ms are numbers." He says: "God formed things as they first arose
according to forms _and_ numbers." See "Timaeus," ch. xiv. and xxvii.]

[Footnote 435: Aristotle's "Metaphysics," bk. i. ch. vi.]

Now the writings of Plato are all extant to-day, and accessible in an
excellent English translation to any of our readers. Cousin has
shown,[436] most conclusively (and we can verify his conclusions for
ourselves), that Aristotle has totally misrepresented Plato. And if, in
the same connection, and in the course of the same argument, and in
regard to the same subjects, he misrepresents Plato, it is most probable
he also misrepresents Pythagoras.

[Footnote 436: "The True, the Beautiful, and the Good," pp. 77-81.]

It is, however, a matter of the deepest interest for us to find the
evidence gleaming out here and there, on the pages of Aristotle, that he
had some knowledge of the fact that the Pythagorean numbers were
regarded as _symbols_. The "numbers" of Pythagoras are, in the mind of
Aristotle, clearly identified with the "forms" of Plato. Now, in Chapter
VI. of the First Book he says that Plato taught that these "forms" were
paradeigmata--models, patterns, exemplars after which created things
were framed. The numbers of Pythagoras, then, are also models and
exemplars. This also is admitted by Aristotle. The Pythagoreans indeed
affirm that entities subsist by an _imitation_ (mimesis) of
numbers.[437] Now if ideas, forms, numbers, were the models or paradigms
after which "the Operator" formed all things, surely it can not be
logical to say they were the "material" out of which all things were
framed, much less the "efficient cause" of things. The most legitimate
conclusion we can draw, even from the statements of Aristotle, is that
the Pythagoreans regarded numbers as the best expression or
representation of those laws of proportion, and order, and harmony,
which seemed, to their eyes, to pervade the universe. Their doctrine was
a faint glimpse of that grand discovery of modern science--that all the
higher laws of nature assume the form of a precise quantitative
statement.

[Footnote 437: Aristotle's "Metaphysics," bk. i. ch. vi.]

The fact seems to be this, the Pythagoreans busied themselves chiefly
with what Aristotle designates "the _formal_ cause," and gave little
attention to the inquiry concerning "the _material_ cause." This is
admitted by Aristotle. Concerning fire, or earth, or the other bodies of
such kind, the