Prior Analytics - Book II   

In the third figure an affirmative syllogism can never be made out

of opposite premisses, for the reason given in reference to the

first figure; but a negative syllogism is possible whether the terms

are universal or not. Let B and C stand for science, A for medicine.

If then one should assume that all medicine is science and that no

medicine is science, he has assumed that B belongs to all A and C to

no A, so that a particular science will not be a science. Similarly if

the premiss BA is not assumed universally. For if some medicine is

science and again no medicine is science, it results that some science

is not science, The premisses are contrary if the terms are taken

universally; if one is particular, they are contradictory.

We must recognize that it is possible to take opposites in the way

we said, viz. 'all science is good' and 'no science is good' or

'some science is not good'. This does not usually escape notice. But

it is possible to establish one part of a contradiction through

other premisses, or to assume it in the way suggested in the Topics.

Since there are three oppositions to affirmative statements, it

follows that opposite statements may be assumed as premisses in six

ways; we may have either universal affirmative and negative, or

universal affirmative and particular negative, or particular

affirmative and universal negative, and the relations between the

terms may be reversed; e.g. A may belong to all B and to no C, or to

all C and to no B, or to all of the one, not to all of the other; here

too the relation between the terms may be reversed. Similarly in the

third figure. So it is clear in how many ways and in what figures a

syllogism can be made by means of premisses which are opposed.

It is clear too that from false premisses it is possible to draw a

true conclusion, as has been said before, but it is not possible if

the premisses are opposed. For the syllogism is always contrary to the

fact, e.g. if a thing is good, it is proved that it is not good, if an

animal, that it is not an animal because the syllogism springs out

of a contradiction and the terms presupposed are either identical or