Chapter XII (2)

40 The always acute and often profound author of _An Outline of
Sematology_ (Mr. B. H. Smart) justly says, “Locke will be much more
intelligible, if, in the majority of places, we substitute ‘the
knowledge of’ for what he calls ‘the Idea of’” (p. 10). Among the
many criticisms on Locke’s use of the word Idea, this is the one
which, as it appears to me, most nearly hits the mark; and I quote
it for the additional reason that it precisely expresses the point
of difference respecting the import of Propositions, between my view
and what I have spoken of as the Conceptualist view of them. Where a
Conceptualist says that a name or a proposition expresses our Idea
of a thing, I should generally say (instead of our Idea) our
Knowledge, or Belief, concerning the thing itself.

41 This distinction corresponds to that which is drawn by Kant and
other metaphysicians between what they term _analytic_ and
_synthetic_, judgments; the former being those which can be evolved
from the meaning of the terms used.

42 If we allow a differentia to what is not really a species. For the
distinction of Kinds, in the sense explained by us, not being in any
way applicable to attributes, it of course follows that although
attributes may be put into classes, those classes can be admitted to
be genera or species only by courtesy.

43 Professor Bain, in his Logic, takes a peculiar view of Definition.
He holds (i., 71) with the present work, that “the definition in its
full import, is the sum of all the properties connoted by the name;
it exhausts the meaning of a word.” But he regards the meaning of a
general name as including, not indeed all the common properties of
the class named, but all of them that are ultimate properties, not
resolvable into one another. “The enumeration of the attributes of
oxygen, of gold, of man, should be an enumeration of the final (so
far as can be made out), the underivable, powers or functions of
each,” and nothing less than this is a complete Definition (i., 75).
An independent property, not derivable from other properties, even
if previously unknown, yet as soon as discovered becomes, according
to him, part of the meaning of the term, and should be included in
the definition. “When we are told that diamond, which we know to be
a transparent, glittering, hard, and high-priced substance, is
composed of carbon, and is combustible, we must put these additional
properties on the same level as the rest; to us they are henceforth
connoted by the name” (i., 73). Consequently the propositions that
diamond is composed of carbon, and that it is combustible, are
regarded by Mr. Bain as merely verbal propositions. He carries this
doctrine so far as to say that unless mortality can be shown to be a
consequence of the ultimate laws of animal organization, mortality
is connoted by man, and “Man is Mortal” is a merely verbal
proposition. And one of the peculiarities (I think a disadvantageous
peculiarity) of his able and valuable treatise, is the large number
of propositions requiring proof, and learned by experience, which,
in conformity with this doctrine, he considers as not real, but
verbal, propositions.

The objection I have to this language is that it confounds, or at
least confuses, a much more important distinction than that which it
draws. The only reason for dividing Propositions into real and
verbal, is in order to discriminate propositions which convey
information about facts, from those which do not. A proposition
which affirms that an object has a given attribute, while
designating the object by a name which already signifies the
attribute, adds no information to that which was already possessed
by all who understood the name. But when this is said, it is implied
that, by the signification of a name, is meant the signification
attached to it in the common usage of life. I can not think we ought
to say that the meaning of a word includes matters of fact which are
unknown to every person who uses the word unless he has learned them
by special study of a particular department of Nature; or that
because a few persons are aware of these matters of fact, the
affirmation of them is a proposition conveying no information. I
hold that (special scientific connotation apart) a name means, or
connotes, only the properties which it is a mark of in the general
mind; and that in the case of any additional properties, however
uniformly found to accompany these, it remains possible that a thing
which did not possess the properties might still be thought entitled
to the name. Ruminant, according to Mr. Bain’s use of language,
connotes cloven-hoofed, since the two properties are always found
together, and no connection has ever been discovered between them:
but ruminant does not mean cloven-hoofed; and were an animal to be
discovered which chews the cud, but has its feet undivided, I
venture to say that it would still be called ruminant.

44 In the fuller discussion which Archbishop Whately has given to this
subject in his later editions, he almost ceases to regard the
definitions of names and those of things as, in any important sense,
distinct. He seems (9th ed., p. 145) to limit the notion of a Real
Definition to one which “explains any thing _more_ of the nature of
the thing than is implied in the name;” (including under the word
“implied,” not only what the name connotes, but every thing which
can be deduced by reasoning from the attributes connoted). Even
this, as he adds, is usually called not a Definition, but a
Description; and (as it seems to me) rightly so called. A
Description, I conceive, can only be ranked among Definitions, when
taken (as in the case of the zoological definition of man) to
fulfill the true office of a Definition, by declaring the
connotation given to a word in some special use, as a term of
science or art: which special connotation of course would not be
expressed by the proper definition of the word in its ordinary
employment.

Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately,
understands by a Real Definition one which contains _less_ than the
Nominal Definition, provided only that what it contains is
sufficient for distinction. “By _real_ definition I mean such an
explanation of the word, be it the whole of the meaning or only
part, as will be sufficient to separate the things contained under
that word from all others. Thus the following, I believe, is a
complete definition of an elephant: An animal which naturally drinks
by drawing the water into its nose, and then spurting it into its
mouth.”—_Formal Logic_, p. 36. Mr. De Morgan’s general proposition
and his example are at variance; for the peculiar mode of drinking
of the elephant certainly forms no part of the meaning of the word
elephant. It could not be said, because a person happened to be
ignorant of this property, that he did not know what an elephant
means.

