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