walking, or generally what happens by chance: for none of these
inclines by nature in the one way more than in the opposite.

  That which is possible in each of its two senses is convertible into
its opposite, not however in the same way: but what is natural is
convertible because it does not necessarily belong (for in this
sense it is possible that a man should not grow grey) and what is
indefinite is convertible because it inclines this way no more than
that. Science and demonstrative syllogism are not concerned with
things which are indefinite, because the middle term is uncertain; but
they are concerned with things that are natural, and as a rule
arguments and inquiries are made about things which are possible in
this sense. Syllogisms indeed can be made about the former, but it
is unusual at any rate to inquire about them.

  These matters will be treated more definitely in the sequel; our
business at present is to state the moods and nature of the
syllogism made from possible premisses. The expression 'it is possible
for this to belong to that' may be understood in two senses: 'that'
may mean either that to which 'that' belongs or that to which it may
belong; for the expression 'A is possible of the subject of B' means
that it is possible either of that of which B is stated or of that
of which B may possibly be stated. It makes no difference whether we
say, A is possible of the subject of B, or all B admits of A. It is
clear then that the expression 'A may possibly belong to all B'
might be used in two senses. First then we must state the nature and
characteristics of the syllogism which arises if B is possible of
the subject of C, and A is possible of the subject of B. For thus both
premisses are assumed in the mode of possibility; but whenever A is
possible of that of which B is true, one premiss is a simple
assertion, the other a problematic. Consequently we must start from
premisses which are similar in form, as in the other cases.

                                14

  Whenever A may possibly belong to all B, and B to all C, there
will be a perfect syllogism to prove that A may possibly belong to all
C. This is clear from the definition: for it was in this way that we
explained 'to be possible for one term to belong to all of another'.
Similarly if it is possible for A to belong no B, and for B to
belong to all C, then it is possible for A to belong to no C. For
the statement that it is possible for A not to belong to that of which
B may be true means (as we saw) that none of those things which can
possibly fall under the term B is left out of account. But whenever
A may belong to all B, and B may belong to no C, then indeed no
syllogism results from the premisses assumed, but if the premiss BC is
converted after the manner of problematic propositions, the same
syllogism results as before. For since it is possible that B should
belong to no C, it is possible also that it should belong to all C.
This has been stated above. Consequently if B is possible for all C,
and A is possible for all B, the same syllogism again results.
Similarly if in both the premisses the negative is joined with 'it
is possible': e.g. if A may belong to none of the Bs, and B to none of
the Cs. No syllogism results from the assumed premisses, but if they
are converted we shall have the same syllogism as before. It is
clear then that if the minor premiss is negative, or if both premisses
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.