Authors/Aristotle/priora/Liber 1/C46

Chapter 46

Greek	Latin	English
	(PL 64 0683A) CAPUT XLII. De syllogismis infinitis, et regulis consequentiarum.	46
50b5 διαφέρει δέ τι ἐν τῶι κατασκευάζειν ἢ ἀνασκευάζειν τὸ ὑπολαμβάνειν ἢ ταὐτὸν ἢ ἕτερον σημαίνειν τὸ μὴ εἶναι τοδὶ καὶ εἶναι μὴ τοῦτο, οἷον τὸ μὴ εἶναι λευκὸν τῶι εἶναι μὴ λευκόν. οὐ γὰρ ταὐτὸν σημαίνει, οὐδ᾽ ἔστιν ἀπόφασις τοῦ εἶναι λευκὸν τὸ εἶναι μὴ λευκόν, ἀλλὰ τὸ μὴ εἶναι λευκόν.	Differt autem in construendo vel destruendo opinari, aut idem, aut diversum significare, non esse hoc, et esse non hoc, ut non esse album, ei quod est esse non album; non enim idem significant, nec est negatio eius quae est esse album ea quae est esse non album, sed non esse album.	In establishing or refuting, it makes some difference whether we suppose the expressions ‘not to be this’ and ‘to be not-this’ are identical or different in meaning, e.g. ‘not to be white’ and ‘to be not-white’. For they do not mean the same thing, nor is ‘to be not-white’ the negation of ‘to be white’, but ‘not to be white’.
λόγος δὲ τούτου ὅδε. ὁμοίως γὰρ ἔχει τὸ δύναται βαδίζειν πρὸς τὸ δύναται οὐ βαδίζειν τῶι ἔστι λευκόν πρὸς τὸ ἔστιν οὐ λευκόν, καὶ ἐπίσταται τἀγαθόν πρὸς τὸ ἐπίσταται τὸ οὐκ ἀγαθόν. τὸ γὰρ ἐπίσταται τἀγαθόν ἢ ἔστιν ἐπιστάμενος τἀγαθόν οὐδὲν διαφέρει, οὐδὲ τὸ δύναται βαδί ζειν ἢ ἔστι δυνάμενος βαδίζειν· ὥστε καὶ τὰ ἀντικείμενα, οὐ δύναται βαδίζειν – οὐκ ἔστι δυνάμενος βαδίζειν. εἰ οὖν τὸ οὐκ ἔστι δυνάμενος βαδίζειν ταὐτὸ σημαίνει καὶ ἔστι δυνάμενος οὐ βαδίζειν ἢ μὴ βαδίζειν, ταῦτά γε ἅμα ὑπάρξει ταὐτῶι (ὁ γὰρ αὐτὸς δύναται καὶ βαδίζειν καὶ μὴ βαδί ζειν, καὶ ἐπιστήμων τἀγαθοῦ καὶ τοῦ μὴ ἀγαθοῦ ἐστί), φάσις δὲ καὶ ἀπόφασις οὐχ ὑπάρχουσιν αἱ ἀντικείμεναι ἅμα τῶι αὐτῶι.	(0683B) Ratio autem huius haec est; similiter enim se habet possibile est ambulare ad possibile non ambulare, id quae est esse album ad esse non album, et scit bonum ad scit non bonum: nam scit bonum vel sciens bonum nihil differt, neque potest ambulare vel est potens ambulare; quare et opposita, non potest ambulare et non est potens ambulare. Si igitur non est potens ambulare idem significat et est potens non ambulare, ipsa simul inerunt eidem, nam idem potest ambulare et non ambulare, et idem sciens bonum et non bonum est. Affirmatio autem et negatio non sunt oppositae simul in eodem.	The reason for this is as follows. The relation of ‘he can walk’ to ‘he can not-walk’ is similar to the relation of ‘it is white’ to ‘it is not-white’; so is that of ‘he knows what is good’ to ‘he knows what is not-good’. For there is no difference between the expressions ‘he knows what is good’ and ‘he is knowing what is good’, or ‘he can walk’ and ‘he is able to walk’: therefore there is no difference between their contraries ‘he cannot walk’-’he is not able to walk’. If then ‘he is not able to walk’ means the same as ‘he is able not to walk’, capacity to walk and incapacity to walk will belong at the same time to the same person (for the same man can both walk and not-walk, and is possessed of knowledge of what is good and of what is not-good), but an affirmation and a denial which are opposed to one another do not belong at the same time to the same thing.
