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negative； the hypothesis must have been that A belongs to some B；
and the original premisses that C belongs to no A and to all B； and
this is the middle figure。 Similarly 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 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
related as whole and part。 It is evident also that in fallacious
reasonings nothing prevents a contradiction to the hypothesis from
resulting； e。g。 if something is odd； it is not odd。 For the
syllogism owed its contrariety to its contradictory premisses； if we
assume such premisses we shall get a result that contradicts our
hypothesis。 But we must recognize that contraries cannot be inferred
from a single syllogism in such a way that we conclude that what is
not good is good； or anything of that sort unless a self…contradictory
premiss is at once assumed； e。g。 'every animal is white and not
white'； and we proceed 'man is an animal'。 Either we must introduce
the contradiction by an additional a