§2.1.24#1Οὔσης δʼ ἀποδείξεως τῆς μὲν καθόλου τῆς δὲ κατὰ μέρος, καὶ τῆς μὲν κατηγορικῆς τῆς δὲ στερητικῆς, ἀμφισβητεῖται ποτέρα βελτίων· ὡς δʼ αὔτως καὶ περὶ τῆς ἀποδεικνύναι λεγομένης καὶ τῆς εἰς τὸ ἀδύνατον ἀγούσης ἀποδείξεως.
Since there is both universal and particular demonstration, and both affirmative and negative, it is disputed which is better; and similarly also concerning that which is said to demonstrate directly and that which leads to the impossible.
πρῶτον μὲν οὖν ἐπισκεψώμεθα περὶ τῆς καθόλου καὶ τῆς κατὰ μέρος· δηλώσαντες δὲ τοῦτο, καὶ περὶ τῆς δεικνύναι λεγομένης καὶ τῆς εἰς τὸ ἀδύνατον εἴπωμεν.
First, then, let us examine the universal and the particular; and having made this clear, let us speak also of that which is said to show directly and that which leads to the impossible.
Δόξειε μὲν οὖν τάχʼ ἄν τισιν ὡδὶ σκοποῦσιν ἡ κατὰ μέρος εἶναι βελτίων.
Now, it might perhaps seem to some who consider the matter in the following way that the particular demonstration is better.
εἰ γὰρ καθʼ ἣν μᾶλλον ἐπιστάμεθα ἀπόδειξιν βελτίων ἀπόδειξις (αὕτη γὰρ ἀρετὴ ἀποδείξεως), μᾶλλον δʼ ἐπιστάμεθα ἕκαστον ὅταν αὐτὸ εἰδῶμεν καθʼ αὑτὸ ἢ ὅταν κατʼ ἄλλο (οἷον τὸν μουσικὸν Κορίσκον ὅταν ὅτι ὁ Κορίσκος μουσικὸς ἢ ὅταν ὅτι ἅνθρωπος μουσικός· ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων), ἡ δὲ καθόλου ὅτι ἄλλο, οὐχ ὅτι αὐτὸ τετύχηκεν ἐπιδείκνυσιν (οἷον ὅτι τὸ ἰσοσκελὲς οὐχ ὅτι ἰσοσκελὲς ἀλλʼ ὅτι τρίγωνον), ἡ δὲ κατὰ μέρος ὅτι αὐτό —εἰ δὴ βελτίων μὲν ἡ καθʼ αὐτό, τοιαύτη δʼ ἡ κατὰ μέρος τῆς καθόλου μᾶλλον, καὶ βελτίων ἂν ἡ κατὰ μέρος ἀπόδειξις εἴη.
For if the demonstration in virtue of which we know more is the better demonstration (for this is the virtue of demonstration), and we know each thing more when we know it in itself than when we know it in virtue of something else (for example, we know the musical Coriscus more when we know that Coriscus is musical than when we know that man is musical; and similarly also in other cases), whereas the universal demonstration shows that something else is the case, not that the thing itself is so (for example, showing that the isosceles has certain angles not because it is isosceles but because it is a triangle), while the particular demonstration shows that the thing itself is so—if, then, the demonstration in itself is better, and the particular demonstration is more like this than the universal, the particular demonstration would be better.
ἔτι εἰ τὸ μὲν καθόλου μὴ ἔστι τι παρὰ τὰ καθʼ ἕκαστα, ἡ δʼ ἀπόδειξις δόξαν ἐμποιεῖ εἶναί τι τοῦτο καθʼ ὃ ἀποδείκνυσι, καί τινα φύσιν ὑπάρχειν ἐν τοῖς οὖσι ταύτην, οἷον τριγώνου παρὰ τὰ τινὰ καὶ σχήματος παρὰ τὰ τινά καὶ ἀριθμοῦ παρὰ τοὺς τινὰς ἀριθμούς, βελτίων δʼ ἡ περὶ ὄντος ἢ μὴ ὄντος καὶ διʼ ἣν μὴ ἀπατηθήσεται ἢ διʼ ἥν, ἔστι δʼ ἡ μὲν καθόλου τοιαύτη (προϊόντες γὰρ δεικνύουσιν ὥσπερ περὶ τοῦ ἀνὰ λόγον, οἷον ὅτι ὃ ἂν ᾖ τι τοιοῦτον ἔσται ἀνὰ λόγον ὃ οὔτε γραμμὴ οὐτʼ ἀριθμὸς οὔτε στερεόν οὔτʼ ἐπίπεδον, ἀλλὰ παρὰ ταῦτά τι)· —εἰ οὖν καθόλου μὲν μᾶλλον αὕτη, περὶ ὄντος δʼ ἧττον τῆς κατὰ μέρος καὶ ἐμποιεῖ δόξαν ψευδῆ, χείρων ἂν εἴη ἡ καθόλου τῆς κατὰ μέρος.