45 In the only attempt which, so far as I know, has been made to refute
the preceding argumentation, it is maintained that in the first form
of the syllogism,

A dragon is a thing which breathes flame,
A dragon is a serpent,
Therefore some serpent or serpents breathe flame,

“there is just as much truth in the conclusion as there is in the
premises, or rather, no more in the latter than in the former. If
the general name serpent includes both real and imaginary serpents,
there is no falsity in the conclusion; if not, there is falsity in
the minor premise.”

Let us, then, try to set out the syllogism on the hypothesis that
the name serpent includes imaginary serpents. We shall find that it
is now necessary to alter the predicates; for it can not be asserted
that an imaginary creature breathes flame; in predicating of it such
a fact, we assert by the most positive implication that it is real,
and not imaginary. The conclusion must run thus, “Some serpent or
serpents either do or are _imagined_ to breathe flame.” And to prove
this conclusion by the instance of dragons, the premises must be, A
dragon is _imagined_ as breathing flame. A dragon is a (real or
imaginary) serpent: from which it undoubtedly follows, that there
are serpents which are imagined to breathe flame; but the major
premise is not a definition, nor part of a definition; which is all
that I am concerned to prove.

Let us now examine the other assertion—that if the word serpent
stands for none but real serpents, the minor premise (a dragon is a
serpent) is false. This is exactly what I have myself said of the
premise, considered as a statement of fact: but it is not false as
part of the definition of a dragon; and since the premises, or one
of them, must be false (the conclusion being so), the real premise
can not be the definition, which is true, but the statement of fact,
which is false.

46 “Few people” (I have said in another place) “have reflected how
great a knowledge of Things is required to enable a man to affirm
that any given argument turns wholly upon words. There is, perhaps,
not one of the leading terms of philosophy which is not used in
almost innumerable shades of meaning, to express ideas more or less
widely different from one another. Between two of these ideas a
sagacious and penetrating mind will discern, as it were intuitively,
an unobvious link of connection, upon which, though perhaps unable
to give a logical account of it, he will found a perfectly valid
argument, which his critic, not having so keen an insight into the
Things, will mistake for a fallacy turning on the double meaning of
a term. And the greater the genius of him who thus safely leaps over
the chasm, the greater will probably be the crowing and vainglory of
the mere logician, who, hobbling after him, evinces his own superior
wisdom by pausing on its brink, and giving up as desperate his
proper business of bridging it over.”

47 The different cases of Equipollency, or “Equivalent Propositional
Forms,” are set forth with some fullness in Professor Bain’s
_Logic_. One of the commonest of these changes of expression, that
from affirming a proposition to denying its negative, or _vicè
versa_, Mr. Bain designates, very happily, by the name Obversion.

48 As Sir William Hamilton has pointed out, “Some A is not B” may also
be converted in the following form: “No B is _some_ A.” Some men are
not negroes; therefore, No negroes are _some_ men (_e.g._,
Europeans).

49 Contraries:
All A is B
No A is B

Subtraries:
Some A is B
Some A is not B

Contradictories:
All A is B
Some A is not B

Also contradictories:
No A is B
Some A is B

Respectively subalternate:
All A is B and No A is B
Some A is B and Some A is not B

50 Professor Bain denies the claim of Singular Propositions to be
classed, for the purposes of ratiocination, with Universal; though
they come within the designation which he himself proposes as an
equivalent for Universal, that of Total. He would even, to use his
own expression, banish them entirely from the syllogism. He takes as
an example,

Socrates is wise,
Socrates is poor, therefore
Some poor men are wise,

or more properly (as he observes) “one poor man is wise.” “Now, if
wise, poor, and a man, are attributes belonging to the meaning of
the word Socrates, there is then no march of reasoning at all. We
have given in Socrates, _inter alia_, the facts wise, poor, and a
man, and we merely repeat the concurrence which is selected from the
whole aggregate of properties making up the whole, Socrates. The
case is one under the head ‘Greater and Less Connotation’ in
Equivalent Propositional Forms, or Immediate Inference.

“But the example in this form does not do justice to the syllogism
of singulars. We must suppose both propositions to be real, the
predicates being in no way involved in the subject. Thus

Socrates was the master of Plato,
Socrates fought at Delium,
The master of Plato fought at Delium.

“It may fairly be doubted whether the transitions, in this instance,
are any thing more than equivalent forms. For the proposition
‘Socrates was the master of Plato and fought at Delium,’ compounded
out of the two premises, is obviously nothing more than a
grammatical abbreviation. No one can say that there is here any
change of meaning, or any thing beyond a verbal modification of the
original form. The next step is, ‘The master of Plato fought at
Delium,’ which is the previous statement cut down by the omission of
Socrates. It contents itself with reproducing a part of the meaning,
or saying less than had been previously said. The full equivalent of
the affirmation is, ‘The master of Plato fought at Delium, and the
master of Plato was Socrates:’ the new form omits the last piece of
information, and gives only the first. Now, we never consider that
we have made a real inference, a step in advance, when we repeat
_less_ than we are entitled to say, or drop from a complex statement
some portion not desired at the moment. Such an operation keeps
strictly within the domain of equivalence, or Immediate Inference.
In no way, therefore, can a syllogism with two singular premises be
viewed as a genuine syllogistic or deductive inference.” (_Logic_,
i., 159.)

