Prior Analytics - Book I   

In particular syllogisms, if the universal premiss is necessary,

then the conclusion will be necessary; but if the particular, the

conclusion will not be necessary, whether the universal premiss is

negative or affirmative. First let the universal be necessary, and let

A belong to all B necessarily, but let B simply belong to some C: it

is necessary then that A belongs to some C necessarily: for C falls

under B, and A was assumed to belong necessarily to all B. Similarly

also if the syllogism should be negative: for the proof will be the

same. But if the particular premiss is necessary, the conclusion

will not be necessary: for from the denial of such a conclusion

nothing impossible results, just as it does not in the universal

syllogisms. The same is true of negative syllogisms. Try the terms

movement, animal, white.



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In the second figure, if the negative premiss is necessary, then the

conclusion will be necessary, but if the affirmative, not necessary.

First let the negative be necessary; let A be possible of no B, and

simply belong to C. Since then the negative statement is

convertible, B is possible of no A. But A belongs to all C;

consequently B is possible of no C. For C falls under A. The same

result would be obtained if the minor premiss were negative: for if

A is possible be of no C, C is possible of no A: but A belongs to


all B, consequently C is possible of none of the Bs: for again we have

obtained the first figure. Neither then is B possible of C: for

conversion is possible without modifying the relation.

But if the affirmative premiss is necessary, the conclusion will not

be necessary. Let A belong to all B necessarily, but to no C simply.

If then the negative premiss is converted, the first figure results.

But it has been proved in the case of the first figure that if the