Note 65 — Chapter VII · ANALYTICA POSTERIORA I.

See Mr. Poste’s note, p. 77, of his translation of this treatise. After saying that the first of Aristotle’s dialectical proofs is faulty, and that the second is a petitio principii, Mr. Poste adds, respecting the so-called analytical proof given by Aristotle:— “It is not so much a proof, as a more accurate determination of the principle to be postulated. This postulate, the existence of first principles, as concerning the constitution of the world, appears to belong properly to Metaphysics, and is merely borrowed by Logic. See Metaph. ii. 2, and Introduction.” In the passage of the Metaphysica (α. p. 994) here cited the main argument of Aristotle is open to the same objection of petitio principii which Mr. Poste urges against Aristotle’s second dialectical argument in this place.

Mr. John Stuart Mill, in his System of Logic, takes for granted that there must be immediate, indemonstrable truths, to serve as a basis for deduction; “that there cannot be a chain of proof suspended from nothing;” that there must be ultimate laws of nature, though we cannot be sure that the laws now known to us are ultimate.

On the other hand, we read in the recent work of an acute contemporary philosopher, Professor Delbœuf (Essai de Logique Scientifique, Liège, 1865, Pref. pp. v, vii, viii, pp. 46, 47:) — “Il est des points sur lesquels je crains de ne m’être pas expliqué assez nettement, entre autres la question du fondement de la certitude. Je suis de ceux qui repoussent de toutes leurs forces l’axiome si spécieux qu’on ne peut tout démontrer; cette proposition aurait, à mes yeux, plus besoin que toute autre d’une démonstration. Cette démonstration ne sera en partie donnée que quand on aura une bonne fois énuméré toutes les propositions indémontrables; et quand on aura bien défini le caractère auquel on les reconnait. Nulle part on ne trouve ni une semblable énumération, ni une semblable définition. On reste à cet égard dans une position vague, et par cela même facile à défendre.”

It would seem, by these words, that M. Delbœuf stands in the most direct opposition to Aristotle, who teaches us that the ἀρχαὶ or principia from which demonstration starts cannot be themselves demonstrated. But when we compare other passages of M. Delbœuf’s work, we find that, in rejecting all undemonstrable propositions, what he really means is to reject all self-evident universal truths, “C’est donc une véritable illusion d’admettre des vérités évidentes par elles-mêmes. Il n’y a pas de proposition fausse que nous ne soyons disposés d’admettre comme axiome, quand rien ne nous a encore autorisés à la repousser” (p. ix.). This is quite true in my opinion; but the immediate indemonstrable truths for which Aristotle contends as ἀρχαὶ of demonstration, are not announced by him as self-evident, they are declared to be results of sense and induction, to be raised from observation of particulars multiplied, compared, and permanently formularized under the intellectual habitus called Noûs. By Demonstration Aristotle means deduction in its most perfect form, beginning from these ἀρχαὶ which are inductively known but not demonstrable (i. e. not knowable deductively). And in this view the very able and instructive treatise of M. Delbœuf mainly coincides, assigning even greater preponderance to the inductive process, and approximating in this respect to the important improvements in logical theory advanced by Mr. John Stuart Mill.

Among the universal propositions which are not derived from Induction, but which serve as ἀρχαὶ for Deduction and Demonstration, we may reckon the religious, ethical, æsthetical, social, political, &c., beliefs received in each different community, and impressed upon all newcomers born into it by the force of precept, example, authority. Here the major premiss is felt by each individual as carrying an authority of its own, stamped and enforced by the sanction of society, and by the disgrace or other penalties in store for those who disobey it. It is ready to be interpreted and diversified by suitable minor premisses in all inferential applications. But these ἀρχαὶ for deduction, differing widely at different times and places, though generated in the same manner and enforced by the same sanction, would belong more properly to the class which Aristotle terms τὰ ἔνδοξα.