Aristotle
actually succeeded in establishing general truths, their analysis of
the inductive operation, even when unexceptionable as to correctness,
has not been specific enough to be made the foundation of practical
rules, which might be for Induction itself what the rules of the
Syllogism are for interpretation of Induction" (Bk. III. ch. i. s. 1.
p. 313.)--"The business of Inductive Logic is to provide rules and
models (such as the Syllogism and its rules are for ratiocination) to
which if inductive arguments conform, those arguments are conclusive,
and not otherwise. This is what the Four Methods profess to be, and
what I believe they are universally considered to be by experimental
philosophers, who had practised all of them long before any one
sought to reduce the practice to theory" (Bk. III. ch. ix. s. 5, p.
471, 5th ed.)--See also the same point of view more copiously set
forth, in Mr. Mill's later work, 'Examination of Sir W. Hamilton's
Philosophy' (ch. xx. pp. 454-462, 3rd ed.): "It is only as a means to
material truth that the formal (or to speak more clearly, the
conditional) validity of an operation of thought is of any value; and
even that value is only negative: we have not made the smallest
positive advance towards right thinking, by merely keeping ourselves
consistent in what is perhaps systematic error. This by no means
implies that Formal Logic, even in its narrowest sense, is not of
very great, though purely negative value."--"Not only however is it
indispensable that the larger Logic, which embraces all the general
conditions of the ascertainment of truth, should be studied in
addition to the smaller Logic, which only concerns itself with the
conditions of consistency; but the smaller Logic ought to be (at
least, finally) studied as part of the greater--as a portion of the
means to the same end; and its relation to the other parts--to the
other means--should be distinctly displayed."]
After adverting to another variety of ratiocinative procedure, which
he calls _Apagoge_ or Abduction (where the minor is hardly more
evident than the conclusion, and might sometimes conveniently become
a conclusion first to be proved),[75] Aristotle goes on to treat of
Objection generally--the function of the dialectical respondent. The
_Enstasis_ or Objection is a proposition opposed not to a conclusion,
but to the proposition set up by the defendant. When the proposition
set up by him is universal, as it must be if he seeks to establish an
universal conclusion, your objection may be either universal or
particular: you may deny either the whole of his proposition, or only
one portion of the particulars contained under it; the denial of one
single particular, when substantiated, being enough to overthrow his
universal. Accordingly, your objection, being thus variously opposed
to the proposition, will lie in the syllogistic figures which admit
opposite conclusions; that is, either in the First or Third; for the
Second figure admits only negative conclusions not opposed to each
other. If the defendant has set up an Universal Affirmative, you may
deny the whole and establish a contrary negative, in the First
figure; or you may deny a part only, and establish a contradictory
negative, in the Third figure. The like, if he has set up an
Universal Negative: you may impugn it either by an universal contrary
affirmative, in the First figure; or by a particular contradictory
affirmative, in the Third figure.[76]
[Footnote 75: Analyt. Prior. II. xxv. p. 69, a. 20-36.]
[Footnote 76: Ibid. II. xxvi. p. 69, a. 37-b. 37.
In objecting to A _universally_, you take a term comprehending the
original subject; in objecting _particularly_, a term comprehended by
it. Of the new term in each case you deny the original predicate, and
have thus, as a major premiss, E. For a minor premiss, you affirm, in
the first case, the new term as predicate of the original subject
(less comprehensive); in the second case, the original subject (more
comprehensive) as predicate of the new term. This gives you, in the
first case, a conclusion in _Celarent_ (Fig. I.), and, in the second,
a conclusion in _Felapton_ (Fig. III.); opposed, the one universally
or contrarily, the other particularly or contradictorily, to the
original proposition.]
The Enthymeme is a syllogism from Probabilities or Signs;[77] the two
being not exactly the same. _Probabilities_ are propositions commonly
accepted, and true in the greater number of cases; such as, Envious
men hate those whom they envy, Persons who are beloved look with
affection on those who love them. We call it a _Sign_, when one fact
is the antecedent or consequent of another, and therefore serves as
mark or evidence thereof. The conjunction may be either constant, or
frequent, or merely occasional: if constant, we obtain for the major
premiss of our syllogism a proposition approaching that which is
universally or necessarily true; if not constant but only frequent or
occasional, the major premiss of our syllogism will at best only be
probable. The constant conjunction will furnish us with a Syllogism
or Enthymeme in the First figure; the significant mark being here a
genuine middle term--subject in the major premiss, and predicate in
the minor. We can then get a conclusion both affirmative and
universally true. In other cases, we cannot obtain premisses for a
syllogism in the First figure, but only for a syllogism in the Second
or Third. In the Third figure, since we get by right no universal
conclusions at all, but only particular conclusions, the conclusion
of the Enthymeme, though it may happen to be true, is open to
refutation. Where by the laws of Syllogism no affirmative conclusion
whatever is possible, as in the Second figure, the conclusion
obtained by Enthymeme is altogether suspicious. In contrast with the
Sign in these figures, that which enters as an effective middle term
into the First figure, should be distinguished under the name of
_Proof_ ([Greek: tekmê/rion].)[78]
[Footnote 77: Ibid. II. xxvii. p. 70, a. 10: [Greek: e)nthu/mêma me\n
ou)=n e)sti\ sullogismo\s e)x ei)ko/tôn ê)\ sêmei/ôn; lamba/netai de\
to\ sêmei=on trichô=s, o(sachô=s kai\ to\ me/son e)n toi=s
schê/masi.]]
