to Timaeus and
Archytas are spurious; and the treatise of Ocellus Lucanus on 'The
Nature of the All' can not have been written by a Pythagorean."[427] The
only writers who can be regarded as at all reliable are Plato and
Aristotle; and the opinions they represent are not so much those of
Pythagoras as "the Pythagoreans." This is at once accounted for by the
fact that Pythagoras taught in secret, and did not commit his opinions
to writing. His disciples, therefore, represent the _tendency_ rather
than the actual tenets of his system; these were no doubt modified by
the mental habits and tastes of his successors.

[Footnote 427: Lewes's "Biographical History of Philosophy," p. 24.]

We may safely assume that the proposition from which Pythagoras started
was the fundamental idea of all Greek speculation--_that beneath the
fleeting forms and successive changes of the universe there is some
permanent principle of unity_[428] The Ionian school sought that
principle in some common physical element; Pythagoras sought, not for
"elements," but for "relations," and through these relations for
ultimate laws indicating primal forces.

[Footnote 428: See Plato, "Timaeus," ch. ix. p. 331 (Bohn's edition);
Aristotle's "Metaphysics," bk. v. ch. iii.]

Aristotle affirms that Pythagoras taught "that _numbers_ are the first
principles of all entities," and, "as it were, a _material_ cause of
things,"[429] or, in other words, "that numbers are substances that
involve a separate subsistence, and are primary causes of
entities."[430]

[Footnote 429: Aristotle's "Metaphysics," bk. i. ch. v.]

[Footnote 430: Id., ib., bk. xii. ch. vi.]

Are we then required to accept the dictum of Aristotle as final and
decisive? Did Pythagoras really teach that numbers are real
entities--the _substance_ and cause of all other existences? The reader
may be aware that this is a point upon which the historians of
philosophy are not agreed. Ritter is decidedly of opinion that the
Pythagorean formula "can only be taken symbolically."[431] Lewes insists
it must be understood literally.[432] On a careful review of all the
arguments, we are constrained to regard the conclusion of Ritter as most
reasonable. The hypothesis "that numbers are real entities" does
violence to every principle of common sense. This alone constitutes a
strong _a priori_ presumption that Pythagoras did not entertain so
glaring an absurdity. The man who contributed so much towards perfec