Authors/Aristotle/priora/Liber 2

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10

Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20

Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27

Chapter 1

Greek	Latin	English
	(PL 64 0685) CAPUT PRIMUM.	1
52b38 Ἐν πόσοις μὲν οὖν σχήμασι καὶ διὰ ποίων καὶ πόσων προτάσεων καὶ πότε καὶ πῶς γίνεται συλλογισμός, ἔτι δ᾽ εἰς ποῖα βλεπτέον ἀνασκευάζοντι καὶ κατασκευά↵ ζοντι, καὶ πῶς δεῖ ζητεῖν περὶ τοῦ προκειμένου καθ᾽ ὁποιανοῦν μέθοδον, ἔτι δὲ διὰ ποίας ὁδοῦ ληψόμεθα τὰς περὶ ἕκαστον ἀρχάς, ἤδη διεληλύθαμεν.	(0685A) In quot ergo figuris, et per quales, et quot propositiones, et quando, et quomodo fit syllogismus, amplius autem ad quae perspiciendum construenti et destruenti, et quomodo oporteat quaerere de proposito secundum unamquamque artem, amplius autem per quam viam sumemus, quae in singulis sunt principia iam pertransivimus.	WE have already explained the number of the figures, the character and number of the premisses, when and how a syllogism is formed; further what we must look for when a refuting and establishing propositions, and how we should investigate a given problem in any branch of inquiry, also by what means we shall obtain principles appropriate to each subject.
ἐπεὶ δ᾽ οἱ μὲν καθόλου τῶν συλλογισμῶν εἰσὶν οἱ δὲ κατὰ μέρος, οἱ μὲν καθόλου πάντες αἰεὶ πλείω συλλογίζονται, τῶν δ᾽ ἐν μέρει οἱ μὲν κατηγορικοὶ πλείω, οἱ δ᾽ ἀποφατικοὶ τὸ συμπέρασμα μόνον. αἱ μὲν γὰρ ἄλλαι προτάσεις ἀντιστρέφουσιν, ἡ δὲ στερητικὴ οὐκ ἀντιστρέφει. τὸ δὲ συμπέρασμα τὶ κατά τινός ἐστιν, ὥσθ᾽ οἱ μὲν ἄλλοι συλλογισμοὶ πλείω συλλογίζον- ται, οἷον εἰ τὸ Α δέδεικται παντὶ τῶι Β ἢ τινί, καὶ τὸ Β τινὶ τῶι Α ἀναγκαῖον ὑπάρχειν, καὶ εἰ μηδενὶ τῶι Β τὸ Α, οὐδὲ τὸ Β οὐδενὶ τῶι Α, τοῦτο δ᾽ ἕτερον τοῦ ἔμπροσθεν· εἰ δὲ τινὶ μὴ ὑπάρχει, οὐκ ἀνάγκη καὶ τὸ Β τινὶ τῶι Α μὴ ὑπάρχειν· ἐνδέχεται γὰρ παντὶ ὑπάρχειν.	Quoniam autem alii quidem syllogismorum sunt universales, alii vero particulares: universales quidem omnes semper plura syllogizant, particularium autem praedicativi quidem plura, negativi vero conclusionem solam. Nam aliae quidem propositiones convertuntur, privativa vero non convertitur. Conclusio vero aliquid de aliquo est, quare alii quidem syllogismi plura syllogizant: ut si A ostensum sit omni aut alicui B inesse, et B alicui A necessarium est inesse, et si nulli B inesse A, et B nulli A, hoc autem aliud est A priore. (0685C) Si autem A alicui B non insit, non necesse est et B alicui A non inesse; contingit enim omni A inesse.	Since some syllogisms are universal, others particular, all the universal syllogisms give more than one result, and of particular syllogisms the affirmative yield more than one, the negative yield only the stated conclusion. For all propositions are convertible save only the particular negative: and the conclusion states one definite thing about another definite thing. Consequently all syllogisms save the particular negative yield more than one conclusion, e.g. if A has been proved to to all or to some B, then B must belong to some A: and if A has been proved to belong to no B, then B belongs to no A. This is a different conclusion from the former. But if A does not belong to some B, it is not necessary that B should not belong to some A: for it may possibly belong to all A.
Αὕτη μὲν οὖν κοινὴ πάντων αἰτία, τῶν τε καθόλου καὶ τῶν κατὰ μέρος· ἔστι δὲ περὶ τῶν καθόλου καὶ ἄλλως εἰπεῖν. ὅσα γὰρ ἢ ὑπὸ τὸ μέσον ἢ ὑπὸ τὸ συμπέρασμά ἐστιν, ἁπάντων ἔσται ὁ αὐτὸς συλλογισμός, ἐὰν τὰ μὲν ἐν τῶι μέσωι τὰ δ᾽ ἐν τῶι συμπεράσματι τεθῆι, οἷον εἰ τὸ Α Β συμπέρασμα διὰ τοῦ Γ, ὅσα ὑπὸ τὸ Β ἢ τὸ Γ ἐστίν, ἀνάγκη κατὰ πάντων λέγεσθαι τὸ Α· εἰ γὰρ τὸ Δ ἐν ὅλωι τῶι Β, τὸ δὲ Β ἐν τῶι Α, καὶ τὸ Δ ἔσται ἐν τῶι Α· πάλιν εἰ τὸ Ε ἐν ὅλωι τῶι Γ, τὸ δὲ Γ ἐν τῶι Α, καὶ τὸ Ε ἐν τῶι Α ἔσται.	Haec ergo communis omnium causa universalium et particularium. Est autem de universalibus, et aliter dicere, quaecunque enim aut sub medio aut sub conclusione sunt, omnium erit idem syllogismus, si illa quidem in medio, haec vero in conclusione ponantur, ut si A B conclusio per C, quaecunque sub B aut sub C sunt, necesse est de omnibus dici A, nam D si in toto B, et B in A, et D erit in A. Rursum si E in toto C, et C in toto A, et E in toto A erit.	This then is the reason common to all syllogisms whether universal or particular. But it is possible to give another reason concerning those which are universal. For all the things that are subordinate to the middle term or to the conclusion may be proved by the same syllogism, if the former are placed in the middle, the latter in the conclusion; e.g. if the conclusion AB is proved through C, whatever is subordinate to B or C must accept the predicate A: for if D is included in B as in a whole, and B is included in A, then D will be included in A. Again if E is included in C as in a whole, and C is included in A, then E will be included in A.
ὁμοίως δὲ καὶ εἰ στερητικὸς ὁ συλλογισμός. ἐπὶ δὲ τοῦ δευτέρου σχήματος τὸ ὑπὸ τὸ συμπέρασμα μόνον ἔσται συλλογίσασθαι, οἷον εἰ τὸ Α τῶι Β μηδενί, τῶι δὲ Γ παντί· συμπέρασμα ὅτι οὐδενὶ τῶι Γ τὸ Β. εἰ δὴ τὸ Δ ὑπὸ τὸ Γ ἐστί, φανερὸν ὅτι οὐχ ὑπάρχει αὐτῶι τὸ Β· τοῖς δ᾽ ὑπὸ τὸ Α ὅτι οὐχ ὑπάρχει, οὐ δῆλον διὰ τοῦ συλλογισμοῦ. καίτοι οὐχ ὑπάρχει τῶι Ε, εἰ ἔστιν ὑπὸ τὸ Α· ἀλλὰ τὸ μὲν τῶι Γ μηδενὶ ὑπάρχειν τὸ Β διὰ τοῦ συλλογισμοῦ δέδεικται, τὸ δὲ τῶι Α μὴ ὑπάρχειν ἀναπόδεικτον εἴληπται, ὥστ᾽ οὐ διὰ τὸν συλλογισμὸν συμβαίνει τὸ Β τῶι Ε μὴ ὑπάρχειν.	Similiter autem et si privativus sit syllogismus. (0685D) In secunda autem figura quod sub conclusione erit, solum erit syllogizare, ut si A insit nulli B, et omni C, conclusio quoniam nulli C inest B; si autem D sub C est, manifestum quoniam non inest ei B, iis autem quae sunt sub A, quoniam B non inest, non palam est per syllogismum, et si non inest B ei quod est E, si est E sub A, sed inesse quidem B nulli C per syllogismum ostensum est, non inesse vero A hoc quod est B, indemonstratum sumptum est, quare nec per syllogismum accidit B non inesse E.	Similarly if the syllogism is negative. In the second figure it will be possible to infer only that which is subordinate to the conclusion, e.g. if A belongs to no B and to all C; we conclude that B belongs to no C. If then D is subordinate to C, clearly B does not belong to it. But that B does not belong to what is subordinate to A is not clear by means of the syllogism. And yet B does not belong to E, if E is subordinate to A. But while it has been proved through the syllogism that B belongs to no C, it has been assumed without proof that B does not belong to A, consequently it does not result through the syllogism that B does not belong to E.
ἐπὶ δὲ τῶν ἐν μέρει τῶν μὲν ὑπὸ τὸ συμπέρασμα οὐκ ἔσται τὸ ἀναγκαῖον (οὐ γὰρ γίνεται συλλογισμός, ὅταν αὕτη ληφθῆι ἐν μέρει), τῶν δ᾽ ὑπὸ τὸ μέσον ἔσται πάντων, πλὴν οὐ διὰ τὸν συλλογισμόν· οἷον εἰ τὸ Α παντὶ τῶι Β, τὸ δὲ Β τινὶ τῶι Γ· τοῦ μὲν γὰρ ὑπὸ τὸ Γ τεθέντος οὐκ ἔσται συλλογισμός, τοῦ δ᾽ ὑπὸ τὸ Β ἔσται, ἀλλ᾽ οὐ διὰ τὸν προγεγενημένον. ὁμοίως δὲ κἀπὶ τῶν ἄλλων σχημάτων· τοῦ μὲν γὰρ ὑπὸ τὸ συμπέρασμα οὐκ ἔσται, ↵ θατέρου δ᾽ ἔσται, πλὴν οὐ διὰ τὸν συλλογισμόν, ἧι καὶ ἐν τοῖς καθόλου ἐξ ἀναποδείκτου τῆς προτάσεως τὰ ὑπὸ τὸ μέσον ἐδείκνυτο· ὥστ᾽ ἢ οὐδ᾽ ἐκεῖ ἔσται ἢ καὶ ἐπὶ τούτων.	In particularibus autem, eorum quidem quae sub conclusione sunt, non erit necessarium. Non enim fit syllogismus, quando ea sumpta fuerit particularis, eorum autem quae sunt sub medio, erit omnium, verumtamen non per syllogismum, ut si A omni B, et B alicui C: nam eius quod sub C est positum, non erit syllogismus, eius vero quod sub B erit, sed non propter eum qui prius factus est syllogismum. (0686A) Similiter autem et in aliis figuris, nam eius quidem quod sub conclusione est non erit, alterius vero erit, verum non per syllogismum, eo quod et in universalibus ex indemonstrata propositione quae sunt sub medio ostendebantur; quare neque hic erit, vel et in illis.	But in particular syllogisms there will be no necessity of inferring what is subordinate to the conclusion (for a syllogism does not result when this premiss is particular), but whatever is subordinate to the middle term may be inferred, not however through the syllogism, e.g. if A belongs to all B and B to some C. Nothing can be inferred about that which is subordinate to C; something can be inferred about that which is subordinate to B, but not through the preceding syllogism. Similarly in the other figures. That which is subordinate to the conclusion cannot be proved; the other subordinate can be proved, only not through the syllogism, just as in the universal syllogisms what is subordinate to the middle term is proved (as we saw) from a premiss which is not demonstrated: consequently either a conclusion is not possible in the case of universal syllogisms or else it is possible also in the case of particular syllogisms.

Chapter 2

Greek	Latin	English
	(PL 64 0686A) CAPUT II. Quod ex falsis in prima figura verum colligatur.	2
53b4 Ἔστι μὲν οὖν οὕτως ἔχειν ὥστ᾽ ἀληθεῖς εἶναι τὰς προ- τάσεις δι᾽ ὧν ὁ συλλογισμός, ἔστι δ᾽ ὥστε ψευδεῖς, ἔστι δ᾽ ὥστε τὴν μὲν ἀληθῆ τὴν δὲ ψευδῆ. τὸ δὲ συμπέρασμα ἢ ἀληθὲς ἢ ψεῦδος ἐξ ἀνάγκης. ἐξ ἀληθῶν μὲν οὖν οὐκ ἔστι ψεῦδος συλλογίσασθαι, ἐκ ψευδῶν δ᾽ ἔστιν ἀληθές, πλὴν οὐ διότι ἀλλ᾽ ὅτι· τοῦ γὰρ διότι οὐκ ἔστιν ἐκ ψευδῶν συλλογισμός· δι᾽ ἣν δ᾽ αἰτίαν, ἐν τοῖς ἑπομένοις λεχθήσεται.	Est ergo sic se habere, ut verae sint propositiones per quas fit syllogismus; est autem ut falsae, est vero ut haec quidem vera, illa autem falsa, conclusio autem aut vera, aut falsa ex necessitate. Ex veris ergo non est falsum syllogizare, ex falsis autem verum, tamen non propter quid, sed quia, nam eius qui est propter quid non est ex falsis syllogismus, ob quam autem causam in sequentibus dicetur.	It is possible for the premisses of the syllogism to be true, or to be false, or to be the one true, the other false. The conclusion is either true or false necessarily. From true premisses it is not possible to draw a false conclusion, but a true conclusion may be drawn from false premisses, true however only in respect to the fact, not to the reason. The reason cannot be established from false premisses: why this is so will be explained in the sequel.
Πρῶτον μὲν οὖν ὅτι ἐξ ἀληθῶν οὐχ οἷόν τε ψεῦδος συλλογίσασθαι, ἐντεῦθεν δῆλον. εἰ γὰρ τοῦ Α ὄντος ἀνάγκη τὸ Β εἶναι, τοῦ Β μὴ ὄντος ἀνάγκη τὸ Α μὴ εἶναι. εἰ οὖν ἀληθές ἐστι τὸ Α, ἀνάγκη τὸ Β ἀληθὲς εἶναι, ἢ συμβήσεται τὸ αὐτὸ ἅμα εἶναί τε καὶ οὐκ εἶναι· τοῦτο δ᾽ ἀδύνατον. μὴ ὅτι δὲ κεῖται τὸ Α εἷς ὅρος, ὑποληφθήτω ἐνδέχεσθαι ἑνός τινος ὄντος ἐξ ἀνάγκης τι συμβαίνειν· οὐ γὰρ οἷόν τε· τὸ μὲν γὰρ συμβαῖνον ἐξ ἀνάγκης τὸ συμπέρασμά ἐστι, δι᾽ ὧν δὲ τοῦτο γίνεται ἐλαχίστων, τρεῖς ὅροι, δύο δὲ διαστήματα καὶ προτάσεις. εἰ οὖν ἀληθές, ὧι τὸ Β ὑπάρχει, τὸ Α παντί, ὧι δὲ τὸ Γ, τὸ Β, ὧι τὸ Γ, ἀνάγκη τὸ Α ὑπάρχειν καὶ οὐχ οἷόν τε τοῦτο ψεῦδος εἶναι· ἅμα γὰρ ὑπάρξει ταὐτὸ καὶ οὐχ ὑπάρξει. τὸ οὖν Α ὥσπερ ἓν κεῖται, δύο προτάσεις συλληφθεῖσαι. ὁμοίως δὲ καὶ ἐπὶ τῶν στερητικῶν ἔχει· οὐ γὰρ ἔστιν ἐξ ἀληθῶν δεῖξαι ψεῦδος.	Primum ergo quoniam ex veris non possibile falsum syllogizare, hinc manifestum. (0686C) Si enim cum est A, necesse est esse B, si non est B, necesse est A non esse; si ergo verum est A, necesse est et B verum esse, aut accidet idem simul et esse et non esse, hoc autem impossibile. Non autem quoniam ponitur A unus terminus, accipiatur, contingere uno aliquo existente, ex necessitate aliquid accidere, non enim potest. Nam quod accidit ex necessitate conclusio est, per quae autem fit ad minimum tres sunt termini, duo autem intervalla et propositiones. Si ergo verum est cui omni inest B et A, cui autem C et B, cui C, necesse est A inesse, et non potest hoc falsum esse, simul enim erit idem et non inerit; ergo A ut unum, positum est duas propositiones colligere. Similiter autem se habet et in privativis, non enim est ex veris ostendere falsum.	First then that it is not possible to draw a false conclusion from true premisses, is made clear by this consideration. If it is necessary that B should be when A is, it is necessary that A should not be when B is not. If then A is true, B must be true: otherwise it will turn out that the same thing both is and is not at the same time. But this is impossible. Let it not, because A is laid down as a single term, be supposed that it is possible, when a single fact is given, that something should necessarily result. For that is not possible. For what results necessarily is the conclusion, and the means by which this comes about are at the least three terms, and two relations of subject and predicate or premisses. If then it is true that A belongs to all that to which B belongs, and that B belongs to all that to which C belongs, it is necessary that A should belong to all that to which C belongs, and this cannot be false: for then the same thing will belong and not belong at the same time. So A is posited as one thing, being two premisses taken together. The same holds good of negative syllogisms: it is not possible to prove a false conclusion from true premisses.
Ἐκ ψευδῶν δ᾽ ἀληθὲς ἔστι συλλογίσασθαι καὶ ἀμφοτέρων τῶν προτάσεων ψευδῶν οὐσῶν καὶ τῆς μιᾶς, ταύτης δ᾽ οὐχ ὁποτέρας ἔτυχεν ἀλλὰ τῆς δευτέρας, ἐάνπερ ὅλην λαμβάνηι ψευδῆ· μὴ ὅλης δὲ λαμβανομένης ἔστιν ὁποτερασοῦν. ἔστω γὰρ τὸ Α ὅλωι τῶι Γ ὑπάρχον, τῶι δὲ Β μηδενί, μηδὲ τὸ Β τῶι Γ. ἐνδέχεται δὲ τοῦτο, οἷον λίθωι οὐδενὶ ζῶιον, οὐδὲ λίθος οὐδενὶ ἀνθρώπωι. ἐὰν οὖν ληφθῆι τὸ Α παντὶ τῶι Β καὶ τὸ Β παντὶ τῶι Γ, τὸ Α παντὶ τῶι Γ ὑπάρξει, ὥστ᾽ ἐξ ἀμφοῖν ψευδῶν ἀληθὲς τὸ συμπέρασμα· πᾶς γὰρ ἄνθρωπος ζῶιον.	(0686D) Ex falsis autem est verum syllogizare, utrisque propositionibus falsis, et una; hac autem non utralibet contingit, sed secunda, si quidem totam sumamus falsam, non tota autem sumpta est utralibet. Insit enim A omni C, ei autem quod est B nulli, nec B insit C; contingit autem hoc, ut nulli lapidi animal, et lapis nulli homini; si igitur sumatur A omni B, et B omni C, A omni C inerit, quare ex utrisque falsis vera est conclusio, omnis enim homo animal.	But from what is false a true conclusion may be drawn, whether both the premisses are false or only one, provided that this is not either of the premisses indifferently, if it is taken as wholly false: but if the premiss is not taken as wholly false, it does not matter which of the two is false. (1) Let A belong to the whole of C, but to none of the Bs, neither let B belong to C. This is possible, e.g. animal belongs to no stone, nor stone to any man. If then A is taken to belong to all B and B to all C, A will belong to all C; consequently though both the premisses are false the conclusion is true: for every man is an animal.
ὡσαύτως δὲ καὶ τὸ στερητικόν. ἔστι γὰρ τῶι Γ μήτε τὸ Α ὑπάρχειν μηδενὶ μήτε τὸ Β, τὸ μέντοι Α τῶι Β παντί, οἷον ἐὰν τῶν αὐτῶν ὅρων ληφθέντων μέσον τεθῆι ὁ ἄνθρωπος· λίθωι γὰρ οὔτε ζῶιον οὔτε ἄνθρωπος οὐδενὶ ὑπάρχει, ἀνθρώπωι δὲ παντὶ ζῶιον. ὥστ᾽ ἐὰν ὧι μὲν ὑπάρχει, λάβηι μηδενὶ ὑπάρχειν, ὧι δὲ μὴ ὑπάρχει, παντὶ ὑπάρχειν, ἐκ ψευδῶν ἀμφοῖν ἀληθὲς ἔσται τὸ συμ↵ πέρασμα. ὁμοίως δὲ δειχθήσεται καὶ ἐὰν ἐπί τι ψευδὴς ἑκατέρα ληφθῆι.	Similiter autem et privativum: insit enim C nulli, nec A, nec B, A autem B omni, ut si eisdem terminis sumptis medium ponatur homo, lapidi enim nec animal, nec homo nulli inest, homini autem omni animal; quare si cui quidem omni inest, sumamus nulli inesse, cui vero non inest, omni inesse, ex falsis utrisque vera erit conclusio. Similiter autem ostendetur et si in aliquo utraque falsa sumatur.	Similarly with the negative. For it is possible that neither A nor B should belong to any C, although A belongs to all B, e.g. if the same terms are taken and man is put as middle: for neither animal nor man belongs to any stone, but animal belongs to every man. Consequently if one term is taken to belong to none of that to which it does belong, and the other term is taken to belong to all of that to which it does not belong, though both the premisses are false the conclusion will be true. (2) A similar proof may be given if each premiss is partially false.
Ἐὰν δ᾽ ἡ ἑτέρα τεθῆι ψευδής, τῆς μὲν πρώτης ὅλης ψευδοῦς οὔσης, οἷον τῆς Α Β, οὐκ ἔσται τὸ συμπέρασμα ἀληθές, τῆς δὲ Β Γ ἔσται. λέγω δ᾽ ὅλην ψευδῆ τὴν ἐναντίαν, οἷον εἰ μηδενὶ ὑπάρχον παντὶ εἴληπται ἢ εἰ παντὶ μηδενὶ ὑπάρχειν. ἔστω γὰρ τὸ Α τῶι Β μηδενὶ ὑπάρχον, τὸ δὲ Β τῶι Γ παντί. ἂν δὴ τὴν μὲν Β Γ πρότασιν λάβω ἀληθῆ, τὴν δὲ τὸ Α Β ψευδῆ ὅλην, καὶ παντὶ ὑπάρχειν τῶι Β τὸ Α, ἀδύνατον τὸ συμπέρασμα ἀληθὲς εἶναι· οὐδενὶ γὰρ ὑπῆρχε τῶν Γ, εἴπερ ὧι τὸ Β, μηδενὶ τὸ Α, τὸ δὲ Β παντὶ τῶι Γ.	(0687A) Si autem altera ponatur falsa, prima quidem tota falsa existente, ut A B, non erit conclusio vera, B C autem erit. Dico autem totam falsam quod contrariam verae, ut si quod nulli inest, omni sumptum est; aut si quod omni, nulli inesse. Insit enim A B nulli, B autem omni C; si ergo B C quidem propositionem sumamus veram, A B autem falsam totam, et omni B inesse A, impossibile est A C conclusionem veram esse, nulli enim inerat A earum quae sunt C, siquidem cui B nulli, B autem omni C.	(3) But if one only of the premisses is false, when the first premiss is wholly false, e.g. AB, the conclusion will not be true, but if the premiss BC is wholly false, a true conclusion will be possible. I mean by ‘wholly false’ the contrary of the truth, e.g. if what belongs to none is assumed to belong to all, or if what belongs to all is assumed to belong to none. Let A belong to no B, and B to all C. If then the premiss BC which I take is true, and the premiss AB is wholly false, viz. that A belongs to all B, it is impossible that the conclusion should be true: for A belonged to none of the Cs, since A belonged to nothing to which B belonged, and B belonged to all C.
ὁμοίως δ᾽ οὐδ᾽ εἰ τὸ Α τῶι Β παντὶ ὑπάρχει καὶ τὸ Β τῶι Γ, ἐλήφθη δ᾽ ἡ μὲν τὸ Β Γ ἀληθὴς πρότασις, ἡ δὲ τὸ Α Β ψευδὴς ὅλη, καὶ μηδενὶ ὧι τὸ Β, τὸ Α – τὸ συμπέρασμα ψεῦδος ἔσται· παντὶ γὰρ ὑπάρξει τῶι Γ τὸ Α, εἴπερ ὧι τὸ Β, παντὶ τὸ Α, τὸ δὲ Β παντὶ τῶι Γ. φανερὸν οὖν ὅτι τῆς πρώτης ὅλης λαμβανομένης ψευδοῦς, ἐάν τε καταφατικῆς ἐάν τε στερητικῆς, τῆς δ᾽ ἑτέρας ἀληθοῦς, οὐ γίνεται ἀληθὲς τὸ συμπέρασμα.	Similiter autem nec si A omni B inest, et B omni C, sumpta sit autem B C quidem vera propositio, A B autem falsa tota, et nulli, cui B inest A, conclusio falsa erit, omni enim C inest A, siquidem cui B omni C et A, B autem omni C. (0687B) Manifestum ergo quoniam prima tota sumpta falsa, sive affirmativa, sive privativa, altera autem vera, non fit vera conclusio.	Similarly there cannot be a true conclusion if A belongs to all B, and B to all C, but while the true premiss BC is assumed, the wholly false premiss AB is also assumed, viz. that A belongs to nothing to which B belongs: here the conclusion must be false. For A will belong to all C, since A belongs to everything to which B belongs, and B to all C. It is clear then that when the first premiss is wholly false, whether affirmative or negative, and the other premiss is true, the conclusion cannot be true.
Μὴ ὅλης δὲ λαμβανομένης ψευδοῦς ἔσται. εἰ γὰρ τὸ Α τῶι μὲν Γ παντὶ ὑπάρχει τῶι δὲ Β τινί, τὸ δὲ Β παντὶ τῶι Γ, οἷον ζῶιον κύκνωι μὲν παντὶ λευκῶι δὲ τινί, τὸ δὲ λευκὸν παντὶ κύκνωι, ἐὰν ληφθῆι τὸ Α παντὶ τῶι Β καὶ τὸ Β παντὶ τῶι Γ, τὸ Α παντὶ τῶι Γ ὑπάρξει ἀληθῶς· πᾶς γὰρ κύκνος ζῶιον. ὁμοίως δὲ καὶ εἰ στερητικὸν εἴη τὸ Α Β· ἐγχωρεῖ γὰρ τὸ Α τῶι μὲν Β τινὶ ὑπάρχειν τῶι δὲ Γ μηδενί, τὸ δὲ Β παντὶ τῶι Γ, οἷον ζῶιον τινὶ λευκῶι χίονι δ᾽ οὐδεμιᾶι, λευκὸν δὲ πάσηι χιόνι. εἰ οὖν ληφθείη τὸ μὲν Α μηδενὶ τῶι Β, τὸ δὲ Β παντὶ τῶι Γ, τὸ Α οὐδενὶ τῶι Γ ὑπάρξει.	Non tota autem sumpta falsa, erit: nam si A C quidem omni inest, B autem alicui, B autem omni C, ut animal, cygno quidem omni, albo autem alicui, album autem omni cygno, si sumatur A omni B, et B omni C, A omni C inerit vere, omnis enim cygnus animal. Similiter autem et si privativa sit A B; possibile est enim A B quidem alicui inesse, C vero nulli, B autem omni C, ut animal alicui albo, nivi vero nulli, album vero omni nivi; si ergo sumatur A quidem nulli B, B autem omni C, A nulli C inerit.	(4) But if the premiss is not wholly false, a true conclusion is possible. For if A belongs to all C and to some B, and if B belongs to all C, e.g. animal to every swan and to some white thing, and white to every swan, then if we take as premisses that A belongs to all B, and B to all C, A will belong to all C truly: for every swan is an animal. Similarly if the statement AB is negative. For it is possible that A should belong to some B and to no C, and that B should belong to all C, e.g. animal to some white thing, but to no snow, and white to all snow. If then one should assume that A belongs to no B, and B to all C, then will belong to no C.
Ἐὰν δ᾽ ἡ μὲν Α Β πρότασις ὅλη ληφθῆι ἀληθής, ἡ δὲ Β Γ ὅλη ψευδής, ἔσται συλλογισμὸς ἀληθής· οὐδὲν γὰρ κωλύει τὸ Α τῶι Β καὶ τῶι Γ παντὶ ὑπάρ- χειν, τὸ μέντοι Β μηδενὶ τῶι Γ, οἷον ὅσα τοῦ αὐτοῦ γένους εἴδη μὴ ὑπ᾽ ἄλληλα· τὸ γὰρ ζῶιον καὶ ἵππωι καὶ ἀνθρώπωι ὑπάρχει, ἵππος δ᾽ οὐδενὶ ἀνθρώπωι. ἐὰν οὖν ληφθῆι τὸ Α παντὶ τῶι Β καὶ τὸ Β παντὶ τῶι Γ, ἀληθὲς ἔσται τὸ συμπέρασμα, ψευδοῦς ὅλης οὔσης τῆς Β Γ προτάσεως. ὁμοίως δὲ καὶ στερητικῆς οὔσης τῆς Α Β προτάσεως. ἐνδέχεται γὰρ τὸ Α μήτε τῶι Β μήτε τῶι Γ μηδενὶ ὑπάρχειν, μηδὲ τὸ Β μηδενὶ τῶι Γ, οἷον τοῖς ἐξ ἄλλου γένους εἴδεσι τὸ γένος· τὸ γὰρ ζῶιον οὔτε μουσικῆι οὔτ᾽ ἰατρικῆι ὑπάρχει, οὐδ᾽ ↵ ἡ μουσικὴ ἰατρικῆι. ληφθέντος οὖν τοῦ μὲν Α μηδενὶ τῶι Β, τοῦ δὲ Β παντὶ τῶι Γ, ἀληθὲς ἔσται τὸ συμπέρασμα.	(0687C) Si autem A B quidem propositio tota sumatur vera, B C autem tota falsa, erit syllogismus verus, nihil enim prohibet A, et B et C omni inesse, B autem nulli C, ut quaecunque eiusdem generis sunt species non subalternae, nam animal et homini et equo inest, equus autem nulli homini inest; si ergo sumatur A omni B, et B omni C, conclusio vera erit, tota falsa B C propositione. Similiter autem cum universalis privativa est A B propositio, contingit enim A neque B, neque C nulli inesse, et B nulli C, ut ex alio genere speciebus diversum genus, nam animal nec musicae, nec medicinae inest, neque musica medicinae. Sumpta ergo A quidem nulli B, B autem omni C, vera erit conclusio. Et si non tota falsa sit B C, sed in aliquo, etiam sic erit conclusio vera.	(5) But if the premiss AB, which is assumed, is wholly true, and the premiss BC is wholly false, a true syllogism will be possible: for nothing prevents A belonging to all B and to all C, though B belongs to no C, e.g. these being species of the same genus which are not subordinate one to the other: for animal belongs both to horse and to man, but horse to no man. If then it is assumed that A belongs to all B and B to all C, the conclusion will be true, although the premiss BC is wholly false. Similarly if the premiss AB is negative. For it is possible that A should belong neither to any B nor to any C, and that B should not belong to any C, e.g. a genus to species of another genus: for animal belongs neither to music nor to the art of healing, nor does music belong to the art of healing. If then it is assumed that A belongs to no B, and B to all C, the conclusion will be true.
καὶ εἰ μὴ ὅλη ψευδὴς ἡ Β Γ ἀλλ᾽ ἐπί τι, καὶ οὕτως ἔσται τὸ συμπέρασμα ἀληθές. οὐδὲν γὰρ κωλύει τὸ Α καὶ τῶι Β καὶ τῶι Γ ὅλωι ὑπάρχειν, τὸ μέντοι Β τινὶ τῶι Γ, οἷον τὸ γένος τῶι εἴδει καὶ τῆι διαφορᾶι· τὸ γὰρ ζῶιον παντὶ ἀνθρώπωι καὶ παντὶ πεζῶι, ὁ δ᾽ ἄνθρωπος τινὶ πεζῶι καὶ οὐ παντί. εἰ οὖν τὸ Α παντὶ τῶι Β καὶ τὸ Β παντὶ τῶι Γ ληφθείη, τὸ Α παντὶ τῶι Γ ὑπάρξει· ὅπερ ἦν ἀληθές. ὁμοίως δὲ καὶ στερητικῆς οὔσης τῆς Α Β προτάσεως. ἐνδέχεται γὰρ τὸ Α μήτε τῶι Β μήτε τῶι Γ μηδενὶ ὑπάρχειν, τὸ μέντοι Β τινὶ τῶι Γ, οἷον τὸ γένος τῶι ἐξ ἄλλου γένους εἴδει καὶ διαφορᾶι· τὸ γὰρ ζῶιον οὔτε φρονήσει οὐδεμιᾶι ὑπάρχει οὔτε θεωρητικῆι, ἡ δὲ φρόνησις τινὶ θεωρητικῆι. εἰ οὖν ληφθείη τὸ μὲν Α μηδενὶ τῶι Β, τὸ δὲ Β παντὶ τῶι Γ, οὐδενὶ τῶι Γ τὸ Α ὑπάρξει· τοῦτο δ᾽ ἦν ἀληθές.	(0687D) Nihil enim prohibet A, et B et C toti inesse, B autem alicui C, ut genus speciei et differentiae, nam animal homini omni et omni gressibili, homo autem alicui gressibili, et non omni; si ergo A omni B, et B omni C sumatur, A omni C inerit, quod quidem erat verum. Similiter autem cum privativa est A, B propositio, contingit enim A nec B, nec C nulli inesse, B vero alicui C, at genus ex alio genere speciei et differentiae, nam animal nec sapientiae nulli inest, nec contemplationi, sapientia vero alicui contemplationi; si ergo sumatur A nulli B, B autem omni C, nulli C inerit A, hoc autem erat verum.	(6) And if the premiss BC is not wholly false but in part only, even so the conclusion may be true. For nothing prevents A belonging to the whole of B and of C, while B belongs to some C, e.g. a genus to its species and difference: for animal belongs to every man and to every footed thing, and man to some footed things though not to all. If then it is assumed that A belongs to all B, and B to all C, A will belong to all C: and this ex hypothesi is true. Similarly if the premiss AB is negative. For it is possible that A should neither belong to any B nor to any C, though B belongs to some C, e.g. a genus to the species of another genus and its difference: for animal neither belongs to any wisdom nor to any instance of ‘speculative’, but wisdom belongs to some instance of ‘speculative’. If then it should be assumed that A belongs to no B, and B to all C, will belong to no C: and this ex hypothesi is true.
Ἐπὶ δὲ τῶν ἐν μέρει συλλογισμῶν ἐνδέχεται καὶ τῆς πρώτης προτάσεως ὅλης οὔσης ψευδοῦς τῆς δ᾽ ἑτέρας ἀληθοῦς ἀληθὲς εἶναι τὸ συμπέρασμα, καὶ ἐπί τι ψευδοῦς οὔσης τῆς πρώτης τῆς δ᾽ ἑτέρας ἀληθοῦς, καὶ τῆς μὲν ἀληθοῦς τῆς δ᾽ ἐν μέρει ψευδοῦς, καὶ ἀμφοτέρων ψευδῶν. οὐδὲν γὰρ κωλύει τὸ Α τῶι μὲν Β μηδενὶ ὑπάρχειν τῶι δὲ Γ τινί, καὶ τὸ Β τῶι Γ τινί, οἷον ζῶιον οὐδεμιᾶι χιόνι λευκῶι δὲ τινὶ ὑπάρχει, καὶ ἡ χιὼν λευκῶι τινί. εἰ οὖν μέσον τεθείη ἡ χιών, πρῶτον δὲ τὸ ζῶιον, καὶ ληφθείη τὸ μὲν Α ὅλωι τῶι Β ὑπάρχειν, τὸ δὲ Β τινὶ τῶι Γ, ἡ μὲν Α Β ὅλη ψευδής, ἡ δὲ Β Γ ἀληθής, καὶ τὸ συμπέρασμα ἀληθές.	In particularibus autem syllogismis contingit, prima propositione tota falsa existente, altera autem vera, veram esse conclusionem, et A B in aliquo falsa existente, B C autem vera, et A B quidem vera, particulari autem falsa, et utrisque existentibus falsis. (0688A) Nihil enim prohibet A B quidem nulli inesse, C autem alicui, et B alicui C inesse, ut animal nulli nivi, albo autem alicui inest, et nix albo alicui. Si ergo ponatur medium nix, primum autem animal, et sumatur A quidem toti B inesse, B autem alicui C, A B tota falsa, B C autem vera, et conclusio vera.	In particular syllogisms it is possible when the first premiss is wholly false, and the other true, that the conclusion should be true; also when the first premiss is false in part, and the other true; and when the first is true, and the particular is false; and when both are false. (7) For nothing prevents A belonging to no B, but to some C, and B to some C, e.g. animal belongs to no snow, but to some white thing, and snow to some white thing. If then snow is taken as middle, and animal as first term, and it is assumed that A belongs to the whole of B, and B to some C, then the premiss BC is wholly false, the premiss BC true, and the conclusion true.
ὁμοίως δὲ καὶ στερητικῆς οὔσης τῆς Α Β προτάσεως· ἐγχωρεῖ γὰρ τὸ Α τῶι μὲν Β ὅλωι ὑπάρχειν τῶι δὲ Γ τινὶ μὴ ὑπάρχειν, τὸ μέντοι Β τινὶ τῶι Γ ὑπάρχειν, οἷον τὸ ζῶιον ἀνθρώπωι μὲν παντὶ ὑπάρχει, λευκῶι δὲ τινὶ οὐχ ἕπεται, ὁ δ᾽ ἄνθρωπος τινὶ λευκῶι ὑπάρχει, ὥστ᾽ εἰ μέσου τεθέντος τοῦ ἀνθρώπου ληφθείη τὸ Α μηδενὶ τῶι Β ὑπάρχειν, τὸ δὲ Β τινὶ τῶι Γ ὑπάρχειν, ἀληθὲς ἔσται τὸ συμπέρασμα ψευδοῦς οὔσης ὅλης τῆς Α Β προτάσεως. καὶ εἰ ἐπί τι ψευδὴς ἡ Α Β πρότασις, ἔσται τὸ συμπέρασμα ἀληθές. οὐδὲν γὰρ κωλύει τὸ Α καὶ τῶι Β καὶ τῶι Γ τινὶ ὑπάρχειν, καὶ τὸ Β τῶι Γ τινὶ ὑπάρχειν, οἷον τὸ ζῶιον τινὶ καλῶι καὶ τινὶ μεγάλωι, καὶ τὸ καλὸν τινὶ μεγάλωι ὑπάρχειν. ἐὰν οὖν ληφθῆι τὸ Α παντὶ τῶι Β καὶ τὸ Β τινὶ τῶι Γ, ↵ ἡ μὲν Α Β πρότασις ἐπί τι ψευδὴς ἔσται, ἡ δὲ Β Γ ἀληθής, καὶ τὸ συμπέρασμα ἀληθές.	Similiter autem et cum privativa est A B propositio, possibile est enim A B quidem toti inesse, C autem alicui non inesse, B vero alicui C inesse, ut animal homini quidem omni inest, album autem aliquod non sequitur, homo vero alicui albo inest; quare si medio posito homine sumatur A nulli B inesse, et B alicui C, vera fit conclusio, cum sit tota falsa A B propositio. Et si in aliquo sit falsa A B propositio, B C vera existente, erit conclusio vera. (0688B) Nihil enim prohibet A, et B, et C, alicui inesse, B autem alicui C, ut animal alicui pulchro, et alicui magno, et pulchrum alicui magno inest; si ergo sumatur A omni B, et B alicui C, et A B, quidem propositio in aliquo falsa erit, B C autem vera, et conclusio vera. Similiter autem et cum privativa est A B propositio, nam iidem erunt termini, et similiter positi ad demonstrationem.	Similarly if the premiss AB is negative: for it is possible that A should belong to the whole of B, but not to some C, although B belongs to some C, e.g. animal belongs to every man, but does not follow some white, but man belongs to some white; consequently if man be taken as middle term and it is assumed that A belongs to no B but B belongs to some C, the conclusion will be true although the premiss AB is wholly false. (If the premiss AB is false in part, the conclusion may be true. For nothing prevents A belonging both to B and to some C, and B belonging to some C, e.g. animal to something beautiful and to something great, and beautiful belonging to something great. If then A is assumed to belong to all B, and B to some C, the a premiss AB will be partially false, the premiss BC will be true, and the conclusion true. Similarly if the premiss AB is negative. For the same terms will serve, and in the same positions, to prove the point.
ὁμοίως δὲ καὶ στερητικῆς οὔσης τῆς Α Β προτάσεως· οἱ γὰρ αὐτοὶ ὅροι ἔσονται καὶ ὡσαύτως κείμενοι πρὸς τὴν ἀπόδειξιν. Πάλιν εἰ ἡ μὲν Α Β ἀληθὴς ἡ δὲ Β Γ ψευδής, ἀληθὲς ἔσται τὸ συμπέρασμα. οὐδὲν γὰρ κωλύει τὸ Α τῶι μὲν Β ὅλωι ὑπάρχειν τῶι δὲ Γ τινί, καὶ τὸ Β τῶι Γ μηδενὶ ὑπάρχειν, οἷον ζῶιον κύκνωι μὲν παντὶ μέλανι δὲ τινί, κύκνος δὲ οὐδενὶ μέλανι. ὥστ᾽ εἰ ληφθείη παντὶ τῶι Β τὸ Α καὶ τὸ Β τινὶ τῶι Γ, ἀληθὲς ἔσται τὸ συμπέρασμα ψευδοῦς ὄντος τοῦ Β Γ.	Rursum si A B quidem vera, B C autem falsa, vera erit conclusio. Nihil enim prohibet A quidem toti inesse B, C autem alicui, et B nulli C inesse: ut animal cygno quidem omni, nigro autem alicui, cygnus vero nulli nigro; quare si sumatur A omni B, et B alicui C, vera erit conclusio, cum sit falsa B C.	(9) Again if the premiss AB is true, and the premiss BC is false, the conclusion may be true. For nothing prevents A belonging to the whole of B and to some C, while B belongs to no C, e.g. animal to every swan and to some black things, though swan belongs to no black thing. Consequently if it should be assumed that A belongs to all B, and B to some C, the conclusion will be true, although the statement BC is false.
ὁμοίως δὲ καὶ στερητικῆς λαμβανομένης τῆς Α Β προτάσεως. ἐγχωρεῖ γὰρ τὸ Α τῶι μὲν Β μηδενὶ τῶι δὲ Γ τινὶ μὴ ὑπάρχειν, τὸ μέντοι Β μηδενὶ τῶι Γ, οἷον τὸ γένος τῶι ἐξ ἄλλου γένους εἴδει καὶ τῶι συμβεβηκότι τοῖς αὑτοῦ εἴδεσι· τὸ γὰρ ζῶιον ἀριθμῶι μὲν οὐδενὶ ὑπάρχει λευκῶι δὲ τινί, ὁ δ᾽ ἀριθμὸς οὐδενὶ λευκῶι· ἐὰν οὖν μέσον τεθῆι ὁ ἀριθμός, καὶ ληφθῆι τὸ μὲν Α μηδενὶ τῶι Β, τὸ δὲ Β τινὶ τῶι Γ, τὸ Α τινὶ τῶι Γ οὐχ ὑπάρξει, ὅπερ ἦν ἀληθές· καὶ ἡ μὲν Α Β πρότασις ἀληθής, ἡ δὲ Β Γ ψευδής.	(0688C) Similiter autem et privativa sumpta A B propositione, possibile enim A B quidem nulli, C autem alicui non inesse, et B nulli C, ut genus ex alio genere speciei et accidenti eius speciebus, nam animal quidem numero nulli inest, albo vero non alicui, numerus autem nulli albo; si ergo medium ponatur numerus, et sumatur A quidem nulli B, B autem alicui C, A alicui C non inerit, quod fuit verum, cum A B quidem sit propositio vera, B C autem falsa.	Similarly if the premiss AB is negative. For it is possible that A should belong to no B, and not to some C, while B belongs to no C, e.g. a genus to the species of another genus and to the accident of its own species: for animal belongs to no number and not to some white things, and number belongs to nothing white. If then number is taken as middle, and it is assumed that A belongs to no B, and B to some C, then A will not belong to some C, which ex hypothesi is true. And the premiss AB is true, the premiss BC false.
καὶ εἰ ἐπί τι ψευδὴς ἡ Α Β, ψευδὴς δὲ καὶ ἡ Β Γ, ἔσται τὸ συμπέρασμα ἀληθές. οὐδὲν γὰρ κωλύει τὸ Α τῶι Β τινὶ καὶ τῶι Γ τινὶ ὑπάρχειν ἑκα- τέρωι, τὸ δὲ Β μηδενὶ τῶι Γ, οἷον εἰ ἐναντίον τὸ Β τῶι Γ, ἄμφω δὲ συμβεβηκότα τῶι αὐτῶι γένει· τὸ γὰρ ζῶιον τινὶ λευκῶι καὶ τινὶ μέλανι ὑπάρχει, λευκὸν δ᾽ οὐδενὶ μέλανι. ἐὰν οὖν ληφθῆι τὸ Α παντὶ τῶι Β καὶ τὸ Β τινὶ τῶι Γ, ἀληθὲς ἔσται τὸ συμπέρασμα. καὶ στερητικῆς δὲ λαμβανομένης τῆς Α Β ὡσαύτως· οἱ γὰρ αὐτοὶ ὅροι καὶ ὡσαύτως τεθήσονται πρὸς τὴν ἀπόδειξιν.	Et si in aliquo sit falsa A B, falsa autem et B C, erit conclusio vera. Nihil enim prohibet A alicui B et alicui C inesse utrique, B autem nulli C, ut si B sit contrarium ipsi C, et ambo accidentia eidem generi, nam animal alicui albo et alicui nigro inest, album autem nulli nigro inest; si ergo sumatur A omni B, et B alicui C, vera erit conclusio. Et privativa quidem sumpta A B, similiter. Nam iidem termini, et similiter ponentur ad demonstrationem.	(10) Also if the premiss AB is partially false, and the premiss BC is false too, the conclusion may be true. For nothing prevents A belonging to some B and to some C, though B belongs to no C, e.g. if B is the contrary of C, and both are accidents of the same genus: for animal belongs to some white things and to some black things, but white belongs to no black thing. If then it is assumed that A belongs to all B, and B to some C, the conclusion will be true. Similarly if the premiss AB is negative: for the same terms arranged in the same way will serve for the proof.
καὶ ἀμφοτέρων δὲ ψευδῶν οὐσῶν ἔσται τὸ συμπέρασμα ἀληθές· ἐγχωρεῖ γὰρ τὸ Α τῶι μὲν Β μηδενὶ τῶι δὲ Γ τινὶ ὑπάρχειν, τὸ μέντοι Β μηδενὶ τῶι Γ, οἷον τὸ γένος τῶι ἐξ ἄλλου γένους εἴδει καὶ τῶι συμβεβηκότι τοῖς εἴδεσι τοῖς αὑτοῦ· ζῶιον γὰρ ἀριθμῶι μὲν οὐδενὶ λευκῶι δὲ τινὶ ὑπάρχει, καὶ ὁ ἀριθμὸς οὐδενὶ λευκῶι. ἐὰν οὖν ληφθῆι τὸ Α παντὶ τῶι Β καὶ τὸ Β τινὶ τῶι Γ, τὸ μὲν συμπέρασμα ἀληθές, αἱ δὲ προτάσεις ἄμφω ψευδεῖς.	(0688D) Et ex utrisque falsis erit conclusio vera. Possibile est enim A B quidem nulli, C autem alicui inesse, B vero nulli C. Ut genus ex alio genere speciei, et accidenti speciebus eius, animal enim numero quidem nulli, albo vero alicui inest, et numerus nulli albo. Si ergo sumatur A omni B, et B alicui C, conclusio quidem vera, propositiones vero ambae falsae.	(11) Also though both premisses are false the conclusion may be true. For it is possible that A may belong to no B and to some C, while B belongs to no C, e.g. a genus in relation to the species of another genus, and to the accident of its own species: for animal belongs to no number, but to some white things, and number to nothing white. If then it is assumed that A belongs to all B and B to some C, the conclusion will be true, though both premisses are false.
ὁμοίως δὲ καὶ στερητικῆς οὔσης τῆς Α Β. οὐδὲν γὰρ κωλύει τὸ Α τῶι μὲν Β ὅλωι ὑπάρχειν τῶι δὲ Γ τινὶ μὴ ὑπάρχειν, μηδὲ τὸ Β μηδενὶ τῶι Γ, οἷον ζῶιον κύκνωι μὲν παντὶ μέλανι δὲ τινὶ οὐχ ὑπάρχει, κύκνος δ᾽ οὐδενὶ μέλανι. ὥστ᾽ εἰ ληφθείη τὸ Α μηδενὶ τῶι Β, τὸ δὲ Β τινὶ τῶι Γ, τὸ Α τινὶ ↵ τῶι Γ οὐχ ὑπάρξει. τὸ μὲν οὖν συμπέρασμα ἀληθές, αἱ δὲ προτάσεις ψευδεῖς.	Similiter autem et cum privativa est A B. Nihil enim prohibet A B quidem toti inesse, C autem alicui non inesse, et neque B nulli C, ut animal cygno quidem omni, nigro autem alicui non inest, cygnus vero nulli nigro: quare si sumatur A nulli B, B autem alicui C A non inerit; ergo conclusio quidem vera, propositiones autem falsae.	Similarly also if the premiss AB is negative. For nothing prevents A belonging to the whole of B, and not to some C, while B belongs to no C, e.g. animal belongs to every swan, and not to some black things, and swan belongs to nothing black. Consequently if it is assumed that A belongs to no B, and B to some C, then A does not belong to some C. The conclusion then is true, but the premisses are false.

