Authors/Aristotle/priora/Liber 1/C6

Chapter 6

Greek	Latin	English
	(PL 64 0645B) CAPUT VI. De syllogismis absolutis tertiae figurae.	6
28a9 Ἐὰν δὲ τῶι αὐτῶι τὸ μὲν παντὶ τὸ δὲ μηδενὶ ὑπάρχηι, ἢ ἄμφω παντὶ ἢ μηδενί, τὸ μὲν σχῆμα τὸ τοιοῦτον καλῶ τρίτον, μέσον δ᾽ ἐν αὐτῶι λέγω καθ᾽ οὗ ἄμφω τὰ κατηγορούμενα, ἄκρα δὲ τὰ κατηγορούμενα, μεῖζον δ᾽ ἄκρον τὸ πορρώτερον τοῦ μέσου, ἔλαττον δὲ τὸ ἐγγύτερον. τίθεται δὲ τὸ μέσον ἔξω μὲν τῶν ἄκρων, ἔσχατον δὲ τῆι θέσει. τέλειος μὲν οὖν οὐ γίνεται συλλογισμὸς οὐδ᾽ ἐν τούτωι τῶι σχήματι, δυνατὸς δ᾽ ἔσται καὶ καθόλου καὶ μὴ καθόλου τῶν ὅρων ὄντων πρὸς τὸ μέσον.	Si autem eidem hoc quidem omni, illud vero nulli inest, vel ambo omni vel nulli, figuram quidem huiusmodi voco tertiam. Medium autem in hac dico, quo ambo praedicamus; extremitates vero, quae praedicantur; maiorem autem extremitatem, quae longius est medio; minorem vero, quae propius. Ponitur autem medium foras quidem extremitatum, ultimum vero positione est. Perfectus igitur non fit syllogismus, nec in hac figura, possibilis vero erit et universaliter, et non universaliter terminis existentibus ad medium.	But if one term belongs to all, and another to none, of a third, or if both belong to all, or to none, of it, I call such a figure the third; by middle term in it I mean that of which both the predicates are predicated, by extremes I mean the predicates, by the major extreme that which is further from the middle, by the minor that which is nearer to it. The middle term stands outside the extremes, and is last in position. A syllogism cannot be perfect in this figure either, but it may be valid whether the terms are related universally or not to the middle term.
Καθόλου μὲν οὖν ὄντων, ὅταν καὶ τὸ Π καὶ τὸ Ρ παντὶ τῶι Σ ὑπάρχηι, ὅτι τινὶ τῶι Ρ τὸ Π ὑπάρξει ἐξ ἀνάγκης· ἐπεὶ γὰρ ἀντιστρέφει τὸ κατηγορικόν, ὑπάρξει τὸ Σ τινὶ τῶι Ρ, ὥστ᾽ ἐπεὶ τῶι μὲν Σ παντὶ τὸ Π, τῶι δὲ Ρ τινὶ τὸ Σ, ἀνάγκη τὸ Π τινὶ τῶι Ρ ὑπάρχειν· γίνεται γὰρ συλλογισμὸς διὰ τοῦ πρώτου σχήματος. ἔστι δὲ καὶ διὰ τοῦ ἀδυνάτου καὶ τῶι ἐκθέσθαι ποιεῖν τὴν ἀπόδειξιν· εἰ γὰρ ἄμφω παντὶ τῶι Σ ὑπάρχει, ἂν ληφθῆι τι τῶν Σ οἷον τὸ Ν, τούτωι καὶ τὸ Π καὶ τὸ Ρ ὑπάρξει, ὥστε τινὶ τῶι Ρ τὸ Π ὑπάρξει.	(0645C) Universaliter quidem quando et p et r inerunt omni s, quoniam alicui r inerit p ex necessitate, nam quoniam convertitur praedicativa, inerit s alicui r. Quare quoniam p inest omni s, et s alicui r, necesse est p alicui r inesse. Fit enim syllogismus per primam figuram. Est autem et per impossibile, et expositione facere demonstrationem: si enim ambo omni s insunt, si sumatur aliquod eorum quae sunt s, ut N huic et p et r inerunt ex necessitate, quare alicui r inerit p.	If they are universal, whenever both P and R belong to S, it follows that P will necessarily belong to some R. For, since the affirmative statement is convertible, S will belong to some R: consequently since P belongs to all S, and S to some R, P must belong to some R: for a syllogism in the first figure is produced. It is possible to demonstrate this also per impossibile and by exposition. For if both P and R belong to all S, should one of the Ss, e.g. N, be taken, both P and R will belong to this, and thus P will belong to some R.
