Authors/Aristotle/priora/Liber 1/C15

Chapter 15

Greek	Latin	English
	(PL 64 0654B) CAPUT XIV. De syllogismis ex una absoluta et altera contingente in prima figura.	15
33b25 Ἐὰν δ᾽ ἡ μὲν ὑπάρχειν ἡ δ᾽ ἐνδέχεσθαι λαμβάνηται τῶν προτάσεων, ὅταν μὲν ἡ πρὸς τὸ μεῖζον ἄκρον ἐνδέχεσθαι σημαίνηι, τέλειοί τ᾽ ἔσονται πάντες οἱ συλλογισμοὶ καὶ τοῦ ἐνδέχεσθαι κατὰ τὸν εἰρημένον διορισμόν, ὅταν δ᾽ ἡ πρὸς τὸ ἔλαττον, ἀτελεῖς τε πάντες, καὶ οἱ στερητικοὶ τῶν συλλογισ μῶν οὐ τοῦ κατὰ τὸν διορισμὸν ἐνδεχομένου, ἀλλὰ τοῦ μηδενὶ ἢ μὴ παντὶ ἐξ ἀνάγκης ὑπάρχειν· εἰ γὰρ μηδενὶ ἢ μὴ παντὶ ἐξ ἀνάγκης, ἐνδέχεσθαί φαμεν καὶ μηδενὶ καὶ μὴ παντὶ ὑπάρχειν.	(0654C) Si autem haec quidem inesse, illa vero contingere sumatur propositionum, quando quae ad maiorem quidem extremitatem contingere significaverit perfecti erunt omnes syllogismi, et contingentis secundum dictam determinationem, quando autem quae ad minorem, et imperfecti omnes, et privativi syllogismi, non contingentis secundum dictam determinationem, sed eius quod est nulli, aut non omni ex necessitate inesse. Si enim nulli, aut non omni ex necessitate contingere dicimus, et nulli, et non omni inesse.	If one premiss is a simple proposition, the other a problematic, whenever the major premiss indicates possibility all the syllogisms will be perfect and establish possibility in the sense defined; but whenever the minor premiss indicates possibility all the syllogisms will be imperfect, and those which are negative will establish not possibility according to the definition, but that the major does not necessarily belong to any, or to all, of the minor. For if this is so, we say it is possible that it should belong to none or not to all.
ἐνδεχέσθω γὰρ τὸ Α παντὶ τῶι Β, τὸ δὲ Β παντὶ τῶι Γ κείσθω ὑπάρχειν. ἐπεὶ οὖν ὑπὸ τὸ Β ἐστὶ τὸ Γ, τῶι δὲ Β παντὶ ἐνδέχεται τὸ Α, φανερὸν ὅτι καὶ τῶι Γ παντὶ ἐνδέχεται. γίνεται δὴ τέλειος συλλογισμός· ὁμοίως δὲ καὶ στερητικῆς οὔσης τῆς Α Β προτάσεως, τῆς δὲ Β Γ καταφατικῆς, καὶ τῆς μὲν ἐνδέχεσθαι τῆς δ᾽ ὑπάρχειν λαμβανομένης, τέλειος ἔσται συλλογισμὸς ὅτι τὸ Α ἐνδέχεται μηδενὶ τῶι Γ ὑπάρχειν.	Contingat enim A omni B, B autem omni C ponatur inesse, quoniam igitur sub B est C, A autem contingit omni B, manifestum quoniam et C omni contingit A, fit ergo perfectus syllogismus. Similiter autem et cum privativa est A B propositio, B C autem affirmativa, et haec quidem contingere, illa vero inesse sumetur, perfectus erit syllogismus, quoniam A contingit nulli C inesse.	Let A be possible for all B, and let B belong to all C. Since C falls under B, and A is possible for all B, clearly it is possible for all C also. So a perfect syllogism results. Likewise if the premiss AB is negative, and the premiss BC is affirmative, the former stating possible, the latter simple attribution, a perfect syllogism results proving that A possibly belongs to no C.
↵ Ὅτι μὲν οὖν τοῦ ὑπάρχειν τιθεμένου πρὸς τὸ ἔλαττον ἄκρον τέλειοι γίγνονται συλλογισμοί, φανερόν· ὅτι δ᾽ ἐναντίως ἔχοντος ἔσονται συλλογισμοί, διὰ τοῦ ἀδυνάτου δεικτέον. ἅμα δ᾽ ἔσται δῆλον καὶ ὅτι ἀτελεῖς· ἡ γὰρ δεῖξις οὐκ ἐκ τῶν εἰ λημμένων προτάσεων.	Quoniam ergo inesse posito ad minorem extremitatem, perfecti syllogismi fiunt, manifestum. Quod autem contrariae se habentes erunt syllogismi, per impossibile monstrandum est, simul autem erit manifestum et quoniam imperfecti, nam ostensio non ex sumptis propositionibus.	It is clear that perfect syllogisms result if the minor premiss states simple belonging: but that syllogisms will result if the modality of the premisses is reversed, must be proved per impossibile. At the same time it will be evident that they are imperfect: for the proof proceeds not from the premisses assumed.
