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should belong to some C； but it is possible for A to belong to C；
and that A should belong to B is not necessary。 For there is no
necessity that some biped should be asleep or awake。 Similarly and
by means of the same terms proof can be made； should the proposition
AC be both particular and necessary。
But if one premiss is affirmative； the other negative； whenever
the universal is both negative and necessary the conclusion also
will be necessary。 For if it is not possible that A should belong to
any C； but B belongs to some C； it is necessary that A should not
belong to some B。 But whenever the affirmative proposition is
necessary； whether universal or particular； or the negative is
particular； the conclusion will not be necessary。 The proof of this by
reduction will be the same as before； but if terms are wanted； when
the universal affirmative is necessary； take the terms
'waking'…'animal'…'man'； 'man' being middle； and when the
affirmative is particular and necessary； take the terms
'waking'…'animal'…'white'： for it is necessary that animal should
belong to some white thing； but it is possible that waking should
belong to none； and it is not necessary that waking should not
belong to some animal。 But when the negative proposition being
particular is necessary； take the terms 'biped'； 'moving'； 'animal'；
'animal' being middle。
12
It is clear then that a simple conclusion is not reached unless both
premisses are simple assertions； but a necessary conclusion is
possible although one only of the premisses is 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 '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
perfe