§2.1.24#2Ἔτι εἰ ἡ ἀπόδειξις μέν ἐστι συλλογισμὸς δεικτικὸς αἰτίας καὶ τοῦ διὰ τί, τὸ καθόλου δʼ αἰτιώτερον (ᾧ γὰρ καθʼ αὑτὸ ὑπάρχει τι, τοῦτο αὐτὸ αὑτῷ αἴτιον· τὸ δὲ καθόλου πρῶτον· αἴτιον ἄρα τὸ καθόλου)· ὥστε καὶ ἡ ἀπόδειξις βελτίων· μᾶλλον γὰρ τοῦ αἰτίου καὶ τοῦ διὰ τί ἐστιν.
Furthermore, if demonstration is a syllogism demonstrative of the cause and of the "why", and the universal is more causal (for that to which something belongs in virtue of itself is itself the cause of this belonging to it; and the universal is first; therefore the universal is the cause); so that the universal demonstration is also better, for it is more of the cause and of the "why".
Ἔτι μέχρι τούτου ζητοῦμεν τὸ διὰ τί, καὶ τότε οἰόμεθα εἰδέναι, ὅταν μὴ ὅτι τι ἄλλο τοῦτο ἢ γινόμενον ἢ ὄν· τέλος γὰρ καὶ πέρας τὸ ἔσχατον ἤδη οὕτως ἐστίν.
Furthermore, we seek the "why" up to this point, and we think we know then, when this is not because something else is coming to be or being; for the ultimate step is already in this way a limit and an end.
οἷον τίνος ἕνεκα ἦλθεν;
For example, for what purpose did he come?
ὅπως λάβῃ τἀργύριον, τοῦτο δʼ ὅπως ἀποδῷ ὃ ὤφειλε, τοῦτο δʼ ὅπως μὴ ἀδικήσῃ· καὶ οὕτως ἰόντες, ὅταν μηκέτι διʼ ἄλλο μηδʼ ἄλλου ἕνεκα, διὰ τοῦτο ὡς τέλος φαμὲν ἐλθεῖν καὶ εἶναι καὶ γίνεσθαι, καὶ τότε εἰδέναι μάλιστα διὰ τί ἦλθεν.
In order to get the money; and this, in order to pay back what he owed; and this, in order not to do an injustice; and proceeding thus, when it is no longer on account of something else nor for the sake of something else, we say that he came, exists, or comes to be on account of this as an end, and then we know best why he came.
εἰ δὴ ὁμοίως ἔχει ἐπὶ πασῶν τῶν αἰτιῶν καὶ τῶν διὰ τί, ἐπὶ δὲ τῶν ὅσα αἴτια οὕτως ὡς οὗ ἕνεκα οὕτως ἴσμεν μάλιστα, καὶ ἐπὶ τῶν ἄλλων ἄρα τότε μάλιστα ἴσμεν, ὅταν μηκέτι ὑπάρχῃ τοῦτο ὅτι ἄλλο.
If indeed it is similar for all causes and "whys", and in the case of those causes which are "that for the sake of which" we know best in this way, then in the other cases also we know best when this no longer belongs because of something else.
ὅταν μὲν οὖν γινώσκωμεν ὅτι τέτταρσιν αἱ ἔξω ἴσαι ὅτι ἰσοσκελές, ἔτι λείπεται διὰ τί τὸ ἰσοσκελές—ὅτι τρίγωνον, καὶ τοῦτο, ὅτι σχῆμα εὐθύγραμμον.
Thus when we know that the external angles are equal to four [right angles] because it is isosceles, there still remains why the isosceles [has them] — because it is a triangle, and this, because it is a rectilinear figure.
εἰ δὲ τοῦτο μηκέτι διότι ἄλλο, τότε μάλιστα ἴσμεν.
And if this is no longer because of something else, then we know best.
καὶ καθόλου δὲ τότε· ἡ καθόλου ἄρα βελτίων.
And it is then [that we know] universally; therefore the universal demonstration is better.
Ἔτι ὅσῳ ἂν μᾶλλον κατὰ μέρος ᾖ, εἰς τὰ ἄπειρα ἐμπίπτει, ἡ δὲ καθόλου εἰς τὸ ἀπλοῦν καὶ τὸ πέρας.
Furthermore, the more it is particular, the more it falls into the infinite, whereas the universal falls into the simple and the limit.
ἔστι δʼ, μὲν ἄπειρα, οὐκ ἐπιστητά, ᾗ δὲ πεπέρανται, ἐπιστητά.
And in so far as things are infinite, they are not knowable, but in so far as they are limited, they are knowable.