πρῶτον δὲ λεκτέον ὅτι εἰ τοῦ Α ὄντος ἀνάγκη τὸ Β εἶναι, καὶ δυνατοῦ ὄντος τοῦ Α δυνατὸν ἔσται καὶ τὸ Β ἐξ ἀνάγκης. ἔστω γὰρ οὕτως ἐχόντων τὸ μὲν ἐφ᾽ ὧι τὸ Α δυνατόν, τὸ δ᾽ ἐφ᾽ ὧι τὸ Β ἀδύνατον. εἰ οὖν τὸ μὲν δυνατόν, ὅτε δυνατὸν εἶναι, γένοιτ᾽ ἄν, τὸ δ᾽ ἀδύνατον, ὅτ᾽ ἀδύ νατον, οὐκ ἂν γένοιτο, ἅμα δ᾽ εἴη τὸ Α δυνατὸν καὶ τὸ Β ἀδύνατον, ἐνδέχοιτ᾽ ἂν τὸ Α γενέσθαι ἄνευ τοῦ Β, εἰ δὲ γενέσθαι, καὶ εἶναι·	(0654D) Primum autem dicendum quoniam si cum est A, necesse est esse B, et cum possibile est esse A, possibile erit B ex necessitate. Sit enim sic se habentibus rebus ut in quo quidem A possibile, in quo autem B impossibile, si ergo aliud possibile quidem est, cum possibile esse, ipsum fiet, hoc vero impossibile, quoniam impossibile, non utique fiet, simul autem si A possibile, et B impossibile, continget fieri praeter B, si autem fieri et esse.	First we must state that if B’s being follows necessarily from A’s being, B’s possibility will follow necessarily from A’s possibility. Suppose, the terms being so related, that A is possible, and B is impossible. If then that which is possible, when it is possible for it to be, might happen, and if that which is impossible, when it is impossible, could not happen, and if at the same time A is possible and B impossible, it would be possible for A to happen without B, and if to happen, then to be.
τὸ γὰρ γεγονός, ὅτε γέγονεν, ἔστιν. δεῖ δὲ λαμβάνειν μὴ μόνον ἐν τῆι γενέσει τὸ ἀδύνατον καὶ δυνατόν, ἀλλὰ καὶ ἐν τῶι ἀληθεύεσθαι καὶ ἐν τῶι ὑπάρχειν, καὶ ὁσα χῶς ἄλλως λέγεται τὸ δυνατόν· ἐν ἅπασι γὰρ ὁμοίως ἕξει.	Nam quod fit, quando factum est, est. Oportet autem accipere non solum in generatione possibile et impossibile, sed et in verum esse, et in quod actu est, et quocunque modo simpliciter aliter dicitur possibile, in omnibus enim similiter se habebit.	For that which has happened, when it has happened, is. But we must take the impossible and the possible not only in the sphere of becoming, but also in the spheres of truth and predicability, and the various other spheres in which we speak of the possible: for it will be alike in all.
ἔτι τὸ ὄντος τοῦ Α τὸ Β εἶναι, οὐχ ὡς ἑνός τινος ὄντος τοῦ Α τὸ Β ἔσται δεῖ ὑπολαβεῖν· οὐ γὰρ ἔστιν οὐδὲν ἐξ ἀνάγκης ἑνός τινος ὄντος, ἀλλὰ δυοῖν ἐλαχίστοιν, οἷον ὅταν αἱ προτάσεις οὕτως ἔχωσιν ὡς ἐλέχθη κατὰ τὸν συλλογισμόν. εἰ γὰρ τὸ Γ κατὰ τοῦ Δ, τὸ δὲ Δ κατὰ τοῦ Ζ, καὶ τὸ Γ κατὰ τοῦ Ζ ἐξ ἀνάγκης· καὶ εἰ δυνατὸν ἑκάτερον, καὶ τὸ συμπέρασμα δυνατόν. ὥσπερ οὖν εἴ τις θείη τὸ μὲν Α τὰς προτάσεις, τὸ δὲ Β τὸ συμπέρασμα, συμβαίνοι ἂν οὐ μόνον ἀναγκαίου τοῦ Α ὄντος ἅμα καὶ τὸ Β εἶναι ἀναγκαῖον, ἀλλὰ καὶ δυνατοῦ δυνατόν.	(0655A) Amplius cum est A, B esse, non tanquam uno aliquo existente A, erit B, oportet opinari, nihil enim est ex necessitate uno aliquo existente, sed duobus ad minus, ut quando propositiones sic se habent (ut dictum est) secundum syllogismum, nam sic dicitur de D, D autem de E, et C de E ex necessitate, et si utrumque possibile, et conclusio erit possibilis. Quemadmodum ergo si quis ponat A quidem propositiones, B autem conclusionem, accidet non solum A existente necessario, et B simul esse necessarium, sed etiam possibili possibile.	Further we must understand the statement that B’s being depends on A’s being, not as meaning that if some single thing A is, B will be: for nothing follows of necessity from the being of some one thing, but from two at least, i.e. when the premisses are related in the manner stated to be that of the syllogism. For if C is predicated of D, and D of F, then C is necessarily predicated of F. And if each is possible, the conclusion also is possible. If then, for example, one should indicate the premisses by A, and the conclusion by B, it would not only result that if A is necessary B is necessary, but also that if A is possible, B is possible.
