language, that thought of
which language is symbolical. Language at the utmost can
but corroborate the analysis of thought, as it must in its
essentials conform to the constitution and laws of thought.
§ 68. Grammar is of use to Logic inasmuch as it offers to it
the forms of words in which thought is expressed, and thus
affords material for analysing and distinguishing the mental
laws embodied in speech, — the reflection of thought. But
Logic considers words only secondarily ; its primary object is
the concept expressed in language. Grammar considers ex-
pression ; and only as universal, not specific or of a particular
language, reaches universal laws. Logic, as dealing with
thought in its nature and laws, reaches a body of principles
common to all human thinking, whatever be the language in
which it is expressed.
§ 69. Logic throws light on grammar, in respect of (a) the
construction and nature of the sentence in all its forms ; (b)
the nature of predication ; (c) the relation of the adjective to
the noun, as a process at once of limitation and increased
attribution, and in respect of other essential points. There
can, indeed, be no true or thoroughgoing science of grammar,
which is not founded on sound logical principles.
§ 70. It is obvious that the parts of speech, if significant at
all, must represent forms of the logical consciousness. And
we may approach the classification of the parts of speech
either from the empirical manifestation of them in language,
that is, by observation and classification ; or we may approach
from reflection on the inner or logical side of the mental
forms which they represent.
THE CATEGORIES OF ARISTOTLE. 51
The grammatical distinctions of the parts of speech cannot
be thoroughly or profoundly studied from the purely empirical
side, that is, from the fact of their manifestation in language.
They exist simply as symbolical of inner or mental forms ;
and it is in these and in their mutual relations that we are to
find the true principles of the science of grammar.
Aristotle has very properly distinguished these points in the
relations of symbols to things, — viz., writing, which represents
words ; words, which represent conceptions ; conceptions,
which represent things.1
With Aristotle ipixrjvua means every expression of thought,
especially expression by the word. This expression may be
simple or combined, as the term or the judgment. In the
Categories, Aristotle considers words singly or apart from
their combination (avev o-u/attAok^s). — (Cat, 2 p. 1, col. a. 1. 16.)
In the De Interpretations, he treats of them in their com-
binations.
He appears very distinctly to look at the parts of speech
from the logical or reflective point of view. He tells us that
the word is the representation of an affection of the mind, just
as writing is an image of the modifications of the voice. He
further grounds the mental form or modification, as is his
consistent doctrine alike in the Categories and Metaphysics,
on things or objects, and on the various forms of existence.
The forms of thought and the things of which thoughts are
the similitudes (oyaoioytara) are the same for all men. Lan-
guage, like writing, varies. — (Cf. De Interpretatione, c. 1.)
(a) The precise relation of Logic, alike to thought and things, is
raised by the doctrine of the Categories of Aristotle. It is, therefore,
necessary to try to put this doctrine properly, as the question is still
of interest to us, as well as of importance in respect of the Aristotelic
theory itself. The place even which the theory of the Categories has
historically occupied in Logic necessitates its consideration.
The synthesis (av/AirXonJi) of terms is, as we have seen (p. 29), essen-
tial to truth. But what of the facts or elements of the synthesis ?
Dissolve the synthesis, and you have certain elements called by Aris-
totle Categories (narriyopiai). These are incomplex elements, out of
which affirmation and negation are constituted. — (So Occam, Logic, i. 4 1 . )
They are ten in number, — viz., oixria, irocrSv, iroi6v, wp6s tj, irov, irtfre,
Kuo-dai, ex^iy, iroiuv, irdcrxeiv- Boethius translated these : Substantia,
Quantitas, Qualitas, Belatio, Ubi, Quando, Situm Esse, Habere, Actio,
Passio. With Aristotle Karriyopla means what can be enunciated or re-
1 Cf. De Int., c. i. — Pacius in loco.
52 INSTITUTES OF LOGIC.
f erred, or what can enter into relation, whether as subject or predicate.
Hence it was translated prcedicamentum by Boethius. Hence also the
word does not originally mean the ultimate classes of things or of
primary notions. — (Cf. Trendelenburg, Elem. Log. Arist., §3.) As ap-
plied to the ten words, its use is restricted. At the same time, as John
of Damascus puts it, these are the ten most general predicaments
under which is found every word simply said, that is, every categore-
matic word, which is neither affirmation nor negation. — (Cf. Prantl,
in. p. 373.)
In the earliest time of the commentators, there were three views as to
what the Categories were intended to denote. Their objects were
variously regarded as words, thoughts, things. Alexander and Eus-
tathius held the first opinion ; Porphyry the second ; Herminus the
third. Later, Boethius held them to be genera of things, with
a view "to comprehend the infinite diversity of things which cannot fall
under science in a few genera, and thus render that which, from its
incomprehensible multitude could not be known, subject to the mind
by the fewness of the genera." — (Ad Porphyr. a se transl., p. 75.
Cf. Prantl., i.-xii. 84, p. 683.) Occam, again, held that the aim of
Aristotle in the Categories is to discuss the first names of things, or
words signifying things, in so far as they are significant. Aristotle,
he holds, is ignorantly supposed to be speaking of things, when he
is only speaking of words and their corresponding concepts. There
is no proposed division of things beyond the mind ; for the categories
are not predicable of these, but only either of words, or concepts, or
conventional signs. There is no substance existing beyond the mind,
except individual substance. — (Cf. Prantl, iii.-xix. p. 866.)
It is clear that whatever be the ultimate application of the catego-
ries, they are originally borrowed from grammatical distinctions. As
Trendelenburg has pointed out, the first four genera are made up of a
substantive and adjectives and a comparative phrase ; the last four are
verbs, representing intransitive, active, and passive senses. The fifth
and sixth are adverbs of place and time. But while thus of gramma-
tical origin, Aristotle has so dealt with them as to apply them alike
to notions and things. They represent, in a general way, alike what
can be conceived, and what exists. They have, in fact, a grammatical,
a conceptual, and an objective reference. Aristotle was here, indeed,
faithful to the lines of his logical, even philosophical method, which
was to pierce through the external form of words to thought and reality.
Hence, in antiquity, Iamblichus was right when he said that the
categories regard at once words, thoughts, and things. If, he argued,
the words treated of have a meaning, then the categories cannot regard
words only. If the categories treat of things, then things are
designated not by the finger but by general ideas, and there is no ex-
pression of general ideas without the help of words. The categories
then treat of ideas or thoughts, but not of pure thoughts, but of
thoughts that repose on things, for philosophy is a study of things
which are, not of things which are not. He concludes, therefore, that
the end of the categories is the study of words, representing things by
the medium of ideas. David the Armenian puts this conclusion still
THE CATEGORIES OF ARISTOTLE. 53
more explicitly by saying that the end of the categories is the study of
the first form of simple words [i. e. , not yet formed into a proposition],
expressing simple things by the medium of simple thoughts, not special
or individual, particular or successive, but the most general. — (Cf. Pro-
legomena by David the Armenian to his indited Commentary given by
St Hilaire, Logique d'Aristot., ii., App., p. 523.)
It is clear, I think, that Aristotle regarded the logical processes or
forms, conception, judgment, syllogism, as based on corresponding
forms of real existence, on, in fact, the crxvtJ-aTa of the categories.
He teaches expressly that ovcria or substance, being proper, is above
demonstration, and yet is the foundation of it ; and that as demon-
stration keeps to it or is parallel with it, we have science proper,
necessary knowledge. This is substance regarded per se. Again, the
other half of knowledge, — phsenomenal knowledge, follows and corre-
sponds to the other categories, which may all be regarded as forms of
Being per aceidens, forms in which Being clothes itself. This is
virtually to say that the logical form in its utmost abstraction cor-
responds with the metaphysical form as discovered in the object of
knowledge, and regarded likewise in its highest generality. He even
says that it is for one and the same science to seek the general princi-
ples of Being, and the general principles of demonstration, and of the
syllogism which constitutes it, expressly, however, guarding against
the supposition that there can be demonstration of Being, while the
latter is yet the only foundation of demonstration. — (Met., v. c. 1,
1025, b. 14.) Being in itself belongs properly to substance. Being per
se or substance, is, moreover, the only true and real Being. Being as
attributed to the other categories, is to be taken only consequentially
(o«x' a.ir\ws a\\' liroyueVcos). — (Cf. Met. vi. 4, 1030, a. 22.)
Occam's view regarding the classification of the categories is that
of things taken simply, or without connotation, there are only three
supreme genera — viz., Substance, Quality, Relation. No quantity, he
holds, is in Aristotle's view, really distinct from substance and quality.
— (Logiea, i. 44. Cf. Prantl, iii. 372.) If genus be taken for every-
thing predicable for itself and in abstraction from another, then there
are ten genera generalissima.
It may be said that, properly speaking, ovcria is a subject, not a
predicate. But the truth on this point is, that ovcria is only second-
arily a subject ; it is a subject in reference to all the nine categories
which presuppose it, and which simply express it in its modifications.
Substance is primarily a predicate in respect of rb ov or Being ; it is
a KaTTjyopla tov Svrbs. It is the first determination of the to 6v, — the
first definitely cognisable conception of it. The genus Being is deter-
minately conceived as substance ; and this latter gives in contrast the
second substances, species and genus. Hence both Ens and Unum
were regarded by the schoolmen as transcendent, or above the cate-
gories. They are of the First Intention, and common to all ; and the
ten prsedicaments are inferior to Ens. As Occam says, we may doubt
whether C is A, or C is B, but not whether C is something ; ens is,
therefore, a common concept. — (See especially Occam, Log., i. 38, and
Prantl, iii. 370.)
54 INSTITUTES OF LOGIC.
Herein lies the point of connection between the metaphysic and the
logic of Aristotle. The categories are forms of predication ; but they
are forms of predication founded on the forms of being. The first
essential form of being is unity, the unity of the individual. This is
the subject alike of being and of thought, or assertion. And all the
genera or kinds of assertion are determined by and correspond to the
forms of being. These are attributions applicable to being, as their
subject either of inherence or of attribution. — {Categories, ii. 145.)
Substance (ovala), the individual, is with Aristotle the first sub-
stance,— first and supreme. It can neither be said of a subject, nor be
in a subject.
Second substance embraces species in which first substances are
(virapxova-iv)) and the genera of these species (ravTa re Kal to twv uSwp
tovtcov yevi)).
The first substances are the ground and principle of all the others,
for they serve as subject to all, either of attribution or inherence.
Without them nothing would be {nh ovaiwv ovv ruv irpdraiv ovaiSiv aSvvarov
twv &\\wv ti ilvai).
The species is more substance than the genus, for it is nearer the
first substance or individual. The species is to the genus that which
the first substance is to the species ; the species serves as foundation to
the genus (uiroKurai yap rb elSos t<# yevet). — (Cat., v. p. 2, a. 11.)
It is thus we find in the first determination of existence the type of
the logical subject, and in subsequent categories or forms of being
the type of the essence (genus) and species, or the judgment and
the principle of the syllogism itself, as the general applied to the
particular.
We ought to note the ambiguity in the term substance. Boethius
translated oha'ia. by substantia, in the sense that it stood by itself, or sub-
sisted apart, — as man, horse. Aristotle, too, denned it as that which
could not be referred to anything as subject, but as that to which other
things could be referred. This is its sense with Descartes and Spinoza.
As the species is so far exemplified in the substance, the term came to
mean the nature or law of the thing. This is more properly essence,
essentia, than substance. In this confusing sense substance is con-
stantly used in some modern systems. — (Cf. Trendelenburg, El. Log.
Arist., § 3.)
Substance or ovcria, as Aristotle understands it, is cognisable only in
the individual ; indeed, exists only in the individual. The individual
is the beginning of knowledge, and the only true point of departure for
Ontology. Substance cannot be really separated from the individual.
It is not materially distinct from it. Apart from sensible objects, sub-
stance is a mere abstraction. It is not a generality separated from all
things, and existing per se. It resides essentially in the lower species,
in individuals. Some, such as Plato, have wrongly attempted to
put general ideas above substances, in fact, to make them sub-
stances. But this is a mere aberration of the logical reason ; it is
AoyiK&s (t)tc7v. Let facts be appealed to, and there is no animal apart
from individual animals. The general rests only on the particular ; it
is never substance. Farther, the particular is known by perception,
THE CATEGORIES OF ARISTOTLE. 55
and the general by the reason in which it resides. The separation of
the general from the particular, since Heraclitus, has been the bane of
philosophy.
With Aristotle, the particular or individual (to. KaO' e/ca<rTa) is the
foundation alike of his theory of being and knowing, — Metaphysic and
Logic. — (See especially Cat. v. ) "With Plato the beginning is the general
and universal. The two are thus apparently diametrically opposed.
Further, being rightly interpreted means unity ; rb eV ical rb 6v —
are one and the same thing. There is no being without unity ; there
is no unity without being. The individual is the true point of depar-
ture, and it is the basis of genera and species. Being is truly only in
the individual. The individual is what it is, because it is one. — (See
end of Categories.)
What, therefore, is predicable of being is predicable of unity.
Unity is, in fact, in all the categories ; it is that of which they are
predicated.
(6) Kant has criticised the categories of Aristotle as empirical and
without order. — (Kritik, Trans. An., i. 1. § iii.) As for the first charge,
his own classification would have been greatly improved in number and
character by more careful analysis of experience. As to the second,
there can be little doubt that there is a certain reference to order
in the Aristotelic scheme ; and no doubt whatever that putting sub-
stance first is much more reasonable than the Kantian or any other
arrangement.
Kant is quite wrong in supposing that Aristotle called the categories
predicaments, or by any term precisely corresponding to this. He is
wrong in supposing that Aristotle added five categories to the original
ten, under the name of post-prsedicaments. — (Cf. St Hilaire, Logique
(VAristote, Pref., p. 83.) All this only shows how little he had read
either of Aristotle or of the history of philosophy after his time.
Kant's categories are the forms or frames under which things, or the
matter of knowledge, must come, in order to be an object of knowledge
at all, that is, intelligible. They are properly subjective and constitu-
tive of the objects of thought. Kant is quite wrong in supposing that
the aim of Aristotle in the scheme of the categories was the same as
his own in the table of the categories of the Understanding. Aris-
totle's reference is distinctly to things as they are, and as their reality
is represented in words, the most general words. With Aristotle
there is no idea of the constitution of objects ; he seeks to enumerate
the classes of things as existing.
The categories of Kant are professed to be " deduced," not to be
got from experience or in experience, to be of transcendental origin.
They are four in number — Quantity, Quality, Relation, and Modality.
Each of these is subdivided into three ; hence twelve species of judg-
ments, and hence twelve forms of judgment. They are simply bor-
rowed from the categories of Aristotle, which are misconceived by
him, and misapplied. They have no proper co-ordination or subordina-
tion ; some are involved in others. Relation is in all of them. They
betray the unfaithfulness of his method, however described, to the facts
of judgment and experience. His limitative judgment is a mere fiction,
56 INSTITUTES OF LOGIC.
resulting from a misconception of wherein negation in a proposition
truly lies. — (Cf. St Hilaire, La Logique iVAristote, Preface.)
The difficulties of the application of Kant's Categories to the matter
or possible objects are, moreover, insuperable. These cannot be applied
to this or that matter, with conscious discrimination, unless on the
supposition of the object being already constituted, and apprehended
as such, in accordance with the category, which is wholly opposed
to the idea of the constitution of the object by category. Indeed, the
difficulty commences at an earlier stage ; for intuition cannot put a
timeless matter into time, or a spaceless matter into space, far less tell
when time alone is to be applied, or both time and space. As has been
well said, the Kritik is really the romance of the Pure Reason.
On Hegel's misconceptions and misrepresentations of the Categories
of Aristotle, see especially Waitz, Organon, i. p. 272 et seq.
57
CHAPTEE VII.
LOGIC THE SCIENCE OF THOUGHT WHAT THOUGHT IS
INTUITION AND THOUGHT.
§ 71. As a term Thought is ambiguous. (1.) It is used as a
general name for every mental phenomenon as in conscious-
ness. In this use, it emphasises the fact of consciousness as
attaching to the mental phenomena in general. It thus em-
braces acts of Intellect, Will, states of Feeling and Desire.
Thought in this application is matter of the science of
Psychology.
(2.) Thought is used to denote all the acts of the Intelli-
gence or Cognitive side of consciousness, whether Percep-
tion, Memory, Imagination, or Understanding. As thus
used, it excludes Feeling, Desire, Volition.
(3.) Thought in its strictest sense denotes the Faculty of
the Understanding. Here it may be used to mark (a) the
Faculty itself ; (b) the Process ; (c) the Product of this
Faculty. These latter are the Concept or Notion, Judgment,
and Inference, including Eeasoning. This faculty has various
names, such as Comparison, Discursive Faculty, Aiavota,
Verstand. Logic contemplates Thought in the sense indi-
cated by this Faculty. It may be called Thought Proper.
§ 72. Intuition is the basis of all thought and of all know-
ledge of objects, whether of outer or inner experience, in so
far as objects are viewed as real. As to possible or ideal
objects or classes of objects, these too depend on intuition.
The limit of construction of the possible object, on its material
side, is the intuition, separately it may be, of the qualities
combined.
§ 73. Every intuition is distinct from every other. This is
58 INSTITUTES OF LOGIC.
founded on the condition of our experience of it — viz., time
or succession. The intuition of one moment differs from
the intuition of the next moment, by the element of succes-
sion, before and after. A continuous intuition is really a
series of intuitions repeated with more or less vivacity.
Even supposing the object of the intuition to be the same
or similar, the intuitions differ by relation to time, and in
respect to external objects in relation also to space.
§ 74. Intuition gives us a unity, the undivided unity of an
object in a given time, or time and space. Thought also
gives us a unity ; but this is a unity of identity or resem-
blance between things, or units numerically different. The
whole of intuition is a Singular ; the whole of thought is a
Universal. Even the combination of parts in intuition, for
example, surface or extension, is but an undivided whole
or singular ; for it is the percept of a definite time, or definite
time or place, and no other.
§ 75. Thought in its rudimentary form is Conception, and
this is the knowledge of the common or general in indi-
viduals, of the one in the many. It is the knowledge or
notion of the point or points in which a plurality of im-
pressions or objects to self-consciousness agree. This feature
of community, or generality of knowledge, is itself the com-
mon character of all the acts and products of Thought or
Understanding — viz., Conception, Judgment, Reasoning. To
know what Judgment and Reasoning mean, we must first
understand what Conception means. Let us illustrate mean-
while the first or rudimentary act of thinking — viz., Con-
ception.
§ 76. In this explanation will come out at least the logical
distinction between Perception or Intuition and Thought.
Let us take any object which is before us, any object of
the senses, say what we call a tree or a house. What ob-
ject exactly means it is not now necessary to consider. To
suppose that it means only impression on consciousness is
enough. We naturally speak of this as what we see ; we
suppose that we obtain all our knowledge of it from the
faculty of vision. The tree I see has a particular size, form,
colour, and shape of leaf. It exists now before me as I see or
perceive it. It is through the sense of vision, or perhaps
the sense of vision combined with the other senses, that I
WHAT THOUGHT IS. 59
apprehend those points about the tree. But supposing that
I get this knowledge from the sense or senses, is this all
which I know about the object before me ? Is this all even
which I say about it, when I call it a tree f If you reflect a
little, you will see that this question must be answered in the
negative, ere I think and say this is a tree. I have already
mentally compared it with other objects which I also call
trees ; I have found that it resembles those other objects ; and
I have already set it along with those other objects in my
mind ; in a word, I have assigned it to a class of things, — I
have classified it. But what does classifying imply ? It im-
plies that while assigning it to a definite class, I have ex-
cluded it from other classes to which an object might have
been assigned. I say it is a tree, — not a house, not a table,
not a chair. I have said further it is a tree — i.e., it is one
among many other trees. Now in order to do all this, I must
have more knowledge than I get in the single act of vision,
by which I see what I call the tree ; for this tells me nothing
but that the object exists before me, now and here. I must
have the knowledge implied in a class-notion, — I must have a
knowledge of the points of resemblance, or the common fea-
tures of all trees, — I must have a knowledge of the relation
which these objects bear to each other ; in a word, I must
have a notion, or concept, or general idea ; and in applying
this general knowledge to the particular case before me, I
apply or exercise thought, logical thought, in its most rudi-
mentary form. This apprehension of points of resemblance,
or of relations between objects, is not an act of sense, nor is
it an object of sense ; it is an act of the Intellect or Under-
standing, by which I break away from or rise superior to the
limitations of my sense knowledge. And this effort, this
rising to a knowledge of relations, renders judgment and
reasoning possible for us.
Its first result in language is the term or general term,
or common noun of our grammars. It is distinguished, of
course, from the singular term or proper noun. City is
a general term, because it is capable of being applied
indefinitely to the objects of the class. Glasgow or this
city are singular terms, because they denote only one object
of the class. Observe that term does not necessarily mean a
single word. Glasgow is a single word and a singular term ;
60 INSTITUTES OF LOGIC.
but this city is as much a singular term, because it is a phrase
which denotes but one object of thought. Whatever word or
set of words indicates the general in our thought is a Com-
mon Term ; whatever word or set of words indicates the
particular, or individual, or one in our thought, is a Singular
Term.
§ 77. There are thus two sides in knowledge or conscious-
ness. There is the function of the Sense or Perception which
notes the features of an object now and here 5 and there is
the function of Thought or Comprehension which grasps them
together by means of the Notion or General Idea, and classifies
and names the object perceived. The one is the intuitive or
particular side of our knowledge ; the other is the general,
even the universal. But for the latter power our sense
knowledge would be chaos ; we should simply be bewildered
amid recurrent and conflicting impressions from things.
What thought does in regard to ordinary objects, science
does in regard to other and more remote objects. It grasps
things by means of conceptions or notions, and laws ; holds
the variety in the unity of thought. It is in this sense, the
true and proper sense, that knowledge is power. It is the
power of the kingdom of man over the world.
§ 78. To explain this more fully, we may say that
thought, as considered by Logic, does not properly begin
until we have compared this thing with that other thing,
and found a point of similarity, — some common mark or at-
tribute. We now have in the community of the attribute
a class of things, either an actual class or an ideal class,
or both. We can now observe and note a third or fourth
thing as possessing an attribute or mark like that we already
know. There is thus a recognition, — the recognition of
similarity in the mark. Having noted and named the mark
lustrous, as in several metals we have seen, we recognise
it in other objects which come up in the course of observa-
tion; and thus know them as lustrous. So with any common
mark, or sum of marks once we hold them. I have in my
mind, as the result of comparison, certain marks which I
include in the name mountain, river, sea, tree. In forming
these, in grouping them, I have exercised thought. There
have been apprehension and recognition. And for the
future, on every occasion on which I recognise the marks as
WHAT THOUGHT IS. 61
in an object of experience, and thus call it a mountain, river,
sea, tree, I also exercise thought. There is thus in every
object of our knowledge a twofold side. There is the appre-
hension of the object, as at this time, or at this time and
place. This is the individual and singular side of the ob-
ject, due to perception or intuition. There is further the
cognition and recognition of the thing as having a mark
or marks like what I already know. This is the universal
side of the object. I speak of this mountain, this tree. The
this indicates the individual or singular in my knowledge.
The mountain or tree indicates the common and universal
in my knowledge. These are really inseparable elements ;
but the one is intuition, the other is thought proper. This
distinction would still be preserved, if I were only to imagine
an object like a mountain or tree. There would still be the
individual side, — the image in my mind ; and the common or
universal side, — the recognition of the likeness in the mark
or marks. There would be an image and a relation of like-
ness conceived as manifested in this individual case, and as
indefinitely applicable to a plurality of similar cases. It is
now clear that we can speak of thought as the recognition
of a thing as through, in, or under another. When I re-
cognise in an object the attributes of life, sensation, and
motion, I know the object for what it is, an animal, and
I know it to be an animal, and not a stone, through these
marks. In this I have also recognised the object as under
a notion, for I have classed it as an animal, or put it under
the class animal, as one of the things included under or
embraced by the notion and name. Thought then as con-
ception, is a process of mentally marking things, and of
classing things by means of the marks.
§ 79. Conception is thus virtually a judgment. There are
two things in the mind, or rather in the indivisible con-
ception of the object. There is the thing and its mark or
class. When I expressly unfold this conception, consciously
set the mark on the object, or consciously set the object
under its class, I judge, I affirm, I conjoin object and mark,
or I include the object under the class notion. I say plant
has organisation. Metals are lustrous. When I proceed fur-
ther and conjoin two judgments, so that by necessary impli-
cation a third follows from them, I reason — As : —
62 INSTITUTES OF LOGIC.
All metals are lustrous ;
Iridium is a metal ;
It is lustrous ; or, iridium is lustrous ; for it is a metal, and
metals are lustrous.
All these acts are the same essentially, whether Concep-
tion, Judgment, or Reasoning. They are all simply forms of
the power of Comparison. Logic is the science of thought,
in so far as this power is concerned.
(a) " On the material given or presented by Perception, that is
Sense, or Reflection, — Internal Perception, — the Understanding works.
It compares ; it recognises similarity or difference ; it conjoins and
disjoins material qualities. This is its first or primary function.
By comparing attributes, and finding a point of similarity, the one
in the many, it makes a concept. By joining or disjoining concepts,
it makes a judgment ; by comparing and joining or disjoining judg-
ments, it makes a reasoning. The essential point in all these acts is
the recognising one thing through or under another. Thought proper
is thus an act of comprehension, or a recognition of one thing as in or
under another. Thought proper is the cognition of one object of
thought by another, in or under which it is mentally included, — in
other words, thought is the knowledge of a thing through a concept or
general notion, or of one notion through another. In thought all that
we think about is considered either as something containing or as some-
thing contained, — in other words, every process of thought is only a
cognition of the necessary relations of two concepts." — (Hamilton, Logic,
L. iii.)
"All thought is a comparison, a recognition of similarity or differ-
ence, a conjunction or disjunction ; in other words, a synthesis or
analysis of its objects. In conception, that is, in the formation of con-
cepts (or general notions), it compares, disjoins or conjoins attributes ;
in an act of judgment it compares, disjoins or conjoins concepts ; in
reasoning it compares, disjoins or conjoins judgments. In each step
of this process there is one essential element ; to think, to compare, to
conjoin or disjoin, it is necessary to recognise one thing through or
under another ; and therefore, in defining thought proper, we may
either define it as an act of comparison or as a recognition of one
notion as in or under another." — (Logic, L. i. pp. 13, 14.)
(b) Hamilton insists strongly on the essential identity of Concept,
Judgment, and Reasoning, or rather, on the element of judgment as
common to all. ' ' Both concepts and reasonings may be reduced to
judgments. ... A concept is a judgment ; for, on the one hand, it
is nothing but the result of a foregone judgment, or series of judg-
ments, fixed and recorded in a word, a sign ; and it is only amplified
by the annexation of a new attribute through a continuance of the same
process. On the other hand, as a concept is thus the synthesis or com-
plexion and the record, I may add, of one or more prior acts of judg-
ment, it can, it is evident, be analysed into these again ; every concept
METAPHYSICAL CONCEPTS. 63
is in fact a judgment or a fasciculus of judgments. These judgments
are not explicitly developed in thought, and not formally expressed in
terms." — (Logic, L. vii. p. 117.)
§ 80. This is Thought, logical thought. But we must not
assume that there is no thought in the intuition or perception
which logical thought supposes, and which is its datum. We
cannot speak of this or that thing even, without thought,
that is, without implying and applying a general or universal
notion. Thing itself is general ; so is existence or being; so are
one and many, identity and difference. And these are implied
in the most elementary intuition. These refer, however, to
the nature and constitution of being, of things as they are,
or, at least, as they are known to us. And Logic does not pro-
fess to investigate the nature and genesis of these notions or
universals. This is the province of Metaphysics or of the
science of Being, its nature and conditions. Further, these
metaphysical notions are ultimately inconceivable, in the sense
of being inexplicable by anything beyond themselves, and
what transcends the explicable or conceivable transcends
Logic. Logic is thus a secondary science ; it is the science
of the conceivable and its relations. This it is necessary to
state, considering the very loose and ambiguous manner in
which Thought is used in current philosophical literature.
§ 81. These extreme metaphysical notions, such as being,
substance, cause, do not afford the means of distinguishing
the individual things of experience. Being is common to all,
and thus affords no distinction ; cause and substance are ex-
treme generalities. They do not help us to distinguish among
individual causes or among individual substances. Things
classed merely as one or many are not known in their essen-
tial properties, or in their distinctive marks. What we
desire to do by thought, after it has passed from the early,
vague, and indefinite consciousness of the world and its
contents, is to mark and group objects, to put them in
classes, and under special laws, to know things clearly and
distinctly, by means of resembling and differing features.
Logic legislates for all processes of this sort. It helps us to
classify, define, arrange, and systematise our knowledge.
§ 82. The only possible conciliation of intuition and
thought, in other words, of experience and abstraction, is
64 INSTITUTES OF LOGIC.
that, in individual instances, category, or what is after-
wards called category, is perceived or apprehended as fact or
object. Thus it is given as real, as real as anything we can
know. This holds of time and space, or a priori intuition,
and of all the possible categories. This, then, as a presenta-
tion, as an intuition of what is definitely real, is represented
by us in the form of a thought, conception, or abstract
divorced from a given time or space. But the representation
gives the presentation, the real ; and the forms of the thought,
the representation, give, in their most general aspect, the
actual facts. The forms might, indeed, be generalised, and
thus regarded as gatherings from experience. They are so,
but they are more ; there is a coincidence between the in-
tuition and the conception generally as to elements ; and
this means constitutional or a priori forms of intelligence,
as well as intuitional and a posteriori generalisation.
(a) This was the doctrine of Occam : —
"Intellectus noster pro statu isto non tantum cognoscit sensibilia, sed
etiam in particulari et intuitive cognoscit aliqua intelligibilia quae
nullo modo cadunt sub sensu. . . . Cujusmodi sunt intellectiones,
actus voluntatis, delectatio, tristitia et cujusmodi, quse potest homo
experiri inesse sibi, quae tamen non sunt sensibilia nobis. " — (Sent. Prol.,
qu. i. H H. Prantl, iii. 751). This may be fairly regarded as com-
prehending the relations, unpicturable, among sensible objects. He
tells us elsewhere, "The intellect not only cognises universals, but even
intuitively cognises those things which the sense cognises." — (Sent.
Prol., qu. i. LL.) First, I cognise some singulars in particular, intui-
tively or abstractively ; and this arises either from the object or from
the habit left over from the first act. After intuition, there follows a
second act, distinct from the first, terminated by some such objective
being (i.e., representative), as it first gave in the subjective being (i. e.,
in the subject existing) ; and that second act produces universals and
second intentions. — (Occam, Sent. ii. qu. 25. Prantl, 784.)
The universal is the first object in the primacy of adequation, not in
the primacy of generation. The object of sense and intellect is abso-
lutely the same ; but the singular is the first object of sense in the order
of generation. Singular means here one in number, and not a sign of
anything. Every cognition is both universal and singular ; but the
question regards cognition properly simple and singular. (1.) The
singular, thus understood, is the first known, because it is a thing out-
side the mind, and all outside the mind is singular. (2. ) This cognition,
as simple, singular, first is intuitive. (3.) The first abstractive cogni-
tion in the primacy of generation is not a cognition properly singular,
but common. Thus, that which from a distance causes sensation,
in virtue of which I can only judge that that seen is being, affords
ORDER OF THOUGHT. 65
the knowledge of being, and nothing lower (more specific), and, there-
fore, not properly a singular concept. Intuitive cognition is properly
singular, not on account of a greater assimilation to one than to another,
but because it is naturally caused by one and not by another. — (Quod.,
1. 911-13. Prantl, ii. 346.)
§ 83. The order and progress of thought in general is a
pyschological question. But the steps may be summarily
indicated. First, the lowest point from which consciousness
as thought can be conceived to begin, is the cognition of
an object as something, something not nothing. There is
apprehension and discrimination. This discrimination is two-
fold : (1.) Through the relation of the object as a form of
being to non-existence or non-appearance, or to other objects,
it may be, contiguous to it ; (2.) Through the relation of the
object to the knowing subject, as an object discriminated
from the knower. Secondly, This something or object is
necessarily apprehended as now, or as now and here — that
is, in time, or in time and space. It becomes this thing, the
thing of the present moment, as opposed to that, either past
or to come. Thirdly, It comes to be known as such or such
a thing ; that is, it is regarded as qualified, and so discrimi-
nated from other things otherwise qualified. Fourthly, It
comes to be known as one of many things ; it is quantified.
Fifthly, It comes to be known either as a permanent or as the
form of a permanent. This is substance, and substance and
phenomenon. Sixthly, It is known in relation to what pre-
ceded it, as in appearance a new form of being, conditioned and
determined by the preceding. This is the form, the relation
of causality, — causality within limited existence. These are
the main metaphysical relations of objects known as existing.
(a) As Occam puts it, the intellect proceeds from potency to act ;
hence no one understands any singular thing whatever, without imme-
diately understanding or being able to understand the most common
being (ens communissimum). — (Sent, i., Dist. 3, qu. 5, B.B. Prantl,
iii. 745.)
When it is said that our cognition begins with the more confused
and more universal, such confusion and universality do not exclude
singularity and designation (signationem) of actual existence in the
thing without, nor is it so confused and universal as to exclude here
and now, but rather to include them. . . . The universal which
we seek is of quite another character, because from its nature (ratione)
it excludes here and now, and designation and actuality of existence.
66 INSTITUTES OF LOGIC.
— (Duns Scotus, In de rer. princ., 13, 3 (vol. iii.), p. 118 A. Prantl, iii.
212, § 119.)
(6) Scotus points out three functions of the intellect in the cognition
of actual existence — (1.) contemplating the reality in the sensation (per-
ception); (2.) reflectively knowing that we know ; (3.) comparison of
the reality perceived with the universal for intellection. Thus white-
ness is not only actually, but it is also colour. — (In dt rer. princ, 13, 3
(vol. iii.), p. 112 A. Prantl, iii. 212, § 119.)
§ 84. Pure thought in the Hegelian sense, or the self-
sufficiency of intellectual power wholly freed from intuition,
or intermixture of organic function, is impossible. It is im-
possible to partition the unity or indeterminateness of ex-
istence into a plurality of distinct notions by means of mere
intellectual function.1 This in fact is equivalent to suppos-
ing that pure or mere Extension in thought can of itself
develop into Comprehension, that the attenuated abstract
can clothe itself in attributes, and so become concrete ; —
that what is not in the cause may yet appear in the effect.
This violates every principle of reason and intelligibility.
Equally baseless is the Kantian view of the outward, or
matter, as a chaos into which the mind is supposed to put
order and system out of its own subjectivity, or from the
spontaneity of the subject. Things are already conformed to
reason and order, and this arrangement is, or is apprehended,
in organic function.2
Unless there be a correlative order in things, and various
forms of that order, the subject is utterly incapable of order-
ing, or determining which kind of a priori form or category
ought to apply in any given circumstances. No application
of category is possible, unless on the condition of the appre-
hension as already existing of the kind or character of the
thing to be categorised.
§ 85. The growth of speech, like that of thought, shows a
progress from the indeterminate to the determinate, corre-
sponding to that of the logical consciousness. " Originally,
in every language, the sound, while significant of meaning
or attribute, indicated indifferently noun and verb, without
declension or conjugation. Parts of speech were thus not
originally discriminated by different words. Thus in the Indo-
Germanic language, the oldest form for the words which now
1 Cf. Schleiermacher, Dialektik, p. 106. 2 Cf. Ueberweg, Logic, p. 108.
THE GROWTH OF SPEECH. 67
sound deed, done, do, doer, doing, was dha (to set, do). This
was the common root of all the subsequent forms of the word.
The one form dha stood for noun, verb, adjective indifferently.
" In the second stage of the language, in order to express
distinctions, they repeated the roots twice, not yet supposed
to be words, along with another root, and linked them to-
gether into one word ; for example, the first person of the
present was dha-dha-mi.
" In the third stage, the elements were fused into one whole,
as dhadhdmi. In that earliest form dha there lay, as yet un-
separated and undeveloped, the different grammatical refer-
ences, their whole verbal and nominal modifications." l
How this separation and discrimination, the assignation of
different sound forms to different logical conceptions, arose,
and was perfected in a suitable and matured language, is
the problem of Comparative Philology.2
1 Schleicher, quoted by Ueberweg, Loyic, pp. 116, 117.
2 On the genesis of naming in reference to Concepts, see below, p. 104
et seq.
68
CHArTER VIII.
LOGIC THE SCIENCE OF THOUGHT, AS THOUGHT, OR OF THE FORMS
OF THOUGHT — WHAT ARE THE FORMS OF THOUGHT.
§ 86. While Logic is thus conversant not with Speech but
with Thought, it is not conversant with everything that is
implied even in Thought Proper. Every thought, whether a
Concept, a Judgment, or a Seasoning, may be viewed in two
aspects, — as to its matter, and as to its form.
The distinction between form and matter in general is one
not difficult to comprehend and illustrate. The form of an
object is, speaking generally, the mode or manner in which
its constituent materials have been arranged. The form of a
house depends on the collocation of the materials, as the form
of a statue depends on their moulding and arrangement.
The material of an object is, in a sense, the unessential part
of the object, seeing that the object itself might remain the
same — the same in form, and thus continue to be the object
it was before, a house of a particular kind, or a statue of an
individual man, even though the material were changed, say
from sandstone to brick, or from brass to marble. The form
is, so to speak, the essential part, that which makes the
object to be what it is, to belong to a definite class, and to
constitute a definite individual.
In analogy, to a certain extent, with this are the matter
and the form of thought. In every thought, be it a concept,
a judgment, or a reasoning, there is form as well as matter.
The form, moreover, is the essential part, that which gives
the thought its character, and which does not change with
a change of the objects or matter about which we think.
E.g., the matter of a judgment lies in the notions or terms,
MATTER AND FORM. 69
the form in the inclusion or exclusion of these terms.
Plant is organised. Here the notions plant and organised
constitute the matter ; the form is indicated by the copula
is, which marks inclusion. The form here makes, so to
speak, the thought, and the thought a judgment ; and all
that can be laid down regarding the laws of inclusion in
a judgment could be laid down regarding this and every
other instance of an inclusive judgment, although the terms
or matter were wholly different from the present one, and
from each other.
§ 87. It may be said further regarding matter and form in
logical thought, that the matter is given to or provided for
thought by other powers than thought itself, very much as
the material of the statue is provided to the artist ; so that
the form is not only what is essential to thought, but is
peculiar to thought. The form is the function or work of
thought. It is the product or result of the operation of
thought on the faculties of experience. This is expressed
otherwise by saying that thought is an elaborative power,
working on data presented to it. But this provision by
perception and memory of materials to thought, does not
imply the existence in the consciousness of the materials
prior to some act of thought ; all that is needed is that they
be simultaneous ; and it should be clearly apprehended that
thought does not create the materials. Nay, further, as will
be shown in the sequel, thought properly speaking, does not
create the form or general relations of the materials.
These relations of Conception, Judgment, and Eeasoning
are definite, necessary, universal ; they can be legislated for ;
they are subject to universal law ; the matter is not.
§ 88. Perhaps the nearest approach to this conception of
Logic as the science of the form of thought was the view
taken of it by the older logicians as the science of second
intentions applied to first. In a concept two degrees of
formality are distinguished. These degrees were named by
the older logicians the first and second intention. A notion
of the first intention is a notion viewed in relation to the
objects which it represents, — in its immediate class relation-
ship. Thus the concepts tree and bird are of the first inten-
tion, when they are regarded as representing the objects of
their respective classes, or as terms for a number of possible
70 INSTITUTES OF LOGTC.
objects. But notions may be viewed not only in relation to
the actual or possible objects which they represent ; they
may be considered in their own mutual relations. Thus the
notions tree and oak may be viewed not merely in relation to
the individuals of the class, but may be compared with each
other. Thus it will be found that tree is a wider notion than
oak, — is, in fact, the genus of which oak is the species, that is,
one of the classes which it embraces. We have thus a new
form of relationship between notions themselves. We may
contemplate this, and name it, making it an object of scientific
investigation. This relationship of notions to each other
was designated by the older logicians as the second intention
of notions. All the Predicables were thus regarded as notions
of the second intention, and Logic was defined as the science
of second intention applied to first, since the former classified
and regulated the latter.1
§ 89. Logic cannot embrace the matter of thought, — of the
concept, judgment, and reasoning. Indeed, no one science
can. For the matter is indefinitely, even, it may be, infinitely
various. There is matter of Sensation, Perception Outer and
Inner, Imagination. Even under each of these heads it is
various. There is the indefinite variety of the sciences, —
mechanical, chemical, vital. The successive variety of the
objects is apprehended here, but we have no principle or
principles from which we can infer what is diverse or what is
common in them. This cannot be demonstrated, far less in
any sense deduced. The variety runs back to no one principle
Ave know or can know. No one form of it could in the nature
of things lead us to predict, even to conceive its subsequent
form. No one science could, therefore, tell us all the variety
of things, far less systematise it. The utmost we can do
is, first, to analyse and state the common principles or cate-
gories which regulate its appearance, or phenomenal being
for us ; and, secondly, by observation and experiment to
test and show what kinds of matter do pass into other kinds,
and by what empirical laws this transmutation is regulated.
This is the province of Metaphysics and Physics. The indef-
inite variety of science seeks to meet, and yet it falls short
of, the infinite variety of things.
§ 90. But if Logic cannot embrace all objects or all the
1 See above, p. 33.
LOGIC THE SCIENCE OF FORM. 71
variety of experience, and legislate for it, it can legis-
late for none of it. If it cannot take in all matter or
objects, it can take in none. It is not at liberty to make
an arbitrary selection ; it would cease to be a science, if it
did. By vindicating for itself the community of form in
things, it vindicates its definite and peculiar sphere. Logic
can only deal with things in all their possible variety, as
they stand in relation to human knowledge, as they exist
for us at' all, by looking not to the matter of experience as
it is objectively, but to this as it stands in relation to our
faculty of Intelligence or Thought, as it is in fact intelligible
or conceivable by us.
§ 91. In what sense and how far is Thought, Pure Thought,
abstract ? Or what is the relation of form and matter ?
In the first place, there is no existence in our mind of
actual form apart from matter of thought, or of actual matter
of thought apart from form. " No object is cogitable except
under some form of thought ; and no form of thought has any
existence in consciousness except some object be thought
under it." The question as to potential form and potential
matter, or how matter and form absolutely arise, is not now
before us. It is enough for us at present to say that matter
and form in thought or to thought are inseparable correlatives,
though by no means identical in fact ; not identical, just be-
cause they are conceived as correlative.
In the second place, it is contended that form can be
separated ideally from matter in the same way and to the
same extent as is done in the method of other abstract know-
ledge,— for example, in Geometry ; and so dealt with as an
object of scientific examination and law. I cannot realise
a form of thought per se ; I cannot realise a matter of thought
per se ; but I can realise, consciously think the same or
similar form of thought apart from this or that matter.
I can conceive the same representative form of the concept in
a thousand successive different notions ; and the same inclu-
sive form of the judgments in a thousand successive different
judgments. And I can discover what is common to the form
in all these different matters, and in all possible different
matters. I can thus reach their laws, the necessary and
universal laws, and state them scientifically. The Geometer,
by showing one figure, say triangle, can demonstrate the
72 INSTITUTES OF LOGIC.
universal properties of the class triangle. He does not need
this or that triangle to show the properties ; he is inde-
pendent of any one ; but he is not independent of every one.
He needs some one figure. So it is with the logician. No
matter which he happens to know or to use restricts him ;
but he needs some matter, of concept, judgment, reasoning,
and by means of that he realises and shows his universal
laws. If the logician can obtain and exhibit universal pro-
perties belonging to every kind of thinking form, as the
mathematician can exhibit universal properties belonging to
every conceivable figure, the reality and the abstract universal-
ity of Logic are vindicated. The proof of this is to be found
in the details and order of the science of Logic to be exhibited.
§ 92. Thought has three forms — viz., Concept or Notion,
Judgment, Inference, including especially Eeaponing.
The first form of Thought is the Concept or Notion. The
thought indicated by the concept man, and expressed by the
term, contains matter and form. The matter is an attribute
or series of attributes. The form consists in this attribute or
sum of attributes having a representative function. Through
means of this function the concept is capable of equally repre-
senting in knowledge any one of a plurality of individuals.
Viewed as to matter or content, concepts differ indefi-
nitely. Stone, plant, animal, man, all differ as to content or
the attributes which constitute them. They all agree in pos-
sessing a representative form, — that is, they are capable of
standing for and helping us to know the individuals which
they respectively embrace. In a word, they are all concepts,
but concepts of differing attributes, and therefore differing
classes and individuals. In technical language, they vary
in matter ; they agree in form. Logically the form is the
essential element, the matter the unessential ; for while the
matter may vary without destroying the concept as concept,
the form cannot vary or be changed without abolishing the
thought as a concept, changing it as a mere concept.
In Judgment there are form and matter. Every judgment
agrees in having the same form. This is inclusion or exclu-
sion, attribution or non-attribution. It either includes the
subject under the predicate, as, The plant is organised — i.e.,
belongs to, forms part of, the class organised ; or it excludes
the subject from the predicate, as, The rock is not organised.
THE FOEMS OF THOUGHT. 73
This is a judgment in Extension, the predicate notion being
a class-term. In Comprehension, the judgment attributes the
predicate to the subject, or declares that it is not attributable
to the subject, as, This man fights bravely. Water does not
violate the law of gravity. In this case, the predicate term
means an attribute, not a class. The form of the judgment
is the same, whatever the terms may be, or whatever we
judge about. And rules can be given regarding the form, in
every kind of matter.
In Eeasoning there is matter, and there is form. The
matter consists of two propositions or premises, and a third
proposition or conclusion. The form lies in the necessary
connection between the two premises and the conclusion.
Thus —
Plant is organised ;
Snowdrop is plant ;
.'. Snowdrop is organised.
Or in letters, — A is B ;
C is A ;
.*. CisB.
As in the Concept and Judgment, so thus in the Eeason-
ing. Our thought as a concept preserves the same form,
whatever be the attributes constitutive of the notion ; our
thought as a judgment preserves the same form, whatever
be the concepts or terms, whose relation is stated, or about
which we judge ; our thought as a reasoning preserves the
same form, whatever be the things about which we reason.
The form is necessary and universal ; the matter temporary
and contingent to thought. Herein lies the central idea of
Logic as a science. It is the science of the permanent and
universal in the relations of human thought.
§ 93. I have hitherto spoken of thought as concept in
relation to the objects of experience or intuition, and shown
its functions in regard to them. But it is now necessary to
say that thought rises to a higher degree than merely the
recognition of the objects of experience, the putting these
under sections or classes. It must be kept in mind that
Perception or Intuition is restricted in several ways. It
apprehends a quality or an object as now and here present to
the mind, — in other words, it is limited by definite conditions
74 INSTITUTES OF LOGIC.
of time and place. And thinking (or conceiving), if it were
exercised only on the matter of perception, could but recog-
nise resemblances amid that matter, and group together
qualities actually presented to it. Thought would thus
follow the footsteps of Perception, and be but the hand-
maid of a limited experience. Now this is not so. Thought
is free. We speak of the freedom of the will. We speak of
that noble power of free choice, which is the great moving
force of all moral life, as the free power pre-eminently —
and so it is. But thought is a free power also. It is free
in a way which enables it to rise above the limitations of
actual perception. Thought is not restricted by the giving
or presenting to it of the quality or individual object of
perception. Once we have obtained the concept or general
idea, thought can, with the concurrence of imagination, con-
struct the individual quality or object which embodies the
attributes of the notion, and thus pass into act without the
aid of Perception.
§ 94. To illustrate this. We may, as I have said, recog-
nise an object which we meet with in experience as like
to an object we have met with before. We thus apply
to the new object our notional or conceptual knowledge.
But it is obvious that, in order to think of an object
which embodies the attributes of our notion, we do not
require to wait for the perception of the second individual
object. We have in our mind the main features of the
class. And in virtue of this possession, potential it may
be, we can at any time, and in any space, construct a
picture or image in the mind of an individual object, be
it mountain, river, shij), or house, like what we formerly
saw, embodying the attributes of our notion. We are no
longer restricted by definite conditions of time and space,
no longer limited to what we merely saw or felt. Thought
now deals with an image — i.e., an individual object which
imagination inspired by it has created or constructed. It
embodies attributes, common to a class, in this one image.
Intelligence has at length awoke to a full consciousness of
its own strength and freedom; and imagination is its ready
servant, — ready to embody in the definite picture or the
glowing image the otherwise dim and unrealised attributes.
Thought has now an unlimited quantitative power ; it has
THE FREEDOM OF THOUGHT. 75
a faculty of constructing individual objects or images which
embody a definite set of qualities. Quantitatively, it is
unlimited ; qualitatively, it is limited by the constituent
attributes of its notion.
§ 95. Perhaps the simplest illustration of this is as follows :
suppose we have somehow in our mind the notion of triangle
or square. It is clear that we can embody these notions, or
represent them as individual pictures, in very various ways.
These pictures may differ very much from each other as to
time, place, and material. But they will agree in possessing
or exhibiting the common features of triangle and square. The
triangle imagined may be equilateral (all sides equal), isosceles
(two sides equal), or scalene (no sides equal). It may be of
wood, or stone, or iron, or silver. It may be black or white,
red or green. In all these particulars it may vary. In all
these we are free, free to construct our individual object as
we choose, provided only we preserve the common features
of a figure formed by the mutual intersection of three straight
lines. Hence all intuition is definite and limited ; all thought
is in a sense unrestricted and free. This exercise of thought,
apart from intuition is Pure or Formal thought, the only
pure thought we know ; whereas when thought is exercised
along with and upon perception, we have Mixed or Material
Thought.
(a) With Schleiermacher pure thinking means thinking with a view
to science, as opposed to ordinary and artistic thinking. "Science is
identical in all the thinking minds producing it, and agrees with the
existence thought about. Pure thought, he maintains against Hegel,
cannot have a peculiar beginning distinct from all other thinking, and
arise originally as something special for itself. In every kind of
thinking the activity of the reason can be exercised only on the basis
of outer and inner perception. There is no act without the ' intellec-
tual function,' and there is none without the 'organic function.'1
Only a relative preponderance of the one or the other function exists
in the different ways of thinking. Agreement with existence is imme-
diately given in inner perception, and is attainable mediately also on
the basis of outer perception.
"There is in the view of Schleiermacher a parallellism, but not an
identity between the forms of thinking and knowing, and the forms of
real existence. Thinking depends upon perception, perception upon
the influence, affection, or impression from the objects or being
without us."2
Ueberweg adds that Schleiermacher's views agree with the results of
1 Dialektik, §107-114. 2 Ueberweg, System of Logic, § 33.
76 INSTITUTES OF LOGIC.
unprejudiced scientific investigation, and correspond more truly than
Hegel's to the idea of the universe as one whole organism, in which the
unity of the whole does not interfere with the manifold and relative
independence of single sides and members ; sameness in common
fundamental characters, does not remove or render meaningless differ-
ence in specific and individual properties, and no one member can be
freed, with respect to his actions, or even his existence, from being
conditioned by any other.1
§96. "Puie thought, as meaning the consciousness of
general notions and of nothing else, is an operation which
never takes place in the human mind. Our only choice
lies between notions as exemplified in individual objects,
and notions as represented in signs, spoken or unspoken.
And the notion as represented in language is but the
substitute for the notion embodied in intuition, and derives
all the conditions of its validity from the possibility of the
latter. Language, though indispensable as an instrument of
thought, lends itself equally to every combination, and thus
furnishes no criterion by which we can distinguish between
sense and nonsense, between the conceivable and the in-
conceivable. A round, square, or a bilinear figure is as a formed
speech, quite as possible as a straight line or an equilateral
triangle. The mere juxtaposition of the words does not
indicate the possibility or the impossibility of the correspond-
ing conception, until we attempt to construct by intuition
an individual object in accordance with it." 2
i Uebervveg, System of Logic, § 33, p. 71. 2 Mansel, Met., p. 187.
CHAPTER IX.
THE CONCEPT HOW FORMED THE GENERAL AND THE
ABSTRACT.
§ 97. We have seen what Thought in general is, what are its
functions, and what are its forms. The next question is, How
does Thought, especially as Conception, arise — what is its
origin and genesis ?
The ground of all thought is the consciousness that some-
thing is or exists. This implies perception of a quality at
a particular time, or time and place, or a sensation, or emo-
tion at a definite time. Lower than this we cannot go ;
and this implies an intuition of reality or being. We have
no conception of abstract being to begin with ; we do not
even know what being means, until we realise it or particular-
ise it in some sensation or quality perceived. The is with
which knowledge begins is totally different from the logical
copula — the is of comparison. The former implies a judgment
of real existence, the latter implies nothing more than a judg-
ment of congruence or harmony between terms.
§ 98. What is at first cognised is thus merely something, or
form of being. But this is vague. The question is — How
from this do we rise to precise logical or scientific thought ?
How are General Ideas, Notions, or Concepts formed in the
mind ? How do we get them ? or make them ? This is
chiefly a psychological question, but we must note the main
features of the process.
First of all, we have certain impressions on the senses.
This is a vague phrase, but it may be regarded as meaning
sensations and perceptions, or what we afterwards name as
such. Each sense is fitted to receive and to give us a definite
78 . INSTITUTES OF LOGIC.
impression. The Eye gives us colours, the Ear sounds, the
Taste certain sensations. We may get these singly or in com-
bination with other impressions. Take them singly first. We
find that they are many, numerous, successive. They occur at
different places and in different times ; but they are not all
unlike. The impressions vary in time, but they are like in
character as impressions. Thus I may have experience of
colours in succession, or at different times, which make the
same or a similar impression on the percipient. Numerically
they are different ; subjectively, or as I perceive them, they
are the same, or they are not distinguishable. The moment
I apprehend likeness or similarity between two separate im-
pressions, I have the ground of the Notion, General Idea, or
Concept. I have thought in the proper sense of that word ;
for thought in its earliest form is the apprehension of relation
— of likeness or resemblance. Now, observe this is the act of
a power higher than Perception, for I now apprehend a rela-
tion ; and a relation is that which I may think, but it is not
that which I can see. It is thus that I get such notions as
that of colour itself — red, black, blue — loud and low, harsh and
soft, sweet and bitter, and so on.
§ 99. Secondly, impressions on the senses are not always
given singly or separately ; they are also given together or
at the same time — i.e., in groups. When I look at an orange,
I have, or seem to have, various impressions — sensations and
perceptions. It is yellow, it is round, it is rough, it has weight,
and when I taste it it has a certain flavour. These various
contemporaneous impressions make up my idea of the object,
which I call an orange.
Other objects, or other bundles of impressions, are presented
or given to me. Besides the orange, I may see what I call a
marble, or a cricket-ball. These, too, mean to me a certain sum
of impressions. But it is clear that I cannot go on for ever
seeing objects or bundles of qualities in this way, without
attempting to connect them in some mode or other. One
object, even one impression, would, if wholly disconnected,
destroy the preceding one and leave me simply the blank of
knowledge. Naturally, therefore, or instinctively, I fix on
some point of connection between those objects more than
mere succession in time. I fix on a point or points of resem-
blance among them — a point of unity, in fact, by means of
THE CONCEPT. 79
which I may be able to join the otherwise various objects
together. The mind is wearied and perplexed with the seem-
ingly infinite variety of the objects of Perception or Intuition.
When, therefore, I discover a point of resemblance among the
otherwise varied objects, I concentrate my attention on that
— I disregard the other qualities in which the objects may
differ ; and this one point or feature — this unity amid diver-
sity— becomes for me a Notion or Concept, which enables me
to class the objects as one. The orange, for example, differs
from the marble in many points, the cricket-ball differs from
both in many points ; but in one point they agree — they are
round; and by means of this concept I class them as one. I
have here gone through three mental processes. The one is Ab-
straction. I have abstracted one special feature from the other
qualities of the object perceived at the same time, and I have
abstracted one quality from the other object ; I have compared
these. I apprehend them as the same or similar ; I have now
performed Generalisation and got the General Idea or Notion.
The Notion or Concept is, therefore, " the knowledge of the
point or points in which two or more objects agree." This is
to conceive or think in its simplest form ; it is to unify — to
think several objects as one. Intuition or Perception is the
faculty of the diverse or varied ; thought of the one — of the
unity amid diversity. In Intuition we are comparatively
passive, liable to be overwhelmed, as it were, by the infinity
of the impressions made upon us. In thought we assert our
true activity, react on the impressions we receive, reduce
them to unity and science, and thus acquire a certain mastery
over the universe of things. Thought is thus a conquering
power.
§ 100. Thirdly, it may be asked why, in any given case,
should we fix on one feature of a complex object or sum of
features rather than another ? Is there any reason for our
abstraction of or attention to one feature amid many, rather
than to another or others ? We have already seen the reason
for our seeking to fix on some feature or other in the object
exclusively. This is because we instinctively, or in the
interest of comprehension, seek to connect objects varied and
varying in time. But the circumstance which leads us to
the particular feature is different from this. This lies in the
fact that a certain feature or certain features of an object are
80 INSTITUTES OF LOGIC.
more striking or impressive than others — i.e., naturally fitted
to evoke a higher degree of attention and interest. The
mind is thus drawn to and fixed upon that feature or those
features to the exclusion of the others. If, at the same time,
this striking feature be a constant or permanent character of
the object, wherever it is offered to our perception, we come
to regard it as a characteristic mark or note. Finding the
same or a similar characteristic feature constantly present
in a succession or plurality of objects, we generalise, — we
take it as the mark or content of our notion of a class of
things. It becomes a concept under which we group a plu-
rality of objects, or form a class- notion. Hence, for example,
such class-notions as flying, swimming, as applied to creatures ;
/lumen or stream, as applied to flowing water ; stagnum or
standing pool, as applied to lake.
§ 101. And here we come upon one distinction between
ordinary and scientific classification. Ordinary thought
looks rather to what is impressive or striking in an object ;
scientific seeks rather for what is primary in nature as op-
posed to what is derivative or secondary. The distinction
between the primary and derivative attributes as grounds of
classification, is well seen in what is known as the Natural
System in Botany. Here attributes upon which other attri-
butes depend, are fixed on as grounds of classification.
Whereas in the system of Linnaeus which preceded the nat-
ural one, it was rather the outward or striking feature, mainly
the number of stamens, which formed the ground of classifica-
tion. This gave a descriptive botany ; the deeper reference
to morphological and structural features led to the better un-
derstanding of the properties of the individual plant, and also
of the natural affinities of plants in general.
The distinction between primary and derivative attributes
is very well shown in geometry. The definitions of point,
line, superficies, and others, are strictly ultimate and primary ;
they give the essence or elements of the concept extension, in
so far as it is the object of pure geometry ; and they are the
grounds of the secondary attributes or properties of figured
extension, as triangle, circle, square. The furthest conclusions
of pure geometrical reasoning presuppose these, and by means
of postulates and axioms flow necessarily from them.
§ 102. Further, it follows from the abstraction involved in
THE CONCEPT. 81
the concept, as the sum of common qualities only, that it
will always represent certain qualities — viz., the common,
to the exclusion of the special or individual. And thus
the name which is given to the concept, and which fixes it
as it were in the objective, will call up only certain features
of an object, these probably the most striking, and will
not mark, though it may suggest the others. " Names, as
has been well said [at least common names or nouns], are in
truth the signs not of things themselves, but of our partial
and generalised conceptions of things." Or as Mr Max
Mtiller has put it, somewhat unguardedly I must observe,
" all nouns express originally one out of the many attributes
of a thing, and that attribute, whether a quality or action, is
necessarily a general idea." x As examples : moon is meas-
urer (ma, Sanscrit) ; flumen is flowing water ; sea is tossed
about water (si) ; stagnum is standing water ; serpent is the
creeper (sarpa); anguis is «?xts (anhi), the throttler ; drum
or druim is ridge, as in Drumalban ; field is felled (feld), the
cleared spot; hope is haven, shelter (Iceland); pen or ben
is head.
(a) Abstraction is used in two senses, which should be distinguished.
(1.) When we look at one object which possesses a variety of qualities,
say a tree, we are sometimes said to abstract one of these qualities
from the other. This we do when we think, for example, of the height
of the object, without precisely regarding anything else in connection
with it. We are thus said to form an abstract idea of the height of
the object ; and we may make the idea still more abstract, by think-
ing and speaking of height and tallness in general. An abstract idea in
this view, is an idea abstracted or withdrawn from other ideas which
enter into a complex object of thought. This is the means of our
gaining definite or precise knowledge, — knowledge prescinded, as it
were, or cut off from other knowledge.
(2.) Abstraction is also employed to indicate the fact, that in looking
at a complex object, we withdraw, turn away, or abstract our regard
from certain qualities of the object, and attend only to one. In this
case we are not said to abstract one quality from the others ; but we
attend to one quality and withdraw or abstract the mind from the
others. In the former case, the single quality regarded out of any
others may be said to be abstracted ; in the latter case, the quality is
viewed as an object of attention, and it is the mind or view of the
mind which is abstracted or withdrawn from the remaining qualities.
It is obvious that all this is merely a matter of terminology. Atten-
tion to one special quality of an object implies abstraction from the
1 P. 362.
F
82 INSTITUTES OF LOGIC.
others ; and abstraction from the others implies attention to the one,
if the object remains a matter of thought at all.
§ 103. The feature, noted abstractly, may be merely an in-
dividual feature so to speak, — it may be merely a something
known in time or space. We may, for example, have the im-
pression of what we afterwards call colour from an object,
although we do not know more of this impression than that
it is merely something distinguished from other impressions
which the object may make. We do not as yet know whether
other things may possess this quality or not. We may
apprehend also what we call hardness in an object, although
we do not consider whether there be other objects in which
we might also find this quality. And we may think of or
apprehend whiteness in an object, without considering its other
qualities, such as its figure, size, &c. This would be called
an abstract idea, because we consider the quality, as it were,
apart from the other qualities of the object. But we might
make this mere abstract idea an abstract and general idea, if
we were to find a similar impression, say whiteness or hard-
ness, in other objects. In this case our notion would involve
a relation of resemblance or similarity, and we should rise to
the abstract yet general idea of redness or hardness; for these
notions imply a quality common to a number of objects. I do
not say that redness or hardness, or any abstract term, is not
possible, simply as in contrast with other qualities of the
object, and as not necessarily implying similarity or relation
of resemblance between several objects. On the contrary,
such terms, and abstract terms in general, — all nouns in ness,
— rather imply originally a contrast between the intuition of
the quality denoted and other qualities of the object. If we
speak of redness in an object, we mean to distinguish this
from its roundness or squareness, its bigness or its littleness;
and in this way we have a perfectly definite knowledge. And
this would be the knowledge of a particular quality as opposed
to other qualities. We go through this process in all atten-
tive and careful acts of knowledge. We desire to attend to
one feature, as contrasted with others ; and it does not matter
to us whether this feature is shared in common with other
objects or not. At first the sense of the savage is thus at-
tracted and abstracted ; but the very same process passes on
in the mind of the very highest culture ; for the faculty of con-
GENERAL AND ABSTRACT. 83
centrated abstraction is that which characterises and marks
the men of strongest intelligence and genius. But, as a rule,
abstract nouns, such as redness, ichiteness, hardness, softness, are
general in their application ; and we mean by them a common
quality, — a quality which is predicable of several objects.
This, of course, implies generalisation. We have gone be-
yond the mere process of abstraction : we have found a similar
feature in objects ; and we have named that similar feature —
abstractly,' no doubt ; we have, in a word, generalised. Yet
we must keep in mind that the abstraction preceded the
generalisation : that we may abstract without generalising,
but cannot generalise without abstraction.
§ 104. It is thus of importance carefully to note that an
abstract idea is not necessarily a general idea, or an idea re-
garded as applicable to more than one object. This has been
recognised theoretically by philosophers ; but it has been not
unfrequently overlooked in practice, and in the construction
of theories of the origin of thought and language. Stewart
has put the true nature of an abstract idea in the following
passage : —
" A person who had never seen but one rose, might
yet have been able to consider its colour apart from its
other qualities ; and, therefore, there may be such a thing
as an idea which is at once abstract and particular. After
having perceived this quality as belonging to a variety
of individuals, we can consider it without reference to any of
them, and thus form the notion of redness or whiteness in
general, which may be called a general abstract idea"1 This
is obvious with regard to the qualities of any individual object
presented to us. We are able to regard any one of its qualities
to the exclusion of the others. I may, for example, make the
hardness of this table an object of my attention, and, in so doing,
may be said to abstract the quality of hardness from the other
qualities of the table, such as its size, figure, &c. Hardness is
in this case an abstract idea ; it is viewed by me in itself and
apart from the other qualities of the object in which it is found.
But it is not yet general, it is not properly a concept. It is
the individual quality of an individual object ; and even if
it were possible to view it apart from any object whatever, it
would not cease to be simply an individual impression.
1 Elements, I. c. iv. § 1.
84 INSTITUTES OF LOGIC.
(a) According to Hamilton, abstraction is not properly a positive
act; it is merely the negation of attention. Concentrated attention on
a single point leads to an abstraction of consciousness from others in an
object. Abstraction should not be applied to that on which attention
is concentrated. Here we prescind, rather than abstract. Of the qual-
ities A, B, and C, we prescind A in abstracting from B and C.
Further, abstraction in this sense, as performed on individual objects,
gives only an individual notion. " The notion of the figure of the desk
before me is an abstract idea — an idea that makes part of the total
notion of that body, and on which I have concentrated my attention,
in order to consider it exclusively. This idea is abstract, but it is at
the same time individual ; it represents the figure of this particular
desk, and not the figure of any other body." — {Met., L. ii. 278.) There
are thus individual abstract notions, and abstract general notions.
§ 105. This gives rise to the distinction between Abstract
and Concrete Terms or names. Humanity is said to be ab-
stract; and man is said to be concrete. Redness is abstract;
red is concrete. The difference is said to be that the latter,
the concrete noun, indicates an attribute or attributes in or
with a being, something existing or conceived as existing ;
whereas the abstract noun is applied to the mere attribute or
attributes. Now I think that this is more a distinction of
language than of thought. It is true that human, man,
coloured, imply directly something to which these attributes
belong; but humanity, colour, imply equally, if not so directly,
an object to which they belong, or subject in which they in-
here. We cannot realise to thought the attributes implied in
the abstract term humanity, without thinking of man in which
they are embodied. So far as language goes, humanity indi-
cates attributes a step further removed from the concrete than
man, but that is all. If we actually give meaning either to
the notions humanity or man, we must equally embody them
in a definite concrete image or object. Mere abstract thought
is an impossibility. The abstract exists only in the term ; it
is not actual thought ; it is the mere possibility of our realis-
ing thought.
§ 106. No doubt we do make abstract terms the subjects
of propositions. We speak of virtue, duty, humanity, as rigid,
obligatory, worthy. But we have a tendency to make abstrac-
tions realities, and to think that these by themselves may
people the universe ; whereas it is our thought of them which
gives them life — even meaning. In this point of view, the
individual object alone is the real — the abstract is a mere
PKIMUM COGNITUM. 85
passing sliow or dim shadow of the individual as the real, im-
perfectly representing the fact of our experience. Neither
the abstract nor the general, as in thought, is the real for us ;
by these we mean at the furthest to imply that there are
beings, definite realities of space and time, and that these
realities have certain mutual relations or attributes. The
very fact of our giving attributes to things means that they
are, and that they are diverse as well ; for all similarity or
likeness implies that the things known as similar are also
diverse — diverse in their true existence as individuals of
space and time. Otherwise similarity would be meaningless;
there would be not similarity, but simple identity. But it is
things or beings, otherwise different, which we hold together
by the bond of resemblance.
§ 107. An abstract idea is thus primarily that of a quality
or attribute, and it may be regarded as opposed to the con-
crete when it forms one of the qualities of a lower notion.
Thus in the scale, organisation is abstract in respect of animal,
for it is higher up and enters into the lower animal as a deter-
mining element or quality. The abstract is thus always a
less determinate notion than the concrete, the lower or con-
crete being fuller as it were of attributes or qualities. In
this way the abstract quality is at the root of the generic idea.
§ 108. The course of inquiry which has now been pur-
sued, in regard to the nature and formation of notions, has a
direct bearing on a question much debated by psychologists
and philologists, — I refer to the origin of our class — know-
ledge ; in other words, the primum cognitum. The question
is, What do we first apprehend — the individual object or the
general idea ?
(1.) We have already found that our knowledge of objects is
at first vague and indefinite ; (2.) we classify them according
to certain very general resemblances, as of time and place ;
(3.) we are attracted by certain striking features in the ob-
jects, which we exclusively attend to; and (4.) we generalise,
or transform these abstracted features into general ideas ;
(5.) we then look upon numerically different objects as pos-
sessing or embodying this attribute or those attributes. We
thus in the end individualise objects by distinguishing them
as members of a class, or as possessing this or that definite
attribute. It is really in virtue of the general idea or notion
86 INSTITUTES OF LOGIC.
that we regard objects as distinguished from each other, as
belonging to this class of things and not to that. So that
our general knowledge is the means of setting the objects
of our experience in the precise light of individual objects,
as special instances of general notions.
§ 109. In reply, accordingly, to the question now pro-
posed — of the primum cognitum — I agree with those who
hold, in opposition to a certain class of philosophers, that we
do not at first know individual objects in their true character
as individuals. Our knowledge of all objects is at first vague
and indefinite ; and the first step towards clear or definite
knowledge is when we attend to the striking feature of an
object, — when, in a word, we begin to abstract. The know-
ledge we gain by abstraction is further transformed into the
general by an increasing experience of new objects with a
feature similar to that in the object we originally observed.
Having reached the point of a general idea, we now have a
clear and distinct apprehension of objects as individuals, —
as the members of different and definite classes. So that our
knowledge may be viewed as progressing from the dimness
of the indefinite, through the abstract, to the clearness of
general and individual vision.
§ 110. This view, however, is not less opposed to the doc-
trine which makes our knowledge begin with the definitely
general, and which has been attributed to Leibnitz, among
other philosophers. It seems to me impossible, from the
nature of the case, to maintain with truth that our know-
ledge begins with the general idea. This involves the
conception of a plurality of individual objects, possessing a
common feature. These objects are necessarily already in
our experience, and intelligence, dealing with them, forms the
general idea. It would, indeed, I believe, be more correct to
say that in a sense our thought begins at once with the
general and the individual, that the two dawn on conscious-
ness together ; that as we are elaborating the concept out
of individuals, we are also making these themselves distinct
objects of consciousness. In truth, as we do not think the
individual apart from the general, or the general apart from
the individual, this process of a double or twofold evolution
of intelligence really takes place. Perfected or matured
thought really commences with the general idea and the
individual instance of it at one and the same time.
PRIMUM COGNITUM. 87
§ 111. The doctrine now advanced thus supersedes the
whole of the old controversy regarding the primum cogni-
tum. And I hold that this view applies very emphatically,
not only to our general ideas but to our universal ideas as
well. We have no universal ideas in any proper sense of
the word before the particular. We have no idea of Being
before we apprehend some being, or being in a definite
form. Nor have we the universal ideas of unity, identity,
quantity, quality, relation, and so on, before the particulars
or perceptions in which they are embodied. Chronologi-
cally, these, the universal and the particular, are realised
together, and each is necessary to the other, though they
have different sources in the mind. And I hold it especially
wrong to say that the universal develops into the particular,
or that the particular is evolved out of it. This is a meaning-
less statement. It supposes the universal to be first in
thought, whereas it has no meaning at all, unless it is along
with the particular in thought. There is a logical con-
comitance between the two, but there is no logical or ideal
priority ; and this is needed for evolution. A theory of this
sort which constantly charges abstraction on the opposite
view, is itself abstraction run mad.
88
CHAPTEE X.
THE CONCEPT ITS CHARACTERISTICS SPECIALLY CONSIDERED.
§ 112. The general characteristics of the Concept or Notion,
viewed as the product of Abstraction and Generalisation, may
be stated as follows : —
(1.) The Concept is Kepresentative.
(2.) It is Partial or Inadequate.
(3.) It is a knowledge of Relation, which is not picturable.
(4.) It has two sides or aspects — that of Comprehension and
that of Extension.
(5.) It is perfected by being expressed in a Term.
§ 113. As the sum of notes or marks in which a plurality
of objects agree, it is a Notion ; as that by means of which
several are grasped as one, or as the ideal unity of several
objects, it is a Concept — holding in one through the common
quality or qualities. Its first and essential function is, there-
fore, the power of representing any one of the individual ob-
jects, actual or possible, which may possess the quality or
qualities it contains.
§ 114. To this it should be added, as Esser has observed,
that a concept is properly the representation of an object not
merely through marks which distinguish it from other objects
in general, but through its distinctive marks, that is, those
marks which distinguish it from the objects which come
nearest to it. The distinctive marks of an object are those
which make it to be this, not that — that is, they are peculiar
and essential. E.g., the concept of a square is not simply
that of a four-sided figure, for this does not distinguish it from
an oblong or a rhombus ; but of a four-sided figure which has
all its sides equal, and all its angles right angles.
CHARACTE11ISTICS OF CONCEPT. 89
(a) The representative function of the Concept was indicated in the
doctrine of vTr6de<ris, or Suppositio, due apparently to the Byzantine
logicians. Suppositio means positio pro alio or aliis—Supponere pro alio
— putting in the place of. The word stands in the place of the thing,
or of the modification of the mind {passio animm), and this convention-
ally {ex institutions, ad placiturn). The passio animce, the intentio,
whether intuitio or conceptus, stands naturally in place of the thing.
But the singular impression, as a passio animae, is an intention, as
much as the concept proper, which represents in one what is common
to many. — (Cf. Occam, Summa Logical, c. xii. et passim.) The Greeks
subdivided tiirodesis, or Suppositio, into common, and discrete (koiv(),
SicaptcriJ.ci'r)). The common is, through a common term, as man — the dis-
crete, through an individual name, as Socrates, or of the demonstrative
pronoun — This is the man. — (Cf. Michael Psellus, in Prantl, ii. 280.)
For the scholastic distinctions of Suppositio, Personalis, Simplex, and
Materialis, see Occam, Sum. Log., i. 70.
§ 115. A notion or concept, as founded on abstraction, is
necessarily a partial and inadequate representation of the
individual, at least in so far as the individual of sense em-
bodies a plurality of qualities. For the notion is but the sum
of the common qualities, and this implies leaving out the
individual ones.
Where the individual is a singular impression, as in the case
of a definite colour — say red or white, or where there is a
simple notion, as resistance — the concept entirely represents
the individual, except as to definite time or space. There
is nothing more in the notion of a definite colour than there
is in the percept, except the apprehension of similarity to
other colours. So it is in the case of the concepts of definite
sounds, tastes, &c.
But a concept, in so far as it relates to a complexus of
qualities apprehended at the same time and in the unity of
an object, is partial and inadequate, for it only brings before
us the object in so far as it possesses a quality or qualities
common to others. In this respect the contrast of Memory
and Thought is complete. The representation of memory is
perfect in proportion as it gives us all the features of the
object, that is, the scene or definite sum of experience appre-
hended in a given time. In memory, our effort is to bring
back every feature of what made up a past whole of experi-
ence. Given but a part of it, we try to recall the other
parts, one after another, until the whole scene flashes again
upon us, as we knew it in its actual past reality. It is the
90 INSTITUTES OF LOGIC.
nature of memory to totalise, and thus to individualise. The
nature of thought is the very opposite. Thought leaves out
all the special individual features or circumstances in its
single act ; it gives us the result, the picture of generalisa-
tion. Notional or conceptual knowledge, viewed in relation
to the complex individual, is thus necessarily inadequate,
incomplete. It gives us a part only of the real individual,
the individual of experience. " We sacrifice completeness of
view to obtain universality."
(a) Hamilton states as a general characteristic of the concept, that
it is a representation of a part only of the various attributes or char-
acters of which an individual object is the sum ; and consequently
affords only " one-sided and inadequate knowledge of the things which
are thought under it." — (Lofiic, L. vii.)
He illustrates this by reference to the individual — Socrates. We
may think him by any one of the concepts — Athenian, Greek, European,
Man, Biped, Animal, Being ; but in doing so we throw out of view
the far greater number of characters of which Socrates is the comple-
ment.— {Ibid.) Mr Mansel acdepts this doctrine when he says that
"a concept is not the adequate and actual representative of any single
object, but an inadequate and potential representative of many."
If, however, we apply this general statement of the nature of the
concept to that of a single attribute, or to an abstract attribute
which may represent the whole nature of a thing, as lineal extension,
time, resistance, it will require modification. The concept in this in-
stance represents the attribute (or attributes) of the thing in its entire-
ness ; and yet it does not cease to be a concept — that is, to be appli-
cable to an indefinite plurality of individuals, and realisable in each.
If there be, as there is, the concept of abstract attributes, the concept
can afford complete knowledge, though it does not usually do so, —
especially in the case of concrete and individual objects of time and
space. With this is closely connected the question, Can there be a
Concept of the Individual ? Hamilton has repeatedly restricted concept
to the common quality or qualities of individual objects, and the
relation which this implies, as more than can be represented in imagina-
tion. It indicates the thought suggested by a general term. Yet
he speaks of " the concept or notion " of Socrates — meaning the whole
attributes " which distinguish him from all other men, and together
make up my notion or concept of him." — (Logic, L. v.) He speaks also
of the concept when at its greatest comprehension as "being a comple-
ment of the whole attributes of an individual object, which by these
attributes it thinks and discriminates from every other." — (L. viii.)
Again, however, he says, speaking of the limits of division: " If a con-
cept be an individual, that is, only a bundle of individual qualities, it
is indivisible, is, in fact, not a proper or abstract concept at all, but
only a concrete representation of imagination." — (L. viii.)
The solution of this apparent discrepancy may be sought in the
following note to the Discussions, p. 13. " The understanding, thought
CHARACTERISTICS OF CONCEPT. 91
proper, notion, concept, &c, may coincide or not with imagination,
representation proper, image, &c. The two faculties do not coincide
in a general notion ; for we cannot represent man or horse in an
actual image without individualising the universal : and thus con-
tradiction emerges. But in the individual, say Socrates or Bucephalus,
they do coincide ; for I see no valid ground why we should not think
in the strict sense of the word, or conceive the individuals which we
represent. "
A notion of all the attributes of the individual, which thus enables
us to discriminate him from other individuals, is a generality, and
thus properly a concept. There is the knowledge of other individuals
in the discrimination, and thus there is a relation of resemblance amid
difference. There is this individual as opposed to that and the other.
That and the other are conceived as belonging to the same class of
individual, but as discriminated from say this, — Socrates, — under the
class. If, however, the attributes be viewed simply as belonging to
this thing or individual — if that be possible, — there would be a mere
image or representation, and no concept proper. But every object of
intuition, and every part of every object, is necessarily thought under
some kind of relation ; there is no absolute or irrespective intuition,
as there is no absolute or irrespective conception. But, as seems to
me, the image of the individual and the concept of it in such a case
do not coincide more than in the case of general notions or concepts
proper. The concept of individual is as much a generality along with
the definite individual attributes, as the concept of horse is along with
the individual attributes of the representation.
§ 116. Thought proper or Concept cannot be imaged, that
is, pictured in a single definite image or representation. For
thus it would cease to convey general or universal know-
ledge, and become but the definite or determinate image of
this or that individual object. A concept cannot thus be
realised in consciousness in the mere representation of one
moment, or of one object. A concept expresses a relation —
a relation of similarity between several objects. It is thus
not only not a single image, it is not even picturable in the
imagination, but is conceived or understood as an intelligible
relation between several objects, actual or ideal.
A concept, as such, is thus always only a potential know-
ledge, that is, there is no imaginable object capable of cor-
responding to its universality. Concepts may be realised " in
relation to some one of the individual objects they classify,
and in this relation can be represented in imagination ; but
then, as so actually represented, they no longer constitute
general attributions, they fall back into mere special deter-
minations of the individual object in which they are repre-
92 INSTITUTES OF LOGIC.
sented. Thus it is, that the generality or universality of con-
cepts is potential, not actual. They are only generals in-
asmuch as they may be applied to any of the various objects
they contain ; but while they cannot be actually elicited into
consciousness, except in application to some one or other of
these, so they cannot be so applied without losing, pro tanto,
their universality." x
(a) Occam has a very clear apprehension of the requisites of intuitive
and representative or abstractive knowledge. In order to intuitive
knowledge, all that is needed is the intellect and the thing known, and no
species. In order to abstractive knowledge, there is needed something
first besides the object and the intellect. Something is left in the imagi-
native power, through the mediation of the intuition of the particular
sense, which was not there before. Otherwise no representation would
be possible. But what is left is not a species, but a habit (habit kx)
— not the object of the act, but a certain habit inclining to represent
the object formerly perceived (sensatum). Simulacra, phantasmata,
idola, imagines, are not anything really distinct from things without,
but indicate the thing itself in respect that it terminates the act of the
internal sense in the absence of the sensible thing. — (Sent., ii., Dist. 27,
qu. 15 C. Prantl, iii. xix. 759.)
When it is said that the intelfcctus aaens makes the universal in the
act, this is true, because it makes something feigned (fictum) and pro-
duces a certain concept in objective being, and in no way subjectively.
(Subjective means in the subject as existing ; objective, in the mind
as intelligising. )
(b) Thomas Aquinas held, in regard to universal intelligible species,
which the intellect gains by abstraction, that the intellect cannot
actually (actu) understand them unless by turning itself to singular
phantasms. — (Prantl, iii. 201.)
§ 117. What, then, it may be asked, does the general term
precisely stand for or represent ? It signifies or symbolises
simply an individual image, which we consider as representing,
though inadequately, the generality. We make this individual
image stand for any or for every other which it resembles in
those essential points which constitute the identity of the class.
We cannot, for example, imagine the genus triangle, but we
can imagine a rectangular triangle alone, or an equilateral
triangle alone, or both together in separate representations.
Conscious of their similarity in one essential feature, we may
imagine only the one, and regard it as the (inadequate) rep-
resentative of the other. The relation of similarity, how-
ever, we cannot imagine. It is wholly unpicturable, but we
1 Hamilton, Logic, L. viii.
CHARACTERISTICS OF COXCEPT. 93
conceive it. When we have two objects before us or the
images of the two individual objects, we can conceive it, —
make it an object of intelligence or thought. This is con-
ceiving or thinking in the proper and fundamental sense of
the term. The whole confusion on this point has arisen
from not distinguishing between the image and the concept —
the Anschauuvg and the Begriff- — as is done in German philo-
sophy. There is the individual object or image : that is rep-
resentable, picturable, in the imagination ; there is the in-
telligible relation or similarity between two or more objects
or representations ; there is the consciousness of identity in
the resembling feature ; and there is the contemplation of
the one individual image as possessing this feature, and,
therefore, representing it in every other resembling indi-
vidual.
§ 11$. Thought, therefore, is the representation, through
imagination, of a whole class of individual objects — actual or
possible. This is the proper doctrine of Nominalism, at once
true and self-evident. The completed act of conception im-
plies at once the knowledge, the image, either of the indi-
vidual object as presented in sense, or as represented in im-
agination, and the knowledge of the relation of resemblance
between it and another or other individual objects, fused in
one act of consciousness. As Hamilton puts it precisely and
succinctly, and in a way that should have absolutely precluded
misconception, " A concept or notion, as the result of a com-
parison, necessarily expresses a relation. It is, therefore, not
cognisable in itself — that is, it affords no absolute or irrespec-
tive object of knowledge, but can only be realised in con-
sciousness by applying it as a term of relation, to one or
more of the objects, which agree in the point or points of
resemblance which it expresses." x This, as he truly says, is
the key to the whole mystery of generalisation and general
terms.
(a) On this point reference may be made to the following passages
as illustrating the doctrine of Hamilton : —
" The terms notion and conception (or more properly concept in this
sense) should be reserved to express what we comprehend but cannot
picture in imagination, such as a relation, a general term," &c. — (Reid's
Works, p. 291, note.)
1 Logic, L. vii. p. 128. See especially L. viii. r-p- 134-186.
94 . INSTITUTES OF LOGIC.
"Imagining should not be confounded with conceiving, &c. ; though
some philosophers, as Gassendi, have not attended to the distinction.
The words conception, concept, notion, should be limited to the thought
of what cannot be represented in the imagination, as the thought sug-
gested by a general term. The Leibnitzians call this symbolical in con-
trast to intuitive knowledge. This is the sense in which conceptio and
conceptus have been usually and correctly employed. "— (Reid's Works,
p. 360, note.)
" Of all such [general notions] we can have no adequate imagination.
A universal, when represented in imagination, is no longer adequate,
no longer a universal. We cannot have an image of those, but only of
some individual of that species. We may, however, have a notion or
conception of it. " — (Reid's Works, p. 364. )
"When abstract and general conceptions are 'particularised,' they
thus cease to be abstract and general, and become merely individual
representations. In precise language they are no longer vo-^fiara, but
(payrdffnara — no longer Begriffe, but Anschauungen ; no longer notions
or concepts, but images. The word ' particularised ' ought to have been
individualised." — (Reid's Works, p. 365, app. 407.)
"A universal, when represented in imagination, is no longer ade-
quate, no longer a universal. We cannot have an image of horse, but
only of some individual of that species. We may, however, have a
notion or conception of it." — (Reid's Works, p. 364.)
§ 119. This solves the problem of Nominalism and Concep-
tualism. The Nominalist showed that a notion could not be
imaged or imagined, — that this, in fact, involved contradic-
tion. The generality, therefore, they attributed to the name.
The Conceptualist held that the object of thought was not
simply a name, but a notion or intelligible object, but those
conceptualists erred who supposed that this was cognisable
by itself.
(a) "The whole controversy of Nominalism and Conceptualism is
founded on the ambiguity of the terms employed. The opposite par-
ties are substantially at one. Had our British philosophers been aware
of the Leibnitzian distinction of intuitive and symbolical knowledge ; and
had we, like the Germans, different terms, like Begriff and Anschauung,
to denote different kinds of thought, there would have been as little
difference of opinion in regard to the nature of general notions in this
country as in the empire." — (Reid's Works, p. 412. Compare note,
p. 360, and Met., L. xxxv. and xxxvi.)
The doctrine of Nominalism, rather Ultra -Nominalism, may be
stated as implying that there is no science of universal things, but only
of the common names of things. There is no connection of things
among themselves, — all that exists is individual, isolated. There is
no thing which is common with any other in nature ; the community
lies wholly in the vocables of the things themselves.
Conceptualism teaches that universals are mere concepts, or that
HAMILTON AND BKOWN. 95
beyond the thought of man there is nothing universal in the universe
of things, common to things among themselves. On the other hand,
some conceptualises hold that there are universal things in nature, and
that these have being per se (ovaidv), although they have not subsist-
ence by themselves, but in singular things, and by them.
Realism implies that universals are not only common names, but
principally things of common natures, which are first signified by
common names. The Realists say, for example, that animal signifies
some nature, in which man and beast agree. Thus the name animal
is not only universal, but the nature animal is so. — (See Goclenius, sub
voce Nominales.)
(b) According to the doctrine ascribed at least to certain thinkers,
known as Conceptualists, we can form an idea corresponding to the
generality of the class term. To this Hamilton in substance replies
that if by idea or conception or notion be meant an image, — one
image, — whether the product of sense, apprehension, or of imagination,
— there can be no one image corresponding to the general term, for
the simple reason that such would be contradictory, self-annihilating.
Take, for example, the notion man. An image adequate to the gener-
ality of this notion would necessarily include male and female, black
and white, copper-coloured, tall and short, &c. Nay, it would need to
represent all and none of these, — it would need to be absolutely general
as the class, and yet not be identifiable with a single individual of it.
This is a manifest impossibility, an absurdity. In the same way an
image adequate to triangle must represent both rectangular and equi-
lateral triangle, and yet neither of these at the same time. There is
thus in the attempt even a twofold violation of the law of non-contra-
diction.
In this connection Hamilton acutely exposes the fallacy of Brown's
doctrine of the generality of the notion as lying in "the feeling of
resemblance," and also his inaccurate statement of the Nominalist
doctrine. Brown criticises the Nominalistic doctrine, on the ground
that it omits what he calls ' ' the feeling of resemblance " between the
objects of perception or conception classed under the same common
name, — omits thus the essential element of the true theory, and leaves
it impossible for us to limit the application of the term to a definite
set of objects. — (See Brown's Lectures, xlvi. and xlvii. ) On the
historical point, Hamilton shows that with the Nominalists uni-
versally— with Hobbes, Berkeley, Hume, Adam Smith, Campbell,
and Stewart, — apprehended resemblance between the objects is the
ground of classification, and the reason of the name. What the
Nominalists deny is, that this conception of similarity could constitute
a general notion. And Brown, in making this a general notion, is
himself wrong. Resemblance is a relation ; a relation supposes certain
objects as related terms ; the resemblance must be in some particular
mode or quality, as colour, figure, &c. ; and the resemblance between
two individual objects in a determinate quality is as individual and
determinate as the objects and their resembling qualities themselves.
The likeness, for example, between a particular snowball and a parti-
cular egg is not more general than the representations of the several
96 INSTITUTES OF LOGIC.
objects. Brown's mistake arises from the lack of an accurate distinc-
tion between the image, product of apprehension or imagination, and
the concept proper which, as involving a relation, is not picturable in
imagination at all, but the object of the intelligence or understanding,
though not such an object per se, or apart from the images of the
related objects. And this mere relation of resemblance between any
two given objects is not more general, though unpicturable, than each of
the individual objects themselves. In the face of all this, Mill actually
assumes, as Hamilton's opinion, that the relation can be thought per
se, and that it can thus be thought as general, and uses against this
opinion, though without acknowledgment, the arguments employed
by Hamilton against Brown's views. — (See Examination, c. xvii. pp.
318, 319.)
Hamilton here has not expressly distinguished the extension and the
comprehension of the concept, and it seems to be the former aspect of
it which he contemplates, in showing the impossibility of forming an
adequate idea or image of it. The question may be asked, Are we
equally unable to image or picture adequately the simple abstract
quality, or the sum of attributes which makes up the comprehension
of the concept ? This question, I think, Hamilton intends also to
answer in the affirmative ; for he agrees with Berkeley in holding that
it is impossible to form abstract ideas of extension, motion, or colour.
— (Met., L. xxxv. pp. 298, 299.) "It is impossible," Berkeley says,
" for me to form the abstract idea of motion distinct from the body
moving, and which is neither swift nor slow, curvilinear, nor recti-
linear; and the like may be said of all other abstract ideas whatever."
This is true of the idea of colour in the abstract ; for this idea as
purely abstract would be neither red, nor blue, nor white, nor any
other determinate colour. In the case, then, even of the attribute or
attributes called abstract, there is the individual image or picture of
some determinate form of the attribute, the reference of it, in fact, to
an individual subject. We cannot think the comprehension apart from
some degree or form of the extension — that is, we must always indi-
vidualise the attribute. This is made perfectly clear in the Lectures
on Logic (Lect. vii. pp. 128, 129), where we are told "that it is alto-
gether impossible to represent any of the qualities expressed by a con-
cept, except as attached to some individual and determinate object;
and their whole generality consists in this, that though we must realise
them in thought under some singular of the class, we may do it under
any." This means, in fact, that along with the comprehension or attri-
bute, we must always realise some part of the extension, some one object,
contained under the class. But it has nothing to do with the circum-
stance of other attributes of the individual, as Mill seems to suppose.
(c) Hamilton in several places speaks of the distinction in German
nomenclature of Anschauung and Beqriff as corresponding to the Leib-
nitzian distinction of Intuitive and Symbolical Thought.
Anschauung, as standing for the presentation of sense and the repre-
sentation of imagination, as Hamilton says (Logic, Lect. x., iii. p. 183),
can hardly be identified with the Intuition or Intuitive Thought of
Leibnitz. The latter is equivalent to mere than the mere presentation
HAMILTON AND MILL. 97
or representation ; it includes thought, and its function as representa-
tive of a class of objects — e.g., the intuition or representation of a
triangle, that is, of all knowledge of the individual figure and its attri-
butes, and the holding it also as the representative of all similar figures.
This is the proper sense and use of the concept. Symbolical thought,
again, with Leibnitz, takes place when we do not image all, or realise any
of the attributes, but put a name in their place, and think and reason
by means of this. Hamilton fully recognises this kind of thinking.
But he does not regard it as the only form, or the first or best form.
And when he speaks of the Begriff as appropriated to " the symbolical
notions of the understanding in contrast to the intuitive presentations
and representations of imagination," he is not to be taken as meaning
the symbolism of the word or name, as Mill assumes, but simply, what
he says, the symbolism or representative character of the notion as
opposed to the mere intuition of sense or the mere representation of
imagination, which agree in being alike individual and immediate. —
{Logic, Lect. vii., p. 127.)
(d) Hamilton's doctrine on the nature of the Concept seems through-
out clear, uniform, and consistent. But Mill, as usual, will have it
that he holds two opposite doctrines, which his critic calls Nominalism
and Conceptualism. But Mill's entire criticism of Hamilton's theory of
Concepts is a mass of misrepresentation and confusion. He attributes
to Hamilton the doctrine that the concept can be thought separately
by the intellect, and at the same time that it cannot be depicted sepa-
rately from the individual in the imagination. He wholly fails to
recognise Hamilton's distinction of image and relation, the connec-
tion of imagination and comparison in the act of thinking or application
of the concept. Hamilton, as we have seen, holds that there is no
mere or absolute concept of a class, whether taken in extension or in
comprehension. He thus denies the so-called or alleged Conceptualism
of Locke and others. This with him is utterly unrealisable in thought.
There is no generality of this sort. On the other hand, he holds that
while the image or determinate representation is essential to the appli-
cation of the concept to objects, this is not the whole of the process,
but the condition under which we think the relation of the image or
determinate object to others of the class, or others possessing the com-
mon feature. The mere image is as little the concept as the mere
relation of resemblance is. Each is equally individual, particular ;
but fuse them in one complete act, and you have thought proper, or
thinking by means of the concept. Of all this Mill has not a single
glimpse ; and the result is a mass of thoroughly irrelevant criticism.
In the first place, Mill entirely mistakes the individualising of the
concept — "We can only be conscious of them [the attributes said to
compose the concept] as forming a representation jointly with other
attributes which do not enter into the concept." — {Examination, p. 402.)
If by this Mill means that other attributes of the one representation
are convertible with the individualising of the concept, the doctrine is
neither that of Hamilton, nor of truth. A concept may be individual-
ised when there is but one single attribute in the objects of the class,
or where there are no attributes besides those contained in the concept ;
G
98 INSTITUTES OF LOGIC.
when, in fact, the individual as existing, and the individual as con-
ceived, are convertible. This holds true of nearly all our most abstract
conceptions — such as Space, Time, One, Being, and of all singulars as
conceived. To individualise the attribute or attributes of a concept is
not to represent it or them in connection with other attributes of the
(existing) individual ; it is merely to form one image or representation
in which the attribute or attributes of the concept are embodied. This
we do by forming for ourselves a present image or individual object,
the image at a given or definite time — now.
In the second place, on the assumption that on Hamilton's doctrine
" concepts are incapable of being realised in thought at all, except as
representations of individual objects," Mill asks, are they, even, " poten-
tially universal," as Hamilton puts it? — (Examination, p. 389.) Hamil-
ton, as we have seen, in no way limits the realisation of the concept
in thought to the mere representation or image. It is not with him
' ' always the mere part of a concrete image. " This is but the condi-
tion, not of representing, as he says, but of our conceiving the relation
of resemblance, which is at the root of the whole. In this concep-
tion there is a potential, as opposed to an actual universality ; for we
are able successively to conceive, always within the limits of the resem-
blance, other objects, and so predicate the common quality of them.
Mill, however, tells us that here we have not ' ' a potential universality, "
but "an universal potentiality." The "universal potentiality " of the
concept is about the oddest property ever attributed to it, — it is
universally capable of everything, but universally incapable of any
one thing.
In the third place, if Mill had kept in view the fact that, according
to Hamilton, a concept is no absolute object of thought, he would
hardly have been puzzled to reconcile Hamilton's statement of wherein
the clearness of a concept lies, and some words which he borrows from
Esser as to the same point. " A concept," says Hamilton, " is said to
be clear when the degree of consciousness is such as enables us to dis-
tinguish it as a whole from others. . . . Distinct, when the degree of
consciousness is such as enables us to discriminate from each other the
several characters, or constituent parts, of which the concept is the
sum." — (Logic, L* ix. p. 158.) In illustration of this, which is from
Krug, he quotes from Esser the following : "A concept is said to be
clear when the degree of consciousness by which it is accompanied is
sufficient to discriminate what we think in and through it, from what
we think in and through other notions." — (Logic, L. ix. p. 161.) This
to Mill is a wonderful and puzzling discrepancy, and shows that " our
author had no clear conception of what makes a conception clear." —
(Examination c. xvii.. p. 413.) It is only wonderful, because the
critic had no "clear perception" of the fact that Hamilton did not
recognise any separate or absolute concept realisable apart from the
object thought in or through it ; and that he supposed, when he spoke
of the concept being distinguishable from other concepts, that people
would remember this, and rightly judge that the two expressions are
precisely convertible, or at least mutually implicative.
Fourthly, wonderful to relate, Mill goes the length of admitting that
" the true theory of concepts needs not, I think, be sought further than
HAMILTON AND MILL. 99
in our author's own account of their origin " — (Examination, p. 392) ;
but presently, as if this were too generous, he adds : ' ' But his theory
is a complete condemnation of his practice. . . . He affirms that
Nominalism and Conceptualism are the same, and on this justification
expounds all the operations of the intellect in the language of Con-
ceptualism, and on the assumptions of Conceptualism." Hamilton has
never affirmed that Nominalism and Conceptualism are "the same,''
though, if he had, a good deal might be said to show that it is in
the main, or substantially, true. But, taking them as two theories,
Hamilton shows that there is truth in each, and showing what this
truth is, brings them into complete harmony by his own doctrine.
And on the basis of the reconstructed theory, he uses language which
only such a critic as Mill would distort as exclusively conceptual.
Mill asks, "Is it correct to say that we think by means of concepts ?
Would it not convey both a clearer and a truer meaning to say that we
think by means of ideas of concrete phenomena, such as are presented
in experience or represented in imagination, and by means of names
which, being in a peculiar manner associated with certain elements of
the concrete images, arrest our attention on those elements ? " Sir W.
Hamilton has told us that a concept cannot, as such, be " realised in
thought," or " elicited into consciousness." Can it be that we think
and reason by means of that which cannot be thought, and of which Ave
cannot become conscious ? To the latter question any tyro would
answer that the same argument would prove that because we cannot
think the half of a whole by itself, or as such, we must think the whole
by means of that of which we cannot become conscious. The same
tyro might answer to the first question, that if we have only the idea
of a concrete phenomenon, and the name of parts of the concrete
image, we cannot think at all, seeing we should never be able to say
whether any other idea or any other phsenomenon agreed with or
differed from the first — never, in a word, be able to perform the first
function of thought — discrimination — name the part or the whole as
we please. Thinking by means of names — the symbolical thinking
of Leibnitz — is putting names "in lieu of notions." This is a kind of
thinking fully recognised by Hamilton ; but it is recognised by him
and others as possible only because there is another sort of thinking in
the first place, and at the root of the whole — viz., Intuitive thinking,
or thinking through a definite representation of the attributes con-
ceived as common to the class. We may think symbolically, but we
must be able to think intuitively, or by means of the image plus the
conceived relation, ere even symbolical thinking can be regarded as
symbolical of anything. And did we only think symbolically, we
should have no test either of clearness, distinctness, or even truth in
our thinking. We could never bring it to the test of experience, or
lend it the enlightenment of intuition. It would be literally " blind
thinking " — the blind leading the blind.
(On Mill's chapters on General Conceptions, Judgment, and Reason-
ing, the reader may refer to an admirable criticism in Hamilton versus
Mill, a publication of which, unfortunately, only two parts appeared
(Edinburgh, 1866). The exposure of the sophistries of the criticism
in those chapters is most thorough.)
100
CHAPTEE XL
THE CONCEPT ITS CHARACTERISTICS SPECIALLY CONSIDERED COM-
PREHENSION AND EXTENSION RELATION TO LANGUAGE —
INTUITIVE AND SYMBOLICAL THINKING.
§ 120. It follows from what has been said on these points
that every concept has a double or twofold side. As em-
bodying the idea of an attribute or attributes, it has a
meaning, content, or comprehension (Inhalt). As through
the attribute or attributes applicable to several objects, it
has a compass, breadth, or extension {Urn fang). It takes
in objects or classes : in the former aspect it indicates attri-
butes, in the latter it denotes objects ; but it cannot denote
unless it first of all indicate or connote.1 So that con-
notation is the ground of denotation — comprehension is the
ground of extension. In the notion Man, the attributes life,
sensation, reason, free-will make up the content or compre-
hension ; in the same notion, white man, black man, copper-
coloured man make up the extension.
The attributes in the comprehension of a concept are fixed ;
these do not vary. But the species, classes, or individuals
contained within the extension, vary according to our prin-
ciple of division. The specification now given is according
to colour, but we may divide man equally well according to
nationality. Here we should speak of Englishman, Scotsman,
Frenchman, Prussian, Russian, and Turk. Or we may divide
man according to his religion, as Mohammedan, Christian, Bud-
dhist. Or under Christian we may take Papist, Presbyterian,
Lutheran. The comprehension is thus invariable ; the ex-
tension is variable, according to the principle of division,
1 For the proper use of this word see below, p. 173.
COMPREHENSION AND EXTENSION. 101
which of necessity introduces a new attribute external to the
comprehension of the notion divided.
As has been well pointed out, — in reply to the question,
What is an object ? — we speak in comprehension. What is art ?
It is sliill in production. Which are the arts ? The answer
is in extension. Painting, Sculpture, Architecture, &c, are arts.
§ 121. The inadequacy of a concept as a representation,
already noticed, is increased in proportion as the width of the
extension of the concept is increased. Thus, take the in-
dividual— say Sir Isaac Newton. First, I represent him as
astronomer. This implies or connotes certain attributes, as
that he is man and intelligent ; but it does not give me the
individual Newton. It leaves out Englishman, Master of the
Mint, Professor of Mathematics. Newton may be astronomer,
though he is none of these. Astronomer applies to him only
in one relation, and in this relation it might apply to, i.e.,
represent, a hundred men besides.
Then, if I represent him simply as a man, the less do I
think of his proper individuality. I have given up even
what is distinctive in astronomer ; for he might be the
former, and not the latter. If I thiuk of him simply as
existing or being, my notion of him falls still short of the
individual. In a word, the more extensive my view of the
individual or his qualities, the less adequate and the more
faint is my picture of the individual. In technical language,
the more extensive my knowledge, the less comprehensive is
it, — the less does it hold the features of the individual.
Thus, let X = astronomer, and A, B, C, D, E, the other
qualities of the individual Newton not implied in X. These
taken together make up a perfect image of him. When I
think of him as one of the X's, I do not think of him — i.e.,
necessarily think of him, as A, B, C, D, E. My knowledge of
him, accordingly, as given in the concept X, is less than an
adequate representation of the individual by A, B, C, D, E.
§ 122. The neglect of attention to this distinction in
our concepts leads to the blank of thought itself, to mere
verbalism, to using terms which are literally nonsensical.
And it is the source of nine-tenths of our controversies ;
for unless we first of all ask ourselves and our opponents
what precisely each means by the term to be applied to an
object — what is its comprehension — it is obvious that, as
102 INSTITUTES OF LOGIC.
opposing parties, we may be fighting absolutely in the dark.
We may literally attach no meaning to the word we rise, or
each of us may attach a totally different meaning to it, and
so be in agreement, while we suppose we are in mortal
conflict. Definition, — the unfoldiDg or explication of the
comprehension of terms, — is the first requisite to clear and
distinct thinking in our own minds, and it is essential to
the understanding of the position of other people.
(a) In the view of the concept now given, I have regarded it as
identical with what other writers call the General Conception, allege-
meine Vorstellung, schema, notio, conceptio, representatio communis, or
generalis, or universalis. But concept or notion has been taken by
some logicians in a narrower sense.
We are told by Ueberweg, for example, that the notion (Begriff, Notio,
Conceptus) is that conception in which the sum total of the essential
attributes, or the essence ( Wesen, essentia) of the object under con-
sideration is conceived. By the phrase — attributes (Merkmale, Notce),
of the object we include not only the outward signs by which it is
known, but all its parts, properties, activities, and relations, — in
short, whatever belongs in any way to the object. The essential
(essentialia) are those attributes which (a) contain the common and
persistent basis for a multitude of others ; and on which (b) the subsist-
ence of the object, its worth and its meaning, depend. . . . Attributes
are also called essential which are necessarily united to marks essen-
tial in the stricter sense, and whose presence, therefore, indicates with
certainty the presence of those others. . . . The other characteristics
of an object are called non-essential {accidentia, modi). The possibility
of modi, or the capability to take this or that modification, must
have its foundation in the essence of the object. . . ."In perfect know-
ledge, notions are valid only as they correspond to the types of the real
groups of their (natural or mental) objects. . . .
We recognise and distinguish the essential (a) in ourselves imme-
diately by feeling and mediately by ideas. . . . The knowledge of our
own essence depends both on the consciousness of the ethical ideas,
and on the amount of our actual existence in them.
(b) By means of the knowledge of the essence in ourselves, we
recognise the essence of persons beyond us more or less adequately in
proportion to their relationship with ourselves. . . .
(c) The essence or the inner purpose of nature is the analogue of
the ethical duty of man, and is to be known in the proportion of this
analogy. . . .
(d) With the inorganic objects of nature, existence, as an end in
itself, and self-determination, come after existence as a mean for
another, and the mechanically becoming determined by another. —
(Ueberweg, Logic, p. 153.)
The construction of a notion "purely according to objective laws,
on the basis of what is most essential for the object in itself," is the
problem of science, in its various departments. It is not the problem
ESSENTIAL ATTRIBUTES. 103
of any one science ; and its laws are simply those treated of in Induc-
tive Logic. To define notion as identical with the knowledge of
essence, is to be guilty of narrowness in definition, or to abuse the
term. It is, besides, to miss the essential character of the notion itself,
and to pass beyond the whole laws of thinking ultimate in the con-
struction of a notion quel notion. When we ask — " According to what
marks are objects to be grouped together and their notions formed ? "
— what are the marks of the essential as distinguished from the non-
essential or accidental attributes? — there are really two questions
involved. ' (1.) What kind of attribute is essential ? (2.) What attribute
in a given case is essential ? An answer might be given by logic proper
to the former question, — in saying that an attribute is essential when
it is of such a kind that the object in which it inheres would not be, or
not be what it is, in its absence. Such an attribute is extension in body.
This would further fulfil the test of being the permanent ground of
other derivative attributes, — such as figure, position, directly ; and
colour indirectly. It will be found, however, that the application of
such a test is limited really to necessary concepts. When we descend
to the properties of individual objects, and to the classes of things, we
may go back a certain way and find grounding attributes, but we can
never be certain that these are the ultimate and thus the absolutely
essential. What attribute in a given case is the essential one ? Shall
we say that it is that without which the object could not be ? But
then this supposes that we have already defined the object in its essen-
tial character. Shall we say that it is an attribute which affords a
permanent ground for other attributes ? But can we call this properly
essential, or constitutive of the being of the object, qud object? Sup-
pose we know, as we only can know, by observation and induction,
what, then, is to be our test of the essential in an object as compared
with the accidental ? Suppose this test is, that at a given point in the
history of physical science we find certain attributes prior to others in
the order of nature, on which those others depend, are we at once to
say that these are the essential attributes of the object ? If so, what hap-
pens when we find, through further analysis, that those so-called essen-
tial attributes are themselves dependent on others ? — are themselves
derivative? And where is this process of analysis to stop? Can we at
any time say that we have found the essential attributes of any object,
taken objectively ? Or rather is it not the case, that in every stage of in-
ductive inquiry we can only say that we have found attributes prior to
others, but the ultimate and permanently essential still necessarily escape
us ? Could we get at the prius of all the objects of our sensible experi-
ence, or of even one object of that experience, then, and then only, could
we determine the essential attribute or attributes of the object. In fact,
the term essential, as objectively implied, has properly only reference to
hypothetical constructions, in which we deal with a limit subjectively
imposed, or to mathematical constructions in which the grounding
concept of extension, necessarily conceived, is modified by us according
to certain implied requirements, by means of definition. Line, sur-
face, triangle, square, can each be given in its essence, but this only
ideally, for there are metaphysical questions regarding the prius of
104 INSTITUTES OF LOGIC.
extension itself. And the true essence may, probably does, lie in unity
of force behind the whole of the extended world.
§ 123. But concepts are naturally expressed in Terms. This
leads to the consideration of the relations between thought
and speech. The essential element in human speech is its
symbolical character. Words are the signs or symbols of intel-
ligence, or rather of the products of intelligence as a mental
act. Intelligence is essential to the formation of language,
and is in exercise previously to the production of the word or
sign. The faculty of language, which depends partly on the
organs of speech and the power of producing sounds, is ob-
viously natural to man, as his intelligence is. But the
faculty comes into play at the prompting of intelligence, and
in order to satisfy the needs of human consciousness. Intel-
ligence is thus the principle and the source of language. Its
conditions are given us in our physical organisation : but no
arrangement of mere articulate sounds can constitute human
language ; for its essential characteristic is, that it is sym-
bolical of meaning or thought. Speech is not merely a series
of words, but a series of word-signs expressive of thought,
feeling, desire, and will.
§ 124. The necessity for language appears to arise at the
point of our earliest generalisation — even our earliest abstrac-
tion, which is made general. We need a sign for that feature,
or those features which several objects present in common.
The moment we begin to generalise, that moment do we give
expression by the word or term. The process of forming
notions is one of disengaging an attribute or variety of attri-
butes from the individual objects of perception. This amounts
to disconnecting those attributes from definite conditions of
time and place. We have, therefore, recourse to the word
or term, which comes in the place of the individual object
of perception, and serves as a point or termination for the
generalising intellectual act, and further, as a nexus which
binds the abstracted attributes together. In virtue, there-
after, of the principle of association by which one object sug-
gests or recalls another that has once been connected with
it, the word brings before us in all time the attribute or sum
of attributes marked, or it recalls to us some individual ob-
ject in which these attributes are embodied. We thus by
association connect the word and the concept, and by the
GENESIS OF NAMING. 105
same principle we are enabled to bring back our notions
to remembrance.
§ 125. The first stage in the process that leads to naming
seems to be that of fixing on or abstracting, as it may be called,
an attribute amid the complexity of attributes presented to
perception. This is the first arrest of intelligence — the con-
centration of consciousness on one out of many of its objects.
This arrest of intelligence is many-sided ; and it is strong as
the powers of the world around us. It is bright and vivid as
that world is clear and intense. It is varied as the wide
sphere of nature itself. In this stage, however, we do not at
first need language, and we do not use it. The thing known
is before us as a reality ; and while this is so we do not need
to name it. The perception is fixed on the percept ; the
percept stands for both thing and name.
§ 126. But there comes a time when this quality perceived
is no longer present to the mind, present in time or in space.
Its reality has become a thing of the past ; yet it is a memory.
And other impressions arrest the perception ; but the under-
standing is vigilant, and it apprehends relations of resem-
blance. The quality originally perceived passes into the term
of a relation, and we have now the ground of the general ab-
stract. But this is an idea, a concept, or thing in the mind,
and it would pass away but for the name. The name thus be-
comes the outward or sensuous sign of the dim abstract ; the
kind of familiar friend of our thought, which fixes and keeps
it, on which, as it were, thought leans. What was originally
perceived, but not named, becomes roundness, or squareness, or
redness, or whiteness, or blackness — this ness indicating being in
each case to begin with, and this round or square indicating
the kind of quality perceived in each case. This gives us the
abstract noun or name, perhaps the first or earliest of names ;
for quality precedes the notion of class, and grounds it. Class
means simply similarity of quality in things, and every quality
in an object is capable of raising that object to a member of a
class, because the quality may be found in other objects.
§ 127. The third stage is that of the class, or concrete com-
mon name or noun. This means that a great number of
things or objects is grasped under a common relation of re-
semblance. We drop the ness, as it were, or whatever stands
for the abstract quality ; and we have the common concrete, —
106 INSTITUTES OF LOGIC.
the round and the square, the red and the white, — that is, we
have the names of classes of things ; and to the name we
transfer, as it were, the burden of thought — the burden of the
whole indefinitude of individuals comprised under the name.
It is now in the generality of thought, when we have passed
from perception, and the real before us, that we have re-
course to the name, and thus designate the generality of
abstraction. To me it appears that the abstract quality is
first named as inner ness, or holloioness, or redness, or whiteness;
and then, by a more concrete form of thought, the common
term arises, and we name not so much the quality, as the
things possessing it, by inner, hollow, red, or white — that is,
we get the class-name.
§ 128. The concept may be said to be imperfect until it is
named, expressed, and fixed in a verbal sign. Concepts are
far from being mere words, — flatus vocis ; the word is but a
sign of thought, and the thought is there before it can receive
the sign. " Speech is not the mother, but the god-mother of
knowledge." Yet it is true " that we could never have risen
above the very lowest degrees in the scale of thought without
the aid of signs." The concept is rendered "permanent for
consciousness by being fixed and ratified in a verbal sign ; " x
and the thought it indicates, from being embodied in the term,
gains in clearness, distinctness, and definiteness.
(a) The generality of the concept does not lie in a community of name.
It is not the essence of the word, says Abelard, as word, which can be
attributed to several ; the vocal sound which constitutes the word is
always actual and particular each time it is pronounced, and not
universal, but it is the signification one attaches to it which is general.
— (Abelard, Glossuhv s. Porphyrium — (Remusat) — Prantl, ii. 175.)
§ 129. This is the primary and normal relation of words
and names to concepts. But there is another relation. It
frequently happens that, in the employment of the word or
sign, this does not suggest the whole amount of thought for
which it is the adequate expression. On the contrary, we
frequently give and take the sign, either with an obscure or
indistinct consciousness of its meaning, or even without an
actual consciousness of its signification at all.2 This was the
point insisted on by Leibnitz in the now well-known distinc-
1 Hamilton, Logic, L. viii., vol. iii. pp. 137, 138.
2 Hamilton, Logic, L. x. , p. 172.
SYMBOLICAL THINKING. 107
tion between Intuitive and Symbolical Thought. The latter
is a common form of thinking ; we use names for concepts,
believing that we can unfold the meaning at will. It is neces-
sary for rapidity in thinking ; it is necessary also in cases
where we cannot actually depict to the mind every point or
individual element of the concept, as in large numbers,
where we proceed through aggregates regarded as units.
But it is a frequent source of error, and often a cloak for
absurdity. The actual unfolding of the meaning or attri-
butes in the imagination — intuitive thinking — is the neces-
sary corrective in ordinary cases of this " blind thinking."
§ 130. In the case especially of a complex concept, that is,
a concept which involves a considerable variety of attributes,
we do not stop each time we use the term which denotes it
to realise fully to the mind each and all of the attributes con-
tained in it. We habitually employ general terms without
fully, or even in any considerable degree, realising their
meaning. When we speak, for example, of Government,
Church, State, Constitution, Commerce, Jurisdiction, &c, we do
not on each occasion of their use unfold to our mind all the
constituent elements of the notions indicated by those terms.
And yet we employ them appropriately enough. Were one
of these terms substituted for another in a discussion, as
Hume has remarked, we should at once detect the incon-
gruity.1 We employ these terms without articulately unfold-
ing the full meaning of each, with a conviction that it is in
our power to do so if required. We can carry out a process
of thought in this abbreviated form ; and as such it is called
symbolical, seeing that we make use of symbols as substitutes
for the contents of notions. The process might appropriately
be called shorthand thinking. When, on the other hand, we
actually realise to the mind all the attributes contained in a
notion, our thought is said to be intuitive ; for the moment
we depart from conception that is purely symbolical, we call
up before the mind an individual representation or embodi-
ment of the attributes contained in the concept, — taking this
representation at the same time as the type of the class.
(a) This distinction of knowledge, or rather of thought, as intuitive
and symbolical — one of the most important analyses at once in psychol-
1 Treatise of Human Nature, i. 7.
108 INSTITUTES OF LOGIC.
ogy and in Logic — was taken by Leibnitz, in a paper published by him
in 16S4, entitled De Cognilione, Veritate, et Ideis. " For the most part,"
says Leibnitz, " especially in an analysis of any length, we do not view
at once the whole characters or attributes of the thing, but in place
of these we employ signs, the explication of which, into what they sig-
nify, we are wont, at the moment of actual thought, to omit, for the
sake of brevity, knowing or believing that we have this explication
always in our power. Thus, when I think a chiliogon (or polygon of a
thousand equal sides) I do not always consider the various attributes of
the side, the equality, and the number of a thousand, but use these
words (whose meaning is obscurely and imperfectly presented to the
mind) in lieu of the notions which I have of them, because I remember
that I possess the signification of these words, though their applica-
tion and explication I do not at present deem to be necessary : this
kind of thinking I am used to call blind or symbolical. We employ it
in algebra and in arithmetic, but in fact, universally. And certainly
where the notion is very complex, we cannot think at once all the in-
gredient notions ; but where this is possible — at least, inasmuch as it
is possible — I call the notion intuitive.'''' — (Quoted, Hamilton, Logic,
L. x.)
§ 131. Symbolical knowledge may thus not inaptly be
compared to a bank-note. We accept and pass a note —
say £1, — from hand to hand without considering each time
we do so how many shillings, sixpences, or pence the
piece of paper represents. We do not unfold to the mind
the exact constituents of the value represented by the
note. This is analogous to our use of general words.
We employ general terms without forming to our minds an
exact representation of the various attributes indicated by
them, just as we do not consider each time we pass a note
that it stands for 240 pence. The process is in both casek.
an abbreviation of labour, and is, in both cases, a symbolical
act. We should render this symbolical act intuitive, if, in-
stead of blindly passing the mark or symbol as a substitute
for the things represented, we set about counting the money
represented in the one case, or picturing to our minds the
attributes represented in the other.
§ 132. It is thus obvious that we may have two kinds of
objects fitted to stand as the type of a class of things. We
may, in the first place, make the representation of any one
individual of a class stand for all the other individuals of that
class, by considering only those points which it has in com-
mon with those other individual objects. In this case we
fully realise the contents of our concept or notion. Leibnitz
SYMBOLICAL THINKING. 109
would call this an intuitive thought, not that it is merely an
intuition, but that it is an intuition constituted into the type
of a class of objects ; it is, in fact, an intuition and a thought.
This is the highest and best form of an act of conception, and
is that towards which, on all occasions, we ought as much as
possible to strive.
In the second place, we may take the symbol or term
which denotes the concept or notion, and rest satisfied with
it, without fully realising the contents of the notion — unfold-
ing them before the mind. This term, from its application
and associations, designates equally any one of a class of
individual objects, and only the individuals of that class.
Whatever, accordingly, we think as applicable to the symbol
or involved in the symbolical knowledge, we regard as ap-
plicable to any one and to all of the individuals which it
represents. We have an illustration of intuitive thought in
the case of Geometry. Here our reasonings refer to an individ-
ual diagram, regarded simply as representing all the possible
figures of the class to which it belongs. We have an ex-
ample of symbolical thought in the case of Algebra, where the
process of investigation is carried on entirely by means of
symbols, representative, it may be, of a quantity which, dur-
ing the process, is regarded by us as entirely unknown
or indefinite. In Algebra, for example, to quote a case, you.
may take the division of unity into any two parts. Here it
is shown that the difference of their squares is equal to the
difference of the parts themselves. It does not matter what
the numbers are. Letters will represent them. This is a
universal law or formula which is worked out, in total un-
consciousness of definite pictures or images attached to the
terms.
§ 133. This distinction of symbolical and intuitive know-
ledge has a very wide and important application. There are
cases in which symbolical thinking is an absolute necessity.
Think of the difference between the idea of a figure of 1000
sides, and that of a triangle or figure of three sides. The latter
we are able quite well definitely to imagine, to picture. The
other we cannot; but we know what it means. And how so?
As appears to me simply by repeating units, which we know
or can picture. Five and ten we can picture, 100 we can
hardly ; but we can realise the 100 through the five or ten.
110 INSTITUTES OF LOGIC.
As we go on to 500, to 1000, the thought grows more dim
as a picture, yet our knowledge is exact enough, because we
go on forming units of which the larger number is composed.
