Книга только для ознакомления
. Thus,
then, geometers speak correctly; they talk about existing things,
and their subjects do exist; for being has two forms-it exists not
only in complete reality but also materially.
Now since the good and the beautiful are different (for the former
always implies conduct as its subject, while the beautiful is found
also in motionless things), those who assert that the mathematical
sciences say nothing of the beautiful or the good are in error. For
these sciences say and prove a great deal about them; if they do not
expressly mention them, but prove attributes which are their results
or their definitions, it is not true to say that they tell us
nothing about them. The chief forms of beauty are order and symmetry
and definiteness, which the mathematical sciences demonstrate in a
special degree. And since these (e.g. order and definiteness) are
obviously causes of many things, evidently these sciences must treat
this sort of causative principle also (i.e. the beautiful) as in
some sense a cause. But we shall speak more plainly elsewhere about
these matters.
4
So much then for the objects of mathematics; we have said that
they exist and in what sense they exist, and in what sense they are
prior and in what sense not prior. Now, regarding the Ideas, we must
first examine the ideal theory itself, not connecting it in any way
with the nature of numbers, but treating it in the form in which it
was originally understood by those who first maintained the
existence of the Ideas
|