The first argument, as will have been seen, rests upon the
supposition that the name Socrates has a meaning; that man, wise,
and poor, are parts of this meaning; and that by predicating them of
Socrates we convey no information; a view of the signification of
names which, for reasons already given (Note to § 4 of the chapter
on Definition, _supra_, pp. 110, 111.), I can not admit, and which,
as applied to the class of names which Socrates belongs to, is at
war with Mr. Bain’s own definition of a Proper Name (i., 148), “a
single _meaningless_ mark or designation appropriated to the thing.”
Such names, Mr. Bain proceeded to say, do not necessarily indicate
even human beings: much less then does the name Socrates include the
meaning of wise or poor. Otherwise it would follow that if Socrates
had grown rich, or had lost his mental faculties by illness, he
would no longer have been called Socrates.

The second part of Mr. Bain’s argument, in which he contends that
even when the premises convey real information, the conclusion is
merely the premises with a part left out, is applicable, if at all,
as much to universal propositions as to singular. In every syllogism
the conclusion contains less than is asserted in the two premises
taken together. Suppose the syllogism to be

All bees are intelligent,
All bees are insects, therefore
Some insects are intelligent:

one might use the same liberty taken by Mr. Bain, of joining
together the two premises as if they were one—“All bees are insects
and intelligent”—and might say that in omitting the middle term
_bees_ we make no real inference, but merely reproduce part of what
had been previously said. Mr. Bain’s is really an objection to the
syllogism itself, or at all events to the third figure: it has no
special applicability to singular propositions.

51 His conclusions are, “The first figure is suited to the discovery or
proof of the properties of a thing; the second to the discovery or
proof of the distinctions between things; the third to the discovery
or proof of instances and exceptions; the fourth to the discovery,
or exclusion, of the different species of a genus.” The reference of
syllogisms in the last three figures to the _dictum de omni et
nullo_ is, in Lambert’s opinion, strained and unnatural: to each of
the three belongs, according to him, a separate axiom, co-ordinate
and of equal authority with that _dictum_, and to which he gives the
names of _dictum de diverso_ for the second figure, _dictum de
exemplo_ for the third, and _dictum de reciproco_ for the fourth.
See part i., or _Dianoiologie_, chap, iv., § 229 _et seqq._ Mr.
Bailey (_Theory of Reasoning_, 2d ed., pp. 70–74) takes a similar
view of the subject.

52 Since this chapter was written, two treatises have appeared (or
rather a treatise and a fragment of a treatise), which aim at a
further improvement in the theory of the forms of ratiocination: Mr.
De Morgan’s “Formal Logic; or, the Calculus of Inference, Necessary
and Probable;” and the “New Analytic of Logical Forms,” attached as
an Appendix to Sir William Hamilton’s _Discussions on Philosophy_,
and at greater length, to his posthumous _Lectures on Logic_.

In Mr. De Morgan’s volume—abounding, in its more popular parts, with
valuable observations felicitously expressed—the principal feature
of originality is an attempt to bring within strict technical rules
the cases in which a conclusion can be drawn from premises of a form
usually classed as particular. Mr. De Morgan observes, very justly,
that from the premises most Bs are Cs, most Bs are As, it may be
concluded with certainty that some As are Cs, since two portions of
the class B, each of them comprising more than half, must
necessarily in part consist of the same individuals. Following out
this line of thought, it is equally evident that if we knew exactly
what proportion the “most” in each of the premises bear to the
entire class B, we could increase in a corresponding degree the
definiteness of the conclusion. Thus if 60 per cent. of B are
included in C, and 70 per cent. in A, 30 per cent. at least must be
common to both; in other words, the number of As which are Cs, and
of Cs which are As, must be at least equal to 30 per cent. of the
class B. Proceeding on this conception of “numerically definite
propositions,” and extending it to such forms as these:—“45 Xs (or
more) are each of them one of 70 Ys,” or “45 Xs (or more) are no one
of them to be found among 70 Ys,” and examining what inferences
admit of being drawn from the various combinations which may be made
of premises of this description, Mr. De Morgan establishes universal
formulæ for such inferences; creating for that purpose not only a
new technical language, but a formidable array of symbols analogous
to those of algebra.

Since it is undeniable that inferences, in the cases examined by Mr.
De Morgan, can legitimately be drawn, and that the ordinary theory
takes no account of them, I will not say that it was not worth while
to show in detail how these also could be reduced to formulæ as
rigorous as those of Aristotle. What Mr. De Morgan has done was
worth doing once (perhaps more than once, as a school exercise); but
I question if its results are worth studying and mastering for any
practical purpose. The practical use of technical forms of reasoning
is to bar out fallacies: but the fallacies which require to be
guarded against in ratiocination properly so called, arise from the
incautious use of the common forms of language; and the logician
must track the fallacy into that territory, instead of waiting for
it on a territory of his own. While he remains among propositions
which have acquired the numerical precision of the Calculus of
Probabilities, the enemy is left in possession of the only ground on
which he can be formidable. And since the propositions (short of
universal) on which a thinker has to depend, either for purposes of
speculation or of practice, do not, except in a few peculiar cases,
admit of any numerical precision; common reasoning can not be
translated into Mr. De Morgan’s forms, which therefore can not serve
any purpose as a test of it.