When I am told that the distance of the sun from the earth is
92,400,000 miles, or that the mean distance of Uranus from
the sun is 1,754,000,000 miles, I confess that I cannot picture
either of these distances to my imagination. I cannot make
what is called an intuitive thought of it, yet I know it in a
symbolical and even definite manner. In the same way, when
I am told that light travels at the rate of 186,000 miles per
second, and thus traverses the distance from the sun to the
earth in eight minutes, I have but a symbolical or unpictur-
able knowledge; yet it is all the knowledge I can have in the
case. We must be content to think those numbers through
the repetition of picturable units merely. We may picture or
construe to the imagination so many units — say five, ten,
fifteen, twenty ; but after that, each of these sums is itself
regarded as a unit, and thus becomes the basis of a higher
calculation or concept. And there is no reason why twenty
units should be regarded as less a unit than one. The twenty
is virtually one, — one as against everything less or more than
itself, — a true unit ; and we may thus add or repeat this
unit, as much as any smaller unit we know. Algebra all
through is very much this kind of knowledge ; geometry, as
I have said, is not so ; for at each step wre have the picture
of a figure before us. For this reason, algebraic training is
not so good a mental discipline as geometry; and both are
inferior as means of culture to the study of the sciences of
intuition, or of fact and probability.
§ 134. It is possible to carry on long trains of reasoning
in this the symbolical method. In fact, it is the most
usual of all methods. But it is this circumstance which
mainly allows contradiction and absurdity to escape us,
which otherwise we should at once detect. It explains,
indeed, how so much is written and accepted as true, which,
nevertheless, we are totally unable to conceive, or even render
intelligible. When contradictory propositions are stated in
terms, whose meaning we fully apprehend, the contradiction
at once flashes on the mind. This would be the case always,
if each of our terms were fully and definitely understood.
But as we use terms symbolically, we may and do employ
SYMBOLICAL THINKING. Ill
terms of contradictory import, form these into propositions
and reasonings, accept the conclusion as valid, without being
at all aware of any incongruity. Yet when our reasoning
encloses a contradiction, however cloaked or concealed, the
whole process is absolutely null ; it is, in a word, nonsensical
or meaningless. To accept the meaningless for the mean-
ing, non-sense for sense, is one marked danger of purely
symbolical thinking. A frequent use of definition, and the
substitution of intuitive for symbolical thinking, are our
main safeguards against contradiction and confusion in any
discussion.
112
CHAPTEE XII.
THE LAWS OF THOUGHT : IDENTITY NON-CONTRADICTION
EXCLUDED MIDDLE DETERMINING REASON.
§ 135. If there be in thought form essential and universal,
this must depend on law necessary in thinking. If, when-
ever we think, or in whatever we call thinking, there is a
type to which the act of thinking conforms, in order to its
very existence, then this type must depend on a law, that
is, a rule so uniform and general as to amount to universality.
The matter of our thinking varies indefinitely ; rules of gener-
ality may apply to it ; difference does not destroy the matter
of thought. Variation from form destroys form, — destroys,
in fact, thought itself. Hence the law which regulates this
unchanging form must itself be an unchanging law, — depen-
• dent, that is, on the very nature of the thinking subject, —
necessary, universal, and thus essential to the very being and
act of thinking.
§ 136. The unchanging character of the form of thought
proves the necessary character of the law of thought ; this,
again, proves the unchanging character of the form of thought.
We may either say that thought as form is necessary, un-
changing, universal ; or that the law of thought is so. The
form is the concrete embodiment of the law ; the law is the
abstract statement of the form.
§ 137. The laws of thought are usually divided into the
contingent and the necessary ; but the latter alone are the
proper laws of thought. We may think successively in
various spheres of knowledge, or of various objects. Where
the objects of thought differ, the laws or conditions of our
thinking them differ also. Thus we may think a state of
LAWS OF THOUGHT. 113
consciousness ; we do so as in time, as contrasted with a
past state, and as void of dimensions. We may thiok an
object of sense, — quality or percept. This we think not
only as now or in time an object of thought, but as in a par-
ticular space related to an object or objects in co-adjacent
spaces. It is contingent whether we think the sensation or
say the sun-dial : and therefore the conditions under which
we think in each case are in so far contingent. These may
metaphysically or really become necessary to the thought
regarded as the thought of the given object ; but there being
no necessity for our thinking the determinate object, there is
no absolute or universal necessity of the condition upon our
thought. These are therefore for thought itself contingent
laws or conditions. They apply only if we happen to think
of certain or determinate objects.
But the laws proper of thought are necessary laws. In
other words, thought of any object is impossible apart from
them. They are the laws of thought as thought. Whatever
be the object we think, we must think it as identical with itself,
as in absolute contrast to its contradictory correlative, and
that on pain of the annihilation of the thought itself. Apart
from the contingent conditions of thinking, certain acts of
thought would not be ; apart from the necessary conditions
of thinking, no act of thought would be. The laws of thought
thus imply a certain abstraction from objects. To them the
object is as to its real nature or characters indifferent. Some
object there must be in order that the law may be manifested
in exercise. But any object is all that is needed. They
bear the same relation to the objects of experience which the
laws of universal grammar bear to the words of different
languages. They contain the intelligible forms of the objects,
as the principles of universal grammar embody the possible
combinations of the words which constitute intelligible, that
is, possible speech.
§ 138. At the same time these laws are inaccurately de-
scribed as independent of all experience. They are not so,
either as to their known origin, — the possibility even of their
conception by us, or of their realisation in our consciousness ;
for this always supposes some instance, either given in ex-
perience or created in the interest of pure thought by the
imagination. They are independent of experience only in
n
114 INSTITUTES OF LOGIC.
the sense of not being merely generalisations from experience,
but conditions even of its possibility as elements correlative
with the matter. Logic is thus the science of the form of
thought, that is, of the laws of the form of thought, or thought
in its utmost generality, as dependent on, or as the expres-
sion of, necessary law.
§ 139. The fundamental virtue of the form of thought is the
consistency of thought with itself. Thought postulates this
in order to its very existence. Thought radically inconsist-
ent is null ; it is not thought, — it is merely words. Neces-
sary connection is the higher virtue of thought. This, how-
ever, is something that follows upon and is superadded to
consistency. Consistency is shown when we can think a
notion without self-destruction. It is the bare possibility of
a notion.
§ 140. The consistency of thought with itself needs explica-
tion. This implies (1) itself — a definite thought (concept), con-
sisting of a definite mark or marks, to begin with. Whatever
transcends definite thought transcends logical law. The
limitation of a concept depends on its constitution through
its marks or attributes. The predicate itself or self, or in
self is utterly inapplicable, unless to a definite concept or
notion.
The laws of thought are thus, in their logical import,
applicable only to definite thought. There must be a con-
cept constituted ere any of them can come into play. They
are in the movement of constitution ; but they are fully real-
ised and applied to the concept or product of the act. But
this concept may be of the utmost generality, provided only
it possess definite content. Hence the laws are applicable
from the earliest movement of thought. The concept must
have at least an attribute, or be an attribute or sum of attri-
butes. Hence they are utterly inapplicable to what is called
pure being or pure thought — the alleged starting-point of the
immanent dialectic or constructive process of the Hegelian
logic. This, as qualityless, cannot come under either the
law of Identity or Non-Contradiction, and it can thus yield
no possibility of movement or construction. The wholly in-
definite is above logical law, and above intelligibility. It can
yield a basis neither for analytic nor for synthetic thought.
(2) They are applicable in the case of mere verbal formulas
HIST01UCAL NOTICES. 115
only hypothetically, but strictly and essentially to whatever
may at any time be comprised in the formula. Thus we
cannot strictly say that an infinite non-commencement of
being in time is contradictory of an absolute commence-
ment of being in time ; but we can say that if we could
actually think what either set of words implies, there would
be two ^contradictories. We can know what would be contra-
dictory from the form of expression, even though that form
is not capable of being translated into an actual or definite
object of thought.
§ 141. A concept being an itself or self — that is, possessing
definite attributes: — it must be thought as such, if thought at
all. In other words, the concept and the sum of characters
which make it up are identical ; and the concept as a whole is
convertible with the sum of characters as its parts. In this is
manifested the force of the law of Identity (principium Iden-
titatis). It implies that a concept in thought is what it is
in thought, and not its opposite — contradictory or contrary.
Every object of thought is conceived as itself — or every A is A —
or, as Baumgarten puts it, following Aquinas, every subject is
predicate of itself. This is the principle at the root of logical
affirmation or position.1 It is at least that without which
affirmation would be impossible.
(a) The earliest expression of the Law of Identity seems to be due
to Parmenides, — xpv T^ *-«7«"' Tt vot tv t' 2m Hfxnevat, — it behoves us to
say and to think this, that which is, is. — (Cf. Ueberweg, Logic, p. 232.)
This is found in the fragments of Parmenides, edited by Mullach. But
the first writer who grasped it in its full significance, and stated it
for modern thought, was Antonius Andreas, a scholar of Scotus, about
the end of the thirteenth century. He died in 1320. In his work,
Quaestiones super XII. Libros Metaphysical — Venetiis, 1481, he makes
the Law of Identity not only co-ordinate with that of Contradiction,
but accords to the Law of Identity the first place. His formula is Ens
est Ens. — (See edition of 1513, Quaest. v. p. 21 a, and Hamilton,
Logic, L. v.)
(b) Plato held in regard to sensible things that, as they are in constant
change, each thing unites opposites, or contradictions. They do not
exist, — they are in a state of flow between being and non- being.
We cannot say that the sensible thing is what it is, or that it is not.
He held, however, that the axiom of Non-Contradiction applies to
Ideas, and to mathematical conceptions, — these being unchangeable.
But he did not properly distinguish between Contrary and Contradic-
tory Opposition. — (Cf. the references in Ueberweg, Logic, p. 249.)
1 Cf. Hamilton, Logic, L. v.
116 INSTITUTES OF LOGIC.
(c) Aristotle recognised the validity of the principle of Identity in
such expressions as "to say that being is not or that not being is, is
false ; to say that being is and not being is not, is true."— (Met., iv. 7,
ix. 10.)
(d) Aquinas says that those propositions are the most known by them-
selves in which the same is predicated of itself, as man is man, or
whose predicates are included in the definition of the subject, as man
is animal. — [Contra Gentiles, i. 10. Quoted by Hamilton, Logic, vol. iv.
Appendix on Laws of Thought.)
(e) Baumgarten expressly distinguished the laws of Identity and Con-
tradiction, and called the former " principium positionis sive identitatis."
His formula is : Every possible A is A, or whatever is, that is, or
every subject is predicate of itself. — (Met., § 11 ; cf. Hamilton, Logic,
L. v. )
(/) Hegel remarks regarding Identity stated as A is A, that no one
thinks or speaks according to it. — (Log. i. 2 ; 32 ff. ; Encyl., § 115.)
The truth is that no one can accurately think otherwise than in accord-
ance with it, whether he make this explicit or not. When we reason,
we do not need to syllogise, though our reasoning is an implicit
syllogism. No more do we need to speak in the formula, or in words
precisely corresponding to it, however rigidly we may assume it. It
would certainly be idle and somewhat ridiculous to say a planet is a
planet, magnetism is magnetism, a spirit is a spirit ; but such a state-
ment is not false, and it may be necessary to identify a concept with
its essential characters, when it is alleged, as by Hegel, that it is other
than it is, or that it is itself and is also other than it is. If a man
says yes is no, one is obliged to formulate the denial by saying yes is
yes, and no is no ; or if he says good is evil, and evil good, we are con-
strained to say no — good is good, and evil is evil.
§ 142. The Law of Identity implies affirmation and nega-
tion— position and exclusion — identity and difference. This
correlation arises from the limitation implied in the constitu-
ent attributes or qualities of a concept. This constitution
or self-hood of the concept is the ground in thought of the
negation, difference, not-selfness. The latter is impossible
apart from the former, is conditioned by it, has no meaning
apart from the positive concept as a sum of attributes.
This negative side may be expressed in the formula — A
which is not B, is not-B. A concept cannot remain identical
with itself, unless in so far as it remains different from what
is not itself. The negation is not necessarily a positive con-
cept, or itself an attribute or sum of attributes. It may be,
and generally is a purely ideal negation, or the conception of
the absence or abstraction of given attributes, e.g., Being
and non-Being, One and None, either generally or of a given
LAW OF IDENTITY. 117
class, Centaur and no-Centaur. Being or Thing is the most
general concept we have. Non-being is a mere relative, sup-
posing being, but is the sublation wholly of being. There
can be no reality or really existing object in negative rela-
tion to being.
(a) Ueberweg adds the axiom of Consistency (principium convent-
entice), as allied to that of Identity. It is expressed,— A which is B,
is B, or every attribute which belongs to the notion may serve as a
predicate to the same. The formula, — Not- A is not- A, is merely
an application of the axiom of Identity to a negative notion. So A
which is not-B, is not-B, is only an application of the principle of Con-
sistency ; and is the ground of negation.
There seems to me to be no necessity for adding this so-called axiom
of Consistency. Everything it can do for us is embraced in the scope
of the Law of Identity. When we say A which is B is B, we merely
apply the Law of Identity, after analysis or definition of A, — A being
B is B. Again, A which is noi-B, is not-B, is the negative side of the
Law of Identity, for A being given as not-B, or lying out of B, is
merely A lying out of B, or A (a definite concept) being given as
different from what is not - itself (B) is simply held different from
what is not - itself (B). We cannot affirm the Law of Identity on its
positive side without implying its negative application. A thing or
concept cannot remain identical with itself, unless in so far as it re-
mains different from what is not-itself.
§ 143. The Law of Identity, in saying that a concept is
itself and nothing else — that A is A, and not not-A — shows,
as we have seen, a negative side, a negation or denial.
While it affirms the identity or convertibility of the concept
with itself, it denies the identity of the opposite (contradic-
tory) of the concept with itself. This implies that a concept
cannot be conceived as itself, and also as its contradictory
opposite in the same act of thought. A cannot be conceived
as A and not-A in the same act or in one act of thought,
or even in two succeeding acts of thought — that is, at all.
This is the Law of Non-Contradiction. The violation of it,
if that were possible to thought, would be the nullity of
thought itself. A and not-A cannot be both thought of the
same concept. Circle and Square cannot be both conceived
of the same figure, or conjoined in one act of thought. A
conceived as equivalent to not-A is conceived as equivalent
to nothing or zero.
The principle of Non-Contradiction has been expressed —
<( Judgments opposed contradictorily to each other, as, A is
118 INSTITUTES OF LOGIC.
B, A is not B, — cannot both be true. The one or the other
must be false. From the truth of the one follows the false-
hood of the other. The double answer, Yes and No, to one
and the same question, in the same sense, is inadmissible." x
§ 144. The law of Non- Contradiction is inaccurately ex-
pressed in the formula — It is impossible for the same thing to be
and not to be. This refers, not to the concept as a concept,
or object of our thought, but to an individual or real object
in time, or in time and space. Existence in time and non-
existence in time are not incompatible unless they be predi-
cated of the same individual at one and the same time. The
individual may pass in succession from existence to non-
existence, or from infancy to maturity, or from black to grey.
But this in no way affects the scope of the law of Non-Con-
tradiction ; for these opposite predicates or concepts of the
same individual can still not be conceived as belonging to
the individual in one and the same act of thought. He cannot
be conceived as existent and non- existent, in one — that is,
in a consistent thought. The element of time as a varying
condition of existence and thought has no effect whatever on
the fundamental consistency or inconsistency of attributes
conceived. Affirmation and negation of contradictory attri-
butes are quite possible, in successive times, of a persistent
or enduring object, but they are not consistent or possible of
the same subject in the same act of thought. The law of
Non-Contradiction is, therefore, of universal applicability in
all definite thought. The only time which Logic knows is
the present, and that not as the time of an actual event, but
as the time merely of an ideal conception. Properly speak-
ing, the is of the proposition has no reference to actual time ;
but to consistency of concept with concept.
(a) "Judgments opposed contradictorily cannot be true at the same
time." But this is inexact. (1) If "at the same time" refers to the
judgments as acts of thought, it says too little. This would not help
us to avoid contradiction, for two judgments might be as to matter
contradictory, if thought at different times — e.g., The Iliad is the pro-
duction of one man ; The Iliad is the production of several authors. The
one might be said in the 17th century, the other in the 18th; yet they
are contradictory judgments. (2) "At the same time " really refers
to the contents of the judgments, and means that judgments contra-
dictorily opposed cannot be true together, or cannot both be true.
i Ueberweg, Logic, p. 235.
LAW OF NON-CONTRADICTION. 119
But in this reference the expression is inexact. — (Ueberweg, Logic,
pp. 236, 237.)
To speak of the same time in connection with the law of Non-Contra-
diction is unduly or accidentally to limit it. Two conceptions which
are contradictory are essentially together in time — i.e. , in the indivisible
act of thought which comprehends them. The effort of thought is to
hold them together at the same moment, while it finds it impossible
to unite them in one subject.
§ 145. The law of Non-Contradiction regulates — (1) the con-
cept as such ; (2) the concept in relation to an attribute (con-
tradictio in adjedo) ; (3) mediate contradiction in corollaries.1
Of two contradictory judgments, we know that both cannot
be true ; but we do not thus necessarily know which is true,
and which false. The principle does not enable us to ascer-
tain this ; but only that having found somehow that one is
true, we are certain that the other is false. Is this man, after
trial, proved guilty or not? He is proved guilty, therefore
it is false that he is proved not guilty. He is proved not
guilty ; therefore it is false that he is proved guilty. Until,
however, we have to do with a definite judgment in time, we
cannot go beyond the merely formal position of saying that
both cannot be true.
(a) Aristotle has expressed the law in various formulas. Thus : "A
thing cannot at once be and not be in one and the same subject and
under the same relation." — (Met., iii. 3. rb yap avrb a/xa i>wapx*iv te ko\
/U7j (nrd.pxi'-v aSuuarop T<j5 avTcp Kal Kara rb avrd.) Again: "The same
thing cannot at the same time be and not be." Again : "Affirmation
and negation cannot be true at the same time of the same subject." —
(Met., iii. 2.) "The same subject does not admit at the same time of
two contrary attributes." — (Cf. An. Pr., ii. 2.) This, according to
Aristotle, is the most certain of all principles. — (Met., iii. 3.) It is
indemonstrable, but the absurdity of its denial can be shown.
Aristotle holds that the principle of contradiction applies to sensible
things, or to the changeable. The same object cannot in actuality or
fact (ii'reAexeia) contain opposites; though it may be capable (86va.fj.ti) of
passing into or through opposites — properly contraries. — (Met., iv. 5.)
" Non-existence is neither in the image nor in the object, but simply
does not exist. The notion of non-existence, however, is primarily
in the negative judgment in which we think the discrepancy be-
tween image and actuality. It can always be used to denote what
does not exist, but is falsely conceived to exist ; never to denote what
does exist. In other words — it is not true that the same thing which
is, also is not ; or, as Aristotle says, — it is impossible that the same
thing is and is not."— (Ueberweg, Logic, p. 253.)
1 Ueberweg, Logic, p. 236. ,
120 INSTITUTES OF LOGIC.
§ 146. The condition of Non - Contradiction is complete
identity in sense, both in the single terms of the judgment,
and in their affirmation and negation. When the sense of
the terms is indefinite, or vacillating, yes and no may be
answered to the (apparently) same question.1 Think exactly,
and state precisely is the rule of contradictories.
Affirmation and negation differ according as we consider
the concepts as absolute, or phenomenal merely of what
transcends them. What, for example, appears to sense may
be affirmed as a sensible fact, and denied as a transcendental
or supersensible fact. We may say what I perceive is, what
I perceive is not, in the sense that it is merely the manifesta-
tion of something beyond itself as cause. These are quite
different senses, and they are only conflicting when con-
fused and regarded as one. The law of Non-Contradiction is,
moreover, in no way affected ; it is still strictly and properly
absolute in respect of the sensible phenomenon ; for this, as
an object of perception or knowledge, is as it is — as it ex-
ists at a given time — and cannot be identified with aught
else, either in the given time or in any other. What rela-
tions it may have to the transcendental is a wholly separate
point, and can in no way be regulated by the law of Non-Con-
tradiction. At the same time, the assertion of the absolute
or real identity of the differences of experience is fatal to the
possibility of any truth whatever. Vacillation in regard to
the sphere of the affirmation and negation is at the root of
most of the current Hegelian fallacies. Their apparent pro-
fundity is only lack of transparency.
(a) " Motion and change have reality (i.e., independently of human
comprehension) ; and judgments opposed to each other contradictorily
cannot both be true.1' — (Ueberweg, Logic, p. 240.)
The change which the judgment represents takes place in a given or
definite time. The conception of the event refers to what takes place
in the time and the points of time — e. g. , the assassination of Caesar
belongs to a definite section of time, and is a continuous happening in
that time. Our judgment of it is true in as far as it reflects the con-
tinuity of the occurrence in conformity with its actual occurrence
during the given time, and as a happening in the historical order of
time — before and after.
" Historical judgments affirming and denying the same about an
occurrence in time — e.g., Socrates was born 469 B.C., and Socrates
was not born 469 B.C., but 470 or 471, are as strictly opposed to each
1 Cf. Ueberweg, Loyic, p. 237.
LAW OF NON-CONTRADICTION. 121
other as contradictories, and can as little be both true as the mathe-
matical judgments which refer to unchangeable existence, — the sum
of the angles of any rectilineal triangle is, and is not, equal to two
right angles. Hegel and Herbart assert that motion and change are in
themselves contradictory, and Hegel teaches that motion is the exist-
ing contradiction. Every moment of passing over from the one circum-
stance into the other (e.g., the beginning of day), unites in itself
predicates which are opposed as contradictories to each other. Hegel
asserts that these contradictory judgments are both true in reference
to the same moment ; but Herbart thinks that that is impossible
according to the irrefragable law of Contradiction, and that the passing
over into and becoming another have no reality. Both opinions are
false. The semblance of contradiction results from the indefiniteness
of the sense, and disappears as soon as every individual expression is
referred to distinct notions. By means of strict definition of notions,
secure points of limitation are at once reached. . . . The axiom
of contradiction may be applied to the notion of motion, if we do not
confine our attention to the proposition which is without difficulty —
Motion is motion; but analyse the notion, and go back to the elements
which are fused together in it, as Trendelenburg himself has done, that
' motion (why not rather that which moves itself ?) is and is not at the
same point at the same time. ' According to our previous explanations,
this being and not being at the same point at the same time is a mere
fiction. Motion is not impossible, because it is not contradictory. " —
(Ueberweg, Logic, pp. 241,242, 244. See there the whole able criticism.)
(6) Wolf's formula is: " Si A est A, fieri non potest, ut simul A non
sit A." — (Logica, §§ 271, 529.) " Propositiones, quibus idem negatur
esse diversum a se ipso, sunt axiomata. . . . Fieri non potest,
ut idem prsedicatum eidem subjecto sub eadem determinatione una
conveniat et non conveniat, immo repugnet. "
(c) Kant expresses the law of Non- Contradiction by " A predicate
does not belong to a subject which contradicts it." — (Kritik, p. 190 ff.,
cf. p. 83 ff.) Its violation abolishes all knowledge, though it is no test
of the (positive) truth of a synthetic judgment.
(d) One of Hegel's objections to the law of Non-Contradiction is that
the form of the proposition contradicts it, for a proposition promises a
distinction between subject and predicate, and this is not fulfilled by
the law. As the form of the proposition lies in the copula, or element
of predication, it is not true that it promises anything of the sort. It
only promises what it does — that is, to unfold the subject by being
more explicit analytically, or to add to it synthetically.
We may have a very valuable addition to our knowledge in the
matter of clearness or explicitness in analytical propositions where no
distinction is added, and we may have an equally important accession
in the case of synthetic judgments. But the form of the proposition
really makes no promise; only if it did, the law of Non-Contradiction
is equally necessary in either case, and essentially regulative. This,
like the other criticisms of the law by Hegel, is of the most super-
ficial order.
The view of Hegel is thus well and summarily put by Ueberweg : —
122 INSTITUTES OF LOGIC.
"Hegel holds that the law of Non-Contradiction is invalidated by
what he calls the axioms or laws of Difference, Opposition, and Excluded
Middle, and that the truth of these laws lies in the unity of identity
and difference, expressed in the category of the Reason. Thought as
Understanding lets tilings stand in their strict determinateness and
distinctness from each other ; then there comes the self-elevation of
those finite determinations and their passing over into their opposites,
wherein lies their dialectic or negative intellectual moment. Then,
finally, there is the unity of the determinations in their opposition —
the speculative, or positively intellectual moment, — in which the dual-
ism of the understanding and the negative monism of the reason be-
come the mutually dependent elements of free speculative truth." —
(Ueberweg, Logic, pp. 257, 258.)
It is only necessary meanwhile to remark on this (1) that truth, as
the unity of identity and difference, so far as simple contradiction is
concerned, is an impossibility to thought.
(2) That such a formula is utterly inapplicable to the conception of
any occurrence in time or historical fact.
(3) That it is inapplicable to the conception of every mathematical
property of extension, — to all the truths of pure geometry.
(4) That it is subversive of all moral distinctions.
(5) That it confounds the unity of identity with the unity of corre-
lation, which asserts and supposes difference in the terms correlated,
and preserves the difference.
(6) The formula is not applicable even in contrary opposition, where
we deal with a plurality of opposites of the same class.
(7) Such a formula is not applicable in any sphere of thought — call
it Reason or anything else. If it held good in the transcendental sphere,
or in any one sphere open to our intelligence, while in the other, or
finite sphere, the law of Non-Contradiction were valid, then we should
have an absolutely irredeemable contradiction in intelligence as pos-
sible to man. There would be no means of deciding which of the two
orders of (so-called) truth we should follow. The results would be
scepticism in thought, and chaos in ideality.
Identity and Difference, as generic concepts or ideas, cannot be
thought apart from each other ; individual existences are identical
with themselves, and different from others, just because they are in-
dividual ; and each being what it is, can be, and be thought, apart
from any other, definite, individual. No other individual is necessary
to the existence of any one individual, as the concept of difference in
general is necessary to the concept of identity in general.
(e) There is one special point in Aristotle's doctrine of Substance which
is well deserving of attention, and which bears in a marked manner on
the theory alike of being and knowing. It is obviously connected with
his view that the forms of thought are related to, dependent on, the
forms of existence. The sixth and last property which he attributes to
Substance is that, while remaining one and identical, it is yet capable
of receiving contraries by a simple change which takes place in itself.
This property is absolutely special to substance, — the individual, — to
it and nothing else, — omni et soli. Nothing else is capable of this.
LAW OF EXCLUDED MIDDLE. 123
One and the same colour does not admit of contraries. A colour numer-
ically one and the same cannot be at the same time black and white :
just as one and the same action cannot be at the same time good and
bad. But the individual, — substance proper, — may remain the same
and yet in turn be black and white, hot and cold, good and bad. In
nature nothing else presents a similar property. Least of all can we
maintain that this is true of word or thought.
It may seem indeed that one and the same assertion may be at once
true and false. If we say of one seated, that he is seated, this assertion
would become false, supposing the person to rise. But there is here
only a formal difference. So far as the individual or substance is con-
cerned, this is susceptible of a change, because it undergoes it in itself,
—in other words, remains the same amid the change. But so far as
word and thought are concerned, these remain absolutely and always
immovable, and contraries only exist for them because the object itself,
■ — what is expressed or thought, — changes. The assertion that some
ene is seated remains not the less always the same ; it is only because
the object changes that it is sometimes true and sometimes false.
Thought is in this respect like the word. Thus then the special pro-
perty of the individual existent is to be as to form susceptible of change,
as undergoing it in itself. But in this sense neither word nor thought
can receive contraries. These are susceptible of contraries, not because
they themselves receive modification, but because something external
to them happens to be modified. It is only because the object is or is
not in such a way, that the assertion can thus be said to be true or
false ; it is not at all because the word itself admits contraries. Word,
thought are not subject to change, and if this did not take place in
objects themselves, they would in nothing receive contraries. — {Cat.,
v. p. 4 a, 21.)
This is an eminently sound and valuable doctrine. So far as it bears
on the nature of thought, it is thoroughly unassailable. And it cuts at
the root of the whole Hegelian assumption of the passage of thought
into its opposite, whether contrary or contradictory. Such a passage
is not consistent with the very conditions of the existence of a concept
to begin with. And, further, as the nature of thought and the nature
of the individual object are shown to be so different, in their essential
properties, it strikes at the very root of the Hegelian assumption of the
identity of thought and being.
§ 147. Given two contradictory opposite concepts, which
though not conceivable as one, are yet conceivable separately,
a third law emerges. Between these there is no third or
middle concept possible to thought. Accordingly, any positive
concept or subject of thought whatever must be thought by
us as lying either within the one sphere, the A or positive,
or the other sphere, the not-A or negative. It cannot be
thought as both, but it must be thought as either in the one
or the other sphere. And if there were proof that the thing
124 INSTITUTES OF LOGIC.
thought did not lie in the one sphere, say the positive, it
must be thought to lie in the other sphere, the negative.
But this never implies a necessity of existence of the object
thought ; it implies only in the actual reality a necessity of
inclusion on a hypothesis of existence. This is the law of
Excluded Middle between two Contradictories, [Lex Exclusi
Tert'd aut Medii inter duo Contradictor id).
The principle of Excluded Third or Middle between two
Contradictories may be thus stated : Judgments opposed
contradictorily, as A is B, A is not B, cannot both be false, but
one or other must be true, there being no third or middle
judgment possible ; or " the double answer yes and no cannot
be given to one and the same question understood in the
same sense."
Considerable misconception has arisen regarding the law
of Excluded Middle from supposing that it warrants "a uni-
versal comparison of any possible subject-notion with any
possible predicate-notion," and that the predicate must either
inhere or not in the subject. This is irrelevant and puerile.
In accordance with the essential nature of logical law, it sup-
poses a definite subject with its definite sphere of at least
possible predication.
§ 148. The laws of Identity and Contradiction warrant us in
concluding from the truth of one contradictory to the false-
hood of the other ; add the law of Excluded Middle, and we
are warranted in concluding from the falsehood of the one
contradictory to the truth of the other. Excluded Middle
thus limits the sphere of the thinkable in relation to affirma-
tion. Of the two forms given in the laws of Identity and
Contradiction, as exclusively possible, the one or the other
must be affirmed as necessary.1
It is necessary to observe that none of those laws has a cate-
gorical reference or import. They are but conditions of our
thinking when we actually think, or they are conditions when
we hypothetically think. They cannot of themselves inform
us of the fact of a real existence or its qualities. This is
clear in regard to Identity and Non-Contradiction, in each
of which cases a datum is presupposed. And it is not less
true of Excluded Middle, where the force of the law is in the
event of the one alternative being affirmed on grounds proper
Hamilton, Logic, L. v.
LAW OF EXCLUDED MIDDLE. 125
to it, the other may be denied, and any third alternative
excluded. And so in the case of negation. Hamilton has
been charged with supposing the law of Excluded Middle to
affirm one of the contradictory alternatives as necessary.
A careful study of his statements shows that this is not the
case. We try, for example, to think an absolute beginning ;
we find we cannot. We try to think infinite non-commence-
ment ; we find we cannot. We conclude that in spite of this
inability, one or other must be real, on the limitation im-
posed by the exclusion of the third or middle. There is here
no affirmation of the one alternative or the other, but only
that the one or other is necessary, and necessary on the
ground of the exclusion of the middle according to the pure
formula. To determine which is or is not, we must go beyond
the logical law. All that Hamilton seeks actually to have
proved is that existence transcends positive thinking, or that
may be real which we cannot actually represent in thought.
(a) Kant, however, apparently has some view of the sort, inaccurately
attributed to Hamilton. For he makes the law of Excluded Middle the
basis of apodictic judgments. The law, as has been said, is incapable
of determining which of the alternatives is to be taken. As Krug puts
it, it is only the principle of reciprocal capacity for determination. —
(Denklehre, § 19, cf. Ueberweg, p. 272.)
(6) Hegel objects to the law of Excluded Middle that it does not
distinguish between cases where the denial is proper and where it is
not proper. It does not distinguish between partial and total negation.
It is, therefore, meaningless. — (Encyl., § 119; Ueberweg, Logic,
p. 261.) Thus it does not tell us that such predicates as green and
not-green, wooden and not-wooden are not applicable to Spirit. To
this the obvious answer is, that this law, like the others, supposes a
definite concept, or, as it has been put, a suitable question, and regu-
lates our thought concerning it. The law does not prescribe playing
with predicates, but assumes that people are reasonable beings and
in earnest in their inquiry. By parity of reasoning, abuse all spec-
tacles, because you have never learned to read.
Hegel varies in his statement of the law of Excluded Middle, at
one time confounding it with that of Non-Contradiction ; at another
time stating it precisely enough under the name of the axiom of the
Opposite, or of Opposition, or Excluded Third. — (Logik, i. 2, p. 67.)
His chief criticism of it consists in saying "that there is always a
third between + A and - A, viz. A in its absolute value ; and O is a
third between + and -. But this is to identify the logical and
mathematical relations which are essentially distinct. Contrary not
Contradictory Opposition exists between positive and negative size in
the mathematical sense. The negative quantity — A is by no means
identical with the logical denial of -I- A. A quantity need not be
126 INSTITUTES OF LOGIC.
either = + A, or = — A. It may be either = + A, or not = + A, and
also either = —A or not= —A. And looked at apart from the signs,
according to its absolute value, it may be either = A or not = A." —
(Ueberweg, Logic, p. 273, cf. Ott., Hegel, p. 197-204. For a fuller
discussion of this and other cognate points see below, chapter xiv.)
(c) Again, it is objected that the mean between the contradicting pre-
dicates is often the true predicate. Between "guilty " and " not guilty "
there is "not proven." Between "full imputation " and "no impu-
tation'' there is " partial imputation." If the knowledge of truth is not
comprehended in a development, says Erdmann in Hegel's sense,
everything is either wholly truth or wholly not-truth. Truth becom-
ing or developing itself is both or neither the one nor the other." —
(Ueberweg, Logic, p. 264.) To this Ueberweg virtually replies : These
statements, even if true, prove nothing against the validity of the
axiom of Excluded Middle, rightly understood. They can only be
held to be exceptions to it by exchanging contradictory for contrary
opposition. This is unwarrantable. The law is not properly expressed
in the formula — A notion, or its opposite, is to be predicated of every
object. The opposing members of contradictory opposition denote
only the presence or absence of a strict agreement of the combina-
tion of conceptions with the actual existence they represent. This is
what is asserted universally by the axiom of Excluded Middle. The
negation cannot be interchangeable with the affirmation of the predicate
opposed as a contrary. Not guilty is not equivalent to guiltless or pure.
Not mortal is not equivalent to immortal or eternal. Not good is not
equivalent to bad or wicked. . . . The contradictory disjunction —
guilty or not guilty, — is not to be charged with the error of denying
the possibility of half-guilt or partial insanity. The error lies in
making reciprocal the negation of this definite guilt with the affirma-
tion of perfect innocence. Forms of transition between different kinds
of the same genus are a mean between existences positively distinct.
They do not stand to each other in the relation of Being and non-Being,
but in that of Being so and otherwise. Such transitions are not excluded
by the law of Excluded Third between the affirmation and negation
of the same. — (See Ueberweg, Logic, p. 264 et seq., and the valuable
remarks which follow.) It comes very much to this, that where you
have a definite concept or subject, and the question is — is this or that
definite attribute to be predicated of it ? the answer must be definitely
yes or no. If the attribute is indefinite, — or variable say as to degree or
quantity, — the howmuch cannot always be definitely given orpredicated.
Is this man sane ? What amount of aberration constitutes insanity ?
This must be first decided. In many cases the question, as put, is
definite, but the answer is made on the principle of a cross-division —
e.g. , Is this man guilty or not guilty? The answer of the jury may
be — It is not proven. This is to mix up two wholly different points
of view. This does not exclude the man's guilt, nor does it include it.
It is, therefore, not a proper answer to the question. But the first
question itself is not the proper question to put to the jury, but really
whether the crime alleged is proven or not proven. Guilty or not guilty,
bo far as the law is concerned, means proven or not proven. The man
LOGICAL LAWS FUNDAMENTAL. 127
is assumed to be innocent until he is proved guilty. The questions of
fact, and of proof of the fact are quite different ; and ought not to be
mixed together. The law should in expression limit itself to what
it actually is limited, —the question of proof.
(d) Plato allowed a third or middle between Being and Nothing —
in sensible things. The Ideas have being — are, — Matter is not ; sen-
sible things as changing neither are, nor are not. They are the flow
in Matter. Aristotle allowed no third between Being and Nothing.—
{Met., iv. § 1, §§ 5, 6, § 9; cf. Ueberweg, p. 271.)
§ 149. The logical laws are fundamental — not derivable
from any other laws, say of Intuition or Experience. They
are the inseparable concomitants even of all Intuition.
(a) It has been said that the logical law of Identity is derived as a
generalisation from the intuition of Identity in things or in experience.
The latter alone is fundamental. To consider this we must distinguish
metaphysical or real, and logical or notional identity. The former
means oneness of the individual at different times ; the latter means,
subjectively, similarity or sameness of the mental impression at different
times, or, objectively, community of attribute among otherwise dif-
erent objects existing at the same or different times. In the former
case there is convertibility through unity ; in the latter, through similar-
ity. Now it is impossible that logical identity can be derived as a gen-
eralisation from metaphysical identity. For oneness at different times
implies already the logical law in its utmost universality. To be per-
ceived as one implies as a concomitant to be known as one out of many
— as in a given time, as this not that ; — it implies in fact the concepts
of unity, identity, difference, applied in a special instance, for all intui-
tion is of the concrete or special. The intuition of the quality or fact
in time with the application to it by the mind of the universal concept
makes up the apprehension of reality — that is, the metaphysical act.
But neither is intuition prior to concept, nor concept to intuition. They
are but the inseparable complementary sides of one and the same act ;
the one, therefore, cannot, properly speaking, generate the other.
(6) It has been said that the logical law of Non- Contradiction is a
generalised application of the intuition of difference to any concept
whatever. A thing or concept is not another ; it is not anyone of the
things or concepts from which it differs. Again, Excluded Middle,—
Every B is either A or Not-A, is said to be the intuition of Difference
and Identity generalised. When A is distinguished from Not-A, it is
discerned by reflection that these divide the extent of all conceivable
existences into two classes.
To this, the answer is, that in the case of Contraries, where there
are two positive qualities or presentations — say colours, as black and
red, green and blue,— there is an intuition of diversity, and the one is
distinguished from the other through the intuition. Still even here the
distinction would not be possible, unless identity involving diversity
were an original scheme or form of thought. To say that black is not
ichite is to say that black remains itself, and does not pass into or be-
128 INSTITUTES OF LOGIC.
come one with white, — that there is diversity. But diversity cannot
be said to be generalised from the intuitional act, as Porter says ; it is
rather so related to this act that the latter is not possible without it.
It is not when a quality is distinguished from its opposite that we gen-
eralise the laws of Identity and Difference, so as to create them ; but it
is because these laws are already implicitly in our possession that intui-
tion is enabled to make the distinction, or that the intuition becomes
possible. Reflection may unfold to us their full extent, — their univer-
sality,— but it does not make them to be, or make them universal, as
ordinary logical thought does in regard to the generalisations of con-
cepts or scientific laws.
(c) Can the law of Non- Contradiction be proved? Or is it ultimate ?
Indirectly, it is shown to be necessary, seeing that no thinking can be
carried on without assuming and using it. Let Yes be also No, and
No also Yes, and there is no one definite conclusion possible, whether
immediate or mediate, as in reasoning. Ueberweg, however, attempts
a direct proof of it, — in substance as follows : —
The highest logical principle is, in his view, "the idea of truth —
that is, the consistency of the content of perception and thinking with
existence." And it is only in so far as the principle of Non-Contradic-
tion has a fundamental significance for a series of other propositions
that it is itself fundamental, while it is derivable from those propo-
sitions. But it may be said that to deduce it from other propositions
can be done only on the supposition that the contradictory cannot be
true. To this it is replied, that the thinking which deduces all logical
laws rests on them. These laws carry with them their own validity,
and are present in our actual thinking, even in that which deduces
them, yet this deduction does not rest upon a scientific knowledge of
those laws, and this is to be carefully distinguished from their actual
validity. — (Logic, p. 239.)
This, I submit, is not a proof of the law ; it is not even a derivation
or deduction of the law. It is true that all logical thinking is con-
formed to the law ; that the law is exemplified in every concept, judg-
ment, and reasoning. It is further true that we come to know the law
as manifest or given in individual cases, — this or that concept, judg-
ment, or reasoning. But as thus itself regulating, conditioning every
possible ground of its proof through a notion or proposition beyond
itself, if that were possible, it is therefore not provable or derivable.
Nor is it a generalisation. It is essential in each act of thought ; as
such, it is necessary ; as necessary, universal. We know and feel its
force in individual instances of thinking ; we reflect on these, realise its
essentiality, its necessity in each case, its universality, therefore, in
all. This is scientific knowledge of it, but it is not a deduction ; it is
an analysis of the matter of our thinking and the reflective recognition
of its ever-present condition. It is in fact coming to know, through
analytic reflection, what our thinking really means. This for us, in
such a sphere of inquiry, is the highest, best, and only method. We
cannot offer direct proof in such a case ; we can only show that those
who deny it, consciously or unconsciously palter with words.
(il) An attempt has been made by Boole and others to derive the
LAW OF SUFFICIENT REASON. 129
logical laws, especially Non-Contradiction, from mathematical rela-
tions, but unsuccessfully. There is no mathematical relation, however
far run back, which does not presuppose those laws, and is embraced
by them. They are the primary conditions of the ultimate mathemati-
cal conceptions, as of all other definite conceptions.
§ 150. It seems necessary to admit another law of thinking
which, if not co-ordinate with the three laws already men-
tioned, is yet auxiliary and important, as connecting pure
and actual thought. The Principle of the Sufficient or De-
termining Keason, or Keason and Consequent, refers to
the deduction of cognitions, especially judgments. " Infer
nothing without a ground or reason." The cognition which
necessitates the inference is the logical reason, ground, or
antecedent; that necessitated is the logical consequent; the
relation between the reason and the consequent is the logical
connection or consequence.1
(a) Leibnitz was the first to make the principle of Sufficient Reason, as
a law of inference co-ordinate with that of Non-Contradiction. — (Theod.,
i. § 44.) His expression of it is "that nothing can be inferred unless
it has a determining cause, or at least reason." It refers to why " a
thing exists, an event happens, a truth has place " — (Lettres a Clarice, v.)
— that is, it is both metaphysical and logical. While the principle
of Contradiction is, with Leibnitz, the ground of necessary truth, the
Sufficient Reason is the ground of contingent truth. — (For references
and quotations regarding these laws, see Hamilton, Logic, L. v., and
relative Appendix ; also Bachmann, Krug, and Ueberweg. )
(b) Ueberweg states the axiom of Sufficient Reason thus : " A judg-
ment can be derived from another judgment (materially different from
it), and find in it its sufficient reason only when the (logical) connection
of thoughts corresponds to a (real) causal connection." — (Logic, p. 281.)
He adds : ' ' The logical form of axiom only asserts that the combination
of judgments, by which a new one is derived from given ones, must
rest on an objective causal nexus. Whether and in what sense every-
thing objective stands in causal relations is to be decided elsewhere
(in Metaphysics and Psychology.)" — (P. 282.)
§ 151. Pure logic as a science is, in the view of some, the
application of the three formal laws to Conception, Judgment,
and Eeasoning. Hamilton at first in the Lectures, and also
originally in the Discussions (p. 160), admitted a fourth co-
ordinate law of thought, — that of Reason and Consequent.
But he finally held that this as a logical relation was nothing
more than a corollary from the law of Non-Contradiction in its
1 Cf. Hamilton, Logic, p. 84, and the references there to Schulze and Krug.
I
130 INSTITUTES OF LOGIC.
three phases, — that is, the three principles already specified.
In an analytical judgment the predicate is obviously affirmed
on the strength of formal law, — Identity. Here there is a mere
logical discrimination of subject and predicate, or of reason
and consequent. In all immediate inferences from a simple
proposition this also is true ; and in all strictly syllogistic
inference, which only evolves the contained and necessitated.
" The principle of Sufficient Eeason," says Hamilton, " should
be excluded from Logic. For, inasmuch as this principle' is
not material (material = non-formal), it is only a derivation
of the three formal laws ; and inasmuch as it is material,
it coincides with the principle of Causality, and is extra-
logical."1 This may be correct. But obviously the principle
of the Sufficient Eeason, or rather of Condition and Con-
ditioned, is a valuable, even indispensable one in all our
practical and scientific thinking. The formal laws regulate
well enough analytical judgments. They enable us to affirm
in the predicate what was in the subject. In synthetical
judgments, they preclude us affirming an attribute contra-
dictory of the subject or its attributes. But we require, at
least for practical purposes, to be cautioned against arbitrary
synthetical judgments. We ought to seek and to have a
ground or reason why we attach the new predicate. Think
not only non-contradictorily, but think with reason. This
caution is, in a very strict sense, extra-logical, but it is very
material, and its application would stop a good deal of loose
talk, especially in philosophy.
When a proposition is challenged, when in fact the right
or propriety of adding a new predicate to a subject is ques-
tioned, to reply that " thought is synthetical," — is as naked
a begging of the question as can well be conceived. What
I ask for is a ground or reason of the addition or synthesis ;
what I get in reply is, there is an addition. Why do you do
this? I do it. This is an absolute confession of mere
arbitrariness, and violates the acknowledged principle, —
think nothing without a (sufficient) reason or ground. From
the universality of this principle there is no escape, unless
in the limited circle of self-evident, self-guaranteeing prin-
ciples. And these, in some form or other, are a necessity of
every philosophy.
1 Discussions, p. 603.
REASON AND CONSEQUENT. 131
§ 152. The relation of Reason and Consequent is not identi-
cal with that of Cause and Effect. Every cause known in
relation to its effect is a reason, and every effect known in
relation to its cause is a consequent. But every reason is not
a cause, and every effect is not a consequent. Cause is a reason
of a thing being ; Reason is a cause of a thing being thought
or known : the one is the ratio essendi ; the other is the ratio
cognoscendi. E.g., the tree being some inches taller than
when I last saw it is the reason why I believe it has grown ;
but the known increase of height is not the cause of its
growth. This is the ratio cognoscendi. The cause or causes
of the increase in the height of the tree are to be sought
in soil, moisture, heat, life. These form the ratio essendi.
If these were known to me, and known also to have had the
effect of increase of height in the past, these would form a
ratio cognoscendi, or ground of anticipating the growth on the
principle of uniformity and of that alone. They would be
in the relation of Reason and (anticipated) Consequent ; but
nevertheless this is a wholly different relation from that of
Cause and Effect. Cause and Effect may pass into Reason
and Consequent ; but Reason and Consequent is not neces-
sarily Cause and Effect.
(a) Ueberweg's statement of the principle (p. 281) is obviously too nar-
row, fivery cause may be a reason ; but every reason is not necessarily
a cause, unless in a very unusual sense of the term. In the case, for
example, of conversion and other forms of immediate inference, it
would be inaccurate to call the convertend or datum the cause of the
converse, though it is the ground and the necessary ground. It may
be doubted also whether in any case the inference is made on the
ground of the antecedent being cause merely. The logical laws will
be found to' afford the nexus, — the cause becomes in fact a reason.
The difference between cause and reason logically is that the complete
knowledge of the cause per se could not lead us to anticipate or pre-
dict, far less necessarily deduce, the effect, while the full knowledge
or consciousness of the reason not only enables, but necessitates us to
anticipate and think the consequent. Thus, no mere knowledge of
motion in any of its forms could enable us apart from experience to
anticipate or predict light or heat, or even thus know what either of
these means. The proposition in immediate inference, the premisses
in a reasoning, lead and necessitate us per se to the consequent or
conclusion.
§•153. The laws of thought as the necessary, though un-
developed, principles of all Conception, Judgment, and Reason-
ing, are assumed and proceeded upon in every act of thought.
132 INSTITUTES OF LOGIC.
Ordinary thought does not find it necessary to state them or
to set them out in their abstract form ; and when reflection
does so, they may appear as too simple for explicit statement.
By some the abstract formula has been derided as " puerile." *
"Puerile" they are not in any proper sense, for they are
known as general principles only to mature reflection. Simple
they are and self-evident as all necessary and universal prin-
ciples are, and the more simple the greater the universality,
and the higher the abstraction. Every axiomatic truth is
simple, but it is not therefore puerile or unimportant. 1 + 1
= 2 is the basis of arithmetic. This is simple, but absolutely
essential and valuable as to results. The laws of Logic are
indeed in themselves more simple ; that is, less charged with
attributes than the laws of any other, even abstract science,
such as geometry : of all laws they have the widest exten-
sion. Geometrical and physical laws in their greatest gen-
erality imply or presuppose the logical laws. Their value
and importance are not manifest from the mere statement of
them, but from their regulative influence over the whole of
human thinking. And their importance is especially mani-
fested as a criticism of, and check upon, aberrations from nor-
mal human thinking — really verbalism — as is manifested in
the basis and method of the so-called Logic of Hegel.
§ 154. Affirmation and negation are implicit in the concept,
but still truly operative. The reference of a given object to
a class, the recognition of the similarity or identity of its
attribute with the class-attribute, is an affirmation, and pro-
ceeds on the assumption of the law of Identity — that similars
are thinkable as one or the same. It proceeds further on
negation — that is, on the assumption provided for by the law
of Non-Contradiction that an attribute is to be discriminated
from non-resembling or differing attributes — is to be excluded
from the contradictory sphere. There is implied further that
this affirmation and negation are the only possible alternatives,
and that, if of a given attribute, we affirm similarity to the
class-attribute, we negate difference ; and if we negate differ-
ence we affirm similarity. This supposes the law of Excluded
Middle or Third. These three laws or axioms, accordingly,
while they may be considered apart for scientific purposes or
statement, are not separable in application. We cannot, in
1 Vera and Hegelians generally.
ANALYTIC AND SYNTHETIC THOUGHT. 133
a word, state one of them without implying all the others.1
As essential to each other, they are essential to every act of
thought.
§ 155. The laws of Identity, Non-Contradiction, Excluded
Middle, primarily regulate thought in its explication, or
thought considered analytically. A concept regarded analyti-
cally is the subject of a judgment, in whose predicate is ex-
plicitly evolved or stated in terms, an attribute implicitly
contained in the subject. For example, we say Body is ex-
tended. Extension is already in the concept of body, and the
judgment which states it explicitly is analytic or explicative.
A concept regarded synthetically is the subject of a judgment
in whose predicate is explicitly evolved, or stated in terms,
an attribute not contained in the subject. This judgment is
synthetic or ampliative. For example, Body is heavy. The
attribute weight is an addition to the notion of body. What
appears to begin to be has a cause. Cause is added on to ap-
parent commencement. The air is elastic.
It is clear that the laws of Identity, Non-Contradiction, and
Excluded Middle regulate analytic thought, for this says no
more than that a concept, as a sum of attributes, is identical
in part or whole with its attribute or attributes. The reason
why we state the predicate and refer it to the concept is to
be found ultimately in the principle of the Identity of the
whole and its parts, — a form or application of the Law of
Identity. The other laws are needed as guarding or con-
serving the application of this principle. These laws not less
regulate synthetic thought, but they do not afford the reason
of it. A predicate added to a subject cannot be contradictory
of that subject. We cannot form a synthetic proposition by
means of A and not- A — Organised and Non-Organised. Every
synthetic predicate while not evolved by means of the law of
Identity, must, nevertheless, conform to the law of Non-Con-
tradiction. Negatively, therefore, the formal laws regulate
synthetic judgments of all kinds, whether experiential or
a priori.
§ 156. But if the reason of the addition of the new predi-
cate be not in the formal law, wherein, it may be asked, does
it lie ? This question is extra-logical. Properly speaking,
Logic cannot tell us where the reason lies for adding a given
1 Compare Hamilton, Logic, iv., Appendix, iv.
134 INSTITUTES OF LOGIC.
predicate, and whence it is drawn. This is for experience
and Psychology to determine, alike in regard to the matter
of Perception or Intuition, and in regard to what are called
synthetic a priori intuitions and judgments. But Logic as
the formal science of thinking is concerned with it to this
extent, that the addition of the predicate be not made wholly
arbitrarily or without a reason of some sort. It thus pro-
vides a form for this mode of judgment as it does for analytic
judgment, — a form of strict and necessary law.
§ 157. Thinking, therefore, which in the synthetic form
added arbitrarily or without some reason a predicate to a
subject, would be not thinking, properly speaking. It would
as arbitrary have no analogy with the highest or strict type
of thought given in analytic thinking. The mind conscious of
thinking is, therefore, compelled to say to itself — Affirm noth-
ing, where an alternative is possible, without a ground or reason.
This principle leaves of course out of view the question as to
what sort of a reason entitles us to affirm a particular predi-
cate or consequent. That must be determined by intuition
and experience, and may be wholly contingent. The prin-
ciple is satisfied if a reason be set forth, and if it can be con-
sistently joined with the consequent or predicate ; and if it be
merely supposed true as a matter of fact. Thereupon it will
regulate the inference, — the necessary inference or relations
between the subject or predicate, — or between the reason
and consequent. In a word, what Logic professes to perform
here is, as usual, merely a hypothetical function : given a
reason, or a reason being supposed, here are the laws which
regulate its connection with its consequent. The influence
of this principle is seen in Hypothetical Propositions and
Reasonings. Logicians have given special applications,
of it in the formulae : (a) Affirm the Condition or Reason,
affirm the Conditioned or Consequent : (b) Deny the Conditioned
or Consequent, deny the Condition or Reason. Posita Conditi-
one, ponitur Conditionatum. Sublato Conditionato, tollitur con-
ditio. A ratione ad rationatum, a negatione rationati ad
negationem rationis, valet consequentia.
§ 158. The applications and modifications of these canons
will be shown subsequently, in connection with Conditional
Inference. Meanwhile it is enough to say that they involve
the essential principles of all indirect or apagogical demon-
ANALYTIC AND SYNTHETIC THOUGHT. 135
stration, so that many of the important demonstrations of
geometry would be impossible without them.
§ 159. The function of the laws of Identity, Non-Contradic-
tion, and Excluded Middle, as applied to synthetic judgments
of contingency, or of contingent predicates, is purely hypo-
thetical. • In the synthetic judgment of experience, it is
always a" question as to which of the new contradictory predi-
cates is to be joined to the subject. Whether fusibility is to
be predicated of gold or not, is an open question for pure or
mere thought. So is in fact every judgment of experience ;
every judgment fairly implying matter of fact. Whether
motion, and what sort of motion, can be predicated as a condi-
tion of light, of heat, of sound, — all these are questions utterly
insoluble for mere thought in any form. Here thought is
perfectly blind. Every law of nature within the sphere of
generalisation, that is, the great body of new predicates, in
a word, of human knowledge, — all this is to be reached by
processes not of thought, but of Intuition and Generalisation,
— processes which thought may regulate, but which it does
not constitute or illumine. Wherever a possible opposite can
be placed, instead of an actual predicate or a supposed pre-
dicate, thought is helpless.
§ 160. But the function of the logical laws in regard to
contingent predicates is twofold. First, of two opposites,
one only can be attributed to the subject. If we say that
fusibility and non-fusibility are possible predicates of gold
before experiment, we are even then shut up to one or other
as applicable. This is the result of the laws of Non-Contradic-
tion and Excluded Middle. Secondly, we may hold thought in
suspense as to the predication or non-predication of the sup-
posed or possible attribute. Thus thought is indeterminate.
This is the scientific attitude before experiment, and should
be carefully distinguished as not really thought, but the sus-
pension of thought. Thirdly, if we do predicate one or other
of these attributes, fusibility or its opposite, we are required
to do so on some ground of reason, or for some sufficient
reason. This is all that formal logic demands ; material or
inductive logic, bringing into play other processes than mere
thinking, will help us to ascertain grounds of sufficiency in
the reason. Observation, analysis, generalisation, induction
are now the processes whose aid is invoked.
136 INSTITUTES OF LOGIC.
§ 161. On this it may be fairly said that while Non-Contra-
diction cannot tell us of a new predicate, — this being due to
observation, experiment, induction, — it yet negatively enacts
that this alleged new predicate is not combinable with the
concept we know, unless as non-contradictory of it, or of its
other attributes. This is its logical application. And further,
as logical thought is that of relation between concepts, or
individuals and concepts, the terms of a judgment, the terms
of a reasoning, it matters nothing to it whether the judg-
ments of a reasoning are (materially) analytical or synthetical,
provided only they are given or placed in the relation of the
containing and the contained. * Thus it matters nothing in a
reasoning whether the major be a synthetical judgment or
not. I may have as a major the synthetical a priori judg-
ment that every event is caused. My reference under this
major to a particular event as caused follows the same rule
' as if the proposition had been analytical. And the same
holds true of all the generalisations of Induction.^ Further,
in the mind of the thinker and speaker, every judgment is
in a sense analytical, for it is the statement explicitly or by
analysis of what he conceives of the subject, and knows of
the subject, or as he enounces. So that logically, for the
purposes of logical dealing and inference, there is no differ-
ence between analytical and synthetical propositions.
\ § 162. While it is true, on the one hand, that Logic, as the
science of the necessary relations of thinking can discover no
new fact, or do anything in this way to amplify science, it
can yet contribute to the progress of science. For it makes
what is already acquired clearer, more distinct, more in-
telligible by classification and arrangement ; it further helps
us to see new relations among the materials accumulated.1
Every time we reach the connection of two terms or notions
of a matter of fact, through the connection of each of these
with a common third which perhaps we had known before,
— though we did not know the common relation of the
notion to the other two, — we add a new truth to the stock
of our knowledge, and we do this in virtue of the operation
of logical law and the canons of logical science. Abstract
these and our progress is paralysed..} In the simplest in-
stances this holds good. The unknown property or proper-
1 Cf. Hamilton, Logic, L. iii.
PROVINCE OF LOGIC. 137
ties of any physical substance may be revealed to us by
finding that the substance belongs to a class which we knew
before, although we now discover for the first time that it
does so belong. Because we may at the same time know of
some property belonging to this class which we now are able
for the first time, in virtue of logical law, to predicate or con-
clude of the substance with which we started. Is this par-
ticular thing — this A — with which I am dealing, possessed
of a particular property or not ? Is it, for example, a poison-
ous substance or not? It belongs, I find, after the proper ob-
servational and experimental methods, to a class of things
which I had not suspected — it belongs to B. All the Bs, I
may already know, have poisonous qualities as part of their
properties. I have now a certainty that A has those pro-
perties. I have here the knowledge of a new relation in
which I can regard A. This is a new truth for me, in a
sense a new fact, upon which I can act ; and but for the aid
of the canons of reasoning supplied by pure logic, working
along with or after the methods of observation and induction,
I could have no certainty of it. If a new planet is discovered,
I can at once infer that it will exhibit in its movements con-
formity to the laws of motion, as established by Kepler and
Newton, simply from a comparison of the notion of it with
other planets which exhibit this conformity. In applying
the general law to a new case, I widen the range of my
science. And this is what logic teaches. It teaches the
general or universal laws of pure inference, whatever be the
"matter or science in which we infer ; and it helps to form the
habit of the correct application of those rules. Clearly, too,
itTollows from this that Observation, Experiment, Induction,
all the means by which we get the materials of knowledge,
and the laws of facts, are prior to the strict logical process of
inference, and that the analysis of this logical process is to
be done independently altogether of the inductive methods.
How we get our premisses is a point of wholly secondary im-
portance in considering what these involve. It is enough
for logic if they be given ; it is indifferent even to it whether
they be actually true or false; the science has a perfectly defi-
nite, and very wide sphere of inquiry, in tracing the laws and
conditions under which these premisses are explicated, and,
their conclusion implicated.
138
CHAPTEE XIII.
THE LAWS OP THOUGHT HAMILTON AND MILL.
§ 163. The true nature and applications of the Laws of
Thought are perhaps best brought out in confronting one
view with another. In this chapter, accordingly, I shall
present the antagonistic views of Hamilton and Mill, and in
a subsequent one the doctrine of Hegel on the subject.
§ 164. On the nature of these laws of thought Hamilton
remarks : " When I speak of laws and of their absolute
necessity in relation to thought, you must not suppose that
these laws and that necessity are the same in the world of
mind as in the world of matter. For free intelligences, a law
is an ideal necessity given in the form of a precept, which
we ought to follow, but which we may also violate if we
please ; whereas, for the existences which constitute the
universe of nature, a law is only another name for those
causes which operate blindly and universally in producing
certain inevitable results. By law of thought or by logical
necessity, we do not, therefore, mean a physical law, such as
the law of gravitation, but a general precept which we are
able certainly to violate, but which if we do not obey, our
whole process of thinking is suicidal or absolutely null." *
Hamilton here very properly marks out the contrast be-
tween the operation of physical and of logical law. In the
former case the law is a sequence, a necessary and inevitable
sequence, at least hypothetically so, given the present con-
stitution of things. The cause or antecedent being given,
[I the effect or consequent must follow ; there is no choice.
iVrhe cause cannot select its effect, the effect cannot select
1 Logic, L. v., p. 78.
PHYSICAL AND LOGICAL LAW. 139
its cause. Bodies gravitate, and they have not the power
to disobey the law. Nor are they conscious of the sequence
or law which they are fulfilling or exemplifying. In these
respects, an intelligence, a free intelligence, though sub-
ject to law, differs from physical agents or causes. It is
open to him to elect to obey the law of his intelligence
or to disobey it. And when he obeys it, there is a certain
degree of choice on his part. When, for example, he fol-
lows the law of Identity in his thinking, or applies it, and
reasons from the whole or genus to the part or species,
thus thinking consistently from all to some, he is so far
electing to obey the law. When in the same way he thinks
that A and not-A must be held to be different, or thought
apart, he follows with a certain election the law. When he
thinks that 2 + 2 = 4, he obeys the law of consistent think-
ing. But he may disobey the law, and think inconsistently.
He may imagine he infers from some to all; he may imagine
he unites two contradictory attributes in one subject ; he
may imagine he thinks 2 + 2 = 5. He may actually express
all this in words. He does so every time he thinks or
reasons inconsistently. His thinking, his concluding from
premisses, is not necessarily valid ; what he concludes, or
says he concludes, may be inconsistent with what he laid
down. The penalty for this is that his so-called or im-
agined thought turns out to be not thought at all, for
the relation which he imagines he constitutes — say the
union of contradictories, or 2 -f- 2 = 5 — does not exist.
The jme half of the thought, so to^speai^^abolishes the ,
r. and no Eaa noTf-tlm Owkifo-TrfchA iTYinoMTipst \\t\ haa. /
other, and he has h^T*1iiB~thi5ught^ he imagines he has.
He sees this as soon as he becomes conscious of the incon-
sistency. It was possible for him to go wrong, and he went
wrong ; it was not possible for the physical sequence to go
wrong, and it did not go wrong. In this sense, and to this
extent, the logical law is an ideal necessity, a precept which
we may or may not obey, but it is also in the strictest sense
a necessary, even inevitable law, or condition of really ex-
istent thinking, or of consistent thinking, for these are exactly
equivalent. Logical law, thus, to a free conscious intelligence,
may be stated in the form of a precept, as every rule of
thought and action must ; but this is not inconsistent, as
Mill alleges, with the rule by law " in the scientific mean-
140 INSTITUTES OF LOGIC.
ing of the term." It does not make the a priori necessary-
law, "like laws made by Parliament," alterable and contin-
gent ; it does not deprive them of the character of " neces-
sities of the thinking act," and make them merely " instruc-
tions for right thinking," or " general precepts which we are
able to violate ; " for they are still the absolutely indispen-
sable conditions of any and all thinking, apart from which it
(j is suicidal and null. Mill's reasoning amounts simply to a
I very pretty fallacy : Logical laws are precepts (Hamilton).
„j 1 Acts of Parliament are precepts (Mill). Therefore, logical
I laws and Acts of Parliament are essentially the same (Mill).
§ 165. Hamilton naturally and properly illustrates, in the
first instance, the law of Identity of the whole and parts in
Comprehension. Seeing that, as he teaches, Comprehension
implies Extension, it hardly probably occurred to him that
further illustration in Extension was needed. But Mill, more
suo, thence at once infers that the law in Hamilton's view
does not apply to the whole in Extension. To say that it
applies to the whole in Comprehension is, forsooth, to say
that it does not apply to the whole in Extension, — that this
application of it in Comprehension is inconsistent with its
application to the whole of Extension, which is yet in Hamil-
ton's view, and properly, implied in the Comprehension !
§ 166. Hamilton does not say, as Mill represents, that
the Principle of Identity is " the peculiar groundwork of any
special kind of reasoning," and he does not deny but affirms
that it is " an indispensable postulate [principle] in all think-
ing." All that he says is that the law of Non-Contradic-
tion, of which the Principle of Identity is the primary
phase, expressly regulates in this its first form, affirmative
thought. Surely a man may be allowed to state one thing at
a time without being held to deny everything else.
§ 167. Mill's own expression of the law of Identity is —
" Whatever is true in one form of words is true in every other
form of words which conveys the same meaning ; or it is " the
reaffirmation in new language of what has been already
asserted." 1
This properly speaking is not the principle of Identity ; for
this law does not regulate simply reaffirmation, and it applies
to the elements of the proposition, or of what is true, in the
1 Examination, p. 482.
MILL ON IDENTITY. 141
first place. Subject and predicate must, in the first instance,
be thought and kept in consistency with themselves, ere any-
thing either true or false can be said. The word true unduly
narrows the scope of the law. It extends beyond what is
true in point of fact to what we can conceive as congruent
or possible. Mill's formula is not a statement of the law, but
of that which supposes and assumes the law, or a special
application of it.
§ 168. Mill denies the principle of Identity to be " the
principle of all logical affirmation." l It applies only to
analytic judgments. If the predicate express a new attribute,
not identical with what pre-existed in the subject, the prin-
ciple does not apply. The reply to this is that the principle
does not apply in the sense of enabling us to add the new
predicate ; but this adding the new predicate is not " logical
affirmation." It is added on the ground of something
external to the original concept and its attributes, either
experience or a priori necessity. Hamilton does not deny
affirmation other than logical, looking to the ground of the
affirmation. But he denies that any kind of affirmation is not
subject to the principle of Non-Contradiction in the added
attribute as compared with the original : so that in the widest
possible sense Non-Contradiction, implied in Identity, regu-
lates all affirmation. Further, the synthesis or addition of a
new attribute to a concept is a process extra-logical, and to be
completed ere we can deal with the full concept, and Logic
does not begin to treat of a concept until it is given us.
As given to Logic, the so-called synthetic concept is, how-
ever found, thus analytic.
§ 169. Hamilton says that " as the law of Contradiction
enjoins the absence of contradiction as the indispensable
condition of thought, it ought to be called the law of Non-
Contradiction." But, says Mill, the law of Contradiction "is
not an injunction ; it does not enjoin the absence of contra-
diction any more than the law of Identity enjoins identity."
What then do they do ? The law of Identity means " that
a proposition which is identical must be true ; " the law of
Contradiction, "that what is contradictory cannot be true."
Does Mill really affect even to imagine that Hamilton said or
meant that the law of Identity, as a condition of affirmation or
1 Examination, p. 483.
142 INSTITUTES OF LOGIC.
thought, enjoined anything but that thought proceeding under
it must affirm, not deny, the identity of the parts with the
whole? Substitute for "true" in Mill's formula "affirmed,"
and you have Hamilton's meaning in the one case ; and
substitute for " cannot be true " " denied," and you have his
meaning in the other case. If " the absence of contradic-
tion be the indispensable condition of thought " — that is,
thought at all, as opposed to fancied but truly non-existent
thought, does not the law of Contradiction as a general
principle or law enjoin this absence, and universally enjoin
it?
§ 170. They are not the fundamental laws of thought,
according to Mill ; they are the laws of consistency. As such
they are the fundamental laws of thought, for thought must
be consistent ere it can be known to be materially true or
false. And they are the only laws which are completely uni-
versal and necessary to logical thought. All others are con-
tingent generalisations.
§ 171. Hamilton says contradictories cannot be thought
together. " Most people," remarks Mill, " would have said
be believed together ; but our author resolutely refuses to
recognise belief as any element in the scientific analysis of a
proposition."1 Hamilton was right, for the reason why they
cannot be believed together is that they cannot be thought
together. And further, Hamilton does recognise the fact that
this incompatibility of thought implies an incompatibility
in existence, which cannot be believed as possible.
§ 172. When Hamilton argues that A and not- A sought to
be united annihilates thought itself, Mill replies that " this
proves only that a contradiction is unthinkable, not that
it is impossible in point of fact."2 Thus, then, a contra-
diction is possible in point of fact, — a non-existent thought
may represent a possible object of reality. There may cor-
respond to zero in thought an actual real object !
§ 173. The law of Contradiction is with Hamilton "the
principle of all logical negation." By logical negation it
must be kept in mind that Hamilton means that negation
which we are entitled to make in virtue of the form of the
proposition. This is symbolised by is and not-is — by A and
not- A. This is a priori, in virtue of the formal law. There
1 Examination, p. 485. 2 Ibid., p. 493.
IDENTITY AND CONTRADICTION. 143
are other forms of negation which are not made in virtue of
the purely formal law, as, for example, the negation of con-
traries or repugnants. Red is not green ; black is not white,
are negations, but not contradictory negations. These are
founded on the facts of intuition, and the laws regulating the
formation" of concepts thence derived. The incompatibility
is real and material. Indirectly, however, there are numer-
ous cases that come under the principle of contradiction.
Thus red and not-red, black and not-black, may be regarded
as implied in the two judgments given. And when we put
white {i.e., a not black) in place of the negation, the contradic-
tion is efficient in the negation, though not the principle of
the whole of it. Whether this should be called logical nega-
tion depends thus on the point of view. When we infer be-
tween contraries, we do so on the principle of contradiction.
We deny of a particular colour that it is red ; this yields us
the inference only that it is some other.
§ 174. The laws of Contradiction and Identity are prin-
ciples of reasoning in the sense of being " generalisations of
a mental act which is of continual occurrence, and which can-
not be dispensed with in reasoning."1 In other words, they
are at once contingent and necessary. They are the general
statements of what continually takes place in reasoning, and
they cannot be dispensed with in reasoning. If the latter,
they are more and other than generalisations. They are in
and constitute the process of the reasoning, the essential
part of the reasoning. To generalise what is already sup-
posed continually to take place, is itself a contradiction in
terms. What continually takes place involves past, present,
and future, and no generalisation can extend to this so as to
give complete universality, far less tell us " what cannot be
dispensed with." The generalisation here supposes alike a
universality and a necessity which it cannot give.
But generalisation itself is impossible without them. In
generalising I apprehend that this case is like that, and so on
indefinitely, and conclude that the general law embraces the
particular cases. If the law of Identity be not true, — if con-
tradictory attributes are not necessarily excluded at every
step in every generalising process — how can the generalisa-
tion move at all, or how can I reach the general law ? But
1 Refer to Examination, p. 487.
144 INSTITUTES OF LOGIC.
if generalisation presuppose identity and non-contradiction,
how are these to be derived from the completion of the
process ? l
§ 175. To subvert the reality of thought by thought itself
is a contradiction. It is to assert the reality of thought and
to deny it at the same time and in the same act. We think
that there is no thought. Mill, more suo, asks, " if the reality
of thought can be subverted, is there any peculiar enormity
in doing it by thought itself?" Simply this, that you would
be asserting the reality of thought in subverting it. Does
he really suppose as he writes, or does he imagine the least
relevancy in this, " that if it were true that thought is an
invalid process, what better proof of this could be given
than that we could by thinking arrive at the conclusion
that our thoughts are not to be trusted?" He adds, "Sir
W. Hamilton always seems to suppose that the imaginary
sceptic who doubts the validity of thought altogether is
obliged to claim a greater validity for his subversive thoughts
than he allows to the thoughts they subvert. But it is
enough for him to claim the same validity, so that all
opinions are thrown into equal uncertainty." There is no
question here of more or less validity in thought, there is
none simply of doubting even, none, properly speaking, of
validity at all. The only point is, if I subvert the reality of
a thought by asserting the (alleged) fact of a contradictory
thought, be it concept or judgment, if I say that a contra-
dictory judgment is and is true, that contradictories thus
may be true, I subvert the act of thought in which I assert
this, for in that case the contradictory of this assertion may
be true. Thought is thus paralysed, and is unable in the
absence of the test of non-contradiction to say anything what-
ever, to assert even its own reality, its own assertion.
§ 176. What is the bearing or scope of these laws, so far
as existence is concerned ? Hamilton's answer is that " what-
ever violates the laws of Identity, of Contradiction, or of Ex-
cluded Middle, we feel to be absolutely impossible, not only in
thought but in existence. Thus we cannot attribute even to
Omnipotence the power of making a thing different from
itself, of making a thing at once to be and not to be, of
making a thing neither to be nor not to be. These three laws
1 Refer to Examination, p. 487 et seq.
SPHERE OF THE LOGICAL LAWS. 145
thus determine to us the sphere of possibility and of impossi-
bility ; and this not merely in thought but in reality, not only
logically, but metaphysically." " They are the laws not only
of human thought but of universal reason." " Very different
is the result of the law of Eeason and Consequent. This
principle merely excludes from the sphere of positive thought
what we cannot comprehend ; for whatever we comprehend,
that through which we comprehend it is its reason. What,
therefore, violates the law of Reason and Consequent merely,
in virtue of this law, becomes a logical zero ; that is, we are
compelled to think it as unthinkable, but not to think it,
though actually non-existent subjectively or in thought, as
therefore necessarily non-existent objectively or in reality." l
§ 177. Mill admits that these laws are laws of all phe-
nomena, and as existence has no meaning but one which
has relation to phenomena, we are safe in admitting them to
be laws of existence. " Existence itself, as we conceive it, is
the power of producing phenomena." But Hamilton cannot
be allowed to hold that these laws are applicable to all
existence. Why, we ask in wonder? Because his opinion
is " that we do know something more than phenomena ; that
we know the primary qualities of bodies as existing in the
noumena, in the things themselves, and not as mere powers
of affecting us." Suppose Hamilton did hold that we knew
something more than phenomena, which is notoriously false,
how does this prove that he cannot hold these laws to
apply to this something more ? It is further in no sense
true that Hamilton held the primary qualities to exist in the
noumena: he does not use the word noumenon. It is bor-
rowed from another philosophy altogether. It is further not
true that phenomenon is to be limited to the meaning of
"affection on us" — the assumption of such a restricted
meaning as the only one is even ludicrous.
§ 178. In supposing a law of thought not to be a law of
existence, the thinking process is not, according to Mill,
thereby invalidated.2 What law of thought does Mill here
refer to? The only one in question at present is non-
contradiction. Does the supposition of this not being a
law of existence, while it is a law of thought, not subvert
all truth, and make our thoughts about existence a mere
1 Led. on Logic, vi. 2 Examination, p. 494.
K
146 INSTITUTES OF LOGIC.
illusion? If non-contradiction be possible in reality, and
impossible in thought, how can thought represent cor-
rectly the real ? What sort of a proof does he give of
this? He says: "If the only real objects of thought,
even when we are nominally speaking of noumena, are
phenomena, our thoughts are true when they are made
to correspond with phenomena : and the possibility of this
being denied by no one, the thinking process is valid whether
our laws of thought are laws of absolute existence or not." x
Suppose the mind incapable of thinking noumena, capable of
thinking only phenomena as coming from noumena, — suppose
the mind under no necessity of thinking these otherwise than
in conformity to what they really are, — then we may refuse
to believe that our generalisations from the phenomenal attri-
butes of noumena can be applied to noumena in any other
aspect, without in the least invalidating thought in regard to
anything to which thought is applicable.2 In other words,
contradictory attributes while they cannot be thought to co-
exist in the phenomenal sphere, and cannot so coexist, may
yet be believed to coexist in the unknown noumenal (unim-
aginable) sphere of being. What is impossible in the pheno-
menal sphere (perceived and imaginable), is yet possible in
the unperceived, unimaginable, sphere of being ; and there-
fore, if actual, thus true, and this possibility in regard to the
unimaginable would not render invalid the (opposite) law in
the sphere of the phenomenal — perceivable and imaginable.
In the first place, the belief in the possibility of the union of
contradictories, whatever they might be, is precluded by the
nature of the so-called thought or judgment which is said to
unite them. Such a judgment is null, has no object, is not
real as a judgment. And Mill, of all people, should be ready
to acknowledge that we cannot believe where there is no
object of belief. In the second place, if the law of non-
contradiction be true or certainly true only in regard to the
existence we perceive and think or imagine, but not in re-
gard to the sphere of things beyond and above this, which
yet produces the perceived and imagined or phenomenal,
then our whole knowledge may be only an illusion ; for this
phenomenal given as non-contradictory may be the product
of what is in itself really and essentially contradictory.
1 Examination, pp. 494, 495. 2 Ibid.
SPHEKE OF THE LOGICAL LAWS. 147
Therefore, truth and falsehood, yes and no, right and wrong,
make after all but the dream of the finite mind, which is for
ever barred from the certainty of true reality. And though
our laws of thought are not invalidated by this supposition
in the phenomenal sphere, the phenomenal sphere is itself
but an uncertain symbolism, perhaps a delusive appearance
of its very contradictory.
148
CHAPTER XIV.
THE LAWS OF THOUGHT THE DOCTRINE OF HEGEL —
STATEMENT AND CRITICISM.
§ 179. The general ground on which Hegel attempts to
abolish the laws of Identity and Non-Contradiction is the
assumption that Identity and Difference, as inseparable in
thought, are the same thing, or at least are mutually creative,
— that identity is only identity as it is not difference, and
difference is only difference as it is not identity, — that each
is not only itself but the special other of itself. This of
course proceeds on the general assumption that what is
necessarily connected in thought is so necessarily connected
in existence, and that opposites are, in so far as real, mutually
constitutive, in fact, mutually creative. The truth is, that
while Identity and Difference are mutually implicative, alike
in apprehension and thought, these are not thus mutually
creative. They cannot be either apprehended or thought
unless as relations already existing, and as existing in
opposition as realities, while known together. Identity and
Difference as mere abstract generalities are not possible,
unless through special apprehension of identities and dif-
ferences : and they are nothing more than terminal abstrac-
tions, unless as realised in this or that specific identity or
difference ; and these are not possible 'unless as forms of
reality, which no thought of ours, or process of thought
passing through us, can create. Further, if identity and
difference disappear in a higher concept or reality, and this
goes on without limit, or ad infinitum, there is no truth, philo-
sophical, moral, or religious, in the world. And there is no
basis possible even for this assertion itself. Identity and
DOCTRINE OF HEGEL. 149
Difference, truth, reality, and laws of thought, all thus
ultimately disappear in a perpetual flow — in fact, a verbal
chaos. The doctrine of Hegel may be thus summarily stated,
almost in his own words : —
(a) " It is very important to conceive identity in its truth, that is
to say, not as identity purely abstract, but as enclosing difference
in itself. . . . Essence is only identity and radiation in itself
in as far as it is negatively relating itself to itself, that is to say,
repulsion of itself by itself : it contains therefore essentially the deter-
mination of difference. . . . Difference, as the mutual relation of
two contraries, is determinate difference, difference in itself properly
called, opposition, the relation of positive and negative. The posi-
tive is only positive in so far as it is not negative, the negative is
only negative in so far as it is not positive. Each being thus only
because it is not the other, each radiates in the other and is only by
the other ; each of the different has not an other in general in face of
it, but its other ; each is the other of its other. Difference is thus con-
tradiction, relation of contradictories which reciprocally suppose each
other.
" The positive is the same thing as identity, but not true identity,
that is to say, determined as not being the negative. The negative is
none other than difference itself ; it is difference with the determination
of not being identity. It is supposed that there is an absolute differ-
ence in positive and negative ; but the two are in themselves the same
thing, and we might call the positive negative, and vice versd. Thus
the same obligation is a positive good for the creditor, a negative good
for the debtor ; — a way to the east is also a way to the west. The
positive and negative are in essential relation, and reciprocally sup-
pose each other. The north pole of the magnet cannot be without
the south pole, the south pole without the north pole. Let one cut the
magnet in two, we have not in the one piece the north pole, in the
other the south pole. In the same way, electricity positive and elec-
tricity negative are not two separate fluids, subsisting the one without
the other.
" Difference in itself gives place to the proposition, — of two opposed
predicates only one can belong to the same thing, and to this, — between
two contradictory predicates there is no middle. This principle of
Contradiction expressly contradicts the principle of Identity, in so
far that, according to the latter, the thing ought to be simple relation
to itself, and that, according to the first, it ought to be relation to
its opposite. It is by the intelligence which is proper to it that
the understanding puts thus alongside of each other two contradic-
tory principles without even comparing them. The understanding
seeks to escape contradiction, and in doing so falls into it. It is pre-
tended that A is necessarily + A or — A, and that there is no third
term. But this third term is A itself ; it is found by this even that
one affirms that it does not exist. If + A signifies a distance of six
miles to the west, — A an equal distance to the east, we may efface
the plus and the minus, the distance does not the less exist. In physics
150 INSTITUTES OF LOGIC.
the idea of polarity is current, and it contains a more true determina-
tion of opposition. In place of saying that there is no middle term
between two contradictories, as the understanding does, it would rather
be necessary to say that all is contradictory. . . . Thus in nature, the
acid is in itself at the same time the base, that is to say, its being
is wholly being in relation with its contrary. The acid does not
therefore rest quietly in the opposition ; its tendency is to posit what
is in itself, reuniting itself to the base. Contradiction is the essence of
all life and all movement : it is the spring of universal activity, it
moves the world, and it is ridiculous to say that it cannot be conceived.
" The positive is that difference, which is for itself, and which at
the same time is in relation with its other. The negative is also for
itself, and at the same time, as subsisting by itself, it is only a relation
with its other."— (Logik, Encycl. § 115, 116, 119, 120, cf. Ott, Hegel,
p. 192 et seq.)
Again (Logik, Part ii. , p. 56), "Contrary and contradictory concepts
— a difference which is here especially noted — lays the ground of the
reflection — determination of difference, and opposition. They are
looked upon as two special kinds, that is, each as firm for itself and
valid against the other, without any thought of the dialectic and the
inner nothingness of this distinction, as if that which is contrary must
not be so severely determined as the contradictory."
" Species are contrary, so far only as they are different, to wit,
through the genus as their objective nature have they an in and for
itself being standing ; they are contradictory, in so far as they are ex-
clusive. Each of these determinations for itself is, however, one-sided,
and without truth : in either — or of the disjunctive judgment is placed
their unity as their truth. "—(Logik, p. 107.)
Again, "Formal thinking makes for itself the determinate ground
proposition that contradiction is not thinkable ; in fact, however, the
thought of contradiction is the essential moment of the concept." —
(P. 342.)
§ 180. Now it is perfectly true that every cognition implies
a relation, and that our highest concepts, logical and meta-
physical, are known in relation to their contraries. We have
thus being and non-being, substance and accident, cause and
effect, and so on. We have light and shade, &c, in our
sensible experience. But it does not follow, as Hegel
assumes, that the one concept in the correlation produces the
other, or that the necessary relation of the contraries or
opposites implies the non-existence of their real opposition
as factors in our experience. The knowledge of opposites is
one, but the opposites known are not therefore one. These
are two wholly different propositions.
§ 181. Identity is ambiguous, and of this ambiguity Hegel
takes advantage : —
IDENTITY AND DIFFERENCE. 151
(1.) There is identity of the one or individual, as against
the flow of time, — that which subsists the same or unchanged
during successive moments is in our experience and meaning
identical in the different moments. The best illustration of
this is in the indivisible Ego of our consciousness, contrasted
with its varying states and conditioning our knowledge of
those states.
(2.) There is the identity of the one or individual as against
the multiplicity of other individuals in experience. The in-
dividual is this, and not that, — this now as against that then,
— this here as against that there.
(3.) There is the identity of the positive, as concept or pro-
position, against the negative of the concept or proposition.
(4.) There is the so-called identity, or rather unity and
homogeneity of all being, both being in itself, and being
in its individual or particular parts. All is one, — homo-
geneous,— or parts of the one homogeneous, call this Pure
Being, or Pure Thought, or Pure Idea, or some common
substance of whatever nature, supposing it to have what we
can call a nature.
§ 182. Now, in regard to the first form of Identity known
to us, difference is not deduced from it or created by it, for
the simple reason that it is already a condition of our know-
ledge that the individual is one and the same, amid the lapse,
change, or difference of time. And it is not true that the
identity of the individual is the difference, or equal to the
difference, or contains the difference. The difference as
against the identity of the Ego in time is difference, and as
against this the identity stands. Further, the difference is
accidental, — any lapse of time may show it, — may illustrate
it ; but the unity or oneness of the Ego is unchanged, whatever
be the particular flow of time in which it subsists. Then,
just because the difference in some form is inseparable in
cognition from the identity, it is inseparable in fact, and
therefore true or real in fact, as a subsisting difference. It
is not true that identity is only as it is difference, or dif-
ference is only as it is identity. They exist in thought and
fact as mutually exclusive ; and unless this be conceded, no
step can be taken in knowledge, or anything result but simple
verbalism. And even although it be admitted that the abstract
concept of identity implies difference, this could never help
152 INSTITUTES OF LOGIC.
us in any case to the knowledge either of individual (or
specific) difference, or of identity and difference. We may
ring verbal changes as we choose, but this thing would be
different from that in a way we thus did not and could not
know, and it would be different as a reality and not identical.
§ 183. With regard to the second form of identity, viz.,
that of the individual as against the many in being, in time
and space, there is here no fusion or equivalence of identity
and difference. The individual as so conceived can subsist
only as it is not the other, and the moment these are identi-
fied, or equalised in any way, individuality ceases. If any
individual be another, it is no longer individual ; if I be you, I
am no longer myself. If every individual be every other, there
is no longer any individual ; if every Ego be every other Ego,
there is no Ego. Hegel affords a perfect reductio ad absurdum
of his vaunted principle when he argues that because an in-
dividual, say this man or this house, can also be called that
man and that house, in of course a different point of view,
this and that do not really distinguish individuals, but mark
the identical !
Manifoldness in being or in individual being no doubt
implies the possibility of likeness and unlikeness ; but it can-
not tell us anything as to what are like or unlike or wherein
that lies. This is wholly a matter of experience, and cannot
be created by us, though it may be apprehended or learned.
Then, it is the greatest of mistakes to suppose that because
things are unlike they are necessarily contradictory. Two
atoms may be unlike in weight and property, but they still
belong to the same class of things. The function of the eye
and that of the hand are very unlike, but they are both help-
ful in sensation and perception. The essential quality of
contradiction is not mere unlikeness or even oj^position, but
absolute exclusion or incompatibility.
§ 184. With regard to the third form of alleged Identity,
positive and negative are not convertible in any form of
opposition. If they are contraries, the negation of one
quality is opposed only by some other ; if contradictories, the
positive is opposed only necessarily by a simple negation.
It may be opposed by a positive, but not necessarily. The
negative has not an equal right to determine the positive ;
the positive is first and definite, and the negative is merely
NEGATION. 153
indefinite, various. It subsists only through the positive, but
not vice versa.
§ 185. The fourth position is a pure hypothesis which it is
the aim of the Dialectic of Hegel to establish, and in which
it wholly fails by sheer internal inconsistency, as well as
gratuitous . assumption. Set up Identity and Difference as
realities which deploy through contradiction, and so make the
Universe. It is easy enough to play at world-making, but it
is play only, and the world is never our world.
Being or thought is throughout the system assumed to be
the same, while we know no such identity in our' experience ;
but wholly different forms of being — spiritual and material :
it clothes itself in difference or different forms, only to return
always to a third form, which includes the first and second
— identity and difference ; and in the end it becomes the
absolute or all expressly, the identity of identity and differ-
ence. The assumption here is that is means a universal
being, which passes into every form of being and is the same
or a unity all through under various forms. It is at the same
time entire in every category into which it passes, and yet it
is transitory through each category, and continuous to a term
of absolute development, when it knows itself as the Universe
and God ; though as there is no limit to Keason there is no
reason why the Absolute should not take a new turn and
pass into something else, but every reason why it should.
Though entire in each category, it is in each incomplete or
untrue. It is only complete or wholly true in the last —
Absolute Idea, in which all the categories are gathered into
one, a unity of method or development. In other words,
Being develops through difference or contradiction, to absorb
in the end all difference and contradiction. It is absolutely
identical ; yet its essential movement is contradiction.
§ 186. But this general doctrine or theory cannot itself be
adduced in disproof of the validity of the laws of Identity
and Non-Contradiction. On the contrary, these have to be
proved invalid, in the first instance, before the theory can be
accepted. That identity passes into difference, negation, or
contradiction is just the point to be proved : it is the point
even which must be rendered conceivable. The assumption
involved is certainly not intuitive ; it is even contrary to
appearance, to thought, and to fact as we know it.
154 INSTITUTES OF LOGIC.
§ 187. The place and power of negation are utterly mis-
conceived and exaggerated in the system. In certain cases
of opposition, one of the terms is merely the negation of the
other. We may, for example, deny absolutely the alleged
position of an object in space, or the existence of a person
in time at all. The negation here gives nothing positive ; it
simply sublates or removes. And this holds in every case of
the is and the is-not in its primary application to reality. The
is or is-not supposes a definite subject of which we speak and
think, and the one is simple affirmation of its reality, the
other of its non-existence. Cause is or it is-not : God is, or He
is-not. Peter the Hermit lived in the eleventh century; he
never lived at all. But there are other contraries which are
equally positive, but not necessarily related, — e.g., yellow and
blue, — wise and foolish. In this case, negation of the one does
not give the other in any sense ; but if the subject spoken of
be capable of admitting the predicate of the genus, say colour,
it is supposed to be indefinitely referred to some one kind of
colour, we may not as yet know which. The thing being first
of all supposed limited to a given class, and one of the mem-
bers of the class being denied of it, it is supposed to be
capable of being found in another member of the class. But
this is a secondary process, not dependent upon the mere
negation of the subject, as say blue, but on the previous affirma-
tion or supposition that there is a class of coloured things,
and that the thing we speak of is capable of belonging to that
class, or admits of colour as an attribute. In fact, it is indef-
inite affirmation following from, and only possible through, a
previous definite affirmation.
Now Hegel confounds these totally different kinds of nega-
tion, and misconceives the real ground and possibility of the
last. The result is that we have constant confusion of contra-
dictory and contrary opposition, and the constant assumption
that the negation of a positive must give a positive.
§ 188. Then there are other cases of opposite terms in which
both are equally positive — e.g., Cause and Effect — Substance
and Accident — Ego and Non-Ego — Subject and Object. Those
specified are necessarily relative or correlative. They are op-
posites and they are positives. Their peculiarity is that if
you think the one, you think also the other ; if you affirm the
one, you affirm the other. But if you negate the former, you
NEGATION. 155
do not affirm the latter, nor in fact do you lay down any-
thing positive by your negation. The negation of cause does
not give effect, or the negation of subject does not give object.
These are in fact a species of contraries.
§ 189. He further constantly proceeds on the counter mis-
take to this — viz., that every negation of a negation gives an
affirmation. But this is ludicrously false. No doubt nega-
tive concepts frequently represent positive qualities — e.g., im-
mortality and immensity. Others again do not — as powerless-
ness, insensibility. In the caee of mere existence, the nega-
tion of not-is, by not not-is, would restore the existence thus
negated. But the question is whether the negation of a
negative would for the first time and of itself give a positive
— e.g., this definite thing is-not. Here I suppress a particular
subject. Again I say — this thing is not correctly stated as
not-being so. The not-is is negated by not. It is not not-is.
No doubt there is here now an affirmation. But an affirmation
of what? Of the subject I started with, — not a new subject.
It may be formulated thus — A, not not-A, therefore, A. Red,
not not-red, therefore red. It is quite clear also that the
mere negation never could give a third notion which would
unite the not and the not-not. All that it can do is to enable
me to recur to the subject from which I started. Yet the
supposition that the negation of negation gives for the first
time new conceptions, — is in fact synthetic, — runs through
the whole logic of Hegel. It is even supposed capable,
given merely a genus, to evolve by the negation of it the
difference which characterises the various species ; whereas
every one must see that no galvanising or negation could do
this, and that the true result in such a case is the negation
simply of the genus itself.
(a) "Hegel makes the affirmative and negative in the relation of
exactly the same force or value — e.g., if the mathematical point be the
negation of space, space is the negation of the mathematical point.
Sight is the negation of darkness, and blue of red. Hegel speaks as if
it were a matter of indifference whether we begin with affirmation or
negation, as if we could as easily infer from the mention of the idea
of darkness that of light, as conclude from light to darkness. But the
negation of negation does not necessarily give an affirmation. Starting
from an affirmation we may deny it and then make it reappear by nega-
tion of the negation. But something positive must be given as known,
and this positive reappears when the negation is denied, but it is not
156 INSTITUTES OF LOGIC.
created in all pieces by the double negation. But according to Hegel
all concepts, save abstract being, are only negations of negations. The
double negation does not only reproduce the point from which it
started, but begets a real affirmation superior to the first. Through the
negation of the thing, we arrive at the thing by negation of that nega-
tion. But out of the ideas of affirmation and negation nothing can
come but themselves. Hegel introduces becoming, but this is a mere
interpolation, at once gratuitous and illegitimate. This is the very
point to be proved ; and it is not even attempted. Becoming is, in
fact, assumed, and assumed from experience or motion in experience.
It may contain being and non-being, but it is not given by affirmation
and negation alone. In fact, it is impossible that negation of an
affirmation, and then negation of that negation can give anything but
the first affirmation, which was given, or assumed, or borrowed from
ordinary consciousness and experience. There is no creation of any
idea, there is the simple manipulation of material already to hand." —
(Ott, Hegel et la Philosophic Allemande, pp. 96-101.)
§ 190. But Hegel alleges certain reasons against the ex-
istence and validity of the fundamental laws of thought : —
(1.) He urges that the law of Identity is contradictory in
form, for every proposition by its form promises a difference
between the subject and attribute or predicate. But the law
of Identity says that A is A, or that A cannot be at the same
time A and not- A. It is sufficient to say in reply to this that
the form of the proposition does not promise a difference be-
tween subject and predicate, for in that case every proposi-
tion would be negative, which is not so. But the form
of the proposition provides for a plurality of notions, —
a subject and a predicate, — whether these be the same or
different. When I say A is A, or the whole is identical
with the sum of its parts, I state a proposition in valid
form, — nay, I state abstractly the principle on which all
affirmation proceeds.
§ 191. (2.) He objects further that it is ridiculous to say that
a planet is a planet, &c. Possibly enough ; but ridicule, as has
been said, is not a proof of truth or falsehood. And it may
be necessary to assert the identity of an object with itself,
when it is sought to confound it with something else. We
may be called upon to say that a planet is a planet, if a man
says it is not a planet out a fixed star. One says the system
of Copernicus is that of Ptolemy. I say no. — The system of
Copernicus is the system of Copernicus — i.e., it is identical with
itself, and not with a different system.
§ 192. (3.) He states the laws of Non-Contradiction and Ex-
hegel's ceiticism of laws of thought. 157
eluded Middle thus : Of two opposite predicates, one only can
belong to the same thing. And : Between two contradictory
predicates, there is no middle. He urges that the law of Non-
Contradiction expressly contradicts that of Identity, because
the latter says the thing ought to be simple relation to itself ;
whereas the former says it ought to be relation to its oppo-
site. But the answer to that is that the two relations are in
no way contradictory or mutually exclusive. A thing may
be in relation to itself, and also in relation to its opposite.
Nay, it must be both. Thus, e.g., the mathematical point is
indivisible. Here I virtually state the relation of the point to
itself, or its essential attribute ; but I no less implicitly state
its relation by negation to the opposite attribute — viz., divisi-
bility. I may state a relation by simple affirmation. This is
indivisible. Or I may do it by negation of negation. This is
not divisible. The Ego or Self is the Ego or Self — not one of
its qualities. The Ego is not the non-Ego or not-Self. These
are compatible statements ; they are, therefore, not contradic-
tories. Nay, if the law of Identity were not previously true
— that is, that a thing is what it is, or is identical with its
attributes — neither the law of Non-Contradiction nor the law
of Excluded Middle would have any sphere of operation. We
can only exclude from negative spheres, when we have a
definite positive to start from, and to make the positive other
than it is, is to abolish it.
§ 193. (4.) He seeks to disprove the law of Excluded Middle
thus : —
It is said, he alleges, that A is necessarily either + A or — A.
There is no third term. But, he adds, this third term is A itself ;
it is found by this that we affirm its non-existence. If + A
signifies a distance of six miles towards the west, and —A
an equal distance towards the east, we can efface the more
and the less [plus and minus), and the space of six miles
still remains. How and where does the space of six miles
remain ? The place is not six miles to the west, it is not six
miles to the east of a given point ; its distance is, therefore,
undetermined ; nay, it is left open to say it may lie to the
north or the south of the point in question. What really
remains is the concept of distance simply, or undetermined.
We are not speaking here of contradictions at all, but of con-
traries under a genus.
158 INSTITUTES OF LOGIC.
But if we say definitely of a given subject called B, that
it is either + A or not + A, that is, that these are the only
two kinds of B, we have excluded any third term. B must
be one or the other, either +A or not +A. Whether not
+ A is — A or A simply is not decided. " We may say A is
alternatively both + A and —A, on the supposition that A
is a genus, which contains species under it. But in this
case we are not stating two contradictories, or mutually
exclusive propositions, but simply two different kinds of the
same quantity.1 If Hegel had attempted to show a middle
between the equal and the unequal in integral numbers, he
would have tried something relevant, however fruitless or
absurd.
The whole of Hegel's proof is thus simply irrelevant. The
positive and negative illustrations which he selects from
magnetism and electricity are simply relatives : these do not
represent either Contrary or Contradictory Opposition. The
plus and minus of a given or even indefinite quantity are merely
contraries, not contradictories ; they express different degrees
of quantity. To confound these either with their relatives,
or with contradictories, is the gravest error possible in a
system of Logic.
§ 194. Aristotle, under the genus of Opposition, specifies
Relation, Contrariety, Privation and Habit, Affirmation and
Negation.2 A Relative, according to Aristotle, is said to
be what it is with reference to something else — e.g., the
double is the double of the half. Knowledge is what it
is with reference to an object known. Hence things rela-
tively opposed are said to be what they are with reference
to opposites. In this respect, Relative Opposition is dis-
tinguished from Contrary Opposition; for contraries are not
said to be what they are with reference to opposites. Thus,
good is not the good of evil, but the contrary of evil ; nor is
white the white of black, but its contrary. On the other hand,
double is the double of half, and knowledge is the knowledge
of object. These are what they are by reference to opposites.
They do not exist, and cannot be conceived out of relation,
relation of contrast and opposition. But Hegel confounds the
merely relative both with Contraries and Contradictories.
§ 195. But all this criticism on the part of Hegel is mere
1 See above, p. 125. 2 Categories, c. x., and below, p. 179.
SPHERE OF LAW OF NON-CONTRADICTION. 159
trifling with the subject. The broad question is : Are there
mutually exclusive conceptions in human knowledge ? That
there are such it is only trifling with meaning and intel-
ligibility to deny. We have examples in a thing being and
not being, in consciousness and unconsciousness, in life and death,
in yes and no. Unless there be this reciprocal exclusion of
predicates, yes and no, truth and error, right and wrong, are
mere illusions of the understanding, to be finally absorbed in
some generic identity of the speculative reason !
§ 196. There can be no doubt that contradiction is accepted
as absurdity by the common consent of mankind, and as de-
structive of the very essence of human reason or knowledge.
The understanding is satisfied that a notion or a proposition
which involves contradiction, properly so called, is a nullity.
Such a proposition can hardly even be called false. It is rather
non-existent ; it is a form of words into which we can put no
meaning. Here one statement destroys the other. If, for
example, a historian says : This man A. B. lived in the
fifteenth century ; another historian says, — no, he did not
live in the fifteenth century or in any other. We know
very well that these statements are exclusive of each other,
and we should certainly be greatly astounded if the specula-
tive philosopher were to appear on the scene and tell us that
both statements are true ; for everything is also the con-
trary of that which it is. We should very properly, I think,
dismiss both him and his philosophy, and hold by the much-
abused common-sense of mankind. If two systems give to me
no guarantee but self-assertion or an appeal to consciousness,
I confess that I feel constrained to accept that one which
does not reverse either the facts of experience or history.
§ 197. Suppose we apply the principle for a moment to
morals. We have what is known as the moral law. It is
supposed to prescribe certain actions, even certain motives,
and to forbid others. It is further absolute, imperative.
We may be doubtful in some cases about what is right or
wrong ; but we know all the same there is a right and
wrong. And we know also definitely enough that particular
actions and particular motives are to be regarded as such.
Veracity, justice, purity, — these are absolute things for us.
Self-sacrifice is a law of moral life. Will it be maintained,
for a moment, that the principle that everything is also the
160 INSTITUTES OF LOGIC.
contrary of what it is holds here ? Is veracity, is justice, is
purity, is self-sacrifice not separated each by an absolute yes
and no from its opposite ? Are the just and the unjust com-
patible things? When I resolve to do a certain thing, is
irresolution not absolutely exclusive of the opposite resolu-
tion or action ? What meaning can there be here in saying
that every one of those notions is identical with its contra-
dictory, or is a union of contradictories, which is the same
thing ? I confess I cannot see that on such a system there
can be either truth or falsehood, right or wrong, at all. There
is an everlasting play of yes and no, successively subverting
each other. Each stage or movement is a third only of the
truth, and as the yes and no of stages one and two gather
themselves up into a third, called yes, — the truth develops.
But then this new yes or notion begins immediately the
same process, and the result of the whole is the absolute
identity of things fully developed. At no stage in history or
in individual life, do we know the whole truth. Every yes
that is evolved is a partial falsehood, until we get to absolute
identity in the end ; and this only shows us how completely
we were deceived in supposing that the difference of truth
and falsehood, of right and wrong, were anything beyond mere
temporary appearances or passing illusions. " If the end of
man," says a writer, " be action, be the accomplishment of
duty, — and if this be as it is the very negation of contradic-
tion,— is it likely that human reason is to find its essence in
contradiction ? The moral law and the Hegelian method are
in insoluble contradiction. You can choose which should go
to the wall."
§ 198. Hegel, indeed, says in regard to some propositions, that
these are not identical in the sense that being and non-being
are — e.g., I am and I am not. This house is there or it is not.
But this does not mend matters. As has been well said,
" the sense in which being and non-being are identical may
be different from that which differences these propositions.
But if everything contain contradiction, and if there be no
affirmation which is not the negation of itself, — these propo-
sitions must be identical in his view, in virtue of the principle
of contradiction itself. Every affirmation, the simplest as well
as the most abstract, is equivalent to its negation, and thus it
matters not whether we take the one form or the other." It
HEGEL'S fokmula of contradiction. 161
is here that practical absurdity shows the theoretical absurdity-
inherent in the system, and it is here that Hegel is found to
recoil from the legitimate consequences of his own principles.
§ 199. Let the system be judged from the point of view of
ordinary reasoning. Let it be tested by the possibility of
reasoning itself. Does Hegel not seek to prove that which is
to be proved, and not the contrary of it ? He does not mean
surely to say no, when he says yes. He proceeds as other
people do, and as every one must, by the ordinary acknow-
ledged canons of reasoning. Then has he established his
peculiar system by this method? In that case, we must
regard the - foundation as utterly rotten. If he accepts the
ordinary canons to any extent whatever, how is his system,
which is wholly subversive of them, to be reconciled with
them ? On the other hand, if his system is based on the sub-
version of those canons, has he not at the outset assumed
what he ought to have proved in the end ? Is not thus the
whole method a gigantic petitio principii t
§ 200. For the ordinary statement — viz., That a thing which is
cannot be the contrary of that which it is, Hegel would substitute
this : — That everything which is is also the contrary of that
which it is. As grounds of a progressive development, neither
formula is of use.
If we take the former principle, it is obvious that we can-
not proceed by negation to a new idea — in other words, we
cannot construct knowledge a priori. It is what is called an
analytic principle — i.e., we can deduce from the notion of the
subject any attribute involved in it ; but we cannot in this
way add to the notion of the subject, particularly, we can-
not add incompatible attributes. From the notion, for example,
of organisation we can draw out, as it were, the attributes of
growth, and end or purpose, and living form conformed to this
end, because we have already fixed these attributes as con-
tained in the notion of organisation. The principle would
keep us to these attributes and only to these — i.e., it would
keep us consistent in our thinking about the object of
thought.
But if you say that the object spoken of is also the oppo-
site, or contrary, or contradictory of that which it is, you
cannot add an attribute in this way. What would come of
identifying, for example, organisation and its opposite ? Or
162 INSTITUTES OF LOGIC.
of negating organisation ? Yet it is supposed that simply by
denying the notion you begin with, you can add a new idea
to the notion, and finally unite this idea and the original notion
in a third term, which again is a new idea. No progress
in knowledge can really be made in this way. It is, in fact,
simply a suicidal process. And if this be so, the whole
system of Hegel is sapped from the foundation.
§ 201. The illustration which is usually given of this process
is that of the growth of a plant or tree. We are supposed to
begin with the germ or seed. This develops into stem, branch,
leaf, &c. And finally there is the union of all these in the plant
or individual thing. The germ or seed is spoken of as the uni-
versal or possibility of the plant ; the stem, branches, leaves,
&c, as the particulars or differences or negations of the germ.
The union of all these is regarded as the individual thing or
plant itself. These three points, universality, particularity,
individuality, are called moments, and it is said that in this
way human knowledge is developed, developed from the
bare abstraction of pure being or pure nothing. The whole
process, including the universal, particular, and individual,
is called the concept or Begriff. This is the type of human
thought, and of all thought human and divine. But the
whole illustration is fallacious. In the first place, it confounds
the order of observation, or, if you choose, thought, with
the order of production. My mere seeing or thinking this
order of development does not make the development itself.
If I say so, I have assumed here that the order of my thought
is the same with the order of being or reality, that, in fact,
my thought is not only observational but creative, that
thought of this order is the divine creative power working in
me. Now I do not admit this general assumption, and I hold
further that merely to state the observed order of the develop-
ment of the plant, and to ticket it with certain big words,
is to leave out of account altogether the essential element
in the process, the causal or productive power at work,
the life within the germ, which, working long silent and
unseen amid the chaos and the decay of matter, gathers,
assimilates, and at length evolves the form of beauty, grace,
and symmetry, — that form which rooted in a darkness as of
the tomb, yet spreads itself out in cheerful greeting to the
light of heaven.
CONTRADICTION NOT DEVELOPMENT. 163
§ 202. But, further, this is no illustration or even analogy
of the true concept of human thought, nor does it properly
illustrate the so-called Begriff of Hegel. The seed or germ is
said to pass into the root, stem, branches, leaves, and fruit.
But how is this known ? I cannot predict this from the
knowledge merely of the germ or seed. I am not now deal-
ing with a comprehensive or individual whole, but with a mere
class or genus, which I have filled up by generalisation, and
which I can unfold at pleasure. I never could tell how or in
what way this germ would develop by any a priori process.
No negation certainly of the germ would help me to this.
This develo'pment is known through intuition or observation
and generalisation. It is seen and followed by me, not made
merely by my seeing it, far less by my thinking it out
from the germ. If I associate the particulars, as they are
called, of stem, branch, leaf, &c, with the germ, I do so not
from an analysis of the notion of the germ, but from direct
experience of what follows in certain circumstances. It is the
germ in the soil and under atmospheric conditions whose
development I follow, — not the germ as germ or seed in pure
thought. The germ is here improperly described as a uni-
versal at all. It is not a genus or class embracing certain
particulars, as organised embraces animal and plant. Or-
ganised can be predicated or affirmed of animal and plant.
These are the species which it contains, and to which it is
applicable. But stem, branch, leaf, &c, cannot be said to be
kinds or species of germ or seed. You may say a plant is
organised, or has organisation, but you cannot say that a leaf
is a germ or seed. That would really be too absurd. And
much less could you go the length of saying that the nega-
tion of the seed led you to the idea of the stem or branch, or
gave you that idea in any way. The seed is not a universal,
properly speaking ; the stem, branch, leaf, &c, are not par-
ticulars, properly speaking. They do not stand to each other
in the relation of genus and species. And as for the indi-
vidual plant being the union of the genus and species, the
thing is simply ridiculous. Genus and species are united in
the individual. Animal and man are united in this man ; but
this man is not constituted by the union of these simply.
Individuality is something higher than mere membership of a
logical class. In this case, the colour red would be an indi-
164 INSTITUTES OF LOGIC.
vidual, because it happened to unite the genus colour and the
species red. But red, though numerically one colour, is not
exactly the kind of indivisible unity which constitutes each
of mankind, or even the unconscious plant or tree which lives
and possesses its own individual being.
§ 203. It is said in regard to limit in thought that the
consciousness of limit transcends limit, that there is only
limit in natural or unconscious things, that the moment
we reach consciousness of limit, limit itself is destroyed.
My answer to this is that so far from consciousness of limit
destroying limit, this consciousness of limit is essential to
consciousness itself. I never could be conscious unless in so
far as I set up limit, either a not-self against myself, or a
negative against my affirmation. If in the act of conscious-
ness, I transcend limit, I necessarily transcend consciousness
itself, and if I do so I pass into the sphere of the meaning-
less. You can no more abolish the eternal yes and no in
truth, than you can abolish by a mere consciousness of limit
right and wrong, virtue and vice, beauty and deformity, in
the ethical and a^sthetical spheres. Nay, the very assertion
is suicidal. How can I know that consciousness transcends
limit, and unconsciousness does not, unless I affirm that
consciousness is one thing, and unconsciousness another — i.e.,
unless I proceed on a principle of strict and definite limitation ?
I distinguish, define, and limit, in order to show that all limit
is really impossible. I seek to show, in fact, that no gun-
powder will explode, by using a train of gunpowder which
explodes the whole magazine.
The truth is, that consciousness or knowledge, as we have
it, is possible only under conscious limitation. Our thought
is constituted by limitation ; we may substitute one kind of
limit for another ; but we have no power of transcending
limit absolutely, any more than the bird can outsoar the
atmosphere.
V
PAET II.
CONCEPTS AND TEEMS.
CHAPTER XV.
CONCEPTS AS NAMED TERMS — THEIR PRINCIPAL DISTINCTIONS.
§ 204. Term in the widest sense may indicate either the
knowledge of an object (quality) apprehended by Outer or
Inner Intuition, an object represented as in Memory or Simple
Representation, or it may mark the concept of the Under-
standing, whether of an abstract quality, or of a subject
(synthesis in one object) of a series of qualities. Term in the
stricter sense of the word indicates the logical concept ; and
it is extended to individual qualities, or objects, only in so
far as these typify a concept whether generalised or uni-
versal a priori ; for it is essential to a term that what it signi-
fies should be discriminated from what is signified by other
terms, that is, it is only applicable where there is discrim-
ination and distinction, therefore unity amid diversity, and
this is a function of logical thinking.
§ 205. Simple Apprehension is wider than Conception, and
has for its object individual quality, image, or concept, merely
as a fact of consciousness. In every case, it involves a
psychological or existential judgment ; it affirms the reality of
its object as a thing apprehended, as subjectively at least
real. When Simple Apprehension realises the meaning of a
166 INSTITUTES OF LOGIC.
concept, it passes into Conception ; because in that case the
concept is thought as representative of an object whether
real or ideal, it matters not. The further question as to
whether we apprehend, intuitively perceive the quality of
an external thing or object, or only an image of it, is a
psychological point of importance. But the decision of it
one way or another need not affect the character of the act
of Conception qua act of Conception. The laws of the act are
the same in either case.
Simple Apprehension is usually limited to our grasp of the
meaning of the concept, as house, man, organised. But there
is no reason in the nature of the case why its object should
not be the relation involved in a proposition, even that in-
volved in a reasoning simply as apprehended, without actual
affirmation or negation on our part. In fact, this was the
ancient and proper extent of the sphere of Apprehension ; for
with the schoolmen term in its widest sense meant what
terminates any act of apprehension ; and this may be either
incomplex, as individual quality, or simple concept, or
complex, as the proposition.
While the term subjectively indicates the completion of the
intellectual act, objectively as applied to the concept, it in-
dicates limitation. A concept implies the limitation of its
object through certain attributes, hence the term in language
which indicates it has for its essential feature the marking
this limitation, this determination, implying distinction from
other concepts. Every term thus implies distinction in
thought of one concept from another.
(a) Occam distinguishes the indicative from the apprehensive act.
The object of the latter is a simple or incomplex knowledge of terms,
propositions, or reasonings. By the former the intellect not only appre-
hends the object, but assents to it, or dissents from it ; and this act
regards the complex only, for in assenting we esteem as true, in dis-
senting we repute as false. — (Sent. Prolog., qu. 10. Prantl, iii.xix. 753.)
§ 206. Words have been divided into Categorematic and
Syncategorematic. The former are held to be significant by
themselves, the latter "only consignificant. The former fully
signify the thing or concept, the latter do not so much signify
as consignify. The noun is categorematic ; the conjunction,
preposition, adverb, and several pronouns only syncategore-
matic. This is properly a grammatical distinction. In the
CATEGOEEMATIC AND SYNCATEGOREMATIC. 167
synthesis of words, called Speech, there are words indicating
subject and predicate and relations of these. The subject
and predicate are, or may be, significant out of relation to
each other, as indicating each a quality, qualities, or a class.
The words of relation, such as conjunction, preposition, are
properly significant in the synthesis or combination called the
sentence. The logical copula is, is properly syncategore-
matic; it is only consignificant, that is, it expresses a relation
between concepts supplied. The relation of course indicated
by each of the consignificant words may be made an object of
abstract contemplation, but still it subsists only as a relation
in some sentence or other, not by itself as an independent or
non-sentential object of thought.
(a) A categorematic word or term has a definite and certain significa-
tion. Thus man signifies all men, whiteness all whitenesses. It has a
definite suppositio, or representative function. A syncategorematic
word has no definite and certain signification, and does not signify any-
thing distinct from what is signified by the predicate. As in arithmetic
the cipher standing by itself signifies nothing, but added to another
figure makes it significant, so the syncategorematic word, properly
speaking, is not significant, but consignificant as added to another term.
It may even give the predicate determinateness, and enable it to stand
definitely for another or others. Such words are all, none, some, whole,
except, only, &c. All, per se, has no fixed signification, but as joined
to man makes the term stand for all men. So also are conjunctions
and prepositions. Significant is here employed, according to the usage
of Boethius, as meaning not merely something determinate, for all, none,
&c, are so, taken per se, but as making significant or able to stand in
the place of something in a certain manner — i.e., giving a term suppo-
sitio, or the function of representation. — (Sum. t. Log., i. c. 4, p. 8.)
Significant and consignificant here are very much equivalent to ab-
stract and applied. The syncategorematic word has a meaning of its
own, as expressing only an abstract relation, conjunctive or preposi-
tional, or adverbial or quantitative ; but as not applied or realised in a
definite subject or predicate, it has not yet a representative force.
§ 207. Term has two meanings — (1) as distinguished
from speech (pratio), it denotes everything incomplex. (2)
Strictly it denotes that which, taken significatively, can be the
subject or predicate of a proposition. In this sense no prepo-
sition, conjunction, adverb, or interjection is a term. These are
syncategorematic. These words taken simply or materially
can of course be placed as subject or predicate of a proposition.
We may say " he reads " is a verb, or " all " is an adjective,
" if" is a conjunction, "from " is a preposition. But thus taken
168 INSTITUTES OF LOGIC.
they are not significant, in the sense of standing for or defi-
nitely representing anything in a fixed mode. — (Cf. Occam,
Log., i. 1, f. 2, 2 B.)
(a)"Opos est nota, qua unum quid et simplex mente repraesentatur. —
(Goclenius, sub voce.)
(b) I call that a term into which a proposition is resolved, as the
predicate and that of which it is predicated, whether to be or not to be
is added or separated. — (An. Prior., I. i. )
(c) Occam makes the term " the proximate part of the proposition "
(pars propinqua propositions) . — (Sum. t. Log., i. c. i.)
(d) Speech, according to Boethius, is threefold — viz. , written, spoken,
conceived, the latter having being in the intellect alone. So term is
written, spoken, conceived (conceptus). The concept or mental term
is the intention or affection (passio) of the mind, naturally signifying or
consignifying something, produced to be part of a mental proposition.
Concepts and propositions composed of them are those mental words
(mentalia verba) which remain alone in the mind, and which, as Augus-
tine says, are of no language, and cannot be externally set forth, al-
though articulate sounds (voces) as signs subordinate to them may be
outwardly pronounced. Articulate sounds, however, are not properly
significant of concepts themselves primarily and properly, but only
secondarily of the same things, which are signified by the concepts of
the mind. As the concept or affection of the mind naturally, from the
nature of the thing, signifies what it does, and as the term spoken or
written is according to voluntary institution, the term may change its
significate at pleasure, but the concept cannot. In other words, the
concept would cease to be the concept it is, or to be significant of that
of which it was formerly the concept.
§ 208. The term may be a single word, or a plurality of
words. The essential point is the preservation of the unity
of the concept, as distinct from the unity of any other concept.
That word, or series of words, is properly a term which is
significant of the total concept of which the predicate is said,
or which is predicated of the subject. Thus we may equally
well designate the concept of triangle by the single term
triangle, or by a figure bounded by three straight lines. We
may equally indicate the same concept by Centaur, or by an
animal with the upper parts human, the lower equine. The
metropolis of Britain and London, the first man and Adam,
signify respectively one and the same object. The con-
cept number is that of continuous addition of unity to unity.
The concept binary is that of unity coalescing with another
unity in one and the same number.1 These expressions are
1 Wolf, Logica, § 34.
CLASSES OF TERMS. 169
all equally limitative and distinctive. The single word has
the advantages of brevity, convenience, and force.
§ 209. Terms have been divided into various classes, chiefly
the following : —
(1.) Univocal, Equivocal, Analogous.
(2.) Singular or Individual, and General or Universal;
corresponding in a measure to Proper and Common Nouns.
(3.) Of the First and Second Imposition and First and
Second Intention.
(4.) Concrete and Abstract.
(5.) Connotative and Non-Connotative or Absolute.
(6.) Distributive or Sejunctive and Collective.
(7.) Definite and Indefinite, or Infinite, Privative and
Negative.
(8.) Categorical and Transcendental.
(9.) Relative and Correlative.
(10.) Contrary and Contradictory.
(11.) Of Possession and Privation.
§ 210. This division is founded on no clear principle, pro-
ceeds, indeed, on the confusion of several points of view.
Some terms, such as the Abstract and Concrete, are so from
the nature of the concept signified by them. The considera-
tion of the distinction thus belongs to the nature of the
concept. Other of the distinctions, such as the Univocal
and Equivocal, may depend on the accident of the naming of
concepts, and are mainly of grammatical import. At the same
time, as the term is so often used as equivalent to the con-
cept, and its distinctions treated as conceptual distinctions,
it is necessary briefly to indicate the meanings of some of
the names applied historically in the Classification of Terms.
§ 211. The distinction of terms as Univocal or Equivocal
is obviously a grammatical one. A word or term may be
equivocal, as Occam has remarked, but not a concept.1 The
univocal term or sign is that which is applied and sub-
ordinated to one concept. It may thus be predicated in one
and the same sense of the many objects under the concept.
The equivocal is that which, signifying many, or having
more than one definite meaning, is applied but not subordi-
nated or restricted to one concept. In this case there is not
one common predicate, but as many predicates as there are
1 Cf. Occam, Sum. t. Log., i. 14; and Wallis, Logica, i. 3.
170 INSTITUTES OF LOGIC.
various meanings. Terms may be equivocal, through acci-
dent, or by design.1 As examples we have light; crab (crab-
fish, crab-apple, crab-tree, constellation).
An Analogous term indicates an identity of relation as
opposed generally to an identity of feature or attribute — e.g.,
the foot of a table and the foot oj a mountain, the foot of a tree,
the foot of a man. The objects in themselves are not resem-
bling, but they fulfil similar relations. These terms are only
indirectly uni vocal. Besides Analogy strictly taken, Likeness
in the things gives rise to similarity in terms. We speak of
a blade of grass and the blade of a sword, though these have
different functions. We say of a portrait, This is the Queen,
though portrait and Queen are only resemblances. Terms of
Simile and Metaphor come under Analogy and Likeness.
§ 212. The Singular or Individual term is opposed to the
general or universal. The singular is logically that which,
indicating an attribute or attributes, is not predicable of
more than one object — as Julius Casar, Edinburgh, Glas-
gow. It may be taken as indicating the individual conceived
as distinct from others, or from what is thought to coexist in
a given moment of time or in another portion of space. The
universal term is that which is predicable of many, as man,
city, mountain. The Singular or Individual should not be
confounded with the Particular, as is generally done. The
particular refers to quantity, and is some of all. But it is
not identical with the one or individual — in fact, is opposed
to it as signifying an indefinite plurality. Some men and
Julius Caesar are by no means convertible. As already
explained, the universality of the concept, and therefore of
the term, is a potential universality. This lies in its being
predicable of several or many. Concept and term alike, as each
act and name, one in number, and not many, are singular.