Furthermore, if the universal is nothing apart from the particulars, whereas the demonstration produces an opinion that this thing in virtue of which it demonstrates is something, and that some such nature exists among beings, for example, a triangle apart from the particular triangles, and a shape apart from the particular shapes, and a number apart from the particular numbers; and if demonstration about what is is better than that about what is not, and that by which one will not be deceived is better than that by which one will; and if the universal demonstration is of this latter kind (for as they proceed, they demonstrate, for example, about proportion, as that whatever is of such a kind will be proportional, which is neither line nor number nor solid nor plane, but something apart from these)—if, then, this demonstration is more universal, but less about what is than the particular, and produces a false opinion, the universal demonstration would be worse than the particular.
Ἤ πρῶτον μὲν οὐδὲν μᾶλλον ἐπὶ τοῦ καθόλου ἢ τοῦ κατὰ μέρος ἅτερος λόγος ἐστίν;
Or, in the first place, is the latter argument not any more applicable to the universal than to the particular demonstration?
εἰ γὰρ τὸ δυσὶν ὀρθαῖς ὑπάρχει μὴ ᾗ ἰσοσκελὲς ἀλλʼ ᾗ τρίγωνον, ὁ εἰδὼς ὅτι ἰσοσκελὲς ἧττον οἶδεν ᾗ αὐτὸ ἢ ὁ εἰδὼς ὅτι τρίγωνον.
For if having angles equal to two right angles belongs to a thing not in so far as it is isosceles but in so far as it is a triangle, he who knows that it is isosceles knows less in so far as it is itself than he who knows that it is a triangle.
ὅλως τε, εἰ μὲν μὴ ὄντος ᾗ τρίγωνον εἶτα δείκνυσιν, οὐκ ἂν εἴη ἀπόδειξις, εἰ δὲ ὄντος, ὁ εἰδὼς ἕκαστον ᾗ ἕκαστον ὑπάρχει μᾶλλον οἶδεν.
And generally, if it demonstrates by assuming what is not in so far as it is a triangle, there would be no demonstration; but if it is about what is, he who knows each thing in so far as each thing belongs knows more.
εἰ δὴ τὸ τρίγωνον ἐπὶ πλέον ἐστί, καὶ ὁ αὐτὸς λόγος, καὶ μὴ καθʼ ὁμωνυμίαν τὸ τρίγωνον, καὶ ὑπάρχει παντὶ τριγώνῳ τὸ δύο, οὐκ ἂν τὸ τρίγωνον ᾗ ἰσοσκελές, ἀλλὰ τὸ ἰσοσκελὲς ᾗ τρίγωνον, ἔχοι τοιαύτας τὰς γωνίας.
If, then, triangle is more extensive, and has the same definition, and 'triangle' is not used homonymously, and the possession of two right angles belongs to every triangle, then it is not the triangle in so far as it is isosceles, but the isosceles in so far as it is a triangle, that has such angles.
ὥστε ὁ καθόλου εἰδὼς μᾶλλον οἶδεν ὑπάρχει ἢ ὁ κατὰ μέρος.
Consequently, he who knows universally knows more in virtue of which it belongs than he who knows particularly.
βελτίων ἄρα ἡ καθόλου τῆς κατὰ μέρος.
Therefore, the universal demonstration is better than the particular.
ἔτι εἰ μὲν εἴη τις λόγος εἷς καὶ μὴ ὁμωνυμία τὸ καθόλου, εἴη τʼ ἂν οὐδὲν ἧττον ἐνίων τῶν κατὰ μέρος, ἀλλὰ καὶ μᾶλλον, ὅσῳ τὰ ἄφθαρτα ἐν ἐκείνοις ἐστί, τὰ δὲ κατὰ μέρος φθαρτὰ μᾶλλον, ἔτι τε οὐδεμία ἀνάγκη ὑπολαμβάνειν τι εἶναι τοῦτο παρὰ ταῦτα, ὅτι ἓν δηλοῖ, οὐδὲν μᾶλλον ἢ ἐπὶ τῶν ἄλλων ὅσα μὴ τὶ σημαίνει ἀλλʼ ἢ ποιὸν ἢ πρός τι ἢ ποιεῖν.
Furthermore, if the universal is some single definition and not a homonymy, it would exist no less than some of the particulars, but even more so, in so far as the imperishable things are among them, whereas the particulars are more perishable. Furthermore, there is no necessity to suppose that this is something apart from these particulars just because it signifies a single thing, any more than in the case of other things which signify not a substance but a quality, a relation, or an action.
εἰ δὲ ἄρα, οὐχ ἡ ἀπόδειξις αἰτία ἀλλʼ ὁ ἀκούων.
If, then, this is supposed, it is not the demonstration that is responsible, but the listener.