Sir William Hamilton’s theory of the “quantification of the
predicate” may be described as follows:

“Logically” (I quote his words) “we ought to take into account the
quantity, always understood in thought, but usually, for manifest
reasons, elided in its expression, not only of the subject, but also
of the predicate of a judgment.” All A is B, is equivalent to all A
is _some_ B. No A is B, to No A is _any_ B. Some A is B, is
tantamount to some A is _some_ B. Some A is not B, to Some A is _not
any_ B. As in these forms of assertion the predicate is exactly
co-extensive with the subject, they all admit of simple conversion;
and by this we obtain two additional forms—Some B is _all_ A, and No
B is _some_ A. We may also make the assertion All A is all B, which
will be true if the classes A and B are exactly co-extensive. The
last three forms, though conveying real assertions, have no place in
the ordinary classification of Propositions. All propositions, then,
being supposed to be translated into this language, and written each
in that one of the preceding forms which answers to its
signification, there emerges a new set of syllogistic rules,
materially different from the common ones. A general view of the
points of difference may be given in the words of Sir W. Hamilton
(_Discussions_, 2d ed., p. 651):

“The revocation of the two terms of a Proposition to their true
relation; a proposition being always an _equation_ of its subject
and its predicate.

“The consequent reduction of the Conversion of Propositions from
three species to one—that of Simple Conversion.

“The reduction of all the _General Laws_ of Categorical Syllogisms
to a single Canon.

“The evolution from that one canon of all the Species and varieties
of Syllogisms.

“The abrogation of all the _Special Laws_ of Syllogism.

“A demonstration of the exclusive possibility of Three Syllogistic
Figures; and (on new grounds) the scientific and final abolition of
the Fourth.

“A manifestation that Figure is an unessential variation in
syllogistic form; and the consequent absurdity of Reducing the
syllogisms of the other figures to the first.

“An enouncement of _one Organic Principle_ for each Figure.

“A determination of the true number of the Legitimate Moods; with

“Their amplification in number (thirty-six);

“Their numerical equality under all the figures; and

“Their relative equivalence, or virtual identity, throughout every
schematic difference.

“That, in the second and third figures, the extremes holding both
the same relation to the middle term, there is not, as in the first,
an opposition and subordination between a term major and a term
minor, mutually containing and contained, in the counter wholes of
Extension and Comprehension.

“Consequently, in the second and third figures, there is no
determinate major and minor premises, and there are two indifferent
conclusions: whereas in the first the premises are determinate, and
there is a single proximate conclusion.”

This doctrine, like that of Mr. De Morgan previously noticed, is a
real addition to the syllogistic theory; and has moreover this
advantage over Mr. De Morgan’s “numerically definite Syllogism,”
that the forms it supplies are really available as a test of the
correctness of ratiocination; since propositions in the common form
may always have their predicates quantified, and so be made amenable
to Sir W. Hamilton’s rules. Considered, however, as a contribution
to the _Science_ of Logic, that is, to the analysis of the mental
processes concerned in reasoning, the new doctrine appears to me, I
confess, not merely superfluous, but erroneous; since the form in
which it clothes propositions does not, like the ordinary form,
express what is in the mind of the speaker when he enunciates the
proposition. I can not think Sir William Hamilton right in
maintaining that the quantity of the predicate is “always understood
in thought.” It is implied, but is not present to the mind of the
person who asserts the proposition. The quantification of the
predicate, instead of being a means of bringing out more clearly the
meaning of the proposition, actually leads the mind out of the
proposition, into another order of ideas. For when we say, All men
are mortal, we simply mean to affirm the attribute mortality of all
men; without thinking at all of the _class_ mortal in the concrete,
or troubling ourselves about whether it contains any other beings or
not. It is only for some artificial purpose that we ever look at the
proposition in the aspect in which the predicate also is thought of
as a class-name, either including the subject only, or the subject
and something more. (See above, p. 77, 78.)

For a fuller discussion of this subject, see the twenty-second
chapter of a work already referred to, “An Examination of Sir
William Hamilton’s Philosophy.”

53 Mr. Herbert Spencer (_Principles of Psychology_, pp. 125–7), though
his theory of the syllogism coincides with all that is essential of
mine, thinks it a logical fallacy to present the two axioms in the
text, as the regulating principles of syllogism. He charges me with
falling into the error pointed out by Archbishop Whately and myself,
of confounding exact likeness with literal identity; and maintains,
that we ought not to say that Socrates possesses _the same_
attributes which are connoted by the word Man, but only that he
possesses attributes _exactly like_ them: according to which
phraseology, Socrates, and the attribute mortality, are not two
things co-existing with the same thing, as the axiom asserts, but
two things coexisting with two different things.