(a) Logically the terms individuum, supposition, singidare, are con-
vertible ; though theologically suppositum means substantia and accidens
contains individuum and singidare.
Individual {individuum) has three meanings : —
(1.) That which is one in number, and not many. In this sense every
universal is individual.
(2.) That which exists without the mind, which is one and not many,
and is not the sign of anything, as Socrates, Plato.
(3.) The sign proper to one, called discrete term. As Porphyry says,
1 Cf. Occam, Sum. t. Log., i. 14, and Wallis, Logica, i. 3.
FIRST AND SECOND INTENTION. 171
the individual is that which is predicated of one only. In other words,
it is not predicated of anything which can stand for many in the
same proposition.
A sign of this sort is (a) Proper Name, as Virgil, London, (b) De-
monstrative Pronoun — this is the man, meaning Socrates, (c) Demon-
strative Pronoun taken along with a common term, as this animal, that
stone. The supposita per se of any common term are demonstrative
pronouns taken along with the same term. — (Occam, Sum. t. Log., i.
19.)
To these may be added designation by Emphasis, through custom
or restricting circumstances, as when an Englishman or Scotsman
speaks of the Queen, he means one person, the reigning monarch, Vic-
toria. The" use of the City by a Londoner, of bird, fish, &c, by sports-
men, implies either an individual or specific reference. — (Cf. Wallis,
Logica, i. 2.)
(b) Occam gives us the true theory of the singular and universal.
The singular is that which is one and not many. In this sense, every
universal as a quality of mind predicable of many is truly and really
singular, just as a word, though common by institution, is really
singular and one in number.
But if singidar mean that which is one and not many, and is the
sign of any singular, no universal is singular, for it is the sign of many.
There is no universal which is not one in number, and is only uni-
versal by signification, as Avicenna teaches. One form in the intellect
is related to a multitude and in this respect is universal, for it is itself
the intention of the mind, whose operation is not varied wherever you
look. In respect of individuals this form is universal ; in respect of
the mind, one of whose forms it is, it is singular. A universal, there-
fore, is one singular intention of the mind itself naturally fitted to be
predicated of many not for itself, but for the things themselves. In
this respect, as predicable of many, it is universal ; as a form really
existing in the mind it is singular. — (Occam, Sum. t. Log., i. 14.)
(c) The doctrine of Scotus was that the universal is in some mode
without the mind, and in individuals, not indeed really distinct from
them, but only formally. Human nature is in Socrates, which is con-
tracted to Socrates, by one individual difference, which is, not really but
formally, distinct from that nature. Hence there are not two things ;
the one, however, is formally not the other. This opinion Occam rejects.
(d) The universal of Occam is in the mind, has no existence out of
the mind, and is a natural sign of things. The term again is a conven-
tional or voluntary imposition of a sign on the universal ; and has no
import apart from this. To call such a doctrine Nominalism is a mis-
nomer. It is a conceptualism, pure and simple, and it shows how
closely the two theories approximated.
§ 213. The distinction of terms of the First and Second
Intention has been already explained in connection with the
definition of Logic.1 A word further is required to show
their relation to terms of the First and Second Imposition.
1 See above, pp. 34, 69.
172 INSTITUTES OF LOGIC.
Impositio and Intentio, as applied to terms, indicate an im-
portant scholastic distinction. It is found in Burleigh and
Armandus (see Prantl, iii. 584, 629) ; but the distinction of
names of the First and Second Intention can be traced at least
to Avicenna. Occam has put the distinction precisely. Some
names signify things beyond the mind ; others the concepts of
the mind ; others significant words themselves ; and there is
the ancient distinction of names of the First and Second Im-
position. Names of the second imposition are those imposed
to signify names themselves, such as noun, verb, pronoun, con-
junction, &c. ; in fact, the different parts of speech, as in
grammar, though syncategorematic words are sometimes
excluded. Names of the first imposition are divided into
names of the first, and names of the second, intention. Those
of the first intention signify real things ; those of the second
concepts of the mind, as genus, species, universal, predicable.
These indicate intentions of the mind, which are natural signs,
or signs voluntarily instituted to indicate these. Second
intentions thus mark what is predicable of the names of
things regarded simply, or apart from their application to the
things signified, in a word, the classes of predicables,
and the abstract relations among the predicable classes or
concepts.1
(a) This distinction may, indeed, at least in matter, be fairly enough
carried back to Aristotle, in his discrimination of First and Second
Substances. First substance is that which is not said of a subject,
and is not found in a subject, as a Alan, a Horse. Second substance is
the species or genus of first substances. A man is in the species man;
man is in the genus animal. Hence man and animal are second sub-
stances.— (Cat. v., §§ 1, 2.) This corresponds pretty closely to First
and Second Intention, and certainly may have suggested it.
§ 214. The proper distinction of Concrete and Abstract is
that the latter may be taken as standing for any quality,
accident or form, inherent in the subject, as whiteness, &c. ;
while the former indicates the subject or object of inherence
as well as the quality, as white. At the same time, logically
it seems impossible to conceive the quality as a pure abstract ;
it must be realised and thought in an individual subject.
The difference is mainly a grammatical one.
Another application of these terms, already noticed, is that
1 Occam, Sum. Logical, i. 12.
ABSOLUTE AND CONNOTATTVE. 173
the abstract is regarded as that which is higher or superior in
the order of generalisation, as animal in regard to man, or
living in regard to animal ; whereas the concrete represents
the lower concept. The abstract is thus ultimately the
highest in the scale of general ideas, the concrete the lowest,
the species or even the individual.
(a) The scholastic usage in regard to concrete and abstract was
much wider than the modern. Three points at least may be noted : —
(1.) The abstract term was used to stand for any accident or form
whatever really inherent in the subject; the concrete for the subject of
the same accident or form — as whiteness, tvhite — conversely, fire, on
fire.
(2. ) The concrete was used to stand for a part, and the abstract for
the whole; or conversely — as life, lit my, — man is living; he is not
life.
(3.) Concrete and abstract sometimes stand for distinct objects, of
which neither is the subject nor the part of the other, as sign and signi-
ficate. — (Occam, Log., i. 5.)
(b) Abstract and Concrete in Hegel have reference to what is called
the development of the concept. The concept (Begrif) is a completed
idea, which in its unity contains difference. The concept is a sub-
stance which contains all its being or properties in itself, and develops
this fully. It has thus a number of moments ; these grasped fully
constitute truth. Each moment by itself is false. When the concept
has arrived at the full development of its moments, it is concrete.
Each moment of the unity taken by itself is abstract. It may be re-
marked on this, that as at any moment of the development, the concept
is not completed, there can be no truth except in the Absolute Idea,
and as then all differences are abolished or identified — even the finite
Ego itself, there is no truth in time at all.
§ 215. An Absolute Term is one which is significant of
some one concept or object without anything conjoined to it ;
or it is that which does not signify something primarily and
also something secondarily, but whatever is signified by it is
equally primarily signified, as Animal signifies Horse, Ass,
Man.
A Connotative Term is that which signifies something
primarily and something secondarily. That which it pri-
marily signifies is usually an attribute, and secondarily the
subject in which the attribute inheres.1
(a) In the definition of a connotative name, there is something straight
and something oblique. Thus, white means something possessing white-
1 Cf . Occam, Log. , i. 10 ; and Goclenius, sub voce.
176 INSTITUTES OF LOGIC.
Kant borrowed the terms, and gave each a different and
both a new signification, though there is a hint of his meaning
of transcendental in ^Egidius Romanus, quoted above. Trans-
cendent with Kant means what is entirely beyond experience,
as given neither in a posteriori datum nor a priori form, and
thus beyond the categories of thought, beyond knowledge in
fact. Transcendental means with him the a priori or neces-
sary conditions of knowledge, which as such transcend the
contingent or adventitious data of experience, yet constitute
the knowledge we have.1
§ 220. A Relative Term is said to be what it is by reference
to something else, or some other term. Thus, double is double
of half.2 Father and child, debtor and creditor, are ordinary
relatives, and make up a complete thought. The term from
which we start in apprehending a relation may be called the
Relative, and that to which it is related the Correlative or
Correlate. Subject is the relative ; object the correlate. But
each term may in turn be relative or correlate — thus, Father
and Son, relative and correlate ; or Son and Father, relative
and correlate.
The true conception of Relation implies (1) Two terms,
and (2) these apprehended in the way of constituting a
whole, of which they are the parts, and which cannot be con-
ceived as a whole without each of the terms. Relatives are
the terms of a sundered totality, which is unthinkable apart
from the union of the terms. Thus King and Subject, — Half
and Double, — Height and Depth. These terms integrate or
make up a complete thought.
§ 221. But relatives are not properly mutually convertible.
For the relation regarded from the one side is not identical
with, nay, is the converse of the relation viewed from the
other. The relation, for example, of Creditor to Debtor is
precisely the reverse of the relation of Debtor to Creditor.
You owe me, — I owe you. Owing to me is not possible with-
out obligation by you. The two terms are necessary, but
the relation, respectively viewed, is by no means the same.
The debtor side may here be regarded as the correlation.
For the positive ground of it is, say, money lent, first of all,
as a matter of fact. Thus the relative is constituted as against
1 Kritik, passim. — Cf. Hamilton, Reid's Works, p. 762.
2 Cf. Aristotle, Cat. x.
RELATIVE TERMS. 177
the correlative, in this case the respondent or defendant. So
the relation of Father to Son, is not convertible with the
relation of Son to Father; the one is the converse of the
other. So with Ruler and Ruled, Master and Vassal. The
relation of the ruler is that of authority, the correlation of
the subject is that of subjection to authority. The master
orders, the vassal or servant obeys.
§ 222. In simple relation the essential thing is a term,
rather concept, positive and determinate, to begin with. Yet
when explicated, or in determining it, this is found to imply
another term, or concept, ere we can put meaning into it.
Thus Uncle is meaningless, unless as we know he is uncle
of Nepheio or Niece ; and so Nephew or Niece is meaningless,
unless as we know Uncle. But Uncle is first of all a deter-
minate concept implying all the attributes of man, and only
on the ground of these is the relation, wholly accidental, of
man as uncle to nephew or niece realised. The relation is
possible, through a previous concept or reality ; the relation
in no way constitutes this, is, in fact, dependent on it, and
this underlying positive or object would remain, whether the
accidental relation were constituted or not. So that relation
between terms or concepts never constitutes the reality of the
term or concept ; but is possible only through a definitely
apprehended or comprehended object. As has been said,
"relation is the accident of a thing, not considered abso-
lutely, but as compared with some other thing. Its essence
depends on comparison." x In fact, relation, ultimately ana-
lysed, means one of the accidents or properties of an object or
concept. And the whole idea of reducing reality to relation
is as suicidal in expression as it is untrue in point of fact.
" There is a great difference," says Aristotle, " between a
thing being relative, and a thing being that which it is,
only because it is said of another thing." Head is head of
some one, but its being does not consist only in this relation,
as that of father in being father to son.2 Even in regard to
simple relatives, we cannot know anything to be relative, until
we know that to which it is relative, and in what respect it
is so relative. If we know a thing, as Aristotle remarks,
to be a double, we must know that of which it is the double. If
we know ten to be the half of another number, we must
1 Wallis, Log. i. 10. 2 Cat. vii., § 26.
M
174 INSTITUTES OF LOGIC.
ness. All concrete names of the first order are connotative, as just,
white, animated. So are all relative names, as similar, which is defined
as that having a quality such as another has, — those belonging to the
genus quantity, as figure, curvity, &c.
Intellect is connotative, inasmuch as it means power and act, so
one, good, true, potency, act, &c. — (Sum. t. Log., i. x. p. 21.)
(6) The concrete term is divided into absolute and connotative, or,
which is almost the same thing, into substantive and adjective. Sub-
stantive indicates that which subsists by itself, as man, stone, colour,
beauty. Adjective is that which signifies a thing as being the accessory
of an other, as human, coloured, beautiful. All abstract terms are sub-
stantives ; although they sometimes signify things which can exist only
in a subject, they yet express them as self-subsisting, as prudence, science,
love. These can be only in a subject, yet in view of the mind they
are self-subsisting. They are substantive by the mode of signification.
— (Aquinas, Logica Minor, Pars I. q. 1.)
(c) This original distinction of Absolute and Connotative Terms is
of considerable importance ; and it is unfortunate that in some modern
works on Logic the proper use of Connotation has been perverted to
designate the comprehension or attributes of a concept. For this we
had already a perfectly unexceptional term, and connotation as thus
applied is really misleading.
§ 216. The scholastic distinction of Concrete and Abstract
terms does not seem well marked off from absolute and con-
notative. It is clear enough that the concrete represents
something different from, or more than the abstract. Thus
just and justice are not convertible. While we can say the
just is virtuous, we cannot put justice as the subject of the
same proposition.1 Yet just as a concept, in its comprehen-
sion, contains no more attributes than justice. It differs from
the latter in its connotation as signifying or consignifying
a subject of inherence, or possessor of the quality justice.
It is, in fact, the quality of justice conceived as inherent or
possessed, that is, as realised in extension. Thus Occam was
right in saying that in one respect concrete and abstract
names are synonymous. Nothing is signified by man more
or other than is signified by humanity, or by Deity than by
the term God?
§ 217. A Distributive or Sejunctive Term is a term indi-
cating attributes common to many individuals, and belonging
to each of the class, — as life, sensation, motion, to horse, cow,
mule, — species of animal. A Collective Term indicates the
repetition of the same or similar quality in a sum of individ-
1 Cf. Occam, Log., i. 5. 2 Occam, Log,, i. c. 7.
CATEGORICAL TERM. 175
uals, as senate, regiment, army, — that is, the quality which
makes each a member of the body. These are made up of
units repeated, and gathered into one whole. The collective
term applies only to the individuals in their totality ; the
distributive is applicable to each individual under it. In the
latter case we naturally say, Each is or Every one is, All are,
— -in the former, The whole is. We predicate only of the
totality, as a singular, or of all considered as one. We can
say of a senate or army what we cannot say of each man in it.
Man is affirmatively predicable of Socrates, but not mankind.
§ 218. Logically a noun is called ddpicrrov, or infinite, better
indeterminate or indefinite, by which all things can be named
except those named by the finite — that is, determinate or defi-
nite noun, to which it is relative, as Homo, Non-homo ; 1 Albus,
Non-albus. This distinction is due to Aristotle, but he de-
clines to call the indefinite a noun — " Not-man is not a noun,
for there is no name which we can apply to it ; it is neither
an affirmation nor a negation ; it is that which I would call
an indeterminate noun, because it agrees equally to all, to
being and to non-being." 2 Not-man, in other words, has no
real determination ; it designates all which is not the thing
or concept spoken of, but it determines nothing.3
Boethius translated aopicrrov by infinitum; not a suitable
word. Hamilton gives indesignate. The true place of the
indeterminate term in Logic will be considered in the sequel.
§ 219. A Categorical Term is any term comprised in the
Ten Categories of Aristotle. A Transcendent or Transcen-
dental Term is one that designates a notion above or beyond
the Categories. The Pseudo-Thomas gives six transcendentia
— viz., Ens, Res, Aliquid, Unum, Bonum, Verum. Res and
Aliquid are new. The others are given by Aquinas.4 iEgidius
Romanus holds these six to be in the knowledge common to
all things, and as belonging to the first conceptions of the
intellect.5
With the schoolmen the transcendental term was held not
only to transcend, but to include the categorical term or terms.6
1 Cf. Goclenius, sub voce. ,
2 De Int. , ii. 4. Waitz omits the last two clauses.
3 Cf. St Hilaire, in loco.
4 Opuscula, 42 f, iv. B. : see Prantl, iii. xix. § 274.
5 See in Prantl, iii. xix. § 355, p. 257.
6 See Aquinas, Logica Minor, pars i. q. 1.
}
178 INSTITUTES OF LOGIC.
know that it is twenty of which it is the half, and so on.
If we know a thing as greater we must know that which
is the less of the two. But this applies in a very limited
way to the objects of knowledge. We may know an object,
whose reality as an object does not in the least consist in the
circumstance of its being a mere relation to another object,
or depend on a relation of reciprocity in reality or cogni-
tion. In fact, mere being in the relation is not possible in
existence, it is possible only as it is grounded by a definite or
positive something which founds the relation. And the true
place of relation alike in knowledge and being is the secondary
one of property or attribute or reference to some other thing.
All or even the ultimate relations of a thing we do not and
can never know, its relations to all actual, far less possible,
objects of experience. We may have a perfectly definite
knowledge of an object without any pretension of this sort.
The primary metaphysical relations are the necessary modes
in which objects exist for us and are known by us. But
these even do not constitute the objects ; rather the objec-
tive, whatever that may be, constitutes them, is their real
ground, and manifests itself through them. To say gener-
ally, as is done, that every object of experience is a relation,
or constituted by a relation, is to assume the possibility of a
relation, while there are not two terms or objects to be related.
A relation in an object is either between the parts of the
object itself, or between it and another object. In either case,
the relation is grounded in something beyond itself, whether
this be a point or object directly cognisable by us, or whether
we have to pierce backwards to something which is only
known to us in the manifestation of the terms of the relation.
Mere relation, as an object of experience or knowledge of ex-
perience, is a pure and simple contradiction. Relation is only
possible through things related ; and its reality is founded on
them.
(a) Founding on Aristotle, relatives are said to be twofold, — some
are secundum did, others secundum esse. The essence of the former
does not lie in mere relation ; the essence of the latter does so lie —
that is, there is nothing in them besides reference to another in some
mode. E.g., scientia et scibile, — cognition and object, — are relations
secundum did, for cognition is a real quality or act ; — so perception
and percept, so quantity and quality. But other relations such as
master and servant, father and son, husband and wife, are secundum
CONTRARY AND CONTRADICTORY TERMS. 179
esse ; for the essence of each relation is in the mere relation of master
to servant, &c. , and is nothing apart from this.
Again, there are four things to be distinguished in Relatives — viz. ,
Subject, Ground. Term, Relation. Subject is always different from
Term in real relatives — e.g. , Virgil is the axithor of the jEneid. Here
we have (a) subject in Virgil, ground in production, term in Mneid,
relation in authorship. — (Cf. Duncan, Inst. Log. L. i. c. viii.)
In the distinction of relatives secundum did and secundum esse, there
seems to be a confusion between the fact of the existing relation, and
the possibility of the subject of it entering into other similar relations
with different terms. Every relation qud relation is that which the
subject has or shows in a definite aspect. The relation of knowledge
and the relation of service, even of double or half, are equally the definite
or specific relations of two things, and subsist only through these ;
though the subjects of them are not necessarily either identical with
the relation or exhausted by it. Mere or pure relation as identical only
with itself is an abstraction.
(b) In the case where an antecedent is supposed, and where what
follows is limited or depends upon it for its place and import, we have
more properly relation than correlation. This is chiefly the case in
what are known as grammatical relatives — e.g., The house tohich stands
there. Here house is antecedent, which is its relative. But which
has no force apart from the antecedent. These are not properly cor-
relatives ; for they are of unequal import and not convertible, so as
still to preserve the knowledge of the relation. The latter supposes
the former, but they cannot change places as in proper correlation. —
(Cf . Note by Latham on Correlation, Johnson's Diet. )
§ 223. Contrary Terms indicate concepts or qualities that
are most opposed in the same class, or general conception —
as good and evil, just and unjust, wise and foolish.1 But these
are not connected or opposed as relatives proper. Good is
not the good of evil, as double is the double of half. And con-
traries do not make up the total thought as simple relatives
do. We can think what is good, a good, say, truthful-
ness or justice, without thinking untruthfulness or injustice
as a part of it, as a necessary constituent of our complete
thought of it, while we cannot think a double without think-
ing it the double of the half. When we think justice we do
think injustice, but not as a part of justice. When we think
the double, we do think the half as an essential part of the
double. This is the only analogue of the Hegelian other; every-
thing is also the other of itself. But it applies only to a few
limited relations, chiefly verbal, and in regard to these it is
but a poor and inaccurate expression of the fact. In regard
1 See Aristotle, Cat. vi.; Met. v. 10.
180 INSTITUTES OF LOGIC.
to the whole wide sphere of thought and experience, espe-
cially contrary opposition, it has no application, and is the
merest illusion of verbalism.
§ 224. Contradictories as terms relate only to concepts, and
they are usually marked in language by not, or its equivalent.
The essential feature of contradictory terms is that they can-
not be combined in the same indivisible act of thought,
they are mutually exclusive, and if the one is thought, the
other is sublated. Thus man and not-man, mortal and im-
mortal, being and non-being, are contradictory terms. These
cannot be joined in one thought of an object. In contra-
dictories a first or positive concept or cognition is always
presupposed ; and the contradictory may be of two kinds.
(1.) It may be the mere indeterminate concept of negation,
indicated by not or its equivalent, which only precisely sig-
nifies the negation of the positive and nothing more, yield-
ing no determinate or significative concept, as one and none,
being and not-being.
(2.) The contradiction may be a positive, like that which it
contradicts. Mortal may be contradicted by immortal, — life
by death — existence at a given time by existence at another time
— the equality of the three angles of a triangle to two right
angles, by their (alleged) inequality — less or more.
(a) In the former kind there is nothing positive. When we say non-ens
est ens, — this is true only as far as non-ens represents the term of a
proposition, but not as taken significatively. One opposite even may
be predicated of another simply or materially, but not significa-
tively— i.e., as standing for a definite object — Non-dictio est dictio,
Non-pars est pars, Non-vox est vox. — (Cf. Occam, Log., i. 36.)
(b) With Aristotle the term to avriKti/uifva does not necessarily
imply contradiction. It designates the two corresponding terms of a
definite relation. It may be translated by Correlatives. Of these
Aristotle makes four classes : —
(1.) Those of Simple Relation (to irp6s ri), as double and half. These
have only a reciprocal reality. Each is dependent on the other in
thought and in fact. This is not the case in any of the three classes
following —
(2.) Contraries (to. ivavTia), as good and evil. These cannot be in the
same subject together in the same respect, but may be in the same
subject in succession.
(3.) Possession and Privation (e|ts kol\ (rrepwis), as Sight and Blind-
ness.
(4.) Contradictories (KaraQcuris Kal air6(pa<ns), as yes and no. These
cannot both be in the same subject at the same time and in the same
CONTRARY AND CONTRADICTORY TERMS. 181
respect. Aristotle, however, holds that Contradictories do not pro-
perly belong to single terms or Concepts (/fori uriStfiiav (tv^ttKok^v
KfySfifva), but are made by affirmation and negation (»caTa<pa<rts kcl\
air6<pa<7is). — (Cat. viii.)
§ 225. Terms of Possession and Privation, or Positive and
Privative terms, are those which on the one hand signify
positively some quality, and on the other signify negatively
the absence of this quality, and yet indicate something other
or opposite in its place, — as sight and blindness. These
terms apply to defects in a given type of objects, and sup-
pose a knowledge of this type oi- concept. Privation is thus
absence of a quality from a subject which is capable of
having it, or ought to be in it at a given time or in given
circumstances, as blindness, deafness, &c, in a person, — or as
darkness from noon, death in man or animal. Truth and
error, right and wrong, honesty and dishonesty, may be taken
as fair illustrations. The privation- may be the result of cir-
cumstances or of a free act on the part of the conscious
subject. Aristotle adds that possession and privation do not
admit of a middle ; and that they can succeed each other
only in a determinate order. Blindness as a privative follows
seeing as a possessive or positive ; and not vice versa.1
1 On this and Opposition generally, see Aristotle, Cat. vii. viii. x. Cf. Met.
v. 22, ix. 1.
182
CHAPTER XVI.
concepts: their kinds.
§ 226. Concepts may be best divided in respect of four
grounds. They may be viewed (1) as to what is primary
and essential in their own nature, (2) in relation to their
objects, (3) to each other, (4) to the subject or thinker.
Under the first head, we shall have the concept as Com-
prehensive or qualitative ; under the second as Extensive, or
quantitative ; under the third as involving various species
of concepts, determined in Comprehension and Extension
respectively ; under the fourth we shall have the quality of
the concept as Clear or Obscure, Distinct or Indistinct,1 &c.
§ 227. The primary and essential element of a concept is
that it is, or contains in it, an attribute or sum of attributes.
This is the ground of the concept of the class : objects are
classed as they possess resembling or corresponding attributes ;
and the real ground of classification is attribution. In other
words, the comprehension of a concept is first ; the extension
follows, and is also limited by the comprehension or attributes
contained in the concept. Concepts are, therefore, first of all
regarded as Comprehensive, or containing attributes.
§ 228. Essence is really the common nature, attribute, or
attributes, in a concept or universal — in a word, its compre-
hension. Whether this is properly constituted, according to
the truth of things, is not to be determined wholly by logical
laws — in fact, only very partially. But still we are able to
say of any given object, regarded as having or lacking this
1 Hamilton, Logic, L. viii., footnote p. 140, suggests a division analogous to
this ; but as will appear in the sequel that now given shows very important
differences.
COMPKEHENSION AND EXTENSION. 183
nature, that it belongs essentially or not to the class. And
there are concepts whose nature or essence is determinable,
necessarily, or not wholly by the mere data of experience, as
causality, substance, &c.
If we take, for example, the concept root, we find that the
attributes or marks which make it up are chiefly tendency,
from origin, towards the centre of the earth, with body, and fibres
which absorb moisture. These are the constituent marks, and
may be said to form the essence of the concept. They are
gathered from observation and generalisation. Innumerable
questions are suggested by this essence, and we can regard it
only as relatively adequate. But it will help us to dis-
tinguish spurious from true roots, as what is called the
" creeping root " of Mint, which is not a root, but a subter-
ranean stem.1
§ 229. While comprehension refers to the attributes, this
again implies objects in which the common attributes are
embodied. These are regarded as classes, or concepts of
classes, or objects of thought. This is the extension of the
concept, which refers to the objects contained under the
concept, to which it is applicable, or of which it is predicable.
Thus Man has sub-classes under it, and is predicable of
European, African, Asiatic, &c. The concept root contains
under it, and is predicable of, fibrous, conical, abrupt, lobed,
granulated, fasciculate roots. These sub-classes are usually
plural, and hence Extension is quantitative. Comprehension
is also ordinarily regarded as quantitative, seeing it con-
tains, or may contain, a plurality of attributes ; but as will be
shown, this is not accurate. Comprehension certainly is not
quantitative in the sense in which Extension is.
§ 230. A whole is that which contains parts. This applies
to Physical Whole as that which is made up of several ele-
ments, each, it may be, different from the other, as an
individual tree or house. This approaches the comprehensive
whole, at least, as in the individual. The logical whole is
properly that which is common to many. The universal is
of two kinds, according to Causality, and according to Predi-
cation. Deity, as the sole cause, is the most universal ; and
in this sense singulars are separable from the universal. But
the universal of predication means merely that which is pre-
1 Hoblyn's Botany, p. 9.
184 INSTITUTES OF LOGIC.
dicable of, and indifferently signifies and stands for, many.
In this sense it is opposed to the singular or concrete.1
The old logical distinction of predication as diet de, and
esse in, really proceeded on the difference of Extension and
Comprehension. In the former case the concept, as universal,
was predicated of all the particulars subject to it. These
were called Subjecta Predicationis, — as animal, plant, under
organised. In the latter case, the concept was said to be in
the subject, or to inhere in the subject, as whiteness in snow,
or knowledge in man. The subject was now Subjectum
Inhaisionis.
§ 231. The Comprehension of a concept is great or small
in proportion to the number of attributes or qualities which
it contains in it, or which constitute it. The Extension of
a notion is great or small in proportion to the number of
objects or classes of objects which it contains under it. When
a concept contains but one attribute, or in as far as more
than one attribute is not distinguishable in it, it is Simple.
When it contains more than one, it is Complex or Compound.
When the Extension of a concept is so small that it con-
tains under it no species or only one object, it is called
individual?
§ 232. In a duly subordinated series of concepts, within a
common sphere of relationship, the law holds good that as the
Extension increases the Comprehension decreases : and as the
Comprehension increases the Extension decreases. The maxi-
mum of the one is the minimum of the other. Thus to take
one individual — say Homer — the related and rising line of
concepts will be poet, Greek, man. Of these the individual
notion is the most comprehensive, comprising as it does all
the common and distinctive attributes. Poet is more exten-
sive and less comprehensive than Homer. Certain attributes
have been thrown out, and only such retained as are common
to others also poets. Greek is still more extensive and less
comprehensive. Man again has greater extension than
Greek and less comprehension.
The lowest, most concrete, or comprehensive concept, the
individual — say Homer — contains all the attributes of the
higher concepts, — as poet, Greek, man. It is the condensa-
tion or concretion of the whole. It contains even more —
1 Occam, Log., i. 35. 2 Hamilton, Logic, L. viii.
DETERMINATION AND GENERALISATION. 185
that is, all the individual peculiarities. And when we throw
out his blindness, his being a native of Chios, &c., and think
of him as poet, we do not say necessarily whether he was
Greek or not ; but as poet is part of the class man, which,
in this instance, is the general class within which we are
relating concepts, man is presupposed. All the same we
can think of the essential features of poet, which are more
than those of man, in contradistinction to the common fea-
tures of man, and so restrict our view to a portion of the
class. This is but an application of the principle involved
in the old logical brocard : — Abstrahentis non est mendacium.
As Wallis puts it : — He who considers sugar' as sweet does
not necessarily think it as white, neither does he deny
it to be so.1
§ 233. The processes by which we increase the Comprehen-
sion and diminish the Extension, and conversely, have been
named Determination or Concretion, and Generalisation or
Abstraction. If we start from the highest point of Extension,
— say, being — we may add on attributes, and thus determine
or restrict the sphere of the concept. Being material, being
spiritual, imply a determination or restriction of the concept.
Being material may be again determined by organic, inorganic ;
organic by animal, plant, &c. In this case we add on deter-
mining attributes, in virtue of which the application or exten-
sion of the notion is limited, while its comprehension or sum
of attribution is increased. The logical part of this process
is ultimately regulated by dichotomy, and that by the law
of Non-Contradiction. We descend through the contrast of
opposites, through the is and the is-not ; the latter or negative
sphere is filled up only by intuition and experience. We can
get no positive attribute by the mere dichotomy, or by pure
thought ; but working under the abstract law or formula, con-
sciously or unconsciously, we fill up the negative sphere
through experience, or the analysis of the contents of notions
gained from experience. Thus, if we take material, we can
divide it into what is organic, and thus by implication into
what is inorganic, or what is excluded as the negative.
As yet we do not know what inorganic is, unless as the nega-
tion of the attribute organic ; and it is for experience to tell
us what things belong either to the one class or the other.
1 Wallis, Logica, i. 22.
186 INSTITUTES OF LOGIC.
But the exclusion keeps our thinking distinct, and affords a
form of classification as our experience grows.
(a) Kant's so-called law of logical affinity or continuity [Kritik, p.
510, ed. Rosenkranz) has been shown to be groundless. It imports
that between all co-ordinate species, other or others intermediate are
conceivable. This is unfounded — (1) in respect of mathematical
species. All angles are either acute or right or obtuse ; there is no
intermediate species, though we may have varieties among the species
through accidental differences of length of line, &c. (2) When the co-
ordinate species are distinguished by contradictory attributes, as when
animal is divided into vertebrate, and invertebrate, that is, with and
without a spinal marrow, there is no intermediate species possibly con-
ceivable.— (Cf. Bachmann, Logik, § 61; Hamilton, Logic, L. xi.)
§ 234. The counter-process of Generalisation is thus obvi-
ous. It is simply that process which is first applied to indi-
viduals, turned upon concepts themselves. Starting from
the individual of experience, already subsumed under a
concept, we abstract from one or other of its attributes ; we
thus rise to greater generality ; and proceeding further in
this way we at every step increase the generality, or exten-
sion, while we decrease the comprehension. From Socrates
we can thus ascend to philosopher, Athenian, man, and so on
upwards to the highest possible concept, some being or being.
Some attempts have been made to invalidate the prin-
ciple of the counter increase and decrease exemplified in the
relations of Comprehension and Extension. It is admitted
that the higher conception has a narrower content but a wider
extent than the lower, while the lower conception has a fuller
content, but a narrower extent. It is denied, however, that
the extent is increased or lessened by every lessening or in-
crease of a given content, and that the content is increased
or diminished with every decrease or increase of a given
extent.1
The grounds on which this view is supported seem to me
to be insufficient and irrelevant. The very admission of the
difference of extent and content between the higher concep-
tion and the lower seems to me to be inconsistent even with
the denial of the uniformity of this difference. How, except
through the attributes given in the concepts or classes, are
we to know anything either of extent and content, or of their
relations of decrease and increase ? We may go beyond the
1 Ueberweg, Logic, p. 135.
THE LAW OF COMPKEHENSION AND EXTENSION. 187
actually contemplated or contained attributes of the concept,
and so make an increase or decrease ; but this has no relevancy
whatever on the relations of the subordinated concepts in the
scheme of graduation with which we chance to deal.
It must be kept in mind that concepts subordinated in
Extension are first of all referable to some common genus, —
it may be of a very wide kind. And here it will be found
that as you lessen the extent by adding on an attribute, you
necessarily increase the content or comprehension. Take
the abstract substance, or something. This is the concept of
being at its widest extent. Add on the attribute corporeal,
and you have a less extensive concept, body or matter as op-
posed to incorporeal or spirit. But substance or something
certainly originally embraced this in its extension, which
body no longer does. If you go still further downwards, and
add on or determine by the attribute life, you have animate
as opposed to inanimate. Add on sentiency, and you have
sentient as opposed to insentient. Add on rational or reason,
and you have man as opposed to brute. Under man you
may have subdivisions or species, but ultimately you must
come to the individual Socrates, Plato, Paul, Peter, &c.
Proceed conversely, by abstraction of the attribute, and you
have a precisely counter result. The greatest sum of attributes
is in the individual, Socrates or Plato. Go on abstracting
an attribute, so as to make the individual less individual, or
common to a species, you necessarily extend the concept which
includes it, as you lessen the content or comprehension, and
so of all the species in the ascending series. The fallacy of
those who deny this law lies in not observing that in no case
need we speak of the number of objects or classes actually
to be found under the concept, but of their potential number,
that is, of the actual and ideal objects possible under the
class. And here the very form of our thinking shows that
there must be a counter decrease and increase, or increase
and decrease. For as attribute is the ground of the class,
each time the number of attributes is lessened, the number
of classes or species is lessened, and the compass of the genus
increased. And conversely, as the number of attributes is
increased, the number of species is increased, or the compass
of the genus is limited by adding on differentia?. It matters
nothing whether in a given species there are more objects
188 INSTITUTES OF LOGIC.
under it, and more sub-species than there were species under
the immediately proximate genus. This is a numerical dif-
ference, not a specific or logical difference. Species depends
on attribute ; and according as you have or have not an
attribute to ground the species, you have or have not the
species, and only the species, whatever be the number of objects
or sub-species contained under it. " If we join the adjective
red to metal," it is said, " we narrow the meaning much more
than if we join the adjective white, for there are at least
twelve times as many white metals as red. So with white
man, and blind man. Thus, in increasing the intension of a
term we may decrease the extension in any degree." 1
How does this bear on the point ? What does it matter
whether under the species white metal there are more metals
than under red ? Does not the genus metal take in all metals,
whether red or white to begin with ? And is not the species
white metal but one species, whether the objects under it
be greater or less than red? Logically, the extension of
metal is diminished as much by red as by white. It is
diminished to the extent of one species by each, and that
is all. No doubt white man and blind man have a different
extension ; the former is much greater than the latter.
It contains more species of man under it, or numerically
more men. This is true, when we compare the one species
with the other ; and have ascertained from observation and
experience the relative numbers under each class. But,
as distinctively or in comprehension only two species, they
are logically to us of equal, that is, any possible, extent. Be-
sides, it may be said, in regard to white and blind, that these
are not separated by any proper dichotomy, — that they are
intersective concepts, — there being nothing in the one which
excludes the other, and therefore not properly co-ordinate
species under the genus. In fact, there is no true division of
the genus, for whatever a proposition may promise, division at
least promises difference, and, if it fails, ceases to be division.
If we add to the intension by properly contradictory, or even
contrary concepts, we must in a constantly uniform ratio
diminish the extension. If we do not so in our division our
process is futile.
1 Jevons, Elementary Lessons in Logic, p. 40.
RELATIONS OF CONCEPTS. 189
§ 235. Concepts are divided according to their mutual
Relations. Concepts admit of comparison in respect (a) of
Extension, (b) of Comprehension.
(1.) In respect of Extension, concepts viewed in relation to
each other are (a) Exclusive, (b) Coextensive, (c) Subordinate,
(d) Co-ordinate, (e) Intersective.
(a) Concepts are Exclusive, when no part or object con-
tained under the one is contained under the other. Thus,
emotion, mineral, — mineral, plant. This refers only to the Ex-
tension, of which we are now speaking. In Comprehension,
or as sums of attributes, some attribute is common to all
concepts. Thus, existence, real or ideal, is predicable of all
concepts.
(V) Concepts are Coextensive, when the sphere of the one
is convertible with that of the other, as equilateral and
equiangular, — living being, organised being.
(c) One concept is Subordinate to another when it occupies
a place or position in the sphere of the other, as rectilineal,
under figure, plant under organised.
(d) Concepts or Species are Co-ordinate, when, while their
spheres are exclusive, they yet immediately go to constitute
the extension of a third concept. Thus triangle, square, and
polygon are exclusive, yet they constitute rectilineal figure.
Man and brute are co-ordinate under animal. Co-ordinates
are thus always also opposed as species.
(e) Concepts are Intersective, when their spheres partly
coincide, and partly do not. In this sense white and cold
coincide ; some white things are cold, and some not ; some
cold things are white, and some not.1
§ 236. The Subordination and Co-ordination of concepts
give rise to distinctions and names of the utmost logical
importance, especially in Judgment and Reasoning. These
are mainly Genus, Species, Difference, Generic and Specific.
In the Subordination of concepts, the higher, wider, or
more extensive, is called a Universal or General Notion Con-
cept, in contrast to the lower or less extensive, which is
known as Particular ; by Aristotle the former is called vovpa.
Ka66kov, the latter vorjf^a fj.tpiK.6v.
1 On these distinctions generally, see Hamilton, Logic, xi. § 31 ; Krug,
Logik, § 41.
190 INSTITUTES OF LOGIC.
(a) A universal, says Occam, is a concept (intentio) of the mind signify-
ing many, for which it can stand {supponere). Therefore one concept
distinct from another is predicated of the other, not indeed for itself,
but for the thing which it signifies ; accordingly, by such propositions
it is not denoted that one concept is another, but it is frequently de-
noted that that which is signified by one concept is that which is
imported by another. — (Log., i. 25.)
§ 237. More definitely, the General Concept is designated
a Genus (y^Vos), inasmuch as it contains an attribute or
attributes common to several classes or concepts under it, and
thus embraces those as part of its sphere; and the Particular
Concept is designated a Species («*8os), inasmuch as while it
too contains an attribute or attributes common to several
classes or individuals under it, and thus embraces them in its
sphere, it is itself regarded as a portion or class under the
wider concept or Genus. Abstraction or Generalisation em-
ployed on concepts to carry up the lower to the higher, the
species to the genus, is called Generification. Determina-
tion, which evolves by attribution species out of genera, is
called Specification.1
Genus and species as considered in Logic have thus nothing
to do with the question of natural science as to whether all
species of plants or animals have arisen from one common
source, and have thus acquired actual diversity through
evolution — whatever that may mean. This is a scientific
question of fact and a metaphysical question of origin and
reality. Logic only seeks to legislate for the forms in which
science has to put its observation, generalisation, and classi-
fication of the actual identities and diversities of our ex-
perience. Logic does not venture so far back in time or so
high in speculation, but, if limited, it knows what it means.
(a) Genus is that which is predicated of several differing in species, in
respect of the what (in to quod quid). When the genus is predicated
of the species, it is meant that that which is imported by the predi-
cate is that which is imported by the subject. — (Occam, Log. , i. 20.)
Genus is usually said to be predicated in quid — that is, in answer
to the question — What is the thing ? What is he ? He is an artist, or
doctor, or lawyer.
§ 238. A Genus or Universal is regarded as a whole,
inasmuch as, in Extension, it contains species or classes of
i Cf. Hamilton, Logic, L. xi. § 35.
GENUS AND SPECIES. 191
objects under it, of which it is predicable. It is thus only
potentially a whole, that is, it is applicable to or predicable
of an indefinite number of objects, actual and ideal. The
species under it represent the parts of the whole or the classes
of which it is predicable. A species is itself a whole in re-
spect of the individuals under it. The individual is the part,
and it is logically individual, inasmuch as it is not predicable
affirmatively of aught but itself.
In Comprehension, the Individual is a whole, inasmuch as
it contains a sum of attributes, which may be represented in
different concepts and in the unity of the individual. This is
the whole of real existence, of time and space, and here the
real and the ideal or logical may coincide. The Genus is
a whole properly in Extension, and is, strictly speaking,
ideal. The Genus contains the species extensively ; the
Species contains the genus comprehensively.
(a) Occam's view is that genus and species do not differ as whole
and part. Genus is not a part of the species, nor species a part of the
genus. Genus is the sign of many, species of few ; animal imports
all animals, man all men, that is fewer objects. Genus and species
equally signify a whole ; but the genus signifies more individuals than
the species. In this sense the species may be taken as the subjective
or subject part. — {Log., i. 21.)
§239. Genera are of two degrees — (1) The 'Highest or
Most General Genus (yeVos ycviKwraToi/, genus summum, general-
issimum) is that which, being a genus, cannot become a species
or form a portion of a class higher than itself. It is that of
which, universally taken, any genus is not predicable.1 (2)
Subaltern or Intermediate Genus (yeVos vTraXkrjkov, genus sub-
alternum, medium) is that which, being a genus, can also
become a species.
Species are also of two degrees — (1) Lowest or Most
Special Species (eTSos dhiKwrarov, species infima, ultima, special-
issima) is that which, being a species, cannot become a genus.
Most Special Species is a concept having no species under it,
or is predicable in quid of no class universally taken. (2)
Subaltern or Intermediate Species (eTSo? virdWrjXov, species sub-
alterna, media) is that which, being a species, may also
become a genus. Subaltern Genus and Subaltern Species
1 Occam, Log., i. 21.
192 INSTITUTES OF LOGIC.
are thus the same.1 The Species Infima can contain under
it only individuals or singular instances of the species,
numerically distinguished.2
A highest genus is usually that concept, in a certain order
of gradation, beyond which observation and generalisation
have not yet advanced, or beyond which it is not necessary
to advance, for the special purpose in view. But absolutely
or objectively viewed, it may not be the highest. Being or
something may be regarded as the only highest genus ; for
this would hold even of Deity or a Universal Cause. This is
in everything that is, whether created or uncreated.
As an example of a Summum Genus in a lower sphere, we
may take figure. The concept of figure is bounded extension.
It may be said extension itself is genus of figure, and em-
braces equally bounded and boundless extension. But figure
ceases to be figure the moment the boundary of the extension
is removed. We have, therefore, in figure itself a highest
genus ; because it cannot be a species of its opposite or
contradictory.
A lowest species, absolutely, it is impossible to reach ; for
differences may always be conceived, say of varying degree,
in the characteristic attributes of a species, so as to consti-
tute a sub-species. But the logical requirements of thought
are satisfied, if the individual under a species be conceived
as embodying the attributes of the species, whether the in-
dividual be real or ideal. This individual, if it cannot be
made again the matter of division into other individuals
of time, or of time and space, is regarded logically as the
individual. " The Highest Genus in a science is the most
general class, whose properties that science investigates ;
the different Lowest Species, the classes at which that
special investigation terminates. In geometry, for example,
the highest genus is magnitude in space ; the infimce species
of triangle are equilateral, isosceles, scalene. The geometri-
cal properties of the figure are not affected by any further
subdivision." 3
§ 240. In a series of subordinate concepts, we have Prox-
imate and Remote Genus and Species. The nearest is that
1 Cf. Hamilton, Logic, L. xi., par. 36.
2 Cf. Porphyry, Eisagoge, ii., where all those distinctions and terms are
explicitly given. Cf. also Aristotle, Topica, i. 5.
* Mansel, Prol., p. 199.
DIFFERENCE. 193
immediately higher in the line of ascent, — this is the proxi-
mum genus; the next superordinate is the remote, genus
remotum, and this increases in degree as we ascend in the
scale. Thus, take the series, body, living, animal, man, —
animal is proximate, living remote, body still more so. This
distinction is readily applicable to species also. Its use and
application are seen in definition.
Take the concept thistle (carduus). This may be divided
according to specific differences into natans (musk thistle),
marianus (milk thistle), lanceolatus (spear thistle), arvensis
(field thistle), &c. &c. These all belong to the genus carduus,
and the mark of this is that the corolla is tubular, generally
spreading, so as to form a hemispherical head, as opposed to
the ligulate or strap-shaped corolla. This again, the carduus
the capitate or headed-flower class, belongs to the higher
genus (order) aequalis — that is, having the florets all perfect,
each having five stamens and a pistil. This order, subaltern
genus and species, is referred to the remote genus Syngenesia
— that is, the class of plants bearing compound flowers, having
their anthers united in a tube.
(Remote or Highest Genus. )
Syngenesia.
(Subaltern Genera and Species.)
Co-ordinate.
I I I
Aequalis. Superflua. Frustranea.
(Subaltern Genus and Species.)
Carduus (Capitate, Tubular Corolla.)
(Proximate Genus and Species.) (Proximate Genus and Species.)
Leaves Decurrent. Leaves Non-Decurrent.
I I
(Species.) (Species.) (Species.)
Musk Thistle. Welted Thistle, &c. Milk Thistle, &c.
§ 241. Difference is that which distinguishes species under
a common genus, and which joined to the genus makes the
species ; as under body we have the difference of life and its
absence, giving animate and inanimate as species of body.
N
194 INSTITUTES OF LOGIC.
" Difference," says Porphyry, " may make an other ; or it may
indicate merely a change in the same. The difference reason-
able joined to animal makes an other — viz., man; the difference
of moving as opposed to being at rest, only makes a change
£n the same. It is by difference that makes an object other,
that genera are divided into species." x
Difference is Divisive and Constitutive ; the former when,
by means of it, we divide the genus into its species as
opposed, — as animal into rational and irrational ; the latter
when, by adding it to the genus, we constitute the species,
as man by rational animal.2
If we take the concept ranunculus as, say, a plant of five
sepals, caducous, some of the petals with nectariferous gland
at base, &c, we shall divide this into its species by differ-
ence, and at the same time so constitute the species. We
find leaves simple, leaves divided. Under the former are the
species less spear wort, and pile wort. Under the latter,
we have wood crowfoot, buttercup, meadow crowfoot, &c.
Thus, too, the brome grass, or soft brome grass, is distin-
guished from the festuca or sheep's fescue grass by being
awned. The festuca is, as a rule, awnless ; and when awned,
the awn is not in normal form.3
In the class lolium, or of flowers in spikes, we have rye-
grass and bearded darnel. The differentia is in the one case
spikelets longer than the glumes; in the latter, spikelets shorter
than the glumes.
§ 242. Difference is Generic, Specific, or Individual. The
attribute, or sum of attributes, which distinguishes a lower
genus or species from the higher genus under which it stands,
and from the other species which are co-ordinate with it
under that genus, is called the Generic or Specific Difference
(8iacf>opa ycvtKrj, Sia<£o/oa €181*77, differentia generica, differentia
specified). Specific Difference is of the Species Infima only, —
of that which being a species can never be a genus. As an
example of generic and specific Difference, we may take
sentient as common to animal and man; of specific Difference,
rational as belonging to the species man only. The attribute
or attributes by which an individual or singular is distin-
guished from the species which contains it, and from the
1 Eisagoge, iii. 5. 2 cf. Porphyry, Eisagoge, iii. 12.
3 Hoblyn's British Plants, p. 30.
CONCEPTS IN COMPREHENSION. 195
other co-ordinate individuals under the species, is called
the Individual, Singular, Numerical Difference {differentia
individualis, singularis, numerica). As subaltern genus and
subaltern species are the same, the difference is called in-
differently generic and specific.1
(a) Difference is a concept expressing a determinate part of a thing,
predicable in quale (what sort) of the same things of which the species
with which it is connected, predicates in quid (what class). Difference
expresses a part, not the whole, because then it would not be distin-
guishable from the species. It expresses further a part and nothing
extrinsic, because otherwise it would be either property or accident.
Difference is always concrete. It is predicated of the same things of
which the species is predicated, and is convertible with the species.
Thus life is not the difference of the living body, but living; and
rational, not reason, is the difference of man. — (Occam, Log. , i. 24. )
§ 243. Difference as predicable of the species is predicable
of the individuals under it, — as rational of man and Socrates.
The Genus and Difference are said to make up the essence, or
essential attributes of the concept. While the Genus answers
the question — Quid est — what is the thing? the Difference
answers the question — Qualis est — of what sort is the thing? As
Difference, taken along with the Genus, completes the concept
or the essence of the concept, it is also said to be predicated
in quale quid — that is, it tells the kind of the what. The
Essence (Essentia) was regarded as equivalent to Quidditas ;
but this did not mean simply the Genus, but the Genus
and Difference combined. These constitute the Essence in
the proper sense of that term.
§ 244. Concepts viewed in Comprehension either coincide
or they do not, that is, they either do or do not comprise the
same character. " Notions are thus divided into Identical and
Different. The Identical are either absolutely or relatively
the same. Of notions Absolutely Identical there are actu-
ally none ; notions Relatively Identical are called, likewise,
Similar or Cognate ; and if the common attributes, by which
they are allied, be proximate and necessary, they are called
Reciprocating or Convertible." 2
§ 245. Concepts in comprehension, viewed in relation to
each other, "are said to be either Congruent or Agreeing,
1 Hamilton, Logic, L. xi., par. 38 ; and Krug, Logik, § 35.
2 Esser, Logik, § 36, quoted by Hamilton, L. xii., par. 41.
196 INSTITUTES OF LOGIC.
inasmuch as they may be connected in thought ; or Conflic-
tive, inasmuch as they cannot. The confliction constitutes
the Opposition of notions. This is twofold : Immediate or
Contradictory Opposition, called likewise Kepugnance; and
Mediate or Contrary Opposition." x In the former case, one
concept abolishes by simple negation what the other posits ;
in the latter it abolishes this through the affirmation of some-
thing else.2 This distinction properly falls to be considered
under Judgment.
§ 246. Concepts compared together in the relation of com-
prehension are further Intrinsic or Extrinsic. " The former
are made up of those attributes which are essential, and,
consequently, necessary to the object of the notion ; these
attributes, severally considered, are called Essentials or
Internal Denominations, conjunctly the Essence (ovo-ia).
The latter consist of those attributes which belong to the
object of the notion only in a contingent manner, or by
possibility; and which are, therefore, styled Accidents, or
Extrinsic Denominations." 3
This raises the question of the distinction of Essence, Prop-
erty, and Accident in concepts. The Essence or Essential attri-
butes of a class representing the order of experience must in
the end be determined by observation, experiment, induction.
And our knowledge of this is relative to scientific progress in
the direction of finding the ultimate or grounding attributes
of things. It is just possible we may never reach absolutely
ultimate knowledge in the matter. In pure science, such as
geometry, we get at essence completely for the purpose of
the science by definition, or, it may be, hypothetical con-
struction. In observational science that attribute or feature
is naturally fixed on as essential which gives the distinctive
character to the concept, or which is subservient to what
may be viewed as the function of the object. Thus the
stamen of a plant consists generally of two parts — -Jilament
and anther containing pollen. The latter feature alone is
regarded as essential to the concept stamen ; the former not,
for the reason that the stamen would cease to be stamen or
to fulfil its function without the anther containing pollen,
1 Aristotle, Cat. vi. ; Met. vi. 10 ; Hamilton, Logic, L. xii., par. 42 ; and
Drobisch, Logik, § 25.
2 Ibid. 3 Hamilton, Logic, L. xii., par 43; Krug, Logik, § 39.
PROPERTY. 197
whereas the presence or absence of the filament would not
affect this.1 Obviously we must be content provisionally to
fix on features as essential, otherwise we could make no
progress in knowledge. Our view, however, is at the best
relative and approximate, so far as the nature of things is
concerned.
The concept force enters into the concepts gravity, cohesion,
chemical affinity. It is essential to each, as we find in experi-
ence. But these three concepts are still to us essentially
different. Gravity acts at a distance ; cohesion on the par-
ticles of a body that are near or in juxtaposition ; chemical
affinity only on bodies of different kinds. This difference,
however, may be only provisional : it may be relative to the
progress we have made in the knowledge of force ; and it is
not impossible that these forms may all be modifications of
one common force, — the particular mode in which it is varied
in its action in each of the three cases being unknown to up.
§ 247. Logicians, following Aristotle, have defined Property
as that which, while it does not constitute the essence, or part
of the essence of the subject or concept, yet follows, results,
or flows from the essence as a necessary consequence. Thus,
if we take as the essence or concept of a straight line " that
which lies just [evenly) (e£ icrov) " as Wallis puts it, " between its
terms" it follows that, of all the lines between the same terms (or
extremes) it is the shortest. This is a property following neces-
sarily from the concept of straight or right line. From the
same concept of right line it follows also as a property that it
is the only straight line between the two extremes. Thus
while Difference is the essentiale constituens, Property is the
essentials consequens.2
§ 248. Hence Property, as immediately flowing from Es-
sence, in the sense already explained, is that which belongs
to a class or species, — all, sole, and always, — omni, soli, et
semper. And hence, also, in regard to property as in regard
to difference, the proposition stating it is of convertible pre-
dication. If risibility be a property of man, then every man
is risible ; and every one risible is a man. If every right line is
the shortest between the same terms, then every line the shortest
between the same terms is a right line. Thus the propositions
are mutually convertible.
i Cf. Hoblyn, Botany, p. 47. « cf. Wallis, Logica, v. 21.
198 INSTITUTES OF LOGIC.
§ 249. To speak of property only as that which necessarily
follows from the subject or essence of the concept, is to iden-
tify the relations of outward objects — observation in general
— with those of mathematical conceptions and definitions.
To adjust the view of property to the requirements of science,
we ought to substitute uniformity for necessity of sequence.
In this case, the logical formula will hold perfectly true. We
have essence, — essential properties, — we have others and
find others uniformly connected with these. These will be
properties whether we can determine a necessary connection
or not. The link of evolution is one thing ; the fact of the
uniform connection is another and the present thing. We
may find a certain amount of motion following uniformly a
certain amount of heat, and vice versa. We should thus get
properties of each, though we know nothing of necessary
connection or even of the inner nature of transmutation, be-
yond superficial quantity of motion and its result. At the
same time, this conception of the nature of property was of
the deepest insight and widest scope. It was a forecast of
all modern science in its true spirit and essence, — the going
backwards in analysis to attribute beyond attribute in the
object, — to principle beyond principle in things, — on which
nearer or observed attributes may be found to depend. In
every scientific classification we, consciously or unconsciously,
follow this law, — every true scientific mind aims at this end.
And to carry the matter wider, all philosophy is in the end
but a seeking of that on the properties of which all the attri-
butes of things depend.
We have numerous illustrations in botany of a uniformity
of sequence in properties following on a point of differ-
ence in classes. To take one instance, — class twelve in
the Linneean arrangement is the Icosandria. The character
or concept of the class is that of a plant bearing flowers
with twenty or more stamens inserted in the Calyx. This is
distinguished from the class Polyandria, which includes
plants bearing flowers with numerous stamens, arising from
the Receptacle. The difference of the two classes is inser-
tion in the Calyx, as opposed to insertion in the Receptacle.
Now with this we have a marked difference of property.
The first class contains as species or sub-classes under the
Orders, which are in their turn merely subaltern genera and
PKOPERTY. 199
species, the Sloe, Wild Pear, Crabtree, Apple, Plum, Pome-
granate, Raspberry, Strawberry, &c. These furnish fruits, in
most cases, of a pleasant and useful sort. The second class
contains in it ranunculaceous plants, such as Larkspur and
Aconite, and papaveraceous plants, such as the common Red
Poppy. The properties of the former are described as
" acridity, causticity, and poison," and the narcotic property
of the poppy is well known.1 It would be rash to infer that
the variation in character of the properties follows or results
from the difference, insertion in Calyx or in Receptacle. But we
have at least here a uniformity or invariable concomitance,
which is sufficient so far for scientific and other purposes.
It may be said that the Essence cannot be conceived apart
from its property, which is a necessary or uniform sequence.
This is quite unfounded and unreasonable. It is perfectly
true that we can conceive essence — say, for example, definition
of triangle or square — without thinking or even knowing
a single property of either, though all may be implied in the
definition. Our definition is clear and distinct knowledge.
After that we may go on, either by deduction or observation,
adding on properties. In this case we should increase our
knowledge. But at the same time this very increase requires
a sum or datum with which to begin.
§ 250. Property is strictly a mark or attribute which belongs
to a class universally taken, and to no other, except that class,
and what is contained under it.2 Thus risible is the property
of man ; inertia is the property of body.
But property may be taken in a wider sense as indicating
the main or constituent marks of a class. Gravity is thus a
property of body; imponderability is a property of ether; trans-
formability into molecular motion is the property of mechanical
motion. Property in the strictest sense may be regarded as
the attribute of a class which is found to follow from, or
which may be added by observation and induction to, the
concept of the class, or the concept of it as originally framed
by us. Given the definitions, for example, of triangle or
square, we thereafter speak of the propositions expressing
truths regarding them as embodying their properties — e.g., any
two angles of a triangle are together less than two right angles.
1 Hoblyn's British Plants, p. 7.
2 Cf. Porphyry, Eisagoge, iv. § 5 ; Occam, Log., i. 25.
200 INSTITUTES OF LOGIC.
Given our conception of a particular metal, we may add on,
by observation or experiment, attributes or properties not
originally known to belong to it.
(a) Property is a concept predicable adequately and convertibly in
quale (what sort), connoting, affirmatively or negatively, something
extrinsic to that which is imported by the subject.
Properties are of four kinds —
(1.) That which belongs to one species or one genus, but not neces-
sarily to all contained under each, as grammarian to man only, but not
to all men. This is the soli sed non omni of later logicians.
(2.) That which belongs to every individual of a species, but not to
this species alone, as biped to man. This is the omni sed non soli.
(3.) That which belongs to any class taken universally, but not
always, only at a particular time, as canescere, to man. This is the
omni et soli sed non semper.
(4.) That which belongs to some class universally taken, and to no
other except that class and what is contained under it, so that it is
convertible with it, and necessarily predicable of the same. This is
property strictly taken ; the other three are accidents. Thus risible is
the property of man, every man is risible, and every risible is man. —
(Occam, Log., i. 25.) This is the omni soli et semper.
These distinctions are given in Porphyry, Eisagoge, v. 1. Cf.
Occam, Log., i. 25.
Property and Difference are distinctions dependent mainly
on our point of view. In the wide sense, every attribute of a
class or concept is a property. The distinction of Difference
and Property especially is relative to the aspect of the object
presented to us, or represented in the class. Difference may
be regarded as a property selected by us to mark off the
particular class under the genus.
§ 251. Accident is that attribute or feature which may be
conceived as present in or absent from the concept of an ob-
ject, without destroying in thought the essential features of
the object itself as conceived by us. Thus we can think as
part of the concept man, the marks laughing, sitting, running,
riding, or the absence of those marks, without in any way
affecting the definite concept itself. Accident thus neither
constitutes the essence, as difference serves to do, nor follows
from it necessarily or uniformly as property does.
Thus the concept of motion is not affected, whether we re-
gard the motion as swift or slow, as uniform or irregular, as
accelerated or retarded. Nor is that of water, as a compound
of the two gases, oxygen and hydrogen, changed in any way,
whether we find water cold or hot, flowing or stagnant. " The
THE PREDICABLES. 201
accident," as Porphyry, following Aristotle, puts it, "is that
which may or may not be in the same subject." x
§ 252. Accidents are distinguished as Separable and In-
separable. The Separable is said to be that which can be
actually or ideally separated from the subject or concept,
while this remains the same, or untouched in its integrity as
a concept. Thus we may separate cold from water, white
from wool or snow, black or red from coat, without destruction
of the subjects from which we make the separation.
The Inseparable accident is said to be that which is not
actually separable from the subject, — as heat from fire, and,
in the old logics, white from swan, black from crow. So far
as species is concerned, separable and inseparable accidents
are utterly unessential. That alone is an accident which is
not necessary to the true concept or essence of the subject,
and which further is not a necessary or a uniform property
of the class or concept.
Accidents may be viewed as Separable and Inseparable in
regard to the individual. In this case we have readily what
is separable — as of a man sitting, standing, running, leaping,
&c. As to the Inseparable, we have such things as native of
Paris, of Rome, of London, — we have tall, short, crooked, &c.
We have an Ethiopian who is black, and not to be made
white by water. These refer wholly to the individual and his
peculiarities. If we think of the individual, they are essen-
tial to him. The Ethiopian is always unwashable. But the
so-called separable accident is not less essential to the in-
dividual, if we think of him at the given time when it belongs
to him. The man sitting at a particular time can for us
as an individual concept only be the man sitting at that par-
ticular time. But the concept of essence which the individual
embodies remains the same through all such forms of change
or accident.
§ 253. Genus, Species, Difference, Property, and Accident are
known in Logic as the Five Predicables, or classes of possible
predicates — at 7revTe <f>wval, quinque voces. What we say of a
subject is supposed to be found under one or other of those
heads. What each has in common is that it is predicable of
many. This classification is due to Porphyry, as given in
the Eisagoge to the Categories of Aristotle.2
1 Eisagoge, v. 3. 2 gee Eisagoge, i. § 1 et sea.
202 INSTITUTES OF LOGIC.
(a) In the view of Aristotle there are four Predicable classes, or the
Four Differences (al Ttrrapts Siatpopal) — viz. , Definition, Genus, Property,
Accident. Definition (Spos, 6pi<x^6s) expresses the essence or essential
qualities of the thing (rb ri fy tlvai). Hence, in the proposition, the
subject may be put for the predicate or the predicate for the subject.
A square is that which has all its sides equal, and all its angles right
angles. This as a definition is convertible.
Genus (yevos) is that which is attributed essentially to several
objects which differ in species. An essential attribute is that which
answers to the question What is the object ? Thus, What is man ?
The answer is conveyed by the genus animal. Here the subject and
predicate are not reciprocally convertible. Animal is a part of man,
but it is wider than man.
Property (rb ftiov) does not express the essence of the thing ; but it
belongs to the thing alone, and can be taken reciprocally for it. Thus
the property of man is to be able to learn grammar : if he is man he
can learn grammar, and if he can learn grammar he is man. We
should not call that property which might belong to another thing ; we
should not say that to sleep is the property of man. Here there can
be no reciprocal attribution or substitution.
Accident ((ru/*)3ej87jieos) is that which may or may not be in one and
the same thing. Thus, to be stated, may or not be present in one and
the same person, and so ichitencss.
Aristotle did not regard Difference as a kind by itself. Difference,
in so far as belonging to the Genus, should be classed with it. It is
the limit which separates one genus from another, and can be predi-
cated of several species. — (Topica, i. c. 3, 4, 5, 6.) Ether may be
regarded as an imponderable fluid with an undulatory motion. If undu-
latory motion be taken as the difference of ether from say mechanical
motion, it may yet be regarded as the concept of a species of mo-
tion, which is capable of being predicated of other objects besides
ether.
It is obvious that the distinctions of difference and property are
relative, and are not always capable of accurate grounding.
Of accidents belonging to a class, the inseparable are those which are
found in all the members simply as a matter of experience, the separ-
able only in some. An inseparable accident of an individual, such as
native of London, is predicable of the subject always. What attributes
are essential, what are properties, and so on, can at the best be deter-
mined only on extra-logical grounds.
§ 254. Notions in Comprehension may be further viewed
as in the relations of Involution and Co-ordination. Involu-
tion corresponds to Subordination in Extension : —
" One notion is involved in another, when it forms a part
of the sum total of characters, which together constitute the
comprehension of that other ; and two notions are in this
quantity (comprehension) co-ordinated, when, whilst neither
DISPAEATE AND DISCRETE NOTIONS. 203
comprehends the other, both are immediately comprehended
in the same lower concept." x The example given is the
notion of the individual Socrates. This contains, among
others, son of Sophroniscus, Athenian, Greek, European, man,
animal, organised being, &c. Of these, some are given
through the others. Socrates is Athenian only through son
of Sophroniscus, only Greek as Athenian, only European as
Greek, only man as European, only animal as man, only
organised being as animal. These characters, as given in
and through others, stand to those others as parts to wholes ;
and it is only on the principle that part of the part is part
of the whole, that the remoter parts are parts of the primary
whole.2
But how, it may be asked, is this relation known ? There
is no a priori connection between son of Sophroniscus and
Athenian. Being son of Sophroniscus does not tell me that
Sophroniscus was an Athenian, or being an Athenian does not
tell me on any logical principle of whole and part that Athenian
was Greek, and so with the others. There is no connection of
whole and part here at all, but of one attribute involving another
through a mere contingent happening or experience. There
is no reasoning here possible on the principle of the dictum of
Aristotle, — that is, from whole to part. This point will be
more fully discussed when we come to treat of Reasoning in
Comprehension.
§ 255. " Notions co-ordinated in the whole of Comprehen-
sion are, in respect of the discriminating characters, different
without any similarity. They are thus, pro tanto, absolutely
different ; and, accordingly, in propriety are called Disparate
Notions. On the other hand, notions co-ordinated in the
quantity or whole of Extension are, in reference to the objects
by them discriminated, different (or diverse) ; but, as we have
seen, they have always a common attribute or attributes in
which they are like. Thus they are only relatively different
(or diverse) ; and, in logical language, are properly called
Disjunct or Discrete Notions." 3
As an illustration of Disparate Notions, we may take
oviparous and warm-blooded as co-ordinate parts of the com-
1 Hamilton, Logic, L. xii., par. 44. 2 Ibid., par. 44 et seq.
3 J bid., par. 45.
204 INSTITUTES OF LOGIC.
prehension of bird. These are relative and correlative, but
not involved in each other. Oviparous is not always warm-
blooded ; and warm-blooded is not always oviparous.1
(a) This view of Disparates does not coincide with that of the earlier
logicians. Disparates are in extension as well. Thus Disparates are
those concepts which are only diverse from each other, and not opposed
as contraries, as earth, vestment, fire. — (Boethius, De Syll. Hyp., p. 608.)
(b) The difference between Disparate and Opposite Concepts lies in
this, that the former are only mutually repugnant, as when one is
opposed equally or in the same mode to many, as man to ox, horse,
dog, lion, and other species of animal. Opposition arises when one is
opposed only to one. — (Cf. Wallis, Logica, i. 16; Duncan, Inst. Log.,
Lect. i. , xiv. § 2 ; Dounam in Rami Dial. i. , xiv. )
Avarice, as opposed equally to liberality and prodigality, would be
taken as representing Disparates ; parent and child, good and bad, see-
ing and non-seeing, Contraries, (the latter rather contradictories. ) But
this principle obviously does not hold universally in simple contraries.
Of colours, red is equally opposed to green and yellow; of figures,
triangle to square and circle. In contradictories alone does the principle
hold completely, and in relatives and privatives as these approximate
to contradictories.
§ 256. Concepts are, in respect of their Quality, regarded as
Clear and Obscure, Distinct and Indistinct. A concept is
clear when in our consciousness of it we are able to distin-
guish it as a whole of attributes, from another or other
concepts. It is obscure when we cannot do this. A con-
cept is distinct when we can distinguish from each other the
various attributes or marks which make it up. It is indis-
tinct when we cannot do this. Obscurity and indistinctness
may arise from defect on the part of the individual think-
er. In some cases it arises from the nature of the object
thought about. In the case of some mathematical figures,
we have both a clear and a distinct knowledge. We can dis-
tinguish triangle as a whole from square, and both from circle;
and we can further specify the marks by which we are able to
do so, and make them distinct to others. We can distinguish
buildings of Norman and of Early English architecture from
each other, and specify the discriminating marks of each.
But it is quite possible for us to have a clear concept of
an object, which is yet indistinct. We can quite well
discriminate red, white, and green from each other ; but it
would puzzle us to tell the marks or express them to others.
] Hamilton, Logic, L. xii.
CLEAK AND DISTINCT NOTIONS. 205
Shades of the same colour can also be discriminated, but not
by specific marks : so with sounds, tones of the voice, and
different odours. The mind of average capacity and activity
is satisfied with being able to distinguish things as wholes or
in a general way ; it is only the active, scientific, or philo-
sophical mind which seeks distinct knowledge.
Descartes laid down Clearness and Distinctness as the
criterion of true knowledge. u I call that clear which is pres-
ent and manifest to the mind giving attention to it, just as
we are said clearly to see objects when, being present to the
eye looking on, they stimulate it with sufficient force, and it
is disposed to regard them ; but the distinct is that which is
so precise and different from all other objects as to compre-
hend in itself only what is clear." x
This criterion is, however, ambiguous in its applications.
When it is said that whatever we clearly and distinctly con-
ceive is true, we may mean that it is possible, that is, an ideal
possibility ; or we may mean that it is real, that is, a matter of
fact or existence.
Leibnitz much more fully and precisely indicates the
various degrees of our conceptual knowledge.2 According
to him, cognition is obscure, when the object is not dis-
tinguished from other objects or the objects around it. Here
the object is a mere something, not nothing ; but what it
precisely is, either in its own class of things, or as contrasted
with other things, we do not apprehend. Cognition again is
clear when we are able definitely to comprehend the object
as in contradistinction from others. Clear Cognition is
further divided into Confused and Distinct. Tt is confused
when we are unable to enumerate the marks or characters
by which the object is discriminated from other objects, while
it yet possesses such marks. Thus we can distinguish colours,
odours, taste, from each other, yet we cannot specify the
marks by which we do so. At the same time such marks
must exist, seeing the objects are resolvable into their respec-
tive causes. Our knowledge again is distinct when we can
specify the discriminating marks, as the assayers in dealing
with gold ; and as we can do in the case of number, magni-
tude, figure. But distinct knowledge may still further be
1 Principles, part i., § 45, p. 212.
2 De Cognitione Veritate et Ideis, Erdmann, p. 19.
206 INSTITUTES OF LOGIC.
Inadequate or Adequate. It is inadequate when the dis-
criminating marks are not analysed or resolved into more
elementary notions, being sometimes clearly, and sometimes
confusedly, thought, — as, for example, the weight and colour
of gold. Knowledge, again, is adequate when the marks in
our distinct cognition are themselves distinctly thought, that is,
carried back by our analysis to an end or termination. Whether
any perfect example of this exists is, in the view of Leibnitz,
doubtful. Number is the nearest approach to it. Then there
is the distinction of the Blind or Symbolical and the Intuitive
in cognition, the former being the potentiality of conception
which lies in terms ; the latter being the clear and distinct or
individual picture of each mark so lying undeveloped. When
cognition is at once Adequate and Intuitive, it is Perfect. But
Leibnitz hesitates to say whether such can be actually realised
by us. Adequate knowledge involves cognition through
means of a priori possibility. But " whether such a perfect
analysis of notions can ever be accomplished by man —
whether he can lead back his thought to first possibles
(prima possibilia) and irresolvable notions, or, what comes to
the same thing, to the absolute attributes of God themselves
— viz., the first causes, I do not now dare to determine." *
1 De Coy., <bc, Erdmann, p. 80.
207
CHAPTER XVII.
CONCEPTS : THEIR EVOLUTION DEFINITION AND DIVISION.
§ 257. Seeing that terms are liable to be used without any
knowledge of their meaning, and in an indeterminate or un-
certain sense, we require Explication and Determination.
These processes come under the head of Definition in its
stricter and wider senses.
When we specify precisely the sense in which a term is
employed, or is intended to be employed by us, we have
Definition of the Name — Nominal Definition. When we
specify the nature or essential attributes of the thing or
object to which the name is applied, we have what is called
Real Definition — Definition of the Nature of the Thing. But
Real Definition, or definition of the nature of the thing,
ought not to be distinguished from Definition proper — that
is, Logical Definition ; for it is the nature of the thing as
conceived by us, or our concept of the thing, which we
actually seek to define. The process of constituting the con-
cept is supposed to be already completed ; and our definition
is an unfolding of what we hold mentally about the object.
Real Definition has, however, a reference to the fact or class
of objects as existing ; and it points to the truth or corre-
spondence of the concept with the universal properties of the
class. But in Logic this is supposed to be given or known,
ere we can explicate it for the purposes of clear thinking by
means of strictly logical definition.
§ 258. In the definition of a term or name — Nominal Defi-
nition—rwe usually employ other terms better known, either
a series of explanatory words instead of one, or a synonymous
term. This is illustrated in the explanations of the diction-
208 INSTITUTES OF LOGIC.
ary. One great aid in the matter is Etymology, though it
is not always to be relied on as giving us the present or actual
sense of a term.
(a) It happens in Geometry, and is so far allowable, that we assign
to a term a specific meaning, even although this is not the one in
ordinary use, or even although it differs from the application of
the same term by others in the same general department, provided
that the assigned meaning be rigidly adhered to. Thus Euclid's
definitions of triangle and cone apply, the one to plane rectilineal, the
other to right or erect cone ; while with Theodosius triangle is so
denned as to take in spherical triangle ; and with Apollonius cone is
so defined as to embrace scalene.1
§ 259. Besides Nominal and Real Definition, we have what
is called Genetic Definition. This applies only to quantities in
time and space. In Mathematics, Genetic Definition is called
Real, as opposed to Nominal. Thus, we have an example,
when we say : — " A circle is formed when we draw around,
and always at the same distance from, a fixed point, a movable
point which leaves its trace, until the termination of the
movement coincides with the commencement." 2 This is
obviously merely a rule for embodying in a concrete form a
definition already existing in the mind. Every time I image
to myself triangle or square, I may be said to define genetically.
But this is no proper application of the term. Nor can it be
correctly said that the notion is the result of the definition ;
the concrete image is, but not the notion. Nor is there any-
thing properly synthetic in the process ; it simply embodies
what we already think.
§ 260. Definition unfolds the Comprehension of a concept ;
Division exhibits the Extension. The Comprehension and the
Extension of a concept ground and render possible the pro-
cesses known as Definition and Division. A concept being
supposed to be constituted through the processes proper to
its construction, it may possess an attribute or mark which
is essential to it in the sense of being universally in it ; and
which is at the same time in another concept higher and
wider in the scale of generalisation (genus) — as animal in
man, — sentient in animal. It may also possess an attribute
which does not belong to the higher or wider concept, and
1 Cf. Wallis, Logica, i. 23.
2 Wolf in Hamilton, Logic, L. 'xxiv.
DEFINITION AND DIVISION. 209
which yet is not possessed by other concepts co-ordinate
with it under the higher notion (difference) as rational or
responsible in man.
Both those attributes, however, may be essential to the
concept, that is, such that if they were taken away it would
no longer be the concept it is, while there are other attributes
which might be abstracted without this happening, — as white
from man, biped from animal. When thus the genus and the
difference of a concept are declared in a proposition, we have
Logical Definition. It is essentially an analytic process ; it
unfolds or declares what we hold to a certain extent implicitly
in thought. It thus makes a notion as a sum of attributes,
essential and characteristic, clear. Thus I say, — man is a
rational animal ; magnet is an iron-ore, having attraction for
iron ; physics is the science of inert matter ; mechanical motion
is the transport of a body from one point in space to another;
molecular motion is the change in the internal particles of a body,
continuing as a whole to occupy relatively the same space.
§ 261. The process which seeks to unfold the essential at-
tributes or comprehension of a concept is called Definition —
Logical Definition 5 that which aims at unfolding or enumer-
ating the classes or species under the genus, is called Division
— Logical Division. So far as our knowledge is concerned,
Definition aims at clearness, and Division at distinctness.
Our knowledge is said to be clear, when we distinguish one
concept from another ; distinct, through division, when we
distinguish the sub-classes or species under a genus. In
another relation, our knowledge is distinct, when we are able
to mark off the attributes in a concept from each other, and so
distinguish the concept from others.
§ 262. Definition and Division, as formal or purely logical
processes, are very limited in their application. All that de-
finition, logically considered, can tell me is, that every defini-
tion is possible in which the attributes combined are non-
contradictory, either directly or indirectly. No logical law
can assure me that the given definition corresponds to an
object in reality, or is adequate to that object. This it is for
observation and generalisation to do.
§ 263. In the same way Division cannot, as a purely logical
process, unfold the extension of a concept. We may divide
every concept contradictorily, that is, by dichotomy. We
210 INSTITUTES OF LOGIC.
can divide figure into rectilinear and what is not rectilinear
say curvilinear. But we cannot do even this much by pure or
logical thought. The one difference or attribute of figure
must be given us, ere we can take a step. Then we can
make the division, and say these are opposite classes ; the one
is not the other. The logical laws, further, do not assure us
that the difference is the real difference, or such as is proper
and adequate to the class of things as existing in nature.
§ 264. At the same time, the logical laws acting along with
actual observation and thinking, regulate it, keep it within
due bounds, aid it in its operations, help to clarify, distin-
guish, and classify. They are not the motive power at work
in the world of science, but they are the ruling and governing
power. They not only ground the possibility of our actual
thinking, but they help it on the way to its highest virtues
of clearness, distinctness, connectedness.
(a) Aristotle, in treating of Definition (bpi(Tfx6s), regards it in the
first place and mainly from the side of the real. His question is prin-
cipally how we are to reach a good, adequate, and true definition of the
thing or real object. Definition is with him the expression of the
essential qualities of a thing or of its specific nature. It answers to
the question ri icrri ; hence the definition is sometimes called rb rl
itTTi. — (An. Post, ii. passim.) From this point of view, accordingly,
definitions will first of all represent the most general classes or prin-
ciples, the necessary and universal concepts, which are the means and
the principles of demonstration. They are such as are fitted to explain
or include all particulars or facts. These universal conceptions are
indemonstrable, yet they are got by observation and induction, — (Cf.
An. Post., ii. §§ 1 to 8.)
The definitions of the most general sort are called by Aristotle imme-
diate (&ntaa). All others are named mediate (fxecrov %x0VTa), and express
secondary qualities and properties, that is, those not constitutive of
the most general essences of things. The principle of demonstration is
an immediate proposition. That is immediate which has nothing prior
to it. These are both forms of what was afterwards known as Real
Definition, definition of things. Definition explains what a thing is
and the substance of the thing (rod ri tun ical ovaias — and 6 6pt<Tfj.bs
obfflas tis yvaipiffixos). — (An. Post., ii. 3.)
But Aristotle farther distinguishes definitions into two classes. He
who defines declares either what a thing is or what the name signifies
(<5 dpi£6fj.€vos Seiicvvcrtv ^ ti ecrriv fj ri awfj.aivei rotivofia). — (An. Post., ii. 7,
cf . 9.) Those who confine themselves to the explanation of the name
alone do not give a definition of the thing. — (Top., i. 5.) This kind of
definition, corresponding to the later Nominal Definition, Aristotle also
calls \6yos bvopurw^.—^Tbid. , 8, 9, 10.) The former, or Real Defini-
LOGICAL DEFINITION. 211
tion, has been called '6pos irpay^arciSSrjs, ovatceSris (essentialis). To this it
should be added that Aristotle regards that definition as alone of im-
portance which unites the knowledge of the cause or origin of a thing
with that of the essence. These are not in truth really separable. In
knowing what a thing essentially is, we do this only through knowing
how it is or has arisen. And that alone which is real has essence. —
(Cf. Alexander Aphrodisienis, Pacius, Waitz, Franck, in An. Post., loc.
cit. See also Ueberweg, Logic, 168.)
Aristotle's ultimate appeal in order to get the definition of the real is
observation and generalisation. What is magnanimity, he asks ? And
how am I to know this ? Only by reference to individual instances. I
must observe Achilles, Ajax, Alcibiades. What they have in common
is the quality of not tolerating an injury. But I may look further. I
find Socrates and Lysander. In them I find an indifference equally to
good and to bad fortune. If I find a resembling feature in those two
qualities, I group them as one ; if not, I leave them separate. Observa-
tion of the individual thus precedes classification or the formation of
the essence.
(b) Leibnitz's view of Real Definition is that of an enumeration of the
marks which render the object possible ; of Nominal Definition that
of the marks which enable us to distinguish it from other objects.
The Real Definition would thus proceed on the ground of the non-con-
tradictory character of the marks, and of certain real or assumed
causes, as possibly operating in the phenomenal sphere. Nothing is
possible that is contradictory, and further nothing is possible that is
beyond the range of existing causes, whether known or unknown.
But this latter test is quite too vague to be of any help. The former,
or non- contradictory test, is definite enough.
(c) Mill makes a strange medley of the whole subject of Definition.
(1.) He broadly lays down the doctrine, that the relation expressed
by propositions is between two matters of fact, not between two
names.
(2.) He holds that all Definitions strictly refer to names and not
to things.
(3.) He holds at the same time that Definitions, though only of
names, are to be founded on a knowledge of the things indicated by
the names.1
In the first place, as a Definition is a proposition it can refer only
to matters of fact, not to names. In the second place, if there be a
knowledge of things grounding the application of the names, and if
definition refers only to names, then our knowledge of things must
be apart from definition or wholly indefinite, and, therefore, useless.
§ 265. Logical Definition, in its strictest and best form, con-
sists of the Proximate Genus, and the Proximate Constitutive
Difference, of the Species which is to be defined. The
proximate genus ought to be given in the interest of the
greatest precision in the ascending scale ; the proximate
1 Logic, i. 160 et seq.; ii. 216 et seq. Cf. Ueberwig, Logic, p. 171, note.
212 INSTITUTES OF LOGIC.
difference ought to be given in the interest of the most pre-
cise discrimination of the species from other species co-
ordinate with it under the common genus.
(a) Every predicate of a thing is either a convertible or non-conver-
tible attribute. If the attribute is convertible with the subject, the
attribute is either a definition or a property, — definition if it expresses
the essence of the thing, property if it does not. If the attribute
makes part of the attributes comprised in the definition, it is either
genus or difference of the subject, since definition is always composed
of genus and difference. — {Top., i. 8.)
(6) Definition as applied to the lowest species or to the individual
may take any essential or constitutive property, that is, attribute
convertible with the subject. Thus we may define man as a risible
animal; horse as a neighing animal.
§ 266. To illustrate this point, Definition, logical defini-
tion, implies two things, first, the statement of the class, or
proximate genus to which an object belongs ; and secondly,
the distinguishing feature or character by which it is marked
off from other objects of the same class — e.g., the Magnet
or Loadstone would be defined, an iron-ore having attraction for
iron. Here iron-ore is the class or genus to which magnet
belongs, — it is also the proximate class or genus, — for it is
that under which it immediately stands, there being no inter-
mediate class between magnet and iron-ore. Having attraction
for iron is the distinguishing feature of magnet, its differentia,
because this is the feature which marks it off from other
kinds of iron-ore. In the same way we define the notion of
responsibility by the notions of free intelligence. Responsibility,
that is, involves intelligence as its genus or class, it involves
also freedom ; for a will to be responsible must not only be
illumined by knowledge, but free to choose between alter-
natives.
Thus we may define triangle as a surface contained or
bounded by three straight lines. Here surface or superficial fig-
ure is the proximate genus ; figure is the more remote. But
surface is more precise, as excluding depth. Surface, however,
takes in circle, square, parallelogram, &c. Triangle is not all
surface; it is only that which is terminated by three lines (differ-
ence), and by three right lines [proximate difference).
§ 267. Definition is thus seen to be a powerful means
of rendering our thoughts clear, of enabling us precisely
to know what we mean in the use of words. (1.) The
LAWS OF DEFINITION. 213
first main caution or rule about Definition is that the defin-
ing clause should not be wider or narrower than the sub-
ject defined, as Aristotle puts it, ovre ttXclov irpoo-KciTat., ovrc
a-rroXeiTrei oi&ev.1 A Definition to be accurate and adequate,
i.e., to be a correct definition, must thus be a convertible pro-
position. Or, the defining clause must be capable of being
put exactly in the place of the thing defined, and of nothing
else. Thus if the definition of Magnet be correct, we must
be able to say, an iron-ore having attraction for iron is a
Magnet. Or, common salt is chloride of sodium. If this be a
correct definition, then it is true that chloride of sodium is com-
mon salt. Suppose we were to define literature as composition
in words, we might test this definition by wheeling it round,
and saying, all composition in words is literature. In this case
we should at once see the inadequacy of the definition, for
we should hardly include under literature a testamentary
document or an Act of Parliament, or a newspaper advertise-
ment, or the local correspondent's paragraph, though these
are all composition in words. So if we were to say, a bird is a
creature that flies in the air, we should take in too much, for
so do butterflies and midges. The test or rule, therefore, of
a sound logical definition is, that the thing defined and the
defining clause are mutually convertible. This is a most
useful practical test in all matters requiring accuracy and
precision of thought. The defining proposition is a propositio
integra ; or, as Aristotle long ago put it, a definition is a
simply or strictly convertible proposition.
§ 268. (2.) We should not seek to define through negative
or merely disjunctive attributes. In this case we do not unfold
what we know or conceive, but what we do not. When we
say of a (supposed) concept or object that it is not so and so,
we do not tell what it is, or what the term positively stands
for in our thought. In the same way, if we say the object I
speak of is either this or that or the other, we fail equally
in defining. There is no proper definition which does not
specify positive attribute. The negative expression may,
however, be useful in clearing the way for a definite or
positive statement.
This caution about negative terms applies fully to a con-
cept taken by itself; but if we consider a concept in relation
1 An. Post., ii. 13.
214 INSTITUTES OF LOGIC.
to another which we already know, and whose attributes we
specify, we may explain, even classify, if not define, by
negation.1 Thus we can give knowledge and classify
scientifically organised and non- organised, vertebrate and in-
vertebrate, phanerogamic and cryptogamic, that is, flowering and
flowerless plants, rectilinear and not-rectilinear. So in regard
to the terms finite and infinite, or non-finite; here knowing
what the finite is, or at least knowing certain positive attri-
butes of it, we can in a way, or negatively, know what that
is which is conceived as devoid of those attributes. So with
personal and impersonal, relative and absolute.
§ 269. (3.) There should be no circle in the proposed Defini-
tion, or what is contained in the clause defined should not be
repeated in the clause defining. As the one clause is thus
defined through the other, we have what is called Diallelon
(8i' dAAi^W), or " circulus in definiendo." Thus to say that
law is a lawful command, or that plant is an organised being
possessing vegetable life, or life is a vitalising power, is to define
in a circle. There is here no explication of the subject de-
fined. " Concealed circular definitions are of very frequent
occurrence when they are at the same time mediate or remote ;
for we are very apt to allow ourselves to be deceived by the
difference of expression, and fancy that we have declared
a notion when we have only changed the language." 2
§ 270. Other rules that the definition should be precise in
terms, perspicuous and direct, that is, not ambiguous, figura-
tive, or metaphorical, are cautions mainly regarding the use
of words, in so far as this may aid or hinder us in attaining
clearness. The readiness with which people are impressed
by figurative and metaphorical words, when the object re-
quires direct and unambiguous thinking, is a proof of how far
the average culture of intelligence is, in our so-called civilisa-
tion, below the normal standard.
§ 271. Description is usually made up of what are known
as Common Accidents, that is, attributes which distinguish
the object or species from others that come under the same
general class. It is in fact a characterisation of the object,
through comprehension, or specifying its marks. Description
refers chiefly to the characteristics of individuals, as each the
sum of its own marks. The laws of Description fall to be
1 Cf. Hamilton, Logic, L. xxiv. 2 Ibid.
LIMIT OF DEFINITION. 215
treated of under the Science of Literary Criticism, or Khetoric.
It will be found, however, as a general rule, that the best
masters of description in verse or prose, follow consciously
or unconsciously certain very definite rules, which are quite
capable of being specified. First among these is the principle
of general picturing or outline, and then the gradual filling in of
characteristic features with a view to the unity of real pres-
ence. Even the most picturesque description never loses
sight of, far less violates, those definite laws of imaginative
construction. Take Scott's ballad of Rosabelle, follow it,
note the commencement, and watch the gradual evolution of
the picture, and this will be found to be true : —
"O'er Roslin all that dreary night,
A wondrous blaze was seen to gleam ;
'Twas broader than the watch-fire's light,
And redder than the bright moonbeam.
It glared on Roslin's castled rock,
It ruddied all the copse- wood glen ;
'Twas seen from Dry den's groves of oak,
And seen from caverned Hawthornden.
Seemed all on fire that chapel proud,
Where Roslin's chiefs uncoffined lie,
Each Baron, for a sable shroud,
Sheathed in his iron panoply.
Seemed all on fire within, around,
Deep sacristy and altar's pale ;
Shone every pillar, foliage-bound,
And glimmered all the dead men's mail."
§ 272. The limit of Definition is met with at the simple
idea, that is, a concept which does not contain a plurality
of attributes, as time, extension, being. Here there is no
higher genus.
At the same time we must not suppose that such notions
are not distinguishable from other notions. But in order to
this they must be given in intuition. This readily founds
a judgment of Difference, though the grounds of it are not
always expressible in terms. Logic carries us to the thresh-
old of the real, but is there arrested.
No form of words in which oral Definition or even Descrip-
tion can be couched is adequate to all the objects of the
senses. The intuition or presentation of the quality is here
216 INSTITUTES OF LOGIC.
indispensable, and it is the mode of conveying the clearest
and most distinct knowledge ; omnis inluitiva notitia est de-
finitio. We are thus enabled actually to experience the per-
ception or sensation. This holds of colours, as red, blue,
yellow; of light, brightness, and darkness; of tastes, odours,
sounds, &c. — indeed of nearly every sensation and percept.
§ 273. All Division supposes a whole of some sort, and.
we must distinguish simple Partition (d7roptfyo7cris), real or
ideal, from Division Proper (Siatpco-is). In the former case
we sunder the whole, generally individual, into its con-
stituent parts, as when we divide a tree into root, trunk,
branch, leaf, or such elements as make up the whole. We
may do this really or ideally only.
Logical Division, on the other hand, deals only with a uni-
versal, that is, where there is a plurality of objects or classes
contained under the concept. And it draws out or specifies
the classes thus contained. The tree, logically divided, would
give, say, deciduous and non-deciduous, and these again oak and
pine. In the case of simple partition, the name of the whole
is not predicable of each of the parts. Tree is not predicable
of root, or trunk, &c. In the case of logical division, it is so
predicable. Tree is predicable of deciduous and non- deciduous,
of pine and oak.
§ 274. As Definition refers to the comprehension of a notion,
and serves to make the meaning clear, so Division refers to
the extension of a notion, and serves to make our meaning
distinct. A notion is clear when I can distinguish it as a
whole from other notions ; a notion is distinct when I can
enumerate or specify the sub-notions or classes contained
under it. Division draws out these.
§ 275. In Division you will find that we come to a point or
object which cannot be further divided. This is the individual
{a.TOfxo<s, individuum) — i.e., literally what is indivisible, or that
notion or name which can be predicated only of one subject,
not of a plurality. The individual cannot be logically divided,
because it contains no species under it. Glasgow cannot be
logically divided, for it contains no lesser Glasgows, no
classes under it. This or that house cannot be divided, for
it is one, logically one. It is only the universal which you
can divide. You may enumerate the parts physical or other
of which this city is composed, the parts of which this tree
DIVISION. 217
is composed ; you may describe each, but you cannot logi-
cally divide either.
§ 276. Logical division cannot proceed until a principle of
division is selected from the whole. This may be either one
of the constitutive features of the concept, or it may be the
relation of the concept to some end or aim which we select or
have in view. The law of Logical Division is strictly that
of Non-contradiction. Starting from a given attribute, we
divide into the classes under it, through its opposite or con-
tradictory. Thus, taking animate, we fix on sentiency, and
divide into the sentient and the non-sentient. What are the
non-sentient under the genus, or whether they actually are
at all, is to be determined, not by the logical law, but by
experience. Still, the ground of exclusion lies there in the
element of opposition or contradiction ; and but for this no
progress were possible. " Contradictio est mensura omnis
oppositionis." x
We may divide plants into flowering (Phanerogamic) and
non-flowering (Cryptogamic). The latter we may again sub-
divide, according to subordinate differences, into ferns,
mosses, lichens, fungi, algce, &c. But what these are, or
how many, is not determinable by any law of pure thinking.
Take what is known as Porphyry's tree : —
Substance.
I
Corporeal
(Body)
Incorporeal
Spirit
(Angels, Souls, &c.)
1
Animate
(Animate)
1
1
Inanimate
(Water, Stones, Minerals, &c.)
1
1
Sentient
(Animal)
1
1.
Insentient
(Plant)
1
J
Rational Irrational
(Man) (Brute).
I
Plato, Socrates, Paul, Peter,2
John, Richard, &c.
1 Duncan, Inst. Log., L. i., xiii. 4. 2 Eisagoge, ii. 23.
218 INSTITUTES OF LOGIC.
Again, heather is of the genus flowering plant, and under
Octandria — i.e., it is a plant bearing flowers with eight stamens,
and, under this class, with one pistil. Under this genus (Mono-
gynia), it is but a co-ordinate species. As a genus, Erica,
it has certain marks, — calyx inferior, four-parted, persistent,
corolla monopetalous, &c. Under this we have various differ-
ences, which mark out the species, — as anthers with two simple
bristles at the base, &c. This gives the cross - leaved heath
(Erica tetralix). Anthers with two serrated appendages at base,
&c, gives the fine-leaved heath [Erica cinered) ; and finally,
through difference of leaf and capsule, we have the common
heather [Erica vulgaris, Calluna vulgaris).
§ 277. In a concept, this or that feature may be fixed on
for the principle of Division. Taking the corolla of a plant,
and looking to the tube, it may be long or short, as in prim-
rose, bell-flower. The throat may be open or closed, as in
digitalis, snap-dragon. The limb may be erect or spreading,
as in hound 's-tongue, primrose} Book I may divide according
to its subject, its size, its antiquity. All are equally valid divi-
sions, provided I preserve the feature or principle from which
I start. Of course no principle of Division is of any real
use which is not a constitutive attribute of the whole.
§ 278. The rules of Division are specially as follow : —
(1.) There ought to be a regulative principle in the Divi-
sion. (Divisio ne careat fundamento.)
(2.) There should be but one principle in one Division.
(3.) The principle should be an actual and constitutive
attribute of the whole to be divided.
(4.) No predicate in the division must, per se, exhaust the
subject.
(5.) The dividing members must together exhaust, and
only exhaust, the subject.
(6.) The divisive members must be mutually exclusive, that
is, there must be no cross-division.
(7.) There should be no leap in the division, but a descent
from immediately higher to immediately lower
classes.2
Thus, for example, to illustrate the main rules, take the
notion figure. I wish to enumerate its species. To do
i Cf. Hoblyn, Botany, p. 43.
2 Cf. Hamilton, Logic, L. xxiv.
ILLUSTRATIONS OF DIVISION. 219
this, I must find a principle of Division. Here the natural
principle is straight or curved line. Taking this, I first divide
figure into rectilinear and curvilinear, i.e., straight - lined
figure and curved-line figure. But I have not yet made my
notion distinct enough. What are the sub-classes under
rectilinear figure? According to the number of sides —
triangle and square. Under curvilinear figure, I draw out
circle and ellipse. My division of figure is now distinct. I
know what object or classes of objects it denotes or contains
in its extension. And observe that this division proceeds
in a regular order from the widest notion to the narrower
ones, from the Genus Summum or highest class to the Species.
Figure is widest or highest notion ; rectilinear and curvilinear
is the next, narrower ; triangle or square still narrower than
rectilinear; circle or ellipse narrower than curvilinear. This
is an important principle in Division, viz., that of preserv-
ing due subordination, making no leaps in the Division
over intermediate classes. If I had divided figure into triangle
and circle, I should have made a bad division, for I should
have omitted the intermediate classes.
§ 279. One most important thing in Logical Division is to
have a principle of Division, and to keep by it. Otherwise
the whole division will get into confusion. Suppose, for
example, I were to divide the notion man or mankind into
Englishmen, Frenchmen, Scotsmen, Episcopalians, Roman Cath-
olics, Presbyterians. This would be a bad division ; for the
members of the division are not exclusive of each other. An
Englishman may be an Episcopalian, a Frenchman may be a
Eoman Catholic, and a Scotsman may be a Presbyterian.
To avoid this, we must keep by one principle of Division ;
state it distinctly. We may divide hook according to its sub-
ject,— historical, philosophical, scientific, — according to its lan-
guage,— French, English, Latin, Greek, — and so on. But we
must not mix up those principles of Division ; for the parts of
the division as inclusive, would be inconsistent with the
nature and process of division itself. This fault is what in
Logic is called a Cross Division.
PAET III.
OF JUDGMENT.
CHAPTER XVIII.
THE NATURE OP JUDGMENT COMPREHENSIVE AND EXTENSIVE.
§ 280. Every act of consciousness is a judgment, or judg-
ment is involved in every mental act. As I am conscious,
I am conscious of some thing or object — some definite
thing, and this I distinguish from another act of conscious-
ness which had for object something different from the
present. There is here affirmation, and there is negation.
Consciousness is thus primarily a judgment or affirmation
of existence, — that some thing is. This form of judgment,
the existential, is prior to the judgment which is a form
of comparison. Through the latter process, based on the
former, we grasp resemblances in several things, and group
them into classes. We may then compare the classes, or the
concepts of the classes, i.e., the attribute or sum of attributes
which make up each concept, and judge them to agree or not,
to be technically congruent or conflictive. We may compare
the individual as a presentation with the concept, and include
or exclude it as a member or not of the class. This would
be logical judgment. Here we look, in the first place, merely
to the congruence of attributes ; or we look, in the second
place, to the relative coincidences of objects as members of
EXISTENTIAL JUDGMENT. 221
the class. We may say — This thing I see is now and here.
I feel cold. These are existential judgments, and have a
reference to a definite time and definite reality. I might say,
the river runs, man is organised, and the three angles of a
triangle are equal to two right angles. These are logical judg-
ments. I do not require the actual existence of the objects,
or imply them. I merely state a congruence or coincidence
between two concepts, or a concept and its property.
(a) This distinction was foreshadowed in the enunciatio apprehensiva
et judicativa of Scotus and Occam. The former referred to the appre-
hension of the relations, say of likeness or equality among sensible or
immediately perceived objects ; the latter, to notions compared by the
intellect. The existential judgment is clearly recognised by Biel, Sup.
Sent. q. 1. Prol.
(6) Mill is pleased to say that to hold both those forms of judgment —
the existential and the logical — is " the very crown of the self-contradic-
tions which we have found to be sown so thickly in Sir W. Hamilton's
speculations." The crown here of the sown contradictions is evidently
a vegetable product. But how the self-destroying contradictions have
had vitality to grow even a crown, we are not told. The existential judg-
ment is, it appears, not a comparison of concepts or of an individual and
a concept. The self-contradiction only emerges as a spectral illusion,
because Mill will insist that Hamilton, in his Logic, is not speaking of
the character of logical judgment, of which he is there bound to speak.
Besides, Hamilton would probably have told Mill that, in the existential
judgment — this is here, that is there, I am conscious of heat or cold —
we do compare and contrast an individual and a concept, though we
at the same time in such an act go beyond this, and relate them to a
given time and space. He would probably have added that, while we
do not get the judgment / am conscious, from a comparison of concepts,
self and being, the consciousness of these is there all the same ; and
that the logical judgment is reflectively reached in the moment in which
the real judgment is given. They are in fact implicative ; and were
there any logical confliction in the concepts, self and being, there
could be no real judgment or union of them. So far, then, from its being
a crowning contradiction to hold the two together, it would be a
crowning absurdity not to hold them together. Logical judgment is
secondary and reflective ; it presupposes the consciousness in the exis-
tential judgment of the special forms of existence, afterwards to be
reflectively realised as categories, and even of features to be generalised
into classes of objects.
§ 281. It is clear from this that judgment, that is, logical
judgment, in no way implies belief in the reality or existence
of the subject and predicate as facts of experience, or in the
truth of the relation of congruence or confliction expressed in
the judgment. We are here dealing with judgment simply
222 INSTITUTES OF LOGIC.
as judgment, or with what is essential to it as an abstract
act, or in its abstract possibility. Its conditions are congru-
ence or confliction of subject and predicate, viewed in com-
prehension. Judgment thus considered obviously does not
involve belief at all in the reality corresponding to the judg-
ment. We cannot disbelieve, unless we have a judgment
before us ; but we may have a judgment before us, and neither
believe nor disbelieve in the truth of it as a statement of
experience. That the notion of man agrees with the notion
of organised, or that man is organised, I can quite well assert,
without believing or disbelieving that there are men in the
world at all. That equilateral is equiangular, I can quite
well assert, though I know no objects of experience corre-
sponding to the one or the other. So I can say that lying is
dishonourable, though I may know no one who is telling a lie
in the world at the present moment. That the Dodo is so
and so characterised, I can assert, though I suspend my belief
as to whether the species is extinct or not. As Occam said :
I may know that a stone is not an ass, though I do not know
that there is either stone or ass at this moment in the world.
(a) Mill challenges Hamilton's definition of judgment, on the ground
that Belief, meaning belief in the objective reality of the judgment or
thing judged of, is essential to a judgment. " The recognition of it [the
judgment] as true is not only an essential part, but the essential element
of it as a judgment ; leave that out, and there remains a mere play of
thought in which no judgment is passed. Every judgment consists in
judging something to be true. The very meaning of a judgment is
something which is capable of being believed or disbelieved ; which
can be true or false ; to which it is possible to say yes or no." — (Exami-
nation, p. 348.) What has been already said disposes of any point
in this criticism ; but it may be added that truth is here ambiguously,
or rather abusively, used for truth of fact. But there is truth of con-
sistency as well, and this is, in the first place, simply in our concepts
and judgments ; and unless this be as a condition, all our judgments
about matters of fact are futile, not judgments at all. Further, " the
recognition of the judgment as true " can hardly be essential to it, if
there be false judgments, as there happen to be ; and if also, as Mill
tells us, a judgment is that which is capable of being true or false.
If a judgment is capable of this, it must be capable of being regarded
as a judgment, ere we either believe or disbelieve it. It is nothing to
Mill that in this criticism of Hamilton he flatly contradicts his own
theory of belief as given in his Logic. — (See i. p. 96, 8th edition.) Belief
in the reality of the things judged is not essential to judgment, if it be
simply possible as it is to form an ideal combination of terms. The
centaur is an animal with the body of a horse and the head of a man.
NATURE OF JUDGMENT. 223
Does any one imagine that if we do not believe in centaurs, that this
statement is therefore not a judgment ?
(6) Mill objects and asks : " Do we never judge or assert anything but
our mere notions of things ? Do we not make judgments and assert
propositions respecting actual things?" — (Examination, p. 346.) In
turn, I ask do we judge or assert anything about things, which we do
not know, or of which we have no notions ? What are actual things for
us but the things as known and conceived by us ? How can we assert
anything about an actual thing, unless we have a notion of the thing
and of that which we assert of it ? And does not this judging through
our conception of things yield the variety in our judgment of things ?
Would it not be a wonderful faculty of judging which could determine
about actual things, not known or conceived by us ? This would be
getting at things in themselves with a wonderful leap ; only what we
overleap is our knowledge of them. But if we cannot compare the naked
actual things, what about them can we compare except our notions, or
symbols of the things ? Does Mill contend that we compare words
minus notions or meaning, or what ?
§ 282. In a Judgment there is obviously a plurality of
thoughts and terms. But as Aristotle long ago pointed out,
there is not necessarily any judgment in such a bare plurality.
We may think of whiteness and wall in succession ; of a, b, and
c ; but unless we join them through a definite relation of is or
is not, we have no judgment. Nay, Aristotle goes further. We
may even have sentences, in which words are joined together,
which are yet not properly judgments. " I deprecate," " I
wish," M I pray ; " in each case I express myself in a sentence,
but I do not properly judge. I do not definitely assert or
deny one thing or another. As Albertus Magnus puts it :
" Nee deprecativa nee optativa, nee infinitiva cum vero vel
falso significant, sed quando est indicativa. . . Oratio per-
fecta dividitur. Non enim omnis oratio enuntiatio est, sed
ilia sola in qua indicative est significatum." 1 Wish and
prayer, threat and command, may indicate convictions on the
part of the person using them ; but these are implicit. There is
as yet no form of judgment as to the matter of them. All the
judgment that even approaches explicitness is the assertion of
the act or state of consciousness in which they are realised.
(a) The first enunciation, in as far as it makes one expression, is, ac-
cording to Aristotle, affirmation, then negation. Affirmation (Kardcpao-is)
is the enunciation of one thing of another thing. Negation (air6<t>a<ris)
is the enunciation of one thing disjoined from another thing. In other
words, affirmation is that which relates one thing to another, negation
1 Periherm, ii. 2, p. 243 A, and i. p. 258 A. Cf. Prantl, iii. p. 104.
224 INSTITUTES OF LOGIC.
that which disjoins one thing from another — (De Int., v. vi.) Reference
and removal are obviously at the root of the Aristotelic conception here,
and very naturally. These are spatial relations, transferred to the
mental act.
(6) Both affirmation and negation belong essentially to the nature
of the act of enunciation. The negative particle is an expression of
the characteristic difference of the mental act of negation, not a mere
accident of expression ; and the negation belongs essentially to the
copula, not to the predicate. Affirmation and negation indicate the
quality of the enunciation or judgment.
(c) For \6yos airo<pavTiic6s, a.ir6<pav<ns we have oratio enunciativa,
enunciatio (Boethius) ; oratio indicativa (Petrus Hispanus) ; effatum
(Sergius) ; proloquhi7n (Varro) ; enunciatum (Cicero) ; propoxitio.
'hir6<pav(m and irpdrao-jj are, according to the usage of Aristotle, to be
distinguished. The former is the general word ; when used as the
premiss of a syllogism, it is called irpiraa-is, proposition. To propose,
irporeiveiv, is to lay down the propositions of a syllogism.
(d) Verbs by themselves are simply nouns. They do not signify
whether a thing is or is not. Neither "to be" nor "not to be"
is a sign of a thing; nor is "being," for that is nothing. They
signify a certain composition, which is unintelligible apart from the
constituent members. Hegel's dictum "Being is nothing," is thus
anticipated by Aristotle, but in a very different sense. Being (rb thai)
is nothing according to Aristotle, unless as a connective of one thing
with another. — (Waitz, in De. Int., c. iii. 1.)
§ 283. In a judgment there is, first of all, to be considered
the precise nature of the copula, is or is not. This may
mean (1.) that the subject contains in it an attribute, as
the sun shines, man is responsible, birds fly.
(2.) That the subject belongs to a class of which it forms
a part, as some men are European, plant is organised, a
good orator is impressive, the cow is ruminant.
In the former case the judgment is in Comprehension. The
subject contains in it the attribute specified at least. In
the latter case, the judgment is in Extension. The subject
is contained under the predicate as a part at least ; other
things may be also contained. This class or object is at
least a portion of a possibly wider class of objects. This
relation of subject and predicate is sometimes expressed as
that the subject is the containing whole (in comprehension),
and that the predicate is the containing whole (in extension),
under which the subject is a part.1
(3.) The copula may indicate an exact equivalence between
subject and predicate, — as Homer was the author of the Iliad.
1 Cf. Hamilton, Logic, L. xiii.
COMPREHENSIVE JUDGMENT. 225
Newton was the author of the Principia. All equilateral is
all equiangular. All the planets are some stars. Some stars
are all the planets. In this case we have Equivalent or Sub-
stitutive propositions.
§ 284. Hamilton holds that the comprehensive proposition
is the first or primary form, and that tins proposition always
implies a corresponding proposition in extension. He does
not maintain that these two kinds of propositions can be
separated, and set apart absolutely, whether in thought or in
fact. But he holds that they are two modes of looking at
the same matter, that every proposition may be expressed
in the one way and in the other, and that we do actually
judge sometimes in the one way and sometimes the other.
When, for example, we say, man is two-legged, we may mean
that the notion man contains as one of its characters the
attribute two-legged. This is a judgment in comprehension.
Obviously, the comprehensive proposition implies an exten-
sive proposition ; for if the subject-notion be an individual
and have an attribute, this attribute is the property of at
least one individual, and ideally of a whole possible class,
and if the subject-notion be a class (or plurality of objects),
extension is equally implied. Conversely, the extensive pro-
position implies a comprehensive, for we cannot have a class
or plurality of objects grouped together unless on the ground
of a common attribute. Otherwise we should fall into the
arbitrary and meaningless.
§ 285. In the ordinary Logic, the predicate had hitherto
been regarded as exclusively the whole, and the subject as
a part of this whole or predicate. The river runs had been
understood in the sense that the river is one or a part of the
class or whole running things. There are other running
things. Man runs and the horse runs. The river is only
one of them. But Hamilton would urge that the subject is
a whole as much as the predicate, and it too may contain the
predicate as a part. Thus in the river runs, the river or
subject may be regarded as containing as a part of its con-
cept the single attribute running ; but this is only one of
its many attributes, and running is but a part of its whole
concept. Here the subject is the whole, and contains in it
the attribute as a part. This, too, is a logical whole ; it is
the relation of whole and part in thought, as much as the
226 INSTITUTES OF LOGIC.
relation in extension of the subject to the predicate as the
whole. Why, then, should Logic neglect this? Every
proposition and every reasoning is, in Hamilton's view,
affected by this distinction, for we may read each proposition,
each reasoning in turn, in the whole of Comprehension and in
the whole of Extension. Nay, the reading in Comprehension
of the subject as whole is the primary and natural reading
of a proposition ; the reading in Extension is only secondary
and derivative, being founded on the Comprehension. The
statement made by Mill that Hamilton separated these forms,
or held the extensive reading to be possible by itself, or real
apart from the implied comprehensive reading, is merely one
of his innumerable misrepresentations of plain and explicit
statement. Comprehension is essential to extension ; exten-
sion is inseparable from comprehension ; where the one exists
the other exists ; yet they express different aspects of the
same matter, different relations in the mind, and so yield
different kinds of reasoning. Hamilton expresses the distinc-
tion in the propositions of extension and comprehension, by
saying that the copula is means in the former is contained
under, whereas in the latter it means comprehends or contains
in it. Thus God is merciful, means in extension is contained
under the notion (or class) merciful; in Comprehension it
means, God comprehends in it the attribute (notion) merciful.
(a) Mill objects to this doctrine that " these two supposed meanings
of the proposition are not two matters of fact or thought reciprocally
inferrible from one another, but one and the same fact written in dif-
ferent ways ; that the supposed meaning in Extension is not a meaning
at all, until interpreted by the meaning in Comprehension ; that all
concepts and general names which enter into propositions require to be
construed in Comprehension, and that their comprehension is the whole
of their meaning." — {Examination, p. 362.) "'All men' and 'the
class man ' are expressions which point to nothing but attributes ;
they cannot be interpreted except in comprehension." There is little
in this that has any relevancy as a counter-statement to Hamilton's
doctrine. To suppose so is a mere mistake. The only thing about
it that calls for notice is the extravagance of the assertions that
extension is not inferrible from comprehension, and that there is
"meaning" in comprehension alone. If by "meaning" Mill means
the attributes of the notion, it is self-evident that meaning belongs
to comprehension alone. But does "the class man" mean "no-
thing but attributes " ? Does it not indicate or imply individuals
with attributes ? Does not any attribute imply some subject of inher-
ence ? And if so, is there not both room and need for the extensive
mill's criticism. 227
proposition ? And is not this further or other meaning or implicate of
the attribute necessarily involved in its very predication ? And if so
involved, is it not a new form of judgment inferrible from the other?
Hamilton says a judgment can be read both in Comprehension and
in Extension — God is merciful means either God is contained under mer-
ciful, that is, under the notion merciful, or class of merciful beings ; or
God comprehends merciful, that is, the notion God contains in it the
attribute merciful.
Mill says no. When we say God is merciful, we speak not of the
notion God, but the Being God. In Comprehension it means, "this
being has the attribute signified by the word merciful. " In Extension
it means, ' ' The Being, God, is either the only being, or one of the
Beings forming the class merciful. The difference is that the second
construction introduces the idea of other possible mercifid beings, an
idea not suggested by the first construction. This suggestion gives
rise to the idea of a class merciful, and of God as a member of that
class ; notions which are not present to the mind at all when it simply
assents to the proposition that God is merciful. " — (Examination, p. 432. )
Has Mill in these statements really said anything that in the least
degree controverts Hamilton's interpretation of propositions in Com-
prehension and Extension ? Nay, has he not fully admitted, even in
words, that very construction which Hamilton puts upon them? In
Mill's view we can have the comprehensive meaning of the proposition in
the mind without having the extensive. We can think God is merciful,
has the attribute, and not think at the same time that God is one
of the class mercifid. Does he not see that the moment God is thought
to possess the attribute, other beings too, at least ideal, may ; and
that thus there is necessarily implied and constituted a class through
the possible application of the attribute ? Worse than all, however,
is the supposition, at once groundless and irrelevant, that we are
not speaking of the notion of God, but of the Being God. Pray,
how can we speak of the Being except through the notion of the
Being God ? How can we with a meaning speak of anything except
through its notion, or as we have the notion of it in our mind ? Is it
words we are speaking of merely ? mere blank unintelligibility ? or
are we speaking of things in themselves which are quite superior to
our notions?
But his whole criticism of this point is a mass of contradiction.
(1.) On the previous page (p. 432) the objection is taken that the judg-
ments in Comprehension and in Extension are totally distinct ; that
the latter introduces what was not at all in the mind while making the
former.
(2.) On page 433, these are affirmed to be " one and the same assertion
in slightly different words." Here he contradicts No. 1.
(3.) The judgment in Comprehension warrants by immediate infer-
ence a judgment respecting Extension, but this judgment respecting
Extension is in Comprehension. In other words, there are two differ-
ent judgments in the case, and yet only one in kind.
(4.) But how does he show both in Comprehension? "A is part of
class B. " " The concept A comprehends the attribute of being in-
228 INSTITUTES OF LOGIC.
eluded in the class B" — or "Man is mortal." "Man comprehends
the attribute of being included in the class mortal," or rather as with
no class predicate, "Man comprehends the attribute of being included
in the attribute mortal," which is neither sense nor truth ; for man is
not included in the attribute, mortal. The attribute may exist with-
out including man, though he includes the attribute, and is included
under the class, which is a very different point. But apart from its
falsity, what a luminous and scientific statement have we here ! ' ' Gold
is in the class mineral. " "Gold includes the attribute of being included
in the class mineral. " Pray, what is the attribute in addition to the
attributes of the class mineral which gold includes or comprehends ?
It includes the attribute of being included ? Is this in addition to
being one of the class mineral, or what ?
(b) Mill admits that the relation of whole and part applies to judgments
in Extension (in affirmative propositions). "The object or class of ob-
jects denoted by the subject is a part (when it is not the whole) of the
class of objects denoted by the predicate. " This holds, too, he admits,
in analytical judgments in comprehension. But in synthetical judg-
ments in comprehension, — " the relation between the two sets of attri-
butes is not a relation of Whole and Part, but a relation of Coexist-
ence." Hoofed animals are ruminant. Supposing this synthetic ru-
minant coexists with hoofed animals, does not the judgment in the
synthetic act join ruminant to the subject hoofed-animal, and make it
a part of my concept of hoofed-animal ? What is the sense of talking
of coexistence except for the purpose of a semblance of difference ? Did
ruminant coexist in my mind with hoofed-animal, before I knew that
hoofed-animal was ruminant? If so, did this coexistence constitute
a judgment? Surely not. At length I knew that ruminant was an
attribute of hoofed-animal, or I felt myself justified in so alleging.
Then I judged or joined them, and I expressed this in a proposition.
But is this any longer mere coexistence ? Is not ruminant now a part
of the whole subject hoofed-animal ? Is this not as much a relation of
whole and part as any case of Extension ? The very act of synthesis
abolishes mere coexistence, makes a union, constitutes whole and part.
(c) "All judgments are really judgments in comprehension, except
where both the terms are proper names. We never really predicate
anything but attributes, though, in the usage of language, we commonly
predicate them by means of words, which are names of concrete ob-
jects." "When I say the sky is blue, my meaning and my whole
meaning is that the sky has that particular colour. I am not thinking
of the class of blue as regards extension at all. I am not caring nor
necessarily knowing what blue things there are, or if there is any blue
thing except the sky. I am thinking only of the sensation of blue,
and am judging that the sky produces this sensation in my sensitive
faculty, or (to express the meaning in technical language) that the
quality answering to the sensation of blue or the power of exciting
the sensation of blue, is an attribute of the sky." "So in all oxen
ruminate. I have nothing to do with the predicate considered in
extension. I may know or be ignorant that there are other rumin-
ating animals besides oxen. The comprehension of the predicate, the
mill's criticism. 229
attribute or set of attributes signified by it, are all that I have in my
mind." — (Examination, pp. 423, 424.)
The subject, too, is an attribute or sum of attributes only. All
oxen ruminate. There is no image of all oxen. I do not know all of
them, and I am not thinking even of all those I do know. All oxen
means "not particular animals, but the objects, whatever they may
be, that have the attributes by which oxen are recognised, and which
compose the notion of an ox." "Wherever these attributes shall be
found, there, as I judge, the attribute of ruminating will be found
also." "This meaning supposes subjects, but merely as all attributes
suppose them." Or if, as Mill admits later, "attributes, even, if they
come to be conceived, cannot be conceived in a detached state, but are
always (as may be said by an adaptation of the Hamiltonian phrase-
ology) thought through objects of some sort." — (Examination, p. 426.)
First, these statements are absolutely contradictory. It cannot be
true that the subject of a proposition is an attribute alone, or sum of
attributes alone, if every attribute implies a subject. That of which
I speak is a subject with attributes.
Secondly, it is not true that the predicate is only and always an
attribute or sum of attributes. This is the first form of predication,
but it is not the only one. It is not true that when I say the sky is
blue, I express only an individual fact. This might have been the case
at the point of the earliest abstraction. But now blue is already a
general concept or term, "applicable, or possibly applicable, to many
objects. My first conscious impression of the sky as blue could not
have been put in words. I could not have said blue, unless I already
had assigned a meaning to it in thought, as a term indicating an
attribute generalised and thus formerly frequently experienced. Blue
means previous knowledge ; it means not red, ivhite, black, or green.
And all this implies generalisation and discrimination. And when I
now speak of the sky as blue, I discriminate it from other colours, and
thus mean more than merely saying it is blue. In this sense there is
already an implicit attribution of quantity to the predicate.
Thirdly, it is contradictory to say all oxen ruminate, and to say that I
do not know whether all do or whether even some do. It is not neces-
sary that I should know every ox in the sense of having seen every ox
past, present, and to come, much less that I should have in my mind
"the images of all oxen." What an image ! But when I speak of all
oxen, it is necessary that I should have in my mind the equivalent or
representative of all oxen as objects.
If all our ordinary, usually all, judgments are in Comprehension
only, Extension not being thought of, perhaps Mill might have told
us how in that case we can speak with discrimination of all or some ?
When I say oxen ruminate, I express only certain attributes of oxen,
but what of the all ? Has this no meaning ? If it has a meaning, is
this meaning in Extension or not ? When I say, some men are vicious,
— are burglars, — what does the some mean ? Does it mean attribute,
or quantity in Extension? Surely if I can speak with knowledge
of all or some of the subject, I have more in my mind than the mere
attributes of the subject. Mill's theory is utterly inconsistent
230 INSTITUTES OF LOGIC.
with the possibility even of a definite proposition, or even ordinary
statement.
He f urther confounds together as equally ' ' collective, though in
definite aggregates," all oxen and some ruminant. He thus abolishes
the very possibility of a discrimination of universality and particularity
in propositions, by identifying the universal and particular as indiffer-
ently expressions of the same.
