§1.1.41Οὐκ ἔστι δὲ ταὐτὸν οὔτʼ εἶναι οὔτʼ εἰπεῖν, ὅτι ᾧ τὸ Β ὑπάρχει, τούτῳ παντὶ τὸ ὑπάρχει, καὶ τὸ εἰπεῖν τὸ ᾧ παντὶ τὸ Β ὑπάρχει, καὶ τὸ παντὶ ὑπάρχει·
It is not the same, either in reality or in statement, to say that to whatever B belongs, to all of this A belongs, and to say to that to all of which B belongs, A also belongs to all.
οὐδὲν γὰρ κωλύει τὸ Β τῷ Γ ὑπάρχειν, μὴ παντὶ δέ.
For nothing prevents B from belonging to C, but not to all of it.
οἷον ἔστω τὸ Β καλόν, τὸ δὲ Γ λευκόν.
For example, let B be beautiful, and C white.
εἰ δὴ λευκῷ τινὶ ὑπάρχει καλόν, ἀληθὲς εἰπεῖν ὅτι τῷ λευκῷ ὑπάρχει καλόν· ἀλλʼ οὐ παντὶ ἴσως.
If then beautiful belongs to some white, it is true to say that beautiful belongs to white; but perhaps not to all.
εἰ μὲν οὖν τὸ τῷ Β ὑπάρχει, μὴ παντὶ δὲ καθʼ οὖ τὸ Β, οὔτʼ εἰ παντὶ τῷ Γ τὸ Β, οὔτʼ εἰ μόνον ὑπάρχει, ἀνάγκη τὸ Α οὐχ ὅτι οὐ παντί, ἀλλʼ οὐδʼ ὑπάρχειν.
If, then, A belongs to B, but not to all of that of which B is predicated, then, neither if B belongs to all of C, nor if it merely belongs to it, is it necessary that A belongs to C—I do not say 'not to all', but not even at all.
εἰ δὲ καθʼ οὗ ἂν τὸ Β λέγηται ἀληθῶς, τούτῳ παντὶ ὑπάρχει, συμβήσεται τὸ Α, καθʼ οὗ παντὸς τὸ Β λέγεται, κατὰ τούτου παντὸς λέγεσθαι.
But if A belongs to all of that of which B is truly said, it will result that A is said of all of that of which B is said.
εἰ μέντοι τὸ Α λέγεται καθʼ οὗ ἂν τὸ Β λέγηται κατὰ παντός, οὐδὲν κωλύει τῷ Γ ὑπάρχειν τὸ Β, μὴ παντὶ δὲ τὸ ἢ ὅλως μὴ ὑπάρχειν.
If, however, A is said of that of which B is said of all, nothing prevents B from belonging to C, but A not belonging to all of C, or not belonging at all.
ἐν δὴ τοῖς τρισὶν ὅροις δῆλον ὅτι τὸ καθʼ οὗ τὸ Β παντὸς τὸ Α λέγεσθαι τοῦτʼ ἔστι, καθ᾿ ὅσων τὸ Β λέγεται, κατὰ πάντων λέγεσθαι καὶ τὸ Α. καὶ εἰ μὲν κατὰ παντὸς τὸ Β, καὶ τὸ Α οὕτως·
So in the case of three terms, it is clear that 'for A to be said of all of that of which B is said' means this: of as many things as B is said, of all of these A also is said.
εἰ δὲ μὴ κατὰ παντός, οὐκ ἀνάγκη τὸ Α κατὰ παντός.
And if B is said of all, A is also thus; but if not of all, it is not necessary that A is said of all.
Οὐ δεῖ δʼ οἴεσθαι παρὰ τὸ ἐκτίθεσθαί τι συμβαίνειν ἄτοπον· οὐδὲν γὰρ προσχρώμεθα τῷ τόδε τι εἶναι, ἀλλʼ ὥσπερ ὁ γεωμέτρης τὴν ποδιαίαν καὶ εὐθεῖαν τήνδε καὶ ἀπλατῆ εἶναι λέγει οὐκ οὔσας, ἀλλʼ οὐχ οὕτως χρῆται ὡς ἐκ τούτων συλλογιζόμενος.
