Aristotle
in this chapter.
Here it will be seen that in place of the words given in Waitz's
text, [Greek: pa=n ga\r to\ _a)/cholon_ makro/bion], Pacius gives
[Greek: pa=n ga\r _to\ G_ makro/bion]: annexing however to the letter
[Greek: G] an asterisk referring to the margin, where we find the
word [Greek: a)/cholon] inserted in small letters, seemingly as a
various reading not approved by Pacius. And M. Barthélemy St. Hilaire
has accommodated his French translation (p. 328) to the text of
Pacius: "Donc A est à C tout entier, car tout C est longève."
Boethius in his Latin translation (p. 519) recognizes as his original
[Greek: pa=n ga\r to\ a)/cholon makro/bion], but he alters the text
in the words immediately preceding:--"Ergo _toti B_ (instead of _toti
C_) inest A, omne enim quod sine cholera est, longævum," &c. (p.
519). The edition of Aldus (Venet. 1495) has the text conformable to
the Latin of Boethius: [Greek: tô=| dê\ B o(/lô| u(pa/rchei to\ A;
pa=n ga\r to\ a)/cholon makro/bion]. Three distinct Latin
translations of the 16th century are adapted to the same text, viz.,
that of Vives and Valentinus (Basil. 1542); that published by the
Junta (Venet. 1552); and that of Cyriacus (Basil. 1563). Lastly, the
two Greek editions of Sylburg (1587) and Casaubon (Lugduni 1590),
have the same text also: [Greek: tô=| dê\ B o(/lô| u(pa/rchei to\ A;
pa=n ga\r [to\ G] to\ a)/cholon makro/bion]. Casaubon prints in
brackets the words [Greek: [to\ G]] before [Greek: to\ a)/cholon].
Now it appears to me that the text of Bekker and Waitz (though Waitz
gives it without any comment or explanation) is erroneous; neither
consisting with itself, nor conforming to the general view enunciated
by Aristotle of the Syllogism from Induction. I have cited two
distinct versions, each different from this text, as given by the
earliest editors; in both the confusion appears to have been felt,
and an attempt made to avoid it, though not successfully.
Aristotle's view of the Syllogism from Induction is very clearly
explained by M. Barthélemy St. Hilaire in the instructive notes of
his translation, pp. 326-328; also in his Preface, p.
lvii.:--"L'induction n'est au fond qu'un syllogisme dont le mineur et
le moyen sont d'extension égale. Du reste, il n'est qu'une seule
manière dont le moyen et le mineur puissent être d'égale extension;
c'est que le mineur se compose de toutes les parties dont le moyen
représente la totalité. D'une part, tous les individus: de l'autre,
l'espèce totale qu'ils forment. L'intelligence fait aussitôt
équation entre les deux termes égaux."
According to the Aristotelian text, as given both by Pacius and the
others, A, the major term, represents _longævum_ (long-lived, the
class-term or total); B, the middle term, represents _vacans bile_
(bile-less, the class-term or total); C, the minor term, represents
the aggregate individuals of the class _longævum_, man, horse, mule,
&c.
Julius Pacius draws out the Inductive Syllogism, thus:--
1. Omnis homo, equus, asinus, &c., est longævus.
2. Omnis homo, equus, asinus, &c., vacat bile.
Ergo:
3. Quicquid vacat bile, est longævum.
Convertible into a Syllogism in Barbara:--
1. Omnis homo, equus, asinus, &c., est longævus.
2. Quicquid vacat bile, est homo, equus, asinus, &c.
Ergo:
3. Quicquid vacat bile, est longævum.
Here the force of the proof (or the possibility, in this exceptional
case, of converting a syllogism in the Third figure into another in
_Barbara_ of the First figure) depends upon the equation or
co-extensiveness (not enunciated in the premisses, but assumed in
addition to the premisses) of the minor term C with the middle term
B. But I contend that this is _not_ the condition peremptorily
required, or sufficient for proof, if we suppose C the minor term to
represent _omne longævum_. We must understand C the minor term to
represent _omne vacans bile_, or _quicquid vacat bile_: and unless we
understand this, the proof fails. In other words, _homo, equus,
asinus, &c._ (the aggregate of individuals), must be co-extensive
with the class-term bile-less or _vacans bile_: but they need not be
co-extensive with the class-term long-lived or _longævum_. In the
final conclusion, the subject _vacans bile_ is distributed; but the
predicate _longævum_ is not distributed; this latter may include,
besides all bile-less animals, any number of other animals, without
impeachment of the syllogistic proof.
Such being the case, I think that there is a mistake in the text as
given by all the editors, from Pacius down to Bekker and Waitz. What
they give, in setting out the terms of the Aristotelian Syllogism
from Induction, is: [Greek: e)/stô to\ A makro/bion, to\ d' e)ph'
ô(=| B, to\ cholên mê\ e)/chon, e)ph' ô(=| de\ G, _to\ kath'
e(/kaston makro/bion_, oi(=on a)/nthrôpos kai\ i(/ppos kai\
ê(mi/onos.] Instead of which the text ought to run, [Greek: e)ph'
ô(=| de\ G, _to\ kath' e(/kaston a)/cholon_, oi(=on a)/nthr. k. i(/p.
k. ê(mi/]. That these last words were the original text, is seen by
the words immediately following: [Greek: tô=| dê\ G o(/lô| u(pa/rchei
to\ A. _pa=n ga\r to\ a)/cholon makro/bion_]. For the reason thus
assigned (in the particle [Greek: ga/r]) is irrelevant and unmeaning
if [Greek: G] designates [Greek: to\ kath' e(/kaston _makro/bion_ ],
while it is pertinent and even indispensable if [Greek: G] designates
[Greek: to\ kath' e(/kaston _a)/cholon_]. Pacius (or those whose
guidance he followed in his text) appears to have perceived the
incongruity of the reason conveyed in the words [Greek: pa=n ga\r to\
a)/cholon makro/bion]; for he gives, instead of these words, [Greek:
pa=n ga\r _to\ G_ makro/bion]. In this version the reason is indeed
no longer incongruous, but simply useless and unnecessary; for when
we are told that A designates the class _longævum_, and that [Greek:
G] designates the individual _longæva_, we surely require no reason
from without to satisfy us that A is predicable of all [Greek: G].
The text, as translated by Boethius and others, escapes that
particular incongruity, though in another way, but it introduces a
version inadmissible on other grounds. Instead of [Greek: tô=| _dê\
G_ o(/lô| u(pa/rchei to\ A, pa=n ga\r to\ a)/cholon makro/bion],
Boethius has [Greek: tô=| _dê\ B_ o(/lô| u(pa/rchei to\ A, pa=n ga\r
to\ a)/cholon makro/bion]. This cannot be accepted, because it
enunciates the conclusion of the syllogism as if it were one of the
premisses. We must remember that the conclusion of the Aristotelian
Syllogism from Induction is, that A is predicable of B, one of the
premisses to prove it being that A is predicable of the minor term C.
But obviously we cannot admit as one of the premisses the proposition
that A may be predicated of B, since this proposition would then be
used as premiss to prove itself as conclusion.
If we examine the Aristotelian Inductive Syllogism which is intended
to conduct us to the final _probandum_, we shall see that the terms
of it are incorrectly set out by Bekker and Waitz, when they give the
minor term [Greek: G] as designating [Greek: to\ kath' e(/kaston
makro/bion]. This last is not one of the three terms, nor has it any
place in the syllogism. The three terms are:
1. A--major--the class-term or class [Greek: makro/bion]--_longævum_.
2. B--middle--the class term or class [Greek: a)/cholon]--bile-less.
3. C--minor--the individual bile-less animals, man, horse, &c.
There is no term in the syllogism corresponding to the individual
_longæva_ or long-lived animals; this last (I repeat) has no place in
the reasoning. We are noway concerned with the totality of long-lived
animals; all that the syllogism undertakes to prove is, that in and
among that totality all bile-less animals are included; whether there
are or are not other long-lived animals besides the bile-less, the
syllogism does not pretend to determine. The equation or
co-extensiveness required (as described by M. Barthélemy St. Hilaire
in his note) is not between the individual long-lived animals and the
class, bile-less animals (middle term), but between the aggregate of
individual animals known to be bile-less and the class, bile-less
animals. The real minor term, therefore, is (not the individual
_long-lived_ animals, but) the individual _bile-less_ animals. The
two premisses of the Inductive Syllogism will stand thus:--
Men, Horses, Mules, &c., are long-lived (major).
Men, Horses, Mules, &c., are bile-less (minor).
And, inasmuch as the subject of the minor proposition is co-extensive
with the predicate (which, if quantified according to Hamilton's
phraseology, would be, _All_ bile-less animals), so that the
proposition admits of being converted simply,--the middle term will
become the subject of the conclusion, All bileless animals are
long-lived.]
[Footnote 54: 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.]]
[Footnote 55: Analyt. Prior. II. **xxiii. p. 68, p. 23: [Greek: ei)
ou)=n a)ntistre/phei to\ G tô=| B, kai\ mê\ u(pertei/nei to\ me/son,
a)na/gkê to\ A tô=| B u(pa/rchein.]
Julius Pacius translates this: "Si igitur convertatur [Greek: to\ G]
cum B, nec medium excedat, necesse est [Greek: to\ A tô=| B] inesse."
These Latin words include the same grammatical ambiguity as is found
in the Greek original: _medium_, like [Greek: to\ me/son], may be
either an accusative case governed by _excedat_, or a nominative case
preceding _excedat_. The same may be said of the other Latin
translations, from Boethius downwards.
But M. Barthélemy St. Hilaire in his French translation, and Sir W.
Hamilton in his English translation (Lectures on Logic, Vol. II. iv.
p. 358, Appendix), steer clear of this ambiguity. The former says:
"Si donc C est réciproque à B, et qu'il ne dépasse pas le moyen, il
est nécessaire alors que A soit à B:" to the same purpose, Hamilton,
_l. c._ These words are quite plain and unequivocal. Yet I do not
think that they convey the meaning of Aristotle. In my judgment,
Aristotle meant to say: "If then C reciprocates with B, and if the
middle term (B) does not stretch beyond (the minor C), it is
necessary that A should be predicable of B." To show that this must
be the meaning, we have only to reflect on what C and B respectively
designate. It is assumed that C designates the sum of individual
bile-less animals; and that B designates the class or class-term
bile-less, that is, the totality thereof. Now the sum of individuals
included in the minor (C) cannot upon any supposition overpass the
totality: but it may very possibly fall short of totality; or (to
state the same thing in other words) the totality may possibly
surpass the sum of individuals under survey, but it cannot possibly
fall short thereof. B is here the limit, and may possibly stretch
beyond C; but cannot stretch beyond B. Hence I contend that the
translations, both by M. Barthélemy St. Hilaire and Sir W. Hamilton,
take the wrong side in the grammatical alternative admissible under
the words [Greek: kai\ mê\ u(pertei/nei to\ me/son]. The only doubt
that could possibly arise in the case was, whether the aggregate of
individuals designated by the minor did, or did not, reach up to the
totality designated by the middle term; or (changing the phrase)
whether the totality designated by the middle term did, or did not,
stretch beyond the aggregate of individuals designated by the minor.
Aristotle terminates this doubt by the words: "And if the middle term
does _not_ stretch beyond (the minor)." Of course the middle term
does not stretch beyond, when the terms reciprocate; but when they do
not reciprocate, the middle term must be the _more_ extensive of the