Authors/Aristotle/priora/Liber 1/C17

Chapter 17

Greek	Latin	English
	(PL 64 0659A) CAPUT XVI. De syllogismis ex ambabus contingentibus in secunda figura.	17
36b26 Ἐν δὲ τῶι δευτέρωι σχήματι ὅταν μὲν ἐνδέχεσθαι λαμβάνωσιν ἀμφότεραι αἱ προτάσεις, οὐδεὶς ἔσται συλλογισμός, οὔτε κατηγορικῶν οὔτε στερητικῶν τιθεμένων, οὔτε καθόλου οὔτε κατὰ μέρος· ὅταν δὲ ἡ μὲν ὑπάρχειν ἡ δ᾽ ἐνδέχεσθαι σημαίνηι, τῆς μὲν καταφατικῆς ὑπάρχειν σημαινούσης οὐδέποτ᾽ ἔσται, τῆς δὲ στερητικῆς τῆς καθόλου ἀεί. τὸν αὐτὸν δὲ τρόπον καὶ ὅταν ἡ μὲν ἐξ ἀνάγκης ἡ δ᾽ ἐνδέχεσθαι λαμβάνηται τῶν προτάσεων. δεῖ δὲ καὶ ἐν τούτοις λαμβάνειν τὸ ἐν τοῖς συμπεράσμασιν ἐνδεχόμενον ὥσπερ ἐν τοῖς πρότερον.	In secunda autem figura quando contingentes quidem sumuntur utraeque propositiones, nullus erit syllogismus, sive sint affirmativae, sive privativae, sive universales, sive particulares. (0659B) Quando autem haec quidem inesse, illa vero contingere significat, affirmativa quidem inesse significante, nunquam erit syllogismus, privativa universali existente, semper. Eodem modo et quando haec quidem ex necessitate, illa vero contingere assumatur, oportet autem et in his accipere quod in conclusionibus est contingens quemadmodum in prioribus.	In the second figure whenever both premisses are problematic, no syllogism is possible, whether the premisses are affirmative or negative, universal or particular. But when one premiss is assertoric, the other problematic, if the affirmative is assertoric no syllogism is possible, but if the universal negative is assertoric a conclusion can always be drawn. Similarly when one premiss is necessary, the other problematic. Here also we must understand the term ‘possible’ in the conclusion, in the same sense as before.
Πρῶτον οὖν δεικτέον ὅτι οὐκ ἀντιστρέφει τὸ ἐν τῶι ἐνδέχεσθαι στερητικόν, οἷον εἰ τὸ Α ἐνδέχεται μηδενὶ τῶι Β, οὐκ ἀνάγκη καὶ τὸ Β ἐνδέχεσθαι μηδενὶ τῶι Α. κείσθω γὰρ τοῦτο, καὶ ἐνδεχέσθω τὸ Β μηδενὶ τῶι Α ὑπάρχειν. οὐκοῦν ἐπεὶ ἀντιστρέφουσιν αἱ ἐν τῶι ἐνδέχεσθαι καταφάσεις ταῖς ἀποφάσεσι, καὶ αἱ ἐναντίαι καὶ αἱ ἀντικείμεναι, τὸ δὲ Β τῶι Α ἐνδέχεται μηδενὶ ὑπάρ ↵ χειν, φανερὸν ὅτι καὶ παντὶ ἂν ἐνδέχοιτο τῶι Α ὑπάρχειν. τοῦτο δὲ ψεῦδος· οὐ γὰρ εἰ τόδε τῶιδε παντὶ ἐνδέχεται, καὶ τόδε τῶιδε ἀναγκαῖον· ὥστ᾽ οὐκ ἀντιστρέφει τὸ στερητικόν.	Primum igitur ostendendum quoniam non convertitur in contingenti, privativa, ut si A contingit nulli B, non necesse est et B contingere nulli A. Ponatur enim hoc et contingat B nulli A inesse, ergo quoniam convertuntur quae sunt in eo quod est contingere affirmationes negationibus, et contrariae, et contraiacentes, B autem contingit nulli A inesse, manifestum est quoniam et omni A contingit B inesse. Hoc autem falsum est. (0659C) Non enim si hoc huic omni contingit, et hoc huic contingat necessarium, quare non convertitur privativa.	First we must point out that the negative problematic proposition is not convertible, e.g. if A may belong to no B, it does not follow that B may belong to no A. For suppose it to follow and assume that B may belong to no A. Since then problematic affirmations are convertible with negations, whether they are contraries or contradictories, and since B may belong to no A, it is clear that B may belong to all A. But this is false: for if all this can be that, it does not follow that all that can be this: consequently the negative proposition is not convertible.