Chapter 3

Greek	Latin	English
	(PL 64 0688D) CAPUT III. Quod colligatur verum ex falsis in secunda figura.	3
55b3 Ἐν δὲ τῶι μέσωι σχήματι πάντως ἐγχωρεῖ διὰ ψευδῶν ἀληθὲς συλλογίσασθαι, καὶ ἀμφοτέρων τῶν προτάσεων ὅλων ψευδῶν λαμβανομένων καὶ ἐπί τι ἑκατέρας, καὶ τῆς μὲν ἀληθοῦς τῆς δὲ ψευδοῦς οὔσης [ὅλησ] ὁποτερασοῦν ψευδοῦς τιθεμένης, [καὶ εἰ ἀμφότεραι ἐπί τι ψευδεῖς, καὶ εἰ ἡ μὲν ἁπλῶς ἀληθὴς ἡ δ᾽ ἐπί τι ψευδής, καὶ εἰ ἡ μὲν ὅλη ψευδὴς ἡ δ᾽ ἐπί τι ἀληθής,] καὶ ἐν τοῖς καθόλου καὶ ἐπὶ τῶν ἐν μέρει συλλογισμῶν. εἰ γὰρ τὸ Α τῶι μὲν Β μηδενὶ ὑπάρχει τῶι δὲ Γ παντί, οἷον ζῶιον λίθωι μὲν οὐδενὶ ἵππωι δὲ παντί, ἐὰν ἐναντίως τεθῶσιν αἱ προτάσεις καὶ ληφθῆι τὸ Α τῶι μὲν Β παντὶ τῶι δὲ Γ μηδενί, ἐκ ψευδῶν ὅλων τῶν προτάσεων ἀληθὲς ἔσται τὸ συμπέρασμα. ὁμοίως δὲ καὶ εἰ τῶι μὲν Β παντὶ τῶι δὲ Γ μηδενὶ ὑπάρχει τὸ Α· ὁ γὰρ αὐτὸς ἔσται συλλογισμός.	(0689A) In media autem figura omnino contingit per falsa verum syllogizare, et utrisque propositionibus totis falsis sumptis, et hac quidem vera, illa tota falsa, utralibet falsa posita, et si utraeque in aliquo falsae, et si haec quidem simpliciter vera, illa autem in aliquo falsa, et in universalibus, et in particularibus syllogismis. Si enim A B quidem nulli inest, C autem omni, ut lapidi animal quidem nulli, homini autem omni, si contrariae ponantur propositiones, et si sumatur A B quidem omni, C vero nulli, ex falsis totis propositionibus erit vera conclusio. Similiter autem et si A inest B quidem omni, C vero nulli, nam idem erit syllogismus.	In the middle figure it is possible in every way to reach a true conclusion through false premisses, whether the syllogisms are universal or particular, viz. when both premisses are wholly false; when each is partially false; when one is true, the other wholly false (it does not matter which of the two premisses is false); if both premisses are partially false; if one is quite true, the other partially false; if one is wholly false, the other partially true. For (1) if A belongs to no B and to all C, e.g. animal to no stone and to every horse, then if the premisses are stated contrariwise and it is assumed that A belongs to all B and to no C, though the premisses are wholly false they will yield a true conclusion. Similarly if A belongs to all B and to no C: for we shall have the same syllogism.
Πάλιν εἰ ἡ μὲν ἑτέρα ὅλη ψευδὴς ἡ δ᾽ ἑτέρα ὅλη ἀληθής· οὐδὲν γὰρ κωλύει τὸ Α καὶ τῶι Β καὶ τῶι Γ παντὶ ὑπάρχειν, τὸ μέντοι Β μηδενὶ τῶι Γ, οἷον τὸ γένος τοῖς μὴ ὑπ᾽ ἄλληλα εἴδεσιν. τὸ γὰρ ζῶιον καὶ ἵππωι παντὶ καὶ ἀνθρώπωι, καὶ οὐδεὶς ἄνθρωπος ἵππος. ἐὰν οὖν ληφθῆι τῶι μὲν παντὶ τῶι δὲ μηδενὶ ὑπάρχειν, ἡ μὲν ὅλη ψευδὴς ἔσται ἡ δ᾽ ὅλη ἀληθής, καὶ τὸ συμπέρασμα ἀληθὲς πρὸς ὁποτερωιοῦν τεθέντος τοῦ στερητικοῦ.	(0689B) Rursum si altera quidem tota falsa, altera autem tota vera. Nihil enim prohibet A et B et C omni inesse, B autem nulli C, ut genus non subalternis speciebus. Nam animal equo omni, et homini inest, et nullus homo equus; si ergo sumatur animal huic quidem omni, illi vero nulli inesse, haec quidem erit falsa, illa vero tota vera, et conclusio vera, ad quodlibet posito privativo.	(2) Again if one premiss is wholly false, the other wholly true: for nothing prevents A belonging to all B and to all C, though B belongs to no C, e.g. a genus to its co-ordinate species. For animal belongs to every horse and man, and no man is a horse. If then it is assumed that animal belongs to all of the one, and none of the other, the one premiss will be wholly false, the other wholly true, and the conclusion will be true whichever term the negative statement concerns.
καὶ εἰ ἡ ἑτέρα ἐπί τι ψευδής, ἡ δ᾽ ἑτέρα ὅλη ἀληθής. ἐγχωρεῖ γὰρ τὸ Α τῶι μὲν Β τινὶ ὑπάρχειν τῶι δὲ Γ παντί, τὸ μέντοι Β μηδενὶ τῶι Γ, οἷον ζῶιον λευκῶι μὲν τινὶ κόρακι δὲ παντί, καὶ τὸ λευκὸν οὐδενὶ κόρακι. ἐὰν οὖν ληφθῆι τὸ Α τῶι μὲν Β μηδενὶ τῶι δὲ Γ ὅλωι ὑπάρχειν, ἡ μὲν Α Β πρότασις ἐπί τι ψευδής, ἡ δ᾽ Α Γ ὅλη ἀληθής, καὶ τὸ συμπέρασμα ἀληθές. καὶ μετατιθεμένου δὲ τοῦ στερητικοῦ ὡσαύτως· διὰ γὰρ τῶν αὐτῶν ὅρων ἡ ἀπόδειξις. καὶ εἰ ἡ καταφατικὴ πρότασις ἐπί τι ψευδής, ἡ δὲ στερητικὴ ὅλη ἀληθής. οὐδὲν γὰρ κωλύει τὸ Α τῶι μὲν Β τινὶ ὑπάρχειν τῶι δὲ Γ ὅλωι μὴ ὑπάρχειν, καὶ τὸ Β μηδενὶ τῶι Γ, οἷον τὸ ζῶιον λευκῶι μὲν τινὶ πίττηι δ᾽ οὐδεμιᾶι, καὶ τὸ λευκὸν οὐδεμιᾶι πίττηι. ὥστ᾽ ἐὰν ληφθῆι τὸ Α ὅλωι τῶι Β ὑπάρχειν τῶι δὲ Γ μηδενί, ἡ μὲν Α Β ἐπί τι ψευδής, ἡ δ᾽ Α Γ ὅλη ἀληθής, καὶ τὸ συμπέρασμα ἀληθές.	Et si altera in aliquo falsa, altera autem tota vera, possibile est enim A B quidem alicui inesse, C autem omni, et B nulli C, ut animal albo quidem alicui, corvo autem omni, album vero nulli corvo. Si ergo sumatur A B quidem nulli, C autem toti inesse, A B quidem propositio in aliquo falsa est, A C autem tota vera, et conclusio vera, et transposita quidem privativa, similiter. (0689C) Nam per eosdem terminos demonstratio. Et si affirmativa quidem propositio in aliquo falsa, privativa autem tota vera, nihil enim prohibet A B quidem alicui inesse, C autem toti non inesse, et B nulli C, ut animal albo quidem alicui, pici autem nulli, album vero nulli pici: quare si sumatur A to i B inesse, C autem nulli, A B quidem in aliquo falsa, A C autem tota vera, et conclusio vera.	(3) Also if one premiss is partially false, the other wholly true. For it is possible that A should belong to some B and to all C, though B belongs to no C, e.g. animal to some white things and to every raven, though white belongs to no raven. If then it is assumed that A belongs to no B, but to the whole of C, the premiss AB is partially false, the premiss AC wholly true, and the conclusion true. Similarly if the negative statement is transposed: the proof can be made by means of the same terms. Also if the affirmative premiss is partially false, the negative wholly true, a true conclusion is possible. For nothing prevents A belonging to some B, but not to C as a whole, while B belongs to no C, e.g. animal belongs to some white things, but to no pitch, and white belongs to no pitch. Consequently if it is assumed that A belongs to the whole of B, but to no C, the premiss AB is partially false, the premiss AC is wholly true, and the conclusion is true.
καὶ εἰ ἀμφότεραι αἱ προτάσεις ἐπί τι ψευδεῖς, ἔσται τὸ συμπέρασμα ἀληθές. ἐγχωρεῖ γὰρ τὸ Α καὶ τῶι Β καὶ τῶι Γ τινὶ ὑπάρχειν, τὸ δὲ Β μηδενὶ τῶι Γ, οἷον ζῶιον καὶ ↵ λευκῶι τινὶ καὶ μέλανί τινι, τὸ δὲ λευκὸν οὐδενὶ μέλανι. ἐὰν οὖν ληφθῆι τὸ Α τῶι μὲν Β παντὶ τῶι δὲ Γ μηδενί, ἄμφω μὲν αἱ προτάσεις ἐπί τι ψευδεῖς, τὸ δὲ συμπέρασμα ἀληθές. ὁμοίως δὲ καὶ μετατεθείσης τῆς στερητικῆς διὰ τῶν αὐτῶν ὅρων.	Et si utraeque propositiones in aliquo falsae, erit conclusio vera, possibile est enim A, et B, et C alicui inesse, B autem nulli C, ut animal, et albo alicui, et nigro alicui, album vero nulli nigro. Si ergo sumator A B quidem omni, C autem nulli, ambae quidem propositiones in aliquo falsae, conclusio autem vera; similiter autem transposita privativa per terminos.	(4) And if both the premisses are partially false, the conclusion may be true. For it is possible that A should belong to some B and to some C, and B to no C, e.g. animal to some white things and to some black things, though white belongs to nothing black. If then it is assumed that A belongs to all B and to no C, both premisses are partially false, but the conclusion is true. Similarly, if the negative premiss is transposed, the proof can be made by means of the same terms.
Φανερὸν δὲ καὶ ἐπὶ τῶν ἐν μέρει συλλογισμῶν· οὐδὲν γὰρ κωλύει τὸ Α τῶι μὲν Β παντὶ τῶι δὲ Γ τινὶ ὑπάρχειν, καὶ τὸ Β τῶι Γ τινὶ μὴ ὑπάρχειν, οἷον ζῶιον παντὶ ἀνθρώπωι λευκῶι δὲ τινί, ἄνθρωπος δὲ τινὶ λευκῶι οὐχ ὑπάρξει. ἐὰν οὖν τεθῆι τὸ Α τῶι μὲν Β μηδενὶ ὑπάρχειν τῶι δὲ Γ τινὶ ὑπάρχειν, ἡ μὲν καθόλου πρότασις ὅλη ψευδής, ἡ δ᾽ ἐν μέρει ἀληθής, καὶ τὸ συμπέρασμα ἀληθές. ὡσαύτως δὲ καὶ καταφατικῆς λαμβανομένης τῆς Α Β· ἐγχωρεῖ γὰρ τὸ Α τῶι μὲν Β μηδενὶ τῶι δὲ Γ τινὶ μὴ ὑπάρχειν, καὶ τὸ Β τῶι Γ τινὶ μὴ ὑπάρχειν, οἷον τὸ ζῶιον οὐδενὶ ἀψύχωι, λευκῶι δὲ τινί οὐχ ὑπάρχει, καὶ τὸ ἄψυχον οὐχ ὑπάρξει τινὶ λευκῶι.	(0689D) Manifestum autem et in particularibus syllogismis, nihil enim prohibet A B quidem omni, C autem alicui inesse, et B alicui C non inesse, ut animal omni homini, albo autem alicui, homo vero alicui albo non inerit. Si ergo ponatur A B quidem nulli inesse, C autem alicui inesse, universalis quidem propositio tota falsa, particularis autem vera, et conclusio vera. Similiter autem et affirmativa sumpta A B, possibile est enim A B quidem nulli, C autem alicui non inesse, et B alicui C non inesse, ut animal nulli inanimato, albo autem alicui, et inanimatum non inerit alicui albo.	It is clear also that our thesis holds in particular syllogisms. For (5) nothing prevents A belonging to all B and to some C, though B does not belong to some C, e.g. animal to every man and to some white things, though man will not belong to some white things. If then it is stated that A belongs to no B and to some C, the universal premiss is wholly false, the particular premiss is true, and the conclusion is true. Similarly if the premiss AB is affirmative: for it is possible that A should belong to no B, and not to some C, though B does not belong to some C, e.g. animal belongs to nothing lifeless, and does not belong to some white things, and lifeless will not belong to some white things.
ἐὰν οὖν τεθῆι τὸ Α τῶι μὲν Β παντὶ τῶι δὲ Γ τινὶ μὴ ὑπάρχειν, ἡ μὲν Α Β πρότασις, ἡ καθόλου, ὅλη ψευδής, ἡ δὲ Α Γ ἀληθής, καὶ τὸ συμπέρασμα ἀληθές. καὶ τῆς μὲν καθόλου ἀληθοῦς τεθείσης, τῆς δ᾽ ἐν μέρει ψευδοῦς. οὐδὲν γὰρ κωλύει τὸ Α μήτε τῶι Β μήτε τῶι Γ μηδενὶ ἕπεσθαι, τὸ μέντοι Β τινὶ τῶι Γ μὴ ὑπάρχειν, οἷον ζῶιον οὐδενὶ ἀριθμῶι οὐδ᾽ ἀψύχωι, καὶ ὁ ἀριθμὸς τινὶ ἀψύχωι οὐχ ἕπεται. ἐὰν οὖν τεθῆι τὸ Α τῶι μὲν Β μηδενὶ τῶι δὲ Γ τινί, τὸ μὲν συμπέρασμα ἔσται ἀληθὲς καὶ ἡ καθόλου πρότασις, ἡ δ᾽ ἐν μέρει ψευδής.	Si ergo ponatur A B quidem omni, C vero alicui non inesse, A B quidem propositio universalis tota falsa, A C autem vera, et conclusio vera. (0690A) Et universali quidem vera posita, minori autem particulari falsa, nihil enim prohibet A nec B nec C nullum sequi, et B alicui C non inesse, ut animal nulli numero nec inanimato, et numerus aliquod inanimatum non sequitur. Si ergo ponatur A B quidem nulli, C autem alicui, et conclusio vera, et universalis propositio vera, particularis autem falsa.	If then it is stated that A belongs to all B and not to some C, the premiss AB which is universal is wholly false, the premiss AC is true, and the conclusion is true. Also a true conclusion is possible when the universal premiss is true, and the particular is false. For nothing prevents A following neither B nor C at all, while B does not belong to some C, e.g. animal belongs to no number nor to anything lifeless, and number does not follow some lifeless things. If then it is stated that A belongs to no B and to some C, the conclusion will be true, and the universal premiss true, but the particular false.
καὶ καταφατικῆς δὲ τῆς καθόλου τιθεμένης ὡσαύτως. ἐγχωρεῖ γὰρ τὸ Α καὶ τῶι Β καὶ τῶι Γ ὅλωι ὑπάρχειν, τὸ μέντοι Β τινὶ τῶι Γ μὴ ἕπεσθαι, οἷον τὸ γένος τῶι εἴδει καὶ τῆι διαφορᾶι· τὸ γὰρ ζῶιον παντὶ ἀνθρώπωι καὶ ὅλωι πεζῶι ἕπεται, ἄνθρωπος δ᾽ οὐ παντὶ πεζῶι. ὥστ᾽ ἂν ληφθῆι τὸ Α τῶι μὲν Β ὅλωι ὑπάρχειν, τῶι δὲ Γ τινὶ μὴ ὑπάρχειν, ἡ μὲν καθόλου πρότασις ἀληθής, ἡ δ᾽ ἐν μέρει ψευδής, τὸ δὲ συμπέρασμα ἀληθές.	Affirmativa autem universali similiter posita, possibile est enim A et B et C toti inesse, B autem aliquod C non sequi, ut genus speciem et differentiam. Nam animal omnem hominem et totum gressibile sequitur, homo vero non omne gressibile: quare si sumatur A B quidem toti inesse, C autem alicui non inesse, universalis quidem propositio vera, particularis falsa, conclusio autem vera.	Similarly if the premiss which is stated universally is affirmative. For it is possible that should A belong both to B and to C as wholes, though B does not follow some C, e.g. a genus in relation to its species and difference: for animal follows every man and footed things as a whole, but man does not follow every footed thing. Consequently if it is assumed that A belongs to the whole of B, but does not belong to some C, the universal premiss is true, the particular false, and the conclusion true.
Φανερὸν δὲ καὶ ὅτι ἐξ ἀμφοτέρων ψευδῶν ἔσται τὸ συμπέρασμα ἀληθές, εἴπερ ἐνδέχεται τὸ Α καὶ τῶι Β καὶ τῶι Γ ὅλωι ὑπάρχειν, τὸ μέντοι Β τινὶ τῶι Γ μὴ ἕπεσθαι. ληφθέντος γὰρ τοῦ Α τῶι μὲν Β μηδενὶ τῶι δὲ Γ τινὶ ὑπάρχειν, αἱ μὲν προτάσεις ἀμφότεραι ψευδεῖς, τὸ δὲ συμπέρασμα ἀληθές. ὁμοίως δὲ καὶ κατηγορικῆς οὔσης τῆς καθόλου προτάσεως, τῆς δ᾽ ἐν μέρει στερητικῆς. ἐγχωρεῖ γὰρ τὸ Α τῶι μὲν Β μηδενὶ τῶι δὲ Γ παντὶ ἕπεσθαι, καὶ τὸ Β τινὶ τῶι Γ μὴ ὑπάρχειν, οἷον ζῶιον ἐπιστήμηι μὲν οὐδεμιᾶι ἀνθρώπωι δὲ παντὶ ἕπεται, ἡ δ᾽ ἐπιστήμη οὐ παντὶ ἀνθρώπωι. ↵ ἐὰν οὖν ληφθῆι τὸ Α τῶι μὲν Β ὅλωι ὑπάρχειν, τῶι δὲ Γ τινὶ μὴ ἕπεσθαι, αἱ μὲν προτάσεις ψευδεῖς, τὸ δὲ συμπέρασμα ἀληθές.	(0690B) Manifestum autem quoniam et utrisque falsis erit conclusio vera, siquidem contingit A et B et C huic quidem omni, illi vero nulli inesse, B vero aliquod C non sequi, nam sumpto A B quidem nulli, C autem alicui inesse, propositiones quidem ambae falsae, conclusio autem vera. Similiter autem et cum praedicativa fuerit universalis propositio, particularis autem privativa, possibile est enim A B quidem nullum, C autem omne sequi, et B alicui C non inesse, ut animal disciplinam quidem nullam, hominem autem omnem sequitur, disciplina vero non omnem hominem. Si ergo sumatur A B quidem toti inesse, C autem aliquod non sequi, propositiones quidem falsae, conclusio autem vera.	(6) It is clear too that though both premisses are false they may yield a true conclusion, since it is possible that A should belong both to B and to C as wholes, though B does not follow some C. For if it is assumed that A belongs to no B and to some C, the premisses are both false, but the conclusion is true. Similarly if the universal premiss is affirmative and the particular negative. For it is possible that A should follow no B and all C, though B does not belong to some C, e.g. animal follows no science but every man, though science does not follow every man. If then A is assumed to belong to the whole of B, and not to follow some C, the premisses are false but the conclusion is true.

Chapter 4

Greek	Latin	English
	(PL 64 0690B) CAPUT IV. Quod ex falsis verum identidem colligatur in tertia figura.	4
56b4 Ἔσται δὲ καὶ ἐν τῶι ἐσχάτωι σχήματι διὰ ψευδῶν ἀληθές, καὶ ἀμφοτέρων ψευδῶν οὐσῶν ὅλων καὶ ἐπί τι ἑκατέρας, καὶ τῆς μὲν ἑτέρας ἀληθοῦς ὅλης τῆς δ᾽ ἑτέρας ψευδοῦς, καὶ τῆς μὲν ἐπί τι ψευδοῦς τῆς δ᾽ ὅλης ἀληθοῦς, καὶ ἀνάπαλιν, καὶ ὁσαχῶς ἄλλως ἐγχωρεῖ μεταλαβεῖν τὰς προτάσεις. οὐδὲν γὰρ κωλύει μήτε τὸ Α μήτε τὸ Β μηδενὶ τῶι Γ ὑπάρχειν, τὸ μέντοι Α τινὶ τῶι Β ὑπάρχειν, οἷον οὔτ᾽ ἄνθρωπος οὔτε πεζὸν οὐδενὶ ἀψύχωι ἕπεται, ἄνθρωπος μέντοι τινὶ πεζῶι ὑπάρχει. ἐὰν οὖν ληφθῆι τὸ Α καὶ τὸ Β παντὶ τῶι Γ ὑπάρχειν, αἱ μὲν προτάσεις ὅλαι ψευδεῖς, τὸ δὲ συμπέρασμα ἀληθές. ὡσαύτως δὲ καὶ τῆς μὲν στερητικῆς τῆς δὲ καταφατικῆς οὔσης. ἐγχωρεῖ γὰρ τὸ μὲν Β μηδενὶ τῶι Γ ὑπάρχειν, τὸ δὲ Α παντί, καὶ τὸ Α τινὶ τῶι Β μὴ ὑπάρχειν, οἷον τὸ μέλαν οὐδενὶ κύκνωι, ζῶιον δὲ παντί, καὶ τὸ ζῶιον οὐ παντὶ μέλανι. ὥστ᾽ ἂν ληφθῆι τὸ μὲν Β παντὶ τῶι Γ, τὸ δὲ Α μηδενί, τὸ Α τινὶ τῶι Β οὐχ ὑπάρξει· καὶ τὸ μὲν συμπέρασμα ἀληθές, αἱ δὲ προτάσεις ψευδεῖς.	(0690C) Erit autem et in postrema figura per falsas totas, et in aliquo utraque, et altera quidem vera, altera autem falsa, et haec quidem in aliquo falsa, illa autem tota vera, et e converso, et quotquot modis aliter possibile est transumere propositiones. Nihil enim prohibet nec A nec B nulli C inesse, A autem alicui B inesse, ut nec homo, nec gressibile, nullum inanimatum sequitur, homo autem alicui gressibili inest; si ergo sumatur A et B omni C inesse, propositiones quidem totae falsae, conclusio autem vera. Similiter autem et cum haec quidem est privativa, illa vero affirmativa. (0690D) Possibile est enim B quidem nulli C inesse, A autem omni, et A alicui B non inesse, ut nigrum nulli cygno, animal autem omni, et animal non omni nigro: quare si sumatur B quidem omni C, A vero nulli, A alicui B non inerit, et conclusio quidem vera, propositiones autem falsae.	In the last figure a true conclusion may come through what is false, alike when both premisses are wholly false, when each is partly false, when one premiss is wholly true, the other false, when one premiss is partly false, the other wholly true, and vice versa, and in every other way in which it is possible to alter the premisses. For (1) nothing prevents neither A nor B from belonging to any C, while A belongs to some B, e.g. neither man nor footed follows anything lifeless, though man belongs to some footed things. If then it is assumed that A and B belong to all C, the premisses will be wholly false, but the conclusion true. Similarly if one premiss is negative, the other affirmative. For it is possible that B should belong to no C, but A to all C, and that should not belong to some B, e.g. black belongs to no swan, animal to every swan, and animal not to everything black. Consequently if it is assumed that B belongs to all C, and A to no C, A will not belong to some B: and the conclusion is true, though the premisses are false.
καὶ εἰ ἐπί τι ἑκατέρα ψευδής, ἔσται τὸ συμπέρασμα ἀληθές. οὐδὲν γὰρ κωλύει καὶ τὸ Α καὶ τὸ Β τινὶ τῶι Γ ὑπάρχειν, καὶ τὸ Α τινὶ τῶι Β, οἷον τὸ λευκὸν καὶ τὸ καλὸν τινὶ ζώιωι ὑπάρχει, καὶ τὸ λευκὸν τινὶ καλῶι. ἐὰν οὖν τεθῆι τὸ Α καὶ τὸ Β παντὶ τῶι Γ ὑπάρχειν, αἱ μὲν προτάσεις ἐπί τι ψευδεῖς, τὸ δὲ συμπέρασμα ἀληθές. καὶ στερητικῆς δὲ τῆς Α Γ τιθεμένης ὁμοίως. οὐδὲν γὰρ κωλύει τὸ μὲν Α τινὶ τῶι Γ μὴ ὑπάρχειν, τὸ δὲ Β τινὶ ὑπάρχειν, καὶ τὸ Α τῶι Β μὴ παντὶ ὑπάρχειν, οἷον τὸ λευκὸν τινὶ ζώιωι οὐχ ὑπάρχει, τὸ δὲ καλὸν τινὶ ὑπάρχει, καὶ τὸ λευκὸν οὐ παντὶ καλῶι. ὥστ᾽ ἂν ληφθῆι τὸ μὲν Α μηδενὶ τῶι Γ, τὸ δὲ Β παντί, ἀμφότεραι μὲν αἱ προτάσεις ἐπί τι ψευδεῖς, τὸ δὲ συμπέρασμα ἀληθές.	Et si in aliquo fuerit utraque falsa, erit conclusio vera, nihil enim prohibet et A et B alicui C inesse, et A alicui B, ut album et pulchrum alicui animali inest, et album alicui pulchro; si ergo ponatur A et B omni C inesse, propositiones quidem in aliquo falsae, conclusio autem vera. Et privativa A C posita, similiter: nihil enim prohibet A quidem alicui C non inesse, B vero alicui inesse, et A non omni B inesse, ut album alicui animali non inesse. (0691A) Pulchrum autem alicui inest, et album non omni pulchro: quare si sumatur A quidem nulli, C B autem omni, utraeque propositiones quidem in aliquo falsae, conclusio autem vera.	(2) Also if each premiss is partly false, the conclusion may be true. For nothing prevents both A and B from belonging to some C while A belongs to some B, e.g. white and beautiful belong to some animals, and white to some beautiful things. If then it is stated that A and B belong to all C, the premisses are partially false, but the conclusion is true. Similarly if the premiss AC is stated as negative. For nothing prevents A from not belonging, and B from belonging, to some C, while A does not belong to all B, e.g. white does not belong to some animals, beautiful belongs to some animals, and white does not belong to everything beautiful. Consequently if it is assumed that A belongs to no C, and B to all C, both premisses are partly false, but the conclusion is true.
Ὡσαύτως δὲ καὶ τῆς μὲν ὅλης ψευδοῦς τῆς δ᾽ ὅλης ἀληθοῦς λαμβανομένης. ἐγχωρεῖ γὰρ καὶ τὸ Α καὶ τὸ Β παντὶ τῶι Γ ἕπεσθαι, τὸ μέντοι Α τινὶ τῶι Β μὴ ὑπάρχειν, οἷον ζῶιον καὶ λευκὸν παντὶ κύκνωι ἕπεται, τὸ μέντοι ζῶιον οὐ παντὶ ὑπάρχει λευκῶι. τεθέντων οὖν ὅρων τοιούτων, ἐὰν ληφθῆι τὸ μὲν Β ὅλωι τῶι Γ ὑπάρχειν, τὸ δὲ Α ὅλωι μὴ ὑπάρχειν, ἡ μὲν Β Γ ὅλη ἔσται ἀληθής, ἡ δὲ Α Γ ὅλη ψευδής, καὶ τὸ συμπέρασμα ἀληθές. ὁμοίως δὲ καὶ εἰ τὸ μὲν Β Γ ψεῦδος, τὸ δὲ Α Γ ἀληθές· οἱ γὰρ αὐτοὶ ὅροι πρὸς τὴν ἀπό- ↵ δειξιν [μέλαν – κύκνος – ἄψυχον]. ἀλλὰ καὶ εἰ ἀμφότεραι λαμβάνοιντο καταφατικαί. οὐδὲν γὰρ κωλύει τὸ μὲν Β παντὶ τῶι Γ ἕπεσθαι, τὸ δὲ Α ὅλωι μὴ ὑπάρχειν, καὶ τὸ Α τινὶ τῶι Β ὑπάρχειν, οἷον κύκνωι παντὶ ζῶιον, μέλαν δ᾽ οὐδενὶ κύκνωι, καὶ τὸ μέλαν ὑπάρχει τινὶ ζώιωι. ὥστ᾽ ἂν ληφθῆι τὸ Α καὶ τὸ Β παντὶ τῶι Γ ὑπάρχειν, ἡ μὲν Β Γ ὅλη ἀληθής, ἡ δὲ Α Γ ὅλη ψευδής, καὶ τὸ συμπέρασμα ἀληθές. ὁμοίως δὲ καὶ τῆς Α Γ ληφθείσης ἀληθοῦς· διὰ γὰρ τῶν αὐτῶν ὅρων ἡ ἀπόδειξις.	Similiter autem et haec quidem tota falsa, illa vero tota vera sumpta. Possibile est enim A et B omne C sequi, et A alicui B non inesse, ut animal et album omne cygnum sequitur, et animal non omni inest albo; positis igitur his terminis, si sumatur B quidem toti C inesse, A vero toti non inesse, B C quidem tota erit vera, A C autem tota falsa, et conclusio vera. Similiter autem et si B C quidem falsa, A C autem vera, nam hi quidem termini ad demonstrationem, nigrum, inanimatum, cygnus. (0691B) Sed et si utraeque assumantur affirmative, nihil enim prohibet B quidem omne C sequi, A autem toti C non inesse, et A alicui B inesse, ut omni cygno animal, nigrum vero nulli cygno, et nigrum inest alicui animali: quare si sumatur A et B omni C inesse, B C quidem tota vera, A C autem tota falsa, et conclusio vera. Similiter autem et A C sumpta vera, nam per eosdem terminos demonstratio.	(3) Similarly if one of the premisses assumed is wholly false, the other wholly true. For it is possible that both A and B should follow all C, though A does not belong to some B, e.g. animal and white follow every swan, though animal does not belong to everything white. Taking these then as terms, if one assumes that B belongs to the whole of C, but A does not belong to C at all, the premiss BC will be wholly true, the premiss AC wholly false, and the conclusion true. Similarly if the statement BC is false, the statement AC true, the conclusion may be true. The same terms will serve for the proof. Also if both the premisses assumed are affirmative, the conclusion may be true. For nothing prevents B from following all C, and A from not belonging to C at all, though A belongs to some B, e.g. animal belongs to every swan, black to no swan, and black to some animals. Consequently if it is assumed that A and B belong to every C, the premiss BC is wholly true, the premiss AC is wholly false, and the conclusion is true. Similarly if the premiss AC which is assumed is true: the proof can be made through the same terms.
Πάλιν τῆς μὲν ὅλης ἀληθοῦς οὔσης, τῆς δ᾽ ἐπί τι ψευδοῦς. ἐγχωρεῖ γὰρ τὸ μὲν Β παντὶ τῶι Γ ὑπάρχειν, τὸ δὲ Α τινί, καὶ τὸ Α τινὶ τῶι Β, οἷον δίπουν μὲν παντὶ ἀνθρώπωι, καλὸν δ᾽ οὐ παντί, καὶ τὸ καλὸν τινὶ δίποδι ὑπάρχει. ἐὰν οὖν ληφθῆι καὶ τὸ Α καὶ τὸ Β ὅλωι τῶι Γ ὑπάρχειν, ἡ μὲν Β Γ ὅλη ἀληθής, ἡ δὲ Α Γ ἐπί τι ψευδής, τὸ δὲ συμπέρασμα ἀληθές. ὁμοίως δὲ καὶ τῆς μὲν Α Γ ἀληθοῦς τῆς δὲ Β Γ ἐπί τι ψευδοῦς λαμβανομένης· μετατεθέντων γὰρ τῶν αὐτῶν ὅρων ἔσται ἡ ἀπόδειξις.	Rursum hac quidem tota vera existente, illa vero in aliquo falsa, possibile est enim B quidem omni C inesse, A autem alicui C et alicui B, ut bipes quidem omni homini, pulchrum non omni, et pulchrum alicui bipedi inest. Si ergo sumatur A et B toti C inesse, B C quidem tota vera, A C autem in aliquo falsa, conclusio autem vera. Similiter autem et A C quidem vera, B C autem falsa in aliquo sumpta, transpositis enim eisdem terminis erit demonstratio.	(4) Again if one premiss is wholly true, the other partly false, the conclusion may be true. For it is possible that B should belong to all C, and A to some C, while A belongs to some B, e.g. biped belongs to every man, beautiful not to every man, and beautiful to some bipeds. If then it is assumed that both A and B belong to the whole of C, the premiss BC is wholly true, the premiss AC partly false, the conclusion true. Similarly if of the premisses assumed AC is true and BC partly false, a true conclusion is possible: this can be proved, if the same terms as before are transposed.
καὶ τῆς μὲν στερητικῆς τῆς δὲ καταφατικῆς οὔσης. ἐπεὶ γὰρ ἐγχωρεῖ τὸ μὲν Β ὅλωι τῶι Γ ὑπάρχειν, τὸ δὲ Α τινί, καὶ ὅταν οὕτως ἔχωσιν, οὐ παντὶ τῶι Β τὸ Α, ἐὰν οὖν ληφθῆι τὸ μὲν Β ὅλωι τῶι Γ ὑπάρχειν, τὸ δὲ Α μηδενί, ἡ μὲν στερητικὴ ἐπί τι ψευδής, ἡ δ᾽ ἑτέρα ὅλη ἀληθὴς καὶ τὸ συμπέρασμα. πάλιν ἐπεὶ δέδεικται ὅτι τοῦ μὲν Α μηδενὶ ὑπάρχοντος τῶι Γ, τοῦ δὲ Β τινί, ἐγχωρεῖ τὸ Α τινὶ τῶι Β μὴ ὑπάρχειν, φανερὸν ὅτι καὶ τῆς μὲν Α Γ ὅλης ἀληθοῦς οὔσης, τῆς δὲ Β Γ ἐπί τι ψευδοῦς, ἐγχωρεῖ τὸ συμπέρασμα εἶναι ἀληθές. ἐὰν γὰρ ληφθῆι τὸ μὲν Α μηδενὶ τῶι Γ, τὸ δὲ Β παντί, ἡ μὲν Α Γ ὅλη ἀληθής, ἡ δὲ Β Γ ἐπί τι ψευδής.	(0691C) Et cum haec quidem est privativa, illa vero affirmativa, quoniam possibile est B quidem toti C inesse, A autem alicui C, et quando sic se habeant, non omni B inesse A. Si ergo assumatur B quidem toti C inesse, A autem nulli, privativa quidem in aliquo falsa, altera autem tota vera, et conclusio erit vera. Rursum quoniam ostensum est quod cum A quidem nulli C inest, et B alicui, evenit A alicui B non inesse, manifestum igitur quoniam et cum A C tota est vera, B C autem in aliquo falsa, contingit conclusionem esse veram; si enim sumatur A quidem nulli C, B autem omni, A C quidem tota vera, B C autem in aliquo falsa.	Also the conclusion may be true if one premiss is negative, the other affirmative. For since it is possible that B should belong to the whole of C, and A to some C, and, when they are so, that A should not belong to all B, therefore it is assumed that B belongs to the whole of C, and A to no C, the negative premiss is partly false, the other premiss wholly true, and the conclusion is true. Again since it has been proved that if A belongs to no C and B to some C, it is possible that A should not belong to some C, it is clear that if the premiss AC is wholly true, and the premiss BC partly false, it is possible that the conclusion should be true. For if it is assumed that A belongs to no C, and B to all C, the premiss AC is wholly true, and the premiss BC is partly false.
Φανερὸν δὲ καὶ ἐπὶ τῶν ἐν μέρει συλλογισμῶν ὅτι πάντως ἔσται διὰ ψευδῶν ἀληθές. οἱ γὰρ αὐτοὶ ὅροι ληπτέοι καὶ ὅταν καθόλου ὦσιν αἱ προτάσεις, οἱ μὲν ἐν τοῖς κατηγορικοῖς κατηγορικοί, οἱ δ᾽ ἐν τοῖς στερητικοῖς στερητικοί. οὐδὲν γὰρ διαφέρει μηδενὶ ὑπάρχοντος παντὶ λαβεῖν ὑπάρ- χειν, καὶ τινὶ ὑπάρχοντος καθόλου λαβεῖν ὑπάρχειν, πρὸς τὴν τῶν ὅρων ἔκθεσιν· ὁμοίως δὲ καὶ ἐπὶ τῶν στερητικῶν.	(0691D) Manifestum autem et in particularibus syllogismis quoniam omnino per falsa erit verum, nam iidem termini sumendi, et quando universales fuerint propositiones, in praedicativis quidem praedicativi, in privativis autem privativi; nihil enim differt, cum nulli inerat, universaliter sumere inesse, et si alicui inerat, universaliter sumere ad terminorum positionem; similiter autem et in privativis.	(5) It is clear also in the case of particular syllogisms that a true conclusion may come through what is false, in every possible way. For the same terms must be taken as have been taken when the premisses are universal, positive terms in positive syllogisms, negative terms in negative. For it makes no difference to the setting out of the terms, whether one assumes that what belongs to none belongs to all or that what belongs to some belongs to all. The same applies to negative statements.
Φανερὸν οὖν ὅτι ἂν μὲν ἦι τὸ συμπέρασμα ψεῦδος, ἀνάγκη, ἐξ ὧν ὁ λόγος, ψευδῆ εἶναι ἢ πάντα ἢ ἔνια, ὅταν δ᾽ ἀληθές, οὐκ ἀνάγκη ἀληθὲς εἶναι οὔτε τὶ οὔτε πάντα, ἀλλ᾽ ἔστι μηδενὸς ὄντος ἀληθοῦς τῶν ἐν τῶι συλλογισμῶι τὸ συμπέρασμα ὁμοίως εἶναι ἀληθές· οὐ μὴν ἐξ ἀνάγκης. αἴτιον δ᾽ ↵ ὅτι ὅταν δύο ἔχηι οὕτω πρὸς ἄλληλα ὥστε θατέρου ὄντος ἐξ ἀνάγκης εἶναι θάτερον, τούτου μὴ ὄντος μὲν οὐδὲ θάτερον ἔσται, ὄντος δ᾽ οὐκ ἀνάγκη εἶναι θάτερον· τοῦ δ᾽ αὐτοῦ ὄντος καὶ μὴ ὄντος ἀδύνατον ἐξ ἀνάγκης εἶναι τὸ αὐτό·	Manifestum igitur quod quando sit conclusio falsa, necesse est ea ex quibus est oratio falsa esse, aut omnia, aut aliqua; quando autem vera, non necesse est verum esse nec aliquod quidem, nec omne. Sed est cum nullum sit verum eorum quae sunt in syllogismis, et conclusionem similiter esse veram, non tamen ex necessitate. Causa autem quoniam cum duo sic se habent ad invicem, ut cum alterum sit, ex necessitate esse alterum, hoc cum non sit quidem, nec alterum erit; cum autem sit, non necesse est esse alterum; idem autem cum sit, et non sit, impossibile ex necessitate esse idem.	It is clear then that if the conclusion is false, the premisses of the argument must be false, either all or some of them; but when the conclusion is true, it is not necessary that the premisses should be true, either one or all, yet it is possible, though no part of the syllogism is true, that the conclusion may none the less be true; but it is not necessitated. The reason is that when two things are so related to one another, that if the one is, the other necessarily is, then if the latter is not, the former will not be either, but if the latter is, it is not necessary that the former should be. But it is impossible that the same thing should be necessitated by the being and by the not-being of the same thing.
λέγω δ᾽ οἷον τοῦ Α ὄντος λευκοῦ τὸ Β εἶναι μέγα ἐξ ἀνάγκης, καὶ μὴ ὄντος λευκοῦ τοῦ Α τὸ Β εἶναι μέγα ἐξ ἀνάγκης. ὅταν γὰρ τουδὶ ὄντος λευκοῦ, τοῦ Α, τοδὶ ἀνάγκη μέγα εἶναι, τὸ Β, μεγάλου δὲ τοῦ Β ὄντος τὸ Γ μὴ λευκόν, ἀνάγκη, εἰ τὸ Α λευκόν, τὸ Γ μὴ εἶναι λευκόν. καὶ ὅταν δύο ὄντων θατέρου ὄντος ἀνάγκη θάτερον εἶναι, τούτου μὴ ὄντος ἀνάγκη τὸ πρῶτον μὴ εἶναι. τοῦ δὴ Β μὴ ὄντος μεγάλου τὸ Α οὐχ οἷόν τε λευκὸν εἶναι. τοῦ δὲ Α μὴ ὄντος λευκοῦ εἰ ἀνάγκη τὸ Β μέγα εἶναι, συμβαίνει ἐξ ἀνάγκης τοῦ Β μεγάλου μὴ ὄντος αὐτὸ τὸ Β εἶναι μέγα· τοῦτο δ᾽ ἀδύνατον. εἰ γὰρ τὸ Β μὴ ἔστι μέγα, τὸ Α οὐκ ἔσται λευκὸν ἐξ ἀνάγκης. εἰ οὖν μὴ ὄντος τούτου λευκοῦ τὸ Β ἔσται μέγα, συμβαίνει, εἰ τὸ Β μὴ ἔστι μέγα, εἶναι μέγα, ὡς διὰ τριῶν.	(0692A) Dico autem, cum sit A album, B esse magnum ex necessitate, et cum non sit A album, B esse magnum ex necessitate; quando enim cum hoc sit (ut A ) album, illud necesse est (ut B ) esse magnum, cum autem sit B magnum, C non esse album, necesse est, si A sit album, C non esse album. Et quando duobus existentibus, cum alterum sit, necesse est alterum esse, hoc autem cum non sit, necesse est A non esse, cum ergo B non sit magnum, A non potest album esse, cum vero A non sit album, necesse est B magnum esse, accidit ex necessitate cum B magnum non sit, idem B esse magnum: hoc autem impossibile, nam si B non est magnum, A non erit album ex necessitate; si ergo cum non sit A album, B erit magnum, accidit, si B non est magnum, B esse magnum, ut per tria.	I mean, for example, that it is impossible that B should necessarily be great since A is white and that B should necessarily be great since A is not white. For whenever since this, A, is white it is necessary that that, B, should be great, and since B is great that C should not be white, then it is necessary if is white that C should not be white. And whenever it is necessary, since one of two things is, that the other should be, it is necessary, if the latter is not, that the former (viz. A) should not be. If then B is not great A cannot be white. But if, when A is not white, it is necessary that B should be great, it necessarily results that if B is not great, B itself is great. (But this is impossible.) For if B is not great, A will necessarily not be white. If then when this is not white B must be great, it results that if B is not great, it is great, just as if it were proved through three terms.