Τούτου δὲ δειχθέντος, φανερὸν ὅτι ψεύδους ὑποτεθέντος καὶ μὴ ἀδυνάτου καὶ τὸ συμβαῖνον διὰ τὴν ὑπόθεσιν ψεῦδος ἔσται καὶ οὐκ ἀδύνατον. οἷον εἰ τὸ Α ψεῦδος μέν ἐστι μὴ μέντοι ἀδύνατον, ὄντος δὲ τοῦ Α τὸ Β ἔστι, καὶ τὸ Β ἔσται ψεῦδος μὲν οὐ μέντοι ἀδύνατον. ἐπεὶ γὰρ δέδεικται ὅτι εἰ τοῦ Α ὄντος τὸ Β ἔστι, καὶ δυνατοῦ ὄντος τοῦ Α ἔσται τὸ Β δυνατόν, ὑπόκειται δὲ τὸ Α δυνατὸν εἶναι, καὶ τὸ Β ἔσται δυνατόν· εἰ γὰρ ἀδύνατον, ἅμα δυνατὸν ἔσται τὸ αὐτὸ καὶ ἀδύνατον.	(0655B) Hoc autem ostenso manifestum est quoniam falso posito, et non impossibili, et quod accidit propter positionem falsum erit, et non impossibile, ut si A falsum quidem est, non tamen impossibile, cum autem sit A et B, et B erit falsum quidem, non tamen impossibile. Nam ostensum est quoniam cum est A, est B, et cum possibile est A, possibile est B. Positum autem est A possibile esse, et B erit possibile, si enim impossibile est B, simul idem erit possibile et impossibile.	Since this is proved it is evident that if a false and not impossible assumption is made, the consequence of the assumption will also be false and not impossible: e.g. if A is false, but not impossible, and if B is the consequence of A, B also will be false but not impossible. For since it has been proved that if B’s being is the consequence of A’s being, then B’s possibility will follow from A’s possibility (and A is assumed to be possible), consequently B will be possible: for if it were impossible, the same thing would at the same time be possible and impossible.
Διωρισμένων δὴ τούτων ὑπαρχέτω τὸ Α παντὶ τῶι Β, τὸ δὲ Β παντὶ τῶι Γ ἐνδεχέσθω· ἀνάγκη οὖν τὸ Α παντὶ τῶι Γ ἐνδέχεσθαι ὑπάρχειν. μὴ γὰρ ἐνδεχέσθω, τὸ δὲ Β παντὶ τῶι Γ κείσθω ὡς ὑπάρχον· τοῦτο δὲ ψεῦδος μέν, οὐ μέντοι ἀδύνατον. εἰ οὖν τὸ μὲν Α μὴ ἐνδέχεται παντὶ τῶι Γ, τὸ δὲ Β παντὶ ὑπάρχει τῶι Γ, τὸ Α οὐ παντὶ τῶι Β ἐνδέχεται· γί νεται γὰρ συλλογισμὸς διὰ τοῦ τρίτου σχήματος. ἀλλ᾽ ὑπέκειτο παντὶ ἐνδέχεσθαι ὑπάρχειν. ἀνάγκη ἄρα τὸ Α παντὶ ↵ τῶι Γ ἐνδέχεσθαι· ψεύδους γὰρ τεθέντος καὶ οὐκ ἀδυνάτου τὸ συμβαῖνόν ἐστιν ἀδύνατον. [ἐγχωρεῖ δὲ καὶ διὰ τοῦ πρώτου σχήματος ποιῆσαι τὸ ἀδύνατον, θέντας τῶι Γ τὸ Β ὑπάρχειν. εἰ γὰρ τὸ Β παντὶ τῶι Γ ὑπάρχει, τὸ δὲ Α παντὶ τῶι Β ἐνδέχεται, κἂν τῶι Γ παντὶ ἐνδέχοιτο τὸ Α. ἀλλ᾽ ὑπέκειτο μὴ παντὶ ἐγχωρεῖν.]	Determinatis autem iis, insit A omni B, B autem contingit omni C, necesse est A igitur contingere omni C inesse. Non enim contingat, B autem omni C ponatur inesse, hoc autem falsum quidem, non tamen impossibile, si ergo A quidem non contingit omni C, B autem omni C insit, A non omni B contingit. Fit enim syllogismus per tertiam figuram. Sed positum erat omni C contingere inesse, necesse est ergo A omni C contingere. Falso enim posito, et non impossibili, quod accidit est impossibile. (0655C) Possibile est autem et primam figuram facere impossibile ponentes B inesse C, nam si B omni C inest, A autem omni B contingit, et omni C continget A, sed positum erat non omni possibile inesse.	Since we have defined these points, let A belong to all B, and B be possible for all C: it is necessary then that should be a possible attribute for all C. Suppose that it is not possible, but assume that B belongs to all C: this is false but not impossible. If then A is not possible for C but B belongs to all C, then A is not possible for all B: for a syllogism is formed in the third degree. But it was assumed that A is a possible attribute for all B. It is necessary then that A is possible for all C. For though the assumption we made is false and not impossible, the conclusion is impossible. It is possible also in the first figure to bring about the impossibility, by assuming that B belongs to C. For if B belongs to all C, and A is possible for all B, then A would be possible for all C. But the assumption was made that A is not possible for all C.