ᾗ ἄρα καθόλου, μᾶλλον ἐπιστητὰ ἢ ᾗ κατὰ μέρος.
Therefore, in so far as they are universal, they are more knowable than in so far as they are particular.
ἀποδεικτὰ ἄρα μᾶλλον τὰ καθόλου.
Therefore, the universal things are more demonstrable.
τῶν δʼ ἀποδεικτῶν μᾶλλον μᾶλλονἀπόδειξις· ἅμα γὰρ μᾶλλον τὰ πρός τι.
And of things more demonstrable, there is more demonstration; for correlative terms increase together.
βελτίων ἄρα ἡ καθόλου, ἐπείπερ καὶ μᾶλλον ἀπόδειξις.
Therefore, the universal demonstration is better since indeed it is also more of a demonstration.
Ἔτι εἰ αἱρετωτέρα καθʼ ἣν τοῦτο καὶ ἄλλο ἢ καθʼ ἣν τοῦτο μόνον οἶδεν· ὁ δὲ τὴν καθόλου ἔχων οἶδε καὶ τὸ κατά μέρος, οὗτος δὲ τὴν καθόλου οὐκ οἶδεν· ὥστε κἂν οὕτως αἱρετωτέρα εἴη.
Furthermore, if that demonstration is more desirable by which one knows both this and something else, than that by which one knows this alone; and he who has the universal knows also the particular, whereas he [who has the particular] does not know the universal; so that even in this way it would be more desirable.
Ἔτι δὲ ὧδε. τὸ γὰρ καθόλου μᾶλλον δεικνύναι ἐστὶ τὸ διὰ μέσου δεικνύναι ἐγγυτέρω ὄντος τῆς ἀρχῆς.
And furthermore in this way: for to demonstrate more universally is to demonstrate through a middle term which is closer to the principle.
ἐγγυτάτω δὲ τὸ ἄμεσον· τοῦτο δʼ ἀρχή.
And the immediate is closest; and this is a principle.
εἰ οὖν ἡ ἐξ ἀρχῆς τῆς μὴ ἐξ ἀρχῆς. ἡ μᾶλλον ἐξ ἀρχῆς τῆς ἧττον ἀκριβεστέρα ἀπόδειξις.
If, then, the demonstration from a principle is [superior to] that not from a principle, that which is more from a principle is a more accurate demonstration than that which is less so.
ἔστι δὲ τοιαύτη ἡ καθόλου μᾶλλον· κρείττων ἄῤ ἂν εἴη ἡ καθόλου.
And the universal demonstration is more of this kind; therefore the universal would be superior.
οἷον εἰ ἔδει ἀποδεῖξαι τὸ Α κατὰ τοῦ Δ· μέσα τὰ ἐφʼ ὧν Β Γ· ἀνωτέρω δὴ τὸ Β, ὥστε ἡ διὰ τούτου καθόλου μᾶλλον.
For example, if it were necessary to demonstrate A of D; and the middle terms are B and C; B is higher, so that the demonstration through this is more universal.
Ἀλλὰ τῶν μὲν εἰρημένων ἔνια λογικά ἐστι· μάλιστα δὲ δῆλον ὅτι ἡ καθόλου κυριωτέρα, ὅτι τῶν τπροτάσεων τὴν μὲν προτέραν ἔχοντες ἴσμεν πως καὶ τὴν ὑστέραν καὶ ἔχομεν δυνάμει, οἷον εἴ τις οἶδεν ὅτι πᾶν τρίγωνον δυσὶν ὀρθαῖς, οἶδέ πως καὶ τὸ ἰσοσκελὲς ὅτι δύο ὀρθαῖς, δυνάμει, καὶ εἰ μὴ οἶδε τὸ ἰσοσκελὲς ὅτι τρίγωνον· ὁ δὲ. ταύτην ἔχων τὴν πρότασιν τὸ καθόλου οὐδαμῶς οἶδεν, οὔτε δυνάμει οὐτʼ ἐνεργείᾳ.
But some of the things mentioned are merely logical; but it is most clear that the universal is more authoritative because, of the premises, when we have the prior one we know in a way also the posterior one, and we have it potentially; for example, if someone knows that every triangle has two right angles, he knows also in a way that the isosceles has two right angles, potentially, even if he does not know that the isosceles is a triangle; whereas he who has this latter premise does not know the universal in any way, neither potentially nor actually.
καὶ ἡ μὲν καθόλου νοητή, ἡ δὲ κατὰ μέρος εἰς αἴσθησιν τελευτῇ.
And the universal is intelligible, while the particular terminates in perception.