Aristotle
two; it can _never_ be the _less_ extensive of the two, since the
aggregate of individuals cannot possibly exceed totality, though it
may fall short thereof.
I have given in the text what I think the true meaning of Aristotle,
departing from the translations of M. Barthélemy St. Hilaire and
Sir** W. Hamilton.]
[Footnote 56: Analyt. Prior. II. xxiii. p. 68, b. 30-38: [Greek:
e)/sti d' o( toiou=tos sullogismo\s tê=s prô/tês kai\ a)me/sou
prota/seôs; ô(=n me\n ga/r e)sti me/son, dia\ tou= me/sou o(
sullogismo/s, ô(=n de\ mê/ e)sti, di' e)pagôgê=s.--phu/sei me\n ou)=n
pro/teros kai\ gnôrimô/teros o( dia\ tou= me/sou sullogismo/s, ê(mi=n
d' e)narge/steros o( dia\ tê=s e)pagôgê=s.]]
From Induction he proceeds to Example. You here take in (besides the
three terms, major, middle, and minor, of the Syllogism) a fourth
term; that is, a new particular case analogous to the minor. Your
purpose here is to show--not, as in the ordinary Syllogism, that the
major term is predicable of the minor, but, as in the Inductive
Syllogism--that the major term is predicable of the middle term; and
you prove this conclusion, not (as in the Inductive Syllogism)
through the minor term, but through the new case or fourth term
analogous to the minor.[57] Let A represent evil or mischievous; B,
war against neighbours, generally; C, war of Athens against Thebes,
an event to come and under deliberation; D, war of Thebes against
Phokis, a past event of which the issue is known to have been
signally mischievous. You assume as known, first, that A is
predicable of D, _i.e._ that the war of Thebes against Phokis has
been disastrous; next, that B is predicable both of C and of D,
_i.e._ that each of the two wars, of Athens against Thebes, and of
Thebes against Phokis, is a war of neighbours against neighbours, or
a conterminous war. Now from the premiss that A is predicable of D,
along with the premiss that B is predicable of D, you infer that A is
predicable of the class B, or of conterminous wars generally; and
hence you draw the farther inference, that A is also predicable of C,
another particular case under the same class B. The inference here
is, in the first instance, from part to whole; and finally, through
that whole, from the one part to another part of the same whole.
_Induction_ includes in its major premiss all the particulars,
declaring all of them to be severally subjects of the major as
predicate; hence it infers as conclusion, that the major is also
predicable of the middle or class-term comprising all these
particulars, but comprising no others. _Example_ includes not all,
but only one or a few particulars; inferring from it or them, first,
to the entire class, next, to some new analogous particular belonging
to the class.[58]
[Footnote 57: Ibid. II. xxiv. p. 68, b. 38: [Greek: paradei=gma d'
e)sti\n o(/tan tô=| me/sô| to\ a)/kron u(pa/rchon deichthê=| dia\
tou= o(moi/ou tô=| tri/tô|.]]
[Footnote 58: Analyt. Prior. II. xxiv. p. 69, a. 1-19**.
Julius Pacius (p. 400) notes the unauthorized character of
this so-called Paradeigmatic Syllogism, contradicting the rules of
the figures laid down by Aristotle, and also the confused manner in
which the scope of it is described: first, to infer from a single
example to the universal; next, to infer from a single example
_through_ the universal to another parallel case. To which we may add
the confused description in p. 69, a. 17, 18, where [Greek: to\
a)/kron] in the first of the two lines signifies the _major_
extreme--in the second of the two the _minor_ extreme. See Waitz's
note, p. 533.
If we turn to ch. xxvii. p. 70, a. 30-34, we shall find Aristotle on
a different occasion disallowing altogether this so-called Syllogism
from Example.]
These chapters respecting Induction and Example are among the most
obscure and perplexing in the Aristotelian Analytica. The attempt to
throw both Induction and Example into the syllogistic form is alike
complicated and unfortunate; moreover, the unsatisfactory reading and
diversities in the text, among commentators and translators, show
that the reasoning of Aristotle has hitherto been imperfectly
apprehended.[59] From some of his phrases, we see that he was aware
of the essential antithesis between Induction and Syllogism; yet the
syllogistic forms appear to have exercised such fascination over his
mind, that he could not be satisfied without trying to find some
abnormal form of Syllogism to represent and give validity to
Induction. In explaining generally what the Syllogism is, and what
Induction is, he informs us that the Syllogism presupposes and rests
upon the process of Induction as its postulate. For there can be no
valid Syllogism without an universal proposition in one (at least) of
the premisses; and he declares, unequivocally, that universal
propositions are obtained only through Induction. How Induction
operates through the particular facts of sense, remembered, compared,
and coalescing into clusters held together by associating similarity,
he has also told us; it is thus that Experience, with its universal
notions and conjunctions, is obtained. But this important process is
radically distinct from that of syllogizing, though it furnishes the
basis upon which all syllogizing is built.
[Footnote 59: Sir W. Hamilton (Lectures on Logic, vol. i. p. 319)
says justly, that Aristotle has been very brief and unexplicit in his
treatment of Induction. Yet the objections that Hamilton makes to
Aristotle are very different from those which I should make. In the
learned and valuable Appendix to his Lectures (vol. iv. pp. 358-369),
he collects various interesting criticisms of logicians respecting
Induction as handled by Aristotle. Ramus (in his Scholæ Dialecticæ,
VIII. xi.) says very truly:--"Quid vero sit Inductio, perobscure ab
Aristotele declaratur; nec ab interpretibus intelligitur, quo modo
_syllogismus_ per medium concludat majus extremum de minore;
_inductio_, majus de medio per minus."
