Prior Analytics - Book I   

particular, a syllogism will be possible, or not, under the

arrangement of the terms as in the case of assertoric propositions.

Suppose that A may possibly belong to all C, and B to some C. We shall

have the first figure again if the particular premiss is converted.

For if A is possible for all C, and C for some of the Bs, then A is

possible for some of the Bs. Similarly if the proposition BC is

universal. Likewise also if the proposition AC is negative, and the

proposition BC affirmative: for we shall again have the first figure

by conversion. But if both premisses should be negative-the one

universal and the other particular-although no syllogistic

conclusion will follow from the premisses as they are put, it will

follow if they are converted, as above. But when both premisses are

indefinite or particular, no syllogism can be formed: for A must

belong sometimes to all B and sometimes to no B. To illustrate the

affirmative relation take the terms animal-man-white; to illustrate

the negative, take the terms horse-man-white--white being the middle

term.



21



If one premiss is pure, the other problematic, the conclusion will

be problematic, not pure; and a syllogism will be possible under the

same arrangement of the terms as before. First let the premisses be

affirmative: suppose that A belongs to all C, and B may possibly

belong to all C. If the proposition BC is converted, we shall have the

first figure, and the conclusion that A may possibly belong to some of

the Bs. For when one of the premisses in the first figure is

problematic, the conclusion also (as we saw) is problematic. Similarly

if the proposition BC is pure, AC problematic; or if AC is negative,

BC affirmative, no matter which of the two is pure; in both cases

the conclusion will be problematic: for the first figure is obtained

once more, and it has been proved that if one premiss is problematic