καὶ ἂν τὸ μὲν Ρ παντὶ τῶι Σ, τὸ δὲ Π μηδενὶ ὑπάρχηι, ἔσται συλλογισμὸς ὅτι τὸ Π τινὶ τῶι Ρ οὐχ ὑπάρξει ἐξ ἀνάγκης· ὁ γὰρ αὐτὸς τρόπος τῆς ἀποδείξεως ἀντιστραφείσης τῆς Ρ Σ προτάσεως. δειχθείη δ᾽ ἂν καὶ διὰ τοῦ ἀδυνάτου, καθάπερ ἐπὶ τῶν πρότερον. ἐὰν δὲ τὸ μὲν Ρ μηδενὶ τὸ δὲ Π παντὶ ὑπάρχηι τῶι Σ, οὐκ ἔσται συλλογισμός. ὅροι τοῦ ὑπάρχειν ζῶιον – ἵππος – ἄνθρωπος, τοῦ μὴ ὑπάρχειν ζῶιον – ἄψυχον – ἄνθρωπος.	Et si r omni quidem s, p autem nulli s inest, erit syllogismus, quoniam p alicui r non inerit ex necessitate. Nam idem modus erit demonstrationis, conversa r s propositione. Ostendetur autem et per impossibile, quemadmodum in prioribus. Si autem insit r, s quidem nulli, p vero omni s, non erit syllogismus. (0645D) Termini inesse, animal, equus, homo; non inesse, animal, inanimatum, homo,	If R belongs to all S, and P to no S, there will be a syllogism to prove that P will necessarily not belong to some R. This may be demonstrated in the same way as before by converting the premiss RS. It might be proved also per impossibile, as in the former cases. But if R belongs to no S, P to all S, there will be no syllogism. Terms for the positive relation are animal, horse, man: for the negative relation animal, inanimate, man.
οὐδ᾽ ὅταν ἄμφω κατὰ μηδενὸς τοῦ Σ λέγηται, οὐκ ἔσται συλλογισμός. ὅροι τοῦ ὑπάρχειν ζῶιον – ἵππος – ἄψυχον, τοῦ μὴ ὑπάρχειν ἄνθρωπος – ἵππος – ἄψυχον·	neque quando ambo de nullo s dicuntur, non erit syllogismus. Termini inesse, animal, equus, inanimatum; non inesse, homo, equus inanimatum, medium, inanimatum.	Nor can there be a syllogism when both terms are asserted of no S. Terms for the positive relation are animal, horse, inanimate; for the negative relation man, horse, inanimate-inanimate being the middle term.