The question between Mr. Spencer and me is merely one of language;
for neither of us (if I understand Mr. Spencer’s opinions rightly)
believes an attribute to be a real thing, possessed of objective
existence; we believe it to be a particular mode of naming our
sensations, or our expectations of sensation, when looked at in
their relation to an external object which excites them. The
question raised by Mr. Spencer does not, therefore, concern the
properties of any really existing thing, but the comparative
appropriateness, for philosophical purposes, of two different modes
of using a name. Considered in this point of view, the phraseology I
have employed, which is that commonly used by philosophers, seems to
me to be the best. Mr. Spencer is of opinion that because Socrates
and Alcibiades are not the same man, the attribute which constitutes
them men should not be called the same attribute; that because the
humanity of one man and that of another express themselves to our
senses not by the same individual sensations but by sensations
exactly alike, humanity ought to be regarded as a different
attribute in every different man. But on this showing, the humanity
even of any one man should be considered as different attributes now
and half an hour hence; for the sensations by which it will then
manifest itself to my organs will not be a continuation of my
present sensations, but a repetition of them; fresh sensations, not
identical with, but only exactly like the present. If every general
conception, instead of being “the One in the Many,” were considered
to be as many different conceptions as there are things to which it
is applicable, there would be no such thing as general language. A
name would have no general meaning if _man_ connoted one thing when
predicated of John, and another, though closely resembling, thing
when predicated of William. Accordingly a recent pamphlet asserts
the impossibility of general knowledge on this precise ground.

The meaning of any general name is some outward or inward
phenomenon, consisting, in the last resort, of feelings; and these
feelings, if their continuity is for an instant broken, are no
longer the same feelings, in the sense of individual identity. What,
then, is the common something which gives a meaning to the general
name? Mr. Spencer can only say, it is the similarity of the
feelings; and I rejoin, the attribute is precisely that similarity.
The names of attributes are in their ultimate analysis names for the
resemblances of our sensations (or other feelings). Every general
name, whether abstract or concrete, denotes or connotes one or more
of those resemblances. It will not, probably, be denied, that if a
hundred sensations are undistinguishably alike, their resemblance
ought to be spoken of as one resemblance, and not a hundred
resemblances which merely _resemble_ one another. The things
compared are many, but the something common to all of them must be
conceived as one, just as the name is conceived as one, though
corresponding to numerically different sensations of sound each time
it is pronounced. The general term _man_ does not connote the
sensations derived once from one man, which, once gone, can no more
occur again than the same flash of lightning. It connotes the
general type of the sensations derived always from all men, and the
power (always thought of as one) of producing sensations of that
type. And the axiom might be thus worded: Two _types of sensation_
each of which co-exists with a third type, co-exist with another; or
Two _powers_ each of which co-exists with a third power co-exist
with one another.

Mr. Spencer has misunderstood me in another particular. He supposes
that the co-existence spoken of in the axiom, of two things with the
same third thing, means simultaneousness in time. The co-existence
meant is that of being jointly attributes of the same subject. The
attribute of being born without teeth, and the attribute of having
thirty-two teeth in mature age, are in this sense co-existent, both
being attributes of man, though _ex vi termini_ never of the same
man at the same time.

54 Supra, p. 93.

55 Professor Bain (_Logic_, i., 157) considers the axiom (or rather
axioms) here proposed as a substitute for the _dictum de omni_, to
possess certain advantages, but to be “unworkable as a basis of the
syllogism. The fatal defect consists in this, that it is ill-adapted
to bring out the difference between total and partial coincidence of
terms, the observation of which is the essential precaution in
syllogizing correctly. If all the terms were co-extensive, the axiom
would flow on admirably; A carries B, all B and none but B; B
carries C in the same manner; at once A carries C, without
limitation or reserve. But in point of fact, we know that while A
carries B, other things carry B also; whence a process of limitation
is required, in transferring A to C through B. A (in common with
other things) carries B; B (in common with other things) carries C;
whence A (in common with other things) carries C. The axiom provides
no means of making this limitation; if we were to follow A
literally, we should be led to suppose A and C co-extensive: for
such is the only obvious meaning of ‘the attribute A coincides with
the attribute C.’”

It is certainly possible that a careless learner here and there may
suppose that if A carries B, it follows that B carries A. But if any
one is so incautious as to commit this mistake, the very earliest
lesson in the logic of inference, the Conversion of propositions,
will correct it. The first of the two forms in which I have stated
the axiom, is in some degree open to Mr. Bain’s criticism: when B is
said to co-exist with A (it must be by a _lapsus calami_ that Mr.
Bain uses the word _coincide_), it is possible, in the absence of
warning, to suppose the meaning to be that the two things are only
found together. But this misinterpretation is excluded by the other,
or practical, form of the maxim; _Nota notœ est nota rei ipsius._ No
one would be in any danger of inferring that because _a_ is a mark
of _b, b_ can never exist without _a_; that because being in a
confirmed consumption is a mark of being about to die, no one dies
who is not in a consumption; that because being coal is a mark of
having come out of the earth, nothing can come out of the earth
except coal. Ordinary knowledge of English seems a sufficient
protection against these mistakes, since in speaking of a mark of
any thing we are never understood as implying reciprocity.

