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are negative； either no syllogism results； or if one it is not
perfect。 For the necessity results from the conversion。
But if one of the premisses is universal； the other particular； when
the major premiss is universal there will be a perfect syllogism。
For if A is possible for all B； and B for some C； then A is possible
for some C。 This is clear from the definition of being possible。 Again
if A may belong to no B； and B may belong to some of the Cs； it is
necessary that A may possibly not belong to some of the Cs。 The
proof is the same as above。 But if the particular premiss is negative；
and the universal is affirmative； the major still being universal
and the minor particular； e。g。 A is possible for all B； B may possibly
not belong to some C； then a clear syllogism does not result from
the assumed premisses； but if the particular premiss is converted
and it is laid down that B possibly may belong to some C； we shall
have the same conclusion as before； as in the cases given at the
beginning。
But if the major premiss is the minor universal； whether both are
affirmative； or negative； or different in quality； or if both are
indefinite or particular； in no way will a syllogism be possible。
For nothing prevents B from reaching beyond A； so that as predicates
cover unequal areas。 Let C be that by which B extends beyond A。 To C
it is not possible that A should belong…either to all or to none or to
some or not to some； since premisses in the mode of possibility are
convertible and it is possible for B to belong to more things than A
can。 Further； this is obvious if we take terms； for if the premisses
are as assumed； the major term is both possible for none of the
minor and must belong to all of it。 Take as terms common to all the
cases under consideration 'animal'…'white'…'man'； where the major
belongs necessarily to the minor； 'animal'…'white'…'garment'； where it
is not possible that the major should belong to the minor。 It is clear
then that if the terms are related in this manner； no syllogism
results。 For every syllogism proves that something belongs either
simply or necessarily or possibly。 It is clear that there is no
proof of the first or of the second。 For the affirmative is
destroyed by the negative； and the negative by the affirmative。
There remains the proof of possibility。 But this is impossible。 For it
has been proved that if the terms are related in this manner it is
both necessary that the major should belong to all the minor and not
possible that it should belong to any。 Consequently there cannot be
a syllogism to prove the possibility； for the necessary （as we stated）
is not possible。
It is clear that if the terms are universal in possible premisses
a syllogism always results in the first figure； whether they are
affirmative or negative； only a perfect syllogism results in the first
case； an imperfect in the second。 But possibility must be understood
according to the definition laid down； not as covering necessity。 This
is sometimes forgotten。
15
If one premiss is a simple proposition； the other a problematic；
whenever the major premiss indicates possibility all the syllogisms
will be perfect and establish possibility in the sense defined； but
whenever the minor premiss indicates possibility all the syllogisms
will be imperfect； and those which are negative will establish not
possibility according to the definition； but that the major does not
necessarily belong to any； or to all； of the minor。 For if this is so；
we say it is possible that it should belong to none or not to all。 Let
A be possible for all B； and let B belong to all C。 Since C falls
under B； and A is possible for all B； clearly it is possible for all C
also。 So a perfect syllogism results。 Likewise if the premiss AB is
negative； and the premiss BC is affirmative； the former stating
possible； the latter simple attribution； a perfect syllogism results
proving that A possibly belongs to no C。
It is clear that perfect syllogisms result if the minor premiss
states simple belonging： but that syllogisms will result if the
modality of the premisses is reversed； must be proved per impossibile。
At the same time it will be evident that they are imperfect： for the
proof proceeds not from the premisses assumed。 First we must state
that if B's being follows necessarily from A's being； B's
possibility will follow necessarily from A's possibility。 Suppose； the
terms being so related； that A is possible； and B is impossible。 If
then that which is possible； when it is possible for it to be； might
happen； and if that which is impossible； when it is impossible；
could not happen； and if at the same time A is possible and B
impossible； it would be possible for A to happen without B； and if
to happen； then to be。 For that which has happened； when it has
happened； is。 But we must take the impossible and the possible not
only in the sphere of becoming； but also in the spheres of truth and
predicability； and the various other spheres in which we speak of
the possible： for it will be alike in all。 Further we must
understand the statement that B's being depends on A's being； not as
meaning that if some single thing A is； B will be： for nothing follows
of necessity from the being of some one thing； but from two at
least； i。e。 when the premisses are related in the manner stated to
be that of the syllogism。 For if C is predicated of D； and D of F；
then C is necessarily predicated of F。 And if each is possible； the
conclusion also is possible。 If then； for example； one should indicate
the premisses by A； and the conclusion by B； it would not only
result that if A is necessary B is necessary； but also that if A is
possible； B is possible。
Since this is proved it is evident that if a false and not
impossible assumption is made； the consequence of the assumption
will also be false and not impossible： e。g。 if A is false； but not
impossible； and if B is the consequence of A； B also will be false but
not impossible。 For since it has been proved that if B's being is
the consequence of A's being； then B's possibility will follow from
A's possibility （and A is assumed to be possible）； consequently B will
be possible： for if it were impossible； the same thing would at the
same time be possible and impossible。
Since we have defined these points； let A belong to all B； and B
be possible for all C： it is necessary then that should be a
possible attribute for all C。 Suppose that it is not possible； but
assume that B belongs to all C： this is false but not impossible。 If
then A is not possible for C but B belongs to all C； then A is not
possible for all B： for a syllogism is formed in the third degree。 But
it was assumed that A is a possible attribute for all B。 It is
necessary then that A is possible for all C。 For though the assumption
we made is false and not impossible； the conclusion is impossible。
It is possible also in the first figure to bring about the
impossibility； by assuming that B belongs to C。 For if B belongs to
all C； and A is possible for all B； then A would be possible for all
C。 But the assumption was made that A is not possible for all C。
We must understand 'that which belongs to all' with no limitation in
respect of time； e。g。 to the present or to a particular period； but
simply without qualification。 For it is by the help of such
premisses that we make syllogisms； since if the premiss is
understood with reference to the present moment； there cannot be a
syllogism。 For nothing perhaps prevents 'man' belonging at a
particular time to everything that is moving； i。e。 if nothing else
were moving： but 'moving' is possible for every horse； yet 'man' is
possible for no horse。 Further let the major term be 'animal'； the
middle 'moving'； the the minor 'man'。 The premisses then will be as
before； but the conclusion necessary； not possible。 For man is
necessarily animal。 It is clear then that the universal must be
understood simply； without limitation in respect of time。
Again let the premiss AB be universal and negative； and assume
that A belongs to no B； but B possibly belongs to all C。 These
propositions being laid down； it is necessary that A possibly
belongs to no C。 Suppose that it cannot belong； and that B belongs
to C； as above。 It is necessary then that A belongs to some B： for
we have a syllogism in the third figure： but this is impo