Prior Analytics - Book II   

universal affirmative and the universal negative, e.g. 'every

science is good', 'no science is good'; the others I call

contradictories.

In the first figure no syllogism whether affirmative or negative can

be made out of opposed premisses: no affirmative syllogism is possible

because both premisses must be affirmative, but opposites are, the one

affirmative, the other negative: no negative syllogism is possible

because opposites affirm and deny the same predicate of the same

subject, and the middle term in the first figure is not predicated

of both extremes, but one thing is denied of it, and it is affirmed of

something else: but such premisses are not opposed.

In the middle figure a syllogism can be made both

oLcontradictories and of contraries. Let A stand for good, let B and C

stand for science. If then one assumes that every science is good, and

no science is good, A belongs to all B and to no C, so that B

belongs to no C: no science then is a science. Similarly if after

taking 'every science is good' one took 'the science of medicine is

not good'; for A belongs to all B but to no C, so that a particular

science will not be a science. Again, a particular science will not be

a science if A belongs to all C but to no B, and B is science, C

medicine, and A supposition: for after taking 'no science is

supposition', one has assumed that a particular science is

supposition. This syllogism differs from the preceding because the

relations between the terms are reversed: before, the affirmative

statement concerned B, now it concerns C. Similarly if one premiss

is not universal: for the middle term is always that which is stated

negatively of one extreme, and affirmatively of the other.

Consequently it is possible that contradictories may lead to a

conclusion, though not always or in every mood, but only if the

terms subordinate to the middle are such that they are either

identical or related as whole to part. Otherwise it is impossible: for

the premisses cannot anyhow be either contraries or contradictories.