And we must not think that any absurdity arises from setting out terms; for we make no use of their being a 'this', but just as the geometer says that this line is a foot long and straight and without breadth when it is not, but he does not use them in such a way as to syllogize from them.
ὅλως γὰρ ὃ μὴ ἔστιν ὡς ὅλον πρὸς μέρος καὶ ἄλλο πρὸς τοῦτο ὡς μέρος πρὸς ὅλον, ἐξ οὐδενὸς τῶν τοιούτων δείκνυσιν ὁ δεικνύων, ὥστε οὐδὲ γίνεται συλλογισμός.
For in general, unless there is something as a whole to a part, and another to this as a part to a whole, the demonstrator does not demonstrate from any such things, so that there is not even a syllogism.
τῷ δʼ ἐκτίθεσθαι οὕτω χρώμεθα ὥσπερ καὶ τῷ αἰσθάνεσθαι, τὸν μανθάνοντʼ ἀλέγοντες· οὐ γὰρ οὕτως ὡς ἄνευ τούτων οὐχ οἷόν τʼ ἀποδειχθῆναι, ὥσπερ ἐξ ὧν ὁ συλλογισμός.
But we use setting out in the same way as we use perception, when we speak to a learner; for we do not use it as though it were impossible to demonstrate without these, as it is from the premises of the syllogism.
§1.1.42Μὴ λανθανέτω δʼ ἡμᾶς ὅτι ἐν τῷ αὐτῷ συλλογισμῶ οὐχ ἅπαντα τὰ συμπεράσματα διʼ ἑνὸς σχήματός ἐστιν, ἀλλὰ τὸ μὲν διὰ τούτου τὸ δὲ διʼ ἄλλου.
And let it not escape us that in the same syllogism not all the conclusions are through one figure, but one through this and another through another.
δῆλον οὖν ὅτι καὶ τὰς ἀναλύσεις οὕτω ποιητέον.
It is clear then that we must also make reductions in this way.
ἐπεὶ δʼ οὐ πᾶν πρόβλημα ἐν ἅπόντι σχήματι ἀλλʼ ἐν ἑκάστῳ τεταγμένα, φανερὸν ἐκ τοῦ συμπεράσματος ἐν ᾧ σχήματι ζητητέον.
And since not every problem is in every figure, but they are ordered in each, it is clear from the conclusion in which figure we must search.
§1.1.43Τούς τε πρὸς ὁρισμὸν τῶν λόγων, ὅσοι πρὸς ἕν τι τυγχάνουσι διειλεγμένοι τῶν ἐν τῷ ὅρῳ, πρὸς ὃ διείλεκται θετέον ὅρον, καὶ οὐ τὸν ἅπαντα λόγον· ἧττον γὰρ συμβήσεται ταράττεσθαι διὰ τὸ μῆκος, οἷον εἰ τὸ ὕδωρ ἔδειξεν ὅτι ὑγρὸν ποτόν, τὸ ποτὸν καὶ τὸ ὕδωρ ὅρους θετέον.
And as for arguments directed to a definition, as many as happen to have argued about some single thing of those in the definition, we must posit as a term that about which it has argued, and not the whole definition; for there will be less confusion because of the length, as for example, if one showed that water is a wet drink, we must posit 'drink' and 'water' as the terms.
§1.1.44Ἔτι δὲ τοὺς ἐξ ὑποθέσεως συλλογισμοὺς οὐ πειρατέο ἀνάγειν·
Further, we must not attempt to reduce hypothetical syllogisms; for it is not possible to reduce them from the premises.
οὐ γὰρ ἔστιν ἐκ τῶν κειμένων ἀνάγειν. οὐ γὰρ διὰ συλλογισμοῦ δεδειγμένοι εἰσίν, ἀλλὰ διὰ συνθήκης ὡμολογημένοι πάντες.
For they have not been shown through a syllogism, but have all been agreed upon through an agreement.
οἷον εἰ ὑποθέμενος, ἂν δύναμίς τις μία μὴ ᾖ τῶν ἐναντίων, μηδʼ ἐπιστήμην μίαν εἶναι, εἶτα διαλεχθείη ὅτι οὐκ ἔστι πᾶσα δύναμις τῶν ἐναντίων, οἱονεὶ τοῦ ὑγιεινοῦ καὶ τοῦ νοσώδους· ἅμα γὰρ ἔσται τὸ αὐτὸ ὑγιεινὸν καὶ νοσῶδες.
