Aristotle

by George Grote

[51] Ibid. II. xxiii. p. 68, b. 13: ἅπαντα γὰρ πιστεύομεν ἢ διὰ συλλογισμοῦ ἢ ἐξ ἐπαγωγῆς.

Though Aristotle might seem, even here, to have emphatically contrasted Syllogism with Induction as a ground of belief, he proceeds forthwith to indicate a peculiar form of Syllogism which may be constructed out of Induction. Induction, and the Syllogism from or out of Induction (he says) is a process in which we invert the order of the terms. Instead of concluding from the major through the middle to the minor (i.e. concluding that the major is predicable of the minor), we now begin from the minor and conclude from thence through the middle to the major (i.e. we conclude that the major is predicable of the middle).[52] In Syllogism as hitherto described, we concluded that A the major was predicable of C the minor, through the middle B; in the Syllogism from Induction we begin by affirming that A the major is predicable of C the minor; next, we affirm that B the middle is also predicable of C the minor. The two premisses, standing thus, correspond to the Third figure of the Syllogism (as explained in the preceding pages) and would not therefore by themselves justify anything more than a particular affirmative conclusion. But we reinforce them by introducing an extraneous assumption:— That the minor C is co-extensive with the middle B, and comprises the entire aggregate of individuals of which B is the universal or class-term. By reason of this assumption the minor proposition becomes convertible simply, and we are enabled to infer (according to the last preceding chapter) an universal affirmative conclusion, that the major term A is predicable of the middle term B. Thus, let A (the major term) mean the class-term, long-lived; let B (the middle term) mean the class-term, bile-less, or the having no bile; let C (the minor term) mean the individual animals — man, horse, mule, &c., coming under the class-term B, bile-less.[53] We are supposed to know, or to have ascertained, that A may be predicated of all C; (i.e. that all men, horses, mules, &c., are long-lived); we farther know that B is predicable of all C (i.e. that men, horses, mules, &c., belong to the class bile-less). Here, then, we have two premisses in the Third syllogistic figure, which in themselves would warrant us in drawing the particular affirmative conclusion, that A is predicable of some B, but no more. Accordingly, Aristotle directs us to supplement these premisses[54] by the extraneous assumption or postulate, that C the minor comprises all the individual animals that are bile-less, or all those that correspond to the class-term B; in other words, the assumption, that B the middle does not denote any more individuals than those which are covered by C the minor — that B the middle does not stretch beyond or overpass C the minor.[55] Having the two premisses, and this postulate besides, we acquire the right to conclude that A is predicable of all B. But we could not draw that conclusion from the premisses alone, or without the postulate which declares B and C to be co-extensive. The conclusion, then, becomes a particular exemplification of the general doctrine laid down in the last chapter, respecting the reciprocation of extremes and the consequences thereof. We thus see that this very peculiar Syllogism from Induction is (as indeed Aristotle himself remarks) the opposite or antithesis of a genuine Syllogism. It has no proper middle term; the conclusion in which it results is the first or major proposition, the characteristic feature of which it is to be immediate, or not to be demonstrated through a middle term. Aristotle adds that the genuine Syllogism, which demonstrates through a middle term, is by nature prior and more effective as to cognition; but that the Syllogism from Induction is to us plainer and clearer.[56]

[52] Analyt. Prior. II. xxiii. p. 68, b. 15: ἐπαγωγὴ μὲν οὖν ἐστὶ καὶ ὁ ἐξ ἐπαγωγῆς συλλογισμὸς τὸ διὰ τοῦ ἑτέρου θάτερον ἄκρον τῷ μέσῳ συλλογίσασθαι· οἷον εἰ τῶν ΑΓ μέσον τὸ Β, διὰ τοῦ Γ δεῖξαι τὸ Α τῷ Β ὑπάρχον· οὕτω γὰρ ποιούμεθα τὰς ἐπαγωγάς.

Waitz in his note (p. 532) says: “Fit Inductio, cum per minorem terminum demonstratur medium prædicari de majore.â€� This is an erroneous explanation. It should have been: “demonstratur majorem prædicari de medio.â€� Analyt. Prior. II. xxiii. 68, b. 32: καὶ τρόπον τινὰ ἀντικεῖται ἡ ἐπαγωγὴ τῷ συλλογισμῷ· ὁ μὲν γὰρ διὰ τοῦ μέσου τὸ ἄκρον τῷ τρίτῳ δείκνυσιν, ἡ δὲ διὰ τοῦ τρίτου τὸ ἄκρον τῷ μέσῳ.

[53] 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.â€� 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,â€� &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.