Chapter 5

Greek	Latin	English
	(PL 64 0692A) CAPUT V. De circulari ostensione in prima figura	5
57b18 Τὸ δὲ κύκλωι καὶ ἐξ ἀλλήλων δείκνυσθαί ἐστι τὸ διὰ τοῦ συμπεράσματος καὶ τοῦ ἀνάπαλιν τῆι κατηγορίαι τὴν ἑτέραν λαβόντα πρότασιν συμπεράνασθαι τὴν λοιπήν, ἣν ἐλάμβανεν ἐν θατέρωι συλλογισμῶι. οἷον εἰ ἔδει δεῖξαι ὅτι τὸ Α τῶι Γ παντὶ ὑπάρχει, ἔδειξε δὲ διὰ τοῦ Β, πάλιν εἰ δεικνύοι ὅτι τὸ Α τῶι Β ὑπάρχει, λαβὼν τὸ μὲν Α τῶι Γ ὑπάρχειν τὸ δὲ Γ τῶι Β [καὶ τὸ Α τῶι Β]· πρότερον δ᾽ ἀνάπαλιν ἔλαβε τὸ Β τῶι Γ ὑπάρχον. ἢ εἰ [ὅτι] τὸ Β τῶι Γ δεῖ δεῖξαι ὑπάρχον, εἰ λάβοι τὸ Α κατὰ τοῦ Γ, ὁ ἦν συμπέ- ρασμα, τὸ δὲ Β κατὰ τοῦ Α ὑπάρχειν· πρότερον δ᾽ ἐλήφθη ἀνάπαλιν τὸ Α κατὰ τοῦ Β.	(0692B) Circulo autem, et ex se invicem ostendere est per conclusionem, et e converso praedicationem alteram sumentem propositionem concludere reliquam, quam sumpserat in altero syllogismo, ut si oportuit ostendere quoniam A inest omni C, ostendat autem per C, rursus si monstret quoniam A inest B, sumens A quidem inesse C, C autem B, et A inerit B, prius autem e converso sumpsit B inesse C, aut si quoniam B inest C, oporteat ostendere si sumat A de C, quae fuit conclusio, B autem de A esse, prius autem sumptum est e converso A de B.	Circular and reciprocal proof means proof by means of the conclusion, i.e. by converting one of the premisses simply and inferring the premiss which was assumed in the original syllogism: e.g. suppose it has been necessary to prove that A belongs to all C, and it has been proved through B; suppose that A should now be proved to belong to B by assuming that A belongs to C, and C to B-so A belongs to B: but in the first syllogism the converse was assumed, viz. that B belongs to C. Or suppose it is necessary to prove that B belongs to C, and A is assumed to belong to C, which was the conclusion of the first syllogism, and B to belong to A but the converse was assumed in the earlier syllogism, viz. that A belongs to B.
ἄλλως δ᾽ οὐκ ἔστιν ἐξ ἀλλήλων δεῖξαι. εἴτε γὰρ ἄλλο μέσον λήψεται, οὐ κύκλωι· οὐδὲν γὰρ λαμβάνεται τῶν αὐτῶν· εἴτε τούτων τι, ἀνάγκη θάτερον μόνον· εἰ γὰρ ἄμφω, ταὐτὸν ἔσται συμπέρασμα, δεῖ δ᾽ ἕτερον.	(0692C) Aliter vero non est ex se invicem ostendere, sive enim aliud medium sumetur, non circulo, nil enim sumitur eorumdem, sive horum quiddam, necesse est alterum solum, nam si ambo, eadem erit conclusio, at oportet diversam esse.	In no other way is reciprocal proof possible. If another term is taken as middle, the proof is not circular: for neither of the propositions assumed is the same as before: if one of the accepted terms is taken as middle, only one of the premisses of the first syllogism can be assumed in the second: for if both of them are taken the same conclusion as before will result: but it must be different.
Ἐν μὲν οὖν τοῖς μὴ ἀντιστρέφουσιν ἐξ ἀναποδείκτου τῆς ἑτέρας προτάσεως γίνεται ὁ συλλογισμός· οὐ γὰρ ἔστιν ἀποδεῖξαι διὰ τούτων τῶν ὅρων ὅτι τῶι μέσωι τὸ τρίτον ὑπάρχει ἢ τῶι πρώτωι τὸ μέσον. ἐν δὲ τοῖς ἀντιστρέφουσιν ἔστι πάντα δεικνύναι δι᾽ ἀλλήλων, οἷον εἰ τὸ Α καὶ τὸ Β καὶ τὸ Γ ἀντιστρέφουσιν ἀλλήλοις. δεδείχθω γὰρ τὸ Α Γ διὰ μέσου τοῦ Β, καὶ πάλιν τὸ Α Β διά τε τοῦ συμπεράσματος καὶ διὰ τῆς Β Γ προτάσεως ἀντιστραφείσης, ὡσαύτως δὲ καὶ τὸ Β Γ διά τε τοῦ συμπεράσματος καὶ τῆς Α Β ↵ προτάσεως ἀντεστραμμένης. δεῖ δὲ τήν τε Γ Β καὶ τὴν Β Α πρότασιν ἀποδεῖξαι· ταύταις γὰρ ἀναποδείκτοις κεχρήμεθα μόναις.	In iis igitur quae non convertuntur ex indemonstrata altera propositione fit syllogismus, non enim est demonstrare per hos terminos, quoniam medio inest tertium, aut primo medium. In iis autem quae convertuntur, erit omnia monstrare per se invicem, ut si A, et B, et C convertuntur sibi invicem: ostendatur enim A C per medium B, et rursum A B per conclusionem, et per B C propositionem conversam; similiter autem et B C, et per conclusionem, et per A B propositionem conversam; oportet autem et C B, et B A propositionem demonstrare, nam his demonstratis usi sumus solis.	If the terms are not convertible, one of the premisses from which the syllogism results must be undemonstrated: for it is not possible to demonstrate through these terms that the third belongs to the middle or the middle to the first. If the terms are convertible, it is possible to demonstrate everything reciprocally, e.g. if A and B and C are convertible with one another. Suppose the proposition AC has been demonstrated through B as middle term, and again the proposition AB through the conclusion and the premiss BC converted, and similarly the proposition BC through the conclusion and the premiss AB converted. But it is necessary to prove both the premiss CB, and the premiss BA: for we have used these alone without demonstrating them.
ἐὰν οὖν ληφθῆι τὸ Β παντὶ τῶι Γ ὑπάρχειν καὶ τὸ Γ παντὶ τῶι Α, συλλογισμὸς ἔσται τοῦ Β πρὸς τὸ Α. πάλιν ἐὰν ληφθῆι τὸ μὲν Γ παντὶ τῶι Α, τὸ δὲ Α παντὶ τῶι Β, παντὶ τῶι Β τὸ Γ ἀνάγκη ὑπάρχειν. ἐν ἀμφοτέροις δὴ τούτοις τοῖς συλλογισμοῖς ἡ Γ Α πρότασις εἴληπται ἀναπόδεικτος· αἱ γὰρ ἕτεραι δεδειγμέναι ἦσαν. ὥστ᾽ ἂν ταύτην ἀποδείξωμεν, ἅπασαι ἔσονται δεδειγμέναι δι᾽ ἀλλήλων. ἐὰν οὖν ληφθῆι τὸ Γ παντὶ τῶι Β καὶ τὸ Β παντὶ τῶι Α ὑπάρχειν, ἀμφότεραί τε αἱ προτάσεις ἀποδεδειγμέναι λαμβάνονται, καὶ τὸ Γ τῶι Α ἀνάγκη ὑπάρχειν.	(0692D) Si ergo sumatur B omni C inesse, et C omni A, syllogismus erit eius quod est B ad A. Rursus si sumatur C omni A inesse, et A omni B, necesse est C inesse omni B. In utrisque ergo syllogismis C A propositio sumpta est indemonstrata, nam aliae probatae erant: quare si hanc ostenderimus, omnes erunt approbatae per se invicem; si ergo sumatur C omni B, et B omni A inesse, utraeque propositiones demonstratae sumuntur, et C necesse est inesse A.	If then it is assumed that B belongs to all C, and C to all A, we shall have a syllogism relating B to A. Again if it is assumed that C belongs to all A, and A to all B, C must belong to all B. In both these syllogisms the premiss CA has been assumed without being demonstrated: the other premisses had ex hypothesi been proved. Consequently if we succeed in demonstrating this premiss, all the premisses will have been proved reciprocally. If then it is assumed that C belongs to all B, and B to all A, both the premisses assumed have been proved, and C must belong to A.
φανερὸν οὖν ὅτι ἐν μόνοις τοῖς ἀντιστρέφουσι κύκλωι καὶ δι᾽ ἀλλήλων ἐνδέχεται γίνεσθαι τὰς ἀποδείξεις, ἐν δὲ τοῖς ἄλλοις ὡς πρότερον εἴπομεν. συμβαίνει δὲ καὶ ἐν τούτοις αὐτῶι τῶι δεικνυμένωι χρῆσθαι πρὸς τὴν ἀπόδειξιν· τὸ μὲν γὰρ Γ κατὰ τοῦ Β καὶ τὸ Β κατὰ τοῦ Α δείκνυται ληφθέντος τοῦ Γ κατὰ τοῦ Α λέγεσθαι, τὸ δὲ Γ κατὰ τοῦ Α διὰ τούτων δείκνυται τῶν προτάσεων, ὥστε τῶι συμπεράσματι χρώμεθα πρὸς τὴν ἀπόδειξιν.	Manifestum est ergo quoniam in solis iis quae convertuntur, circulo et per se invicem contingit fieri demonstrationes, in aliis vero quemadmodum prius diximus. (0693A) Accidit autem et in iis eodem quod monstratur uti ad demonstrationem, nam C de B, et B de A monstratur sumpto C de A dici, C autem de A per has ostenditur propositiones: quare conclusione utimur ad demonstrationem.	It is clear then that only if the terms are convertible is circular and reciprocal demonstration possible (if the terms are not convertible, the matter stands as we said above). But it turns out in these also that we use for the demonstration the very thing that is being proved: for C is proved of B, and B of by assuming that C is said of and C is proved of A through these premisses, so that we use the conclusion for the demonstration.
Ἐπὶ δὲ τῶν στερητικῶν συλλογισμῶν ὧδε δείκνυται ἐξ ἀλλήλων. ἔστω τὸ μὲν Β παντὶ τῶι Γ ὑπάρχειν, τὸ δὲ Α οὐ- δενὶ τῶι Β· συμπέρασμα ὅτι τὸ Α οὐδενὶ τῶι Γ. εἰ δὴ πάλιν δεῖ συμπεράνασθαι ὅτι τὸ Α οὐδενὶ τῶι Β, ὁ πάλαι ἔλαβεν, ἔστω τὸ μὲν Α μηδενὶ τῶι Γ, τὸ δὲ Γ παντὶ τῶι Β· οὕτω γὰρ ἀνάπαλιν ἡ πρότασις. εἰ δ᾽ ὅτι τὸ Β τῶι Γ δεῖ συμπεράνασθαι, οὐκέθ᾽ ὁμοίως ἀντιστρεπτέον τὸ Α Β (ἡ γὰρ αὐτὴ πρότασις, τὸ Β μηδενὶ τῶι Α καὶ τὸ Α μηδενὶ τῶι Β ὑπάρχειν), ἀλλὰ ληπτέον, ὧι τὸ Α μηδενὶ ὑπάρχει, τὸ Β παντὶ ὑπάρχειν. ἔστω τὸ Α μηδενὶ τῶι Γ ὑπάρχειν, ὅπερ ἦν τὸ συμπέρασμα· ὧι δὲ τὸ Α μηδενί, τὸ Β εἰλήφθω παντὶ ὑπάρχειν· ἀνάγκη οὖν τὸ Β παντὶ τῶι Γ ὑπάρχειν. ὥστε τριῶν ὄντων ἕκαστον συμπέρασμα γέγονε, καὶ τὸ κύκλωι ἀποδεικνύναι τοῦτ᾽ ἔστι, τὸ τὸ συμπέρασμα λαμβάνοντα καὶ ἀνάπαλιν τὴν ἑτέραν πρότασιν τὴν λοιπὴν συλλογίζεσθαι.	In privativis autem syllogismis hoc modo monstratur ex se invicem: sit B quidem omni C inesse, A autem nulli B, conclusio autem quoniam A nulli C. Si ergo rursum oporteat concludere quoniam A nulli B, quod prius sumptum erat, erit A quidem nulli C, C autem omni B, sic enim e converso propositio. Si autem quoniam B inest C, oporteat concludere, non iam similiter convertendum A B, nam eadem propositio est B nulli A, et A nulli B inesse, sed sumendum, cui A nulli inest, huic B omni inesse. (0693B) Sit enim A nulli C inesse, quod quidem fuit conclusio, cui autem A nulli B, si sumatur omni inesse, necesse est ergo B omni C inesse: quare cum sint tria, unumquodque conclusio est facta, et circulo demonstrare, hoc est conclusionem sumentem et e converso alteram propositionem, reliquam syllogizare.	In negative syllogisms reciprocal proof is as follows. Let B belong to all C, and A to none of the Bs: we conclude that A belongs to none of the Cs. If again it is necessary to prove that A belongs to none of the Bs (which was previously assumed) A must belong to no C, and C to all B: thus the previous premiss is reversed. If it is necessary to prove that B belongs to C, the proposition AB must no longer be converted as before: for the premiss ‘B belongs to no A’ is identical with the premiss ‘A belongs to no B’. But we must assume that B belongs to all of that to none of which longs. Let A belong to none of the Cs (which was the previous conclusion) and assume that B belongs to all of that to none of which A belongs. It is necessary then that B should belong to all C. Consequently each of the three propositions has been made a conclusion, and this is circular demonstration, to assume the conclusion and the converse of one of the premisses, and deduce the remaining premiss.
Ἐπὶ δὲ τῶν ἐν μέρει συλλογισμῶν τὴν μὲν καθόλου πρότασιν οὐκ ἔστιν ἀποδεῖξαι διὰ τῶν ἑτέρων, τὴν δὲ κατὰ μέρος ἔστιν. ὅτι μὲν οὖν οὐκ ἔστιν ἀποδεῖξαι τὴν καθόλου, φανερόν· τὸ μὲν γὰρ καθόλου δείκνυται διὰ τῶν καθόλου, τὸ δὲ συμπέρασμα οὐκ ἔστι καθόλου, δεῖ δ᾽ ἐκ τοῦ συμπεράσματος δεῖξαι καὶ τῆς ἑτέρας προτάσεως. ἔτι ὅλως οὐδὲ γίνεται ↵ συλλογισμὸς ἀντιστραφείσης τῆς προτάσεως· ἐν μέρει γὰρ ἀμφότεραι γίνονται αἱ προτάσεις.	In particularibus autem syllogismis universalem quidem propositionem non est demonstrare per alias, particularem autem est; quoniam autem non est demonstrare universalem, manifestum, nam universale monstratur per universalia, conclusio autem non est universalis, oportet autem ostendere ex conclusione et altera propositione. Amplius, omnino non fit syllogismus conversa propositione, nam particulares fiunt utraeque propositiones.	In particular syllogisms it is not possible to demonstrate the universal premiss through the other propositions, but the particular premiss can be demonstrated. Clearly it is impossible to demonstrate the universal premiss: for what is universal is proved through propositions which are universal, but the conclusion is not universal, and the proof must start from the conclusion and the other premiss. Further a syllogism cannot be made at all if the other premiss is converted: for the result is that both premisses are particular.
τὴν δ᾽ ἐπὶ μέρους ἔστιν. δεδείχθω γὰρ τὸ Α κατὰ τινὸς τοῦ Γ διὰ τοῦ Β. ἐὰν οὖν ληφθῆι τὸ Β παντὶ τῶι Α καὶ τὸ συμπέρασμα μένηι, τὸ Β τινὶ τῶι Γ ὑπάρξει· γίνεται γὰρ τὸ πρῶτον σχῆμα, καὶ τὸ Α μέσον. εἰ δὲ στερητικὸς ὁ συλλογισμός, τὴν μὲν καθόλου πρότασιν οὐκ ἔστι δεῖξαι, δι᾽ ὁ καὶ πρότερον ἐλέχθη· τὴν δ᾽ ἐν μέρει ἔστιν, ἐὰν ὁμοίως ἀντιστραφῆι τὸ Α Β ὥσπερ κἀπὶ τῶν καθόλου, [οὐκ ἔστι, διὰ προσλήψεως δ᾽ ἔστιν,] οἷον ὧι τὸ Α τινὶ μὴ ὑπάρχει, τὸ Β τινὶ ὑπάρχειν· ἄλλως γὰρ οὐ γίνεται συλλογισμὸς διὰ τὸ ἀποφατικὴν εἶναι τὴν ἐν μέρει πρότασιν.	Particulare autem est, ostendatur enim A de aliquo C per B, si ergo sumatur B omni A, et conclusio maneat, B alicui C inerit, fit enim prima figura, et est A medium. (0693C) Si autem fit privativus syllogismus, universalem quidem propositionem non est ostendere, propter hoc quod prius dictum est, particularem (si simpliciter convertatur A B quemadmodum et in universalibus) non est, per assumptionem autem est, ut cui A alicui non insit, B alicui inesse; nam aliter se habentibus non fit syllogismus, eo quod negativa est particularis propositio.	But the particular premiss may be proved. Suppose that A has been proved of some C through B. If then it is assumed that B belongs to all A and the conclusion is retained, B will belong to some C: for we obtain the first figure and A is middle. But if the syllogism is negative, it is not possible to prove the universal premiss, for the reason given above. But it is possible to prove the particular premiss, if the proposition AB is converted as in the universal syllogism, i.e ‘B belongs to some of that to some of which A does not belong’: otherwise no syllogism results because the particular premiss is negative.

Chapter 6

Greek	Latin	English
	(PL 64 0693C) CAPUT VI. De eadem cyclica circulari ostensione in secunda figura.	6
58b13 Ἐν δὲ τῶι δευτέρωι σχήματι τὸ μὲν καταφατικὸν οὐκ ἔστι δεῖξαι διὰ τούτου τοῦ τρόπου, τὸ δὲ στερητικὸν ἔστιν. τὸ μὲν οὖν κατηγορικὸν οὐ δείκνυται διὰ τὸ μὴ ἀμφοτέρας εἶναι τὰς προτάσεις καταφατικάς· τὸ γὰρ συμπέρασμα στερητικόν ἐστι, τὸ δὲ κατηγορικὸν ἐξ ἀμφοτέρων ἐδείκνυτο καταφατικῶν. τὸ δὲ στερητικὸν ὧδε δείκνυται. ὑπαρχέτω τὸ Α παντὶ τῶι Β, τῶι δὲ Γ μηδενί· συμπέρασμα τὸ Β οὐδενὶ τῶι Γ. ἐὰν οὖν ληφθῆι τὸ Β παντὶ τῶι Α ὑπάρχον, [τῶι δὲ Γ μηδενί,] ἀνάγκη τὸ Α μηδενὶ τῶι Γ ὑπάρχειν· γίνεται γὰρ τὸ δεύτερον σχῆμα· μέσον τὸ Β. εἰ δὲ τὸ Α Β στερητικὸν ἐλήφθη, θάτερον δὲ κατηγορικόν, τὸ πρῶτον ἔσται σχῆμα. τὸ μὲν γὰρ Γ παντὶ τῶι Α, τὸ δὲ Β οὐδενὶ τῶι Γ, ὥστ᾽ οὐδενὶ τῶι Α τὸ Β· οὐδ᾽ ἄρα τὸ Α τῶι Β. διὰ μὲν οὖν τοῦ συμπεράσματος καὶ τῆς μιᾶς προτάσεως οὐ γίνεται συλλογισμός, προσληφθείσης δ᾽ ἑτέρας ἔσται.	In secunda autem figura affirmativam quidem non est ostendere per hunc modum, privativam autem est; ergo praedicativa quidem non ostenditur, eo quod non sunt utraeque propositiones affirmativae, nam conclusio privativa, praedicativa autem ex utrisque ostendebatur affirmativis. (0693D) Privativa autem sic ostenditur: insit enim A omni B, C autem nulli, conclusio quoniam B nulli C; si ergo sumatur B omni A inesse, et nulli C, necesse est A nulli C inesse, fit enim secunda figura, medium B. Si autem A B privativa sumpta sit, altera vero praedicativa, prima erit figura, nam C quidem omni A, B autem nulli C, quare B nulli A, ergo nec A B, medium C; ergo per conclusionem quidem et unam propositionem non fit syllogismus, assumpta autem altera erit.	In the second figure it is not possible to prove an affirmative proposition in this way, but a negative proposition may be proved. An affirmative proposition is not proved because both premisses of the new syllogism are not affirmative (for the conclusion is negative) but an affirmative proposition is (as we saw) proved from premisses which are both affirmative. The negative is proved as follows. Let A belong to all B, and to no C: we conclude that B belongs to no C. If then it is assumed that B belongs to all A, it is necessary that A should belong to no C: for we get the second figure, with B as middle. But if the premiss AB was negative, and the other affirmative, we shall have the first figure. For C belongs to all A and B to no C, consequently B belongs to no A: neither then does A belong to B. Through the conclusion, therefore, and one premiss, we get no syllogism, but if another premiss is assumed in addition, a syllogism will be possible.
εἰ δὲ μὴ καθόλου ὁ συλλογισμός, ἡ μὲν ἐν ὅλωι πρότασις οὐ δείκνυται διὰ τὴν αὐτὴν αἰτίαν ἥνπερ εἴπομεν καὶ πρότερον, ἡ δ᾽ ἐν μέρει δείκνυται, ὅταν ἦι τὸ καθόλου κατηγορικόν· ὑπαρχέτω γὰρ τὸ Α παντὶ τῶι Β, τῶι δὲ Γ μὴ παντί· συμπέρασμα Β Γ. ἐὰν οὖν ληφθῆι τὸ Β παντὶ τῶι Α, τῶι δὲ Γ οὐ παντί, τὸ Α τινὶ τῶι Γ οὐχ ὑπάρξει· μέσον Β. εἰ δ᾽ ἐστὶν ἡ καθόλου στερητική, οὐ δειχθήσεται ἡ Α Γ πρότασις ἀντιστραφέντος τοῦ Α Β· συμβαίνει γὰρ ἢ ἀμφοτέρας ἢ τὴν ἑτέραν πρότασιν γίνεσθαι ἀποφατικήν, ὥστ᾽ οὐκ ἔσται συλλογισμός. ἀλλ᾽ ὁμοίως δειχθήσεται ὡς καὶ ἐπὶ τῶν καθόλου, ἐὰν ληφθῆι, ὧι τὸ Β τινὶ μὴ ὑπάρχει, τὸ Α τινὶ ὑπάρχειν.	Si autem non universalis sit syllogismus, quae in toto quidem est propositio non ostenditur, propter eamdem causam quam quidem diximus et prius, quae autem in parte, ostenditur quando universalis sit praedicativa. (0694A) Insit enim A omni B, C autem non omni, conclusio B C; si ergo sumatur B omni A, C autem non omni, conclusio A alicui C non inerit medium B. Si autem est universalis privativa, non ostenditur A propositio, conversa A B, accidit enim utrasque aut alteram propositionem fieri negativam: quare non erit syllogismus; sed similiter ostendetur quemadmodum et in universalibus, si sumatur, cui B alicui non inest, A alicui inesse.	But if the syllogism not universal, the universal premiss cannot be proved, for the same reason as we gave above, but the particular premiss can be proved whenever the universal statement is affirmative. Let A belong to all B, and not to all C: the conclusion is BC. If then it is assumed that B belongs to all A, but not to all C, A will not belong to some C, B being middle. But if the universal premiss is negative, the premiss AC will not be demonstrated by the conversion of AB: for it turns out that either both or one of the premisses is negative; consequently a syllogism will not be possible. But the proof will proceed as in the universal syllogisms, if it is assumed that A belongs to some of that to some of which B does not belong.

Chapter 7

Greek	Latin	English
	(PL 64 0694A) CAPUT VII. De cyclica ratiocinatione in tertia figura.	7
58b39 Ἐπὶ δὲ τοῦ τρίτου σχήματος ὅταν μὲν ἀμφότεραι αἱ προτάσεις καθόλου ληφθῶσιν, οὐκ ἐνδέχεται δεῖξαι δι᾽ ἀλλήλων· τὸ μὲν γὰρ καθόλου δείκνυται διὰ τῶν καθόλου, τὸ ↵ δ᾽ ἐν τούτωι συμπέρασμα ἀεὶ κατὰ μέρος, ὥστε φανερὸν ὅτι ὅλως οὐκ ἐνδέχεται δεῖξαι διὰ τούτου τοῦ σχήματος τὴν καθόλου πρότασιν. Ἐὰν δ᾽ ἡ μὲν ἦι καθόλου ἡ δ᾽ ἐν μέρει, ποτὲ μὲν ἔσται ποτὲ δ᾽ οὐκ ἔσται. ὅταν μὲν οὖν ἀμφότεραι κατηγορικαὶ ληφθῶσι καὶ τὸ καθόλου γένηται πρὸς τῶι ἐλάττονι ἄκρωι, ἔσται, ὅταν δὲ πρὸς θατέρωι, οὐκ ἔσται.	In tertia autem figura, quando utraeque propositiones universaliter sumentur, non contingit ostendere per se invicem propositionem. (0694B) Nam universalis quidem ostenditur per universalia, in hac autem conclusio semper est particularis: quare manifestum quoniam omnino non contingit ostendere per hanc figuram universalem propositionem. Si autem haec quidem universalis sit, illa vero particularis, quandoque quidem erit, quandoque vero non inerit; quando ergo utraeque praedicativae sumantur, et universalis sit ad minorem extremitatem, erit; quando vero ad alteram, non erit.	In the third figure, when both premisses are taken universally, it is not possible to prove them reciprocally: for that which is universal is proved through statements which are universal, but the conclusion in this figure is always particular, so that it is clear that it is not possible at all to prove through this figure the universal premiss. But if one premiss is universal, the other particular, proof of the latter will sometimes be possible, sometimes not. When both the premisses assumed are affirmative, and the universal concerns the minor extreme, proof will be possible, but when it concerns the other extreme, impossible.
ὑπαρχέτω γὰρ τὸ Α παντὶ τῶι Γ, τὸ δὲ Β τινί· συμπέρασμα τὸ Α Β. ἐὰν οὖν ληφθῆι τὸ Γ παντὶ τῶι Α ὑπάρχειν, τὸ μὲν Γ δέδεικται τινὶ τῶι Β ὑπάρχον, τὸ δὲ Β τινὶ τῶι Γ οὐ δέδεικται. καίτοι ἀνάγκη, εἰ τὸ Γ τινὶ τῶι Β, καὶ τὸ Β τινὶ τῶι Γ ὑπάρχειν. ἀλλ᾽ οὐ ταὐτόν ἐστι τόδε τῶιδε καὶ τόδε τῶιδε ὑπάρχειν· ἀλλὰ προσληπτέον, εἰ τόδε τινὶ τῶιδε, καὶ θάτερον τινὶ τῶιδε. τούτου δὲ ληφθέντος οὐκέτι γίνεται ἐκ τοῦ συμπεράσματος καὶ τῆς ἑτέρας προτάσεως ὁ συλλογισμός. εἰ δὲ τὸ Β παντὶ τῶι Γ, τὸ δὲ Α τινὶ τῶι Γ, ἔσται δεῖξαι τὸ Α Γ, ὅταν ληφθῆι τὸ μὲν Γ παντὶ τῶι Β ὑπάρχειν, τὸ δὲ Α τινί. εἰ γὰρ τὸ Γ παντὶ τῶι Β, τὸ δὲ Α τινὶ τῶι Β, ἀνάγκη τὸ Α τινὶ τῶι Γ ὑπάρχειν· μέσον τὸ Β. καὶ ὅταν ἦι ἡ μὲν κατηγορικὴ ἡ δὲ στερητική, καθόλου δ᾽ ἡ κατηγορική, δειχθήσεται ἡ ἑτέρα. ὑπαρχέτω γὰρ τὸ Β παντὶ τῶι Γ, τὸ δὲ Α τινὶ μὴ ὑπαρχέτω· συμπέρασμα ὅτι τὸ Α τινὶ τῶι Β οὐχ ὑπάρχει. ἐὰν οὖν προσληφθῆι τὸ Γ παντὶ τῶι Β ὑπάρχειν, ἀνάγκη τὸ Α τινὶ τῶι Γ μὴ ὑπάρχειν· μέσον τὸ Β.	Insit enim A omni C, B autem alicui C, conclusio A B. (0694C) Si ergo sumatur C omni A inesse conversa universali, et A inesse B, quod erat conclusio, C quidem ostensum est alicui B inesse, B autem alicui C, non est ostensum, quamvis necesse est si C alicui B, et B alicui C inesse; sed non idem est hoc illi, et illud huic inesse, sed assumendum est, si hoc alicui illi, et alterum alicui huic, hoc autem sumpto iam non sit ex conclusione et altera propositione syllogismus. Si autem B quidem omni C, A autem alicui C, erit ostendere A C, quando sumatur C quidem omni B inesse, A autem alicui; nam si C omni B inest, A autem alicui B, necesse est A alicui C inesse, medium B. Et cum fuerit haec praedicativa quidem, illa vero privativa, universalis autem praedicativa, ostendetur altera. Insit enim B omni C, A autem alicui non insit, conclusio quoniam A alicui B non inest. Si ergo assumatur C B omni inesse, inerat autem et A non omni B, necesse est A alicui C non inesse medium B.	Let A belong to all C and B to some C: the conclusion is the statement AB. If then it is assumed that C belongs to all A, it has been proved that C belongs to some B, but that B belongs to some C has not been proved. And yet it is necessary, if C belongs to some B, that B should belong to some C. But it is not the same that this should belong to that, and that to this: but we must assume besides that if this belongs to some of that, that belongs to some of this. But if this is assumed the syllogism no longer results from the conclusion and the other premiss. But if B belongs to all C, and A to some C, it will be possible to prove the proposition AC, when it is assumed that C belongs to all B, and A to some B. For if C belongs to all B and A to some B, it is necessary that A should belong to some C, B being middle. And whenever one premiss is affirmative the other negative, and the affirmative is universal, the other premiss can be proved. Let B belong to all C, and A not to some C: the conclusion is that A does not belong to some B. If then it is assumed further that C belongs to all B, it is necessary that A should not belong to some C, B being middle.
ὅταν δ᾽ ἡ στερητικὴ καθόλου γένηται, οὐ δείκνυται ἡ ἑτέρα, εἰ μὴ ὥσπερ ἐπὶ τῶν πρότερον, ἐὰν ληφθῆι, ὧι τοῦτο τινὶ μὴ ὑπάρχει, θάτερον τινὶ ὑπάρχειν, οἷον εἰ τὸ μὲν Α μηδενὶ τῶι Γ, τὸ δὲ Β τινί· συμπέρασμα ὅτι τὸ Α τινὶ τῶι Β οὐχ ὑπάρχει. ἐὰν οὖν ληφθῆι, ὧι τὸ Α τινὶ μὴ ὑπάρχει, τὸ Γ τινὶ ὑπάρχειν, ἀνάγκη τὸ Γ τινὶ τῶι Β ὑπάρχειν. ἄλλως δ᾽ οὐκ ἔστιν ἀντιστρέφοντα τὴν καθόλου πρότασιν δεῖξαι τὴν ἑτέραν· οὐδαμῶς γὰρ ἔσται συλλογισμός.	(0694D) Cum autem privativa universalis sit, non ostenditur altera nisi sicut in prioribus, si sumatur cui hoc alicui non inest, alterum alicui inesse, ut si A nulli C, B autem alicui, conclusio quoniam A alicui B non inest. Si ergo sumatur cui A alicui non inest, eidem C alicui inesse, necesse est C alicui B inesse, aliter autem non est convertentem universalem propositionem ostendere alteram, nullo enim modo erit syllogismus.	But when the negative premiss is universal, the other premiss is not except as before, viz. if it is assumed that that belongs to some of that, to some of which this does not belong, e.g. if A belongs to no C, and B to some C: the conclusion is that A does not belong to some B. If then it is assumed that C belongs to some of that to some of which does not belong, it is necessary that C should belong to some of the Bs. In no other way is it possible by converting the universal premiss to prove the other: for in no other way can a syllogism be formed.
[Φανερὸν οὖν ὅτι ἐν μὲν τῶι πρώτωι σχήματι ἡ δι᾽ ἀλλήλων δεῖξις διά τε τοῦ τρίτου καὶ διὰ τοῦ πρώτου γίνεται σχήματος. κατηγορικοῦ μὲν γὰρ ὄντος τοῦ συμπεράσματος διὰ τοῦ πρώτου, στερητικοῦ δὲ διὰ τοῦ ἐσχάτου· λαμβάνεται γάρ, ὧι τοῦτο μηδενί, θάτερον παντὶ ὑπάρχειν. ἐν δὲ τῶι μέσωι καθόλου μὲν ὄντος τοῦ συλλογισμοῦ δι᾽ αὐτοῦ τε καὶ διὰ τοῦ πρώτου σχήματος, ὅταν δ᾽ ἐν μέρει, δι᾽ αὐτοῦ τε καὶ τοῦ ἐσχάτου. ἐν δὲ τῶι τρίτωι δι᾽ αὐτοῦ πάντες. φανερὸν δὲ καὶ ὅτι ἐν τῶι τρίτωι καὶ τῶι μέσωι οἱ μὴ δι᾽ αὐτῶν γινόμενοι συλλογισμοὶ ἢ οὐκ εἰσὶ κατὰ τὴν κύκλωι δεῖξιν ἢ ἀτελεῖς.	Manifestum igitur quoniam in prima quidem figura per se invicem est ostensio, et per primam, et per tertiam figuram fit: nam cum praedicativa quidem est conclusio, per primam, cum autem privativa, per postremam; sumitur enim cui hoc nulli, alterum omni inesse. In media autem, cum universalis est quidem syllogismus et per ipsam, et per primam figuram, et per postremam; cum autem particularis, et per ipsam, et per postremam. In tertia vero per ipsam, omnes. (0695A) Manifestum etiam quoniam in media et in tertia qui non per ipsas fiunt syllogismi, aut non sunt secundum eam quae circulo est ostensionem, aut imperfecti sunt.	It is clear then that in the first figure reciprocal proof is made both through the third and through the first figure-if the conclusion is affirmative through the first; if the conclusion is negative through the last. For it is assumed that that belongs to all of that to none of which this belongs. In the middle figure, when the syllogism is universal, proof is possible through the second figure and through the first, but when particular through the second and the last. In the third figure all proofs are made through itself. It is clear also that in the third figure and in the middle figure those syllogisms which are not made through those figures themselves either are not of the nature of circular proof or are imperfect.