[Footnote 78: Analyt. Prior. II. xxvii. p. 70, a. 31-b. 6.
Aristotle throws in the remark (a. 24), that, when one premiss only
of the Enthymeme is enunciated, it is a Sign; when the other is
added, it becomes a Syllogism. In the examples given to illustrate
the description of the Enthymeme, that which belongs to the First
figure has its three terms and two propositions specified like a
complete and regular Syllogism; but when we come to the Third and
Second figures, Aristotle gives two alternate ways of stating each:
one way in full, with both premisses enunciated, constituting a
normal, though invalid, Syllogism; the other way, with only one of
the premisses enunciated, the other being suppressed as well-known
and familiar.
Among logicians posterior to Aristotle, the definition given of the
Enthymeme, and supposed to be derived from Aristotle was, that it was
a Syllogism with one of the premisses suppressed--[Greek:
monolê/mmatos]. Sir W. Hamilton has impugned this doctrine, and has
declared the definition to be both absurd in itself, and not
countenanced by Aristotle. (Lectures on Logic, Vol. I. Lect. xx. p.
386, seq.) I think Hamilton is mistaken on this point. (See Mr.
Cope's Introd. to Arist. Rhetoric, p. 103, seq.) Even in the present
chapter Aristotle distinctly alludes to the monolemmatic enunciation
of the Enthymeme as one mode of distinguishing it from a full
Syllogism; and in the Rhetorica he brings out this characteristic
still more forcibly. The distinction is one which belongs to Rhetoric
more than to Logic; the rhetor, in enunciating his premisses, must be
careful not to weary his auditors; he must glance at or omit reasons
that are familiar to them; logical fulness and accuracy would be
inconsistent with his purpose. The writers subsequent to Aristotle,
who think much of the rhetorical and little of the logical point of
view, bring out the distinction yet more forcibly. But the rhetorical
mode of stating premisses is often not so much an omission either of
major or minor, as a confused blending or packing up of both into
one.]
Aristotle concludes his Analytica Priora by applying this doctrine of
Signs to determine the limits within which Physiognomy as a science
is practicable. The basis upon which it rests is this general fact or
postulate: That in all natural affections of the animal, bodily
changes and mental changes accompany each other. The former,
therefore, may become signs or proofs of the latter,[79] if, in each
class of animals, we can discriminate the one specific bodily
phenomenon which attaches to each mental phenomenon. Thus, the lion
is a courageous animal. What is the bodily sign accompanying a
courageous disposition? It is (we assume here) the having extremities
of great size. This belongs to all lions, as a _proprium_; in the
sense that, though it may or does belong also to some individuals of
other races (as men), it does not belong to any other entire race.
Physiognomy as a science will, then, be possible, if we can find
races of animals which have only one characteristic mental attribute,
and if we can discover what is the physical attribute correlating
with it.[80] But the difficulties are greater when the same race has
two characteristic mental attributes (_e.g._ lions are both
courageous and generous), each with its correlative physical
attribute; for how can we tell which belongs to which? We have then
to study individuals of other races possessing one of these
attributes without the other; thus, if we find that courageous men,
who are not generous, agree in having large extremities, we may infer
that this last circumstance is, in the lion, the correlative mark of
his courage and not of his generosity. The physiognomonic inference
will be expressed by a syllogism in the First figure, in which the
major term (A) reciprocates and is convertible with the middle term
(B), while B stretches beyond (or is more extensive than) the minor
(C); this relation of the terms being necessary, if there is to be a
single mark for a particular attribute.[81]
[Footnote 79: Analyt. Prior. II. xxvii. p. 70, b. 7-16: [Greek: ei)/
tis di/dôsin a(/ma metaba/llein to\ sô=ma kai\ tê\n psuchê/n, o(/sa
phusika/ e)sti pathê/mata;--sumpa/schein ga\r a)llê/lois
u(pokei=tai.] See the Aristotelian treatise entitled [Greek:
Phusiognômonika/], pp. 808-809, Bekk.]
[Footnote 80: Ibid. II. xxvii. p. 70, b. 22. About the
characteristics of the lion see Aristot. Physiognom. p. 809, b.
14-36: [Greek: ta\ peri\ tê\n psuchê\n dotiko\n kai\ e)leu/theron,
megalo/psuchon kai\ philo/nikon, kai\ prau+\ kai\ di/kaion kai\
philo/storgon pro\s a(\ a)\n o(milê/sê|.]]
[Footnote 81: Ibid. II. xxvii. p. 70, b. 31-36.]
Here the treatise ends; but the reader will remember that, in
describing the canons laid down by Aristotle for the Syllogism with
its three Figures and the Modes contained therein, I confined myself
to the simple Assertory syllogism, postponing for the moment the long
expositions added by him about Modal syllogisms, involving the
Possible and the Necessary. What is proper to be said about this
complicated and useless portion of the Analytica Priora, may well
come in here; for, in truth, the doctrines just laid down about
Probabilities, Signs, and Proofs, bring us back to the Modals under a
different set of phrases. The Possible or Problematical is that, of
the occurrence or reality of which we doubt, neither believing nor
disbelieving it, not being prepared to assert either that it is, or
that it is not; _that which may be or may not be_. It is our manner