§2.1.6Εἰ οὖν ἐστιν ἡ ἀποδεικτικὴ ἐπιστήμη ἐξ ἀναγκαίων ἀρχῶν (ὃ γὰρ ἐπίσταται, οὐ δυνατὸν ἄλλως ἔχειν), τὰ δὲ καθ᾿ αὑτὰ ὑπάρχοντα ἀναγκαῖα τοῖς πράγμασιν (τὰ μὲν γὰρ ἐν τῷ τί ἐστιν ὑπάρχει· τοῖς δʼ αὐτὰ ἐν τῷ τί ἐστιν ὑπάρχει κατηγορουμένοις αὐτῶν, ὧν θάτερον τῶν ἀντικειμένων ἀνάγκη ὑπάρχειν), φανερόν ὅτι ἐκ τοιούτων τινῶν ἂν εἴη ὁ ἀποδεικτικὸς συλλογισμός· ἅπαν γὰρ ἢ οὕτως ὑπάρχει ἢ κατὰ συμβεβηκός, τὰ δὲ συμβεβηκότα οὐκ ἀναγκαῖα.
If, then, demonstrative science is from necessary principles (for what one knows cannot be otherwise), and those things that belong to things in themselves are necessary to them (for some belong in the definition of what they are, while for others, the things themselves belong in the definition of what their predicates are, of which one of the opposites must belong), it is clear that the demonstrative syllogism must be from some such premises; for everything belongs either in this way or accidentally, and accidental properties are not necessary.
Ἣ δὴ οὕτω λεκτέον, ἢ ἀρχὴν θεμένοις ὅτι ἡ ἀπόδειξις ἀναγκαίων ἐστί, καὶ εἰ ἀποδέδεικται, οὐχ οἷόν τʼ ἄλλως ἔχειν· ἐξ ἀναγκαίων ἄρα δεῖ εἶναι τὸν συλλογισμόν.
Or indeed we must speak in this way, or by laying down as a principle that demonstration is of necessary things, and if it has been demonstrated, it cannot be otherwise; the syllogism must therefore be from necessary premises.
ἐξ ἀληθῶν μὲν γὰρ ἔστι καὶ μὴ ἀποδεικνύντα συλλογίσασθαι, ἐξ ἀναγκαίων δʼ οὐκ ἔστιν ἀλλʼ ἢ ἀποδεικνύντα· τοῦτο γὰρ ἤδη ἀποδείξεως ἐστιν.
For from true premises one can reason without demonstrating, but from necessary premises one cannot do so except by demonstrating; for this is already the characteristic of demonstration.
σημεῖον δʼ ὅτι ἡ ἀπόδειξις ἐξ ἀναγκαίων, ὅτι καὶ τὰς ἐνστάσεις οὕτω φέρομεν πρὸς τοὺς οἰομένους ἀποδεικνύναι ὅτι οὐκ ἀνάγκη, ἂν οἰώμεθα ἢ ὅλως ἐνδέχεσθαι ἄλλως ἢ ἕνεκά γε τοῦ λόγου.
And a sign that demonstration is from necessary premises is that we also bring objections in this way against those who think they are demonstrating, by saying "it is not necessary," if we think that it is possible to be otherwise, either altogether or at least for the sake of the argument.
δῆλον δʼ ἐκ τούτων καὶ ὅτι εὐήθεις οἱ λαμβάνειν οἰόμενοι καλῶς τὰς ἀρχάς, ἐὰν ἔνδοξος ᾖ ἡ πρότασις καὶ ἀληθής, οἶον οἱ σοφισταὶ ὅτι τὸ ἐπίστασθαι τὸ ἐπιστήμην ἔχειν.
It is also clear from these things that those who think they grasp their principles well are simple-minded, if the premise is acceptable and true—as the sophists assume that to know is to possess knowledge.
οὐ γὰρ τὸ ἔνδοξον ἡμῖν ἀρχή ἐστιν, ἀλλὰ τὸ πρῶτον τοῦ γένους περὶ ὃ δείκνυται· καὶ τἀληθὲς οὐ πᾶν οἰκεῖον.
For it is not the acceptable that is a principle for us, but the primary thing of the genus about which the demonstration is made; and not every truth is appropriate.
ὅτι δʼ ἐξ ἀναγκαίων εἶναι δεῖ τὸν συλλογισμόν, φανερόν καὶ ἐκ τῶνδε.
And that the syllogism must be from necessary premises is also clear from the following.