μέσον ἄψυχον. φανερὸν οὖν καὶ ἐν τούτωι τῶι σχήματι πότ᾽ ἔσται καὶ πότ᾽ οὐκ ἔσται συλλογισμὸς καθόλου τῶν ὅρων ὄντων. ὅταν μὲν γὰρ ἀμφότεροι οἱ ὅροι ὦσι κατηγορικοί, ἔσται συλλογισμὸς ὅτι τινὶ ὑπάρχει τὸ ἄκρον τῶι ἄκρωι, ὅταν δὲ στερητικοί, οὐκ ↵ ἔσται. ὅταν δ᾽ ὁ μὲν ἦι στερητικὸς ὁ δὲ καταφατικός, ἐὰν μὲν ὁ μείζων γένηται στερητικὸς ἅτερος δὲ καταφατικός, ἔσται συλλογισμὸς ὅτι τινὶ οὐχ ὑπάρχει τὸ ἄκρον τῶι ἄκρωι, ἐὰν δ᾽ ἀνάπαλιν, οὐκ ἔσται. Ἐὰν δ᾽ ὁ μὲν ἦι καθόλου πρὸς τὸ μέσον ὁ δ᾽ ἐν μέρει, κατηγορικῶν μὲν ὄντων ἀμφοῖν ἀνάγκη γίνεσθαι συλλογισμόν, ἂν ὁποτεροσοῦν ἦι καθόλου τῶν ὅρων. εἰ γὰρ τὸ μὲν Ρ παντὶ τῶι Σ τὸ δὲ Π τινί, ἀνάγκη τὸ Π τινὶ τῶι Ρ ὑπάρχειν. ἐπεὶ γὰρ ἀντιστρέφει τὸ καταφατικόν, ὑπάρξει τὸ Σ τινὶ τῶι Π, ὥστ᾽ ἐπεὶ τὸ μὲν Ρ παντὶ τῶι Σ, τὸ δὲ Σ τινὶ τῶι Π, καὶ τὸ Ρ τινὶ τῶι Π ὑπάρξει· ὥστε τὸ Π τινὶ τῶι Ρ.	Manifestum est igitur et in hac figura et quando erit, et quando non erit syllogismus ex universalibus terminis. Quando enim ambo termini sunt praedicativi, erit syllogismus, quoniam inest alicui extremitas extremitati; quando vero privativi, non erit syllogismus; quando autem hic quidem privativus, ille vero affirmativus; si maior quidem fuerit privativus, alter vero affirmativus, erit syllogismus, quoniam alicui non inest extremitas extremitati. Si autem e converso, non erit. (0646A) Si autem hic quidem sit universaliter ad medium, alter vero particulariter, si uterque sit praedicativus, necesse est fieri syllogismum, et si alteruter sit universalis terminorum; nam si r omni s insit, p vero alicui s, necesse est et p alicui r inesse, nam quoniam convertitur affirmativa, inerit s alicui p, quare quoniam r omni s inest, s autem alicui p, et r alicui p inerit, quare et p alicui r.	It is clear then in this figure also when a syllogism will be possible and when not, if the terms are related universally. For whenever both the terms are affirmative, there will be a syllogism to prove that one extreme belongs to some of the other; but when they are negative, no syllogism will be possible. But when one is negative, the other affirmative, if the major is negative, the minor affirmative, there will be a syllogism to prove that the one extreme does not belong to some of the other: but if the relation is reversed, no syllogism will be possible. If one term is related universally to the middle, the other in part only, when both are affirmative there must be a syllogism, no matter which of the premisses is universal. For if R belongs to all S, P to some S, P must belong to some R. For since the affirmative statement is convertible S will belong to some P: consequently since R belongs to all S, and S to some P, R must also belong to some P: therefore P must belong to some R.