ὥσπερ οὖν οὐ ταὐτό ἐστι τὸ μὴ ἐπίστασθαι τἀγαθὸν καὶ ἐπίστασθαι τὸ μὴ ἀγαθόν, οὐδ᾽ εἶναι μὴ ἀγαθὸν καὶ μὴ εἶναι ἀγαθὸν ταὐτόν. τῶν γὰρ ἀνάλογον ἐὰν θάτερα ἦι ἕτερα, καὶ θάτερα. οὐδὲ τὸ εἶναι μὴ ἴσον καὶ τὸ μὴ εἶναι ἴσον· τῶι μὲν γὰρ ὑπόκειταί τι, τῶι ὄντι μὴ ἴσωι, καὶ τοῦτ᾽ ἔστι τὸ ἄνισον, τῶι δ᾽ οὐδέν. διόπερ ἴσον μὲν ἢ ἄνισον οὐ πᾶν, ἴσον δ᾽ ἢ οὐκ ἴσον πᾶν.	(0683C) Quemadmodum ergo non idem est, non scire bonum et scire non bonum, nec esse non bonum et non esse bonum idem, nam proportionalium, si alterum sit, et alterum, nec esse non aequale et non esse aequale idem, huic enim quod est non aequale subiacet aliquid, et hoc est inaequale, illi vero nihil, eo quod aequale quidem vel inaequale non omne est, aequale autem vel non aequale omne;	As then ‘not to know what is good’ is not the same as ‘to know what is not good’, so ‘to be not-good’ is not the same as ‘not to be good’. For when two pairs correspond, if the one pair are different from one another, the other pair also must be different. Nor is ‘to be not-equal’ the same as ‘not to be equal’: for there is something underlying the one, viz. that which is not-equal, and this is the unequal, but there is nothing underlying the other. Wherefore not everything is either equal or unequal, but everything is equal or is not equal.
ἔτι τὸ ἔστιν οὐ λευκὸν ξύλον καὶ οὐκ ἔστι λευκὸν ξύλον οὐχ ἅμα ὑπάρχει. εἰ γάρ ἐστι ξύλον οὐ λευκόν, ἔσται ξύλον· τὸ δὲ μὴ ὂν λευκὸν ξύλον οὐκ ἀνάγκη ξύλον εἶναι. ὥστε φανερὸν ὅτι οὐκ ἔστι τοῦ ἔστιν ἀγαθόν τὸ ἔστιν οὐκ ἀγαθόν ἀπόφασις. εἰ οὖν κατὰ παντὸς ἑνὸς ἢ φάσις ἢ ἀπόφασις ἀληθής, εἰ μὴ ἔστιν ἀπόφασις, δῆλον ὡς κατάφασις ἄν πως εἴη. καταφάσεως δὲ πάσης ἀπόφασις ἔστιν· καὶ ταύτης ἄρα τὸ οὐκ ἔστιν οὐκ ἀγαθόν.	amplius, est non album lignum et non est album lignum non simul sunt, si enim est lignum non album, erit lignum, quod autem non est album lignum, non necesse est esse lignum: quare manifestum est quoniam non est eius quod est bonum, est non bonum, negatio; si ergo de omni uno vel affirmatio, vel negatio vera, si non est negatio, palam quoniam affirmatio aliquo modo erit; affirmationis autem omnis, negatio est, et huius ergo, ea quae est non est, non bonum.	Further the expressions ‘it is a not-white log’ and ‘it is not a white log’ do not imply one another’s truth. For if ‘it is a not-white log’, it must be a log: but that which is not a white log need not be a log at all. Therefore it is clear that ‘it is not-good’ is not the denial of ‘it is good’. If then every single statement may truly be said to be either an affirmation or a negation, if it is not a negation clearly it must in a sense be an affirmation. But every affirmation has a corresponding negation. The negation then of ‘it is not-good’ is ‘it is not not-good’.
