Note 53 — Chapter VI · ANALYTICA PRIORA II.

Ibid. II. xxiii. p. 68, b. 18: οἷον ἔστω τὸ Α μακρόβιον, τὸ δ’ ἐφ’ ᾧ Β, τὸ χολὴν μὴ ἔχον, ἐφ’ ᾧ δὲ Γ, τὸ καθ’ ἕκαστον μακρόβιον, οἷον ἄνθρωπος καὶ ἵππος καὶ ἡμίονος. τῷ δὴ Γ ὅλῳ ὑπάρχει τὸ Α· πᾶν γὰρ τὸ ἄχολον μακρόβιον· ἀλλὰ καὶ τὸ Β, τὸ μὴ ἔχειν χολήν, παντὶ ὑπάρχει τῷ Γ. εἰ οὖν ἀντιστρέφει τὸ Γ τῷ Β καὶ μὴ ὑπερτείνει τὸ μέσον, ἀνάγκη τὸ Α τῷ Β ὑπάρχειν.

I have transcribed this Greek text as it stands in the editions of Buhle, Bekker, Waitz, and F. Didot. Yet, notwithstanding these high authorities, I venture to contend that it is not wholly correct; that the word μακρόβιον, which I have emphasized, is neither consistent with the context, nor suitable for the point which Aristotle is illustrating. Instead of μακρόβιον, we ought in that place to read ἄχολον; and I have given the sense of the passage in my English text as if it did stand ἄχολον in that place.

I proceed to justify this change. If we turn back to the edition by Julius Pacius (1584, p. 377), we find the text given as follows after the word ἡμίονος (down to that word the text is the same): τῷ δὴ Γ ὅλῳ ὑπάρχει τὸ Α· πᾶν γὰρ τὸ Γ μακρόβιον· ἀλλὰ καὶ τὸ Β, τὸ μὴ ἔχον χολήν, παντὶ ὑπάρχει τῷ Γ. εἰ οὖν ἀντιστρέφει τὸ Γ τῷ Β, καὶ μὴ ὑπερτείνει τὸ μέσον, ἀνάγκη τὸ Α τῷ Β ὑπάρχειν. Earlier than Pacius, the edition of Erasmus (Basil. 1550) has the same text in this chapter.

Here it will be seen that in place of the words given in Waitz’s text, πᾶν γὰρ τὸ ἄχολον μακρόβιον, Pacius gives πᾶν γὰρ τὸ Γ μακρόβιον: annexing however to the letter Γ an asterisk referring to the margin, where we find the word ἄχολον 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 πᾶν γὰρ τὸ ἄχολον μακρόβιον, 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: τῷ δὴ Β ὅλῳ ὑπάρχει τὸ Α· πᾶν γὰρ τὸ ἄχολον μακρόβιον. 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: τῷ δὴ Β ὅλῳ ὑπάρχει τὸ Α· πᾶν γὰρ [τὸ Γ] τὸ ἄχολον μακρόβιον. Casaubon prints in brackets the words [τὸ Γ] before τὸ ἄχολον.

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: ἔστω τὸ Α μακρόβιον, τὸ δ’ ἐφ’ ᾧ Β, τὸ χολην μὴ ἔχον, ἐφ’ ᾧ δὲ Γ, τὸ καθ’ ἕκαστον μακρόβιον, οἷον ἄνθρωπος καὶ ἵππος καὶ ἡμίονος. Instead of which the text ought to run, ἐφ’ ᾧ δὲ Γ, τὸ καθ’ ἕκαστον ἄχολον, οἷον ἄνθρ. κ. ἵπ. κ. ἡμί. That these last words were the original text, is seen by the words immediately following: τῷ δὴ Γ ὅλῳ ὑπάρχει τὸ Α. πᾶν γὰρ τὸ ἄχολον μακρόβιον. For the reason thus assigned (in the particle γάρ) is irrelevant and unmeaning if Γ designates τὸ καθ’ ἕκαστον μακρόβιον, while it is pertinent and even indispensable if Γ designates τὸ καθ’ ἕκαστον ἄχολον. Pacius (or those whose guidance he followed in his text) appears to have perceived the incongruity of the reason conveyed in the words πᾶν γὰρ τὸ ἄχολον μακρόβιον; for he gives, instead of these words, πᾶν γὰρ τὸ Γ μακρόβιον. 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 Γ designates the individual longæva, we surely require no reason from without to satisfy us that A is predicable of all Γ. 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 τῷ δὴ Γ ὅλῳ ὑπάρχει τὸ Α, πᾶν γὰρ τὸ ἄχολον μακρόβιον, Boethius has τῷ δὴ Β ὅλῳ ὑπάρχει τὸ Α, πᾶν γὰρ τὸ ἄχολον μακρόβιον. 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 Γ as designating τὸ καθ’ ἕκαστον μακρόβιον. 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 μακρόβιον — longævum. 2. B — middle — the class term or class ἄχολον — 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.