Prior Analytics - Book I   

then that in universal attribution the terms of the negative premiss

should be convertible, e.g. if no pleasure is good, then no good

will be pleasure; the terms of the affirmative must be convertible,

not however, universally, but in part, e.g. if every pleasure,is good,

some good must be pleasure; the particular affirmative must convert in

part (for if some pleasure is good, then some good will be

pleasure); but the particular negative need not convert, for if some

animal is not man, it does not follow that some man is not animal.

First then take a universal negative with the terms A and B. If no B

is A, neither can any A be B. For if some A (say C) were B, it would

not be true that no B is A; for C is a B. But if every B is A then

some A is B. For if no A were B, then no B could be A. But we

assumed that every B is A. Similarly too, if the premiss is

particular. For if some B is A, then some of the As must be B. For

if none were, then no B would be A. But if some B is not A, there is

no necessity that some of the As should not be B; e.g. let B stand for

animal and A for man. Not every animal is a man; but every man is an

animal.



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The same manner of conversion will hold good also in respect of

necessary premisses. The universal negative converts universally; each

of the affirmatives converts into a particular. If it is necessary

that no B is A, it is necessary also that no A is B. For if it is

possible that some A is B, it would be possible also that some B is A.

If all or some B is A of necessity, it is necessary also that some A

is B: for if there were no necessity, neither would some of the Bs

be A necessarily. But the particular negative does not convert, for

the same reason which we have already stated.

In respect of possible premisses, since possibility is used in

several senses (for we say that what is necessary and what is not