It is clear, then, from these facts that, since its substance is
the cause of each thing's being, we must seek in these differentiae
what is the cause of the being of each of these things. Now none of
these differentiae is substance, even when coupled with matter, yet it
is what is analogous to substance in each case; and as in substances
that which is predicated of the matter is the actuality itself, in all
other definitions also it is what most resembles full actuality.
E.g. if we had to define a threshold, we should say 'wood or stone
in such and such a position', and a house we should define as
'bricks and timbers in such and such a position',(or a purpose may
exist as well in some cases), and if we had to define ice we should
say 'water frozen or solidified in such and such a way', and harmony
is 'such and such a blending of high and low'; and similarly in all
other cases.
Obviously, then, the actuality or the formula is different when
the matter is different; for in some cases it is the composition, in
others the mixing, and in others some other of the attributes we
have named. And so, of the people who go in for defining, those who
define a house as stones, bricks, and timbers are speaking of the
potential house, for these are the matter; but those who propose 'a
receptacle to shelter chattels and living beings', or something of the
sort, speak of the actuality. Those who combine both of these speak of
the third kind of substance, which is composed of matter and form (for
the formula that gives the differentiae seems to be an account of
the form or actuality, while that which gives the components is rather
an account of the matter); and the same is true of the kind of
definitions which Archytas used to accept; they are accounts of the
combined form and matter.
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