Δεῖ δὲ λαμβάνειν τὸ παντὶ ὑπάρχον μὴ κατὰ χρόνον ὁρίσαντας, οἷον νῦν ἢ ἐν τῶιδε τῶι χρόνωι, ἀλλ᾽ ἁπλῶς· διὰ τοιούτων γὰρ προτάσεων καὶ τοὺς συλλογισμοὺς ποιοῦμεν, ἐπεὶ κατά γε τὸ νῦν λαμβανομένης τῆς προτάσεως οὐκ ἔσται συλλογισμός· οὐδὲν γὰρ ἴσως κωλύει ποτὲ καὶ παντὶ κινου- μένωι ἄνθρωπον ὑπάρχειν, οἷον εἰ μηδὲν ἄλλο κινοῖτο· τὸ δὲ κινούμενον ἐνδέχεται παντὶ ἵππωι· ἀλλ᾽ ἄνθρωπον οὐδενὶ ἵππωι ἐνδέχεται. ἔτι ἔστω τὸ μὲν πρῶτον ζῶιον, τὸ δὲ μέσον κινού μενον, τὸ δ᾽ ἔσχατον ἄνθρωπος. αἱ μὲν οὖν προτάσεις ὁμοίως ἕξουσι, τὸ δὲ συμπέρασμα ἀναγκαῖον, οὐκ ἐνδεχόμενον· ἐξ ἀνάγκης γὰρ ὁ ἄνθρωπος ζῶιον. φανερὸν οὖν ὅτι τὸ καθόλου ληπτέον ἁπλῶς, καὶ οὐ χρόνωι διορίζοντας.	Oportet autem accipere omni inesse non secundum tempus determinantes, ut nunc, aut in hoc tempore, sed simpliciter (per huiusmodi enim propositiones et syllogismos facimus), quoniam secundum nunc sumpta propositione, non erit syllogismus. Nihil enim fortasse prohibet quandoque et omni moventi hominem inesse, ut si nihil aliud moveatur, movens autem contingit omni equo, sed homo nulli equo contingit. Amplius: sit primum quidem animal, medium vero movens, postremum vero homo, ergo propositiones quidem similiter se habebunt, conclusio vero erit necessaria, non contingens. (0655D) Ex necessitate enim homo est animal, manifestum igitur quoniam universale sumendum simpliciter, et non tempore determinantes.	We must understand ‘that which belongs to all’ with no limitation in respect of time, e.g. to the present or to a particular period, but simply without qualification. For it is by the help of such premisses that we make syllogisms, since if the premiss is understood with reference to the present moment, there cannot be a syllogism. For nothing perhaps prevents ‘man’ belonging at a particular time to everything that is moving, i.e. if nothing else were moving: but ‘moving’ is possible for every horse; yet ‘man’ is possible for no horse. Further let the major term be ‘animal’, the middle ‘moving’, the the minor ‘man’. The premisses then will be as before, but the conclusion necessary, not possible. For man is necessarily animal. It is clear then that the universal must be understood simply, without limitation in respect of time.
Πάλιν ἔστω στερητικὴ πρότασις καθόλου ἡ Α Β, καὶ εἰλήφθω τὸ μὲν Α μηδενὶ τῶι Β ὑπάρχειν, τὸ δὲ Β παντὶ ἐνδεχέσθω ὑπάρχειν τῶι Γ. τούτων οὖν τεθέντων ἀνάγκη τὸ Α ἐνδέχεσθαι μηδενὶ τῶι Γ ὑπάρχειν. μὴ γὰρ ἐνδεχέσθω, τὸ δὲ Β τῶι Γ κείσθω ὑπάρχον, καθάπερ πρότερον. ἀνάγκη δὴ τὸ Α τινὶ τῶι Β ὑπάρχειν· γίνεται γὰρ συλλογισμὸς διὰ τοῦ τρίτου σχήματος· τοῦτο δὲ ἀδύνατον. ὥστ᾽ ἐνδέχοιτ᾽ ἂν τὸ Α μηδενὶ τῶι Γ· ψεύδους γὰρ τεθέντος ἀδύνατον τὸ συμβαῖνον.	Rursum: sit privativa propositio universalis A B, et sumatur A quidem nulli B inesse, B autem contingat omni C inesse. His igitur positis necesse est A contingere nulli C inesse, non enim contingat, B autem ponatur inesse C sicut prius, necesse est igitur A alicui B inesse, fit enim syllogismus per tertiam figuram. Hoc autem impossibile, quare contingit A, nulli C. Posito enim falso, et non impossibili, impossibile est quod accidit.	Again let the premiss AB be universal and negative, and assume that A belongs to no B, but B possibly belongs to all C. These propositions being laid down, it is necessary that A possibly belongs to no C. Suppose that it cannot belong, and that B belongs to C, as above. It is necessary then that A belongs to some B: for we have a syllogism in the third figure: but this is impossible. Thus it will be possible for A to belong to no C; for if at is supposed false, the consequence is an impossible one.