Chapter 8

Greek	Latin	English
	(PL 64 0695A) CAPUT VIII. De syllogismo conversivo.	8
↵ Τὸ δ᾽ ἀντιστρέφειν ἐστὶ τὸ μετατιθέντα τὸ συμπέρασμα ποιεῖν τὸν συλλογισμὸν ὅτι ἢ τὸ ἄκρον τῶι μέσωι οὐχ ὑπάρξει ἢ τοῦτο τῶι τελευταίωι. ἀνάγκη γὰρ τοῦ συμπεράσματος ἀντιστραφέντος καὶ τῆς ἑτέρας μενούσης προτάσεως ἀναιρεῖσθαι τὴν λοιπήν· εἰ γὰρ ἔσται, καὶ τὸ συμπέρασμα ἔσται. διαφέρει δὲ τὸ ἀντικειμένως ἢ ἐναντίως ἀντιστρέφειν τὸ συμπέρασμα· οὐ γὰρ ὁ αὐτὸς γίνεται συλλογισμὸς ἑκατέρως ἀντιστραφέντος· δῆλον δὲ τοῦτ᾽ ἔσται διὰ τῶν ἑπομένων. λέγω δ᾽ ἀντικεῖσθαι μὲν τὸ παντὶ τῶι οὐ παντὶ καὶ τὸ τινὶ τῶι οὐδενί, ἐναντίως δὲ τὸ παντὶ τῶι οὐδενὶ καὶ τὸ τινὶ τῶι οὐ τινὶ ὑπάρχειν.	Convertere autem est transponentem conclusionem facere syllogismum, quoniam vel extremum medio non inerit, vel hoc postremo; necesse est enim conclusione conversa, et altera remanente propositione, interimi reliquam; nam si erit, et conclusio erit: differt autem opposite aut contrarie convertere conclusionem, non enim fit idem syllogismus utrolibet conversa; palam autem hoc erit per sequentia. (0695B) Dico autem opponi quidem omni inesse non omni, et alicui nulli, contrarie autem omni nulli, et alicui non alicui inesse.	To convert a syllogism means to alter the conclusion and make another syllogism to prove that either the extreme cannot belong to the middle or the middle to the last term. For it is necessary, if the conclusion has been changed into its opposite and one of the premisses stands, that the other premiss should be destroyed. For if it should stand, the conclusion also must stand. It makes a difference whether the conclusion is converted into its contradictory or into its contrary. For the same syllogism does not result whichever form the conversion takes. This will be made clear by the sequel. By contradictory opposition I mean the opposition of ‘to all’ to ‘not to all’, and of ‘to some’ to ‘to none’; by contrary opposition I mean the opposition of ‘to all’ to ‘to none’, and of ‘to some’ to ‘not to some’.
ἔστω γὰρ δεδειγμένον τὸ Α κατὰ τοῦ Γ διὰ μέσου τοῦ Β. εἰ δὴ τὸ Α ληφθείη μηδενὶ τῶι Γ ὑπάρχειν, τῶι δὲ Β παντί, οὐδενὶ τῶι Γ ὑπάρξει τὸ Β. καὶ εἰ τὸ μὲν Α μηδενὶ τῶι Γ, τὸ δὲ Β παντὶ τῶι Γ, τὸ Α οὐ παντὶ τῶι Β καὶ οὐχ ἁπλῶς οὐδενί· οὐ γὰρ ἐδείκνυτο τὸ καθόλου διὰ τοῦ ἐσχάτου σχήματος. ὅλως δὲ τὴν πρὸς τῶι μείζονι ἄκρωι πρότασιν οὐκ ἔστιν ἀνασκευάσαι καθόλου διὰ τῆς ἀντιστροφῆς· ἀεὶ γὰρ ἀναιρεῖται διὰ τοῦ τρίτου σχήματος· ἀνάγκη γὰρ πρὸς τὸ ἔσχατον ἄκρον ἀμφοτέρας λαβεῖν τὰς προτάσεις. καὶ εἰ στερητικὸς ὁ συλλογισμός, ὡσαύτως. δεδείχθω γὰρ τὸ Α μηδενὶ τῶι Γ ὑπάρχον διὰ τοῦ Β. οὐκοῦν ἂν ληφθῆι τὸ Α τῶι Γ παντὶ ὑπάρχειν, τῶι δὲ Β μηδενί, οὐδενὶ τῶι Γ τὸ Β ὑπάρξει. καὶ εἰ τὸ Α καὶ τὸ Β παντὶ τῶι Γ, τὸ Α τινὶ τῶι Β· ἀλλ᾽ οὐδενὶ ὑπῆρχεν.	Sit enim ostensum A de C per medium B; si igitur sumatur A nulli C inesse, omni autem B, nulli C inerit B, et si A quidem nulli C, B autem omni C, A non omni B, et non omnino nulli, non enim ostendebatur universale per tertiam figuram. Omnino autem eam quae est ad maiorem extremitatem propositionem non est destruere universaliter per conversionem, semper enim interimitur per tertiam figuram, necesse enim ad postremam extremitatem utrasque sumere propositiones. Et si privativus sit syllogismus, similiter: ostendatur, enim A nulli C inesse per B, ergo si sumatur A omni C inesse, nulli autem B, nulli C inerit B. Et si A et B omni C, A alicui B, sed nulli inerat.	Suppose that A been proved of C, through B as middle term. If then it should be assumed that A belongs to no C, but to all B, B will belong to no C. And if A belongs to no C, and B to all C, A will belong, not to no B at all, but not to all B. For (as we saw) the universal is not proved through the last figure. In a word it is not possible to refute universally by conversion the premiss which concerns the major extreme: for the refutation always proceeds through the third since it is necessary to take both premisses in reference to the minor extreme. Similarly if the syllogism is negative. Suppose it has been proved that A belongs to no C through B. Then if it is assumed that A belongs to all C, and to no B, B will belong to none of the Cs. And if A and B belong to all C, A will belong to some B: but in the original premiss it belonged to no B.
Ἐὰν δ᾽ ἀντικειμένως ἀντιστραφῆι τὸ συμπέρασμα, καὶ οἱ συλλογισμοὶ ἀντικείμενοι καὶ οὐ καθόλου ἔσονται. γίνεται γὰρ ἡ ἑτέρα πρότασις ἐν μέρει, ὥστε καὶ τὸ συμπέρασμα ἔσται κατὰ μέρος. ἔστω γὰρ κατηγορικὸς ὁ συλλογισμός, καὶ ἀντιστρεφέσθω οὕτως. οὐκοῦν εἰ τὸ Α οὐ παντὶ τῶι Γ, τῶι δὲ Β παντί, τὸ Β οὐ παντὶ τῶι Γ· καὶ εἰ τὸ μὲν Α μὴ παντὶ τῶι Γ, τὸ δὲ Β παντί, τὸ Α οὐ παντὶ τῶι Β. ὁμοίως δὲ καὶ εἰ στερητικὸς ὁ συλλογισμός. εἰ γὰρ τὸ Α τινὶ τῶι Γ ὑπάρχει, τῶι δὲ Β μηδενί, τὸ Β τινὶ τῶι Γ οὐχ ὑπάρξει, οὐχ ἁπλῶς οὐδενί· καὶ εἰ τὸ μὲν Α τῶι Γ τινί, τὸ δὲ Β παντί, ὥσπερ ἐν ἀρχῆι ἐλήφθη, τὸ Α τινὶ τῶι Β ὑπάρξει.	(0695C) Si autem opposite convertatur conclusio, et alii syllogismi oppositi, et non universales erunt, fit enim altera propositio particularis, quare conclusio erit particularis. Sit enim praedicativus syllogismus, et convertatur sic, ergo si A non omni C, B autem omni B, non omni C. Et si A quidem non omni C, B autem omni A, non omni B. Similiter autem et si privativus sit syllogismus, nam si A alicui C inest, B autem nulli, B alicui C non inerit, et non simpliciter nulli, et si A quidem alicui C, B autem omni, quemadmodum in principio sumptum est, A alicui B inerit.	If the conclusion is converted into its contradictory, the syllogisms will be contradictory and not universal. For one premiss is particular, so that the conclusion also will be particular. Let the syllogism be affirmative, and let it be converted as stated. Then if A belongs not to all C, but to all B, B will belong not to all C. And if A belongs not to all C, but B belongs to all C, A will belong not to all B. Similarly if the syllogism is negative. For if A belongs to some C, and to no B, B will belong, not to no C at all, but-not to some C. And if A belongs to some C, and B to all C, as was originally assumed, A will belong to some B.
Ἐπὶ δὲ τῶν ἐν μέρει συλλογισμῶν ὅταν μὲν ἀντικειμένως ἀντιστρέφηται τὸ συμπέρασμα, ἀναιροῦνται ἀμφότεραι αἱ προτάσεις, ὅταν δ᾽ ἐναντίως, οὐδετέρα. οὐ γὰρ ἔτι συμβαίνει, καθάπερ ἐν τοῖς καθόλου, ἀναιρεῖν ἐλλείποντος τοῦ συμπεράσματος κατὰ τὴν ἀντιστροφήν, ἀλλ᾽ οὐδ᾽ ὅλως ↵ ἀναιρεῖν.	In particularibus autem syllogismis quando opposite convertitur conclusio, interimuntur utraeque propositiones, quando vero contrariae, neutra; non enim iam accidit quemadmodum in universalibus interimere deficiente conclusione secundum conversionem, sed nec omnino interimere.	In particular syllogisms when the conclusion is converted into its contradictory, both premisses may be refuted, but when it is converted into its contrary, neither. For the result is no longer, as in the universal syllogisms, refutation in which the conclusion reached by O, conversion lacks universality, but no refutation at all.
δεδείχθω γὰρ τὸ Α κατὰ τινὸς τοῦ Γ. οὐκοῦν ἂν ληφθῆι τὸ Α μηδενὶ τῶι Γ ὑπάρχειν, τὸ δὲ Β τινί, τὸ Α τῶι Β τινὶ οὐχ ὑπάρξει· καὶ εἰ τὸ Α μηδενὶ τῶι Γ, τῶι δὲ Β παντί, οὐδενὶ τῶι Γ τὸ Β. ὥστ᾽ ἀναιροῦνται ἀμφότεραι. ἐὰν δ᾽ ἐναντίως ἀντιστραφῆι, οὐδετέρα. εἰ γὰρ τὸ Α τινὶ τῶι Γ μὴ ὑπάρχει, τῶι δὲ Β παντί, τὸ Β τινὶ τῶι Γ οὐχ ὑπάρξει, ἀλλ᾽ οὔπω ἀναιρεῖται τὸ ἐξ ἀρχῆς· ἐνδέχεται γὰρ τινὶ ὑπάρχειν καὶ τινὶ μὴ ὑπάρχειν. τῆς δὲ καθόλου, τῆς Α Β, ὅλως οὐδὲ γίνεται συλλογισμός· εἰ γὰρ τὸ μὲν Α τινὶ τῶι Γ μὴ ὑπάρχει, τὸ δὲ Β τινὶ ὑπάρχει, οὐδετέρα καθόλου τῶν προτάσεων. ὁμοίως δὲ καὶ εἰ στερητικὸς ὁ συλλογισμός· εἰ μὲν γὰρ ληφθείη τὸ Α παντὶ τῶι Γ ὑπάρχειν, ἀναιροῦνται ἀμφότεραι, εἰ δὲ τινί, οὐδετέρα. ἀπόδειξις δ᾽ ἡ αὐτή.	(0695D) Ostendatur enim A de aliquo C per B; ergo si sumatur A nulli C inesse, B autem alicui C, A alicui B non inerit, et si A nulli C, B autem omni, nulli C inerit B; quare interimentur utraeque. Si autem contrarie convertantur, neutra; nam si A alicui C non inest, B autem omni, B alicui C non inerit, sed nondum interimitur quod ex principio, contingit, enim alicui inesse, et alicui non inesse: universali autem sublato A B, omnino non fit syllogismus. Si enim A quidem alicui C non inest, B autem alicui inest, neutra propositionum universalis est. Similiter autem et si privativus sit syllogismus, si enim sumatur A omni C inesse, interimuntur utraeque; si autem alicui, neutra; demonstratio autem eadem.	Suppose that A has been proved of some C. If then it is assumed that A belongs to no C, and B to some C, A will not belong to some B: and if A belongs to no C, but to all B, B will belong to no C. Thus both premisses are refuted. But neither can be refuted if the conclusion is converted into its contrary. For if A does not belong to some C, but to all B, then B will not belong to some C. But the original premiss is not yet refuted: for it is possible that B should belong to some C, and should not belong to some C. The universal premiss AB cannot be affected by a syllogism at all: for if A does not belong to some of the Cs, but B belongs to some of the Cs, neither of the premisses is universal. Similarly if the syllogism is negative: for if it should be assumed that A belongs to all C, both premisses are refuted: but if the assumption is that A belongs to some C, neither premiss is refuted. The proof is the same as before.

Chapter 9

Greek	Latin	English
	(PL 64 0695D) CAPUT IX. De syllogismo conversivo in secunda figura.	9
60a15 Ἐν δὲ τῶι δευτέρωι σχήματι τὴν μὲν πρὸς τῶι μείζονι ἄκρωι πρότασιν οὐκ ἔστιν ἀνελεῖν ἐναντίως, ὁποτερωσοῦν τῆς ἀντιστροφῆς γινομένης· ἀεὶ γὰρ ἔσται τὸ συμπέρασμα ἐν τῶι τρίτωι σχήματι, καθόλου δ᾽ οὐκ ἦν ἐν τούτωι συλλογισμός. τὴν δ᾽ ἑτέραν ὁμοίως ἀναιρήσομεν τῆι ἀντιστροφῆι. λέγω δὲ τὸ ὁμοίως, εἰ μὲν ἐναντίως ἀντιστρέφεται, ἐναντίως, εἰ δ᾽ ἀντικειμένως, ἀντικειμένως.	(0696A) In secunda autem figura, eam quidem quae est ad maiorem extremitatem propositionem, non est interimere contrarie, quolibet modo conversione facta, semper erit conclusio in tertia figura, universalis autem non fuit in hac syllogismus, alteram autem in hac interimemus, similiter conversione. Dico autem similiter: si contrarie quidem convertitur, contrarie; si opposite, opposite.	In the second figure it is not possible to refute the premiss which concerns the major extreme by establishing something contrary to it, whichever form the conversion of the conclusion may take. For the conclusion of the refutation will always be in the third figure, and in this figure (as we saw) there is no universal syllogism. The other premiss can be refuted in a manner similar to the conversion: I mean, if the conclusion of the first syllogism is converted into its contrary, the conclusion of the refutation will be the contrary of the minor premiss of the first, if into its contradictory, the contradictory.
ὑπαρχέτω γὰρ τὸ Α παντὶ τῶι Β, τῶι δὲ Γ μηδενί· συμπέρασμα Β Γ. ἐὰν οὖν ληφθῆι τὸ Β παντὶ τῶι Γ ὑπάρχειν καὶ τὸ Α Β μένηι, τὸ Α παντὶ τῶι Γ ὑπάρξει· γίνεται γὰρ τὸ πρῶτον σχῆμα. εἰ δὲ τὸ Β παντὶ τῶι Γ, τὸ δὲ Α μηδενὶ τῶι Γ, τὸ Α οὐ παντὶ τῶι Β· σχῆμα τὸ ἔσχατον. ἐὰν δ᾽ ἀντικειμένως ἀντιστραφῆι τὸ Β Γ, ἡ μὲν Α Β ὁμοίως δειχθήσεται, ἡ δὲ Α Γ ἀντικειμένως. εἰ γὰρ τὸ Β τινὶ τῶι Γ, τὸ δὲ Α μηδενὶ τῶι Γ, τὸ Α τινὶ τῶι Β οὐχ ὑπάρξει. πάλιν εἰ τὸ Β τινὶ τῶι Γ, τὸ δὲ Α παντὶ τῶι Β, τὸ Α τινὶ τῶι Γ, ὥστ᾽ ἀντικείμενος γίνεται ὁ συλλογισμός. ὁμοίως δὲ δειχθήσεται καὶ εἰ ἀνάπαλιν ἔχοιεν αἱ προτάσεις.	Insit enim A omni B, C autem nulli, conclusio B C. Si ergo sumatur B omni C inesse, et A B maneat, A omni C inerit, fit enim prima figura. Si autem B omni C, A autem nulli C, A non omni B, figura postrema. (0696B) Si autem opposite convertatur B C, A B quidem similiter ostendetur, A C autem opposite: nam si B alicui C, A autem nulli C, A alicui B non inerit; rursum si B alicui C, A autem omni B, A alicui C, quare oppositus fit syllogismus. Similiter autem ostendetur et si e converso se habeant propositiones.	Let A belong to all B and to no C: conclusion BC. If then it is assumed that B belongs to all C, and the proposition AB stands, A will belong to all C, since the first figure is produced. If B belongs to all C, and A to no C, then A belongs not to all B: the figure is the last. But if the conclusion BC is converted into its contradictory, the premiss AB will be refuted as before, the premiss, AC by its contradictory. For if B belongs to some C, and A to no C, then A will not belong to some B. Again if B belongs to some C, and A to all B, A will belong to some C, so that the syllogism results in the contradictory of the minor premiss. A similar proof can be given if the premisses are transposed in respect of their quality.
εἰ δ᾽ ἐστὶν ἐπὶ μέρους ὁ συλλογισμός, ἐναντίως μὲν ἀντιστρεφομένου τοῦ συμπεράσματος οὐδετέρα τῶν προτάσεων ἀναιρεῖται, καθάπερ οὐδ᾽ ἐν τῶι πρώτωι σχήματι, ἀντικειμένως δ᾽ ἀμφότεραι. κείσθω γὰρ τὸ Α τῶι μὲν Β μηδενὶ ὑπάρχειν, τῶι δὲ Γ τινί· συμπέρασμα Β Γ. ἐὰν οὖν τεθῆι τὸ Β τινὶ τῶι Γ ὑπάρχειν καὶ τὸ Α Β μένηι, συμπέρασμα ἔσται ὅτι τὸ Α τινὶ τῶι Γ οὐχ ὑπάρχει, ἀλλ᾽ οὐκ ἀνήιρηται τὸ ἐξ ἀρχῆς· ἐνδέχεται γὰρ τινὶ ὑπάρχειν καὶ μὴ ὑπάρχειν. πάλιν εἰ τὸ Β τινὶ τῶι Γ καὶ τὸ Α τινὶ τῶι Γ, οὐκ ἔσται συλλογισμός· οὐδέτερον γὰρ καθόλου τῶν εἰλημμένων. ↵ ὥστ᾽ οὐκ ἀναιρεῖται τὸ Α Β. ἐὰν δ᾽ ἀντικειμένως ἀντιστρέφηται, ἀναιροῦνται ἀμφότεραι. εἰ γὰρ τὸ Β παντὶ τῶι Γ, τὸ δὲ Α μηδενὶ τῶι Β, οὐδενὶ τῶι Γ τὸ Α· ἦν δὲ τινί. πάλιν εἰ τὸ Β παντὶ τῶι Γ, τὸ δὲ Α τινὶ τῶι Γ, τινὶ τῶι Β τὸ Α. ἡ αὐτὴ δ᾽ ἀπόδειξις καὶ εἰ τὸ καθόλου κατηγορικόν.	Si autem particularis est syllogismus, contrarie quidem conversa conclusione neutra propositionum interimitur, quemadmodum nec in prima figura, opposite autem, utraeque. Ponatur enim A B quidem nulli inesse, C autem alicui, conclusio B C. Si igitur ponatur B alicui C inesse, et A B maneat, conclusio erit quoniam A alicui C non inest, sed non interimitur quod ex principio, contingit enim alicui inesse et non inesse. Rursum si B alicui C, et A alicui C, non erit syllogismus, neutrum enim universale eorum quae sumpta sunt, quare non interimitur A B. (0696C) Si autem opposite convertatur, interimuntur utraeque, non si B omni C, A autem nulli B, nulli C, A erit autem alicui. Rursum si B omni C, A autem alicui C, alicui B, A . Eadem autem demonstratio et si universalis sit praedicativa.	If the syllogism is particular, when the conclusion is converted into its contrary neither premiss can be refuted, as also happened in the first figure,’ if the conclusion is converted into its contradictory, both premisses can be refuted. Suppose that A belongs to no B, and to some C: the conclusion is BC. If then it is assumed that B belongs to some C, and the statement AB stands, the conclusion will be that A does not belong to some C. But the original statement has not been refuted: for it is possible that A should belong to some C and also not to some C. Again if B belongs to some C and A to some C, no syllogism will be possible: for neither of the premisses taken is universal. Consequently the proposition AB is not refuted. But if the conclusion is converted into its contradictory, both premisses can be refuted. For if B belongs to all C, and A to no B, A will belong to no C: but it was assumed to belong to some C. Again if B belongs to all C and A to some C, A will belong to some B. The same proof can be given if the universal statement is affirmative.

Chapter 10

Greek	Latin	English
	(PL 64 0696C) CAPUT X. De syllogismo conversivo in tertia figura.	10
60b6 Ἐπὶ δὲ τοῦ τρίτου σχήματος ὅταν μὲν ἐναντίως ἀντιστρέφηται τὸ συμπέρασμα, οὐδετέρα τῶν προτάσεων ἀναιρεῖται κατ᾽ οὐδένα τῶν συλλογισμῶν, ὅταν δ᾽ ἀντικειμένως, ἀμφότεραι καὶ ἐν ἅπασιν. δεδείχθω γὰρ τὸ Α τινὶ τῶι Β ὑπάρχον, μέσον δ᾽ εἰλήφθω τὸ Γ, ἔστωσαν δὲ καθόλου αἱ προτάσεις. οὐκοῦν ἐὰν ληφθῆι τὸ Α τινὶ τῶι Β μὴ ὑπάρχειν, τὸ δὲ Β παντὶ τῶι Γ, οὐ γίνεται συλλογισμὸς τοῦ Α καὶ τοῦ Γ. οὐδ᾽ εἰ τὸ Α τῶι μὲν Β τινὶ μὴ ὑπάρχει, τῶι δὲ Γ παντί, οὐκ ἔσται τοῦ Β καὶ τοῦ Γ συλλογισμός.	In tertia vero figura quando contrarie quidem convertitur conclusio, neutra propositionum interimitur secundum nullum syllogismorum; quando autem opposite, utraeque in omnibus. Si enim ostensum A alicui B inesse, medium autem sumptum C, et sint universales propositiones, si ergo sumatur A alicui B non inesse, B autem omni C, non fit syllogismus eius quod est A de C. Neque si A B alicui non inest, C autem omni, non erit eius quod est B C syllogismus.	In the third figure when the conclusion is converted into its contrary, neither of the premisses can be refuted in any of the syllogisms, but when the conclusion is converted into its contradictory, both premisses may be refuted and in all the moods. Suppose it has been proved that A belongs to some B, C being taken as middle, and the premisses being universal. If then it is assumed that A does not belong to some B, but B belongs to all C, no syllogism is formed about A and C. Nor if A does not belong to some B, but belongs to all C, will a syllogism be possible about B and C.
ὁμοίως δὲ δειχθήσεται καὶ εἰ μὴ καθόλου αἱ προτάσεις. ἢ γὰρ ἀμφοτέρας ἀνάγκη κατὰ μέρος εἶναι διὰ τῆς ἀντιστροφῆς, ἢ τὸ καθόλου πρὸς τῶι ἐλάττονι ἄκρωι γίνεσθαι· οὕτω δ᾽ οὐκ ἦν συλλογισμὸς οὔτ᾽ ἐν τῶι πρώτωι σχήματι οὔτ᾽ ἐν τῶι μέσωι. ἐὰν δ᾽ ἀντικειμένως ἀντιστρέφηται, αἱ προτάσεις ἀναιροῦνται ἀμφότεραι. εἰ γὰρ τὸ Α μηδενὶ τῶι Β, τὸ δὲ Β παντὶ τῶι Γ, τὸ Α οὐδενὶ τῶι Γ· πάλιν εἰ τὸ Α τῶι μὲν Β μηδενί, τῶι δὲ Γ παντί, τὸ Β οὐδενὶ τῶι Γ. καὶ εἰ ἡ ἑτέρα μὴ καθόλου, ὡσαύτως. εἰ γὰρ τὸ Α μηδενὶ τῶι Β, τὸ δὲ Β τινὶ τῶι Γ, τὸ Α τινὶ τῶι Γ οὐχ ὑπάρξει· εἰ δὲ τὸ Α τῶι μὲν Β μηδενί, τῶι δὲ Γ παντί, οὐδενὶ τῶι Γ τὸ Β.	(0696D) Similiter autem ostendetur et si non universales sint propositiones, aut enim utrasque necesse est particulares esse per conversionem, aut universalem ad minorem extremitatem fieri, sic autem non fiet syllogismus, nec in prima figura, nec in media. Si autem opposite convertantur propositiones, interimuntur utraeque, nam si A nulli B, B autem omni C, A nulli C. Rursum si A B quidem nulli, C autem omni, B nulli C. Et si altera non sit universalis, similiter; si enim A nulli B, B autem alicui C, A alicui C non inerit. Si autem A quidem nulli, C autem omni, nulli C, B.	A similar proof can be given if the premisses are not universal. For either both premisses arrived at by the conversion must be particular, or the universal premiss must refer to the minor extreme. But we found that no syllogism is possible thus either in the first or in the middle figure. But if the conclusion is converted into its contradictory, both the premisses can be refuted. For if A belongs to no B, and B to all C, then A belongs to no C: again if A belongs to no B, and to all C, B belongs to no C. And similarly if one of the premisses is not universal. For if A belongs to no B, and B to some C, A will not belong to some C: if A belongs to no B, and to C, B will belong to no C.
Ὁμοίως δὲ καὶ εἰ στερητικὸς ὁ συλλογισμός. δεδείχθω γὰρ τὸ Α τινὶ τῶι Β μὴ ὑπάρχον, ἔστω δὲ κατηγορικὸν μὲν τὸ Β Γ, ἀποφατικὸν δὲ τὸ Α Γ· οὕτω γὰρ ἐγίνετο ὁ συλλογισμός. ὅταν μὲν οὖν τὸ ἐναντίον ληφθῆι τῶι συμπεράσματι, οὐκ ἔσται συλλογισμός. εἰ γὰρ τὸ Α τινὶ τῶι Β, τὸ δὲ Β παντὶ τῶι Γ, οὐκ ἦν συλλογισμὸς τοῦ Α καὶ τοῦ Γ. οὐδ᾽ εἰ τὸ Α τινὶ τῶι Β, τῶι δὲ Γ μηδενί, οὐκ ἦν τοῦ Β καὶ τοῦ Γ συλλογισμός. ὥστε οὐκ ἀναιροῦνται αἱ προτάσεις.	(0697A) Similiter et si privativus sit syllogismus; ostendatur enim A alicui B non inesse; si autem praedicativa quidem B C, A C autem negativa, sic enim fiebat syllogismus. Quando igitur contrarium sumitur conclusioni, non erit syllogismus, nam si A alicui B, B autem omni C, non fit syllogismus eius quod est A et C. Neque si A alicui B, nulli autem C, non fuit eius quod est A B et C syllogismus, quare non interimuntur propositiones.	Similarly if the original syllogism is negative. Suppose it has been proved that A does not belong to some B, BC being affirmative, AC being negative: for it was thus that, as we saw, a syllogism could be made. Whenever then the contrary of the conclusion is assumed a syllogism will not be possible. For if A belongs to some B, and B to all C, no syllogism is possible (as we saw) about A and C. Nor, if A belongs to some B, and to no C, was a syllogism possible concerning B and C. Therefore the premisses are not refuted.
ὅταν δὲ τὸ ἀντικείμενον, ἀναιροῦνται. εἰ γὰρ τὸ Α παντὶ τῶι Β καὶ τὸ Β τῶι Γ, τὸ Α παντὶ τῶι Γ· ἀλλ᾽ οὐδενὶ ὑπῆρχεν. πάλιν εἰ τὸ Α παντὶ τῶι Β, τῶι δὲ Γ μηδενί, τὸ Β οὐδενὶ τῶι Γ· ἀλλὰ παντὶ ὑπῆρχεν. ὁμοίως δὲ δείκνυται καὶ εἰ μὴ καθόλου εἰσὶν αἱ προτάσεις. γίνεται γὰρ τὸ Α Γ καθόλου τε καὶ στερητικόν, θάτερον δ᾽ ἐπὶ μέρους καὶ κατηγορικόν. εἰ μὲν οὖν τὸ Α παντὶ τῶι Β, τὸ δὲ Β τινὶ τῶι Γ, τὸ Α τινὶ τῶι Γ συμβαίνει· ἀλλ᾽ οὐδενὶ ὑπῆρχεν. πάλιν εἰ τὸ Α παντὶ τῶι Β, τῶι δὲ Γ ↵ μηδενί, τὸ Β οὐδενὶ τῶι Γ· ἔκειτο δὲ τινί. εἰ δὲ τὸ Α τινὶ τῶι Β καὶ τὸ Β τινὶ τῶι Γ, οὐ γίνεται συλλογισμός· οὐδ᾽ εἰ τὸ Α τινὶ τῶι Β, τῶι δὲ Γ μηδενί, οὐδ᾽ οὕτως. ὥστ᾽ ἐκείνως μὲν ἀναιροῦνται, οὕτω δ᾽ οὐκ ἀναιροῦνται αἱ προτάσεις.	Quando vero oppositum, interimuntur; nam si A omni B, et B omni C, A omni C, sed nulli inerat. Rursum si A omni B, nulli autem C, B nulli C, sed omni inerat. Similiter autem monstratur, et si non universales sint propositiones: sit enim A C universalis et privativa, altera autem particularis et praedicativa, ergo si A quidem omni B, B autem alicui C, A alicui C accidit, sed nulli inerat. Rursum si A omni B, nulli autem C, et B nulli C. (0697B) Si autem A alicui B, et B alicui C, non fit syllogismus. Neque si A alicui B, et nulli C, nec sic. Quare illo quidem modo interimuntur, sic autem non interimuntur propositiones.	But when the contradictory of the conclusion is assumed, they are refuted. For if A belongs to all B, and B to C, A belongs to all C: but A was supposed originally to belong to no C. Again if A belongs to all B, and to no C, then B belongs to no C: but it was supposed to belong to all C. A similar proof is possible if the premisses are not universal. For AC becomes universal and negative, the other premiss particular and affirmative. If then A belongs to all B, and B to some C, it results that A belongs to some C: but it was supposed to belong to no C. Again if A belongs to all B, and to no C, then B belongs to no C: but it was assumed to belong to some C. If A belongs to some B and B to some C, no syllogism results: nor yet if A belongs to some B, and to no C. Thus in one way the premisses are refuted, in the other way they are not.
Φανερὸν οὖν διὰ τῶν εἰρημένων πῶς ἀντιστρεφομένου τοῦ συμπεράσματος ἐν ἑκάστωι σχήματι γίνεται συλλογισμός, καὶ πότ᾽ ἐναντίος τῆι προτάσει καὶ πότ᾽ ἀντικείμενος, καὶ ὅτι ἐν μὲν τῶι πρώτωι σχήματι διὰ τοῦ μέσου καὶ τοῦ ἐσχάτου γίνονται οἱ συλλογισμοί, καὶ ἡ μὲν πρὸς τῶι ἐλάττονι ἄκρωι ἀεὶ διὰ τοῦ μέσου ἀναιρεῖται, ἡ δὲ πρὸς τῶι μείζονι διὰ τοῦ ἐσχάτου· ἐν δὲ τῶι δευτέρωι διὰ τοῦ πρώτου καὶ τοῦ ἐσχάτου, ἡ μὲν πρὸς τῶι ἐλάττονι ἄκρωι ἀεὶ διὰ τοῦ πρώτου σχήματος, ἡ δὲ πρὸς τῶι μείζονι διὰ τοῦ ἐσχάτου· ἐν δὲ τῶι τρίτωι διὰ τοῦ πρώτου καὶ διὰ τοῦ μέσου, καὶ ἡ μὲν πρὸς τῶι μείζονι διὰ τοῦ πρώτου ἀεί, ἡ δὲ πρὸς τῶι ἐλάττονι διὰ τοῦ μέσου.	(0697C) Manifestum est ergo ex iis quae dicta sunt quomodo conversa conclusione in unaquaque figura fit syllogismus, et quando contrarie propositioni, et quando opposite; et quoniam in prima quidem figura per mediam et postremam fiunt syllogismi, et quae quidem ad minorem extremitatem semper per mediam interimitur, quae vero ad maiorem per postremam; in secunda autem, per primam et postremam, quae quidem ad minorem extremitatem semper per primam figuram, quae vero ad maiorem, per postremam; in tertia vero, per primam et per mediam, et quae quidem ad maiorem per primam semper, quae vero ad minorem per mediam semper.	From what has been said it is clear how a syllogism results in each figure when the conclusion is converted; when a result contrary to the premiss, and when a result contradictory to the premiss, is obtained. It is clear that in the first figure the syllogisms are formed through the middle and the last figures, and the premiss which concerns the minor extreme is alway refuted through the middle figure, the premiss which concerns the major through the last figure. In the second figure syllogisms proceed through the first and the last figures, and the premiss which concerns the minor extreme is always refuted through the first figure, the premiss which concerns the major extreme through the last. In the third figure the refutation proceeds through the first and the middle figures; the premiss which concerns the major is always refuted through the first figure, the premiss which concerns the minor through the middle figure.

Chapter 11

Greek	Latin	English
		11
61a17 Τί μὲν οὖν ἐστὶ τὸ ἀντιστρέφειν καὶ πῶς ἐν ἑκάστωι σχήματι καὶ τίς γίνεται συλλογισμός, φανερόν. ὁ δὲ διὰ τοῦ ἀδυνάτου συλλογισμὸς δείκνυται μὲν ὅταν ἡ ἀντίφασις τεθῆι τοῦ συμπεράσματος καὶ προσληφθῆι ἄλλη πρότασις, γίνεται δ᾽ ἐν ἅπασι τοῖς σχήμασιν· ὅμοιον γάρ ἐστι τῆι ἀντιστροφῆι, πλὴν διαφέρει τοσοῦτον ὅτι ἀντιστρέφεται μὲν γεγενημένου συλλογισμοῦ καὶ εἰλημμένων ἀμφοῖν τῶν προτάσεων, ἀπάγεται δ᾽ εἰς ἀδύνατον οὐ προομολογηθέντος τοῦ ἀντικειμένου πρότερον, ἀλλὰ φανεροῦ ὄντος ὅτι ἀληθές. οἱ δ᾽ ὅροι ὁμοίως ἔχουσιν ἐν ἀμφοῖν, καὶ ἡ αὐτὴ λῆψις ἀμφοτέρων. οἷον εἰ τὸ Α τῶι Β παντὶ ὑπάρχει, μέσον δὲ τὸ Γ, ἐὰν ὑποτεθῆι τὸ Α ἢ μὴ παντὶ ἢ μηδενὶ τῶι Β ὑπάρχειν, τῶι δὲ Γ παντί, ὅπερ ἦν ἀληθές, ἀνάγκη τὸ Γ τῶι Β ἢ μηδενὶ ἢ μὴ παντὶ ὑπάρχειν. τοῦτο δ᾽ ἀδύνατον, ὥστε ψεῦδος τὸ ὑποτεθέν· ἀληθὲς ἄρα τὸ ἀντικείμενον. ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων σχημάτων· ὅσα γὰρ ἀντιστροφὴν δέχεται, καὶ τὸν διὰ τοῦ ἀδυνάτου συλλογισμόν.	Quid ergo est convertere, et quomodo in unaquaque figura, et quis fit syllogismus, manifestum. (PL 64 0697C) [CAPUT XI. De syllogismo per impossibile]. Per impossibile autem syllogismus ostenditur quidem, quando contradictio ponitur conclusionis, et assumitur altera propositio. Fit autem in omnibus figuris, simile enim est conversioni. Verumtamen differt in tantum quoniam convertitur quidem facto syllogismo, et sumptis utrisque propositionibus. Deducitur autem ad impossibile non confesso opposito prius, sed manifesto quoniam est verum. (0697D) Termini vero similiter se habent in utrisque, et eadem sumptio utrorumque, ut si A inest omni B, medium autem C, si supponitur A non omni vel nulli B inesse, C vero omni, quod fuit verum, necesse est C B aut nulli aut non omni inesse, hoc autem impossibile, quare falsum est quod suppositum est. Verum ergo oppositum; similiter autem in aliis figuris, quaecunque enim conversionem suscipiunt, et per impossibile syllogismum.	It is clear then what conversion is, how it is effected in each figure, and what syllogism results. The syllogism per impossibile is proved when the contradictory of the conclusion stated and another premiss is assumed; it can be made in all the figures. For it resembles conversion, differing only in this: conversion takes place after a syllogism has been formed and both the premisses have been taken, but a reduction to the impossible takes place not because the contradictory has been agreed to already, but because it is clear that it is true. The terms are alike in both, and the premisses of both are taken in the same way. For example if A belongs to all B, C being middle, then if it is supposed that A does not belong to all B or belongs to no B, but to all C (which was admitted to be true), it follows that C belongs to no B or not to all B. But this is impossible: consequently the supposition is false: its contradictory then is true. Similarly in the other figures: for whatever moods admit of conversion admit also of the reduction per impossibile.
Τὰ μὲν οὖν ἄλλα προβλήματα πάντα δείκνυται διὰ τοῦ ἀδυνάτου ἐν ἅπασι τοῖς σχήμασι, τὸ δὲ καθόλου κατηγορικὸν ἐν μὲν τῶι μέσωι καὶ τῶι τρίτωι δείκνυται, ἐν δὲ τῶι πρώτωι οὐ δείκνυται. ὑποκείσθω γὰρ τὸ Α τῶι Β μὴ παντὶ ἢ μηδενὶ ὑπάρχειν, καὶ προσειλήφθω ἄλλη πρότασις ὁποτερωθενοῦν, εἴτε τῶι Α παντὶ ὑπάρχειν τὸ Γ εἴτε τὸ Β παντὶ τῶι Δ· οὕτω γὰρ ἂν εἴη τὸ πρῶτον σχῆμα. εἰ μὲν οὖν ὑπόκειται μὴ παντὶ ὑπάρχειν τὸ Α τῶι Β, οὐ γίνεται συλλο↵γισμὸς ὁποτερωθενοῦν τῆς προτάσεως λαμβανομένης,	(0698A) Ergo alia quidem proposita omnia ostenduntur per impossibile in omnibus figuris, universale autem praedicativum in media et in tertia monstratur, in prima autem non monstratur: supponatur enim A non omni B aut nulli inesse, et assumatur alia propositio, utrolibet modo, sive A omni inest C, sive B omni D (sic enim erat prima figura); si ergo supponatur A non omni B inesse, non fiet syllogismus quomodolibet sumpta propositione.	All the problems can be proved per impossibile in all the figures, excepting the universal affirmative, which is proved in the middle and third figures, but not in the first. Suppose that A belongs not to all B, or to no B, and take besides another premiss concerning either of the terms, viz. that C belongs to all A, or that B belongs to all D; thus we get the first figure. If then it is supposed that A does not belong to all B, no syllogism results whichever term the assumed premiss concerns; but if it is supposed that A belongs to no B, when the premiss BD is assumed as well we shall prove syllogistically what is false, but not the problem proposed.
εἰ δὲ μηδενί, ὅταν μὲν ἡ Β Δ προσληφθῆι, συλλογισμὸς μὲν ἔσται τοῦ ψεύδους, οὐ δείκνυται δὲ τὸ προκείμενον. εἰ γὰρ τὸ Α μηδενὶ τῶι Β, τὸ δὲ Β παντὶ τῶι Δ, τὸ Α οὐδενὶ τῶι Δ. τοῦτο δ᾽ ἔστω ἀδύνατον· ψεῦδος ἄρα τὸ μηδενὶ τῶι Β τὸ Α ὑπάρχειν. ἀλλ᾽ οὐκ εἰ τὸ μηδενὶ ψεῦδος, τὸ παντὶ ἀληθές. ἐὰν δ᾽ ἡ Γ Α προσληφθῆι, οὐ γίνεται συλλογισμός, οὐδ᾽ ὅταν ὑποτεθῆι μὴ παντὶ τῶι Β τὸ Α ὑπάρχειν. ὥστε φανερὸν ὅτι τὸ παντὶ ὑπάρχειν οὐ δείκνυται ἐν τῶι πρώτωι σχήματι διὰ τοῦ ἀδυνάτου.	Si autem nulli B, D quidem assumatur, syllogismus quidem erit falsi, non ostenditur autem propositum; nam si A nulli B, B autem omni D, A nulli D, hoc autem sit impossibile, falsum igitur est nulli B inesse A, sed non si nulli falsum, omni verum. Si autem C A assumatur, non fit syllogismus, nec quando supponitur non omni B inesse A; quare manifestum quoniam omni inesse non ostenditur in prima figura per impossibile.	For if A belongs to no B, and B belongs to all D, A belongs to no D. Let this be impossible: it is false then A belongs to no B. But the universal affirmative is not necessarily true if the universal negative is false. But if the premiss CA is assumed as well, no syllogism results, nor does it do so when it is supposed that A does not belong to all B. Consequently it is clear that the universal affirmative cannot be proved in the first figure per impossibile.
Τὸ δέ γε τινὶ καὶ τὸ μηδενὶ καὶ μὴ παντὶ δείκνυται. ὑποκείσθω γὰρ τὸ Α μηδενὶ τῶι Β ὑπάρχειν, τὸ δὲ Β εἰλήφθω παντὶ ἢ τινὶ τῶι Γ. οὐκοῦν ἀνάγκη τὸ Α μηδενὶ ἢ μὴ παντὶ τῶι Γ ὑπάρχειν. τοῦτο δ᾽ ἀδύνατον – ἔστω γὰρ ἀληθὲς καὶ φανερὸν ὅτι παντὶ ὑπάρχει τῶι Γ τὸ Α – ὥστ᾽ εἰ τοῦτο ψεῦδος, ἀνάγκη τὸ Α τινὶ τῶι Β ὑπάρχειν. ἐὰν δὲ πρὸς τῶι Α ληφθῆι ἡ ἑτέρα πρότασις, οὐκ ἔσται συλλογισμός. οὐδ᾽ ὅταν τὸ ἐναντίον τῶι συμπεράσματι ὑποτεθῆι, οἷον τὸ τινὶ μὴ ὑπάρχειν. φανερὸν οὖν ὅτι τὸ ἀντικείμενον ὑποθετέον.	Alicui autem, et nulli, et non omni ostenditur. Supponatur enim A nulli B inesse, B autem sumptum sit omni aut alicui C, ergo necesse est A nulli aut non omni C inesse, hoc autem impossibile. Sit enim verum et manifestum quoniam omni C inest A, quare si hoc falsum, necesse est A alicui B inesse. (0698B) Si autem ad A sumatur altera propositio, non erit syllogismus, neque quando subcontrarium conclusioni supponitur ut alicui non inesse; manifestum ergo quoniam oppositum sumendum est.	But the particular affirmative and the universal and particular negatives can all be proved. Suppose that A belongs to no B, and let it have been assumed that B belongs to all or to some C. Then it is necessary that A should belong to no C or not to all C. But this is impossible (for let it be true and clear that A belongs to all C): consequently if this is false, it is necessary that A should belong to some B. But if the other premiss assumed relates to A, no syllogism will be possible. Nor can a conclusion be drawn when the contrary of the conclusion is supposed, e.g. that A does not belong to some B. Clearly then we must suppose the contradictory.
Πάλιν ὑποκείσθω τὸ Α τινὶ τῶι Β ὑπάρχειν, εἰλήφθω δὲ τὸ Γ παντὶ τῶι Α. ἀνάγκη οὖν τὸ Γ τινὶ τῶι Β ὑπάρχειν. τοῦτο δ᾽ ἔστω ἀδύνατον, ὥστε ψεῦδος τὸ ὑποτεθέν. εἰ δ᾽ οὕτως, ἀληθὲς τὸ μηδενὶ ὑπάρχειν. ὁμοίως δὲ καὶ εἰ στερητικὸν ἐλήφθη τὸ Γ Α. εἰ δ᾽ ἡ πρὸς τῶι Β εἴληπται πρότασις, οὐκ ἔσται συλλογισμός. ἐὰν δὲ τὸ ἐναντίον ὑποτεθῆι, συλλογισμὸς μὲν ἔσται καὶ τὸ ἀδύνατον, οὐ δείκνυται δὲ τὸ προτεθέν. ὑποκείσθω γὰρ παντὶ τῶι Β τὸ Α ὑπάρχειν, καὶ τὸ Γ τῶι Α εἰλήφθω παντί. οὐκοῦν ἀνάγκη τὸ Γ παντὶ τῶι Β ὑπάρχειν. τοῦτο δ᾽ ἀδύνατον, ὥστε ψεῦδος τὸ παντὶ τῶι Β τὸ Α ὑπάρχειν. ἀλλ᾽ οὔπω γε ἀναγκαῖον, εἰ μὴ παντί, μηδενὶ ὑπάρχειν. ὁμοίως δὲ καὶ εἰ πρὸς τῶι Β ληφθείη ἡ ἑτέρα πρότασις· συλλογισμὸς μὲν γὰρ ἔσται καὶ τὸ ἀδύνατον, οὐκ ἀναιρεῖται δ᾽ ἡ ὑπόθεσις· ὥστε τὸ ἀντικείμενον ὑποθετέον.	Rursum supponatur A alicui B inesse, sumptum autem sit C omni A, necesse est igitur C alicui B inesse, hoc autem sit impossibile, quare falsum quidem suppositum est; si autem sic, verum est nulli inesse. Similiter autem et si privativa sumpta sit C A. Si autem ad B sumpta sit propositio, non erit syllogismus. Si autem contrarium supponatur, syllogismus erit et impossibile, non tamen ostenditur quod est propositum: supponatur enim A omni B, et C sumptum sit omni A, ergo necesse est C omni B inesse: hoc autem impossibile, quare falsum est omni B inesse A, sed nondum erit necessarium, si non omni, nulli inesse. (0698C) Similiter autem et si A D B sumatur altera propositio: nam syllogismus quidem erit et impossibile, non interimitur autem hypothesis, quare oppositum supponendum.	Again suppose that A belongs to some B, and let it have been assumed that C belongs to all A. It is necessary then that C should belong to some B. But let this be impossible, so that the supposition is false: in that case it is true that A belongs to no B. We may proceed in the same way if the proposition CA has been taken as negative. But if the premiss assumed concerns B, no syllogism will be possible. If the contrary is supposed, we shall have a syllogism and an impossible conclusion, but the problem in hand is not proved. Suppose that A belongs to all B, and let it have been assumed that C belongs to all A. It is necessary then that C should belong to all B. But this is impossible, so that it is false that A belongs to all B. But we have not yet shown it to be necessary that A belongs to no B, if it does not belong to all B. Similarly if the other premiss taken concerns B; we shall have a syllogism and a conclusion which is impossible, but the hypothesis is not refuted. Therefore it is the contradictory that we must suppose.
Πρὸς δὲ τὸ μὴ παντὶ δεῖξαι ὑπάρχον τῶι Β τὸ Α, ὑποθετέον παντὶ ὑπάρχειν· εἰ γὰρ τὸ Α παντὶ τῶι Β καὶ τὸ Γ παντὶ τῶι Α, τὸ Γ παντὶ τῶι Β, ὥστ᾽ εἰ τοῦτο ἀδύνατον, ψεῦδος τὸ ὑποτεθέν. ὁμοίως δὲ καὶ εἰ πρὸς τῶι Β ἐλήφθη ἡ ἑτέρα πρότασις. καὶ εἰ στερητικὸν ἦν τὸ Γ Α, ὡσαύτως· καὶ γὰρ οὕτω γίνεται συλλογισμός. ἐὰν δὲ πρὸς τῶι Β ἦι τὸ στερητικόν, οὐδὲν δείκνυται. ἐὰν δὲ μὴ παντὶ ἀλλὰ τινὶ ὑπάρχειν ὑποτεθῆι, οὐ δείκνυται ὅτι οὐ παντὶ ἀλλ᾽ ὅτι οὐδενί. εἰ γὰρ τὸ Α τινὶ τῶι Β, τὸ δὲ Γ παντὶ τῶι Α, τινὶ ↵ τῶι Β τὸ Γ ὑπάρξει. εἰ οὖν τοῦτ᾽ ἀδύνατον, ψεῦδος τὸ τινὶ ὑπάρχειν τῶι Β τὸ Α, ὥστ᾽ ἀληθὲς τὸ μηδενί. τούτου δὲ δειχθέντος προσαναιρεῖται τὸ ἀληθές· τὸ γὰρ Α τῶι Β τινὶ μὲν ὑπῆρχε, τινὶ δ᾽ οὐχ ὑπῆρχεν.	Ad ostendendum autem non omni B inesse A, supponendum omni inesse, nam si A omni B, et C omni A, omni B inerit C; si ergo hoc impossibile, falsum quod suppositum est; similiter autem et si ad B sumpta sit altera propositio. Et si privativa sit C A, similiter, nam et sic fit syllogismus. Si autem ad B sumpta sit privativa, nihil ostenditur. (0698D) Si autem non omni, sed alicui inesse supponatur, non ostenditur quoniam non omni, sed quoniam nulli: si enim A alicui B, C autem omni A, alicui B inerit C; si ergo hoc impossibile, falsum est alicui B inesse A, quare verum nulli; hoc autem ostenso, interimitur verum, nam A alicui quidem B inerat, alicui vero non inerat.	To prove that A does not belong to all B, we must suppose that it belongs to all B: for if A belongs to all B, and C to all A, then C belongs to all B; so that if this is impossible, the hypothesis is false. Similarly if the other premiss assumed concerns B. The same results if the original proposition CA was negative: for thus also we get a syllogism. But if the negative proposition concerns B, nothing is proved. If the hypothesis is that A belongs not to all but to some B, it is not proved that A belongs not to all B, but that it belongs to no B. For if A belongs to some B, and C to all A, then C will belong to some B. If then this is impossible, it is false that A belongs to some B; consequently it is true that A belongs to no B. But if this is proved, the truth is refuted as well; for the original conclusion was that A belongs to some B, and does not belong to some B.
ἔτι οὐδὲν παρὰ τὴν ὑπόθεσιν συμβαίνει [τὸ] ἀδύνατον· ψεῦδος γὰρ ἂν εἴη, εἴπερ ἐξ ἀληθῶν μὴ ἔστι ψεῦδος συλλογίσασθαι· νῦν δ᾽ ἐστὶν ἀληθές· ὑπάρχει γὰρ τὸ Α τινὶ τῶι Β. ὥστ᾽ οὐχ ὑποθετέον τινὶ ὑπάρχειν, ἀλλὰ παντί. ὁμοίως δὲ καὶ εἰ τινὶ μὴ ὑπάρχον τῶι Β τὸ Α δεικνύοιμεν· εἰ γὰρ ταὐτὸ τὸ τινὶ μὴ ὑπάρχειν καὶ μὴ παντὶ ὑπάρχειν, ἡ αὐτὴ ἀμφοῖν ἀπόδειξις.	Amplius autem non tam propter hypothesin accidit impossibile, falsa enim erit, siquidem ex veris non est falsum syllogizare: nunc autem est vera, inest enim A alicui B, quare non supponendum alicui inesse, sed omni. Similiter autem et si alicui B non inest A, ostenderemus; si enim idem est alicui non inesse, et non omni inesse, eadem in utrisque demonstratio.	Further the impossible does not result from the hypothesis: for then the hypothesis would be false, since it is impossible to draw a false conclusion from true premisses: but in fact it is true: for A belongs to some B. Consequently we must not suppose that A belongs to some B, but that it belongs to all B. Similarly if we should be proving that A does not belong to some B: for if ‘not to belong to some’ and ‘to belong not to all’ have the same meaning, the demonstration of both will be identical.
Φανερὸν οὖν ὅτι οὐ τὸ ἐναντίον ἀλλὰ τὸ ἀντικείμενον ὑποθετέον ἐν ἅπασι τοῖς συλλογισμοῖς. οὕτω γὰρ τό τε ἀναγκαῖον ἔσται καὶ τὸ ἀξίωμα ἔνδοξον. εἰ γὰρ κατὰ παντὸς ἡ φάσις ἢ ἡ ἀπόφασις, δειχθέντος ὅτι οὐχ ἡ ἀπόφασις, ἀνάγκη τὴν κατάφασιν ἀληθεύεσθαι. πάλιν εἰ μὴ τίθησιν ἀληθεύεσθαι τὴν κατάφασιν, ἔνδοξον τὸ ἀξιῶσαι τὴν ἀπόφασιν. τὸ δ᾽ ἐναντίον οὐδετέρως ἁρμόττει ἀξιοῦν· οὔτε γὰρ ἀναγκαῖον, εἰ τὸ μηδενὶ ψεῦδος, τὸ παντὶ ἀληθές, οὔτ᾽ ἔνδοξον ὡς εἰ θάτερον ψεῦδος, ὅτι θάτερον ἀληθές.	(0699A) Manifestum ergo quoniam non contrarium, sed oppositum supponendum in omnibus syllogismis, sic enim necessarium erit et axioma probabile; nam si de omni vel affirmatio vel negatio, ostenso quoniam non negatio, necesse est affirmationem veram esse; rursum si non ponant veram esse affirmationem, constat veram esse negationem; contrariam vero neutro modo contingit ratum facere. enim necessarium, si nulli falsum, omni verum, neque probabile ut sit alterum falsum, quoniam alterum verum. Manifestum ergo quoniam in prima figura alia quidem proposita omnia ostenduntur per impossibile, universale autem affirmativum non ostenditur.	It is clear then that not the contrary but the contradictory ought to be supposed in all the syllogisms. For thus we shall have necessity of inference, and the claim we make is one that will be generally accepted. For if of everything one or other of two contradictory statements holds good, then if it is proved that the negation does not hold, the affirmation must be true. Again if it is not admitted that the affirmation is true, the claim that the negation is true will be generally accepted. But in neither way does it suit to maintain the contrary: for it is not necessary that if the universal negative is false, the universal affirmative should be true, nor is it generally accepted that if the one is false the other is true.

