rdness, texture, etc. Either these qualities must be originally in
the primal air, or not. If the qualities existed in it then it was not
really one homogeneous matter like air, but must have been simply a
mixture of different kinds of matter. If not, how do these properties
arise? How can this air which has not in it the qualities of things we
see, develop them? The simplest way of getting out of the difficulty
is to found quality upon quantity, and to explain the former by the
amount or quantity, more or less, of matter existent in the same
volume. This is precisely what is meant by rarefaction and
condensation. Condensation would result in compressing more matter
into the same volume. Rarefaction would give rise to the opposite
process. Great compression of air, a great amount of it in a small
space, might account for the qualities, say, of earth and stones, for
example, their heaviness, hardness, colour, etc.

Hence Anaximenes was to some extent a more logical and definite
thinker than Anaximander, but cannot {30} compare with him in audacity
and originality of thought.

Other Ionic Thinkers

We have now considered the three chief thinkers of the Ionic School.
Others there were, but they added nothing new to the teaching of these
three. They followed either Thales or Anaximenes in stating the first
principle of the world either as water or as air. Hippo, for example,
followed Thales, and for him the world is composed of water, Idaeus
agreed with Anaximenes that it is derived from air. Diogenes of
Apollonia is chiefly remarkable for the fact that he lived at a very
much later date. He was a contemporary of Anaxagoras, and opposed to
the more developed teachings of that philosopher the crude materialism
of the Ionic School. Air was by him considered to be the ground of all
things.

{31}

CHAPTER III

THE PYTHAGOREANS

Not much is known of the life of Pythagoras. Three so-called
biographies have come down to us from antiquity, but they were written
hundreds of years after the event, and are filled with a tissue of
extravagant fancies, and with stories of miracles and wonders worked
by Pythagoras. All sorts of fantastic legends seem to have gathered
very early around his life, obscuring from us the actual historical
details. A few definite facts, however, are known. He was born
somewhere between 580 and 570 B.C. at Samos, and about middle age he
migrated to Crotona in South Italy. According to legend, befo