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Prior Analytics - Book II   

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.

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



To convert a syllogism means to alter the conclusion and make

another syllogism to prove that either the extreme cannot belong to

the middle or the middle to the last term. For it is necessary, if the

conclusion has been changed into its opposite and one of the premisses

stands, that the other premiss should be destroyed. For if it should

stand, the conclusion also must stand. It makes a difference whether

the conclusion is converted into its contradictory or into its

contrary. For the same syllogism does not result whichever form the

conversion takes. This will be made clear by the sequel. By

contradictory opposition I mean the opposition of 'to all' to 'not

to all', and of 'to some' to 'to none'; by contrary opposition I

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