
Prior Analytics  Book II
Book
1
WE have already explained the number of the figures, the character
and number of the premisses, when and how a syllogism is formed;
further what we must look for when a refuting and establishing
propositions, and how we should investigate a given problem in any
branch of inquiry, also by what means we shall obtain principles
appropriate to each subject. Since some syllogisms are universal,
others particular, all the universal syllogisms give more than one
result, and of particular syllogisms the affirmative yield more than
one, the negative yield only the stated conclusion. For all
propositions are convertible save only the particular negative: and
the conclusion states one definite thing about another definite thing.
Consequently all syllogisms save the particular negative yield more
than one conclusion, e.g. if A has been proved to to all or to some B,
then B must belong to some A: and if A has been proved to belong to no
B, then B belongs to no A. This is a different conclusion from the
former. But if A does not belong to some B, it is not necessary that B
should not belong to some A: for it may possibly belong to all A.
This then is the reason common to all syllogisms whether universal
or particular. But it is possible to give another reason concerning
those which are universal. For all the things that are subordinate
to the middle term or to the conclusion may be proved by the same
syllogism, if the former are placed in the middle, the latter in the
conclusion; e.g. if the conclusion AB is proved through C, whatever is
subordinate to B or C must accept the predicate A: for if D is
included in B as in a whole, and B is included in A, then D will be
included in A. Again if E is included in C as in a whole, and C is
included in A, then E will be included in A. Similarly if the
syllogism is negative. In the second figure it will be possible to
infer only that which is subordinate to the conclusion, e.g. if A
belongs to no B and to all C; we conclude that B belongs to no C. If