Ἔχει δὲ τάξιν τήνδε πρὸς ἄλληλα. ἔστω τὸ εἶναι ἀγαθὸν ἐφ᾽ οὗ Α, τὸ δὲ μὴ εἶναι ἀγαθὸν ἐφ᾽ οὗ Β, τὸ δὲ εἶναι μὴ ἀγαθὸν ἐφ᾽ οὗ Γ, ὑπὸ τὸ Β, τὸ δὲ μὴ εἶναι μὴ ἀγαθὸν ἐφ᾽ οὗ Δ, ὑπὸ τὸ Α. παντὶ δὴ ὑπάρξει ἢ τὸ Α ἢ τὸ Β, καὶ οὐδενὶ τῶι αὐτῶι· καὶ ἢ τὸ Γ ἢ τὸ Δ, καὶ οὐδενὶ τῶι αὐτῶι. καὶ ὧι τὸ Γ, ἀνάγκη τὸ Β παντὶ ὑπάρχειν	(0683D) Habent autem ordinem hunc ad invicem, sit esse quidem bonum in quo A, non esse autem bonum in quo B, esse autem non bonum in quo C sub B, non esse autem non bonum in quo D sub A, omni ergo inerit aut A, aut B, et nulli eidem, et omni aut C, aut D, et nulli eidem, et cui C inest, necesse est B omni inesse.	The relation of these statements to one another is as follows. Let A stand for ‘to be good’, B for ‘not to be good’, let C stand for ‘to be not-good’ and be placed under B, and let D stand for not to be not-good’ and be placed under A. Then either A or B will belong to everything, but they will never belong to the same thing; and either C or D will belong to everything, but they will never belong to the same thing. And B must belong to everything to which C belongs.
(εἰ ↵ γὰρ ἀληθὲς εἰπεῖν ὅτι ἐστὶν οὐ λευκόν, καὶ ὅτι οὐκ ἔστι λευκὸν ἀληθές· ἀδύνατον γὰρ ἅμα εἶναι λευκὸν καὶ εἶναι μὴ λευκόν, ἢ εἶναι ξύλον οὐ λευκὸν καὶ εἶναι ξύλον λευκόν, ὥστ᾽ εἰ μὴ ἡ κατάφασις, ἡ ἀπόφασις ὑπάρξει), τῶι δὲ Β τὸ Γ οὐκ ἀεί (ὁ γὰρ ὅλως μὴ ξύλον, οὐδὲ ξύλον ἔσται οὐ λευκόν).	Si enim verum est dicere quoniam est non album, et quoniam non est album, verum; impossibile est enim simul esse album et esse non album, aut esse lignum album et esse lignum non album: quare si non affirmatio, et negatio inerit. Ei autem quod est B, non semper C, quod enim omnino non est lignum, neque lignum erit album, nec non album.	For if it is true to say ‘it is a not-white’, it is true also to say ‘it is not white’: for it is impossible that a thing should simultaneously be white and be not-white, or be a not-white log and be a white log; consequently if the affirmation does not belong, the denial must belong. But C does not always belong to B: for what is not a log at all, cannot be a not-white log either.
ἀνάπαλιν τοίνυν, ὧι τὸ Α, τὸ Δ παντί (ἢ γὰρ τὸ Γ ἢ τὸ Δ· ἐπεὶ δ᾽ οὐχ οἷόν τε ἅμα εἶναι μὴ λευκὸν καὶ λευκόν, τὸ Δ ὑπάρξει· κατὰ γὰρ τοῦ ὄντος λευκοῦ ἀληθὲς εἰπεῖν ὅτι οὐκ ἔστιν οὐ λευκόν), κατὰ δὲ τοῦ Δ οὐ παντὸς τὸ Α (κατὰ γὰρ τοῦ ὅλως μὴ ὄντος ξύλου οὐκ ἀληθὲς τὸ Α εἰπεῖν, ὡς ἔστι ξύλον λευκόν, ὥστε τὸ Δ ἀληθές, τὸ δ᾽ Α οὐκ ἀληθές, ὅτι ξύλον λευκόν). δῆλον δ᾽ ὅτι καὶ τὸ Α Γ οὐδενὶ τῶι αὐτῶι καὶ τὸ Β καὶ τὸ Δ ἐνδέχεται τινὶ τῶι αὐτῶι ὑπάρξαι.	E converso autem cui inest A, et D omni inest, aut enim C, aut D: quoniam autem non possunt simul esse non album et esse album, D inerit, nam de eo quod est album verum est dicere quoniam non est non album. (0684A) De D autem non omnino A erit, nam de eo quod omnino non est lignum, non verum est dicere A quoniam est lignum album; quare D verum est, et A non verum, quoniam est lignum album. Palam autem quoniam et A et C nulli eidem insunt sed B et D contingit eidem alicui inesse.	On the other hand D belongs to everything to which A belongs. For either C or D belongs to everything to which A belongs. But since a thing cannot be simultaneously not-white and white, D must belong to everything to which A belongs. For of that which is white it is true to say that it is not not-white. But A is not true of all D. For of that which is not a log at all it is not true to say A, viz. that it is a white log. Consequently D is true, but A is not true, i.e. that it is a white log. It is clear also that A and C cannot together belong to the same thing, and that B and D may possibly belong to the same thing.
