Authors/Aristotle/priora/Liber 2/C7

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.