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than one conclusion； e。g。 if A has been proved to to all or to some B；
then B must belong to some A： and if A has been proved to belong to no
B； then B belongs to no A。 This is a different conclusion from the
former。 But if A does not belong to some B； it is not necessary that B
should not belong to some A： for it may possibly belong to all A。
This then is the reason common to all syllogisms whether universal
or particular。 But it is possible to give another reason concerning
those which are universal。 For all the things that are subordinate
to the middle term or to the conclusion may be proved by the same
syllogism； if the former are placed in the middle； the latter in the
conclusion； e。g。 if the conclusion AB is proved through C； whatever is
subordinate to B or C must accept the predicate A： for if D is
included in B as in a whole； and B is included in A； then D will be
included in A。 Again if E is included in C as in a whole； and C is
included in A； then E will be included in A。 Similarly if the
syllogism is negative。 In the second figure it will be possible to
infer only that which is subordinate to the conclusion； e。g。 if A
belongs to no B and to all C； we conclude that B belongs to no C。 If
then D is subordinate to C； clearly B does not belong to it。 But
that B does not belong to what is subordinate to A is not clear by
means of the syllogism。 And yet B does not belong to E； if E is
subordinate to A。 But while it has been proved through the syllogism
that B belongs to no C； it has been assumed without proof that B
does not belong to A； consequently it does not result through the
syllogism that B does not belong to E。
But in particular syllogisms there will be no necessity of inferring
what is subordinate to the conclusion （for a syllogism does not result
when this premiss is particular）； but whatever is subordinate to the
middle term may be inferred； not however through the syllogism； e。g。
if A belongs to all B and B to some C。 Nothing can be inferred about
that which is subordinate to C； something can be inferred about that
which is subordinate to B； but not through the preceding syllogism。
Similarly in the other figures。 That which is subordinate to the
conclusion cannot be proved； the other subordinate can be proved； only
not through the syllogism； just as in the universal syllogisms what is
subordinate to the middle term is proved （as we saw） from a premiss
which is not demonstrated： consequently either a conclusion is not
possible in the case of universal syllogisms or else it is possible
also in the case of particular syllogisms。
2
It is possible for the premisses of the syllogism to be true； or
to be false； or to be the one true； the other false。 The conclusion is
either true or false necessarily。 From true premisses it is not
possible to draw a false conclusion； but a true conclusion may be
drawn from false premisses； true however only in respect to the
fact； not to the reason。 The reason cannot be established from false
premisses： why this is so will be explained in the sequel。
First then that it is not possible to draw a false conclusion from
true premisses； is made clear by this consideration。 If it is
necessary that B should be when A is； it is necessary that A should
not be when B is not。 If then A is true； B must be true： otherwise
it will turn out that the same thing both is and is not at the same
time。 But this is impossible。 Let it not； because A is laid down as
a single term； be supposed that it is possible； when a single fact
is given； that something should necessarily result。 For that is not
possible。 For what results necessarily is the conclusion； and the
means by which this comes about are at the least three terms； and
two relations of subject and predicate or premisses。 If then it is
true that A belongs to all that to which B belongs； and that B belongs
to all that to which C belongs； it is necessary that A should belong
to all that to which C belongs； and this cannot be false： for then the
same thing will belong and not belong at the same time。 So A is
posited as one thing； being two premisses taken together。 The same
holds good of negative syllogisms： it is not possible to prove a false
conclusion from true premisses。
But from what is false a true conclusion may be drawn； whether
both the premisses are false or only one； provided that this is not
either of the premisses indifferently； if it is taken as wholly false：
but if the premiss is not taken as wholly false； it does not matter
which of the two is false。 （1） Let A belong to the whole of C； but
to none of the Bs； neither let B belong to C。 This is possible； e。g。
animal belongs to no stone； nor stone to any man。 If then A is taken
to belong to all B and B to all C； A will belong to all C；
consequently though both the premisses are false the conclusion is
true： for every man is an animal。 Similarly with the negative。 For
it is possible that neither A nor B should belong to any C； although A
belongs to all B； e。g。 if the same terms are taken and man is put as
middle： for neither animal nor man belongs to any stone； but animal
belongs to every man。 Consequently if one term is taken to belong to
none of that to which it does belong； and the other term is taken to
belong to all of that to which it does not belong； though both the
premisses are false the conclusion will be true。 （2） A similar proof
may be given if each premiss is partially false。
（3） But if one only of the premisses is false； when the first
premiss is wholly false； e。g。 AB； the conclusion will not be true； but
if the premiss BC is wholly false； a true conclusion will be possible。
I mean by 'wholly false' the contrary of the truth； e。g。 if what
belongs to none is assumed to belong to all； or if what belongs to all
is assumed to belong to none。 Let A belong to no B； and B to all C。 If
then the premiss BC which I take is true； and the premiss AB is wholly
false； viz。 that A belongs to all B； it is impossible that the
conclusion should be true： for A belonged to none of the Cs； since A
belonged to nothing to which B belonged； and B belonged to all C。
Similarly there cannot be a true conclusion if A belongs to all B； and
B to all C； but while the true premiss BC is assumed； the wholly false
premiss AB is also assumed； viz。 that A belongs to nothing to which
B belongs： here the conclusion must be false。 For A will belong to all
C； since A belongs to everything to which B belongs； and B to all C。
It is clear then that when the first premiss is wholly false；