Ὁμοίως δ᾽ ἔχουσι καὶ αἱ στερήσεις πρὸς τὰς κατηγορίας ταύτηι τῆι θέσει. ἴσον ἐφ᾽ οὗ τὸ Α, οὐκ ἴσον ἐφ᾽ οὗ Β, ἄνισον ἐφ᾽ οὗ Γ, οὐκ ἄνισον ἐφ᾽ οὗ Δ.	Similiter autem tem se habent et privationes ad praedicationes eadem positione: sit enim aequale in quo A, non aequale in quo B, inaequale in quo C, non inaequale in quo D.	Privative terms are similarly related positive ter terms respect of this arrangement. Let A stand for ‘equal’, B for ‘not equal’, C for ‘unequal’, D for ‘not unequal’.
Καὶ ἐπὶ πολλῶν δέ, ὧν τοῖς μὲν ὑπάρχει τοῖς δ᾽ οὐχ ὑπάρχει ταὐτόν, ἡ μὲν ἀπόφασις ὁμοίως ἀληθεύοιτ᾽ ἄν, ὅτι οὐκ ἔστι λευκὰ πάντα ἢ ὅτι οὐκ ἔστι λευκὸν ἕκαστον· ὅτι δ᾽ ἐστὶν οὐ λευκὸν ἕκαστον ἢ πάντα ἐστὶν οὐ λευκά, ψεῦδος.	In pluribus autem quorum his quidem inest, illis vero non inest idem, negatio quidem similiter vera fit, ut quoniam non sunt alba omnia, aut quoniam non est album unumquodque, aut quoniam est non album unumquodque, aut quoniam omnia sunt non alba, falsum est.	In many things also, to some of which something belongs which does not belong to others, the negation may be true in a similar way, viz. that all are not white or that each is not white, while that each is not-white or all are not-white is false.
ὁμοίως δὲ καὶ τοῦ ἔστι πᾶν ζῶιον λευκόν οὐ τὸ ἔστιν οὐ λευκὸν ἅπαν ζῶιον ἀπόφασις (ἄμφω γὰρ ψευδεῖσ), ἀλλὰ τὸ οὐκ ἔστι πᾶν ζῶιον λευκόν. Ἐπεὶ δὲ δῆλον ὅτι ἕτερον σημαί νει τὸ ἔστιν οὐ λευκόν καὶ οὐκ ἔστι λευκόν, καὶ τὸ μὲν κατάφασις τὸ δ᾽ ἀπόφασις, φανερὸν ὡς οὐχ ὁ αὐτὸς τρόπος τοῦ δεικνύναι ἑκάτερον, οἷον ὅτι ὁ ἂν ἦι ζῶιον οὐκ ἔστι λευκὸν ἢ ἐνδέχεται μὴ εἶναι λευκόν, καὶ ὅτι ἀληθὲς εἰπεῖν μὴ λευκόν· τοῦτο γάρ ἐστιν εἶναι μὴ λευκόν.	(0684B) Similiter autem et eius quae est omne animal album, non haec (est non album omne animal) negatio, ambae enim falsae, sed es, non omne animal album. Quoniam autem palam quod aliud significat est non album, et non est album, et illa quidem affirmatio, haec vero negatio, manifestum quoniam non est idem modus monstrandi utrumque, ut quoniam quidquid est animal, non est album, aut contingit non esse album, et quoniam verum dicere non album, hoc enim est esse non album.	Similarly also ‘every animal is not-white’ is not the negation of ‘every animal is white’ (for both are false): the proper negation is ‘every animal is not white’. Since it is clear that ‘it is not-white’ and ‘it is not white’ mean different things, and one is an affirmation, the other a denial, it is evident that the method of proving each cannot be the same, e.g. that whatever is an animal is not white or may not be white, and that it is true to call it not-white; for this means that it is not-white.