εἰ γὰρ ὁ μὴ ἔχων λόγον τοῦ διὰ τί οὔσης ἀποδείξεως οὐκ ἐπιστήμων, εἴη δʼ ἂν ὥστε τὸ Α κατὰ τοῦ Γ ἐξ ἀνάγκης ὑπάρχειν, τὸ δὲ Β τὸ μέσον, διʼ οὗ ἀπεδείχθη, μὴ ἐξ ἀνάγκης, οὐκ οἶδε διότι. οὐ γάρ ἐστι τοῦτο διὰ τὸ μέσον· τὸ μὲν γὰρ ἐνδέχεται μὴ εἶναι, τὸ δὲ συμπέρασμα ἀναγκαῖον.
For if one who does not have the explanation of "why," when there is a demonstration, is not a man of science, and it should be that A belongs to C of necessity, but B, the middle term through which it was demonstrated, is not of necessity, he does not know "why." For this is not because of the middle term; for the one may not be, but the conclusion is necessary.
ἔτι εἴ τις μὴ οἶδε νῦν ἔχων τὸν λόγον καὶ σῳζόμενος, σῳζομένου τοῦ πράγματος, μὴ ἐπιλελησμένος, οὐδὲ πρότερον ᾔδει.
Furthermore, if someone does not know now, though he still has the explanation and is preserved, and the object is preserved, and he has not forgotten, then he did not know before either.
φθαρείη δʼ ἂν τὸ μέσον, εἰ μὴ ἀναγκαῖον, ὥστε ἕξει μὲν τὸν λόγον σῳζόμενος σῳζομένου τοῦ πράγματος, οὐκ οἶδε δέ.
But the middle term might be destroyed if it is not necessary, so that though he is preserved and the object is preserved, he will have the explanation but not know it.
οὐδʼ ἄρα πρότερον ἤδει.
Therefore, he did not know before either.
εἰ δὲ μὴ ἔφθαρται, ἐνδέχεται δὲ φθαρῆναι, τὸ συμβαῖνον ἂν εἴη δυνατὸν καὶ ἐνδεχόμενον.
And if it has not been destroyed, but is capable of being destroyed, that which follows would be possible and contingent.
ἀλλʼ ἔστιν ἀδύνατον οὕτως ἔχοντα εἰδέναι.
But it is impossible to know when one is in such a state.
Ὅταν μὲν οὖν τὸ συμπέρασμα ἐξ ἀνάγκης ᾖ, οὐδὲν κωλύει τὸ μέσον μὴ ἀναγκαῖον εἶναι διʼ οὗ ἐδείχθη (ἔστι γὰρ τὸ ἀναγκαῖον· καὶ μὴ ἐξ ἀναγκαίων συλλογίσασθαι, ὥσπερ καὶ ἀληθὲς μὴ ἐξ ἀληθῶν)·
Therefore, when the conclusion is necessary, nothing prevents the middle term through which it was demonstrated from not being necessary (for it is possible to reason to a necessary conclusion even from premises that are not necessary, just as one can reason to a true conclusion from premises that are not true).
ὅταν δὲ τὸ μέσον ἐξ ἀνάγκης, καὶ τὸ συμπέρασμα ἐξ ἀνάγκης, ὥσπερ καὶ ἐξ ἀληθῶν ἀληθὲς ἀεί (ἔστω γὰρ τὸ Α κατὰ τοῦ Β ἐξ ἀνάγκης, καὶ τοῦτο κατὰ τοῦ Γ· ἀναγκαῖον τοίνυν καὶ τὸ Α τῷ Γ ὑπάρχειν)·
But when the middle term is necessary, the conclusion is also necessary, just as from true premises a true conclusion always follows (for let A belong to B of necessity, and this to C; then it is necessary for A also to belong to C).
ὅταν δὲ μὴ ἀναγκαῖον ᾖ τὸ συμπέρασμα, οὐδὲ τὸ μέσον ἀναγκαῖον οἷόν τʼ εἶναι (ἔστω γὰρ τὸ τῷ Γ μὴ ἐξ ἀνάγκης ὑπάρχειν, τῷ δὲ Β, καὶ τοῦτο τῷ Γ ἐξ ἀνάγκης· καὶ τὸ Α ἄρα τῷ Γ ἐξ ἀνάγκης ὑπάρξει· ἀλλʼ οὐχ ὑπέκειτο).
But when the conclusion is not necessary, it is also impossible for the middle term to be necessary (for let [A] not belong to C of necessity, but to B [of necessity], and this to C of necessity; then A will also belong to C of necessity, but this was not assumed).
