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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'
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