[40] Aristot. De Interpr. p. 22, a. 14-b. 28.
[41] Aristot. De Interpr. p. 22, b. 22, λείπεται τοίνυν &c.; Ammonius, Schol. p. 133, b. 5-27-36.
Aristotle also intimates (p. 23, a. 18) that it would be better to reverse the order of the propositions in the tables, and to place the Necessary before the Possible. M. Barthélemy St. Hilaire has inserted (in the note to his Translation, p. 197) tables with this reversed order.
[42] Aristot. De Interpret. p. 22, b. 29-p. 23, a. 15.
Having thus stated that possible to be, in this unilateral and equivocal sense but in no other, is a legitimate consequence of necessary to be, Aristotle proceeds to lay down a tripartite distinction which surprises us in this place. “It is plain from what has been said that that which is by Necessity, is in Act or Actuality; so that if things sempiternal are prior, Actuality is prior to Possibility. Some things, like the first (or celestial) substances, are Actualities without Possibility; others (the generated and perishable substances) which are prior in nature but posterior in generation, are Actualities along with Possibility; while a third class are Possibilities only, and never come into Actuality� (such as the largest number, or the least magnitude).[43]
[43] Ibid. p. 23, a. 21-26.
Now the sentence just translated (enunciating a doctrine of Aristotle’s First Philosophy rather than of Logic) appears decidedly to contradict what he had said three lines before, viz., that in one certain sense, the necessary to be included and implied the possible to be; that is, a possibility or potentiality unilateral only, not bilateral; for we are here told that the celestial substance is Actuality without Possibility (or Potentiality), so that the unilateral sense of this last term is disallowed. On the other hand, a third sense of the same term is recognized and distinguished; a sense neither bilateral nor unilateral, but the negation of both. This third sense is hardly intelligible, giving as it does an impossible Possible; it seems a self-contradictory description.[44] At best, it can only be understood as a limit in the mathematical sense; a terminus towards which potentiality may come constantly nearer and nearer, but which it can never reach. The first, or bilateral potentiality, is the only sense at once consistent, legitimate, and conformable to ordinary speech. Aristotle himself admits that the second and third are equivocal meanings,[45] departing from the first as the legitimate meaning; but if equivocal departure to so great an extent were allowed, the term, put to such multifarious service, becomes unfit for accurate philosophical reasoning. And we find this illustrated by the contradiction into which Aristotle himself falls in the course of a few lines. The sentence of First Philosophy (which I translated in the last page) is a correction of the logical statement immediately preceding it, in so far as it suppresses the necessary Possible, or the unilateral potentiality. But on the other hand the same sentence introduces a new confusion by its third variety — the impossible Potential, departing from all clear and consistent meaning of potentiality, and coinciding only with the explanation of Non-Ens, as given by Aristotle elsewhere.[46]
[44] M. Barthélemy St. Hilaire, in the note to his translation (p. 197) calls it justly — “le possible qui n’est jamais; et qui par cela même, porte en lui une sorte d’impossibilité.â€� It contradicts both the two explanations of δυνατὸν which Aristotle had given a few lines before. 1. δυνατὸν ὅτι ἐνεργεῖ. 2. δυνατὸν ὅτι ἐνεργήσειεν ἄν (p. 23, a. 10).
[45] Aristot. De Interpr. p. 23, a. 5. τοῦτο μὲν τούτου χάριν εἴρηται, ὅτι οὐ πᾶσα δύναμις τῶν ἀντικειμένων, οὐδ’ ὅσαι λέγονται κατὰ τὸ αὐτὸ εἶδος. ἔνιαι δὲ δυνάμεις ὁμώνυμοί εἰσιν· τὸ γὰρ δυνατὸν οὐχ ἁπλῶς λέγεται, ἀλλὰ τὸ μὲν ὅτι ἀληθὲς ὡς ἐνεργείᾳ ὄν, &c.
If we read the thirteenth chapter of Analytica Priora I. (p. 32, a. 18-29) we shall see that τὸ ἐνδεχόμενον is declared to be οὐκ ἀναγκαῖον, and that in the definition of τὸ ἐνδεχόμενον, the words οὗ μὴ ὄντος ἀναγκαίου are expressly inserted. When τὸ ἀναγκαῖον is said ἐνδέχεσθαι, this is said only in an equivocal sense of ἐνδέχεσθαι — τὸ γὰρ ἀναγκαῖον ὁμωνύμως ἐνδέχεσθαι λέγομεν.