ἔτι δ᾽ οὐδὲν κωλύει τὸ μὲν Α τῶι Β ἐνδέχεσθαι μηδενί, τὸ δὲ Β τινὶ τῶν Α ἐξ ἀνάγκης μὴ ὑπάρχειν, οἷον τὸ μὲν λευκὸν παντὶ ἀνθρώπωι ἐνδέχεται μὴ ὑπάρχειν (καὶ γὰρ ὑπάρχειν), ἄνθρωπον δ᾽ οὐκ ἀληθὲς εἰπεῖν ὡς ἐνδέχεται μηδενὶ λευκῶι· πολλοῖς γὰρ ἐξ ἀνάγκης οὐχ ὑπάρχει, τὸ δ᾽ ἀναγκαῖον οὐκ ἦν ἐνδεχόμενον.	Amplius autem nihil prohibet A quidem contingere nulli B, B autem alicui A ex necessitate non inesse, ut album quidem contingit omni homini non inesse, nam et inesse hominem autem non verum est dicere, quoniam contingit nulli albo, pluribus enim ex necessitate non inest, necessarium autem non inerat contingens.	Further, these propositions are not incompatible, ‘A may belong to no B’, ‘B necessarily does not belong to some of the As’; e.g. it is possible that no man should be white (for it is also possible that every man should be white), but it is not true to say that it is possible that no white thing should be a man: for many white things are necessarily not men, and the necessary (as we saw) other than the possible.
Ἀλλὰ μὴν οὐδ᾽ ἐκ τοῦ ἀδυνάτου δειχθήσε ται ἀντιστρέφον, οἷον εἴ τις ἀξιώσειεν, ἐπεὶ ψεῦδος τὸ ἐνδέχεσθαι τὸ Β τῶι Α μηδενὶ ὑπάρχειν, ἀληθὲς τὸ μὴ ἐνδέχεσθαι μηδενί (φάσις γὰρ καὶ ἀπόφασισ), εἰ δὲ τοῦτ᾽, ἀληθὲς ἐξ ἀνάγκης τινὶ τῶι Α ὑπάρχειν· ὥστε καὶ τὸ Α τινὶ τῶι Β· τοῦτο δ᾽ ἀδύνατον. οὐ γὰρ εἰ μὴ ἐνδέχεται μηδενὶ τὸ Β τῶι Α, ἀνάγκη τινὶ ὑπάρχειν. τὸ γὰρ μὴ ἐνδέχεσθαι μηδενὶ διχῶς λέγεται, τὸ μὲν εἰ ἐξ ἀνάγκης τινὶ ὑπάρχει, τὸ δ᾽ εἰ ἐξ ἀνάγκης τινὶ μὴ ὑπάρχει· τὸ γὰρ ἐξ ἀνάγκης τινὶ τῶν Α μὴ ὑπάρχον οὐκ ἀληθὲς εἰπεῖν ὡς παντὶ ἐνδέχεται μὴ ὑπάρχειν, ὥσπερ οὐδὲ τὸ τινὶ ὑπάρχον ἐξ ἀνάγκης ὅτι παντὶ ἐνδέχεται ὑπάρχειν.	Sed nec ex impossibili ostendet convertens, ut si quis putet quoniam falsum est B contingere nulli A inesse, verum non contingere nulli A, affirmatio enim et negatio, si autem hoc verum, ex necessitate alicui A inesse B, quare et A alicui B inesse, hoc autem impossibile. Non enim si A non contingit nulli B, necesse est A alicui B inesse. (0659D) Nam non contingere nulli dicitur dupliciter, hoc quidem si ex necessitate alicui inest, illud vero si ex necessitate alicui non inest. Nam quod ex necessitate alicui eorum quae sunt A non inest, non est verum dicere quoniam omni contingit non inesse, quemadmodum nec alicui inest ex necessitate, quoniam omni contingit inesse.	Moreover it is not possible to prove the convertibility of these propositions by a reductio ad absurdum, i.e. by claiming assent to the following argument: ‘since it is false that B may belong to no A, it is true that it cannot belong to no A, for the one statement is the contradictory of the other. But if this is so, it is true that B necessarily belongs to some of the As: consequently A necessarily belongs to some of the Bs. But this is impossible.’ The argument cannot be admitted, for it does not follow that some A is necessarily B, if it is not possible that no A should be B. For the latter expression is used in two senses, one if A some is necessarily B, another if some A is necessarily not B. For it is not true to say that that which necessarily does not belong to some of the As may possibly not belong to any A, just as it is not true to say that what necessarily belongs to some A may possibly belong to all A.