ἀλλὰ τὸ μὲν ἀληθὲς εἰπεῖν ἔστι λευκόν εἴτε μὴ λευκόν ὁ αὐτὸς τρόπος· κατασκευαστικῶς γὰρ ἄμφω διὰ τοῦ πρώτου δείκνυται σχήματος· τὸ γὰρ ἀληθὲς τῶι ἔστιν ὁμοίως τάττεται· τοῦ γὰρ ἀληθὲς εἰπεῖν λευκὸν οὐ τὸ ἀληθὲς εἰπεῖν μὴ λευκὸν ἀπόφασις, ἀλλὰ τὸ μὴ ἀληθὲς εἰπεῖν λευκόν. εἰ δὴ ἔσται ἀληθὲς εἰπεῖν ὁ ἂν ἦι ἄνθρωπος μουσικὸν εἶναι ἢ μὴ μουσικὸν εἶναι, ὁ ἂν ἦι ζῶιον ληπτέον ἢ εἶναι μουσικὸν ἢ εἶναι μὴ μουσικόν, καὶ δέδεικται. τὸ δὲ μὴ εἶναι μουσικὸν ὁ ἂν ἦι ἄνθρωπος, ἀνασκευαστικῶς δείκνυται κατὰ τοὺς εἰρημένους τρόπους τρεῖς.	Sed verum quidem dicere, est album, sive non album, idem modus. Constructive enim ambae per primam ostenduntur figuram, nam verum ei quod est similiter ordinatur, eius enim quae est, verum dicere album, non haec, verum dicere non album, negatio, sed haec, non est verum dicere album. (0684C) Si enim verum est dicere quidquid est homo musicum esse, aut non musicum esse, quidquid est animal sumendum musicum esse, aut non musicum esse, et ostensum est. Non esse autem musicum quidquid est homo, destructive monstratur secundum dictos tres modos.	But we may prove that it is true to call it white or not-white in the same way for both are proved constructively by means of the first figure. For the expression ‘it is true’ stands on a similar footing to ‘it is’. For the negation of ‘it is true to call it white’ is not ‘it is true to call it not-white’ but ‘it is not true to call it white’. If then it is to be true to say that whatever is a man is musical or is not-musical, we must assume that whatever is an animal either is musical or is not-musical; and the proof has been made. That whatever is a man is not musical is proved destructively in the three ways mentioned.