For example, if having hypothesized that if there is not one single power of contraries, neither is there one science, one should then argue that not every power is of contraries, as for instance of the healthy and the diseased; for the same thing will be at once healthy and diseased.
ὅτι μὲν οὖν οὐκ ἔστι μία πάντων τῶν ἐναντίων δύναμις, ἐπιδέδεικται, ὅτι δʼ ἐπιστήμη οὐκ ἔστιν, οὐ δέδεικται.
That, then, there is not one power of all contraries has been shown, but that there is not one science has not been shown.
καίτοι ὁμολογεῖν ἀναγκαῖον· ἀλλʼ οὐκ ἐκ συλλογισμοῦ, ἀλλʼ ἐξ ὑποθέσεως.
And yet it is necessary to agree; but not from a syllogism, but from a hypothesis.
τοῦτον μὲν οὖν οὐκ ἔστιν ἀναγαγεῖν, ὅτι δʼ οὐ μία δύναμις, ἔστιν· οὗτος γὰρ ἴσως καὶ ἦν συλλογισμός, ἐκεῖνο δʼ ὑπόθεσις.
This, then, cannot be reduced, but that there is not one power can be; for this latter was perhaps indeed a syllogism, but the former a hypothesis.
Ὁμοίως δὲ καὶ ἐπὶ τῶν διὰ τοῦ ἀδυνάτου περαινομένων· οὐδὲ γὰρ τούτους οὐκ ἔστιν ἀναλύειν, ἀλλὰ τὴν μὲν εἰς τὸ ἀδύνατον ἀπαγωγὴν ἔστι (συλλογισμῷ γὰρ δείκνυται), θάτερον δʼ οὐκ ἔστιν· ἐξ ὑποθέσεως γὰρ περαίνεται.
Similarly also in the case of those concluded through the impossible; for indeed we cannot reduce these either, but we can reduce the reduction to the impossible (for it is shown by a syllogism), but the other part we cannot; for it is concluded from a hypothesis.
διαφέρουσι δὲ τῶν προειρημένων ὅτι ἐν ἐκείνοις μὲν δεῖ προδιομολογήσασθαι, εἰ μέλλει συμφήσειν, οἷον ἂν δειχθῇ μία δύναμις τῶν ἐναντίων, καὶ ἐπιστήμην εἶναι τὴν αὐτήν· ἐνταῦθα δὲ καὶ μὴ προδιομολογησάμενοι συγχωροῦσι διὰ τὸ φανερόν εἶναι τὸ ψεῦδος, οἷον τεθείσης τῆς διαμέτρου συμμέτρου τὸ τὰ περιττὰ ἴσα εἶναι τοῖς ἀρτίοις.
But they differ from the aforementioned in that, in those, one must agree beforehand if one is going to assent, as for example that if one power of contraries is shown, the science of them is also the same; whereas here, even without agreeing beforehand, they assent because the falsehood is obvious, as for example, if the diagonal is assumed to be commensurate, that odd numbers are equal to even numbers.
Πολλοὶ δὲ καὶ ἕτεροι περαίνονται ἐξ ὑποθέσεως, οὓς ἐπισκέψασθαι δεῖ καὶ διασημῆναι καθαρῶς.
And many others also are concluded from a hypothesis, which we must investigate and distinguish clearly.
τίνες μὲν οὖν αἱ διαφοραὶ τούτων, καὶ ποσαχῶς γίνεται τὸ ἐξ ὑποθέσεως, ὕστερον ἐροῦμεν· νῦν δὲ τοσοῦτον ἡμῖν ἔστω φανερόν, ὅτι οὐκ ἔστιν ἀναλύειν εἰς τὰ σχήματα τοὺς τοιούτους συλλογισμούς.
What, then, are the differences of these, and in how many ways conclusion from a hypothesis occurs, we will say later; but for now let this much be clear to us, that it is not possible to reduce such syllogisms into the figures.
καὶ διʼ ἣν αἰτίαν, εἰρήκαμεν.
And we have stated the reason why.