πάλιν εἰ τὸ μὲν Ρ τινὶ τῶι Σ τὸ δὲ Π παντὶ ὑπάρχει, ἀνάγκη τὸ Π τινὶ τῶι Ρ ὑπάρχειν· ὁ γὰρ αὐτὸς τρόπος τῆς ἀποδείξεως. ἔστι δ᾽ ἀποδεῖξαι καὶ διὰ τοῦ ἀδυνάτου καὶ τῆι ἐκθέσει, καθάπερ ἐπὶ τῶν πρότερον. Ἐὰν δ᾽ ὁ μὲν ἦι κατηγορικὸς ὁ δὲ στερητικός, καθόλου δὲ ὁ κατηγορικός, ὅταν μὲν ὁ ἐλάττων ἦι κατηγορικός, ἔσται συλλογισμός. εἰ γὰρ τὸ Ρ παντὶ τῶι Σ, τὸ δὲ Π τινὶ μὴ ὑπάρχει, ἀνάγκη τὸ Π τινὶ τῶι Ρ μὴ ὑπάρχειν. εἰ γὰρ παντί, καὶ τὸ Ρ παντὶ τῶι Σ, καὶ τὸ Π παντὶ τῶι Σ ὑπάρξει· ἀλλ᾽ οὐχ ὑπῆρχεν. δείκνυται δὲ καὶ ἄνευ τῆς ἀπαγωγῆς, ἐὰν ληφθῆι τι τῶν Σ ὧι τὸ Π μὴ ὑπάρχει.	Rursum si r alicui s, p vero omni s insit, necesse est et p alicui r inesse, nam idem modus demonstrationis. Est autem demonstrare et per impossibile, et expositione, quemadmodum in prioribus. (0646B) Si autem unus quidem sit praedicativus, alius vero privativus, universaliter autem praedicativus, quando minor quidem fuerit praedicativus, erit syllogismus; nam si r omni s, p vero alicui s non inest, necesse est p alicui r non inesse, si enim p omni r, et r omni s, et p omni s inerit, sed non inerat. Monstratur autem et sine deductione, si sumatur aliquid eorum quae sunt s, cui p non inest.	Again if R belongs to some S, and P to all S, P must belong to some R. This may be demonstrated in the same way as the preceding. And it is possible to demonstrate it also per impossibile and by exposition, as in the former cases. But if one term is affirmative, the other negative, and if the affirmative is universal, a syllogism will be possible whenever the minor term is affirmative. For if R belongs to all S, but P does not belong to some S, it is necessary that P does not belong to some R. For if P belongs to all R, and R belongs to all S, then P will belong to all S: but we assumed that it did not. Proof is possible also without reduction ad impossibile, if one of the Ss be taken to which P does not belong.
ὅταν δ᾽ ὁ μείζων ἦι κατηγορικός, οὐκ ἔσται συλλογισμός, οἷον εἰ τὸ μὲν Π παντὶ τῶι Σ, τὸ δὲ Ρ τινὶ τῶι Σ μὴ ὑπάρχει. ὅροι τοῦ παντὶ ὑπάρχειν ἔμψυχον – ἄνθρωπος – ζῶιον. τοῦ δὲ μηδενὶ οὐκ ἔστι λαβεῖν ὅρους, εἰ τινὶ μὲν ὑπάρχει τῶι Σ τὸ Ρ, τινὶ δὲ μή· εἰ γὰρ παντὶ τὸ Π τῶι Σ ὑπάρχει, τὸ δὲ Ρ τινὶ τῶι Σ, καὶ τὸ Π τινὶ τῶι Ρ ὑπάρξει· ὑπέκειτο δὲ μηδενὶ ὑπάρχειν. ἀλλ᾽ ὥσπερ ἐν τοῖς πρότερον ληπτέον· ἀδιορίστου γὰρ ὄντος τοῦ τινὶ μὴ ὑπάρχειν καὶ τὸ μηδενὶ ὑπάρχον ἀληθὲς εἰπεῖν τινὶ μὴ ὑπάρχειν· μηδενὶ δὲ ὑπάρχοντος οὐκ ἦν συλλογισμός. φανερὸν οὖν ὅτι οὐκ ἔσται συλλογισμός.	Quando vero maior fuerit praedicativus, non erit syllogismus, ut si p insit omni s, r autem alicui s non insit. Termini vero omni inesse, animatum, homo, animal. Nulli vero, non est sumere terminos si r inest alicui quidem s, alicui autem non. Si enim omni s inest p, r autem alicui s, et p inerit alicui r, sed positum erat nulli r inesse. (0646C) Sed quemadmodum in prioribus dicendum est; nam cum indefinitum est alicui non inesse, et quod nulli inest, verum est dicere alicui non inesse, nulli vero cum inesset, non erat syllogismus; manifestum ergo est, quoniam non erit syllogismus.	But whenever the major is affirmative, no syllogism will be possible, e.g. if P belongs to all S and R does not belong to some S. Terms for the universal affirmative relation are animate, man, animal. For the universal negative relation it is not possible to get terms, if R belongs to some S, and does not belong to some S. For if P belongs to all S, and R to some S, then P will belong to some R: but we assumed that it belongs to no R. We must put the matter as before.’ Since the expression ‘it does not belong to some’ is indefinite, it may be used truly of that also which belongs to none. But if R belongs to no S, no syllogism is possible, as has been shown. Clearly then no syllogism will be possible here.
