View source for Authors/Aristotle/priora/Liber 1/C24

==Chapter 24==
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|(PL 64 0666C) CAPUT XXIV. De qualitate et quantitate terminorum syllogismi.

|24

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|{{a|bk41b6|41b6}} Ἔτι τε ἐν ἅπαντι δεῖ κατηγορικόν τινα τῶν ὅρων εἶναι καὶ τὸ καθόλου ὑπάρχειν· ἄνευ γὰρ τοῦ καθόλου ἢ οὐκ ἔσται συλλογισμὸς ἢ οὐ πρὸς τὸ κείμενον, ἢ τὸ ἐξ ἀρχῆς αἰτήσεται. κείσθω γὰρ τὴν μουσικὴν ἡδονὴν εἶναι σπου δαίαν. εἰ μὲν οὖν ἀξιώσειεν ἡδονὴν εἶναι σπουδαίαν μὴ προσθεὶς τὸ πᾶσαν, οὐκ ἔσται συλλογισμός· εἰ δὲ τινὰ ἡδονήν, εἰ μὲν ἄλλην, οὐδὲν πρὸς τὸ κείμενον, εἰ δ᾽ αὐτὴν ταύτην, τὸ ἐξ ἀρχῆς λαμβάνει. 

|Amplius autem in omnibus oportet aliquem terminorum praedicativum esse et universalem, sine universali enim non erit syllogismus, aut non ad hoc quod positum est, aut quod ex principio est petet. Ponatur enim musicam voluptatem esse studiosam, si ergo poposcerit voluptatem esse studiosam, non addens omnem, non erit syllogismus, si autem aliquam voluptatem esse studiosam, si aliam quidem, nihil ad hoc quod positum est, si autem eamdem, quod ex principio erat, sumit. 



|Further in every syllogism one of the premisses must be affirmative, and universality must be present: unless one of the premisses is universal either a syllogism will not be possible, or it will not refer to the subject proposed, or the original position will be begged. Suppose we have to prove that pleasure in music is good. If one should claim as a premiss that pleasure is good without adding ‘all’, no syllogism will be possible; if one should claim that some pleasure is good, then if it is different from pleasure in music, it is not relevant to the subject proposed; if it is this very pleasure, one is assuming that which was proposed at the outset to be proved. 

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|μᾶλλον δὲ γίνεται φανερὸν ἐν τοῖς διαγράμμασιν, οἷον ὅτι τοῦ ἰσοσκελοῦς ἴσαι αἱ πρὸς τῆι βάσει. ἔστωσαν εἰς τὸ κέντρον ἠγμέναι αἱ Α Β. εἰ οὖν ἴσην λαμβάνοι τὴν Α Γ γωνίαν τῆι Β Δ μὴ ὅλως ἀξιώσας ἴσας τὰς τῶν ἡμικυκλίων, καὶ πάλιν τὴν Γ τῆι Δ μὴ πᾶσαν προσλαβὼν τὴν τοῦ τμήματος, ἔτι δ᾽ ἀπ᾽ ἴσων οὐσῶν τῶν ὅλων γωνιῶν καὶ ἴσων ἀφηιρημένων ἴσας εἶναι τὰς λοιπὰς τὰς Ε Ζ, τὸ ἐξ ἀρχῆς αἰτήσε- ται, ἐὰν μὴ λάβηι ἀπὸ τῶν ἴσων ἴσων ἀφαιρουμένων ἴσα λείπεσθαι.

|(0666D) Magis autem fit manifestum in figuris, ut quoniam aequicruris aequales sunt anguli, qui sunt ad basim: sint enim in centrum ductae A B, si ergo aequalem sumpserit A C angulum ei qui est B D, non omnino petens aequales eos qui sunt semicirculorum, et rursum C ei qui est D, non omnem assumens eum qui est incisionis. Amplius, ab aequalibus existentibus totis angulis, aequalibus demptis, aequales esse reliquos, scilicet E F, quod ex principio est petet, nisi sumat ab omnibus aequalibus, aequis demptis, aequalia relinqui.