A more fundamental objection is stated by Mr. Bain in a subsequent
passage (p. 158). “The axiom does not accommodate itself to the type
of Deductive Reasoning as contrasted with Induction—the application
of a general principle to a special case. Any thing that fails to
make prominent this circumstance is not adapted as a foundation for
the syllogism.” But though it may be proper to limit the term
Deduction to the application of a general principle to a special
case, it has never been held that Ratiocination or Syllogism is
subject to the same limitation; and the adoption of it would exclude
a great amount of valid and conclusive syllogistic reasoning.
Moreover, if the _dictum de omni_ makes prominent the fact of the
application of a general principle to a particular case, the axiom I
propose makes prominent the condition which alone makes that
application a real inference.

I conclude, therefore, that both forms have their value, and their
place in Logic. The _dictum de omni_ should be retained as the
fundamental axiom of the logic of mere consistency, often called
Formal Logic; nor have I ever quarreled with the use of it in that
character, nor proposed to banish it from treatises on Formal Logic.
But the other is the proper axiom for the logic of the pursuit of
truth by way of Deduction; and the recognition of it can alone show
how it is possible that deductive reasoning can be a road to truth.

_ 56 Logic_, p. 239 (9th ed.).

57 It is hardly necessary to say, that I am not contending for any such
absurdity as that we _actually_ “ought to have known” and considered
the case of every individual man, past, present, and future, before
affirming that all men are mortal: although this interpretation has
been, strangely enough, put upon the preceding observations. There
is no difference between me and Archbishop Whately, or any other
defender of the syllogism, on the practical part of the matter; I am
only pointing out an inconsistency in the logical theory of it, as
conceived by almost all writers. I do not say that a person who
affirmed, before the Duke of Wellington was born, that all men are
mortal, _knew_ that the Duke of Wellington was mortal; but I do say
that he _asserted_ it; and I ask for an explanation of the apparent
logical fallacy, of adducing in proof of the Duke of Wellington’s
mortality, a general statement which presupposes it. Finding no
sufficient resolution of this difficulty in any of the writers on
Logic, I have attempted to supply one.

58 The language of ratiocination would, I think, be brought into closer
agreement with the real nature of the process, if the general
propositions employed in reasoning, instead of being in the form All
men are mortal, or Every man is mortal, were expressed in the form
Any man is mortal. This mode of expression, exhibiting as the type
of all reasoning from experience “The men A, B, C, etc., are so and
so, therefore _any_ man is so and so,” would much better manifest
the true idea—that inductive reasoning is always, at bottom,
inference from particulars to particulars, and that the whole
function of general propositions in reasoning, is to vouch for the
legitimacy of such inferences.

59 Review of Quetelet on Probabilities, _Essays_, p. 367.

_ 60 Philosophy of Discovery_, p. 289.

_ 61 Theory of Reasoning_, chap. iv., to which I may refer for an able
statement and enforcement of the grounds of the doctrine.

62 On a recent careful reperusal of Berkeley’s whole works, I have been
unable to find this doctrine in them. Sir John Herschel probably
meant that it is implied in Berkeley’s argument against abstract
ideas. But I can not find that Berkeley saw the implication, or had
ever asked himself what bearing his argument had on the theory of
the syllogism. Still less can I admit that the doctrine is (as has
been affirmed by one of my ablest and most candid critics) “among
the standing marks of what is called the empirical philosophy.”

_ 63 Logic_, book iv., chap. i., sect. 1.

64 See the important chapter on Belief, in Professor Bain’s great
treatise, _The Emotions and the Will_, pp. 581–4.

65 A writer in the “British Quarterly Review” (August, 1846), in a
review of this treatise, endeavors to show that there is no _petitio
principii_ in the syllogism, by denying that the proposition, All
men are mortal, asserts or assumes that Socrates is mortal. In
support of this denial, he argues that we may, and in fact do, admit
the general proposition that all men are mortal, without having
particularly examined the case of Socrates, and even without knowing
whether the individual so named is a man or something else. But this
of course was never denied. That we can and do draw conclusions
concerning cases specifically unknown to us, is the datum from which
all who discuss this subject must set out. The question is, in what
terms the evidence, or ground, on which we draw these conclusions,
may best be designated—whether it is most correct to say, that the
unknown case is proved by known cases, or that it is proved by a
general proposition including both sets of cases, the unknown and
the known? I contend for the former mode of expression. I hold it an
abuse of language to say, that the proof that Socrates is mortal, is
that all men are mortal. Turn it in what way we will, this seems to
me to be asserting that a thing is the proof of itself. Whoever
pronounces the words, All men are mortal, has affirmed that Socrates
is mortal, though he may never have heard of Socrates; for since
Socrates, whether known to be so or not, really is a man, he is
included in the words, All men, and in every assertion of which they
are the subject. If the reviewer does not see that there is a
difficulty here, I can only advise him to reconsider the subject
until he does: after which he will be a better judge of the success
or failure of an attempt to remove the difficulty. That he had
reflected very little on the point when he wrote his remarks, is
shown by his oversight respecting the _dictum de omni et nullo_. He
acknowledges that this maxim as commonly expressed—“Whatever is true
of a class, is true of every thing included in the class,” is a mere
identical proposition, since the class _is_ nothing but the things
included in it. But he thinks this defect would be cured by wording
the maxim thus—“Whatever is true of a class, is true of every thing
which _can be shown_ to be a member of the class:” as if a thing
could “be shown” to be a member of the class without being one. If a
class means the sum of all the things included in the class, the
things which can “be shown” to be included in it are part of the
sum, and the _dictum_ is as much an identical proposition with
respect to them as to the rest. One would almost imagine that, in
the reviewer’s opinion, things are not members of a class until they
are called up publicly to take their place in it—that so long, in
fact, as Socrates is not known to be a man, he _is not_ a man, and
any assertion which can be made concerning men does not at all
regard him, nor is affected as to its truth or falsity by any thing
in which he is concerned.