εἰ οὖν τις ἀξιοίη, ἐπεὶ οὐκ ἐνδέχεται τὸ Γ τῶι Δ παντὶ ὑπάρχειν, ἐξ ἀνάγκης τινὶ μὴ ὑπάρχειν αὐτό, ψεῦδος ἂν λαμβάνοι· παντὶ γὰρ ὑπάρχει, ἀλλ᾽ ὅτι ἐνίοις ἐξ ἀνάγκης ὑπάρχει, διὰ τοῦτό φαμεν οὐ παντὶ ἐνδέχεσθαι.	Si ergo aliquis putet quoniam contingit C omni D inesse, ex necessitate alicui non inesse ipsum, falsum sumet, omni enim inest, si contingat, sed quoniam quibusdam ex necessitate inest, propter hoc dicimus non omni contingere.	If any one then should claim that because it is not possible for C to belong to all D, it necessarily does not belong to some D, he would make a false assumption: for it does belong to all D, but because in some cases it belongs necessarily,
ὥστε τῶι ἐνδέχεσθαι παντὶ ὑπάρχειν τό τ᾽ ἐξ ἀνάγ κης τινὶ ὑπάρχειν ἀντίκειται καὶ τὸ ἐξ ἀνάγκης τινὶ μὴ ὑπάρχειν. ὁμοίως δὲ καὶ τῶι ἐνδέχεσθαι μηδενί. δῆλον οὖν ὅτι πρὸς τὸ οὕτως ἐνδεχόμενον καὶ μὴ ἐνδεχόμενον ὡς ἐν ἀρχῆι διωρίσαμεν οὐ τὸ ἐξ ἀνάγκης τινὶ ὑπάρχειν ἀλλὰ τὸ ἐξ ἀνάγκης τινὶ μὴ ὑπάρχειν ληπτέον. τούτου δὲ ληφθέντος οὐδὲν συμβαίνει ἀδύνατον, ὥστ᾽ οὐ γίνεται συλλογισμός. φανερὸν οὖν ἐκ τῶν εἰρημένων ὅτι οὐκ ἀντιστρέφει τὸ στερητικόν.	Quare ei quod est contingere omni inesse, et ea quae est ex necessitate alicui inesse, opponitur, et ea quae est ex necessitate alicui non inesse, similiter autem et ei quae est contingere nulli. (0660A) Palam ergo quoniam ad sic contingens, et non contingens, ut in principio definivimus, non solum ex necessitate alicui inesse, sed et ex necessitate alicui non inesse sumendum. Hoc autem sumpto, nihil accidit impossibile, quare non fit syllogismus. Manifestum ergo ex iis quae dicta sunt quoniam non convertitur privativa.	therefore we say that it is not possible for it to belong to all. Hence both the propositions ‘A necessarily belongs to some B’ and ‘A necessarily does not belong to some B’ are opposed to the proposition ‘A belongs to all B’. Similarly also they are opposed to the proposition ‘A may belong to no B’. It is clear then that in relation to what is possible and not possible, in the sense originally defined, we must assume, not that A necessarily belongs to some B, but that A necessarily does not belong to some B. But if this is assumed, no absurdity results: consequently no syllogism. It is clear from what has been said that the negative proposition is not convertible.
Τούτου δὲ δειχθέντος κείσθω τὸ Α τῶι μὲν Β ἐνδέχεσθαι μηδενί, τῶι δὲ Γ παντί. διὰ μὲν οὖν τῆς ἀντιστροφῆς οὐκ ἔσται συλλογισμός· εἴρηται γὰρ ὅτι οὐκ ἀντιστρέφει ἡ τοιαύτη πρό τασις. ἀλλ᾽ οὐδὲ διὰ τοῦ ἀδυνάτου· τεθέντος γὰρ τοῦ Β ‹μὴ› παντὶ τῶι Γ ἐνδέχεσθαι ‹μὴ› ὑπάρχειν οὐδὲν συμβαίνει ψεῦδος· ἐνδέχοιτο γὰρ ἂν τὸ Α τῶι Γ καὶ παντὶ καὶ μηδενὶ ὑπάρχειν.	Hoc autem ostenso ponatur A, B quidem contingere nulli, C vero omni, per conversionem ergo non erit syllogismus. Dictum est enim quoniam non convertitur huiusmodi propositio. Sed nec per impossibile, nam posito B omni C contingere inesse, nihil accidit falsum, continget enim A et omni et nulli C inesse.	This being proved, suppose it possible that A may belong to no B and to all C. By means of conversion no syllogism will result: for the major premiss, as has been said, is not convertible. Nor can a proof be obtained by a reductio ad absurdum: for if it is assumed that B can belong to all C, no false consequence results: for A may belong both to all C and to no C.
