Leonid Zhmud The Origin of the History of Science in Classical Antiquity

Phileb. 55d 5–8, 55e–56c, Leg. 747b 1f., Epin. 977d 7f. On Philolaus’ epistemol-
ogy and its influence on Plato, see Huffman.
Philolaus, 172ff.
140
Burnyeat. Plato. See above, 72 n. 112.
141
Note, however, the special role of medicine in Aristotle’s model of técnh, especially
in his ethico-political treatises (Fiedler, W.
Analogiemodelle bei Aristoteles, Amster-
dam 1978, 180ff.). For the Stoic view on técnh as a model for philosophy, see below,
287.

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5. The theory and history of science in the Academy
111
notice it. The elementary character of fifth-century mathematics can hardly ex-
plain this: in the Hellenistic period, the exact sciences could boast of greater
achievements, which did not prevent the major philosophical schools of the
period from criticizing or ignoring them (8.1). Plato himself criticized the
mathematical sciences; his criticism, however, showed interest and was sym-
pathetic, and aimed at the common task of achieving a more exact knowledge.
His suggestion was to bring astronomy and harmonics closer to geometry and
arithmetic by ‘removing’ the physical foundations that prevented them from
becoming mathematical sciences proper. This is what underlies Plato’s critical
attitude toward these two sciences in the
Republic (530b, 531c) and his sugges-
tions to reform astronomy and harmonics by making them follow methods ac-
cepted in geometry.
142
For Speusippus and Xenocrates, tà maqhmatiká proved still more import-
ant than for Plato, since in their ontology mathematical numbers, magnitudes,
and bodies took the place of the Platonic Forms, which they rejected.
143
Freed
from Plato’s interest in técnai, which he inherited from Socrates, the Aca-
demics vigorously develop the philosophy of mathematics.
144
“Mathematics
has come to be identical with philosophy for modern thinkers, though they say
that it should be studied for the sake of other things.” (
Met. 992a 31) This com-
ment by Aristotle on his former colleagues from the Academy leaves no doubt
about his critical attitude toward the place they accorded to mathematics. In
fact, even while theorizing about mathematical objects, the Academics did it
for the sake of philosophy, and not for mathematics proper. Aristotle’s range of
interests was richer and more varied. Still in the Academy, he defends and ad-
vocates in the
Protrepticus the ideal of vita contemplativa, while developing in
his logical works, especially in the
Second Analytics, the methodology of scien-
tific research based chiefly on those means of acquiring new knowledge that
were elaborated in mathematics. In spite of the obvious influence of mathemat-
ics on Aristotelian logic and the wealth of mathematical examples and anal-
ogies that we find in his writings,
145
only a few small works of his enormous
heritage are devoted to exact sciences as such.
146
Aristotle does not seem to be
142
Plato emphasizes that harmonics’ application of numbers to real physical phenom-
ena is the same as what is done in astronomy (
Res. 531c 1). Hence, his criticism of
both sciences is identical: both should “rise to the consideration of general prob-
lems” following the example of geometry.
143
Krämer,
op. cit., 28f.
144
See above, 90 n. 40–41. Speusippus’ Tecnõn Élegco~ (D. L. IV, 5) must have been
devoted to rhetorical treatises (Tarán.
Speusippus, 195).
145
On mathematical analogies and examples in Aristotle, see Fiedler,
op. cit., 47ff.,
64ff.
146
See the titles in the list of Aristotle’s works (D. L. V, 24–26): ^Astronomikón
(No. 112), ^Optikón (No. 113), Mhcanikón (No. 122). Moraux, P. Les listes an-