were resolved. Diogenes of Apollonia adopted
the idea of Anaximenes, but gave a deeper significance to it. The older
thinker conceived the vital air as a kind of soul; the younger man
conceived the soul as a kind of air--an invisible force, permeating and
actuating everything. This attribution of intelligence to the primal
power or matter was certainly a progress in speculation; but another
line of thought was struck out by Anaximander of Miletus, who had been a
friend of Thales. He was passionately addicted to mathematics, and a
great many inventions are ascribed to him; among others, the sun-dial
and the geographical map.

In his view, any one single thing could not be all things, and in his
famous saying, "The infinite is the origin of all things," he introduced
into metaphysics an abstract conception in place of the inadequate
concrete principles of Thales and his disciples. Pythagoras was a
contemporary of Anaximander, and, like him, one of the great founders of
mathematics. He held that the only permanent reality in the cosmos was
the principle of order and harmony, which prevented the universe from
becoming a blank, unintelligible chaos; and he expressed this idea in
his mystic doctrine: "Numbers are the cause of the material existence of
things." The movement which he spread by means of a vast, secret
confraternity ended, however, in a barren symbolism, and it is
impossible to trace what relation his strange theories of the
transmigration of souls and the music of the spheres have to his general
system of thought.

Far more influence on the progress of speculation was exercised by
Xenophanes of Colophon. Driven by the Persian invasion of 546 B.C. to
earn his living as a wandering minstrel, he developed the ideas of
Anaximander, and founded the school of great philosophic poets, to which
Parmenides, Empedocles and Lucretius belong. He is the grand monotheist,
and he has published his doctrines in his verses:

There is one God alone, the greatest of spirits and mortals,
Neither in body to mankind resembling, neither in ideas.

Shelley's line: "The One remains, the Many change and pass," sums up the
teaching of the line of thinkers which culminated in Plato. In their
view, knowledge derived from the senses was fallacious because it
touched only the diverse and changing appearances of things; absolute
knowledge of the one abiding spiritual reality could, they held, only be
obtained by the exercise of spiritual