εἰδέναι <πόση>20 ἐστὶν εἰδέναι τὸν ἀριθμόν; τὸ γὰρ ἄπειρον καὶ ἀναρίθμητον ταὐτόν, καὶ πλέον ἀεὶ τὸ ἄπειρον τοῦ ὡρισμένου. ὥσπερ οὖν εἰ ᾔδει ὅτι τοσήδε 15ἐστί, πεπερασμένην αὐτὴν ἀνάγκη εἶναι, | οὕτως εἰ μὴ οἶδε πόση τίς ἐστιν, ὡς ἀντιστρέφοντος παραλογίζεται ἡ ψυχή, καὶ φαίνεται αὕτη εἶναι ἄπειρος. ἔτι21 τὸ ποσὸν ὡρισμένον ἐστὶ καὶ τὸ ὡρισμένον ποσόν. ὅταν τοίνυν μὴ φαίνηται ὡρισμένον, ὥσπερ ἄπειρον δόξει εἶναι, διὰ τὸ τὸ πεφυκὸς ὡρίσθαι, ἂν μὴ ᾖ ὡρισμένον, 20ἄπειρον εἶναι, | καὶ τὸ φαινόμενον μὴ ὡρίσθαι φαίνεσθαι ἀνάγκη πως ἀπέραντον.
5. Διὰ τί πρεσβύτεροι μὲν γινόμενοι μᾶλλον νοῦν ἔχομεν, νεώτεροι δ᾿ ὄντες θᾶττον μανθάνομεν; ἢ ὅτι ὁ θεὸς ὄργανα ἐν ἑαυτοῖς ἡμῖν δέδωκε δύο, ἐν οἷς χρησόμεθα 25τοῖς ἐκτὸς | ὀργάνοις, σώματι μὲν χεῖρα, ψυχῇ δὲ νοῦν; ἔστι γὰρ καὶ ὁ νοῦς τῶν φύσει ἐν ἡμῖν ὥσπερ ὄργανον ὑπάρχων· αἱ δὲ ἄλλαι ἐπιστῆμαι καὶ τέχναι τῶν ὑφ᾿ ἡμῶν ποιητῶν εἰσίν, ὁ δὲ νοῦς τῶν φύσει. καθάπερ οὖν τῇ χειρὶ οὐκ εὐθὺς γενόμενοι χρώμεθα 30βέλτιστα, ἀλλ᾿ ὅταν ἡ φύσις αὐτὴν ἐπιτελέσῃ | (προϊούσης γὰρ τῆς ἡλικίας ἡ χεὶρ μάλιστα δύναται ἀποτελεῖν τὸ ἑαυτῆς ἔργον), τὸν αὐτὸν τρόπον καὶ ὁ νοῦς τῶν φύσει οὐκ εὐθὺς ἀλλ᾿ ἐπὶ γήρως ἡμῖν μάλιστα
because knowing <how long it is>, is to know the number? 39 For the infinite and unnumbered are the same, and the infinite is always greater than the determinate. Therefore, just as if one knows that it is such a length, it must be limited, so too if one does not know how long it is, as though converting (the proposition),40 the soul is led to a false conclusion, and this41 appears to be infinite. Further, a quantity is determinate and what is determinate is a quantity. So when something does not appear to be determinate, it seems to be as it were infinite, because that which is naturally determinate, if it is not determinate, seems to be infinite, and what appears not to be determinate must appear in a sense infinite.
5.42 Why do we have more understanding when we get older, whereas we learn more quickly when we are younger? Is it because god has given us two instruments within ourselves, in which we will use external instruments, the hand for the body, understanding for the soul? For the understanding is among the things existing in us by nature as an instrument; and while the other sciences and arts are among the things produced by us, understanding is among the things existing by nature. So, just as we do not use the hand in the best way immediately after we are born, but when nature perfects it (for as our age progresses the hand is most able to complete its function), in the same way too, among the things existing by nature, understanding is present in us most not immediately but in old age, and
- 39I.e., to be able to specify its length arithmetically.
- 40The word translated here is a form of the standard term in Aristotle’s logical works for “to convert” (ἀντιστρέφειν), e.g., to convert “every A is B” into “every B is A” (see, e.g., Pr.An. 25a6).
- 4See Sophocles, Ajax.
- 5Il. 6.200-202.
- 6Or “temperament.”
- 41This (αὕτη) must refer to the length (“how long,” πόση).
- 42Cf. EN 6.11, 1143b7-9, Rh. 2.13.