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Metaphysics   


however, the soul is something different and is not identical with the
animal, even so some parts must, as we have maintained, be called
prior and others must not.
11

Another question is naturally raised, viz. what sort of parts
belong to the form and what sort not to the form, but to the
concrete thing. Yet if this is not plain it is not possible to
define any thing; for definition is of the universal and of the
form. If then it is not evident what sort of parts are of the nature
of matter and what sort are not, neither will the formula of the thing
be evident. In the case of things which are found to occur in
specifically different materials, as a circle may exist in bronze or
stone or wood, it seems plain that these, the bronze or the stone, are
no part of the essence of the circle, since it is found apart from
them. Of things which are not seen to exist apart, there is no
reason why the same may not be true, just as if all circles that had
ever been seen were of bronze; for none the less the bronze would be
no part of the form; but it is hard to eliminate it in thought. E.g.
the form of man is always found in flesh and bones and parts of this
kind; are these then also parts of the form and the formula? No,
they are matter; but because man is not found also in other matters we
are unable to perform the abstraction.
Since this is thought to be possible, but it is not clear when
it is the case, some people already raise the question even in the
case of the circle and the triangle, thinking that it is not right
to define these by reference to lines and to the continuous, but
that all these are to the circle or the triangle as flesh and bones
are to man, and bronze or stone to the statue; and they reduce all
things to numbers, and they say the formula of 'line' is that of
'two'. And of those who assert the Ideas some make 'two' the
line-itself, and others make it the Form of the line; for in some
cases they say the Form and that of which it is the Form are the same,
e.g. 'two' and the Form of two; but in the case of 'line' they say
this is no longer so.
It follows then that there is one Form for many things whose
form is evidently different (a conclusion which confronted the
Pythagoreans also); and it is possible to make one thing the
Form-itself of all, and to hold that the others are not Forms; but
thus all things will be one.
We have pointed out, then, that the question of definitions
contains some difficulty, and why this is so. And so to reduce all
things thus to Forms and to eliminate the matter is useless labour;
for some things surely are a particular form in a particular matter,
or particular things in a particular state. And the comparison which
Socrates the younger used to make in the case of 'animal' is not
sound; for it leads away from the truth, and makes one suppose that
man can possibly exist without his parts, as the circle can without
the bronze. But the case is not similar; for an animal is something
perceptible, and it is not possible to define it without reference
to movement-nor, therefore, without reference to the parts' being in a
certain state. For it is not a hand in any and every state that is a
part of man, but only when it can fulfil its work, and therefore
only when it is alive; if it is not alive it is not a part.
Regarding the objects of mathematics, why are the formulae of
the parts not parts of the formulae of the wholes; e.g. why are not
the semicircles included in the formula of the circle? It cannot be
said, 'because these parts are perceptible things'; for they are
not. But perhaps this makes no difference; for even some things
which are not perceptible must have matter; indeed there is some
matter in everything which is not an essence and a bare form but a
'this'. The semicircles, then, will not be parts of the universal
circle, but will be parts of the individual circles, as has been
said before; for while one kind of matter is perceptible, there is

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