Further, though propositions with him are only in Comprehension,
yet logicians were right in admitting only into their logical system
reasoning in Extension. "They did not concern themselves witli pro-
positions or reasonings as they exist in thought, but only as they are
expressed in language." — (Examination, p. 429.) A very philosophical
procedure this. They did not concern themselves with what is ad-
mitted to be the true reality of the proposition or reasoning, what
it is in thought, but with what it is in language, which is not
as it is in thought, not necessarily in thought at all. Whatever
absurdity or inconsistency is to be perpetrated, let it be done if a
position of Hamilton can be contradicted. ' ' The propositions in Ex-
tension being, in this sense, exactly equivalent to the judgments in
Comprehension, served quite as well to ground forms of ratiocination
upon." "They are practically equivalent — that is, so long as the
propositions in words are always time or false, according as the judg-
ments in thought are so." — (Examination, p. 429.) Will any one
explain how it is possible that a judgment in thought can be equivalent
to a proposition in language which has no counterpart in thought ? Or
if the comprehensive judgment is the same with the extensive, while
"the mode of contemplating the fact is different," the act of thought
being not only a distinct act, but an act of a different kind," will
it not be necessary philosophically to vindicate this ere we can accept
the form of reasoning in Extension for form in Comprehension ? Nay,
these things being so, is not Hamilton right in saying that the ordinary
logicians have erred in neglecting reasoning in comprehension, the
primary essential form of reasoning, the reasoning of the very inner
thought, arid instead dealt with reasoning as vulgarly expressed in
ordinary language, without telling us what it really represents ?
§ 286. Determination, that is, fixing or settling, is essential
to judgment, whether it be in Comprehension or Extension.
In the former, where predicate is an attribute, we determine
the subject by the attribute, as — plant has organisation,
man dies, beauty fades. Thus we limit or determine the sub-
ject by the predicate, and exclude it from the opposite or in-
definite class.
In Extension, determination means the setting of a sub-
ject under one definite class, to the exclusion of other classes,
as man is mortal, critics are fallible, insects are short-lived,
dogs are sagacious.
Logical determination is impossible apart from a previous
LOGICAL DETERMINATION. 231
knowledge of the characters of the subject and predicate.
And any determination in regard to actual experience is either
by means of what we already know, and, therefore, secondary,
or in virtue of the first spontaneous acts of intelligence con-
ditioned by what is actually presented to us, and what, therefore,
determines us, rather than we it. There is no determination
by us even possible, apart from the secondary logical process, or
the spontaneous cognition through intuition of objects and
relations, given us to know. We can put nothing into objects
which are either wholly indefinite, or which are not cognised
by us as already furnished with definite relations.
(a) Mill utterly mistakes the meaning of Determination, and this has
helped to lead him astray on this point. He asserts that it means only
' ' our conceiving one of two notions as adding on additional attributes
to the other." Hamilton of course uses no such redundant phrase
in connection with the verb " to determine," or with determina-
tion. And Mill's representation of Hamilton's meaning has really
nothing whatever to do with determination itself. It is a clumsy and
inaccurate way of stating what Hamilton had explained, when Deter-
mination was used "in a particular relation," &c. — viz., the process
of Specification, ' ' when descending from the highest notion, we, step
by step, add on the several characters from which we had abstracted
in our ascent . . . and thus limit or determine more and more the
abstract vagueness or extension of the notion." — (Logic, xi. , iii. p. 94.)
We determine a notion, whether the predicate be an addition to the
subject or not, whenever we make an affirmation. When we say that
the number four, or our notion of it is made up of the units 1, 1, 1, 1
in succession, we have determined our notion, though we have added no
new attribute. And when we say that the conscious act is or exists,
we have determined our subject-notion, though we have added nothing
to it. When we say this colour I perceive is red, we have deter-
mined, because we have restricted the subject we speak of to a definite
class of things : the determination lies in the act of judging, and, as
Hamilton points out, only in that ; for until we have judged congruence
(or confliction), there are only floating, unconnected concepts.
§ 287. Concepts and Judgments, as Hamilton expressly
holds, and constantly repeats, are the results of the same
process, Comparison. Every concept is, in fact, a judgment
fixed and ratified in a sign. In consequence of this acquired
permanence, concepts afford the principal means of all subse-
quent comparisons and judgments. A concept may be viewed
as an implicit or undeveloped judgment ; a judgment as an
explicit or developed concept. He, accordingly, defines judg-
ment, logical judgment, thus : "To judge is to recognise
232 INSTITUTES OF LOGIC.
the relation of congruence or of confliction, in which two
concepts, two individual things, or a concept and an indi-
vidual compared together, stand to each other." x
Congruent concepts are such as are mutually compatible and
representable in the same indivisible act of thought. They
may differ in themselves from each other — as learning and
virtue, beauty and riches, magnanimity and stature; but as
each of these pairs may be easily combined in the notion we
form of one thing or subject, they are congruent. Conflic-
tive notions, again, are those only whose difference is so great
that each involves the negation of the other, as virtue and
vice, beauty and deformity, wealth and poverty." Congruence
and confliction, it should be carefully noted, express a re-
lation of concepts under comprehension, and viewed as
attribute or sum of attributes.3 As attributes, congruent
concepts are said by Hamilton to coincide or coexist to-
gether, in thought, though they are not in themselves
identical, because they form elements of one mental image
or representation. As attributes, conflictive concepts can-
not be united in one representation, either because one im-
mediately negates another — contradictory opposition — that
is, the one abolishes directly what the other establishes ; or
because one mediately negates another — contrary opposition
— that is, when one concept abolishes what the other estab-
lishes through the affirmation of something else. It should
be observed that concepts are not in themselves affirmative
or negative. In so far, however, as two concepts afford the
elements, and, if brought into relation, necessitate the for-
mation of an affirmative and negative proposition, they may
be considered affirmative and negative.4 To give, thus, the
distinction between two concepts simply as congruent, or two
concepts simply as conflictive, and judgment proper, we
have to accentuate the recognition and expression of this
congruence or confliction. We advance, in fact, from the
simple representation or mere conception to the stage of the
is and the is not, as expressing the relation conceived be-
tween the concepts as elements or terms of the judgment.
Thus, for example, we may have the three concepts or
thoughts, water, iron, rusting. These as mere concepts are
i Logic, L. xiii., pp. 225, 226. 2 Logic, L. xii., p. 214.
8 Logic, L. xii., p. 213. 4 Logic, L. xii., pp. 215, 216.
WHAT JUDGMENT SUPPOSES. 233
congruent ; they are capable of being represented in imagi-
nation in one notion, or as the elements of a single notion,
that is, a complex notion. If, however, we proceed beyond
this, and, so to speak, articulate the relation subsisting among
them, we form a judgment, an affirmative judgment, and we
say water rusts iron. In this, of course, we meanwhile pro-
nounce no judgment on the matter of fact, whether this is
truly and really a fact of experience or not. All that we are
supposed to have before us is the material or constituted
concepts in which we find or are supposed to find no incom-
patibility. And the act of judgment is the recognition and
expression of this compatibility.
(b) Mill actually criticises this illustration as if Hamilton had con-
tended that we know or discover the truth or fact that ivater rusts iron,
from comparing merely the concepts or thoughts water, iron, rusting.
The proposition, he holds, expresses a sequence or connection between
the facts, not between our concepts. " If we lived till doomsday, we
should never find the proposition that water rusts iron in our concepts, if
we had not first found it in the outward phenomena. " Did Mill for a
moment seriously imagine that Hamilton, or any sane person, ever held
the converse of what he here states ? or that when Hamilton speaks of
the congruence, he meant to imply that ? But did Mill suppose that
when he substituted the word facts for thoughts, he could possibly deal
with the phenomena water, iron, rusting, per se, or apart from our con-
cepts or thoughts of them ? Yet this must be so, if Hamilton is to be
corrected. What is the fact of water, iron, rusting, apart from our
knowledge or thought of the fact ? When we compare these, present
or absent in sense, what are we comparing but our thoughts or con-
cepts of them ? Even in a real judgment, or judgment about a matter
of fact, it is, after all, our thought, knowledge, or concept of the fact
with which we are dealing, and which we compare in the subject and
predicate of a judgment. Does Mill suppose that we can deal with
facts which are not thought and known facts ? When he further talks
of such a judgment as resulting from "direct remembrance of the
facts," his position is quite as suicidal, unless he can show that remem-
brance of the facts is a thing apart from conception of the facts.
§ 288. Judgment, that is, logical judgment, supposes the
concepts given. It thus supposes them to be in themselves
conceivable, that is, actually concepts, each conceivable by
itself, therefore, not in themselves self- contradictory, not vio-
lating any logical law of conception, and not violating any mate-
rial law of conception. Logically, then, judgment is restricted
to recognising congruence or confliction under the condition
of non-contradiction. What is non-contradictory is logically
234 INSTITUTES OF LOGIC.
congruent ; and hence " all positive and affirmative notions
are congruent, that is, they can, as far as their form is con-
cerned, be thought together ; but whether in reality they can
coexist, that cannot be decided by logical rules." x Hence,
even contrary opposition is not decided on logical grounds,
but on material, on the incompatibilities of intuition, or of
the matter of the concepts. A, B, C, — sitting, standing, lying,
— black, red, blue — are groups of contraries, because we can-
not unite the attributes they represent in one image. But
this we learn from experience. While A and not A — sitting
and not sitting, we can at once, a priori or logically, pro-
nounce to be conflictive, the moment the terms are enounced.
Mediate or contrary opposition (confliction) comes under logical
rule only indirectly. Sitting is incompatible with standing,
blue with white, because perception does not give us and we
cannot represent each pair together, but only in separate
intuitions. But logical law can deal with contrary opposites
the moment they are known to be such, and constituted
into the members of a sphere of opposition. Logical law can
regulate the passage from the one to the other, by affirmation
or by negation.
§ 289. It would seem from this that what attributes are op-
posed mediately or in contrary opposition, must be learned
from experience ; while contradictory opposition may be deter-
mined by simple logical law. I must learn, for example,
that sitting, standing, lying, walking, are conflictive concepts
from experience wholly ; while sitting and not-sitting, standing
and not-standing, are known a priori, or from the concept
itself, to be conflictive. The congruence or compatibility of
attributes must thus in the main be learned from intuition,
the observation of the realities which are combined in the
outward or inward world of our experience. In our concept
of tree, we combine form, colour, growth, organisation. Our
only means of knowing these to be compatible is through a
reference to intuition and representation working on the
data of sense. The confliction of attributes must be learned
in the same way, all except those that are immediately con-
tradictory. We cannot combine in one and the same surface
black and white, or red or green, because intuition never gives
us such a combination, but the opposite. There is a material
1 Hamilton, Logic, L, xii., p. 216.
CONGKUENCE IN JUDGMENT. 235
barrier in this case to unifying, or to congruence. But in
whatever way congruence between attributes may arise,
whatever its ground or conditions, its test logically is the
power of representing the two attributes as in the one sub-
ject, or the one attribute as a mark or attribute of the other.
When we can do this, and when we recognise and enounce
the congruence, we have an act of judgment, — properly logical
judgment.
(a) It has been remarked on this point of the congruence of notions,
that it may be of two different kinds. The concepts or attributes may
be such as we must necessarily unite in thought, or such as we may or
may not unite, according to circumstances. Man and animal are con-
cepts of the former kind ; man and the concept ten feet high are of the
latter. — (Monck's Hamilton, p. 132.) Hamilton has himself touched
on this distinction, when he distinguishes notions in Comprehension as
Intrinsic and Extrinsic. The former are made up of those attributes which
are essential, and, consequently, necessary to the object of the notion.
The latter consist of those attributes which belong to the object of the
notion only in a contingent manner or by possibility. — (Logic, L. xii. ,
iii. p. 216.) But this is wholly extra-logical.
The knowledge of what is essential to the object of a notion is obvi-
ously a process subsequent to the formation of the notion itself. The
object of a notion is simply that of which the attributes of the notion
can be predicated ; and when the attributes of the notion can be predi-
cated, there is the object of the notion. Animal or organised is necessary
and essential to the notion man, because we have already determined
the notion as that which possesses this particular attribute. This is a
wholly hypothetical necessity ; it is an analytical exposition of the con-
tents of a given notion. Ten feet high, again, is a possibility and a
contingency of the notion ; it is compatible with it, but not essential
to it, or an element of the definition of that which would constitute a
man. But the congruence needed for the judgment is the same in both
cases, and it is fulfilled in both cases. If we say man is animal, or
man is organised, we judge, — we enounce congruence, and congruence
between man and one of its essential, because already determined,
characters. If we say man is ten feet high, we judge equally, — we
enounce congruence between man and a character not essential to the
notion or a part of it. We have fulfilled all the conditions of (formal)
judgment in this latter case ; but we have erred if we imply that the
attribute ten feet high is an essential, that is, already defined, charac-
ter of man, the concept. This distinction, accordingly, of the essential
and the non-essential characters of the concept is extra-logical, and
in no way affects the nature of logical judgment- as in itself simply
the enouncement of congruence or confliction.
§ 290. This leads to the further question — Is Judgment,
as thus defined, limited to Analytical Judgments alone ? Or
236 INSTITUTES OF LOGIC.
does it also include Synthetical ? In the analytical predicate
we enounce an attribute already contained in the subject, as
body is extended. In the synthetical judgment we add or
enounce a new predicate not already contained, or rather
not known to be already contained in it. The law of Iden-
tity warrants the former enunciation ; it cannot of itself
warrant the latter, or lead us to it. I do not see that this
should give rise to any difficulty. In the first place, the
distinction between synthetical and analytical judgments is
in a great measure relative. What is synthetical at one
stage becomes analytical at another, when the concept is
more fully determined. This is the case with most scientific
concepts. In the second place, even though the attribute
confronted with the existing concept be new, its congru-
ence with it alone satisfies the affirmative judgment. Ex-
perience may evolve a new attribute, congruence is still the
logical test of its (possible) combination. That it is actu-
ally combined is grounded on conditions not involved in the
mere congruence. This is to confuse congruence with belief
in the reality of the congruent. In case of synthetical judg-
ments a priori, as cause added to the concept of an event
apparently beginning, the ground of the assertion is extra-
logical, not found in the law of Identity ; but the recognition
of congruence between the concept of an event apparently
commencing and a cause is still there, and there as a condition
of its assertion as a law of reality. The distinction of syn-
thetical and analytical judgments, whether well founded or
not, in no way affects the doctrine that congruence of repre-
sentation is the condition of the logical judgment, and that
this judgment consists in apprehending and enouncing the
congruence.
§ 291. In synthetical judgments a priori, there is of course
no preliminary comparison of two concepts. The subject
concept is supposed to be given, and to this we add the new
predicate concept. We have, for example, an apparent com-
mencement of an event in time ; we add on the concept of
cause and form a synthetical judgment. The relation between
the two concepts is said to be necessary. Thinking the one,
I must think the other. But in this case, are we correct in
holding that the subject concept is conceived first and inde-
pendently, and then the predicate concept is added to it ? If
JUDGMENT ANALYTIC. 237
the concept event and the concept cause be correlatives, and
necessary correlatives, can the one be conceived apart from
the other ? Is not the true state of the case this, — that there
is the coequal revelation of one double-sided concept ; and the
so-called synthesis or adding on of the predicate is a mere
making explicit of what we think implicitly and vaguely ? If
this be so, the so-called synthetical a priori judgment is simply
the full consciousness of a necessary relation, and different
altogether from judgments of experience, in which we add on
not by way of necessity, new attributes or concepts to the
subject. The nearest approach to the synthetical a priori
apprehension is in those cases where an attribute is ultimately
seen to be necessarily implied in a given attribute, as divisi-
bility in extension, although this judgment is synthetical only
relatively to the development of our knowledge, and not in
relation to the nature of the original notion.
§ 292. Logically all judgments are analytic, for judgment
is an assertion by the person judging of what he knows of
the subject spoken of. To the person addressed, real or
imaginary, the judgment may contain a predicate new — a
new knowledge. But the person making the judgment speaks
analytically, and analytically only ; for he sets forth a part of
what he knows belongs to the subject spoken of. In fact, it is
impossible any one can judge otherwise. We must judge by
our real and supposed knowledge of the thing already in the
mind. Even when we add a wholly new predicate to the sub-
ject, as in scientific discovery, we, in the judging, state only
analytically what we already know. Even when we form a syn-
thetic judgment a priori, we analyse a complex notion ; for as
the so-called new predicate is a necessary one, a necessary
correlative, we never really had the subject in the mind
per se, but always with the predicate implicitly.
§ 293. What, then, it may be asked further, is the import or
nature of this act of judgment? What is the condition, so to
speak, implied in it? The answer, in the first place, is, that
this recognition, when affirmative, or of the congruent, is a
determination, a limitation. It is also, in a sense, a deter-
mination, when negative, or of the conflictive. How in one
complex notion, first, can we conceive two notions as in one,
or as united in an affirmative judgment ? Clearly the notions
cannot be regarded as both subjects in a judgment, that is,
238 INSTITUTES OF LOGIC.
as both equally determined or limited, for there is nothing
here in the one to limit the other. They are still represented
or conceived apart. But an affirmative judgment requires and
expresses union, — the union of two. Hence the one notion
must stand to the other in the relation of subject to predi-
cate, that is, something must be attributed to the subject,
or the subject must be included under some class-notion.
For the same reason, the two notions, if attributes, cannot be
regarded as one, or as united in a judgment, if neither deter-
mines or qualifies the other. There must thus in a judgment
be a relation of the thing or concept determined (the subject),
that by which it is determined (the predicate), the relation or
determination between the two (the copula). These three
elements constitute one indivisible act of thought. Thus a
judgment is a determination, a limitation. For example,
we say iron is a mineral. The subject iron is limited to or by
the notion mineral. If mineral be regarded as a class, iron
is a part of it, or included under it, that is, limited to it, as
distinguished from the sphere outside of it. If mineral be
regarded as an attribute, it is a part, mark, or character of the
notion iron, that is, it is limited to it or distinguished from
what does not possess it. The electrical is polar. Electrical,
if taken as attribute, has polar as an attribute or mark of it.
It is subject, or determined ; polar is predicate or determining.
In each case, however, whether the predicate be class or
attribute, the subject is thereby marked off, limited, distin-
guished from what it is not, from other things not possessing
the distinctive mark or belonging to the definite class. Ham-
ilton, accordingly, finally defines logical judgment " to be the
product of that act in which we pronounce that of two notions
thought as subject and predicate, the one does or does not
constitute a part of the other, either in the quantity of Exten-
sion or in the quantity of Comprehension." *
The phrase, " a part of the other," will mean, in the case
of Extension, that is, where we compare a subject with a
class-notion, as man with organised, a portion of the class,
an object or individual under the extension of the class, and
thus one with it when actually thought in connection with it.
In the case of Comprehension, "a part of the other" will
mean that the predicate is thought as a mark, character, or
1 Logic, L. xiii., p. 229.
CONGRUENCE IN JUDGMENT. 239
attribute of the subject, and thus conceived as one with it,
as it may be either inseparably connected with it, or as, for
the time at least, actually connected with it in the unity of a
single complex notion. Congruence, as thus finally ex-
plained or elucidated by Hamilton, does not imply in the case
of the comprehensive predicate that it is identified with the
subject. He does not say that the electrical is polarity, or
that electricity is polarity, — that free-intelligent is responsibility,
or that free-intelligence is responsibility. He says the electrical
contains polarity as a mark or attribute, or that polarity is
a mark of electricity, or that free-intelligent contains in it
responsibility. There is a congruence, a unity between the
notions, when, compared as subject and predicate, the one
forms part of the other.
(a) Mill puzzles himself sadly over these two statements or defini-
tions of Judgment, and regards them, as usual, as inconsistent. He
cannot reconcile the "congruence" of the first with "a part of the
other " of the second statement. So far from being inconsistent, the
latter phrase simply renders the former more explicit. " Congruence "
does not mean, as Mill conceives, that "the attributes comprehended
in both of them [the concepts] can be simultaneously possessed by the
same object. " Hamilton says no such thing. All the congruence he
needs or asks for is that they can be simultaneously thought or con-
ceived as possessed by the same object, or better, united in the
same subject of thought, — that they be not in thought repugnant.
Nor does the phrase "a part of. the other" mean, as he imagines, that
"the one concept is actually a part of the other." It means simply
that the one concept is conceived and pronounced to be in thought an
object under a given class, or a subject possessing a definite attribute.
There is no distinction here corresponding to " a part of " and " along
with. " Learning and virtue are congruent, since I can conceive them
together in the same object of thought, and in the same indivisible act
of representation. They are thus conceived along with each other in
one act, while virtue and vice cannot be so represented. But I do not
say, or need to say, that learning is virtue, or virtue is learning. So
when I say that learning and virtue are parts of the comprehension of
the notion of Socrates, or of the notion of an ideally perfect man, I
no more say, or need to say, that learning is virtue, or virtue learning.
But, as parts of the same complex notion, they are congruent. The
latter statement about judgment simply explains the two forms of
Congruence, that which lies in a subject possessing, or conceived as
possessing, parts or attributes ; and that which lies in a subject con-
ceived as being a portion of a (wider) class than itself.
There is not the slightest contradiction in Hamilton's doctrine here.
Two attributes, or groups of attributes, are congruent when we can
think them as one, or in one notion as coincident, as the one qualify-
240 INSTITUTES OF LOGIC.
ing the other, and not unless this be so. We cannot think wisdom
and circle as one or congruent, or the one as qualifying the other,
but we can think circle as white or black, as thus qualified and deter-
mined. And in this case the blackness or the whiteness is part of the
concept we form of the circle, not along with it merely, but one of
its qualities in the group of qualities which we name this circle.
Hamilton illustrates this by the notions electrical and polar. He says
"we cannot think the two attributes electrical and polar as a single
notion, unless we convert the one of these attributes into a subject to
be determined or qualified by the other." — (Lo;jic, iii. p. 227.) Mill
asks, ' ' Do we ever think the two attributes electrical and polar as a
single notion ? We think them as distinct parts of the same notion,
that is, as attributes which are constantly conjoined." — (Examination,
p. 344. ) Does Mill not know what a single notion in Logic means ?
Does he suppose that a single notion means only one or a single attri-
bute, or two attributes identified ? Does he not know that a single
notion is not necessarily a simple notion, but may be a complex notion,
provided only the attributes which make it up can be thought in one
representation, and not merely successively, or as repugnant?
Hamilton has not two meanings of the word " congruent," as ap-
plied to the concepts of attributes. He does not mean by it " along
with " at one time, and at another ' ' actually a part of. " His sole test
of congruence is compatibility of representation of the two attributes
in the same subject ; but he does not make the one attribute a part of
the other. He does not say that beauty is a part of riches ; but he says
we may represent and affirm these attributes to belong to one and the
same subject, or that the beautiful one is rich. And then rich or riches
is a part of the subject-notion, a part of that subject which is beautiful.
We might no doubt form a judgment in which we should make one
attribute a part of another attribute, as when we say extension is
(contains in it) divisibility. We know that divisibility is a necessary
implicate of extension. But we do not identify the two ; we say only
divisibility is a mark of extension, or the subject-notion extension has
as part of it divisibility. It would certainly be ridiculous in this case
to say that the judgment states that divisibility is conceived merely
' ' along with " extension ; that thus the two can be conceived apart ;
and that all we assert in the judgment is a separable conjunction.
(b) Mill conjures up another inconsistency, in what he calls Hamil-
ton's first theory of judgment Judgment is regarded as the recognition
of congruence or confliction not only between concepts, but between
"two individual things." But as in the so-called second theory,
Hamilton declares it to be " the product of that act in which we pro-
nounce that of two notions, thought as subject and as predicate, the
one does or does not constitute a part of the other, either in Extension
or in Comprehension," he is to be held as denying that one individual
thing is predicable of another ; ' ' one at least of the terms of compari-
son must be a concept. " It would be enough to say, in regard to this,
that Hamilton recognises a "notion" of the individual, where the
image of the individual and concept proper coincide. But Mill further
contends that " if the predicate in a judgment be held to be part of the
CONGRUENCE IN JUDGMENT. 241
subject, then the individual cannot be predicable of an individual ; for
one notion of an individual object cannot be a part of another notion
of an individual object. One object may be an integrant part of
another, but it cannot be a part in Comprehension or in Extension. St
Paul's is an integrant part of London, but neither an attribute of it,
nor an object of which it is predicable."1 Here we may well ask,
Did Mill know what is meant by predicable ? Evidently he supposes
that predicable means only affirmatively predicable, and, in fact, identifi-
cation. We cannot say London is St Paul's, but we can say what is
correct, that London is not St Paul's ; and thus St Paul's, the indi-
vidual thing or notion, is the predicate of London, the individual
thing or notion. We cannot say, The donkey is its leg, but we can say,
it is not. And here we as truly predicate, as if we had identified the
donkey and its leg. But is it so certain that one individual cannot
stand as a logical part, say attribute or determination in relation to
another individual object? Can the individual as predicate not be
logically a part of the subject? The truth is, that one individual
notion can be part of another, can be affirmatively predicated of
another. We affirm this every day. We do it when we speak of Sir
Isaac Newton as the author of the Principia, or of Victoria as the
Queen of England. In these subject and predicate are strictly indi-
vidual notions, and the predicate is part, and in a good sense a part
only, of the subject. A little further on, Mill, in pursuance of his
chimerical contradictions, represents Hamilton as holding that, in
order to form concepts, we first of all compare and judge between
individual objects ; and he maintains this doctrine to be true. If we
so judge apart from concepts, do we not predicate, both affirm and
deny, one individual thing of another ; and in so predicating, do we
not pronounce the one thing to be or not to be a part of the other ?
Hamilton is perfectly consistent ; Mill is neither accurate nor consistent,
(c) It may be objected that congruence between two concepts is
sometimes partial, and thus that the same two concepts may be
described as both congruent and conflictive, as the ground thus
equally of affirmative and negative judgments. Thus, tall and man
are congruent, — some men are tall. Again, they are conflictive, — some
men are not tall — they are dwarfs. But this has nothing to do with
congruence in comprehension, or attribute : and Hamilton is dealing
with congruence as a relation under comprehension. Alan and tall are
congruent as attributes ; and we may unite them formally, that is,
unite them in one subject in a judgment. We may also unite them
really, or as in presentation. This implies also that so far their
extensions coincide. Comprehension implies always some (imaginary
or real) extension. But it does not imply absolute coincidence or co-
equality of extension. That the extension of a congruent concept, say
tall, is wider than the extension of that with which it is congruent,
say man, is no proof that the two concepts are not congruent in com-
prehension or as attributes, or, in other words, that as attributes they
are to be regarded as both congruent and conflictive. Further, when
tall is predicated of some men, and not-tall of others, there is no conflic-
1 Examination, p. 422.
Q
242 INSTITUTES OF LOGIC.
tion, for we are speaking of different subjects or portions of the same
class.
(d) This mode of speaking of Judgment as the comparison of one notion
with another, and the recognition of the one as a part, comprehensively
or extensively of the other, or as not a part, requires some slight modi-
fication to suit Hamilton's later doctrine that a proposition is, in exten-
sion, an equation or non-equation of subject and predicate. It needs
no change to suit it to his later statements of the comprehensive pro-
position, for from this he properly excludes the notion of quantity (see
Logic, Appendix iv. 271 and 276) in the sense in which it is applicable
to the proposition in extension. But even with regard to the judgment
in extension there is no conflict between the earlier and the later doc-
trines. In the four affirmative propositional forms, the earlier language
applies strictly, — to (Afl) all is some; (IfA) some is all; (Ifl) some is
some. With regard to Af A, — or all is all, — we compare two wholes,
and regard them as convertible. But logically the predicate whole is
declared to be the constituent of the subject whole. All equilateral is
all equiangular. Equiangular is "a part" of equilateral in the logical
sense of the coincidence of one notion with another. That they wholly
coincide, or are coextensive, does not destroy the concept of them as
reciprocally parts of the whole notion of equiangular-equilateral.
§ 294. The element of determination of the judgment in
comprehension may, in a sense, be said to depend on the
amount or degree of the specification of action and object.
(1.) This may be said to be incomplete, as Bruce gained a
victory, or the man was killed. (2.) Or complete, as Bruce
gained a victory at Bannockburn over Edward II. ; the man
was killed by being run over by the express, Sfc. Complete-
ness and incompleteness of determination are relative to the
purpose or end of the judgment. It depends, indeed, on
what we mean precisely to assert, or need precisely to deny.
The distinction made by some between objective completion
and objective determination is wholly groundless, from a
logical point of view. Every determination by any attribute
whatever, or by any class whatever, is a completion of the
judgment ; because this is a case of determination against
indetermination, — of a definite affirmative against a negative.
Of course, looking to the actual fact or possibility of obser-
vation and generalisation, any determination, through a
predicate, is incomplete. But this has no logical signifi-
cance. The logical essence of the judgment is as clear
and marked in the first predicate as in the most advanced,
or in the most complex series. When I say this is, my
judgment is perfectly complete or determinate, as contrasted
JUDGMENT IN RELATION TO EXISTENCE. 243
with its negation, this is not. And when I say this is a metal,
the judgment is really not more determinate as a judgment,
though the predicate contains more attributes, for the deter-
mination is always in relation not merely to the possible
predicates of the subject, but to what I know definitely of
the subject. As against the knowledge asserted there is
always the negation of the opposite determination.
§ 295. Judgment in its objective relation may be supposed
to represent all the actual and possible forms or relations of
existence. The first relation of existence is a thing and its
quality, — a substantive or permanent, and its action or pro-
perty. This is equivalent to the relation of inherence or of
subject and phenomenon. The subject of the judgment may
be taken as representing the thing or permanent subject, the
predicate as representing the action, quality, or property. In
language these are expressed by the noun and the verb.
This form of judgment is in logical language the comprehen-
sive,— the predicate is regarded as quality or attribute.
Under this head of comprehension is included every judg-
ment which expresses the relation of causality between thing
or cause and its effect, as the sun is the cause of heat, opium
causes sleep. The action or the passion in a given case may
be related to the subject as a singular effect, or it may be
regarded as the fixed and constant effect of the thing. This
would yield one feature of the distinction between accident
and property.
Sequence, concomitance, and coexistence may fairly be
regarded as coming under Comprehension. The sun is fol-
lowed or accompanied by day. A is constantly followed or
accompanied by B, or A and B always coexist. Things re-
lated alike in time and space, through uniformity or con-
stancy of conjunction, come under the head of subject and
property. There may be simple simultaneity, and simple
co-adjacency, as in the case of my writing while the clock
strikes twelve, or the co-adjacency of the planets in space.
This and that may be together in time or in time and space,
apart from the relation of cause and effect, or of substance
and accident; but a judgment regarding these would come
under the head either of simple individuals or of classifica-
tion by resemblance in time or in time and space. And
this suggests the second great relation of things indicated
244 INSTITUTES OF LOGIC.
by judgment, that is, similarity or resemblance among the
objects or qualities of objects. This does not take into
account either substance or causality, or even properly time
or space. It only considers whether two given qualities are
like or unlike, compatible or incompatible, unifiable or not
in thought, and this gives rise to the notion of the class,
to the judgment in Extension or Classification. Here we
may be said to state the relation between two ideas, and to
refer to, include in or exclude from, a class. These two forms
of judgment, — the Comprehensive and Extensive, — are,
logically considered, wholly independent of their actual or
metaphysical relations ; at the same time, they represent in
a general and scientific form those various metaphysical rela-
tions,— are, in fact, fitted for thinking those relations, stated
in their highest abstraction. It indicates simply a narrow, in-
adequate, and one-sided view, to represent logical judgment
as founded on or expressing coexistence, or concomitance of
attributes, or immediate succession, and to deny reference to
a class, — as is done by Mill. Logical judgment is, on its real
side or application to reality, as wide as the relations of things
themselves, and that mainly because, while indifferent to
special relations, it formulises all. It is a remarkable theory
of judgment which, while limiting judgment to coexistence,
and excluding inherence, would tell us that three-sided figure
only coexists with triangle, or extension with tody. And
not less so would be the theory which implies that while
consuming paper succeeds flame, the power of consuming is
not a property inherent in flame.
(a) " In the judgment A is a coward, the combination of the notion of
A with his deeds is the basis of the judgment ; its subsumption under
the notion of cowardice is the judgment proper. The logical element is
the analytic subsumption of the less general subject-notion (or subject-
conception) under the more general predicate notion. "— (Beneke, in
Ueberweg, Logic, p. 193.) The combination of A with his deeds is
simply, to begin with, a judgment. Mere coexistence of A with his
deeds, as in Mill's view, is no judgment. There might quite well co-
exist in my mind the conceptions of competent learning in metaphysical
philosophy and Mr A B ; but I need not, therefore, think of combin-
ing them. Their coexistence and the attribution of the former to
the latter might be to me wide as the poles asunder. When I combine
A with certain deeds, and say that A is the author of them, I judge as
much as when, having referred those deeds to the class cowardly, I
predicate cowardice of A, and refer him to the class of cowards.
JUDGMENT WITH HEGEL. 245
(b) Judgment with Hegel is equivalent to "the determination given
to the notion by itself, or the notion making itself particular, or the
original self- division of the notion into its moments with distinguishing
reference of the individual to the universal, and the subsumption of the
former under the latter, not as a mere operation of subjective thought,
but as a universal form of all things." — (Ueberweg, Logic, p. 192.)
Ueberweg's only objection to this is the confounding of reference to
reality with reality. But the fundamental objections to such a state-
ment are (1) the absurdity of hypostatising the notion, as yet a pure
abstract without individual instance, and regarding this as capable of
passing into the individual, confounded usually with the particular.
(This, that, with some of all.) (2) The attribution to the notion per se,
or notion in any way, the power of consciously passing into the indi-
vidual, or the power of conscious process at all, which is competent
only to a conscious subject cognisant of itself and difference. The
notion, in fact, as a pure abstraction, is credited with all the attributes
of a conscious subject or thinker. In other words, simply and ulti-
mately because there is a (supposed) necessity of connection between
notion and individual, this connection is hypostatised as a thing per se,
and regarded as the universal in things ; whereas it is and can only be,
and be intelligible, in this or that individual consciousness, and thus
subject to all its conditions. (For a fuller statement and examination
of Hegel's theory of Judgment, see below, chapter xxii. )
246
CHAPTER XIX.
JUDGMENTS SIMPLE OR CATEGORICAL AND COMPOSITE THE
CATEGORICAL — ITS ELEMENTS AND KINDS — AFFIRMATIVE AND
NEGATIVE — UNIVERSAL, PARTICULAR, SINGULAR.
§ 296. Judgments considered as to the most general relation
of subject and predicate are divided into Categorical or Simple,
and Composite, — called also Conditional. When the predi-
cate is referred to the subject simply or absolutely, that is,
without contingency, we have the Categorical Judgment or
Proposition, — as A is B ; A is not B. When the judgment is
contingent, and the statement is made under a condition or
with an alternative, we have the Composite Judgment or
Proposition, — If A is, B is. A is either C or D.
§ 297. Looking specially meanwhile to the Categorical, it is
essential to a judgment, as already defined, that there should be
subject, copula, and predicate, whether implicitly involved,
or explicitly stated. In order to judge we must have that of
which we predicate — the subject ; we must have that which
is predicated — the predicate ; and we must have that by
means of which we predicate, that is, affirm or deny, — the
copula. Thus, the sunset is lurid; the moon is bright; the
temperature is 32°. The Subject of a judgment was called
vTroK€L(Aevov, subjectuvx ; the Predicate Kar-qyopov/xevov, prcedica-
tum. A concept as predicable of a subject is, with Aris-
totle, KaTrr/oprjfia • as actually predicated, Kanrjyopovfitvov. The
subject and predicate are naturally called the terms or limits
of the Judgment (opoi, S.Kpa, Trepara, termini),1 because it is
within these that the predication, — affirmation or denial, is
made. Thus, we may say,— plant is organised. Plant is sub-
1 Hamilton, Logic, L. xiii.
SUBJECT AND PKEDICATE. 247
ject ; organised, predicate ; is, copula. Some marble is white.
A judgment expressed in words is a Proposition (enunciatio}
a.7r6<f>a.V(Ti.s).
(a) There is sometimes the assertion of mere action, without definite
reference to a subject which acts. It rains, it snows, it thunders. There
is rain, snow, thunder. This is the first stage. Then there comes the
definite subject; then the definite subject with reference to the specifica-
tion and object. This is substantially the view of Schleiermacher and
others. — (Cf. Ueberweg, Logic, p. 200.) It may be said there is no
assertion of action without reference to a subject which acts, though
there may be reference to a subject which we do not wholly know.
When we say it rains or snows, we simply express a reference to the
ultimate power beyond the sensible phsenomena ; but in so far as we
regard this as the subject or cause of rain or snow, we regard it as a
perfectly definite subject or cause. There is no such thing in human
thought or experience as the apprehension or conception of an action
or property without reference to a subject or substance, whether this be
wholly known or not.
§ 298. The Subject of a proposition has sometimes been
called the Minor Term ; the Predicate the Major. This arises
from considering one special kind of proposition, in which the
subject is either species or individual. When I say man is
organised, or triangle is figure, the subject term is less, under-
stood as less, than the predicate. It is part at least of its
sphere or ambitus. But there may be more, or the sphere of the
predicate may be larger than that of which it is predicated.
Organised is or may be wider than man ; figure is or may be
wider than triangle. Or if we say Bucephalus is horse, we
have a predicate of which only a part is taken. But there are
cases in which this distinction does not exist. Whenever
the subject and predicate are substitutive, or convertible, there
can in the proposition be no distinction of major or minor term.
This at least is clear, that the extension of the predicate can
never, in a true or competent predication, be less than that
of the subject. In fact, this distinction of less and greater,
of species and genus, is that expressed in the relation of
subject and predicate in Universal Affirmative Propositions.
The universal affirmative was usually regarded as propositio
potissima. The relations of Minor and Major are most pro-
perly applicable when terms are compared in the syllogism.
§ 299. It ought to be noticed that a subject may be either
incomplex or complex. The subject of which we speak may
be man, plant, mineral. Or it may be grammatically a com-
248 INSTITUTES OF LOGIC.
plex expression, as, to obey the law of truth is incumbent on
every man; or to shun vice is a virtue. Here the infinitive
phrase is as much a term or subject as if it had been put
in a single word. Logically these phrases, whether single
terms or a plurality of words, indicate one concept, regarded
as subject or predicate, as that whole of which something
is said, or as that whole which is said of something.
§ 300. Terms and the parts of propositions are not given
explicitly in ordinary language. The complex or irreflective
expression is matter of analysis. If I say, / walk, or leap, or
run, I express what I say in an implicit propositional form,
and the science of logic has to ask me to make my meaning
or mental act explicit in words. I must, therefore, resolve
each expression into subject, copula, and predicate.
(a) Each proposition recognised by Aristotle represents a universal
and invariable form of words, and a universal and invariable act of
thinking, — the former apart from the particular words, the latter apart
from the particular matter. Thus, the affirmative proposition is a
synthesis by which we unite one representation to another. The words
and the form of thought in one proposition may be used in all. The
Categories of Kant represent the universal forms of thought. These
functions of the understanding are united in a supreme act, the pri-
mordial fact of pure apperception. But while Aristotle considers the
judgment to have a reference to existence and non-existence, Kant's
expression, objectivity, has not a similar reference. This means merely
the (fixed or universal) relations of knowledge, as the material is acted
on by the Ego, and subsumed under the Categories. It is bringing,
for one thing, the special under the universal ; but the universal itself,
with its relations and connections, is the product of the Ego, — the out-
come of its activity. Aristotle's objective reference, if we may use the
expression, was wholly different from this, which is simply subjective,
though necessary.
(b) 'TiroKfiixivov with Aristotle has two grand meanings, — it indicates
the subject of a judgment, and also the substance or substrate to actions
in the nature of things. This was indifferently translated subjectum
by the Latins, as by Boethius. 'AvriKei/j.ei'ov or object was translated
by Boethius oppositum. Hence subject in the middle ages is equivalent
to substrate, and so it is with Descartes and Spinosa. Esse subjectivum
means with Occam that the thing in nature is placed beyond the mental
species, and is not framed by thought alone. On the other hand, esse
objectivum is that whose reality is known as a mental product or crea-
tion. Objective reality with Descartes is thus in modern language sub-
jective or a representational notion. Kant and Fichte reverse this
usage. The subject is he who knows ; the object is the thing, as far in-
deed as it is subjected to the knower, and yet preserves its own nature
free from the opinion of the knower. Hence it happens that that is
JUDGMENTS OF QUALITY. 249
called subjective which lies in the varying condition of the knower, and
that objective which lies in the constant nature of the thing itself.
Wherefore if truth be defined the harmony of the subjective with
the objective, nothing more is postulated than that the thing is simply
thought as it is, and the cognition is adequate to the thing known. —
(Trendelenburg, Elementa Logices Aristotelece, pp. 52, 53, ed. 1845.
Compare Descartes, English Translation, Appendix, Notes iii. and vii.)
(c) KaTriyopetv is sometimes simply to say, at other times to prove
by certain arguments, as with Plato in the Thecetetus. In logic, kottj-
yopovfjievov is the predicate, or principal predicate ; wpocrKaTvyopoviji.evoi',
or appredicate, is that which is placed to the predicate, or rather
placed before it, that it may be enunciated of the subject — viz., is,
since it has the force of a tie, and is not itself predicated. SwyKanj-
yopovfieva are those words which belong to the principal predicate —
e.g., Alexander is the son of Philip of Macedon. Here son is the prin-
cipal predicate ; the other words are syncategorematic ; is is not pre-
dicated, but it is the instrument and medium through whose interven-
tion the predicate is attributed to the subject. — (Goclenius, sub voce.)
(d) The infinitive is very commonly the subject of a proposition. It
is a virtue to shun vice. Here to shun vice is subject. The infinitive
is, of course, simply a form of the noun, as containing merely the
attribute indicated by the verb.
In the resolution of a proposition, grammatically considered, we may
have various subjects and predicates, according to the emphasis or
intention of the person employing the set of words. I ought to love my
neighbour. This may be resolved : (a) I (subject) am one who ought to
love my neighbour, (b) To love my neighbour (subject) is my duty,
(c) My duty (subject) is to love my neighbour, fee.1
In the case of a proposition referring to past time, as Homer was a
poet, we may consider the element of time part of the predicate, or
resolving the toas into is, we can say Homer is a poet, or to be reckoned
as a poet, and conversely some poet is Homer.*
§ 301. It is usual in logical treatises to consider judgments
in respect of their Quantity, before treating of them in re-
spect of their Quality. This seems to me to be an ill-
grounded arrangement. The form of a judgment, — what is
essential to it, — lies in the copula, and in the copula as
marking inclusion or exclusion, attribution or non-attribution.
Affirmation and negation, dependent on quality, as it is
technically understood, are thus the essential characters of
the judgment. We can have either the one or the other,
while the subject is an indivisible unity, and does not admit
of more or less in quantity. And it is not essential to affirma-
tion or negation whether we take the subject, being a com-
mon term or concept, as in all its extent or in some. All
1 Wallis, Logica, ii. 2. 2 Ibid.
250 INSTITUTES OF LOGIC.
and some are indeed, in a sense, syncategorematic. Hence
the relations of Quality ought to be considered before those
of Quantity, in judgments. Predication, in truth, and the
forms of it, lie at the very heart of judgment. And as ex-
pressed in language a proposition is always essentially a
sentence indicative, not expressive merely of apprehension,
or wish, or threat.
§ 302. Further, predication, as involving affirmation or
negation, is a point antecedent wholly to the quality of truth
or falsity in a judgment. It lies nearer to its nature or
essence, — in fact makes it. A judgment can only be true or
false, as it in the first instance affirms or denies. This is the
strict logical presupposition of truth and falsity alike ; and
these are only possible as the judgment is a predication, — an
inclusion or exclusion of a given subject and class, or
an attribution or definite non-attribution of a quality to a
subject. Hence it is a mistake to place, as Mill does, the
truth or falsity of a proposition in the foreground. This
is necessarily a property or result, because it is only possible
through a full-formed judgment.1 And we must know about
the nature of the subject and predicate from intuition and
actual conception, before we can pronounce on the truth or
falsity of their synthesis or disjunction. In a word, the form
of the proposition precedes, is independent of the matter;
and can be legislated for apart from consideration of this
altogether, though originally, no doubt, we were led to join
or disjoin subject and predicate through the force of intuition
and the conditions of actual conception, as we actually
numbered or measured, before we thought of the pure rela-
tions of number or extension.
(a) Ueberweg makes judgment essentially consist in "a conscious refer-
ence to what actually exists, or, at least, to the objective phsenomena.
This gives the judgment its character of a logical function. " — {Logic, p.
188.) What has been already said shows that this is a secondary ref-
erence in strict logical judgment, and is possible only in and through
the constitution of the judgment, for which logic legislates.
§ 303. A judgment (or proposition) is properly negative
only when the negation affects the copula. The negation
may be joined to the subject or to the predicate, while the pro-
position remains affirmative. An animal which is not rational
1 Cf. Wallis, Logica, ii. 1.
DEGEEES OF NEGATION. 251
is a h'ute ; what is not an animal is not a man — or not-animal
is not man. These are affirmative propositions, because the
negation in no way affects the copula. We may say not-
animal is not man. In this case the proposition is negative.1
(a) In Latin the negative particle (non) is usually put before the sub-
stantive verb (est) ; in English it is put after it — Non est, is not.
— (Wallis, Logica, ii. 3.)
(b) Every man is not loise. If this is taken distributively, then no man
is wise. But if we say, not every man is wise, we leave it to be inferred
that some are or may be. We do not absolutely negate. — (Wallis,
Log., iii. 2.) u Not every one that saith unto me, Lord, Lord, shall enter
into the kingdom of heaven." — (Matt. vii. 21.) This does not mean
none who say so shall enter ; but only some who so speak shall not.
§ 304. We ought to distinguish two degrees, or rather effects,
of negation. In the first place, we may deny an attribute of
a subject, as the pine is not deciduous. Here the subject
still remains, although the attribute has been negated. And
the subject may be either what we find actually to be, or
what we suppose ideally may be, for the whole class pine is
to us an object of thought, an ideal class. In the second
place, our negation may be such that the subject itself does
not survive the negation. If I say a square circle does not exist,
or is an impossibility in thought and fact, or there never
was such a person as Presbyter John, I abolish not merely all
attributes, but I wholly sweep away the subject of the pro-
position. In the former case, the subject is but a form of
words, with no unity of meaning or representation to begin
with ; and I assert this of the proposition. In the latter, the
subject has a definite meaning ; I do attach some conception
to Presbyter John, but I sweep away the subject as a real
existence.
§ 305. " Non-homo is not a noun, for none is constituted
which can be applied to it. It is neither enunciation nor
negation. Let it be an indefinite noun (ovo/^a aopio-Tov), because
it can be equally predicated of every, whether what is or
what is not." — (De Int., c. ii.)
The ovofxa dopio-Tov has only the form of affirmation. It
really posits nothing ; hence it has been translated by
Boethius nomen infinitum. The elephant is not man, is a
finite or definite negative. The elephant is not-man means
1 Wallis, Log., iii. 2.
252 INSTITUTES OF LOGIC.
that the elephant is something which is not man ; hence infinite,
or better indefinite. To attach the negative particle to the
predicate is an artificial form of expression.1 In a proper
negation, the negative belongs to the copula, or act of judg-
ment.
(a) Non-homo is not said in reference to man only, but in reference
to horse and dog, and goat, stag, and hippocentaur, and all things
absolutely existing and non-existing. — (Ammonius Hermise, quoted by
Trendelenburg, in loco.)
The elephant is something not man, or something which is not in-
cluded under man as a class, or as a sum of attributes. If I know
men, and the attributes of man, I know what does not belong to the
elephant, or objects among which the elephant is not to be classed.
But this does not tell me what attribute or attributes elephant
possesses, or what objects it is like. So far as this affirmation is con-
cerned, elephant might not possess life, sensation, locomotion, organ-
isation, &c. — all these being in man. It tells me nothing, there-
fore, of elephant more than that as subject of a proposition it means
something, — something conceived only, it may be, but I do not know
what or more. If elephant as a simple concept be held as a subject
defined, its attributes would be less than those of man, though in some
respects congruent. To say it is not-man would be only to say that it
is a concept having definite attributes, but less than those in the concept
man. But obviously such a judgment would add nothing to our know-
ledge of elephant ; it would only negatively say what already we posi-
tively know of the subject. It would not even articulately develop
what we knew. It would not amount even to an analytical judgment.
The logical developments, or more properly manifestations of this form
of the indefinite concept are founded on an essential misconception of
the nature of negation, and a wholly artificial form of expression.
Without a verb, says Aristotle, there is neither affirmation nor negation.
(b) The judgment a.6pi<rrov of Aristotle has been supposed to mean
unlimited judgment (unendliches Urtheil), for although the predicate
non-homo be excluded from one thing, there may remain a limitless
space (sphere) of those things to which it may belong. — (Kant, d. r.
Vernunft, p. 97.) But the judgment is properly indefinite, Unbe-
stimmtes, not unlimited.
This interpretation supposes that the noun or subject concept is
already defined, and hence may be found in the sphere outside man,
or the infinite noun ; but as a defining judgment it is wholly indefinite.
Kant's third form of judgment, the Limitative or Infinite, is sup-
posed to arise when the negation is connected with the predicate, not
with the copula. But the essence of the form of judgment lies in the
affirmative or negative copula ; and if the copula affirms the combina-
tion of the subject with the (negative) predicate, the judgment is
affirmative. There is no real ground for the distinction of the limita-
tive judgment from affirmative and negative judgments.
1 Cf. Trendelenburg, in loco.
JUDGMENT OF QUANTITY. 253
(c) Kant, again, divides judgments into three kinds — viz., Analytic,
Synthetic a posteriori, Synthetic a priori. In the analytic judgment, the
predicates state merely what is already contained, known to be con-
tained, in the subject : in the synthetic, the predicates add something
to our knowledge of the subject, founded either on experience (a pos-
teriori), or on pure intuition of time and space, or pure concept of
the understanding (a priori). With Kant, a priori is used to denote a
knowledge independent of experience. If by that he meant wholly
independent, there is no such knowledge and no such judgment.
Experience as known, and intuition and concept of category as a priori,
are inseparably related and inseparably given in experience, and so
apprehended in one. The setting up of a priori, or pure intuition, or
pure category, as a distinct kind of knowledge is, in itself, a meaning-
less process, and has been the source of endless aberration and fallacy.
That there is an a priori synthesis, or synthetic act on occasion of ex-
perience, and in relation to experience, is true ; that this is an imposition
of the mind on experience, is false. It is simply experience itself re-
vealing itself to the full reach of the cognitive faculty.
Again, the distinction of analytic and synthetic judgments of ex-
perience is relative, relative especially to the progress of knowledge.
Unless we can get back to ultimate essence in each thing, we can never
determine what is absolutely analytic in knowledge. And what is syn-
thetic to-day may be analytic to-morrow, in the progress of science.
Moreover, logically every predicate is analytic. It is explanatory of
what is already conceived in the mind of the subject. It is explicit of
the implicit.
Aristotle meant by a priori a knowledge of a thing through its cause
or causes, which are prior in the order of nature ; by a posteriori, a
knowledge from effects which are posterior in the order of nature. As
Ueberweg remarks, Kant's application of the Aristotelic phrases, and
the consequent use of them, have done more harm than good in philo-
sophy (Logic, p. 224). They have, in fact, led to verbalism, fantastic
and lawless construction of systems and theories, which are neither
applicable to experience, nor verifiable by it, or by any test competent
to the knowledge of actual fact or reality.
§ 306. According to Quantity, Judgments (Propositions)
are usually divided, since the time of Aristotle, into three
classes, viz. : —
(1.) Universal or General (7rpoTao-et? at kcl66\ov).
(2.) Particular (7rpoTao-£ts fteptKat', at iv //.epet).
(3.) Individual or Singular (7rpoTacreis at ko.6' eKaarov, to.
arofxaj.1
§ 307. Hamilton's principle of the division of Judgments
is a simple one. Looking to the subject, Judgments, in his
view, are either of a determinate quantity, according as their
sphere is circumscribed, or of an indeterminate or indefinite
1 De Int. c. 7 ; An. Pr. i. 2 ; and below, p. 255, for the Indefinite Proposition.
254 INSTITUTES OF LOGIC.
quantity, according as their sphere is uncircumscribed. The
subject as a determinate quantity may be either a whole
undivided [all, every, the whole) ; in this case we have a
General or Universal Proposition. Or it may be an indi-
visible unity (a proper name, this or that) ; in this case we
have a Singular or Individual Proposition. Further, the
subject of the judgment may be an indeterminate quantity
(some) ; in this case we have a Particular Proposition.1 As
examples of a Universal Proposition, we may take : — All man
is organised ; all equilateral is equiangular ; all A is B. Of a
Particular — Some men are courageous ; some men are white ;
some men are blind ; some As are Bs. Of a Singular or Indi-
vidual— Bacon was the author of the Novum Organum, ; this
man was the thief. In a Universal judgment the predicate
refers to all of the subject, as : — All A is B, or every A is B ;
all men are mortal ; all plants are organised ; no A is B ; or any
A is not B ; any man is not a stone. The subject is here taken
in its compass or extension ; of everything or all in or under
the subject is the predicate affirmed or denied.
In a Particular judgment, the predicate refers to some part
of the subject at least, as — Some A is B ; some A is not B ;
some man is learned ; some man is not learned. The subject of
the particular judgment is some at least, one at least, of the
class. We may add on to this others, until we come to all
of the class. Some at least means some one certainly, pos-
sibly all. The particular, therefore, provides for the possi-
bility of the universal.
In an Individual judgment the subject is an indivisible
unit, as a person or individual object. Thus Aristotle is a philo-
sopher. Here philosopher is predicated of Aristotle in its whole
extent, that is, as one or the minimum of extension. Nor
can the subject be less, without changing or destroying it.
The individual subject may be indicated in language by a
proper name, as Virgil, or, ex hypothesi, as the Bard of
Mantua, or the author of the JEneid ; or this man? The
essential part of the individual representation is its deter-
minateness, or definite totality.
§ 308. An Individual judgment is thus distinguished from
a subject, which is a common concept or term, by this, that
the common term may be a particular subject, and yet not
1 Logic, L. xiii. 2 Wallis, ii. 4.
INDEFINITE JUDGMENTS. 255
cease to indicate the class for which it stands, as some men
are learned; whereas the individual subject or term, if
lessened in extension, would no longer represent the indi-
vidual. The predication must always be of the whole. Aris-
totle does not include under the head of particular the in-
dividual or singular. The one is Kara fic/ao?, the other aro//.os.
§ 309. The individual may be constituted by a unity of
aggregation, as this heap of stones ; or by organisation, as
this man, this tree.
The individual may be further constituted collectively into
one subject, so that the predicate refers to the whole of it,
and not to each of the parts, — as, all the planets are eight ; all
the apostles are twelve. In all the planets are stars — that
is, every planet is a star ; all the apostles were called — that
is, every apostle was called ; the predicate refers to each. The
universality in the former case is that of Definite Omnitude ;
in the latter that of Complete Distribution.
(a) Herbart's view of the individual judgment is that it is to be re-
garded as universal only when the subject is distinctly marked. A
man, a tree, a house, is to be taken as indicating a particular judgment,
that is, some or one out of all. But a or an may equally well indicate
any one, and therefore all.
§ 310. Logicians, following Aristotle, have set up as a fourth
class of judgments, rather propositions, what is called the In-
definite. The subject of such a proposition has no mark of
quantity, neither all nor some, and it is thus left indefinite
in expression. Propositions of this sort have been called
■jr/DOTao"ets dStopio-TOL, airpoahiopio-roi.
Hamilton prefers to call them preindesignate, that is, lack-
ing the mark of quantity.
There is, properly speaking, no indefinite or mentally in-
designate subject, and therefore no indefinite judgment. When
we speak of a subject, we are supposed to know that the pred-
icate applies either to the whole of it or to a part of it at
least. If the former, the subject is mentally definite or
universal ; if the latter, the subject is particular. As we
cannot reasonably speak at all of a subject unless we know
that the predicate applies to some at least of it, our proposi-
tion must always mean this much. To leave the subject un-
marked in expression is thus an accident or inaccuracy of
language, and does not constitute a ground for a separate
256 INSTITUTES OF LOGIC.
class of judgments. When we omit the mark of quantity in
the subject, we do so either for the sake of abbreviation of
speech in ordinary usage, or because the subject is well under-
stood to be taken universally, or because it is not necessary
for the purpose of the statement that the proposition should
be more than particular. In the case of the subject being a
singular term or indicating an individual, no mark of quantity
is needed. It is taken as an indivisible unity.
(a) The marks of universality are : — All, every, the whole, each, both
both one and the other, none not, none, nobody, neither, always, every
where, &c.
The marks of particularity are : — Some one, somebody, any one, some
thing, or some one at least ; not none, several, few, not-nobody, one, two
three; some not, not all, at some time, somewhere, &c.
(6) These signs are more explicit in Latin and Greek than in English
For universal signs we have omnis, which is equivalent to every, all,
the distributive whole, and also to the collective. Totus means all, the
whole, the completed class or collective whole ; and so does cunctus.
Other signs indicate the whole from the point of view of one or every
one, each, as eaaffros, unusquisque, singuli.
Every and each both refer to one selected, but every to one selected
out of a whole definite, — every one of the men was drowned; every one
of hoofed animals ruminates. Each refers to one selected out of several
or many, or two. Each of them got a shilling; or each of the two was
killed in turn. The effect of every and each is to concentrate attention
on one or a unit of a more or less definite whole.
The Greek iras indicates all, and this either (a) of one — the whole
entire — that is, Definite Individuality ; (b) of several, every, in plural all.
aO\os is equivalent to the former of these meanings. liar ris means
every one taken one by one, every single one. Quisquis, quicunque (who-
ever, whatever), implicitly mean all, every one.
Adverbial signs of universality are omnino, prorsus, semper, ubique,
undique, &c.
Of particles of quantification in Particulars, we have in Latin chiefly
Quis, Aliquis, Quidam. Quis means some (very indefinitely), some at
least, any one, somebody, <Src. It does not even imply actual existence, and
hence is used in conditional clauses with si, nisi, &c. Aliquis means some
one, somebody, any one, &c. , — that is, not-none, but with no reference to
its kind or individuality. It is any one, as opposed to a certain one.
Quidam means some one, a certain one, whom I know, but do not choose
or need farther to specialise. In the plural, quidam would seem to mean
some of a definite class, as opposed to others of the same class. Exces-
serunt urbe quidam, alii mortem sibi consciverunt. The some here refers
to one part of a definite class — those in the city — at the time. There
is some or other (or not-some) of the same class. Nonnullus is some or
several at least — as nonnulla pars militum. Nonnulli, so?ne.
The distinction of quidam and aliquis is important as bearing on the
legitimacy of the Negative proposition with a particular predicate, —
INDEFINITE PKOPOSITIONS. 257
some is not some (In I), noticed below. Quidam means some one, yet
a certain one whom I know or have in mind, though I may not choose
to specify him. In quidam vestrum me vocavit, it means one whom I
know. Aliquis would mean some one whom I do not necessarily know.
Quidam thus means one only, or a definite one, and implies not the
other one or other of you. As Valla puts it, quidam is biparticidaris,
— that is, it is both affirmative and negative. Aliquis, quisquam, quis-
piam, may be taken as particulars of the universal quisquis (whoever,
whatever, &c.) Adverbial particular signs are unquam, usquam, uspiam,
aliquando, alicubi, alicunde, &c. Quidam, in fact, is singular in mean-
ing rather than particular.
In Greek, ns, masculine and feminine, one, any one, some one ; equi-
valent sometimes to our a, an ; neuter, anything, something.
Like efcao-Tos or iras, it means each, each one, every one. Hence
starting from the individual, and running through the class, it may
stand, like aliquis, as particular or universal.
In negatives, we have as universal signs nullus — that is, we ullus — we
ullus quidem, not one, not even one, none, not any. Similarly in Greek
we have ovScls and /urjSels. With all the Aristotelic commentators,
the subject of the Particular negative is not taken as rives od, but as
ov 7r5s. — (See Philoponus on Scheme of First Figure.) Nullus currit,
i.e., ullus non currit. Elephanto belluarum nulla prudentior. Ullus,
used almost exclusively in negatives, is unulus, from unus ; as meaning
one, any one, it is properly universal. Nequis (we aliquis) is not even some
one, that is, none — so universal. Nihil, nihilum, nothing (nihil non,
everything; non nihil, something). Nemo (we homo), no man, no one
(nemo non, every one; non nemo, many a one). Adverbial negative
signs are nunquam, nuspiam, &c. Aliquis, as other particulars, with
negation is commonly a universal. Aliquis non est me fortunatior,
quisquam non est te melior, ullus non est illo modestior — that is, nemo, no
one. We should not use quidam in those instances — that is, a certain
one — for we really mean any one whatever. Particulars as a rule, when
they receive a negation, become universal. — (Cf. Laurentius Valla,
Dial. L. ii. c. xxviii.)
Singular signs are hie, ille, iste, mens, tuus, &c. , and proper names ;
also adverbs of time, as nunc, eras, tunc, &c. — (On this point see
especially Valla, Dialectica, L. ii. cap. xxv. et seq.)
§ 311. Indefinite propositions can only be enunciated where
the subject is a common term, and capable thus of being taken
universally or particularly. Propositions whose subject is
singular or individual are necessarily taken universally, or
definitely of the whole subject, as Homer was an epic poet ;
Plato was the author of the Republic.
(a) It has been laid down as a rule that the indefinite (or indesignate)
is when affirmative universal, and when negative particular. This is
not absolutely trustworthy.
(6) It is not correct to maintain, as Ueberweg does, that in indefinites,
R
258 INSTITUTES OF LOGIC.
when the subject is a general notion (e.g., a man, or a great general),
the proposition is to be regarded as particular, or " that the subject
is to be taken as an indefinite part of the sphere of the subject-notion."
— (Logic, p. 214.) It .must be so taken at least, but more may be
meant and mentally asserted, more may be assumed in reasoning
upon the proposition. The subject may in such cases quite well be a
universal.
In Greek the article has the force of all in universals. 'O HvOpusiros (wov
means man is animal, and all man is animal (was &p6pwiros fa0")- The
article has the power of universal determination (praefinition), (rod
KaBoAov wpoatiiopianov). But the article agrees to the unifying of the
universal subject ; wherefore it is conjoined to each of singulars (juov-
adtK&y) and of individuals (dr6fiwv), for we say 6 9)\tos (the sun) and
6 2&>Kf>oT7)s (Socrates), and sometimes we apply to what is excellent
amid the like, as when we say, 6 ironrr)?s (the poet), 6 frhrwp (the orator).
— (Ammonius Hermehe, M. De Int. f. 67b; Latine", p. 108 — cf. pp. 118,
188, 299, 300. Ed. Venetiis : 1549.) The force of the Greek article,
therefore, is twofold: (1.) To render the noun universal, to gather
up the individuals of the class into a whole — that is, to render the
concept universal, and therefore definitely general ; (2.) To mark in
singulars and individuals their definitude as such, and thus to individ-
ualise, or render the noun definitely individual. — This testimony of
expression goes to confirm the logical accuracy of the classifying of
the universal and the singular under the common head of the Definite.
We have other examples of the power of the article to render definite,
or to mark precise determination in the case of abstract nouns in which
the unity or completeness of the attribute is indicated by the prefixing
of the article, as v aper-fr, rj Sidvota-
So 6 (rb? vlbs means thy son — that is, one definite one ; while vUs <rov
means any one of thy so7is ; rb iroKirtKbv means the citizens as a body ;
rb papfSapinbv, the barbarians taken collectively; ol 6vi]toI means the
class ; Qvr)To\, mortals, some at least, though it may mean the whole class ;
oZtos esrl 6 Miviiriros means this is the distinguished Menippus ; <p(\ovs
■KOiilffOai means to make friends, — that is, some indefinitely ; rovs <pi\ovs
irotelffdcu, means to make the friends spoken of.
So in German, when we speak of the class (definitely), the article is
prefixed, as das Metall ist niitzlich — metal (that is, the class) is useful.
Die Stadt, the town, indicates definitely the single or individual town.
Das Brod, bread, the class ; ein Brod, a loaf.
In English the usage is rather the other way. The man would mean
the individual ; whereas der Mensch means the class man. But if we
say the dog, the cat, &c, we generally mean the class.
In French the articles show whether a subject is taken universally
(definitely) or particularly. When we say Vhomme est capable de bitn
et de mal, we mean tous les hommes, or the whole or class. As in
Greek, the article is prefixed to abstract nouns, as la beaute', le courage,
&c. This has the effect of individualising, and yet indicates the uni-
versal quality in all of the class. So long as there is no express restric-
tion, the term is understood universally. — (Cf. Delariviere, Nouvelle
Logique Classique, § 580-1.)
aeistotle's view of judgments. 259
§ 312. Judgments considered according to Quantity and
Quality are usually divided into four kinds : —
A. Universal affirmative — All A is B.
E. Universal negative — No A is B.
I. Particular affirmative — Some A is B.
0. Particular negative — Some A is not B.
Asserit A, negat E, sunt universaliter ambse ;
Asserit I, negat 0, sunt particulariter ambse.
In those forms, the subject in universals, whether affirma-
tive or negative, is taken in its whole extent, or distribu-
tively ; in particulars, in part of its extent. The predicate
in affirmatives, whether universal or particular, is held to be
taken in part of its extent, only, or at least ; in negatives,
whether universal or particular, the predicate is held to be
taken in the whole of its extent. This classification of judg-
ments, accordingly, must be regarded as referring to their
extension only, and we shall consider below what modifica-
tions and additions require to be made to it.
(a) Aristotle's test of the universal (rb 8e H.a06\ov) is that it may be
predicated of many (Be Int., c. vii.) ; of the singular (icad' Ijcootop) that
it cannot be so predicated. In Met., iii. 4, he says the individual is that
which is one in number. Man is a universal ; Callias is a singular.
As a proposition is an enunciation affirmative or negative, it is either
universal, particular («V M€'pe')> or indefinite (aSiSpiffros). I call the
universal, says Aristotle, the being present (uirdpx6"') with all or with
none ; the particular, the being present with some, or not with some,
or not with all ; indefinite, the being or not being present, the mark of
the whole, or the part being omitted, as the knowledge of opposites is
one, or pleasure is not a good. — {An. Pr., i. 2.)
\b) 'Yirdpxtiv, with Aristotle, means that what is in the nature of the
thing may be predicated in enunciation of the thing as subject. Pred-
ication would thus be opposed to arbitrary mental creation, and would
be an expression of reality. — (Cf. Trendelenburg, El., § 6.)
'Tirapxeiv is held to have two meanings —
(1.) One in which the predicate, is said to be in the subject, as all
B is A, — A is predicated of every B.
(2.) One in which the subject is said to be in the predicate, as all A
is B, — A is in the whole B. This is said to be the reverse of the
former.
Every B is A, means every one, hence all, — omnitude. A is predi-
cated of every one of the subject, taken distributively. A is in the
whole (of) B, means in the totality represented by B as subject. Hamil-
ton's view, however, of the statement (in An. Pr., i. 1) is that it is
260 INSTITUTES OF LOGIC.
"the preliminary explanation of the two ordinary modes of stating a
proposition, subsequently used by Aristotle. In both convertibles he
descends from extension to comprehension, from the predicate to the
subject." — (Log., iv. 302.)
(c) Universal and particular are taken relatively. The universal
may be predicated of many, and yet be itself a part of a wider notion.
The genus which comprehends individuals may be a species of a higher
genus, — as man, Callias, animated.
The universal is more excellent than the particular. Thus of two
propositions, he who holds the prior (the universal), also, in a certain
manner, knows the posterior ; as if any one knows that every triangle
has angles equal to two right, in a certain manner also he potentially
knows this of an isosceles triangle, even although he does not know
that the isosceles is a triangle. But he who knows the other proposi-
tion [the particular] in no way holds the universal, either in faculty
or in act. Further, the universal proposition is apprehended by the
intellect alone ; the particular falls under the sense. — (An. Post., i. 24.)
There are three classes of objects of thought, according to Aristotle.
(1.) Some things are such that they cannot be universally predicated
of any other thing, as Cleon, Callias, the singular thing, and the object
of sense alone, — the percept. These are properly only subjects.
(2.) But of such subjects there are things which may be universally
predicated, as man, animated. These express the genus or general
nature of the subject.
(3.) There are notions which may be predicated of others, but of
them nothing prior or higher can be predicated. These are summa
genera, to which nothing is prior and more universal, so that there is
nothing which can be predicated of them. If being or unity be attrib-
uted to these, this, according to Aristotle, is not true predication.
Being and unity are only true predicates when they define the singular,
by itself indefinite. — (An. Pr., i. 27, and Trendelenburg, in loco.)
In the Categories, c. 2, Aristotle says that ' ' individuals, and all that
is numerically one, cannot be said (predicated) of any subject. But
nothing prevents these being sometimes in a subject ; for example,
grammar is one of the things which are in a subject, and yet it is not
predicated of any subject." But, as Hamilton remarks, this is refuted
by the admitted reciprocation of the singular. — (An. Pr., ii. 23, § 4.)
" Let A be long-lived, B that which has no gall, and C all long-lived
animals, as man, horse, mule, &c. Then A is in all C, for all C is long-
lived ; but B also, that tvhich has no bile, is in all C ; if, then, C is
reciprocal to B, and does not extend beyond the middle, A must be in
B."— ( Cf. Logic, iv. p. 301.)
(4.) Aristotle hesitates as to whether what were afterwards known
as transcendent notions are to be regarded as universals. — (Met., iii. cc.
3, 4; Eth., i. c. 6; Met., iv. c. 2.) Being, thing, something, are tran-
scendent; animal, virtue, colour, figure, &c, are determinate and circum-
scribed by certain limits of predication. The former are universal in
the sense of being applicable to a plurality of objects ; but they are
not so universal or applicable in so precise a signification as the deter-
minate concepts. — (Cf. Mark Duncan, Inst. Log., i. 2 ; Salmurii, 1612.)
261
CHAPTEE XX.
OF MODALITY IN PROPOSITIONS.
§ 313. When the predicate is said of the subject barely or
merely, as by is or is not, we have a pure, simple, absolute, or
categorical proposition, that is, one merely assertory. When
the proposition is wholly resolvable into its three logical
elements, — subject, copula, predicate, — we have this kind of
proposition, as A is B, A is not B, the sun shines, bodies gravi-
tate. When, however, the proposition contains a modification
or qualification, which affects the copula, we have what is
called a Modal Proposition. It is certain that A is B. It is
believed that A is not B. It is perhaps true that C hilled D.
It is impossible that he can run over the ground in that time.
Some modes of propositions appear to strengthen the
statement ; others to lessen its effect, or the effect of a simple
assertion. It is certain, absolutely certain, above doubt, &c,
may be taken as intensifying the assertion. Perhaps, it
seems, it may be, &c, may be regarded as diminishing the
force of the simple statement. At the same time, the simple
unqualified statement conveyed by is or is not, really often
conveys a higher sense of assurance on the part of the
speaker, than the use of epithets implying absolute certainty,
or the absence of doubt. These epithets rather suggest an
attempt to suppress doubt in the mind of the writer or
speaker.1 In the language of the older and more exact
logicians, Modal Enunciation consists of the Dictum and
Mode. The Dictum corresponds to the subject, the Mode to
the Predicate of a Pure Enunciation. The Dictum is an
expression consisting of the case of the noun and the verb of
1 Cf. Wallis, Logica, ii. 8.
262 INSTITUTES OF LOGIC.
the infinitive mood, as Hominem esse animal necesse est. Here
the Dictum is hominem esse animal; the Mode, necesse est.
The Mode, it is added, is not the attribute in the Modal Enun-
ciation, and the Dictum is not the subject, but correspond
proportionally to the attribute and subject in the pure propo-
sition.1
§ 314. The so-called modality of a proposition in many cases
depends on the use of the adverb, and its natural expression
of an attribute, and an attribute usually of the verb, or it
may be adjective. We may happen to express in language
an attribute which is one only of the complex attributes
expressed by the predicate ; but thus to regard our proposition
as essentially different from the simple or assertory, would
be the merest bowing down before the husk, the accident
of expression, and worthy only of the weakest nominalism.
Whenever the mode is in the form of the adverb, it is resolv-
able into an attribute of the predicate. This man was justly
convicted, is readily resolved into a case of just conviction,
and so with all ordinary adverbial phrases or clauses. Proper
logical modality affects the cohesion of subject and predicate
alone.
(a) Every proposition expresses either that the subject is in the predi-
cate, or is in it necessarily, or may be in it. — (An. Pr., i. 2.) The first
is the absolute proposition, the propositia pura of the schoolmen. It
is called categorical by Kant and others ; but categorical with Aristotle
means the universal affirmative proposition or simply the affirmative
proposition. Under the necessary, Aristotle comprehends the impossi-
ble, under the contingent the possible. — (St Hilaire, in loco.)
The terms modal and modality are due to the commentators, not to
Aristotle; and they are akin to the grammatical moods of the verb.
With Aristotle, mood {rpSiros), primarily and properly, means any ad-
verbial qualification, as swiftly, beautifully, always, &c, and hence
mood came to mean the most general classes of those qualifications,
especially necessity, possibility, contingency, impossibility. Boethius
translated rp6iros by modus, borrowing it probably from the gram-
marians.
The corresponding modern names are Assertory, Apodictic, Proble-
matic. The rb iv8ex<S(J-wov of Aristotle was translated by Boethius
contingens, i.e., in which the issue is such that whether it may or may
not take place, is left undecided. The other meaning of contingent is
that which is, but is opposed to what is necessary. — (Cf. Trendelen-
burg, in loco.) Properly the possible is that which is not, and might
be ; the contingent is that which is, and might not be. Aristotle has
1 Cf. Duncan, Inst. Log., L. ii. c. ii. § 4 ; and Wallis, Log., L. ii. 8.
NECESSITY OF THOUGHT. 263
distinctly noted these two meanings, but apparently uses them without
always discriminating them. — (Cf. Zabarella, In De Int., c. 12.) It is
clear that the modality of a proposition, as such, depends wholly on
the form of the copula. As Vives has well said, those propositions to
which the mode is added have not a dialectical but a grammatical
significance. — (Cf. Mark Duncan, Inst. Log., L. ii. c. 2, § 4.)
§ 315. Logicians who have admitted modality into the
science have usually contented themselves, though illegiti-
mately, with recognising four kinds — viz., Necessity, Con-
tingency, Possibility, Impossibility. By Necessity is meant
that the thing or subject spoken of cannot be otherwise ; by
Contingency it is, but it might have been otherwise ; by
Possibility it is not, but may be ; by Impossibility it cannot
be, it is against the nature of the thing.
Of Necessity, such an example as this may be given ;
animal \is sentient, that is, sentiency is of the essence of
animal. It belongs to animal, and this cannot be otherwise.
Of Impossibility, the example may be given, man is not
a stone. Man being sensitive, he cannot be stone.
Of Possibility, Aristotle might have been a king, though he
was not.
Of Contingency, — Alexander was a king, and Aristotle was
a philosopher. Such things were so, but they might have been
otherwise.
(a) Kant joins together Possibility and Impossibility, Existence and
non-Existence, Necessity and Accidentally or Contingency. But the
impossible has no proper relation to the problematic. What is impos-
sible is what cannot be; and the statement is given in a negative judg-
ment, necessarily negative or apodictic. A cannot be B. Of necessity,
no A is any B.
Again, the accidental or contingent, what is, but may not be, or
might not be, is assertory, and ought not to be coupled with what is
necessary, or xohat must be, that is, with what is apodictic. — (Cf.
TJeberweg, Logic, p. 208.)
§ 316. Obviously there is no necessity in sentiency as an
attribute of animal. There is the simple fact that such a
feature is a part of the concept animal, and that this is war-
ranted by experience ; and further, that it is in all animals,
or a property of the class. But a necessity of thought there
is not in this case, nor in any case of generalisation from
experience. We find certain objects distinguished by this
feature, and we, therefore, classify them as one, or of the
264 INSTITUTES OF LOGIC.
game kind. But we do so simply on the ground of a constant
or never-failing experience ; and the feature becomes essen-
tial to any individual object to which we give the class
name, because we have already fixed on it as part of the con-
cept, for reasons sufficient or insufficient. But necessity of
thought there is none, only constancy or uniformity of experi-
ence. So with consuming paper as a feature of fire, so with
a stone falling to the ground when thrown into the air. All
is matter simply of experience, and our concepts are, as to
their constitution, relative to given experience. The essence,
or essential features of a concept, are first of all determined,
and then, of course, it is necessary that the object classifiable
under it should possess the corresponding essence or sum of
features. But this is a purely hypothetical necessity ; and
in no way makes the concept itself a necessity of thought,
however well founded as a generalisation from experience.
Impossibility has as little reference to the facts of experi-
ence. It is, in truth, merely the converse or negative of
necessity. It is necessity that a thing should not be in
such and such a manner. But so far as our ordinary and
scientific knowledge go, we have no such necessity. To
logical law, numbers, relations of space, even to meta-
physical law, impossibility of conception distinctly applies ;
but it stops there. There is no impossibility in conceiving
the reverse of any purely physical law or relation of things.
As applied to ordinary thought, it is a mere confusion of uni-
versal negation with proper impossibility.
§ 317. Necessity as applied to propositions of experience,
ordinary or scientific, means only universal affirmation ; and
this, run back to its elements, is grounded mainly on sci-
entific induction. It is equivalent, in fact, to the universal
affirmative of the logical treatises. Impossibility, in the same
relations, may be fairly translated into Universal Negation.
Thus A is necessarily B — i.e., all A is B. It is impossible that
A can be B — i.e., no A is B.
Contingency has the same references as possibility. Plato
was a philosopher, but might have been something else. Some
of the As are Bs, but they might have been otherwise. Some
men are prudent, all the men in the ship were drowned. The
cases of Possibility are obviously instances of hypotheses, or
propositions to be tested by material evidence, and thus do not
MODALITY. 265
fall within Pure Logic. Contingency is wholly extn.-logical,
and depends on our view of the nature of reality and its rela-
tions. Possibility and Contingency may apply to the indi-
vidual subject, to the particular, or even universal.
Possibility — This city may possibly be ruined by an earth-
quake. The Pretender might possibly have been a King. Some
of the sailors may have been drowned. All of the As may be Bs.
§ 318. The true view of the modal proposition is that
which makes what is called the dictum, or subordinate pro-
position, the subject of the whole proposition, and the mode,
whether necessary, possible, or contingent, the predicate of
the dictum. In this way every modal proposition really
becomes a singular, either affirmative or negative. Thus,
it is possible that all metals are electrical, in other words, this
definite proposition, all metals are electrical, is one of our possible
conceptions or propositions. There is here, properly speaking,
no question of whether the proposition (subject) is true or
false. The reference is wholly to its possible verification.
So in the case of a particular affirmative dictum, as it
may be that some men are rogues or red-coloured. The some men
are rogues or some men are red-coloured is the subject, and the
predicate of contingency is affirmed of it. Here the subject
is one definite individual statement. It is not possible, it is not
contingent, it is not necessary, — these would indicate singular
negative propositions.1 It is of no consequence to the defin-
iteness or individuality of the proposition, taken as subject,
whether it be of universal or particular quantity. It is re-
garded simply as a complete or integral statement or proposi-
tion. The subject and predicate are to be regarded merely
as simple terms, seeing that they indicate one simple definite
conception.
Modality is wholly indefinite, in fact, infinite. And there is
no reason whatever why, if any modality is admitted in Logic,
all may not. Thus we might take anything in the form of a
proposition as the dictum — anything, in fact, which the in-
definitude of expression might afford or the licence of fancy
suppose. Then the modes might be as varied, and we should
have every indirect form of speech, evasive or suggestive
phraseology, possible in rhetoric or language, to consider, and
all this, forsooth, that Logic may be expanded to the neces-
1 Cf. Wallis, Logica, ii. 8.
266 INSTITUTES OF LOGIC.
sities of what is called human thought or experience, — an
expression which is made to stand for accurate thinking and
discrimination of points that differ. All modal expressions
are, in fact, syncategorematic, and wholly external to the true
nature of the proposition, of which even they form part.
§ 319. But what is necessity ? On what ground is a proposi-
tion necessary ? Is there more than one kind of necessity ?
These questions require to be answered in regard to the first
form of modality. What branch of philosophy is to give the
answers ? Clearly that which deals with the nature, origin,
guarantee of human knowledge. But this is obviously, at
least, a very different science, or series of sciences, from that
which deals with the nature and relations of concepts in
every matter, judgments of every kind, and propositions in
every form of reasoning.
As to the possible, — that which may or may not issue, —
what is to be our test of this? Clearly something in the
character of the matter or cause, something, therefore, to
be determined by observation and induction. The possible
may depend on a law or rule of doubtful application, on a
converging series of causes, whose total result we cannot
beforehand predict with certainty. Is it seriously maintained
that an inquiry into principles which would help us to reg-
ulate knowledge or anticipation of this sort, is to be classed
with the laws which regulate actual and possible conception,
judgment, and reasoning ? We should thus require to have
recourse not only to the whole rules of Induction, but to those
of the estimate of Proof. And if the conclusiveness of our
inference from the proposition were to depend on its character
as contingent, this would be paralysed in a thousand cases,
and never be absolutely strict in any. At any rate, we should
be driven to a set of inquiries wholly foreign to the precise
and useful rules of consistent and connected thinking, with
the prospect only of indefinite delay. To reproach the
Science of Formal or Deductive Logic for not taking into
account the modality of propositions, is utterly beside the
point and futile, just as much so as to say that Geometry
does not tell you of the particular spaces it can measure, or
Arithmetic the properties of the things, pears, apples, or
cherries, which it can help you to number.
(a) Aristotle said, iracra irp6raais iffrtv if) tov virdpxetv $1 tov i£ avdyK-qs
ueberweg's view of modality. 267
tiirdpxetv ^ tov ivSexecOai. dirdpxeu'. — (An. Pr., i. 2.) From this hint
logicians have worked out modal judgments ; and though it may be
said that Aristotle's statement refers to the relations of existence or
actuality, this may readily further be taken as the ground of the
various degrees of certainty regarded as represented by modal judg-
ments.
According to Ueberweg, the notion of affirmation is " the conscious-
ness of the agreement of the combination of conceptions with actual
existence; the notion of negation, "the consciousness of the want of
agreement of the combination of conceptions with actual existence."
According to modality, "the judgment is problematic, assertory, or
apodictic. Its problematic character lies in the uncertainty of coming
to a decision upon the agreement of the combination of conceptions
with actual existence. Its assertory character lies in the immediate
certainty (based on one's own or another's perception) ; and its apo-
dictic character in the mediately acquired (based on demonstration,
a.Tr6S(t^ts) certainty of coming to such decision." — (Logic, p. 206.)
From what I have already said, it is, I think, clear that no one science,
call it Logic or anything else, could possibly deal with all the grounds
on which such judgments ought to be made, even as with a view
simply to specify the conditions, laws, and methods of determining
matter of fact, what only may be, what cannot be, what must
be. This would be the most heterogeneous science conceivable, or a
series of logics of the most varying order. One's own perception is
the basis in some cases; "authentic witness" in others; inference,
necessary inference, from another judgment. How can these be dis-
cussed from a single point of view ? Or how can they be discussed at
all, apart from the whole range of Mental Philosophy ?
Avvaffdai (to be capable), in the Aristotelic use, may be taken as
meaning possibility in the sense of the existence of the cause, and thus
of its possible operation, as a matter of fact. The seed is capable of
developing into the plant ; the plant is capable of flowering ; eVSe'xecflou
may be taken as meaning the absence of hindering or hostile circum-
stances, in other words, causes that might frustrate the possible (natural)
effect, as frost in respect to the seed in the earth. Hindering circum-
stances may further be represented by the absence of concauses, as
apart from moisture, air, suitable soil, &c, the seed will not develop
into what is potentially in it. These concauses, sometimes called con-
ditions, are truly parts or elements of the cause, which is generally
the sum of concauses. — (On this point cf. Waitz, Org., i. 376, and
Ueberweg, Logic, p. 208 et seq.) Supposing the sum of concauses or
the cause to be present, and there being no counteracting cause, the
effect will follow with necessity, that is, hypothetical necessity, or uni-
formly without exception. There is, however, even here no true logical
or even metaphysical necessity.
In an Assertory Judgment, the certainty is said to depend on the cor-
respondence between the judgment and our observation or generalisa-
tion of facts, as bodies gravitate. All the planets move with the sun in
space. Some A is B. This refers to what is known as a matter of fact.
But there is really no true distinction in respect of generalisations from
268 INSTITUTES OF LOGIC.
experience between assertory and problematic judgments. The assert-
ory judgment all bodies gravitate is not a matter of past experience, it is
not even a matter of fact. It is a matter partly of fact and partly of objec-
tive possibility, or probability, and therefore of belief. Some bodies
have been found to gravitate ; all bodies will or may gravitate. This lat-
ter proposition is not strictly assertory ; it is a problematic proposi-
tion, with the highest degree of subjective certainty. It is a descrip-
tion of the state of my knowledge or assurance regarding fact, rather
than of fact itself. It is my belief that all bodies will or can gravitate, is
the true form of the universal assertory judgment, and it is simply a
modification of the problematic.
Then the Problematic Judgment has no proper place by itself. It,
too, describes a state of my knowledge or a limited degree of assurance
regarding fact. It is the case or I know that this event can happen,
either because I know the sum of its concauses exist, or more
slightly still, because I do not know anything that can prevent it hap-
pening. This seed can or may grow into a tree, — this person may com-
mit suicide ; either because there is nothing to hinder the one, or it is
in the power of the person to do what I suppose possible. But this
indicates merely a state of limited certainty or expectancy on my
part. The subject of the judgment, if it can be so called, is not pri-
marily, as in the assertory judgment, the seed or the person spoken
of, but the state of my mind is such that I believe that the seed
can grow, or the person destroy himself. The problematic judg-
ment is simply the statement of a hypothesis which is not itself a
judgment but a conception. As far as the problematic judgment is
one, it is simply assertory. The problem is merely a stage on the
way to judgment proper, in which quite different terms will appear,
for we shall then be able to say, the seed has become a tree, — not, it is
my belief that it may.
The Apodictic Judgment has no better title to be considered as a
separate form. It, too, refers to the degree of certainty or assur-
ance, and is properly expressed in the assertory form — it is the case, or
I knoiv or believe that A must follow B. In the first place, must here is
ambiguous. It may refer to a mere physical sequence, in which must
simply represents unexceptional uniformity, as, all bodies must gravitate;
or to a sequence, metaphysical or other, in which must is strictly taken
as representing a relation the reverse of which is inconceivable, as, this
change has a cause; 5 + 5 = 10 ; all the angles of a triangle are equal
to two right angles ; nothing is less than something ; one is not none.
In the former case there is no necessity, that is, absolute necessity, in
the sequence. There is simply the high, very high, certainty which
attends a sound generalisation from experience ; and this in its univer-
sality is always only problematical, only relative to grounds of belief,
the actual facts not having, from the nature of the case, happened.
In the latter case, the judgment is simply assertory of a state of my
knowledge or belief, or of a condition of my knowledge. A change
has a cause, and I know it must have a cause, for the reason that I can-
not think it otherwise ; 2 + 2 = 4, for the reason I cannot conceive
the sum any more or less. The objective necessity lies properly in the
uebeeweg's view of modality. 269
matter of the judgment, or in that about which I think. I express the
state of mind produced by this necessity by must, as I might express a
generalisation from experience by will, or an objective possibility by may
or can; but all these are properly distinctions arising from the matter or
application of the complex subject or predicate, which is really change
having a cause, all bodies gravitating, this seed growing. These refer to
degrees of my knowledge, founded no doubt on objective fact, but none
the less capable of being stated in a plainly assertory form.
That the simple assertion is the essential and only necessary thing,
is proved by the fact that it alone is sufficient to guarantee a necessity
of inference. All A is B, all G is A, all C is B, is as valid as all A
must be B, all O must be A , therefore all C must be B. Whatever be
the relation of the terms, as to material connection, this does in no
way affect the necessity of the inference.
(6) "There is no modal enunciation," says Valla; "there is neces-
sity and possibility in the conclusion, as there is truth in all parts of
the argumentation. For all must be true whether you say it is neces-
sary, or possible, or easy, or honourable, or anything else. In this
respect the true is the same as the certain, for nothing is true that is
not certain and confessed But the truth of the two prior parts of the
syllogism and argumentation is placed as certain and confessed ; in the
last, however — that is, in the conclusion — it is extorted, and therefore
there is in it necessity or quasi necessity." — (Dialectica, L. ii. c. 39, f.
50a, ed. 1530.)
270
CHAPTER XXL
COMPOSITE JUDGMENTS HYPOTHETICAL OR CONDITIONAL,
DISJUNCTIVE, DILEMMATIC.
§ 320. Looking to the special relation of the subject to the
predicate of a judgment, as direct (or unconditional), or in-
direct (or conditional), we have, as has been already said, the
various forms of judgment, known as Categorical, and Com-
posite or Conditional. For we may assert directly, absolutely,
or simply one thing of another — that an attribute belongs to
the subject — or that something will be or happen, or needs
to be thought, if only something else in the first place hap-
pens or is thought. We may say A is B, or if A is, then B is.
If the sun is up, then it is day. A is either B or not-B. A is
either B or C or D. The world is either eternal or not-eternal.
The world is either the work of chance, or the ivork of intelligence.
This intelligence is either a single act in a remote past, or it is a
continuous act. We have thus the Hypothetical Judgment
(called also Conjunct and Conjunctive) — if is, there is ; or the
Disjunctive Judgment — this is either, or. To these should
be added the Hypothetico-Disjunctive, also called Dilem-
matic, being a combination of the two first-mentioned, as if
A is B, it is either C or D.
(a) With Aristotle categorical (Ka.Tt\yopiK6s) means affirmative. In later
usage, it is applied to a judgment of simple or absolute assertion or denial,
as opposed to the hypothetical or disjunctive judgment. — (Cf. Hamilton,
Logic, L. xiii.) Aristotle cannot be said to have recognised the dis-
tinction of categorical and conditional (conjunctive and disjunctive)
judgments, at least as grounds of reasoning, so as to form hypothetical
and disjunctive syllogisms. This distinction or addition to the Aris-
totelian view seems to be due to Theophrastus and Eudemus. It was
among the Latins elaborated by Boethius. — (De Syllogisimo Hypothetico. )
HYPOTHETICAL JUDGMENT. 271
(6) With regard to the use of Hypothetical and Conditional, it
ought to be noted that the former is sometimes employed to mark the
genus of Conditional and Disjunctive judgments, as by Aldrich and
Whately. This usage ought not to be followed. Conditional is better
suited to mark the genus of which hypothetical and disjunctive are
species, though even this term is not unambiguous. — (Cf. Hamilton,
Logic, L. xiii.)
§ 321. The Hypothetical or Conditional judgment is a
statement of relation between an antecedent and a conse-
quent, or reason and result. The form lies in the connection
or consequence. If A is, B is; or B is on the supposition
or condition that A is. Should a stormy wind blow, that wall
will fall. In this form of judgment, the condition or hypo-
thesis is attached to the antecedent or subject.
§ 322. The hypothetical judgment thus differs from the
categorical, inasmuch as the latter affirms an attribute existing
in a subject, or a subject as belonging to a certain class ;
whereas the affirmation, mental or real, of the consequent
in a hypothetical judgment, depends on the previous or con-
temporaneous affirmation of the subject. It is one thing to
say — Lying is dishonourable; it is quite another to say — If
this man lies, he dishonours himself. In the former case we
affirm an attribute of a subject ; in the latter we do not pro-
perly affirm, but state a supposition or sequence following
the realisation of a definite hypothesis. This is simply a
preparation for absolute affirmation. It is not wholly deter-
minate.
§ 323. In the hypothetical judgment there are three ele-
ments— the Antecedent, the Consequent, the Connection or
Sequence — as, If A is B, C is D. A being B is the antecedent,
C is D is the consequent. If is, or if then, is the copula, and
indicates the sequence. The effect of the copula is to bind
up antecedent and consequent into one act of judgment. It
is, in fact, a statement simply of connection. As Ammonius
Hermieas puts it : " Hypothetic enouncements are made up
of categoric. For they express the consequence or opposi-
tion of one categoric proposition and another, uniting them
with each other, by either the conjunctive or disjunctive
particles, in order to show that they constitute together a single
enouncement." l
1 On De Interpretatione, f. 3, 1546. Quoted by Hamilton, Logic ii. , Ap-
pendix B, p. 389.
272 INSTITUTES OF LOGIC.
§ 324. The sequence, moreover, is a necessary one ; for we
are supposed to have in the antecedent a reason, full and
adequate, otherwise there would be no reason at all for the
consequent. This may be founded on material considerations
of causality in the antecedent ; but this is merely the ground,
more or less valid, of the reason, or cause as a reason, — in a
word, of the necessary form into which we suppose ourselves
entitled to put the particular sequence. If the one thing is, the
other thing is. This formula, however grounded in any partic-
ular sequence, is yet independent of the given sequence, and
raises the connection to the form of a necessary one, — neces-
sary in our thinking. Even if the reason or antecedent given
were found to be insufficient to warrant the consequent, this
would not affect the validity of the principle of connection,
but only its material truth. At the same time, the principal
value in practice of hypothetical judgment and reasoning is
the material truth or actual sufficiency of connection between
antecedent and consequent in any given case.
§ 325. The Hypothetical judgment may be regarded as in
Extension, and as in Comprehension. In the former case, the
formula will be, — If A is, B is ; if man is, animal is. If all
A is B, then C (a part of A) is D (a part of B). Or, If all man
is animal, European (a part of man) is mortal (a part of ani-
mal). Here the supreme law or canon regulating the infer-
ence will be simply that of Identity. In this case Keason
and Consequent will be completely identified with the formal
law of the relation of whole and part.
In the latter case — in Comprehension — the formula will
be — (a) If A is, B is ; if the sun is up, it is day. (b) If A have
for its mark B, then C (a mark of B) is a mark of A. If the
moon presents always the same face to the earth, then, having no
diurnal revolution on her axis (a mark of always presenting the
same face to the earth) is a mark of the moon. The law which
immediately governs this proposition, or rather the inference
from it, is — A mark of the mark is a mark of the thing itself, or
Pratdicatum prazdicati est pr&dicatum subjecti. Nota noto3 est
nota rei ipsius.
The subject in this case is taken comprehensively, as that
which has immediate and mediate marks or attributes. The
strength or validity of the assertion lies in the connection,
however materially grounded, between the immediate and the
DISJUNCTIVE JUDGMENT. 273
mediate attributes. This may depend on inherence or caus-
ality, on coexistence or succession, and affects the actual
truth of the judgment ; but the form or supposition being
given, we are able logically, independently of this, to educe the
formal consequence.
§ 326. In the Disjunctive judgment, the essence or form
lies in the opposition or contrast of the several members of
the predicate, — as A is either B or not-B ; A is either B or 0
or D. The opposition among the disjunct members means
that one is to be affirmed, and one only. There is just this
much truth or assumption, that the subject is to be found in
one or other of the members, and, if found in one, is not to be
found in the other or others. In the former case, or strictest
kind of disjunction, the logical form alone necessitates the
exclusion ; in the latter case, the whole of disjunction has
been constituted through intuition ; the members are given
as exclusive on this ground ; and hence the inclusion in one
(or affirmation) implies the exclusion from the others. The
world is either eternal or non-eternal, is an instance of the
former — contradictory disjunction. A was born either in 1801,
or 1802, or 1803 ; the burglar made his escape either by leaping
from the window, or from the roof or by sliding down the rone,
are instances of the latter — contrary disjunction. Contrary
alternatives are properly, in the end, forms of contradictory.
A is either B or C or D, means really, A or not- A, B or not-B,
0 or not-C. The world is either eternal, or it is the work of
chance or of intelligence. This, strictly taken, means the world
is either eternal or non-eternal (that is, it had a beginning in
time) ; it is either the work of chance or not, — i.e., it is the work
of intelligence. As the work of intelligence, it may be of a single
act or not ; that is, it is plural or continuous. The disjunctive
statement is thus also a preparation for determinate affirma-
tion or negation, rather than affirmation itself.
§ 327. In the case of the disjunctive judgment, the copula
is eithei — or j this brings together the alternatives in one act
of conception. And this synthesis is the preliminary to the
analysis or ultimate exclusion of the one from the other. All
disjunction is affirmation and negation through affirmation, or
it is affirmation through negation. For when we say A is B,
then it is neither C nor D. It is neither spring nor summer ;
therefore is is either autumn or winter.
s
274 INSTITUTES OF LOGIC.
(a) It should be noted that disjunction has nothing whatever to
do with Community or Reciprocity, as Kant would have it. Disjunc-
tion may refer to exclusive alternatives in time, or place, or quality,
or quantity, which admit of not the slightest possibility of community
or reciprocity, in any scientific sense of the terms, or in any logical or
metaphysical sense. This time, that time, this place, that place, this
quality, that quality, &c, have, as to real reference, or logical reference,
not the semblance of reciprocity. All actual fact, indeed, is fact,
whether there is reciprocity or not ; for all fact of intuition — every per-
cept— is exactly as it is perceived, as every concept is exactly as it is
apprehended, whatever may be its possible or discoverable relations.
§ 328. There is a distinction between the hypothetical and
disjunctive, which has not received sufficient attention. In
the case of the hypothetical, as usually put, the consequent,
while dependent on the antecedent, may not be dependent on
it alone. When we say, if it rains, the earth will be wet, we
connect reason and consequent, but we do not (materially) con-
nect the consequent exclusively with the antecedent, for dew
or pouring water on the ground may make it wet. Or when
we say, if this ma)i is sick, he is not fit to travel, the consequent
may depend or be realised through other causes or reasons
than the one specified. But in the case of disjunction, there
is a wholly different conception. Our predicate in disjunc-
tion implies, from its very form, a whole, — the distribution,
in fact, of a genus into its parts or species, — and these taken
exhaustively or exclusively. This is either A or not- A. This is
either A, or B, or C, or D. The season is either spring or summer,
or autumn or winter. This planet is one or other of the eight.
In all these cases we have determined a whole within which
the subject of which we speak must be found or thought.
There is no room for an indefinite number or plurality of dis-
junct members, as there is for a plurality of antecedents, as in
the case of the hypothetical judgment. The disjunctive
judgment, therefore, approaches much more closely strict
logical form — of whole and part — than the hypothetical, at
least as commonly understood and interpreted.
275
CHAPTER XXII.
hegel's theory of judgment.
§ 329. In the following paragraphs my aim is to notice the
principal points in Hegel's doctrine of Judgment. I do this
chiefly because I find that they have been adopted without
any definite acknowledgment by writers who have referred to
certain logical points, or have expressly treated of them. I
notice them, also, because they are brought forward as speci-
mens of " advanced thought." In themselves they are of the
very slightest value — indeed, none. But as they are fitted to
impose on people, simply from their novelty — a great charm
in these times — the truth of a thing, if old, being rather
against it — they require notice.
§ 330. According to the principle of the immanent dialectic,
which has been laid down as absolute, and foreclosing a
system of the universe, an idea posited opposes itself to
its negation. This, in its turn, produces a new idea, neces-
sarily better defined or more true than the first. In this
second part, however, of the Science of Logic, called the Sub-
jective Logic, it seems that development — that is, from notion
to judgment and judgment to reasoning — does not take place
according to the principle of negation, but quite another, viz.,
that of evolution or development, akin to the progress of
organism in nature. The grain becomes the plant ; it be-
comes in an explicit form what it was virtually before. Thus
the notion passes into the judgment. The notion is the ab-
stract form, the judgment the dialectical, and the reasoning
the speculative form. Notions exist in things — things are
only living notions, also things are judgments realised ; and
reasoning is the reality in its true or speculative form.1
1 Compare for this chapter Die Subjective Logik, being the second part of
276 INSTITUTES OF LOGIC.
§ 331. But supposing the notion to be the grain from
which the judgment is evolved or which evolves the judgment,
what of the origin of the notion itself? It will surely be
admitted that the concepts of experience, and of science, are
generalisations, — that they depend upon, are due to some pro-
cess of elaboration or constitution by the mind. We need not
at present refer to the universal concepts of intelligence, such
as cause, substance, quantity, quality, &o. — which may be sup-
posed to have another origin and character. The generalised
concept is at least a cognition or relation among individual
objects of time and space, — a cognition, in fact, of similarity
amid objects or impressions at different times. Can this
be cognised without a judgment? — without judgments of
various orders? We judge surely when we apprehend a
reality or impression in time. We judge or subsume under
certain universal concepts of being, unity, difference, &c.
We remember, compare, generalise. Not one of these
acts is possible apart from judgment, — apart even from what
is essential to logical judgment ; and yet, according to Hegel,
we have to wait for judgment until the notion develops itself
into it, — the notion or so-called grain of the judgment being,
in the first instance, the product of it. By judgment we form
notions ; notions, again, evolve into judgment ; and thus judg-
ment is explained ! Such is the theory of advance in Psychol-
ogy and Logic.
§ 332. The notion or idea of a thing is precisely the gener-
ality which exists in its individual. It is neither abstract
nor distinct from things, nor posterior to them, but, on the
contrary, pre-exists in them. Our religious understanding
proves it in saying that God made the world out of nothing,
or that the world is the work of thought, or of the ideas of
God. This clearly proves that The Idea has by itself a crea-
tive power which has no need, in order to manifest itself, that
things are already produced, but which, on the contrary,
precedes their birth !
§ 333. The idea is at first general ; but its proper dialectic
force obliging it to determine itself, it becomes particular in
denying itself; and this particularising, which is the negation
Wissenschaft der Logik, ed. Berlin 1841. Of this there is an excellent abridg-
ment in La Logique Subjective de Hegel, by Sloraan and Wallon (Paris, 1854),
■which I have found of much use.
HEGEL'S theory of judgment. 277
of the general, is manifested or comes to existence under the
form of the individual. The particular and the individual are
not, therefore, separate or distinct from the general ; this
takes these forms without changing its nature ; it particu-
larises and individualises itself, but always remains what it
was at first.
§ 334. From the decrease in comprehension and the increase
of extension in the ascending scale of generalisation, Hegel
argues that God or the Supreme Being, as the last or highest
notion, is necessarily to be regarded as the poorest of all in
attributes, instead of, as He ought to be, the richest. In this
it is assumed that God or the Supreme Being is identical
with the abstraction Being, which is the summum genus in
generalisation. Of this there is no proof; in fact, it is a
perversion of accurate logical phraseology, and it is disproved
by the fact, that while Being as a general notion can be predi-
cated of all lower in the scale, God or the Supreme Being
cannot properly be predicated of any.
§ 335. The general and the particular always subsist in
the individual ; hence there are no individual notions . . .
Every individual thing is at the same time general and par-
ticular ; and this union of the general and the particular in
its bosom is precisely that which constitutes its proper
notion or its individuality, which is thus only the product or
image.1
It follows from this that in the case of a generalised con-
cept, as book, house, — this book, this house, is, as individual only,
an image or instance, represented in the imagination of the
general (concept) and the (individual) picture, and that this
in no way differs from the book or the house, which I perceive
or reach by intuition, — that is, it is untrue to our experience.
All individuals, accordingly, in time or in history, are simply
instances of general concepts embodied. Their whole in-
dividuality lies there. Proper names ought, therefore, to be
discarded from language as a superfluity. Only the particular
{some or one of all) is vindicable.
§ 336. In Hegel's view, the body and the soul of a judg-
ment are its individuality and generality, — that is, the subject
and predicate. The answer to a question gives necessarily
a subject, which is only a simple word without meaning, on
1 Cf. Die Subjective Logik, § i. c. 1.
278 INSTITUTES OF LOGIC.
which I arrest my attention to find the predicate of it. This
is a thing without attributes or qualities, which is about to
receive its determination, but which is yet absolutely noth-
ing. It is only a name or sound.
§ 337. Modern logicians say or assume, that in the judg-
ment the subject and predicate are two things or substances
equally real, having the same value, existing on the same
title and the same line, to be met with here or there in the
world, and that the human intelligence unites or relates
them in the judgment. But this hypothesis contradicts com-
mon sense and language, according to which the copula is,
which joins the subject to the predicate, says that the first
is the second ; that which proves that the act of our mind
called judgment, does not unite two things which without it
would be separated, but, on the contrary, that it separates or
divides into two parts, named subject and predicate, things
or notions, which by themselves are at the same time that
which marks the subject and the predicate. Judgment is,
therefore, an act of the mind by which we divide into subject
and predicate an idea or a thing which had not yet been
divided, before this act, into its two constitutive parts. Thus
the copula is marks not a conjunction but a disjunction, not
only an identity but a difference between the subject and
predicate, which by it are at once united and separated.
There is a thing total or one, cut, so to speak, into two by
judgment, which enables us to see it under the form of sub-
ject and predicate. In the eyes of the grammarian, the sub-
ject and predicate have an independent and distinct existence ;
but in logic, as in reality, there is absolutely none. The pre-
dicate is the subject, or rather the thing is actually the
subject and the predicate together.1
§ 338. (1.) There is no meaning in a subject taken by
itself. If this means merely that a notion or concept can-
not be realised in the mind without thinking its attribute or
attributes, or the marks which make it up, it is an idle truism.
If it means to call this process attaching a predicate to the
subject by a definite assertion implied in the copula ts, —
that is, a definite judgment, — it is psychologically false.
The marks contained in a concept as subject, can be realised
in the imagination as a picture without any such explicit
1 Die Subjective Logilc, § i. c. 2. , especially pp. 66, 67.
HEGEL'S THEORY OF JUDGMENT. 279
or express assertion. This representation is, moreover, the
ground or condition of any such judgment.
If there be no meaning in a subject — that is, a notion or
individual taken by itself, on what ground do I add a predi-
cate to it? If it is on the ground of identity, or as an
analysis of the subject, how can I predicate at all if the sub-
ject is purely a void notion ? If it is that I add on a new
predicate, how is it that I can attach in any way a predicate,
new or old, to a void subject ? When I say something of a
thing, surely I know the thing to some extent ere I say
something of it.
§ 339. (2.) Logicians, in saying or assuming that the sub-
ject and predicate in a judgment, or in some judgments,
are actually separate, either in the world or in thought, until
they are conjoined by the intelligence in an act of judgment,
are quite right. For they are speaking not immediately of
things, but of concepts simply, or of the individual and the
concept. When I say that water rusts iron, or that fire con-
sumes paper, I join together two concepts representative of
things or facts in my sense-experience. And until I have done
so, or have knowledge enough to do so, the facts lie out of
my experience. Nor in this case do I need to say that the
subject is the predicate, or that the subject is identical with
the predicate ; which would simply be false. Water is not
rusting iron, fire is not consuming paper ; but they form two
elements in one synthesis, and the latter is an attribute of the
former. I may represent water rusting iron, or fire consuming
paper, as a whole or one thing — one complete fact — which by
the act of judgment I divide or separate into two parts — sub-
ject and predicate — at once separating or conjoining and dis-
joining in the same mental act ; but all the same, I have not
identified the two concepts, — I have not even found the two
things, water and rusting iron, together only at one time, for
these are generalised concepts. I have, in order to make
this one representation in the mind of water rusting iron,
or water wearing the rock, been obliged to collect together
facts from various points of time and space ; and this gathered
experience is the ground at once of my total representation
of the thing and the judgment which follows. If the thing
be " a judgment realised," there is simply a judgment before
my judgment, which I come to learn, and to gather, through
280 INSTITUTES OF LOGIC.
generalisation, extending over time, and varied particulars,
not necessarily set together, and not yet gathered into one
total representation.
§ 340. (3.) One would be curious, too, to learn how such a
theory of judgment, even when applied to experience, would
suit those cases in which we add a new predicate to the sub-
ject,— as when Newton said, the planetary motions are due to
gravity. Was it that this hitherto unknown fact was reached
by him by dividing in the first instance a totality in his mind
— gravitating-motion, or by coming to unite, through experience
and inference, gravity to motion, which, though joined in
point of fact, had been hitherto separated in all human in-
telligences? Is not the representation as one or a whole
of gravitating-motion, of motion due to gravity, or light flowing
from ethereal undulation, the result of a synthetic judgment,
rather than the ground of it ? And is it not an abuse of words
to call the complex fact in nature a judgment, unless as
the supposed act or result of an intelligence conscious of
realising the synthesis ? And are we to talk of this with an
assurance as complete as we can of our own act of judgment ?
§ 341. (4.) Further, if the judgment be the breaking up of a
known whole, containing what we then call subject and predi-
cate, and we do not know which is which until the judgment
shows it, how can we by judging show it, and how can the
subject judging know the difference ? Is this not simply to
suppose that we have a judgment before we have a judgment ?
§ 342. The essential character of every judgment, whatever
its form, is to express that an individual thing posited as sub-
ject, is a general notion given as predicate, — in other words,
that the generality marked by the predicate is (or exists) in
the individual thing expressed by the subject. . . . The
subject or individual thing is raised to the sphere of its predi-
cate, and the predicate or the general, in its turn, is placed
in existence or realised by the subject.1 Hence, an enuncia-
tion which expresses an individual thing by its characters is
not a judgment, as, Aristotle died in the fourth year of the one
hundred and fifteenth Olympiad, aged seventy-three ; or, Ccesar
was born in Rome ; he made war on the Gauls for ten years, and
passed the Rubicon. Such statements are propositions, but
not judgments.2
1 Die Subjective Logik, pp. 69, 70. 2 Hid., pp. 67, 68.
HEGEL'S theory of judgment. 281
§ 343. There is a judgment, only when an individual
thing is determined by a general notion. Therefore, one
subject cannot be a concept, — it cannot be an abstract gen-
eral concept, — we cannot state the relation between con-
cept and concept ; we cannot speak of an abstract term ; we
can only predicate in a judgment of the individual. Nor if
the predicate be singular have we a judgment. I venture
to say that such a criterion of proposition and judgment was
never before proposed, and none more groundless or futile
could be given. We cannot say, this is not the man you mean,
or took him for. The predicate is singular, therefore there is
no judgment. Is there any further reductio ad absurdum
needed of reckless speculation or assertion?
§ 344. Hegel seems to find this doctrine rather too much
even for him. He therefore hastens to add that individual
enouncements are judgments, if they be stated in answer to
a doubt. If the time of the death or the age of the philoso-
pher were put in doubt, or if it were asked whether an indi-
vidual was really dead, or only seemingly so, the answer to
such a question would be a judgment, because generality is
involved — Has the train really passed the station or not ? It
has passed the station. This is now a judgment ; but if we
had not been in doubt about it, and asked the question, it
would not have been one ! It comes to this, that no histori-
cal proposition is a judgment.
§ 345. To show that the predicate fills the subject, regarded
as essentially void, with content, Hegel gives us the example
— God is all-powerful. Without this predicate, God would be
an empty frame. This, as the proof of a universal feature of
judgment, is simply worthless. Even as filling the subject
with content, it is not true ; it is simply adding a predicate
to what we know and may know of God otherwise. Because
we happen to add a predicate to a subject, it does not follow
that the subject was originally void. Had the predicate
embodied an adequate definition of God, it might have been
plausibly said to have filled the subject with content ; but
the predicate in this case is not such. All-powerful is not
convertible with God ; and were the statement even true of
defining propositions, this would not make it true of all.
Nay, the predicate here is even analytic, for we use it because
we already know that, if this attribute were lacking, the sub-
282 INSTITUTES OF LOGIC.
ject spoken of would not merit the name God. And what,
on such a doctrine, becomes of synthetic propositions, in
which we are supposed to add a new predicate to that which
we already know of the subject?
§ 346. The qualitative judgment represents the agreement
or disagreement of two notions. This, according to Hegel,
neglects what merits more attention — the coupling of the
individual to a general notion.
Starting from the position that judgments are enunciations
expressive of individual things by means of general notions,
Hegel divides judgments into four kinds, viz. : —
(1.) Qualitative, or of Simple Apperception.
(2.) Keflective.
(3.) Necessary.
(4.) Ideal.
§ 347. The Qualitative Judgment or Judgment of Apper-
ception affirms or denies a quality. But under this qualita-
tive form, judgment is not yet developed : for the subject,
which is nothing in itself, is here supposed essential ; the
predicate, on the other hand, being nothing in itself, and
only united to it in an accidental manner. By this form of
judgment is obviously meant the comprehensive or attributive
judgment of modern logicians.
§ 348. One of the greatest errors of logicians, according to
Hegel, is to hold that such a proposition as this violet is blue
or not blue, necessarily embraces in one or other of its alterna-
tives the truth. This may be true or false without reaching
the reality of things. That which is just is not always true.
We reply to this that the proposition is both just and true,
so far as it aims or need aim at truth. Whether violet be blue
or not, is not here the question ; nor is such a point decided.
All that is said is, these are exclusive alternatives ; they
cannot coexist in the subject ; if one is there, the other is not.
Our intuitional perception prevents us making the union. A
subject — say violet, which would unite both, would be meaning-
less, void in the true sense of the word ; — as void and mean-
ingless as to say this is a case of murder or it is not ; and yet
it may be both murder and suicide, or both murder and accident.
Hegel's argument in support of his paradox is as weak as
the absurdity of the paradox is strong. What is just is not
always true, is proved, according to him, by such examples as
HEGEL'S THEOEY OF JUDGMENT. 283
a man is sick ; some one has committed a robbery. These judg-
ments may be just or accurate, but they are not true ; for a
sick organism is not a true organism, and theft does not enter
into the true notion of humanity !
§ 349. There is nothing peculiar to this first form of judg-
ment, which does not belong to the third and fourth forms.
It merely says, — the individual (I) is a generality (G), — that
is, I — G. The violet is blue, or the individual violet is the
generality colour blue.
That the individual is a generality is expressed in the same
judgment under another form ; for this proposition, — the violet
is blue, expresses, rather implies, two things at once, — that the
violet is a whole endowed with several qualities, and that it
has that of blue. But it does not expressly say the former,
as it does not expressly say that the colour blue may belong
to other individual objects besides the violet. This first form
of judgment is imperfect, and therefore untrue.
§ 350. It is a wonderful test of the truth of a judgment,
even of its imperfection, to find it stated that as the form of
it does not express all that is possible about the matter, or
all that is implied in the matter, though what it expresses
may be both consistent and accurate, it is yet to be set down
as imperfect and untrue. Pray, what single judgment would
stand this test, except, perhaps, strict logical definition ? Are
the exigencies of thought as a process of abstraction and con-
centration to have no fitting form of expression or judgment?
§ 351. About equally instructive and convincing is the proof
that every negative judgment is necessarily affirmative.
This violet is not red, implies that it has a colour ! This ob-
viously is not implied in the form of the proposition, — it is
inferred from the matter ; because we are already supposed
to know, regarding violet, that it belongs to the class of
coloured things. But this is a wholly secondary form of
judgment, — an accident, indeed, of the matter about which we
judge. The negation of the predicate as the form of judgment
does not put a positive in the place of the negation, even
in the case of the qualitative or comprehensive proposition.
For we may say, The man of whom you speak did not inherit
the property. This, certainly, does not imply that he inherited
anything else, or that there was anything else to inherit.
§ 352. The insufficiency, according to Hegel, betrayed in
284 INSTITUTES OF LOGIC.
those two sorts of judgments, — the qualitative affirmative and
negative, is corrected by making the two terms of the proposi-
tion identical. Thus, this blue violet is a blue violet. But this
is not a judgment, it is simply a tautology. So with all nega-
tive judgments called impossible or infinite, — as this table is not
an animal; the rose is not a plant. In the case of tautology,
the predicate is absolutely identical with the subject ; in the
other case, absolutely different. There is no putting an
individual subject (I) in relation with a general predicate.
All qualitative judgments issue either in tautology or in a
futile infinity. And yet, as if to show the very licence of
the possibility of differing, Hegel holds that negative infinite
judgments exist. A crime is a negative infinite judgment,
for the criminal not only denies the right of the individual,
but the right of the State. Death, too, is a negative infinite
judgment, for soul and body are separated so as to have no
further relation.
§ 353. One fails rather to see the point of the imperfection
of the form of the qualitative judgment ; and certainly, if
there be imperfection, we shall not find the correction in the
formula given by Hegel, which is a simple travesty of fact
and form. This violet is blue, means, it seems, this blue violet
is a blue violet. It means necessarily nothing of the sort, and
it can only be travestied into this on the basis of another
previous judgment and meaning. This violet is blue means
— (1) that I select or attend to the colour or blueness of the
violet I see, and not to its shape or form, or other qualities, to
which I might have attended ; (2) that it has the mark blue,
and not that of any other colour which it might have had.
All this implies judgment, and judgment of an important and
essential kind. It is the foundation, and affords the formula,
of all observation, all concentration, and therefore of accu-
rate thinking and science. Nothing of this is formulated
in saying this blue violet is a blue violet, for this is a secondary
or derivative statement, founded on the primary observation
and judgment — that of fact regarding the object I see, and
only possible after I have apprehended the predicate blue as
its mark. I am not first speaking of what I know to be a
blue violet, for violet and blue violet are not identical ; and
this statement, this blue violet is a blue violet, is only
possible through an addition to my experience, — that is, the
HEGEL'S theory of judgment. 285
other natural judgment by which I superadd a new predicate
to the subject.
§ 354. As to negative infinite judgments, as Hegel calls
them, it is clear that he does not know precisely what an
infinite or rather indefinite term, ovofia aopta-rov, is.1 The
so-called predicate in such a judgment is not in the least
degree more in analogy with the predicate of a qualitative
judgment than with that of any other.
§ 355. But as there is thus tautology in identifying the
two terms, there is no correction of the imperfect form of the
qualitative judgment. Also, when the two terms are abso-
lutely unlike, there is as little correction of the imperfect form.
Hence the dialectic force drives us to the following form —
Reflective Judgment.
§ 356. The Keflective judgment explicitly translates the
truth of the qualitative — viz., that the subject does not exist
alone, but that there is a predicate, that is, a relation to a
thing which exists out of it.
When we say this violet or this flower is blue, we may con-
sider the subject or individual (I) as existing of itself; in
this reflective judgment, on the other hand, as this plant is
salutary, besides the thing in itself, we always think of some
other thing, as the malady which the plant can cure.
In the Qualitative judgment, the individual was the prin-
cipal thing, in which only the predicate appeared to inhere.
In the Keflective, it is the predicate or general which becomes
the important element. Thus — Man is mortal ; all matter is
heavy ; all things are perishable ; certain forms of matter are
elastic.
§ 357. There is no such difference in those two kinds of
judgments as is here supposed. The qualitative judgment
about the individual passes readily into the reflective, really
extensive judgment. The predicate in the former case may
be at first individual, but as such it is the ground of a class
— actual or ideal. And this class it grounds or forms is
just as much a generality as that given in salutary, useful,
&c, or any other common term. The whole of this is a
mere wandering from what is essential and relevant, and
shows a constant confusion of matter and form.
§ 358. What can be more arbitrary or more misnamed as
1 See above, p. 175.
286 INSTITUTES OF LOGIC.
necessary evolution or dialectic than this progress from the
reflective judgment to the necessary ?
Certain forms of body are elastic, means, it seems, that elas-
ticity belongs to all bodies, but more particularly to some !
Hence the subject loses its character of individuality, becomes
general, and thus the subject and the predicate may be substi-
tuted for each other ! But when the generality enters ex-
pressly into the subject, as all bodies are elastic, it is no longer
a fact which we express, but a necessity. Hence the tran-
sition from reflective to necessary judgments. A doctrine
which is based on the identification of some and all, which
confounds universality with necessity, and is supposed to
be bolstered up by a hypothetical dictum, — what can be said
of all the individuals belongs necessarily to the species, — may
be fairly left without comment.
§ 359. In necessary judgments, the subject and predicate
are so related that the one is the true essence or substance of
the other, and reciprocally. Further, they are subordinated
as individual to the species of which it forms part. Thus,
the violet is a flower, this ring is of gold, gold is a metal.
The copula is here marks not simple existence, or relation,
but absolute necessity. To say that gold is dear, and gold is
a metal, is to state two totally different judgments. Dear is
an accident, and metal marks the essence.
The form of proposition, gold is a metal, says implicitly
that the quality of metal belongs not only to gold, but to
silver, copper, iron, &c. Whence it follows that judgment
does not carry in itself the proof or reason of its truth or
necessity. This reason is expressed in the second form of
necessary judgment, — the Hypothetical or Conditional — as,
if this thing is, this other thing must be also, or if A is, B is.
Judgments of this class almost deny the existence of the
two terms A and B, by showing that neither A nor B can
exist alone by themselves, because A is not only A but B.
Without losing the one, we recover the other in the Dis-
junctive form — that is, the third and last form of the neces-
sary judgments. Thus A [genus] is either B, or C, or D
[species). These are the only species and all the species.
But we need science to show us that the species actually
enumerated complete the genus. We need, therefore, another
form of judgment to show this.
hegel's theory of judgment. 287
§ 360. This leads to the highest of all, — the Ideal Judg-
ments. These are conformed to the idea by which we judge
that which is according to that which ought to be. Here the
copula is has acquired all the energy which it ought to have.
