Prior Analytics - Book I   

in the universal syllogisms. Nor again, if the negative statement is

necessary but particular, will the conclusion be necessary. The

point can be demonstrated by means of the same terms.



11



In the last figure when the terms are related universally to the

middle, and both premisses are affirmative, if one of the two is

necessary, then the conclusion will be necessary. But if one is

negative, the other affirmative, whenever the negative is necessary

the conclusion also will be necessary, but whenever the affirmative is

necessary the conclusion will not be necessary. First let both the

premisses be affirmative, and let A and B belong to all C, and let

AC be necessary. Since then B belongs to all C, C also will belong

to some B, because the universal is convertible into the particular:

consequently if A belongs necessarily to all C, and C belongs to

some B, it is necessary that A should belong to some B also. For B

is under C. The first figure then is formed. A similar proof will be

given also if BC is necessary. For C is convertible with some A:

consequently if B belongs necessarily to all C, it will belong

necessarily also to some A.

Again let AC be negative, BC affirmative, and let the negative

premiss be necessary. Since then C is convertible with some B, but A

necessarily belongs to no C, A will necessarily not belong to some B

either: for B is under C. But if the affirmative is necessary, the

conclusion will not be necessary. For suppose BC is affirmative and

necessary, while AC is negative and not necessary. Since then the

affirmative is convertible, C also will belong to some B

necessarily: consequently if A belongs to none of the Cs, while C

belongs to some of the Bs, A will not belong to some of the Bs-but not

of necessity; for it has been proved, in the case of the first figure,

that if the negative premiss is not necessary, neither will the