Chapter 12

Greek	Latin	English
	(PL 64 0699A) CAPUT XII. De syllogismo per impossibile in secunda figura.	12
62a20 Φανερὸν οὖν ὅτι ἐν τῶι πρώτωι σχήματι τὰ μὲν ἄλλα προβλήματα πάντα δείκνυται διὰ τοῦ ἀδυνάτου, τὸ δὲ καθόλου καταφατικὸν οὐ δείκνυται. ἐν δὲ τῶι μέσωι καὶ τῶι ἐσχάτωι καὶ τοῦτο δείκνυται. κείσθω γὰρ τὸ Α μὴ παντὶ τῶι Β ὑπάρχειν, εἰλήφθω δὲ τῶι Γ παντὶ ὑπάρχειν τὸ Α. οὐκοῦν εἰ τῶι μὲν Β μὴ παντί, τῶι δὲ Γ παντί, οὐ παντὶ τῶι Β τὸ Γ. τοῦτο δ᾽ ἀδύνατον· ἔστω γὰρ φανερὸν ὅτι παντὶ τῶι Β ὑπάρχει τὸ Γ, ὥστε ψεῦδος τὸ ὑποκείμενον. ἀληθὲς ἄρα τὸ παντὶ ὑπάρχειν. ἐὰν δὲ τὸ ἐναντίον ὑποτεθῆι, συλλογισμὸς μὲν ἔσται καὶ τὸ ὀδύνατον, οὐ μὴν δείκνυται τὸ προτεθέν. εἰ γὰρ τὸ Α μηδενὶ τῶι Β, τῶι δὲ Γ παντί, οὐδενὶ τῶι Β τὸ Γ. τοῦτο δ᾽ ἀδύνατον, ὥστε ψεῦδος τὸ μηδενὶ ὑπάρχειν. ἀλλ᾽ οὐκ εἰ τοῦτο ψεῦδος, τὸ παντὶ ἀληθές.	In media autem figura et postrema et hoc ostenditur. Ponatur enim A non omni B inesse, sumptum sit autem omni C inesse A ; ergo si B quidem non omni inest A, C autem omni, non omni B inest C, hoc autem impossibile. Sit enim manifestum quoniam omni B inest C, quare falsum quod suppositum est, verum est ergo omni inesse. (0699B) Si autem contrarium supponatur, syllogismus quidem erit ad impossibile, non tamen ostenditur quod propositum est. Si enim A nulli B, omni autem C, nulli B, C, hoc autem impossibile, quare falsum est, nulli inesse, sed non si hoc falsum, verum omni.	It is clear then that in the first figure all problems except the universal affirmative are proved per impossibile. But in the middle and the last figures this also is proved. Suppose that A does not belong to all B, and let it have been assumed that A belongs to all C. If then A belongs not to all B, but to all C, C will not belong to all B. But this is impossible (for suppose it to be clear that C belongs to all B): consequently the hypothesis is false. It is true then that A belongs to all B. But if the contrary is supposed, we shall have a syllogism and a result which is impossible: but the problem in hand is not proved. For if A belongs to no B, and to all C, C will belong to no B. This is impossible; so that it is false that A belongs to no B. But though this is false, it does not follow that it is true that A belongs to all B.
ὅτι δὲ τινὶ τῶι Β ὑπάρχει τὸ Α, ὑποκείσθω τὸ Α μηδενὶ τῶι Β ὑπάρχειν, τῶι δὲ Γ παντὶ ὑπαρχέτω. ἀνάγκη οὖν τὸ Γ μηδενὶ τῶι Β. ὥστ᾽ εἰ τοῦτ᾽ ἀδύνατον, ἀνάγκη τὸ Α τινὶ τῶι Β ὑπάρχειν. ἐὰν δ᾽ ὑποτεθῆι τινὶ μὴ ὑπάρχειν, ταὐτ᾽ ἔσται ἅπερ ἐπὶ τοῦ πρώτου σχήματος.	Quando autem alicui B inest A, supponatur A nulli B inesse, C autem omni insit, necesse est ergo C nulli B inesse, quare si hoc impossibile, necesse est A alicui B inesse. Si autem supponatur alicui non esse, eadem erunt quae in prima figura.	When A belongs to some B, suppose that A belongs to no B, and let A belong to all C. It is necessary then that C should belong to no B. Consequently, if this is impossible, A must belong to some B. But if it is supposed that A does not belong to some B, we shall have the same results as in the first figure.
πάλιν ὑποκείσθω τὸ Α τινὶ τῶι Β ὑπάρχειν, τῶι δὲ Γ μηδενὶ ὑπαρχέτω. ἀνάγκη οὖν τὸ Γ τινὶ τῶι Β μὴ ὑπάρχειν. ἀλλὰ παντὶ ὑπῆρχεν, ὥστε ψεῦδος τὸ ὑποτεθέν· οὐδενὶ ἄρα τῶι Β τὸ Α ὑπάρξει.	Rursum supponatur A alicui B inesse, C autem nulli insit, necesse est igitur C alicui B non inesse; sed omni inerat, quare falsum quod suppositum est, nulli ergo B inerat A.	Again suppose that A belongs to some B, and let A belong to no C. It is necessary then that C should not belong to some B. But originally it belonged to all B, consequently the hypothesis is false: A then will belong to no B.
ὅτι δ᾽ οὐ παντὶ τὸ Α τῶι Β, ὑποκείσθω παντὶ ὑπάρχειν, τῶι ↵ δὲ Γ μηδενί. ἀνάγκη οὖν τὸ Γ μηδενὶ τῶι Β ὑπάρχειν. τοῦτο δ᾽ ἀδύνατον, ὥστ᾽ ἀληθὲς τὸ μὴ παντὶ ὑπάρχειν. φανερὸν οὖν ὅτι πάντες οἱ συλλογισμοὶ γίνονται διὰ τοῦ μέσου σχήματος.	(0699C) Quando autem non omni B inest A, supponatur omni inesse: C autem nulli, necesse est ergo C nulli B inesse, hoc autem impossibile, quare verum est non omni inesse. Manifestum ergo quoniam omnes syllogismi fiunt per mediam figuram.	When A does not belong to an B, suppose it does belong to all B, and to no C. It is necessary then that C should belong to no B. But this is impossible: so that it is true that A does not belong to all B. It is clear then that all the syllogisms can be formed in the middle figure.

Chapter 13

Greek	Latin	English
	(PL 64 0699C) CAPUT XIII. De ostensione per impossibile in tertia figura.	13
62b5 Ὁμοίως δὲ καὶ διὰ τοῦ ἐσχάτου. κείσθω γὰρ τὸ Α τινὶ τῶι Β μὴ ὑπάρχειν, τὸ δὲ Γ παντί· τὸ ἄρα Α τινὶ τῶι Γ οὐχ ὑπάρχει. εἰ οὖν τοῦτ᾽ ἀδύνατον, ψεῦδος τὸ τινὶ μὴ ὑπάρχειν, ὥστ᾽ ἀληθὲς τὸ παντί. ἐὰν δ᾽ ὑποτεθῆι μηδενὶ ὑπάρχειν, συλλογισμὸς μὲν ἔσται καὶ τὸ ἀδύνατον, οὐ δείκνυται δὲ τὸ προτεθέν· ἐὰν γὰρ τὸ ἐναντίον ὑποτεθῆι, ταὐτ᾽ ἔσται ἅπερ ἐπὶ τῶν πρότερον. ἀλλὰ πρὸς τὸ τινὶ ὑπάρχειν αὕτη ληπτέα ἡ ὑπόθεσις.	Similiter autem et per ultimam. Ponatur enim A alicui B non inesse, C autem omni B, ergo A alicui C non inerit; si ergo hoc impossibile, falsum alicui non inesse, quare verum est omni. Si vero supponatur nulli inesse, syllogismus quidem erit, et impossibile, non ostendit autem quod propositum est; si enim contrarium supponatur, eadem erunt quae in prioribus.	Similarly they can all be formed in the last figure. Suppose that A does not belong to some B, but C belongs to all B: then A does not belong to some C. If then this is impossible, it is false that A does not belong to some B; so that it is true that A belongs to all B. But if it is supposed that A belongs to no B, we shall have a syllogism and a conclusion which is impossible: but the problem in hand is not proved: for if the contrary is supposed, we shall have the same results as before.
εἰ γὰρ τὸ Α μηδενὶ τῶι Β, τὸ δὲ Γ τινὶ τῶι Β, τὸ Α οὐ παντὶ τῶι Γ. εἰ οὖν τοῦτο ψεῦδος, ἀληθὲς τὸ Α τινὶ τῶι Β ὑπάρχειν. ὅτι δ᾽ οὐδενὶ τῶι Β ὑπάρχει τὸ Α, ὑποκείσθω τινὶ ὑπάρχειν, εἰλήφθω δὲ καὶ τὸ Γ παντὶ τῶι Β ὑπάρχον.	Sed ad ostendendum alicui inesse, eadem sumenda est hypothesis, nam si A nulli B, C autem alicui B, A non omni C; si ergo hoc falsum, verum est A alicui B inesse. (0699D)	But to prove that A belongs to some B, this hypothesis must be made. If A belongs to no B, and C to some B, A will belong not to all C. If then this is false, it is true that A belongs to some B.
οὐκοῦν ἀνάγκη τῶι Γ τινὶ τὸ Α ὑπάρχειν. ἀλλ᾽ οὐδενὶ ὑπῆρχεν, ὥστε ψεῦδος τὸ τινὶ τῶι Β ὑπάρχειν τὸ Α. ἐὰν δ᾽ ὑποτεθῆι παντὶ τῶι Β ὑπάρχειν τὸ Α, οὐ δείκνυται τὸ προτεθέν, ἀλλὰ πρὸς τὸ μὴ παντὶ ὑπάρχειν αὕτη ληπτέα ἡ ὑπόθεσις.	Quando autem nulli B inest A, supponatur alicui inesse, sumptum sit autem et C omni B inesse, ergo necesse est A alicui C inesse; sed nulli inerat, quare falsum est alicui B inesse A. Si autem supponatur omni B inesse A, non ostenditur propositum:	When A belongs to no B, suppose A belongs to some B, and let it have been assumed that C belongs to all B. Then it is necessary that A should belong to some C. But ex hypothesi it belongs to no C, so that it is false that A belongs to some B. But if it is supposed that A belongs to all B, the problem is not proved.
εἰ γὰρ τὸ Α παντὶ τῶι Β καὶ τὸ Γ παντὶ τῶι Β, τὸ Α ὑπάρχει τινὶ τῶι Γ. τοῦτο δὲ οὐκ ἦν, ὥστε ψεῦδος τὸ παντὶ ὑπάρχειν. εἰ δ᾽ οὕτως, ἀληθὲς τὸ μὴ παντί. ἐὰν δ᾽ ὑποτεθῆι τινὶ ὑπάρχειν, ταὐτ᾽ ἔσται ἃ καὶ ἐπὶ τῶν προειρημένων.	sed ad ostendendum non omni inesse, eadem sumenda hypothesis, nam si A omni B, et C alicui B, A inest alicui C; hoc autem non fuit, quare falsum est omni inesse, si autem sic, verum non omni. Si autem supponatur alicui inesse, eadem erunt quae et in iis quae prius dicta sunt.	But this hypothesis must be made if we are prove that A belongs not to all B. For if A belongs to all B and C to some B, then A belongs to some C. But this we assumed not to be so, so it is false that A belongs to all B. But in that case it is true that A belongs not to all B. If however it is assumed that A belongs to some B, we shall have the same result as before.
Φανερὸν οὖν ὅτι ἐν ἅπασι τοῖς διὰ τοῦ ἀδυνάτου συλλογισμοῖς τὸ ἀντικείμενον ὑποθετέον. δῆλον δὲ καὶ ὅτι ἐν τῶι μέσωι σχήματι δείκνυταί πως τὸ καταφατικὸν καὶ ἐν τῶι ἐσχάτωι τὸ καθόλου.	Manifestum ergo quoniam in omnibus per impossibile syllogismis oppositum supponendum. Palam autem et quoniam in media figura ostenditur quodammodo affirmativum, et in postrema universale.	It is clear then that in all the syllogisms which proceed per impossibile the contradictory must be assumed. And it is plain that in the middle figure an affirmative conclusion, and in the last figure a universal conclusion, are proved in a way.

Chapter 14

Greek	Latin	English
	(PL 64 0699D) CAPUT XIV. Quo rusta, et quae ad impossibile ducit demonstratio, differant.	14
62b29 Διαφέρει δ᾽ ἡ εἰς τὸ ἀδύνατον ἀπόδειξις τῆς δεικτικῆς τῶι τιθέναι ὁ βούλεται ἀναιρεῖν ἀπάγουσα εἰς ὁμολογούμε- νον ψεῦδος· ἡ δὲ δεικτικὴ ἄρχεται ἐξ ὁμολογουμένων θέσεων. λαμβάνουσι μὲν οὖν ἀμφότεραι δύο προτάσεις ὁμολογουμένας· ἀλλ᾽ ἡ μὲν ἐξ ὧν ὁ συλλογισμός, ἡ δὲ μίαν μὲν τούτων, μίαν δὲ τὴν ἀντίφασιν τοῦ συμπεράσματος. καὶ ἔνθα μὲν οὐκ ἀνάγκη γνώριμον εἶναι τὸ συμπέρασμα, οὐδὲ προϋπολαμβάνειν ὡς ἔστιν ἢ οὔ· ἔνθα δὲ ἀνάγκη ὡς οὐκ ἔστιν. διαφέρει δ᾽ οὐδὲν φάσιν ἢ ἀπόφασιν εἶναι τὸ συμπέρασμα, ἀλλ᾽ ὁμοίως ἔχει περὶ ἀμφοῖν.	(0700A) Differt autem quae ad impossibile demonstratio ab ea quae est ostensiva, eo quod ponat quod vult interimere, deducens ad confessum falsum, ostensiva autem incipit A confessis positionibus veris. Sumunt ergo utraeque duas propositiones confessas, sed haec quidem ex quibus est syllogismus, illa vero unam quidem harum, alteram vero contradictionem conclusionis. Et hinc quidem non necesse est notam esse conclusionem, neque prius opinari quoniam est, aut non est; illinc vero necesse est, quoniam non est. Differt autem nihil affirmativam, vel negativam esse conclusionem, sed similiter se habet in utrisque.	Demonstration per impossibile differs from ostensive proof in that it posits what it wishes to refute by reduction to a statement admitted to be false; whereas ostensive proof starts from admitted positions. Both, indeed, take two premisses that are admitted, but the latter takes the premisses from which the syllogism starts, the former takes one of these, along with the contradictory of the original conclusion. Also in the ostensive proof it is not necessary that the conclusion should be known, nor that one should suppose beforehand that it is true or not: in the other it is necessary to suppose beforehand that it is not true. It makes no difference whether the conclusion is affirmative or negative; the method is the same in both cases.
Ἅπαν δὲ τὸ δεικτικῶς περαινόμενον καὶ διὰ τοῦ ἀδυνάτου δειχθήσεται, καὶ τὸ διὰ τοῦ ἀδυνάτου δεικτικῶς διὰ τῶν αὐτῶν ὅρων [οὐκ ἐν τοῖς αὐτοῖς δὲ σχήμασιν]. ὅταν μὲν γὰρ ὁ συλλο↵γισμὸς ἐν τῶι πρώτωι σχήματι γένηται, τὸ ἀληθὲς ἔσται ἐν τῶι μέσωι ἢ τῶι ἐσχάτωι, τὸ μὲν στερητικὸν ἐν τῶι μέσωι, τὸ δὲ κατηγορικὸν ἐν τῶι ἐσχάτωι. ὅταν δ᾽ ἐν τῶι μέσωι ὁ συλλογισμός, τὸ ἀληθὲς ἐν τῶι πρώτωι ἐπὶ πάντων τῶν προβλημάτων. ὅταν δ᾽ ἐν τῶι ἐσχάτωι ὁ συλλογισμός, τὸ ἀληθὲς ἐν τῶι πρώτωι καὶ τῶι μέσωι, τὰ μὲν καταφατικὰ ἐν τῶι πρώτωι, τὰ δὲ στερητικὰ ἐν τῶι μέσωι.	(0700B) Omnis enim quae ostensive concluditur, et per impossibile monstrabitur, et quae per impossibile ostensive, et per eosdem terminos, non autem in eisdem figuris. Nam quando per impossibile syllogismus fit in prima figura, quod verum est in media erit, aut in postrema, privativum quidem in media, praedicativum autem in postrema. Quando autem syllogismus in media fit, quod verum est erit in prima figura in omnibus propositionibus, quando autem in postrema syllogismus, quod verum est erit in prima et in media, affirmativa quidem in prima, privativa autem in media.	Everything which is concluded ostensively can be proved per impossibile, and that which is proved per impossibile can be proved ostensively, through the same terms. Whenever the syllogism is formed in the first figure, the truth will be found in the middle or the last figure, if negative in the middle, if affirmative in the last. Whenever the syllogism is formed in the middle figure, the truth will be found in the first, whatever the problem may be. Whenever the syllogism is formed in the last figure, the truth will be found in the first and middle figures, if affirmative in first, if negative in the middle.
ἔστω γὰρ δεδειγμένον τὸ Α μηδενὶ ἢ μὴ παντὶ τῶι Β διὰ τοῦ πρώτου σχήματος. οὐκοῦν ἡ μὲν ὑπόθεσις ἦν τινὶ τῶι Β ὑπάρχειν τὸ Α, τὸ δὲ Γ ἐλαμβάνετο τῶι μὲν Α παντὶ ὑπάρχειν, τῶι δὲ Β οὐδενί· οὕτω γὰρ ἐγίνετο ὁ συλλογισμὸς καὶ τὸ ἀδύνατον. τοῦτο δὲ τὸ μέσον σχῆμα, εἰ τὸ Γ τῶι μὲν Α παντὶ τῶι δὲ Β μηδενὶ ὑπάρχει. καὶ φανερὸν ἐκ τούτων ὅτι οὐδενὶ τῶι Β ὑπάρχει τὸ Α. ὁμοίως δὲ καὶ εἰ μὴ παντὶ δέδεικται ὑπάρχον. ἡ μὲν γὰρ ὑπόθεσίς ἐστι παντὶ ὑπάρχειν, τὸ δὲ Γ ἐλαμβάνετο τῶι μὲν Α παντί, τῶι δὲ Β οὐ παντί. καὶ εἰ στερητικὸν λαμβάνοιτο τὸ Γ Α, ὡσαύτως· καὶ γὰρ οὕτω γίνεται τὸ μέσον σχῆμα.	(0700C) Sit enim ostensum A nulli aut non omni B per primam figuram, ergo hypothesis quidem erat alicui B inesse A, C autem sumebatur A quidem omni inesse, B autem nulli, sic enim fiebat syllogismus ad impossibile. Hoc autem media figura, si C A quidem omni, B autem nulli inest, et manifestum ex his quoniam B nulli inest A. Similiter autem et si non omni ostensum sit inesse, nam hypothesis quidem est omni B A inesse, C autem sumebatur A quidem omni, B autem non omni, et si privativa sit sumpta C A, similiter etenim sic fit in media figura.	Suppose that A has been proved to belong to no B, or not to all B, through the first figure. Then the hypothesis must have been that A belongs to some B, and the original premisses that C belongs to all A and to no B. For thus the syllogism was made and the impossible conclusion reached. But this is the middle figure, if C belongs to all A and to no B. And it is clear from these premisses that A belongs to no B. Similarly if has been proved not to belong to all B. For the hypothesis is that A belongs to all B; and the original premisses are that C belongs to all A but not to all B. Similarly too, if the premiss CA should be negative: for thus also we have the middle figure.
πάλιν δεδείχθω τινὶ ὑπάρχον τῶι Β τὸ Α. ἡ μὲν οὖν ὑπόθεσις μηδενὶ ὑπάρχειν, τὸ δὲ Β ἐλαμβάνετο παντὶ τῶι Γ ὑπάρχειν καὶ τὸ Α ἢ παντὶ ἢ τινὶ τῶι Γ· οὕτω γὰρ ἔσται τὸ ἀδύνατον. τοῦτο δὲ τὸ ἔσχατον σχῆμα, εἰ τὸ Α καὶ τὸ Β παντὶ τῶι Γ. καὶ φανερὸν ἐκτούτων ὅτι ἀνάγκη τὸ Α τινὶ τῶι Β ὑπάρχειν. ὁμοίως δὲκαὶ εἰ τινὶ τῶι Γ ληφθείη ὑπάρχον τὸ Β ἢ τὸ Α.	Rursum sit ostensum alicui B inesse A, ergo hypothesis quidem est nulli inesse, B autem sumebatur omni C inesse, et A vel omni vel alicui C, sic enim erit impossibile. Hoc autem postrema figura, si A et B omni C, et manifestum ex his quia necesse est A alicui B inesse, similiter autem et si alicui C sumatur inesse B vel A.	Again suppose it has been proved that A belongs to some B. The hypothesis here is that is that A belongs to no B; and the original premisses that B belongs to all C, and A either to all or to some C: for in this way we shall get what is impossible. But if A and B belong to all C, we have the last figure. And it is clear from these premisses that A must belong to some B. Similarly if B or A should be assumed to belong to some C.
Πάλιν ἐν τῶι μέσωι σχήματι δεδείχθω τὸ Α παντὶ τῶιΒ ὑπάρχον. οὐκοῦν ἡ μὲν ὑπόθεσις ἦν μὴ παντὶ τῶι Β τὸΑ ὑπάρχειν, εἴληπται δὲ τὸ Α παντὶ τῶι Γ καὶ τὸ Γ παντὶ τῶι Β· οὕτω γὰρ ἔσται τὸ ἀδύνατον. τοῦτο δὲ τὸ πρῶτονσχῆμα, τὸ Α παντὶ τῶι Γ καὶ τὸ Γ παντὶ τῶι Β. ὁμοίως δὲ καὶ εἰ τινὶ δέδεικται ὑπάρχον· ἡ μὲν γὰρ ὑπόθεσις ἦν μηδενὶ τῶι Β τὸ Α ὑπάρχειν, εἴληπται δὲ τὸ Α παντὶ τῶι Γ καὶ τὸ Γ τινὶ τῶι Β.	(0700D) Rursum in media figura ostensum sit A omni B inesse, ergo hypothesis quidem fuit, non omni B inesse A, sumptum est autem A omni C, et C omni B, sic enim erit impossibile; hoc autem prima figura, si A omni C, et C omni B. Similiter autem et si ostensum sit alicui inesse, nam hypothesis quidem fuit, nulli B inesse A, sumptum est autem A omni C, et C alicui B.	Again suppose it has been proved in the middle figure that A belongs to all B. Then the hypothesis must have been that A belongs not to all B, and the original premisses that A belongs to all C, and C to all B: for thus we shall get what is impossible. But if A belongs to all C, and C to all B, we have the first figure. Similarly if it has been proved that A belongs to some B: for the hypothesis then must have been that A belongs to no B, and the original premisses that A belongs to all C, and C to some B.
εἰ δὲ στερητικὸς ὁ συλλογισμός, ἡ μὲν ὑπόθεσις τὸ Α τινὶ τῶι Β ὑπάρχειν, εἴληπται δὲ τὸ Α μηδενὶ τῶι Γ καὶ τὸ Γ παντὶ τῶι Β, ὥστε γίνεται τὸ πρῶτον σχῆμα.	Si autem privativus fit syllogismus, hypothesis quidem A alicui B inesse, sumptum est autem A nulli C, et C omni B, quare fit prima figura.	If the syllogism is negative, the hypothesis must have been that A belongs to some B, and the original premisses that A belongs to no C, and C to all B, so that the first figure results.
καὶ εἰ μὴ καθόλου ὁ συλλογισμός, ἀλλὰ τὸ Α τινὶ τῶι Β δέδεικται μὴ ὑπάρχειν, ὡσαύτως. ὑπόθεσις μὲν γὰρ παντὶ τῶι Β τὸ Α ὑπάρχειν, εἴληπται δὲ τὸ Α μηδενὶ τῶι Γ καὶ τὸ Γ τινὶ τῶι Β· οὕτω γὰρ τὸ πρῶτον σχῆμα.	Et si non universalis sit syllogismus, sed A alicui B ostensum sit non inesse, similiter: nam hypothesis quidem omni B inesse A, sumptum est autem A nulli C, et C alicui B, sic enim prima figura.	If the syllogism is not universal, but proof has been given that A does not belong to some B, we may infer in the same way. The hypothesis is that A belongs to all B, the original premisses that A belongs to no C, and C belongs to some B: for thus we get the first figure.
Πάλιν ἐν τῶι τρίτωι σχήματι δεδείχθω τὸ Α παντὶ τῶι Β ὑπάρχειν. οὐκοῦν ἡ μὲν ὑπόθεσις ἦν μὴ παντὶ τῶι Β τὸ ↵ Α ὑπάρχειν, εἴληπται δὲ τὸ Γ παντὶ τῶι Β καὶ τὸ Α παντὶ τῶι Γ· οὕτω γὰρ ἔσται τὸ ἀδύνατον. τοῦτο δὲ τὸ πρῶτον σχῆμα. ὡσαύτως δὲ καὶ εἰ ἐπὶ τινὸς ἡ ἀπόδειξις· ἡ μὲν γὰρ ὑπόθεσις μηδενὶ τῶι Β τὸ Α ὑπάρχειν, εἴληπται δὲ τὸ Γ τινὶ τῶι Β καὶ τὸ Α παντὶ τῶι Γ. εἰ δὲ στερητικὸς ὁ συλλογισμός, ὑπόθεσις μὲν τὸ Α τινὶ τῶι Β ὑπάρχειν, εἴληπται δὲ τὸ Γ τῶι μὲν Α μηδενί, τῶι δὲ Β παντί· τοῦτο δὲ τὸ μέσον σχῆμα.	(0701A) Rursum in tertia figura ostensum sit A inesse omni B, ergo hypothesis quidem fuit non omni B inesse A, sumptum est autem C omni B, et A omni C, sic enim erit impossibile, hoc autem prima figura. Similiter autem et si in aliquo sit demonstratio, non hypothesis quidem erit nulli B inesse A, sumptum est autem C alicui B, et A omni C. Si autem privativus sit syllogismus, hypothesis quidem A alicui B inesse, sumptum est autem C A quidem nulli, B autem omni, hoc autem media figura.	Again suppose it has been proved in the third figure that A belongs to all B. Then the hypothesis must have been that A belongs not to all B, and the original premisses that C belongs to all B, and A belongs to all C; for thus we shall get what is impossible. And the original premisses form the first figure. Similarly if the demonstration establishes a particular proposition: the hypothesis then must have been that A belongs to no B, and the original premisses that C belongs to some B, and A to all C. If the syllogism is negative, the hypothesis must have been that A belongs to some B, and the original premisses that C belongs to no A and to all B, and this is the middle figure.
ὁμοίως δὲ καὶ εἰ μὴ καθόλου ἡ ἀπόδειξις. ὑπόθεσις μὲν γὰρ ἔσται παντὶ τῶι Β τὸ Α ὑπάρχειν, εἴληπται δὲ τὸ Γ τῶι μὲν Α μηδενί, τῶι δὲ Β τινί· τοῦτο δὲ τὸ μέσον σχῆμα.	Similiter autem et si non universalis sit demonstratio, nam hypothesis quidem erit omni B inesse A, sumptum est autem C A quidem nulli, B autem alicui, hoc autem media figura.	Similarly if the demonstration is not universal. The hypothesis will then be that A belongs to all B, the premisses that C belongs to no A and to some B: and this is the middle figure.
Φανερὸν οὖν ὅτι διὰ τῶν αὐτῶν ὅρων καὶ δεικτικῶς ἔστι δεικνύναι τῶν προβλημάτων ἕκαστον [καὶ διὰ τοῦ ἀδυνάτου]. ὁμοίως δ᾽ ἔσται καὶ δεικτικῶν ὄντων τῶν συλλογισμῶν εἰς ἀδύνατον ἀπάγειν ἐν τοῖς εἰλημμένοις ὅροις, ὅταν ἡ ἀντικειμένη πρότασις τῶι συμπεράσματι ληφθῆι. γίνονται γὰρ οἱ αὐτοὶ συλλογισμοὶ τοῖς διὰ τῆς ἀντιστροφῆς, ὥστ᾽ εὐθὺς ἔχομεν καὶ τὰ σχήματα δι᾽ ὧν ἕκαστον ἔσται. δῆλον οὖν ὅτι πᾶν πρόβλημα δείκνυται κατ᾽ ἀμφοτέρους τοὺς τρόπους, διά τε τοῦ ἀδυνάτου καὶ δεικτικῶς, καὶ οὐκ ἐνδέχεται χωρίζεσθαι τὸν ἕτερον.	Manifestum ergo quoniam per eosdem terminos et ostensive est demonstrare unumquodque propositum, et per impossibile. (0701B) Similiter autem erit, et cum sint ostensivi syllogismi, ad impossibile deducere in terminis sumptis, quando opposita propositio conclusioni sumpta fuerit, nam fiunt iidem syllogismi iis qui sunt per conversionem, quare statim habemus et figuras per quas unumquodque erit. Palam ergo quoniam omne propositum ostenditur per utrosque modos et per impossibile et ostensive, et non contingit separari alterum ab altero.	It is clear then that it is possible through the same terms to prove each of the problems ostensively as well. Similarly it will be possible if the syllogisms are ostensive to reduce them ad impossibile in the terms which have been taken, whenever the contradictory of the conclusion of the ostensive syllogism is taken as a premiss. For the syllogisms become identical with those which are obtained by means of conversion, so that we obtain immediately the figures through which each problem will be solved. It is clear then that every thesis can be proved in both ways, i.e. per impossibile and ostensively, and it is not possible to separate one method from the other.