Ἁπλῶς δ᾽ ὅταν οὕτως ἔχηι τὸ Α καὶ τὸ Β ὥσθ᾽ ἅμα μὲν τῶι αὐτῶι μὴ ἐνδέχεσθαι, παντὶ δὲ ἐξ ἀνάγκης θάτε ↵ ρον, καὶ πάλιν τὸ Γ καὶ τὸ Δ ὡσαύτως, ἕπηται δὲ τῶι Γ τὸ Α καὶ μὴ ἀντιστρέφηι, καὶ τῶι Β τὸ Δ ἀκολουθήσει καὶ οὐκ ἀντιστρέψει· καὶ τὸ μὲν Α καὶ Δ ἐνδέχεται τῶι αὐτῶι, τὸ δὲ Β καὶ Γ οὐκ ἐνδέχεται. πρῶτον μὲν οὖν ὅτι τῶι Β τὸ Δ ἕπεται, ἐνθένδε φανερόν. ἐπεὶ γὰρ παντὶ τῶν Γ Δ θάτερον ἐξ ἀνάγκης, ὧι δὲ τὸ Β, οὐκ ἐνδέχεται τὸ Γ διὰ τὸ συνεπιφέρειν τὸ Α, τὸ δὲ Α καὶ Β μὴ ἐνδέχεσθαι τῶι αὐτῶι, φανερὸν ὅτι τὸ Δ ἀκολουθήσει. πάλιν ἐπεὶ τῶι Α τὸ Γ οὐκ ἀντιστρέφει, παντὶ δὲ τὸ Γ ἢ τὸ Δ, ἐνδέχεται τὸ Α καὶ τὸ Δ τῶι αὐτῶι ὑπάρχειν. τὸ δέ γε Β καὶ τὸ Γ οὐκ ἐνδέχεται διὰ τὸ συνακολουθεῖν τῶι Γ τὸ Α· συμβαίνει γάρ τι ἀδύνατον. φανερὸν οὖν ὅτι οὐδὲ τῶι Δ τὸ Β ἀντιστρέφει, ἐπείπερ ἐγχωρεῖ ἅμα τὸ Δ καὶ τὸ Α ὑπάρχειν.	Simpliciter autem quando sic se habent A et B, ut simul quidem eidem non contingant, omni autem de necessitate alterum, et rursum C et D similiter. Sequitur autem id quod est C, A, et non convertitur, et id quod est B sequetur D, et non convertitur, et A quidem et D contingunt eidem, B autem et C non contingunt. Primum ergo quoniam id quod est B sequitur D, hinc manifestum quoniam eorum quae sunt C D alterum ex necessitate omni inest, cui autem B non contingit C, eo quod simul infert A, A autem et B non contingunt eidem, manifestum quoniam D sequetur B. (0684D) Rursum quoniam ei quod est A non convertitur C, omni autem vel C, vel D, contingit A, et D eidem inesse; B autem et C non contingit, eo quod consequitur A id quod est C, accidit enim quiddam impossibile. Manifestum est ergo quoniam nec B ei quod est D convertitur, eo quod contingit simul A, D inesse.	In general whenever A and B are such that they cannot belong at the same time to the same thing, and one of the two necessarily belongs to everything, and again C and D are related in the same way, and A follows C but the relation cannot be reversed, then D must follow B and the relation cannot be reversed. And A and D may belong to the same thing, but B and C cannot. First it is clear from the following consideration that D follows B. For since either C or D necessarily belongs to everything; and since C cannot belong to that to which B belongs, because it carries A along with it and A and B cannot belong to the same thing; it is clear that D must follow B. Again since C does not reciprocate with but A, but C or D belongs to everything, it is possible that A and D should belong to the same thing. But B and C cannot belong to the same thing, because A follows C; and so something impossible results. It is clear then that B does not reciprocate with D either, since it is possible that D and A should belong at the same time to the same thing.
Συμβαίνει δ᾽ ἐνίοτε καὶ ἐν τῆι τοιαύτηι τάξει τῶν ὅρων ἀπατᾶσθαι διὰ τὸ μὴ τὰ ἀντικείμενα λαμβάνειν ὀρθῶς ὧν ἀνάγκη παντὶ θάτερον ὑπάρχειν· οἷον εἰ τὸ Α καὶ τὸ Β μὴ ἐνδέχεται ἅμα τῶι αὐτῶι, ἀνάγκη δ᾽ ὑπάρχειν, ὧι μὴ θάτερον, θάτερον, καὶ πάλιν τὸ Γ καὶ τὸ Δ ὡσαύτως, ὧι δὲ τὸ Γ, παντὶ ἕπεται τὸ Α. συμβήσεται γὰρ ὧι τὸ Δ, τὸ Β ὑπάρχειν ἐξ ἀνάγκης, ὅπερ ἐστὶ ψεῦδος. εἰλήφθω γὰρ ἀπόφασις τῶν Α Β ἡ ἐφ᾽ ὧι Ζ, καὶ πάλιν τῶν Γ Δ ἡ ἐφ᾽ ὧι Θ. ἀνάγκη δὴ παντὶ ἢ τὸ Α ἢ τὸ Ζ· ἢ γὰρ τὴν φάσιν ἢ τὴν ἀπόφασιν.	(0685A) Accidit autem aliquoties in huiusmodi terminorum ordine falli, eo quod opposita non sumantur recte, quorum necesse est omni alterum inesse: ut si A et B non contingunt simul eidem, necesse est autem inesse cui non alterum, alterum, et rursus C et D similiter, cui autem C omni sequitur A, accidet enim cui D, B inesse ex necessitate, quod falsum est; si sumatur enim negatio eorum quae sunt A B, ea quae est in quibus F, et rursus eorum quae sunt C D, ea quae est in quibus G. Necesse est igitur omni inesse vel A, vel F, aut enim affirmationem aut negationem,	It results sometimes even in such an arrangement of terms that one is deceived through not apprehending the opposites rightly, one of which must belong to everything, e.g. we may reason that ‘if A and B cannot belong at the same time to the same thing, but it is necessary that one of them should belong to whatever the other does not belong to: and again C and D are related in the same way, and follows everything which C follows: it will result that B belongs necessarily to everything to which D belongs’: but this is false. ‘Assume that F stands for the negation of A and B, and again that H stands for the negation of C and D. It is necessary then that either A or F should belong to everything: for either the affirmation or the denial must belong.
