87 b ἐπισκέψασθαι δὲ καὶ διὰ τῶν ἄλλων σχημάτων ὁσαχῶς ἐνδέχεται τοῦ αὐτοῦ γενέσθαι συλλογισμόν.
XXX. Τοῦ δ᾿ ἀπὸ τύχης οὐκ ἔστιν ἐπιστήμη δι᾿ 20ἀποδείξεως. οὔτε γὰρ ὡς ἀναγκαῖον οὔθ᾿ ὡς ἐπὶ τὸ πολὺ τὸ ἀπὸ τύχης ἐστίν, ἀλλὰ τὸ παρὰ ταῦτα γιγνόμενον· ἡ δ᾿ ἀπόδειξις θατέρου τούτων. πᾶς γὰρ συλλογισμὸς ἢ δι᾿ ἀναγκαίων ἢ διὰ τῶν ὡς ἐπὶ τὸ πολὺ προτάσεων· καὶ εἰ μὲν αἱ προτάσεις ἀναγκαῖαι, 25καὶ τὸ συμπέρασμα ἀναγκαῖον, εἰ δ᾿ ὡς ἐπὶ τὸ πολύ, καὶ τὸ συμπέρασμα τοιοῦτον. ὥστ᾿ εἰ τὸ ἀπὸ τύχης μήθ᾿ ὡς ἐπὶ τὸ πολὺ μήτ᾿ ἀναγκαῖον, οὐκ ἂν εἴη αὐτοῦ ἀπόδειξις.
XXXI. Οὐδὲ δι᾿ αἰσθήσεως ἔστιν ἐπίστασθαι. εἰ γὰρ καὶ ἔστιν ἡ αἴσθησις τοῦ τοιοῦδε καὶ μὴ τοῦδέ 30τινος, ἀλλ᾿ αἰσθάνεσθαί γε ἀναγκαῖον τόδε τι καὶ ποὺ καὶ νῦν. τὸ δὲ καθόλου καὶ ἐπὶ πᾶσιν ἀδύνατον αἰσθάνεσθαι· οὐ γὰρ τόδε οὐδὲ νῦν· οὐ γὰρ ἂν ἦν καθόλου· τὸ γὰρ ἀεὶ καὶ πανταχοῦ καθόλου φαμὲν εἶναι. ἐπεὶ οὖν αἱ μὲν ἀποδείξεις καθόλου, ταῦτα δ᾿ οὐκ ἔστιν αἰσθάνεσθαι, φανερὸν ὅτι οὐδ᾿ ἐπίστασθαι 35δι᾿ αἰσθήσεως ἔστιν, ἀλλὰ δῆλον ὅτι καὶ εἰ ἦν αἰσθάνεσθαι τὸ τρίγωνον ὅτι δυσὶν ὀρθαῖς ἴσας ἔχει τὰς γωνίας, ἐζητοῦμεν ἂν ἀπόδειξιν καὶ οὐχ
examine this point in the other figures to see in how many ways it is possible to draw the same inference.a
XXX. There can be no demonstrative knowledge There is no science of the fortuitous. of the fortuitous.b What happens by chance is neither a necessary nor a usual event, but something which happens in a different way from either; whereas demonstration is concerned with one or the other of them. Every syllogism proceeds through premisses which are either necessary or usual; if the premisses are necessary, the conclusion is necessary too; and if the premisses are usual, so is the conclusion. Hence if the fortuitous is neither usual nor necessary, there can be no demonstration of it.
XXXI. Scientific knowledge cannot be acquired Sense-perception cannot give scientific knowledge by sense-perception. Even granting that perception is of the object as qualified, and not of a mere particular,c still what we perceive must be a particular thing at a particular place and time. On the other hand a universal term of general application cannot be perceived by the senses, because it is not a particular thing or at a given time; if it were, it would not be universal; for we describe as universal only that which obtains always and everywhere. Therefore since demonstrations are universal, and universals cannot be perceived by the senses, obviously knowledge cannot be acquired by sense-perception. Again it is obvious that even if it were possible to perceive by the senses that the sum of the angles of a triangle is equal to two right angles, we should still require a proof of this; we should not (as somed
- aIt is tempting to regard this observation as a sort of “marginal jotting” in Aristotle’s lecture notes. The project is not carried out.
- bFor chance see Physics II. iv–vi, and cf. Met. 1064 b 32 ff.
- cWhen we perceive a sensible object, what we perceive is, in one sense, a complex of sensible qualities (colour, shape, size, etc.) which constitute a recognizable type. But the fact remains that the object perceived is only one particular instance of the type.
- de.g., Protagoras—if Plato represents his meaning fairly (which is questionable) in Theaetetus 151 e. Cf. Diogenes Laertius ix. 51.