Chapter 15

Greek	Latin	English
	(PL 64 0701B) CAPUT XV. De ratiocinatione ex oppositis.	15
63b22 Ἐν ποίωι δὲ σχήματι ἔστιν ἐξ ἀντικειμένων προτάσεων συλλογίσασθαι καὶ ἐν ποίωι οὐκ ἔστιν, ὧδ᾽ ἔσται φανερόν. λέγω δ᾽ ἀντικειμένας εἶναι προτάσεις κατὰ μὲν τὴν λέξιν τέτταρας, οἷον τὸ παντὶ τῶι οὐδενί, καὶ τὸ παντὶ τῶι οὐ παντί, καὶ τὸ τινὶ τῶι οὐδενί, καὶ τὸ τινὶ τῶι οὐ τινί, κατ᾽ ἀλήθειαν δὲ τρεῖς· τὸ γὰρ τινὶ τῶι οὐ τινὶ κατὰ τὴν λέξιν ἀντίκειται μόνον. τούτων δ᾽ ἐναντίας μὲν τὰς καθόλου, τὸ παντὶ τῶι μηδενὶ ὑπάρχειν, οἷον τὸ πᾶσαν ἐπιστήμην εἶναι σπουδαίαν τῶι μηδεμίαν εἶναι σπουδαίαν, τὰς δ᾽ ἄλλας ἀντικειμένας.	In qua autem figura est ex oppositis propositionibus syllogizare, et in qua non est, sic erit manifestum. (0701C) Dico autem oppositas esse propositiones, secundum locutionem quidem quatuor, ut omni et nulli, et omni et non omni, et alicui et nulli, et alicui et non alicui inesse; secundum veritatem autem tres, nam alicui et non alicui secundum locutionem opponuntur solum; harum autem contrarias quidem universales, omni nulli inesse, ut omnem disciplinam esse studiosam, nullam esse studiosam, alias vero oppositas.	In what figure it is possible to draw a conclusion from premisses which are opposed, and in what figure this is not possible, will be made clear in this way. Verbally four kinds of opposition are possible, viz. universal affirmative to universal negative, universal affirmative to particular negative, particular affirmative to universal negative, and particular affirmative to particular negative: but really there are only three: for the particular affirmative is only verbally opposed to the particular negative. Of the genuine opposites I call those which are universal contraries, the universal affirmative and the universal negative, e.g. ‘every science is good’, ‘no science is good’; the others I call contradictories.
Ἐν μὲν οὖν τῶι πρώτωι σχήματι οὐκ ἔστιν ἐξ ἀντικειμένων προτάσεων συλλογισμός, οὔτε καταφατικὸς οὔτε ἀποφατικός, καταφατικὸς μὲν ὅτι ἀμφοτέρας δεῖ καταφατικὰς εἶναι τὰς προτάσεις, αἱ δ᾽ ἀντικείμεναι φάσις καὶ ἀπόφασις, στερητικὸς δὲ ὅτι αἱ μὲν ἀντικείμεναι τὸ αὐτὸ τοῦ αὐτοῦ κατηγοροῦσι καὶ ἀπαρνοῦνται, τὸ δ᾽ ἐν τῶι πρώτωι μέσον οὐ λέγεται κατ᾽ ἀμφοῖν, ἀλλ᾽ ἐκείνου μὲν ἄλλο ἀπαρνεῖται, αὐτὸ δὲ ἄλλου κατηγορεῖται· αὗται δ᾽ οὐκ ἀντίκεινται.	In prima igitur figura non est ex oppositis propositionibus syllogismus, neque affirmativus, neque negativus; affirmativus quidem, quoniam oportet utrasque affirmativas esse propositiones, oppositae autem affirmatio et negatio; privativus autem, quoniam oppositae quidem idem de eodem praedicant et negant, in prima autem medium non dicitur de utrisque, sed de illo quidem aliud negatur, idem autem de alio praedicatur, hae vero non opponuntur.	In the first figure no syllogism whether affirmative or negative can be made out of opposed premisses: no affirmative syllogism is possible because both premisses must be affirmative, but opposites are, the one affirmative, the other negative: no negative syllogism is possible because opposites affirm and deny the same predicate of the same subject, and the middle term in the first figure is not predicated of both extremes, but one thing is denied of it, and it is affirmed of something else: but such premisses are not opposed.
	(PL 64 0701C) CAPUT XVI. De ratiocinatione ex oppositis in secunda figura.
Ἐν δὲ τῶι μέσωι σχήματι καὶ ἐκ τῶν ἀντικειμένων καὶ ἐκ τῶν ἐναντίων ἐνδέχεται γίγνεσθαι συλλογισμόν. ἔστω γὰρ ↵ ἀγαθὸν μὲν ἐφ᾽ οὗ Α, ἐπιστήμη δὲ ἐφ᾽ οὗ Β καὶ Γ. εἰ δὴ πᾶσαν ἐπιστήμην σπουδαίαν ἔλαβε καὶ μηδεμίαν, τὸ Α τῶι Β παντὶ ὑπάρχει καὶ τῶι Γ οὐδενί, ὥστε τὸ Β τῶι Γ οὐδενί· οὐδεμία ἄρα ἐπιστήμη ἐπιστήμη ἐστίν. ὁμοίως δὲ καὶ εἰ πᾶσαν λαβὼν σπουδαίαν τὴν ἰατρικὴν μὴ σπουδαίαν ἔλαβε· τῶι μὲν γὰρ Β παντὶ τὸ Α, τῶι δὲ Γ οὐδενί, ὥστε ἡ τὶς ἐπιστήμη οὐκ ἔσται ἐπιστήμη. καὶ εἰ τῶι μὲν Γ παντὶ τὸ Α, τῶι δὲ Β μηδενί, ἔστι δὲ τὸ μὲν Β ἐπιστήμη, τὸ δὲ Γ ἰατρική, τὸ δὲ Α ὑπόληψις· οὐδεμίαν γὰρ ἐπιστήμην ὑπόληψιν λαβὼν εἴληφε τινὰ εἶναι ὑπόληψιν.	(0701D) In media autem figura, et ex oppositis, et ex contrariis contingit fieri syllogismum. Sit enim bonum quidem in quo A, disciplina autem in quo B et C; si ergo omnem disciplinam studiosam sumpsit, et nullam, A inest omni B, et nulli C, quare B nulli C, nulla ergo disciplina disciplina est. Similiter autem et si omnem sumens studiosam disciplinam, medicinam vero non studiosam sumpsit, nam A B quidem omni, C autem nulli, quare aliqua disciplina non erit disciplina. Et si A C quidem omni, B autem nulli, est autem B quidem disciplina, C autem medicina, A vero opinio, nullam enim disciplinam opinionem sumens, sumpsit aliquam disciplinam esse opinionem.	In the middle figure a syllogism can be made both oLcontradictories and of contraries. Let A stand for good, let B and C stand for science. If then one assumes that every science is good, and no science is good, A belongs to all B and to no C, so that B belongs to no C: no science then is a science. Similarly if after taking ‘every science is good’ one took ‘the science of medicine is not good’; for A belongs to all B but to no C, so that a particular science will not be a science. Again, a particular science will not be a science if A belongs to all C but to no B, and B is science, C medicine, and A supposition: for after taking ‘no science is supposition’, one has assumed that a particular science is supposition.
διαφέρει δὲ τοῦ πάλαι τῶι ἐπὶ τῶν ὅρων ἀντιστρέφεσθαι· πρότερον μὲν γὰρ πρὸς τῶι Β, νῦν δὲ πρὸς τῶι Γ τὸ καταφατικόν. καὶ ἂν ἦι δὲ μὴ καθόλου ἡ ἑτέρα πρότασις, ὡσαύτως· ἀεὶ γὰρ τὸ μέσον ἐστὶν ὁ ἀπὸ θατέρου μὲν ἀποφατικῶς λέγεται, κατὰ θατέρου δὲ καταφατικῶς. ὥστ᾽ ἐνδέχεται τἀντικείμενα περαίνεσθαι, πλὴν οὐκ ἀεὶ οὐδὲ πάντως, ἀλλ᾽ ἐὰν οὕτως ἔχηι τὰ ὑπὸ τὸ μέσον ὥστ᾽ ἢ ταὐτὰ εἶναι ἢ ὅλον πρὸς μέρος. ἄλλως δ᾽ ἀδύνατον· οὐ γὰρ ἔσονται οὐδαμῶς αἱ προτάσεις οὔτ᾽ ἐναντίαι οὔτ᾽ ἀντικείμεναι.	(0702A) Differt autem A priore in terminis converti, nam prius quidem ad B, nunc autem ad C affirmativum. Et si sit non universalis altera propositio, similiter; semper enim medium est, quod ab altero quidem negative dicitur, de altero vero affirmative. Quare contingit opposita quidem perfici, non autem semper, neque omnino, sed sic se habeant, quae sunt sub medio, ut vel eadem sint, vel totum ad partem; aliter autem impossibile, non enim erunt propositiones ullo modo, neque contrariae, neque oppositae.	This syllogism differs from the preceding because the relations between the terms are reversed: before, the affirmative statement concerned B, now it concerns C. Similarly if one premiss is not universal: for the middle term is always that which is stated negatively of one extreme, and affirmatively of the other. Consequently it is possible that contradictories may lead to a conclusion, though not always or in every mood, but only if the terms subordinate to the middle are such that they are either identical or related as whole to part. Otherwise it is impossible: for the premisses cannot anyhow be either contraries or contradictories.
	(PL 64 0702A) CAPUT XVII. De syllogismo ex oppositis in tertia figura.
Ἐν δὲ τῶι τρίτωι σχήματι καταφατικὸς μὲν συλλογισμὸς οὐδέποτ᾽ ἔσται ἐξ ἀντικειμένων προτάσεων διὰ τὴν εἰρημένην αἰτίαν καὶ ἐπὶ τοῦ πρώτου σχήματος, ἀποφατικὸς δ᾽ ἔσται, καὶ καθόλου καὶ μὴ καθόλου τῶν ὅρων ὄντων. ἔστω γὰρ ἐπιστήμη ἐφ᾽ οὗ τὸ Β καὶ Γ, ἰατρικὴ δ᾽ ἐφ᾽ οὗ Α. εἰ οὖν λάβοι πᾶσαν ἰατρικὴν ἐπιστήμην καὶ μηδεμίαν ἰατρικὴν ἐπιστήμην, τὸ Β παντὶ τῶι Α εἴληφε καὶ τὸ Γ οὐδενί, ὥστ᾽ ἔσται τις ἐπιστήμη οὐκ ἐπιστήμη. ὁμοίως δὲ καὶ ἂν μὴ καθόλου ληφθῆι ἡ Β Α πρότασις· εἰ γάρ ἐστί τις ἰατρικὴ ἐπιστήμη καὶ πάλιν μηδεμία ἰατρικὴ ἐπιστήμη, συμβαίνει ἐπιστήμην τινὰ μὴ εἶναι ἐπιστήμην. εἰσὶ δὲ καθόλου μὲν τῶν ὅρων λαμβανομένων ἐναντίαι αἱ προτάσεις, ἐὰν δ᾽ ἐν μέρει ἅτερος, ἀντικείμεναι.	In tertia vero figura affirmativus quidem syllogismus nunquam erit ex oppositis propositionibus propter causam dictam, et in prima figura. (0702B) Negativus autem erit syllogismus, et universalibus, et non universalibus terminis. Sit enim disciplina in quo B et C, medicina autem in quo A; si ergo sumat omnem medicinam disciplinam, et nullam medicinam disciplinam, B omni A sumpsit, et C nulli A, quare erit aliqua disciplina non disciplina. Similiter autem et si non universaliter sumpta sit A B propositio, nam si est aliqua medicina disciplina, et rursum nulla medicina disciplina, accidit disciplinam aliquam non esse disciplinam. Sunt autem universaliter quidem sumptis terminis contrariae propositiones, si autem particularis altera sit, oppositae.	In the third figure an affirmative syllogism can never be made out of opposite premisses, for the reason given in reference to the first figure; but a negative syllogism is possible whether the terms are universal or not. Let B and C stand for science, A for medicine. If then one should assume that all medicine is science and that no medicine is science, he has assumed that B belongs to all A and C to no A, so that a particular science will not be a science. Similarly if the premiss BA is not assumed universally. For if some medicine is science and again no medicine is science, it results that some science is not science, The premisses are contrary if the terms are taken universally; if one is particular, they are contradictory.
Δεῖ δὲ κατανοεῖν ὅτι ἐνδέχεται μὲν οὕτω τὰ ἀντικείμενα λαμβάνειν ὥσπερ εἴπομεν πᾶσαν ἐπιστήμην σπουδαίαν εἶναι καὶ πάλιν μηδεμίαν, ἢ τινὰ μὴ σπουδαίαν· ὅπερ οὐκ εἴωθε λανθάνειν. ἔστι δὲ δι᾽ ἄλλων ἐρωτημάτων συλλογίσασθαι θάτερον, ἢ ὡς ἐν τοῖς Τοπικοῖς ἐλέχθη λαβεῖν.	(0702C) Oportet autem scire quoniam contingit opposita sic sumere quemadmodum diximus, omnem disciplinam studiosam esse, et rursum nullam aut aliquam non esse studiosam, quod non solet latere; erit autem per alias interrogationes syllogizare alteram, et quemadmodum in Topicis dictum est, sumere.	We must recognize that it is possible to take opposites in the way we said, viz. ‘all science is good’ and ‘no science is good’ or ‘some science is not good’. This does not usually escape notice. But it is possible to establish one part of a contradiction through other premisses, or to assume it in the way suggested in the Topics.
ἐπεὶ δὲ τῶν καταφάσεων αἱ ἀντιθέσεις τρεῖς, ἑξαχῶς συμβαίνει τὰ ἀντικείμενα λαμβάνειν, ἢ παντὶ καὶ μηδενί, ἢ παντὶ καὶ μὴ παντί, ἢ τινὶ καὶ μηδενί, καὶ τοῦτο ἀντιστρέψαι ἐπὶ ↵ τῶν ὅρων, οἷον τὸ Α παντὶ τῶι Β, τῶι δὲ Γ μηδενί, ἢ τῶι Γ παντί, τῶι δὲ Β μηδενί, ἢ τῶι μὲν παντί, τῶι δὲ μὴ παντί, καὶ πάλιν τοῦτο ἀντιστρέψαι κατὰ τοὺς ὅρους. ὁμοίως δὲ καὶ ἐπὶ τοῦ τρίτου σχήματος. ὥστε φανερὸν ὁσαχῶς τε καὶ ἐν ποίοις σχήμασιν ἐνδέχεται διὰ τῶν ἀντικειμένων προτάσεων γενέσθαι συλλογισμόν.	Quoniam autem affirmationum oppositiones sunt tres, sexies accidit opposita sumere, aut omni et nulli, aut omni et non omni, aut alicui et nulli; et hoc converti in terminis, ut A omni B et nulli C, aut omni C et nulli B, aut huic quidem omni, illi vero non omni, et rursum hoc converti secundum terminos; similiter autem et in tertia figura. Quare manifestum est et quoties et in quibus figuris contingit per oppositas propositiones fieri syllogismum.	Since there are three oppositions to affirmative statements, it follows that opposite statements may be assumed as premisses in six ways; we may have either universal affirmative and negative, or universal affirmative and particular negative, or particular affirmative and universal negative, and the relations between the terms may be reversed; e.g. A may belong to all B and to no C, or to all C and to no B, or to all of the one, not to all of the other; here too the relation between the terms may be reversed. Similarly in the third figure. So it is clear in how many ways and in what figures a syllogism can be made by means of premisses which are opposed.
Φανερὸν δὲ καὶ ὅτι ἐκ ψευδῶν μὲν ἔστιν ἀληθὲς συλλογίσασθαι, καθάπερ εἴρηται πρότερον, ἐκ δὲ τῶν ἀντικειμέ- νων οὐκ ἔστιν· ἀεὶ γὰρ ἐναντίος ὁ συλλογισμὸς γίνεται τῶι πράγματι, οἷον εἰ ἔστιν ἀγαθόν, μὴ εἶναι ἀγαθόν, ἢ εἰ ζῶιον, μὴ ζῶιον, διὰ τὸ ἐξ ἀντιφάσεως εἶναι τὸν συλλογισμὸν καὶ τοὺς ὑποκειμένους ὅρους ἢ τοὺς αὐτοὺς εἶναι ἢ τὸν μὲν ὅλον τὸν δὲ μέρος. δῆλον δὲ καὶ ὅτι ἐν τοῖς παραλογισμοῖς οὐδὲν κωλύει γίνεσθαι τῆς ὑποθέσεως ἀντίφασιν, οἷον εἰ ἔστι περιττόν, μὴ εἶναι περιττόν. ἐκ γὰρ τῶν ἀντικειμένων προτάσεων ἐναντίος ἦν ὁ συλλογισμός· ἐὰν οὖν λάβηι τοιαύτας, ἔσται τῆς ὑποθέσεως ἀντίφασις,	(0702D) Manifestum est quoniam ex falsis est verum syllogizare, quemadmodum dictum est prius; ex oppositis autem non est, semper enim contrarius syllogismus fit rei (ut si est bonum non esse bonum, aut si animal non animal) eo quod ex contradictione est syllogismus, et subiecti termini aut iidem sunt, aut hic quidem totum, ille autem pars. Palam autem quoniam in paralogismis nihil prohibet fieri hypotheseos contradictionem, ut si est impar non esse impar, nam ex oppositis propositionibus contrarius erit syllogismus; si ergo sumpserit hoc modo, hypotheseos erit contradictio.	It is clear too that from false premisses it is possible to draw a true conclusion, as has been said before, but it is not possible if the premisses are opposed. For the syllogism is always contrary to the fact, e.g. if a thing is good, it is proved that it is not good, if an animal, that it is not an animal because the syllogism springs out of a contradiction and the terms presupposed are either identical or related as whole and part. It is evident also that in fallacious reasonings nothing prevents a contradiction to the hypothesis from resulting, e.g. if something is odd, it is not odd. For the syllogism owed its contrariety to its contradictory premisses; if we assume such premisses we shall get a result that contradicts our hypothesis.
δεῖ δὲ κατανοεῖν ὅτι οὕτω μὲν οὐκ ἔστιν ἐναντία συμπεράνασθαι ἐξ ἑνὸς συλλογισμοῦ ὥστ᾽ εἶναι τὸ συμπέρασμα τὸ μὴ ὂν ἀγαθὸν ἀγαθὸν ἢ ἄλλο τι τοιοῦτον, ἐὰν μὴ εὐθὺς ἡ πρότασις τοιαύτη ληφθῆι (οἷον πᾶν ζῶιον λευκὸν εἶναι καὶ μὴ λευκόν, τὸν δ᾽ ἄνθρωπον ζῶιον), ἀλλ᾽ ἢ προσλαβεῖν δεῖ τὴν ἀντίφασιν (οἷον ὅτι πᾶσα ἐπιστήμη ὑπόληψις [καὶ οὐχ ὑπόληψισ], εἶτα λαβεῖν ὅτι ἡ ἰατρικὴ ἐπιστήμη μέν ἐστιν, οὐδεμία δ᾽ ὑπόληψις, ὥσπερ οἱ ἔλεγχοι γίνονται), ἢ ἐκ δύο συλλογισμῶν. ὥστε δ᾽ εἶναι ἐναντία κατ᾽ ἀλήθειαν τὰ εἰλημμένα, οὐκ ἔστιν ἄλλον τρόπον ἢ τοῦτον, καθάπερ εἴρηται πρότερον.	(0703A) Oportet autem considerare quoniam sic quidem non est contraria concludere ex uno syllogismo (ut sit conclusio quoniam non est bonum, bonum aut aliud quiddam tale), nisi statim huiusmodi propositio sumatur, ut omne animal esse album et non album, hominem autem animal, sed vel assumere oportet contradictionem, ut quoniam omnis disciplina opinio et non opinio, deinde sumere quoniam medicina disciplina quidem est. , nulla autem opinio, quemadmodum redargutiones fiunt, vel ex duobus syllogismis. Quare esse quidem contraria secundum veritatem quae sumpta sunt, non est alio modo quam hoc quemadmodum dictum est prius.	But we must recognize that contraries cannot be inferred from a single syllogism in such a way that we conclude that what is not good is good, or anything of that sort unless a self-contradictory premiss is at once assumed, e.g. ‘every animal is white and not white’, and we proceed ‘man is an animal’. Either we must introduce the contradiction by an additional assumption, assuming, e.g., that every science is supposition, and then assuming ‘Medicine is a science, but none of it is supposition’ (which is the mode in which refutations are made), or we must argue from two syllogisms. In no other way than this, as was said before, is it possible that the premisses should be really contrary.

Chapter 16

Greek	Latin	English
	(PL 64 0703A) CAPUT XVIII. De petitione principii.	16
64b28 Τὸ δ᾽ ἐν ἀρχῆι αἰτεῖσθαι καὶ λαμβάνειν ἐστὶ μέν, ὡς ἐν γένει λαβεῖν, ἐν τῶι μὴ ἀποδεικνύναι τὸ προκείμενον, τοῦτο δὲ συμβαίνει πολλαχῶς· καὶ γὰρ εἰ ὅλως μὴ συλλογίζεται, καὶ εἰ δι᾽ ἀγνωστοτέρων ἢ ὁμοίως ἀγνώστων, καὶ εἰ διὰ τῶν ὑστέρων τὸ πρότερον· ἡ γὰρ ἀπόδειξις ἐκ πιστοτέρων τε καὶ προτέρων ἐστίν. τούτων μὲν οὖν οὐδέν ἐστι τὸ αἰτεῖσθαι τὸ ἐξ ἀρχῆς· ἀλλ᾽ ἐπεὶ τὰ μὲν δι᾽ αὑτῶν πέφυκε γνωρίζεσθαι τὰ δὲ δι᾽ ἄλλων (αἱ μὲν γὰρ ἀρχαὶ δι᾽ αὑτῶν, τὰ δ᾽ ὑπὸ τὰς ἀρχὰς δι᾽ ἄλλων), ὅταν μὴ τὸ δι᾽ αὑτοῦ γνωστὸν δι᾽ αὑτοῦ τις ἐπιχειρῆι δεικνύναι, τότ᾽ αἰτεῖται τὸ ἐξ ἀρχῆς.	In principio autem petere et accipere est quidem, ut in genere, sumere in eo quod non est demonstrare propositum. Hoc autem accidit multipliciter, nam et si omnino non syllogizatur, et si per ignotiora aut similiter ignota, et si per posteriora quod prius est, demonstratio enim ex prioribus et notioribus est. (0703B) Horum ergo nullum est petere quod ex principio est, sed quia haec quidem nata sunt per se cognosci, illa vero per alia (nam principia quidem per se, quae autem sub principiis, per alia), quando quod non per se notum est, per se aliquis conatur ostendere, tunc petit quod ex principio est.	To beg and assume the original question is a species of failure to demonstrate the problem proposed; but this happens in many ways. A man may not reason syllogistically at all, or he may argue from premisses which are less known or equally unknown, or he may establish the antecedent by means of its consequents; for demonstration proceeds from what is more certain and is prior. Now begging the question is none of these: but since we get to know some things naturally through themselves, and other things by means of something else (the first principles through themselves, what is subordinate to them through something else), whenever a man tries to prove what is not self-evident by means of itself, then he begs the original question.
τοῦτο δ᾽ ἔστι μὲν οὕτω ποιεῖν ὥστ᾽ εὐθὺς ἀξιῶσαι τὸ προκείμενον, ἐνδέχεται δὲ καὶ μεταβάντας ἐπ᾽ ἄλλα ἄττα τῶν πεφυκότων δι᾽ ἐκείνου δείκνυσθαι διὰ τούτων ↵ ἀποδεικνύναι τὸ ἐξ ἀρχῆς, οἷον εἰ τὸ Α δεικνύοιτο διὰ τοῦ Β, τὸ δὲ Β διὰ τοῦ Γ, τὸ δὲ Γ πεφυκὸς εἴη δείκνυσθαι διὰ τοῦ Α· συμβαίνει γὰρ αὐτὸ δι᾽ αὑτοῦ τὸ Α δεικνύναι τοὺς οὕτω συλλογιζομένους. ὅπερ ποιοῦσιν οἱ τὰς παραλλήλους οἰόμενοι γράφειν· λανθάνουσι γὰρ αὐτοὶ ἑαυτοὺς τοιαῦτα λαμβάνοντες ἃ οὐχ οἷόν τε ἀποδεῖξαι μὴ οὐσῶν τῶν παραλλήλων. ὥστε συμβαίνει τοῖς οὕτω συλλογιζομένοις ἕκαστον εἶναι λέγειν, εἰ ἔστιν ἕκαστον· οὕτω δ᾽ ἅπαν ἔσται δι᾽ αὑτοῦ γνωστόν· ὅπερ ἀδύνατον.	Hoc autem est sic facere quidem ut statim postulet id quod propositum est: contingit autem et transgredientes et ad alia eorum quae nata sunt per illa ostendi per haec monstrare quod ex principio est, ut si A ostendatur per B, et B per C, C autem natum sit ostendi per A, accidit enim idem A per se demonstrare eos qui sic syllogizant, quod faciunt qui parallelas arbitrantur scribere, latent enim ipsi seipsos talia sumentes quae non valent demonstrare, cum non sint parallelae. (0703C) Quare accidit sic syllogizantibus unumquodque esse dicere si est unumquodque, sic autem omne erit per se notum, quod est impossibile.	This may be done by assuming what is in question at once; it is also possible to make a transition to other things which would naturally be proved through the thesis proposed, and demonstrate it through them, e.g. if A should be proved through B, and B through C, though it was natural that C should be proved through A: for it turns out that those who reason thus are proving A by means of itself. This is what those persons do who suppose that they are constructing parallel straight lines: for they fail to see that they are assuming facts which it is impossible to demonstrate unless the parallels exist. So it turns out that those who reason thus merely say a particular thing is, if it is: in this way everything will be self-evident. But that is impossible.
Εἰ οὖν τις ἀδήλου ὄντος ὅτι τὸ Α ὑπάρχει τῶι Γ, ὁμοίως δὲ καὶ ὅτι τῶι Β, αἰτοῖτο τῶι Β ὑπάρχειν τὸ Α, οὔπω δῆλον εἰ τὸ ἐν ἀρχῆι αἰτεῖται, ἀλλ᾽ ὅτι οὐκ ἀποδείκνυσι, δῆλον· οὐ γὰρ ἀρχὴ ἀποδείξεως τὸ ὁμοίως ἄδηλον. εἰ μέντοι τὸ Β πρὸς τὸ Γ οὕτως ἔχει ὥστε ταὐτὸν εἶναι, ἢ δῆλον ὅτι ἀντιστρέφουσιν, ἢ ἐνυπάρχει θάτερον θατέρωι, τὸ ἐν ἀρχῆι αἰτεῖται. καὶ γὰρ ἂν ὅτι τῶι Β τὸ Α ὑπάρχει δι᾽ ἐκείνων δεικνύοι, εἰ ἀντιστρέφοι (νῦν δὲ τοῦτο κωλύει, ἀλλ᾽ οὐχ ὁ τρόποσ). εἰ δὲ τοῦτο ποιοῖ, τὸ εἰρημένον ἂν ποιοῖ καὶ ἀντιστρέφοι διὰ τριῶν.	Si ergo aliquis dubitat assumpto dubio quoniam A inest C, similiter et quoniam B, petat autem i inesse B, nondum manifestum si quod in principio est petat, sed quoniam non demonstravit manifestum, non enim est principium demonstrationis, quod similiter est incertum. Si autem B ad C sic se habet ut idem sit, aut manifestum quod convertuntur, aut inest alterum alteri, quod in principio est petit, nam et quoniam A inest B, per illa monstrabit si convertantur, nunc autem hoc prohibet, sed non modus. (0703D) Si autem hoc faciat, quod dictum est faciet, et convertet per tria,	If then it is uncertain whether A belongs to C, and also whether A belongs to B, and if one should assume that A does belong to B, it is not yet clear whether he begs the original question, but it is evident that he is not demonstrating: for what is as uncertain as the question to be answered cannot be a principle of a demonstration. If however B is so related to C that they are identical, or if they are plainly convertible, or the one belongs to the other, the original question is begged. For one might equally well prove that A belongs to B through those terms if they are convertible. But if they are not convertible, it is the fact that they are not that prevents such a demonstration, not the method of demonstrating. But if one were to make the conversion, then he would be doing what we have described and effecting a reciprocal proof with three propositions.
ὡσαύτως δὲ κἂν εἰ τὸ Β τῶι Γ λαμβάνοι ὑπάρχειν, ὁμοίως ἄδηλον ὂν καὶ εἰ τὸ Α, οὔπω τὸ ἐξ ἀρχῆς, ἀλλ᾽ οὐκ ἀποδείκνυσιν. ἐὰν δὲ ταὐτὸν ἦι τὸ Α καὶ Β ἢ τῶι ἀντιστρέφειν ἢ τῶι ἕπεσθαι τῶι Β τὸ Α, τὸ ἐξ ἀρχῆς αἰτεῖται διὰ τὴν αὐτὴν αἰτίαν· τὸ γὰρ ἐξ ἀρχῆς τί δύναται, εἴρηται ἡμῖν, ὅτι τὸ δι᾽ αὑτοῦ δεικνύναι τὸ μὴ δι᾽ αὑτοῦ δῆλον.	similiter autem et si B sumat inesse C, quod similiter incertum sit, ut et si A inest C, nondum quod ex principio petit, sed neque demonstrat. Si autem idem sit A et B, aut eo quod convertuntur, aut eo quod A sequitur ei quod est B, quod ex principio est petit propter eamdem causam, nam ex principio quod valet, prius dictum est A nobis, quoniam per se monstrabitur quod non est per se manifestum.	Similarly if he should assume that B belongs to C, this being as uncertain as the question whether A belongs to C, the question is not yet begged, but no demonstration is made. If however A and B are identical either because they are convertible or because A follows B, then the question is begged for the same reason as before. For we have explained the meaning of begging the question, viz. proving that which is not self-evident by means of itself.
Εἰ οὖν ἐστι τὸ ἐν ἀρχῆι αἰτεῖσθαι τὸ δι᾽ αὑτοῦ δεικνύναι τὸ μὴ δι᾽ αὑτοῦ δῆλον, τοῦτο δ᾽ ἐστὶ τὸ μὴ δεικνύναι, ὅταν ὁμοίως ἀδήλων ὄντων τοῦ δεικνυμένου καὶ δι᾽ οὗ δείκνυσιν ἢ τῶι ταὐτὰ τῶι αὐτῶι ἢ τῶι ταὐτὸν τοῖς αὐτοῖς ὑπάρχειν, ἐν μὲν τῶι μέσωι σχήματι καὶ τρίτωι ἀμφοτέρως ἂν ἐνδέχοιτο τὸ ἐν ἀρχῆι αἰτεῖσθαι, ἐν δὲ κατηγορικῶι συλλογισμῶι ἔν τε τῶι τρίτωι καὶ τῶι πρώτωι.	(0704A) Si ergo est in principio petere per se monstrare quod non per se est manifestum, hoc autem est non ostendere quando similiter dubitantur quod monstratur et per quod monstratur, vel eo quod eadem eidem, vel eo quod idem eisdem inesse sumitur, in media quidem figura et tertia utrorumque continget similiter quod est in principio petere, in praedicativo quidem syllogismo et in tertia figura, et in prima,	If then begging the question is proving what is not self-evident by means of itself, in other words failing to prove when the failure is due to the thesis to be proved and the premiss through which it is proved being equally uncertain, either because predicates which are identical belong to the same subject, or because the same predicate belongs to subjects which are identical, the question may be begged in the middle and third figures in both ways, though, if the syllogism is affirmative, only in the third and first figures.
ὅταν δ᾽ ἀποφατικῶς, ὅταν τὰ αὐτὰ ἀπὸ τοῦ αὐτοῦ· καὶ οὐχ ὁμοίως ἀμφότεραι αἱ προτάσεις (ὡσαύτως δὲ καὶ ἐν τῶι μέσωι), διὰ τὸ μὴ ἀντιστρέφειν τοὺς ὅρους κατὰ τοὺς ἀποφατικοὺς συλλογισμούς.	negative autem quando eadem ab eodem, et non similiter utraeque propositiones, similiter autem et in media, eo quod non convertuntur termini secundum negativos syllogismos.	If the syllogism is negative, the question is begged when identical predicates are denied of the same subject; and both premisses do not beg the question indifferently (in a similar way the question may be begged in the middle figure), because the terms in negative syllogisms are not convertible.
ἔστι δὲ τὸ ἐν ἀρχῆι αἰτεῖσθαι ἐν μὲν ταῖς ἀποδείξεσι τὰ κατ᾽ ἀλήθειαν οὕτως ἔχοντα, ἐν δὲ τοῖς διαλεκτικοῖς τὰ κατὰ δόξαν.	Est autem in principio petere in demonstrationibus quidem quae secundum veritatem sic se habent, in dialecticis autem, quae secundum opinionem.	In scientific demonstrations the question is begged when the terms are really related in the manner described, in dialectical arguments when they are according to common opinion so related.

Chapter 17

Greek	Latin	English
	(PL 64 0704A) CAPUT XIX. De non propter hoc accidere falsum.	17
65a38 Τὸ δὲ μὴ παρὰ τοῦτο συμβαίνειν τὸ ψεῦδος, ὁ πολλάκις ἐν τοῖς λόγοις εἰώθαμεν λέγειν, πρῶτον μέν ἐστιν ἐν τοῖς εἰς τὸ ἀδύνατον συλλογισμοῖς, ὅταν πρὸς ἀντίφασιν ἦι ↵ τούτου ὁ ἐδείκνυτο τῆι εἰς τὸ ἀδύνατον. οὔτε γὰρ μὴ ἀντιφήσας ἐρεῖ τὸ οὐ παρὰ τοῦτο, ἀλλ᾽ ὅτι ψεῦδός τι ἐτέθη τῶν πρότερον, οὔτ᾽ ἐν τῆι δεικνυούσηι· οὐ γὰρ τίθησι ὁ ἀντίφησιν.	Non propter hoc autem accidere falsum (quod saepe in disputationibus solemus dicere) primum quidem est in iis qui ad impossibile syllogismis, quando ad contradictionem est huius quod monstratum est ea quae ad impossibile. (0704B) Nam neque qui non contradicit dicit non propter hoc, sed quoniam falsum est aliquid positum priorum, neque in ostensiva, non enim ponit quod contradicit.	The objection that ‘this is not the reason why the result is false’, which we frequently make in argument, is made primarily in the case of a reductio ad impossibile, to rebut the proposition which was being proved by the reduction. For unless a man has contradicted this proposition he will not say, ‘False cause’, but urge that something false has been assumed in the earlier parts of the argument; nor will he use the formula in the case of an ostensive proof; for here what one denies is not assumed as a premiss.
ἔτι δ᾽ ὅταν ἀναιρεθῆι τι δεικτικῶς διὰ τῶν Α Β Γ, οὐκ ἔστιν εἰπεῖν ὡς οὐ παρὰ τὸ κείμενον γεγένηται ὁ συλλογισμός. τὸ γὰρ μὴ παρὰ τοῦτο γίνεσθαι τότε λέγομεν, ὅταν ἀναιρεθέντος τούτου μηδὲν ἧττον περαίνηται ὁ συλλογισμός, ὅπερ οὐκ ἔστιν ἐν τοῖς δεικτικοῖς· ἀναιρεθείσης γὰρ τῆς θέσεως οὐδ᾽ ὁ πρὸς ταύτην ἔσται συλλογισμός. φανερὸν οὖν ὅτι ἐν τοῖς εἰς τὸ ἀδύνατον λέγεται τὸ μὴ παρὰ τοῦτο, καὶ ὅταν οὕτως ἔχηι πρὸς τὸ ἀδύνατον ἡ ἐξ ἀρχῆς ὑπόθεσις ὥστε καὶ οὔσης καὶ μὴ οὔσης ταύτης οὐδὲν ἧττον συμβαίνειν τὸ ἀδύνατον.	Amplius autem quando interimitur aliquid ostensive per A B C, non est dicere quoniam non propter quod positum est factus est syllogismus, nam non propter hoc fieri tunc dicimus, quando interempto hoc nihilominus perficitur syllogismus, quod non est in ostensivis, interempta enim propositione, nec qui ad hanc est erit syllogismus. Manifestum igitur quoniam in iis qui ad impossibile sunt dicitur non propter hoc, et quando sic se habet ad impossibile quae ex principio est hypothesis, ut cum sit, vel cum non sit haec, nihilominus accidit impossibile.	Further when anything is refuted ostensively by the terms ABC, it cannot be objected that the syllogism does not depend on the assumption laid down. For we use the expression ‘false cause’, when the syllogism is concluded in spite of the refutation of this position; but that is not possible in ostensive proofs: since if an assumption is refuted, a syllogism can no longer be drawn in reference to it. It is clear then that the expression ‘false cause’ can only be used in the case of a reductio ad impossibile, and when the original hypothesis is so related to the impossible conclusion, that the conclusion results indifferently whether the hypothesis is made or not.
Ὁ μὲν οὖν φανερώτατος τρόπος ἐστὶ τοῦ μὴ παρὰ τὴν θέσιν εἶναι τὸ ψεῦδος, ὅταν ἀπὸ τῆς ὑποθέσεως ἀσύναπτος ἦι ἀπὸ τῶν μέσων πρὸς τὸ ἀδύνατον ὁ συλλογισμός, ὅπερ εἴρηται καὶ ἐν τοῖς Τοπικοῖς. τὸ γὰρ τὸ ἀναίτιον ὡς αἴτιον τιθέναι τοῦτό ἐστιν, οἷον εἰ βουλόμενος δεῖξαι ὅτι ἀσύμμετρος ἡ διάμετρος, ἐπιχειροίη τὸν Ζήνωνος λόγον, ὡς οὐκ ἔστι κινεῖσθαι, καὶ εἰς τοῦτο ἀπάγοι τὸ ἀδύνατον· οὐδαμῶς γὰρ οὐδαμῆι συνεχές ἐστι τὸ ψεῦδος τῆι φάσει τῆι ἐξ ἀρχῆς.	(0704C) Ergo manifestissimus quidem modus est non propter suppositionem esse falsum, quando ab hypothesi inconiunctus est A mediis syllogismus ad impossibile, quod dictum est in Topicis; quod enim non est causa, ut causam ponere hoc est; ut si volens ostendere quoniam asymeter est diameter, conetur Zenonis ratione quoniam non est moveri, et ad hoc inducat impossibile, nullo enim modo continuum est falsum locutioni quae est ex principio.	The most obvious case of the irrelevance of an assumption to a conclusion which is false is when a syllogism drawn from middle terms to an impossible conclusion is independent of the hypothesis, as we have explained in the Topics. For to put that which is not the cause as the cause, is just this: e.g. if a man, wishing to prove that the diagonal of the square is incommensurate with the side, should try to prove Zeno’s theorem that motion is impossible, and so establish a reductio ad impossibile: for Zeno’s false theorem has no connexion at all with the original assumption.
ἄλλος δὲ τρόπος, εἰ συνεχὲς μὲν εἴη τὸ ἀδύνατον τῆι ὑποθέσει, μὴ μέντοι δι᾽ ἐκείνην συμβαίνοι. τοῦτο γὰρ ἐγχωρεῖ γενέσθαι καὶ ἐπὶ τὸ ἄνω καὶ ἐπὶ τὸ κάτω λαμβάνοντι τὸ συνεχές, οἷον εἰ τὸ Α τῶι Β κεῖται ὑπάρχον, τὸ δὲ Β τῶι Γ, τὸ δὲ Γ τῶι Δ, τοῦτο δ᾽ εἴη ψεῦδος, τὸ τὸ Β τῶι Δ ὑπάρχειν. εἰ γὰρ ἀφαιρεθέντος τοῦ Α μηδὲν ἧττον ὑπάρχοι τὸ Β τῶι Γ καὶ τὸ Γ τῶι Δ, οὐκ ἂν εἴη τὸ ψεῦδος διὰ τὴν ἐξ ἀρχῆς ὑπόθεσιν.	Alius autem modus, si continuum quidem sit impossibile hypothesi, non tamen propter illam accidat, hoc autem possibile est fieri, et in hoc quod superius, et in hoc quod inferius sumenti continuum, ut si A ponatur inesse B, B autem C, C vero D, hoc autem sit falsum B inesse D, nam (si ablato A, nihilominus B inest C, et C D ) non erit falsum propter eam quae ex principio est hypothesin.	Another case is where the impossible conclusion is connected with the hypothesis, but does not result from it. This may happen whether one traces the connexion upwards or downwards, e.g. if it is laid down that A belongs to B, B to C, and C to D, and it should be false that B belongs to D: for if we eliminated A and assumed all the same that B belongs to C and C to D, the false conclusion would not depend on the original hypothesis.
ἢ πάλιν εἴ τις ἐπὶ τὸ ἄνω λαμβάνοι τὸ συνεχές, οἷον εἰ τὸ μὲν Α τῶι Β, τῶι δὲ Α τὸ Ε καὶ τῶι Ε τὸ Ζ, ψεῦδος δ᾽ εἴη τὸ ὑπάρχειν τῶι Α τὸ Ζ· καὶ γὰρ οὕτως οὐδὲν ἂν ἧττον εἴη τὸ ἀδύνατον ἀναιρεθείσης τῆς ἐξ ἀρχῆς ὑποθέσεως. ἀλλὰ δεῖ πρὸς τοὺς ἐξ ἀρχῆς ὅρους συνάπτειν τὸ ἀδύνατον· οὕτω γὰρ ἔσται διὰ τὴν ὑπόθεσιν, οἷον ἐπὶ μὲν τὸ κάτω λαμβάνοντι τὸ συνεχὲς πρὸς τὸν κατηγορούμενον τῶν ὅρων (εἰ γὰρ ἀδύνατον τὸ Α τῶι Δ ὑπάρχειν, ἀφαιρεθέντος τοῦ Α οὐκέτι ἔσται τὸ ψεῦδοσ)·	(0704D) Aut rursum si quis in superiori sumat continuum, ut si A quidem B, E autem A, F vero E, falsum autem sit F inesse A, nam et sic nihilominus erit impossibile, interempta quae est ex principio hypothesi. Sed oportet ad eos qui ex principio terminos copulare impossibile, sic enim erit propter hypothesin, ut in inferiori quidem sumenti continuum ad praedicatum terminum; nam si impossibile est A inesse D, interempto A, non amplius erit falsum.	Or again trace the connexion upwards; e.g. suppose that A belongs to B, E to A and F to E, it being false that F belongs to A. In this way too the impossible conclusion would result, though the original hypothesis were eliminated. But the impossible conclusion ought to be connected with the original terms: in this way it will depend on the hypothesis, e.g. when one traces the connexion downwards, the impossible conclusion must be connected with that term which is predicate in the hypothesis: for if it is impossible that A should belong to D, the false conclusion will no longer result after A has been eliminated.
ἐπὶ δὲ τὸ ἄνω, καθ᾽ οὗ κατηγορεῖται (εἰ γὰρ τῶι Β μὴ ἐγχωρεῖ τὸ Ζ ὑπάρχειν, ἀφαιρεθέντος τοῦ Β οὐκέτι ἔσται τὸ ἀδύνατον). ὁμοίως δὲ καὶ στερητικῶν τῶν συλλογισμῶν ὄντων.	In superiori autem de quo praedicatur; nam si F non possibile est inesse B, interempto B non amplius erit impossibile; similiter autem et cum privativi sint syllogismi.	If one traces the connexion upwards, the impossible conclusion must be connected with that term which is subject in the hypothesis: for if it is impossible that F should belong to B, the impossible conclusion will disappear if B is eliminated. Similarly when the syllogisms are negative.
↵ Φανερὸν οὖν ὅτι τοῦ ἀδυνάτου μὴ πρὸς τοὺς ἐξ ἀρχῆς ὅρους ὄντος οὐ παρὰ τὴν θέσιν συμβαίνει τὸ ψεῦδος. ἢ οὐδ᾽ οὕτως ἀεὶ διὰ τὴν ὑπόθεσιν ἔσται τὸ ψεῦδος; καὶ γὰρ εἰ μὴ τῶι Β ἀλλὰ τῶι Κ ἐτέθη τὸ Α ὑπάρχειν, τὸ δὲ Κ τῶι Γ καὶ τοῦτο τῶι Δ, καὶ οὕτω μένει τὸ ἀδύνατον	Manifestum ergo quoniam cum impossibile non ad priores terminos, non propter positionem accidit falsum; an nec sic semper propter hypothes in erit falsum? (0705A) nam si non ei quod est B, sed ei quod est k positum est inesse A, k autem C, et hoc D, et sic manet impossibile;	It is clear then that when the impossibility is not related to the original terms, the false conclusion does not result on account of the assumption. Or perhaps even so it may sometimes be independent. For if it were laid down that A belongs not to B but to K, and that K belongs to C and C to D, the impossible conclusion would still stand.
(ὁμοίως δὲ καὶ ἐπὶ τὸ ἄνω λαμβάνοντι τοὺς ὅρουσ), ὥστ᾽ ἐπεὶ καὶ ὄντος καὶ μὴ ὄντος τούτου συμβαίνει τὸ ἀδύνατον, οὐκ ἂν εἴη παρὰ τὴν θέσιν. ἢ τὸ μὴ ὄντος τούτου μηδὲν ἧττον γίνεσθαι τὸ ψεῦδος οὐχ οὕτω ληπτέον ὥστ᾽ ἄλλου τιθεμένου συμβαίνειν τὸ ἀδύνατον, ἀλλ᾽ ὅταν ἀφαιρεθέντος τούτου διὰ τῶν λοιπῶν προτάσεων ταὐτὸ περαίνηται ἀδύνατον, ἐπεὶ ταὐτό γε ψεῦδος συμβαίνειν διὰ πλειόνων ὑποθέσεων οὐδὲν ἴσως ἄτοπον, οἷον τὰς παραλλήλους συμπίπτειν καὶ εἰ μείζων ἐστὶν ἡ ἐντὸς τῆς ἐκτὸς καὶ εἰ τὸ τρίγωνον ἔχει πλείους ὀρθὰς δυεῖν;	similiter autem et in sursum sumenti terminos, quare (quoniam cum est, et cum non est, hoc accidit impossibile) non erit propter positionem, aut cum non est hoc, nihilominus fieri falsum. Nec sic sumendum ut alio posito accidat impossibile, sed quando ablato hoc idem per reliquas propositiones concluditur impossibile, eo quod idem falsum accidere per plures hypotheses nihil fortasse inconveniens est, ut parallelas, contingere, et si maior est qui interius est, eo qui exterius, et si triangulus habet plures rectos duobus.	Similarly if one takes the terms in an ascending series. Consequently since the impossibility results whether the first assumption is suppressed or not, it would appear to be independent of that assumption. Or perhaps we ought not to understand the statement that the false conclusion results independently of the assumption, in the sense that if something else were supposed the impossibility would result; but rather we mean that when the first assumption is eliminated, the same impossibility results through the remaining premisses; since it is not perhaps absurd that the same false result should follow from several hypotheses, e.g. that parallels meet, both on the assumption that the interior angle is greater than the exterior and on the assumption that a triangle contains more than two right angles.

Chapter 18

Greek	Latin	English
	(PL 64 0705A) CAPUT XX. De falsa ratiocinatione, catasyllogismo, hoc est corratiocinatione, et elencho.	18
66a16 Ὁ δὲ ψευδὴς λόγος γίνεται παρὰ τὸ πρῶτον ψεῦδος. ἢ γὰρ ἐκ τῶν δύο προτάσεων ἢ ἐκ πλειόνων πᾶς ἐστι συλλογισμός. εἰ μὲν οὖν ἐκ τῶν δύο, τούτων ἀνάγκη τὴν ἑτέραν ἢ καὶ ἀμφοτέρας εἶναι ψευδεῖς· ἐξ ἀληθῶν γὰρ οὐκ ἦν ψευδὴς συλλογισμός. εἰ δ᾽ ἐκ πλειόνων, οἷον τὸ μὲν Γ διὰ τῶν Α Β, ταῦτα δὲ διὰ τῶν Δ Ε Ζ Η, τούτων τι ἔσται τῶν ἐπάνω ψεῦδος, καὶ παρὰ τοῦτο ὁ λόγος· τὸ γὰρ Α καὶ Β δι᾽ ἐκείνων περαίνονται. ὥστε παρ᾽ ἐκείνων τι συμβαίνει τὸ συμπέρασμα καὶ τὸ ψεῦδος.	(0705B) Falsa autem oratio fit propter primum falsum; aut enim ex duabus propositionibus aut ex pluribus omnis est syllogismus; ergo si ex duabus quidem, harum necesse est alteram, aut etiam utrasque esse falsas, nam ex veris non erat falsus syllogismus; si vero ex pluribus (ut sic quidem per A B, hoc autem per D F G ), horum erit aliquid superiorum falsum, et propter hoc oratio, nam A et B per illa concluduntur, quare propter illorum aliquid, accidit conclusio et falsum.	A false argument depends on the first false statement in it. Every syllogism is made out of two or more premisses. If then the false conclusion is drawn from two premisses, one or both of them must be false: for (as we proved) a false syllogism cannot be drawn from two premisses. But if the premisses are more than two, e.g. if C is established through A and B, and these through D, E, F, and G, one of these higher propositions must be false, and on this the argument depends: for A and B are inferred by means of D, E, F, and G. Therefore the conclusion and the error results from one of them.

Chapter 19

Greek	Latin	English
		19
66a25 Πρὸς δὲ τὸ μὴ κατασυλλογίζεσθαι παρατηρητέον, ὅταν ἄνευ τῶν συμπερασμάτων ἐρωτᾶι τὸν λόγον, ὅπως μὴ δοθῆι δὶς ταὐτὸν ἐν ταῖς προτάσεσιν, ἐπειδήπερ ἴσμεν ὅτι ἄνευ μέσου συλλογισμὸς οὐ γίνεται, μέσον δ᾽ ἐστὶ τὸ πλεονάκις λεγόμενον. ὡς δὲ δεῖ πρὸς ἕκαστον συμπέρασμα τηρεῖν τὸ μέσον, φανερὸν ἐκ τοῦ εἰδέναι ποῖον ἐν ἑκάστωι σχήματι δείκνυται. τοῦτο δ᾽ ἡμᾶς οὐ λήσεται διὰ τὸ εἰδέναι πῶς ὑπέχομεν τὸν λόγον.	Ut autem non catasyllogizetur, observandum, quando sine conclusionibus interrogat orationem, ut non detur bis idem in propositionibus, eo quod scimus quoniam sine medio syllogismus non fit, medium autem est quod plerumque dicitur. (0705C) Quomodo autem oportet ad unamquamque conclusionem observare medium manifestum est, eo quod scitur quale in unaquaque figura ostenditur, hoc autem nos non latebit, eo quod videmus quomodo submittimus orationem.	In order to avoid having a syllogism drawn against us we must take care, whenever an opponent asks us to admit the reason without the conclusions, not to grant him the same term twice over in his premisses, since we know that a syllogism cannot be drawn without a middle term, and that term which is stated more than once is the middle. How we ought to watch the middle in reference to each conclusion, is evident from our knowing what kind of thesis is proved in each figure. This will not escape us since we know how we are maintaining the argument.
Χρὴ δ᾽ ὅπερ φυλάττεσθαι παραγγέλλομεν ἀποκρινομένους, αὐτοὺς ἐπιχειροῦντας πειρᾶσθαι λανθάνειν. τοῦτο δ᾽ ἔσται πρῶτον, ἐὰν τὰ συμπεράσματα μὴ προσυλλογίζωνται ἀλλ᾽ εἰλημμένων τῶν ἀναγκαίων ἄδηλα ἦι, ἔτι δὲ ἂν μὴ τὰ σύνεγγυς ἐρωτᾶι, ἀλλ᾽ ὅτι μάλιστα ἄμεσα. οἷον ἔστω δέον συμπεραίνεσθαι τὸ Α κατὰ τοῦ Ζ· μέσα Β Γ Δ Ε. δεῖ οὖν ἐρωτᾶν εἰ τὸ Α τῶι Β, καὶ πάλιν μὴ εἰ τὸ Β τῶι Γ, ἀλλ᾽ εἰ τὸ Δ τῶι Ε, κἄπειτα εἰ τὸ Β τῶι Γ, καὶ οὕτω ↵ τὰ λοιπά. κἂν δι᾽ ἑνὸς μέσου γίνηται ὁ συλλογισμός, ἀπὸ τοῦ μέσου ἄρχεσθαι· μάλιστα γὰρ ἂν οὕτω λανθάνοι τὸν ἀποκρινόμενον.	Oportet autem quod custodire praecipimus respondentes, ipsos argumentantes tentare latere, hoc autem erit primum quidem si conclusiones non prius syllogizent, sed sumptis necessariis non manifestae sint. Amplius autem si non propinqua interrogant, sed quam maxime longe media, ut si sit opportunum concludere A D E F, media B E D E, oportet ergo inquirere si A B, et rursum non si B E, sed si D E, deinde si B C, et sic reliqua, et si per unum medium sit syllogismus, A medio incipere, maxime enim sic latebit respondentem.	That which we urge men to beware of in their admissions, they ought in attack to try to conceal. This will be possible first, if, instead of drawing the conclusions of preliminary syllogisms, they take the necessary premisses and leave the conclusions in the dark; secondly if instead of inviting assent to propositions which are closely connected they take as far as possible those that are not connected by middle terms. For example suppose that A is to be inferred to be true of F, B, C, D, and E being middle terms. One ought then to ask whether A belongs to B, and next whether D belongs to E, instead of asking whether B belongs to C; after that he may ask whether B belongs to C, and so on. If the syllogism is drawn through one middle term, he ought to begin with that: in this way he will most likely deceive his opponent.

