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:—