The first form of the Ideal Judgment is purely Assertory,
as, this action is good, this house is beautiful. But as doubt is
not resolved, this judgment is really problematic.
The second form, — the Problematic Judgment, — is more
advanced, since it is more explicit. It says, In this or that
point of view this house is beautiful. But in this form there is
still a doubt. Hence the need of another form — the Judg-
ment Apodictic. This tends by itself to reject all uncertainty,
repel all objection. This (which shows the individual thing)
house (which marks the general) built in such and such a way
(which indicates that which it has of the particular) is bad or
beautiful (which formulates the apodictic judgment). Hence this
(individual) is finally a genus, rendered manifest in particu-
larising itself. The dialectical force disengages itself from
the apodictic judgment, and passes into reasoning.1 These
latter dogmata may very fairly be left without comment.
1 Die Subjective Logik, p. 89 et seqq. Cf. the summary given in La Logique
Subjective, p. 40 et seqq.
288
CHAPTER XXIII.
THE POSTULATE OF LOGIC THE QUANTIFICATION OF THE
PREDICATE NEW PROPOSITIONAL FORMS.
§ 361. Logic, as the science of the form of thought, neces-
sarily demands that in the case of every given thought, — be
it Concept, Judgment, or Seasoning, — the thought should
be strictly analysed and determined, so that all that is in the
thought, and nothing but what is in the thought as a mental
fact, should be expressly set forth in language or symbols.
In this Logic asks nothing more than is required by every
science which seeks its own perfection. Every science, in
dealing with a matter or datum, seeks to know precisely and
determinately what that datum is ; and Logic as the science
of the form of thought, requires to know exactly the thought,
and its precise limitations, as in the mind.
Hamilton has expressed this in what he calls the Postu-
late of Logic. " The only postulate of Logic which requires
an articulate enouncement is the demand that, before dealing
with a judgment or reasoning expressed in language, the
import of its terms should be fully understood. In other
words, Logic postulates to be allowed to state explicitly in
language what is implicitly contained in the thought."1 This
is essential to a scientific Logic. As a science of law and of
the laws of thought, it must know precisely what it has got
to regulate. The ambiguities and ellipses of language are
thus, first, to be cleared up. Neither purely empty terms, nor
ambiguous terms, nor so-called indefinite judgments, nor enthy-
mematic reasonings can be accepted by Logic as they occur.
Logic demands that these be rigorously cleared. And, in this
1 Logic, ii. sect. 6, and ii., Appendix, p. 252 et scq.
POSTULATE OF LOGIC. 289
precision, there is revealed the true state or process of the
thought. Whatever amount of elliptical expression may be
permissible in ordinary or in rhetorical speech, Logic allows
none. It is not necessary as a speaker or writer that one
should use the explicit form of thought which logical analysis
demands, but it is necessary that the logician should make
articulate the state of any concept, judgment, or reasoning,
or that it should be given to him in an articulate form.
Logic will thus teach us how we really think, when we seem
to think otherwise than we do. Contradiction, vagueness,
want of consecution, in our thinking, can thus, and thus only,
be scientifically exposed. Such a postulate is a simple
necessity for logical purposes. Thus only can we extricate
the meaning clothed or hid in words. A proposition, as ex-
pressed in language, may have various meanings, according to
intention and emphasis. It may be involved, defective,
redundant, obscure, and until it is stated directly, categori-
cally, in the case of a purely affirmative or negative judgment,
it is unfit to be dealt with logically.
This postulate not only may, but must be made by logic ;
and it underlies the practice of every logical analyst. " It
is the function of the logician, from the various formulas
of speech (however involved), and from the scope of the
oration or speaker, like a skilled anatomist to resolve or to
dissect, member by member, what is said, that he may dis-
tinctly perceive (at least in his own mind) what is said of
what, and how far, whether of the whole or of the part."1
As has been said, whatever helps to exclude error, and to
simplify logic, is a real addition to the science.
§ 362. It is from an application of this postulate that
Hamilton reaches his doctrine of a Quantified Predicate ; and
on it as a general principle this doctrine rests for its vindi-
cation. It is clear that the postulate must be admitted, in
other words, ordinary language must be translated into exact
terms ; ellipses must be supplied. We must state in language
what is efficient in thought ; and before proceeding to deal
logically with any proposition or reasoning, we must be
allowed to determine and express what it means.2 The pos-
tulate is demanded by the ordinary logic not less than by that
1 Wallis, Logica,ii. 11.
2 Logic, ii., Appendix, p. 270.
290 INSTITUTES OF LOGIC.
of Hamilton. And if Hamilton's application of it in the
analysis of judgment and reasoning show elements essential
to those processes in our ordinary or actual thinking, it only
carries out the Aristotelic analysis to a fuller and more sci-
entific issue ; and its pretensions to this must be tested by
the accuracy of the analysis, and the necessity of the new
forms in thought.
§ 363. The first application of the Postulate may be fairly
taken in reference to the subject of Propositions. Here as
everywhere we need explicitness in the data. Hamilton's
classification of Propositions (Judgments) according to
Quantity is new and important. The judgment is the pro-
position as thought ; the proposition is the judgment as
expressed in language. The judgment is (a) either of de-
terminate (definite) quantity, according as we know and cir-
cumscribe the objects of which we speak ; or (b) it is of
indeterminate (indefinite) quantity, according as the sphere
is not known and not circumscribed. Determinate or Definite
Judgments relate either (a) to an undivided whole, and thus
form a General and Universal Proposition, or (b) to a unity
indivisible, and thus form an Individual or Singular Pro-
position. An Indeterminate (indefinite) judgment refers to
some indefinite number less than the whole of a class, and
thus forms a Particular Proposition. Thus, every X is Y ;
every mineral acid is a poison — is a Universal Proposition.
Here we speak of the whole number of objects in the class.
Catiline is ambitious — is an Individual Proposition. Here
we speak of the whole, but it is a single object. Some men
are virtuous — is a Particular Proposition. Here we speak of
some indefinite number less than the whole.
The quantity of a judgment is thus always either indefinite
or definite. In judging, we must judge either of some, or of
the whole, taken universally or individually. These are the
only quantities of which we ought to hear in Logic ; and the
expression, — the propositional form of the inner thought, —
must, for purposes of exact logical analysis, adequately and
thoroughly indicate the extent of the judgment. Hence what
are called Indefinite Propositions — that is, propositions which
do not indicate by their language the extent in which the sub-
ject is taken, whether indefinite or definite, cannot as such be
dealt with logically. They should be called Preindesignate
QUANTIFICATION OF PKEDICATE. 291
Propositions — that is, propositions to which in language no
mark or designation of their quantity, as in thought, is
attached. When this is done, when a verbal sign, some or
all, marks the extent in which they are actually thought,
we have Predesignate Propositions.
§ 364. The new propositional forms arising from the Quan-
tification of the Predicate are vindicated as legitimate, — as
proper material of the science of logic, the moment they are
shown to be possible forms of judgment or thought, and they
can be shown to be more than that, — even necessary forms.
Logic, as a science, must be " an unexelusive reflex of thought,
and not merely an arbitrary selection out of the forms of think-
ing." What may be the frequency or infrequency of the
use of the form, — its importance or comparative insignifi-
cance,— has really little to do with the question of the legiti-
macy and necessity of it in the pure science of logic. All
that is required to be shown is that the form in question is
at work in our actual thinking, — it may be to us wholly
unconsciously at work, — but if it be so, it is the function of
Logic as a science to detect and unfold it, to bring it clearly
out in the light of consciousness and explicit knowledge.
And Logic is not complete as a science, until it has done
this with every form of thought, be it judgment or reason-
ing, actually in operation in the mental processes. And
this can be shown by even the weakest of the propositional
forms — parti-partial negation. In other words, Logic, as
at least the science of inference, must know as a requisite to
inference the precise meaning of the concept, or proposition,
from which the inference is supposed to be possible. And
if there be even the shadow of a lurking " meaning " in the
proposition, that must be explicitly stated, otherwise Logic
cannot begin even to exercise its function. And this com-
pletely vindicates Hamilton's Quantified Predicate ; for the
express quantification is, as he says, to be produced "on
demand," and that is all which his doctrine requires.
(«) Mill actually regards the logical postulate as a particular case
of the Principle of Identity " in, as he says, its most generalised shape.
It is a case of postulating to be allowed to express a given meaning in
another form of words. " — {Examination, p. 483.) It is a case of nothing
of the kind. There is no "given meaning" to commence with. It is a case
of asking that the person speaking should expressly say what he means
to say, and all that he means to say. His meaning is only given when
292 INSTITUTES OF LOGIC.
it is fully expressed. If, for example, he is speaking of all of a thing,
he should say so ; or of some, that he should say so. Or, if he is reason-
ing with a suppressed premiss or reason in his mind, that he should
state it in order that it may be scientifically — that is, logically, dealt
with.
§ 365. " In fact, says Hamilton, ordinary language quanti-
fies the predicate, so often as this determination becomes of
the smallest import." l This is done, for example, when we
speak of any definite number, as all of a class. The three boys
here are all that were in the field. Eight stars are all the planets.
These were certainly some of the rioters.
§ 366. We further expressly quantify the predicate every
time we frame a definition, for in a definition proper, sub-
ject and predicate are not only convertible, but alone con-
vertible— as man is rational animal. The test of this is
that all rational animal is man. A good government is that
which has the happiness of the governed for its object ; hence
every government which has the happiness of the governed for its
object is a good one. Common salt is chloride of sodium, and
conversely. Unless the universal quantification of the predi-
cate be here admitted, and that in an affirmative proposition,
it will follow that a definition cannot be stated in a single
proposition. In fact, every simply convertible universal
affirmative, implies that the predicate is taken in its fullest
quantity, as all, — either every one or the whole. This occurs
every time we identify one class with another — one total
or whole with another.
(a) The quantification of the predicate is further justified by gram-
matical usage — that is, by the form which expresses the ordinary
requirements of speech. In Greek the definite article, as we have
seen, has a power of specification, in other words, of rendering definite,
— either in the form of universality or singularity. — (See above, p. 258. )
And the rule as laid down by Ueberweg is as follows: "Whenever
the predicate in Greek has the article, the spheres of the subject and
predicate notions coincide ; when the spheres of the subject and predi-
cate notions do not coincide, the predicate in Greek has never the
article." — (Logic, p. 315.) When we say eipfy-o ecrrl ra.ya.d6v, peace is
the good, or highest good, we quantify the predicate by the article, both
in Greek and English.
Quantification of the predicate by the superlative degree is of course
of the commonest occurrence, as kIvvuis ya.p aurv fxtylffrri 5^ rots
"EWrja-iy eyevtro ; just as we might say in English — Sirius is the
brightest star in the heavens.
1 Logic, iv., Appendix v. (c).
EXPONIBLES. 293
The formation of what are called Substantival Phrases by means of
the article with the infinitive is really the specification of an attribute,
as rb afxaprdvav, sinning, rb ehai, rb <pi\siv. The article prefixed to
the neuter singular of the adjective also specifies attribute, or abstract
name, as rb nak6v, the beautiful ; ra, KaXd, beautiful things — that is, in
extension. So in German das Gute, the good ; die Guten, the good people.
The definite article in Greek is used as a pronoun, as in Homer, —
NeVTWfj 6 yepwv, — Nestor, that aged man. In this case there is equiva-
lence of subject and predicate, as in a singular judgment.
The child plays alone (solus) is ix6vos d irals irai(et (predicative) ; 5 fi6vos
7rcus traiCfi, the only child plays (unicus). — (See Clyde's Greek Syntax,
pp. 18, 19.)
In the connection of was with numerals, we have an example of the
quantified predicate of absolute totality, as rb. ■na.vra titica, ten in all.
Take away the article, and say ndvra Sena, and then it means ten oj
each — that is, there is the difference between totality and distribution.
§ 367. There are certain propositions regarded as com-
pound, which proceed on a total quantification of the predi-
cate, even in affirmatives, and which are most readily and
properly resolved into the logical formula of A is all B, or
all A is all B. These are chiefly Exclusive and Exceptive
Propositions.
Exclusive and Exceptive Propositions are known in the
Parva Logicalia, and in subsequent logical treatises as Pro-
positions Exponibiles. They formed the stock-in-trade of the
Terminalists from Hispanus downwards. Scheibler, among
others of the moderns, has given an exposition of them.
One general rule is that every exclusive proposition is
resolvable into an affirmative and a negative, — man alone
is rational is equivalent to man is rational, and what is not
man is not rational ; the first is the propositio exponibilis, the
other two the propositiones exponentes.1
In Exclusive Propositions, or rather " inclusive limited by
an exclusion,"2 there is a tacit quantification of the predi-
cate, thus, God alone is worthy of being loved for His own sake
is called an exclusive. It is held to contain two judgments,
— (a) that God is to be loved for His own sake, and (b) that
other things are not to be loved for their own sake, or ought
to be loved for God's sake. According to the principle of
the quantified predicate, this would make one proposition
— viz., God is all that is worthy of being loved for its own sake.
1 See Scheibler, Op. Log. iii. 7. Hamilton, Logic, iv., Appendix v. (c).
2 Hamilton, Logic, iv., Appendix v. (c).
294 INSTITUTES OF LOGIC.
And this is convertible. Others may be similarly resolved,
as — Quas dederis soles semper habebis opes. Nobilitas sola est
atque unica veritus. Hoc iiniim scio quod nihil scio. Una
salus victis — nidlam sperare salutem. Unus Dominus, una
fides, unum baptismum.
These and other apposite examples of Exolusives x may be
readily reduced to one proposition, on the principle of the
Quantified Predicate. At the same time, every such propo-
sition may be contradicted or negated in three ways, — for
(a) we may deny, for example, that virtue is nobility, or
agrees with the subject at all ; (b) we may maintain that
birth confers nobility as well — that is, agrees with something
else ; and (c) that birth confers nobility and not virtue — that
is, we may maintain both.2
It is certain that there is nothing certain — or, uncertainty is
all (the only) certainty. This may be denied (a) by saying,
with the dogmatists, there are things of which we are certain,
and there is certainty ; or (b) with the Pyrrhonists, everything
is so uncertain, that it is doubtful whether there is nothing
certain.3
§ 368. It is clear, I think, in such cases, that the proper
opposite of such propositions is that which denies the exclu-
sion. We deny, for example, that virtue is the only nobility,
or is all nobility. Other propositions may follow from this as
immediate inferences, as, for example, that other things make
nobility, or that there are some things which are noble,
though not virtues. To maintain that virtue is not nobility
at all, is to go beyond the limit of the negation which we
need to assert as the opposite of the proposition.
§ 369. In Exceptive Propositions, we affirm something of
the whole subject, with the exception of certain subordinate
objects or clauses under it. This is indicated by an excep-
tive particle. Thus, none of the philosophers, except the Pla-
tonists, recognised the spirituality of God. Except the wise man
(of the Stoics) all men are tridy fools. Avarus nisi cum moritur,
nihil rectefacit. Nemo Imditur nisi a seipso*
These are obviously resolvable into, those who recognised the
spirituality of God were all Platonists ; or better, Platonists
were all who recognised the spirituality of God. The wise man
of the Stoics is all the class wise, or the wise man of the Stoics is
1 See Port Royal Logic, Part II. c. 10. 2 pM. 3 Ibid. 4 Ibid.
QUANTIFICATION OF PREDICATE. 295
•>
the wise man. The proper opposites here are, other besides
Platonists recognised the spirituality of God, — or Platonists were
not all who recognised the spirituality of God. So other men were
wise besides the wise man of the Stoics, or he does not exhaust the
class wise. This is all we need to assert for purposes of
denial. We need simply to deny the convertibility of the
proposition. We do not require to say, the wise man of the
Stoics was a fool, or he was a fool and other men were not, — as
has been suggested ; * though no doubt such propositions
would have the effect of denial. It may thus be admitted
that Exclusive and Exceptive Propositions may be regarded
as compound, but it is obvious that they do involve the
quantification of the predicate, and the simple and scientific
way of treating them is to resolve them into this logical
form. Thus only can we set against them their proper and
relevant contradictory, or bring them to the test of the mutual
convertibility of subject and predicate.
When it is said that pain is the greatest of all evils, we need
only to deny its maximum degree, not the fact of its being an
evil, or to assert that it is no evil, as has been suggested.2
§ 370. But in truth the express quantification of the predi-
cate follows as a necessity from the very nature of predication
in extension. The predicate in extension indicates a class.
Affirmative predication is the reference of the subject to the
class. It must have some place in the class — some at least.
This is the first requisite of the act. Plant is organised — that
is, some at least. This I must know before I say it, — before
I express predication at all. Why, then, not designate the
extent in which I mean the predicate term to be taken?
Again, I may know and mean that the place of the subject in
the class is that it occupies the whole of it. I say, all tri-
lateral is triangular, — meaning all triangular. Why not, even,
to avoid ambiguity, express this? I may, of course, only
need, for the purposes of my argument, to say that it is some
at least. Then let me say so. But if I mean all, I am equally
bound to express it in logical argument. So with not any, and
with not some, as a mark of particularity in negatives. If what
I have in my mind is not any of the class in a negative, I
am bound • to express it designately. If only not some, I am
under a similar obligation, for these are very different state-
1 See Port Royal Logic, Part II. c. 10. 2 Ibid.
296 INSTITUTES OF LOGIC.
ments. I am not bound, of course, to express in language
more of the predicate than I mean, or use, or need, in the
argument. I am thus not bound always to say, though I
know it to be the case, that all of the subject is all of the
predicate, if some of it will suit the needs of my argument.
But I am bound in logical strictness to state whether I use
all or some. This is really all which the quantification of the
predicate implies. And as such, it is a simple necessity of
logical exactness, and therefore of logical science.
§ 371. While the predicate of any one of the four ordinary
logical forms remains without express quantification, the pro-
position is left ambiguous. If I say, for example, All A is B, —
I may mean some of the Bs, — or all of the Bs. I may mean
all A is some B, or all A is all B. If I say no A is B, I
may mean no A is any B, or no A is some B. No plant is any
animal ; no planet is some star.
The ordinary Logic assumes that men usually, or rather
universally intend to assert in a universal affirmative (A)
that all A is [some) B, and in a universal negative (E) that all
A is not any B, or in a particular (0) that some A is not any B.
But even adding to these the particular affirmative (/), do these
exhaust the possible or scientifically valid forms of statement
or proposition ? Do they exhaust even the necessary and
useful forms ? Hamilton answers no ; and he claims the
right (1) to give express, not merely understood, quantifica-
tion to the predicate alike in affirmative and negative pro-
positions recognised on the ordinary system, and (2) in virtue
of the same principle to give an express quantification to the
predicate in other propositional forms. He further challenges
the validity of the two received logical canons (a) that in
all affirmatives the predicate is particular, and (b) in all
negatives this predicate is universal. Hamilton's procedure
is in no way a departure from logical method or principle. It
is simply a demand that what is understood in thought, as the
nature of certain propositions, should not remain implicit or
understood, but should be expressly set forth, and that this
demand, realised in some propositions, should be applied to all.
§ 372. The vindication of the quantifying of the predicate
depends mainly on this, as to whether it subserves the end of
testing inference, the main aim of Logic. That it does so, as
regards immediate and mediate inference alike, is indisputable.
QUANTIFICATION OF PREDICATE. 297
When I apply the predicate to a subject, do I mean to say-
that it applies to the subject only, or to the subject at least ?
Plant is organised — do I mean by organised some at least —
or do I mean that organised applies to nothing more than
plant ? These are two very different statements indeed ; and
they afford very different kinds of inference. Organised as a
predicate, and therefore as a middle term in a reasoning, is
wholly ambiguous, until the specific limit of it is precisely
cleared in expression. Logic to be scientific, to exhibit pro-
perly inferences, must demand the explicit quantification as a
preliminary. Common thought and speech may be satisfied
with the minimum of quantification — the some at least. Logic
must know whether or not the maximum is intended and meant.
(a) " The syllogistic theory is not an analysis of the reasoning process,
but only furnishes a test of the validity of reasonings, by supplying
forms of expression into which all reasoning may be translated if valid,
and which, if they are invalid, will detect the hidden flaw. " — (Examina-
tion, p. 513.) That is, we can have a test of valid and invalid reasoning,
which is not founded on an analysis of the reasoning process. A form of
expression which does not express any analysis whatever of the reason-
ing process, might be — nay, is alleged to be, the test of the validity
and invalidity of all reasoning. Words are higher than thought — the
test of its validity — words that do not in any way necessarily express
the inner process of thinking ! On this supposition, Mill for a moment
admits that " a form which always exhibited the quantity of the predi-
cate might be an improvement on the common form." — (Ibid.) He is
even " not disposed to deny that for occasional use, and for purposes of
illustration, it is so. "
(6) " There is not a single instance, nor is it possible in the nature
of things that there should be an instance, in which a conclusion that
is provable from quantified premisses, could not be proved from the
same premisses unquantified, if we set forth all those which are really
involved. If there could be such an instance, the quantified syllogism
would be a real addition to the theory of Logic ; if not, not. "— ^(Ibid, p.
518.) In other words, there is not a single instance in which a conclusion
that is provable from quantified premisses could not be proved from
the same premisses unquantified, if we quantify these. What is the
setting forth all those which are "really involved," but the express
statement of the degree of distribution or quantification of the terms ?
And this is the summary of Mill's criticism of a new logical theory,
which, whether competent logicians accept all its details or not, has
certainly modified all logical doctrine since its promulgation.
(c) The climax of objections to the quantified predicate is reached
in the grand, undefined, verbalism — "a psychological irrelevance."
Yet Mill tells us this process, in general forms of proposition, is
familiar to the ordinary logic which represents accurately processes of
thought. That which is essentially sound in several cases, and,
298 INSTITUTES OF LOGIC.
therefore, in its principle, becomes "a psychological irrelevance," —
when extended to other cases.
§ 373. Hamilton says every predicate is quantified in
thought — at least in extension. But what is meant by
quantified? In the first place, when we say that the predi-
cate applies to the subject, be it attribute or class, we must
mean and say that it is coextensive with the subject at
least. The predicate is thus necessarily quantified in
thought, whether taken comprehensively or extensively.
In comprehension the attribute does not vary ; in exten-
sion the class does vary. In extension the predicate may
not be quantified at more than the necessary minimum ;
but it is quantified. In the second place, if the predicate
apply to more than the subject, as it may, and if we know
this, as we may, the predicate is quantified in thought by
some only. The river runs, — it is one only of the running
things. Other things run also. In the third place, if the
predicate apply to the subject only, — as equiangular to equi-
lateral,— and we know this, then it is quantified in thought.
It is a very odd ground of objection to the doctrine that the
predicate is always quantified in thought — that there is al-
ways a minimum amount of quantification in thought — that
there may be a higher known to us — that is, in thought.
Why not, therefore, to remove ambiguity, on demand, state
expressly in language what we think and mean ? How else
can we logically deal with the thought? Hamilton's state-
ment is thus thoroughly vindicated, that in every case there
is a quantity in thought, and this ought to be set forth in
expression. The habit of looking explicitly at the quantity of
the predicate — considering in all cases exactly what we mean,
is of the greatest utility in simplifying our logical statement,
in restricting it, guarding it against ambiguity and the possi-
bility of invalid conclusions.
(a) Mill has no correct conception of what quantification of the
predicate means. He has no conception that when the subject is
regarded as coextensive with the part at least of a class, — this is
quantifying the predicate — i.e., particularly. His confusion is that
he imagines that to quantify the predicate means always thinking of
it as embracing other things (or subjects) besides the present subject —
or subject spoken of. This, no doubt, is quantifying the predicate,
but it is only one case of it. The river runs is one only of the running
things, — this is quantification ; but there is no less quantification when
OBJECTIONS TO QUANTIFICATION. 299
I say the river ruiis at least, or simply the river runs, because I have
made the quantity of the predicate coextensive at least with the sub-
ject— river ; it is one at least of the running things. This comes out
quite clearly in the statement that the predicate has usually no quantity
in thought, because it is simply thought as coextensive with the sub-
ject ; and in the statement that in a universal proposition we think
of the subject "as its several parts." — (Ex., p. 512 and note.)
(b) Mill imagines that he disproves the existence of a quantitative
judgment in thought, because we can judge qualitatively — or in com-
prehension— without reference to quantity. He appeals triumphantly
to "every reader's consciousness" that we can judge that all oxen
ruminate, without knowing or considering whether anything else does.
He might have learned from Hamilton himself that in the comprehen-
sive judgment the predicate as attribute appears without quantifica-
tion. But this in no wise settles the question as to whether, judging in
quantity with the predicate as a class, we can judge without a specific
meaning as to quantity. In this case we must mean that oxen are
some at least of the ruminant, or all of the ruminant, or some only of
the ruminant. It is true, as Hamilton lays down, that " in reality
and in thought every quantity is necessarily either all, or some, or
none."
It is as ridiculous to say that no predicate is universally quantified
in thought as to say that every predicate is. If we understand our
meaning, — if we have a definite meaning, which we ought to have, —
we either think of the predicate as some, or all.
§ 374. It is not true that "the logic of the quantified pred-
icate takes the comprehension out of propositions, and leaves
them a caput mortuum" x A proposition in Extension derives
its meaning from the corresponding proposition in Compre-
hension, on the general principle of the correlation of the two
quantities. This is Hamilton's doctrine from beginning to
end of the whole matter.
(a) Mill admits everything for which Hamilton contends as to the
fact of our judging and reasoning in Comprehension as well as in
Extension. He admits that the former is prior and more natural ;
that the latter flows from the former — is, in a sense, identical with
it, true if it is true ; that the ordinary logics proceed exclusively on
Extension in judgments and reasonings ; that this is hurtful in practice.
I appeal to the pages of his Examination, in chapter xxii., p. 497 et
seqq., for the truth of these statements. Yet he makes these admis-
sions as a preliminary to an attack on Hamilton for holding them —
for introducing Comprehension into Logic ! On this and other points
in Mill's criticism, see the admirable exposure given in Hamilton versus
Mill [by Mr Simon]. It is greatly to be regretted, in the interest alike
of fair criticism and the science of Logic, that the author has not yet
given Part III. to the public.
(b) But the critic waxes still bolder. We do not, according to Mill,
1 Examination, p. 517.
300 INSTITUTES OF LOGIC.
usually quantify even the subject in thought, in the sense which Sir
W. Hamilton's theory requires. "In an universal proposition we do
not think the subject as an aggregate whole, but as its several parts.
We do not judge that all A is B, but that all As are Bs. All A is a
very different notion from each A. What is true of A only as a whole
forms no element of a judgment concerning its parts." . . . "If all
A is all B is time at all, it is true only of A considered as a whole,
and expresses a relation between the two classes as totals, not between
either of them and its parts." — {Examination, pp. 512, 513.)
Hamilton's theory requires only what in fact and reason must be
admitted the two meanings of all, as every and the whole. In a
proposition with a universal subject, do we not speak of all the
parts — that is, of every one gathered into a whole ? All plants are
organised, means that organised applies to the whole sum of objects
classed as plants ; or that we shall find the totality called plant under
the class organised. This supposes, of course, that organised is pred-
icable of every plant, and that we have summed up the every into
a whole or all. But do we now continue to think or to speak merely
of " the several parts " ? Nay, do we not think and speak of plant,
the class, rather than of this or that plant ? It is not merely of " the
several parts " we speak, but of every one, and, if of every one, then
of the whole class. We never can, according to this view, predicate
of a sum or class of objects regarded as a whole ; we must always
predicate of each part forsooth ! If we speak but of the parts sev-
erally or separately, how is it possible thus to say that the whole
class is included under organised ? Each plant is in its turn a part
of organised, no doubt ; but this is a very different judgment from
the whole are, or the whole class plant is so included. Again, Mill reads
all A is all B as all A only is all B, or, A regarded as a whole is all
B. A taken as a class only. This is not the necessary meaning of all
A. It is only the meaning in the case of a Collective notion proper,
made up of units different from the sum — as an army, a regiment,
a ministry, a presbytery, &c. Here what is true of the whole is
not necessarily true of each unit ; but this is a special kind of
whole — not the ordinary logical whole— in which the class -name is
always predicable of each of the parts. Army, regiment, is not predi-
cable of soldier — he is not the regiment ; nor presbytery of presbyter —
he is not the presbytery. But in the case of the ordinary logical
whole, the class-name is predicable of each member of the class.
Animal is predicable of man, bird, and beast. And if we speak of all
the class, or all A, in this sense, we can say that it is all B. We can
say, for example, that all equilateral is all equiangular, or that the
whole class equilateral is identical with the whole class equiangular.
And this expresses not only a relation, as Mill alleges, between the
two classes as totals, but between them as parts — {ibid., p. 513) — for
it implies that every A (equilateral) is to be found in every B (equi-
angular). Otherwise we should have the absurdity, the contradiction,
that the whole objects included in the class A are convertible with the
whole objects included in the class B, and yet there is an A which is
not a B !
OBJECTIONS TO QUANTIFICATION. 301
(c) Again, it is said, all A is B is not spontaneously quantified in thought
as all A is some B. When the speaker or learner is told this, it is a
new idea to him. — (Ibid., p. 512.) Suppose it were, what then? Has
he not now been told what his statement must at least mean ? Is it
not necesary to the coherency, to say nothing of the truth, of the state-
ment, that A is some at least of the Bs ? And whether the individual
thinker had this or more in his mind, does not the thought he ex-
presses demand him to mean this, or something more than this ? And
if he be confused or ambiguous, does not this very confusion justify
the logical postulate that the thought must be explicitly stated in lan-
guage ? And of what highest use or precision is such a judgment, if
the speaker does not know whether he means some, or all ?
As it has been well put, when I say all A is B, or all asses bray,
it is not maintained by Hamilton that we must know whether braying
actually extends beyond asses, or not ; but he maintains that we must
know it extends to all asses. And it is not true that, in order to
form a proposition in Extension, we must know this greater extension.
All we need to form such a proposition is that the braying extends to
the asses at least. This is to quantify the predicate (particularly). —
(Hamilton versus Mill, Pt. ii. p. 216.)
§ 375. Hamilton has indeed already answered these and
other objections made to the quantification of the predicate.
(1.) In the case of Universal Affirmatives, the universal
quantification of the predicate is " always untrue," — all man
is animal, but all animal is man, — the supposed converse is
not true. This is of course materially untrue ; but what
then ? It so happens to be so in this particular case ; but is
it untrue, much less formally illegal in all ? What, then, of
the propositions, — all rational is all risible, all trilateral is all
triangular, all triangle is all figure with its angles equal to
three right angles? Aristotle, who makes this objection in
practice, proceeds, as he must proceed, on the quantification
of the predicate, as in Induction and Demonstration.
(2.) In the case of Keciprocating Propositions — as all man
is all risible — it is alleged that if the predicate were quanti-
fied, the all as applied to the subject being distributively
taken, this would imply that every individual man, Socrates,
Plato, is all (that is, the whole class) risible. There is
nothing in this. All may be used either distributively or
collectively ; but if it be used in the one sense in the subject,
it ought to be used in the same sense in the predicate. " In
the same logical unity (proposition or syllogism), the same
term or quantification should not be changed in import."
Thus we should have, collectively, all (the whole class) man is
302 [institutes of logic.
all {the whole class) risible; distributively, all (every several)
man is all (every several) risible.
(3.) With regard to the objection that the quantification of
the predicate is useless, Hamilton points to its consequences
as shown in the changes thereby introduced into the science
of Logic. There is in the main the restoration of the science
of logic to simplicity and truth ; and especially (1) the sim-
plified and scientific treatment of Exponibles — Exclusive
and Exceptive Propositions ; (2) simplification of Conver-
sion ; (3) of Mood and Figure, and their rules ; (4) restora-
tion of forms of Seasoning illegitimately and inconsistently
excluded ; (5) theory of Proposition and Reasoning as Equa-
tion.1 All these points will be illustrated in the sequel.
§ 376. The term quantity has been indiscriminately applied
to a concept viewed in Extension and in Comprehension. In
this, as it seems to me, there is both confusion and inaccu-
racy. A concept viewed extensively has obviously a quan-
tity— it is a whole which contains objects, and it may be
greater or less ; it may be taken in the whole of its extent,
or only in part of its extent. Animal is a whole ; it contains
species and individuals under it, and we may speak of the
whole of the class — all, or of a part of the class — some.
The conception of quantity is not, however, as appears to
me, so strictly, if at all, applicable to the concept in Compre-
hension. No doubt, if a notion contain in it a plurality of
attributes, it may be said to possess quantity ; for it contains
a variety of constituent elements. At the same time, it is
obvious that a notion as a sum of attributes cannot be subject
to degrees of greater or less ; for if we take from any notion
even one of the attributes which it contains, it ceases to be
the notion which it was before. If, for example, we take from
animal the attribute sensation, leaving only being with life, &c,
what remains is not the notion of animal. So that a notion,
viewed as a sum of attributes, is absolutely indivisible, and
cannot in strict propriety be said to possess quantity. This
is even more apparent respecting a notion which has only
one attribute — as mortal (subject to death), extension, succes-
sion, unity. An attribute is absolutely indivisible, and as
such has properly no logical quantity. When we think or
speak of the attribute mortal or sentient, it is of the attribute
1 Logic, ii., Appendix, p. 295 et seq.
COMPREHENSION IN PROPOSITIONS. 303
as absolutely entire or indivisible. When we use the term
mortal as the name of a class, we think and speak of all or
some of the beings of the class ; but when we use mortal as
the name of an attribute, we must think and speak of the
attribute in its indivisible integrity. Sentient or mortal as the
name of a class is repeated in each of its portions or sub-
classes ; mortal as an attribute, if divided, is destroyed.
§ 377. It does not affect this doctrine that the indivisible
mark or attribute may be also in other objects besides the
subject or predicate of the given proposition. It may quite
well inhere in other subjects or objects. Wood is combustible,
so is coal. Iron is a mineral, gold is a mineral. All the
same, the attribute as attribute is entire in each — it is capable
of distribution over many subjects ; but it is complete, indi-
visible in each ; and is thus wholly different from the predi-
cate as a class-notion.
§ 378. This distinction does not appear sufficiently marked
in the doctrine of Propositions in the ordinary logic, or in
that of Hamilton. In the Lectures on Logic, the term quantity
is applied indiscriminately to concepts in Extension and in
Comprehension. In the later forms of his theory, Hamilton
recognises the distinction in words ; but he makes no thorough-
going application of it to the theory of Propositions. He
says : " A judgment or proposition is only a comparison
resulting in a congruence, an equation, or non-equation, of
two notions in the quantity of extension ; and that these
compared notions may stand to each other, as the one subject
and the other predicate, as both the subject, or as both the
predicate of the judgment."1 "I say in respect to their
Extension — for it is this quantity alone which admits of
ampliation or restriction — the comprehension of a notion
remaining always the same, being always taken at its full
amount." 2
§ 379. But the view has a very important bearing on Pro-
positions, especially on the doctrine of a Quantified Predicate.
Whether the attribute stand as subject or as predicate, it is
to be taken as a unit — as indivisible. We speak of the whole
of it or not at all. As a predicate, therefore, it does not admit
of greater or less, unless intensively, which does not affect
its character or mark ; it has no extensive quantity, or it is
» Logic, App., iv., 276. 2 iud., p, 271.
304 INSTITUTES OF LOGIC.
always quantified to the full, if we may apply quantity at all.
In an affirmative judgment, therefore, the attribute is predi-
cated as a unit or whole. Man is mortal, animal is sentient —
that is, everything in the mark mortality is in man, and every-
thing in sentiency is in animal. In a negative judgment, the
attribute or mark is denied of the subject, wholly or com-
pletely. Sugar is not chloride of sodium ; ether is not ponder-
able ; matter is not a thinking substance ; some sins are not
crimes. Here the attribute as predicate is wholly or absolutely
denied of the subject ; and we could not do less without
destroying the judgment itself.
It may be maintained, as with the Port Eoyalists, that
" the negative proposition does not separate from the subject
all the parts contained in the comprehension of the attribute,
but separates only the total and complete idea composed of
all these attributes." This can only even seem to apply to
a case where the predicate is complex, or the sum of a plurality
of attributes, — as in thinking substance. Matter is not a thinking
substance, but it is not said that it is not a substance. The
total or complete concept alone is denied. Animal is not
a rational and responsible being — it may still be a being of
another sort. This does not affect the main position ; the
comprehensive concept as a predicate is a unity, and as such
it is absolutely or wholly denied of the subject. Whether
another notion, containing a part of the one element of the
complex concept may be affirmed or not, in no way appears
from the proposition itself, or what are the other marks of the
subject. A does not contain in him magnanimity. Other virtues
he may have, and virtue is an element in magnanimity ; but
the exclusion is complete, for we deny the virtue represented
by or in magnanimity, the substance represented by or in think-
ing, the being represented by or in rational and responsible.
(a) The author of the Logic of Poi't Royal — the acute Antony
Arnauld — has the merit of at least partially recognising this principle
of the indivisibility of the attribute predicate.
" An idea is always affirmed according to its Comprehension, because
in taking away one of its essential attributes we utterly destroy and
annihilate it, so that it is no longer the same idea ; and, consequently,
when it is affirmed, it is always affirmed in relation to everything which
it comprehends within itself. Thus, when I say that a rectangle is a
parallelogram, I affirm of rectangle everything contained in the idea of
parallelogram. For if there were any part of this idea that did not belong
PROPOSITIONAL FORMS. 305
to a rectangle, it would follow that the whole idea did not belong to it,
but only a part of that idea ; and thus the word parallelogram, which
signifies the whole idea, ought to be denied and not affirmed of the
rectangle." — (Part II. c. 17.)
With regard to affirmatives, the rules are : —
(a) The attribute of an affirmative proposition is affirmed according
to its whole comprehension ; and (6) affirmed not according to its whole
extension, if it is in itself greater than that of the subject ; (c) the
extension of the attribute is restricted by that of the subject, so that
it denotes no more than that part of its extension which agrees with its
subject. In men are animals, animals means not all, but simply those
animals which are men. — (L., Part. II. c. xvii.)
With regard to negatives, it is held (a) that the proposition does not
separate all the parts of the comprehension of the attribute from the
subject, but only its totality ; whereas (/>) the proposition separates
from the subject the idea of the attribute according to the whole of its
extension. — (Part II. c. 19.) The distinction of comprehension and
extension in the rules is not clearly marked ; nor is the conception of
the true nature of the comprehensive predicate steadily applied to
negatives.
§ 380. The theoretically valid forms of proposition, on the
principle of the quantified predicate, are, when fully stated,
as follow : —
(1.) All X is all Y—AfA.
(A) (ii.) All X is some Y—Afl.
(3.) Some X is all Y—IfA.
(I) (iv.) Some X is some Y — If I.
(E) (v.) Any X is not any Y — An A.
(6.) Any X is not some Y — AnI.
(0) (vii.) Some X is not any Y — InA.
(8.) Some X is not some Y — Inl.
§ 381. Thomson's classification is as follows : —
1. A. All plants grow — Universal Affirmative Attributive.
2. E. No right action is inexpedient — Universal Negative.
3. I. Some muscles act without our volition — Particular
Affirmative Attributive.
4. 0. Some plants do not grow in the tropics — Particular
Negative.
5. U. Common salt is chloride of sodium — Universal Affir-
mative Substitutive.
6. Y. Some stars are all the planets — Particular Affirmative
Substitutive.
u
306 INSTITUTES OF LOGIC.
§ 382. In what may be regarded as his final logical doctrine,
Hamilton explains, first of all, the nature of Affirmation and
Negation. Affirmation means inclusion, and absolute affirma-
tion absolute inclusion. The subject in this case is definite.
It is this or all, — the individual or the class of individuals.
We say, this man is tall ; all planets are stars. Negation, on
the other hand, is exclusion ; and absolute negation is absolute
exclusion. We say, this man is not a European ; all plant is
not any animal ; no plant is an animal.
Looking merely to the class-notion, affirmation proceeds
downwards or inwards from the greatest to the least, from
the whole to the parts. Negation proceeds upwards or out-
wards from the least to the greatest, from the parts to the
whole. Thus we say all A is B, or A contains the part B.
On the other hand, we say any A is not any B, or taking
any one A — the least — it is not any one B, even though you
go through the whole class B, or accumulate all the Bs
to confront it. Any man — any one — is not any horse, even
suppose all the class horse is examined or brought to con-
front the one man, or any one man.
At the maximum of Breadth, affirmation predicates the least
of the most, — the fewest attributes of the greatest number
of things ; as, Man is or exists — animal is organised.
Negation, again, here says the most of the least. It with-
draws the greatest number of attributes from the fewest things.
At the maximum of Depth, affirmation says the most of
the least, — it predicates the greatest number of attributes of
the individual. Man is living, sentient, rational, organised.
Negation here says the least of the most, — it withdraws the
fewest attributes from the greatest number of things.1
§ 383. In ordinary language, Negation is a privative or
correlative act — that is, it supposes an affirmation or inclusion
which it reverses. We deny what has been affirmed. But here
we must distinguish between all, and not any. The former,
all, we use in universal affirmatives, and we say all is, all are.
This may mean the whole, collectively ; or every, each, each
several, distributively. When we deny a universal affirmative,
so expressed, as all As are Bs, we assert that some are not ;
when we deny that all the men in the ship were drowned, we
assert that some were not. In the same way, when we deny
1 Discussions, p. 680.
DEFINITUDE AND INDEFIN1TUDE. 307
that all the men in the ship were not drowned, we affirm that
some were.
To avoid this ambiguity, the proper logical predesignation
in universal negation is not any (none), is. All are thus
excluded, through the non-inclusion of any. Any stone is not
any plant ; any A is not any B ; any one of the persons accused
of this theft is not any one of those guilty ; or none — not one —
of them is guilty.
§ 384. It should be noted that any is not properly adapted to
affirmation, but only to negation. It is the same with ullus,
and means primarily (even) one, (even) the least or fewest, j It
ranges from least to greatest — from the non-inclusion of the
least to the exclusion of the whole. Any one is not, — thus all
are not. We can say, the whole (or class) triangle is the whole
(or class) trilateral; or, every (or each several) triangle is every
(or each several) trilateral. If we were to say, any triangle is
any trilateral, we should speak nonsense, confounding every
triangle with every other. Or if we were to say some one X
is any one Y — that is, some one figure is any one triangle, some
one animal is any one man — we should say what is absurd
in terms, and we should not express what the proposition is
intended to mean. Any is contained under some, as the genus.
Any, any one, must always be some ; some is not always any.1
§ 385. Hamilton has analysed anew the doctrine of par-
ticular quantity, and formally introduced into Logic a new
meaning of the designation some. In the ordinary or Aris-
totelic logic, some means, in affirmatives, some at least — some,
perhaps all. Some itself here is indefinite, but it does not
definitely exclude all. In negatives, not some means not
some at least, not some perhaps none. Not some is itself thus
indefinite, but it does not definitely exclude not any, or none.
This sense of some, — some at least — Hamilton names Indefinite
Definitude. But there is another meaning of some. It may
mean, in affirmatives, some at most, — some not all — some only.
Some itself is here indefinite, but it is definitely exclusive of
all. In negatives, not some means not some at most — not some
and yet not none — not some only. The not some is itself in-
definite, but it is definitely exclusive of not any or none. This
meaning of some — some at most — Hamilton names Definite
Indefinitude.
1 Discussions, p. 683.
308 INSTITUTES OF LOGIC.
§ 386. Hamilton holds that the latter meaning of some —
some at most, or some only — is the more prominent in ordinary-
thought and language ; while the former — some at least — is a
mere accident, depending on our ignorance in special cases.
Every quantity is necessarily either all, or none, or some. The
third is formally exclusive of the other two. Some only
excludes equally all and none. Aristotle confounded what
was indefinitely thought, with what was thought as indefinite,
and thus hindered the scientific development of the logical
theory of propositions. Hamilton would thus introduce some
only into the theory of propositions, without, however, dis-
carding the meaning of some at least. On this principle he
has constructed a table of the mutual relations of the Eight
Propositional forms on either system of particularity. This
shows what propositions are incompossible (inconsistent,
contrary, contradictory), and what yield immediate infer-
ences (integration, restriction).1 It is thus not correct to
say, as has been said, that Hamilton discarded the ordinary
logical meaning of some. He simply supplemented it by
introducing into the propositional forms that of some only.
§ 387. But there may be a question as to whether some only
is equally fundamental with some at least. I rather think it is
not. It is quite clear that I can speak of some at least, with-
out advancing to the more definite stage of some only. I may
know that all the metals are at least conductors — that is, some
conductors — without knowing that they are some only, — if this
should chance to be true. Some at least does not imply some
only; but some only implies some at least, and more. It
implies some at least are, and some at most are.
No doubt there is an inference from some only to some other.
Some only is, therefore, some other is not. Only some of the As
are Bs ; therefore some other of the As are not Bs ; or there
are other As which are not Bs. But before I can speak of some
only, must I not have formed two judgments, — the one that
some are, the other that others of the same class are not ?
Only some presupposes this, or these judgments. The in-
tegration, then, is rather a re-integration, — it is a filling up
of what I have already thought or determined, — of what I
have already presented only in part. The some only would
thus appear as the composite of two propositions already
1 Discussions, p. 692.
DEFINITUDE AND INDEFINITUDE. 309
formed — first, that some are; secondly, that some (others of
the class) are not. It seems to me that we must, first of all,
work out logical principles on the indefinite meaning of some
at least. This is the primary requisite and meaning of affirma-
tion— the least possible — in dealing with a class. Some only,
as appears to me, is a secondary and derivative judgment.
Still this need not interfere with the recognition of the mean-
ing in propositions. Nor does it make it less a single judg-
ment, after the process of formation has been completed. It
is then no more a double judgment than all are ; and, like
it, may appear as a single premiss in a reasoning.
§ 388. There can be no doubt of the common use of this
definite meaning of some in ordinary thought and speech.
When I say, some of the men in the ship were drowned, I natur-
ally mean only some ; I oppose this definite particularity to
all, — all the men in the ship were drowned. I should not,
in this connection, naturally say, some of the men in the ship
were not drowned. The positive element in the occurrence
is that to which I should naturally refer, and in wishing to
express that all were not, I should say some were, — that is,
only some were.
(a) " I saw some of your children to-day." These words, according to
Mill, do not mean that I saw some only. But we are led to infer that
they do, because it is most likely, if I had seen them all, that I should
have said so ; " and it is further presupposed that I must have known
whether the children I saw were all or not. " Any tyro in Logic would
say in reply to this, that if I say I saw some, I must mean not all, but
only some, in whatever way I may have come to know this. Logic
begins with the assertion made, and demands its explicit meaning.
Is it conceivable that even Mill could have imagined that some, said
of what had been seen, might mean more than the some seen ? or that
the some expressed did not exclude all ?
(b) In Greek we have a means of distinguishing the some and some.
In the case of an individual object, say in space, we have one part of
the object distinguished from the other by a definite form of expression.
Thus, if we only mean to speak of the middle market-place, we should
say r\ fxi(Ti\ dyopd ; but if of the middle of the market-place, we should
say, y ayopa /xea-rj. So t2> eaxaT0V fyos means the outmost mountain, but
icxarov rb opos means the outmost part of the mountain. — (Clyde's
Greek Syntax, p. 21.) This is simply the some and some, or the some
and some not of the logical conception 6 fiev . . . 6 Se. These may ex-
press opposition ; they also often express different or divided parts of the
same thing— portions of the same class — the one, the other, hie and ille
— as this species and that species of the same class — in logical form
some and some (other) (of organisms)
310 INSTITUTES OF LOGIC.
" In English, as in Greek, the attributive formula marks a distinction
of persons and things, whereas the predicative formula marks a dis-
tinction of conditions in the same person or thing. The stone is soft
here, v vtrpa /ia\aKr} 4cttiv ivravda, is predicative ; the soft stone is here,
t) fiakaicfi werpa £<tt\v ivravda, is attributive — marking a difference in the
kind of stone. / see the mountains white (predicative) ; / see the white
mountains (attributive)." — (Clyde's Greek Syntax, p. 19.)
(c) Laurentius Valla, long ago, vindicated the practical use of the
bi- particular proposition (propositio biparticularis) — some is not some.
"Non totus orbis," he said, "paruit Alexandre," i.e., "pars orbis
paruit, pars non paruit." So " tota Gnecia non paruit Alexandre,"
i.e., "non tota Grsecia." This was a distinct and formal anticipation,
as well as vindication, of the necessity for thought and expression of
the some and the some not in reference to the same class. — (See Diabe-
tica, c. xxvi.)
311
CHAPTER XXIV.
OBJECTIONS TO QUANTIFIED PROPOSITIONAL FORMS GENERAL
CONSEQUENCES OF QUANTIFICATION OF PREDICATE.
§ 389. It has been urged, that if we expressly quantify the
predicate, we shall have a form or formula of judgment
which is a simple repetition or tautology. This criticism must
be held to be taken to the form of the proposition in Exten-
sion. Indeed, those who urge it seem utterly ignorant of
any other form of proposition. In Comprehension, as we have
seen, the predicate as attribute is, in affirmatives, necessarily
taken in its totality, as an indivisible unity. No attribute
is properly divisible, and is thus necessarily taken in its in-
tegrity. When we say A is B, or the river runs, the attribute
is taken wholly or completely, but it could not be represented
in the formula A is A B, the river is the river running. This
is a different statement from the river runs, or has this par-
ticular mark. Gold is soluble in aquafortis — does not mean
that gold is gold soluble in aquafortis; for we are speaking of
gold itself, and we have added a mark, and until the mark
has been added it is not, to begin with, gold soluble in aqua-
fortis. The Black Watch were the first in the breach, does not
mean that the Black Watch were the Black Watch first in the
breach; for this is precisely what we have to add to what
the Black Watch already is or is known to bek
§ 390. In any affirmative judgment, we necessarily, in
thought, quantify the predicate to the full extent of the sub-
ject. A is B, means A is some B at least ; or B is in A, all or
some A ; man is organised — that is, some part of the class at
least, or organised is in A, all or some. If, therefore, the criti-
cism have any force at all, it must imply that in every such
312 INSTITUTES OF LOGIC.
judgment, whether the predicate be expressly quantified or
not, the meaning is A is A B ; and it is thus not an objec-
tion, even if it be an objection at all, to the express quantifi-
cation of the predicate but to the judgment as thought — that
is, to the judgment as a judgment.
§ 391. But suppose the predicate expressly quantified, as
A is (some) B — water is a (some) useful thing, — does this mean
only or at all that A is A B, or water is water useful f In no
way whatever. It means simply, that taking the two con-
cepts or classes of things represented by A and B, water and
useful, the subject is a part at least, some at least, of the
predicate class, but whether all, or how far short of all, we
cannot tell. Water and water useful are quite distinct con-
cepts; we are speaking of the former, not of the latter. Use-
ful water is not the subject of which I speak, but water; and
these are two very different things. The extent of useful, of
which I speak, is limited to the extent of the subject — water ;
but I am still speaking of water, not merely of useful water,
and I am not repeating what I said in the subject, but adding
to it — specifying and relating it to a class which may or
may not be coextensive with it. The oak is a deciduous tree —
that is, some part of the deciduous. The oak is the oak decidu-
ous, are wholly different propositions — not the least of the
same import. All equilateral is (all) equiangular, — the totality
in the one case is convertible with that in the other ; but all
equilateral is equilateral-equiangular, does not assure me of
the convertibility of the subject and predicate.
§ 392. It is further contended, that in the case of the ex-
press quantification of the predicate, the subject should be
qualified (!) by the predicate. Why we are not told, nor what
qualified judgment means in such a case. But it seems that if
we say all man is some mortal, we ought to say all man is man
mortal, and then man mortal is man mortal ; or A is B, then A B
is A B. I submit there is no equivalence in those statements or
propositions, no necessary connection between them. When
I say all man is some mortal, I am speaking of the class man
and the whole class man. But when I say man mortal, or
mortal man are so and so, I speak of a part of the class man
— viz., the mortal part, and I imply that there is or may be
another part of which I am not speaking at all — viz., the non-
mortal or immortal part. The one is a universal proposition
PREDICATES EXTENSIVE AND COMPREHENSIVE. 313
in which I speak of the whole subject ; the other is a par-
ticular proposition, in which I speak only of some of the class,
a supposed part of the subject. To say that the violet is blue,
is not the same as to say that the blue violet is the blue violet.
In the former case I am supposed to speak of all the class
violet, and to say it is blue ; in the latter case I am supposed
to take a part of the class by restriction — viz., the blue violet,
and to say simply that it is identical with itself. This arises
from the elementary principle that any adjective applied to a
subject is limitative. Mortal man is necessarily less than all
man, and blue violet is necessarily less than all violet or all of
the class. Hence to say that all of one class is equivalent to
some of another or possibly wider class, is one thing ; but
when I say man mortal is man mortal, this does not tell me
that I am speaking of the whole of the subject, and the pro-
position is not the convertible equivalent of all man is some
mortal. It is simply a narrower proposition, and at the ut-
most a puerile verbal inference from it, which depends on
the wider proposition.
But if the some in the predicate means some only, which it
might do, the attempted equation of the two propositions is
even ludicrous. All men are (only some) mortal, cannot be
translated into all men are men mortal, — for this does not in
the least tell me what I said originally that all men do not
exhaust the class mortal, but are only a part of it. And to
put men mortal for the predicate all men, is merely to repeat
the blunder already exposed.
The formula becomes even more inappropriate when the
subject and predicate are each universally quantified. We
may say, all the men at the bar are all the rioters. This, ac-
cording to the formula, should be, all the men at the bar are the
men at the bar-rioters. And this paltry tautology is actually
to be regarded as representing the statement made in the
original proposition !
Again, let us take such a proposition as some stars are all
the planets. Here, according to the formula, we ought to
mean some stars are star-planets — which is pretty well non-
sensical, and certainly not in the least the equivalent of the
original proposition.
§ 393. The criticism, indeed, proceeds on the confusion of
the Comprehensive and Extensive Predicates.
314 INSTITUTES OF LOGIC.
(1.) In regard to concepts, — when we translate man is
some mortal, into man is man mortal, — we pass from the pred-
icate in extension to that in comprehension — from what has
quantity to what has none, but is indivisible. The some mortal
of the first proposition indicates the limited place of the subject
in the class ; the man mortal of the other clumsily indicates
mortality as an attribute of man. Instead of saying this
simply, we say man is man (the) mortal, or man is the (or a)
subject which possesses the mark mortal. To pass from the
comprehensive predicate to the extensive is natural and legit-
imate ; to repass from the extensive to the comprehensive is
arbitrary and wholly unnecessary, and it does not proceed on
any equivalence of quantity ; for we really pass from what has
quantity to what has none — from extension to comprehension.
To take an individual subject : — Simon is a tanner — that is,
one of the tanners or class. If, however, we thus quantify the
predicate, we ought, on the principle stated above, to have
this form — Simon is Simon tanner, as man is man mortal.
Now this is not the equivalent of the original proposition at
all. 'This means that of those named Simon, the one of
whom I now speak is tanner, or the tanner, as opposed to
Simon the miller or butcher, or some one else of the same
name. He is marked, in fact, by an attribute as one of the
Simons ; whereas, when I say Simon is a tanner, or one of the
class, I am not considering whether there are other Simons,
but only that he is one or a part of a definite class. He
is in the class, but does not necessarily exhaust the whole
extension. The proposition, Simon is Simon (the) tanner, is
in Comprehension as giving the mark of the individual ; the
proposition, Simon is a tanner, is in Extension, and gives the
place of the subject in the class.
§ 394. Objections have been made to the scientific validity
of certain of the Propositional Forms : —
(1.) Toto-total affirmation. All is all. All X is all Y.
It is objected by De Morgan —
(1) This is complex. (2) It cannot be denied by a simple
proposition.
(1.) It is complex ; and all Xs are Ys is compounded of
all Xs are some Ys, and some Xs are all Ys.
(a) All Xs are all Ys is not more complex than its alleged
constituents — all Xs are some Ys, or some Xs are all Ys. One
OBJECTIONS TO QUANTIFIED FORMS. 315
quantity cannot be more complex than another. All is
not compound, while some is simple. The truth is that some
is made up of several, as this, that, &c., just as all is made
up of every one. It is the business of Logic to consider a
judgment as a completed or finished product. The psycho-
logical complexity of the judgment is a wholly different
point. Moreover, to admit that some is all — some figure is all
triangle — is simple, renders it impossible to conceive that
all is all, or all triangle is all trilateral, is compound. All
and some are both made up of a plurality. The attempt
has been made to show the composition in question, on
the ground that the propositions which make up all X is
all F— viz., all X is Y, and all Y is X, are independent of
each other ; while the propositions which make up all X is
some Y — viz., all X is Y, and some Y is X, are not, the one
being inferrible from the other by conversion. But when we
find that this proceeds on the assumption (1) that the predi-
cate as predicate has no quantity, and (2) nevertheless, that
in conversion the quantity acquired is particular when the
convertend is affirmative, and universal when it is nega-
tive, we need not argue the point. If the predicate in
the convertend had no quantity, and yet acquired it in
the conversion, the acquisition was at once arbitrary and
illogical.
§ 395. (b) All Xs are all Ys is said to be compounded of two
propositions— viz., all Xs are some Ys, and some Xs are all Ys.
In concrete language, all triangle is all trilateral, is said to be
made up of all triangle is some trilateral — some triangle is all
trilateral. But these are incompatible propositions. If either
of them is true, the other is false. Nay, if either of these
alleged generating propositions be true, the so-called product,
all triangle is all trilateral, is false. Here some is used in the
sense of some only. All triangle is (only some) trilateral is con-
tradictory of (only some) triangle is all trilateral; and either
of these is contradictory of all triangle is all trilateral. Nor
can it be shown that this form AfA is made up of these two
forms, even if we take some in the ordinary Aristotelic sense
of some at least. Thus (a) all triangle is some at least trilateral ;
and (6) some at least of triangle is all trilateral. For the
quantity of the predicate in (a) is wholly indefinite, and the
quantity of the subject in (b) is wholly indefinite, and the two
316 INSTITUTES OF LOGIC.
indefinites put together cannot logically yield the definitude
or totality of the same subject and the same predicate in a
conclusion. Thus : —
(a) All triangle is (some) trilateral.
(b) (Some) triangle is all trilateral.
(c) All triangle is all trilateral.
All triangle is some trilateral at least, perhaps all, how much I
know not ; some triangle at least, how much I know not, is
all trilateral. These propositions are vague, even if they
were consistent, and cannot form the elements of the com-
pound, all triangle is all trilateral.1
(2) The objection that all X is all Y, all man is all mortal,
cannot be denied by a simple proposition, is groundless. We
can say readily the whole class man is not identical with the
whole class mortal. That is all we need to say in order to
deny, and it is conveyed in one proposition.
The denial here is perfectly definite. We deny the equiv-
alence of the terms as wholes. It is said by De Morgan that
such a proposition all X is all Y, can be denied only by the
disjunctive assertion, " Either no Xs are some Ys, or some
Xs are no Ys." Though one of these were true, the power of
denying all is all in an elementary form is refused me.
Hamilton, in dealing with this objection, shows that De
Morgan does not distinguish contrary from contradictory de-
nial. In contrary opposition the original statement may be
denied by a plurality of propositions. A denial need not rest
on a single alternative case — on a contradictory proposition —
but on one or other of two incompossible contraries, and it
will be valid if one or other of the contraries be true.
" All (class, whole, every, $c.) triangle is all (class, whole,
every, fyc.) trilateral, is contradictorily denied by the proposi-
tion. All (class, fyc.) triangle — is not — all (class*, fyc.) trilateral,
in the sense ' This proposition, All triangle is all trilateral,
is untrue.' The denial here is necessarily vague, for there
are five several cases, any of which it may mean, and of
these any will validly support the negation of the affirmative
proposition. These are: 1°, Not-all triangle is all trilateral,
— i.e., Some triangle is all trilateral. 2°, All triangle is not-
all trilateral, — i.e., All triangle is some trilateral. These are
inconsistents. The following are contraries — viz., 3°, No
1 Cf, Hamilton, Discussions, p. 688.
OBJECTIONS TO QUANTIFIED FORMS. 317
triangle is any trilateral. 4°, Some triangle is no trilateral.
5°, No triangle is some trilateral.'1 x
All that needs to be done in the case seems to me to make
such a denial as will affect the equality of the two classes, —
that is, the point asserted. An antagonist does not require
to do more in the first instance. The special proof or oppo-
site case on which he relies is a secondary point. If it be
said, — all the men at the bar were all the men in the field, Ifcan
deny this by saying this was not so. I may yet hold my proof
in reserve. I may be able to show that one man in the field
leaped the wall and escaped, or that one of the men at the
bar was not in the field at all, or that none of the men at the
bar was in the field, and so on. Either of these alternative
cases would disprove the assertion, — that is, the equivalence
of subject and predicate alleged. I can legitimately make a
contradictory negation in the first place, though this in the
end may depend on the truth of one or other of several
alternatives.
§ 396. The use of the form, all is all, is common and
necessary. Every adequate Definition supposes it. If I
say proportion is the similitude of ratios, then, the defini-
tion being accepted, the predicate can be put in the place
of the subject, and nothing else. This is simply AfA.
And surely, if I can think the subject and predicate of
a definition — nay, must think them as precisely convert-
ible, it is ridiculous to suppose that I cannot express this in
a single propositional form, — that I am to be called upon to
define, and then in another proposition to say this is a good
definition, or its terms are convertible. The form is further
obviously necessary and useful in expressing equivalence
between two undivided wholes, as copper is sulphate of iron —
that is, all of the one is all of the other. Common salt is chloride
of sodium, and so on. In ordinary language we do, wher-
ever it is necessary, attach a sign of universality to the
predicate by limitative and exceptive particles. We say,
God alone is good ; Virtue is the only nobility ; Of animals man
alone is rational. We use besides one, only, precisely, just,
sole, &c.
§ 397. In Induction and in practical reasoning, the need of
the form is obvious. As Professor Bowen well illustrates this
1 Discussions, p. 689 et seq.
318 INSTITUTES OF LOGIC.
point : " If I am playing chess, and my king is in fatal check,
I must reason thus — I can neither move my king, nor inter-
pose a man, nor capture the attacking piece. But these are
all the modes of obviating check. Then I am-checkmated." x
(a) " All A is all B is inadmissible, because it is not the equivalent
of any single proposition capable of being asserted in an unquantified
form." — {Examination, p. 514.) It is the equivalent of two separate
judgments, All As are Bs, and all Bs are As. All man is all rational.
This means, every man has the attribute reason, and nothing which is
not man has that attribute. It is not possible to make only one judg-
ment out of an assertion divisible into two parts, one of which may
be known and the other unknown." — (Ibid., p. 515.)
"Unless Sir W. Hamilton was prepared to maintain that, whenever
the universal converse of an universal affirmative proposition would be
true, we cannot know the one without knowing the other, it is in vain
for him to contend that a form which asserts both of them at once is
only one proposition. . . . If ' all equilateral triangles are all equi-
angular,' is only one judgment, what is the proposition that all equi-
lateral triangles are equiangular ? Is it half a judgment ? " — (Ibid.)
In the first place, all A is all B, or all man is all rational, does not
mean what Mill says it means. It is a judgment of quantity —
equivalence in quantity, and not directly in quality at all. It is a
judgment of two convertible totalities, not merely of equivalence in
attributes. In the second place, the argument amounts to this, that
all A is" all B is a compound proposition, and therefore is not ad-
missible as one propositional form. Without referring expressly to the
test of the proposition as compound given by Mill, his argument is
futile ; for if it held good, no proposition would be admissible as one
propositional form except a Singular Judgment. This is the only pro-
position which is strictly indivisible — its subject being an indivisible
unit, — one, this, that. Every other proposition, whether the subject be
quantified as some or all, would in this case be compound and inad-
missible as a single propositional form. Some is compound of several
units, all is made up of every unit of the class. Some men are just, all
metals are conductors, are in this case compound propositions. And it
matters nothing, so far as this point is concerned, whether we also
speak of all in the predicate. We may say, Some stars are all the
planets, or all equilateral is all equiangular. These propositions are
not, in principle, more compound than all the planets are stars, or all
equilateral is equiangular. Mill, in fact, confuses the process of the
psychological formation of judgments with its logical results. The
logical unit, whether concept or judgment, is necessarily compound,
but it still remains and can be dealt with as a logical unit. And
the propositions which Mill regards as compound, because they are
" divisible into two parts, one of which may be known and the other
unknown," are not more compound than those which he regards as
single. We may know that some metals are electrical without knowing
that all are, though we cannot make this assertion without knowing
1 Logic, p. 134.
PARTI-PARTIAL NEGATION. 319
the former ; just as we may know that all equilateral is (some) equi-
angular, without knowing that they are all equiangular, though we
cannot know this without knowing the former. No doubt, whatever
proposition is capable of division into two separate assertions, one of
which may be true or assumed without involving the other, is psycho-
logically a compound proposition ; but this applies to every proposition
except the Singular, whose subject is logically an indivisible unit.
(b) " Some A is some B, i.e., only some B, is a double proposition, com-
pounded of some A is some B and some (other) A is not any B. The
one statement affirms, the other denies, a different predicate of a differ-
ent subject, and these are, therefore, two distinct judgments." — (Exam-
ination, p. 517.) Do they really? (Some) man is (only some) of the
six-feet things — (some) (other) man is not any of the six-feet things. Does
the subject man differ because we speak of some and some other of the
class ? Does the predicate, six-feet things, differ because we speak of
some and any of the class ? Are we not still dealing with the same
genus in each case, and simply subdividing it? And even if this
were true, would this prove the judgment with some only in it to
be any more compound than that all A is some B implies the fore-
gone judgment that some (at least) are ?
(c) " All Xs are all Ys," says De Morgan, is compounded of " all Xs
are some Ys," and "some Xs are all Ys." No, replies Hamilton —
these are incompatible, — mutually exclusive. They cannot unite to
form one proposition. X cannot be thought both as only some Y,
and as all or every Y. Mill rejoins : yes ; for if all Xs are some Ys
identifies X with only some Y, some Xs are all Ys "superadds the
remainder"! — (Examination, p. 516.) In other words, we first say
X is only some Y, and then we say no, it is the whole of Y. We
thus make one proposition — every X is every Y. Some only may mean
more than some only !
§ 398. But Hamilton answered this and other objections
by anticipation. To the objection that in Reciprocating pro-
positions the predicate is taken in its full extent, vi materia,
Hamilton replies, "that as form is merely the necessity of
thought, it is as easy to think two notions as toto-totally
coinciding (say, triangle and trilateral) as two notions toto-
partially, and parti-totally coinciding, say, triangle &nd figure.
Accordingly we can equally abstractly represent their rela-
tions both by geometric quantities (lines or figures) and by
purely logical symbols. Taking lines : — the former I ;
the latter | . Taking the symbols : the former
C : fc^— : r ; the latter A, bm^— : B- — But if the recipro-
cation were determined by the mere matter, by the object con-
tingently thought about, all abstract representation would be
impossible." x
1 Logic, ii. Appendix, p. 297.
320 INSTITUTES OP LOGIC.
§ 399. The objection made by Thomson to the forme AnI
and Inl, is that they have the semblance but not the power of
a denial, is unfounded. To take AnI.
If we say, any bird is not some animal, we can still say,
any bird is some animal. This is no proper objection to the
original form, for the some animal spoken of in the two propo-
sitions is different. In fact, we are dividing a class or genus
into its parts and species. We suppose animal the genus, and
divide it into some and some. These are exclusive, and yet
possess a common quality. All roses are some flowering shrubs,
and all roses are not some flowering shrubs — that is, flowering
shrubs contain roses and some other shrubs. As Professor
Bowen has well remarked : " Any limitation of the predicated
class by a limiting adjective is equivalent to quantifying that
predicate particularly. Pines are not deciduous trees — that is,
pines are not some trees.'1 x
§ 400. The same principle justifies parti-partial negation —
Inl — Some is not some.
The peculiar use of this form is to express the divisibility
of any whole. When we say, some A is not some A, we assert
parts, and that these can be divided, or that there are parts and
parts. If we deny this statement, we assert that the thing
spoken of is indivisible or a unity. This form is implicitly at
work in every science — in every case, in fact, in which we
divide a genus into its species, or a species into sub-species,
or these, again, into individuals. When we speak of some and
other men, for example, we have presupposed this form that
some is not some — that the class man is capable of division,
capable of being sundered and separated, and yet remaining
the supreme whole which contains the some and the other —
say, the European and the Asiatic. We may say there are
men and men. We say, as we do every day, there are poli-
ticians and politicians, there are ecclesiastics and ecclesias-
tics, there are sermons and sermons. These are but covert
forms of the some is not some, and unless this is formally
vindicable, the greater part of our ordinary language is wholly
baseless in reason.2
§ 401. Is some is not some not an available proposition?
May I not say — do I not need to say — planting is not some
planting t Planting monotonous larches all over a hillside is
1 Logic, p. 139. 2 Cf. Discussions, p. 695 et seq.
CONSEQUENCES OF QUANTIFIED PREDICATE. 321
not planting the same xoiih graceful birches. Planting in one
sort of way is not planting in another sort of way. And yet
both are planting. Only the one is good, the other bad.
And if I can state this propositionally, why may it not appear
in a reasoning? Again, some vivisection is not vivisection.
This is nonsense ; but some vivisection is not some vivisection,
is true and important ; for the one may be with an anesthetic,
the other without it.
§ 402. There are objections against their scientific and prac-
tical necessity. (1.) Some X is all Y — IfA. This is merely
a new mode of expressing Afi — A, all X is some Y; for we
can convert Afi into IfA — and say all X is some Y, and some
Y is all X. So with AnI and In A — any X is not some Y — some
Y is not any X. These are thus virtually identical forms, and
the new ones, IfA and InA, are, though valid, not scientifi-
cally or practically necessary.
That some stars are all the planets, and all the planets are some
stars, are no doubt deducible directly the one from the other.
But that does not bear on the point, that the logical doctrine
of the universal particularity of the predicate in an affirmative
proposition, is by the admitted legitimacy of IfA at once dis-
proved, as that of the invariable universality of the predicate
in a negative proposition is equally disproved by the admitted
legitimacy of AnI. And if these forms be legitimate, their
scientific value in reasoning is at once vindicated, and we can
now employ these propositions as premisses, and draw conclu-
sions directly from them. This we could not do before on the
ordinary logical principles, being driven to the circuitous
process of reduction in order to reach what is now a direct
conclusion. And being thus both legitimate and valuable in
a scientific aspect, it may happen practically that we approach
the knowledge of the proposition through the new form —
Some stars are all the planets, or all A is not some Y — rather
than in the old. This being so, there is no reason why we
should be debarred from their direct use, and be made to state
each in the form of an equivalent.1
§ 403. Among the consequences of the doctrine of the quan-
tified predicate, we note (1) propositions become equations or
non-equations of subject and predicate. They are equations
or non- equations in quantity proper — that of Extension;
1 For further vindication, see Discussions, p. 662 et seq.
X
322 INSTITUTES OF LOGIC.
for, as I have said, quantification of the predicate does not and
cannot apply to comprehension. All the same this relation
of equation need not abolish the relation of whole and part.
(a) It has been supposed that when Hamilton said "every proposi-
tion expresses an equation between its subject and its predicate," he
meant to speak of the terms taken absolutely, or each regarded for
itself. — (Cf. St Hilaire, art. Proposition Diet, de S.P.) Hamilton has
no such meaning. He refers merely to the proposition in question,
to the proposition as determinate, as far as it expresses the quantity of
the terms. This is shown by the very nature of explicit quantification ;
for example, all man is some mortal. By this he does not mean an
equation absolutely between the terms man and mortal, but only
between as much of them as is taken or considered — in the one case
all, and in the other some. It is not that all terms are equivalent or
identical, but that the proposition expresses how far they are so.
It is actually objected by the same writer that the idea of equa-
tion is inapjdicable to negative propositions, as if Hamilton had not
repeatedly and expressly said that the relation is one either of equa-
tion or non-equation.
(b) Hamilton nowhere says that "every proposition which I affirm
respecting a subject must include all I know about it," and there-
fore, that if I know all trilateral figures to be triangular, I must
say not "all triangles are trilateral" but " all triangles are all tri-
lateral."— (Examination, p. 516.) What Hamilton says is, that what
I know, judge, and mean to say in a propositional form — in language
— I should say expressly, that it may be clear to myself and others,
and that logical science may unambiguously deal with it. If, for
example, I mean merely to state that the predicate extends to all of
the subject, I should say all trilateral is triangular; and if I mean to
say that it is coextensive with it, and not more, I should say all trilateral
is all triangular.
(2.) Propositions (in extension) are seen to be immediately
convertible. The predicate can be immediately put in the
place of the subject, and a proposition of precisely the same
force or import emerges. The various methods of Conversion
devised by logicians are thus abolished, and all conversion
becomes absolutely simple, and by a single method — mere
transposition of the terms, — as every A is (some) B ; some B
is every A ; any A is not (some) B ; some B is not any A.
§ 404. The scientific value of the quantification of the pred-
icate is, in Hamilton's view, shown expressly in regard to
Syllogism. Its necessity and logical importance are vindi-
cated by the fact that it is really assumed in the ordinary
syllogistic view, though not acknowledged — in fact, repudiated.
CONSEQUENCES OF QUANTIFIED PKEDICATE. 323
In the First Figure, there is the acknowledged peculiarity of
indirect moods — such as Bamalip, Celanes, Dabitis, Fapesmo,
Frisesmo. These moods, as well as all the moods of the Fourth
Figure, are simply sub-conclusions from the direct conclusions
of the premisses employed. There is the secret conversion of
the undeclared direct conclusion. But there is the further
peculiarity, not acknowledged, that these indirect conclusions
are immediate inferences from a proposition which, on the
ordinary logical doctrine, is illegitimate — viz., a negative pro-
position with a particular predicate (AnI, InA.) To take
Fesapo, for instance : —
No planet is [any] comet ; (An A).
All comets are some (stars) revolving round the sun; (Afl).
(.*. No planet is some star revolving round the sun) ; AnI.
.'. Some stars revolving round the sun are no planets; (InA).
The proposition within brackets, AnI, is the immediate,
though undeclared, conclusion from the premisses. The last
proposition, InA, is merely an inference from this immediate
conclusion. The logicians are thus here obliged to acknow-
ledge as efficient in thought a judgment which they regard as
illogical — viz., the negative with a particular predicate (AnI).
For the converse of this proposition cannot be true or legiti-
mate, unless it is so itself. The contracted views of logicians
as to the indefinite quantification of the negative predicate are
thus refuted by their own practice. The general result of this
analysis is that all the indirect moods of the first figure, and
all the moods of the fourth, are only mediate conclusions from
moods (or conjugations) of the first figure. Consequently
there is no ground for maintaining a fourth figure at all.
The conclusion of each of the indirect moods of the first figure
is simply a process of conversion from one quantity into an-
other ; the moods of the fourth figure are merely the indirect
moods of the first figure, the premisses being held to be
transposed — a circumstance which can cause no syllogistic
difference.1
§ 405. While, since the time of the Port-Royalists, the doc-
trine of Comprehension has been recognised and received into
logical systems, it seems to me that the salient and essential
feature of the doctrine in its relation to judgments has either
been generally overlooked, or when noticed at all most im-
1 Discussions, p. 663.
324 INSTITUTES OF LOGIC.
perfectly appreciated. This is the individuality or totality of
the attribute as predicate, — which gives an entirely new and
yet natural form of proposition and series of propositional
forms. In regard to these, quantity is of no consequence ; it
falls out of consideration.
§ 406. This new classification of propositions is formally
legitimate, and is at the same time suitable to the actual
facts of our experience and the needs of our thought. Taking
Comprehension first as the basis of the whole, we have : —
A. All man is mortal (indivisible attribute or mark) ;
.*. Mortal is a mark of all man.
E. No man is quadruped ;
:. Quadruped is not a mark of any man.
I. Some man is learned ;
.'. Learning is a mark of some man.
0. Some man is not learned ;
.'. Learning is not a mark of some man.
U1. This man is artist ;
.'. Artist is a mark of this man.
U2. This man is not an assassin ;
.'. Assassin is not a mark of this man.
In each predicate there is quality, not quantity. The judg-
ment is simple, natural, and easy ; it is suitable to experience ;
it is simply convertible, and may be expressed in either form
— as convertend or converse. To distinguish such proposi-
tional forms, we might call them — A Comp., E Comp., I Gomp.,
0 Comp., U Comp.1, U Comp.2
It is to be observed that the predicate (attribute) is
taken in its whole comprehension, whether the judgment be
affirmative or negative. When we say this man is not an
assassin, we speak of the whole comprehension of the concept,
as marked off from every other, either fuller or less in compre-
hension. We do not deny anything of him, except the com-
plete whole essentially involved in the concept assassin. He
may be homicide, or he may not ; but this is neither (im-
plicitly) affirmed nor denied in our judgment.
§ 407. In Extension, the following will be the scheme of
forms : —
PROPOSITION AL FORMS. 325
•
A1. All man is (some) mortal.
A2. All man is (all) risible.
E1. Any man is not (any) stone.
E2. Any man is not (some) biped.
I. Some man is (some) biped.
01. Some man is not (any) happy.
02. Some man is not (some) biped.
U1. This man is not a thief {any).
U2. This man is not biped (some).
These may be marked :— A Ex.1, A Ex.2 ; E Ex.1, E Ex.2 ;
I Ex. ; 0 Ex.1, 0 Ex.2 ; U Ex.1, U Ex.2.
(a) The Port Royal Logicians were really the first to give effective
prominence to the distinction between Extension and Comprehension
in Notions and Propositions. But there are references to the distinction
by other writers, before and after the date of the Port Royal Logic
(1662). To say nothing meanwhile of the obvious references to the dis-
tinction in Aristotle himself, we have its apprehension and statement
by Cardinal Cajetan in 1496. — (See Port Royal Logic, Introd. p. 33.)
Collection of many is twofold ; intensively, and thus the species is
more collective, because it rather unites the adunata ; extensively, and
thus the genus is more collective, because many more fall under its
unification (adunatione) than under the compass (ambitu) of the species.
The species and genus are like generals — the one of which has a small
army, but wholly unanimous ; the other great, but of diverse factions.
For that collects more intensively, this more extensively. Porphyry
speaks of the extensive collection, and therefore says the genus is more
collective. — (Cajetanus in Porph. De Geneve et Specie.)
The species is in itself more one than the genus, since the species ex-
presses a nature absolutely indivisible formally, whence it is called
atoma ; but the genus imports a nature divisible. — (Cajetanus in
Porph. De Geneve et Specie, quoted by Stahl, Jtegulce Philosophical,
Tit. xii. Reg. v., p. 381 : London, 1672; first ed. 1635.)
(b) Avicenna had said — Predication is of two sorts, either univocal or
denominative. Socrates is a man, is univocal. Here there is true and
univocal predication. Man is white, or man has ivhiteness, — this is
denominative. Man is not said to be whiteness ; as Socrates is said to
be man. — (Log., p. 3 v. B. ; Prantl, ii. p. 325.)
(c) The universal which Logic examines contains three things : the
name, which expresses several things ; the idea, which represents
general things ; and the nature, which is in several things. — (La
Dialectique du Sieur de Launay, Dissert, iii. p. 72 : Paris, 1673.)
(d) Universale inest singulis inferiorum, et de illis potest praedicari,
non secundum extensionem, seu univevsalitatem, sed secundum naturam
tantum et comprehensionem. Ut tota essentia naturae sensitivae,
secundum omnia attributa sua, est in singulis animalibus ; non autem
in tota extensione, qua: una cum convenientia eorum in quibus extendi-
326 INSTITUTES OF LOGIC.
tur, est forma universalis. — (Goveanus, Logica Elenctica, Disp. x. p.
128 : Dublinii, 1683.)
There are explicit and intelligent notices of the distinction in Hutche-
son, Locj. Comp, pp. 24, 25 (ed. 1754) ; in William Duncan's Elements
of Logick, I. iv. § 2 ; Kirwan, Logick, i. p. 41 (1807). With all this,
the doctrine has remained comparatively unfruitful until our own day.
§ 408. The table of propositional forms given by Hamilton
is defective, in so far as it does not specially provide a form
for Singulars. The form which is the nearest approach to
this is AfA, but this is not adequate, and does not mark out
the Singular either properly or without ambiguity. The
following scheme may be given as a complete and specific
statement of Categorical Propositional forms : —
Affirmative —
I. X is Y. Singular Definite, Comprehensive only, in
two forms.
(a) Newton is the author of the Principia. Concrete.
(b) Veracity is the harmony between expression and
conviction. Abstract.
II. All X is all Y. Definite Omnitude — Double, — cor-
responding in Extension to Definite Singularity in
Comprehension.
III. All X is (some) Y. Definite Omnitude — Single.
IV. Some X is (all) Y.
V. Some X is (some) Y.
Negative —
X is not Y.
I. Newton is not the author of the Principia.
II. Any X is not (any) Y.
. III. Any X is not (some) Y.
IV. Some X is not (any) Y.
V. Some X is not (some) Y.
No. I. is in Comprehension alone ; No. II. is in Extension
alone. All the others may be read both in Extension and in
Comprehension. In the latter, the predicate is taken as in-
divisible and unquantified. If the predicate Y be taken as a
class, we have an Extensive Proposition ; if it be taken as a
mark or indivisible attribute, we have a Comprehensive Pro-
position, and that in both cases, whether Affirmative or
Negative.
327
CHAPTER XXV.
QUANTIFIED PREDICATE HISTORICAL NOTICES.
§ 409. The history of opinions regarding the legitimacy or
the opposite of quantifying the predicate is one in itself of much
interest, and it has acquired importance from its bearing on
the logical theories of Hamilton, Thomson, and De Morgan,
and other recent developments in formal logic. So far as
Aristotle is concerned, the principle of quantifying the predi-
cate was rejected by him, when he had the doctrine expressly
before him.1
On other occasions, Aristotle may be regarded as having
proceeded on the legitimacy of the doctrine, and thus accepted
it in practice. This is seen especially in his treatment of the
formal Inductive Syllogism.2 The great body of logicians,
since the time of Aristotle, have been content to acquiesce in
Aristotle's rejection of a quantified predicate, and generally
for the reasons he has given, which are by no means cogent
or satisfactory.3 The notices hitherto given of writers favour-
able to the doctrine of a Quantified Predicate, either in theory
or in assumption in practice, are to be found mainly in Hamil-
ton's Logic, and in Mr Baynes' New Analytic of Logical Forms*
Neither Prantl nor Ueberweg has given adequate attention to
this point in their historical references.
Mr Baynes, in the New Analytic, published in 1850, refers
to certain names as recognising the doctrine in theory or in
1 See Categories, ii. § 1, v, § 7. De Int., c. vii. §§ 2-4 c. x. An. Prior., i.
c. xxvii. § 9. An. Post., i. c. xii. § 10.
2 See below, p. 449 et seq.
3 For a statement and criticism of Aristotle's views, see Hamilton, Logic, iv.
Appendix g, p. 298 et seq.
4 New Analytic, App. i. p. 81.
328 INSTITUTES OF LOGIC.
practice. The first is Laurentius Valla (1408-1457), in his De
Dialectica, libri. iii. The references are to the edition at Paris
of 1530, though the work was probably first published much
earlier.1 Following Valla, is Ambrosius Nolanus in his Casti-
gationes adversus Averroem: Venetiis, 1517. Then, Jodocus
Isenacensis, or Jodoc Trutfeder of Eisenach, who was the
instructor in philosophy of Luther, — by no means a sympa-
thetic pupil, — and who died in 1519. His work is Summxdce
Totius Logicce, 1501. In England we have Joshua Oldfield, in
his Essay towards the Improvement of Reason, 1707; and there
is a reference to Godfrey Ploucquet, Fundamenta Philosophic
Speculative, 1759. Thynne, in his notes to Walker's Com-
pendium of Logic, — the Trinity College, Dublin, text-book of
the time, — makes applications of the doctrine.
Hamilton refers to authorities for and against the prin-
ciple,— among the former Titius, Ars Cogitandi (1721), and
Ploucquet. His reference to Titius is, however, very incom-
plete.2
§ 410. Valla recognises the principle alike theoretically and
practically, though he cannot be said to have carried it out
with anything like scientific development or precision. He
adduces a number of instances of express quantification in
ordinary language, for his criticisms of the approved logical
doctrines of his day were made chiefly from a grammatical
standpoint. There is universality in the predicate in such
expressions as these — Nego aliquem esse beatum. Aliquem is
here equivalent to ullum. Veto ullum intrare ; prohibeo quem-
quam loqui.s Then he recognises the equivalence of subject
and predicate in such expressions as the lion roars (rugit), the
horse neighs (hinnit), man laughs (ridet). The predicate here
is coextensive with the subject, and precisely convertible.4
Valla's doctrine acquires its importance from his application
of it to the Conversion of Propositions. His doctrine on this
point proceeds on the postulate of an express quantification
of the predicate, and is perhaps the earliest application of it
to this subject, affording at the same time a legitimate and
useful simplification of the ordinary logical rules.
1 There is a later edition — Laurentii Vallce Romani dialecticarum dispu-
talionum libri tres eruditiss. Opera Joannis Noviomagi castigati diligenter—
Colonics, 1541.
2 See Logic, iv. Appendix g., and below, p. 334.
3 De Dial., ii. c. xxix. See above, pp. 257, 310. 4 De Dial., ii. xxii.
CORONEL. 329
(a) "Although the signification of the predicate may be wider than that
of the subject, yet it is not taken [in the proposition] as wider ; and
therefore subject and predicate are convertible — as every man is animal.
This is not taken as the whole genus animal, but as some part of this
genus ; therefore some part of animal is in every man. In the same way,
some man is animal means some part of animal ; therefore some part of
animal is some man. ... In negation the principle is different, as
no man is a satyr — that is, no man is any satyr, therefore, no satyr is
any man. Collectively, satyr is not a species of man, that is, any species
of man, therefore any species of man is not a satyr. . . . In negatives,
that or this fish is not foetus-bringing forth, but ova-laying ; to wit, of
those which bring forth fetus, but do not lay eggs, is not that or this fish.
" Thales is one of the seven wise men — that is, some one (aliquis) of the
seven — therefore some one of the seven is Thales. Pythagoras was not of
the seven wise men — that is, any of the seven ; therefore any of the seven
ivas not Pythagoras." In arguing against the opinion that two sub-
contraries are sometimes false together, when their predicates have a
universal sign, as Plato is every animal, Plato is not any animal,
Valla says: "These are not true sub- contraries, of which the second
does not negate what the prior affirms. Plato is every animal has
for its negative Plato is not every animal ; and this negative has for
affirmative, Plato is some animal, because we are not now able to
say any."1
§ 411. But the treatise which first most fully anticipated
the main results of the doctrine of a Quantified Predicate, in re-
spect not only to Conversion but the Moods and Figures of Syl-
logism, is one entirely unnoticed in the history of logical doc-
trine. It bears the following main title : Habes studiose lector
Magistri Lodovici Coronelli in sacra pagina doctoris eximii
amplissimum non solum syllogismorum trium figurarum de medio
communi tractatum ; sed et syllogismorum expositoriorum in ter-
minis divinis arlem syllogisandi. Necnon conversiones simplicem
et per accidens continentem. Omnemque ferine difficultatem dia-
lectices enodantem Magistri Joannis Guidonis magna diligentia
recognitum et emendatum. Veneunt Parrhissiis in via Jacobea in
edibus honesti viri Bernardi Aubry. (1518).
The sub-title is : Syllogismoram tractatus a Magistro Ludo-
vico Coronet Hispano artium professore editus auspicato incipit.
(a) Guido is the editor of the work or treatise, and he calls himself
" Billarensis " in the preface to his pupils. He speaks of Coronel in
the highest terms both as to character and learning.
Neither Ludovicus Coronel nor Guido is noticed by Prantl, while there
is mention by him of Antonius Coronel, a prolific logical writer, who
1 Dialectica, L. ii. c. 24.
330 INSTITUTES OF LOGIC.
taught in Paris in the early part of the sixteenth century, and who, like
Ludovicus, was a native of Segovia. They were probably brothers. An-
tony dedicates his commentary on the Later Analytics to a brother, Fran-
ciscus Fernandus Coronel, a distinguished soldier, 1510. The treatise of
Ludovicus Coronel, which is exceedingly rare, is in the spirit of Petrus
Hispanus and the Terminalists. He and Antony had evidently come
under the influence, at that time very powerful in Paris, of the Scot —
John Major (1478-1540) — now almost only a name, but in his day and
for more than a generation afterwards, one of the most influential of
thinkers, and especially successful in creating a line of followers, — the
last representatives of a retreating and modified scholasticism. Among
these we can reckon Robert Caubraith, Scot ; David Cranston, from
Glasgow ; William Manderston, Scot ; George Lockhart, Scot ; Caspar
Lax and Johannes Dolz, both of Arragon, Johann Mayr or Eck, Antonius
and Ludovicus Coronel, Joannes Dullaert of Ghent, and several others.
The line of Major and his school was nominalistic, terminalistic in
fact, which meant an attempt to render the scholastic logical abstractions
more concrete by bringing them face to face with the forms of lan-
guage, and thus nearer to actual human thinking. The line of Major,
— the relations ultimately of Logic and Grammar, — requires still to be
worked out.
§ 412. Ludovicus Coronel does not lay down explicitly or
as a principle the doctrine of a quantified predicate, but he
criticises the ordinary theory of Conversion, the general and
special rules of Syllogism, even the distinctions of Mood and
Figure, on a tacit assumption and application of this doctrine.
And he proceeds, as will appear, on the principle which
grounds the whole doctrine of express quantification, that we
ought to distribute according to meaning, or enounce as we
think. He is very cautious in dealing with the received
rules, and the authority of Aristotle, which he tries con-
stantly to claim ; but he seeks, if not to substitute new
rules for the old, at least to supplement them by others
which he holds to be equally valid, and to yield " good and
formal consequences." In regard to Conversion, the author
comes in the end to the view that all conversion is simple.
Only let the same quantity remain in the process of conver-
sion, and let us suppose the terms of the conversa and con-
vertens in the same species of representation (in eadem specie
suppositionis), and conversion is effected simply. Thus, by
simple conversion, we can say, All man is animal, — therefore,
animal is all man. Man is Socrates, — therefore, Socrates is
man — (fol. xxxb). This mode of it is to be applied to the
imperfect moods. Conversion, moreover, is an inference, —
COKONEL. 331
implying antecedent, consequent, and illation. To say all
man is animal, therefore all animal is man, — is not conversion ;
because this is made from a suppositio confusa, — in modern
language, from a lack of explicit quantification of the predicate.
But we can convert simply all propositions by distributing
according to the kinds of each (distribuendo pro generibus
singulorum), as the sense may be. Thus even the universal
affirmative proposition is converted simply, as all man is
all animal is convertible into all animal is all man. About
the Universal Negative there is no doubt. The Particular
Negative thus admits of simple conversion, — as, man is not
animal, therefore animal is not man (fol. xxxvib). Then he
says, that every proposition is converted per accidens, by dis-
tributing according to the kinds of eacb, as Universal Nega-
tive and Universal Affirmative, and so may the Particular
Negative, as, Socrates is not an ass, therefore no ass is
Socrates ; and some man is not an ass, therefore every {any) ass
is not some man. The Particular Affirmative may also be thus
converted, — Some man is all animal, therefore all animal is
man (fol. xxxvib). We have here an express recognition of
several of the new propositional forms in Hamilton's table,
— viz., AfA, IfA, Afl, AnI, InA — and their simple con-
vertibility.
If it be said, it is added, that these views are opposed to
the common mode of speech, that two kinds of propositions
are converted simply, and two per accidens, — the reply is,
that the common method refers to propositions taken in the
accustomed manner. Let the same quantity remain and let
the logical proprieties be accepted in all respects in the same
manner, — which is nothing else than that the terms in the
conversa and convertens should stand in the same relation (kind)
of representation (suppositionis), — then all conversion is
simple (fol. xxxvib).
§ 413. In accordance with these views, a particular pro-
position is defined as that in which no term is distributed ;
a universal as that in which either term, subject or predicate,
is distributed. He holds also that the rule regarding the
invalidity of a conclusion from pure particulars does not apply
to pure singulars, or the expository syllogism, which is
" argumentum efficacissimum." The rule against pure par-
ticulars refers to common terms. Further, if the antecedent
332 INSTITUTES OF LOGIC.
be formally impossible, or the consequent formally necessary,
the consequence is good from pure particulars, or from pure
negatives, as — (1) Man is not man; (2) Man is or is not
animal ; Socrates is or is not running (fol. vb).
It is also held that there is consequence, which is non-
syllogistic, and therefore not disposed in mood and figure.
This does not depend on the premisses and the union of the
extremes with the middle, but on the inference from the
disjunctive part to the disjunctive whole (fol. iib).
(a) Coronel criticises the special rules of Syllogism, on the same
principle.
The Second Rule, the major in the first figure, being particular,
nothing follows ; for as the middle term is the highest it is not dis-
tributed, and being the predicate in the minor (affirmative) it is not
distributed. Against this you may argue, and well, these senses of the
two rules of the First Figure are superfluous.
Other rules of the First Figure commonly assigned are : The middle
ought to be the total predicate of the minor. But, on the other hand,
it follows validly —
Every man (quilibet homo) is running,
Some ass is the ass of a man, therefore,
Some ass is the ass of one miming.
Nor in a like form is an objection (instantia) capable of being given,
yet the middle, which is the term man, is not total predicate of the
minor, as is clear ; therefore, it is said that that rule is not always to
be observed. Secondly, the middle in the minor ought not to be ac-
cepted for others, nor for more than in the major. On the other hand
it validly follows, all man runs, all white was all man, all white runs, —
or thus, all white was running, yet the middle in the minor is taken
for more (as well present and past) than in the major, in which it was
precisely taken for the present. Therefore it is said that that rule is
not absolutely to be observed.
The Third Rule majore de inesse et minore de praterito velfuturo aut
possibili consequentia non valet. On the contrary it validly follows, all
man is running, all white was all man, therefore all wshite was running.
Hence it is said that rule does not hold, and ought to be limited.
In the criticism of the moods of the different Figures, there is some
well-founded argument, but also a good deal of verbal and irrelevant
remark after the fashion of the subtleties of terminalism, and often
grounded on a change of the terms themselves. In the First Figure,
the following is held valid : —
All man is risible.
Some rational is all man (or ass.)
Therefore, some rational is risible {or ass.) This may be taken as
eqvrivalent to the mood Afl, If A, If I. The rule is, — that from a
negative minor in the First Figure nothing follows, (1) because this
would be arguing from the non-distributed to the distributed ; (2) be-
cause the conclusion is unusual. Thus,
CAKAMUEL. 333
All man is running,
No ass is man,
Therefore, no ass is running. But put it thus : —
All man is all running (AfA).
No ass is a man (AnA).
Therefore, no ass is running, (AnA). ' ' This is a good and formal
consequence, but" (it is added, by way of salvo, to the received views)
' ' it does not proceed against those instituting that rule, who were not
using an affirmative proposition, whose predicate might be distributed.
Also in thus inferring ; — therefore, any (quilibet) ass is not running,
although the predicate of the major be not distributed, it validly fol-
lows. Nor does this even proceed against them, because that mood is
not used among them. But for all instances which can even be ad-
duced, it is said that the sense of this rule, — the minor being negative
in the first figure, nothing follows, — is that it is not inferred from the
non-distributed to the distributed in respect of the major term ; — with
this it stands that Fapesmo anAFrisesmorum are good inferences, although
the minor is negative."
Again, with regard to the distribution of the middle term, there is,
it is held, a good syllogism in Barbara, apart from perfect distribu-
tion of the middle, which is contrary to the common opinion. Let
the minor term in the minor be completely distributed, and thus let the
sense of the minor be all which is man is animal; if, therefore, the
distribution of the middle, according to the kinds of each, be sufficient
to Barbara, it would be legitimate from those premisses to infer all
man is running, the subject being completely distributed (fol. viiia).
The major here supposed is evidently animal is running.
Again: —
Omnis homo est currens,
Risibile quilibet homo est,
Ergo, risibile est currens.
This may be said not to be in Darii, — for it does not consist of
a universal affirmative major, and a particular affirmative minor, for
both premisses are universal. Of the first there can be no doubt.
As to the second, one of the terms is distributed, and this is enough.
§ 414. Joannes Caramuel reduces all Conversion to Simple
by explicit quantification of subject and predicate, and ex-
pressly recognises all the new propositional forms. He indi-
cates the universality, particularity, singularity, and indefini-
tude of subject and predicate in a proposition by U, P, S, I.
Thus, All man is animal, is U I. All man is some animal, is
U P. Some animal is all man, is P U. Some man is not some
stone, is P P. Some man is not this stone, is P S. Some animal
is this man, is P S. The defect of his doctrine is that he does
not perfectly distinguish between material . and formal truth
and falsity.1
1 See Logica Vocalis, Opera, p. 220 : Francofurti, 1654.
334 INSTITUTES OF LOGIC.
§ 415. Titius, in his Ars Cogitandi, first published in 1701,
very fully and explicitly anticipated the doctrine of the
quantification of the Predicate ; he recognises it not only in
Propositions, but applies it to Conversion and Syllogism.
Titius holds that in universal affirmative propositions the
predicate, for the most part particular, is sometimes attributed
to the subject, according to its whole comprehension, but not
according to its whole extension; while in negative propo-
sitions, although particular, the predicate for the most part
being universal, is removed from the subject according both
to its whole comprehension and its whole extension.1
(a) Titius recognises universal affirmatives with universal predicate
— as Ever;/ man is (every) risible, and a negative with particular predi-
cate— as no Turk is (some) man — viz., Christian — or, some doctor is not
some man. — (Ars Cogitandi, c. vi. §§ 44, 45.)
The error of the common doctrine of Conversion lies in the supposi-
tion that the predicate should assume the sign and quantity of the
subject. — (Ars Cogitandi, c. vii. § 3 et seq. 1721.)
Titius holds conversion to be a simple transposition of subject and
predicate, with the quantities of the convertend unchanged. Hence
all conversion is simple and uniform. For example, (1) No man is a
stone ; no stone is a man. (2) Some man is not medical (any) ; any medical
is not some man. (3) This Peter is not learned (any) ; any learned is not
this Peter. (4) Every man is animal (some) ; some animal is man. (5)
Some man runs (any) ; some runner is man. (6) This Paul is learned,
(some) ; some learned is this Paul. — (Ars Cogitandi, c. vii. § 3 et seq.)2
§ 416. In 1827 appeared the work of George Bentham,
Outline of a New System of Logic. In this we have a very
close approach to the new Propositional Forms. Speaking of
Propositions, he says : —
(a) " In the case where both terms of a proposition are collective
entities, identity and diversity may have place : —
1. Between any individual referred to by one term, and any individual
referred to by the other. Ex. The identity between equiangular and
equilateral triangles.
2. Between any individual referred to by one term and any one of a
part only of the individuals referred to by the other term. Ex. The
identity between quadrupeds and swimming animals. Whenever a
term is intended to be applied to any individual referred to by a
common name, that term is called universal. Wherever it is intended
to be applied to any one of a part only of such individuals, the term is
called partial.
1 Ars Cogitandi, c. vi. sections 37 et seq.
2 See the editorial references in Hamilton, Logic, iv., Appendices V. (g), p.
298, VIII. A. p. 375, X. p. 442.
BENTHAM. 335
In .affirmative propositions, universality is ascribed to the first term
by prefixing to the common name the words every or any, to the second
term by the word any ; but, in the latter case, it seems necessary to
express identity more distinctly than by the simple copula is ; by some
such expression as is the same as. In the same propositions, partiality
is ascribed to the first term by the words some or some one (in Latin
aliquis) ; to the last term by the same words when the first term is
partial ; by the word a when the first is universal. Ex. :
Every horse is a quadruped (partial).
Some quadrupeds (partial) are some flying animals (partial).
Every equiangular triangle (universal) is the same as any equilateral
triangle (universal).
In negative propositions, universality is ascribed in the same manner,
as also partiality to the first term ; but in the case of the first term
being universal, the negative sign (in the English language) must be
combined with the sign of extent of the second, in order to avoid
ambiguity. Ex. gr. :
Every horse (universal) is no cow (partial or universal).
Some quadrupeds (partial) are not flying animals (partial).
Every equiangular triangle (universal) is the same as no isosceles
triangle (universal or partial).
Simple propositions, considered in regard to the above relations, may
therefore be either affirmative or negative ; and each term may be either
universal or partial. These propositions are, therefore, reducible to
the eight following forms, in which, in order to abstract every idea
not connected with the substance of each species, I have expressed the
two terms by the letters X and Y, their identity by the mathematical
sign = , diversity by the sign 1 1, universality by the words in toto, and
partiality by the words ex parte. These forms are : —
1. X in toto = Y ex parte.
2. X in toto || Y ex parte.
3. X in toto = Y in toto.
4. X in toto || Y in toto.
5. X ex parte = Y ex parte.
6. X ex parte || Y ex parte.
7. X ex parte = Y in toto.
8. X ex parte || Y in toto."
Bentham rejects Some X is all Y, some X is not all Y, as identical
with all X is some Y, and all X is not some Y. He retains : (1) All
is all ; (2) all is some ; (3) all is not all or some ; (4) some is some ; (5)
some is not some. But beyond thus stating these propositional forms,
he attempts no application of them in the science of Logic, except to
say that the ordinary rules regarding distribution are not correct, and
that for conversion, which he regards as a " conversive syllogism," the
extent of the terms should always be distinctly expressed. — (Outline
of Logic, chap. viii. p. 130 et seq.)
§ 417. As early as 1833, Hamilton had recognised the
necessity for quantifying the predicate in affirmative propo-
330 INSTITUTES OF LOGIC.
sitions. This appears from the exposition of the Inductive
Syllogism given by him in the contribution to the Edinburgh
Review in April of that year. Therein is the principle
assumed and applied. Before 1840, he had become con-
vinced of the necessity of applying it to negative Proposi-
tions.1
(a) Ueberweg remarks that the quantification of the predicate "has
been carried out by Hamilton on the basis of assertions of Aristotle, and
according to partial precedents in the Logique ou Vart de Penser, and
in Beneke." — (Logic, p. 219.) The first portion of this statement is not
exact ; the whole only shows the small degree of attention which Ueber-
weg has given to the subject of the quantification of the predicate and
its history.
1 Discussions, Appendix II. A.
PART IV.
OF INFEBENCE.
CHAPTER XXVI.
INFERENCE IMMEDIATE AND MEDIATE IMMEDIATE (1) TERMINAL
EQU1POLLENCE (2) PRO-POSITIONAL EQUIPOLLENCE SUBAL-
TERNATION CONVERSION.
§ 418. The third product of the Faculty of the Understand-
ing is Inference. This is of two kinds — Immediate and
Mediate Inference, or Reasoning. The nature of each of
those kinds of inference lies in what I would call necessary
implication. As our basis we have a judgment, or judg-
ments. As, in order to form the judgment, we advance from
concepts or terms to their junction or disjunction ; so, in in-
ference, we advance from a judgment or series of judgments
to another founded on that or those.
If we have but one judgment as a basis or ground, and
if this yields another necessarily, as every judgment must,
we have immediate inference. If we have two judgments
so related that they necessitate a third, we have Mediate
Inference, or what is known as Reasoning. As an ex-
ample of the former, wo may take what is popularly known
as the Conversion of Propositions. Conversion arises when,
retaining the same subject and predicate, we inferentially
put the predicate in the place of the subject, and the
Y
338 INSTITUTES OF LOGIC.
subject in the place of the predicate. Thus, if I say no
planet is inhabited, I am entitled forthwith to say anything
inhabited is not a planet. Or if I say every X is Y, I am
entitled forthwith to say some Y is every X ; or if every X
be included under (some) Y, then some Y includes every X.
Now these are cases of immediate inference, because I do not
require to go beyond the terms or data of the proposition
given to be able, or even necessitated, to affirm the other or
consequent proposition.
§ 419. Hamilton states the distinction between those two
kinds of inference thus : " Keasoning [better Inference] is
the showing out explicitly that a proposition not granted or
supposed is implicitly contained in something granted or
supposed. What is granted or supposed is either a single
proposition or more than a single proposition." Immediate
Inference arises when a second proposition is necessitated
directly and without a medium by the first. In this species
of inference there are only two notions and two propositions.
In Mediate Inference, on the other hand, or Reasoning
proper, there is the mediate eduction of one proposition out
of the correlation of two others, and there are thus three
collated notions.1
| 420. While it may be admitted that there is a difference
between Immediate and Mediate Inference, it seems to me
that it would be a mistake to suppose that those processes
are regulated by different laws. They are simply forms, less
or more complex, of the same process, and they are regulated
by the same laws. The Law of Identity, for example, applies
as readily — nay, more proximately — to immediate inference
as to mediate, and is truly the ground of both. If I say
every A is B, or every covetous man is needy, I can say with
formal necessity some A is B ; some, or this covetous man, is
needy. Here I am really saying that if the whole is or is
affirmed, the part is, or may be stated as being also. There is a
direct application of the principle of containing and contained.
There is no need of any third and mediating term or proposi-
tion in order to necessitate the conclusion, and this is truly
all the difference between immediate and mediate inference.
The law of inference or validity is the same in both cases.
If I say A is B — that is, a part of B, but G is apart of A,
1 Discussions, p. 651.
TERMINAL INFERENCE. 339
therefore, C is a part of B, I apply precisely the same law
as in the former case ; only here I directly apply it to a
part of the whole (A), in order to make it clear that this part
(C) is also a part of B. The explicit application of the law
to a part of the inferior whole A, and through that to another
part of the superior whole B, is merely an additional step in
a process substantially identical with that of direct inference
from whole to part.
§ 421. The cases of immediate inference are varied ; and
to this head may be reduced many logical processes which
have not been considered as inferences at all, but which
are truly such. It is necessary to show that these are re-
ducible to a single head or principle, in the interest of a
scientific logic. The practical use of their consideration is to
bring out clearly what lurks in everyday statements, often
without consciousness of it on the part of those making them.
§ 422. Immediate Inference may be divided into Terminal
and Propositional. The main form of Immediate Terminal
Inference is Equipollence. Equipollence is the complete agree-
ment in meaning of two propositions which are enounced in
different forms of expression, so that, given the one form of ex-
pression, we may translate this strictly into the other. This
is obviously not so much a case of immediate inference — that
is, inference grounded on the thought — as a case of recog-
nised equivalence between two different forms of expression
for the same concept, degree of quantity, or proposition. It
may thus be described as immediate terminal inference or
equivalence, and properly belongs to the domain of Grammar.
Here the postulate of logic imperatively applies : State in a
definite form of language what you definitely think as to
meaning, quantity, and quality. The consideration of the
Equipollentia of propositions has occupied a large space in
Logic, especially since the time of William of Shyrewood
and the date of the Summulce of Petrus Hispanus. But the
whole discussion, while of grammatical and general import,
is strictly extra - logical, and only requires a passing
reference.
(a) "Equipollence is that by which two or more enunciations, a
negation mediating, are reduced to the same value of quantity and
quality."— (Stier, Prcecepta Doctrinal, Tract, ii. p. 17. 1659.)
§ 423. Equipollence in propositions arose very much from
340 INSTITUTES OF LOGIC.
the use of the negative particle in Latin, before signs of
universality, and also before signs of negation. Thus, when
we say non omnia (not every one), we mean some are not.
Omnis non, every one not, means nullus, not any one. Non
nullus, not none, means quidam, some. Nullus non, none not,
means every one; and so on. Thus, non omne peccatum est
crimen, not every sin is a crime — that is, some is not. If we
had said omne peccatum non est crimen, we should mean no
sin is a crime, which is a very different proposition. Hamilton
recognises Equipollence as a form of Immediate Inference ;
but he restricts it considerably, and identifies it mainly with
Double Negation. Thus, A is not not-A. This is merely
translating an affirmation into a double negation, and is, as
he remarks, of merely grammatical import.1
(a) The forms of Equipollence have been expressed by the Latin
logicians in mnemonic lines. Shy re wood, probably the oldest (died
after 1249), gives : —
" ^Equivalent omnis, nullus non, non aliquis non;
Nullus, non aliquis, omnis non, requiparantur ;
Quidam, non nullus, non omnis non, sociantur ;
Quidam non, non nullus non, non omnis, adherent.
Or all together : —
Pra? Contradic, Post Contrar, Prre Postque Subalter."
(See also Lambert of Auxerre, quoted in Prantl, iii. 28.)
Non omnis, quidam non. Omnis non quasi nullus.
Non nullus, quidam ; sed nullus non valet omnis.
Non alter, neuter. Neuter non prastat uterque.
(b) (1.) Sign of negation prefixed to a universal or particular sign im-
plies the contradictory.
(2.) Sign of negation placed after a universal sign implies the contrary.
(3.) Sign of negation placed before and after a universal or particular
sign implies the subaltern.
Hence, (4.) when two universal negative signs are placed in the same
expression, one in the subject and another in the predicate, then the
first is equipollent to its contrary by the second rule, and the second
to its contradictory by the first rule. — (Hispanus, Summul., i. 3, 2,
f. 36 A. Prantl, iv. 44.)
The forms of expression and rules have been repeated by logicians
with very slight variations since the time of Hispanus. On the author-
ship of these and other mnemonic lines, see below, p. 399.
§ 424. (1.) The first and simplest form of Immediate Preposi-
tional Inference is that of Subaltern ation or Eestriction, usu-
ally placed under Conversion. This arises when we infer
some from all, or restrict the quantity either of the subject or
1 Loyic, iv. p. 269.
CONVERSION. 341
predicate, or both. Thus all X is Y, therefore some X is Y.
Some X is all Y, therefore some X is some Y. All X is all Y,
therefore some X is some Y. Here some means some at least.1
This obviously proceeds on the Law of Identity of whole and
part. Subalternation is commonly regarded as a form of
opposition. It is really not so. There is no opposition be-
tween all or the whole of a class, and some of the same, pro-
vided some be taken as meaning some at least. If some be
taken as meaning some only, there is not only opposition, but
contradiction. All men are civilised, and some only are civilised,
are opposed as negatives and contradictories.
§ 425. (2.) Conversion is commonly spoken of as a transposi-
tion of terms — that is, of subject and predicate. It is this ;
but it is so only through the necessity of inference or con-
sequence. It is because from the original form of the propo-
sition or convertend we can infer the same proposition or an
equivalent in a new form, that conversion is possible. No
conversion is true or real which is not strictly inferential,
or dependent on a necessity of consequence. There is and
can be no change, as is supposed, in the quantity of the
terms, — no change from universal to particular in legitimate
conversion. The warrant of the inference is in the original
proposition, and in that alone ; hence conversion is inference,
and properly immediate inference.
§ 426. Conversion arises only when the convertens, better
conversa, follows necessarily from the given proposition or
convertend. It is, in fact, a process from equal to equal. But
this necessity can never be accurately ascertained until the
terms of the proposition are definitely — that is, in the case of
Extension, quantitatively given. All conversion in extension
supposes explicit quantification alike of subject and predi-
cate ; it is only thus that conversion is logically or scien-
tifically possible, and that we can avoid the mistake of sup-
posing a change or accommodation of terms different from
the original, and in the interest of artificial processes and rules.
§ 427. The canon of Conversive Inference may be thus
stated : The predicate of a proposition, in so far as it is
affirmed or denied of the subject, may become subject to the
original or given subject, now predicate. Thus All X is some Y;
hence some Yis all X. No Xis any Y; therefore no Yis any X.
1 Cf. Hamilton, Logic, App. p. 269.
342 INSTITUTES OF LOGIC.
(a) Conversion proceeds on the necessity of the consequence, through
this, that the predicate is said of the subject. In this Conversion dif-
fers from Syllogism and Enthymeme. Because it is necessary, it differs
from the conversion of a particular negative, for although that may be
transposition of subject and predicate, it is not conversion, because it
is not a formal consequence. Whence it follows that conversion is a
hypothetical, conditional, or rational proposition, whose antecedent is
called the Converse (conversa), the consequent the Converting (con-
vertens) ; and therefore the proposition given to be converted (conver-
tenda) is the converse, and the other through which it is converted
the converting (convert ens). — (Duns Scotus, In Universam Aristotelis
Logicam Exactissimce Qcestiones. In An. Pr., i. qucest. xii.)
§ 428. According to the ordinary logical doctrine, we have
three kinds of Conversion. (1.) Simple Conversion is that
in which are preserved, in the converse, the quality and
quantity of the original proposition. Universal negatives
and particular affirmatives are thus convertible. Thus, no
(not any) X is F; therefore, no (not any) Y is X. No horse
is a biped; hence, no biped is a horse. Some men are tall ;
therefore, some tall things are men. Some animals are short-
lived ; therefore, some short-lived are animals. Some X is Y;
therefore, some Y is X.
§ 429. (2.) Conversio per accidens, or Kara /xepo's, is that in
which the quality is preserved, but the quantity is diminished.
The universal, in a word, is converted into the particular of
the same quality. All universal affirmatives are thus con-
vertible— as, every man is animal; therefore, some animal is
man. Every A is B ; therefore, some B is A. It is further
held generally that where a universal affirmative is con-
vertible into a universal affirmative, or rather an affirmative
proposition with a universal subject, this takes place, not by
reason of the form, but of the matter — as, every man is capable
of philosophy ; hence, every one capable of philosophy is a man ;
otherwise, we might infer from every man is an animal, that
every animal is a man.1 This represents the common view of
logicians on the point.
§ 430. (3.) Conversion per contrapositionem is simply through
contradiction and then transposition of subject and predicate.
In place of the subject of the proposition, we have the con- •
tradictory of the predicate laid down; and in place of the
predicate, the contradictory of the subject. Thus, every man
1 Cf. Mark Duncan, Inst. Log., ii. 4.
CONVERSION. 343
is capable of being a grammarian ; hence, he who is not capable
of being a grammarian is not a man. Every A is B ; therefore,
everything that is not B is not A. Aristotle recognised this
form of conversion, and called it indirect consecution in con-
tradictories.1 This is a form of Equipollence.
(a) FEcI simpliciter convertitur, EvA per accid,
AstO per contra, sic fit conversio tota.
— (Petrus Hispanus, Summ., i. 24, p. 30 B. Prantl, iv. 43.)
§ 431. The rules for these processes in the ordinary logical
system are cumbrous, and, in several respects, inadequate.
They do not always accomplish what they profess, and they
often assume other hidden processes which are necessary to
their working.
§ 432. Conversion per accidens is applied to A and E.
But in neither case is the process a scientific one. To take
A, as has been pointed out, conversion per accidens is not a
conversion of A, but of the particular included in A. Thus :
all X is Y, is converted into some Y is X. But some Y is X
is the direct converse of some X is Y, and only indirectly of
all X is Y, because all X includes some X. This is not pro-
perly conversion, but Immediate Inference of Subalternation,
because all is, some is.
The conversion of 0, some X is not Y, is done by Contra-
position— attaching the not to the predicate. This is rather
evading conversion than accomplishing it. There is a change
of terms. Neither Conversion by Limitation nor by Contra-
position is a self-sufficient process. There is always in each
another process implied, but not unfolded.2
§ 433. According to Hamilton, the first great source of
error in the ordinary doctrine of Conversion is that the
quantities are not converted with the quantified terms.
Logicians have looked at the naked terms of the proposition ;
whereas the terms with which they ought to have dealt, are
the terms as quantified in the original proposition. When we
say all plant is organised, we ought not to consider merely
plant and organised in the conversion, but the quantity of
each term as well. The moment we do this, the so-called
limitation of all to some disappears ; for it was all and some to
begin with, and we can say by Simple Conversion some organ-
ised is all plant. The quantity of the proposition in Conver-
1 Top., it 8. 2 Logic, App. v. (c) p. 275.
344 INSTITUTES OF LOGIC.
sion is thus shown to remain always the same. That of the
Converse is exactly equal to that of the convertend or original
proposition. Logicians, looking only to the quantity of the
subject, and not considering that the predicate has always a
quantity in thought as well, called the one proposition uni-
versal, and the other particular, whereas in quantity they
were precisely equivalent — All X is (some) Y is precisely
equivalent to Some Y is all X. It is not maintained that this
express quantification of the predicate is always necessary in
ordinary thought and language. It is sufficient if the predi-
cate be as extensive as the subject, which every affirmative
judgment must assume. Whether it be in itself more exten-
sive is generally of little moment. But as soon as we have
to find its immediate implicate by Conversion, we must ask
the quantity of the predicate which subsists in thought to be
explicitly stated. This being done, all Conversion of Propo-
sitions becomes one — simple, natural, and thorough-going.
There can be no doubt that Hamilton has for the first time
clearly shown the true character of Conversion, its requisite,
and its rule. Wherever thought needs to seek the converse
of a proposition, its best, easiest, and most scientific way is to
conform to the simple principle which Hamilton has given.
§ 434. The table of Hamilton, with the Eight Propositional
Forms, shows at a glance the convertibility of each :
AfA, All X is all Y = AfA.
(A) Afl, All X is some Y = IfA.
IfA, Some X is all Y = AfI.
(I) Iff, Some X is some Y = IfI.
(E) An A, Any X is not any Y = An A.
AnI, Any X is not some Y = InA.
(0) InA, Some X is not any Y = A n I.
Inl, Some X is not some Y = Inl.
(a) The attempts at modifying the current doctrine of conversion by
the older logicians are curious and suggestive.
Universal Negative is twofold, — (1) in which the predicate is distrib-
uted, as no man is an ass; (2) in which the predicate is not distributed,
as when the predicate precedes the negation, as omnis homo animal non
est (every man is not animal.)
In the first case, the conversion is simple, as every suppositum in the
subject is removed from it in the predicate, so every suppositum in the
predicate is removed from it in the subject.
ERRONEOUS IMMEDIATE INFERENCES. 345
In the second case, there cannot be simple conversion, as every phoenix
is not animal (omnia phoenix animal non est), therefore, some animal is
not phoenix. This per accidens. — (Duns Scotus, In An. Pr., L. i. c. xii.)
The particular affirmative proposition is of two sorts, (1) with the
predicate discrete, as some man is Socrates. This cannot be converted
simply, but only per accidens into one singular, Socrates is a man. But,
with addition, this can be converted simply, as aliquid quod est Socrates
est homo. Such a particular implies a universal from the terms trans-
posed, as some man is Socrates, therefore, all which is Socrates is man.
This does not hold in divine things, as, this essence is the father,
therefore, everything which is this divine essence is the father. The son is
this divine essence, and he is not the father. This consequence is,
therefore, not formal. — (Duns Scotus, In An. Pr., L. i. c. xiii.)
Scotus recognises a particular affirmative proposition with a distrib-
uted predicate, as some moon is every moon {quazdam luna est omnia
luna). ' This can be simply converted, every moon is (the) moon. Here
the predicate stands for every one of its supposita; the subject for one
suppositum, and these are equivalent. — (Ibid.)
(b) yEqualis vero est subjectus terminus predicate, ut si quis dicat
"homo risibilis est " ; ut vero id quod subjectum est majus possit esse
prsedicato, nulla prorsus enuntiatione contingit, ipsa enim prsedicata
natura minora esse non patitur. — (Boethius, Introd. ad Syll. Gat. , p.
562. Prantl, i. p. 696.)
(c) Mark Duncan argues against simple conversion of Particular Nega-
tive thus : Some man is not stone ; e converso, some stone is not man.
This is not formally good. For, by parity of conversion, if some animal
is not man, some man is not animal ; therefore some stone is not man, not
because some man is not stone, but because no man is stone. — (Inst. Log. ,
L. ii. c. v. § 5.)
(d) The particular affirmative is not converted per contrapositionem —
Something intelligent is man ; something not man is not intelligent. —
(Shyrewood. Prantl, iii. 15.)
On Conversion, see especially Marsilius von Inghen. — (Prantl, iv. 97.)
§ 435. Some logicians, among others Thomson, regard the
following as cases of Immediate Negative Conceptions. A
statement made in a positive predicate regarding a subject
inference, implies a statement regarding its opposite, or con-
tradictory. The bodily organism is material ; this implies that
it is not immaterial. All human virtues are not without alloy
or imperfection. This implies that all human virtues are short
of their type, and that a perfect act of virtue is not within the
power of man. These are virtually the same statements, but
they are made from different points of view, and they may be
supposed to bring out what is implied in the original state-
ments. It is clear, however, that, unless in the case of the
simple contradictory, there is here no purely formal inference.
346 INSTITUTES OF LOGIC.
It is either a case of the same predicate in other words ; or of
a predicate implied through a medium or process of reasoning.