Chapter 20

Greek	Latin	English
		20
66b4 Ἐπεὶ δ᾽ ἔχομεν πότε καὶ πῶς ἐχόντων τῶν ὅρων γίνεται συλλογισμός, φανερὸν καὶ πότ᾽ ἔσται καὶ πότ᾽ οὐκ ἔσται ἔλεγχος. πάντων μὲν γὰρ συγχωρουμένων, ἢ ἐναλλὰξ τιθεμένων τῶν ἀποκρίσεων, οἷον τῆς μὲν ἀποφατικῆς τῆς δὲ καταφατικῆς, ἐγχωρεῖ γίνεσθαι ἔλεγχον. ἦν γὰρ συλλογισμὸς καὶ οὕτω καὶ ἐκείνως ἐχόντων τῶν ὅρων, ὥστ᾽ εἰ τὸ κείμενον ἐναντίον τῶι συμπεράσματι, ἀνάγκη γίνεσθαι ἔλεγχον· ὁ γὰρ ἔλεγχος ἀντιφάσεως συλλογισμός.	(0705D) Quoniam ergo habemus quando et quomodo se habentibus terminis fit syllogismus, manifestum et quando erit, et quando non erit elenchus, nam omnibus affirmativis, vel permutatim positis responsionibus (ut hac quidem affirmativa, illa vero negativa), contingit fieri elenchum: erit enim syllogismus, et sic in illo modo se habentibus terminis; quare si id quod positum est contrarium sit conclusioni, necesse est fieri elenchum, nam elenchus syllogismus contradictionis est.	Since we know when a syllogism can be formed and how its terms must be related, it is clear when refutation will be possible and when impossible. A refutation is possible whether everything is conceded, or the answers alternate (one, I mean, being affirmative, the other negative). For as has been shown a syllogism is possible whether the terms are related in affirmative propositions or one proposition is affirmative, the other negative: consequently, if what is laid down is contrary to the conclusion, a refutation must take place: for a refutation is a syllogism which establishes the contradictory.
εἰ δὲ μηδὲν συγχωροῖτο, ἀδύνατον γενέσθαι ἔλεγχον· οὐ γὰρ ἦν συλλογισμὸς πάντων τῶν ὅρων στερητικῶν ὄντων, ὥστ᾽ οὐδ᾽ ἔλεγχος· εἰ μὲν γὰρ ἔλεγχος, ἀνάγκη συλλογισμὸν εἶναι, συλλογισμοῦ δ᾽ ὄντος οὐκ ἀνάγκη ἔλεγχον. ὡσαύτως δὲ καὶ εἰ μηδὲν τεθείη κατὰ τὴν ἀπόκρισιν ἐν ὅλωι· ὁ γὰρ αὐτὸς ἔσται διορισμὸς ἐλέγχου καὶ συλλογισμοῦ.	Si vero nihil affirmetur, impossibile est fieri elenchum, non enim erat syllogismus, cum omnes termini erant privativi, quare nec elenchus: nam si elenchus, necesse est syllogismus esse; cum autem est syllogismus, non necesse est elenchum esse. (0706A) Similiter autem si nihil positum sit secundum responsionem universaliter; nam eadem erit definitio syllogismi et elenchi.	But if nothing is conceded, a refutation is impossible: for no syllogism is possible (as we saw) when all the terms are negative: therefore no refutation is possible. For if a refutation were possible, a syllogism must be possible; although if a syllogism is possible it does not follow that a refutation is possible. Similarly refutation is not possible if nothing is conceded universally: since the fields of refutation and syllogism are defined in the same way.

Chapter 21

Greek	Latin	English
	(PL 64 0706A) CAPUT XXI. De fallacia secundum opinionem.	21
66b18 Συμβαίνει δ᾽ ἐνίοτε, καθάπερ ἐν τῆι θέσει τῶν ὅρων ἀπατώμεθα, καὶ κατὰ τὴν ὑπόληψιν γίνεσθαι τὴν ἀπάτην, οἷον εἰ ἐνδέχεται τὸ αὐτὸ πλείοσι πρώτοις ὑπάρχειν, καὶ τὸ μὲν λεληθέναι τινὰ καὶ οἴεσθαι μηδενὶ ὑπάρχειν, τὸ δὲ εἰδέναι. ἔστω τὸ Α τῶι Β καὶ τῶι Γ καθ᾽ αὑτὰ ὑπάρχον, καὶ ταῦτα παντὶ τῶι Δ ὡσαύτως. εἰ δὴ τῶι μὲν Β τὸ Α παντὶ οἴεται ὑπάρχειν, καὶ τοῦτο τῶι Δ, τῶι δὲ Γ τὸ Α μηδενί, καὶ τοῦτο τῶι Δ παντί, τοῦ αὐτοῦ κατὰ ταὐτὸν ἕξει ἐπιστήμην καὶ ἄγνοιαν.	Accidit autem quandoque (quemadmodum in positione terminorum fallebamur) et secundum opinionem fieri fallaciam, ut si contingat idem pluribus principaliter inesse, et hoc quidem latere aliquem, et putare nulli inesse, illud autem scire, ut insit A B et C per se, et haec omni D similiter. Si igitur B quidem putet omni A inesse, et hoc D, C autem nulli A, et hoc omni D, eiusdem secundum idem habebit disciplinam et ignorantiam.	It sometimes happens that just as we are deceived in the arrangement of the terms, so error may arise in our thought about them, e.g. if it is possible that the same predicate should belong to more than one subject immediately, but although knowing the one, a man may forget the other and think the opposite true. Suppose that A belongs to B and to C in virtue of their nature, and that B and C belong to all D in the same way. If then a man thinks that A belongs to all B, and B to D, but A to no C, and C to all D, he will both know and not know the same thing in respect of the same thing.
πάλιν εἴ τις ἀπατηθείη περὶ τὰ ἐκ τῆς αὐτῆς συστοιχίας, οἷον εἰ τὸ Α ὑπάρχει τῶι Β, τοῦτο δὲ τῶι Γ καὶ τὸ Γ τῶι Δ, ὑπολαμβάνοι δὲ τὸ Α παντὶ τῶι Β ὑπάρχειν καὶ πάλιν μηδενὶ τῶι Γ· ἅμα γὰρ εἴσεταί τε καὶ οὐχ ὑπολήψεται ὑπάρχειν. ἆρ᾽ οὖν οὐδὲν ἄλλο ἀξιοῖ ἐκ τούτων ἢ ὁ ἐπίσταται, τοῦτο μὴ ὑπολαμβάνειν; ἐπίσταται γάρ πως ὅτι τὸ Α τῶι Γ ὑπάρχει διὰ τοῦ Β, ὡς τῆι καθόλου τὸ κατὰ μέρος, ὥστε ὅ πως ἐπίσταται, τοῦτο ὅλως ἀξιοῖ μὴ ὑπολαμβάνειν· ὅπερ ἀδύνατον.	(0706B) Rursum si quis fallatur circa ea quae sunt ex eadem coniugatione, ut si A inest B, hoc autem C, et C D, opinetur autem A inesse omni B, et rursum nulli C. Simul enim sciet, et non opinabitur inesse; ergo nihil aliud existimat ex iis quam scit, hoc non opinari, scit enim aliquo modo quoniam A inest C per B, velut in universali hoc quod est particulare; quare quod aliquo modo scit, hoc omnino existimat non opinari, quod est impossibile.	Again if a man were to make a mistake about the members of a single series; e.g. suppose A belongs to B, B to C, and C to D, but some one thinks that A belongs to all B, but to no C: he will both know that A belongs to D, and think that it does not. Does he then maintain after this simply that what he knows, he does not think? For he knows in a way that A belongs to C through B, since the part is included in the whole; so that what he knows in a way, this he maintains he does not think at all: but that is impossible.
Ἐπὶ δὲ τοῦ πρότερον λεχθέντος, εἰ μὴ ἐκ τῆς αὐτῆς συστοιχίας τὸ μέσον, καθ᾽ ἑκάτερον μὲν τῶν μέσων ἀμφοτέρας τὰς προτάσεις οὐκ ἐγχωρεῖ ὑπολαμβάνειν, οἷον τὸ Α τῶι μὲν Β παντί, τῶι δὲ Γ μηδενί, ταῦτα δ᾽ ἀμφότερα παντὶ τῶι Δ. συμβαίνει γὰρ ἢ ἁπλῶς ἢ ἐπί τι ἐναντίαν λαμβάνεσθαι τὴν πρώτην πρότασιν.	In eo autem quod prius dictum est, si non ex eadem coniugatione sit medium; secundum utrumque quidem mediorum ambas propositiones non possibile est opinari, ut A B quidem omni, C autem nulli, haec autem utraque omni D; accidit autem aut simpliciter aut in aliquo contrariam sumere primam propositionem.	In the former case, where the middle term does not belong to the same series, it is not possible to think both the premisses with reference to each of the two middle terms: e.g. that A belongs to all B, but to no C, and both B and C belong to all D. For it turns out that the first premiss of the one syllogism is either wholly or partially contrary to the first premiss of the other.
εἰ γὰρ ὧι τὸ Β ὑπάρχει, παντὶ τὸ Α ὑπολαμβάνει ↵ ὑπάρχειν, τὸ δὲ Β τῶι Δ οἶδε, καὶ ὅτι τῶι Δ τὸ Α οἶδεν. ὥστ᾽ εἰ πάλιν, ὧι τὸ Γ, μηδενὶ οἴεται τὸ Α ὑπάρχειν, ὧι τὸ Β τινὶ ὑπάρχει, τούτωι οὐκ οἴεται τὸ Α ὑπάρχειν. τὸ δὲ παντὶ οἰόμενον ὧι τὸ Β, πάλιν τινὶ μὴ οἴεσθαι ὧι τὸ Β, ἢ ἁπλῶς ἢ ἐπί τι ἐναντίον ἐστίν. Οὕτω μὲν οὖν οὐκ ἐνδέχεται ὑπολαβεῖν, καθ᾽ ἑκάτερον δὲ τὴν μίαν ἢ κατὰ θάτερον ἀμφοτέρας οὐδὲν κωλύει, οἷον τὸ Α παντὶ τῶι Β καὶ τὸ Β τῶι Δ, καὶ πάλιν τὸ Α μηδενὶ τῶι Γ.	(0706C) Si enim cui B inest omni A opinatur inesse, B autem D novit, et quoniam A D novit, quare si rursum cui C nulli, putat A inesse, cui B alicui inest, huic non putat A inesse, quod autem omni putat cui B, rursum alicui non putare cui B, aut simpliciter, aut in aliquo contrarium et; sic ergo non contingit opinari. Secundum utrumque autem unam, aut secundum alterum utrasque, nihil prohibet A omni B, et B D, et rursum A nulli C.	For if he thinks that A belongs to everything to which B belongs, and he knows that B belongs to D, then he knows that A belongs to D. Consequently if again he thinks that A belongs to nothing to which C belongs, he thinks that A does not belong to some of that to which B belongs; but if he thinks that A belongs to everything to which B belongs, and again thinks that A does not belong to some of that to which B belongs, these beliefs are wholly or partially contrary. In this way then it is not possible to think; but nothing prevents a man thinking one premiss of each syllogism of both premisses of one of the two syllogisms: e.g. A belongs to all B, and B to D, and again A belongs to no C.
ὁμοία γὰρ ἡ τοιαύτη ἀπάτη καὶ ὡς ἀπατώμεθα περὶ τὰς ἐν μέρει, οἷον εἰ ὧι τὸ Β, παντὶ τὸ Α ὑπάρχει, τὸ δὲ Β τῶι Γ παντί, τὸ Α παντὶ τῶι Γ ὑπάρξει. εἰ οὖν τις οἶδεν ὅτι τὸ Α, ὧι τὸ Β, ὑπάρ- χει παντί, οἶδε καὶ ὅτι τῶι Γ. ἀλλ᾽ οὐδὲν κωλύει ἀγνοεῖν τὸ Γ ὅτι ἔστιν, οἷον εἰ τὸ μὲν Α δύο ὀρθαί, τὸ δ᾽ ἐφ᾽ ὧι Β τρίγωνον, τὸ δ᾽ ἐφ᾽ ὧι Γ αἰσθητὸν τρίγωνον. ὑπολάβοι γὰρ ἄν τις μὴ εἶναι τὸ Γ, εἰδὼς ὅτι πᾶν τρίγωνον ἔχει δύο ὀρθάς, ὥσθ᾽ ἅμα εἴσεται καὶ ἀγνοήσει ταὐτόν. τὸ γὰρ εἰδέναι πᾶν τρίγωνον ὅτι δύο ὀρθαῖς οὐχ ἁπλοῦν ἐστιν, ἀλλὰ τὸ μὲν τῶι τὴν καθόλου ἔχειν ἐπιστήμην, τὸ δὲ τὴν καθ᾽ ἕκαστον. οὕτω μὲν οὖν ὡς τῆι καθόλου οἶδε τὸ Γ ὅτι δύο ὀρθαί, ὡς δὲ τῆι καθ᾽ ἕκαστον οὐκ οἶδεν, ὥστ᾽ οὐχ ἕξει τὰς ἐναντίας.	(0706D) Nam similis huiusmodi fallacia, veluti fallimur circa particularia, ut si A omni B inest, B autem omni C, A omni C inerit; si ergo aliquis novit quoniam A cui B inest omni, novit et quoniam ei quod est C; sed nihil prohibet ignorare C quoniam est, ut si A quidem duo recti, in quo autem B triangulus, in quo vero C sensibilis triangulus; opinabitur enim aliquis non esse C, sciens quoniam omnis triangulus habet duos rectos: quare simul sciet et ignorabit idem, nam scire omnem triangulum quoniam duobus rectis, non simplex est, sed hoc quidem universalem habet disciplinam, illud vero singularem. Sic ergo in universali novit C, quoniam duobus rectis, in singulari autem non novit, quare non habebit contrarias.	An error of this kind is similar to the error into which we fall concerning particulars: e.g. if A belongs to all B, and B to all C, A will belong to all C. If then a man knows that A belongs to everything to which B belongs, he knows that A belongs to C. But nothing prevents his being ignorant that C exists; e.g. let A stand for two right angles, B for triangle, C for a particular diagram of a triangle. A man might think that C did not exist, though he knew that every triangle contains two right angles; consequently he will know and not know the same thing at the same time. For the expression ‘to know that every triangle has its angles equal to two right angles’ is ambiguous, meaning to have the knowledge either of the universal or of the particulars. Thus then he knows that C contains two right angles with a knowledge of the universal, but not with a knowledge of the particulars; consequently his knowledge will not be contrary to his ignorance.
ὁμοίως δὲ καὶ ὁ ἐν τῶι Μένωνι λόγος, ὅτι ἡ μάθησις ἀνάμνησις. οὐδαμοῦ γὰρ συμβαίνει προεπίστασθαι τὸ καθ᾽ ἕκαστον, ἀλλ᾽ ἅμα τῆι ἐπαγωγῆι λαμβάνειν τὴν τῶν κατὰ μέρος ἐπιστήμην ὥσπερ ἀναγνωρίζοντας. ἔνια γὰρ εὐθὺς ἴσμεν, οἷον ὅτι δύο ὀρθαῖς, ἐὰν ἴδωμεν ὅτι τρίγωνον. ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων.	Similiter autem est quae in Menone est oratio, quoniam disciplina est reminiscentia; nunquam enim accidit praescire quod singulare est, sed simul inductione sumere particularium disciplinam, velut recognoscentes. Nam quaedam scientes, statim scimus, ut quoniam duobus rectis, si scimus quoniam triangulus, similiter autem et in aliis.	The argument in the Meno that learning is recollection may be criticized in a similar way. For it never happens that a man starts with a foreknowledge of the particular, but along with the process of being led to see the general principle he receives a knowledge of the particulars, by an act (as it were) of recognition. For we know some things directly; e.g. that the angles are equal to two right angles, if we know that the figure is a triangle. Similarly in all other cases.
Τῆι μὲν οὖν καθόλου θεωροῦμεν τὰ ἐν μέρει, τῆι δ᾽ οἰκείαι οὐκ ἴσμεν, ὥστ᾽ ἐνδέχεται καὶ ἀπατᾶσθαι περὶ αὐτά, πλὴν οὐκ ἐναντίως, ἀλλ᾽ ἔχειν μὲν τὴν καθόλου, ἀπατᾶσθαι δὲ τὴν κατὰ μέρος.	Ergo universali quidem speculamur particularia, propria autem non scimus; quare contingit et falli circa ea, verum non contrarie, sed habere quidem universale, decipi autem particulari.	By a knowledge of the universal then we see the particulars, but we do not know them by the kind of knowledge which is proper to them; consequently it is possible that we may make mistakes about them, but not that we should have the knowledge and error that are contrary to one another: rather we have the knowledge of the universal but make a mistake in apprehending the particular.
ὁμοίως οὖν καὶ ἐπὶ τῶν προειρημένων· οὐ γὰρ ἐναντία ἡ κατὰ τὸ μέσον ἀπάτη τῆι κατὰ τὸν συλλογισμὸν ἐπιστήμηι, οὐδ᾽ ἡ καθ᾽ ἑκάτερον τῶν μέσων ὑπόληψις. οὐδὲν δὲ κωλύει εἰδότα καὶ ὅτι τὸ Α ὅλωι τῶι Β ὑπάρχει καὶ πάλιν τοῦτο τῶι Γ, οἰηθῆναι μὴ ὑπάρχειν τὸ Α τῶι Γ, οἷον ὅτι πᾶσα ἡμίονος ἄτοκος καὶ αὕτη ἡμίονος οἴεσθαι κύειν ταύτην· οὐ γὰρ ἐπίσταται ὅτι τὸ Α τῶι Γ, μὴ συνθεωρῶν τὸ καθ᾽ ἑκάτερον.	(0707A) Similiter autem in praedictis, non enim contraria quae est secundum medium ei quae est secundum syllogismum disciplinae, nec quae est secundum utrumque mediorum opinatio, nihil enim prohibet scientem, et quoniam A toti B inest, et rursum hoc toti C, putare non inesse, ut quoniam omnis mula sterilis, et haec mula, putare hanc habere in utero; non enim scit quoniam A, C qui non conspicit, quod est secundum utrumque.	Similarly in the cases stated above. The error in respect of the middle term is not contrary to the knowledge obtained through the syllogism, nor is the thought in respect of one middle term contrary to that in respect of the other. Nothing prevents a man who knows both that A belongs to the whole of B, and that B again belongs to C, thinking that A does not belong to C, e.g. knowing that every mule is sterile and that this is a mule, and thinking that this animal is with foal: for he does not know that A belongs to C, unless he considers the two propositions together.
ὥστε δῆλον ὅτι καὶ εἰ τὸ μὲν οἶδε τὸ δὲ μὴ οἶδεν, ἀπατηθήσεται· ὅπερ ἔχουσιν αἱ καθόλου πρὸς τὰς κατὰ μέρος ἐπιστήμας. οὐδὲν γὰρ τῶν αἰ↵σθητῶν ἔξω τῆς αἰσθήσεως γενόμενον ἴσμεν, οὐδ᾽ ἂν ἠισθημένοι τυγχάνωμεν, εἰ μὴ ὡς τῶι καθόλου καὶ τῶι ἔχειν τὴν οἰκείαν ἐπιστήμην, ἀλλ᾽ οὐχ ὡς τῶι ἐνεργεῖν.	Quare manifestum quoniam et si hoc quidem novit, illud vero non novit, falletur, quod habent universales ad particulares disciplinas; nullum enim sensibilium cum extra sensum fit scimus, nec si sentientes fuerimus scimus, nisi ut in universali, et in eo quod habet propriam disciplinam, sed non in eo quod est in actum.	So it is evident that if he knows the one and does not know the other, he will fall into error. And this is the relation of knowledge of the universal to knowledge of the particular. For we know no sensible thing, once it has passed beyond the range of our senses, even if we happen to have perceived it, except by means of the universal and the possession of the knowledge which is proper to the particular, but without the actual exercise of that knowledge.
τὸ γὰρ ἐπίστασθαι λέγεται τριχῶς, ἢ ὡς τῆι καθόλου ἢ ὡς τῆι οἰκείαι ἢ ὡς τῶι ἐνεργεῖν, ὥστε καὶ τὸ ἠπατῆσθαι τοσαυταχῶς. οὐδὲν οὖν κωλύει καὶ εἰδέναι καὶ ἠπατῆσθαι περὶ ταὐτό, πλὴν οὐκ ἐναντίως. ὅπερ συμβαίνει καὶ τῶι καθ᾽ ἑκατέραν εἰδότι τὴν πρότασιν καὶ μὴ ἐπεσκεμμένωι πρότερον. ὑπολαμβάνων γὰρ κύειν τὴν ἡμίονον οὐκ ἔχει τὴν κατὰ τὸ ἐνεργεῖν ἐπιστήμην, οὐδ᾽ αὖ διὰ τὴν ὑπόληψιν ἐναντίαν ἀπάτην τῆι ἐπιστήμηι· συλλογισμὸς γὰρ ἡ ἐναντία ἀπάτη τῆι καθόλου.	(0707B) Nam scire tripliciter dicitur, aut ut universali, aut ut propria, aut ut in actu, quare et decipi totidem modis, nihil ergo prohibet et scire, et deceptum esse circa idem, verumtamen non contrarie. Quod accidit et ei qui secundum utramque scit propositionum, et non pertractavit prius, nam opinans in utero habere mulam, non habet secundum ac um disciplinam, neque propter opinionem fallaciam contrariam disciplinae, syllogismus enim est contraria fallacis in universali.	For to know is used in three senses: it may mean either to have knowledge of the universal or to have knowledge proper to the matter in hand or to exercise such knowledge: consequently three kinds of error also are possible. Nothing then prevents a man both knowing and being mistaken about the same thing, provided that his knowledge and his error are not contrary. And this happens also to the man whose knowledge is limited to each of the premisses and who has not previously considered the particular question. For when he thinks that the mule is with foal he has not the knowledge in the sense of its actual exercise, nor on the other hand has his thought caused an error contrary to his knowledge: for the error contrary to the knowledge of the universal would be a syllogism.
Ὁ δ᾽ ὑπολαμβάνων τὸ ἀγαθῶι εἶναι κακῶι εἶναι, τὸ αὐτὸ ὑπολήψεται ἀγαθῶι εἶναι καὶ κακῶι. ἔστω γὰρ τὸ μὲν ἀγαθῶι εἶναι ἐφ᾽ οὗ Α, τὸ δὲ κακῶι εἶναι ἐφ᾽ οὗ Β, πάλιν δὲ τὸ ἀγαθῶι εἶναι ἐφ᾽ οὗ Γ. ἐπεὶ οὖν ταὐτὸν ὑπολαμβάνει τὸ Β καὶ τὸ Γ, καὶ εἶναι τὸ Γ τὸ Β ὑπολήψεται, καὶ πάλιν τὸ Β τὸ Α εἶναι ὡσαύτως, ὥστε καὶ τὸ Γ τὸ Α. ὥσπερ γὰρ εἰ ἦν ἀληθές, καθ᾽ οὗ τὸ Γ, τὸ Β, καὶ καθ᾽ οὗ τὸ Β, τὸ Α, καὶ κατὰ τοῦ Γ τὸ Α ἀληθὲς ἦν, οὕτω καὶ ἐπὶ τοῦ ὑπολαμβάνειν.	Qui autem opinatur quod bonum esse est malum esse, idem opinabitur bonum esse et malum. Sit enim bonum esse in quo A, malum autem esse in quo B, rursum bonum esse in quo C; quoniam igitur idem opinatur et B et C, et esse C B opinabitur, et rursum B esse A similiter, quare et C A, nam quemadmodum si erat verum de quo C B, et de quo B A, et de quo C A verum erat, sic et in opinatione.	But he who thinks the essence of good is the essence of bad will think the same thing to be the essence of good and the essence of bad. Let A stand for the essence of good and B for the essence of bad, and again C for the essence of good. Since then he thinks B and C identical, he will think that C is B, and similarly that B is A, consequently that C is A. For just as we saw that if B is true of all of which C is true, and A is true of all of which B is true, A is true of C, similarly with the word ‘think’.
ὁμοίως δὲ καὶ ἐπὶ τοῦ εἶναι· ταὐτοῦ γὰρ ὄντος τοῦ Γ καὶ Β, καὶ πάλιν τοῦ Β καὶ Α, καὶ τὸ Γ τῶι Α ταὐτὸν ἦν· ὥστε καὶ ἐπὶ τοῦ δοξάζειν ὁμοίως. ἆρ᾽ οὖν τοῦτο μὲν ἀναγκαῖον, εἴ τις δώσει τὸ πρῶτον; ἀλλ᾽ ἴσως ἐκεῖνο ψεῦδος, τὸ ὑπολαβεῖν τινὰ κακῶι εἶναι τὸ ἀγαθῶι εἶναι, εἰ μὴ κατὰ συμβεβηκός· πολλαχῶς γὰρ ἐγχωρεῖ τοῦθ᾽ ὑπολαμβάνειν. ἐπισκεπτέον δὲ τοῦτο βέλτιον.	Similiter autem et in eo quod est esse. (0707C) Nam cum idem sit C et B, et rursum B et A, C A idem erit, quare et opinatione similiter; ergo hoc quidem necessarium si quis det primum. Sed fortasse illud falsum opinari aliquem quod malum esse est bonum esse, nisi secundum accidens; multipliciter enim possibile est hoc opinari, perspiciendum autem hoc melius.	Similarly also with the word ‘is’; for we saw that if C is the same as B, and B as A, C is the same as A. Similarly therefore with ‘opine’. Perhaps then this is necessary if a man will grant the first point. But presumably that is false, that any one could suppose the essence of good to be the essence of bad, save incidentally. For it is possible to think this in many different ways. But we must consider this matter better.

Chapter 22

Greek	Latin	English
	(PL 64 0707C) CAPUT XXII. De conversionibus terminorum.	22
67b27 Ὅταν δ᾽ ἀντιστρέφηι τὰ ἄκρα, ἀνάγκη καὶ τὸ μέσον ἀντιστρέφειν πρὸς ἄμφω. εἰ γὰρ τὸ Α κατὰ τοῦ Γ διὰ τοῦ Β ὑπάρχει, εἰ ἀντιστρέφει καὶ ὑπάρχει, ὧι τὸ Α, παντὶ τὸ Γ, καὶ τὸ Β τῶι Α ἀντιστρέψει καὶ ὑπάρξει, ὧι τὸ Α, παντὶ τὸ Β διὰ μέσου τοῦ Γ· καὶ τὸ Γ τῶι Β ἀντιστρέψει διὰ μέσου τοῦ Α. καὶ ἐπὶ τοῦ μὴ ὑπάρχειν ὡσαύτως, οἷον εἰ τὸ Β τῶι Γ ὑπάρχει, τῶι δὲ Β τὸ Α οὐχ ὑπάρχει, οὐδὲ τὸ Α τῶι Γ οὐχ ὑπάρξει. εἰ δὴ τὸ Β τῶι Α ἀντιστρέφει, καὶ τὸ Γ τῶι Α ἀντιστρέψει. ἔστω γὰρ τὸ Β μὴ ὑπάρχον τῶι Α· οὐδ᾽ ἄρα τὸ Γ· παντὶ γὰρ τῶι Γ τὸ Β ὑπῆρχεν. καὶ εἰ τῶι Β τὸ Γ ἀντιστρέφει, καὶ τὸ Α ἀντιστρέψει· καθ᾽ οὗ γὰρ ἅπαντος τὸ Β, καὶ τὸ Γ. καὶ εἰ τὸ Γ καὶ› πρὸς τὸ Α ἀντιστρέφει, καὶ τὸ Β ἀντιστρέψει. ὧι γὰρ τὸ Β, ↵ τὸ Γ· ὧι δὲ τὸ Α, τὸ Γ οὐχ ὑπάρχει. καὶ μόνον τοῦτο ἀπὸ τοῦ συμπεράσματος ἄρχεται, τὰ δ᾽ ἄλλα οὐχ ὁμοίως καὶ ἐπὶ τοῦ κατηγορικοῦ συλλογισμοῦ.	Quando vero convertuntur extremitates, necesse est et medium converti ad utramque; si enim A de C per B est, si convertitur et inest cui A omni, C et B A convertitur, et inest cui A omni, B per medium C, et C B convertitur per medium A. Et in non esse itidem, ut si B inest C, A vero non inest B, neque A inerit C. (0707D) Si ergo B convertatur ad A, et C ad A convertetur: sit enim B nulli A inexistens, ergo neque C, omni enim C inerat B, et si B convertitur ad C, et A convertetur ad C; nam de quocunque omnino B, et C. Et si C ad A convertitur, et B convertetur ad A: cui enim B inest, et C; cui autem C, A non inest; et solum hoc A conclusione incipit, alia autem non similiter, ut in praedicativo syllogismo.	Whenever the extremes are convertible it is necessary that the middle should be convertible with both. For if A belongs to C through B, then if A and C are convertible and C belongs everything to which A belongs, B is convertible with A, and B belongs to everything to which A belongs, through C as middle, and C is convertible with B through A as middle. Similarly if the conclusion is negative, e.g. if B belongs to C, but A does not belong to B, neither will A belong to C. If then B is convertible with A, C will be convertible with A. Suppose B does not belong to A; neither then will C: for ex hypothesi B belonged to all C. And if C is convertible with B, B is convertible also with A, for C is said of that of all of which B is said. And if C is convertible in relation to A and to B, B also is convertible in relation to A. For C belongs to that to which B belongs: but C does not belong to that to which A belongs. And this alone starts from the conclusion; the preceding moods do not do so as in the affirmative syllogism.
Πάλιν εἰ τὸ Α καὶ τὸ Β ἀντιστρέφει, καὶ τὸ Γ καὶ τὸ Δ ὡσαύτως, ἅπαντι δ᾽ ἀνάγκη τὸ Α ἢ τὸ Γ ὑπάρχειν, καὶ τὸ Β καὶ Δ οὕτως ἕξει ὥστε παντὶ θάτερον ὑπάρχειν. ἐπεὶ γὰρ ὧι τὸ Α, τὸ Β, καὶ ὧι τὸ Γ, τὸ Δ, παντὶ δὲ τὸ Α ἢ τὸ Γ καὶ οὐχ ἅμα, φανερὸν ὅτι καὶ τὸ Β ἢ τὸ Δ παντὶ καὶ οὐχ ἅμα [οἷον εἰ τὸἀγένητον ἄφθαρτον καὶ τὸ ἄφθαρτον ἀγένητον, ἀνάγκη τὸγένομενον φθαρτὸν καὶ τὸ φθαρτὸν γεγονέναι]· δύο γὰρ συλλογισμοὶ σύγκεινται.	(0708A) Rursum si A et B convertuntur, et C et D similiter, omni autem necesse est A aut C inesse, et B et D sic se habebunt, ut omni alterum insit; quoniam enim cui A B, E cui C D, omni autem A aut C, et non simul, manifestum quoniam et B aut D omni, et non simul, ut si ingenitum, incorruptibile, et incorruptibile ingenitum, necesse est quod factum est corruptibile et corruptibile factum esse, duo enim syllogismi constituti sunt.	Again if A and B are convertible, and similarly C and D, and if A or C must belong to anything whatever, then B and D will be such that one or other belongs to anything whatever. For since B belongs to that to which A belongs, and D belongs to that to which C belongs, and since A or C belongs to everything, but not together, it is clear that B or D belongs to everything, but not together. For example if that which is uncreated is incorruptible and that which is incorruptible is uncreated, it is necessary that what is created should be corruptible and what is corruptible should have been created. For two syllogisms have been put together.
πάλιν εἰ παντὶ μὲν τὸ Α ἢ τὸ Β καὶ τὸ Γ ἢ τὸ Δ, ἅμα δὲ μὴ ὑπάρχει, εἰ ἀντιστρέφει τὸ Α καὶ τὸ Γ, καὶ τὸ Β καὶ τὸ Δ ἀντιστρέφει. εἰ γὰρ τινὶ μὴ ὑπάρχει τὸ Β, ὧι τὸ Δ, δῆλον ὅτι τὸ Α ὑπάρχει. εἰ δὲ τὸ Α, καὶ τὸ Γ· ἀντιστρέφει γάρ. ὥστε ἅμα τὸ Γ καὶ τὸ Δ. τοῦτο δ᾽ ἀδύνατον. οἷον εἰ τὸ ἀγένητον ἄφθαρτον καὶ τὸ ἄφθαρτον ἀγένητον, ἀνάγκη τὸ γενόμενον φθαρτὸν καὶ τὸ φθαρτὸν γεγονέναι›. Ὅταν δὲ τὸ Α ὅλωι τῶι Β καὶ τῶι Γ ὑπάρχηι καὶ μηδενὸς ἄλλου κατηγορῆται, ὑπάρχηι δὲ καὶ τὸ Β παντὶ τῶι Γ, ἀνάγκη τὸ Α καὶ Β ἀντιστρέφειν· ἐπεὶ γὰρ κατὰ μόνων τῶν Β Γ λέγεται τὸ Α, κατηγορεῖται δὲ τὸ Β καὶ αὐτὸ αὑτοῦ καὶ τοῦ Γ, φανερὸν ὅτι καθ᾽ ὧν τὸ Α, καὶ τὸ Β λεχθήσεται πάντων πλὴν αὐτοῦ τοῦ Α. πάλιν ὅταν τὸ Α καὶ τὸ Β ὅλωι τῶι Γ ὑπάρχηι, ἀντιστρέφηι δὲ τὸ Γ τῶι Β, ἀνάγκη τὸ Α παντὶ τῶι Β ὑπάρχειν· ἐπεὶ γὰρ παντὶ τῶι Γ τὸ Α, τὸ δὲ Γ τῶι Β διὰ τὸ ἀντιστρέφειν, καὶ τὸ Α παντὶ τῶι Β ὑπάρξει.	Rursum si omni quidem, A vel B, et C vel D, simul autem non insunt, si convertitur A et C, et B et D convertetur. Nam si alicui non inest B, cui D, palam quoniam A inest; si autem A, et C, convertuntur enim; quare simul C et D, hoc autem impossibile. Quando autem A toti B et C inest, et de nullo alio praedicatur, inest autem et B omni C, necesse est A et B converti, quoniam enim de solis B C dicitur A, praedicatur autem B et idem dese et de C, manifestum quoniam de quibus A, et B dicetur omnibus, verum et de A. Rursum quando A et B, toti C insunt convertitur autem C B, necesse est A omni B inesse, quoniam enim omni C A, C autem B, eo quod convertuntur, et A omni B inerit. (0708B)	Again if A or B belongs to everything and if C or D belongs to everything, but they cannot belong together, then when A and C are convertible B and D are convertible. For if B does not belong to something to which D belongs, it is clear that A belongs to it. But if A then C: for they are convertible. Therefore C and D belong together. But this is impossible. When A belongs to the whole of B and to C and is affirmed of nothing else, and B also belongs to all C, it is necessary that A and B should be convertible: for since A is said of B and C only, and B is affirmed both of itself and of C, it is clear that B will be said of everything of which A is said, except A itself. Again when A and B belong to the whole of C, and C is convertible with B, it is necessary that A should belong to all B: for since A belongs to all C, and C to B by conversion, A will belong to all B.
Ὅταν δὲ δυοῖν ὄντοιν τὸ Α τοῦ Β αἱρετώτερον ἦι, ὄντων ἀντικειμένων, καὶ τὸ Δ τοῦ Γ ὡσαύτως, εἰ αἱρετώτερα τὰ Α Γ τῶν Β Δ, τὸ Α τοῦ Δ αἱρετώτερον. ὁμοίως γὰρ διωκτὸν τὸ Α καὶ φευκτὸν τὸ Β (ἀντικείμενα γάρ), καὶ τὸ Γ τῶι Δ (καὶ γὰρ ταῦτα ἀντίκειται). εἰ οὖν τὸ Α τῶι Δ ὁμοίως αἱρετόν, καὶ τὸ Β τῶι Γ φευκτόν· ἑκά- τερον γὰρ ἑκατέρωι ὁμοίως, φευκτὸν διωκτῶι. ὥστε καὶ τὰ ἄμφω τὰ Α Γ τοῖς Β Δ. ἐπεὶ δὲ μᾶλλον, οὐχ οἷόν τε ὁμοίως· καὶ γὰρ ἂν τὰ Β Δ ὁμοίως ἦσαν.	Quando autem duo fuerint opposita, ut A magis eligendum sit quam B, cum sint opposita, et D quam C similiter, si magis eligenda sunt A C quam B D, A magis eligendum quam D. Similiter enim sequendum A, et fugiendum B, opposita enim, et C ei quod est D, nam et haec opponuntur; si ergo A ei quod est D similiter eligendum, et B ei quod est C fugiendum, utrumque enim utrique similiter fugiendum eligendo; quare et haec ambo A C iis quae sunt B D, quoniam autem magis, non possibile similiter, nam et B D similiter erunt.	When, of two opposites A and B, A is preferable to B, and similarly D is preferable to C, then if A and C together are preferable to B and D together, A must be preferable to D. For A is an object of desire to the same extent as B is an object of aversion, since they are opposites: and C is similarly related to D, since they also are opposites. If then A is an object of desire to the same extent as D, B is an object of aversion to the same extent as C (since each is to the same extent as each-the one an object of aversion, the other an object of desire). Therefore both A and C together, and B and D together, will be equally objects of desire or aversion. But since A and C are preferable to B and D, A cannot be equally desirable with D; for then B along with D would be equally desirable with A along with C.
εἰ δὲ τὸ Δ τοῦ Α αἱρετώτερον, καὶ τὸ Β τοῦ Γ ἧττον φευκτόν· τὸ γὰρ ἔλαττον τῶι ἐλάττονι ἀντίκειται. αἱρετώτερον δὲ τὸ μεῖζον ἀγαθὸν καὶ ἔλαττον κακὸν ἢ τὸ ἔλαττον ἀγαθὸν καὶ μεῖζον κακόν· καὶ τὸ ἅπαν ἄρα, τὸ Β Δ, αἱρετώτερον τοῦ Α Γ. νῦν δ᾽ οὐκ ἔστιν. τὸ Α ἄρα αἱρετώτερον τοῦ Δ, καὶ τὸ Γ ἄρα τοῦ Β ἧττον φευκτόν.	Si autem D magis eligendum quam A, et B quam C minus fugiendum; nam quod minus est minori opponitur; magis autem eligendum est maius bonum et minus malum quam minus bonum et maius malum. (0708C) Universum igitur B D magis eligendum quam A C, nunc autem non est, ergo magis A eligendum quam D, et C ergo minus fugiendum quam B.	But if D is preferable to A, then B must be less an object of aversion than C: for the less is opposed to the less. But the greater good and lesser evil are preferable to the lesser good and greater evil: the whole BD then is preferable to the whole AC. But ex hypothesi this is not so. A then is preferable to D, and C consequently is less an object of aversion than B.
εἰ δὴ ἕλοιτο πᾶς ὁ ἐρῶν κατὰ τὸν ἔρωτα τὸ Α τὸ οὕτως ἔχειν ὥστε χαρίζεσθαι, καὶ τὸ μὴ χαρίζεσθαι τὸ ἐφ᾽ οὗ Γ, ἢ τὸ χαρίζεσθαι τὸ ἐφ᾽ οὗ Δ, καὶ ↵ τὸ μὴ τοιοῦτον εἶναι οἷον χαρίζεσθαι τὸ ἐφ᾽ οὗ Β, δῆλον ὅτι τὸ Α τὸ τοιοῦτον εἶναι αἱρετώτερόν ἐστιν ἢ τὸ χαρίζεσθαι. τὸ ἄρα φιλεῖσθαι τῆς συνουσίας αἱρετώτερον κατὰ τὸν ἔρωτα. μᾶλλον ἄρα ὁ ἔρως ἐστὶ τῆς φιλίας ἢ τοῦ συνεῖναι.	Si ergo eligat omnis amans secundum amorem A sic se habere, ut concedere, et non concedere in quo C, aut concedere in quo D, et non tale esse ut concedere in quo B, manifestum quoniam A huiusmodi esse, magis eligendum est quam concedere; ergo diligi quam conventio magis eligendum secundum amorem; magis ergo amor est in amicitia quam convenire.	If then every lover in virtue of his love would prefer A, viz. that the beloved should be such as to grant a favour, and yet should not grant it (for which C stands), to the beloved’s granting the favour (represented by D) without being such as to grant it (represented by B), it is clear that A (being of such a nature) is preferable to granting the favour. To receive affection then is preferable in love to sexual intercourse. Love then is more dependent on friendship than on intercourse.
εἰ δὲ μάλιστα τούτου, καὶ τέλος τοῦτο. τὸ ἄρα συνεῖναι ἢ οὐκ ἔστιν ὅλως ἢ τοῦ φιλεῖσθαι ἕνεκεν· καὶ γὰρ αἱ ἄλλαι ἐπιθυμίαι καὶ τέχναι οὕτως. Πῶς μὲν οὖν ἔχουσιν οἱ ὅροι κατὰ τὰς ἀντιστροφὰς καὶ τὸ αἱρετώτεροι ἢ φευκτότεροι εἶναι, φανερόν·	Si autem maxime huius, et finis haec, ergo convenire aut non est omnino, aut diligendi gratia, nam et aliae concupiscentiae et artes sic fiunt. Quomodo ergo se habent termini secundum conversiones, et in eo quod magis fugiendum vel magis eligendum sit, manifestum est.	And if it is most dependent on receiving affection, then this is its end. Intercourse then either is not an end at all or is an end relative to the further end, the receiving of affection. And indeed the same is true of the other desires and arts.

