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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 assumption； assuming； e。g。； that
every science is supposition； and then assuming 'Medicine is a
science； but none of it is supposition' （which is the mode in which
refutations are made）； or we must argue from two syllogisms。 In no
other way than this； as was said before； is it possible that the
premisses should be really contrary。
16
To beg and assume the original question is a species of failure to
demonstrate the problem proposed； but this happens in many ways。 A man
may not reason syllogistically at all； or he may argue from
premisses which are less known or equally unknown； or he may establish
the antecedent by means of its consequents； for demonstration proceeds
from what is more certain and is prior。 Now begging the question is
none of these： but since we get to know some things naturally
through themselves； and other things by means of something else （the
first principles through themselves； what is subordinate to them
through something else）； whenever a man tries to prove what is not
self…evident by means of itself； then he begs the original question。
This may be done by assuming what is in question at once； it is also
possible to make a transition to other things which would naturally be
proved through the thesis proposed； and demonstrate it through them；
e。g。 if A should be proved through B； and B through C； though it was
natural that C should be proved through A： for it turns out that those
who reason thus are proving A by means of itself。 This is what those
persons do who suppose that they are constructing parallel straight
lines： for they fail to see that they are assuming facts which it is
impossible to demonstrate unless the parallels exist。 So it turns
out that those who reason thus merely say a particular thing is； if it
is： in this way everything will be self…evident。 But that is
impossible。
If then it is uncertain whether A belongs to C； and also whether A
belongs to B； and if one should assume that A does belong to B； it
is not yet clear whether he begs the original question； but it is
evident that he is not demonstrating： for what is as uncertain as
the question to be answered cannot be a principle of a
demonstration。 If however B is so related to C that they are
identical； or if they are plainly convertible； or the one belongs to
the other； the original question is begged。 For one might equally well
prove that A belongs to B through those terms if they are convertible。
But if they are not convertible； it is the fact that they are not that
prevents such a demonstration； not the method of demonstrating。 But if
one were to make the conversion； then he would be doing what we have
described and effecting a reciprocal proof with three propositions。
Similarly if he should assume that B b