The difference between the reviewer’s theory and mine may be thus
stated. Both admit that when we say, All men are mortal, we make an
assertion reaching beyond the sphere of our knowledge of individual
cases; and that when a new individual, Socrates, is brought within
the field of our knowledge by means of the minor premise, we learn
that we have already made an assertion respecting Socrates without
knowing it: our own general formula being, to that extent, for the
first time _interpreted_ to us. But according to the reviewer’s
theory, the smaller assertion is proved by the larger: while I
contend, that both assertions are proved together, by the same
evidence, namely, the grounds of experience on which the general
assertion was made, and by which it must be justified.

The reviewer says, that if the major premise included the
conclusion, “we should be able to affirm the conclusion without the
intervention of the minor premise; but every one sees that that is
impossible.” A similar argument is urged by Mr. De Morgan (_Formal
Logic_, p. 259): “The whole objection tacitly assumes the
superfluity of the minor; that is, tacitly assumes we know Socrates
(Mr. De Morgan says ‘Plato,’ but to prevent confusion I have kept to
my own _exemplum_.) to be a man as soon as we know him to be
Socrates.” The objection would be well grounded if the assertion
that the major premise includes the conclusion, meant that it
individually specifies all it includes. As, however, the only
indication it gives is a description by marks, we have still to
compare any new individual with the marks; and to show that this
comparison has been made, is the office of the minor. But since, by
supposition, the new individual has the marks, whether we have
ascertained him to have them or not; if we have affirmed the major
premise, we have asserted him to be mortal. Now my position is that
this assertion can not be a necessary part of the argument. It can
not be a necessary condition of reasoning that we should begin by
making an assertion, which is afterward to be employed in proving a
part of itself. I can conceive only one way out of this difficulty,
viz., that what really forms the proof is _the other_ part of the
assertion: the portion of it, the truth of which has been
ascertained previously: and that the unproved part is bound up in
one formula with the proved part in mere anticipation, and as a
memorandum of the nature of the conclusions which we are prepared to
prove.

With respect to the minor premise in its formal shape, the minor as
it stands in the syllogism, predicating of Socrates a definite class
name, I readily admit that it is no more a necessary part of
reasoning than the major. When there is a major, doing its work by
means of a class name, minors are needed to interpret it: but
reasoning can be carried on without either the one or the other.
They are not the conditions of reasoning, but a precaution against
erroneous reasoning. The only minor premise necessary to reasoning
in the example under consideration, is, Socrates is _like_ A, B, C,
and the other individuals who are known to have died. And this is
the only universal type of that step in the reasoning process which
is represented by the minor. Experience, however, of the uncertainty
of this loose mode of inference, teaches the expediency of
determining beforehand what _kind_ of likeness to the cases
observed, is necessary to bring an unobserved case within the same
predicate; and the answer to this question is the major. The minor
then identifies the precise kind of likeness possessed by Socrates,
as being the kind required by the formula. Thus the syllogistic
major and the syllogistic minor start into existence together, and
are called forth by the same exigency. When we conclude from
personal experience without referring to any record—to any general
theorems, either written, or traditional, or mentally registered by
ourselves as conclusions of our own drawing—we do not use, in our
thoughts, either a major or a minor, such as the syllogism puts into
words. When, however, we revise this rough inference from
particulars to particulars, and substitute a careful one, the
revision consists in selecting two syllogistic premises. But this
neither alters nor adds to the evidence we had before; it only puts
us in a better position for judging whether our inference from
particulars to particulars is well grounded.

66 Infra, book iii., chap. ii.

67 Infra, book iii., ch. iv., § 3, and elsewhere.

68 It is justly remarked by Professor Bain (_Logic_, ii., 134) that the
word Hypothesis is here used in a somewhat peculiar sense. An
hypothesis, in science, usually means a supposition not proved to be
true, but surmised to be so, because if true it would account for
certain known facts; and the final result of the speculation may be
to prove its truth. The hypotheses spoken of in the text are of a
different character; they are known not to be literally true, while
as much of them as is true is not hypothetical, but certain. The two
cases, however, resemble in the circumstance that in both we reason,
not from a truth, but from an assumption, and the truth therefore of
the conclusions is conditional, not categorical. This suffices to
justify, in point of logical propriety, Stewart’s use of the term.
It is of course needful to bear in mind that the hypothetical
element in the definitions of geometry is the assumption that what
is very nearly true is exactly so. This unreal exactitude might be
called a fiction, as properly as an hypothesis; but that
appellation, still more than the other, would fail to point out the
close relation which exists between the fictitious point or line and
the points and lines of which we have experience.