οὗτος οὖν ὁ συλλογισμὸς οὐκ ἔστι τοῦ κατὰ τὸν διορισμὸν ἐνδεχομένου, ἀλλὰ τοῦ μηδενὶ ἐξ ἀνάγκης (αὕτη γάρ ἐστιν ἡ ἀντίφασις τῆς γενομένης ὑποθέσεως· ἐτέθη γὰρ ἐξ ἀνάγ κης τὸ Α τινὶ τῶι Γ ὑπάρχειν, ὁ δὲ διὰ τοῦ ἀδυνάτου συλλογισμὸς τῆς ἀντικειμένης ἐστὶν φάσεωσ).	Hic ergo syllogismus non est contingentis secundum definitionem, sed nulli inesse ex necessitate. Haec est contradictio factae hypothesis. (0656A) Positum est enim ex necessitate A alicui C inesse, syllogismus autem per impossibile, oppositae est contradictionis.	This syllogism then does not establish that which is possible according to the definition, but that which does not necessarily belong to any part of the subject (for this is the contradictory of the assumption which was made: for it was supposed that A necessarily belongs to some C, but the syllogism per impossibile establishes the contradictory which is opposed to this).
ἔτι δὲ καὶ ἐκ τῶν ὅρων φανερὸν ὅτι οὐκ ἔσται τὸ συμπέρασμα ἐνδεχόμενον. ἔστω γὰρ τὸ μὲν Α κόραξ, τὸ δ᾽ ἐφ᾽ ὧι Β διανοούμενον, ἐφ᾽ ὧι δὲ Γ ἄνθρωπος. οὐδενὶ δὴ τῶι Β τὸ Α ὑπάρχει· οὐδὲν γὰρ διανοούμενον κόραξ. τὸ δὲ Β παντὶ ἐνδέχεται τῶι Γ· παντὶ γὰρ ἀνθρώπωι τὸ διανοεῖσθαι. ἀλλὰ τὸ Α ἐξ ἀνάγκης οὐδενὶ τῶι Γ· οὐκ ἄρα τὸ συμπέρασμα ἐνδεχόμενον. ἀλλ᾽ οὐδ᾽ ἀναγκαῖον ἀεί. ἔστω γὰρ τὸ μὲν Α κινούμενον, τὸ δὲ Β ἐπιστήμη, τὸ δ᾽ ἐφ᾽ ὧι Γ ἄνθρωπος. τὸ μὲν οὖν Α οὐδενὶ τῶι Β ὑπάρξει, τὸ δὲ Β παντὶ τῶι Γ ἐνδέχεται, καὶ οὐκ ἔσται τὸ συμπέρασμα ἀναγκαῖον· οὐ γὰρ ἀνάγκη μηδένα κινεῖσθαι ἄνθρωπον, ἀλλ᾽ ↵ οὐκ ἀνάγκη τινά. δῆλον οὖν ὅτι τὸ συμπέρασμά ἐστι τοῦ μηδενὶ ἐξ ἀνάγκης ὑπάρχειν. ληπτέον δὲ βέλτιον τοὺς ὅρους.	Amplius autem et ex terminis manifestum quoniam non erit conclusio contingens, sit enim A quidem corvus, in quo autem B intelligens, in quo autem C homo, nulli ergo B inest A, nam nullum intelligens, corvus, B autem contingit omni C, omni enim homini inest intelligere, sed A ex necessitate nulli C, non igitur conclusio contingens. Sed nec necessaria semper: sit enim A quidem movens, B autem scientia, in quo autem C homo, ergo A quidem nulli B inerit, B autem omni C contingit, et non erit conclusio necessaria, non enim necesse est nullum hominem moveri, sed necesse est aliquem. (0656B) Manifestum igitur quoniam est conclusio eius quod est nulli ex necessitate inesse. Sumendum autem melius terminos.	Further, it is clear also from an example that the conclusion will not establish possibility. Let A be ‘raven’, B ‘intelligent’, and C ‘man’. A then belongs to no B: for no intelligent thing is a raven. But B is possible for all C: for every man may possibly be intelligent. But A necessarily belongs to no C: so the conclusion does not establish possibility. But neither is it always necessary. Let A be ‘moving’, B ‘science’, C ‘man’. A then will belong to no B; but B is possible for all C. And the conclusion will not be necessary. For it is not necessary that no man should move; rather it is not necessary that any man should move. Clearly then the conclusion establishes that one term does not necessarily belong to any instance of another term. But we must take our terms better.
