[20] Ibid. p. 93, a. 30-b. 14.
Aristotle has thus shown how the Essence or Quiddity (τί ἐστι) may become known in this class of cases. There is neither syllogism nor demonstration thereof, yet it is declared through syllogism and demonstration: though no demonstration thereof is possible, yet you cannot know it without demonstration, wherever there is an extraneous cause.[21]
[21] Ibid. b. 15-20: ὥστε συλλογισμὸς μὲν τοῦ τί ἐστιν οὐ γίνεται οὐδ’ ἀπόδειξις, δῆλον μέντοι διὰ συλλογισμοῦ καὶ δι’ ἀποδείξεως.
Mr. Poste translates an earlier passage (p. 93, a. 5) in this very difficult chapter as follows (p. 107): “If one cause is demonstrable, another indemonstrable cause must be the intermediate; and the proof is in the first figure, and the conclusion affirmative and universal. In this mode of demonstrating the essence, we prove one definition by another, for the intermediate that proves an essence or a peculiar predicate must itself be an essence or a peculiar predicate. Of two definitions, then, one is proved and the other assumed; and, as we said before, this is not a demonstration but a dialectical proof of the essence.â€� Mr. Poste here translates λογικὸς συλλογισμός “dialectical proof.â€� I understand it rather as meaning a syllogism, τοῦ ὑπάρχειν simply (Top. I. v. p. 102, b. 5), in which all that you really know is that the predicate belongs to the subject, but in which you assume besides that it belongs to the subject essentially. It is not a demonstration because, in order to obtain Essence in the conclusion, you are obliged to postulate Essence in your premiss. (See Alexander ad Topic. I. p. 263, Br.). You have therefore postulated a premiss which required proof as much as the conclusion.
But the above doctrine will hold only in cases where there is a distinct or extraneous cause; it will not hold in cases where there is none. It is only in the former (as has been said) that a middle term can be shown; rendering it possible that Quiddity or Essence should be declared by a valid formal syllogism, though it cannot be demonstrated by syllogism. In the latter, where there is no distinct cause, no such middle term can be enunciated: the Quiddity or Essence must be assumed as an immediate or undemonstrable principium, and must be exposed or set out in the best manner practicable as an existent reality, on Induction or on some other authority. The arithmetician makes his first steps by assuming both what a monad is and that there exists such a monad.[22]
[22] Analyt. Post. II. ix. p. 93, b. 21. ἔστι δὲ τῶν μὲν ἕτερόν τι αἴτιον, τῶν δ’ οὐκ ἔστιν. ὥστε δῆλον ὅτι καὶ τῶν τί ἐστι τὰ μὲν ἄμεσα καὶ ἀρχαί εἰσιν, ἃ καὶ εἶναι καὶ τί ἐστιν ὑποθέσθαι δεῖ ἢ ἄλλον τρόπον φανερὰ ποιῆσαι. ὅπερ ὁ ἀριθμητικὸς ποιεῖ· καὶ γὰρ τί ἐστι τὴν μονάδα ὑποτίθεται, καὶ ὅτι ἔστιν.
Themistius, p. 80: ἃ καὶ εἶναι καὶ τί ἐστιν ὑποθέσθαι δεῖ, ἢ ἄλλον τρόπον φανερὰ ποιῆσαι ἐξ ἐπαγωγῆς ἢ πίστεως ἢ ἐμπειρίας. Rassow, De Notionis Definitione, pp. 18-22.
We may distinguish three varieties of Definition. 1. Sometimes it is the mere explanation what a word signifies; in this sense, it has nothing to do with essence or existence; it is a nominal definition and nothing more.[23] 2. Sometimes it enunciates the Essence, cause, or reason of the definitum; this will happen where the cause is distinct or extraneous, and where there is accordingly an intervening middle term: the definition will then differ from a demonstration only by condensing into one enunciation the two premisses and the conclusion which together constitute the demonstration.[24] 3. Sometimes it is an immediate proposition, an indemonstrable hypothesis, assuming Essence or Quiddity; the essence itself being cause, and no extraneous cause — no intervening middle term — being obtainable.[25]
[23] Analyt. Post. II. x. p. 93, b. 29-37.
[24] Ibid. p. 93, b. 38, seq. οἷον ἀπόδειξις τοῦ τί ἐστιν, τῇ θέσει διαφέρων τῆς ἀποδείξεως· — συλλογισμὸς τοῦ τί ἐστι, πτώσει διαφέρων τῆς ἀποδείξεως — differing “situ et positione terminorumâ€� (Julius Pacius, p. 493).