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It is clear then that when the first premiss is wholly false；
whether affirmative or negative； and the other premiss is true； the
conclusion cannot be true。
（4） But if the premiss is not wholly false； a true conclusion is
possible。 For if A belongs to all C and to some B； and if B belongs to
all C； e。g。 animal to every swan and to some white thing； and white to
every swan； then if we take as premisses that A belongs to all B；
and B to all C； A will belong to all C truly： for every swan is an
animal。 Similarly if the statement AB is negative。 For it is
possible that A should belong to some B and to no C； and that B should
belong to all C； e。g。 animal to some white thing； but to no snow；
and white to all snow。 If then one should assume that A belongs to
no B； and B to all C； then will belong to no C。
（5） But if the premiss AB； which is assumed； is wholly true； and the
premiss BC is wholly false； a true syllogism will be possible： for
nothing prevents A belonging to all B and to all C； though B belongs
to no C； e。g。 these being species of the same genus which are not
subordinate one to the other： for animal belongs both to horse and
to man； but horse to no man。 If then it is assumed that A belongs to
all B and B to all C； the conclusion will be true； although the
premiss BC is wholly false。 Similarly if the premiss AB is negative。
For it is possible that A should belong neither to any B nor to any C；
and that B should not belong to any C； e。g。 a genus to species of
another genus： for animal belongs neither to music nor to the art of
healing； nor does music belong to the art of healing。 If then it is
assumed that A belongs to no B； and B to all C； the conclusion will be
true。
（6） And if the premiss BC is not wholly false but in part only； even
so the conclusion may be true。 For nothing prevents A belonging to the
whole of B and of C； while B belongs to some C； e。g。 a genus to its
species and difference： for animal belongs to every man and to every
footed thing； and man to some footed things though not to all。 If then
it is assumed that A belongs to all B； and B to all C； A will belong
to all C： and this ex hypothesi is true。 Similarly if the premiss AB
is negative。 For it is possible that A should neither belong to any
B nor to any C； though B belongs to some C； e。g。 a genus to the
species of another genus and its difference： for animal neither
belongs to any wisdom nor to any instance of 'speculative'； but wisdom
belongs to some instance of 'speculative'。 If then it should be
assumed that A belongs to no B； and B to all C； will belong to no C：
and this ex hypothesi is true。
In particular syllogisms it is possible when the first premiss is
wholly false； and the other true； that the conclusion should be
true； also when the first premiss is false in part； and the other
true； and when the first is true； and the particular is false； and
when both are false。 （7） For nothing prevents A belonging to no B； but
to some C； and B to some C； e。g。 animal belongs to no snow； but to
some white thing； and snow to some white thing。 If then snow is
taken as middle； and animal as first term； and it is assumed that A
belongs to the whole of B； and B to some C； then the premiss BC is
wholly false； the premiss BC true； and the conclusion true。
Similarly if the premiss AB is negative： for it is possible that A
should belong to the whole of B； but not to some C； although B belongs
to some C； e。g。 animal belongs to every man； but does not follow
some white； but man belongs to some white； consequently if man be
taken as middle term and it is assumed that A belongs to no B but B
belongs to some C； the conclusion will be true although the premiss AB
is wholly false。 （If the premiss AB is false in part； the conclusion
may be true。 For nothing prevents A belonging both to B and to some C；
and B belonging to some C； e。g。 animal to something beautiful and to
something great； and beautiful belonging to something great。 If then A
is assumed to belong to all B； and B to some C； the a premiss AB
will be partially false； the premiss BC will be true； and the
conclusion true。 Similarly if the premiss AB is negative。 For the same
terms will serve； and in the same positions； to prove the point。
（9） Again if the premiss AB is true； and the premiss BC is false；
the conclusion may be true。 For nothing prevents A belonging to the
whole of B and to some C； while B belongs to no C； e。g。 animal to
every swan and to some black things； though swan belongs to no black
thing。 Consequently if it should be assumed that A belongs to all B；
and B to some C； the conclusion will be true； although the statement
BC is false。 Similarly if the premiss AB is negative。 For it is
possible that A should belong to no B； and not to some C； while B
belongs to no C； e。g。 a genus to the species of another genus and to
the accident of its own species： for animal belongs to no number and
not to some white things； and number belongs to nothing white。 If then
number is taken as middle； and it is assumed that A belongs to no B；
and B to some C； then A will not belong to some C； which ex
hypothesi is true。 And the premiss AB is true； the premiss BC false。
（10） Also if the premiss AB is partially false； and the premiss BC
is false too； the conclusion may be true。 For nothing prevents A
belonging to some B and to some C； though B belongs to no C； e。g。 if B
is the contrary of C； and both are accidents of the same genus： for
animal belongs to some white things and to some black things； but
white belongs to no black thing。 If then it is assumed that A
belongs to all B； and B to some C； the conclusion will be true。
Similarly if the premiss AB is negative： for the same terms arranged
in the same way will serve for the proof。
（11） Also though both premisses are false the conclusion may be
true。 For it is possible that A may belong to no B and to some C；
while B belongs to no C； e。g。 a genus in relation to the species of
another genus； and to the accident of its own species： for animal
belongs to no number； but to some white things； and number to
nothing white。 If then it is assumed that A belongs to all B and B
to some C； the conclusion will be true； though both premisses are
false。 Similarly also if the premiss AB is negative。 For nothing
prevents A belonging to the whole of B； and not to some C； while B
belongs to no C； e。g。 animal belongs to every swan； and not to some
black things； and swan belongs to nothing black。 Consequently if it is
assumed that A belongs to no B； and B to some C； then A does not
belong