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By Alexander of Aphrodisias

Within the moment half booklet 1 of the previous Analytics, Aristotle displays at the software of the formalized common sense he has constructed within the first part, focusing rather at the non-modal or assertoric syllogistic built within the first seven chapters. those reflections lead Alexander of Aphrodisias, the nice overdue second-century advert exponent of Aristotelianism, to provide an explanation for and infrequently argue opposed to next advancements of Aristotle's common sense and possible choices and objections to it, rules linked regularly along with his colleague Theophrastus and with the Stoics. the opposite major subject of this a part of the previous Analytics is the specification of a mode for locating real premises had to end up a given proposition.Aristotle's presentation is typically tough to persist with, and Alexander's dialogue is intensely important to the uninitiated reader. In his statement at the ultimate bankruptcy translated during this quantity, Alexander presents an insightful account of Aristotle's feedback of Plato's approach to department.

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R e m i n d i n g us of w h a t has been shown, he says t h a t i t is impossible for there to be a syllogism from t w o negative premisses. For, he says, ' i t is necessary t h a t one of the t e r m s be categorical', t h a t is, t h a t one of the premisses be a f f i r m a t i v e , i f there is going to be a syllogism. H e has shown t h a t t h i s is h o w t h i n g s are by s h o w i n g t h a t i n every figure combinations consisting of t w o negative premisses are not syllogistic. For even i n the cases i n w h i c h there w o u l d seem to be < a syllogism w i t h t w o negative premisses> as w i t h contingent premisses, f i r s t of all, contingent negatives are not simple negations, a n d f u r t h e r m o r e , a syllogism results, w h e n one or b o t h are t r a n s f o r m e d i n t o the a f f i r m a t i v e , b u t not o t h e r w i s e .

I summarize here the m a i n content of chapter 2 8 . A r i s t o t l e is interested i n describing a procedure for finding proofs of conclusions i n w h i c h A is predicated of E. He proposes ( 4 4 a l l - 1 7 ) t h a t one set out for A : 25 2 6 B (the consequents of A, those X such that X belongs to all A) A D (what 'cannot' belong to A, those X such that X belongs to no A (and, therefore, A belongs to no X)), C (the antecedents of A, those X such that A belongs to all X) and for E: F (the consequents of E, those X such that X belongs to all E) E H (what 'cannot' belong to E, those X such that X belongs to no E (and, therefore, E belongs to no X)), G (the antecedents of E, those X such that E belongs to all X) 23 Introduction I n 43b39-44a38 a n d a g a i n i n 44b8-19, A r i s t o t l e associates t h e discov­ ery of a p r o o f w i t h f i n d i n g a n X c o m m o n to a class for A a n d a class for E: For ' A belongs to a l l E' one looks for an X i n b o t h F a n d C so t h a t the conclusion follows from ' A belongs to a l l X ' a n d ' X belongs to a l l E' by B a r b a r a i .

Syllogism> from the s i m i l a r is also l i k e t h i s . B u t A r i s t o t l e alone calls from the more or the less or the s i m i l a r ' i n v o l v i n g quality', a n d he alone calls w h a t are called prosleptic (such as m i x e d ) ' i n v o l v i n g a t r a n s f o r m a t i o n ' , as we w i l l l e a r n as t h e discussion proceeds. 46 C h a p t e r 24 41b6-14 F u r t h e r m o r e i n every syllogism i t is necessary t h a t one of the terms be categorical and t h a t there be u n i v e r s a l holding; [for w i t h o u t the u n i v e r s a l either there w i l l be no syllo­ gism or i t w i l l not relate to w h a t is proposed or i t w i l l beg the question.

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