But if on the other
hand one supposes this, many impossible results, as we have said,
follow. But either this or the other must be the case, so that if
neither is, number cannot exist separately.
It is evident, also, from this that the third version is the
worst,-the view ideal and mathematical number is the same. For two
mistakes must then meet in the one opinion. (1) Mathematical number
cannot be of this sort, but the holder of this view has to spin it out
by making suppositions peculiar to himself. And (2) he must also admit
all the consequences that confront those who speak of number in the
sense of 'Forms'.
The Pythagorean version in one way affords fewer difficulties than
those before named, but in another way has others peculiar to
itself. For not thinking of number as capable of existing separately
removes many of the impossible consequences; but that bodies should be
composed of numbers, and that this should be mathematical number, is
impossible. For it is not true to speak of indivisible spatial
magnitudes; and however much there might be magnitudes of this sort,
units at least have not magnitude; and how can a magnitude be composed
of indivisibles? But arithmetical number, at least, consists of units,
while these thinkers identify number with real things; at any rate
they apply their propositions to bodies as if they consisted of
those numbers.
If, then, it is necessary, if number is a self-subsistent real
thing, that it should exist in one of these ways which have been
mentioned, and if it cannot exist in any of these, evidently number
has no such nature as those who make it separable set up for it.
Pages:
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362