All actual human virtues may be imperfect, without the con-
sequence that all possible virtues of man are so. There is no
immediate connection between those two statements. This
so-called form of immediate inference, in so far as it is non-
contradictory, comes properly under the head of Equipollence,
— being purely terminal.
§ 436. Immediate Inference through Determination. — De-
termination means adding a predicate or term to a notion, so
as to make it more specific or determinate. We determine
every time we proceed from higher genera to lower species.
Thus, an animal is like ourselves a sentient creature ; therefore,
an animal struck or wounded is a creature in suffering like our-
selves. There is here no purely formal immediate inference ;
the connection between a sentient creature, struck or
wounded and suffering, is known through induction, and 'is
here inferred through a major. Sentiency, wounded, suffering,
are after observation associated or connected, but the con-
cept of the one does not necessarily lead in any way to that of
the other.
§ 437. Immediate Inference by Complex Conceptions. — This
arises when the subject and predicate, that is, the entire pro-
position, is added comprehensively to the original conception.
Thus, the molecule of sand consists of silicon and oxygen ; there-
fore, the analysis of the molecule of sand into those elements would
be an analysis of a molecule. Not, certainly, of a molecule,
meaning any molecule, but simply of the molecule of sand.
But to call this an inference, immediate or other, is a simple
misnomer. It is a mere tautology. The doctrine of Ex-
ponibles, with the old logicians, and the propositional impli-
cates unfolded according to their rules, were much better
grounded than this.
347
CHAPTER XXVII.
IMMEDIATE INFERENCE OPPOSITION — CONTRARY AND
CONTRADICTORY.
§ 438. " Since it may happen that what is may be enun-
ciated as if it were not, and what is not as if it were, and
what is as if it were, and what is not as if it were not ;
further, as this applies equally to the present and to other
times, therefore it is lawful to deny all those things which
any one has affirmed, as well as to affirm those things which
any one has denied. Whence it appears that to every affirma-
tion is opposed a negation, to every negation an affirmation ;
let this be contradiction (dvTt^ao-ts), the affirmation and nega-
tion of the opposite. But I call opposed that which is of
the same concerning the same, not the species alone of one
expression." x
§ 439. Aristotle here raises a very important and fundamental
question. We seek frequently to deny or contradict, to state
the opposite of a given proposition. The question arises,
How can we best do so? In other words, how are we to
make a statement which shall deny a given statement or
proposition without doing more than exactly denying it —
that is, without doing more than is logically required of us ?
Out of this need or question arises what is called the doctrine
of the Opposition of Propositions. And this is one of the
most important and also one of the nicest points in Logic. It
depends essentially on the negation or negative proposition
which is strictly implied in any advanced or given proposi-
tion. The proposition we advance may be an affirmative.
In this case, what we have to look for is the negative which
1De Int., c. 6.
348 INSTITUTES OF LOGIC.
will precisely deny it, and do nothing more. The proposition
advanced may be a negative. In this case, what we have to
look for is the affirmative which will directly confront and
conflict with it, and which, if established, will render it un-
tenable. These propositions will be regarded as opposites
of various kinds, and the test of them in each case will be
the strictness of the Immediate Inference with which, as
negatives or affirmatives, they are implied in and follow from
the original proposition. He who makes a statement is bound
to accept all that which it logically implies, and only that
which it logically implies, — in affirmation, therefore, to ex-
clude the immediately involved negation ; in negation to
exclude the immediately conflictive affirmation.
§ 440. In dealing with this point, it may be well to sketch
generally, before proceeding to detail, the main forms and
features of the Opposition of propositions. This will be found
to admit of degrees. Let us take, first, universal affirmative
and universal negative propositions. If it is said that every
X is Y, I can deny this by saying that no X is Y. Or, to
take a concrete example, — if it is said that every planet is
inhabited, this may be denied by saying that no planet is
inhabited. Now, look at these two propositions. The one,
every planet is inhabited, is a universal affirmative ; the other,
no planet is inhabited, is a universal negative. They agree in
quantity, but they differ in quality. They are both universals :
they speak of the whole of the subject ; but the one is affirma-
tive, and the other negative. The opposition, therefore, here
is tolerably complete ; for the one affirms universally of the
subject, or affirms of the whole subject ; the other denies
universally of the subject, or of the whole subject. Yet this
is not the highest or the extreme form of opposition. For
while the assertion or the truth of the one proposition implies
the denial or the falsity of the other, the denial or the falsity
of the one does not imply the affirmation or the truth of the
other. Thus it cannot possibly be asserted or be true that
every planet is inhabited, and that no planet is inhabited ; that
every X is Y, and that no X is Y. If the former of these
statements be true, the latter is false. But the denial of the
former statement does not imply the truth of the latter. It
may be false that every planet is inhabited, yet it does not
follow that all planets are not inhabited; for if even one planet,
CONTRADICTORY OPPOSITION. 349
or some planets were not inhabited, it would be false that every
one is. All, therefore, which I have to prove or assert in
order to deny that every X is Y, is not that every X is not Y,
but only that some X is not Y And if I did not see this in
an argument, and did not keep by it, I should simply be giv-
ing up my fair logical position and advantage. This kind of
opposition between Propositions is what is called Contrary
Opposition, or the Opposition of Contraries. It holds only
between A and E.
§ 441. But there is still another and a stronger degree of
opposition between propositions than this. This degree con-
sists in such a contrast or opposition, that if the one propo-
sition be true, the other is necessarily false ; or if the one
proposition be false, the other is necessarily true. Or, to put
it in logical language, if the one proposition be affirmed, its
opposite must be denied ; or if the one proposition be denied,
the other must necessarily be affirmed. This mutual relation
holds only when the opposing propositions differ alike in
quantity and in quality. Thus, we may say, — (A) every
planet is inhabited, and in opposition we may say, (0) some
planets are not inhabited. If it be true that every planet is
inhabited, it is false that some are not. If it be false that
every planet is inhabited, then it is at least true that some are
not. In other words, the truth of the one proposition implies
the falsity of the other ; and the falsity of the one implies the
truth of the other. So it is also with E and I — universal neg-
ative and particular affirmative. This form of opposition is
called Contradictory Opposition ; it is the strongest or the
extreme form known to human thought. It is absolutely
insuperable. No compromise, no conciliation is possible
between those two forms of statement, — of affirmation and
negation, — of yes and no. Between Contrary Propositions
there is a possible medium or middle position ; we do not
necessarily pass from the one to the other, — from all to none,
— we may rest in some. But in the case of contradictory
opposition, there is no such medium or resting-place possible.
Between saying that every one is, and that some are not, — we
cannot find a compromise or resting-place for thought. These
statements are absolutely exclusive of each other. Hence it
is laid down as an imperative logical rule — that is, a supreme
law of human thinking — that there is no medium or middle
350 INSTITUTES OF LOGIC.
between contradictory propositions. This is called the law
of Excluded Middle between Contradictories. Contradictory
opposition holds between A and 0, and E and I.
§ 442. It is right to say that these two kinds of opposition
— Contrary and Contradictory — hold in relation not only to
Propositions but to Terms or Notions. Thus, e.g., black
and white are contrary terms, for an object cannot be both at
once ; and there may be objects that are neither the one nor
the other. A stone cannot be both ; but a feeling, or a desire,
or a volition cannot be either the one or the other.
Again, organised and non-organised cannot be applied to the
same thing in one act of conception or judgment ; and there is
nothing, in extreme logical exactness, of which we can think,
which does not fall under the one head or the other. So that
these notions exhaust the whole sphere of the thinkable.
Being and non-being, for example, are absolute contradic-
tories, to those who understand the meaning of the terms.
There is no possibility of conciliating these by a medium or
middle notion. Nothing can at once be and not-be ; to say
that these are the same because the term being occurs in the
second half of the thought, is arbitrarily to leave out the
difference expressed by not, and thus say that there is a
unity when you have merely abolished the real difference — i.e.,
changed the terms. This application, however, of negation to
concepts seems to me to be a secondary one, grounded on the
negation properly expressed in the judgment, and transferred
for the sake of brevity and grammatical purposes to language.
(a) That the same, in the same reference, at the same time, should
belong and not belong to the same thing is impossible. This is the
most certain of all principles ; for it is impossible that any one can con-
ceive as the same being and not-being. Wherefore, all recall demon-
stration to this ultimate belief.— -(Met., iv. 3.) Aristotle says — rb avro
'djxa koX Kara rb avro, because affirmation and negation of the same thing
or the one after the other, or the one in respect of the other, there may
be. If the same, at the same time, and in the same thing, could both
be and not be, and in reason be affirmed and denied, all things would
be mixed, and nothing stable. There would be no species which you
could define as universal ; there would be no necessity, nothing of which
the nature is not to be both one way and another. To pursue truth
would be to follow the flying (to ireT6/Jt.ei>a SiwKetv) ; but it is the nature
of intelligence to intelligise unity. The sublation of this principle,
that is, non-contradiction, is the abolition of cognition and of reality. —
(Cf. Met. iv. 3-7, xi. 5, and Trendelenburg, El. Log. § 9.)
CONTRADICTORY AND CONTRARY OPPOSITION. 351
§ 443. There is a good deal of misconception prevalent re-
garding the true character and import of Contradictory and
Contrary Opposition, whether as regards propositions or con-
cepts. People talk in a vague and inaccurate manner about
these two kinds of opposition, and continually confound
them. But the truth is that Contradictory Opposition means
an absolute or irreconcilable opposition, while Contrary
Opposition does not. If a beggar asks me for a halfpenny,
and I say no, or I shall give you none, I should be properly
understood to say absolutely none, not even one halfpenny.
If I gave him a halfpenny, he would have something — what
is positive ; if I gave him no halfpenny, he would have
nothing — what is negative. This seems tolerably clear,
but we are told that Contradictory Opposites are equally
positive, or real ; that halfpenny and no-halfpenny, or penny
and no-penny, are equally positive in thought and in reality.
I am perfectly certain that the beggar does not think so.
The assumption underlying this view must be, that we
cannot negate except by putting something positive on
the other side. We cannot say no halfpenny without im-
plying a farthing, or a penny, or a sixpence, or something
of that sort. Now I venture to think this a total miscon-
ception of the nature of negation. We may deny, and
deny absolutely, without supposing or implying a positive
at all. We do so in every case of Contradictory Negation.
The apparent exceptions are really cases of an inferior kind
of opposition — Contrary Opposition. E.g., to take number.
We say one and two are opposites. When we deny or
negate one, when we say there is not one, we may of
course be supposed to mean there is more than one — there
are two. We here, however, first of all suppose that the
thing we speak of is and may of course be numbered. We
regard it as coming under a class, and as belonging to some
portion of that class — viz., number — either one, two, three,
or four, &c. But tivo or three is not the true contradictory
of one. This is none — not even one — not any • and in the
denial here we lay down nothing, we simply sweep abso-
lutely away. That is true contradictory denial ; and here
there is no possible alternative, and no positive notion laid
down in opposition. The importance of this distinction is
seen the moment you come to deal with a philosophy which
352 INSTITUTES OF LOGIC.
professes to construct all thought and reality by the law of
contradiction, which alleges that the contradictory actually
passes into its opposite, and so passing forms knowledge and
reality. Nothing can be more futile, and even meaningless,
than such a pretension. When we abolish or supersede the
law of contradiction, we abolish all knowledge, we reduce
everything to chaos.
§ 444. True logical opposition, whether contrary or contra-
dictory, is an opposition of quality in concepts, and as such
it is independent of time. But when we apply opposition to
experience, the element of time necessarily comes into con-
sideration. A subject of a judgment may be quite capable of
contraries in successive times — as a body at rest and in motion.
And so of contradictories even, — for what lives may pass into
what does not live ; what feels into what does not feel. This,
however, in no way affects the laws regulating what is
ideally contrary or contradictory. It only modifies their
application. It makes not the slightest difference in the
concepts of the qualities as different, or even in the fact of
their difference as a matter of experience.
§ 445. Opposition in propositions, as founded on opposi-
tion in qualities of things, and in their concepts, is of
those qualities or concepts which differ the most in the same
genus. In colour we have the various forms of colour, such
as black and white ; in the sensible sphere we have pleasure
and pain, heat and cold, light and darkness, motion and rest,
&c.; in the moral sphere, good and evil, avarice, prodigality ;
in the intellectual sphere, belief, doubt, unbelief. In other
words, Contraries are positive concepts which exclude each
other from a subject capable of them.1
§ 446. The older logicians recognised different grounds in
the opposition of judgments. Some they regarded as opposed
materially, others formally. In this, indeed, they followed
Aristotle.2 The chief principle of difference is, that material
opposites admit of a medium, while formal opposites do not.
The application of this principle is not always quite clear;
but probably concepts under a genus, as red, green, yellow,
rich and poor, &c, might be regarded as materially opposed,
seeing that any one of these affirmed and denied as a predi-
i Cf. Cat. vi., Met. vi. 10.
2 See De Int., vi., De Soph. Elench., v., An. Pr., ii. 35.
CONTRADICTORY AND CONTRARY OPPOSITION. 353
cate would admit of a medium. The object might be neither
one nor other of two, yet something else under the genus.
In formal opposition, affirmation and mere negation — is, or
is-not — there is no medium, as rich and not rich. The same
is affirmed and denied of the same in name and thing. In
modern language we should say that the former kind of
opposition depends on difference of intuition, this being
ultimately referable to the constitution of the outer and
inner faculties of observation and reflection ; while the
latter depends on the simple application of the formula of
non-contradiction.
But the truth is, that all opposition depends for its force
ultimately on Contradiction. The first in every genus, as
Aristotle remarks, is the measure of the rest. Contradiction
is the first, simplest, and truest form of opposition. Con-
tradiction is, therefore, the measure of all opposition. White
is opposed to black through intuition, but the intuition is
founded on the implied difference or contradiction of white and
not-white. The world is either eternal, or the work of chance, or
the work of intelligence. This division is primarily through
the contradictory — The world is either eternal or non-eternal —
that is, it had a beginning in chance or in intelligence}
§ 447. Now the question arises as to the possibility of a
middle or uniting term. In the case of Contraries, as they
belong to the same genus, they may be conceived as each a
species of the genus — e.g., white and black is each a species
of colour, as pleasure and pain is each a species of sensation.
In the case of Contradictories, affirmation and negation of one
and the same attribute may be regarded as included under
Consciousness. But this is the genus of the acts of mind ; it
is not the genus, properly speaking, of the attribute affirmed
and denied, as sensation is the genus of pleasure and pain.
The attribute and its contradictory negation do not come
under the same genus. The attribute and its contrary nega-
tion do so. This genus may be said to unite in a sense the
two contraries ; bxit the position and the negation of the same
attribute cannot be so united.
§ 448. It follows from this that, while in Contrary opposi-
tion the mutual exclusion of the attributes is through two
positive attributes, the mutual exclusion of the attributes in
1 Cf. Aristotle, Met. , x., and Duncan, Inst. Log., i. 13.
z
354 INSTITUTES OF LOGIC.
Contradictory opposition is not necessarily through two posi-
tive attributes, but through a positive attribute and its bare
negation — the mere absence of it. Hence, when I negate
contradictorily, I do not necessarily posit another attribute in
the place of the negated attribute ; I only absolutely take it
away. I negate, e.g., contradictorily sensation. I say this
subject is insentient, or it is incapable of vision. Here I put
nothing in the place of the sensation or the vision negated ;
I merely leave the subject of which I speak to be referred to
any one in the sphere of possible predicates — the only limit
to this being that the predicate is compatible with the nature
of the subject, whatever that may be. The negation affirms
nothing beyond the indefinite possibility of some other com-
petent predicate.
In the case of Contraries, affirmation and negation differ.
Here I am dealing with a class of things already constituted.
I am dealing with opposites or the greatest opposites in that
class. I affirm one of them ; I necessarily deny the other. I
say this figure is a square, it is not a circle ; this sensation is
pleasurable, it is not painful. Here I select, as it were, among
the members of a constituted genus. But what of negation ?
Suppose I say of the sensation, it is not painful, or of an
object of vision, it is not green. Do these necessarily put
anything in the place of the attribute negated ? I have made
the object I speak of more determinate, in the sense of having
excluded it from a particular predicate in the class to which
it belongs. But that is all. The sensation may be either
pleasurable or indifferent. The object seen is some other
colour. But I do not by this act say definitely what other
colour it is. It is not green ; it may be red, or blue, or white
— since it must be one or other. That I know independently.
But all that my negation of the particular attribute implies
is that some predicate of colour may be attributed to it ;
beyond this indefinite possibility nothing is implied.
§ 449. Accordingly, while it is true that every determina-
tion is a negation, the contrary is not true that every negation
is a determination. A negation is a determination only in the
sense of excluding from a particular attribute, and leaving the
subject to be referred to some other class, or to be clothed in
some other attribute not specified. The negation itself does
not fix anything, — does not really determine, — unless where
IMMEDIATE AND MEDIATE OPPOSITION. . 355
we have already restricted the sphere of predication to two
possibilities, which supposes the principle of Non - Contra-
diction. If the possible predicates be more, we know only
that the subject is in one or other — a case, in fact, of contrary
disjunction. And contrariety itself, as restricted to the species
under a class, supposes also the principle of Non-Contradic-
tion ; for this class must first of all by it be discriminated
from other classes.
§ 450. As to a medium between two Contradictories, the
very conception of its possibility is precluded. Affirmation
and negation of the same attribute in respect of the same
stibject are not only impossible ; they are irreconcilable by
any third notion, for the reason either that the subject of the
predication itself has been sublated, as A is, A is not, or that
the attribute and its contradictory opposite abolish the attri-
bute itself, as organised and non-organised.
11 In all attributions," says Aristotle, " where there is no con-
tradiction, although even the definitions are substituted for
names, and where the attributes are in the subject by them-
selves and not by accident, we can always, without deceiving
ourselves, apply absolutely the isolated attributes to the
thing. Nevertheless, non-being, simply because it is rational,
cannot with truth be expressed as being; for the thought
which we form of it is not that it is, but on the contrary, that
it is not." x
§ 451. Opposites are thus, according to Aristotle, of two
kinds, Immediate and Mediate.
The Immediate Contraries (i.e., Contradictories) are such
that one of them must necessarily be in those things in which
it can naturally be, or of which it is predicated. These have
nothing intermediate. Thus, number must be odd or even.
Here there is nothing intermediate — no middle.
§ 452. Mediate Contraries, on the other hand, have some-
thing intermediate, in which one of them need not be inherent.
Thus, black and white are both predicable of body, yet it need
not be either. Beauty and strength are predicable of man, but
he need not possess either. The intermediate is sometimes
named, as dark brown, pale, with regard to black and white.
The intermediate again is sometimes the negation of both
extremes, as what is neither good nor bad, just nor unjust,
1 De Int., c. xi. §11.
356 INSTITUTES OF LOGIC.
§ 453. Out of this hint of a discrimination of media in Con-
traries, logicians following Aristotle explicitly developed the
distinction between the media forma and the medium sub-
jectum. The middle form in contrary opposition is found
when of the extremes in their nature predicable of an object
it is yet neither, but, it may be, a third of the same class, as
red is a middle form between white and black, and body may
be neither of the two latter, but the first mentioned. This
is called the middle from participation of the extremes.
The middle subject is found when of two contrary predicates
neither is applicable to the subject, as black and white, neither
of which is applicable to soul ; or blind and seeing, neither of
which is applicable to stone. The middle subject is so called
from a negation of the extremes. The middle form was said
to have an application in all or most contraries, and the sub-
ject middle was said to be given in all opposites, contradictories
alone excepted.1
§ 454. The question thus arises, — Can we have a form
of opposition that is so extensive as to include every sub-
ject, as well as to exclude every forma media ? If we take
the abstract formula of contradiction or Immediate Con-
trariety already given, we should have something like this :
A — any given subject whatever — is either B or not-B.
Everything we definitely conceive — every concept we can
make — falls under one or other of those heads. A be-
longs to this definite class of things or thoughts, or it does
not. This is obviously an allowable form of thought about
things or concepts. A lies in ( B J or not-B. But this kind
of opposition is only truly possible beween a definite and in-
definite class of things, regarded as predicates. And the
moment we substitute for A any subject whatever, a definite
concrete subject, we have an illustration of Immediate Con-
trariety, and consequently of the possibility of a medium sub-
jectum, or subject that is neither, because incapable of one or
other. As, animal is either organised or not-organised ; but
volition is neither, as belonging to a sphere incapable of the
one or the other. It would thus seem that the only absolutely
1 Compare Zabarella, Tn Lib. Prcedicament. Tabulae. Opera Logica —
Francofurti, 1608, pp. 127, 670.
VIEW OF ARISTOTLE. 357
comprehensive contradictory — that which excludes every media
forma, and at the same time includes every medium subjectum —
is the abstract formula, A is either B or not-B, translated into
the most abstract of all concepts, being and not-being, when
we should have A- — any subject whatever — either is or is not.
There is here no medium possible, either of form or of sub-
ject. For between the is and the is not there is no middle
form, and nothing whatever can escape lying within one or
other of those terms, being and non-being.
(a) The following passages contain the essential points of the doctrine
of Aristotle on the subject of Opposition : —
Contradiction lies essentially in this, that in the negation of what is
affirmed, and in the affirmation of what is denied, no middle or third
can intervene. There is thus the mere or simple negation of the other.
These propositions are said to be contradictorily opposed, — dvri(partKws
avTiKeiixevai. Thus, every man is white ; not every man is white — that
is, some man is not white. But if you oppose every man is white to
no man is white, this amounts to more than mere negation, for it asserts
something new, and this is as far as possible different from the other,
and is manifestly contrary opposition — evavrlcas avriKtifuvov.
Those which in the same genus are the most distant from each other
are defined Contraries. — (Cat., vi.)
I say, therefore, that affirmation is contradictorily opposed to nega-
tion. When the one enunciation is universally significant, the other
is not universally so in the same thing itself, as every man is white,
not every man is white [that is, some man is not white] ; no man is
white, some man is white. There is contrary opposition when there is
affirmation of the universal and negation of the same universal, as all
man is white, no man is white; every man is just, no man is just.
These, therefore, cannot be both true at the same time. — (De Int., vii.)
Contradiction suffers no middle, Contraries admit a middle. — (Met.,
x. 4.)
Contradiction is opposition, in which nothing intervenes between the
twofold enunciation by itself ; but part of the contradiction is one
affirmation, by which something is drawn to something, the other
negation, by which something is removed from something. — (An. Post.,
i. 2.)
All contraries, Aristotle holds, must be either in the same genus, or
in contrary genera, or be genera themselves. Thus white and black
are in the same genus of colour ; justice and injustice in contrary genera —
viz. , virtue and vice ; and good and bad are themselves genera. But
the truth is, that in the examples here given, justice and injustice are as
much in the same genus as black and white are, — in that, to wit of
ethical quality, and good and bad may also be referred to one genus,
viz., quality. So that contraries come to be the opposites of the same
class. And thus the exception indicated by the forma media, and inter-
mediate possibility, paralyses the strictness of the predication all
358 INSTITUTES OF LOGIC.
through contraries. The middle subject to be found in all contraries
is really that which distinguishes Contrary from Contradictory Opposi-
tion, as Aristotle himself virtually says. The opposition of Affirmation
and Negation is, he tells us, different from all the other modes of opposi-
tion, since in it alone it is always necessary that the one should be true
and the other false. This is not always necessary in contraries, nor in
Relatives, nor in Habit and Privation. Health and disease are con-
traries, yet neither of them is necessarily true or false ; double and
half are relatives ; sight and blindness illustrate Habit and Privation;
yet neither of these is necessarily true or false. What is predicated
without conjunction is not necessarily either true or false, and all the
above-named are predicated without conjunction. It is clear from
this that contrariety rests all through upon the assumption that we
are dealing with things classed. The subject in contrariety may be
a class notion, or it may be an individual, and the sphere of our predi-
cation is limited to classes or qualities that may as a matter of fact or
experience belong to it. The subjects spoken of are supposed to have
natures or constituent qualities which distinguish them from other
subjects, with different natures or qualities. Here, therefore, the
Laws of Identity and Diversity are assumed and employed, in refer-
ence primarily to the subject of the proposition. This necessity of
being true or false may appear to happen in contraries, but it is not so.
" Socrates is well," " Socrates is sick." While Socrates lives, one will
be true and the other false, but when he is dead both will be false.
But in affirmation and negation, one is always either true or false, as
Socrates is sick, Socrates is not sick. When he exists, one is either true
or false ; when he is dead, one is either true or false, for that he is sick
is false, but that he is not sick is true. — (Cf. Cat., x.)
But it may be said that Socrates dead is no longer capable of sick-
ness, and, therefore, that the not-sick does not apply to him, any
more than to a stone. And, therefore, that here the dead or moulder-
ing Socrates is a subjectam medium, and consequently that we have not
a true contradictory. If we throw the matter into a hypothetical
form, i.e., limit the sphere of the subject, — we may have contradiction
within the same class of things, as Socrates, — a supposed sentient or-
ganism,— is either sick or not sick, tvell or ill. If Socrates is living, he is
either sick or not. He is not both, but he must be either. If Socrates is
alive, he has either a fever or not. Both cannot be true : one must. If
one is true, the other is false ; if one is false, the other is true. So that
the affirmation and negation of Aristotle here illustrated does not differ
essentially from what is called Immediate Contrariety. Every number
is either even or odd. This payment is either just or unjust. Given an
object of a specific or known nature, and you are able to state two
alternatives regarding it which are purely contradictories, both of
which cannot be held regarding it, while one must. Body is either white,
or not white — is a true contradictory, though there are things incapable
of colour. Body is either red or green, is not from the terms or form
a true contradictory, for it does not preclude formally the possibility
of its being blue. The proper contrariety is contrariety with a media
forma. The medium subjectum is perfectly compatible with contradic-
LAW OF NON-CONTRADICTION. 359
tory opposition, for the essence of this lies in the absolutely exclusive
form of the predication.
§ 455. The statement that the law of Non-Contradiction is
not " absolute," has already been dealt with.1 It is enough
here to say that it is " absolute," or that the contradictory
concepts are completely mutually exclusive in all our concep-
tion, and in all our true or even possible knowledge of objects.
Even suppose we introduce the element of time and succes-
sion through the changes of a permanent subject or substance,
the law cannot be described as not absolute.
" Ice the solid, water the liquid, and steam the gas, are
three states of one natural object ; the condition of each state
being a certain amount of heat." We shall find on examina-
tion that the main thing implied in saying that there is one
natural object here or substance, through all the changes of
state, is the weight of the original substance. This remains
the same all through the changes, — as does also the weight
of the two gases, oxygen and hydrogen, which alone are found
in it.2 But though there be a substance here capable of trans-
mutation into contraries, if you choose, would any one rea-
sonably say that these states, as objects of sense, are not dif-
ferent or opposed ? Would it be correct here to speak of the
opposition, so far as perceived by us, in successive varying
times, as " not absolute " ? And to apply such an expres-
sion at all — especially without careful explanation — is it not
misleading, and a mere mixing up of totally different points
of view ?
§ 456. But the statement that this law is not absolute, de-
stroys the statement that the law is not absolute. This is
the same as to say, there is absolutely no no ; and when I
deny the absoluteness or complete mutual excmsiveness —
or, which is the same thing, assert the compatibility of two
contradictory propositions — I destroy each, even that one
in which I make the assertion. There is no longer either
assertion, affirmation, or denial. The test of contradiction
as a criterion of the absurd falls to the ground.
(a) Much confusion on this point has arisen from inaccuracy in
determining what, in point of fact, are contraries and what contradic-
tories. Thus, / am conscious, or the Ego and its conscious mode, are
1 See above, p. 120. 2 Huxley.
360 INSTITUTES OF LOGIC.
not true contradictories. For they are not mutually incompatible
either in thought or existence ; on the contrary, we do not know, as
we cannot think the one without the other.
The mode is me partially, for it is mine, and I am in mine. But
it is in no sense a contradictory of me. It does not exclude me.
It involves me, as I am in it. There is mutual involution, not mutual
exclusion or abolition.
The true contradictory of / am is / am not. These are mutually
exclusive, in thought and being. The true contradictory of / am
conscious, is / am not conscious. In / am conscious of what is not-me
— of extension, resistance, &c. , there is no true contradiction ; for
my consciousness of the not-me does not abolish the me, or the me
conscious. The true contradictory here of me would be / am the not-me,
or I am consciously the not-me — the extension, the resistance I perceive.
I am confronted with a negation of myself ; but I am not the negation.
I must even be in order to be so confronted. The negation does not
make me to be or to be conscious ; it is only possible through my
being, and my being is realised in me as successively conscious, even
though only conscious of ideas in me.
§ 457. A question may be raised in regard to tlie two con-
tradictories,— the two inconditionates — the Absolute and
Infinite in Hamilton's doctrine of the Conditioned, — which is
of fundamental importance, though I do not chance to have
met with it among the critics. It may be said that the two
opposites — e.g., an absolute beginning of being and an in-
finite non-beginning of being, or of time — cannot be regarded
properly as contradictories, because we cannot, ex hypothesi,
conceive either. When we cannot form a definite conception
of an object, we are not entitled to say that this other concep-
tion, itself also indefinite or negative, is the contradictory
of the former. If I cannot positively conceive time or being
as absolutely commencing — commencing without being or
time before it, — how can I say that an infinite regress of time
or being, which I can as little positively conceive, is its
contradictory ?
§ 458. In reply to this it may be said, in the first place,
that two contradictories do not require to be equally definite.
If I definitely know one object, in its quality or qualities,
I am able to say that the mere negation of these qualities is
the contradictory of the object — as, for example, organised
and non-organised, — as one and none, — as living and dead.
And this is not necessarily anything definite. But, in the
second place, it may be urged that, in respect of the two
inconditionates, I can conceive neither positively, and conse-
LAW OF NON-CONTRADICTION. 361
quently I have no definite object to negate. Hence a contra-
dictory opposite is impossible, and hence also I could not be
justified in saying that of the two inconditionates one or other
must be real or true. This seems, however, to be an objec-
tion more apparent than real. All that is necessary to be
able to say that these two forms of thought or speech are
contradictory, is to be able to understand what is intended to
be designated by them. The contradiction here is thus,
indeed, purely formal or terminal. It means merely that if
we were able to think positively each of those inconditionates,
we could not but regard them as contradictories. We can
say of the abstract term or form of thought, an infinite non-
commencement, that it is contradictory of the abstract term
or form of thought, an absolutely first or commencement.
Unconditional limitation and unconditional non-limitation are
in a contradictory relation. The statement, therefore, of such
contradictories would be, though purely hypothetical, still
effectual. It would mean that if any object were thought as
infinitely non-commencing, and as absolutely commencing,
these would be contradictory conceptions. And if it were
proved that the one alternative is impossible or unreal, the
other is necessarily possible or real. But it must be admitted
that this alternative inference has no force, unless we first of
all accept being or time as a positive datum, or fact ; and
then try to think it as either absolute or infinite. We begin
with a conception of being in some form — space, time,
quality — and we try to think it as the inconditionate of
limitation, absolute, finished, completed, or as the incon-
ditionate of non-limitation, endless, unfinishable, and we find
ourselves unable to do either ; and yet there being something
thought, and thought as real, it must be in either of those
two alternative inconceivabilities, — either capable of being
absolutely determinate or infinitely indeterminate. In
the sense, therefore, of terminal formulae, these incondition-
ates are legitimate contradictories ; and as applied to any
object of possible thought, they are hypothetically mutually
exclusive.
362
CHAPTER XXVIII.
IMMEDIATE INFERENCE OPPOSITION CONTRARY — CONTRADICTORY
SUB-CONTRARIES INTEGRATION.
§ 459. True logical opposition thus arises only when there
is such an incompatibility between two judgments that the
holding of the one necessarily excludes the holding of the
other. In other words, both propositions cannot be true,
or held together consistently. In opposition, thus, the first
essential point is that the propositions have the same subject
and predicate, the difference being in quantity or in quality,
or in both. With a given subject and predicate, a proposition
being stated, there is necessarily inferred the removal or
falsity of another proposition, the opposite; even in some
cases the removal or falsity of the one gives the positive or
truth of the other.
§ 460. The table of Opposition usually given is as follows : —
Contrary
-f Sub-Contrary 0
The provision that the subject and predicate must be
I
SUB-CONTKARIES. 363
identical in the two propositions, relieves us of two grand
mistakes : —
(1.) That there is opposition between what is known as
Sub-contraries, that is, a particular affirmative and a particular
negative proposition, even though these relate to the same
genus, as some man is learned, some man is not learned, for
the identity of the subject, that is, the part of the class, is not
here guaranteed, and therefore there is no ground for opposi-
tion. Both may be true ; a third judgment is required to tell us
that the some in the two cases is identical. This alone shows
that the terms of the judgment are not, per se, mutually ex-
clusive, and there is thus neither opposition nor immediate
inference.
(2.) That contradiction may subsist between judgments
whose predicates are opposed contradictorily ; whereas con-
tradiction only exists between judgments whose subject
and predicate are identical, and in which accordingly the
affirmation and negation bear on the same thing or point. It
is, in fact, secundum idem, ad idem, ex eodem. This is really
the doctrine of Aristotle, and it is the sound one.1 Thus or-
ganised and non-organised are contradictory predicates, but
can form part of contradictory judgments only when predi-
cated of the same subject. The importance of this principle
will appear in reference to certain theories of Seasoning.
(re) An elenchus is a contradiction of one and the same, not of a word,
but of a thing, and of a word not synonymous but the same, collected
necessarily from the data, not co-enumerating the original question ;
according to the same, and with reference to the same, in a similar
manner, and in the same time. — (Soph. El., v.)
(b) All opposites are diverse ; but all diverse are not opposites, as
whiteness and sweetness in milk. These can be predicated of the same.
Opposites are those which cannot be truly predicated either of them-
selves in turn, or of the same third, according to the same (part), in re-
ference to the same, and in the same time. — (Duncan, Inst. Log., i. 13.)
(1.) According to the same — i.e., the same part — as white and black.
(2.) To the same — double and half axe opposed, and yet the same may
be double and half, but not to the same.
(3.) At the same time — heat and cold, sight and blindness, riches and
poverty. The same man may be hot or cold, but not at the same time.
— (Cf. Arist. Soph. Elen., c. v. Duncan, Inst. Log., i. 13 § 1.)
Heat may be predicated of the subject of ivhiteness and blackness,
though whiteness and blackness cannot be predicated of the same. —
(Ibid.)
1 Cf. Knauer, Contrar und Contradictorisch, 1868.
364 INSTITUTES OF LOGIC.
(c) Aristotle tells us that some propositions are opposed Kara A«f'|jp
(vocem), others /cot' &\ri6ctav (veritatem).
Thus, (1.) the dog barks and the dog does not bark are opposed accord-
ing to expression, but not according to truth. The domestic dog barks,
but not the constellation. Here there is no opposition in meaning.
(2.) Some man is just, some man is not just, are opposed merely accord-
ing to expression, for the some is uncertain and may refer to different
parts of man — say, Cicero and Catiline. These propositions may both
be true, and as such they are not properly opposites.
(d) Duncan (so Thomson, Outline, p. 193) holds that sub-contraries
cannot be both false. He argues that if it be false that some man is
just, the contradictory will be true that no man is just. If it be
false that some man is not just, the contradictory will be true that all
man is just. If, therefore, these are both false, — some man is just,
some man is not just — the following will be both true, that every man
is just, and that no man is just. — (Instit. Log., ii. vi.)
Some man is just ; some (other) man is not just. Some man has the
mark Y ; some (other) man has not the mark Y. If it be false that
some man has the mark Y, then it is true that some man has not the
mark Y. If it be false that some man has not the mark Y, then it is
true that some man has the mark Y. These thus may be true together ;
but they cannot be false together.
Might it not be in regard to sub-contraries that man is neither just
nor unjust, but simply not acting, or acting in circumstances where
neither justice nor injustice is possible ? All man may conceivably be
sleeping or fishing, or shooting, or running, &c. , — and some or no part,
therefore, acting either justly or unjustly. When sub-contraries cannot
be both false, we are supposing some men — the subject — to be acting in
circumstances to which the predicate is possibly and naturally appli-
cable— that is, a certain or definite some.
§ 461. The contradictory opposites usually given are A and
0, E and I. Thus (A), all X is Y; (0), some X is not Y.
(E) No X is Y; (I) some X is Y.
The rule is, position implies sublation ; sublation implies
position. There is no medium between contradictory oppo-
sites. If A be posited, 0 is sublated ; if 0 be posited, A is
sublated ; and so of E and I.
Posit, All animal is sentient (A) ; sublate, some animal is not
(any) sentient (0).
Posit, Some animal is not (any) sentient (0) ; sublate, all
animal is sentient (A).
If we sublate 0, some (even a part of) animal is not sentient;
we posit A, all animal is (some) sentient, that is, every one is.
THOMSON'S DOCTRINE. 365
A 0
It is not true that some men are not civilised ; therefore it is
true that all men are civilised.
Posit, No miser is (any) happy (E) ; sublate, some (even one)
miser is happy (I).
Posit, Some (at least) miser is happy (I) ; sublate, no miser
is (any) happy (E).
§ 462. Thomson disputes the propriety of regarding A and
0 as contradictories. He says, " the fact is, that we cannot
tell from the removal of 0 whether we ought to replace
it by A or U. Let the 0, some men are not rational animals,
be removed, that is, its truth denied, and that removal will
not establish the A, that all men are (some) rational animals.
A third judgment is possible, namely, that all men are (all)
rational animals, — the only rational animals there are ; and
which of these two is to apply cannot be inferred from the
0, but must be inferred from the facts of the case." l This
criticism proceeds on a misconception of what logical illa-
tion is, and the confusion of formal and material sequence.
In logical illation we have not to consider what is possible
in inference, but what is necessary — in fact, the necessary
consequent is all with which we have got to do. And in
this case the necessary consequent and the only one is A,
or, all men are (some at least) of rational animals. If it be not
true, or rather if it be denied, that some (even some) men are
not rational animals, it follows that all men are rational — that
is, some of rational animals at least. Whether all men he all
rational animals, or all the rational animals that are, is not
decided, and it is irrelevant. What we have only to look
for, or need to look for, in such a case is a proposition which
necessarily follows at least from the denial of the original
one, whether this inferred proposition represents all the truth
or not.
1 Outline, p. 190.
366 INSTITUTES OF LOGIC.
§ 463. But while this criticism is inept, the ordinary theory-
is open to objection, and needs amendment. Some seems to
have three distinct meanings, and it is only in two of these
that the contradiction between 0 and A is sustained. (1.)
Some, taken in its ordinary logical acceptation, means some
at least, perhaps all, I don't know whether or not. If, then,
I deny that some at least of men are not civilised, I do not
necessarily assert that all men are, I only imply that some
are civilised, though I do not know whether the whole are,
whether even others are or not. This is the extreme of in-
definitude, and here 0 does not yield A as contradictory,
but only I.
(2.) If some means some only, and I deny that only some men
are not civilised, I imply that all men are civilised, — that is,
0 implies A as its contradictory. Not some only are clearly
means all are. Some only is thus seen to be tacitly and
without proper acknowledgment accepted in the ordinary
logical formulae.
(3.) Some may be taken as meaning even some, or even some
part. Thus, even some part of man is not without a sense of
a transcendent Being. This (0) implies (A) that every pari of
man or all man has a sense of transcendent Being. This comes
very near the definitude of any — ullus. It is denied that
some (even one) X is not Y, therefore every X is Y.
(a) Some {at least). This is all that is necessary to a Particular Pro-
position. To sublate Universality, some one requires to be excepted.
Between some (plural, several) and none, there intervenes some one.
To deny that all the apostles of Christ were faithful to their Lord — it is
not necessary to assert several were unfaithful, but only one — some one.
It ought to be noted that while of contradictories one is
always true and the other false, it often happens that we
cannot, as a matter of fact, tell which is true or which is
false. This happens especially in future contingents. Thus,
it will rain to-morrow, it will not rain to-morrow ; but which is
true or to happen we cannot determine.1
§ 464. Contradictories, considered in reference to the sub-
ject, are of two kinds — (a) The subject in the one is a Uni-
versal, or (b) a Singular, certain, and designate, — as every
man is just, not every man is just — Cato is just, Cato is not just.
1 Duncan, Instil. Log., vi. 2.
Hamilton's view. 367
In the case of the universal subject, the contradiction requires
difference both in quantity and in quality, or between A and
0. These two forms are expressly recognised by Aristotle.
(a) With Aristotle contradiction is of (1.) Universals, as, all man is
white, some man is not white ; no man is white, some man is white.
(2.) Singulars, as, Socrates is white, Socrates is not white. — (Cf. De
Int., c. vi. vii.)
(b) Occam recognises a form of Contradiction which he names Inferen-
tial. Thus, no animal runs, some man runs. The latter implies the
contradictory of the former, for if some man runs, some animal runs. —
(Summ. Log., i. 36.) This, however, is not contradictory to any one
who has not identified some man and some animal. It thus makes
no new form.
§ 465. On Hamilton's system there is no contradiction be-
tween any two propositions which contain whole and part.
The only true contradiction is between Singulars and Totali-
ties indivisible, that is, regarded as Singulars. Socrates is
sick ; Socrates is not sick. The whole of A is (identical with)
the whole of B}
In the doctrine of the Opposition of Propositions, the
modifications introduced by Hamilton arise mainly from the
semi-definite meaning of some, as some at most, some only.
Some, according to Hamilton, is always thought as semi-
definite — that is, some at most or only, when the other term
of the judgment is universal. Thus, some animals are (all)
carnivorous, means negation of all are carnivorous — that is,
not all are carnivorous or some only of animals are carnivorous.
(Only) some sunsets are stormy — that is, others are not, or not
all are.
In the case of Subalterns, we infer I from A and 0 from
E — All is some, .'. some is some; all is not, ,', some is not.
This only holds good if we mean some at least. If we mean
some only, the two propositions are inconsistent — that is, they
cannot both be true.
Thus, All African is (some) black (only) ; ;. some African is
(some) black (only.) — (Afl, IfA.) All men are copper-col-
oured; some men only (not all) are copper-coloured — are in-
consistent. Some horses (only) are not swift is opposed to no
horses are swift.
§ 466. In Sub-contrary Opposition (so called) there is
an inference from some only to some other. If I say all men
1 See Bowen, Logic, p. 173.
368 INSTITUTES OF LOGIC.
are some animals or some animals are all men, I can infer all
men are not some animals, or some animals are not some men.
Some animals only, implies that men are a certain some, and
not any other animals, or other part of the class. This infer-
ence Hamilton calls Integration, inasmuch as it is a com-
pleting of the whole, of which a part only has been given.
§ 467. Under Immediate Inference, Hamilton further lat-
terly included the two forms of Hypothetical Seasoning, —
the Conjunctive and Disjunctive. This doctrine appears in
the note to " The Essay on the New Analytic of Logical
Forms" (1850). "All mediate inference is one; that in-
correctly called Categorical ; for the Conjunctive and Dis-
junctive forms of Hypothetical Reasoning are reducible to
Immediate Inferences."1 The nature of Hypothetical Rea-
soning had occupied Hamilton's attention specially for
some time from 1848 to 1852. Certain fragmentary re-
sults are given in the Appendix to the Lectures on Logic.2
From these we gather that he held all inference to be
hypothetical, and that what have been called Hypothetical
Syllogisms are not more hypothetic than others. In
one of the fragmentary papers, he says that Aristotle in
ignoring them as forms of reasoning was right, that they
are not composite by contrast to the regular Syllogism, but
more simple, that if inferences at all they are immediate,
not mediate, that they are not argumentations, but pre-
parations for augmentation, as only putting the question in
preparation for the syllogistic process. Hamilton cannot be
said to have reached a conclusion on this subject wholly
definite, clear, or satisfactory. He inclines on the whole
to the view that Conjunctive and Disjunctive Syllogisms are
reducible to forms of Immediate Inference, at once resem-
bling and different from each other.3
(a) In 1848, he gave as kinds of Immediate Inference, i. Sub-alter-
nation ; ii. Conversion ; iii. Opposition, (a) of Contradiction, (b) of
Contrariety, (c) of Sub-contrariety ; iv. Equipollence ; v. Modality ;
vi. Contraposition ; vii. Correlation ; viii. Identity. — (Logic, App. VIII.
iv. p. 373. )
1 DlSCUS SZ07ZS T) 65 1
2 Appendix VIII., vol. iv. p. 369 et seq. 3 IV. p. 387.
369
CHAPTEE XXIX.
MEDIATE INFERENCE REASONING ITS NATURE AND LAWS
THE SYLLOGISM — ORDER OF ENUNCIATION.
§ 468. Inference in every form means necessary implication.
In other words, given a certain proposition or statement,
another proposition or statement must also be admitted along
with it or in consequence of it. That other statement is
implied in it, and necessarily implied in it. This is infer-
ence,— the first form of Inference, — Immediate Inference.
Thus, if I say : No Christian can be cruel to the creatures
whom God has wade, I am entitled to say that the man who is
cruel to these creatures is not a Christian. If the first proposi-
tion be granted, the second must be granted. The first pro-
position may, of course, be disputed ; but, given that, the
second, follows, and necessarily follows. Thus the inference
is immediate ; that is, I do not need any third or other term
beyond what I have in my original statement to warrant my
inference.
A single proposition may thus yield an inference, apart
altogether from what is called reasoning. And one of the
most necessary things in our ordinary practical dialectic is
simply to be able at once to catch at the immediate in-
ference which a statement implies, — unknown, it may be, to
the person who makes it. Every proposition, if we but
definitely understand, and, much more, definitely state the
character of our terms, must yield a direct or immediate
inference.
§ 469. But there is another kind of Inference besides this,
— the inference which we usually call Argument or Reason-
ing. Now, what is the type or form of a perfect reasoning ?
2 A
370 INSTITUTES OF LOGIC.
It is that I have two propositions, not one merely, as in the
case of Immediate Inference, and out of these two I not
only get, but I am obliged to get a third. This, for example,
will stand as a type of reasoning : —
(A) (B) _
A free-intelligent is responsible ;
(C) _ (A) _
Man is a free-intelligent ;
(C) t (B)<
Therefore, Man is responsible.
Now, the conclusiveness of this reasoning — i.e., the connec-
tion between the premisses and the conclusion — is entirely
independent of the matter or subject about which we reason.
It is of no consequence whatever what the terms of the
reasoning are, whether they are free-intelligent, responsible,
and man, or what they are. These may be quite changed,
yet if we preserve the connection between the terms, our
reasoning will be equally valid or conclusive. Thus, suppose
I substitute for free-intelligent, A ; and for responsible, B ; and
for man, C ; then I might reason thus : —
Every A is B ;
Every C is A ;
.'. Every C is B.
It matters thus nothing what are the notions or terms of our
reasonings, — the law of reasoning is the same. In technical
language, the matter of our reasoning may vary ; but the
form remains the same. I have got here, as it were, the
mould of human reasoning. I care not whether it be applied
to science, to ordinary matter of fact, to history, or to philoso-
phy. The reasoning process is all the same in these. I
have got the law, or form, or type of reasoning which runs
through the infinity of things about which I can think. Amid
changing matter, I have got the unchanging form, — the ideal
of accurate sequence in thought. This is the conception
which regulates the chaos of associated impressions. This is
the golden band that runs through and holds together all
the materials of thought.
(a) Mill's conception of inference is that of proceeding from the
known to the unknown, or from truths known to others really distinct
from them. Inference with him is of three kinds — from generals to
MEDIATE INFERENCE. 371
particulars, particulars to generals, particulars to particulars. This
last is the foundation of both the others.
(b) Mill, as might be looked for, rejects immediate inference, on the
ground that there is no real progression from one truth to another, —
the logical consequent being a mere repetition of the logical antecedent.
This is not the case, as is clear from the illustrations given ; and it is
as incorrect to hold that there is only a change of expression in im-
mediate inference ; there is a distinction in judgment.
(c) Kant regards immediate inference as inference of the Under-
standing, mediate as that of the Reason. — (K. d. r. V., p. 360 ; Log.,
§41.)
§ 470. Mediate Inference is of two kinds — viz., Syllogism
and Induction. Syllogism proceeds (a) from the general to
the particular, or (b) from the equal to the equal. Induction
proceeds from the individual or from the particular to the
general. Syllogism, in so far as it proceeds in the first line,
is a reasoning from the higher or wider to the lower or
narrower ; Induction is a reasoning from the lower or parts
to the whole or totality which is thus constituted.
(a) We believe all either through Syllogism (<xv\\oytfffiov) or through
Induction (e ir ay ay rjs). — (An. Pr., ii. 23.)
We learn either from induction or from demonstration (airoSei^ei) ;
demonstration is from universals, induction is from parts (particulars).
— (An. Post., i. 18.)
As the proposition in demonstration is a necessary one, and of im-
mediate certainty, these statements of Aristotle are not to be construed
as implying an empirical theory of knowledge.
§ 471. In this case we have Mediate Inference or Season-
ing, because we have not merely two propositions, but
because we have introduced into each of the two propositions
or premisses a term common to both, called the Middle
Term. And let it be observed that these two proposi-
tions are not merely arbitrarily or voluntarily connected.
They are connected in virtue of the law of whole and part
in thought. Thus, I may find or know from observation
that the crocus is a plant, and I may find, further, that
plant belongs to the class organised. Each of these proposi-
tions, taken by itself, would not lead me far. I might be
able from it to state the proposition in another form, but
that is not much. But if I put the two propositions together,
— and I am led to do this because the term or concept plant
belongs to or is common to both, — I shall find that a
372 INSTITUTES OF LOGIC.
proposition, distinct from either, necessarily emerges. I say,
first of all, every plant is organised ; then, the crocus is a
plant; and thus I get the new proposition, that the crocus is
organised, or, in virtue of its being a plant, belongs to the
class organised. Now this, whatever view we may take of
its nature, is the fundamental form and type of all human
reasoning, — that to which valid reasoning may be reduced,
and by which it may be tested. And if we seek to analyse
the principle or law which regulates and necessitates this
evolution, we shall find that it is analogous to that of whole
and part, — that it is, in fact, that of genus and species. Thus,
crocus is found to be a part of plant ; plant is found to be a
part of organised, therefore the whole organised, inasmuch as
it includes the part or species, plant, includes also the part
or species of plant — viz., crocus. There you have the ground-
principle of direct or categorical reasoning, — that form of
thought into which the working of the mind naturally and
chiefly flows. This reasoning is called mediate, because
we connect crocus and organised through their participation
in a common notion or term — viz., plant.
(a) Reasoning, says Wolff, is an operation of the mind, in which,
from two propositions having a common term, there is formed a third,
by combining the diverse terms in both. Syllogism is an expression
in which the reasoning (argument, ratiocinium) or discourse (discursus)
is expressly set forth. — (Logica, § 50, 332.)
(b) What is a Reasoning ? Hamilton, following Esser, in the Logic
Lectures, brings out its nature and scope in this manner. We have
before us two notions, which are opposed to each other, — repugnant
or contradictory. We wish to know which is to be affirmed of a given
subject. But we are unable from an examination of the notions them-
selves to determine this point. We are thus in doubt, and we must
remain in this state of indecision, until we get further knowledge. The
knowledge, moreover, must be a general rule which will extinguish the
doubt. It must be a rule with an application to the present case.
For example, we have before us the two contradictory predicates
free-agent and necessary agent. We ask the question — Which of these
applies to man ? Is man a free-agent or is he a necessary agent ? How
is this question to be decided, and the doubt solved ? Not certainly by
a mere inspection of the two contradictory predicates. But suppose I
take one — say free-agent — and find by a competent process that a free-
agent is one morally responsible, or that every morally responsible agent
is free, I have thus advanced a step in the line of solution. Suppose
I further find that man is morally responsible, — I have thus got two
related propositions, or one notion related to the two notions, freedom
and moral responsibility. Now the question or problem with which I
MEDIATE INFERENCE.
373
started may be solved, and I can with necessity or absolute certainty
infer that man is a free-agent. Thus —
Every morally responsible agent is a free-agent ;
Man is a morally responsible agent. ;
Therefore, man is a free-agent.
It is obvious that the cogency of the reasoning depends on the ascer-
tained relations of the middle term, morally responsible agent, at once to
man and to free-agent.
(c) To Mill it appears that we can never discover that two notions
stand in the relation of whole and part, by comparing each of them
with a third. E.g., we should say this: A is a part of B, B is a part
of C. By putting these together, we find that A is a part of C.
Thus :—
(All) A is apart of B (some B);
(All) B is a part of C (some C);
.'. (All) A is a part of G (some C).
But Mill does not admit this. A, according to him, is perceived to
be A and something more. We thus perceive A and something more
to be a part of C, without perceiving that A is a part of C. In other
words, we perceive that (all) A is a part of B, and that (all) B is a
part of C. We must, therefore, have perceived from the very first, or
before putting these two propositions together, that A was a part of G.
Why ? we ask in wonder. Because otherwise you would have the
absurdity of supposing that you perceived A and something more to be
a part of C, without perceiving that A is a part of C ! Suppose we
perceive in this way, according to the terms : —
(a) All A is B.
(b) All Bis C.
Is the second proposition here an advance on the first or not ? Is
the one necessarily involved in the other ? May I not know that all
374 INSTITUTES OF LOGIC.
mineral acids art poison, without knowing that salt is a mineral acid ?
Suppose a child being taught geography, might it not learn first that
Jerusalem is in or a part of Palestine, without knowing that Palestine
is in or a part of Asia ? And once it knows these two things, would
it not, through them, know, and necessarily know, that Jerusalem is
in or a part of Asia ?
Yet if Mill's contention be correct, the second is as necessarily in-
volved in the first as the conclusion, A is C, is involved in the other
two. As it has been well put, even if we grant " that we perceive B
to be A and something more, quite as soon as we perceive it to be so,
— quite as soon as we perceive A itself to be a part of B, how can we
be said to perceive A and something more to be part of C, be/ore we
can perceive it to be so ? " But the truth is, that Mill's assumption
here is simply contradictory. It is this, that if all or every A be a
part of B, it is A and something more. How possibly, if only every
A be B, can A be itself and something more ? What more, if only
every A be a B? If every mineral acid be a poison, how is every
mineral acid more than the poisons with which it is convertible ? If a
pound is a pound of lead, how can or why should a pound be more
than a pound ?
§ 472. The act of reasoning is, in Hamilton's view, as a
mental act, — that is, once the relations of the three terms are
grasped in the mind, — one organic, indivisible whole. We
may state in language its different parts or propositions suc-
cessively; but in the mental reasoning or in mutual relation,
they have a wholly different significance from what they have
considered apart. This significance is to be found in the
light which they mutually reflect on each other in the reason-
ing. In consciousness the three notions and their reciprocal
relations, the moment they are grasped, constitute only one
identical and simultaneous cognition. To consider reasoning
as a mere whole made up of judgments, is an illustration
simply of " the mechanical mode of cleaving the mental phe-
nomena into parts ; and holds the same relation to a genuine
analysis of mind which the act of the butcher does to that of
the anatomist." *
(a) The intellect knows in one act the conclusion of a syllogism ; and
also in that act the terms of the conclusion ; — yet in that act it knows
nothing incomplex of the conclusion. In the same act, thus, in respect
of the conclusion there is knowledge, but no knowledge in respect
of the terms. — (Occam, In Sent., i. Dist. 1, qu. 1 L. Prantl, iii. xix.
755.)
§ 473. Hamilton expressly and consistently holds that all
i Logic, L. XV. iii. p. 275.
LAW OF MEDIATE INFERENCE. 375
inference, — be it mediate or immediate, be it categorical or
so-called hypothetical, — is truly and ultimately hypothetical ;
and thus that what are called conjunctive and disjunctive
reasonings, are not more hypothetical than categorical rea-
sonings. In immediate inference, given a proposition, the
question is, What are the inferences which its commutations
afford ? In categorical reasoning, given three notions, two
related, and at least one postively to a third — what are the
inferences, afforded in the relations to each other, which this
comparison of the two notions to the third determines <i1 It
is for this reason that he regards the terms sumption and
subsumption on the whole the best names for the premisses.
Logic considers these not as absolutely, but only as hypo-
thetically true. Logic does not warrant their truth, it only
guarantees the legitimacy of the inference — the necessity of
the conclusion.
§ 474. Now there must be a law here — a law, necessary
and universal — regulating my thought, and all human
thought ; and what is that ? It is, that when you have gen-
eralised, or brought things into a class, you are entitled to
affirm or to deny of the things contained in the class, what
you may affirm or deny of the class itself. If, for example, I
am entitled to affirm responsibility of a free-intelligent, and if
I am entitled to affirm free-intelligent of man, I am bound to
affirm responsibility of man. Now that is really the whole —
the essence — of human reasoning. But observe the points
here implied. When we have got the premisses, we must
get the conclusion. That follows necessarily, or, as I have
said, by necessary implication. But we may have a great
deal to do in getting the premisses. This need not be dis-
guised. The getting the premisses, or the best rales for
getting them, belong to what we call Inductive Logic. But
it is a very important thing all the same to be able to get
the rules for drawing valid conclusions, — for keeping us
right in our reasonings, — and that is what formal Logic
professes absolutely to do, and can do.
§ 475. The ultimate law or rule which regulates categorical
reasoning is a maxim founded on the laws of Identity and
Non-Contradiction — viz., whatever belongs, or does not belong,
to the genus, belongs, or does not belong, to the species or in-
1 Loyic, Appendix iv. p. 371.
376 INSTITUTES OF LOGIC.
dividuals contained under it — or, as it is more commonly put,
in the words of the Dictum of Aristotle, — Whatever is predi-
cated, affirmatively or negatively, of a term distributed, may
be predicated in like manner of everything contained under it.
This rule is a universal rule. It regulates all reasoning,
whatever be the things or matter about which we reason.
We may see this, taking for the terms of the reasoning letters
of the alphabet, thus :
Every X is Y ;
Every Z is X ;
.'. Every Z is Y.
Or, Y is predicated of X ; Z is contained under X ; therefore
Y must be predicated of Z. Terms related, as X, Y, and Z are
in this reasoning, must necessarily give the same kind of con-
clusion, whatever these terms may happen to represent.
(a) Ueberweg holds "the most important doctrine in the whole of syllo-
gistic" to be embodied in the following paragraph : " The possibility
of the Syllogism as a form of knowledge rests on the hypothesis that
a real conformity to law exists and can be known. . . . Perfect
knowledge rests on the coincidence of the ground of knowledge with
the real cause. Hence that syllogism is most valuable, in which the
mediating part (the middle notion, the middle term), which is the
ground of the knowledge of the truth of the conclusion, also denotes
the real cause of its truth." — (Logic, p. 337.)
It is a serious objection to this view (1.) that it implies a distinction
of Syllogism as more or less valuable or valid, and therefore syllogisms
of different grades. There is one law which regulates the essence and
process of valid reasoning, otherwise there is no science or ultimate
criterion of it. (2.) " The truth of the conclusion " is ambiguous. If
it means the validity of the conclusion, that is one thing ; if it means
the absolute or irrespective truth of the conclusion, that is another
thing.
Ueberweg supports his view by arguing apparently that unless the
conviction of the universally valid truth of the premisses is not founded
on the presupposition of a real conformability to law, it must first be
reached by a comparison of all individual cases. If the latter alterna-
tive be true, the truth of the conclusion must be established ere we get
the truth of the premiss or premisses. If, for example, all men be
sentient, and Caius be a man, then Caius must have been known to be
sentient ere we could say all men are sentient. We thus knew the
truth of the conclusion before that of the premisses, and in order to
get the universality of the premiss, must assume the truth of the con-
clusion. This is really the objection of Sextus Empiricus to syllogism —
viz., that the major premiss can only be established by induction, and
that this supposes the examination and testing of every individual,
and hence that we fall into a petitio principii in syllogistic deduction.
ueberweg's view. 377
If we say that all animals move the under jaw, this might be refuted
by a single negative instance, — as, for example, the crocodile, which
moves only the upper jaw. — (Hypot., ii. 194.)
The answer to that is, we do not get the universality of the premiss
through the comparison and enunciation of all particular cases. This
is a simple impossibility, for cases under a concept or genus are ideally
infinite, and need not be actual cases at all. There is a confusion here
of generic and numerical totality. The universality from which we
start is that of a class, constituted by certain definite attributes, one
or a mark attaching to one of which may be stated as a predicate. All
that we require to know to bring the individual — actual or ideal — un-
der the predicate of the class, is to know that he possesses the marks of
the class or genus,— that he is man in this instance. The predicate
of the class or the mark of the predicate of the class may, therefore,
become predicate of him,. — the individual. We do not, for example,
require to wait until Caius dies to predicate of him, mortal or subject to
death, — for we are supposed to know that this is a mark attaching to
man or some mark of man. We do not need to examine every kind or case
of triangle to predicate equality of the three angles to two right angles,
for this is a mark which is already attached universally to a three-sided
figure, or to the class triangle, by implication in the definition.
Our inference would be perfectly good, and contain all the elements
essential to inference, were we to say, if all men are sentient, and Caius
is a man, he is sentient, — the question, as to how we get the univer-
sality of our major premiss, or whether it correspond to anything in
reality or not, being wholly independent points. Our major may be a
generalisation from experience, it may be the statement of an a priori
law, or essential principle of reality, which no examination of indi-
vidual instances could give ; but in either case the conclusion from it
may be stated in the form of hypothetical inference, its formal validity
thus tested, and its character as the type of a universal formal infer-
ence in any kind of matter vindicated.
(1.) Is the middle term in every proper or scientific syllogism a
cause ?
(2.) Is the inference dependent on this, or is it dependent on the
fact that a cause is only a case of coming under the law of whole and
part?
It is not universally true, or nearly so, that "in a syllogism the
ground of the knowledge of the truth of the conclusion also denotes
the real cause of its truth " (Ueberweg, Logic, p. 337). If man be sen-
tient, and Caius man, Caius is sentient ; but the middle term man
cannot be said to be the cause of sentiency or of Caius being sentient.
Sentiency is a property of the class, and as such belongs to any dis-
coverable member of the class, — known, possibly, to belong to it by
other marks. Much less is this so in the case of a reasoning through
equivalents, which obviously Ueberweg does not contemplate. A is
equal to B, B is equal to C, — therefore A is equal to C. A may be
known to be equal to B for a hundred years before B is known to be
equal to C, and yet until this discovery is made, there is no possibility
of the conclusion. And would any one say, in this case, that the middle
378 INSTITUTES OF LOGIC.
B is a cause, or the cause of the truth of the conclusion ? It is cer-
tainly the ground or condition, but cause it is not in any proper sense
of the word. The relation in which it stands to the other terms is
much wider than anything embraced under Causality.
In the second place, even where the middle term may be a cause, the
conclusion does not depend on the relation of cause and effect for its
necessity, since there is no example of the relation of cause and effect
in our experience which is necessary, or the opposite of which cannot be
represented in thought. The example given by Ueberweg is: "An
opaque body which comes between a luminary and a body which, dark
in itself, is light by means of the other, causes an eclipse of the latter.
The earth is an opaque body which, at certain times, comes between the
luminary, the sun, and the moon which is dark in itself and made
luminous by the sun. Hence, at certain times, the earth causes an
eclipse of the moon."
The force of this reasoning does not depend at all on the causal re-
lation of an opaque body to the eclipse, but on the circumstance of its
universality ; otherwise it would not take place in the case of the earth.
We may get at the universality through the causality ; but get at the
universality we must somehow, ere we can include the special case, and
thus we depend on the reference to the class, not the reference to the
cause, for the validity of our conclusion. In a word, we fall back on
the formal reference, in the case of a class constituted, it may be, by
the relation of causality, but still constituted somehow, and by us
accepted as universal. It is only now that our inference can reach the
character of necessary implication. The particular effect does so
happen in the circumstances, or from the cause (or causes) ; but that it
must do so, we could not before experience have told, — that it must
always do so, we cannot, after experience, assert, — and, therefore, we
never would, from this relation alone, say that the eclipse of the moon
must follow from the position of the earth.
§ 476. Aristotle thus enounces the supreme Canon of
Syllogism : —
When it is said that a thing is in the totality (eV oXw) of
another, or that a thing is attributed to all of another (Kara
7ravTos), these expressions are the same in sense. To say
that a thing is attributed to all of another (or to another in
its entireness), is to say that we suppose there is no part of
the subject of which the other thing cannot be said ; and,
in the same way, the not being attributed to any. — (An.
Pr., i. 1.)
We have here apparently a formula of the Syllogistic
Canon, which is much wider than most subsequent logicians
have supposed, or at least accepted and applied. The Canon
takes in reasoning alike in Extension and in Comprehension.
" To be comprised in the totality," " to be attributed to
DEFINITION OF SYLLOGISM. . 379
all," are different expressions, with the same logical effect,
referring to different aspects or forms of reasoning.
The former refers to the subject as forming part of the
extension of the predicate — as, all gold is (some) metal. The
latter refers to the predicate as forming a part of the total
comprehension of the subject — as, every mineral acid is a
poison, or has the mark poison. The former proposition states
the relation of the part to the whole (species to genus) ; the
latter states the relation of the whole to the part — as min-
eral acid to its part or one of its marks, poison. The one
is the relation of the particular or species to the universal
or genus ; the other is the relation of the universal to the
particular, or at least the complex to the particular or indi-
vidual mark.1
(a) Trendelenburg, however, remarks that the expression iv '6K<p dvai
T(p /j.4ffcfi, signifies only that the subject is as a part in the whole genus.
The proposition £v does not indicate the mark which is in, but the
species which is under, the genus. In Categ. V. we have, as some man
is in the species man (ev tfSti viripxa). But this refers only to one form
of the expression.
§ 477. An argument exhibited in strict form is called a
Syllogism. This consists of two propositions or premisses,
and a third or conclusion. Of these, one proposition is called
the major, the other the minor. Of the three terms one is
major, another minor, a third middle.
There are three terms in every Demonstration, and no
more. The syllogism is made up of two propositions. The
three terms constitute two propositions.2
§ 478. The Syllogism may be denned as " an enunciation
in which certain propositions being posited, another proposi-
tion different from these necessarily follows, because of this
only, that these are posited. When I say because of this
only that these are posited, I mean that it is because of these
that the other proposition follows, and by following from
these I mean that there is no need of any extraneous notion
in order to effect the necessary conclusion." 3
(a) Aulus Gellius, speaking of Aristotle's definition of Syllogism,
describes it thus : ' ' Syllogismus est oratio in qua consensis quibusdam
1 Cf. St Hilaire, in loco. 2 ^n# pr^ i 25.
3 An. Pr., i. 1. This definition is repeated almost verbatim — Top., i. 1, § 3.
380 INSTITUTES OF LOGIC.
et concessis, aliud quid, quam quae concessa sunt, per ea, quae concessa
sunt, necessario conficitur " (xv. 26). On this Trendelenburg remarks
that rtdivTa and Kelfatva are wider than concessa and consensa — the latter
referring to what is granted by an opponent, the former to what holds
through the force of the things themselves. — (§ 21.) But so far as the
formal inference is concerned, this matters nothing.
(b) The necessary with Aristotle, as Biese pointedly remarks, is either
simply per se or absolute, on account of which others are ; or hypo-
thetical, which is on account of others. — (Trendelenburg, § 21.)
(c) Syllogism is literally and essentially collection into one. This
may be from and through the general, as in Deduction, or through
the particular, as in Induction. Etymologically <rv\\oyi(e<r6cu is to con-
join by reckoning or reasoning. In Plato it means to collect into one
what follows from two statements posited, and usually the ascertain-
ment of the universal from the particular. — (See Theaeteius, p. 186d ;
Phcedrus, p. 2496; Phil. 41c.) By syllogism Aristotle means such a union
of three notions that the third and first can be joined or collected in
one enunciation — as man and animal through mortal, or A and B
through a common C. When Aristotle speaks of syllogism from induc-
tion (6 «£ iiraywyrjs <rv\\oyi<Tfi6s), he is influenced by the earlier and more
general meaning of the word, — collection generally. — (Cf. Trendelen-
burg, in loco. )
2,v\\oyicrfj.6s is literally a reckoning all together or up, and logically it
is a reckoning or bringing together before the mind of premisses so as
to be summed up or completed in one conclusion. The same idea is
conveyed in colligere, collectio. Cicero's equivalent to <Tv\\oyi<rix6s is
ratiocinatio. In the widest sense with Aristotle, <rv\\oyi<r/j.6s may be
based on the merely general, or on the necessary in which case we have
demonstration. Or it may even refer to particulars, and in this case we
have a syllogism from induction.
On Hegel's blunder about the Syllogism and Aristotle, see Waitz in
An. Pr., i. p. 371. After quoting the Aristotelic definition, Waitz says :
" Quare non recte Hegel (Wke, xiv. p. 408) ' Der (7v\\oyi<TiJ.6s ist ein
Grund (4<tt\ \6yos, Begrtinden) in welchem wenn Einiges gesetzt ist, ein
Anderes als das Gesetzte nach der Nothwendigkeit folgt ; ' neglexit enim
verba r<j> ravra elvai bene expressa a Biesio 1. p. 1 30, ' so dass sich
dieses an jene in mittelbar anschliefst,' neque recte vertit \6yov,
quern haud scio an optime reddamus Gallico vocabulo utentes, ' rais-
onnement' (raison, \6yos)." In fact this is but an illustration of the
inaccuracies which pervade the impossible encyclopaedic knowledge of
Hegel. He is a man who frequently speaks at second-hand, and his
representations of Aristotle are on a par of inaccuracy with his repre-
sentations of Descartes. What with his preconceived formulae and his
pretensions to cover the whole field of philosophy, Hegel is about the
least trustworthy of men who have professed to represent historical
opinions.
§ 479. Aristotle's point of contrast between Induction and
Syllogism is, that the former yields knowledge through par-
ticulars ; the latter through generals. Particulars are more
TEEMS AND PREMISSES. .381
known to sense, generals are nearer to the productive prin-
ciples of nature. For example, all generous metal is ductile ;
gold is a generous metal ; therefore gold is ductile : this is a
specimen of Syllogism. On the other hand, Induction de-
pends on particulars. Thus gold, silver, iron, and the rest are
ductile ; therefore, all metal is ductile. Or, the angles of every
parallelogram are equal to four right angles. A rhombus is a
parallelogram, therefore the angles of a rhombus are equal to
four right angles. By induction we have — the angles of
a rectangle, square, rhombus, rhomboid, are equal to four right
angles, therefore the angles of every parallelogram are.1
(a) 'Eiraywyrj, literally a bringing to or on, was translated by Cicero
Inductio. In the phrases tirdyeiv \6yov (Met., i. vii.), irapaSiy/xara, the
term might appear to be better translated by afferre than inducere ; for
in 4-iraywyr) certain singulars are brought to (afferuntur) and almost
piled up (congeruntur). But inductio has this meaning, and reasons
are said to be induced (induci) (Cicero, Fat. 10. ) With Plato lir&yuv
and iiraywyri have not this logical signification. — (See Trendelburg, El.
Log. Ar., § 20.) In a military sense, iiraywyf) is bringing up one body
after another — that is, in a consecutive order. With Aristotle, and
logically, eiraywy-fi in its widest sense is the bringing to or forward of
particular or individual instances, in order to form or reach a general
conclusion.
§ 480. The premisses, as in a Syllogism, are called by Aris-
totle 7rpoTao-eis. Among the Latins, the major premiss is
known as propositio, the minor as assumptio; the conclusion
is o-vfnripacrjxa, because it follows from the union of the terms
(irtpaTa) — (An. Pr., i. 9 ; ii. 6) ; o-vfifidivew indicates the con-
sequence— the turning out or resulting from the premisses.
§ 481. Term, syllogistically considered, is the notion into
which a proposition is resolved as predicate, or that of which
there is predication. — (An. Pr., i. 1.) Term (6po<;, terminus), as
predicate, is thus the limiting or determining notion. The sub-
ject and predicate of a proposition are the terms or limits by
which it is circumscribed, as lines do a figure.2 To determine
is thus properly to limit or circumscribe a subject by means
of a predicate. The determination lies in the limit implied
in the predicate notion or term, whether this be an analysis
of the subject notion, or an attribute added to it, or the
reference of it to a class. This limit is realised through the
1 Cf. Trendelenburg, El. Log. Arid. § 20.
2 Cf. Trendelenburg, § 22.
382 INSTITUTES OF LOGIC.
opposition of its negation — in quality or in quantity merely,
or in both.
§ 482. Apart from the middle, the other terms are called
the extremes (a*cpa), for the one occupies the highest place, so
that it embraces the other notions as subjects ; the other the
lowest place, so that it is subject to the others. Hence, the
one of the extremes which is wider is called the major term —
that which is narrow, the minor term. The major is predi-
cate, the minor subject of the conclusion.1
(a) The different constitutents of the Syllogism are named as fol-
lows, viz. : —
(1.) The middle notion or term is called medium, terminus medius,
nota intermedia, argumentum, rb fiecrov, '6pos ixtcros.
(2.) The given judgments or premisses are called propositions prce-
missa>, judicia pnemissa, posita, irpoTdcms, rh irpoTeiv6/j.eva, ra rfdtvra,
rk Kfifneva, sumptiones, acceptiones, Aij/u/xaTo.
(3. ) The minor premiss, or that which contains the subject or subor-
dinate propositional member of the conclusion, is called propositio
minor, assumptio, subsumptio, irp6<rArpf/is, irpSraffis 77 ixdrrcov.
(4.) The major premiss, as containing the superordinate propositional
member of the conclusion, is called propositio major, propositio, sumptio,
\rj/j.fxa, rb /le'i^ov. •
(5.) The conclusion is called conclusio, judicium conclusum, illatio,
ffvfjLiripacTfia, iiricpopd. — (See Hamilton, Logic, iii. L. xv. ; and Ueber-
weg, Logic, p. 335.)
§ 483. The major term is thus the greatest whole in the
reasoning ; the minor is the least ; the middle the less. In
the following example, the major term is organised ; the minor
or least is crocus; the middle or less is plant. The major
proposition is that which states the relation of the greatest
quantity to the less, —
Every plant is organised.
The minor proposition is that which states the relation of the
least quantity to the less, —
The crocus is a plant.
The conclusion is that which states the relation of the least
quantity to the greatest, —
The crocus is organised.
Aristotle, in speaking of major, minor, and middle terms,
had reference to the first figure, in which these terms may be
taken as relatively wider, middle, and narrower or less. But
this distinction does not properly hold in the other figures,
1 Trendelenburg, El. Log. § 24.
ENUNCIATION OF SYLLOGISM. 383
and in the Unfigured or Expository Syllogism does not hold
at all.
§ 484. The usual logical tests of the major and minor
terms in a reasoning are obviously of a wholly superficial
nature. The main one is really the relative local position of
the terms. Hamilton goes deeper, seeks a scientific ground,
and founds the distinction on the two counter-quantities of
Breadth and Depth — Extension and Comprehension. That is
major in Breadth which contains the part of the class — the
minor is the part contained. That is major in Depth which
contains the attribute, and the minor is the attribute contained.
And when these terms are translated the one into the other,
the major of the one quantity becomes the minor of the other.
Further, there is formally or logically no major or minor term
or premiss in the Unfigured Syllogism, or in the second or
third figures of the Figured Syllogism. In these forms the
extremes are either in no quantity or in the same. The dis-
tinction holds only in the first figure ; and here either ex-
treme may be major or minor, according as we take it in
Breadth or Depth.
§ 485. In his final doctrine of Syllogism, Hamilton distin-
guishes two ways of stating a categorical reasoning — viz.,
the Synthetic and the Analytic. In the former, which is the
more common, we proceed from the premisses to the conclu-
sion ; though, as the reasoning is mentally one, premisses and
conclusions are inappropriate expressions. In the latter way
— the analytic — we first state the conclusion, and then state
the premisses as the reasons. Here the conclusion would
properly be called the Question or Qucesitum, and the premisses
the proofs. The analytic method Hamilton regards as the
more natural. We are in doubt, and we put the question, Is
G in A t Analytically we reply, Yes (or G is in A) ; for G is
in B, and B is in A.
This is more natural than the synthetical order, which
would be : —
B is in A, and G is in B, therefore G is in A.
Or analytically : —
7s spirit of salt a poison ? Yes ;
For spirit of salt is a mineral acid,
And all mineral acid is a poison.
Synthetically : —
384 INSTITUTES OF LOGIC.
All the mineral acids are poison ;
Spirit of salt is a mineral acid ;
Therefore it is a poison.
The expression of the Syllogism in either of these ways
shows that it is originally one in thought ; and the Analytic
or Synthetic form, as the case may be, follows the needs of
expression. It might be added to this that while the ana-
lytic mode is that which we should naturally adopt for
research, the synthetic is better fitted for teaching or expo-
sition.
§ 486. As Hamilton has observed, the analytical order of
the Syllogism thoroughly disposes of the common but super-
ficial objection that the Syllogism is a petitio principii. This,
which has been urged by Mill and others, is that the truth
of the conclusion must be known before the truth of the
major premiss which states the general rule. Before I am
able to say all men are mortal, I must know that Socrates is
mortal, — I must know that every individual man, including
Socrates, is mortal. Otherwise I could not state the general
principle or rule. But if I know that Socrates is mortal,
there is nothing to be inferred from the general — all men are
mortal.
This objection is beside the point in even the Synthetic
reasoning, but its irrelevancy is clearly shown by the Ana-
lytic form. I am in doubt, and ask — Is man a responsible
agent t I reason thus : —
Man is a responsible agent ;
For man is a free-intelligent agent ;
(And all free-intelligent agents are responsible.)
In what way is there any begging of the question asked
here ? I compare man with the class free - intelligent agent,
and I therefore determine the question of his responsibility.
But my real difficulty here is to know whether man is to be
classed with free-intelligent. The moment I know that, I
know that he is responsible. The general rule that free-
intelligent is responsible did not involve the truth to me that
man was responsible, because I might quite well know that,
and yet not know that man was a free-intelligent. My ulti-
mate appeal is no doubt to the rule ; but that which decides
the question, or quaesitum, of the reasoning is the ascer-
taining that the rule is capable of being applied to the case
SYLLOGISM NOT A PET1TIO PRINCIP1I. 385
in hand, — that in fact the case in hand can be subsumed
under it. The analytic mode of reasoning is thus the type
of the method of search and inquiry ; it is that naturally
followed by one as yet ignorant of the truth of the conclu-
sion. The synthetic, on the other hand, is that adopted
when one knows the truth of the conclusion already, and
is called upon to teach or expound it through its grounds.
These, — the premisses, — are then placed first. To the teacher
thus the conclusion is known ; to the learner it is not, or
only when both premisses are unfolded. The Analytic
method is for the learner ; the Synthetic for the teacher.
§ 487. Or to take an illustration in practice — Ought this
man to he punished or not for an offence which he has committed?
How is this question to be decided — yea or nay ? Only
by considering whether it would be just or expedient that
the offence committed in the given circumstances should
have the usual punishment, or whether there are mitigat-
ing circumstances which might render it just or expedient
to allow the actor to go. Suppose the crime were classed
under the former, or the latter head, we should simply be
referring it to a general law or rule — in fact, a major
premiss. This in no way contained it from the first or
beforehand, — the rule was not generalised from it, but it,
a new case with resembling features, is subsumed under
the rule. It would be an inaccurate account of such a
process to say that it is simply a reading out of a general
law or induction which I have before me, of a decision
already come to, for the case is a wholly new one. And
it would be quite as inaccurate and inadequate to say that
I have only to generalise the conclusion, and say all such
crimes ought to be punished, or any such crime ought
not to be punished, since this is the very question which
I must decide ere I reach the conclusion at all, — which of
these general alternatives, in fact, I must proceed upon in
determining the conclusion itself.1
§ 488. On this point one other remark may be made.
The objection urged by Mill and others to the syllogism
as a petitio principii is shown to be futile even as regards
the Synthetic form, the moment it is shown that every general
rule or major proposition of a reasoning is not got by
i Cf. Janet, Rev. Phil., 1881, t. 12, p. 117.
2 B
386 INSTITUTES OF LOGIC.
induction. The objection, to have any weight, requires this
to be established, — that every general rule or universal prin-
ciple at the head of a reasoning is a simple generalisation,
or product of induction, — nay, it even requires the rule to
be the result of the inspection of every individual, actual and
possible, under it. This is ridiculous, even as an account
of the inductive process. But if it be not shown that we
have no universal a priori truths, the objection to synthetic
syllogistic reasoning is futile. If we have such, and one
principle is enough, the moment it is applied to an exist-
ence under it, be it actual or possible, that moment is the
allegation of the petitio principii in the reasoning disproved.
If it be true a priori that every event which takes place has
a cause, then the subsumption of any particular event
under the rule annihilates the whole of this criticism.1
1 For a very able and complete exposure of the fallacies in the theory of the
Syllogism as a reasoning from particular to particular, see Janet, De la Valeur
du Syllogisme Rev. Phil., tome 12, p. 105 (1881).
387
CHAPTER XXX.
CATEGORICAL SYLLOGISMS ON ARISTOTELIC PRINCIPLES
MOOD AND FIGURE.
§ 489. Syllogism as a combination of propositions must be
stated in the forms and relations of those propositions. The
number of syllogistic forms must, therefore, be limited by the
number of propositions, and their possible combinations.
This, in the first place, is quite independent of Figure, or the
position of the middle term with reference to the extremes.
But, as will appear, the validity of the possible moods will be
limited or determined by the general rules of reasoning, and
the special rules applicable to Syllogistic Figure. If Mood
in the end be emancipated wholly from Figure, then we shall
have moods determined only by the general syllogistic rules
or conditions of reasoning.
§ 490. The mood of a syllogism (modus, tpottos) represents
the nature of the combination of the premisses, or of the pre-
misses and conclusion, according to quantity and quality.
The early logicians regard Mood as composed of two propo-
sitions only, — the major and minor premiss. In this case
there would be but sixteen moods. If, however, we extend
mood to the conclusion, the three propositions of the Syllo-
gism, taken along with the four Aristotelic kinds of propo-
sition,— A, E, I, 0, — would give us sixteen pairs of premisses
and four different conclusions, — in all sixty-four moods.
The sixteen pairs of premisses are as follows : —
AA EA IA OA
AE EE IE OE
AI EI II 01
AO EO 10 00
388 INSTITUTES OF LOGIC.
The combinations now spoken of are wholly numerical ;
their logical validity remains to be tested by the general
rules of Syllogism, and by the special rules of each Figure.
§ 491. The essence of the Categorical Syllogism being that
there are three terms, and one of them common, the rules of
valid syllogistic inference follow from the application of the
Laws of Identity and Non-Contradiction to the construction
of the Syllogism itself, or to its form. These are — (1.) No in-
ference follows from two negative premisses, for the community
of the middle term with the extremes is thus excluded.
There is no means of mediation, no ground of comparison,
and therefore no ground of inclusion or exclusion in the
conclusion. There is no constitution of the relation of whole
and part. Thus —
No Y is (any) X.
No Z is (any) Y.
The possibilities here are either (1) No Z is any X ; or (2)
Some Z is X ; or (3) All Z is X. But nothing is determined.
So equally with negative premisses, universal and particular,
and both particular. Hence the moods EE, EO, OE, 00 are
logically inadmissible.
§ 492. (2.) The second rule of exclusion applicable to all
the figures follows on the same principle — viz., that there is
no valid conclusion from two particular premisses ; ex meris
particularibus nihil sequitur. The general ground of this rule
is that no community of the middle term with the extremes —
major and minor — is laid down. The part of the one pro-
position is not necessarily identical with the part of the other.
If, for example, it is said : —
Some Y is X,
Some Z is Y;
RULES OF SYLLOGISM. 389
Or,
Some men are negroes,
Some Africans are men.
I am not told whether the some Y [men) who are negroes in
the major are the same or not with the some men who are
Africans in the minor. So long as this doubt remains, infer-
ence is paralysed. The same principle applies whether the
premisses be particular affirmative and particular negative, or
both particular negatives.
The moods inadmissible on this rule are obviously —
II, 10, 01.
(a) 111 all Syllogisms, according to Aristotle, it is necessary that some
term be affirmative and universal. Without a universal there will
either be no syllogism, or it will not relate to the point proposed, or
what is sought from the commencement will be begged. Thus, — Is
the pleasure of learning honourable ? If it be said pleasure is honour-
able, not adding all, there will be no conclusion. If only some pleasure
be understood, either another pleasure may be posited, which i3 nothing
to the point, or the pleasure of learning itself, in which case we beg and
accept that which was to be demonstrated from the first. — {An. Pr., i.
24.) (Thus—
Some pleasure is honourable;
Learning brings pleasure;
.". The pleasure of learning is honourable.)
§ 493. (3.) There is given as a third general rule of exclu-
sion that no valid conclusion follows from a particular major
premiss combined with a negative minor premiss. Thus —
Some A is (some) M,
No B is {any) M,
it does not follow either that some B is not any A, for all B
may not be quite separated from all A ; and thus some of B
may be A, or even all B may be included in A as a part,
although some other part of A is included in M. Thus —
(1)
390 INSTITUTES OF LOGIC.
In other words, there is no conclusion in the form B A.1
According to this view, the mood I E is specially excluded in
all the figures, and I 0, 0 E, 0 0 ; these, however, fall to be
excluded on other grounds as well. This leaves only eight
forms of combination of the premisses. I confess I do not see
that there is proper ground for the exclusion of I E. It is
made to depend on a certain arbitrary distinction of majority
and minority in the premisses which does not necessarily
exist, especially in the second and third figures. With the
premisses I and E,
Some A is (some) M,
No B is (any) M,
it follows, even on Aristotelic principles, that some A (at least)
— namely, that which is M, is not any B. And there follows
also a conclusion in terms of B A, on the full scheme of pro-
positional forms ; for we can infer some B is not (some) A, and
convert some A is not (some) B.
(A)< _ (M)
Some organised is some animal,
(B) (M)
No plant is any animal,
(A)_ (B)
Some organised is not any plant,
(B) (A)_
but not Some plant is not any organised.
§ 494. Supposing always the Syllogism to be simple, or to
include three terms and three propositions, we have (1.) The
middle term must be distributed — that is, taken in its full extent
or quantity, once at least in the premisses.
(2.) No term may be distributed — that is, taken at its full quan-
tity in the conclusion, which was not distributed in one of the prem-
isses ; or no term may be taken in the conclusion at more than
the greatest quantity assigned to it in the premisses. The viola-
tion of this rule results in an illicit process of major or minor
term.
(3.) If one premiss be negative, the conclusion must be negative.
(4.) If one premiss be partiadar, the conclusion must be par-
ticular.
1 Ueberweg, Logic, p. 388.
FIGUKE. 59 L
§ 495. Of the eight generally admissible combinations,
some are to be rejected in certain of the figures, and others
are useless, as marking only a particular conclusion when a
universal could be drawn, as A A I in the first figure. The
application of the general and special rules leaves nineteen
moods both valid and useful. We have thus now to explain
what is meant by the Figure of Syllogism.
§ 496. Categorical Syllogisms are divided, according to
the position of the Middle Term, into several forms, known as
Figures (Jigitrce, crx^a-Ta). The position of the Middle Term
depends on its relation as subject or predicate of the other
two terms. (1.) If the Middle Term be subject in one premiss
and predicate in another, we have the First Figure ; (2.) if it
be predicate in both premisses, we have the Second Figure ;
(3.) if it be subject in both premisses, we have the Third
Figure. As Aristotle has put it : the Middle Term must be
in both propositions. If, therefore, the middle is attributed
to another term, or another attributed to it, or if it is affirmed
of one term and another is denied of it, this is the First
Figure. If it is itself affirmed and denied of some term, this
is the Middle Figure. If the other terms are attributed to
it, or if one be denied and the other affirmed of it, this is the
Last Figure. Thus we have the position which the middle
occupies in each figure.1 Let Y be middle, X major, Z minor,
we have —
I. Figure— Y X
Z Y
.'. Z X
II. Figure— X Y
Z Y
.\ Z X
III. Figure— Y X
Y Z
/. Z Y
§ 497. The statement of the Middle Term, as in the First
Figure subject and predicate, may be regarded as enabling
us to include the First Figure Proper, and what is known as
the Fourth Figure. In the one case, the middle is subject to
1 An. Pr.,i. 32, §7.
392 INSTITUTES OF LOGIC.
the major and predicate to the minor ; in the other case, it is
predicate to the major and subject to the minor.
IV. Fourth or Second Form of First Figure : —
XY
YZ
.'. zx
§ 498. In the Second and Third Figures, the middle term
preserves the same relation to each of the other two terms in
both premisses, — in the one subject, in the other predicate.
§ 499. The First Figure is regarded by Aristotle as the
perfect one, or as giving the perfect moods. It gives the
order of subordination from the highest or most general to the
lowest or most special — the major or next general term being
in the conclusion predicated of the minor.
Thus—
All mammals are viviparous,
All whales are mammals,
Therefore all whales are viviparous.
In other words, mammals are under [a species of) vivip-
arous.
Whales are under (a species of) mammals,
Therefore whales are under [a species of) viviparous.
§ 500. " When three terms," says Aristotle, " are so related,
that the extreme (major) is in the whole middle, and the middle,
again, is or is not in the whole first (minor), there is neces-
sarily a perfect conclusion (syllogism) of the extremes.
" I call that term the middle which is both itself in another
and another in it — which is thus middle by position ; the
extremes both the term which is in another and that in which
another is.
" For if A is enunciated of every B, and B of every C, A
must be enunciated of every C. I call this the First Figure." 1
(B) _ (A)
Every plant is organised,
(C) (B)
Every crocus is a plant,
(C) (A)
Every crocus is organised.
i An. Pr., i. 4, § 2, 3, 4.
akistotle's fokmula. 393
Here A the major term is in the whole B, the middle ; and
B the middle, is in the whole C, the minor ; therefore the
whole C, the minor, is in (some at least) A, the major.
This formula may fairly be taken as fitted and probably
intended to embrace reasoning, both in Comprehension and
Extension.
In Extension—
All B is some part of the class A,
All G is some part of the class B,
.'. All C is some part of the class A.
In Comprehension —
The whole B contains the mark A,
The whole G contains the mark B,
.'. The whole C contains the mark A.
Or—
The whole G contains the mark B,
The whole B contains the mark A,
.'. The whole G contains the mark A.
(3) (M) (1)
Take — gold, metal, ductile —
(M) _ (1)
(All) metal is ductile.
(3) _ (M)
(Alt) gold is metal.
(3) _ (1)
Therefore gold is ductile.
The third is subject to or contained under the middle ;
the middle is subject to or contained under the first ; the first
is necessarily predicated of, or contained under, the third.
This is the relation of stibsumption.1
(a) 0-xw"* Trp&Tov — from material figure and form — hence applied
to diction and the categories. The Latins translated vxv/J-a by figura.
— (Trendelenburg, El. Log., § 24.)
A B r with Aristotle always indicates the first figure.
(b) Aristotle, looking only to the essential relations of the terms, usually
put the predicate first. Thus —
If A can be predicated of all B,
And B of all V,
Then A is to be predicated of all I\
1 Cf. Trendelenburg, El. Log., § 24.
394 INSTITUTES OF LOGIC.
That is—
All B is A,
All r is B,
Then all T it A .
§ 501. Aristotle thus distinguishes complete or perfect and
incomplete or imperfect Syllogism. Syllogism is complete
when there is no need of any other datum than the data pre-
viously admitted, in order that the necessary proposition may,
as conclusion, appear in all its evidence. It is incomplete
when there is needed one or more other data, which may be
necessary after the terms first posited, but which have not yet
been precisely formulated in the premisses.
The complete syllogism is in this view that afforded by
the moods of the First Figure, and those only. The moods
of the Second and Third Figure are incomplete, inasmuch as, in
order to evince their perfect cogency, the propositions, one or
more, need conversion, through which they are brought back
to moods in the first figure.1
§ 502. The formula of the Second Figure with Aristotle is
exemplified as follows : —
Let M be enunciated of no N and of every X. Because,
therefore, the negative proposition is convertible, in no M
will there be N ; but M was placed in every X ; therefore
N will be in no X Thus —
No N is M = E ^
Every X is M = A >- = Cesare.
:. No X is N = E j
With the conversion : —
No M is N = E ^
Every X is M = A V = Celarent.
.;. No X is N = E )
So of the other moods.
In this figure there is no affirmative syllogism, but all
negative, either universally or particularly.2
The middle is posited beyond the extremes, and indeed
in the first place. The middle term is predicate in both
premisses.
§ 503. In the Third Figure we have : —
1 An. Pr., i. 1. 2 a%i pr<) j. V-
FOURTH FIGURE. 395
(a) All Y is X\
All Y is Z > =Darapti.
.'. Some Z is X )
(b) No Y is X \
All Y is Z U Felapton.
.'. Some Z is not X )
When one term, says Aristotle, is in all, but another term
in none, of the same term, or when both terms are or are not
universally in this same term, I call this the Third Figure ;
the middle in this I call that notion to which both are re-
ferred as predicates, and the extremes the predicates ; the
major extreme is that furthest removed from the middle, the
minor that which is nearest it ; but the middle is thus placed
beyond the extremes, that it may occupy the last place. The
conclusion is valid, whether the terms are universally or not
referred to the middle notion.
When P and R are in all S (as subject), then necessarily
P is in some R (as part). Thus —
All S is P\
All S is R > = Darapti.
.'. Some R is P J
By conversion, since all S is R, some R is S. Then all S is
P, some R is S (as predicate), therefore some R is P. This is
Darii of the First Figure.
There is no universal conclusion in this figure, either
affirmative or negative.1
§ 504. Aristotle did not recognise the Fourth or (so-called)
Galenic Figure as distinct ; but he has indicated some moods
which were afterwards referred to it.2 Theophrastus and
Eudemus, according to the testimony of Alexander of Aphro-
disias and Boethius, added five new moods — that is, what
are known as indirect moods of the First Figure. These
are Bamalip, Calemes, Dimatis, Fesapo, Fresison. These at
first given as indirect or imperfect moods of the First
Figure, got through conversion, were constituted into moods
of a new or Fourth Figure.3 The attribution of the Fourth
Figure to Galen as his creation has not been proved. It
1 An. Pr., i. 6. 2 Ibid. i. c. vii. 3 Cf. Ueberweg, Logic, p. 368.
396 INSTITUTES OF LOGIC.
rests mainly on a statement of Averroes ; and what of Galen's
writings remain show no proof of his authorship. But the
truth is, that the moods of the Fourth Figure were recognised
long before his time, and all that he could have done was to
call them moods of a new or Fourth Figure. The moods Fa-
pesmo and Frisesmo are also regarded as indirect moods of
the First Figure.
(a) The form of syllogism with Aristotle depends, according to
Trendelenburg, on the different relations of the terms, grounded on the
principle of the wider containing the narrower. Hence there are but
three positions : (1.) When the middle term is in the middle position,
as in the first figure ; (2.) when it is highest, as in the second figure —
that is, predicate in both premisses ; (3. ) when it is lowest, as in the
third figure — that is, subject in both premisses. With three terms in
the syllogism, and the relations of the middle, these are properly all
the figures.
The so-called Fourth Figure does not depend on any new necessary
relation of the terms, but on the fortuitous position of these in the
premisses. This is quite a different principle of division, and really
arbitrary. Further, there is nothing in the arrangement of the Fourth
Figure which can yield a conclusion different from what can be reached
in the others. It is, therefore, unnecessary and useless. It is simply
not a new figure but a variation of arrangement, founded on the pos-
sible place of the middle term in the premisses. — (Trendelenburg, El.
Log. Arist., § 28.) On Trendelenburg's view in relation to Aristotle,
see Ueberweg, Logic, p. 358. On the difference between Hegel's view
of the figures and that of Aristotle, see Trendelenburg, Logische Un-
tersuchungen, iv. p. 251.
(b) Against Kant's conclusion in The False Subtlety of the Four Syllo-
gistic Figures (1762), Ueberweg urges that the conclusion in the other
figures besides the first may be directly found without reduction to the
first. They are simple, as much as the first. — {Logic, p. 373.)
(c) Hegel places the third figure before the second, or rather names
the third second, and the second third. The change, if it be not a
historical blunder, has no ground in reason.
(d) Herbart and Drobisch reject the moods of the Fourth Figure.
Trendelenburg rejects those of the third, on the ground of ambiguity
and tendency to error. But this is excluded by a strict determination
of the nature of particular judgment. — (Ueberweg, Logic, p. 375.)
(e) Hamilton's view of the Fourth Figure is, that it is a hybrid
reasoning. Its two premisses run in one quantity — Comprehension;
its conclusion is in another — Extension. Further, the conclusion is in-
direct or mediate, being the converse of what is natural. The Fourth
Figure is really the First, with premisses transposed, and the indirect
conclusion of the First given as a direct conclusion. — (See Logic, iv.,
App. D. (a), p. 449.)
Thus Bamalip is only Barbara, with transposed premisses and con-
verted conclusion : —
MOODS. 397
(2.) All irons are some metals,
(1.) All metals are some minerals,
All irons are some minerals.
(By conversion)
,*. Some minerals are all irons. And so of the others.
(/) Ueberweg seems to suppose that the spherical representation may
equally symbolise Extension and Comprehension. — (Logic, p. 379.) In
this he is wrong. Of course whether Extension and Comprehension
can be united in the same reasoning, as Trendelenburg supposes, is a
different question. If Ueberweg further supposes, as he seems to do,
that the representation by spheres of propositions and syllogistic moods
really proves anything regarding their congruence or confliction, he
is equally mistaken. Diagrams only show — only can show — what is
valid on a law of thought. Picturing to the eye by diagram is nothing
more than individualising, and this is only the shadow of proof. The
truth is, seeing that the concept is essentially unpicturable, spherical
diagrams are inadequate as representations, and only rude aids to
thinking.
§ 505. In consequence of the application of the rules
already specified : —
In the First Figure the moods are —
AAA, EAE, All, EIO.
In the Second —
EAE, AEE, EIO, AOO.
In the Third—
AAI, IAI, All, EAO, OAO, EIO.
In the Fourth, or Indirect Moods of the First —
AAI, AEE, IAI, EAO, EIO.
§ 506. These are summed up in the mnemonic lines : —
(1.) bArbArA, cElArEnt, dArll, fErlOque prioris.
(2.) cEsArE, cAmEstrEs, fEstlnO, bArOkO, secundas.
(3.) Tertia, dArAptl, dlsAmls, dAtlsI, fElAptOn, bOk-
ArdO, fErlso, habet : quarta insuper addit.
(4.) brAmAntlp, cAmEnEs, dlmArls,1 fEsApO, frEsIsOn.
§ 507. The first mood of the First Figure, Barbara, is in
letters : —
All Yis X.
All Z is Y.
All Z is X.
i Otherwise, bAmAUp, cAlEmEs, dlmAtls.
398 INSTITUTES OF LOGIC.
Symbolically (in extension) : —
All animal is sentient,
All man is animal,
Therefore all man is sentient.
§ 508. In the Second Figure we have the mood Cesare.
This is in letters : —
No X is Y.
All Z is Y.
:. No Z is X.
Symbolically (in extension) : —
Anything lasting is not violent,
Every unjust law is violent,
Therefore any unjust law is not lasting.
§ 509. In the Third Figure the mood Darapti is in
letters : —
All Y is X.
All Y is Z.
.'. Some Z is X.
Symbolically (in extension) : —
MNEMONIC LINES. 399
All temperance is a virtue,
All temperance is praiseworthy,
Therefore some virtue is praiseworthy.
(a) There is a sharp controversy in regard to the original authorship
of these and other of the logical mnemonic lines. Prantl and others at-
tribute them to Michael Psellus (the second) ; while Hamilton, Thurot,
and Val Rose, hold that the author of the Synopsis, which has passed
under the name of Psellus since 1597, was the borrower. Psellus was
born in 1018 or 1020, and he died after 1077. He was the author
of a paraphrase of the De Interpretatione, published at Venice in
1503, and of a 'Svvoipis t&v irivTt (povaiv ko.1 rwv S^kcl Kartiyopiuiv, pub-
lished at Venice, 1532. In 1597, Ehinger edited a MS. entitled "Ztivotyis
els tV 'ApurroTfAovs AoyiK^v 'Emorr-ftp-wi'. This MS. was without name
of author ; but Ehinger attributed it to Psellus. The Synopsis is almost
identical with a work which was undoubtedly by Petrus Hispanus
(1226-1277), entitled Summulce, and consisting of Seven Tractatus, —
printed in 1486, — of which some forty-seven editions, mostly with
commentaries, appeared between this date and 1516. The authenticity
and authorship of the Synopsis, attributed to Psellus, are disputed, on
the following, among other grounds — (1.) That there is no authority
from any designation in the MS. used by Ehinger to assign the author-
ship to Psellus ; (2.) that there are other MSS. in existence in Europe,
identical with the Ehinger one, in which the treatise professes to be
merely a translation from Hispanus ; (3. ) that in four out of these five (or
more MSS.), the name of the author or translator is given as Georgius
Scholaris, known as Gennadius and Patriarch of Constantinople in
1453 ; (4.) that though the Synopsis contains Greek equivalents for the
Latin memorial verses, those for the Syllogistic moods are greatly
inferior in precision and suitableness, as compared with the lines ap-
pearing in the Summulm of Hispanus. To the reasons now adduced
might with probability be added the presumption that Hispanus,
living at the period he did, was not Greek scholar enough to be able
to translate the work of Psellus. It is thus inferred that, instead of
the Synopsis of Psellus being the original work, this was merely a
translation, by a later hand, from the Summulce of Hispanus. In this
case the memorial verses are to be assigned to Hispanus as the original,
relatively, and not to Psellus.
But it would be a hasty inference to assign the lines — whether of
the Syllogistic moods or others — to Hispanus as absolutely the original
source among the Latins. These, or very close equivalents, had been
in circulation before the time of Hispanus himself. They occur in the
writings (unpublished) of William of Shyrewood (or Shyrwode), who
died Chancellor of Lincoln in, it is said, 1249. There is evidence,
however, that he was alive considerably after this date. Shyrewood
was a very distinguished logician, — of whom Roger Bacon says :
" longe sapientior Alberto, nam in philosophia communi nullus major
est eo." His treatise anticipated the terminalist doctrines of Hispanus.
Prom Shyrewood, the verses seem to have passed to a pupil of his, —
Lambert of Auxerre, — who lived in the middle of the thirteenth cen-
400 INSTITUTES OF LOGIC.
tury. Through one or both of those sources the mnemonics passed to
Hispanus, whose versions show some slight deviations from those of
his predecessors. — (Cf. Prantl, ii. p. 275; Thurot, Revue ArchAologique,
October 1864 ; Revue Critique, March 30, and July 6, 1867; Hamilton,
Discussions, pp. 128, 671.)
Shyrewood gives : —
Sub Prae Prima, bis Prae Secunda, tertia bis Sub.
He gives also for the first time in Latin (? first absolutely) : —
Barbara, Celarent, Darii, Ferio, Baralipton,
Celantes, Dabitis, Fapesmo, Frisesomorum,
Cesare, Campestres, Festino, Boroco, Darapti,
Felapton, Disamis, Datisi, Bocardo, Ferison.
Shyrewood adds : A signifies universal affirmative ; E universal
negative ; I particular affirmative, 0 particular negative ; S simple
conversion ; P per accidens ; M transposition of premisses ; B and R in
the same phrase reductio ad impossibile.
The two first verses serve the first figure, the four terms of the
third verse the second figure, and all the others the third figure. To
the first four moods of the first figure all the others are reducible.
Prantl conjectures that A, E, I, 0, are due respectively to the
vowels in iras, rls, ovfiels (ov8«V), ov jtSs (ii. p. 277). But these vowels
appear to be rather of Latin origin. A and I may very well be sup-
posed to represent the two first vowels in Affirmo, and E and 0 the
two in Nego.
§ 510. The special rules of the First Figure are — (1.) that
the major premiss must be universal; (2.) that the minor premiss
must be affirmative.
§ 511. The special rules of the Second Figure — are (1.) the
major premiss must be universal ; (2.) one of the premisses must
be negative.
(a) In the second figure, the middle term is the predicate alike of
Proposition and Assumption. As predicate it is taken as the wider
or more general notion in each premiss, — the subject being regarded
as part of the genus. Thus —
Whatever lives is nourished,
No stone is nourished,
Therefore no stone lives.
Hence both premisses must be universal, one affirmative and the other
negative, or one at least universal, whether it affirm or deny. From
mere particulars nothing follows.
In the second figure there is no affirmative conclusion according to
Aristotle ; for in order to this, both proposition and assumption would
require to be affirmative : and as the middle term is predicate in both,
and is necessarily taken only particularly, there would not necessar-
ily be a comparison of the extremes with a common third. If both
premisses be negative, there is no positive relation of either with the
THIRD FIGURE. 401
middle term, but mere exclusion. — (Cf. Trendelenburg, El. Log. Arist.,
§25.)
§ 512. The special rule of the Third Figure is that the minor
premiss must be affirmative.
(a) In the third figure, the middle term is subject alike of proposition
and assumption. Hence it is regarded as less general than either of
the other terms. Thus —
S P
Every square has right angles,
S R
Every square is a parallelogram,
R P
.'. There are parallelograms which have right angles.
In the third figure there is no universal conclusion. P as predicate
is conjoined with R in the conclusion ; and P and R are predicates of
the same subject. Since the predicate commonly is wider than the
subject, P and R are wider than the same subject. Because, therefore,
P and R either agree or disagree with the narrower (the middle), you
cannot infer that P and R universally agree or disagree with each other.
There is reference only to a part of both. Wherefore, in the third
figure there is no universal conclusion ; and there is no conclusion from
mere negatives. — (Trendelenburg, El. Log. Arist., § 26.)
Lambert has for rule of first figure the dictum de Omni et de Nullo ;
for the second, a dictum de Diver so, "things which are different
do not belong to each other ; " for the third, a dictum de Exemplo,
"if As are Bs, then there are As which are Bs ; " for the fourth, a
dictum de Reciproco ; "if no M is B, no B is this or that M ; if C is
or is not this or that B, there is B which is or is not C."
The first figure proves qualities, the second differences, the third
examples and conceptions, the fourth reciprocities. — (Cf. Ueberweg,
Logic, pp. 372, 373.)
§ 513. It follows from these rules that in all the figures
the conclusion can be (1.) affirmative only, if both premisses
are affirmative ; (2.) negative, if one premiss be negative ; (3.)
sometimes universal, if both premisses are universal, some-
times particular, if both premisses are universal; (4.) par-
ticular if one premiss is particular.
§ 514. It appears also that every kind of proposition — viz.,
A, E, I, 0, may be proved in the first figure. There can be
proved in the second, negatives only — viz., E, 0 ; in the
third, particulars only — viz., I, 0 ; in the fourth, particular
affirmative, universal negative, and particular negative — viz.,
I, E, 0.
2 c
402 INSTITUTES OF LOGIC.
§ 515. Universal affirmative conclusions have the highest
scientific value, because they advance our knowledge in a posi-
tive manner, and admit of reliable application to the individual.
The universal negatives come next ; they guarantee not only a
negative, but a distinctly definite view. Then come the par-
ticular affirmatives, which promise a positive advance, but
leave us helpless in the application to individual cases.
Lastly, the particular negative conclusions are of the lowest
value. Their special service is to ward off false general-
isation.1
(a) Science which embraces the nature of the thing, can be neither
negative nor particular. It shows the genesis of the thing, and lays
down its nature. Negation merely takes away, and the particular
does not embrace knowledge extending to all of the class. As the
second figure is negative, the third particular, it is only the first which
can contain science.
TS)V 5* <rxiM^Ta"/ iirurrntt.oviKbv h&Xhtto. rb izpwr6i/ icrriv. aire yap fiaOri-
IxariKaX rwv (iriarrinwv 8ia tovtov (ptpovat ras airoSfl^tis otov dp 16 '/xt/t ik^
Kcil ycw(i.(Tpla ical dirTiK-f). — (An. Post., i. 14.)
§ 516. Keduction in the Aristotelic sense, means the bring-
ing back of a mood of the Second and Third Figures, and
latterly of the Fourth, to one of the First Figure — as
perfect. The means of doing this are two : (1.) Conversion
of the premisses or conclusion ; (2.) Transposition of the pre-
misses. To this may be added Contraposition. We thus can
get from the given premisses either the original conclusion,
all in the First Figure, or a conclusion from which the
original conclusion follows by "conversion. In the mnemonic
lines those means of reduction are marked by the letters
s, m, p. These, in their order, mark simple conversion, trans-
position of the premisses, conversion per accidens. The initial
consonant of the mood of the figures after the first indicates
the mood of the first to which the mood in question is to be
reduced. Thus Cesare of the Second Figure is to be reduced,
as indicated, to Celarent of the First.
Cesare : —
No X is Y,
aii z is r,
.-.. No Z is X.
1 Ueberweg, Logic, p. 437.
REDUCTION. 403
No plant feels,
Every animal feels,
So Therefore no animal is a plant.
Gelarent : —
No Y is X,
AllZ is Y,
.\ No Z is X.
Nothing that feels is a plant,
Every animal feels,
Therefore no animal is a plant.
In the Second Figure — Camestres : —
Every animal lives,
No stone lives,
Therefore no stone is an animal.
This is converted into Celarent thus : —
Nothing living is a stone,
Every animal lives,
Therefore no animal is a stone,
Therefore no stone is an animal.
So Darapti : —
All Yis X,
All Yis Z,
.'. Some Z is X.
This is reduced to Darii : —
All Yis X,
Some Z is Y,
.'. Some Z is X.
And so with the others, according to indication — affording
a good enough exercise for beginners in logic.
Here we have employed Conversion and transposition of
the premisses. This is known as Ostensive Reduction.
§ 517. Reductio or Deductio ad Impossibile is that in which
from the contradictory of the conclusion to be proved, and
another proposition manifestly true, or at least conceded by
an opponent, we infer the absurd or impossible. If in a
mood of the Second and Third Figures the premisses are con-
ceded, but the conclusion denied, as not necessarily following
from the premisses, the contention may be reduced to
absurdity by the syllogism being reconstituted in the First
Figure, one of the premisses being preserved and the con-
404 INSTITUTES OF LOGIC.
tradictory of the conclusion put in the place of the other.
In the Second Figure, the major is preserved, and the con-
tradictory of the conclusion put in place of the minor ; in the
Third Figure, the minor is preserved, and the contradictory
of the conclusion is put in place of the major : —
Servat majorem, variatque secunda minorem ;
Tertia majorem variat, servatque minorem}
Thus, Baroko : —
All X is Y;
Some Z is not Y ;
Some Z is not X.
Every animal feels ;
Some living thing does not feel ;
Therefore, some living thing is not animal.
Keduced to Barbara : —
All X is Y (conceded) ;
All Z is X ;
.: All Z is Y;
Every animal feels ;
Every living is animal ;
Therefore, every living feels.
As this conclusion is the contradictory of the original
(given) Minor Premiss, it must be false ; one of the premisses
must, therefore, be false. But the original major as given is
(supposed) true. The falsity is thus in the minor. This is
the contradictory of the original conclusion ; therefore, the
original conclusion is true.2
The K in Baroko and Bokardo means that the premiss
indicated by the vowel before it is to have the contradictory
of the conclusion put in its place. In the one case, this is
the major premiss ; in the other, the minor.
But the whole of reduction is simply unnecessary ; the
moods of the Second and Third Figures are on any system
equally and as directly valid as those of the First. The
superiority of the First Figure over the others lies not in a
higher cogency or necessity of sequence, but in greater per-
spicuity in respect of the principle of inference.
1 Cf. Duncan, Inst. Log., L. iv. c. iii.
2 Cf. Whately, Logic, B. ii. c. iii. § 6.
CONTRAPOSITION. 405
Reduction by Contraposition has also, though not gener-
ally, been employed. Thus Gamestres : —
Every animal feels ;
No plant feels /
Therefore, no plant is animal.
Convert the major by Contraposition —
What does not feel is not animal,
preserve the minor, and we have the same conclusion in
Gelarent : —
What does not feel is not animal ;
No plant feels ;
Therefore, no plant is animal.
So Baroko to Ferio. This was not generally received, be-
cause the converse of the minor is less clear as in effect affirm-
ative than the simple affirmation which has been transposed
into it.1
1 Cf. Duncan, Inst. Log., L. iv. c. iii.
406
CHAPTER XXXI.
CATEGORICAL SYLLOGISMS ON HAMILTON'S PRINCIPLES FIGURED
AND UNFIGURED SYLLOGISM ULTRA-TOTAL DISTRIBUTION.
§ 518. Hamilton has singular merit in his analysis of
Figure, Major and Minor Terms, and Propositions. The
whole tendency of his inquiries on this point is to simplifica-
tion,— scientific completeness and unity, — leading ultimately,
in fact, to the position that Figure, with all its complexities,
is unessential to reasoning. The ordinary view rather led to
the notion that reasoning depended on the order of expres-
sion,— certainly that the difference of Major and Minor in
terms and propositions did. Hamilton has shown that reason-
ing depends on the internal thought, — on the essential mental
relations of Containing and Contained, — of Inclusion and
Exclusion in thought. His view on this point was developed
prior to that of the quantification of the predicate. But this
doctrine completed the theory.
§ 519. Mediate or Syllogistic Reasoning (Categorical) is,
according to Hamilton, divided into two kinds — the Unfigured
and the Figured. In the former, which results directly from
the quantification of the predicate, and from regarding the
proposition as an equation, the terms compared do not stand
to each other in the reciprocal relation of subject and predi-
cate, being in the same proposition, either both subjects or
(possibly) both predicates. The canon for this form of reason-
ing is : " In as far as two notions (notions proper or indi-
viduals) either both agree, or one agreeing, the other does
not, with a common third -notion ; in so far these notions do
or do not agree with each other."
§ 520. In the Figured Syllogism Proper, again, the terms
aristotle's doctrine of figure. 407
compared are severally subject and predicate, and thus con-
taining and contained. Its general canon is : " What worse
relation of subject and predicate subsists between either of
two terms and a common third term, with which one at least
is positively related ; that relation subsists between the two
terms themselves." 1 The Figured Syllogism runs in the
counter wholes of Intension and Extension.
§ 521. According to Aristotle's mode of statement, the
middle term was intermediate in nature and in position in
the two premisses. Thus : —
P is in M ;
M is in S ;•
.'. P is in S.
This shows the middle term, M, as lying in the middle and
between the two extremes, P and S. But later logicians did
not so enounce such a reasoning. They said : —
Mis P;
S is M ;
.-. s is p.
Here the middle term does not lie between the extremes ;
and in the Second and Third Figures it no more does so,
being in the one twice predicate, in the other twice subject.
The Aristotelic form indeed is suitable at once to reasoning
in comprehension and in extension.
§ 522. To preserve the Aristotelic position of the middle
term in extension, — the subject being usually first, — it was
necessary to state the minor premiss first, even in the First
Figure. This was done by a majority of the older logicians.
But subsequently this order was departed from, and the
major premiss was stated first, thus displacing the middle
term from its intermediate position in the syllogism. Now
the question arises — Is there any natural rule or law regulat-
ing the order of enouncement 1 In Figured Syllogism, the
true principle is the relation of the middle term, as including
or included under the subject of the conclusion. It matters
nothing as to which premiss is placed first or last in the
expression. But to avoid ambiguity that premiss which
expresses the relation of the greatest to the less, — that
which expresses the relation of the less to the least, — should
1 Discussions, p. 654.
408 INSTITUTES OF LOGIC.
be placed first and second. The conclusion would, of course,
state the relation of the least to the greatest. Thus, in Ex-
tension in the First Figure, we should have : —
M is contained under P;
S is contained under M ;
.'. S is contained under P.
Here P is major, predicate of major premiss ; S is minor,
subject of minor premiss ; S is subject of conclusion, P pre-
dicate. P= the greatest whole ; At = the less ; $=the least.
This being so, S the least must be contained in P the greater.
§ 523. In Comprehension, the same principle would lead
to the reversal of the order of the premisses. Thus : —
S is At;
Mis P;
.: Sis P.
This means S, the greatest whole, contains in it one mark At;
At, the less, contains in it one mark, the least, P ; .". S, the
greatest whole, contains in it one mark P, the least.
Animal contains in it sentient;
Sentient contains in it life ;
.". Animal contains in it life.
It is clear from this that as the premisses in this First Figure
determine the relation of the subject of the conclusion to the
predicate, as either a part contained under the predicate, or as
a whole containing the predicate in it, — there can be but one
immediate or direct conclusion in each of the moods, and in
Extension and Comprehension. The First Figure thus still
retains and admits of the distinction of major and minor terms,
major and minor propositions, and the conclusion is single or
direct, — in each of the quantities of Extension and Compre-
hension. It admits, however, of two conclusions, — a direct
and an immediately inferred conclusion.1 We can say :—
1 Discussions,, p. 658.
ARISTOTLE'S DOCTRINE OF FIGURE. 409
All M is (some) C ;
All T%is (some) M ;
.'. All YJs (some) G.
Or, some C is all T.
§ 524. But let us look at the Second and Third Figures, and
we shall find that we no longer have the same kind of rela-
tions between the terms, and consequently, no longer the
distinction of major and minor in terms and premisses. We
shall thus have two conclusions equally direct, either extreme
being taken as subject or as predicate of the conclusion. In
the Second Figure, the middle term is the predicate of both
premisses, — not as in the first the subject of one extreme and
the predicate of the other.
CisM.
r is M.
This form thus merely tells us that each extreme is contained
under the middle, but it says nothing of the relation of the
one extreme to the other. There is no subordination of
greater or least. We may thus reason : —
(Some) G is (some) M ;
(Some) r is (all) M ;
.'. (Some) G is (some) T.
Or, (Some) T is (some) G.
Here each extreme is major or minor, or neither. And there
are two direct conclusions, differing only according to the
manner of reading.
In the Third Figure the same holds. Here the middle term
is subject in both premisses, — it is contained under each
extreme. Thus : —
(Some) M is (some) G ;
(All) M is (some) T ;
.". (Some) G is (some) T.
Or, (Some) Y is (some) C.
Here there is as little subordination of extreme to extreme —
of C to ]? — and consequently the relation majority and
minority in extremes is abolished. And we have two
equally direct conclusions.
410 INSTITUTES OF LOGIC.
§ 525. Now it is obvious that wo are very near the aboli-
tion of Figure altogether. We may. now reason that as C is
M, and T is M, C is T or T is C. Indeed, if we quantify the
predicate, and thus reduce the proposition to a simple equa-
tion, the identity of a reasoning in all the three Figures
becomes clear. The Second Figure is only the First, with
the major premiss converted and transposed ; the Third
Figure is only the First, with its minor premiss converted
and transposed. Figure is thus unessential to the validity
of a reasoning. Mood alone is the essential thing. In prac-
tice, the Figures have at the same time special uses and
functions. The First Figure affords a form for reasoning in
Extension and in Comprehension alike. The Second Figure
naturally fits Extension ; for the middle term is predicate in
both premisses, — each extreme is contained under it as a
common whole. The Third Figure equally suits Comprehen-
sion ; for the middle term, as subject of both premisses, nat-
urally contains in it each of the extremes, as the parts of a
common whole. It will thus be found, further, that the
Second and Third Figures are specially suited — the one to
Deductive Eeasoning in Extension ; the other to Inductive
Eeasoning in Comprehension. The general distinction be-
tween Deductive and Inductive reasoning, regarded here as
processes of formal inference, is that in the former we reason
downwards from the greatest whole or law to the particular
instance or fact contained under it ; in the latter we reason
upwards from the particular instances or facts to the whole or
general law. In the former case we proceed on the principle
that " what belongs to the containing whole belongs also to
the contained parts ; " in the latter case on the principle
that " what belongs to the constituent parts belongs also to
the constituted whole." Now, Deductive Reasoning naturally
takes the form of Extensive Reasoning ; Inductive that of
Comprehensive Reasoning. For in Extension we begin with
the widest notion ; in Comprehension with the particular or
individual fact. Thus, in the Second Figure, we should
naturally have a Deductive Reasoning in Extension : —
X Y Z are [contained under) all M ;
a b c are [contained under) all M;
.'. a b c are X Y Z.
DISTINCTION OF SUBJECT AND PKEDICATE. 411
Responsible persons are all man ;
Black, white, copper-coloured are all man ;
.'. Black, white, copper-coloured are responsible persons.
This inference is to the similarity or identity of the parts,
through the common whole M, which contains them.
The Third Figure would suit an Inductive Reasoning in
Comprehension.
XYZ are all P ;
XYZ are As;
.', Some As are all P.
Peter, John, fyc. (12), are all the apostles ;
Peter, John, fyc. (12), are zealous persons ;
.: Some zealous are all the apostles.
