The Complete Aristotle (eng.)

be’ implies a twofold
possibility, while, if either of the two former propositions is
true, the twofold possibility vanishes. For if a thing may be, it
may also not be, but if it is necessary that it should be or that
it should not be, one of the two alternatives will be excluded. It
remains, therefore, that the proposition ‘it is not necessary that
it should not be’ follows from the proposition ‘it may be’. For
this is true also of that which must necessarily be.
    Moreover the proposition ‘it is not necessary that it should not
be’ is the contradictory of that which follows from the proposition
‘it cannot be’; for ‘it cannot be’ is followed by ‘it is impossible
that it should be’ and by ‘it is necessary that it should not be’,
and the contradictory of this is the proposition ‘it is not
necessary that it should not be’. Thus in this case also
contradictory propositions follow contradictory in the way
indicated, and no logical impossibilities occur when they are thus
arranged.
    It may be questioned whether the proposition ‘it may be’ follows
from the proposition ‘it is necessary that it should be’. If not,
the contradictory must follow, namely that it cannot be, or, if a
man should maintain that this is not the contradictory, then the
proposition ‘it may not be’.
    Now both of these are false of that which necessarily is. At the
same time, it is thought that if a thing may be cut it may also not
be cut, if a thing may be it may also not be, and thus it would
follow that a thing which must necessarily be may possibly not be;
which is false. It is evident, then, that it is not always the case
that that which may be or may walk possesses also a potentiality in
the other direction. There are exceptions. In the first place we
must except those things which possess a potentiality not in
accordance with a rational principle, as fire possesses the
potentiality of giving out heat, that is, an irrational capacity.
Those potentialities which involve a rational principle are
potentialities of more than one result, that is, of contrary
results; those that are irrational are not always thus constituted.
As I have said, fire cannot both heat and not heat, neither has
anything that is always actual any twofold potentiality. Yet some
even of those potentialities which are irrational admit of opposite
results. However, thus much has been said to emphasize the truth
that it is not every potentiality which admits of opposite results,
even where the word is used always in the same sense.
    But in some cases the word is used equivocally. For the term
‘possible’ is ambiguous, being used in the one case with reference
to facts, to that which is actualized, as when a man is said to
find walking possible because he is actually walking, and generally
when a capacity is predicated because it is actually realized; in
the other case, with reference to a state in which realization is
conditionally practicable, as when a man is said to find walking
possible because under certain conditions he would walk. This last
sort of potentiality belongs only to that which can be in motion,
the former can exist also in the case of that which has not this
power. Both of that which is walking and is actual, and of that
which has the capacity though not necessarily realized, it is true
to say that it is not impossible that it should walk (or, in the
other case, that it should be), but while we cannot predicate this
latter kind of potentiality of that which is necessary in the
unqualified sense of the word, we can predicate the former.
    Our conclusion, then, is this: that since the universal is
consequent upon the particular, that which is necessary is also
possible, though not in every sense in which the word may be
used.
    We may perhaps state that necessity and its absence are the
initial principles of existence and non-existence, and that all
else must be regarded as posterior to these.
    It is plain from what has been said that that which is of
necessity is actual. Thus, if that which is eternal is prior,
actuality also is prior to potentiality. Some things are
actualities without potentiality, namely, the primary substances; a
second class consists of those things which are actual but also
potential, whose actuality is in nature prior to their
potentiality, though posterior in time; a third class comprises
those things which are never actualized, but are pure
potentialities.
14
    The question arises whether an