innumerable degrees, from the
most complicated to the most simple: it is now a Triad, combining the
Monad and the Duad, and partaking of the nature of both; now a Tetrad,
the form of perfection; now a Decad, which, in combining the four
former, involves, in its mystic nature, all the possible accordances of
the universe.[442]

The psychology of the Pythagoreans was greatly modified by their
physical, and still more, by their moral tenets. The soul was arithmos
eauton kinon--a self-moving number or Monad, the copy (as we have seen)
of that Infinite Monad which unfolds from its own incomprehensible
essence all the relations of the universe. This soul has three elements,
Reason (nous), Intelligence (phren), and Passion (Thymos). The two last,
man has in common with brutes, the first is his grand and peculiar
characteristic. It has, hence, been argued that Pythagoras could not
have held the doctrine of "transmigration." This clear separation of man
from the brute, by this signal endowment of reason, which is
sempiternal, seems a refutation of those who charge him with the
doctrine.

In the department of morals, the legislator of Crotona found his
appropriate sphere. In his use of numerical notation, moral good was
essential unity--evil, essential plurality and division. In the fixed
truths of mathematical abstractions he found the exemplars of social and
personal virtue. The rule or law of all morality is resemblance to God;
that is, the return of number to its root, to unity,[443] and virtue is
thus a harmony.

[Footnote 442: That is, 1+2+3+4=10. There are intimations that the
Pythagoreans regarded the Monad as God, the Duad as matter, the Triad as
the complex phenomena of the world, the Tetrad as the completeness of
all its relations, the Decad as the cosmos, or harmonious whole.]

[Footnote 443: Aristotle, "Nichomachian Ethics," bk. i. ch. vi.]

Thus have we, in Pythagoras, the dawn of an _Idealist_ school; for
mathematics are founded upon abstractions, and there is consequently an
intimate connection between mathematics and idealism. The relations of
space, and number, and determinate form, are, like the relations of
cause and effect, of phenomena and substance, perceptible _only in
thought_; and the mind which has been disciplined to abstract thought by
the study of mathematics, is prepared and disposed for purely
metaphysical studies. "The looking into mathematical learning is a kind
of prelude to the contempla