Ἐπεὶ τοίνυν εἰ ἐπίσταται ἀποδεικτικῶς, δεῖ ἐξ ἀνάγκης ὑπάρχειν, δῆλον ὅτι καὶ διὰ μέσου ἀναγκαίου δεῖ ἔχειν τὴν ἀπόδειξιν· ἢ οὐκ ἐπιστήσεται οὔτε διότι οὔτε ὅτι ἀνάγκη ἐκεῖνο εἶναι, ἀλλʼ ἢ οἰήσεται οὐκ εἰδώς, ἐὰν ὑπολάβῃ ὡς ἀναγκαῖον τὸ μὴ ἀναγκαῖον, ἢ οὐδʼ οἰήσεται, ὁμοίως ἐάν τε τὸ ὅτι εἰδῇ διὰ μέσων ἐάν τε τὸ διότι καὶ διʼ ἀμέσων.
Since, then, if one knows demonstratively, it must belong of necessity, it is clear that one must have the demonstration through a necessary middle term; otherwise one will know neither "why" nor "that" it is necessary for it to be so, but either he will think so without knowing, if he supposes what is not necessary to be necessary, or he will not even think so, equally whether he knows "that" through middle terms or "why" and through immediate terms.
Τῶν δὲ συμβεβηκότων μὴ καθʼ αὑτά, ὃν τρόπον διωρίσθη τὰ καθʼ αὑτά, οὐκ ἔστιν ἐπιστήμη ἀποδεικτική.
Of accidental properties that are not in themselves, in the way in which "in themselves" was defined, there is no demonstrative science.
οὐ γὰρ ἔστιν ἐξ ἀνάγκης δέξαι τὸ συμπέρασμα· τὸ συμβεβηκὸς γὰρ ἐνδέχεται μὴ ὑπάρχειν· περὶ τοῦ τοιούτου γὰρ λέγω συμβεβτηκότος.
For it is not possible to prove the conclusion of necessity; for an accidental property may not belong (since it is of this kind of accidental property that I am speaking).
καίτοι ἀπορήσειεν ἄν τις ἴσως τίνος ἕνεκα ταῦτα δεῖ ἐρωτᾶν περὶ τούτων, εἰ μὴ ἀνάγκη τὸ συμπέρασμα εἶναι· οὐδὲν γὰρ διαφέρει εἴ τις ἐρόμενος τὰ τυχόντα εἶτα εἴπειεν τὸ συμπέρασμα.
And yet one might perhaps wonder why we need to ask questions about these things, if the conclusion is not to be necessary; for it makes no difference if someone, having asked arbitrary questions, then states the conclusion.
δεῖ δʼ ἐρωτᾶν οὐχ ὡς ἀναγκαῖον εἶναι διὰ τὰ ἠρωτημένα, ἀλλʼ ὅτι λέγειν ἀνάγκη τῷ ἐκεῖνα λέγοντι, καὶ ἀληθῶς λέγειν, ἐὰν ἀληθῶς ᾖ ὑπάρχοντα.
But we must ask questions not because the conclusion is necessary because of the things asked, but because it is necessary for the one who concedes those premises to state the conclusion, and to state it truly if the premises belong truly.
Ἐπεὶ δʼ ἐξ ἀνάγκης ὑπάρχει περὶ ἕκαστον γένος ὅσα καθʼ αὑτὰ ὑπάρχει καὶ ᾗ ἕκαστον, φανερὸν ὅτι περὶ τῶν καθʼ αὑτὰ ὑπαρχόντων αἱ ἐπιστημονικαὶ ἀποδείξεις καὶ ἐκ τῶν τοιούτων εἰσίν.
And since those things which belong in themselves to each genus, and insofar as each is what it is, belong of necessity, it is clear that scientific demonstrations are about things that belong in themselves, and are from such things.
τὰ μὲν γὰρ συμβεβηκότα οὐκ ἀναγκαῖα, ὥστʼ οὐκ ἀνάγκη τὸ συμπέρασμα εἰδέναι διότι ὑπάρχει, οὐδʼ εἰ ἀεὶ εἴη, μὴ καθʼ αὐτὸ δέ, οἷον οἱ διὰ σημείων συλλογισμοί.
For accidental properties are not necessary, so that one does not of necessity know "why" the conclusion belongs, not even if it should always be the case, but not in itself—as, for example, with reasoning through signs.
τὸ γὰρ καθʼ αὐτὸ οὐ καθʼ αὑτὸ ἐπιστήσεται, οὐδὲ διότι (τὸ δὲ διότι ἐπίστασθαί ἐστι τὸ διὰ τοῦ αἰτίου ἐπίστασθαι).
For one will not know that which is in itself as in itself, nor will one know "why" (and to know "why" is to know through the cause).
διʼ αὐτὸ ἄρα δεῖ καὶ τὸ μέσον τῷ τρίτῳ καὶ τὸ πρῶτον τῷ μέσῳ ὑπάρχειν.
Therefore, the middle term must belong to the third, and the first to the middle term, because of itself.