necessary premisses. The universal negative converts universally; each
of the affirmatives converts into a particular. If it is necessary
that no B is A, it is necessary also that no A is B. For if it is
possible that some A is B, it would be possible also that some B is A.
If all or some B is A of necessity, it is necessary also that some A
is B: for if there were no necessity, neither would some of the Bs
be A necessarily. But the particular negative does not convert, for
the same reason which we have already stated.

  In respect of possible premisses, since possibility is used in
several senses (for we say that what is necessary and what is not
necessary and what is potential is possible), affirmative statements
will all convert in a manner similar to those described. For if it
is possible that all or some B is A, it will be possible that some A
is B. For if that were not possible, then no B could possibly be A.
This has been already proved. But in negative statements the case is
different. Whatever is said to be possible, either because B
necessarily is A, or because B is not necessarily A, admits of
conversion like other negative statements, e.g. if one should say,
it is possible that man is not horse, or that no garment is white. For
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