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in the former case the one term necessarily does not belong to the
other； in the latter there is no necessity that it should： and the
premiss converts like other negative statements。 For if it is possible
for no man to be a horse； it is also admissible for no horse to be a
man； and if it is admissible for no garment to be white； it is also
admissible for nothing white to be a garment。 For if any white thing
must be a garment； then some garment will necessarily be white。 This
has been already proved。 The particular negative also must be
treated like those dealt with above。 But if anything is said to be
possible because it is the general rule and natural （and it is in this
way we define the possible）； the negative premisses can no longer be
converted like the simple negatives； the universal negative premiss
does not convert； and the particular does。 This will be plain when
we speak about the possible。 At present we may take this much as clear
in addition to what has been said： the statement that it is possible
that no B is A or some B is not A is affirmative in form： for the
expression 'is possible' ranks along with 'is'； and 'is' makes an
affirmation always and in every case； whatever the terms to which it
is added； in predication； e。g。 'it is not…good' or 'it is not…white'
or in a word 'it is not…this'。 But this also will be proved in the
sequel。 In conversion these premisses will behave like the other
affirmative propositions。
4
After these distinctions we now state by what means； when； and how
every syllogism is produced； subsequently we must speak of
demonstration。 Syllogism should be discussed before demonstration
because syllogism is the general： the demonstration is a sort of
syllogism； but not every syllogism is a demonstration。
Whenever three terms are so related to one another that the last
is contained in the middle as in a whole； and the middle is either
contained in； or excluded from； the first as in or from a whole； the
extremes must be related by a perfect syllogism。 I call that term
middle which is itself contained in another and contains another in
itself： in position also this comes in the middle。 By extremes I
mean both that term which is itself contained in another and that in
which another is contained。 If A is predicated of all B； and B of
all C； A must be predicated of all C： we have already explained what
we mean by 'predicated of all'。 Similarly also； if A is predicated
of no B； and B of all C； it is necessary that no C will be A。
But if the first term belongs to all the middle； but the middle to
none of the last term； there will be no syllogism in respect of the
extremes； for nothing necessary follows from the terms being so
related； for it is possible that the first should belong either to all
or to none of the last； so that neither a particular nor a universal
conclusion is necessary。 But if there is no necessary consequence；
there cannot be a syllogism by means of these premisses。 As an example
of a universal affirmative relation between the extremes we may take
the terms animal； man； horse； of a universal negative relation； the
terms animal； man； stone。 Nor again can syllogism be formed when
neither the first term belongs to any of the middle； nor the middle to
any of the last。 As an example of a positive relation between the
extremes take the terms science； line； medicine： of a negative
relation science； line； unit。
If then the terms are universally related； it is clear in this
figure when a syllogism will be possible and when not； and that if a
syllogism is possible the terms must be related as described； and if
they are so related there will be a syllogism。
But if one term is related universally； the other in part only； to
its subject； there must be a perfect syllogism whenever universality
is posited with reference to the major term either affirmatively or
negatively； and particularity with reference to the minor term
affirmatively： but whenever the universality is posited in relation to
the minor term； or the terms are related in any other way； a syllogism
is impossible。 I call that term the major in which the middle is
contained and that term the minor which comes under the middle。 Let
all B be A and some C be B。 Then if 'predicated of all' means what was
said above； it is necessary that some C is A。 And if no B is A but
some C is B； it is necessary that some C is not A。 The meaning of
'predicated of none' has also been defined。 So there will be a perfect
syllogism。 This holds good also if the premiss BC should be
indefinite； provided that it is affirmative： for we shall have the
same syllogism whether the premiss is indefinite or particular。
But if the universality is posited with respect to the minor term
either affirmatively or negatively； a syllogism will not be
possible； whether the major premiss is positive or negative；
indefinite or particular： e。g。 if some B is or is not A； and all C
is B。 As an example of a positive relation between the extremes take
the terms good； state； wisdom： of a negative relation； good； state；
ignorance。 Again if no C is B； but some B is or is not A or not
every B is A； there cannot be a syllogism。 Take the terms white；
horse； swan： white； horse； raven。 The same terms may be taken also
if the premiss BA is indefinite。
Nor when the major premiss is universal； whether affirmative or
negative； and the minor premiss is negative and particular； can
there be a syllogism； whether the minor premiss be indefinite or
particular： e。g。 if all B is A and some C is not B； or if not all C is
B。 For the major term may be predicable both of all and of none of the
minor； to some of which the middle term cannot be attributed。
Suppose the terms are animal； man； white： next take some of the
white things of which man is not predicated…swan and snow： animal is
predicated of all of the one； but of none of the other。 Consequently
there cannot be a syllogism。 Again let no B be A； but let some C not
be B。 Take the terms inanimate； man； white： then take some white
things of which man is not predicated…swan and snow： the term
inanimate is predicated of all of the one； of none of the other。
Further since it is indefinite to say some C is not B； and it is
true that some C is not B； whether no C is B； or not all C is B； and
since if terms are assumed such that no C is B； no syllogism follows
（this has already been stated） it is clear that this arrangement of
terms will not afford a syllogism： otherwise one would have been
possible with a u