The Complete Aristotle (eng.)

if the
demonstration is not universal. The hypothesis will then be that A
belongs to all B, the premisses that C belongs to no A and to some
B: and this is the middle figure.
    It is clear then that it is possible through the same terms to
prove each of the problems ostensively as well. Similarly it will
be possible if the syllogisms are ostensive to reduce them ad
impossibile in the terms which have been taken, whenever the
contradictory of the conclusion of the ostensive syllogism is taken
as a premiss. For the syllogisms become identical with those which
are obtained by means of conversion, so that we obtain immediately
the figures through which each problem will be solved. It is clear
then that every thesis can be proved in both ways, i.e. per
impossibile and ostensively, and it is not possible to separate one
method from the other.
15
    In what figure it is possible to draw a conclusion from
premisses which are opposed, and in what figure this is not
possible, will be made clear in this way. Verbally four kinds of
opposition are possible, viz. universal affirmative to universal
negative, universal affirmative to particular negative, particular
affirmative to universal negative, and particular affirmative to
particular negative: but really there are only three: for the
particular affirmative is only verbally opposed to the particular
negative. Of the genuine opposites I call those which are universal
contraries, the 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.
    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