Ἐὰν δὲ τὸ στερητικὸν τεθῆι πρὸς τὸ ἔλαττον ἄκρον ἐνδέχεσθαι σημαῖνον, ἐξ αὐτῶν μὲν τῶν εἰλημμένων προτάσεων οὐδεὶς ἔσται συλλογισμός, ἀντιστραφείσης δὲ τῆς κατὰ τὸ ἐνδέχεσθαι προτάσεως ἔσται, καθάπερ ἐν τοῖς πρότερον. ὑπαρχέτω γὰρ τὸ Α παντὶ τῶι Β, τὸ δὲ Β ἐνδεχέσθω μηδενὶ τῶι Γ. οὕτω μὲν οὖν ἐχόντων τῶν ὅρων οὐδὲν ἔσται ἀναγκαῖον· ἐὰν δ᾽ ἀντιστραφῆι τὸ Β Γ καὶ ληφθῆι τὸ Β παντὶ τῶι Γ ἐν δέχεσθαι, γίνεται συλλογισμὸς ὥσπερ πρότερον· ὁμοίως γὰρ ἔχουσιν οἱ ὅροι τῆι θέσει. τὸν αὐτὸν δὲ τρόπον καὶ στερητικῶν ὄντων ἀμφοτέρων τῶν διαστημάτων, ἐὰν τὸ μὲν Α Β μὴ ὑπάρχειν, τὸ δὲ Β Γ μηδενὶ ἐνδέχεσθαι σημαίνηι· δι᾽ αὐτῶν μὲν γὰρ τῶν εἰλημμένων οὐδαμῶς γίνεται τὸ ἀναγκαῖον, ἀν τιστραφείσης δὲ τῆς κατὰ τὸ ἐνδέχεσθαι προτάσεως ἔσται συλλογισμός. εἰλήφθω γὰρ τὸ μὲν Α μηδενὶ τῶι Β ὑπάρχειν, τὸ δὲ Β ἐνδέχεσθαι μηδενὶ τῶι Γ. διὰ μὲν οὖν τούτων οὐδὲν ἀναγκαῖον·	Si autem privativum ponatur ad maiorem extremitatem contingere significans, ex ipsis quidem sumptis propositionibus, nullus erit syllogismus, conversa autem secundum contingens propositione, erit quemadmodum in prioribus. Insit enim A omni B, B autem contingat nulli C, sic ergo habentibus se terminis, nihil erit necessarium. Si autem convertatur B C, et sumatur B contingere omni C, fiet syllogismus quemadmodum prius, similiter enim habent se termini positione. (0656C) Eodem autem modo et cum privativa sunt utraque intervalla, si A B quidem non inesse, B C autem nulli, contingere significat, nam per ea quidem quae sumpta sunt nullo modo fit necessarium, conversa autem secundum contingens propositione erit syllogismus, sumatur enim A quidem, nulli B inesse, B autem contingere nulli C, per haec quidem nihil necessarium.	If the minor premiss is negative and indicates possibility, from the actual premisses taken there can be no syllogism, but if the problematic premiss is converted, a syllogism will be possible, as before. Let A belong to all B, and let B possibly belong to no C. If the terms are arranged thus, nothing necessarily follows: but if the proposition BC is converted and it is assumed that B is possible for all C, a syllogism results as before: for the terms are in the same relative positions. Likewise if both the relations are negative, if the major premiss states that A does not belong to B, and the minor premiss indicates that B may possibly belong to no C. Through the premisses actually taken nothing necessary results in any way; but if the problematic premiss is converted, we shall have a syllogism. Suppose that A belongs to no B, and B may possibly belong to no C. Through these comes nothing necessary.
ἐὰν δὲ ληφθῆι τὸ Β παντὶ τῶι Γ ἐνδέχεσθαι, ὅπερ ἐστὶν ἀληθές, ἡ δὲ Α Β πρότασις ὁμοίως ἔχηι, πάλιν ὁ αὐτὸς ἔσται συλλογισμός. ἐὰν δὲ μὴ ὑπάρχειν τεθῆι τὸ Β παντὶ τῶι Γ καὶ μὴ ἐνδέχεσθαι μὴ ὑπάρχειν, οὐκ ἔσται συλλογισμὸς οὐδαμῶς, οὔτε στερητικῆς οὔσης οὔτε καταφατικῆς τῆς Α Β προτάσεως. ὅροι δὲ κοινοὶ τοῦ μὲν ἐξ ἀνάγκης ὑπάρχειν λευκόν – ζῶιον – χιών, τοῦ δὲ μὴ ἐνδέχεσθαι λευκόν – ζῶιον – πίττα.	Si autem sumatur B omni C contingere, quod verum est, A B autem propositio similiter se habeat, rursus erit idem syllogismus. Si autem non inesse ponatur B omni C, et non contingere non inesse, non erit syllogismus nullo modo, sive privativa sit, sive affirmativa A B propositio. Termini autem communes ex necessitate quidem inesse, album, animal, nix. Non contingere autem, album, animal, pix.	But if B is assumed to be possible for all C (and this is true) and if the premiss AB remains as before, we shall again have the same syllogism. But if it be assumed that B does not belong to any C, instead of possibly not belonging, there cannot be a syllogism anyhow, whether the premiss AB is negative or affirmative. As common instances of a necessary and positive relation we may take the terms white-animal-snow: of a necessary and negative relation, white-animal-pitch.