The Inductive Syllogism, as constructed by Aristotle, requires a
reciprocating minor premiss. It may, indeed, be cited (as I have
already remarked) in support of Hamilton's favourite precept of
quantifying the predicate. The predicate of this minor must be
assumed as _quantified in thought_, the subject being taken as
co-extensive therewith. Therefore Hamilton's demand that it shall be
_quantified in speech_ has really in this case that foundation which
he erroneously claims for it in all cases. He complains that Lambert
and some other logicians dispense with the necessity of quantifying
the predicate of the minor by making it disjunctive; and adds the
remarkable statement that "the recent German logicians, Herbart,
Twesten, Drobisch, &c., following Lambert, make the Inductive
Syllogism a byeword" (p. 366). I agree with them in thinking the
attempted transformation of Induction into Syllogism very
unfortunate, though my reasons are probably not the same as theirs.
Trendelenburg agrees with those who said that Aristotle's doctrine
about the Inductive Syllogism required that the minor should be
disjunctively enunciated (Logische Untersuchungen, xiv. p. 175, xvi.
pp. 262, 263; also Erläuterungen zu den Elementen der Aristotelischen
Logik, ss. 34-36, p. 71). Ueberweg takes a similar view (System der
**Logik, sect. 128, p. 367, 3rd ed.). If the Inductive Inference
is to be twisted into Syllogism, it seems more naturally to fall into
an _hypothetical_ syllogism, _e. g._:--
If this, that, and the other magnet attract iron, all magnets attract
iron;
But this, that, and the other magnet do attract iron: _Ergo_,
&c.]
The central idea of the Syllogism, as defined by Aristotle, is that
of a conclusion following from given premisses by _necessary_
sequence;[60] meaning by the term _necessary_ thus much and no
more--that you cannot grant the premisses, and deny the conclusion,
without being inconsistent with yourself, or falling into
contradiction. In all the various combinations of propositions, set
forth by Aristotle as the different figures and modes of Syllogism,
this property of necessary sequence is found. But it is a property
which no Induction can ever possess.[61] When Aristotle professes to
point out a particular mode of Syllogism to which Induction conforms,
he can only do so by falsifying the process of Induction, and by not
accurately distinguishing between what is observed and what is
inferred. In the case which he takes to illustrate the Inductive
Syllogism--the inference from all particular bile-less animals to the
whole class bile-less--he assumes that we have ascertained the
attribute to belong to _all_ the particulars, and that the inductive
inference consists in passing from all of them to the class-term; the
passage from premisses to conclusion being here necessary, and thus
falling under the definition of Syllogism; since, to grant the
premisses, and yet to deny the conclusion, involves a contradiction.
But this doctrine misconceives what the inductive inference really is.
We never can observe _all_ the particulars of a class, which is
indefinite as to number of particulars, and definite only in respect
of the attributes connoted by the class-term. We can only observe
_some_ of the particulars, a greater or smaller proportion. Now it is
in the transition from these _to_ the totality of particulars, that
the real inductive inference consists; not in the transition _from_
the totality to the class-term which denotes that totality and
connotes its determining common attribute. In fact, the distinction
between the totality of particulars and the meaning of the
class-term, is one not commonly attended to; though it is worthy of
note in an analysis of the intellectual process, and is therefore
brought to view by Aristotle. But he employs it incorrectly as an
intermediate step to slur over the radical distinction between
Induction and Syllogism. He subjoins:[62]--"You must conceive the
minor term C (in the Inductive Syllogism) as composed of all the
particulars; for Induction is through all of them." You may say that
Induction is _through_ all the particulars, if you distinguish this
totality from the class-term, and if you treat the class-term as the
ultimate _terminus ad quem_. But the Induction must first travel _to_
all the particulars; being forced to take start from a part only, and
then to jump onward far enough to cover the indefinite unobserved
remainder. This jump is the real Induction; and this can never be
brought under the definition of Syllogism; for in the best and most
certain Induction the sequence is never a necessary one: you may
grant the premisses and deny the conclusion without contradicting
yourself.
[Footnote 60: Alexander intimates that Aristotle enunciated
"necessary sequence" as a part of his definition of Syllogism, for
the express purpose of distinguishing it from Induction, which is a
sequence _not necessary_ (Schol. ad Top. p. 253, a. 19, Br.): [Greek:
to\ d' _e)x a)na/gkês_ proskei/menon e)n tô=| o(/rô|, tê=s
**e)pagôgê=s chôri/zei to\n sullogismo/n; **e)/sti me\n ga\r kai\
e)pagôgê\ lo/gos e)n ô(=| tethe/ntôn tinô=n e(/tero/n ti tô=n
keime/nôn sumbai/nei, a)ll' _ou)k_ e)x a)na/gkês.]]
[Footnote 61: Alexander (in his Scholia on the Metaphysica, E. i. p.
406**, ed. Bonitz) observes truly: [Greek: a)ll' ei) e)k tê=s
ai)sthê/seôs kai\ tê=s e)pagôgê=s pi/stis, ou)k e)/stin a)po/deixis,
pro\s pa=san ga\r e)pagôgê\n du/natai/ tis e)ni/stasthai kai\ mê\
e)a=|n to\ katho/lou sumperai/nein.]]
[Footnote 62: Analyt. Prior. II. xxiii. p. 68, b. 27: [Greek: dei=
de\ noei=n to\ G to\ e)x a(pa/ntôn tô=n kath' e(/kaston sugkei/menon;
ê( ga\r e)pagôgê\ dia\ pa/ntôn.] See Professor Bain's 'Inductive
Logic,' chap. i. s. 2, where this process is properly criticised.]