By Aristotle, Smith (trans.)
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ConsequencJy, if A belongs to every C of necessity, and C belongs to some B, then it is also necessary for A to belong to some B (for B is under C). The first figure therefore comes about. And it will also be proved in the same way if Be is necessary. For C converts to some A; consequently, if B belongs to every C of necessity, then it will also belong to some A of necessity. Next, let AC be privative, Be affirmative, and the privative necessary. Then, since C converts to some B and A belongs of necessity to no C , A will also of necessity not belong to some B: for B is bclowC.
It will be demon strative if it is (cue and has been obtained by means of the initial assumptions; a dialectical premise, on the other hand, is the posing of a contradiction as a question (when one is getting answers) and the taking of something apparent and accepted (when one is deducing), as was explained in the Topics. 1 24010 15 20 25 30 24bl0 2 15 20 30 1 What a premise is, then, and how deductive, demonstrative, and dialectical premises differ, will be explained morc precisely in what follows; let the distinctions just made be sufficient for our present ne\,ds.
For if they are otherwise, a necessary result does nOt come about. If the middle is universal only in relation to one term, then when it is universal in relation to the major extreme (whether positively or privatively) but particularly with respect to the minor and oppositely to the universal (by 'oppositely' I mean that if the universal is privative then the particular is affirmative, while if the universal is positive then the particular is privative), then it is necessary for a privative particular deduction to come about.