ἐὰν δ᾽ ὁ στερητικὸς ἦι καθόλου τῶν ὅρων, ὅταν μὲν ὁ μείζων ἦι στερητικὸς ὁ δὲ ἐλάττων κατηγορικός, ἔσται συλλογισμός. εἰ γὰρ τὸ Π μηδενὶ τῶι Σ, τὸ δὲ Ρ τινὶ ὑπάρχει τῶι Σ, τὸ Π τινὶ τῶι Ρ οὐχ ὑπάρξει· πάλιν γὰρ ἔσται τὸ πρῶτον σχῆμα τῆς Ρ Σ προτάσεως ἀντιστραφείσης.	Si autem privativus sit universalis terminus, quando maior quidem privativus fuerit, minor autem praedicativus, erit syllogismus. Si enim p nulli s, r autem alicui inest s, et p alicui r non inerit. Rursum enim prima erit figura, r s propositione conversa.	But if the negative term is universal, whenever the major is negative and the minor affirmative there will be a syllogism. For if P belongs to no S, and R belongs to some S, P will not belong to some R: for we shall have the first figure again, if the premiss RS is converted.
ὅταν δὲ ὁ ἐλάττων ἦι στερητικός, οὐκ ἔσται συλλογισμός. ὅροι τοῦ ὑπάρχειν ζῶιον – ἄνθρωπος – ἄγριον, τοῦ μὴ ὑπάρχειν ζῶιον – ἐπιστήμη – ἄγριον· μέσον ἐν ἀμφοῖν τὸ ἄγριον.	Quando autem minor fuerit privativus, non erit syllogismus. Termini inesse, animal, homo, ferum. Non inesse, animal, scientia, ferum, medium in utrisque ferum.	But when the minor is negative, there will be no syllogism. Terms for the positive relation are animal, man, wild: for the negative relation, animal, science, wild-the middle in both being the term wild.
οὐδ᾽ ὅταν ἀμφότεροι στερητικοὶ τεθῶσιν, ἦι δ᾽ ὁ μὲν καθόλου ὁ δ᾽ ἐν μέρει. ὅροι ↵ ὅταν ὁ ἐλάττων ἦι καθόλου πρὸς τὸ μέσον, ζῶιον – ἐπιστήμη – ἄγριον, ζῶιον – ἄνθρωπος – ἄγριον· ὅταν δ᾽ ὁ μείζων, τοῦ μὲν μὴ ὑπάρχειν κόραξ – χιών – λευκόν. τοῦ δ᾽ ὑπάρχειν οὐκ ἔστι λαβεῖν, εἰ τὸ Ρ τινὶ μὲν ὑπάρχει τῶι Σ, τινὶ δὲ μὴ ὑπάρχει. εἰ γὰρ τὸ Π παντὶ τῶι Ρ, τὸ δὲ Ρ τινὶ τῶι Σ, καὶ τὸ Π τινὶ τῶι Σ· ὑπέκειτο δὲ μηδενί. ἀλλ᾽ ἐκ τοῦ ἀδιορίστου δεικτέον.	Nec quando ambo privativi ponuntur, est autem unus quidem universalis, alter vero particularis. Termini inesse, quando minor est universalis ad medium, animal, homo, ferum, non inesse, animal, scientia, ferum. (0646D) Quando autem maior, non inesse quidem, corvus, nix, album; inesse vero non est sumere si r alicui quidem inest s, alicui autem non inest. Si enim p omni r insit, r autem alicui s, et p inerit alicui s. Positum est autem nulli, sed ex indefinito monstrandum est.	Nor is a syllogism possible when both are stated in the negative, but one is universal, the other particular. When the minor is related universally to the middle, take the terms animal, science, wild; animal, man, wild. When the major is related universally to the middle, take as terms for a negative relation raven, snow, white. For a positive relation terms cannot be found, if R belongs to some S, and does not belong to some S. For if P belongs to all R, and R to some S, then P belongs to some S: but we assumed that it belongs to no S. Our point, then, must be proved from the indefinite nature of the particular statement.