This inference is to the common whole through the similarity
or identity of the parts which constitute it.1
§ 526. The distinction of Subject and Predicate, as usually
taken in Extension, by the Aristotelic logicians, arises mainly
from the circumstance that the predicate is supposed to be a
wider notion than the subject. The subject is contained under
the predicate as a part of it at least. The genus thus was pre-
dicated of the species, as the oak is a tree, — the species was
predicated of the individual, this tree is a birch. The subject
notion, therefore, was regarded as of less extent than the pre-
dicate. In comprehension, however, the subject might be
regarded as the greater, seeing that the predicate usually
expresses only one of its attributes, as fire burns ; water runs :
burning and running, being only each a small part of the notions
oifire or water. The subject thus comprehends the attribute,
and more or others. The quantification of the predicate in
extension abolishes the essential distinction of subject and
predicate. We may say as we please : all plant is some or-
ganised, or some organised is all plant. The only difference of
subject and predicate here would be in the accidental interest
we have in the one or other, as first in thought.
(a) Robert Kilwardby, Archbishop of Canterbury (1276) (died 1279),
who does not use the Byzantine art words or memorial verses, speaking
of the Second Figure, says : The middle is that by which one extreme
is distant from another, but, as predicated of both extremes, there is
no difference in the distance, and therefore no medium. The middle
1 Cf. Discussions, App. II.
412 INSTITUTES OF LOGIC.
is equally distant from both extremes (terms) ; therefore the terms
are equidistant from the middle. — (Kilwardby in Prantl, iii. p. 186.)
§ 527. And carrying out this principle to its ultimate issue,
we may have the simplest form of reasoning in the Unfigured
Syllogism. This is the simplest form, for here we have
no longer the distinction of Extension and Intension, and
the order of the premisses is thus wholly arbitrary. The
terms do not stand to each other in the relation of subject and
predicate, being in the same proposition either both subjects
or (possibly) both predicates. The formula for this is : —
Subjects : —
All C and some B are (some) convertible ;
All B and all A are (some) convertible ;
.'. All C and some A are (some) convertible.
Predicates : —
(Some) convertibles are all 0 and some B ;
(Some) convertibles are all B and all A ;
.'. (Some) convertibles are all 0 and some A.
§ 528. The canon for this reasoning is : —
" In as far as two notions (notions proper or individuals)
either both agree, or one agreeing, the other does not, with
a common third notion ; in so far, these notions do or do not
agree with each other." This canon excludes (1.) an undis-
tributed middle term, as then no common notion ; (2.) two
negative premisses, as then no agreement of either of the
other notions therewith. In ordinary discourse we regularly
use the unfigured form of reasoning when we apply the prin-
ciple that, as A is equal to B, and B to C, A is equal to C.
This form regulates our dealings with quantities, and our
processes in Geometry.
§ 529. The Unfigured Syllogism of Hamilton is closely akin
to what is known as the Expository Syllogism (Syllogismus
Expositiorius, Sensilis) of the Peripatetics and other subse-
quent logicians. Its principle was given as : Those things
which agree with the same singular third agree with each
other. (Quai congruunt eidem tertio singulari ea congruunt
inter se.) This syllogism was usually run through the three
Figures, but it was held to be less natural in the First and
Second than in the Third, where the middle was subject, —
EXPOSITOEY SYLLOGISM. 413
it being held that a singular is less properly a predicate than
a subject. Thus we may have in the First Figure : —
Aristotle was a Greek ;
The author of the Analytics was Aristotle ;
Therefore the author of the Analytics was a Greek.
In the Second Figure : —
Aristotle was the tutor of Alexander ;
The author of the Iliad was not the tutor of Alexander ;
Therefore he was not Aristotle.
In the Third Figure :—
Epicurus was bold;
Epicurus was a philosopher ;
Therefore some (a) philosopher was bold.
This form, which is not recognised by Aristotle as a syllo-
gism, because there is nothing in it universal, was called by
him eK^eVts — that is, expositio or exhibition on account of its
use in exhibiting the necessary sequence in the Third Figure
— in those moods in which (the subject) middle term is
universal. Thus, to take Datisi: —
Every man may err ;
Some man is wise ;
Therefore some wise may err.
This is expounded or exhibited by substituting for the
common term man the individual, say Plato. We should thus
have : —
Plato may err ;
Plato was wise ;
Therefore some (a) wise may err.
Here the middle is what is known as Singidare Sensile.1
Kamus regarded this form of reasoning as Syllogism
Proper. It is no doubt a simple and natural form ; it pro-
ceeds on the principle of equation, better equivalence in
subject and predicate ; and, whether affirmative or negative,
is independent of Figure. Hamilton's canon for the Un-
figured Syllogism applies to it directly and completely.
As this form proceeds neither from the more general to
1 Cf. Mark Duncan, Inst. Log., L. iv. c. iv.
414 INSTITUTES OF LOGIC.
the less, nor from the less to the more, but from equal to
equal, it has in these times been called Traduction. Only
the name is new, or rather it is borrowed from Bacon (Nov.
Org., i. 70).
§ 530. This analysis of Figure and the Figured Syllogism
enabled Hamilton to reduce all the general laws of Categor-
ical Syllogisms to a single canon. This is really a summary
statement of the Six Rules of Syllogism usually given. This
canon is : " What worse relation of subject and predicate sub-
sists between either of two terms and a common third term,
with which one at least is positively 1 (affirmatively) related,
that relation subsists between the two terms themselves."
The six rules of Syllogism, as usually stated, are all con-
tained under this general canon, and may be readily evolved
out of it. Hamilton has added to the general canon the forms
which are specially applicable to each of the Three Figures.
For the First Figure, the canon is : —
"What worse relation of determining (predicate), and of
determined (subject), is held by either of two notions to a
third, with which one at least is positively related ; that
relation do they immediately (directly) hold to each other,
and indirectly (mediately) its converse." This latter clause
provides for the distinction between the direct and indirect
conclusions in the First Figure, — the latter being obtained
through immediate inference or conversion.
For the Second Figure, the canon is : —
" What worse relation of determined (subject) is held by
either of two notions to a third, with which one at least is
positively related ; that relation do they hold indifferently to
each other."
For the Third Figure, the canon is : —
" What worse relation of determining (predicate) is held by
either of two notions to a third, with which one at laest is
positively related ; that relation do they hold indifferently to
each other."
The last clause in each of these rules points to the two
possible conclusions in those Figures, each of which is as
direct as the other.
§531. The expression here, "the worse relation," needs
explanation. " Sectetur partem conclusio deteriorem," said
1 Positively is misprinted possibly in Discussions, p. 654, ed. 1853.
AFFIRMATION AND NEGATION. 415
the old logicians. Particular quantity [some) was worse or
weaker than universal quantity (all) ; and negation was
worse or weaker than affirmation. I could only predicate of
some, not of all. I could not even assert anything about
the subject proposed. But as they did not admit two nega-
tive propositions, the one with a particular predicate, they did
not, and did not need to, determine which of two negatives,
a particular or a universal, was the worse. Hamilton's sys-
tem of propositional forms requires this to be done, especially
as applied to Syllogism. With him thus, affirmation, as with
the old logicians, is always better than negation. And the
best affirmation is where we affirm all of all — all X is all Y;
and the worst when we affirm of some only — some X is
some Y.
In negation, again, the worst is when we deny of all or any
— any is not any. This is in contrast to the best of affirma-
tion, when we affirm all of all. The best of negation is when
we deny only of some — some is not some. The worse grades
of negation are some is not any, any is not some.
Any is not any is the worst in negation. If I can say that
not even one is true of the subject, or is a part of it, I have
said the utmost — the worst — which I can say against any
assertion, that a part of the predicate is true of the subject.
Any mineral is not any organised thing, is the utmost or worst
I can deny of the subject mineral, especially if some one has
affirmed any positive relation to organised about it.
All is all is the best affirmation ; as all man is all risible. It
is the best between these terms. If I had said all man is some
risible, I don't know how many, or all man is only some, I
should not have affirmed so much of the subject as when
I said all is all. I have said it is not only some of which I
speak, but all of which I speak. And I predicate of it not
only some, but all.
§ 532. The following table shows the whole order of best
and worst quantification throughout the two qualities, and
how affirmation commences with the whole in inclusion (all),
and negation with the parts in exclusion (any) : —
416
INSTITUTES OF LOGIC.
Besty^!. Toto-total — all is all.
'2. Toto-partial — all is some.
•3. Parti-total — some is all.
•4. Parti-partial — some is some.
'5. Parti-partial — some is not some.
•6. Parti-total — some is not any.
-7. Toto-partial — any is not some.
Tfbrst^-8. Toto-total — any is not any.
Affirmative.
Negative.
§ 533. To the universality of the canon there is an appar-
ent, but only an apparent exception. That is, in those moods
in which the particular quantity of the affirmative conclusions
disappears in the negative moods — giving place to a univer-
sal quantity in the negative. This occurs in the (negative)
moods IXa., Xb., XP., and XII*.1 In these—
Take the following— (IX.)
Affirmatively we read : —
All Mis all 0;
All r is some M ;
.'. All r is some C ;
Or, Some C is all T.
Negatively this becomes — (IXa.)
Any M is not any C ;
All T is some M ;
.'. Any r is not any C.
Or, any G is not any V.
Take the following— (X.)
Affirmatively we read : —
Some M is all C ;
All r is all M;
.'. Some Y is all C.
Negatively— (Xb.)
Some M is all 0 ;
Any r is not any M ;
.'. Any r is not any C.
1 From the table of moods, Logic, iv., App. v. (e) Syllogisms, p. 285.
HAMILTON'S SYLLOGISTIC MOODS. 417
Affirmatively —
Some animal is all man ;
All sentient is all animal ;
.'. Some sentient is all man.
Deny the minor —
Some animal is all man ;
Any sentient is not any animal ;
.'.Any sentient is not any man.
Or, Some animal is all man ;
Any mineral is not any animal ;
.'. Any mineral is not any man.
§ 534. Here the change is from a particular affirmative
conclusion to a universal negative. But this is a passage
simply from the worst in affirmation to the worst in negation.
Had the change been from a particular affirmation to a uni-
versal affirmation, it would have been from the worse to the
better, or best. But seeing that it is a change from particular
in affirmation to universal in negation, it is a passage only
from the worst in the one quality to the worst in the other.
The validity and applicability of the canon are thus not
shaken but confirmed. (So in XIa. and XIIb.) As Hamilton
has remarked : " The worst relation between either extreme
and middle is here preserved in the conclusion. As affir-
mation comes in from the greatest whole, while negation
goes out from the least part, so, in point of fact, the some of
the one may become the not any of the other." x
m § 535. With the Eight Propositional Forms as a basis, there
is a corresponding increase of the syllogistic moods. A
simple arithmetical calculation of the combinations (syzygies)
gives 512 conceivable moods. But applying the canon,
these are reduced to 36 valid moods, — 12 affirmative and
24 negative. These are essentially the same through
the Three Figures, — the Fourth Figure being excluded by
Hamilton as illegitimate. If we pass the moods through
each of the Three Figures, we get the 36 moods three
times repeated, making 108 moods in all. But these are
really only got through a change in expression, — the mood is
always essentially the same — figure making no valid differ-
1 Logic, App. iv. p. 286.
2 D
418 INSTITUTES OF LOGIC.
ence. No mood can be valid in one figure which is not
valid in every one. Indeed, looking at the mere formal
equivalence of the moods, we may reduce the number
of affirmative moods to 7, and of negative to 14, —
21 in all. This arises from the circumstance of the
possible interconversion of certain of the moods. In some
the middle term is balanced, — that is, it is universal in both
premisses. The extremes are balanced when both are taken
universally ; tmbalanced when the one is so taken, and the
other not. If we take the unbalanced moods iv., vi., viii., x.,
xii., as simply the converse of the one preceding it, which they
are, only seven valid affirmative moods are left. With these
five affirmatives, ten corresponding negative moods would be
struck out, or reduced to the corresponding negatives of the
affirmative mood which afforded the (abolished) converse.
This would leave fourteen negative moods, or twenty-one
affirmative and negative. The cumbrous rules of reduction
are thus abolished, — simple conversion (with transposition)
will enable us to turn any mood into any figure. And taking
the quantification of the predicate into account, we abolish as
not only useless, but false, the special rules of each figure.
By admitting the universality of the predicate in affirmative
judgments, — the particularity of the predicate in negative
judgments, — right in the face of the Aristotelic prescriptions,
— we show that the usual rules of the First, Second, and Third
Figures are false, and the syllogistic process stands out vin-
dicated as one, evident, and simple, — conformable to a Single
Universal Canon.
§ 536. Hamilton's Table of the Moods of Figured Syllo-
gisms is printed at the end of the Lectures on Logic — the
moods being also given or symbolised in the forms of his
notation. The diagram representing Figured and Unfigured
Syllogism alike, and in Extension and Comprehension, is to
be found in the Discussions, p. 658. Eeference may be
made to these for details. The following are the twelve
moods in Extension of the First Figure : —
(1.) All M is all C ;
All r is all M ;
.'. AUT is all C.
Hamilton's syllogistic moods. 419
(2.) All M is some G ;
Some r is all M ;
.'. Some Y is some G.
(3.) All M is some G ;
All Y is some M ;
.'. All Y is some C.
(4.) Some M is all G ;
Some Y is all M ;
.'. Some r is some C.
(5.) All M is some C ;
Some r is some M ;
.'. Some T is some C.
(6.) Some M is some C ;
Some T is all M ;
.'. Some T is some G.
(7.) All Mis all 0;
Some r is all M ;
.'. Some r is all C.
(8.) All M is some C ;
AllY is all M;
.*. All r is some G.
(9.) All M is all C;
All T is some M ;
.'. All r is some C.
(10.) Some M is all G ;
AllY is all M ;
.". Some Y is all G.
(11.) All M is some G;
Some Y is some M ;
.*. Some Y is some C.
(12.) Some M is some G ;
All Y is all M;
.*. Some Y is some G.
The first mood of the First Figure is thus symbolised : —
420 INSTITUTES OF LOGIC.
Read in Extension it runs : —
All M is [included under) all C ;
All T is (included under) all M ;
.'. All r is (included under) all C.
Or, as an indirect conclusion, —
All C is (included under) all T.
Read in Comprehension, it runs thus : —
All M is (includes in it) all T ;
All C is (includes in it) all M ;
.'. All G is (includes in it) all T.
Or—
All C is (includes in it) all T ;
All M is (includes in it) all T :
.'. All C is (includes in it) all T.
§ 537. Twelve pairs of premisses, with the same quantities
as in the First Figure, may be run through the Second and
Third Figures, and each mood may be read in Extension
and in Comprehension. Thus, to take No. 2 in the Second
Figure, we have : —
In Extension, this reads : —
Some C is all M ;
Some r is all M;
.'. Some Y is some C.
Or—
Some C is some T.
In Comprehension, it reads : —
All M is some C ;
All M is some V ;
.'. Some C is some T.
Or—
Some T is some C.
Hamilton's notation. 421
§ 538. There are thus 12 affirmative moods in each of the
Three Figures — in all 36 affirmative moods. As each of these
affirmatives yields by negation in turn of major and of minor
premiss, two negative moods, there will be 24 negative moods
in each figure, in all 72 negatives — some of which are, how-
ever, of little or no actual value. Thus, to take No. 2 of the
First Figure, we have —
(a)
No M is any C ;
Some T is all M ;
.'. Some r is not some C.
(b) C, -:M: — H-,r.
All M is some 0 ;
Some r is not any M ;
.'. Some ]? is not some C.
§ 539. The symbolical notation here employed, though
simple, requires a word of explanation. It is that devised by
Hamilton. He has the merit of having added to Logic a
system of notation which is at once simple, perspicuous, and
adequate. First of all, a proposition is represented by a
horizontal line. If either of the terms can stand as subject
or as predicate — if, in a word, there be no distinction of Sub-
ject and Predicate, as in the Unfigured Syllogism — the line
is drawn as of equal thickness throughout. Thus —
C Ill Willi! I
C is r, or r is G, or O and T are equal.
But if the one term be regarded as Subject and the other
as Predicate, the line is represented thus —
c — r
And this proposition may be read in either of two ways, as
in Breadth or in Depth. The thick end of the line represents
the subject of the proposition in Breadth, and is read —
C is I1, or C is contained or included under T.
422 INSTITUTES OF LOGIC.
The thin end of the line represents the subject in Depth,
and is read —
r is C, or r includes or contains in it C.
This applies to affirmative propositions. Negation is de-
noted by a perpendicular line drawn through the horizontal.
Thus—
C | r, is read, C is not Y.
The quantity or distribution of the terms, is indicated by
points. Thus a comma ( , ) placed after a term indicates that
it is to be taken particularly or indefinitely; a colon (:) that
it is to be taken universally or definitely. As the middle
term appears twice in the syllogism, it will have two separate
marks of quantity. That on the right — colon or comma —
indicates how it is to be taken, universally or particularly,
with the term on the right ; that on the left — colon or comma
— with the term on the left. Further, in a syllogism the
conclusion is indicated, in Breadth and Depth, by a line sim-
ilar to the lines of the premisses, extending from the one
extreme to the other. The following will readily illustrate
the notation.
In the First Figure we may take the following : —
This is read in —
(a) Breadth. (b) Depth.
All M is some C ; Some M is all Y ;
All Y is some M ; Some C is all M ;
.'. All Y is some C. .*. Some C is all Y.
Negation is thus indicated —
(a) Breadth. (b) Depth.
Any M is not any C ; Some M is all Y ;
All Y is some M ; Any C is not any M ;
.'. Any Y is not any C. .'. Any C is not any Y.
In the Second Figure we may take the following : —
HAMILTON'S NOTATION.
423
C,
M,
(a) Breadth.
Some C is all M ;
All r is some M ;
.'. All r is some C.
(Or, Some C is all T.)
In the Third Figure : —
(b) Depth.
Some M is all Y ;
All M is some C ;
.'. Some C is all T.
(Or, All r is some C.)
C,
M,
(a) Breadth.
All M is some C ;
Some M is all T ;
.'. All T is some C.
(b) Depth.
All T is some M ;
Some G is all M ;
.'. Some C is all F.
(Or, All r is some O.)
In the Second and Third Figures there are two horizontal
lines above and below the extremes, indicating that two
equally direct and immediate conclusions may be drawn in
these figures. In these figures there is properly no distinc-
tion of major and minor terms, and consequently no distinction
of major and minor propositions. This is true equally of the
Unfigured Syllogism. It .is only in the First Figure that
the distinction of Breadth and Depth is preserved, and conse-
quently that of major and minor in terms and propositions.
§ 540. The Canon of Syllogism laid down by Hamilton,
§ 520 et seq., as proceeding on the mere formal possibility of
reasoning, necessarily comprehends all the legitimate forms of
quantification. " This Canon supposes that the two extremes
are compared together through the same common middle, and
this cannot but be if the middle, whether subject or predi-
cate, in both its quantifications together, exceed its totality,
though not taken in that totality in either premiss.1 Ac-
cordingly, " the rule of the logicians, that the middle term
should be once at least distributed [or indistributable], (i.e.,
taken universally or singularly = definitely), is untrue. For
1 Logic, iv. p. 355.
424 INSTITUTES OF LOGIC.
it is sufficient if, in both the premisses together, its quantifica-
tion be more than its quantity as a whole (Ultratotal).
Therefore, a major part (a more or most), in one premiss,
and a half in the other, are sufficient to make it effective. It
is enough for a valid syllogism, that the two extreme notions
should (or should not), of necessity, partially coincide in the
third or middle notion ; and this is necessarily shown to be
the case, if the one extreme coincide with the middle, to the
extent of a half (Dimidiate Quantification) ; and the other,
to the extent of aught more than a half (Ultradimidiate
Quantification.) " *
Thus we may reason : —
One-half of A is B ;
Two-thirds of A is C ;
.'. Some C is B.
Or—
Three-fourths of A is B ;
Two-thirds of A is C ;
.'. Some C is B.
Or—
Most of the As are Bs ;
Most of the As are Cs ;
.'. Some Cs are Bs.
In concrete examples : —
Three-fourths of the army were French ;
Three-fourths of the army were hilled ;
Therefore some French were killed.
Three-fourths of the twelve pears were ripe ;
Three-fourths of the twelve pears were stolen ;
Therefore some that were ripe were stolen.
This form of quantification and reasoning was first sug-
gested by Lambert [Neues Organon, Dianoiologie, § 193 et
seq.) It has since been adopted by De Morgan. Hamilton's
view of it is, so far, a sound one : " These two quantifications
should be taken into account by Logic as authentic forms,
but then relegated as of little use in practice, and cumber-
ing the science with a superfluous mass of moods."2 Again,
1 Logic, iv. p. 355. 2 Ibid.
ULTRA-TOTAL DISTRIBUTION. 425
he lays down the principles which ought to limit a genuine
science of Logic in the following words : " Such quantifica-
tions are of no value or application in the one whole (the uni-
versal, potential, logical), or, as I would amplify it, in the two
correlative and counter wholes (the logical and the formal,
actual, metaphysical), with which Logic is conversant. For
all that is out of classification, all that has no reference to
genus and species, is out of Logic, indeed out of Philosophy ;
for Philosophy tends always to the universal and necessary.
Thus, the highest canons of Deductive Keasoning — the Dicta
de Omni et de Nullo — were founded on, and for, the procedure
from the universal whole to the subject parts ; whilst, con-
versely, the principle of inductive reasoning was established
on, and for, the (real or presumed) collection of all the subject
parts as constituting the universal whole. 2°, The integrate
or mathematical whole, on the contrary (whether continuous
or discrete), the philosophers contemned. For whilst, as Aris-
totle observes, in mathematics genus and species are of no
account, it is, almost exclusively, in the mathematical whole
that quantities are compared together, through a middle
term, in neither premiss equal to the whole. But this rea-
soning, in which the middle term is never universal, and the
conclusion always particular, is — as vague, partial, and con-
tingent— of little or no value in Philosophy. It was accord-
ingly ignored in Logic ; and the predesignations more, most,
&c, as I have said, referred to universal, or (as was most
common) to particular, or to neither, quantity."1 This is a
true insight into the real essence and needs of logical reason-
ing, as a universal means of thinking, and consequently of
logical science. These words hold in themselves the con-
demnation, scientifically and practically, of the " advances "
in Formal Logic, made on geometrical and algebraical lines,
of De Morgan and Boole, and even of the more enlightened
Jevons.
§ 541. A reasoning in which the middle term is never de-
finitely known, and in which accordingly we have always a
vacillating and particular conclusion, is of no use practically,
or in the wide sphere of probable thought. Scientifically, it
is a mere tentative, — ending in some is some, — a mere ap-
1 Logic, iv. pp. 353, 354.
426 INSTITUTES OF LOGIC.
proach to satisfactory certainty. And even when the prem-
isses are made numerically definite, as with De Morgan, the
reasoning is of not the slightest use unless in reference to
numbers and a numerical or mathematical whole. It is
really of not the smallest consequence, as a rule, that we
should know the exact numerical proportion of the middle
term to the extremes. We seldom do know it, as a matter
of fact, and when we do, we may remit the calculation to
arithmetic.
§ 542. It ought further, I think, to be noted in connection
with this form of reasoning, that it readily lends itself to ma-
terial fallacy, or a conclusion materially untrue. No doubt,
in the abstract, if £ of Y are X, and £ of Y are Z, some of
the Zs are Xs. So if X contains {the part) Y, and Y contains
(the part) Z, X contains Z. But this latter formula embodies
the law of inference from genus to species, or from whole to
part. The other formula does not. It does not tell us in
what relation X stands to Y, or Z to Y, whether that of part
and whole, or of subject and attribute. Nor do we know,
taking X and Z as attributes, whether they are compatible
with each other or not. The practical application of the bare
formula is therefore of but little use, and readily leads to
material error. Thus, if we say : —
f of the potatoes were diseased ;
\ was eaten by the crows ;
Therefore the crows must have eaten some of the diseased ;
this is correct, because there was not a half left not diseased.
If, however, we substitute for diseased, hard as a stone, we
should on the same formula have the conclusion that the
crows ate some potatoes hard as a stone. There is nothing in
the formula itself to prevent us substituting for X and Z
incompatible attributes. Thus the following is quite com-
patible with the formula : —
Three-fourths of men are saints ;
Three-fourths of men are sinners ;
Therefore some who are saints are sinners.
Such a formula can thus give a valid and true conclusion
only in certain matter, — where the distribution refers to a
whole of which the predicates are parts, or in which they
ULTEA-TOTAL DISTRIBUTION. 427
are compatible attributes. In fact, the necessary premisses
are: —
Three-fourths of the Ys are Xs ;
Three-fourths of the Ys are [also] Zs ;
Therefore some of the Zs are Xs.
Or, if three-fourths of Y are X,
And if three-fourths of Y are Z,
And if X and Z represent things which coexist in the
same (or are compatible),
Then some Z is X, or some Z may be thought to be X.
428
CHAPTER XXXII.
CATEGORICAL SYLLOGISMS — COMPREHENSIVE REASONING
THE FIVE SYLLOGISTIC FORMS.
§ 543. The Aristotelic Categorical Syllogism proceeds
mainly, if not exclusively, in the quantity of Extension.
But according to later views, as we have seen, we have
reasoning in Comprehension as well.
§ 544. In the view of Hamilton, every notion has not only
an Extensive but an Intensive quantity — breadth and depth —
and these quantities always stand in an inverse ratio to each
other. It would thus seem likely that if notions bear a cer-
tain relation to each other in Extension, they must bear a
counter -relation to each other in Comprehension. Hence
there will be reasoning in Comprehension, as there is reason-
ing in Extension. In Extension the reasoning runs : —
All responsible agents are free-agents (i.e., are contained
under the class) ;
Man is a responsible agent (i.e., contained under the class) ;
Therefore man is a free-agent (i..e., contained under the class).
In comprehension we necessarily invert the process of this
reasoning. The notion free-agent, which in the extensive
reasoning is the greatest whole or major term, becomes in
comprehension the smallest part or minor term, and the
notion man, which is in extension the smallest part or minor
term, now becomes the greatest whole or major term. The
notion responsible agent remains the middle term in both
reasonings ; but what was formerly its part is now its whole,
and what was formerly its whole is now its part. In Com-
prehension we reason thus : —
REASONING IN COMPREHENSION AND EXTENSION. 429
The notion man comprehends in it the notion responsible agent ;
The notion responsible agent comprehends in it the notion free-
agent ;
Therefore the notion man comprehends in it the notion free-
agent.
In Extension. In Intension.
B is A ; C is B ;
G is B ; B is A ;
.'. C is A. .'. G is A.
Thus, by reversing the order of the premisses and the mean-
ing of the copula, we can always change a categorical syllogism
of Extension into one of Intension, and vice versa. The
reasoning in Comprehension has been generally overlooked
by logicians ; but it is genuine, and it is prior to extensive
reasoning in the order both of nature and knowledge. Aris-
totle gives a definition of the middle term, which applies to
the comprehensive reasoning.1
§ 545. Hamilton holds broadly that whatever mood and
figure is valid in the one quantity is valid in the other, and
every anomaly is equally an anomaly in both. The rules of
Extensive reasoning are equally applicable to the Compre-
hensive reasoning, with the single proviso that all that is said
of the sumption (major premiss) in extension is to be under-
stood of the subsumption (minor premiss) in comprehension,
and vice versa.
§ 546. Of course the mere transposition of the premisses does
not constitute the difference between reasoning in Comprehen-
sion and in Extension ; that depends on the inner relation of
the subject and predicate of the propositions as whole and part,
or as part and whole. The transposition of the premisses in
Extension or in Comprehension might, as Hamilton elsewhere
remarks, be made without changing the essential character
of the reasoning. It would not be natural, but it would not
affect the reasoning as a mental process. But the position
of the premisses as indicated is the natural way of showing
when we reason in Comprehension or in Extension. Of
course, it is hardly necessary to say in passing that Hamilton
does not, as Mill states, make the distinction of Comprehen-
sion and Extension depend merely on the transposition of
the premisses.2
1 Logic, L. xvi. p. 299, and above, p. 407. " Examination, p. 505,
430 INSTITUTES OF LOGIC.
§ 547. The quantities of Breadth and Depth are explicitly
held by Hamilton to be merely views of the same relation
from opposite points, not things in themselves different.1
He combats the view that the reading a proposition in depth
in contrast to its reading in breadth is " not another reading
of the same proposition, but another proposition derived in-
ferentially, though not syllogistically."
He holds very distinctly that Breadth and Depth, though
named quantities, are really one and the same quantity, viewed
in counter-relations and from opposite ends. Nothing is the
one which is not, pro tanto, the other. Though different in
the order of thought (ratione), the two quantities are identical
in the nature of things (re). In effect it is precisely the same
reasoning, whether we argue in Depth or in Breadth. Thus,
in Depth, we may argue the individual Z is (or contains in it
attribute) some Y ; all Y is some U ; all U is some 0 ; all 0 is
some I ; all I is some E ; all E is some A ; therefore Z is some
A. (Take Socrates, Athenian, Greek, European, Man, Mammal,
Animal.)
In Breadth, the argument would be the same: Some A
(i.e., as class contains under it the subject part) is all E ; some
E is all I ; some I is all 0; some 0 is all U ; some U is all Y ;
some Y is Z; therefore some A is Z. (Keverse the concrete
concepts already given.) Hamilton adds that as the propo-
sition in either quantity is only an equation, only an affir-
mation of identity or its negation, the substantive verb is or
is not expresses the relation more accurately, than containing
and contained, — whether in or under. We are told, also, that
in syllogisms the contrast of the two quantities is abolished,
and the differences of figure, major and minor, premiss and
term, likewise disappear.
§ 548. It has been objected to this that " the two modes
of reading propositions in Depth and Breadth are not convert-
ible ; the extensive mode gives the intensive, but not vice
versd in all cases." " In the affirmative, any portion of the
intension of the predicate may be affirmed of the subject ; in
the negative, it is not true that any portion of the intension
of the predicate may be denied of the subject. Thus, 'No
1 See Discussions, p. 697. Hamilton gives the fullest and most explicit
account of his views on Breadth and Depth in Reasoning in connection with
the Table figured in Discussions, p. 699.
REASONING IN COMPREHENSION. 431
planet moves in a circle,' gives us a right to deny any consti-
tutive attribute of circular motion to that of a planet, but not
any attribute ; not, for example, the progression through
every longitude." x
Against this Hamilton strongly maintains that the correla-
tion of Breadth and Depth in Propositions and Syllogisms is
thoroughgoing, — universal, — applying equally to affirmative
and negative. The rule is : " The predicate of the predicate
is, with the predicate, affirmed or denied of the subject." " All
that enters into the predicate notion is denied of the subject,
if the predicate itself be denied." There is no difference
whatever between " constitutive " and " attributive " in the
case. We have nothing to do with what has been previously
known or discovered. We have only to do with what we
formally think.
In saying, " No planet moves in a circle," we do not uni-
versally deny of a planet any progression through every
longitude, but we deny of it a circular progression — that is,
a particular kind. And so it is also when we say Newton is
not Leibnitz. Here every attribute of Leibnitz is denied of
Newton — contradictorily denied. But we say again, Leibnitz
is a mathematician, or mathematician is an attribute of Leibnitz.
Do we infer that Newton is not a mathematician ? That the
attribute mathematician does not belong to Newton ? We do,
and we do not. We deny that Newton is a certain mathema-
tician— this mathematician who is Leibnitz. But we deny in-
ferentially nothing more. We do not exclude Newton from
the whole of the class mathematician. We only exclude him
from that unit of it which is identical with Leibnitz. We
infer that Newton is not the mathematician Leibnitz, — we
spoke of nothing more than this in connection with Leibnitz ;
but it would be going beyond our premisses to deny abso-
lutely that Newton is a mathematician. So far as De Morgan's
criticism is concerned, the answer is complete ; but there
are some points about the nature of comprehensive reason-
ing which require attention and examination.
§ 549. It seems to me that in Hamilton's vindication of
the Comprehensive Reasoning there is a tacit change in the
minor premiss from Comprehension to Extension. To put it
formally : —
1 Discussions, p. 697. De Morgan, as there quoted.
432 INSTITUTES OF LOGIC.
(The concept) Newton does not contain in it (the concept)
Leibnitz ;
i.e., the one sum of attributes in Newton does not contain in
it any of the other sum in Leibnitz.
But (the concept) Leibnitz contains the concept (attribute)
mathematician ;
Therefore (the concept) Newton does not contain the concept
(or attribute) mathematician.
Here it seems to me that the proper and logical conclusion
is that Newton does not contain the attribute mathematician.
We avoid this only by reading the minor premiss in Exten-
sion, not in Comprehension ; and think of a mathematician or
one of the class mathematicians, and thus only are we able to
allow in the conclusion that Newton is not a mathematician,
or this one of the class. But this seems to me to be a reason-
ing which does not proceed wholly in Comprehension, but
really both in Comprehension and in Extension.
To put it in letters : —
X (the individual Newton) does not contain in it Y (the indivi-
dual Leibnitz) ;
Y (Leibnitz) contains in it the mark Z (mathematician) ;
Therefore X (Newton) does not contain in it the mark Z
(mathematician).
No, only the mark Z in so far as it is in Y ; but this
amounts to making the predicate "the mark Z (mathema-
tician)" equivalent to one or some mathematician only, — for
we have not said that Y alone contains the mark Z, in which
case X could not contain the mark Z. We have thus intro-
duced into the minor premiss the conception of distributed
quantity — that is, extension.
§ 550. If we mean by the sum of attributes certain specific
attributes, a, b, c, &c. — man, mathematician, &c. — the concept
Newton, or other attributes regarded as in it, are not those
which are actually or numerically in Leibnitz. But then the
denial here is not in respect of the attributes properly re-
garded, but of the distribution of them, and would mean that
while the same attributes logically considered may be or are
in both individuals, they are yet numerically different ; or
there are several of the same kind — only the one individual
REASONING IN COMPREHENSION. 433
has them as well as the other. In this case, our denial
merely amounts to saying that the individuality of Newton
is not the individuality of Leibnitz, or there are two units,
possessing, it may be, logically identical attributes. But this
cannot be regarded as a conclusion wholly in comprehension.
§ 551. It seems to me that in all this the nature of reason-
ing in Depth or Comprehension is virtually identified with
that in Extension or Breadth. If the proposition in each be
an equation, we have in each extensive quantity. It matters
little or nothing to the nature of a reasoning whether we
begin with the individual or the genus, if in each process we
require to introduce all and some, or extensive quantity into
the premisses. We are no longer reasoning from one indi-
visible attribute, or indivisible sum of attributes, to another ;
but from one quantity of these to another, and that is pre-
cisely reasoning in Breadth. If Hamilton had persistently
kept in view the principle of the indivisibility of the attribute
which he laid down some time before these views were given
in the Discussions,1 he might have developed a doctrine of
strictly Comprehensive Reasoning ; but as it is, he does not
seem to me to have done so.
§ 552. The defects of the theory of reasoning in Compre-
hension come out most markedly in relation to negative con-
clusions. Here, in fact, it seems to me to break down, when
left wholly to itself.
The law for affirmatives as given by Hamilton is : " The
predicate of the predicate is, with the predicate, affirmed of
the subject." Thus : —
Man includes in it sentient ;
Sentient includes in it capable of suffering ;
Therefore man includes in it capable of suffering.
Or—
Socrates is son of Sophroniscus ;
Sophroniscus is Athenian;
Therefore Socrates is Athenian.
This is quite valid, — and is strictly a reasoning in Com-
prehension. But take the other half of the rule — that for
negatives — " The predicate of the predicate is, with the
predicate, denied of the subject." Thus : —
1 See Logic, iv. Appendix v. (c), p. 271.
2 E
432 INSTITUTES OF LOGIC.
( The concept) Newton does not contain in it (the concept)
Leibnitz ;
i.e., the one sum of attributes in Newton does not contain in
it any of the other sum in Leibnitz.
But (the concept) Leibnitz contains the concept (attribute)
mathematician ;
Therefore (the concept) Newton does not contain the concept
(or attribute) mathematician.
Here it seems to me that the proper and logical conclusion
is that Newton does not contain the attribute mathematician.
We avoid this only by reading the minor premiss in Exten-
sion, not in Comprehension ; and think of a mathematician or
one of the class mathematicians, and thus only are we able to
allow in the conclusion that Newton is not a mathematician,
or this one of the class. But this seems to me to be a reason-
ing which does not proceed wholly in Comprehension, but
really both in Comprehension and in Extension.
To put it in letters : —
X (the individual Newton) does not contain in it Y (the indivi-
dual Leibnitz) ;
Y (Leibnitz) contains in it the mark Z (mathematician) ;
Therefore X (Newton) does not contain in it the mark Z
(mathem atician) .
No, only the mark Z in so far as it is in Y ; but this
amounts to making the predicate "the mark Z (mathema-
tician)" equivalent to one or some mathematician only, — for
we have not said that Y alone contains the mark Z, in which
case X could not contain the mark Z. We have thus intro-
duced into the minor premiss the conception of distributed
quantity — that is, extension.
§ 550. If we mean by the sum of attributes certain specific
attributes, a, b, c, &c. — man, mathematician, &c. — the concept
Newton, or other attributes regarded as in it, are not those
which are actually or numerically in Leibnitz. But then the
denial here is not in respect of the attributes properly re-
garded, but of the distribution of them, and would mean that
while the same attributes logically considered may be or are
in both individuals, they are yet numerically different ; or
there are several of the same kind — only the one individual
REASONING IN COMPREHENSION. 433
has them as well as the other. In this case, our denial
merely amounts to saying that the individuality of Newton
is not the individuality of Leibnitz, or there are two units,
possessing, it may be, logically identical attributes. But this
cannot be regarded as a conclusion wholly in comprehension.
§ 551. It seems to me that in all this the nature of reason-
ing in Depth or Comprehension is virtually identified with
that in Extension or Breadth. If the proposition in each be
an equation, we have in each extensive quantity. It matters
little or nothing to the nature of a reasoning whether we
begin with the individual or the genus, if in each process we
require to introduce all and some, or extensive quantity into
the premisses. We are no longer reasoning from one indi-
visible attribute, or indivisible sum of attributes, to another ;
but from one quantity of these to another, and that is pre-
cisely reasoning in Breadth. If Hamilton had persistently
kept in view the principle of the indivisibility of the attribute
which he laid down some time before these views were given
in the Discussions,1 he might have developed a doctrine of
strictly Comprehensive Reasoning ; but as it is, he does not
seem to me to have done so.
§ 552. The defects of the theory of reasoning in Compre-
hension come out most markedly in relation to negative con-
clusions. Here, in fact, it seems to me to break down, when
left wholly to itself.
The law for affirmatives as given by Hamilton is : " The
predicate of the predicate is, with the predicate, affirmed of
the subject." Thus : —
Man includes in it sentient ;
Sentient includes in it capable of suffering ;
Therefore man includes in it capable of suffering.
Or—
Socrates is son of Sophroniscus ;
Sophroniscus is Athenian;
Therefore Socrates is Athenian.
This is quite valid, — and is strictly a reasoning in Com-
prehension. But take the other half of the rule — that for
negatives — " The predicate of the predicate is, with the
predicate, denied of the subject." Thus : —
1 See Logic, iv. Appendix v. (c), p. 271.
2 E
436 INSTITUTES OF LOGIC.
I cannot infer that blameworthy is not in prudence; but only
not in that part of prudence which is convertible with virtue.
If I say : —
Man comprehends animal life ;
No animal life has weight ;
I cannot, therefore, say that no man has weight, but only
that weight is not in that part of man which is convertible
with animal life. But weight may be an attribute of man,
after all.
Praiseworthy ($) is a mark of learning (M) ;
Learning (M) is not a mark of prudence (P)',
Therefore praiseworthy (S) is not a mark of prudence (P).
Taking S, M, and P to represent attributes throughout, and
each attribute in its indivisibility, this is a bad reasoning.
We have, in fact, in the premisses compared attributes as
indivisible wholes with each other, and in the conclusion
drawn an inference limiting their distribution or distributive
application.
§ 555. As thus put, reasoning in Comprehension with a
negative conclusion is illogical. There are two special condi-
tions which must be fulfilled, ere it is at all valid. These are
(1.) Where the attribute of the subject is assumed to be alone
or single. In this case, we could argue from the attribute
wanting another specific attribute, that this is also absent
from the subject —
E.g., S has the (single) mark M ;
M wants the mark P ;
.'. S has not the mark P.
In the case of a Defining Proposition, in which the subject
and predicate are necessarily convertible, we may have a
negative reasoning in Comprehension.
Thus we may reason : —
Oratory is the art of persuasive speaking;
Sculpture is not a mark or part of persuasive speaking;
.*. Sculpture is not a part or mark of oratory.
In this case, however, the predicate or mark of the subject
must be convertible with it — that is, it must be its single mark.
(2.) Where the mark of the mark is in contradictory rela-
tion,— or absolute repugnance. As : —
REASONING IN COMPREHENSION. 437
S (Animal) comprehends M (Organisation) ;
M (Organisation) does not comprehend P = not-M (Non-or-
ganisation) ;
.*. S does not comprehend P.
But this is hardly worthy of the name of reasoning. We
have immediately implied the absence of P (not-M) in the
assertion of M.
(3) There is a third case where the mark implies the neces-
sary exclusion of another mark — as contrary, incompatible, or
repugnant.
The soul is an indivisible unity;
An indivisible unity has not extension {is contradictory of exten-
sion, or extension is contradictory of indivisible unity) ;
Therefore the soul has not extension.
M is an invariable mark of S ;
P never is a mark of M ;
.'. P never is a mark of S.
If M be supposed in every S, and P never in any M ; yet
P may be a mark of S, — for it may have other marks than M.
But if it be alleged that P cannot coexist with M, or is re-
pugnant to M being at all, then we may infer, on the sup-
position that M is an invariable mark of S, that P never is a
mark of S. But this is to state much more in the premisses
than the simple fact of the one being or not being a mark of
the other. Thus : —
Electricity (s) has the mark (m) of travelling along a tied nerve ;
The nervous fluid (p) has not the mark (rn) of travelling along
a tied nerve ;
. : Electricity (s) is not the nervous fluid (p).
Here the marks are absolutely repugnant — contradictory — tra-
velling and not-travelling along a tied nerve. Hence the reason-
ing is sound.
(a) Professor Bowen in his able and clear exposition of the logical
doctrines of Hamilton, offers a solution of the difficulty here stated,
which I cannot regard as satisfactory. He says — " In intension the
parts are not species, but attributes or marks, and these do not exclude
each other. Each part or attribute here interpenetrates, so to speak,
and informs the whole. Black is a part of negro in the sense of being
only one of his attributes, since he has many others, such as being long-
heeled, prognathous, &c. ; but it is a part which colours the whole, for the
438 INSTITUTES OF LOGIJ.
negro is black all over. . . . The maxim for the reasoning in com-
prehension is that a mark of the mark is also a mark of the thing itself,
of the whole thing. Free agency, which is a mark of responsibility, is
also a mark of man, because responsibility is a mark of the whole
man." Thus read, the above syllogism would be valid. " S has M
for one of its marks or attributes. M, though only one of the attributes
of S, affects or colours the whole of S ; therefore P, which is not an
attribute of M, is not an attribute of S. Thus —
A negro has a black skin ;
But a black skin is not an invariable sign of a brute intellect ;
Therefore a negro is not necessarily brutish in intellect."
It seems to me that this does not meet the difficulty. We have
here a totally different conclusion from that alleged in the formula.
S comprehends M ;
M does not comprehend P ;
.', S does not comprehend P.
The parallel reasoning should have been : —
A negro has a black skin ;
The notion of a black skin has not the mark or notion of a brute intellect ;
Therefore the notion negro has not the mark or notion of a brute intellect.
This absolutely stated is illogical. And when we argue that because
being brutish in intellect is not the mark of a black skin, the negro is
not brutish in intellect, we state a very different conclusion from that
which follows when we argue that because a black skin is not invari-
ably or necessarily a sign of a brutish intellect, a brutish intellect
is not invariably or necessarily a sign of the negro. This means merely
that so far as these signs go, it is not proved that the negro is brutish
in intellect. But it is not proved that he is not brutish in intellect,
which is the conclusion required. The two cautions already laid down
are necessary. Either the mark of the subject is single, exclusive of
others, or convertible with the subject ; or the mark of the mark is
essentially repugnant to — contradictory of the mark of the subject.
§ 556. The Canon of Comprehension should, therefore (for
negatives), run thus : —
A mark repugnant to a mark of the subject is repugnant to the
subject itself.
Or, A mark contradictory of a mark of the subject is contra-
dictory of the subject itself.
For affirmatives : A mark essential to a mark of the subject
is essential to the subject. This is necessary : —
S contains M ;
M contains P ;
S contains P.
KINDS OF CATEGORICAL REASONING. 439
It is only as M contains P always, or essentially as part of
it, or identical with it, that we can be sure that S always
or essentially contains P. If M contains P only sometimes,
or now has it, and then not, we cannot have the conclusion
that S contains P.
Thus, if we reason : —
Poison is a mark of every mineral acid ;
No mineral acid has for its mark digitalis ;
Therefore poison is not a mark of digitalis.
This is clearly incorrect. It is equivalent to : —
If this be a mineral acid, it is a poison; but it is not a
mineral acid ; therefore, it is not a poison.
Here is the usual hypothetical or equivalent categorical
fallacy.
But we may reason validly thus : —
Man has the mark morally responsible ;
Necessitated volition is repugnant to {^incompatible with) moral
responsibility ;
Therefore man does not possess the mark necessitated volition.
In Extension this would run : —
A Man is morally responsible ;
E A being with necessitated volition is not morally responsible;
E Therefore a being with necessitated volition is not man.
=. Camestres.
The result is that mere exclusion is not sufficient for a
comprehensive negative conclusion. As we are not dealing
with classes, but with attributes, and as these are indivisible,
the attributes must not only lie out of each other simply, but
mxist be mutually incompatible.
This, I apprehend, was what was dimly and imperfectly
recognised in the phraseology of the negative rule — Re-
pugnans notm est repugnans rei ipsi.
§ 557. From what has been said under the head of the
Categorical Syllogism, it may be inferred that there are at
least three kinds of Categorical Eeasoning, To these I pro-
pose to add other two — viz., those marked (3.) and (5.)
(1.) There is the Extensive Reasoning. In this the predi-
cate in both premisses is taken as the genus of the subject.
Thus :—
440 INSTITUTES OF LOGIC.
Animal js organised;
Man isjanimal;
Therefore man is organised.
The characteristic of this reasoning is, that as it passes
from genus to species and individual, what is predicated in
the genus of the subject is predicated of the species or indi-
viduals of the subject, but not conversely. For what may be
said of the species need not be said of the genus, and so of
the individual and species. Animal is, therefore man is, does
not follow. Animal is, therefore risible is, does not follow.
§ 558. (2.) There is the Comprehensive Reasoning, strictly
so called, in which the predicate is taken as attribute of the
subject, be it mark, property, action. Thus : —
Plant has organisation ;
Organisation has reciprocity of vital action ;
Therefore plant has reciprocity of vital action.
§ 559. (3.) There is the Combined Extensive and Comprehen-
sive Eeasoning. Here the predicate will be taken in one
premiss as genus, in the other as attribute. Thus : —
All Xs have the mark Y (Comprehension) ;
All Zs belong to the class ofXs (Extension) ;
Therefore all Zs have the mark Y (Comprehension).
All gold is a metal ;
All metal has the mark lustrous ;
Therefore all gold has the mark lustrous.
This form of reasoning, though not usually recognised in
Logic, is in common, even necessary, use ; and, in fact, is the
formula according to which we most usually subsume the
individual under the general. How am I to know, I may
ask myself, whether this substance I have found is a metal
or not? Only by some mark — say lustrous. Thus through
the mark I refer it to its class. Will the oats be a good or
bad crop this season ? I might determine this through cer-
tain marks — as the yellow look of the braird, the shortness of
the straw, the poverty of the ear, &c, and so on. This is
really a mixed reasoning, partly in Comprehension and partly
in Extension. It occurs constantly in pure Geometry.
KINDS OF CATEGORICAL REASONING. 441
§ 560. (4.) There is the Syllogism of Equivalence, — the rea-
soning from equal to equal. This is the Unfigured Syllogism
of Hamilton — the Expository Syllogism of others. The
former is wider than the latter, which referred only to Singu-
lars ; but Hamilton, by making equivalents in quantity,
widened its scope. There is not only reasoning from this to
that, or individual A to individual B, but from the equivalence
of all of one class to some of another. The formula of the
Syllogism of Equivalence is, however, in all cases the same.
What are equivalent, or non-equivalent, to a common third
term, are equivalent or non-equivalent to each other.
If X be equivalent to Y,
and Y to Xi
X is equivalent to Y.
If all X be equivalent to some Y,
and all Z be equivalent to all X,
all Z is equivalent to some Y.
§ 561. (5.) To these I am disposed to add a fifth form —
what I would call the Syllogism of Collection. Here we
literally gather into one in the conclusion what we stated
separately, yet as implicated, in the premisses. Thus : —
The crops this season are good in quality ;
The crops this season are good in quantity ;
Therefore the crops this season are good both in quality and
in quantity.
So negatively : —
The crops this season are not good in quality ;
They are not good in quantity ;
Therefore they are not good either in quality or quantity.
This is a perfectly simple form of reasoning, — in common
use, — though not fitting into any of the received formulas, —
nay, in the negative form, even apparently violating the rule
against two negative premisses. The law may be generalised
thus : Where the same middle term admits of predicates of
opposite kinds or genera, these, when both positively related,
may be affirmed, or, when both negatively related, may be
denied, of the middle term as subject of the conclusion. This
reasoning differs from the ordinary forms by admitting
middle as subject of the conclusion, and in the negative
442 INSTITUTES OF LOGIC.
form the rule against double negatives does not apply, for
the comparison has been instituted not through comparing
major and minor through the middle, but collating major and
minor in succession with the middle. The middle again
appearing as subject of conclusion, with the gathered predi-
cates, constitutes the conclusion naturally and simply a col-
lectio — collection.
443
CHAPTER XXXIII.
OF COMPLEX AND INCOMPLETE REASONINGS DEDUCTIVE
CHAIN - REASONING : EPICHEIREMA SORITES ORDINARY
ENTHYMEME.
§ 562. According mainly to the manner of enouncement or
expression, a reasoning may be Simple or Complex, Complete
or Incomplete. A reasoning is simple in nature when it con-
tains three and only three related propositions, constituting
a single reasoning. It is simple in expression when these
propositions are explicitly stated in the order either of Ex-
tension, Comprehension, or Equivalence. This is properly a
Monosyllogism — that is, a single independent reasoning.
§ 563. But Syllogisms may be connected in a succession or
series, and thus stand to each other in the relation of antece-
dent and consequent. This is regarded as a composite or
complex reasoning, and is called a Poly syllogism, also a Chain-
syllogism or Chain of Reasoning.
§ 564. In a Chain of Reasoning the order may be either
that of thing proved and reason, or of reason and thing
proved. In other words, " each successive syllogism is the
reason of that which precedes it, or the preceding syllogism
is the reason of that which follows it." The former order is
called the Analytic or Regressive ; the latter is the Synthetic
or Progressive. The reason-containing Syllogism is called
the Prosyllogism ; the consequent-containing Syllogism is
called the Episyllogism.1 If the Chain of Reasoning be com-
posed of more than two links, the same syllogism may be, in
different relations, prosyllogism and episyllogism.
§ 565. A polysyllogism, not explicitly enounced, is made
1 Cf. Krug, Logik, § iii. ; and Hamilton, Logic, iii. 364.
444 INSTITUTES OF LOGIC.
up either of partially complete and partially abbreviated
syllogisms, or of syllogisms all equally abbreviated. Tn the
former case we have what logicians call the Epicheirema
(i7rix^pr]fj.a) ; in the latter the Sorites.1 Of the Epicheirema or
Reason-rendering Syllogism, the following is an example : —
X is Y;
But Z is X, for it is D ;
Therefore Z is also Y.
It is permissible to take the life of a man who lays an ambush
with the purpose of taking yours ;
Milo, therefore, was justified in killing Clodius, for Clodius
had laid an ambush against Milo's life.2
§ 566. The Chain-syllogism proper or Sorites (o-wpeir^s,
coacervatio, congeries, gradatio, climax, de primo ad ultimum)
arises when we carry on the principle of Inference beyond
the part of the highest part, and take in the part of that part,
and so on through a series of successive parts.3 Thus a simple
syllogism would run : —
(All) B is apart of A ;
(All) C is a part of B ;
.'. (All) C is a part of A.
But we may proceed thus : —
B is A — i.e., A contains B ;
G is B — i.e., B contains C ;
D is 0 — i.e., C contains D ;
E is D — i.e., D contains E ;
Therefore E is A — i.e., A contains E.
In this case we have the Chain-syllogism or Sorites, and
this example in Extension. The predicate is the containing
whole.
But the ordinary logical Sorites — sometimes called the
Aristotelian — really proceeds in Comprehension, and this is
the more natural form. Thus : —
1 Esser, Logik, § 104 ; Hamilton, Logic, iii. 364.
2 Cicero, pro Milone. See Port Royal Logic, p. 231.
3 See especially Hamilton, Logic, iii. L. xix. , who gives the best analysis of
this form of reasoning, and who for the first time accurately stated its history.
SOKITES. 445
E is D — i.e., has the mark D ;
D is C — i.e., has the mark C ;
G is B — i.e., has the mark B ;
B is A — i.e., lias the mark A ;
Therefore E is A — i.e., has the mark A.
Here the subject is the containing whole, and the predicate
the contained part. Both of these forms are Progressive, in
the sense of proceeding from whole to part in the respective
quantities.1
A concrete example in Comprehension is found in the
following : —
Every body is in space;
What is in space is in one part of space;
What is in one part of space may be in another;
What may be in another part of space may change its space;
What may change its space is movable;
Therefore every body is movable.2
(a) Sorites, a heaper, is from crwpbs, a heap, and originally desig-
nated the sophism named by Cicero acervalis. The Sorites, as the
name for a form of reasoning, is not to be found in Aristotle. Nor
was the form of reasoning afterwards designated Sorites developed
by him, though it is improperly named the Aristotelian form. — (See
the reference in An. Pr., i. 25.) The name was probably first applied
to the reasoning by Valla in his Dialecticce Disputationes, published
after the midddle of the fifteenth century. — (See Hamilton, Logic, iii.
p. 377.) Mark Duncan thinks this form is called the heaper, because
as grain is superadded to grain in a heap, so proposition is superim-
posed on proposition in the reasoning. His definition of it is "an
argumentation in which the attribute of every prior proposition is the
subject of the posterior until, through several middles, we reach the
term to be connected with the subject of the first proposition. It con-
tains as many syllogisms as there are propositions between the first and
the last." — (Inst. Log., L. iv. c. vii. § 6.)
§ 567. It is easy enough to state each of these in a
Kegressive form.
Hamilton lays down the rules : " In the Progressive Sorites
of Comprehension and in the Eegressive Sorites of Extension,
the middle terms are the predicates of the prior premisses
and the subjects of the posterior ; the middle term is here
in position intermediate between the extremes. On the con-
trary, in the Progressive Sorites of Extension and in the
1 Hamilton, Logic, iii. p. 366. 2 Hamilton, Logic, iii. p. 381.
446 INSTITUTES OF LOGIC.
Regressive Sorites of Comprehension, the middle terms are
the subjects of the prior premisses and the predicates of the
posterior ; the middle term is here in position not intermediate
between the extremes." x
§ 568. The Sorites known as the Goclenian — being that
first formulated by Rudolph Goclenius of Marburg2 — is the
Regressive Sorites in Comprehension. The difference may
be shown thus : —
(1.) Progressive Comprehensive, (2.) Regressive Compre-
hensive.
(1.) EisD; (2.) Bis A;
DisC; CisB;
CisB; DisC;
B is A ; E is D;
.'. E is A. .'. E is A.
(1.) Bucephalus is a horse ;
A horse is a quadruped ;
A quadruped is an animal ;
An animal is a substance ;
Therefore Bucephalus is a substance.
(2.) An animal is a substance ;
A quadruped is an animal ;
A horse is a quadruped ;
Bucephalus is a horse ;
Therefore Bucephalus is a substance.
It is to be noted that these reasonings are both progressive,
in the sense that prosyllogism precedes episyllogism in each.
§ 569. The rules of the common Sorites are as follow :
" 1°, The number of the premisses is unlimited. 2°, All the
premisses, with the exception of the last, must be affirmative,
and, with the exception of the first, definite. 3°, The first pre-
miss may be either definite or indefinite (Universal or Singular,
or Particular ). 4°, The last may be either negative or affir-
mative." 3 The reasoning would thus be vitiated in two
waj's — (1.) by a particular premiss in the series after the first ;
(2.) by a negative premiss between the first and the last.
i Logic, iii. pp. 379, 380.
2 Ooclenii Isagoge in Organum Aristolelis. Francof., 1598: p. 255.
3 Hamilton, Logic, iii. pp. 371, 372.
ENTHYMEME. 447
To these it should be added that in the case of a negative
conclusion in Comprehension, the mere denial of the predicate
is not enough. This denial must, in accordance with the
principles already laid down, be a statement of incompati-
bility or contradiction between subject and predicate.
§ 570. If it be thought necessary to resolve the Sorites into
Simple Syllogisms, the rule is that there are as many simple
syllogisms as there are middle terms between the subject and
predicate of the conclusion, or propositions between the first
and the last. But the truth is, that the Sorites is simply the
natural form of a sequence in reasoning ; without the use-
less repetition of conclusions, which everybody of ordinary
intelligence is able to supply.
§571. The Enthymeme is usually regarded as an incom-
plete or defective reasoning, — one of the premisses, major
or minor, being suppressed, or retained in the mind.
Thus : (a) The air has weight, for it is body. The major is
here suppressed, (b) Every murderer deserves death; there-
fore this man deserves death. The minor is here suppressed.
As Hamilton has pointed out, even the conclusion may be
understood or suggested merely. Thus : —
" Sunt monachi nequam ; nequam non unus et alter :
Prseter Petrum omnes : est sed et hie monachus. " 1
§ 572. The Enthymeme is wrongly regarded as a special
form of reasoning co-ordinate with syllogism. It arises sim-
ply from the need of expressing thought in a terse and abbre-
viated form. As Mark Duncan has well put it : " Dicitur
syllogismus imperfectus non respectu mentis, sed prola-
tionis : nam in mente proponentis integer esse potest et
solidus syllogismus, etsi proferatur truncatus." 2
Duncan and the older logicians, who really knew something
of the literature of the subject, were well aware that Aristotle
gave no countenance to the view of the Enthymeme as a
specific form of reasoning. They were also well aware of the
fact that, with Aristotle, Enthymeme does not signify a syllo-
gism or abbreviated expression at all, but a reasoning from
signs and likelihoods, — a reasoning, in fact, of probability.3
i Logic, iii. p. 393. 2 jnst. Log., L. iv. p. 252.
3 See Duncan. Inst. Log., L. iv. p. 251. On the nature and literature of the
Enthymeme, see especially Hamilton, Lectures on Logic, L. xx., and Discus-
sions, p. 154. He there clears up the whole matter, — leaving almost nothing
more to he clone.
448 INSTITUTES OF LOGIC.
§ 573. Enthymematic expression is not simply an accident,
but a necessity of language in a rhetorical interest. What is
evident is passed over. What is prolix is avoided. What is
brief is sought after ; and what can be left through suggestion
to the imagination or reason of a hearer or reader, is allowed
to make for itself its special effect. Some of the finest effects
alike in oratory and in poetry are made through enthymematic
expression. Thus : —
'A6a.va.Tov opy-qv fir) <f>v\aTTe, dvrjrbs wv.
(Mortal, cherish not immortal hate.)
" When, fast as shaft can fly',
Blood-shot his eyes, his nostrils spread,
The loose rein dangling from his head,
Housing and saddle bloody red,
Lord Marmion's steed rushed by."
— Scott.
449
•CHAPTER XXXIV.
INDUCTION FORMAL AND MATERIAL ANALOGY.
§ 574. According to the view of Categorical Seasoning
which makes it dependent on the Law of Identity, or whole
and part, it is obvious that we may reason not only from the
whole or genus to the parts, but conversely from the parts to
the whole. In the former case we have Deductive Categorical
Reasoning, in the latter Inductive Categorical Reasoning.
In the latter case we argue from u the notion of all the con-
stituent parts discretively, to the notion of the constituted
whole collectively. Its general laws are identical with those
of the Deductive Categorical Syllogism, and it may be ex-
pressed, in like manner, either in the form of an Intensive or
of an Extensive Syllogism." 1
§ 575. Strictly formal induction has been named Perfect
Induction or Perfect Enumeration, as compared with Imper-
fect Induction or Enumeration. In the former case, there is
an enumeration of all the singulars under the species, or of
all the species under the genus — i.e., under the universal in
question. The latter founds merely on some of the singulars
under the species, or some of the species under the genus —
i.e., under the universal in question. Aristotle recognised the
distinction of reasoning either from singulars or from parts
to the whole. He regards Induction as iTrayaryr] -f] airb tu>v
ko.B ckclcttov Zirl to. KaOoXov !<£oSos, and as €K twv Kara fxipos.2
Thus, to take singulars, we have Perfect Induction in the
following : —
Mercury, Venus, the Earth, Mars, Jupiter, Saturn, Uranus,
Neptune, are opaque bodies lit by the sun ;
1 Hamilton, Logic, iii. p. 318. 2 An. Post., j. 18.
2 F
450 INSTITUTES OF LOGIC.
These are all the primary planets;
Therefore all the primary planets are opaque bodies lit by
the sun.
To take species : —
Gold, silver, copper, tin, lead, zinc, platinum, iron, are
{all) the most malleable metals ;
These are (all) the most useful;
Therefore all the most malleable are the most useful metals.
In Imperfect Induction we may reason thus : —
TJiis, that, and the other magnet attracts iron;
This, that, and the other magnet represent all magnets ;
Therefore all magnets attract iron.
Or—
This, that, and the other criminal was about 25 years
of age ;
This, that, and the other criminal represent the majority
of criminals ;
Therefore criminals of about 25 years of age are the majority.
§ 576. Aristotle recognised Formal Induction ; and thus dis-
tinguished Syllogism and Induction. In propositions which
have a middle term, syllogism takes place by this middle ; in
those which have not, it takes place by induction. We. may
thus say that induction is in some sort opposed to Syllogism ;
for this demonstrates the extreme of the' third term through
the middle ; that demonstrates the extreme of the middle
through the third term. Thus then the syllogism which is
produced by a middle term is, in nature, prior and more
known ; but that which is formed by induction is for us more
evident.1
§ 577. To illustrate this by his own example : —
(C) = minor. (A) = major.
Every man, horse, mule is long-lived ;
(C) = minor. (B) = middle.
Man, horse, mule is all devoid of bile ;
(B) (A)
Therefore all devoid of bile is long-lived.
1 An. Pr. , ii. 23.
akistotle's induction. 451
Or—
Every X Y Z is A ;
X Y Z is all B;
■ Therefore all B is A.
This is a reason apparently in the Third Figure ; but in it,
according to the ordinary rule, it is illegitimate, because the
conclusion is universal. But the conclusion is legitimated
on the principle that when two terms are attributed wholly
to a third, and when this third is reciprocal to the second of
the two terms, the first of these terms is also attributable to
the second. On this ground Aristotle may be supposed to
rest the inductive syllogism as a valid independent form. No
doubt he seems to suggest in (§ 4) the conversion of the minor
premiss into
All devoid of bile is man, horse, mide.
We should thus have the inference in Barbara of the First
Figure. Thus : —
Every man, horse, mule is long-lived ;
All devoid of bile is man, horse, mide ;
Therefore all devoid of bile is long-lived.
But this is by no means conclusive, though through the
emphasis given to the moods of the First Figure by subse-
quent logicians, the validity of the inductive form has been
made unwarrantably to depend on its capability of reduction
to this Figure. The validity of the inductive form obviously
depends on the principle, which Aristotle himself elsewhere
expressly disavows, of the universality of the predicate in an
affirmative proposition — in fact, on the recently much-ques-
tioned form all is all. But this may be taken as an instance
at once of its validity and utility.
(a) Aristotle evidently recognises Material Induction when he tells
us that "induction is a progress from singulars to the universal, as if
the skilled pilot is the best, and the skilled charioteer, the skilled in
every genus is the best ; " and especially when he adds that " induction
is more fitted for persuasion, and more certain as well as more evident
to the sense and common to the many ; but syllogism presses with a
greater necessity and repels opponents with greater force." — (Top., i.
12.) Formal induction is, of course, as cogent as (Deductive) syllogism.
We have also the recognition of Imperfect Induction as the basis of the
reasoning from Example (see below, p. 484 et seq.)
In the following passage, however, he refers obviously to that form
452 INSTITUTES OF LOGIC.
of Induction in which the Universal is constituted through a complete
enumeration of the parts.
"There is, therefore, induction, and inference from induction, when
we conclude one of the extremes of the middle by the other extreme.
Thus, for example, if B is middle of A r, to demonstrate by r, that
A is B ; for this is how we make the induction. Let A be long-lived, B
that which has not bile, and C all long-lived animals, as man, horse,
mule, &c. Then A is in C all entire ; for all C is long-lived ; but B also,
that is, that which has no bile, is in all C ; if, then, C is reciprocal to
B, and does not exceed the middle, it is therefore necessary that A is
in B ; for it has been demonstrated that any two things being the attri-
butes of the same subject, if the extreme is reciprocal to one of them,
it is necessary that the other attribute should also be in the reciprocal
attribute. Further, it ought to be supposed that C is composed of all
the particular cases ; for induction comprehends all. Such is the syl-
logism of the primitive and immediate proposition." — (An. Pr., ii. 23.)
There are other passages in which Aristotle referred to what we call
material induction, as, for example, An. Post., i. 18; ii. 19. He tells
us expressly that imperfect induction is only allowable, where there is
no contrary instance (ivinaffis). — (Top., vii. 8.) And he certainly prac-
tised it not without success in his History of Animals. In this use of
the inductive method he but followed Hippocrates in medicine. But
the truth is, there has been no time in the history of observational
science in which Material Induction has not been followed more or less
faithfully. Even Bacon, who signalised and emphasised the method —
mistaking, at the same time, the place and scope of the Formal Induc-
tion and Deduction of Aristotle — had before him, as exemplifying the
method, Copernicus, Kepler, and Galileo. Newton but took up the
thread of the predecessors of Bacon, with the advantage of the illumina-
tion which Bacon had thrown on the method. Even Newton's deduc-
tion could be verified only by Bacon's observation and induction, as to
coincidence with actual fact.
§ 578. Hamilton regards Induction as proceeding equally
in Comprehension and Extension, and gives the following
formulae for Induction : —
A. In Comprehension —
(1.) (The parts holding the place of the major term S.)
X Y Z constitute M ;
M comprehends P ;
Therefore X Y Z comprehend P.
(2.) (The parts holding the place of the middle term) —
>S comprehends X Y Z ;
X Y Z constitute P ;
Therefore S comprehends P.
PERFECT INDUCTION. 453
B. In Extension —
(1.) (The parts holding the place of the major term P) —
X Y Z constitute M ;
& is contained under M ;
Therefore S is contained under X Y Z.
(2.) (The parts holding the place of the middle term) —
X Y Z are contained under P ;
X Y Z constitute S ;
Therefore S is contained under P.
§ 579. Perfect Induction may very properly be extended
to cases in which there has been the observation or analysis
of the individual constituent elements of a concrete, say
physical whole. Thus we may reason : —
Quartz, felspar, and mica are all the constituents of ordinary
granite ;
Ordinary granite is an igneous rock ;
Therefore quartz, felspar, and mica are all the constituents oj
an (some) igneous rock.
Or—
Cognition, feeling, desire, will, are all the phenomenal mani-
festations of mind in man ;
Mind in man is the only mind we directly know ;
Therefore cognition, feeling, desire, will, are all the phenomenal
constituents of mind directly known to us.
This principle applies very strictly to the constitution of
geometrical figures, to all chemical analysis of bodies ; and it
serves to explain how, from a single analysis of a body or
description of a figure, we are able to extend our analysis or
description to all similars.
Thus geometrical demonstration may be taken as a form of
Perfect Induction, although in it we specify only a single
[figure. Exhibiting only a single diagram, we are able in a
valid demonstration to draw a conclusion which is not only
true, but necessarily true. As the latter it is universal, that
is, applies to every figure of the same character. Thus, given
a parallelogram, or a four-sided figure of which the opposite
sides are parallel, it can be proved that the opposite sides
454 INSTITUTES OF LOGIC.
and angles of this figure are equal to one other ; and that the
diameter bisects the parallelogram, that is, divides it into two
equal parts.1 This, as a consequence, necessary and neces-
sarily true, applies to all parallelograms whatever, and we
need but the one figure through which we demonstrate the con-
clusion. The confidence with which we extend our conclusion
to all figures of the same class, — whether these actually exist
or are only ideally conceived, whether they agree or not in
size, material, &c, with the one figure we know, — is based on
the conception and conviction of the essential similarity of
all the other figures to the one before us. This may pos-
sibly in the end be found to depend on the nature of the
matter — space or extension — about which we reason, and
its adaptability to explicit or essential definition. In the
same way, we may demonstrate the most abstract relations
of numbers in Algebra, through formulae which, while in-
dependent of any given number, are yet applicable to all
which fall under the specified conditions. In Arithmetic there
is an approach to this universality, for we know, for example,
that 10 + 10 = 20 in all instances and in every kind of
matter, whether we speak of pence, pounds, or shillings — of
pears, apples, or men.
In the case of Chemical Analysis, the resolution of a single
body, that is, specimen of a class, may enable us to ascertain
the exact constituents of each substance of the class — as in
the case of water. Here electricity enables us to decompose
water " into two perfectly different substances, oxygen and
hydrogen gases, and into nothing else," and to show " that
water when thus decomposed yields twice as large a volume
of hydrogen as it does of ogygen."2 We are confident after
this analysis that any example of water afterwards taken
will yield those elements. This is founded, however, partly
on the direct evidence afforded by the analysis of the single
sample, and on an inductive law already established, that
chemical combination is constant in its nature. — that it takes
place according to uniform law ; one feature of this law being
that it does so most readily between those bodies which least
resemble each other.
§ 580. The practical value of Perfect Induction lies in its
enabling us to summarise particulars or details in one total
1 Euclid, Prop. 34. 2 Roscoe.
MATERIAL INDUCTION. 455
concept or expression. Under its guidance we may unite in
one expression particulars which otherwise we should be
obliged specially and tediously to enumerate. It has thus an
important synthetic value, as enabling us to predicate of the
whole of a series of particulars or individuals known to lie
within certain limits. We can predicate definitely of all the
apostles, all the months of the year, all the people in this room,
all the objects at a given time, or in a given space, &c, only
through the form of Perfect Induction.1
"■^ § 581. Material Induction and Analogy are both founded on
the principle known as the presumption of the Uniformity of
Nature. Without, meanwhile, entering into a consideration
of the ground and genesis of this principle, it is enough for
the present purpose to refer to the two applications of it in
Induction and Analogy.
In Material Induction we proceed from the parts — that is,
some of the parts — to predicate of the whole or class of things
to which these belong. The part may be an individual thing,
or a species ; but ultimately what we found on is the individual
of observation or experience. Thus —
This, that, and the other metal has a peculiar lustre ;
But this, that, and the other metal represent all metals ;
Therefore all metals have a peculiar lustre.
Or—
A B G D have each the attribute Y ;
A B G D belong to the same class X ;
Therefore the whole class X has the attribute Y.
Such an inference supposes at least two things — (l.) That
J no negative or contradictory instance be given or known ;
/ and (2.) That the attribute is not a merely temporary, passing,
/ or accidental state of the individual, but permanent and essen-
A tial. This, of course, raises the question as to what an essential
| attribute is. To this point I have already referred.2 It
I means in this connection, as we shall see, causal relation or
sequence.
(a) " Material or Philosophical Induction," says Hamilton, " is not
so simple as commonly stated ; but consists of two syllogisms and two
deductive syllogisms, and one of them an Epicheirema. Thus : —
1 Cf. Jevons, Logic, p. 214. 2 See above, p. 102 et seq.
456 INSTITUTES OF LOGIC.
" I. What is found true of some constituents of a natural class, is to
be presumed true of the whole class ( for nature is always uni-
form) ; a a' a" are some constituents of the class A ; therefore
what is true of a a' a" is to be presumed true of A .
" II. What is true of a a' a" is to be presumed true of A; but Z is true
of a a' a" ; therefore Z is true of A.
1 ' It will be observed that all that is here inferred is only a presump-
tion founded, 1°, on the supposed uniformity of nature ; 2°, That A is
a natural class ; 3°, On the truth of the observation that a a' a" are
really constituents of that class A ; and 4°, That Z is an essential qual-
ity, and not an accidental." — (Hamilton, Logic, iv. p. 368.)
§ 582. In regard to the statement that Induction supposes
a natural class, it ought to be noted that it is often required
to establish a natural class. Induction is indeed necessary
iu order to establish the concepts of species and genera, in
all cases in which these do not depend on mere observation
and description of coexisting features, as in Descriptive
Botany, Zoology, &c. A species or genus which is consti-
tuted through a knowledge of the essential attributes of a
thing, — through its properties, — is the concept of the causal
or constant relation of that thing to its properties.
In many cases we have the concept of the causal sequence
when we do not know more than the immediate terms, and
are unable to run back the relation to anything higher, — as
in gravity, chemical affinity, electrical attraction of two metals
in^juxtaposition.
§ 583. The difference between Formal and Material Induc-
tion appears to lie in this, — that in the former case there is
an actual enumeration of all the individuals in the class ; in
the latter there is no such enumeration, but only a statement
of some. In the former case, we infer of all in the conclusion
because we have supposed or are certain that all the in-
dividuals constituting the class have been enumerated ; in
the latter we infer of all in the conclusion because the some
— one or several — are taken on extra-logical grounds known
to us. to be capable, in a given respect or attribute, to repre-
sent all of the class. In both cases the whole is supposed to
be constituted, but in different ways ; and in both cases the
mere formal inference may be regarded as hypothetically neces-
sary,— the one on the assumption of the actual enumeration of
all, the other on the assumption of the guaranteed equivalence
of some in a given respect to the all in that respect. So far
>i
MATERIAL INDUCTION. 457
as the formal inference is concerned, there is no difference;
for before we infer, logic receives or accepts the totality.
§ 584. In elevating the some observed into the all unob-
served in the minor premiss of the Material Inductive Syllog-
ism, there is always a weakness in the assumption made that
the observed cases acttially represent the whole of the un-
observed or possibly observable cases. And a single instance
to the contrary — an instantia — is sufficient to destroy the
universality. " Una instantia, cadit inductio." Thus, let us
reason : —
This, that, and the other metal are between seven and eight times
heavier than an equal bulk of water ;
This, that, and the other metal represent all metals ;
Therefore all metals are between seven and eight times heavier
than an equal bulk of water.
This is formally good ; but we have been given erroneous
data, for the metal lithium, to say nothing of potassium and
sodium, is lighter than an equal bulk of water. The validity
of the formal inference in such a case is really of subordinate
importance. The point to be attended to is the ground of
the equivalence stated in the minor premiss.
§ 585. It must at the same time be admitted that there are
very few cases in actual practice in which we can have ab-
solute assurance of a perfect enumeration. We may have it
in the case of numerical definitude, as the number of the
apostles, or the number of the primary planets — though in
the case of the planetoids it would have been rash and wrong,
as a matter of fact, to stop at any ascertained number during
the last forty years, as it would be rash to do so now. In
Geometry, our enumeration of the species of triangle, &c,
may be quite definite and complete. But usually, even in
what is known as perfect enumeration, there is a certain
amount of assumption ; and one contrary instance would de-
stroy the universality, just as one contrary instance in. the
minor premiss in material induction would destroy the uni-
versality. Considered as formal inference, both — as seems to
me — are only hypothetical^ necessary, and in this respect
the one is as strict as the other.
(a) As Bacon remarks, perfect induction is especially liable to be con-
tradicted by a simple opposite instance turning up, or may depend
458 INSTITUTES OF LOGIC.
on imperfect knowledge of the existing cases. The true or material
induction is through an analysis of experience, by means of proper re-
jections and exclusions, and after or through negations to conclude the
affirmation. — (Nov. Ory., i. 105.)
§ 586. Whately, without properly distinguishing Formal and
Material Induction, makes the Inductive Syllogism deductive
with the expressed major, which is usually understood.
" What belongs (or does not belong) to the individuals we
have examined, belongs (or does not belong) to the whole
class under which they are contained." But in truth there
is neither really nor formally any such principle as thus ex-
pressed, and such a proposition could form no valid major
premiss for a reasoning — no law that could necessitate an
inference. This is really an inadequate expression of the
minor premiss in the Material Inductive Syllogism. The ob-
server working on experience thinks himself justified, by
wholly extra-formal considerations, in saying that the in-
stances which he has examined warrant him in making them
stand for or represent all the possible instances of the kind or
class. It is true that they are only some, but on their nature
or character he judges them to be equivalent to all. This
handed over to the formal logicians is translated into the pro-
position that these — some — represent all, or are conceived to
represent all, — and the proper conclusion is, that the property
which they manifest is thus conceived as applicable to the
whole class. If we take the common illustration, this, that,
and the other magnet represent all magnets, or are all mag-
nets, the conclusion is necessary that all magnets attract
iron ; but the conclusion is only necessary on the formal law
of whole and part, and it is only necessary hypothetically —
that is, given these as being all, the conclusion follows.1
(«) Induction, in the view of Trendelenburg, " only sums up the
fact of the universal from the individuals, while Analysis seeks the
universal cause from the given phenomenon." But Ueberweg objects
" that the so-called analytical procedure must take the inductive form,
and scientific induction the ' analytical ' element, which refers to the
causal nexus. Hence evei-y such distinction only corresponds to that
of the ' formal' and ' real ' sides of Induction." — (Loylc, p. 487.)
§ 587. Syllogistically in Imperfect Induction a particular
conclusion alone is possible. If this, that, and the other magnet
1 Cf. Hamilton, Discussions, p. 167 et seq.
MATERIAL INDUCTION. 45?
attracts iron, then it follows that some magnet attracts iron.
This can hardly be called a syllogistic inference : it is merely
a summation, or at best an immediate inference, for there is
as yet no third term. But what we have to establish further
is, that attracting iron is a property not only of the individual
magnets we have observed, but of every one or all. How is
this to be done ? How is it possible ? It is possible, in the
first instance, on the supposition or assumption or ascertained
principle that the two things, magnet and attracting iron, may
stand in the general relation of cause and effect ; and, in the
second instance, on the ascertainment, through certain tests
or rules, that they do as a matter of fact so stand. If it can
be found that magnet in this case is a cause, and that its pro-
perty is attracting iron, then we have found what in point of
fact is an invariable or universal relation between the subject
and the predicate. And on this ground we extend the limited
or observed relation^all that actual experience can give us —
to the unlimited and unobserved, and constitute our partial
observation but essential knowledge into the type of the class,
or the condition of future possibility. This leads us back to
the notion and principle of Causality, and to the principle of
uniformity or in variableness in the manifestations of Causality
— in other words, to the law that similar antecedents are fol-
lowed by similar consequents. This is not itself the law of
Causality : it is a most inadequate expression for the law ;
but it is a manifested property of the law, and it is that
through which we are able actually to determine what things
are causes and what effects amid the numerous relations of
mere sequence or succession.
(a) Does the predicate, asks Ueberweg, belong to the subject because
of its generic nature or its individual nature ? or because of accidental
circumstances ? — that is the problem of Induction. — (Ueberweg, Loyic,
p. 485.) If the first question can be answered in the affirmative by
the experience of a single instance, as is quite possible, we need no
more cases : we have got the causal relation, and this is universal.
§ 588. The reference of Induction, says George, to the 4
objective causal nexus is a circle, since the knowledge of the I
real nexus is always based upon incomplete inductions. To
this U°^QT,wpgjpplies : The causal nexus as existing precedes
our inductions ; but our knowledge of it in a universal form
460 INSTITUTES OF LOGIC.
results after a multiplicity of special inductions.1 But the
question really is : How are we to know that the predicate —
say, attracting iron — is an effect of each magnet observed ?
This can only be by observing that one after another of
magnets attracts iron — that this actually happens. How
many of these observations entitle us to say that magnet is
cause in this case ? — that it is of the nature of the magnet to
attract iron ? The force of the inductive illation lies there, —
that is, in our knowing from observation that a causal relation
really is, — for the causal relation is, as a matter of general-
isation, only another expression for universal and invariable
relation. What, in other words, enables us to pass from
the mere sequence, from which we could never infer uni-
versality, to the causal sequence from which we can?
Only the number and kind of the instances. But our test
of this cannot be the causal nexus itself in the things, for
as yet we do not know it — we are seeking to find whether
it exists or not in the instances in question. A sequence
that has occurred in a given number of instances in cer-
tain circumstances may be supposed or presumed by us to
happen again in similar circumstances, from the number of
times or the frequency with which it has already occurred.
That this sequence is the result of a cause, and a permanent
cause, if known to us, would no doubt explain the expecta-
tion of the recurrence ; but as we cannot know it to be due
to a permanent cause until we have generalised the succes-
sive instances of the sequence, we cannot possibly say that
the knowledge of a causal nexus in things is the only ground
of our expectancy for the future. We have in this three dis-
tinct stages — (1.) The experience, more or less frequent, of
the sequence. (2.) The reference of the sequence to a cause
and a permanent cause in nature — definitely known. (3.) The
expectation based on this of the invariable recurrence of the
sequence in the future, provided the antecedent be the same
or similar.
This would be the strongest form of Inductive Expectation,
or the widest universality. But it is conceivable — nay, a
fact — that we have experience of uniformities of sequence,
whose cause we cannot discover, — or which are not known to
be connected causally, — as day and night, light and darkness ;
1 Logic, p. 490.
MATERIAL INDUCTION. 461
and yet we expect the recurrence of these with as much con-
fidence as if we knew them to be causally related. It is thus,
as seems to me, to be a narrowing of the grounds of the In-
ductive Inference to limit it to a knowledge of causal relations
among things. Mere constancy in experience is as frequently
the ground of our inference. This is essential to our know-
ledge of the causal relation itself in any given instance, and
we should properly cherish a probable expectancy even where
we could not discover causality at all, or at least were not
aware of its actual existence. Mankind confidently expected
the recurrence of night after day, and day after night, long
before any one was aware of the daily revolution of the earth
round its axis. And even now we should confidently expect
rain rapidly to dissolve limestone rock, although we might
not be aware that the main causal efficiency lies in the car-
bonic acid taken up by the rain.
§ 589. For the inductive illation proper, — from the some to
the all, — no one formula — no a priori formula — can be stated,
nor can we prescribe by formula beforehand the number of
cases which warrant a universal inference. For syllogism we
can lay down one universal rule, founded on the very condi-
tions— the very possibility of human thinking ; for Induction
we can do no such thing. Violate the syllogistic law and
thinking no longer exists ; it is only in appearance. Violate
any of the laws of Induction, and you do not abolish the
process ; you only conduct it wrongly. There is thus the
absolute distinction between what is fundamental in human
thought — the very condition of it — and what is needed in the
application of thinking. An incoherent syllogism is not a
syllogism ; is not even thinking. An imperfect, hasty, or un-
warranted induction is still an induction, only a bad one.
§ 590. "Almost all induction," says Hamilton, " is necessarily
imperfect ; and Logic can inculcate nothing more important
on the investigators of nature than that sobriety of mind
which regards all its past observations only as hypothetically
true, only as relatively complete, and which, consequently,
holds the mind open to every new observation, which may
correct and limit its former judgments."1 Mr Jevons has
amply endorsed this opinion.2 "No imperfect induction,"
he says, " can give a certain conclusion. It may be highly
1 Logic, iv. p. 170. 2 El. Logic, p. 213, cf. p. 223.
462 INSTITUTES OF LOGIC.
probable or nearly certain, that the cases unexamined will
resemble those which have been examined, but it can never
be certain. It is quite possible, for instance, that a new
planet might go round the sun in an opposite direction to the
other planets. . . . Mistakes have constantly occurred in science
from expecting that all new cases would exactly resemble old
ones. Imperfect induction thus gives only a certain degree
of probability, or likelihood that all instances will agree with
those examined."
§ 591. This is not the place to enter on a discussion of the
ground of the principle of the Uniformity of Nature, as it is
called, or of the belief in Cosmical Order. I can afford space
only for a remark, in passing, on Hume's well-known view on
the subject, and for a few paragraphs in which what seems to
me the true theory may be indicated.
It may fairly be said that the ground Hume alleges — viz.,
custom or customary experience — is obviously insufficient as a
ground, on his own theory of knowledge, or on any theory of
knowledge. Custom is but repetition, or the constant recur-
rence of impressions in a certain uniform order. Whence, we
ask, is this recurrence, — this uniform recurrence, — this order
in the subjective impressions? From the Ego, is it? Does
it depend on a permanent self in consciousness amid the im-
pressions ? No ; for, according to Hume, there is no such
thing, — no self or subject of impressions. But whence, then,
does the order come, — the custom of the uniformity in the
impressions ? Not surely from the custom itself ; for while
this may be put forward to explain the expectancy of the
recurrence in the future, it cannot reasonably be taken as ex-
plaining itself. Whence still, one asks, a customary uniform
order of impressions, if there be nothing behind it, or along-
side of it, acting in a customary and uniform manner ? Would
this not be not only the most mysterious but the most irra-
tional of all conceptions of the fact, to say nothing of the
origin, of experience ? And, further, how possibly can there
be a known series or order of impressions, — many, varied,
successive, — if there be no permanent knower in or amid the
series subsisting through time, — looking behind and before,
— and through a continuous knowledge grasping the isolated
impressions, as they fly, into one comprehended whole of
succession ?
GROUND OF INDUCTION. 463
§ 592. The principle known as that of the Uniformity of
Nature, which is at the root of inductive illation, may, as I
think, be regarded as founded on causality, and as simply its
manifest application. We have, in inductive illation, the fol-
lowing stages — (1.) The ascertainment by observation, analy-
sis, experiment of the number of cases, which varies in dif-
ferent matter, necessary for the inference that they depend
on a definite cause. The problem here is truly to distinguish
casual sequence from causal sequence. For this no one gen-
eral rule can be given, either a priori or founded on experi-
ence, such as we have in Deductive Inference.
(2.) Once the step is taken from merely casual to causal
sequence, we then attach the uniformly observed to a cause,
and to this or that cause. The cause is known as existing,
and as manifesting certain definite relations or properties.
It has now two features, (a)_ that of permanency or stability,
and (b) that of uniformity implying generality. For if a
cause acts, and always in a similar way, the law of its action
is general. If the mode of action is changed, the cause itself
is changed.
§ 593. (3.) Induction is not confined to cases in which the
causes are merely similar ; it operates where the cause is it-
self single, but subsists during a continuance of time. When
precisely the same cause — numerically one — is found after a
lapse of time, by inductive inference we predict that its mani-
festations will be as they were originally inductively estab-
lished. The same hammer which split the stone yesterday,
is expected, when applied in the same circumstances, to split
another stone to-day. Let the wind withdraw the cloud from
the sun, and it will be expected to shine now as it did an
hour ago.
§ 594. (4.) The inductive illation of cause from observed
uniformity of sequence extends beyond the same permanent
cause to similar causes — that is, to causes sensibly similar — ■
for thus only by sense-appearance can we judge of similarity
in causes. Hence we get the general principle at the root of
all induction which takes in similars — viz., that of general
' effects of the same genus the causes are the same, or similar
causes produce similar effects, or similar antecedents are
followed by similar consequents.
§ 595. (5.) The principle, accordingly, of the uniformity of
464 INSTITUTES OF LOGIC.
nature, or of the expectation of similar consequents from
similar antecedents, is resolved into two elements : —
(a) The conception of a cause as manifesting certain prop-
erties or effects.
(b) The presumed stahility of the cause, on the ground
mainly that we do not know, or have not observed, that its
causal efficiency has been impaired or destroyed. This could
only be done by the supposition of another cause acting in
the interval, and impairing, destroying the efficiency of the
cause whose operations were inductively known. On the
absence of any knowledge to this effect, we continue to expect
that the cause we have known as operating will subsist and
operate as before. This applies especially and in the first
instance to a cause which is the same in time, or numerically
one. It applies, in the second place, and not less, to a cause
similar to the cause which we have known as operating. For
here we connect the sensible appearance of the cause with its
causal efficiency, as we did in the first instance observed. We
suppose that under a similar appearance we shall find a
similar causal efficiency, and this because we have not
observed or do not know that another cause has been in
operation to deprive it of this supposed efficiency. This
seems to me to be the genesis of the principle known as the
uniformity of nature. It is the only theory of it which fully
accounts for its place and character in our knowledge, — for
the principle, while it is almost universally operative in
ordinary experience, in the conduct of affairs, in the guidance
of life, in professional work, and in the highest science, is
never necessary, — never gives results of absolute irreversible
import, yet leads with probability, and even cogently con-
strains. And this feature of it — its most characteristic
feature — is at once explained by the fact that our expectation
of recurrence in the future is determined by the condition that
we do not know that any negative or destructive cause has
been at work. This theory of the Inductive Principle is at
once positive and negative, or rather is positive and non-
negative. It supposes a cause, and a cause to subsist, until
the proof of its negation or destruction has been given. It is
thus in its essence a principle simply of Probability.
§ 596. (6.) This principle of uniform expectation being once
in operation, it receives confirmation from the fulfilment of
ANALOGY. 465
the expectation in given cases. Every time we expect a
similar consequent from a similar antecedent, and find it
follows, our belief in the principle of uniformity is strengthened.
This confirmatory experience reacts on the original pre-
sumption of uniformity, until it gradually becomes one of
our most familiar, most firmly established, and most trusted
principles.
§ 597. While Syllogism is an inference from whole to part,
and Induction an inference from the parts to the whole,
Analogy may be regarded as inference from individual to
individual, or from part to part.1 Generally speaking, the
inference of Analogy is founded on similarity, and it proceeds
from partial to total similarity in objects, — from likeness in
some points to likeness in all. The formula of it is : Many
in one, therefore all in one.
In Induction we proceed from the fact that a property or
mark belongs to many objects of a class, and infer that it
belongs to all of the class. The formula is : One in many,
therefore one in all.2
§ 598. Analogy must not be confounded with Proportion,
or a resemblance of ratios. Thus we have proportion when two
numbers agree in being half of another yet different number,
as — 2 is to 4, as 5 is to 10. These are definite or known ratios
in each case. In Analogy proper there is a similarity of
objects in certain known properties, and an inference to
similarity in certain other unknown or unobserved properties.
§ 599. The Inference of Analogy has two main forms, —
(1.) It may proceed from some individuals of a class to another
or other individuals of the class ; (2.) From several known
attributes in an object to other attributes in that object not
known or observed. In both cases, however, it proceeds
from the known to the unknown — from the individual to the
individual, or from the mark to the mark. These are not
essentially different forms of Analogy.
§ 600. Of the First Form of Analogy the rule may be thus
generalised : (1.) A property which is known to belong to
several members of a class, probably belongs to another
member of that class, in which it is not observed or not
capable from circumstances of being observed, provided
i Cf. Aristotle, An. Pr., ii. 24.
2 Cf. Kant, Logik, § 84. Krug, Logik, § 168. Hamilton, Logic, iv. p. 173.
2 G
466 INSTITUTES OF LOGIC.
always the known property belongs to the several members
of the class in their generic capacity.
Thus, in letters : —
A, B, C, D (individuals of a class X), have the property Y ;
F also belongs to the class X ;
Therefore probably F has the property Y.
Ceres, Pallas, Juno (all of them planetoids), have the property
of greater eccentricity of orbit ;
Vesta is also a planetoid ;
Therefore probably Vesta has the property of greater eccen-
tricity of orbit.
§ 601. Of the Second Form of Analogical Inference the
rule may be generalised as follows : —
(2.) If one object agrees with another in certain known
properties, it is probable that it will also agree with it in all
its other properties, in so far as these are generic and not
individual merely.
Thus, in letters : —
If we find in X the marks a, b, c, d, and if we find in Y a, b,
the probability is, that Y also contains the marks c and d.
Or—
This disease has the marks a and b ; a and b are usually
accompanied with c and d in jaundice ;
This disease will probably develop the marks c and d ;
In other words, The disease will probably be jaundice.
The Earth, — a planet, revolving on its axis, having an atmos-
phere, water, change of seasons, §c, — supports organic life;
Mars is a planet, revolving on its axis, having an atmosphere,
water, change of seasons, fyc. ;
Therefore Mars probably supports organic life.
§ 602. In both those forms the force of the argument will
increase in proportion to the number of the resembling fea-
tures, their nature as not temporary and individual, but as
permanent and generic. We shall fall into error, as we found
on attributes known to be common to the two objects, while
the unobserved attribute inferred is connected not with these
but with points of difference between the objects. Thus X
may resemble Y in the points a, b, and it may also possess the
ANALOGY. 467
points c, d, because it is one individual and Y is another, —
in this case we should have no inference. If X be a statesman,
able, eloquent, modest, and truthful ; and Y is a statesman, able
and eloquent; it does not follow that Y is modest and truthful.
For modest and truthful are by no means generic properties of
a statesman.
§ 603. Another element which adds to the force of Analogical
Inference — especially in the Second Form — is that of time or
circumstance in which a particular set of marks may be ob-
served. If, for example, in the course of a disease, not exactly
known as to its nature, the physician were to note the develop-
ment in succession, or in anticipated circumstances grounded
on previous observation, of certain symptoms, he would, with
the probability of being right in the end, infer that the other
symptoms which usually follow these would in due course be
developed, and thus be able to forecast the real nature of the
malady. He would, in a word, infer the unknown from the
known — the undeveloped from the developed — on the principle
of Analogy ; and the force of the inference would depend not
only on the nature of the symptoms, but on the fact of their
specification or precise limitation in time.
§ 604. One special form of analogy — the Third — may be
called that of Analogy of Function. Thus the geologist who
finds a fossil skeleton similar to the structure of an animal
of the present clay fitted to browse on herbage, will readily
infer that this also was a function of the creature whose fossil
remains are found. This can hardly be said to be similarity
in another or new property, but the completion or integra-
tion of the idea involved in structure. Yet it is properly an
Analogical Inference.
§ 605. Both Astronomy and Geology are now prosecuted in
the large spirit of analogy. Laws of motion, similar to those
on this planet are supposed to hold in regard to the planetary
bodies. And the causes and laws of change operative on the
globe at the present time, are accepted as the grounds of ex-
plaining the geological phenomena of the past.
§ 606. In Induction, and also in Analogy, the essential
point is the determination of the value of the individuals or
of the attributes as capable in the one case of standing for
the whole members of the class ; in the other, of guaranteeing
the community of the further attribute or attributes inferred.
468 INSTITUTES OF LOGIC.
And the inference in each case points to a common cause or
principle upon which the individuals and the attributes, ob-
served and unobserved, but inferred, are to be taken as
dependent.
§ 607. Induction and Analogy are to a large extent the
grounds of syllogistic inference, inasmuch as it is from them
that we obtain our major proposition ; but they are not the
regulative principles of the pure illation. Nor is it correct
to say, as Hegel apparently does,1 that these are the only
grounds or bases of universality in the inference. Geometry,
not less than Metaphysics, repudiates this.
1 Encyl.,% 90.
469
CHAPTER XXXV.
THE METHODS OP INDUCTION.
§ 608. It has been said — (1.) " That in the complexity of
things or sequences, observation and experiment are needed to
analyse the accidental from the essential or permanent, and to
determine regarding a given phenomenon that upon which
its real existence depends — that is, its cause or condition —
for all the finite is conditioned.
(2.) " That we must seek not only the conditions which
determine the existence of a phenomenon, but the properties
which exclude it or which are indifferent to it." x
We thus need certain rules and methods of Observation
and Induction, in virtue of which we may find what is in-
variably connected in experience ; mainly, in a word, distin-
guish the casual from the causal, — what is connected simply
by arbitrary or contingent association from what is linked
together objectively, or in the order of nature.
§ 609. The aim of Inductive Method with Bacon is the search
after " Form." Concrete substances are made up of " simple
natures " or qualities — they are " forme copulate " ; if we can
reach the form of the simple nature, we can see how it is pro-
duced, and thus proceed to the composition of substances. The
forms of substances are, at least, ultimately discoverable. A
substance with him means a congeries of qualities. Qualities
are " simple natures " ; but form is ambiguous. It is taken
to mean essence, definition, &c, of a thing, and the cause,
hence law, of a thing. Form thus applies to the essential
1 Franck, Diet. Phil. hid.
470 INSTITUTES OF LOGIC.
qualities of a class, to the attributes of a concrete substance,
or to a quality itself.1
§ 610. As in an object the essential qualities are those upon
which certain other or derivative qualities depend — may depend
— even as their cause ; and as the form of a quality is really
the cause of that quality, the two meanings of form come
to coincide. The essential qualities, for example, of a trian-
gle or square are given in the definition, and on these all
the demonstrated properties depend. The form or cause of
heat, to use Bacon's illustration, is motion — a kind of motion.
Thus the search after form resolves itself practically into
the search after causes. If by cause we understand, as we
ought to do, not only what as a determination precedes the
effect or consequent in time, but that also which is concomi-
tant with the effect in time, the expression "form" may
well take in the whole scope of causal relation as sought for
by induction.
§ 611. The essential point of Bacon's inductive Method lies
in Exclusion (Exclusiva) : " Inductio mala est qua? per enu-
merationem simplicem principia concludit scientiarum, non
adhibitis exclusionibus et solutionibus, sive separationibus
natures debitis." 2 Again : " Naturam separare debet, per re-
jectiones et exclusiones debitas ; ac deinde, post negativas
tot quot sufficiunt, super affirmativas concludere." 3 Again,
more particularly, he says : " Est itaque Inductionis verse
opus primum (quatenus ad inveniendas formas) rejectio sive
exclusiva naturarum singularum, quje non inveniuntur in
aliqua instantia, ubi natura data adest ; aut inveniuntur in
aliqua instantia, ubi natura data abest ; aut inveniuntur in
aliqua instantia crescere, cum natura data decrescat ; aut
decrescere, cum natura data crescat. Turn vero post rejec-
tionem et exclusivam debitis modis factam, secundo loco
(tanquam in fundo) manebit (abeuntibus in fumum opinion-
ibus volatilibus), forma affirmativa, solida, et vera, et bene
terminata." 4
§ 612. As aids to the Method of Exclusion, Bacon gives
the three tables — viz. :
(1.) The table of Presence or the appearance (comparcntia)
to the intellect of all known instances, which agree in the
i Cf. Fowler, Nov. Org., Int. 2 Nov. Org., i. 69.
3 Ibid., i. 105 ; cf. ii. 15, 16, 19, * Nov. Org., ii. 16 ; cf. ii. 19.
bacon's rules. 471
same nature, although the matter or circumstances are most
unlike.
(2.) The table of Absence, or the appearance to the intel-
lect of instances which want the given nature ; because the
form, as has been said, ought to be not less absent when
the given nature is absent, than to be present when it is
present.
(3.) The table of. Comparison, or the appearance to the
intellect of instances in which the nature, regarding which
there is inquiry, is present according to greater and less ;
whether the appearance made be of increment or decrement
in the same subject or by turns in diverse subjects. . . .
Any nature may not be received for the time as form, unless
it uniformly decrease when the nature itself decreases ; and,
in like manner, is constantly increased when the nature itself
is increased.1
§ 613. After the tables, Bacon proceeds to state certain re-
maining auxiliaries of the intellect in seeking a true and per-
fect interpretation of nature and induction. Under this head
he gives the first place to "the Prerogatives of Instances"
(Prcerogativis Instantiarurti. These are " characteristic phe-
nomena selected from the great miscellaneous mass of facts
which occur in nature, and which, by their number, indis-
tinctness, and complication, tend rather to confuse than to
direct the mind in its search for causes and general heads
of induction." 2
§ 614. First among the Prerogative Instances, Bacon
places the Solitary Instances (Instantias Solitarias). Those
are solitary instances, he says, which exhibit the nature
concerning which there is inquiry in such subjects as have
nothing in common with other subjects, except that nature
itself ; or again, which do not exhibit the nature regarding
which there is inquiry in such subjects as. are similar through
all with other subjects, except in that very nature itself. It
is manifest that instances of this sort remove doubts, and
accelerate and strengthen the exclusion ; so that a few of
these are equivalent to many. This and other examples which
follow in illustration, leave but little to make explicit Mill's
i Nov. Org., ii. 11, 12, 13.
2 Herschel, Discourse on Study of Natural Philosophy, § 190. Cf, Fowler,
Nov. Org., ii. 21.
/
472 INSTITUTES OF LOGIC.
methods of agreement and difference.1 Bacon even speaks of
the instances solitary, " quatenus ad similitudinem " ; and
those solitary, " quatenus ad discrepantiam." 2 The Instantm
Migrantes, under the Prerogative, readily suggest the method
of Concomitant Variations.8
§ 615. Among the Prerogative Instances, Bacon has the
Crucial Instance (Instantia Cruris). This means an observation
or experiment which by its nature definitely settles one or
other of two or more hypotheses, or possible antecedents, as
the true one. We suppose nothing changed, except a partic-
ular antecedent as present or absent ; and with this we find
the effect in question, present or absent. This readily sug-
gests the method of Difference.4
§ 616. The Tables given by Bacon, and other statements,
seem to indicate that he supposed science was to be built
up, first, by observation of facts arranged as the same or
different ; secondly, by induction therefrom, giving us laws
of more or less generality, the axiomata media ; and thirdly,
from these intermediate laws rising to the highest generalisa-
tions. This cannot be taken as the sole mode in which
science has progressed since his ^ime ; for the element of
Deduction, making use of the imperfect or limited general-
isation in new spheres, and where the antecedent or cause
was not observable, has done most to build up our know-
ledge of the physical universe. But the method of Bacon
did forecast the mode of certain discoveries, and in its re-
verse form it is that in which the ascertained laws of science
are best stated. And its influence as a protest against
arbitrary anticipation of the order of nature cannot be over-
estimated.
§ 617. As has been pointed out by Herschel, Mill, and
frequently illustrated by Professor Fowler, Bacon's Method
of Exclusions " proceeds on the assumption that every pheno-
menon has only one cause, that is to say, is due to only one
set of conditions. Of the ' simple natures ' there is some one,
and one only, which, if it could be found, is the ' form ' of the
natura data. But the same event may be due to one set of
conditions at one time, and to a different set at another.
1 Novum, Organum, ii. 22.
2 Of. Professor Fowler's admirable edition of the Novum Organum, p. 409.
3 Nov. Org., ii. 23. * Nov. Org., ii. 36.
METHODS OF INDUCTION. 473
Hence, though it is invariably true that the same cause is
always followed by the same effect, the converse proposition
that the same effect is always due to the same cause would
frequently be misleading." l
§ 618. Mill has well analysed the methods of Induction, i
and gives certain Kules or Canons, which, though open to ^f .
criticism in expression and details, are in substance those \fO
generally received. Mill, in fact, has made explicit what I
Bacon foreshadowed, and what Herschel had already in thee/
main put more clearly.
The First Method — called the Method of Agreement — is
thus stated : " If two or more instances of the phenomenon
under investigation have only one circumstance in common,
the circumstance in which alone all the instances agree, is
the cause (or effect) of the given phenomenon ; " or, as it has /
been put, — " the sole invariable antecedent of a phenomenon ^
is probably its cause." 2
§ 619. In order to make this canon available, the first re-
quisite is ample observation of the circumstances or actual
antecedents of the phenomenon in question. When we find
among those antecedent circumstances that there are some
whose presence or absence does not affect the actual occur-
ence of the phenomenon or event, — we infer that these are /
not essential to it ; in a word, that they are casual not causal. v
If, however, we be able to find an antecedent, either one cir-
cumstance or sum of circumstances, which alone invariably
precedes or accompanies the phenomenon, we are entitled to
infer with probability that that is the cause, or that the
phenomenon depends on it as effect. But we ought to ob- ,
serve in regard to this method, that all which it tells us is
simply that the antecedent is the cause in the given circum- ^jNfc>
stances ; in other words, it is a cause of the effect, but not
necessarily the only cause, or the cause at all times and in (
all circumstances.
§ 620. As has been pointed out by numerous logicians,
and in these days emphasised by Mill and others, the
same (similar) phenomenon, or event, or effect, may follow
from several different causes.
This was the very commonplace of logic and of usual prac-
tice ere modern ignorance invested it with the dignity of a
1 Fowler, Nov. Org., Int., p. 62. 2 Jevons, Logic, 241.
^
474 INSTITUTES OF LOGIC.
discovery. Even Koger Bacon taught it, as common-sense
had forestalled him.
Electricity, for example, may be excited by friction, cleav-
age, pressure, change of temperature, motion of the magnet,
&c. Supposing, therefore, that electricity as an effect is pres-
ent in different times and circumstances, it does not follow
that this particular antecedent, which is a known cause of it,
is the actual cause in each of the instances. One of the
other causes may be in operation. But if we find one ante-
cedent constantly present when the phenomenon occurs, and
constantly absent when the phenomenon does not occur, there
being no other change in the circumstances, we may infer
that that antecedent is the cause of the phenomenon in
question.1
Hence the need of the second Rule or Canon — the Method of
Difference. It is thus stated : " If an instance in which the
phenomenon under investigation occurs, and an instance in
which it does not occur, have every circumstance in common
save one, that one occurring only in the former, — the circum-
stance in which alone the two instances differ, is the effect
or the cause, or an indispensable part of the cause, of the
phenomenon."
" We learn," says Jevons, " that sodium or any of its com-
pounds produces a spectrum having a bright yellow double
line, by noticing that there is no such line in the spectrum of
light when sodium is not present, but that if the smallest
quantity of sodium be thrown into the flame or other source
of light, the bright yellow line instantly appears." 2
A dead body is found floating in the river. We might
infer at once that drowning, or suffocation through drowning,
was the cause of death. This would be simply on the Method
of Agreement. This would_be a_sjiffietgBfcdcause, and it is
(possibly) present. But suppose we find a sword-wound in
the body, obviously dealt while living, sufficient to cause
death, we should at once attribute the death or event to
another cause or antecedent. Here the circumstance in
which the two cases differ is the cause.
We find, for example, that electricity can be produced by
friction ; and seeing that the body thus electrified loses its
electricity after a time, when the friction has ceased, we
1 Cf. Jevons, Logic, p. 242. 2 Logic, p. 243.
METHODS OF INDUCTION. 475
prove that this was the cause, as by renewing the friction
we again electrify the body. Here we have, first, the presence
of the antecedent, then its absence and the absence of the
consequent ; we have the renewed presence of the antecedent
and the renewed appearance of the consequent.
This is the great Canon of Experiment, and of what may
be called Concentrated or Exclusive Observation.
We ask what, among other concomitant circumstances, is
the cause, or at least indispensable condition of life in the
animal ? We isolate one known circumstance, — we with-
draw from the breathable atmosphere one of its elements
— oxygen — and the animal speedily dies. Oxygen is thus
proved indispensable to life.
In order to test the effect or consequents of a particular
cause, the essential preliminary is its isolation as far as pos-
sible from the concomitant circumstances, or placing it in a
position where its specific action can be definitely ascer-
tained. It is thus only we can truly study its proper or
specific effects.
Of this Pascal's well-known experiment on the column of
mercury in the Torricellian tube may be given as a good
illustration. It was surmised that the column of mercury in
the tube was sustained or counterpoised by the weight of the
air. Is this so ? was the question. Pascal argued if it be so,
when the weight of the air is diminished, the mercury ought
to stand lower. On carrying the mercury in the tube up the
mountain — the Puy de Dome, — " the weight of the incum-
bent air was diminished, because a shorter column of air was
to be sustained ; the mercury in the barometer ought to sink,
and it was found to do so accordingly." l This experiment
proceeded on a certain isolation of the main circumstance,
and it may be taken also as illustrating the Method of Con-
comitant Variations. Bacon would probably have called it
</ an Instantia Migrans.
§ 621. Mill's third canon is the Joint Method of Agreement
and Difference. It is thus expressed : u If two or more
instances in which the phenomenon occurs have only one
circumstance in common, while two or more circumstances in
which it does not occur have nothing in common save the
absence of that circumstance, — the circumstance in which alone
1 See Playfair, Prel. Diss. En. Brit.
476 INSTITUTES OF LOGIC.
the two sets of instances (always or invariably) differ is the
effect or the cause, or an indispensable part of the cause, of
the phenomenon." This is the rule, as amended by Jevons.1
There is a reference in this canon to those cases in which
the effect is present, and also to those cases in which the
effect is absent. This is virtually a union of Bacon's two
i tables — Presentice and Absentia.
*/ § 622. By a cause we ought not to understand merely a
single antecedent. As a rule the cause of a phenomenon
o is itself a sum of phenomena or antecedents. The cause,
in fact, is made up of con-causes or conditions, all acting
together, and producing a "definite effect. Now there are
cases in which the resultant effect is wholly different in kind
from that which would follow from each of the con-causes,
supposing them to act separately. Thus oxygen and hy-
drogen together produce water, but neither of them would
produce it by itself. And so generally of chemical com-
binations. The man, the gun, the shot, the powder, the
percussion-cap together, produce a result which neither of
them has separately. But it may happen that the total effect
is of the same kind as that which would be produced by each
of the antecedents taken singly, though probably less in
degree or quantity. The result, as it has been phrased, is
homogeneous. Thus, to borrow an illustration, friction, com-
bustion, compression, &c, all in operation at one time will
produce the same common effect — heat. The cuirassier and
his armour will both result in weight for the horse. The
question thus arises how, in such instances, we are to deter-
mine what or how much of the joint common effect is due
to each con-cause ? How are we to find the proportionate
result? In order to this, we must know or ascertain the
amount due to one or more of the con-causes. Mill gives
the following direction or rule — called that of the Method of
Residues. " Subduct from any phenomenon such part as is
known by previous inductions to be the effect of certain
antecedents, and the residue of the phenomenon is the effect
of the remaining antecedents." Thus it would be easy in
the instance given to tell the weight which the rider con-
tributed to the sum total, if, knowing that sum, we knew also
the weight of the armour.
i Logic, pp. 245, 246.
METHODS OF INDUCTION. 477
In Dynamics, where we are dealing with the sum of a
series of forces, we can ascertain the relative degrees only
by separating the effect of each concomitant force.
In Chemistry this method is constantly employed " to
determine the proportional weights of substances which com-
bine together." Thus after an ingenious process, known to
chemical analysis, it is found that " 88*89 parts by weight
of oxygen unite with 11 "11 parts of hydrogen to form 100
parts of water." x
In Astronomy its use is constant. The residual irregular-
ity of Uranus, after deduction had been made of the effects
of all known attractions on it, led Adams and Leverrier to
the inference of the existence of a planet beyond, and thus to
the discovery of Neptune.
It is easier, perhaps, to lay down this rule of induction, like
some of the others, than to put it in practice. We may take
the effect known in these days as the depression of trade.
To this no doubt several causes concur. We have, probably,
over-production, excessive competition at home, foreign com-
petition, the appreciation or comparatively higher value of gold,
exclusion from foreign markets, the result of sending shoddy
exports abroad, &c. ; but it would puzzle most people to tell
how much depression is due to each cause. And it does not
help us much to ask us to determine, in the first place,
through previous induction, how much is due to this or that
of the complex causes or con-causes actually in operation.
In the case of a complexity of motives, terminating in a
single action, the application of this rule would be exceedingly
difficult, if not impossible. The motives or con-causes of the
action might be self-interest, fear of consequences, shame of
exposure, sense of duty. It is conceivable that any one of
these, taken singly, would not have been powerful enough to
lead to the action in question ; but all combined might result
in the particular action or course of conduct. But how would
it be possible in such circumstances to estimate the force of
each ? The canon is obviously of use only where the causes
are quantitative and capable of separate measurement, or where
each cause is known to be related to a definite part of the
total effect.
§ 623. But a phenomenon or effect not only depends on a
1 Cf. Jevons, Logic, p. 254 ; Roseoe, El. Chem., p. 88.
478 INSTITUTES OF LOGIC.
certain antecedent or cause, it may depend for its quantity or
degree on the quantity or degree of the cause. For precise
scientific statement, it is not enough merely to ascertain the
uniform antecedent, we must further seek in most cases to
ascertain the relation between the degree of the antecedent
and that of the effect. This seems to be what Bacon points
to in the tables of Comparison or Proportion.
In the case of an effect which admits of more or less
of quantity, it is clear that the cause, as more or less, will
produce an effect differing in quantity or degree. Effect is
always proportioned to cause, and a less degree or quantity is
as much effect of its cause, as if that cause were exercised to
the full. The degree of temperature which makes water
simply warmer, is as much a cause as that which makes it
boil. The difference is not in the causal relation, but simply
in the degree of it, or in the correlation of the cause and effect.
There may be, as Sir John Herschel has put it, " increase or
diminution of the effect, with the increased or diminished
intensity of the cause, in cases which admit of increase and
diminution."
" It is necessary to inquire," says Franck, " whether prop-
erties which we have recognised in an individual, in a species,
or in a genus, are not produced in different proportions
according to different circumstances, and whether these pro-
portions themselves can be led back to a uniform rule. It
is thus only that induction can attain the knowledge of laws,
and that these laws, in certain cases, can receive the sanction
of reasoning and the calculus."
Hence the further canon, as stated by Mill, that of the
Method of Concomitant Variations: " Whatever phenomenon
varies in any manner wherever another phseomenon varies
in some particular manner, is either a cause or an effect of
that phenomenon, or is connected with it through some fact
of causation." The canon as thus put, points to the proof of
the cause which variation gives us ; but its true value rather
lies in the precision of proportion to which the canon con-
tributes.
We have familiar examples of this rule in our ordinary ex-
perience. Every time we exert force or pressure, we know
that the effect — say the degree of motion of the body on
which we act — is determined by the degree of force or pressure
METHODS OF INDUCTION. 479
which we put forth. In the case of heat, we find that a body
expands, generally speaking, according to the degree of tem-
perature. We find that water grows warm, and finally boils,
according to the continuance and increase of the temperature
applied to it.
The " waxing " and " waning " of the moon may be taken
as a jrood illustration of the method of Concomitant Varia-
tions. Both in the " waxing " and in the " waning," the
varying amount of illuminated surface displayed by the moon
to a spectator on this globe, depends on and corresponds with
the varieties in her motions and positions as receding from
or approaching the sun. We have with increase of distance,
increase of light, and with decrease of distance, decrease of
light. After what is known as " new moon," the moon, from
a thin crescent, with the horns turned to the east, grows, as
she increases her angular distance from the sun, to a semi-
circle of light. When the moon, after passing through the
" gibbous " stage, reaches the position of 180° in advance of
the sun, she appears as full moon, and the whole illuminated
disc is visible. From this point, beginning to draw nearer
to the sun, she gradually wanes, passing again through the
" gibbous " phase to the stage of the last quarter or semicircle
of light. Nearing the sun still more, she reassumes the
crescent form, with the horns turned to the west, and grad-
ually passes into the darkness of the position of the " new
moon." Here you have a series of concomitant variations be-
tween the elements of motion, distance, position, on the one
hand, and degrees and forms of illumination on the other.
Jevons gives a very good illustration of variations " in the
connection which has of late years been shown to exist be-
tween ^he aurora borealis, magnetic storms, and the spots on
the sun. It has only in the last thirty or forty years become
known that the magnetic compass needle is subject at inter-
vals to very slight but curious movements, and that at the
same time there are usually natural currents of electricity
produced in telegraph wires, so as to interfere with the trans-
mission of messages. These disturbances are known as mag-
netic storms, and are often observed to occur when a fine
display of the northern or southern lights is taking place in
some parts of the earth. Observations during many years
have shown that these storms come to their worst at the end
480 INSTITUTES OF LOGIC.
of every eleven years, the maximum taking place about the
present year, 1870, and then diminish in intensity until the
next period of eleven years has passed. Close observations
of the sun during thirty or forty years have shown that the
size and number of the dark spots, which are gigantic storms
going on upon the sun's surface, increase and decrease exactly
at the same periods of time as the magnetic storms upon the
earth's surface. No one can doubt, then, that these strange
phenomena are connected together, though the mode of the
connection is quite unknown. It is now believed that the
planets Jupiter, Saturn, Venus, and Mars are the real causes
of the disturbances ; for it has been shown that an exact
correspondence exists between the motions of these planets
and the periods of the sun-spots. This is a most remark-
able and extensive case of concomitant variations."1 At the
same time, it must be observed that this is a wholly em-
pirical concomitance. We know only that great variations
mutually correspond, but we do not see or know the link
of connection.
§ 624. Where the relation of Cause and Effect enters into
the strictly inductive illation, — that is, truly the valid con-
stitution of the minor premiss, that some stands for, or is
equal to all — Ueberweg has well summed up the rules in
operation : —
(1.) " Inductive inference has strict universality when S (the
subject) contains the sufficient reason of P (the predicate) ;
and when P is related to S as its only possible cause or con-
ditio sine qua non ; and, lastly, when S and P are both neces-
sary consequences of a common cause, sufficient for P and the
only possible cause of S."
(2.) " Induction leads only to comparative universality, or to
rules which may be limited by exceptions, when S is only a
single co-operative cause or condition of P : or when, on the
other hand, P is not the possible cause of S, or when S and
P are consequences of a common cause, but may also result
singly under different conditions."2
§ 625. The place of Hypothesis in science and of a limited
induction, which comes to be much the same thing, is that of
inciting to testing and verification. The question really is, —
Does the hypothesis in question — does the limited law I
1 Logic, p. 251. 2 Logic, p. 486.
HYPOTHESIS. 481
have already got by induction — explain the facts, — more of the
facts, all of the facts ? Does it extend to cases where I can-
not observe the cause already in operation, but the results of
which seem to be in conformity with this as the cause ?
What is its probability, its generality ? This is frequently
to be tested by deduction — Material Deduction. This means
taking the conception formulated in the hypothesis, or taking
the limited uniformity, and calculating with this as a basis
what should happen in certain circumstances, or in a sphere
wider than that already embraced by us. This is experimen-
tal rather than observational. Newton might apply the con-
ception of gravity to the motion of the moon to discover
whether attraction subsisted between it and the earth. Ob-
servation of the facts corresponded with the results of the
deduction — that is, what ought to be the hypothesis or
limited law extended to this new sphere. And so with the
moon and the sun. Doubtless this is the way in which
science progresses, and this was not a form of method, at
least explicitly contemplated by the modern founder of In-
ductive Method — Lord Bacon. At the same time it is not
just to say that Bacon limited scientific method simply to
observation and induction from facts and laws of increasing
generality. His Prerogative Instances, especially the Mi-
grantes and Crucial, show how he could look at characteristic
facts, and specially select them. Modern Deductive Method
is in no way incompatible with Baconianism. Bacon's de-
nunciation of "the anticipation of nature," as opposed to
" the interpretation of nature," was eminently sound. In warn-
ing men against projecting their mere "conceits" into the
course of nature, and thinking they find them there, Bacon did
an incalculable service to science. Facts are the first thing
— conceptions, hypotheses, modes of explanation may follow.
He fully admits the value of hypotheses — that is, of questions
to put to nature. The most and best questioning man will be
the discoverer in the end, provided he has caution, zeal, ap-
plication, as Newton had. But testing, verification, deduc-
tion are in the end to appear before the bar of Observa-
tion ; and it is because of the harmony which subsists
between the most laborious, the most ingenious deductive
results and the facts as tested by observation, that Deduc-
tion as a method has its value — in relation, at least, to the
2 H
482 INSTITUTES OF LOGIC.
physical universe. We use deduction when we cannot ob-
serve the cause, but only suppose it. All the same, the result
of the deduction, in order to have any validity, must harmon-
ise with the facts, or supposed effects as observed by us. If
Newton showed that there was attraction between the earth
and the moon, by reasoning deductively, the criterion of this
reasoning was the harmony between the actual motions and
positions and the result of the deduction. And so it is in
all cases where a conclusion arrived at deductively reaches
full verification or certainty ; otherwise, the supposition in-
volved is only a probable hypothesis. Of this we have an
illustration in the supposition that the brighter parts of the
moon consist of mountains. These, in themselves, are be-
yond direct observation : yet this hypothesis explains certain
appearances which those parts present. They are found —
(1.) to cast shadows when the sun's rays fall upon them
obliquely ; (2.) in the interior illuminated border of the
moon there are points illuminated before the others, thus
showing them to be higher. The hypothesis, thus, of a
mountainous surface is rendered highly probable. The facts
we observe, are as if there were mountains of a great ele-
vation.
