In general, too, all the ways of showing that the whole is
not the same as the sum of its parts are useful in meeting the type
just described; for a man who defines in this way seems to assert that
the parts are the same as the whole. The arguments are particularly
appropriate in cases where the process of putting the parts together
is obvious, as in a house and other things of that sort: for there,
clearly, you may have the parts and yet not have the whole, so that
parts and whole cannot be the same.
If, however, he has said that the term being defined is not 'A and
B' but the 'product of A and B', look and see in the first place if
A and B cannot in the nature of things have a single product: for some
things are so related to one another that nothing can come of them,
e.g. a line and a number. Moreover, see if the term that has been
defined is in the nature of things found primarily in some single
subject, whereas the things which he has said produce it are not found
primarily in any single subject, but each in a separate one. If so,
clearly that term could not be the product of these things: for the
whole is bound to be in the same things wherein its parts are, so that
the whole will then be found primarily not in one subject only, but in
a number of them.
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