The Complete Aristotle (eng.)

necessary. But in
both cases, whether the syllogisms are affirmative or negative, it
is necessary that one premiss should be similar to the conclusion.
I mean by ‘similar’, if the conclusion is a simple assertion, the
premiss must be simple; if the conclusion is necessary, the premiss
must be necessary. Consequently this also is clear, that the
conclusion will be neither necessary nor simple unless a necessary
or simple premiss is assumed.
13
    Perhaps enough has been said about the proof of necessity, how
it comes about and how it differs from the proof of a simple
statement. We proceed to discuss that which is possible, when and
how and by what means it can be proved. I use the terms ‘to be
possible’ and ‘the possible’ of that which is not necessary but,
being assumed, results in nothing impossible. We say indeed
ambiguously of the necessary that it is possible. But that my
definition of the possible is correct is clear from the phrases by
which we deny or on the contrary affirm possibility. For the
expressions ‘it is not possible to belong’, ‘it is impossible to
belong’, and ‘it is necessary not to belong’ are either identical
or follow from one another; consequently their opposites also, ‘it
is possible to belong’, ‘it is not impossible to belong’, and ‘it
is not necessary not to belong’, will either be identical or follow
from one another. For of everything the affirmation or the denial
holds good. That which is possible then will be not necessary and
that which is not necessary will be possible. It results that all
premisses in the mode of possibility are convertible into one
another. I mean not that the affirmative are convertible into the
negative, but that those which are affirmative in form admit of
conversion by opposition, e.g. ‘it is possible to belong’ may be
converted into ‘it is possible not to belong’, and ‘it is possible
for A to belong to all B’ into ‘it is possible for A to belong to
no B’ or ‘not to all B’, and ‘it is possible for A to belong to
some B’ into ‘it is possible for A not to belong to some B’. And
similarly the other propositions in this mode can be converted. For
since that which is possible is not necessary, and that which is
not necessary may possibly not belong, it is clear that if it is
possible that A should belong to B, it is possible also that it
should not belong to B: and if it is possible that it should belong
to all, it is also possible that it should not belong to all. The
same holds good in the case of particular affirmations: for the
proof is identical. And such premisses are affirmative and not
negative; for ‘to be possible’ is in the same rank as ‘to be’, as
was said above.
    Having made these distinctions we next point out that the
expression ‘to be possible’ is used in two ways. In one it means to
happen generally and fall short of necessity, e.g. man’s turning
grey or growing or decaying, or generally what naturally belongs to
a thing (for this has not its necessity unbroken, since man’s
existence is not continuous for ever, although if a man does exist,
it comes about either necessarily or generally). In another sense
the expression means the indefinite, which can be both thus and not
thus, e.g. an animal’s walking or an earthquake’s taking place
while it is 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