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

Pace
Krämer (
op. cit., 75f.), who tries to prove Heraclides’ priority, there is no evidence
of Plato’s influence on Ecphantus (noñ~ in A 1 is clearly from Anaxagoras), nor are
there any reasons to date the latter in the last third of the fourth century: by that time
no Pythagoreans remained.
115
Interestingly, Proclus himself studied mathematics with the mathematician Hero of
Alexandria, not in the Academy of Athens (Marin.
Vit. Procl. 9). – For a different
view of the relations between Platonism and mathematics, see Burkert, W. Konstruk-
tion und Seinsstruktur: Praxis und Platonismus in der griechischen Mathematik,
ABrWG 34 (1982) 125–141.
116
Aristoxenus gathered all the gossip about Plato (fr. 61–68, 131), Dicaearchus wrote
that Plato raised and then destroyed philosophy (Dorandi.
Filodemo, 125, col. I),
Eudemus sometimes preferred Archytas to Plato (fr. 60, but see fr. 31), and Aristotle
himself was known for his inordinate criticism for his teacher.

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4. Plato on science and scientific directorship
105
ship between Plato and contemporary mathematicians, but his dialogues. It is
here that we should look for, and can find, the basis for the idea of Plato as an
architect of the sciences, which the Academics then developed further.
So far I have neglected the issue of the extent to which the Academics’ ef-
forts to emphasize Plato’s role in establishing the methodology of the exact
sciences reflected his own position. Plato often criticized the scientific method-
ology of his contemporaries, especially in books VI–VII of the
 Republic, where
he outlines a program of education for future guardians of the ideal polis. Let us
compare, for example, Archytas’ description of the numerous acoustic obser-
vations and some simple experiments (47 B 1) with Plato’s remark that the true
science of harmonics must be independent of all this, measuring mathematical
and not audible consonances, which is exactly what the Pythagoreans fail to
realize (531c). While Archytas sings the praises of the social and even moral
consequences of practical arithmetic,
117
Plato insists that arithmetic should be
pursued mainly for the sake of pure knowledge (525c–d). The geometers derive
their propositions from several premises, which they consider self-evident and
do not further explain (510c–e); solid geometry is in a very undeveloped state
(528b–c). For Plato, true astronomy is concerned not with the movement of the
visible heavenly bodies, but with ideal kinematics of mathematical heavens
(529a–530c).
118
These well-known passages were discussed and interpreted many times,
now in support of Plato’s anti-empiricism and of his hostility toward the real
sciences of that time, and now as an example of his foresight of future math-
ematical astronomy.
119
I do not think it possible to add anything significantly
new to what has already been said on this subject. If, however, one tries to con-
centrate on what is uncontroversial, or at least to avoid the extreme points of
view, then it should be said that the position of external and competent critic
was only natural for Plato, as were his efforts to put the results and methods of
the exact sciences to the use of his favorite science – dialectic. It is also obvious
117
47 B 3. See above, 71f.
118
Admittedly, the emphasis in the
Timaeus is rather different.
119
See e.g. Taylor,
op. cit.; Cornford, F. M. Mathematics and dialectic in the Republic
VI–VII (1932),
Studies in Plato’s metaphysics, ed. by R. E. Allen, London 1965,
61–95; Hare, R.M. Plato and the mathematicians,