Sophists (Heath, [1921] 1981: 1:220–231; Fowler, 1987: 294–308). Not only
Plato but Eudoxus as well built on this milieu; Eudoxus’ school at Cyzicus was
famous above all as a school of mathematics and astronomy. But it was also
a full-fledged philosophical school, propounding the doctrine of Ideas in much
the same form as Plato (Reale, 1985: 63–64; DSB, 1981: 4:465–467), while
diverging in ethics by holding a hedonistic doctrine that brought the school
closer to the Cyrenaics. Eudoxus’ school was the prime center of mathematical
creativity in its day; Plato acquired some of the prestige of mathematics by
drawing in individual mathematicians such as Theaetetus, Philip of Opus, and
Heraclides Ponticus, and having Eudoxus himself visit the Academy with his
followers to teach the more advanced subjects.
This source of rivalry soon collapsed; the Cyzicus school moved and then
disappeared, enriching the next generation of the Academy with mathemati-
cians. It is possible that there was a struggle at Cyzicus itself between two
factions; we know of an early follower of Epicurus who had apparently
converted from the Cyzicus mathematical school, and of Epicurean charges
which circulated at that time implying at least one of the factions had attached
its astronomy to Babylonian star worship (Rist, 1972: 7). At about this time,
Plato’s third-generation successor as head of the Academy (ca. 340–314 b.c.e.),
Xenocrates, promoted star worship for a while, making astronomy a sacred
practice attached to demonology (Dillon, 1977: 24–38; Cumont, [1912] 1960:
29–30). The general drift seems clear: the Cyzicus school and the Academy
more or less divided the same turf for a generation, leaving Plato leeway to
experiment with other intellectual strands. When the Cyzicus school collapsed,
its doctrines became predominant at the Academy, and mathematics was
exalted as the major form of knowledge. Speusippus, Plato’s successor in 348
b.c.e., placed all emphasis on supra-sensible reality, and hence on numbers as
the first principles of the world (Guthrie, 1961–1982, 5:459–461).
The mathematicians’ takeover had the further consequence that Aristotle
split off to establish his own school. Aristotle developed the doctrine that num-
bers are inessential, since mathematics contributes nothing to understanding
movement and change. Since a mathematics of change eventually proved pos-
sible, one should say that Aristotle was not interested in encouraging a mathe-
matics along these lines; his structural motivation was to break with the
mathematical faction, representing the side of the Academy that held out for
non-mathematical pursuits.^18 Aristotle seems to have taken the empirical re-
searchers with him; first on his biological expeditions around the Aegean, and
later into his rival foundation at Athens.
The Academy in its first generation appears to have been rather non-doc-
trinaire. Not only did Plato explore a diversity of positions, as indicated in the
range of his own writings, but also the Academy included specialists not
100 •^ The Skeleton of Theory