And its tradition of matter theory are an important

and its tradition of matter theory are an important element of pre-
Socratic thought, but consideration of the intellectual dynamic driving
the Milesians reveals another feature of the enterprise of early Greek
science: the rise of science as rational debate. In a word, the Milesian
philosophers disagreed, and they used reason, logic, and observation
to attack the ideas of others and to bolster their own propositions.
Thales’s notion that water is the primary substance had its prob-
lems, notably to explain how water could give rise to fire, its opposite,
water and fire being mutually destructive, as in fire boiling away water
or water quenching fire. Anaximander of Miletus (flourished 555 bce )
dealt with this problem in the generation following Thales by rejecting
water as the underlying agent and by putting forth the much vaguer
notion of some “boundless” or formless initial state (the Apeiron ) out
of which duality and the world grew. By allowing duality to emerge
from unity, as it were, Anaximander’s “boundless” explained hot and
cold, which Thales could not, but the concept of the “boundless” re-
mained forbiddingly abstract and metaphysical. The next Milesian,
Anaximenes, responded to this difficulty and to the same general ques-
tion around 535 bce . His answer was to suggest air (or the “ pneuma ”)
as the primeval element. More down to earth, this suggestion would
also seem to suffer from the problem of opposites that troubled Thales’s
water theory, except that Anaximenes posited two conflicting forces in
the universe, rarefaction and condensation, which variously con-
densed air into liquids and solids and rarefied it into fire. The tradition
of the Milesian school culminated a century later with the thought of
Empedocles (fl. 445 bce ), who as an adult lived in Greek Italy. In a the-
GREEKS BEARING GIFTS 61

ory that remained influential for 2 , 000 years Empedocles postulated
four primary elements—earth, air, fire, and water—and the attracting
and repelling forces of (what else?) Love and Strife.
The pluralistic and abstract character of natural knowledge among
the early Greeks is no better illustrated than by another pre-Socratic
“school,” the cult of the Pythagoreans. The Pythagoreans, centered in
Italy, formed an organized religious brotherhood and sect, and individ-
ual innovator-adepts submerged their contributions to the collectivity
by giving credit to their founding guru, Pythagoras (fl. 525 bce ), orig-
inally from the island of Samos off the Ionian coast. The Pythagoreans
embodied a certain “orientalism” reminiscent of the master’s sixth-
century Persian contemporary, Zoroaster.
The Pythagoreans are famed for introducing mathematics into nat-
ural philosophy. Their mathematics was not the crude arithmetic of the
marketplace or the practical geometrical procedures of the surveyor or
architect, or even the exact mathematical tools of Babylonian astron-
omers. Rather, the Pythagoreans elevated mathematics to the level of