καὶ πάλιν ἢ τὸ Γ ἢ τὸ Θ· φάσις γὰρ καὶ ἀπόφασις. καὶ ὧι τὸ Γ, παντὶ τὸ Α ὑπόκειται. ὥστε ὧι τὸ Ζ, παντὶ τὸ Θ. πάλιν ἐπεὶ τῶν Ζ Β παντὶ θάτερον καὶ τῶν Θ Δ ὡσαύτως, ἀκολουθεῖ δὲ τῶι Ζ τὸ Θ, καὶ τῶι Δ ἀκολουθήσει τὸ Β· τοῦτο γὰρ ἴσμεν. εἰ ἄρα τῶι Γ τὸ Α, καὶ τῶι Δ τὸ Β. τοῦτο δὲ ψεῦδος· ἀνάπαλιν γὰρ ἦν ἐν τοῖς οὕτως ἔχουσιν ἡ ἀκολούθησις. οὐ γὰρ ἴσως ἀνάγκη παντὶ τὸ Α ἢ τὸ Ζ, οὐδὲ τὸ Ζ ἢ τὸ Β· οὐ γάρ ἐστιν ἀπόφασις τοῦ Α τὸ Ζ. τοῦ γὰρ ἀγαθοῦ τὸ οὐκ ἀγαθὸν ἀπόφασις· οὐ ταὐτὸ δ᾽ ἐστὶ τὸ οὐκ ἀγαθὸν τῶι οὔτ᾽ ἀγαθὸν οὔτ᾽ οὐκ ἀγαθόν. ὁμοίως δὲ καὶ ἐπὶ τῶν Γ Δ· αἱ γὰρ ἀποφάσεις αἱ εἰλημμέναι δύο εἰσίν.	et rursum, aut C, aut G; affirmatio enim et negatio, et cui C omni A subiacet, quare cui F omni hoc quod est G. Rursum quoniam eorum quae sunt F B omni alterum, et eorum quae sunt G D similiter. Sequitur autem G id quod est F, et id quod est D sequitur B, hoc enim scimus. (0686A) Si ergo A id quod est C, et id quod est D sequetur B, hoc autem falsum; E contrario enim erat in his (quae sic se habent) consequentia. Non enim fortasse necessarium omni inesse, aut A aut F, nec F aut B: non enim est negatio eius quod est A hoc quod est F, nam boni non bonum negatio; non autem est idem hoc quod est non bonum ei quod est neque bonum neque non bonum; similiter autem et in C D, nam negationes quae sumptae sunt, duae sunt.	And again either C or H must belong to everything: for they are related as affirmation and denial. And ex hypothesi A belongs to everything ever thing to which C belongs. Therefore H belongs to everything to which F belongs. Again since either F or B belongs to everything, and similarly either H or D, and since H follows F, B must follow D: for we know this. If then A follows C, B must follow D’. But this is false: for as we proved the sequence is reversed in terms so constituted. The fallacy arises because perhaps it is not necessary that A or F should belong to everything, or that F or B should belong to everything: for F is not the denial of A. For not good is the negation of good: and not-good is not identical with ‘neither good nor not-good’. Similarly also with C and D. For two negations have been assumed in respect to one term.