|This is more obvious in geometrical proofs, e.g. that the angles at the base of an isosceles triangle are equal. Suppose the lines A and B have been drawn to the centre. If then one should assume that the angle AC is equal to the angle BD, without claiming generally that angles of semicircles are equal; and again if one should assume that the angle C is equal to the angle D, without the additional assumption that every angle of a segment is equal to every other angle of the same segment; and further if one should assume that when equal angles are taken from the whole angles, which are themselves equal, the remainders E and F are equal, he will beg the thing to be proved, unless he also states that when equals are taken from equals the remainders are equal.

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|φανερὸν οὖν ὅτι ἐν ἅπαντι δεῖ τὸ καθόλου ὑπάρχειν, καὶ ὅτι τὸ μὲν καθόλου ἐξ ἁπάντων τῶν ὅρων καθόλου δείκνυται, τὸ δ᾽ ἐν μέρει καὶ οὕτως κἀκείνως, ὥστ᾽ ἐὰν μὲν ἦι τὸ συμπέρασμα καθόλου, καὶ τοὺς ὅρους ἀνάγκη καθόλου εἶναι, ἐὰν δ᾽ οἱ ὅροι καθόλου, ἐνδέχεται τὸ συμπέρασμα μὴ εἶναι καθόλου. δῆλον δὲ καὶ ὅτι ἐν ἅπαντι συλλογισμῶι ἢ ἀμφοτέρας ἢ τὴν ἑτέραν πρότασιν ὁμοίαν ἀνάγκη γίνεσθαι τῶι συμπεράσματι. λέγω δ᾽ οὐ μόνον τῶι καταφατικὴν εἶναι ἢ στερητικήν, ἀλλὰ καὶ τῶι ἀναγκαίαν ἢ ὑπάρχουσαν ἢ ἐνδεχομένην. ἐπισκέψασθαι δὲ δεῖ καὶ τὰς ἄλλας κατηγορίας. 

|Manifestum igitur quoniam in omni syllogismo oportet universale esse. Et quoniam universale quidem ex omnibus terminis universalibus monstratur, particulare autem et sic, et aliter. (0667A) Quare si conclusio sit universalis, et terminos necesse est universales esse, si autem universales sint termini, contingit conclusionem non universalem esse. Palam etiam quoniam in omni syllogismo aut utramque, aut alteram propositionem similem necesse est fieri conclusioni, dico autem non solum in eo quod affirmativa sit, vel negativa, sed in eo quod necessaria aut inesse, aut contingens: considerare autem oportet et alia praedicamenta. 

|It is clear then that in every syllogism there must be a universal premiss, and that a universal statement is proved only when all the premisses are universal, while a particular statement is proved both from two universal premisses and from one only: consequently if the conclusion is universal, the premisses also must be universal, but if the premisses are universal it is possible that the conclusion may not be universal. And it is clear also that in every syllogism either both or one of the premisses must be like the conclusion. I mean not only in being affirmative or negative, but also in being necessary, pure, problematic. We must consider also the other forms of predication.

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|Φανερὸν δὲ καὶ ἁπλῶς πότ᾽ ἔσται καὶ πότ᾽ οὐκ ἔσται συλλογισμός, καὶ πότε δυνατὸς καὶ πότε τέλειος, καὶ ὅτι συλλογισμοῦ ὄντος ἀναγκαῖον ἔχειν τοὺς ὅρους κατά τινα τῶν εἰρημένων τρόπων. 

|Manifestum autem et simpliciter quando erit, et quando non erit syllogismus, et quando perfectus, et quoniam si est syllogismus, necessarium est habere terminos secundum aliquem dictorum modorum.

|It is clear also when a syllogism in general can be made and when it cannot; and when a valid, when a perfect syllogism can be formed; and that if a syllogism is formed the terms must be arranged in one of the ways that have been mentioned.

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==Notes==
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