Chapter 23

Greek	Latin	English
	(PL 64 0708C) CAPUT XXIII. De epagoge, id est inductione.	23
68b8 ὅτι δ᾽ οὐ μόνον οἱ διαλεκτικοὶ καὶ ἀποδεικτικοὶ συλλογισμοὶ διὰ τῶν προειρημένων γίνονται σχημάτων, ἀλλὰ καὶ οἱ ῥητορικοὶ καὶ ἁπλῶς ἡτισοῦν πίστις καὶ ἡ καθ᾽ ὁποιανοῦν μέθοδον, νῦν ἂν εἴη λεκτέον. ἅπαντα γὰρ πιστεύομεν ἢ διὰ συλλογισμοῦ ἢ ἐξ ἐπαγωγῆς.	(0708D) Quoniam autem non solum dialectici et demonstrativi syllogismi per praedictas fiunt figuras, sed et rhetorici, sed et simpliciter quaecunque fides est, et secundum unamquamque artem, nunc erit dicendum. Omnia enim credimus per syllogismum aut ex inductione;	It is clear then how the terms are related in conversion, and in respect of being in a higher degree objects of aversion or of desire. We must now state that not only dialectical and demonstrative syllogisms are formed by means of the aforesaid figures, but also rhetorical syllogisms and in general any form of persuasion, however it may be presented. For every belief comes either through syllogism or from induction.
Ἐπαγωγὴ μὲν οὖν ἐστι καὶ ὁ ἐξ ἐπαγωγῆς συλλογισμὸς τὸ διὰ τοῦ ἑτέρου θάτερον ἄκρον τῶι μέσωι συλλογίσασθαι, οἷον εἰ τῶν Α Γ μέσον τὸ Β, διὰ τοῦ Γ δεῖξαι τὸ Α τῶι Β ὑπάρχον· οὕτω γὰρ ποιούμεθα τὰς ἐπαγωγάς. οἷον ἔστω τὸ Α μακρόβιον, τὸ δ᾽ ἐφ᾽ ὧι Β τὸ χολὴν μὴ ἔχον, ἐφ᾽ ὧι δὲ Γ τὸ καθ᾽ ἕκαστον μακρόβιον, οἷον ἄνθρωπος καὶ ἵππος καὶ ἡμίονος. τῶι δὴ Γ ὅλωι ὑπάρχει τὸ Α (πᾶν γὰρ τὸ Γ μακρόβιον)· ἀλλὰ καὶ τὸ Β, τὸ μὴ ἔχειν χολήν, παντὶ ὑπάρχει τῶι Γ.	ergo si inductio quidem est, et ex inductione syllogismus per alteram extremitatem medio syllogizare. Ut si eorum quae sunt A C medium sit B, per C ostendere A inesse B, sic enim facimus inductiones. Ut sit A longaevum, in quo autem B choleram non habere, in quo vero C singulare longaevum, ut homo, equus, et mulus. (0709A) Ergo toti B inest A, omne enim quod sibi cholera est, longaevum, sed et B non habere choleram, omni inest C;	Now induction, or rather the syllogism which springs out of induction, consists in establishing syllogistically a relation between one extreme and the middle by means of the other extreme, e.g. if B is the middle term between A and C, it consists in proving through C that A belongs to B. For this is the manner in which we make inductions. For example let A stand for long-lived, B for bileless, and C for the particular long-lived animals, e.g. man, horse, mule. A then belongs to the whole of C: for whatever is bileless is long-lived. But B also (’not possessing bile’) belongs to all C.
εἰ οὖν ἀντιστρέφει τὸ Γ τῶι Β καὶ μὴ ὑπερτείνει τὸ μέσον, ἀνάγκη τὸ Α τῶι Β ὑπάρχειν. δέδεικται γὰρ πρότερον ὅτι ἂν δύο ἄττα τῶι αὐτῶι ὑπάρχηι καὶ πρὸς θάτερον αὐτῶν ἀντιστρέφηι τὸ ἄκρον, ὅτι τῶι ἀντιστρέφοντι καὶ θάτερον ὑπάρξει τῶν κατηγορουμένων. δεῖ δὲ νοεῖν τὸ Γ τὸ ἐξ ἁπάντων τῶν καθ᾽ ἕκαστον συγκείμενον· ἡ γὰρ ἐπαγωγὴ διὰ πάντων.	si ergo convertatur C ei quod est B, et non transcendat medium, necesse est C inesse B. Ostensum enim est prius quoniam, si duo aliqua eidem insunt, et ad alteram eorum convertatur extremum, converso et alterum inerit praedicatorum. Oportet autem intelligere C ex singularibus omnibus compositum, nam inductio per omnia.	If then C is convertible with B, and the middle term is not wider in extension, it is necessary that A should belong to B. For it has already been proved that if two things belong to the same thing, and the extreme is convertible with one of them, then the other predicate will belong to the predicate that is converted. But we must apprehend C as made up of all the particulars. For induction proceeds through an enumeration of all the cases.
Ἔστι δ᾽ ὁ τοιοῦτος συλλογισμὸς τῆς πρώτης καὶ ἀμέσου προτάσεως· ὧν μὲν γὰρ ἔστι μέσον, διὰ τοῦ μέσου ὁ συλλογισμός, ὧν δὲ μὴ ἔστι, δι᾽ ἐπαγωγῆς. καὶ τρόπον τινὰ ἀντίκειται ἡ ἐπαγωγὴ τῶι συλλογισμῶι· ὁ μὲν γὰρ διὰ τοῦ μέσου τὸ ἄκρον τῶι τρίτωι δείκνυσιν, ἡ δὲ διὰ τοῦ τρίτου τὸ ἄκρον τῶι μέσωι. φύσει μὲν οὖν πρότερος καὶ γνωριμώτερος ὁ διὰ τοῦ μέσου συλλογισμός, ἡμῖν δ᾽ ἐναργέστερος ὁ διὰ τῆς ἐπαγωγῆς.	Syllogismus autem huiusmodi est primae et immediatae propositionis: quarum enim est medium, per medium est syllogismus; quorum vero non est, per inductionem. Et quodam modo opponitur inductio syllogismo, nam hic quidem per medium extremum de tertio ostendit, illa autem per tertium extremum de medio. Ergo natura quidem prior et notior per medium syllogismus, nobis autem manifestior qui est per inductionem.	Such is the syllogism which establishes the first and immediate premiss: for where there is a middle term the syllogism proceeds through the middle term; when there is no middle term, through induction. And in a way induction is opposed to syllogism: for the latter proves the major term to belong to the third term by means of the middle, the former proves the major to belong to the middle by means of the third. In the order of nature, syllogism through the middle term is prior and better known, but syllogism through induction is clearer to us.

Chapter 24

Greek	Latin	English
	(PL 64 0709A) CAPUT XXIV. De paradigmate, hoc est exemplo.	24
68b38 Παράδειγμα δ᾽ ἐστὶν ὅταν τῶι μέσωι τὸ ἄκρον ὑπάρχον δειχθῆι διὰ τοῦ ὁμοίου τῶι τρίτωι. δεῖ δὲ καὶ τὸ μέσον τῶι τρίτωι καὶ τὸ πρῶτον τῶι ὁμοίωι γνώριμον εἶναι ὑπάρχον. οἷον ἔστω τὸ Α κακόν, τὸ δὲ Β πρὸς ὁμόρους ἀναιρεῖσθαι ↵ πόλεμον, ἐφ᾽ ὧι δὲ Γ τὸ Ἀθηναίους πρὸς Θηβαίους, τὸ δ᾽ ἐφ᾽ ὧι Δ Θηβαίους πρὸς Φωκεῖς. ἐὰν οὖν βουλώμεθα δεῖξαι ὅτι τὸ Θηβαίοις πολεμεῖν κακόν ἐστι, ληπτέον ὅτι τὸ πρὸς τοὺς ὁμόρους πολεμεῖν κακόν. τούτου δὲ πίστις ἐκ τῶν ὁμοίων, οἷον ὅτι Θηβαίοις ὁ πρὸς Φωκεῖς. ἐπεὶ οὖν τὸ πρὸς τοὺς ὁμόρους κακόν, τὸ δὲ πρὸς Θηβαίους πρὸς ὁμόρους ἐστί, φανερὸν ὅτι τὸ πρὸς Θηβαίους πολεμεῖν κακόν.	(0709B) Exemplum autem est, quando medio extremum inesse ostenditur per id quod est simile tertio. Oportet autem et medium tertio, et primum simili notius esse, inesse. Ut sit A malum, B autem contra confines inferre bellum, in quo autem C Athenienses contra Thebanos, in quo autem D Thebanos contra Phocenses. Si ergo volumus ostendere quoniam Thebanis pugnare malum est, sumendum quoniam contra confines pugnare est malum, huius autem fides ex similibus, ut quoniam Thebanis contra Phocenses. Quoniam ergo contra confines malum, contra Thebanos autem contra confines est, manifestum quoniam contra Thebanos pugnare malum.	We have an ‘example’ when the major term is proved to belong to the middle by means of a term which resembles the third. It ought to be known both that the middle belongs to the third term, and that the first belongs to that which resembles the third. For example let A be evil, B making war against neighbours, C Athenians against Thebans, D Thebans against Phocians. If then we wish to prove that to fight with the Thebans is an evil, we must assume that to fight against neighbours is an evil. Evidence of this is obtained from similar cases, e.g. that the war against the Phocians was an evil to the Thebans. Since then to fight against neighbours is an evil, and to fight against the Thebans is to fight against neighbours, it is clear that to fight against the Thebans is an evil.
ὅτι μὲν οὖν τὸ Β τῶι Γ καὶ τῶι Δ ὑπάρχει, φανερόν (ἄμφω γάρ ἐστι πρὸς τοὺς ὁμόρους ἀναιρεῖσθαι πόλεμον), καὶ ὅτι τὸ Α τῶι Δ (Θηβαίοις γὰρ οὐ συνήνεγκεν ὁ πρὸς Φωκεῖς πόλεμοσ)· ὅτι δὲ τὸ Α τῶι Β ὑπάρχει, διὰ τοῦ Δ δειχθήσεται. τὸν αὐτὸν δὲ τρόπον κἂν εἰ διὰ πλειόνων τῶν ὁμοίων ἡ πίστις γένοιτο τοῦ μέσου πρὸς τὸ ἄκρον.	(0709C) Quoniam ergo B C et D inest, manifestum, utrumque enim est contra confines inferre bellum, et quoniam A D, Thebanis enim non fuit utile contra Phocenses bellum. Quoniam autem A inest B, per D ostendetur, eodem autem modo et si per plura similia fides fiat medii ad extremum.	Now it is clear that B belongs to C and to D (for both are cases of making war upon one’s neighbours) and that A belongs to D (for the war against the Phocians did not turn out well for the Thebans): but that A belongs to B will be proved through D. Similarly if the belief in the relation of the middle term to the extreme should be produced by several similar cases.
φανερὸν οὖν ὅτι τὸ παράδει- γμά ἐστιν οὔτε ὡς μέρος πρὸς ὅλον οὔτε ὡς ὅλον πρὸς μέρος, ἀλλ᾽ ὡς μέρος πρὸς μέρος, ὅταν ἄμφω μὲν ἦι ὑπὸ ταὐτό, γνώριμον δὲ θάτερον. καὶ διαφέρει τῆς ἐπαγωγῆς, ὅτι ἡ μὲν ἐξ ἁπάντων τῶν ἀτόμων τὸ ἄκρον ἐδείκνυεν ὑπάρχειν τῶι μέσωι καὶ πρὸς τὸ ἄκρον οὐ συνῆπτε τὸν συλλογισμόν, τὸ δὲ καὶ συνάπτει καὶ οὐκ ἐξ ἁπάντων δείκνυσιν.	Manifestum ergo quoniam exemplum est neque ut totum ad partem, neque ut pars ad totum, sed ut pars ad partem, quando ambo quidem insunt sub eodem, notum autem alterum. Et differt ab inductione, quoniam haec quidem ex omnibus individuis ostendebat inesse extremum medio, et ad extremum non copulabat syllogismum, hoc autem et copulat, et non ex omnibus ostendit.	Clearly then to argue by example is neither like reasoning from part to whole, nor like reasoning from whole to part, but rather reasoning from part to part, when both particulars are subordinate to the same term, and one of them is known. It differs from induction, because induction starting from all the particular cases proves (as we saw) that the major term belongs to the middle, and does not apply the syllogistic conclusion to the minor term, whereas argument by example does make this application and does not draw its proof from all the particular cases.

Chapter 25

Greek	Latin	English
	(PL 64 0709C) CAPUT XXV. De apagoge deductioneque.	25
69a20 Ἀπαγωγὴ δ᾽ ἐστὶν ὅταν τῶι μὲν μέσωι τὸ πρῶτον δῆλον ἦι ὑπάρχον, τῶι δ᾽ ἐσχάτωι τὸ μέσον ἄδηλον μέν, ὁμοίως δὲ πιστὸν ἢ μᾶλλον τοῦ συμπεράσματος· ἔτι ἂν ὀλίγα ἦι τὰ μέσα τοῦ ἐσχάτου καὶ τοῦ μέσου· πάντως γὰρ ἐγγύτερον εἶναι συμβαίνει τῆς ἐπιστήμης. οἷον ἔστω τὸ Α τὸ διδακτόν, ἐφ᾽ οὗ Β ἐπιστήμη, τὸ Γ δικαιοσύνη. ἡ μὲν οὖν ἐπιστήμη ὅτι διδακτόν, φανερόν· ἡ δ᾽ ἀρετὴ εἰ ἐπιστήμη, ἄδηλον.	(0709D) Deductio autem quando medio quidem primum palam est inesse, postremo autem medium dubium quidem, similiter autem credibile aut magis conclusione. Amplius, si pauciora sunt media postremo et medio, omnino enim propinquius esse accidit scientiae. Ut sit A docibile, in quo B disciplina, C iustitia, ergo disciplina quoniam docibilis, manifestum; iustitia autem si disciplina, dubium.	By reduction we mean an argument in which the first term clearly belongs to the middle, but the relation of the middle to the last term is uncertain though equally or more probable than the conclusion; or again an argument in which the terms intermediate between the last term and the middle are few. For in any of these cases it turns out that we approach more nearly to knowledge. For example let A stand for what can be taught, B for knowledge, C for justice. Now it is clear that knowledge can be taught: but it is uncertain whether virtue is knowledge.
εἰ οὖν ὁμοίως ἢ μᾶλλον πιστὸν τὸ Β Γ τοῦ Α Γ, ἀπαγωγή ἐστιν· ἐγγύτερον γὰρ τοῦ ἐπίστασθαι διὰ τὸ προσειληφέναι τὴν Α Β ἐπιστήμην, πρότερον οὐκ ἔχοντας. ἢ πάλιν εἰ ὀλίγα τὰ μέσα τῶν Β Γ· καὶ γὰρ οὕτως ἐγγύτερον τοῦ εἰδέναι. οἷον εἰ τὸ Δ εἴη τετραγωνίζεσθαι, τὸ δ᾽ ἐφ᾽ ὧι Ε εὐθύγραμμον, τὸ δ᾽ ἐφ᾽ ὧι Ζ κύκλος· εἰ τοῦ Ε Ζ ἓν μόνον εἴη μέσον, τὸ μετὰ μηνίσκων ἴσον γίνεσθαι εὐθυγράμμωι τὸν κύκλον, ἐγγὺς ἂν εἴη τοῦ εἰδέναι. ὅταν δὲ μήτε πιστότερον ἦι τὸ Β Γ τοῦ Α Γ μήτ᾽ ὀλίγα τὰ μέσα, οὐ λέγω ἀπαγωγήν. οὐδ᾽ ὅταν ἄμεσον ἦι τὸ Β Γ· ἐπιστήμη γὰρ τὸ τοιοῦτον.	Si igitur similiter aut magis credibile sit B C quam A C, deductio est, propinquius enim scientiae, per quod assumpserint A C, disciplinam prius non habentes. Aut rursum si pauciora media sint B C, nam et sic propinquius est scientiae. (0710A) Ut si D sit quadrangulare, in quo autem E rectilineum, in quo F circulus, si ergo eius quod est E F unum solum sit medium, per lunares figuras aequalem fieri rectilineo circulum propinquius erit scientiae. Quando autem neque credibilius est B C quam A C, neque pauca media, non dico deductionem, neque quando immediata est B C, disciplina enim quod eiusmodi est.	If now the statement BC is equally or more probable than AC, we have a reduction: for we are nearer to knowledge, since we have taken a new term, being so far without knowledge that A belongs to C. Or again suppose that the terms intermediate between B and C are few: for thus too we are nearer knowledge. For example let D stand for squaring, E for rectilinear figure, F for circle. If there were only one term intermediate between E and F (viz. that the circle is made equal to a rectilinear figure by the help of lunules), we should be near to knowledge. But when BC is not more probable than AC, and the intermediate terms are not few, I do not call this reduction: nor again when the statement BC is immediate: for such a statement is knowledge.

Chapter 26

Greek	Latin	English
	(PL 64 0710A) CAPUT XXVI. De instantia, quam enstasin dicunt.	26
69a37 Ἔνστασις δ᾽ ἐστὶ πρότασις προτάσει ἐναντία. διαφέρει δὲ τῆς προτάσεως, ὅτι τὴν μὲν ἔνστασιν ἐνδέχεται εἶναι ἐπὶ μέρους, τὴν δὲ πρότασιν ἢ ὅλως οὐκ ἐνδέχεται ἢ οὐκ ἐν τοῖς ↵ καθόλου συλλογισμοῖς. φέρεται δὲ ἡ ἔνστασις διχῶς καὶ διὰ δύο σχημάτων, διχῶς μὲν ὅτι ἢ καθόλου ἢ ἐν μέρει πᾶσα ἔνστασις, ἐκ δύο δὲ σχημάτων ὅτι ἀντικείμεναι φέρονται τῆι προτάσει, τὰ δ᾽ ἀντικείμενα ἐν τῶι πρώτωι καὶ τῶι τρίτωι σχήματι περαίνονται μόνοις.	Instantia autem est propositio propositioni contraria. Differt autem A propositione, quoniam contingit quidem instantiam esse in parte, propositionem vero aut omnino non contingit, aut non in universalibus syllogismus. (0710B) Fertur autem instantia duobus modis et per duas figuras: duobus modis quidem, quoniam aut universalis aut particularis omnis instantia; per duas autem figuras, quoniam oppositae feruntur propositioni, opposita autem in prima et tertia figura perficiuntur solis.	An objection is a premiss contrary to a premiss. It differs from a premiss, because it may be particular, but a premiss either cannot be particular at all or not in universal syllogisms. An objection is brought in two ways and through two figures; in two ways because every objection is either universal or particular, by two figures because objections are brought in opposition to the premiss, and opposites can be proved only in the first and third figures.
ὅταν γὰρ ἀξιώσηι παντὶ ὑπάρχειν, ἐνιστάμεθα ἢ ὅτι οὐδενὶ ἢ ὅτι τινὶ οὐχ ὑπάρχει· τούτων δὲ τὸ μὲν μηδενὶ ἐκ τοῦ πρώτου σχήματος, τὸ δὲ τινὶ μὴ ἐκ τοῦ ἐσχάτου. οἷον ἔστω τὸ Α μίαν εἶναι ἐπιστή- μην, ἐφ᾽ ὧι τὸ Β ἐναντία. προτείναντος δὴ μίαν εἶναι τῶν ἐναντίων ἐπιστήμην, ἢ ὅτι ὅλως οὐχ ἡ αὐτὴ τῶν ἀντικειμένων ἐνίσταται, τὰ δ᾽ ἐναντία ἀντικείμενα, ὥστε γίνεται τὸ πρῶτον σχῆμα, ἢ ὅτι τοῦ γνωστοῦ καὶ ἀγνώστου οὐ μία· τοῦτο δὲ τὸ τρίτον· κατὰ γὰρ τοῦ Γ, τοῦ γνωστοῦ καὶ ἀγνώστου, τὸ μὲν ἐναντία εἶναι ἀληθές, τὸ δὲ μίαν αὐτῶν ἐπιστήμην εἶναι ψεῦδος.	Nam quando postulatur omni inesse, instamus quoniam nulli, aut quoniam alicui non inest. Horum autem nulli quidem ex prima figura, alicui autem non ex postrema. Ut sit A unam esse disciplinam, in quo B contraria; proponit ergo unam esse contrariorum disciplinam, aut quoniam omnino non est eadem oppositorum instant. Contraria autem opposita, quare fit prima figura; aut quoniam noti et ignoti non una, haec autem tertia. Nam secundum tertiam notum et ignotum contraria quidem esse verum, unam autem esse eorum disciplinam, falsum.	If a man maintains a universal affirmative, we reply with a universal or a particular negative; the former is proved from the first figure, the latter from the third. For example let stand for there being a single science, B for contraries. If a man premises that contraries are subjects of a single science, the objection may be either that opposites are never subjects of a single science, and contraries are opposites, so that we get the first figure, or that the knowable and the unknowable are not subjects of a single science: this proof is in the third figure: for it is true of C (the knowable and the unknowable) that they are contraries, and it is false that they are the subjects of a single science.
πάλιν ἐπὶ τῆς στερητικῆς προτάσεως ὡσαύτως. ἀξιοῦντος γὰρ μὴ εἶναι μίαν τῶν ἐναντίων, ἢ ὅτι πάντων τῶν ἀντικειμένων ἢ ὅτι τινῶν ἐναντίων ἡ αὐτὴ λέγομεν, οἷον ὑγιεινοῦ καὶ νοσώδους· τὸ μὲν οὖν πάντων ἐκ τοῦ πρώτου, τὸ δὲ τινῶν ἐκ τοῦ τρίτου σχήματος.	(0710C) Rursum in privativa propositione similiter: cum postulat enim non esse contrariorum unam disciplinam, aut quoniam omnium oppositorum, aut quoniam contrariorum aliquorum est eadem disciplina, dicimus, ut sani et aegri, ergo omnium quidem ex prima, aliquorum vero ex tertia figura.	Similarly if the premiss objected to is negative. For if a man maintains that contraries are not subjects of a single science, we reply either that all opposites or that certain contraries, e.g. what is healthy and what is sickly, are subjects of the same science: the former argument issues from the first, the latter from the third figure.
Ἁπλῶς γὰρ ἐν πᾶσι καθόλου μὲν ἐνιστάμενον ἀνάγκη πρὸς τὸ καθόλου τῶν προτεινομένων τὴν ἀντίφασιν εἰπεῖν, οἷον εἰ μὴ τὴν αὐτὴν ἀξιοῖ τῶν ἐναντίων, πάντων εἰπόντα τῶν ἀντικειμένων μίαν. οὕτω δ᾽ ἀνάγκη τὸ πρῶτον εἶναι σχῆμα· μέσον γὰρ γίνεται τὸ καθόλου πρὸς τὸ ἐξ ἀρχῆς.	Simpliciter autem in omnibus universaliter quidem instantibus, necesse est ad id quod universale est proposito contradictionem dicere (ut si non unam existimet contrariorum omnium, dicere oppositorum unam; sic autem necesse est primam esse figuram, medium enim fit universale ad hoc quod ex principio);	In general if a man urges a universal objection he must frame his contradiction with reference to the universal of the terms taken by his opponent, e.g. if a man maintains that contraries are not subjects of the same science, his opponent must reply that there is a single science of all opposites. Thus we must have the first figure: for the term which embraces the original subject becomes the middle term.
ἐν μέρει δέ, πρὸς ὅ ἐστι καθόλου καθ᾽ οὗ λέγεται ἡ πρότασις, οἷον γνωστοῦ καὶ ἀγνώστου μὴ τὴν αὐτήν· τὰ γὰρ ἐναντία καθόλου πρὸς ταῦτα. καὶ γίνεται τὸ τρίτον σχῆμα· μέσον γὰρ τὸ ἐν μέρει λαμβανόμενον, οἷον τὸ γνωστὸν καὶ τὸ ἄγνωστον. ἐξ ὧν γὰρ ἔστι συλλογίσασθαι τοὐναντίον, ἐκ τούτων καὶ τὰς ἐνστάσεις ἐπιχειροῦμεν λέγειν. διὸ καὶ ἐκ μόνων τούτων τῶν σχημάτων φέρομεν· ἐν μόνοις γὰρ οἱ ἀντικείμενοι συλλογισμοί· διὰ γὰρ τοῦ μέσου οὐκ ἦν καταφατικῶς.	quod autem ad hoc in parte est universale, dicitur propositio, ut noti et ignoti non eamdem, nam contraria universale ad haec, et fit tertia figura, medium enim in parte sumptum, ut notum et ignotum. (0710D) Nam ex quibus est syllogizare contrarium, ex iis et instantias conamur dicere, quare et ex his solis figuris ferimus, nam in his solis oppositi syllogismi, per mediam enim figuram non fuit affirmare.	If the objection is particular, the objector must frame his contradiction with reference to a term relatively to which the subject of his opponent’s premiss is universal, e.g. he will point out that the knowable and the unknowable are not subjects of the same science: ‘contraries’ is universal relatively to these. And we have the third figure: for the particular term assumed is middle, e.g. the knowable and the unknowable. Premisses from which it is possible to draw the contrary conclusion are what we start from when we try to make objections. Consequently we bring objections in these figures only: for in them only are opposite syllogisms possible, since the second figure cannot produce an affirmative conclusion.
ἔτι δὲ κἂν λόγου δέοιτο πλείονος ἡ διὰ τοῦ μέσου σχήματος, οἷον εἰ μὴ δοίη τὸ Α τῶι Β ὑπάρχειν διὰ τὸ μὴ ἀκολουθεῖν αὐτῶι τὸ Γ. τοῦτο γὰρ δι᾽ ἄλλων προτάσεων δῆλον· οὐ δεῖ δὲ εἰς ἄλλα ἐκτρέπεσθαι τὴν ἔνστασιν, ἀλλ᾽ εὐθὺς φανερὰν ἔχειν τὴν ἑτέραν πρότασιν. [διὸ καὶ τὸ σημεῖον ἐκ μόνου τούτου τοῦ σχήματος οὐκ ἔστιν.]	Amplius autem et si sit, oratione indiget plurima, quae est per mediam figuram, ut si non concedant A inesse B, eo quod non sequitur hoc C, hoc enim per alias propositiones manifestum; non oportet autem instantiam converti ad alia, sed statim manifestam habere alteram propositionem. Quapropter et signum ex sola hac figura non est.	Besides, an objection in the middle figure would require a fuller argument, e.g. if it should not be granted that A belongs to B, because C does not follow B. This can be made clear only by other premisses. But an objection ought not to turn off into other things, but have its new premiss quite clear immediately. For this reason also this is the only figure from which proof by signs cannot be obtained.
Ἐπισκεπτέον δὲ καὶ περὶ τῶν ἄλλων ἐνστάσεων, οἷον περὶ τῶν ἐκ τοῦ ἐναντίου καὶ τοῦ ὁμοίου καὶ τοῦ κατὰ δόξαν, καὶ ↵ εἰ τὴν ἐν μέρει ἐκ τοῦ πρώτου ἢ τὴν στερητικὴν ἐκ τοῦ μέσου δυνατὸν λαβεῖν.	Perspiciendum autem et de aliis instantiis, ut de iis quae sunt ex contrario, et simili, et secundum opinionem, et si particularem ex prima, vel privativam ex media possibile est sumere.	We must consider later the other kinds of objection, namely the objection from contraries, from similars, and from common opinion, and inquire whether a particular objection cannot be elicited from the first figure or a negative objection from the second.

Chapter 27

Greek	Latin	English
	(PL 64 0710D) CAPUT XXVII. De eicote, hoc est consentaneo signo, indicio, et enthymemate.	27
Ἐνθύμημα δὲ ἐστὶ συλλογισμὸς ἐξ εἰκότων ἢ σημείων,› 70a2 εἰκὸς δὲ καὶ σημεῖον οὐ ταὐτόν ἐστιν, ἀλλὰ τὸ μὲν εἰκός ἐστι πρότασις ἔνδοξος· ὁ γὰρ ὡς ἐπὶ τὸ πολὺ ἴσασιν οὕτω γινόμενον ἢ μὴ γινόμενον ἢ ὂν ἢ μὴ ὄν, τοῦτ᾽ ἐστὶν εἰκός, οἷον τὸ μισεῖν τοὺς φθονοῦντας ἢ τὸ φιλεῖν τοὺς ἐρωμένους.	(0711A) Eicos autem et signum non idem est, sed eicos quidem est propositio probabilis. Quod enim ut in pluribus sciunt sic factum; vel non factum, aut esse vel non esse, hoc est eicos, ut odire invidentes, vel diligere amantes.	A probability and a sign are not identical, but a probability is a generally approved proposition: what men know to happen or not to happen, to be or not to be, for the most part thus and thus, is a probability, e.g. ‘the envious hate’, ‘the beloved show affection’.
σημεῖον δὲ βούλεται εἶναι πρότασις ἀποδεικτικὴ ἢ ἀναγκαία ἢ ἔνδοξος· οὗ γὰρ ὄντος ἔστιν ἢ οὗ γενομένου πρότερον ἢ ὕστερον γέγονε τὸ πρᾶγμα, τοῦτο σημεῖόν ἐστι τοῦ γεγονέναι ἢ εἶναι.	Signum autem vult esse propositio demonstrativa, vel necessaria, vel probabilis; nam quo existente est, vel quo facto prius vel posterius res, signum est vel fuisse vel esse.	A sign means a demonstrative proposition necessary or generally approved: for anything such that when it is another thing is, or when it has come into being the other has come into being before or after, is a sign of the other’s being or having come into being.
[ἐνθύμημα μὲν οὖν ἐστὶ συλλογισμὸς ἐξ εἰκότων ἢ σημείων] λαμβάνεται δὲ τὸ σημεῖον τριχῶς, ὁσαχῶς καὶ τὸ μέσον ἐν τοῖς σχήμασιν· ἢ γὰρ ὡς ἐν τῶι πρώτωι ἢ ὡς ἐν τῶι μέσωι ἢ ὡς ἐν τῶι τρίτωι, οἷον τὸ μὲν δεῖξαι κύουσαν διὰ τὸ γάλα ἔχειν ἐκ τοῦ πρώτου σχήματος· μέσον γὰρ τὸ γάλα ἔχειν. ἐφ᾽ ὧι τὸ Α κύειν, τὸ Β γάλα ἔχειν, γυνὴ ἐφ᾽ ὧι Γ.	Enthymema ergo est syllogismus imperfectus ex eicotibus et signis. (0711B) Accipitur autem signum tripliciter, quoties et medium in figuris, aut enim ut in prima, aut ut in media, aut ut in tertia: ut ostendere quidem parientem esse, eo quod lac habeat, ex prima figura, medium enim lac habere, in quo A parere B, lac habere mulier in quo C.	Now an enthymeme is a syllogism starting from probabilities or signs, and a sign may be taken in three ways, corresponding to the position of the middle term in the figures. For it may be taken as in the first figure or the second or the third. For example the proof that a woman is with child because she has milk is in the first figure: for to have milk is the middle term. Let A represent to be with child, B to have milk, C woman.
τὸ δ᾽ ὅτι οἱ σοφοὶ σπουδαῖοι, Πιττακὸς γὰρ σπουδαῖος, διὰ τοῦ ἐσχάτου. ἐφ᾽ ὧι Α τὸ σπουδαῖον, ἐφ᾽ ὧι Β οἱ σοφοί, ἐφ᾽ ὧι Γ Πιττακός. ἀληθὲς δὴ καὶ τὸ Α καὶ τὸ Β τοῦ Γ κατηγορῆσαι· πλὴν τὸ μὲν οὐ λέγουσι διὰ τὸ εἰδέναι, τὸ δὲ λαμβάνουσιν.	Quoniam autem sapientes, studiosi, nam Pittacus est studiosus, per postremam, in quo A studiosum, in quo B sapientes, in quo C Pittacus. Verum igitur A et B de C praedicari; sed hoc quidem non dicunt quia notum sit, illud vero sumunt.	The proof that wise men are good, since Pittacus is good, comes through the last figure. Let A stand for good, B for wise men, C for Pittacus. It is true then to affirm both A and B of C: only men do not say the latter, because they know it, though they state the former.
τὸ δὲ κύειν, ὅτι ὠχρά, διὰ τοῦ μέσου σχήματος βούλεται εἶναι· ἐπεὶ γὰρ ἕπεται ταῖς κυούσαις τὸ ὠχρόν, ἀκολουθεῖ δὲ καὶ ταύτηι, δεδεῖχθαι οἴονται ὅτι κύει. τὸ ὠχρὸν ἐφ᾽ οὗ τὸ Α, τὸ κύειν ἐφ᾽ οὗ Β, γυνὴ ἐφ᾽ οὗ Γ. Ἐὰν μὲν οὖν ἡ μία λεχθῆι πρότασις, σημεῖον γίνεται μόνον, ἐὰν δὲ καὶ ἡ ἑτέρα προσληφθῆι, συλλογισμός, οἷον ὅτι Πιττακὸς ἐλευθέριος· οἱ γὰρ φιλότιμοι ἐλευθέριοι, Πιττακὸς δὲ φιλότιμος.	Peperisse autem quoniam pallida, per mediam figuram vult esse; quoniam enim sequitur parientes pallor, sequitur autem et hanc, ostensum esse arbitrantur quoniam peperit. Pallor in quo A, parere in quo B, mulier in quo C. Ergo si una quidem dicatur propositio, signum fit solum, si autem et altera sumitur, syllogismus. Ut Pittacus liberalis, nam ambitiosi liberales, Pittacus autem ambitiosus.	The proof that a woman is with child because she is pale is meant to come through the middle figure: for since paleness follows women with child and is a concomitant of this woman, people suppose it has been proved that she is with child. Let A stand for paleness, B for being with child, C for woman. Now if the one proposition is stated, we have only a sign, but if the other is stated as well, a syllogism, e.g. ‘Pittacus is generous, since ambitious men are generous and Pittacus is ambitious.’
ἢ πάλιν ὅτι οἱ σοφοὶ ἀγαθοί· Πιττακὸς γὰρ ἀγαθός, ἀλλὰ καὶ σοφός. οὕτω μὲν οὖν γίνονται συλλογισμοί, πλὴν ὁ μὲν διὰ τοῦ πρώτου σχήματος ἄλυτος, ἂν ἀληθὴς ἦι (καθόλου γάρ ἐστιν), ὁ δὲ διὰ τοῦ ἐσχάτου λύσιμος, κἂν ἀληθὲς ἦι τὸ συμπέρασμα, διὰ τὸ μὴ εἶναι καθόλου μηδὲ πρὸς τὸ πρᾶγμα τὸν συλλογισμόν· οὐ γὰρ εἰ Πιττακὸς σπουδαῖος, διὰ τοῦτο καὶ τοὺς ἄλλους ἀνάγκη σοφούς.	(0711C) Aut rursus, quoniam sapientes boni, Pittacus autem bonus, sed et sapiens, sic ergo fiunt syllogismi. Verum quidem per primam figuram insolubilis, si verus sit, universalis enim est. Qui autem per postremam, est solubilis, et si vera sit conclusio, eo quod non universalis, est in tertia, nec ad rem syllogismus, non enim si Pittacus est studiosus, propter hoc et alios necesse est esse sapientes.	Or again ‘Wise men are good, since Pittacus is not only good but wise.’ In this way then syllogisms are formed, only that which proceeds through the first figure is irrefutable if it is true (for it is universal), that which proceeds through the last figure is refutable even if the conclusion is true, since the syllogism is not universal nor correlative to the matter in question: for though Pittacus is good, it is not therefore necessary that all other wise men should be good.
ὁ δὲ διὰ τοῦ μέσου σχήματος ἀεὶ καὶ πάντως λύσιμος· οὐδέποτε γὰρ γίνεται συλλογισμὸς οὕτως ἐχόντων τῶν ὅρων· οὐ γὰρ εἰ ἡ κύουσα ὠχρά, ὠχρὰ δὲ καὶ ἥδε, κύειν ἀνάγκη ταύτην. ἀληθὲς μὲν οὖν ἐν ἅπασιν ὑπάρξει τοῖς σημείοις, διαφορὰς δ᾽ ἔχουσι τὰς εἰρημένας.	Qui vero per mediam figuram est, semper et omnino solubilis, nunquam enim syllogismus fit, sic se habentibus terminis. Non enim si quae peperit pallida, pallida autem et haec, necesse est parere hanc; ergo verum est quidem in omnibus figuris, differentias autem habent iam dictas.	But the syllogism which proceeds through the middle figure is always refutable in any case: for a syllogism can never be formed when the terms are related in this way: for though a woman with child is pale, and this woman also is pale, it is not necessary that she should be with child. Truth then may be found in signs whatever their kind, but they have the differences we have stated.
↵ Ἢ δὴ οὕτω διαιρετέον τὸ σημεῖον, τούτων δὲ τὸ μέσον τεκμήριον ληπτέον (τὸ γὰρ τεκμήριον τὸ εἰδέναι ποιοῦν φασὶν εἶναι, τοιοῦτο δὲ μάλιστα τὸ μέσον), ἢ τὰ μὲν ἐκ τῶν ἄκρων σημεῖον λεκτέον, τὰ δ᾽ ἐκ τοῦ μέσου τεκμήριον· ἐνδοξότατον γὰρ καὶ μάλιστα ἀληθὲς τὸ διὰ τοῦ πρώτου σχήματος.	An igitur sic dividendum signum? (0712A) horum autem medium indicium sumendum, nam indicium dicunt esse quod scire facit, tale autem maxime medium, an vero quae quidem ab extremitatibus signa dicenda, quae autem ex medio indicium? probabilissimum enim et maxime veram est quod est per primam figuram.	We must either divide signs in the way stated, and among them designate the middle term as the index (for people call that the index which makes us know, and the middle term above all has this character), or else we must call the arguments derived from the extremes signs, that derived from the middle term the index: for that which is proved through the first figure is most generally accepted and most true.
	(PL 64 0712A) CAPUT XXVIII. De syllogismo physiognomico.
Τὸ δὲ φυσιογνωμονεῖν δυνατόν ἐστιν, εἴ τις δίδωσιν ἅμα μεταβάλλειν τὸ σῶμα καὶ τὴν ψυχὴν ὅσα φυσικά ἐστι παθήματα· μαθὼν γὰρ ἴσως μουσικὴν μεταβέβληκέ τι τὴν ψυχήν, ἀλλ᾽ οὐ τῶν φύσει ἡμῖν ἐστὶ τοῦτο τὸ πάθος, ἀλλ᾽ οἷον ὀργαὶ καὶ ἐπιθυμίαι τῶν φύσει κινήσεων.	Naturas autem cognoscere possibile est, si quis concedat simul transmutare corpus et animam, quaecunque sunt naturales passiones; discens enim aliquis fortasse musicam, transmutavit secundum quid animam, sed non earum quae natura nobis insunt, haec est passio, sed ut irae et concupiscentiae, et naturalium motionum.	It is possible to infer character from features, if it is granted that the body and the soul are changed together by the natural affections: I say ‘natural’, for though perhaps by learning music a man has made some change in his soul, this is not one of those affections which are natural to us; rather I refer to passions and desires when I speak of natural emotions.
εἰ δὴ τοῦτό τε δοθείη καὶ ἓν ἑνὸς σημεῖον εἶναι, καὶ δυναίμεθα λαμβάνειν τὸ ἴδιον ἑκάστου γένους πάθος καὶ σημεῖον, δυνησόμεθα φυσιογνωμονεῖν. εἰ γάρ ἐστιν ἰδίαι τινὶ γένει ὑπάρχον ἀτόμωι πάθος, οἷον τοῖς λέουσιν ἀνδρεία, ἀνάγκη καὶ σημεῖον εἶναί τι· συμπάσχειν γὰρ ἀλλήλοις ὑπόκειται. καὶ ἔστω τοῦτο τὸ μεγάλα τὰ ἀκρωτήρια ἔχειν· ὁ καὶ ἄλλοις ὑπάρχειν γένεσι μὴ ὅλοις ἐνδέχεται.	(0712B) Si igitur et hoc det, et unum unius signum esse, et possumus sumere proprium uniuscuiusque generis passionem et signum, poterimus naturas cognoscere. Si enim est proprie alicui generi individuo existens passio, ut si leonibus fortitudo, necesse est et signum esse aliquod, compati enim sibi invicem positum est, et sit hoc magnas summitates habere, quod et aliis generibus, non totis contingit.	If then this were granted and also that for each change there is a corresponding sign, and we could state the affection and sign proper to each kind of animal, we shall be able to infer character from features. For if there is an affection which belongs properly to an individual kind, e.g. courage to lions, it is necessary that there should be a sign of it: for ex hypothesi body and soul are affected together. Suppose this sign is the possession of large extremities: this may belong to other kinds also though not universally.
τὸ γὰρ σημεῖον οὕτως ἴδιόν ἐστιν, ὅτι ὅλου γένους ἴδιόν ἐστι [πάθοσ], καὶ οὐ μόνου ἴδιον, ὥσπερ εἰώθαμεν λέγειν. ὑπάρξει δὴ καὶ ἐν ἄλλωι γένει τοῦτο, καὶ ἔσται ἀνδρεῖος [ὁ] ἄνθρωπος καὶ ἄλλο τι ζῶιον. ἕξει ἄρα τὸ σημεῖον· ἓν γὰρ ἑνὸς ἦν.	Nam signum sic proprium est, quoniam totius generis propria passio est, et non solius proprium, sicut solemus dicere. Erit ergo et in alio genere hoc, et erit fortis homo, et aliquod aliud animal; habebit ergo signum, unum enim unius erat.	For the sign is proper in the sense stated, because the affection is proper to the whole kind, though not proper to it alone, according to our usual manner of speaking. The same thing then will be found in another kind, and man may be brave, and some other kinds of animal as well. They will then have the sign: for ex hypothesi there is one sign corresponding to each affection.
εἰ τοίνυν ταῦτ᾽ ἐστί, καὶ δυνησόμεθα τοιαῦτα σημεῖα συλλέξαι ἐπὶ τούτων τῶν ζώιων ἃ μόνον ἓν πάθος ἔχει τι ἴδιον, ἕκαστον δ᾽ ἔχει σημεῖον, ἐπείπερ ἓν ἔχειν ἀνάγκη, δυνησόμεθα φυσιογνωμονεῖν.	(0712C) Si ergo haec sunt, poterimus talia signa colligere in iis animalibus quae solum unam passionem habent aliquam propriam, unaquaeque autem habet signum, et quoniam unum habere necesse est, poterimus naturas cognoscere.	If then this is so, and we can collect signs of this sort in these animals which have only one affection proper to them-but each affection has its sign, since it is necessary that it should have a single sign-we shall then be able to infer character from features.
εἰ δὲ δύο ἔχει ἴδια ὅλον τὸ γένος, οἷον ὁ λέων ἀνδρεῖον καὶ μεταδοτικόν, πῶς γνωσόμεθα πότερον ποτέρου σημεῖον τῶν ἰδίαι ἀκολουθούντων σημείων; ἢ εἰ ἄλλωι τινὶ μὴ ὅλωι ἄμφω, καὶ ἐν οἷς μὴ ὅλοις ἑκάτερον, ὅταν τὸ μὲν ἔχηι τὸ δὲ μή· εἰ γὰρ ἀνδρεῖος μὲν ἐλευθέριος δὲ μή, ἔχει δὲ τῶν δύο τοδί, δῆλον ὅτι καὶ ἐπὶ τοῦ λέοντος τοῦτο σημεῖον τῆς ἀνδρείας.	Si vero duo habet propria totum genus, ut leo, forte et communicativum, quomodo cognoscemus utrum utrius sit signum, eorum signorum quae proprie sequuntur? An si et alii alicui non toti ambo, et in quibus non totis utrumque, quando hoc quidem habet, illud autem non? nam si fortis quidem, liberalis autem non, habet autem duorum hoc, palam quoniam et in leone hoc signum fortitudinis.	But if the kind as a whole has two properties, e.g. if the lion is both brave and generous, how shall we know which of the signs which are its proper concomitants is the sign of a particular affection? Perhaps if both belong to some other kind though not to the whole of it, and if, in those kinds in which each is found though not in the whole of their members, some members possess one of the affections and not the other: e.g. if a man is brave but not generous, but possesses, of the two signs, large extremities, it is clear that this is the sign of courage in the lion also.
Ἔστι δὴ τὸ φυσιογνωμονεῖν τῶι ἐν τῶι πρώτωι σχήματι τὸ μέσον τῶι μὲν πρώτωι ἄκρωι ἀντιστρέφειν, τοῦ δὲ τρίτου ὑπερτείνειν καὶ μὴ ἀντιστρέφειν, οἷον ἀνδρεία τὸ Α, τὰ ἀκρωτήρια μεγάλα ἐφ᾽ οὗ Β, τὸ δὲ Γ λέων. ὧι δὴ τὸ Γ, τὸ Β παντί, ἀλλὰ καὶ ἄλλοις. ὧι δὲ τὸ Β, τὸ Α παντὶ καὶ οὐ πλείοσιν, ἀλλ᾽ ἀντιστρέφει· εἰ δὲ μή, οὐκ ἔσται ἓν ἑνὸς σημεῖον.	Est vero naturas cognoscere in prima quidem figura, eo quod medium priori extremitati convertitur, tertiam autem transcendit, et non convertitur, ut sit fortitudo A, summitates magnas habere in quo B, C autem leo; ergo cui C, B omni, sed et aliis, cui autem B, A omni, et non pluribus, sed; convertitur si autem non, non erit unum unius signum.	To judge character from features, then, is possible in the first figure if the middle term is convertible with the first extreme, but is wider than the third term and not convertible with it: e.g. let A stand for courage, B for large extremities, and C for lion. B then belongs to everything to which C belongs, but also to others. But A belongs to everything to which B belongs, and to nothing besides, but is convertible with B: otherwise, there would not be a single sign correlative with each affection.