Φανερὸν οὖν ὅτι καθόλου τῶν ὅρων ὄντων, καὶ τῆς μὲν ὑπάρχειν τῆς δ᾽ ἐνδέχεσθαι λαμβανομένης τῶν προτάσεων, ὅταν ἡ πρὸς τὸ ἔλαττον ἄκρον ἐνδέχεσθαι λαμβάνηται πρότασις, ἀεὶ γίνεται συλλογισμός, πλὴν ὁτὲ μὲν ἐξ αὐτῶν ὁτὲ δ᾽ ἀντιστραφείσης τῆς προτάσεως. πότε δὲ τούτων ἑκάτε ρος καὶ διὰ τίν᾽ αἰτίαν, εἰρήκαμεν. Ἐὰν δὲ τὸ μὲν καθόλου τὸ δ᾽ ἐν μέρει ληφθῆι τῶν διαστημάτων, ὅταν μὲν τὸ πρὸς τὸ μεῖζον ἄκρον καθόλου τεθῆι καὶ ἐνδεχόμενον, εἴτ᾽ ἀποφατικὸν εἴτε καταφατικόν, τὸ δ᾽ ἐν μέρει καταφατικὸν καὶ ὑπάρχον, ἔσται συλλογισμὸς τέλειος, καθάπερ καὶ καθόλου τῶν ὅρων ὄντων. ἀπόδειξις δ᾽ ἡ αὐτὴ ἣ καὶ πρότερον.	(0656D) Manifestum est igitur quoniam cum universales sunt termini, et haec quidem propositionum inesse, illa vero sumitur contingens, quando quae ad minorem est extremitatem contingere sumitur propositio, semper fit syllogismus, verumtamen quandoquidem ex ipsis, quando autem propositione conversa, quando vero utrumque horum, et ob quam causam, diximus. Si autem hoc quidem universale, illud vero particulare sumitur intervallorum, quando ad maiorem quidem extremitatem universale ponitur, et contingens sive negativum, sive affirmativum, particulare autem affirmativum et inesse, erit syllogismus perfectus, quemadmodum et cum universales sunt termini, demonstratio autem eadem quae et prius.	Clearly then if the terms are universal, and one of the premisses is assertoric, the other problematic, whenever the minor premiss is problematic a syllogism always results, only sometimes it results from the premisses that are taken, sometimes it requires the conversion of one premiss. We have stated when each of these happens and the reason why. But if one of the relations is universal, the other particular, then whenever the major premiss is universal and problematic, whether affirmative or negative, and the particular is affirmative and assertoric, there will be a perfect syllogism, just as when the terms are universal. The demonstration is the same as before.
ὅταν δὲ καθόλου μὲν ἦι τὸ πρὸς τὸ μεῖζον ἄκρον, ὑπάρχον δὲ καὶ μὴ ἐνδεχόμενον, θάτερον δ᾽ ἐν μέρει καὶ ἐνδεχόμενον, ἐάν τ᾽ ἀποφατικαὶ ἐάν τε καταφατικαὶ τεθῶσιν ἀμφότεραι, ἐάν τε ἡ μὲν ἀποφατικὴ ἡ δὲ καταφατική, πάντως ἔσται συλλογισμὸς ἀτελής. πλὴν οἱ μὲν διὰ τοῦ ἀδυνάτου δειχθήσονται, ↵ οἱ δὲ καὶ διὰ τῆς ἀντιστροφῆς τῆς τοῦ ἐνδέχεσθαι, καθάπερ ἐν τοῖς πρότερον. ἔσται δὲ συλλογισμὸς διὰ τῆς ἀντιστροφῆς [καὶ] ὅταν ἡ μὲν καθόλου πρὸς τὸ μεῖζον ἄκρον τεθεῖσα σημαίνηι τὸ ὑπάρχειν [ἢ μὴ ὑπάρχειν], ἡ δ᾽ ἐν μέρει στερητικὴ οὖσα τὸ ἐνδέχεσθαι λαμβάνηι, οἷον εἰ τὸ μὲν Α παντὶ τῶι Β ὑπάρχει ἢ μὴ ὑπάρχει, τὸ δὲ Β τινὶ τῶι Γ ἐνδέχεται μὴ ὑπάρχειν· ἀντιστραφέντος γὰρ τοῦ Β Γ κατὰ τὸ ἐνδέχεσθαι γίνεται συλλογισμός. ὅταν δὲ τὸ μὴ ὑπάρχειν λαμβάνηι ἡ κατὰ μέρος τεθεῖσα, οὐκ ἔσται συλλογισμός.	(0657A) Quando autem universale quidem fuerit, ad maiorem extremitatem inesse, et non contingens, alterum vero particulare, et contingens, sive affirmative, sive negative ponantur utraeque, sive haec quidem negativa, illa vero affirmativa, omnino erit syllogismus imperfectus. Verum hi quidem per impossibile ostenduntur, illi vero per conversionem contingentis, quemadmodum in prioribus. Erit autem syllogismus per conversionem, et quando universalis quidem ad maiorem extremitatem posita significaverit inesse, vel non inesse, particularis vero cum sit privativa, sumatur contingens, ut si A quidem omni B inest, vel non inest, B autem alicui contingit non inesse, conversa enim B C, secundum contingere fit syllogismus. Quando autem non inesse sumetur particulariter posita propositio, non erit syllogismus.	