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.e. the Forms which we posit. If it is for
this reason, because the objects of mathematics, while they differ
from the things in this world in some other respect, differ not at all
in that there are many of the same kind, so that their first
principles cannot be limited in number (just as the elements of all
the language in this sensible world are not limited in number, but
in kind, unless one takes the elements of this individual syllable
or of this individual articulate sound-whose elements will be
limited even in number; so is it also in the case of the
intermediates; for there also the members of the same kind are
infinite in number), so that if there are not-besides perceptible
and mathematical objects-others such as some maintain the Forms to be,
there will be no substance which is one in number, but only in kind,
nor will the first principles of things be determinate in number,
but only in kind:-if then this must be so, the Forms also must
therefore be held to exist. Even if those who support this view do not
express it articulately, still this is what they mean, and they must
be maintaining the Forms just because each of the Forms is a substance
and none is by accident.
But if we are to suppose both that the Forms exist and that the
principles are one in number, not in kind, we have mentioned the
impossible results that necessarily follow.
(13) Closely connected with this is the question whether the
elements exist potentially or in some other manner
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