Οὐδ᾽ ἂν ἑκάτερος τινὶ τῶι μέσωι ὑπάρχηι ἢ μὴ ὑπάρχηι, ἢ ὁ μὲν ὑπάρχηι ὁ δὲ μὴ ὑπάρχηι, ἢ ὁ μὲν τινὶ ὁ δὲ μὴ παντί, ἢ ἀδιορίστως, οὐκ ἔσται συλλογισμὸς οὐδαμῶς. ὅροι δὲ κοινοὶ πάντων ζῶιον – ἄνθρωπος – λευκόν, ζῶιον – ἄψυχον – λευκόν.	Neque si uterque alicui medio inest, vel non inest, vel unus quidem inest, alter vero non inest, vel hic quidem alicui, ille vero non omni, vel indefinite, nullo modo erit syllogismus. Termini autem communes omnium, animal, homo, album, animal, inani matum, album.	Nor is a syllogism possible anyhow, if each of the extremes belongs to some of the middle or does not belong, or one belongs and the other does not to some of the middle, or one belongs to some of the middle, the other not to all, or if the premisses are indefinite. Common terms for all are animal, man, white: animal, inanimate, white.
Φανερὸν οὖν καὶ ἐν τούτωι τῶι σχήματι πότ᾽ ἔσται καὶ πότ᾽ οὐκ ἔσται συλλογισμός, καὶ ὅτι ἐχόντων τε τῶν ὅρων ὡς ἐλέχθη γίνεται συλλογισμὸς ἐξ ἀνάγκης, ἄν τ᾽ ἦι συλλογισμός, ἀνάγκη τοὺς ὅρους οὕτως ἔχειν. φανερὸν δὲ καὶ ὅτι πάντες ἀτελεῖς εἰσὶν οἱ ἐν τούτωι τῶι σχήματι συλλογισμοί (πάντες γὰρ τελειοῦνται προσλαμβανομένων τινῶν) καὶ ὅτι συλλογίσασθαι τὸ καθόλου διὰ τούτου τοῦ σχήματος οὐκ ἔσται, οὔτε στερητικὸν οὔτε καταφατικόν.	Manifestum est igitur, et in hac figura, quando erit, et quando non erit syllogismus, et quoniam habentibus se terminis, ut dictum est, fit syllogismus ex necessitate, et si sit syllogismus, necesse est terminos sic se habere. (0647A) Manifestum est etiam, quia omnes imperfecti sunt in hac figura syllogismi, omnes enim perficiuntur quibusdam assumptis. Et quoniam syllogizare universale per hanc figuram non erit, neque privativum, neque affirmativum.	It is clear then in this figure also when a syllogism will be possible, and when not; and that if the terms are as stated, a syllogism results of necessity, and if there is a syllogism, the terms must be so related. It is clear also that all the syllogisms in this figure are imperfect (for all are made perfect by certain supplementary assumptions), and that it will not be possible to reach a universal conclusion by means of this figure, whether negative or affirmative.