But whenever the major premiss is universal, but assertoric, not problematic, and the minor is particular and problematic, whether both premisses are negative or affirmative, or one is negative, the other affirmative, in all cases there will be an imperfect syllogism. Only some of them will be proved per impossibile, others by the conversion of the problematic premiss, as has been shown above. And a syllogism will be possible by means of conversion when the major premiss is universal and assertoric, whether positive or negative, and the minor particular, negative, and problematic, e.g. if A belongs to all B or to no B, and B may possibly not belong to some C. For if the premiss BC is converted in respect of possibility, a syllogism results. But whenever the particular premiss is assertoric and negative, there cannot be a syllogism.
ὅροι τοῦ μὲν ὑπάρχειν λευκόν – ζῶιον – χιών, τοῦ δὲ μὴ ὑπάρχειν λευκόν – ζῶιον – πίττα· διὰ γὰρ τοῦ ἀδιορίστου ληπτέον τὴν ἀπόδειξιν.	Termini inesse, album, animal, nix; non inesse autem, album, animal, pix, per indefinitum enim est sumenda demonstratio.	As instances of the positive relation we may take the terms white-animal-snow; of the negative, white-animal-pitch. For the demonstration must be made through the indefinite nature of the particular premiss.
ἐὰν δὲ τὸ καθόλου τεθῆι πρὸς τὸ ἔλαττον ἄκρον, τὸ δ᾽ ἐν μέρει πρὸς τὸ μεῖζον, ἐάν τε στερητικὸν ἐάν τε καταφατικόν, ἐάν τ᾽ ἐνδεχόμενον ἐάν θ᾽ ὑπάρχον ὁποτερονοῦν, οὐδαμῶς ἔσται συλλογισμός. Οὐδ᾽ ὅταν ἐν μέρει ἢ ἀδιόριστοι τεθῶσιν αἱ προτάσεις, εἴτ᾽ ἐνδέχεσθαι λαμβάνουσαι εἴθ᾽ ὑπάρχειν εἴτ᾽ ἐναλλάξ, οὐδ᾽ οὕτως ἔσται συλλογισμός. ἀπόδειξις δ᾽ ἡ αὐτὴ ἥπερ κἀπὶ τῶν πρότερον. ὅροι δὲ κοινοὶ τοῦ μὲν ὑπάρχειν ἐξ ἀνάγκης ζῶιον – λευκόν – ἄνθρωπος, τοῦ δὲ μὴ ἐνδέχεσθαι ζῶιον – λευκόν – ἱμάτιον. φανερὸν οὖν ὅτι τοῦ μὲν πρὸς τὸ μεῖζον ἄκρον καθόλου τεθέντος ἀεὶ γίνεται συλλογισμός, τοῦ δὲ πρὸς τὸ ἔλαττον οὐδέποτ᾽ οὐδενός.	(0657B) Si autem universale quidem ponatur ad minorem extremitatem, particulare autem ad maiorem sive privativum, sive affirmativum, sive contingens, sive inesse utrumvis, nullo modo erit syllogismus. Nec cum particulares, vel indefinitae ponentur propositiones, sive contingere sumptae, sive inesse, seu permutatim, nec sic erit syllogismus, demonstratio autem eadem quae in prioribus. Termini autem communes inesse quidem, ex necessitate, animal, album, homo; non contingere vero, animal, album, tunica. Manifestum est igitur quoniam universali posito ad maiorem extremitatem semper erit syllogismus, ad minorem autem nunquam.	But if the minor premiss is universal, and the major particular, whether either premiss is negative or affirmative, problematic or assertoric, nohow is a syllogism possible. Nor is a syllogism possible when the premisses are particular or indefinite, whether problematic or assertoric, or the one problematic, the other assertoric. The demonstration is the same as above. As instances of the necessary and positive relation we may take the terms animal-white-man; of the necessary and negative relation, animal-white-garment. It is evident then that if the major premiss is universal, a syllogism always results, but if the minor is universal nothing at all can ever be proved.