§ 626. The rules of Induction are, as it seems to me, not
really by themselves rules of discovery; they are rather rules
of guidance and verification or testing in the process of dis-
covery. The discoverer must start with an hypothesis — a
question to put to nature or the facts. This is the guiding
spirit of investigation : if, with this in his mind, he tests
its applicability according to the canons of induction, he will
do well either in finding in it a probable solution, or in
casting it aside as useless. And, certainly, before he can
vindicate his theory to the world, he must show that his
hypothesis has fulfilled those conditions.
As to the value of the rules of Induction in the matter of
culture, they are wholly secondary as compared with the
high abstract training, the precision of logical thinking, the
orderliness of thought, the power of consecution, which
are developed by the study of Formal or General Logic.
Compared to this, their influence is weak and unsteady as is
the swaying chaos of fact in the world compared with the
grasp of the universal laws which regulate concepts, proposi-
VALUE OF RULES OF INDUCTION. 48b
tions, and reasonings. And while in the world of physical
phenomena — definite, visible, tangible, or to be reached by
microscope or telescope — they are valuable and important,
they cannot for a moment be placed on the same high level
as those laws which regulate all human thinking in its very
essence, its very possibility — form, in fact, the conditions of
any concept, any judgment, any reasoning whatever. These
are the first things to be studied, and the man who knows not
these in their grounds and basis, is, whatever he may know of
rules applied to so-called phenomena, a mere empiric.
484
CHAPTEE XXXVI.
QUASI-SYLLOGISMS EXAMPLE ARISTOTELIC ENTHYMEME.
§ 627. What is known as Reasoning from Example has an
apparent likeness to Analogy. In Example the process is
from one particular to another particular, similar to the former.
Thus we may say : —
Socrates (a philosopher) was modest; therefore Diogenes (a
philosopher) was modest. In this there is really no valid in-
ference— the one particular does not necessarily imply the
other.
If, further, we explicate what is apparently involved in the
one premiss, we should have Socrates is modest ; therefore all
philosophers are modest, which is a paralogism. We need
somehow to connect modest and philosopher into a universal
proposition, — All philosophers are modest, — and this is not
provided for by the terms of the propositions or data given
us.1 Yet this is typical of the reasoning from Example set
forth by Aristotle.
His reasoning from Example (TrapaScL-y/xa) is really a com-
plex process, consisting (1.) of an inference so-called, from
one single case to every case of the same kind ; (2.) of a
syllogism properly constituted, in which the supposed uni-
versal conclusion of the first reasoning becomes the major
proposition of the second. Aristotle defines Example as that
in which, among three notions, the extreme is affirmed of the
middle through a term similar to the third. But we must
know, he adds, that the middle is with the third term, and
that the first is with the similar term.
1 Cf. Duncan, Inst. Log., L. iv. c. vii. § 2.
EXAMPLE. 485
Thus, to take his own illustration, which may be put
thus : —
(a) The war by the Thebans (neighbours) against the Phocians
was destructive ;
Therefore the war by the Athenians (neighbours) against
the Thebans will be destructive.
This implies the reasoning —
(b) The war waged by the Thebans against the Phocians was
destructive (A is A) ;
That was a war against neighbours (A is P>) ;
Therefore every war against neighbours is destructive
(B is A).
Then we have the following : — ■
(c) B is A
T isB
;. r is a
Or—
Every ivar against neighbours is destructive ;
The war of the Athenians against the Thebans would be a war
against neighbours ;
Therefore this war would be destructive.
§ 628. The latter reasoning is perfect ; but the major, every
war against neighbours is destructive, depends on the preceding
reasoning, if it can be called such, which it is not in any
proper sense. It may be brought under the head of Imperfect
Induction ; but it is a thoroughly weak case. The point to
be established, which is not, but is simply assumed or left to
be inferred from the nature of the case as known to us, is
the connection between the destructiveness of the war and
its being between neighbours. As Aristotle himself points
out, the reasoning in the former case is really only of rhetorical
import or influence — fitted to persuade, but not cogent enough
for conviction.
Or, to take another illustration : —
(a) A (a statesman) is patriotic ;
Therefore B (a statesman) is patriotic.
This implies the reasoning —
486 INSTITUTES OF LOGIC.
(b) A is patriotic ;
A is a statesman ;
Therefore all statesmen are patriotic.
Hence we reason —
(c) All statesmen are patriotic ;
B is a statesman /
Therefore B is patriotic.
The reasoning (b) is obviously a paralogism, — while the
reasoning (c) is formally valid ; but, as borrowing its major
from an unsound reasoning, is materially wrong.
(a) It is evident that Example is not a relation of the whole to the
part, nor of the part to the whole ; it is the relation of a part to a part,
since the two terms are the subjects of one and the same, and that only
the one is more known than the other.
Example differs from Induction in this, that the one demonstrates,
through all the particular cases, that the extreme is in the middle, and
does not bind the syllogism (conclusion) to the other extreme, while
example does so, and does not demonstrate through all the particular
cases. — (An. Pr., ii. 24.)
(b) Pacius gives this illustration of the difference of Syllogism from
Induction and Example : —
(1.) Syllogism —
All war against neighbours is fatal ;
The war of the Athenians against the Thebans is a war against
neighbours ;
Therefore the war of the Athenians against the Thebans will
be fatal.
(2.) Induction —
The war of the Thebans against the Phocians, the war of the
Athenians against the Thebans, and all similar wars, are
fatal ; hence all war against neighbours is fatal.
(3.) Example —
The war of the Thebans against the Phocians has been fatal ;
hence the war of the Athenians against the Thebans will be
fatal.
(c) Example is an argument in which some Singular is inferred
through one or other similar. Formally, it has no force of proba-
tion, because there is no process from one singular to another unless .
through the universal, which cannot be concluded from the one or
the other singular. — (Duncan, Inst. Log., L. iv., c. vii. p. 249.)
§ 629. The inference from one case to another similar is not
a necessity but a simple presumption or probability. In a
given instance, A1 has been followed by B1 ; in another in-
stance A2 occurring will not necessarily be followed by B2.
EXAMPLE.
487
The presumption is that it may ; or, owing to the specific
character of the instances, we may be certain that A2 will bo
followed by B2, as in the case of the elements of a chemical
analysis. But there is here no real syllogistic inference as
from whole to part, or all parts to whole. Example is but a
stage in induction, and is often a good practical rule to act on
in the interest of caution and the avoidance of danger. But
that is all. It is no doubt the form of reasoning, — if it
may be called reasoning, — which appeals most strongly to
the average irreflective intellect. The average intelligence
seldom rises above process from similar to similar, or from
particular to particular. The moment the question is raised,
— similar in what, and why is this particular result likely to
follow ? — we get into the sphere of Induction and the search
after causes. At the same time, the presumption on which
example is founded often strikes home. When, after the
slaughter of King Ahaziah, Jezebel, looking from the window,
called out to Jehu — " Had Zimri peace, who slew his master ? "
the question passed with winged force to the heart of the
reddianded Jehu.1
§ 630. Example may be of use in illustration, though it is
not a reasoning. It has, however, semblance enough to infer-
ence to pass as such in popular oratory, and even in other
departments of literature, as a valid argument. The majority
of men are much more ready to catch at and fix on an example
as at least convincing or persuasive, than to follow the links
of sound argumentation, however clearly stated. The proper
use of Example is to lead us to inquire whether the attribute
alleged to be predicable of the second subject is really con-
nected with the quality common to both. In some cases
there may be a strong presumption that the attribute is con-
nected with the common quality. Thus A (a Christian) was
put to death under Nero, therefore B (a Christian) was put to
death under Nero. If we find that B died in Nero's reign at
Borne, and while other Christians were being put to death,
the likelihood of his also having been a sufferer is increased.
And thus example may be a help to discovery, or, at least,
to some form of probability in a doubtful matter.
(a) To allow, as Duncan does, that Example may be valid per
1 2 Kings ix. 31.
488 INSTITUTES OF LOGIC.
accidens or by help of the matter is simply to give up the form, as a
proper mode of reasoning. Thus, Plato is by nature risible, there/ore so
is Socrates, since the nature of all men is the same. The by nature
introduces a universal. It is equivalent to man naturally or all man is
risible. — (Ibid.)
§ 631. The Enthymeme is a reasoning from likelihood or
signs, or from both in the single reasoning. It is unessential
to the Enthymeme of Aristotle whether a premiss be sup-
pressed or not, as is the case in the ordinary enthymeme; the
reasoning would still be an enthymeme — that is, " of a pecu-
liar matter from signs and likelihoods."
§ 632. Likelihood and Sign (eucos S« xal o-qfxciov), says Aris-
totle, are not the same. The likely is a proposition based on
opinion. What people know for the most part as happening
or not happening, or being or not being, this is the likely.
For example, the envious hate, lovers love. The Sign, on
the other hand, tends to be a proposition capable of demon-
strating, either necessary or proved by the opinion of men.
That which existing implies the existence of another thing,
or which having been produced, another thing is implied as
produced, before or after, — this is the Sign, indicating that
the thing is produced or exists. The Enthymeme, accor-
dingly, is a syllogism from the likely or from signs.1
(a) The term incomplete (drf\^is t£ (IkStwv) is usually added to Syllo-
gism in this definition ; but it has no authority, and it has been pro-
perly rejected by Pacius, the Berlin editors, St Hilaire, and others. —
(Cf. St Hilaire, in loco.) The examples of enthymeme given by Aris-
totle have their two premisses ; otherwise there would be nothing to
suggest reasoning.
§ 633. Hrj/xciov and eiVos differ as genus and species.
'Srjfjieiov is generally a sign or mark, and it is divided into (1.)
a sign necessary and certain, which is called tck/xt/jplov, as
there is a scar, therefore there was a wound; the mountains cast
a shadow, therefore they are illumined ; and (2.) a probable sign
(eiKos) which may sometimes fail, as he is a soldier, therefore he
is renowned.2 In the first case the T^Kfuqpiov is peculiar, and
can indicate but the one thing or fact, and in this case it is
necessary. In the second case the cikos may belong equally
to, and thus indicate, several things. The reKfirjpLov has the
1 An. Pr., ii. 27. 2 Cf. Duncan, Inst. Log., L. iv. c. vii.
ENTHYMEME. 489
power of demonstration. The cases of this class are, how-
ever, rare.1
§ 634. The true character of the cikos is thus a proposition
very generally accepted, nearly universal, but not quite so,
and such as, if used in a reasoning, would give a probable
conclusion, as : — ■
Envious men usually hate ;
This man is envious ;
He probably, therefore, hates.
It is, in fact, a proposition founded on experience, but not
satisfying the requirements of sound induction.
§ 635. The Sign, in order to be of use in reasoning by
Enthymeme, must be capable of assuming a propositional
form, and thus becoming the indication (or sign) of some other
truth or fact capable of being propositionally stated. The
force of the reasoning must further turn on the relevancy or
appropriateness of the sign or significative character of the
proposition. " If one proposition should be stated, there is
only a sign ; but if the other also be assumed, there is a syl-
logism, as that Pittacus is liberal, for the ambitious are liberal,
and Pittacus is ambitious." Thus, - this man's face is yellow,
therefore he is suffering from jaundice, would be an enthy-
mematic relation of two propositions. The argument would
be completed by supplying the general proposition. Whoso-
ever's face is yellow is suffering from jaundice. But the weak-
ness of the Enthymeme comes out here, for the sign elevated
to a general proposition is not identical with a proposition
strictly universal, or admitting of no exception. It may be a
proposition generally received, but it is not proved to be uni-
versal, and hence the peculiar character of the reasoning,
arising from a consideration of the matter.2
§ 636. The Sign in the Enthymeme may have the three
positions of the middle — (a) subject and predicate, as the middle
in the First Figure ; (6) predicate of the two extremes, as the
middle in the Second Figure ; (c) subject of the two extremes,
as the middle in the Third Figure.
Thus, First Figure : —
1 Cf. Trendelenburg in loco.
2 Cf. Crakanthorpe, Trendelenburg, Waitz, St Hilaire in loco.
490 INSTITUTES OF LOGIC.
(B) , (A)
(a) Any dog which shuns water is mad ;
(C) • (B)
This dog shuns water ;
(C) (A)
Therefore he is mad.
Second Figure : —
(C) (A)
(b) Pittacus is a worthy man ;
(C) (B)
Pittacus is a wise man ;
(B) (A)
Therefore (some) wise are worthy.
Third Figure : —
(B) (A)
(c) All mad dogs shun water ;
(C) (A)
This dog shuns water ;
(0) (B)
Therefore this dog is mad.
§ 637. This sense of the Enthymeme is that constant in Aris-
totle. But the term has had various meanings assigned to
it. Quintilian gives these, among others — (a) signifying
all things conceived in the mind ; (b) an opinion (sententia)
with reason ; (c) a certain form of argument ; (d) epicheirema ;
(e) rhetorical syllogism ; (/) imperfect or abbreviated syllo-
gism, in which one or more of the propositions of the perfect
form are suppressed. This has come to be the prevailing
meaning of the term.1
(a) Aristotle, in the Topics, divides syllogisms thus : —
(1.) Philosophema, or Demonstrative Syllogism, — highest and hest
form.
(2.) Epicheirema, or Dialectical Syllogism.
(3.) Sophisma, or Eristic Syllogism.
(4.) Aporema, or Dialectical Syllogism of Contradiction. — (Top., viii.
11; i. 1.)
There is demonstration when the conclusion is from what is true and
primary, or from what is based on this as its principle of certainty.
i See Trendelenburg, El. Log., § 37.
Aristotle's division of syllogisms. 491
The dialectical syllogism is that which draws its conclusion from pro-
positions commonly received (simple probabilities). True and primary
propositions are. held as certain, not through other propositions, but
through themselves ; for there is no need to investigate the why of
principles which give us science ; but each principle ought to be per-
fectly credible by itself. That is probable which appears such, either
to all men, or to the majority, or to the wise ; and among these, either
to all or some, either the most illustrious or the most trustworthy.
The Eristic or Contentious Syllogism is that which proceeds on pro-
positions that seem probable, which yet are not so. They are apt
for a conclusion, or seem to be so. This is the semblance of a Syllo-
gism. It seems to conclude, but does not. — (Top., i. 1; viii. 12. Soph.
Elench., i. 2.)
The equality of contrary reasonings would seem to be that which
causes doubt. When in reasoning it appears to us that the reasons are
equal on both sides, we doubt which of the two we ought to adopt in
action. — (Top., vi. 6.)
492
CHAPTER XXXVII.
HYPOTHETICAL DISJUNCTIVE, HYPOTHETICO-DISJUNCTIVE,
FORMS OF REASONING.
§ 638. Besides the Categorical Form of Reasoning, we have
others which outwardly differ from it, in being made up of
two kinds of propositions — a hypothetical, or disjunctive,
along with a categorical premiss. The Hypothetical and the
Disjunctive Reasoning cannot, as seems to me, be said to
differ essentially from the Categorical. For the laws which
regulate them are the same in all the cases — viz., those of
Identity, Non-Contradiction, and Excluded Middle. The law
of Reason and Consequent is in its relation to Hypothetical
and Disjunctive Reasonings only an application of those other
laws — it is, in fact, those laws in motion. At the same time,
the law of Reason and Consequent should not be excluded
from Logic, as a special expression of those laws, and also
as a general postulate which requires us to think always with
a reason in some form.
§ 639. The Hypothetical, Conditional, or Conjunctive Syllo-
gism has for its major premiss a hypothetical judgment, which
enounces the connection between a reason and consequent, or
condition and conditioned. This premiss has nothing to do
meanwhile with the question of the actual or isolated reality
of the condition or conditioned. It states only that between
the antecedent and the consequent there is such a connection
that if the one is, the other is also. Thus, if A is, B is ; or,
A being given, B is also given. If the sun is up, it is day. This
is the major premiss or sumption of the reasoning, — and the
whole reasoning turns on the connection or sequence between
the terms.
HYPOTHETICAL REASONINGS. 493
The major being given, we may proceed (a) to the cate-
gorical affirmation of the Antecedent or Condition, and thus
necessarily reach an affirmative conclusion. Thus : —
If A is, B is ;
But A is ;
There/ore B is.
If the sun is up, it is day ;
But the sun is up ;
Therefore it is day.
Or—
If there he no difference in weight between a given quantity of
water and the ice or the steam into which it may be converted,
then the heat which is added to or taken from the water to give
rise to these several states possesses no weight. But there is no
difference, fyc, therefore heat possesses no weight.1
This is known as the Constructive Hypothetical, or as the
modus ponens.
Or (b) we may proceed to the categorical denial of the Con-
sequent or Conditioned, and thence backwards to the denial
of the Antecedent or Condition. Thus : —
If A is, B is ;
But B is not ;
Therefore A is not.
If the sun is up, it is day ;
But it is not day ;
Therefore the sun is not up.
This is the Destructive Hypothetical or modus tollens.
11 In Hypothetical, the reason or antecedent means the
condition, that is, the complement of all without which some-
thing else would not be ; and the consequent means the
conditioned, that is, the complement of all that is determined
to be by the existence of something else." 2
§ 640. The rules of these two forms have been given
thus : — Posita conditione ponitur conditionatum ; sublato condi-
tional, tollitur conditio.
The special rules commonly given for the Hypothetical
Syllogism are (1.) the major or Sumption is always Definite
1 Huxley. J Hamilton, Logic, L. xviii., iii. p. 356.
494 INSTITUTES OF LOGIC.
in quantity, and Affirmative in quality ; the Subsumption
may vary in these respects.
(2.) The conclusion is regulated by that member of the
major which is not subsumed in the minor.
It should be explained that by affirmative as applied to
the major or hypothetical premiss, it means simply the
assertion of the relation of dependence between antecedent
and consequent. Further, quantity in the antecedent in the
major only comes into account in some cases, — as from genus
to species, — but not properly from mark to mark.
§ 641. According to the common view, thus, we can con-
clude from the truth of the antecedent to the truth of
the consequent, or from the falsehood of the consequent
to the falsehood of the antecedent. But we cannot validly
reverse those processes. (1.) Thus, to take the first case,
we cannot conclude from the truth of the consequent to the
truth of the antecedent —
If A is, B is ;
But B is ;
Therefore A is.
The fact of B does not give the fact of A, for B may
depend on other facts besides A. We have not said in
our major, A is the only antecedent on which B depends;
and therefore supposing we find B to be, it does not follow
that A is. Or, concretely —
If X made that statement, he is foolish ;
But X is foolish ;
Therefore he made the statement.
This by no means follows from the datum.
(2.) To take the second case : —
If X made the statement, he is foolish ;
But X did not make the statement ;
Therefore he is not foolish.
This does not follow from the datum, for we only asserted
a connection between making the statement and being foolish,
and as X is disconnected from the condition, we cannot say
either that he is foolish or that he is not, — so far as our
data are concerned.
HYPOTHETICAL REASONINGS. 495
(a) These are the two direct forms of the principle of what is
known as the Sufficient Reason; and these indicate its sphere as a
logical principle.
Looked at as bearing on truth, — truth of fact, — this law has two
important applications— as Kant puts them :
"(1.) The truth of the consequent yields negatively only the truth
of the principle or reason. If a false consequent follows from a
principle, this principle is false. For if the principle were true,
equally ought the consequent to be true, the consequent being de-
termined by the principle. But the converse does not hold, — that
if from a principle false consequences did not flow, that principle
would be true; for true consequents may follow from a false prin-
ciple.
" (2.) If all the consequents of a principle be true, this principle
is itself true ; for if the principle were false in any respect, some
false consequence would follow.
' ' The first mode of inferring that which gives only a sufficient nega-
tive and indirect criterion of the truth of a principle, is called the
apagogical (modus tollens). This mode is applicable in geometry, and
enables us to demonstrate the falsity of a principle by this alone, that
a false consequent follows from it. E.g., if the earth be flat, the
polar star ought always to appear at the same height ; but this is not
so ; therefore, the earth is not flat.
" The second mode of inference, positive and direct (modus po7iens),
cannot recognise apodictically the universality of the consequents, and
is thus only led to a probable and hypothetically true conclusion, by
the supposition that if several consequents be true, all the others are
equally so" (Kant, Logik, Int.).
§ 642. But, as seems to me, we may in Hypothetical Keason-
ing have a form in which the consequent is dependent on a
single antecedent, and where, consequently, we may proceed
from the truth of the consequent to the truth of the ante-
cedent, and from the falsehood of the antecedent to the false-
hood of the consequent. Thus —
(a) If education is good, it both develops and informs the
mind ;
But this education both develops and informs the mind ;
Therefore this education is good.
Or—
(b) This education is not good ;
Therefore it does not develop and inform the mind.
Or, If the sun, earth, and moon are in a straight line (that of
syzygies), and the earth is between the sun and moon, the whole
of the illuminated face of the moon may be seen from the earth.
496 INSTITUTES OF LOGIC.
This is true whether we affirm the antecedent or the con-
sequent, because the antecedent is sole cause. Equally we
may say, If the moon be in the line of syzygies with the earth
and sun, and between the earth and sun, no part of her disc can
be seen from the earth. This is equally valid whether we
affirm antecedent or consequent, and for the same reason.
The force of the inference here depends on the converti-
bility of the sphere of the antecedent and the consequent.
The consequent here is really given as dependent on one
antecedent, and hence we can proceed indifferently from one
to other, either by affirmation or negation.
Again, we may have perfect equivalence in the spheres,
although the relationship of the terms is reversed. Thus —
If A is the son of B, B is the father of A ;
But B is the father of A ;
Therefore A is the son of B.
Or—
A is not the son of B ; therefore B is not the father of A.
§ 643. And even in regard to those cases in which the
spheres of the antecedent and consequent are not convertible,
the reasoning in the form of the modus tollens may fairly be
reduced to the same formula. Thus : from the falsehood of
the antecedent : —
If X made the statement in question, he is foolish ;
But he did not make the statement in question ;
Therefore (so far as our datum goes) he is not foolish — i.e., not
proved foolish, or not the fool this would make him.
This is virtually saying there is no proved connection suffi-
cient to found the conclusion that he belongs to the class
foolish.
But in no case of this sort could we conclude from the
truth of the consequent to the truth of the antecedent : —
If X made the statement in question, he is foolish ;
But he is foolish ;
Therefore he made the statement in question.
Here the converse process is not legitimate, whether we
regard foolish as taken extensively or comprehensively.
HYPOTHETICAL REASONINGS. 497
From the fact of a man belonging to a class, it does not follow
that he commits or has committed a given or definite action
characteristic of the class.
If man is, animal is. — Let this be quantified : — ■
If (all) man is, (some) animal is ;
But some animal is ;
Therefore all man is.
No — for the some animal of the minor may not be the some
animal of the major. We should need to say this some
animal is.
(a) The property is a reciprocal attribution to the subject ; the genus
is not. Animal is, therefore man is, does not follow. Animal is, there-
fore risibility is, does not follow. But man is, therefore risible is; risible
is, therefore man is. — (Porphyry, Eisagoge, ix. 6.)
§ 644. The Hypothetical is obviously a useful and much
needed form of reasoning. We frequently know that if one
event takes place, another certainly will follow. Thus an
astronomer might be able to tell us that if the moon has
always the same face to the earth, it has no diurnal revolution
on its axis. These two things may be known to be essen-
tially connected ; yet I may not be able from imperfect obser-
vation to say absolutely that either is so. But as soon as I
am able to affirm the antecedent part of the proposition, and
to say the moon has always the same face to the earth, I can
conclude to the consequent in the form of the hypothetical
reasoning, that the moon has no diurnal revolution on its
axis. This enables us to extend our knowledge ; for we thus
connect what is within our observation with what may be be-
yond it,— as the physician may connect an observed symptom
with an unobservable poison in the system of the patient.
§ 645. There is in appearance a more complex form of the
Hypothetical reasoning, in which seemingly there are four
terms. Thus : —
If A is B, Cis D;
But A is B ;
Therefore C is D.
2 i
498 INSTITUTES OF LOGIC.
Or—
If the rains be heavy, the river will be flooded ;
But the rains have been heavy ;
Therefore the river is flooded.
There is, however, no real difference here between this and
the apparently simpler form. There are more terms, taken
isolatedly, in the antecedent and in the consequent ; but the
point of the 'whole is as simple as in the form in which there
are only two terms — antecedent and consequent. For what
is asserted is a certain connection between the antecedent as
a whole and the consequent as a whole. This is in no way
affected by the seeming complexity, either of antecedent or
consequent. The same rules and the same remarks apply to
this as to the other form.
§ 646. It may be said that, as in Hypothetical Reasoning
there are but antecedent and consequent, there are only two
terms, and the inference is, therefore, not mediate, but imme-
diate. But on the other hand, it may be urged that the
minor premiss really supplies a new term. When we say, if
the sun shines, it is day, we merely state a general or universal
fact or law. When we categorically add, the sun does shine,
or does now shine, we have made a new statement — a state-
ment coming under the general rule, no doubt, but still
specifically distinct and definite. It is a new proposition, or
new matter of fact. And it is through this minor alone that
we can apply the connection stated in the major to the con-
sequent in the conclusion. The mere hypothesis of the major
is per se powerless for inference.
(a) Hamilton's final view may perhaps be stated as follows : — Tak-
ing Conditional as the genus, he includes under it Conjunctive (Hypo-
thetical) and Disjunctive. In either form, however, there is no reach-
ing a conclusion through a middle term. There is thus no mediate in-
ference, or reasoning syllogistically. The so-called major premiss in
either form is not properly a major premiss. There is but one premiss ;
and all that it does is to state a relation or dependence between the
judgments or propositions. If A is, C is, or if A is B, Cis D. You have
but to apply the rule of the Condition and Conditioned. This granted,
— affirm the condition (or antecedent), and you affirm the consequent.
Deny the consequent, you deny the antecedent or condition. We do
not need to go beyond the given relation or dependence, we do not need
another term or proposition, in addition. We have only to apply the
rule of inference to what we have — in a word, the inference is imme-
Hamilton's view. 4P9
diate. And it belongs to what may be called Explicative Inference.
"Given two or more propositions; related and conditionally, — what
are the inferences which the relative propositions, explicated under
these conditions, afford ?" — {Logic, iv. p. 371. Appendix viii.)
The Conjunctive, properly stated, is : — As B, so A ;
or as B is, so is A ; or as C is B, so is B A. This is
the Explicand ; then follows the Explicative proposi-
tion,— B is ; then the Explicate, A is. Thus : —
If Bis C, A is B,—
Explicated thus,— The cases of B being C, are cases of
A being B. Therefore, this case of B being C is a case
of A being B.
If the rock is metamorphosed, it has been subjected to heat.
Every case of a rock being metamorphosed, is a case of having been sub-
jected to heat.
This case of a rock being metamorphosed {hyper sthene), is a case of hav-
ing been subjected to heat.
If any A is, B is ;
This A is, B is.
I venture to think that conjunctive (or hypothetical) reasoning, and
disjunctive as well, are not reducible to mere explication of the so-
called major premiss. Explication of what is conditional, can never
go beyond stating the condition in a particular form. But as thus
stated, it is still conditioned. We do not reach any categorical result
or conclusion.
Thus :—
If rain has fallen, the ground is wet ;
But rain has fallen, therefore the ground is wet.
Is this a mere explication of the dependence between the condition
and conditioned of the premiss ? When it is said rain has fallen, this
is a new statement or proposition, not evolved out of the conjunctive
premiss. It is in fact a particular instance, which is brought under a
general rule. This is a very different thing from saying, supposing
rain falls on a particular occasion, that will be a case of the ground
being wet. This would be an immediate inference from the conjunc-
tive premiss. But the categorical statement is not at all implied in
this premiss. And on the categorical statement rests the whole efficacy
of the reasoning. In fact, the conjunctive premiss may betaken as the
statement of a law of nature, gained somehow or other ; and the minor
or categorical premiss is the reference of an actual instance to the
general law.
Whenever rain falls, the ground is wet ;
The case of rain falling is the case of the ground being wet ;
Suppose there is a case of rain falling, then there is a case of the ground
being wet.
This is obviously an immediate inference ; it merely says this would
be a particular instance of a general relation between two things,
500 INSTITUTES OF LOGIC.
provided that relation were granted or existed. But it is idle and
tautological.
But suppose we say — rain has fallen (to-day) ; hence the ground is
wet. Here we go heyond supposition or hypothesis ; and categorically
assert. In this case we practically introduce new terms, — terms of
fact, — as opposed to terms of mere concept. And the true force of the
Conjunctive Conditional lies here. It helps us to apply our general
knowledge to new or particular instances, which otherwise we could
not have done. This is a very different thing from mere explication, —
which, as applied to a conditional (or hypothetical) reasoning, must
always remain conditional (or hypothetical).
§ 647. The true view of the Hypothetical or Conjunctive
Reasoning seems to me to be that it is of three special kinds,
— regulated by principles which are in a manner different, but
which may yet be held as coalescing under the head of the
Sufficient Reason. In the first place, the hypothetical or
conjunctive premiss may state the relation of whole or part ;
and thus the nexus or connection of antecedent and conse-
quent may be based on this relation, — on, in fact, the Law
of Identity. Thus, if all A is a part of B, C (a part of A)
is D (a part of B). This connection is wholly analytic, and
it is governed by the law of whole and part — of genus and
species. Explicitly stated, it would run : —
As the notion (genus) animal contains the notion (species)
man, this man (or the man we speak of) is animal ; or If
every tyrant is worthy of death, Nero (a tyrant) is worthy of
death.
We suppose Nero to be part of the class tyrant, and conse-
quently that what is applicable to the whole is applicable
to the part.
§ 648. In the second place the hypothetical premiss may
state the relation of Cause and Effect, — this in thought be-
coming reason and consequent. In this case, the reasoning
fully evolved is synthetical, and states the relation between
two facts (or concepts) known only through experience, not
implied in the concepts employed. Thus : —
If rain should fall for four hours in the west, this river will be
flooded ;
But rain has so fallen ;
Therefore this river is flooded.
The connection here between the antecedent and the con-
FORMS OF HYPOTHETICALS. ' 501
sequent in the major depends on observation and general-
isation, which have enabled us to reach a cause upon which
a general or universal consequent depends.
§ 649. In the third place, we may have the connection in
the major between antecedent and consequent determined
through the relation of the sign and the thing signified.
Thus :—
If the barometer falls, rain will fall ;
But the barometer has fallen ;
Therefore rain will fall.
Here the falling of the barometer is not the cause of the
rain falling, but the indication or sign. It is the reason
why we believe that the other event will follow.
§ 650. The truth seems to be in regard to Hypotheticals,
that the reasoning runs naturally in comprehension ; it is a
reasoning through marks or attributes of the subject, rather
than through the quantity of the subject. It proceeds on the
principle that a mark of the mark is a mark of the subject
itself. Thus :—
If education is good, it informs and develops the mind ;
But this education is good ;
Therefore it informs and develops the mind.
Here good is the mark of education; informing and developing
the mind is the mark of good; and hence it is the mark of this
education. This is a simple, natural, and easy form of reason-
ing. It amounts to this, that when an individual object is
found to possess a particular attribute, we are warranted to
refer to it any attribute essential to that attribute. In obser-
vational science, as in the study of bodily and mental charac-
teristics, we shall find this formula of the greatest use,
provided we are careful to ascertain the essential connection
of the marks with each other. The physician knows that a
certain mark (antecedent) indicates a certain disease (conse-
quent) ; and finding the mark present in a given subject, he
infers the disease — say poisoning from tetanus. This is simply
an unconscious hypothetical reasoning in comprehension.
The application of the principle no doubt requires great
caution, and this depends on the observer. We must be care-
ful to ascertain that the mark (or antecedent) is either exclu-
sively or at least conclusively connected with the consequent,
502 INSTITUTES OF LOGIC.
otherwise we have no true mark of the mark. Spasm and
rigidity of muscle may, for example, be a mark of other things
besides poisoning, as epilepsy. We must therefore, if we
can, ascertain the special feature of rigidity which indicates
poisoning. Otherwise our inference might be made from an
insufficient mark. But all this is a matter of experience and
analysis prior to the actual inference. It is, in fact, an appli-
cation of Induction.
§ 651. It is by this method that physical science, in so far
as observational and generalising, has progressed since the
time of Bacon. For the principle is truly synthetic ; it in-
volves an addition to our conception of any given fact or
thing. We add to our thoughts of things by finding that
other thoughts or other things are essentially connected with
them. But for this, we should go on merely making explicit,
by analysis and deduction, our received or supposed knowledge.
When we add fact to fact, we get beyond the mere analytic
judgment, and progress by synthesis or a true addition to our
experimental knowledge.
§ 652. But whatever be the ground on which the connection
between antecedent and consequent be established — whether
that of genus and species, or of cause and effect, or of sign
and thing signified, or mark of the mark, — the connection
itself is only of one kind for the logician. It is given as that
of condition and conditioned, determining and determined,
or as Keason and Consequent. The antecedent or reason-
one concept or proposition — is given as that upon which
another concept or proposition is to be thought as dependent,
and necessarily dependent, in whatever way we may have
come to know this dependency, and after this the rules of the
reasoning are purely formal, and applicable in all matter and
under every form of connection. The formula really is : —
Think this, and you must think that.
(a) There is some controversy as to whether Aristotle recognised
hypothetical syllogism in the modern sense of the phrase. "It is not
necessary," he says, "further to analyse hypothetical syllogisms, for
it cannot be done with the initial data, since they conclude not by syllo-
gism, but only in consequence of convention admitted on both sides "
(An. Pr., i. 44). "We suppose that if such a thing is demonstrated,
such another will be equally so. Thus, if contraries have one and the
same quality, the notion of contraries will be single — that is, it will be a
knowledge in one and the same time. Hence, this being posited, we
Aristotle's doctrine. 503
prove, by an ostensive syllogism, that certain contraries have not one
and the same quality, and taking for middle term the contraries salu-
brious and insalubrious, we demonstrate that they have different quali-
ties. Thus : — The salubrious and the insalubrious have not the same
qualities, but the salubrious and the insalubrious are contraries, therefore,
some contraries have not the same qualities. The supposition has been
proved, and by that alone, according to the convention, the principal
conclusion is also proved, — the concept of contraries is not single. But
this demonstration does not result from a syllogism ; it results only
from the hypothesis ; and it cannot be reduced to any figure by analy-
sis. We might further prove the major, — the salubrious and the in-
salubrious have not the same qualities, — by reduction to the absurd ;
for the contradictory would lead to this conclusion, evidently inadmis-
sible, that the salubrious and the insalubrious are identical. The initial
proposition would then be true." — (St Hilaire, in loco.)
Hamilton holds that Aristotle did not recognise as syllogism the
later hypothetical reasoning. In one place (An. Pr., i. 32, § 5) Aris-
totle describes the process of the Hypothetic Syllogism (that called by
Alexander 8t' o\wv), but denies it to be a syllogism. His syllogisms
from hypothesis are therefore different. Thus, if man existing, it
be necessary that animal exist, and if animal, that substance; man
existing, it is necessary that substance exist ; but this, though neces-
sary, is not syllogism. Hamilton further points out that, in Aristotle's
view, Thesis or Position is the genus opposed to Axiom, and contains
under it, as species, Hypothesis or Supposition and Definition. " Hypo-
thesis is that thesis which assumes one or other alternative by a con-
tradiction. Definition is that thesis which neither affirms nor denies.
Hypothetical is thus that which affirms or denies one alternative or
other, — which is not possibly either, and, consequently, includes both.
They are thus, as complete, neither propositions nor syllogisms, as not
affirming one alternative to the exclusion of the other." — (Logic, iv.
p. 388.)
Pacius, St Hilaire, and Prantl, again, hold that Aristotle recognised
the later Hypothetical Syllogism. Ammonius Hermeiae is strong
on the other side (see In De Int., p. 3, ed. Aid. 1546, quoted in Hamil-
ton, Logic, iv. p. 388 : see the other authorities there referred to).
Ueberweg holds that "Aristotle did not formally comprehend, under
his notion of inferences, e£ uwodecreus, hypothetical inferences in the
later sense. He reckoned indirect proof among the syllogisms hypo-
thetical, in this sense, — tov e£ inro9e<reais fitpos rb Sia tov ddwdrov, — be-
cause in it a false proposition — viz., the contradictory opposite of the
proposition to be proved — is hypothetically taken as true, and so serves
as an i>Tr6decris, and forms the basis of a syllogism, by means of which
something evidently untrue is inferred." — (Logic, p. 449.)
Theophrastus developed more fully hypothetical inference ; still,
however, giving special attention to the hypothetical character in the
three propositions (ol 5<a Tpiwv inroOeTinol). Thus, if A is, B is ; if B is,
T is ; therefore if A is, r is. He and Eudemus, however, admitted as
hypothetical reasonings those with a categorical minor, and through
them these forms have come into Logic. Theophrastus laboured, as
504 INSTITUTES OF LOGIC.
other logicians have done since, to reduce to or find parallels for the
hypothetical forms in the categoricals of the figures. There is neither
need nor use for the reduction of hypotheticals to the categorical form.
The essence of the hypothetical judgment is a statement of the rela-
tion of connection and dependence of predicate on subject. This can
be regulated directly by a law of thinking, — is as direct and cogent as
any categorical form. And every disjunctive judgment is immediately
regulated by the law of Excluded Middle.
§ 653. A Disjunctive Syllogism is a reasoning in which the
major premiss is a disjunctive proposition, and according to
the common doctrine, either of Contradiction or of Contrariety.
Thus, A is either B or not B ; A is either B or C or D. The
force of the disjunctive proposition is to state and exhaust a
totality, or total conception, so that while each of the con-
cepts constituting the totality is possibly predicable of the
subject, one or other of them is necessarily predicable. In
order to constitute a reasoning with such a proposition as a
major, we must have a minor premiss which is categorical.
This either (a) affirms one of the possible predicates, and thus
the conclusion will deny the other or others ; or (b) it denies
one or more of them, and thus the conclusion must determin-
ately affirm the other, or indeterminately affirm the others.
Thus, to take the first case — affirmative — or Modus ponens, or
Modus ponendo tollens, —
Conti'adictory Disjunction : —
(a) A is either B or not-B (i.e., C) ;
A is B;
Therefore it is not not-B (i.e., C).
The world is either eternal or non-eternal (i.e., had a beginning
in time) ;
The icorld had a beginning in time ;
Therefore it is not eternal.
(b) Modus tollens or tollendo ponens : — -
A is either B or not-B (i.e., C) ;
A is not B ;
Therefore A is not not-B (i.e., C).
A is either a slave or he is dead ;
A is not a slave ;
Therefore he is dead.
DISJUNCTIVE REASONINGS. 505
This tree is either deciduous or non-deciduous ;
It belongs to the non-deciduous ;
Therefore it is not a deciduous.
§ 654. This is the simplest or barest form of Disjunctive
Inference, and it ought to be noted regarding this and every
other form of it, that its essential feature lies in the actual or
assumed opposition among the possible predicates, — this being
the point upon which the whole force of the conclusion de-
pends. It is not enough to state a disjunctive proposition as
major premiss. This may give rise merely to a categorical
reasoning, according to treatment. Thus we may say : —
The men taken are either in a state of captivity or they are
dead ;
B was one of those taken ;
Therefore B is either a captive or dead.
The minor premiss makes no reference to the mutual ex-
clusion or opposition of the possible predicates ; the conclu-
sion, therefore, does not turn on this ; and the reasoning is
thus simply a categorical one with an indeterminate predicate.
As the form of a disjunctive lies in the statement of an alter-
native, the conclusion from it must turn on the alternative
exclusion.
§ 655. The principle which regulates disjunctive reasoning
is the law of Excluded Middle, or that which provides that
between two contradictory extremes there is no third conceiv-
able ; and consequently, if the one be posited, the other is
negated, and if the one be negated, the other is posited.
This applies obviously, in the first place, to simple disjunc-
tion, or the opposition of two contradictory terms, whether
these be positive and negative, or two positives — as B and
not-B, or B and C. This law will be found to apply even to
the more complex case in which there are more than two
opposing predicates — as A is either B or C or D. This is in
reality a complex disjunctive proposition. When analysed it
means —
(a) A is either B or not B (i.e., C or D);
(b) A is either C or not C (i.e., B or D) ;
(c) A is either D or not D (i.e., either B or C).
In a concrete example —
506 INSTITUTES OF LOGIC.
A is either a lime, a plane, or an elm.
This means —
(a) A is either a lime or not (i.e., a plane or elm).
(b) A is either a plane or not (i.e., a lime or elm).
(c) A is either an elm or not (i.e., a lime or a plane).
Or—
The world is either eternal, or the work of intelligence, or the
work of chance.
This means —
(a) The world is either eternal or non- eternal.
(b) The non-eternal (i.e., what commences) is either the work
of the intelligent or the non-intelligent (i.e., chance).
The same analysis applies to the form, either A is B, or C
is D. The one cannot coexist with the other, or be thought
as coexisting.
§ 656. In those cases in which we have only two disjunct
members, it may be questioned whether, when the minor pre-
miss is negative, there is properly a mediate reasoning at all.
When we say —
This tree is either deciduous or non-deciduous,
and then say it is non-deciduous, or belongs to the class of
non-deciduous, we have said it is not a deciduous tree, in other
words. There is really no progress to a conclusion here, but
simply a statement in a positive form of what we have stated
in a negative way. So equally when the minor premiss is
affirmative, as —
This tree is either deciduous or non-deciduous ;
It is deciduous.
This implies that it is not non- deciduous ; but to state this in
the form of a third proposition is really no advance in thought
on the minor premiss, but simply putting the minor itself in
other words. Such reasonings may fairly be regarded as forms
of Immediate Inference. The term and its contradictory op-
posite may be regarded, not as two terms, but as two aspects
of the same notion.
§ 657. In cases where the opposing predicates are more
RULES OF DISJUNCTIVES. 507
than two, we have Contrary Disjunction — in other words, we
have predicates generally of the same class opposed on the
ground of subordinate differences. Thus : A is either B or O
or D. The colour is either blue, or red, or yellow. The tree is
either maple, or ash, or birch.
Here the forms are as follow. In the modus ponens we
have —
(a) A is either B or C or D ;
A is B ;
Therefore A is neither 0 nor D.
(b) A is either B or G or D ;
A is either B or C ;
Therefore it is not D.
This rock is either sedimentary, or organic, or igneous ;
It is sedimentary ;
Therefore it is neither organic nor igneous.
In the modus tollens we have —
(a) A is either B or C or D ;
A is not B ;
Therefore A is either C or D.
Or—
(b) A is either B or C or D ;
A is neither B nor C ;
Therefore A is D.
Sedimentary rock consists either of gravel, sand, or mud ;
This sedimentary rock does not consist of gravel ;
Therefore it consists either of sand or mud.
§ 658. The rules usually given for the Disjunctive Syllo-
gism are: (1.) It must have three terms and three proposi-
tions. (2.) The major is always uniform, being universal
and affirmative. (3.) The minor premiss may be of any form,
— that is, universal or particular, affirmative or negative.
(4.) The conclusion follows the minor in quantity, and is
opposed to it in quality.1
1 Cf. Esser, Logik, § 95 ; Krug, Logik, § 86 ; and Hamilton, Logic,' iii.
pp. 332, 333.
508 INSTITUTES OF LOGIC.
(a) Mark Duncan, in this case not showing his usual precision and grasp
of principle, holds that the modus ponens or the position of the one
part to the sublation of the other fails, or is inadmissible in Disjunc-
tive Reasoning. In this he has been followed by other logicians, —
among whom we are to reckon substantially Mill and Jevons — the
latter at least in principle. Duncan's ground, moreover, is exactly the
ground adopted by those following him. It is this, that there are dis-
junctions which are not exclusive. Thus, the highwayman lies in wait
either for your life or for your purse. Upright conduct secures for a
man either the esteem of his fellow-men or the favour of Deity. Posit the
one of these, it is said, and you do not therefore deny or sublate the
other. Of course not. As a matter of fact, the highwayman will not
scruple, in certain circumstances, to take both life and purse ; and the
esteem of men is quite compatible with the favour of Deity. But
what then ? All that can be said is, there is a blunder in stating such
things as alternatives. The whole presupposition of Disjunctive Rea-
soning is alternation, — the opposition of alternatives. It does not say
that anything any one chooses to say is opposed, is actually opposed.
With this it has nothing whatever to do. What it says is, that if you
give certain alternatives, — certain opposites, — you can deal with them,
— you must deal with them according to the laws of Excluded Middle.
It would be just as reasonable to object to the law regulating Categori-
cal Inference, that you might put as a whole or genus that which is
not so, and so wrongly include something under it as a species, or
make a mistake about a certain genus and species.
(b) Mill has a remarkable criticism of the disjunctive proposition
and reasoning. He says gravely, " X is either a man or brute is not a
judgment founded on the principle of Excluded Middle, since brute is
not a bare negation of man, but includes the positive attribute of being
an animal, which X may possibly not be." So far as the logician is
concerned, — so far as the Principle of Excluded Middle is concerned,
— nothing is known or can be known of X beyond what is stated or
given in the proposition. This is, that X either has the qualities of
man, which are more than those of brute, or the qualities of brute,
which are less than those of man. X is one or other, not both, — that
is all that is stated or known about X — all that is given in the propo-
sition ; and Logic as a science can take cognisance of nothing more. It
knows nothing of possibilities, — especially possibilities retained in the
mind. Nor can any one with a correct insight into what inference
implies go beyond this. The terms here are given as materially and
formally opposed, and that is the whole point at issue. Let X possibly
not be animalr what then ? What has that to do with the logical
exclusion of the terms man and brute ? It only means that we have
blundered in regard to our subject, but not in regard to the exclusion.
If X is possibly, to begin with, not an animal at all, it was folly to
include him in either of two classes, man or brute, each of which
implies animal. The fault here is a material or extra-logical one.
But once X is included, or better thought as included, — for there lies
the confusion of Mill and others, — in either the one or the other, the
HYPOTHETICO-DISJUNCTIVE. 509
term must be dealt with as belonging either to the one or the other,
and this is all that logical law professes to do.
Again, Mill gives us the following : —
Every son of A is either B or C or D ;
But a son of A is dead ;
Therefore either B or C or D is dead.
The major proposition here, we are told, does not rest on the law of
Excluded Middle, or on any necessity of thought, but on my know-
ledge of the fact. Did Mill really for a moment suppose that any
one with common intelligence of the sphere of the Law of Excluded
Middle ever imagined that the law informed him of this fact or any
fact? At the same time, once the logician is furnished with this major,
— that every son of A is either B or C or D, — the law of Identity
will tell him, that every absolutely precludes more sons than those
specified, — that every cannot be interchanged with more than those
specified. And on the strength of this Law and that of Excluded
Middle, I am able to conclude that the dead son must be either B, 0,
or D, — for if these were not thought as exhaustive, and as thus limit-
ing the inference within them, — if there might be more, — the dead son
need not be either B, C, or D, but possibly E.
But we are immediately told by Mill that the judgment, every animal
is either a man or a brute, is founded on the Law of Excluded Middle.
Such a judgment is not in any proper sense " founded " on this law ;
the law simply regulates the mutual exclusion of the terms. The true
form of this judgment is, — every animal is either a man or not a man.
That is all that the law says or can say. It does not enable us to
identify not-man and brute. We must have the further knowledge,
through comparison of the features of man and brute, that brute can be
identified with what is not-man. The principle of Excluded Middle is
here simply the scheme or form under which the otherwise known
opposition of man and brute becomes logically available. Having found
these, or having been given them, as opposed, we state the opposition
in virtue of, or as a case of, the law of Exclusion between opposites.
§ 659. There is still a third form of Syllogism, which results
from a major proposition which is at once hypothetical and
disjunctive. Thus : — If A is, then either B or 0 is. Here the
relation of the antecedent to the consequent is not affirmed
directly, but only through mutually exclusive predicates.
The reasoning then proceeds to sublate or remove the entire
consequent : —
If A is, then either B or C is ;
But neither B nor G is ;
Therefore A is not.
We have now what is known as the Hypothetico-Disjunc-
510 INSTITUTES OF LOGIC.
tive Syllogism, or the Dilemma, called also Cornutus or
Horned Syllogism.1 It is called horned, because in the sump-
tion the disjunctive members of the consequent are opposed
like horns to the assertion of the adversary. With these we
throw it from one side to the other in the subsumption, in
order to toss it altogether away in the conclusion.2
§ 660. Krug gives the following cautions regarding the
legitimacy of the Dilemma, and they are well deserving of
consideration. In sifting a dilemma, we ought to ask —
(1.) Whether a veritable consequence subsists between the
antecedent and consequent of the sumption ?
(2.) Whether the opposition in the consequent is thorough-
going and valid?
(3.) Whether in the subsumption the disjunctive members
are legitimately sublated?3
Krug gives the following example which violates those con-
ditions : —
If virtue were a habit worth acquiring, it must ensure either
power, or wealth, or honour, or pleasure ;
But virtue ensures none of these ;
Therefore virtue is not a habit worth acquiring.*
Ueberweg borrows from Krug the following, which he char-
acterises as " a scientifically justifiable trilemma " : —
If the actually existing world were not the best of all possible
worlds, then God did not either know the best, or could not create
and preserve it, or did not wish to create or preserve it. But
{because of the divine wisdom, omnipotence, and goodness) neither
the first, second, nor third is true. Hence the actual world is
the best of all possible worlds.5
§ 661. The older view of logicians regarding the Dilemma
takes in more than this form. It was recognised by Hamilton
as a reasoning having a conditional major premiss with several
antecedents, and a disjunctive minor. This is the view,
among others, of Whately and Mansel. Dilemma would
properly indicate two antecedents, but it is used to include
1 Cf. Hamilton, Logic, iii. p. 350.
2 Krug, Logik, § 85 ; Hamilton, Logic, iii. p. 352.
3 Logik, § 87.
4 Cf. Hamilton, Logic, iii. pp. 352, 353.
6 See Krug, Logik, § 87 ; Ueberweg, Logic, p. 459.
t
DILEMMA. 511
more than two — and in this case may properly be Trilemma,
Tetralemma, Polylemma.
§ 662. Its forms are as follow, and they are regulated by
the combined laws of Hypothetical and Disjunctive Season-
ing :—
I. Simple Constructive.
If A is B, C is D, and if X is Y, C is D ;
But either A is B, or X is Y ;
Therefore C is D.
Here the common consequent is inferred.
II. Complex Constructive.
If A is B, C is D, and if X is Y, E is F;
But either A is B, or X is Y;
Therefore either C is D, or E is F.
The point of these two forms is, that whatever alternative
be chosen, the same conclusion is inevitable.
III. Destructive.
If A is B, C is D, and if X is Y, E is F;
But either C is not D, or E is not F ;
Therefore either A is not B, or X is not Y.
512
CHAPTER XXXVIII.
FALLACIES —FORMAL AND MATERIAL. (1.) FORMAL FALLACIES.
§ 663. Fallacy, in the widest sense of the term, includes
every form of reasoning, or apparent reasoning, which leads
to a conclusion either invalid, or such as ought not to be
accepted, because of a fault in one or both of the premisses.
A reasoning may be bad (1.) because the conclusion does not
follow from the premisses ; (2.) because the premiss or pre-
misses are false in point of fact, or unduly assumed ; (3.)
because the conclusion is not the proof of the point which
it is adduced to prove, or which the reasoner professes to
prove.
§ 664. A fallacy is regarded either as a Paralogism or a
Sophism, — the former when the person reasoning is in error,
either as to premiss or conclusion, and is at the same time
unaware of it ; the latter, when a reasoning, bad either in
matter or form, or in both, is employed with a full conscious-
ness of it on the part of the writer or speaker, and thus with
the purpose of deceiving. This, of course, is of no logical
importance. What the science of Logic professes to do is
to deal with the essential character of the reasoning itself,
— so far as its rules can reach it.
§ 665. Aristotle divides fallacies into two classes — viz.,
those irapb. rrjv \e£w and c£w rrjs Ai^etos, or, as it was after-
wards put, in dictione et extra dictionem — in the expression and
beyond it. Under the first head — in Dictione — he classes six
fallacies — viz. (1.) ofxiaw^ia [equivocation) ; (2.) d/x,<£i/3oA.ia {am-
biguity) ; (3.) crw0eo-is (fallacia a sensu diviso ad sensum com-
DIVISION OF FALLACIES. 513
positum) ; (4.) Staipecrts (fallacia a sensu composite ad sensum
divisum) ; (5.) 7rpoo-a)Sta (accent)) (6.) o-x^fia rrjs Ac'^cws (figura
dictionis).
§ 666. Under the second head — extra Dictionem — he has
seven classes : (1.) irapa to o-v//./3e/&7Kos (fallacia ratiocinationis
ex accidente) ; (2.) to on-Aw? ^ /x.^ an-Aws (« dicto simpliciter ad
dictum secundum quid) ; (3.) yj tov iXeyxpv ayvota (ignoratio
elenchi) ; (4.) 7rapa to €7to/acvov (fallacia ratiocinationis ex
consequente ad antecedens) ; (5.) to cv apxi? Aajn/Javeiv cutcict^cu
(petitio principii) 5 (6.) to /at) amov ws aiTiov rtOevai (fallacia
de non causa ut causa) ; (7.) to Ta 7rAct'cj (.puyrrjfxaTa ev ttouiv
(fallacia plurium interrogationum).1
§ 667. Aristotle has thus really anticipated all the forms
of fallacy which have been dealt with by subsequent logicians.
But the division into in Dictione et extra Dictionem is not
satisfactory or well founded. The class, in Dictione, may pro-
perly be referred to fallacies in the inference, — to cases, in
fact, in which the conclusion does not follow from the pre-
misses,— that is, Formal Fallacies.
§ 668. Those under the second head, extra Dictionem, may
as a rule be referred either to the class of formal fallacies,
or to that of Material Fallacies, in which the conclusion, while
following from the premisses, is based on false or irrelevant
premisses. This will appear as we proceed.
§ 669. There is, properly speaking, no specific class of the
fallacies of language (in Dictione). Language may doubtless
give rise to incorrect or invalid inference, but it does so
because it leads to a violation of formal or logical law, —
chiefly, in fact, to the making use of four instead of three
terms in a reasoning. This is known as quaternio terminorum,
or the logical quadruped. This is most commonly manifested
in what is known as Ambiguous Middle ; in other words, in
the use of a term which indicates more than one notion, and
which is taken in a double sense in the reasoning. For the
ambiguity of a word does not necessarily lead to invalidity of
inference, unless in so far as the ambiguity is made use of in
the reasoning process.
§ 670. The only sound division of Fallacies accordingly
is into — (1.) those in which the fault is in the reasoning
process itself, — in other words, those in which the conclusion
1 Top. viii. 11 ; De Soph. Elench., § i., c. iv. v.
2 K
514 INSTITUTES OF LOGIC.
does not follow from the premisses ; and (2.) those in which,
while the conclusion is justly drawn, one or more of the prem-
isses is incorrect, in point of fact, unduly assumed, or such
as, while professedly meeting the point at issue, really do not,
and only yield a conclusion irrelevant to the question pro-
posed. Thus there emerge only two grand kinds of Fallacies
— those in the Form and those in the Matter of the reasoning.
§ 671. It should be noted generally regarding fallacies,
that several of them have a tendency to run into each other,
and that a so-called reasoning may be fallacious in more than
one way. It is enough, however, if a bad reasoning can be
fairly referred to one class or species of fallacy. All that can be
aimed at in the classification of fallacies is to make the classes
as exact as possible, — to specify their discriminating feature,
and to show generally how the particular fallacy is to be
avoided. And this classification at present must be based
on the logical point of view. The sources of fallacy and of
sophism, lying in natural tendencies and in surrounding
circumstances — in the intelligence, and in the moral and
imaginative nature of man, in impulses and preconceptions
— form quite an independent sphere of inquiry. This was
sketched in general, and, at the same time, grand outline by
Bacon in his well-known Idola:1 "A complete history of
sophism," says a French writer, "would be the political history
of mankind."
§ 672. Under the first head — the class of Formal Fallacy
— we have the following : —
(1.) Those which violate the essential principle of the con-
stitution of syllogism, as involving more than three terms.
(2.) Those which proceed on the non-distribution of the
middle term — that is, on its particular distribution in each
premiss.
(3.) Those that proceed on the universal distribution or
quantification of major or minor term in the conclusion, while
it was not taken universally in the premisses.
(4.) Those which proceed to an affirmative conclusion,
while one premiss is negative.
(5.) Those which proceed on a so-called reasoning, in which
neither premiss is affirmative.
(6.) (In Hypothetical Keasonings.) Those which proceed
1 See Novum- Organum, Book I. aph. xxxviii. et seq.
FOKMAL FALLACIES. 515
from the denial of the antecedent to the denial of the con-
sequent.
(7.) Those which proceed from the affirmation of the con-
sequent to the affirmation of the antecedent.
These exhaust the possibilities of formal error in Mediate
Inference. There are other possibilities of error in Immediate
Inference, as in Conversion, Opposition, Integration, Restric-
tion ; but these have already been provided for in the rules
laid down regarding them.1
§ 673. (1.) To the first of those heads — the quaternio ter-
minorum — may be referred all the cases of what is known as
Ambiguous Middle. Here we have really two middle terms
whose difference is cloaked under some accident of expres-
sion ; and thus, as we have a different concept in each of the
premisses, the extremes of the conclusion have not been com-
pared with the same third. Whately regards Ambiguous
Middle as a semilogical fallacy — that is, partly in the matter
(or expression), and partly in the form. It is essentially the
latter — a formal fallacy, for it misleads only through its in-
formality.
§ 674. Fallacies whose invalidity arises from ambiguity
in terms, and the formal vice of which is a quaternio termino-
rum, may be classed as follows : —
(1.) Homonymia, or Equivocation.
(2.) Prosodia, or Accent.
(3.) Amphiboly.
(4.) Figura Dictionis, including Paronymous Words, Etymol-
ogy, Figurative and Direct Sense.
(5) Composition and Division, including the fallacy of In-
terrogation.
(6.) Fallacia a dicto secundum quid ad dictum simpliciter;
and the converse, A dicto simpliciter ad dictum secundum quid.
§ 675. Those kinds of fallacies may be found in any term
of a reasoning ; but as a rule they are cases of what is known
as Ambiguous Middle, — the middle term being that upon
which the conclusion essentially depends. In the case where
a premiss is not false, or unduly assumed, and where the con-
clusion is not invalidly drawn from the premisses, the fault
will usually be found in the double sense of the Middle Term.
There we ought to look for it.
1 See above, chapters xxvii. and xxviii.
516 INSTITUTES OF LOGIC.
§ 676. It is obvious that if the middle term in a reasoning
be ambiguous, or equivocal — i.e., capable of being taken in
either of two senses — our reasoning is likely to be utterly-
futile. And no form of fallacy is more common and more
difficult to detect than this, especially when the two prem-
isses containing the middle term stand far apart from each
other.
Thus, for example, the word expedient may be used as
meaning conducive to the greatest good, or conducive to temporary
prosperity. I may argue that a particular course of conduct
is expedient, by showing simply that I should by it secure
a temporary object which I have in view. There would be
no harm in my thus arguing, and thus acting even. But
if I attempted further to vindicate my conduct by saying that
it was expedient in the other or higher sense of being conduc-
ive to the greatest good — in fact, being absolutely useful and
right — I should be guilty of identifying the two senses of
the word, and substituting for the lower sense of the term
the higher one, which I had not vindicated, or shown to be the
sense in which my action was originally understood. This
would be a case of Ambiguous Middle, in which I took a
term in one sense in the one premiss, and in a different,
even it might be conflicting, sense in the other.
As a simple instance of Ambiguous Middle, take the fol-
lowing : —
Cicero's style entitled him to rank in the highest class ;
So did the style of Beau Brummell ;
Therefore Cicero and Beau Brummell both rank in the highest
class.
The Middle Term here is, of course, style ; but the style of
the one referred to the turn of his sentences, that of the
other to the fashion of his garments.
On a par with this is such a so-called reasoning as the
following : —
This side of the river is different from the other side ;
But the other side is a this side as well (say to the man opposite
to me) ;
Therefore this side and the other side (that is, the different sides)
are the same.
§ 677. The most common type of ambiguity in the Middle
FORMAL FALLACIES. 517
Term is when it appears to be one, but in point of fact is not.
In the major premiss, it may be coupled with a condition ;
in the minor, it may be taken singly. Of this sort is the old
fallacy called the Horned (Cornutus, Kepartv-rj). As —
He who has not lost a thing, has it;
You have not lost horns ;
Therefore you have them.
Here the major refers only to what was actually in pos-
session.
This is the key to the solution of many sophisms, as Aris-
totle shows in the De Sophisticis Elenchis.1
§ 678. The first form of ambiguity in terms is known as
Homonymia (6/xwi/v^ta), or Equivocation. This arises when a
term, taken by itself, has more than one signification, — that is,
denotes more than one concept, and is thus capable of being
taken in two different senses in the reasoning. Common
examples are light, meaning not heavy, and not dark ; and box,
meaning a tree, a chest, a blow.
As an example of fallacy arising from this source, we may
take this : —
The end of a thing is its perfection ;
Death is not the perfection of life ;
Therefore death is not the end of life.
End is here ambiguous ; it means final cause, or that for
the sake of which a thing is ; and it means termination. Hence
the seeming paradox in the conclusion.
Again, the various meanings of the term substance give rise
to fallacies of the same sort. Thus : — '■
Substance is not quantity ;
Body is substance;
Therefore body is not quantity.
Some of the examples given by the older logicians are
simply a play on words, or species of verbal pleasantry.
Thus :—
Every dog can bark;
Some star is a dog ;
Therefore some star can bark.
i Cf. Trendelenburg, El. Log., § 27.
518 INSTITUTES OF LOGIC.
§ 679. The term truth, from its various applications or
denotations, lends itself readily to the fallacy of Ambiguous
Middle. It may mean truth of fact, truth of consistency,
truth of possibility, as opposed to actuality, &c. Some
demonstrative systems of philosophy confuse the two first
mentioned meanings, and thus make consistency in think-
ing equivalent to harmony of thinking with experience. Des-
cartes, apparently, in his Criterion of Truth, — clearness and
distinction, — confounds the conditions of possible thinking
with the conditions of thinking a thing as it really is.
§ 680. Sensation, Impression, Reason, Idea, Individual, and
Individualistic, Subjective, Objective, and many of the terms in
Psychology, are peculiarly liable to ambiguous meaning and
application.
Sensation is constantly confounded with Perception, with-
out remark or explanation on the part of those using it.
And thus the whole controversy between Kealism and Ideal-
ism in Perception is obscured, and the point in many cases
begged from the beginning.
§ 681. Hume's use of the term impression is of the most
varied and misleading sort. It starts with an unproved
assumption, and it ends in confounding together mere sensa-
tion, apprehension, emotion, desire, and volition. Impression,
as he employs it, is of no valid use whatever as a middle term
in a reasoning.
§ 682. Reason is nearly equally misleading. It is used
for Understanding, Reasoning, Reason as source of principles,
what is called Pure Reason, and in a host of other ways.
Idea means almost anything, and therefore practically
nothing, in connection with knowledge. And the Idea, the
Universal, &c, as used for the bare form of knowledge, has
the worst possible suggestion of the separability of matter
and form, and the hypostatising of the latter as, first, a dis-
tinct entity, and then as all in all in the end.
Individualistic, as applied in these days to systems of phil-
osophy of the most opposite sort, has the vaguest and most
shifting of meanings.
Individual, individualism, or individualistic, may be em-
ployed in at least the following applications, which are
varied, and some of wThich are conflicting.
(1.) Individual may be used for singular and particidar.
AMBIGUITY IN TEEMS. 519
In the former case, it means this, that, one ; in the latter case,
it means some (at least). In the first meaning it is opposed to
the plurality of units in time ; in the second, to the univer-
sality of the concept. It is one of many, and some of all. This
is the logical ambiguity of the term.
(2.) Individualism in philosophy may mean that knowledge
is the impression or state of the consciousness of each indi-
vidual in the world; that, however different, these impressions
are equally true or the truth, simply because they are the im-
pressions of the individual. The truth, thus, for the individ-
ual in his youth may be wholly different from the truth for
the same individual in his prime ; and what is true for one,
may be false for another. This is in substance the Protagor-
ean Homo mensura.
(3.) Individualism may mean a series of sense impressions,
regarded simply as conscious states, and as forming the sense
experience of each individual, and even being all that is of
world reality.
(4.) Individualism may mean that, in the last resort in hu-
man thinking, the test of a principle or universal condition of
knowledge is the self-evidence and necessity which constrain
each individual to accept it as a principle or condition of our
knowledge. This constraint, as not peculiar to one individual
more than to another, would be a common or universal pro-
perty of all human thinkers ; such a theory would be quite
opposed to the Protagorean Homo mensura.
(5.) Again, it may be held that as man thinks only as
sharing or being a part of the consciousness of God, a philo-
sophy which repels this view is individualistic. A classifi-
cation of philosophies under this negative head would lead to
the most indiscriminate grouping which it is possible to
conceive.
(6.) Individualism may further mean the negation of Pan-
theism, or the assertion of finite reality in a sense which is
incompatible with Pantheism, understood as the doctrine of a
single consciousness pervading the world.
§ 683. Subjective and Objective admit of various meanings.
In contrast, the one marks the knower, the other the known.
The known may be regarded as (1.) that which is in relation
to the knower ; (2.) that which is independent, and subsists
per se ; (3.) that which transcends the known and definitely
520 INSTITUTES OF LOGIC.
knowable. Objective is, however, sometimes used for that
which is necessarily or universally connected in knowledge.
This may, after all, be but a series of sensations, and there-
fore wholly subjective as to matter, and even form.
To these may be added such phrases as the government, the
church, experience, wealth, &c. Definition, consistently held
by, is the only remedy for ambiguous terms.
§ 684. The second form is Fallacy of Prosody, or Accent
(7T/30(T<J)8(!a).
This arises when the same word, having different significa-
tions, receives its meaning from the mode of pronunciation.
Words vary in meaning according to accent proper, quantity
of syllable, spiritus lenis et asper, &c. Accentuation may
either remove or cause ambiguity.
The same word or phrase may be so pronounced, accent-
uated, or emphasised as to convey one of two wholly distinct
meanings. And if the term or phrase be a quotation, it may,
by the accent or mode of pronunciation which accompanies
it, be made to convey a meaning wholly different from that
originally intended. What was ironically said, or said in
joke, may thus be made to appear as if it were seriously
spoken, and conversely. In quotation, by the introduction of
italics, as has been remarked, we may wholly change the
scope of a statement.
§ 685. The third form of ambiguity is Amphiboly. This
is a double meaning in or through the structure of the sen-
tence, or somehow from the context, while the words them-
selves may have but one definite signification. It depends,
in fact, frequently, on that fault in syntactical construction
through which a word or expression may be connected either
with what goes before or with what follows it. Thus : — Qui
scit literas hodie didicit. This may mean either qui scit
liter as hodie, didicit, or qui scit literas, hodie eas didicit.1
I have made thee free a slave.
Then there is the well-known line, which has come down in
nearly all logical compends : —
Aio te, JEacida, Romanos vincere posse.
(Pyrrhus the Romans shall I say subdue.)
1 Given by Duncan as an example of the Fallacy of Division, but better as
Amphiboly.
FIGUEA DICTIONIS. 521
And we may add : —
TTiVTTjKOVT OLvBp(x)V eKClTOV XlTTC SlOS 'A^tXXfUS.
But as Achilles could not out of fifty men leave a hundred,
we must suppose that out of a hundred he left fifty.
§ 686. The fourth form is Figura Dictionis (ar^rjfjLa ttjs Xe£ea>s).
Aristotle describes this as taking place when that which is
not the same thing is expressed in the same way, as masculine
taken for feminine, or feminine for masculine, or neuter for
either, or action for suffering. Thus, because to burn and to
cut are actions, we may suppose that to rest, to be well, &c,
are also actions.
More important forms of this fallacy arise when, under the
same word, different categories, or kinds of categories, are con-
founded. Thus : —
What is snow, that is not milk;
But snow is white;
Therefore milk is not white.
Here the reference in the what (quod) is to snow as a sub-
stance or distinct object, while the conclusion refers to
quality. So : —
Qui heri eras idem hodie es;
At qui heri eras sanus ;
Ergo hodie sanus es.1
§ 687. To this may fairly be referred the commonplace
fallacy usually classed under the head of Fallacia ex Acci-
dente : —
What is bought in the market is eaten ;
Raw meat is bought in the market ;
Therefore raw meat is eaten.
Raw meat is not properly an answer to what, but to what
sort of meat.
§ 688. Under this head may, also, be included the fallacy
known as that of Paronymous or Conjugate Terms.
Paronymous terms are terms derived from the same root.
They may be substantive, adjective, or verb. Thus we have
presume and presumption, project and projector, assume and as-
sumption, expedient (noun), expedient (adjective), expediency
1 Top., i. iv. ; Duncan, Inst. Log., L. v. c. vii.
522 INSTITUTES OF LOGIC.
(noun). Each of these sets of words is from the same root.
But they have not necessarily the same or a synonymous
meaning. If we employ them in a reasoning as if they had,
we shall probably draw a false conclusion. To take a common
example : —
Projectors are not to be trusted ;
This man has formed a project ;
. • . He is not to be trusted.
In this case the ambiguity lies in the middle term, and it
leads us wholly wrong. So with assume, assumption, and
assumptive. We may innocently assume a thing to be true ;
we may be guilty of assumption in our conduct. These are
paronymous terms, but they are not synonymous.
§ 689. To the Figura Dictionis may be referred the Fallacy
of Etymology. This arises when it is supposed that, because
of the original meaning of a word being such an one, it must
necessarily retain that meaning through all subsequent usage,
or that this meaning is to override or supersede an acquired,
and, it may be, extended or purified signification. Most of
the words in the science of mind had originally a material
reference. And in this instance the fallacy would consist in
assuming or maintaining that such words have thus neces-
sarily no wider or higher reference.
We have illustrations of the fallacy of Etymology in such
cases as right, truth, &c. As right is from rectus, and this from
rego to rule, it has been inferred that all right is a creation of
the law. There is here as gross a hiatus in the proof as can
well be conceived. So with truth. As this comes from trow,
to believe, it has been inferred that truth can only mean what
each believes, or individual opinion, — the Protagorean Homo
Mensura. Spiritus, animus, anima, ave/Aos, signifying originally
breath and air, are not to be held as only signifying these.
Comprehension, Conception, meaning originally a grasping or
holding several sensible things, as one or in one, are not
on that account to be limited merely to sensible objects or
singulars. In all these cases there is a hiatus which virtually
begs the question regarding the present meaning of the word.
§ 690. To the Figura Dictionis may be referred the fallacy
arising from a change of the Figurative to the Direct Sense —
thus : —
COMPOSITION AND DIVISION. 523
The mind sees ;
Seeing is an organic act ;
Therefore the mind in seeing puts forth an organic act.1
§ 691. The fifth form includes the fallacies from Composition
and Division. Fallacia a sensu diviso ad sensum compositum,
and A sensu composito ad sensum divisum.
(1.) The fallacy of Composition (o-wflecm) arises from the
conjunction of the separate. Here the composite meaning is
false, while the divided is true.
(2.) The fallacy of Division (Siaipco-is) arises from the separ-
ation of the conjoint. Here the composite meaning is true,
and the divided false.
In other words, the fallacy of Composition arises when we
first of all take a term distributively, and then argue from it as
if it had been taken collectively. Thus, in numbers, we may
say 6 and 5 are even and odd (taken distributively) ; 11 is 6
and 5, therefore 11 is even and odd. The fallacy lies in the
Composition.
Again, if we take a term collectively, and argue as if it had
been taken distributively, we have the fallacy of Division.
By distributively, we mean each of several things, and in
speaking of them we predicate of each. By collectively, we
mean the whole of several things, and in speaking of them we
predicate of the whole. This ambiguity comes out in the
word all. All may mean every one, or it may mean the whole;
and these are two very different things indeed. We may say,
all prudent men are thoughtful. Here we mean to predicate
thoughtfulness of every one of them taken singly. When we
say all these fish weigh 100 pounds, we do not express ourselves
unambiguously, but we would naturally be taken to mean
not every one, but the whole taken together. If we argue
from all meaning every one, as if it meant the whole, we should
have the fallacy of Composition ; if from all meaning the
whole, to all meaning every one, we should have the fallacy
of Division.
Examples : Fallacy of Composition. Thus we may say : —
This man is good, and a workman /
Therefore he is a good workman.
1 Cf. Reiffenberg, Logique, p. 69.
524 INSTITUTES OF LOGIC.
One of the learned men at the table of the Emperor
Conrad III. asked him one day — " Have you an eye .?" " Yes,
certainly," said the Emperor. "Have you two?" "As-
suredly," was the reply. " But one and two make three ; you
have, therefore, three eyes." The Emperor was puzzled, but
did not believe the Scholastic.
Examples : Fallacy of Division : —
This man is a good workman;
Therefore he is good, or a good man.
Or—
The planets are eigM ;
But the Earth and Mars are planets ;
Therefore the Earth and Mars are eight.
§ 692. The Fallacy of Interrogation, Fallacia plurium Inter-
rogationum, may be fairly referred to the head of Fallacy from
Division. Here we ask several questions in a way which
makes them appear to be but one. In giving our assent to
the question, we probably mean to assent but to one of the
questions really involved, but it may be taken as an assent
to another of the concealed questions, to which we should
probably demur. Our assent to the one may, then, be taken
as an assent to another wholly different, or to each involved ;
and on this assumption a reasoning is founded.
Perhaps the commonest form of the fallacy is that kind of
question which assumes or implies a thing to be true by
asking about the time or manner of it. How long is it since
you ceased to be temperate f When did you leave off stealing f
How did you contrive to effect your escape ? Who is the man on
the wall ?
Another form is that of asking the cause of a fact, before
the fact itself is ascertained to be real.
Commonly, several different qualities are grouped in the
interrogation. Was not Cicero an excellent citizen, orator,
poet, and soldier f If the answer be in the affirmative, the
quality which he did not possess might be seized upon as
that which was admitted. The obvious solution is an analysis
of the composite question into its parts, and separate reply
to each.
§ 693. Fallacia a dicto secundum quid ad dictum simpliciter;
and the converse — A dicto simpliciter ad dictum secundum quid.
A DICTO SECUNDUM QUID. 525
(1.) The first form arises when we take what is pre-
dicated with restriction as true absolutely, or make what is
said only generally to be true universally. A statement is
true in some respects, with certain qualification ; it is taken
as true absolutely. Thus it may be true that, in the case of
sleeplessness, to take an opiate is desirable ; but it does not
follow that taking an opiate, as a general rule, or even in all
cases of sleeplessness, is a good thing. So a war in self-
defence, or to protect the oppressed, may be proper ; but war
itself, or as a general condition, is not therefore desirable or
proper. The fallacy is prompted by the common tendency
to hasty generalisation.
If the principle of this fallacy were admitted, we might
argue that because the negro has white teeth, he is white ;
or that bullion ought to be thrown into the sea, because it
ought to be thrown into the sea to avoid shipwreck.
We should be guilty of this fallacy if we passed from the
proposition that non-being is conceivable, to this, that non-being
is. Or if we said, being is not really, because it is not one of the
things which are, for example, not man; for not to be this
or that thing, and not to be absolutely, are by no means
identical.1
To this may be referred the old fallacy, or joke, known as
the masqued (eyKCKoAt^/Aeyos) attributed to Diodorus (Cronos),
of the School of Megara. A man in a mask is introduced. It
is asked, Do you know him f No. This man is your father;
therefore, you don't know your father.
; § 694. To this head may be fairly enough referred the Fal-
lacia ex Accidente.
This arises when it is supposed that, because there may
be various accidents in a subject, all these accidents are in
the attributes of the subject, or in the subject itself. Thus,
taking Aristotle's negative illustration : —
Coriscus is other than Socrates ;
Socrates is a man ;
Therefore Coriscus is not a man.
Here we are speaking of the individual Socrates, or of
Socrates in what distinguishes him from other men, and,
therefore, man as not distinctive is not an essential, but, so to
1 Top., i. v.
526 INSTITUTES OF LOGIC.
speak, in this reference, an accidental mark of the individual.
We here affirm of the accident what is true only of the sub-
ject.1 This fallacy is properly a reasoning from the unessen-
tial to the essential. It consists in attributing to a thing
as constitutive and constant, that which belongs to it only
accidentally or temporarily, yet does not follow from its nature.
" An isolated fact," says Marmontel, " rare and without con-
sequence, given as constant ; a passing or special abuse taken
for the state of things habitual and general, — there is the
means of revolutions."
§ 695. The converse — A dicto simpliciter ad dictum secun-
dum quid — arises when we take what is said or admitted
generally, or of the nature of the thing, as true or admitted
with unrestricted universality. Thus we may admit that
mountain-climbing is a pleasant and exhilarating exercise,
but it would be going beyond what we meant if we extended
the statement to all circumstances whatever, even in mist or
a snow-storm. A soft voice is no doubt agreeable, but not
necessarily at all times. We may sometimes even prefer the
silence that is said to be golden.
It may be a sound principle, that what has been intrusted
to you to keep should be returned to its owner on demand ;
but not a sword or a rifle, if the owner asks it in a state of
drunkenness, fury, or madness.
§ 696. All the fallacies now mentioned are to be solved by
distinguishing the double meaning of the ambiguous term.
This may be either major or minor ; usually it is the middle
term. When the distinction is made, the so-called reasoning
appears with four terms, and is thus invalid in its very con-
stitution.
§ 697. (2.) The second of the formal fallacies to be con-
sidered is that of Undistributed Middle. This is a viola-
tion of the rule which prescribes that the middle term in a
reasoning must be taken in its full extent (or distribution),
once at least "in the premisses. This law holds on every
theory of reasoning, — whether Aristotelic or other. There
must always be a common third, and the community is only
secured through distribution of the middle term. The ap-
parent exception in the case of Ultra-total Distribution has
already been dealt with, and its value estimated.2
1 De Soph. Elench. , i. v. 2 See above, p. 423 et seq.
UNDISTRIBUTED MIDDLE. 527
§ 698. A person may argue, or rather seem to argue, in this
way : —
Food is necessary to life •
Mutton is food ;
Therefore, mutton is necessary to life.
We know instinctively that there is something wrong in
this reasoning. But can we lay our finger on the fallacy, and
expose it on intelligible and assured grounds ? Not unless
we apply logical rule. Let us look at the propositions. We
say food is necessary to life. We mean by this, of course, food
in some form — some kind of food. Then we say — Mutton is
food — i.e., a kind of food, or a part of food. Now these two
statements do not warrant our conclusion that mutton is
necessary to life ; for this would be to imply that mutton only
is food, or is all food, whereas we have not said any such
thing. The middle term of the reasoning here is [some) food ;
it is taken in one part of its application in the major proposi-
tion ; in another part, not necessarily the same part, in the
other proposition. We have not, therefore, the same term
with which to compare the other two terms of the conclusion ;
and thus we cannot draw or prove our conclusion. This is
what is called the fallacy of Undistributed Middle. The
middle term is not taken in its full extent or application in
any one of the premisses, and, therefore, the major and minor
terms have not been compared with the same or a common
term. We have illustrations of the same fallacy in such an
apparent reasoning as this : —
Blue is a colour ;
Red is a colour ;
Therefore blue is red.
Here we speak in each proposition only of some portion of
the class colour ; but it does not follow that this is the same
portion in both cases ; therefore we cannot have a conclusion
at all. We might as well argue that because men and whales
are animals, all men are whales. They are both animals, no
doubt, but they belong to wholly different portions of the
class animal — i.e., the term with which they are compared is
not distributed ; they are not, therefore, compared with the
same thing, only with different portions of the same thing,
and there is, therefore, no inference.
528 INSTITUTES OF LOGIC.
§ 699. Cases of Undistributed Middle occur only in the
quantity of Extension.
Obviously a term distributed in a reasoning must remain
the same, as predicate or as subject of predication through
the reasoning. When I say —
All the stars have a movement;
All the stars are subject to the law of gravity ;
I speak of the same subject, and on these premisses I can
found an inference. When I say —
Some stars are luminous;
Some stars are subject to eclipse;
I do not know whether they are the same stars or not, and
therefore cannot found an inference.
This, then, refers to a term taken in Extension. A singular
term, or a term taken in Comprehension, is to be regarded
as distributed, or rather taken as an indivisible totality. In
Plato was pupil of Socrates, and Plato wrote the Republic,
there is reference to the same subject. So in the case of
abstract terms — that is, really terms taken in comprehen-
sion— as justice, virtue, courage, &c. Here we necessarily
speak of the whole, and therefore of the same.1
§ 700. (3.) The third case is that of fallacies which arise
from a violation of the rule that no term shall be taken in
the conclusion at a greater quantity or distribution than that
which was given to it in the premisses. Of this fallacy we
have two forms — (1.) If the predicate of the conclusion be
taken at more than its right, we have illicit process of the
Major Term. (2.) If the subject of the conclusion be so taken,
we have illicit process of the Minor Term.
§ 701. To take an example : —
Whoever is capable of deliberate crime is responsible ;
A lunatic is not capable of deliberate crime ;
Therefore a lunatic is not responsible.
Now you will perhaps not dispute the conclusion here that
a lunatic is not responsible. But the question is, does this
conclusion follow from the premisses which you have laid
down ? In other words, have you proved it ? You have not
in this case. This is about as bad a specimen of reasoning as
1 Cf. Delariviere, Nouv. Log., Classique, L. II., § ii. c. iii.
ILLICIT PROCESS, 529
could well be given. Yet it looks plausible enough. But
analyse it ; apply to it the rule of reasoning which has been
stated. Whatever is predicated, affirmatively or negatively, of a
term distributed, may be predicated in like manner of everything
contained under it. We predicate, then, in our apparent
reasoning, responsible of every one capable of deliberate crime.
So far good. But then we merely say that a lunatic does not
belong to the class that is capable of deliberate crime. We
have no right, therefore, to infer from this that a lunatic is not
responsible ; for, for aught we have said, responsibility may
be wider than those capable of deliberate crime. Having
affirmed responsibility of a class of people, we have no right,
on that ground, to deny it of a person or persons who do not
belong to that class. The fault here lies in taking one of the
terms — viz., the major, responsible — in a particular or limited
application only in the major premiss, while in the conclusion
you take it universally or in the whole, of its application.
This is called, technically, illicit process of the major term.
§ 702. Again :—
Stories of massacre related of the Russians are shown to be false ;
Stories of massacre related of the Turks are shown to be false ;
Therefore all stories of massacre related of either are false.
Now this conclusion says that all stories of massacre re-
lated either of Bussians or Turks are false. But it is a bad
conclusion ; for in each of the premisses we have spoken only
of some stories of massacre related of both, and we have no
right, therefrom, to include that all the stories of massacre
related of them are untrue. This is what is called illicit
process of the Minor Term. We take the minor term particu-
larly in the premisses — i.e., we take but a part of it — and in
the conclusion we make an assertion regarding the whole
of it.
§ 703. There is more chance of our falling into the mistake
of Illicit Brocess of the Major than of the Minor Term. In
ordinary reasoning, and in ordinary syllogistic form, we are
not careful to express the precise quantity of the predicate,
as usually particular in affirmative propositions. When we
say — All Y is X, we usually mean some X, but we do not say
so. It is enough if Y be some X for our affirmation. But in
drawing our inference this point requires attention. We may
2 L
530 INSTITUTES OF LOGIC.
readily be led to suppose that we spoke of all the X's as well
as of all the F's. In this case we should go wrong. We may
say:—
Every animal lives ;
A plant is not an animal ;
Therefore no plant lives.
In the major premiss we really mean to say that every
animal is some living thing, but not being careful enough to
express this, we find ourselves landed in the conclusion that
plant is not any living thing. As to the subject we are usually
on our guard, and we generally know whether we are speak-
ing of all or some ; hence we do not so readily fall into the
error of taking the subject of the conclusion at a greater
quantity than that which we have assigned to it in the
premisses.
§ 704. (4.) The fourth fallacy in form, is, when we proceed
to an affirmative conclusion, while one premiss is negative.
This arises from a violation of the fundamental law of
syllogism, already explained.
§ 705. (5.) The fifth form of bad reasoning arises when we
proceed to any conclusion whatever, while neither premiss is
affirmative. This fallacy also arises from a violation of a
fundamental law.1
This form may be typified thus : —
A cat is not a biped ;
A dog is not a biped.
Therefore, you can say nothing either about dogs or cats.
Cannot you say, in this case, that dogs and cats agree in not
being biped ? Well, if you choose to think this worthy of the
name of inference, you may. Can you say that bipeds are
neither dogs nor cats ? No ; because you have not asserted
that bipeds even exist. You have only said that the notion
of a dog and the notion of a cat do not harmonise with the
notion of a biped. But whether there are really cats or dogs
you have not said, far less whether there are bipeds. From
negative premisses you can infer nothing ; for the simple
reason that you have not affirmed the agreement of any one
of the supposed terms of the conclusion with a middle term.
i See above, pp. 388, 390.
HYPOTHETICAL FALLACIES. 531
And the conclusion is always the assertion — the necessary
assertion of a relation between terms.
§ 706. (6.) In Hypothetical Eeasonings, those which pro-
ceed on the denial of the antecedent to the denial of the con-
sequent. The principle of this fallacy has been already
explained. Thus : —
If this thing be sentient, it is living ;
But it is not sentient ;
Therefore it is not living.
This is equivalent to the fallacy in Categoricals, known as
Illicit Process of the major term. Thus : —
All sentient is {some) living ;
This thing is not sentient ;
Therefore it is not {any) living.
But if we specify or quantify the terms, we may have an
inference that is valid on this process. Thus : —
A 11 sentient is (some) living ;
This thing is not [any] sentient ;
Therefore this thing is not {some) living.
So in the hypothetical. Thus : —
If the penal laws against Papists were enforced, they would
be aggrieved ;
But these laws are not enforced ;
Therefore Papists are not aggrieved.
This conclusion is invalid, as it stands, since Papists may,
as a matter of fact, have other sources of grievance than that
here specified. But if we quantify the terms, we get a per-
fectly valid inference. Thus : —
If the penal laws against Papists were enforced, they would
be {some) aggrieved ;
Or — They would have a definite grievance ;
But these laws are not enforced ;
Therefore Papists are not (some) aggrieved ;
Or — They have not the definite grievance winch follows from
the enforcement of the penal laws.
§ 707. (7.) Those which proceed on the affirmation of the
consequent to the affirmation of the antecedent. Thus : —
532 INSTITUTES OF LOGIC.
If this thing is sentient, it lives ;
But it lives ;
Therefore it is sentient.
This, as it stands, is incorrect ; and the fallacy corre-
sponds to that of the Undistributed Middle in Categoricals.
Thus :—
All sentient is (some) living;
This thing is (some) living;
Therefore it is sentient.
This proceeds in Extension. If we take it in Comprehen-
sion, it will read thus : —
If this thing has the mark sentiency, it will have the mark life ;
But it has the mark life;
Therefore it has the mark sentiency.
Here we have not said that everything having the mark life
has the mark sentiency, only that everything sentient has the
mark life. But on this assumption the conclusion turns,
and it is thus invalid ; for the living or the mark life may
be found, for aught we know, in other than the sentient. If
there be sentiency, there is at least life, states the connection
between two terms, but not their convertibility, or the sin-
gularity of the connection. The mistake lies, as Aristotle
pointed out, in supposing the consecution to be reciprocal.1
The following are Aristotle's examples : —
If a thing has been created, it had a beginning ;
This tiling had a beginning ;
Therefore it was created.
If this man has a fever, he is hot ;
But he is hot;
Therefore he has a fever?
§ 708. Even in the denial of the consequent, we must be
careful to observe that the denial is precise, otherwise we
have no inference. Thus : —
If this thing be sentient it is (some) living ;
But it is not (some) living ;
Therefore it is not sentient.
i Top., i. 5. ilbid.
HYPOTHETICAL FALLACIES. 533
This conclusion is only valid on the supposition that the
some living spoken of in the sumption is identical with the
some living spoken of in the subsumption. What we really
mean to assert is, that it is not this some living, which is
included in sentient, for if it were some other living, we have
introduced a proposition which is not the denial of the con-
sequent. In the ordinary form, the subsumption appears as
a universal negative, and hence there is no difficulty : btit
if quantification be introduced, we may, without care, have
an irrelevant subsumption.
534
CHAPTEK XXXIX.
FALLACIES — (2.) MATERIAL FALLACIES.
§ 709. Before proceeding to consider the Material Fallacies,
or those in which, while the conclusion actually follows from
the premisses, it is yet incorrect in point of fact, or irrelevant
to the point at issue, it is necessary to observe the relations
of true and false premisses to the character of the conclusion,
as itself true or false.
On this subject the following rules may be laid down : —
(1.) If both premisses be true, that is, correct representa-
tions of reality, and if the conclusion be validly drawn there-
from, we have the certainty of a true conclusion, or judgment
in harmony with fact.
This is grounded, as Aristotle has pointed out, on the law
of Non-contradiction. If A being, B necessarily is ; and B
not being, A necessarily is not ; then if A is true, B is neces-
sarily true : otherwise, the same thing (A) would at one and
the same time be and not be.1
(2.) If one premiss be true, and the other false, or even if
both premisses be false, and the conclusion be correctly
drawn from them, the conclusion may yet be true in point of
fact. In this case we have not a sufficient reason for our
belief in the truth of the conclusion, so far as this argument
goes ; but we may still correctly hold the conclusion as true
in point of fact.
(a) One premiss false. Thus : —
No white is animate;
All snow is white;
Therefore no snow is animate.
i An. Pr., ii. 2.
MATERIAL FALLACIES. 535
Here the conclusion is true in point of fact, but not because
of the reason given.
(b) Both premisses false. Thus : —
No man is animate ;
Every stone is a man ;
Therefore no stone is animate.
Here, also, the conclusion is true in point of fact, but not
because of the reason given. In these cases the true emerges
by chance, as Aristotle remarks — not from the necessity of
things.
To suppose this rule otherwise would be to fall into one
form of the hypothetical fallacy already noticed — viz., the
antecedent is not, therefore the consequent is not : —
If man is, animal is;
But man is not ;
Therefore animal is not.
This is really equivalent to the fallacy of supposing that be-
cause the reason is false, the conclusion alleged to be founded
on it is false ; or because a reason adduced has been dis-
proved, the conclusion has necessarily and absolutely been
disproved.
Suppose a person argues for the existence of Deity from
the alleged fact of its being universally believed, or believed
by all nationalities, an opponent might conceivably overthrow
the proof by adducing an instance of a nation in which no
such belief exists. In this case the proof would go for
nothing ; but it would be a fallacy to suppose that the con-
clusion was absolutely disproved.
§ 710. (3.) If the conclusion be false, and there be no flaw
in the reasoning, one or other of the premisses must be false.
If the conclusion be true, the truth of the premisses is not
thereby guaranteed ; but if the conclusion, formally valid, is
false, the falsity of a premiss, one or both, is established.1
This principle is of the utmost importance in examining
a hypothesis. From a false hypothesis you may deduce a
true proposition, as Ptolemy did, when, from an incorrect de-
scription of the celestial movements, he deduced the nature
1 See An. Pr., ii. 4.
536 INSTITUTES OF LOGIC.
and periods of the eclipse of the moon, and the duration of
the month and year. In these cases, conclusions true in
point of fact were drawn from erroneous premisses. It comes
to this, that the antecedent may, and therefore commonly
does, extend more widely than the antecedent as predicate to
the subject ; for what springs from this cause may also issue
from another. For example, if you cut a right cone so by
the plane, that the section is parallel to the base, there will
be a circle ; but if there be a circle, this is rarely the cause
of it.1
§ 711. Material Fallacies depend either (1.) on the falsity of
the premiss or premisses, or (2.) on the undue assumption of a
premiss, or (3.) on the irrelevancy of the conclusion in respect
of the question proposed or point at issue.
§ 712. (1.) With regard to false premisses, the conclusion
correctly drawn from them may be either true or false. But
this of course is by accident ; and there is no reason or neces-
sity which, in the argument, can be held as guaranteeing it.
This is known as the fallatia falsi medii, as it is on the con-
nection of the middle term with the extremes, in this case
unreal, that the conclusion is supposed to turn.
§ 713. The fallacy of Imperfect Disjunction may be taken
as an instance of a false premiss. In Indirect Proof, which
depends mainly on disjunction, and a disjunctive major
premiss, fallacy frequently arises from an incompleteness in
the disjunctive statement. The principle of disjunction is, as
we have seen, the full statement or exhaustion of the pos-
sibilities of the case, and a consequent reasoning from affirma-
tion to negation, or negation to affirmation. Clearly, then,
if we omit a possible case to start with, our conclusion will be
materially false.
§ 714. In Mathematics, complete disjunction is easily accom-
plished— as when we say, rectilineal triangle is either rectan-
oular, or obtuse angular, or acute angular. If this figure is not
the first, it is either the second or third. But in the Observa-
tional and Moral Sciences this is not so easily carried out.
In Theology our disjunction is often purely nominal, as turn-
ing on a subject which is incapable, from its nature, as trans-
cending experience, of strict definition and exhaustive possi-
bilities.
1 Cf. An. Pr., ii. 4 ; and Trendelenburg in loco, El Log., § 32.
KINDS OF MATERIAL FALLACIES. 537
Thus, it has been argued that we cannot live happily in
this world, since in life we must either abandon ourselves to our
passions, or combat them.1 If we do the former, we have no
happiness, but a feeling of shame and dissatisfaction. If we ,
do the latter, we live in a constant state of internal warfare,
and, therefore, of pain. This disjunction is incomplete, inas-
much as we omit the alternative of reasonable control and tem-
perance in life, which may lead to happiness, perhaps alone
to what people call happiness.
We have an illustration of imperfect disjunction in the
case of the reasoning of the Islanders of Otaheite, when
Captain Cook arrived on their shores, bringing a sheep in his
vessel. They were puzzled at first, not having seen quite
such an animal before. How was it to be classed ? All the
creatures known to them were pigs, dogs, rats, and birds.
The new object appeared to be neither a pig, nor a dog, nor
a rat, therefore they concluded it was a bird of some new
sort, for birds were to them of varied kinds.
§ 715. In a reasoning, whether simple or complex, there
are two essential rules. (1.) " That no proposition [which is
provable] be employed as a principle of probation, which
stands itself in need of proof.
(2.) " That nothing else be proved than the proposition for
whose proof the probation was instituted." 2 The first of
these rules should be qualified by the terms in square brackets.
There are propositions of immediate certainty, which may be
employed legitimately in probation.
These two rules embrace the various forms of formal fallacy,
known as (1.) Petitio principii, or Fallacia quasiti medii,
TO iv CLpXti ttlTCMT&U.
(2.) *Y(TTepov irporepov.
(3.) Circulus in demonstrando, — diallelus, — 6 Si' oAAt/Awv
T/307T09.
(4.) Saltus vel Hiatus in demonstrando, Leap in Probation.
(5.) Heterozetesis, Ignoratio vel Mutatio Elenchi, and Tran-
situs in aliud genus, vel a genere ad genus, — /x.€Ta/?ao-is cis
aAAo yevos.
§ 716. Petitio Principii, taken first in its wider sense, de-
1 Cf. Reiffenberg, Logique, p. 101. For some excellent illustrations of in-
complete disjunction in Apagogical Demonstration, see Ueberweg, Logic, p. 532.
2 Hamilton, Logic, iv., L. xxvi. p. 52.
538 INSTITUTES OF LOGIC.
notes any reasoning in which a premiss is assumed, the cer-
tainty of which is not greater than that of the conclusion
it is adduced to prove, and which may be doubted on the
same grounds as the conclusion itself. This is the undue
assumption of a premiss in the widest sense, — a premiss
open to doubt, uncertain, not conceded by the opponent, or
not properly to be conceded by him, unless it can be estab-
lished on grounds similar to those which would establish
the conclusion. By the older logicians this was expressed
by the assumption, " Id quod asque ignotum est ac ipsa
quaestio." l Hamilton gives as an illustration of Petitio Prin-
cipii in this its wider sense, Aristotle's argument for slavery.
The barbarians, as of inferior intellect, are the bondsmen of the
Greeks, and the Greeks, as of superior intellect, are the born
masters of the barbarians. Here, of course, the assumption in
the premisses of relative inferiority would be questioned by
an opponent as much as the conclusion itself.2 An opponent
of slave-holding might be met by the proposition or argument
that slavery is to be upheld because it brings cheap labour,
and this is an advantage to the general social wellbeing.
The opponent might very fairly reply that this advantage —
even if admitted — is not proved to counterbalance the dis-
advantages of slave-holding, in its bearings on the moral
and social character of the people among whom it subsists.
He might urge, besides, that the conclusion is irrelevant to
the true and higher point at issue — as to whether slavery is
permissible at all on moral grounds. This runs into a case
of the fallacy to be noticed below — known as Ignoratio
Elenchi.
§ 717. What is known as the saltus or leap in a probation
may, as Hamilton points out, be reduced to the first form of
the Petitio Principii. We may, for the sake of brevity, omit
propositions in a proof ; this is not the saltus proper. We
do so in the Sorites, which is quite valid. But when, in a
series of reasonings, we pass from one proposition to another,
which is not logically connected with the former, except
through another intermediate proposition, which we have not
proved, then we commit a saltus. This, in fact, is simply
an instance of an unduly assumed premiss, — generally, as if
it did not need proof, while it does require it. Thus : —
1 Cf. Duncan, InsL Log,, v. p. 321. 2 Logic, iv. L. xxvi.
PETITIO PRINCIPIL 539
A. B. committed the murder ; therefore, he was more or less
insane.
Or, to take an example from Krug : —
Socrates was not a Christian ; therefore his good works were
only sirks.
This thing had a beginning ; therefore it was created.
This man stole the apples ; because he was in the garden an
hour before it was discovered that they were stolen.
We commit a saltus every time we pass directly from fancy
to reality, or from the possible to the actual. One practical
form of the fallacy is the contention made by idealising yet
indiscreet reformers, when they assume that because their
scheme of government or social change is sound and good, it
ought to be applied to a given state of society, without
consideration of the actual conditions or circumstances which
might actually frustrate its beneficial operation.
§ 718. The second form of Petitio Principii, known also as
varepov TrpoTtpov — hysteron proteron — is that usually considered
as a petitio, or begging of the question at issue. This arises
when a proposition is employed as a ground of proof, the truth
of which depends on the truth of the proposition — that is, con-
clusion— which it is adduced to prove.
One solution of the question at issue is assumed in the
premiss,- and this assumption involves the truth of the
conclusion which it is set up to prove. This is strictly
begging the question, borrowing, or snatching an answer.
This is not properly reasoning, but re-assertion ; and it is
usually cloaked by a change of terms, while the meaning or
effect is the same. This was expressed by the older logicians
as assuming "pro medio id quod in quasstione est verbis
aliquantum mutatis."1
§ 719. Technically, the mistake here arises from our in-
ferring, or supposing that we infer, a conclusion from itself.
There is here no proper syllogism ; for our conclusion is not
drawn from two different propositions taken together, but
really from one proposition only. We repeat, in the so-called
conclusion, one of the premisses, and there are thus not three
distinct propositions in the syllogism. Thus, I may ask — Is
this decision of the Synod to be accepted as sound? And I
may be told Yes, because the deliverances of the Synod are right.
1 Duncan, Ibid.
540 INSTITUTES OF LOGIC.
The question here, of course, is — Is this particular decision
a sound one t I am told it is, because the deliverances of the
Synod are right. But I may doubt this general proposition
precisely on the grounds on which I doubt the soundness of
the particular decision in question ; and to accept this as a
reason for the conclusion is no clearing whatever of my
doubt, — no giving me anything more certain than my original
state of mind. Nay, that the decision is sound, is assumed in
the reason, which refers to all the deliverances of the Synod.
Whereas this particular decision might give me fair grounds
for questioning the soundness of all the deliverances, or of
every deliverance.
§ 720. (3.) Reasoning in a Circle, as it is called, is the third
form of Petitio Principii. This is the more complex form.
In this case we have not one syllogism only, but two at least,
sometimes a series ; hence the fallacy is less easy of detec-
tion. Usually in the Circle, the antecedent in the first
reasoning is proved by its own consequent in the second.1
Thus we may reason : E is D, because F is D ; and F is D,
because E is D.
It is said, — John stole the apples. How do you know that
John stole the apples ? Because the man in the garden was
John, and he stole the apples. This is merely grounding the
same proposition on itself.
Krug gives, as an example, a reasoning of Plato for the
immortality of the soul. In the Phado, Plato grounds its im-
mortality on its simplicity / in the Republic, the simplicity on
the immortality.2
Thus we might reason : God exists, and is all-powerful,
good, and wise, because there is a divine revelation of Him ; and
the revelation is divine, because God exists and is all-powerful,
good, and wise.8
This is clearly a reasoning in a Circle. But if we were to
reason : There is a God who is all-powerful, good, and wise ;
therefore He has divinely revealed Himself , — the reasoning would
not be open to the charge of the Circle.
Descartes is commonly represented as seeking to prove the
veracity of the testimony of our intelligence from the existence
and truthfulness' of Deity ; and this latter proposition from
1 Cf. Krug, Logik, § 133, and Hamilton, Logic, iv. L. xxvi.
2 Logik, § 133. 3 Cf. Krug, Logik, § 133, An. 3.
THE CIRCLE. 541
the veracity of our faculties. This, of course, would be a
Petitio Principii or Circle ; but a more comprehensive inter-
pretation of his statements shows that what he means is a
belief or natural presumption in the truth of our perceptions,
on the ground of non-repugnance between the deliverances of
sense, memory, and understanding.1
As Ueberweg has well pointed out, Kant's argument for the
false subtlety of the Four Syllogistic Figures, or rather for the
exclusive normal character of the First Figure, rests on a Petitio
Principii, and, it may be added, on a very common form of it,
— that is, narrow definition. He first of all defines syllogistic
inference, or, as he calls it, " inference of the reason," as " the
knowledge of the necessity of a proposition by subsuming
what conditions it under a general rule." This applies to the
First Figure, and to it alone. But he has not thus proved the
point at issue, which is, that no normal syllogism can take the
form of the Second and Third Figures. He has thus virtually
begged from the commencement his conclusion as to u the
false subtlety" of those figures.2 This illustration may in-
deed be taken as a mixture of Petitio Principii with Ignoratio
Elenchi.
This fallacy seems simple enough when exposed. But all
fallacies do. They are none the less deceitful for all that. It
is only necessary for them to be cloaked in words to pass for
good arguments with many readers and hearers.
§ 721. In the case of the first principles of knowledge,
where we have self-evidence and necessity, there is no pos-
sible proof. If we say A is A, or A and not- A are not, we
have no proof in any higher proposition ; and we might argue
that if these be not accepted thought is impossible, — in other
words, all that we know and call thought falls to the ground.
This, in a sense, is reasoning to the truth or fact of the ante-
cedent from the fact of the consequent. But the Circle proper
refers to definite provable propositions, — propositions the
reason of which lies in other propositions beyond them. The
Circle is a bad reasoning within the sphere of knowledge, but
cannot be held as applying to those laws without which any
knowledge would be impossible.
§ 722. Heterozetesis (a-epo^-nyo-is) embraces Mutatio or Ig-
1 Cf. Meditations, vi. p. 169 (Eng. trans.)
2 Cf. Ueberweg, Logic, p. 535.
542 INSTITUTES OF LOGIC.
noratio Elenchi in its general forms — irrelevant conclusion,
proving too little, proving too much. The general character
of this fallacy is to be found in a change of the point to be
proved. In other words, we prove something different from
what we profess to do, or what we ought to do as strictly-
relevant to the point at issue. As this fallacy generally
occurs in discussion, it is said to be an ignoring or passing
by of the proof of the contradictory of the conclusion in an
opponent's argument. In order to expose it, we require to
specify that element or condition which has been omitted,
and which is needed to constitute a valid opposition in the
circumstances.
This fallacy has three forms — (1.) That in which the terms
of the proposition to be proved are changed. This is pro-
perly a passing into another genus, — transitus ad aliud genus.
Thus : Is the soul immortal ? It is proved, or attempted to
be proved, that the soul has not always been, and, therefore, it is
not eternal. This is a conclusion which, as it stands, is wholly
irrelevant to the point at issue. There is, in fact, a hiatus
unproved — viz., that that cannot always be which once was not.
Or : Is the person at the bar guilty or not of the charge made
against him ? A counsel might prove the heinousness of the
crime charged, the dreadful aggravations in this case, the
need for making a public example of such a wretch ; and so
on. But all the same, such points are wholly irrelevant until
the man's guilt has been established. Yet if an irrelevant
conclusion is clearly proved, some people are very apt to
suppose that this is the conclusion which was required to be
proved. The clear proof of mysterious noises in a house at
night goes a long way with many people to establish the
existence of the ghost ; and the clear vision of the corpse-
lights on the moor may convince the belated traveller of the
buried dead below.
§ 723. One very common form of irrelevant conclusion is,
for a person arguing to suppose that when he has demolished
an opponent's alleged proofs or reasons, he has established his
own, that is, the opposite conclusion. All that he has done
is to show that the arguments adduced in support of a definite
conclusion were unsound.
§ 724. {2.) The second case of Mutatio Elenchi is when we
MUTATIO ELENCHI. 543
prove less than we proposed to do or ought to do, in order to
establish our point, or to form a true opposition or contradiction.
Thus : Were the Pharisees virtuous t We prove that they
observed the law even in every respect. As virtue is properly a
matter of motive, and as our proof does not touch this ques-
tion,— whether the observance was due to love of the law, or
to ostentation, or love of praise, — we have proved less than
we ought to have proved. At the same time, in a proof of
this sort, — the too little, — our conclusion might be wholly
relevant, though insufficient. It may, in fact, be one step,
and that an important one, in the direction of the full or ade-
quate conclusion. It may be admitted, as has been said,
that the physico-theological argument, or argument from
design, proves too little to establish the full conception of
God ; but if it proves power and knowledge, it is one
step in the process, and it may be supplemented on other
grounds.
§ 725. (3.) The third case is that of proving too much, —
more than we need to do in order to establish our point.
Qui nimium probat, nihil probat. But proving too much has
two forms, (1.) In the one case, our conclusion may be per-
fectly true, only wider than we actually need ; and in this
instance it contains under it the conclusion in question. Thus,
the question may be — Was a particular substance thrown
into the fire actually consumed t I might prove that it was
incombustible. Here I prove too much, — at least more than
was needed for the point at issue. But it includes and settles
the question of actual fact in the instance in hand. Or : Is
the soul immortal f If I prove that from its nature it is im-
perishable, I have proved more than the mere fact of its im-
mortality, but my conclusion includes the latter. In this first
case, the common rule about proving too much is not to be
taken strictly.
(2.) In the second case, we prove too much when, if the
general principle on which our conclusion is necesarily based
were admitted, we should have false inferences. This is the
true nimium probat. This implies that the universal from which
the conclusion is perhaps tacitly drawn is false. Thus : Pity
ought to be gratified because it is a natural feeling. On the
same principle ought revenge, anger, &c. Here, at least, we
544 INSTITUTES OF LOGIC.
have assumed too much, — more than is needed for our conclu-
sion, and what equally justifies other conclusions which are
unwarrantable.
§ 726. Persecution for the sake of opinion, as has been
remarked, may be regarded as a practical form of Ignoratio
Elenchi. The reformer who is executed, or the martyr
who is burned at the stake, is not by this act necessarily
proved in error ; it is only shown that his opponents were
stronger than he, — which is a very different point indeed.
To make an end of man by violence or bullying, does not
refute, by reason, or even make an end eventually of his
conclusions.
§ 727. This fallacy is exceedingly common. When an
opinion is propounded, we find people attacking it on the
ground of its traditional character, its being nothing new,
or its bearing, real or supposed, upon existing interests
and institutions. These considerations are entirely out of
place, until the truth or falsity of the opinion has been dis-
cussed and established on grounds of evidence. It is no
reproach to truth that it is new ; it is no reproach to truth
that it is old. It is, or ought to be, no aid to falsehood
that it has tradition in its favour. Novelty and antiquity
are but shifting accidents ; the real light to truth is the
light of experience, which is both old and new, — which, as
Bacon said, is never passing, but eternal.
§ 728. The Argumentum ad Hominem, as it is called, may be
regarded as a foi'm of Irrelevant Conclusion. This argument is
a cheap and popular way of disposing of an opponent's reason-
ing. It consists in saying: This is your opinion now, and
these are the reasons you give ; but don't you remember that
you held an entirely opposite opinion, just, say, two years ago?
Your argument now is accordingly of no value. You are re-
futed out of your own mouth. This is the usual clap-trap of the
popular orator. It is cheap, easy, and superficial. It is per-
fectly competent to say to him in return : Your reasoning is
grossly fallacious. Even admitting that I have changed my
opinion on the point in question, that does not prove my present
argument or proof of the opinion to be false or invalid. I
ask you to look at my reasons before you decide that. And
so far as I am personally concerned for the change of my
ARGUMENTUM AD HOMINEM. 545
opinion, that does not necessarily imply moral delinquency.
I may have been seeking for, and may have got more light ;
you may be remaining in the blindness of your original
bigotry. But this, too, is to be settled in a great measure by
a consideration of the grounds of my opinion now adduced.
And until you have examined these, and shown them to be
worthless, you really have not advanced the counter-opinion
one whit. This should settle the argumentum ad hominem
style of attack ; but those who use it are generally so much
of the irrelevant type, that they do not know when they are
overthrown in argument.
Of course, it must be admitted that there may be ground
for a personal charge against a man who changes his opinions.
But in this case the charge must be founded on the man-
ner and circumstances of the change, not on the mere fact
of the change itself. This really means nothing unworthy;
it may mean something in the highest degree worthy and
commendable.
§ 729. The Argumentum ad Hominem may, however, fairly
be employed within certain limits. It is a legitimate form
of reasoning to show that the assumptions or principles on
which a person proceeds in a discussion, ought logically to
lead him to certain conclusions. These may be conclusions
which he desires to repudiate, or which, from their recognised
falsity, show the falsity of the premisses which he has as-
sumed. In the former case, he is proved an inconsistent
reasoner ; in the latter case, his principles themselves are
controverted.
§ 730. What is known as the Fallacy of Objections comes
under the head of Mutatio Elenchi.
This fallacy assumes that if objections of more or less force
can be stated to a proposition or proposal, it is necessarily
false, and ought to be abandoned. Some minds delight in
objections, and are satisfied, if they can find them, without
inquiring into their sufficiency or even relevancy. But it is
hardly possible to state any proposition in general matter to
which no objection can be made. The limited intelligence sees
only a part, fixes on that, and a difficulty which it may
suggest ; sees a thing in one of its aspects, disapproves, and
concludes that the whole proposition is not true, or the whole
2 M
546 INSTITUTES OF LOGIC.
scheme undesirable. The real question is as to the balance
of objections or difficulties, — the side upon which the least
are found to lie is that to be adopted. This applies espe-
cially to social changes, which never can take place without
disadvantage to some interest or other — that is, to some indi-
viduals. The true question is as to the bearing of the change
on the whole, and in the long-run.
§ 731. To the head of Mutatio Elenchi may fairly be re-
ferred a fallacy, or rather sophism, not uncommon in these
days, which might be named, Trick of Title. Thus a critic,
even in an infallible daily print, may blunder as to a matter
of fact, — in a word, misrepresent the author he criticises.
Should the person misrepresented write to the newspaper
to set the critic right, his communication will probably be
immediately labelled " An Author on his Defence," when
" Our Critic's Misrepresentation " would have been more to
the point. Qui s'excuse, s'accuse, is by no means true with
an unlimited generality.
§ 732. The Fallacia ad Verecundiam may fairly enough be
classed under the head of the Mxdatio Elenchi. It is prac-
tically an appeal to one's reverence for authority — one's
modesty in face of a great author or his opinion. Of this it
may be said, that it contains a very good element, — the
propriety of recognising the value of an opinion advanced by
a man who has studied a particular subject. In many cases
we should hardly think of disputing the judgment of an
authority, — as, for example, the analysis of a recognised
chemical expert. In some cases, even, we might respect the
opinion of a doctor of medicine. But in general subjects,
where we know thought is progressing, science is widening,
historical research becoming more critical and discriminating,
we should be more ready to withhold our assent from mere
authority. In certain departments, no quality, be it careful
observation, or exact thinking, or speculative insight, or
genius in any form, can give us an absolutely trustworthy
result. For a time the modes or styles and the opinions of
powerful men have their dominating influence. All literary
history shows this. We have had Aristotle dominant for
centuries, — the philosopher, the master ; and no human in-
tellect ever deserved these appellations more. None ever
AD IGNORANTIAM. 547
struck out lines so new and so profound as the Stagirite.
Yet even he was not broad enough for human experience
or human thought. And those who for centuries knew and
believed only him, shut themselves out from the fulness of
human knowledge, and that by one of the ways against which
he had warned them — practically a Mutatio Elenchi. For the
question, as Aristotle himself taught, was not whether a
conclusion was accepted, but whether it was the conclusion
to be accepted. In the same way we had Ciceronianism in
style, Johnsonese, and latterly, to some extent, Carlylese, —
all probably representing advances on the past, and thus
things relatively good, but altogether unworthy of exclusive
acceptance and worship. There was no question here by
people as to what was the best, — only a yielding to a power-
ful influence, or a regard to what, for the time, would be ac-
cepted or approved. This was a true Mutatio Elenchi.
§ 733. The Fallacia ad Ignorantiam may well come under
the same head. This implies an appeal to the ignorance,
limited reading, education, or reflection of the hearer or reader.
A man says : Here is my opinion ; here are my arguments.
Can you refute this opinion? can you answer those argu-
ments ? No, I cannot ; I confess I am beaten. Well, then,
accept the arguments, or, at least, the conclusion. This
appeal, as wholly relative to the ignorance of the hearer or
reader, is entirely beside the mark. The ground of it is in no
way decisive, either of the force of the arguments or of the
truth of the conclusion. It amounts to this : You don't know
any better, therefore accept this as true.
With this is closely connected the Fallacia ad Populum, or
appeal to the passions, prejudices, interests of a mob, sect, or
political party, in virtue of which they are led to accept an
unsifted or unproved conclusion.
§ 734. The fallacy of Mutilated or Isolated Quotation may
be brought under the head of Mutatio Elenchi. These practi-
cally issue in an irrelevant conclusion. Had the full quota-
tion, or that taken in connection with the text, been given,
the conclusion would have been different, and probably
irrelevant to the point at issue.
§ 735. What is known as the Fallacia Supponentis may be
referred to the head of Mutatio Elenchi. This, by appealing
548 INSTITUTES OF LOGIC.
to a man's preconceptions, interests, personal vanity, may
induce him readily to recognise in things, probably only
similar to what he knows and has studied, a true affinity,
and thus lead him to an irrelevant conclusion, or a conclusion
not justified by the data.
§ 736. Nothing contributes more to the prevention, or,
not least, the shortening of discussion, than a preliminary
attention to the state of the question. What is really the
point at issue ought to be the first inquiry in the interest of
intellectual honesty. Strong feeling or moral dishonesty may
lead a man to attribute to an opponent a position which he
does not hold ; and not unfrequently a person will attack a
position which his opponent does not dispute, simply because
he is conscious of being unable successfully to impugn the
point at issue.
§ 737. Sophisma non causa pro causa, or cum hoc ergo propter
hoc.
This arises when we take for cause that which is not cause,
or mistake casual for causal sequence. When one event fol-
lows another, the question is whether the former is the cause
of the latter, determines it, or whether it is a case of mere
following, or simple conjunction. If we mistakenly hold the
first for cause, we have no sufficient reason for inferring the
second, should the first again occur ; yet we may make this
inference. When Eousseau assigned the commencement of
the decay in manners in all countries to the first moment of
the culture of letters, he might fairly be held guilty of the
non causa pro causa. Instances of the same are the old
fancies that the waning moon had a bad, and the full, or
new, moon a good influence on human affairs.
Besides attributing causality where it does not exist, we
may give as a reason of a conclusion a proposition which is
insufficient to justify it. Thus : —
Orators are apt to mislead ; therefore banish them from the
State.
Heresy sometimes arises from the reading of Scripture ; there-
fore prohibit the reading.
Religion has been the cause of civil wars ; therefore suppress it.
These may be taken as instances at the same time of a
NON CAUSA PRO CAUSA. 549
hiatus in the reasoning. We need proof of an intermediate
proposition.
The fallacy here may equally lie in mistaking for an effect
or consequent that which is not so, or which does not at all
follow. Thus — from the connection between the nervous
system and the consciousness, we may infer that the latter is
a simple effect or result of the former ; or because the brain
is a condition of thinking, the brain is actually the thinker.
This is the cum hoc ergo propter hoc.
§ 738. The non causa pro causa may be taken as extending
to a subtle form of deception, in which one concept is, to some
extent, unconsciously substituted for another, and so accepted
as a reason, or at least as satisfying the preconceptions of what
a reason ought to be in the circumstances. Of this the fol-
lowing may be given as an illustration : —
" The nebular hypothesis," says a writer, " was a recrement
of ancient traditions about the origin of the universe from
Nothing. The original mist of the nebular hypothesis is
assumed to be of extreme tenuity, — of a density less than
the one hundredth thousand part of hydrogen, the lightest
gaseous body known to the chemist. By reason of this
ethereal subtlety it was readily substituted, in the conceptions
of the popular mind, for the old void from which the world
was said to have emerged, and in the imaginations of those
who look upon matter as a sort of inspissation of mind for the
universal antemundane impersonal Spirit. It thus conformed
to the assumption that, on any hypothesis respecting the
mode of the world's formation, it must, 'in the beginning,'
have - been ' without form and void,' and at the same time
satisfied the mystic yearnings after the ethereal and 'spirit-
ualistic' " 1
§ 739. One very common form of the non causa pro causa,
is not simply the mistaking of the individual object for a cause
when it is not so, but the general misapprehension of law for
cause. Physical law, in particular, is, as observed by us, simply
uniformity of sequence. It is no doubt much more than this ;
but this is what we observe, and what we are too ready to
identify with the whole of it. In this way we come to
attribute efficiency or causality to what we call law, whereas
1 Stallo, Concepts of Modem Physics, p. 292.
550 INSTITUTES OF LOGIC.
law is but the mode, the uniform mode, in which causality is
displayed. Laws are not causes, but the modes of action of
causes. An event is not explained by being referred to its
law, or the uniform kind of occurrence to which it belongs ; it
is only properly explained when we refer this law to a cause ;
and this cause, again, may be carried backwards to another,
and must be carried ultimately to a First Cause or Power in
things ; the only other alternative being the suicidal one of
an endless regress.
§ 740. The connection between supposed sign and thing
signified comes under this head. The common illustrations
are the old popular impressions of the connection between
an eclipse or a comet, and the death of an eminent person,
or a war which might follow in time. Belief in dreams
and various prognostics, as signs of events to follow, is of
the same class.
" Solem quis dicere falsum
Audeat ? ille etiam caecos instare tumultus
Saepe monet : fraudemque et operta tumescere bella.
Ille etiam extincto miseratus Caesare Romam ;
Cum caput obscura nitidum ferrugine texit,
Impiaque aeternam timuerunt saacula noctem." 1
§ 741. What is known as the Fallacia fictce Universalitatis,
arises either from imperfect induction, or perhaps more com-
monly from the non causa pro causa — the cum hoc ergo propter
hoc. Because the subject has been followed b3r the predicate
in one or two instances, we hastily generalise the subject or
antecedent as cause. The examples already given of the non
causa pro causa illustrate this point.
But in truth the liability to this fallacy is inseparable from
the fullest Observation and the most ample Induction. Uni-
versal laws, or laws accepted as such in the course of science,
have frequently proved to be by no means universal. Nothing
appeared to be more completely established by Observation
and Induction, carried on through the ages, than that the
satellites in the planetary system moved round each planet
in a uniform direction. But what turned out to be the fact ?
The addition of Uranus to the system, as has been noticed,
1 Virgil, Oeorg., I.
NON CAUSA PRO CAUSA. 551
showed planets moving in a direction wholly contrary to what
had been supposed the universal mode ; and the further dis-
covery of Neptune, with its satellites moving like those of
Uranus, gave the coup de grace to the assumptive universal
law. In this there is a sound practical lesson of modesty,
and a rebuke to dogmatism, which can be appreciated only
by those physical observers who not only note, but think.
THE END.
PRINTED BY WILLIAM BLACKWOOD AND SONS.
CORRIGENDA.
Page 17, line 16, for "a great part," read "the whole."
, 43,
i 271,
. 294,
i 310,
. 310,
25, for "precepts," read "percepts."
35, for "Hermiese," read "Hermeiae."
3, for "veritus," read "veritas."
4, read " ixaXaK-fi.''
5, read " /Aa\aKT)."
X,
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