_ 69 Mechanical Euclid_, pp. 149 _et seqq._

70 We might, it is true, insert this property into the definition of
parallel lines, framing the definition so as to require, both that
when produced indefinitely they shall never meet, and also that any
straight line which intersects one of them shall, if prolonged, meet
the other. But by doing this we by no means get rid of the
assumption; we are still obliged to take for granted the geometrical
truth, that all straight lines in the same plane, which have the
former of these properties, have also the latter. For if it were
possible that they should not, that is, if any straight lines in the
same plane, other than those which are parallel according to the
definition, had the property of never meeting although indefinitely
produced, the demonstrations of the subsequent portions of the
theory of parallels could not be maintained.

71 Some persons find themselves prevented from believing that the
axiom, Two straight lines can not inclose a space, could ever become
known to us through experience, by a difficulty which may be stated
as follows: If the straight lines spoken of are those contemplated
in the definition—lines absolutely without breadth and absolutely
straight—that such are incapable of inclosing a space is not proved
by experience, for lines such as these do not present themselves in
our experience. If, on the other hand, the lines meant are such
straight lines as we do meet with in experience, lines straight
enough for practical purposes, but in reality slightly zigzag, and
with some, however trifling, breadth; as applied to these lines the
axiom is not true, for two of them may, and sometimes do, inclose a
small portion of space. In neither case, therefore, does experience
prove the axiom.

Those who employ this argument to show that geometrical axioms can
not be proved by induction, show themselves unfamiliar with a common
and perfectly valid mode of inductive proof; proof by approximation.
Though experience furnishes us with no lines so unimpeachably
straight that two of them are incapable of inclosing the smallest
space, it presents us with gradations of lines possessing less and
less either of breadth or of flexure, of which series the straight
line of the definition is the ideal limit. And observation shows
that just as much, and as nearly, as the straight lines of
experience approximate to having no breadth or flexure, so much and
so nearly does the space-inclosing power of any two of them approach
to zero. The inference that if they had no breadth or flexure at
all, they would inclose no space at all, is a correct inductive
inference from these facts, conformable to one of the four Inductive
Methods hereinafter characterized, the Method of Concomitant
Variations; of which the mathematical Doctrine of Limits presents
the extreme case.

72 Whewell’s _History of Scientific Ideas_, i., 140.

73 Dr. Whewell (_Philosophy of Discovery_, p. 289) thinks it
unreasonable to contend that we know by experience, that our idea of
a line exactly resembles a real line. “It does not appear,” he says,
“how we can compare our ideas with the realities, since we know the
realities only by our ideas.” We know the realities by our
sensations. Dr. Whewell surely does not hold the “doctrine of
perception by means of ideas,” which Reid gave himself so much
trouble to refute. If Dr. Whewell doubts whether we compare our
ideas with the corresponding sensations, and assume that they
resemble, let me ask on what evidence do we judge that a portrait of
a person not present is like the original. Surely because it is like
our idea, or mental image of the person, and because our idea is
like the man himself.

Dr. Whewell also says, that it does not appear why this resemblance
of ideas to the sensations of which they are copies, should be
spoken of as if it were a peculiarity of one class of ideas, those
of space. My reply is, that I do not so speak of it. The peculiarity
I contend for is only one of degree. All our ideas of sensation of
course resemble the corresponding sensations, but they do so with
very different degrees of exactness and of reliability. No one, I
presume, can recall in imagination a color or an odor with the same
distinctness and accuracy with which almost every one can mentally
reproduce an image of a straight line or a triangle. To the extent,
however, of their capabilities of accuracy, our recollections of
colors or of odors may serve as subjects of experimentation, as well
as those of lines and spaces, and may yield conclusions which will
be true of their external prototypes. A person in whom, either from
natural gift or from cultivation, the impressions of color were
peculiarly vivid and distinct, if asked which of two blue flowers
was of the darkest tinge, though he might never have compared the
two, or even looked at them together, might be able to give a
confident answer on the faith of his distinct recollection of the
colors; that is, he might examine his mental pictures, and find
there a property of the outward objects. But in hardly any case
except that of simple geometrical forms, could this be done by
mankind generally, with a degree of assurance equal to that which is
given by a contemplation of the objects themselves. Persons differ
most widely in the precision of their recollection, even of forms:
one person, when he has looked any one in the face for half a
minute, can draw an accurate likeness of him from memory; another
may have seen him every day for six months, and hardly know whether
his nose is long or short. But every body has a perfectly distinct
mental image of a straight line, a circle, or a rectangle. And every
one concludes confidently from these mental images to the
corresponding outward things. The truth is, that we may, and
continually do, study nature in our recollections, when the objects
themselves are absent; and in the case of geometrical forms we can
perfectly, but in most other cases only imperfectly, trust our
recollections.

_ 74 Logic_, i., 222.

75 Ibid., 226.

_ 76 History of Scientific Ideas_, i., 65–67.

77 Ibid., i., 60.

78 Ibid., 58, 59.

79 “If all mankind had spoken one language, we can not doubt that there
would have been a powerful, perhaps a universal, school of
philosophers, who would have believed in the inherent connection
between names and things, who would have taken the sound _man_ to be
the mode of agitating the air which is essentially communicative of
the ideas of reason, cookery, bipedality, etc.”—De Morgan, _Formal
Logic_, p. 246.