ὅλως δ᾽ εἰ ἔστι συλλογισμός, δῆλον ὅτι τοῦ ἐνδέχεσθαι ἂν εἴη διὰ τὸ μηδετέραν τῶν προτάσεων εἰλῆφθαι ἐν τῶι ὑπάρ- χειν, καὶ οὗτος ἢ καταφατικὸς ἢ στερητικός· οὐδετέρως δ᾽ ἐγ ↵ χωρεῖ. καταφατικοῦ μὲν γὰρ τεθέντος δειχθήσεται διὰ τῶν ὅρων ὅτι οὐκ ἐνδέχεται ὑπάρχειν, στερητικοῦ δέ, ὅτι τὸ συμπέρασμα οὐκ ἐνδεχόμενον ἀλλ᾽ ἀναγκαῖόν ἐστιν. ἔστω γὰρ τὸ μὲν Α λευκόν, τὸ δὲ Β ἄνθρωπος, ἐφ᾽ ὧι δὲ Γ ἵππος. τὸ δὴ Α, τὸ λευκόν, ἐνδέχεται τῶι μὲν παντὶ τῶι δὲ μηδενὶ ὑπάρχειν. ἀλλὰ τὸ Β τῶι Γ οὔτε ὑπάρχειν ἐνδέχεται οὔτε μὴ ὑπάρχειν.	(0660B) Omnino autem si est syllogismus, palam quoniam contingens erit, eo quod neutra propositionum sumpta est in eo quod est inesse, et hic vel affirmativus, vel privativus: neutro autem modo possibile est, affirmativo enim posito, ostendetur per terminos quoniam non contingit inesse; privativo autem, quoniam conclusio non est contingens, sed necessaria. Sit enim A quidem album, B autem homo, in quo autem C equus, ergo album A contingit huic quidem omni, illi vero nulli inesse, sed B neque inesse contingit C, neque non inesse.	In general, if there is a syllogism, it is clear that its conclusion will be problematic because neither of the premisses is assertoric; and this must be either affirmative or negative. But neither is possible. Suppose the conclusion is affirmative: it will be proved by an example that the predicate cannot belong to the subject. Suppose the conclusion is negative: it will be proved that it is not problematic but necessary. Let A be white, B man, C horse. It is possible then for A to belong to all of the one and to none of the other. But it is not possible for B to belong nor not to belong to C.
ὅτι μὲν οὖν ὑπάρχειν οὐκ ἐγχωρεῖ, φανερόν· οὐδεὶς γὰρ ἵππος ἄνθρωπος. ἀλλ᾽ οὐδ᾽ ἐνδέχεσθαι μὴ ὑπάρχειν· ἀνάγκη γὰρ μηδένα ἵππον ἄνθρωπον εἶναι, τὸ δ᾽ ἀναγκαῖον οὐκ ἦν ἐνδεχόμενον. οὐκ ἄρα γίνεται συλλογισμός.	Quoniam igitur inesse non possibile, est manifestum, nullus enim equus homo, sed neque contingere non inesse, necesse est enim nullum equum hominem esse, necessarium autem non erat contingens, non igitur fit syllogismus.	That it is not possible for it to belong, is clear. For no horse is a man. Neither is it possible for it not to belong. For it is necessary that no horse should be a man, but the necessary we found to be different from the possible. No syllogism then results.
ὁμοίως δὲ δειχθήσεται καὶ ἂν ἀνάπαλιν τεθῆι τὸ στερητικόν, κἂν ἀμφότεραι καταφατικαὶ ληφθῶσιν ἢ στερητικαί (διὰ γὰρ τῶν αὐτῶν ὅρων ἔσται ἡ ἀπόδειξισ)· καὶ ὅταν ἡ μὲν καθόλου ἡ δ᾽ ἐν μέρει, ἢ ἀμφότεραι κατὰ μέρος ἢ ἀδιόριστοι, ἢ ὁσα χῶς ἄλλως ἐνδέχεται μεταλαβεῖν τὰς προτάσεις· ἀεὶ γὰρ ἔσται διὰ τῶν αὐτῶν ὅρων ἡ ἀπόδειξις. φανερὸν οὖν ὅτι ἀμφοτέρων τῶν προτάσεων κατὰ τὸ ἐνδέχεσθαι τιθεμένων οὐδεὶς γίνεται συλλογισμός.	Similiter autem ostendetur, et si e converso ponatur privativa, et si utraeque affirmative ponantur, vel privative, nam per eosdem terminos erit demonstratio. (0660C) Et quando haec quidem universalis, illa vero particularis, vel utraeque particulares, vel indefinitae, aut quolibet modo aliter contingit permutari propositiones, semper enim erit per eosdem terminos demonstratio. Manifestum ergo quoniam utrisque propositionibus secundum contingere positis, nullus fit syllogismus.	A similar proof can be given if the major premiss is negative, the minor affirmative, or if both are affirmative or negative. The demonstration can be made by means of the same terms. And whenever one premiss is universal, the other particular, or both are particular or indefinite, or in whatever other way the premisses can be altered, the proof will always proceed through the same terms. Clearly then, if both the premisses are problematic, no syllogism results.