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

New essays on Plato and Aristotle,
ed. by R. Brumbaugh, London 1965, 21–38; Barker, A. Súmfwnoi @riqmoí: A note
on
Republic 531c 1–4, CPh 73 (1978) 337–342; Science and the sciences in Plato,
ed. by J. P. Anton, New York 1980; Mourelatos, A. P. D. Astronomy and kinematics
in Plato’s project of rationalist explanation,
SHPS 12 (1981) 1–32; Annas, J. An in-
troduction to Plato’s Republic, Oxford 1981, 272ff.; Gaiser, K. Platons Zusammen-
schau der mathematischen Wissenschaften,
A & A 32 (1986) 89–124; Robins, I.
Mathematics and the conversion of the mind,
Republic vii 522c 1–531e 3, AncPhil
15 (1995) 359–391; Gregory, A. Astronomy and observation in Plato’s
Republic,
SHPS 27 (1996) 451–471; Kouremenos, T. Solid geometry, astronomy and construc-
tions in Plato’s
Republic, Philologus 148 (2004) 34–49.

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Chapter 3: Science in the Platonic Academy
106
that the disciplines that constituted the quadrivium variously suited Plato’s
goal: arithmetic and geometry to a greater extent and astronomy and harmonics
to a lesser, for they were connected with mathematical interpretation of natural
phenomena, which, according to Plato, could not be a subject for scientific
study. The controversy begins when, based on Plato’s often rather vague re-
marks, we try to understand what stands behind his criticism: is he proposing
an alternative program for developing the exact sciences, anticipating the work
of Euclid and Ptolemy, or is he simply worried about how to adapt the exact
sciences to his own pedagogical purposes, how to make them a true preliminary
for dialectic. I personally prefer the second answer,
120
but I am ready to admit
that these passages
 could be interpreted as valuable methodological instruc-
tions on how to develop the exact sciences. I think they were understood
exactly in this way in the Academy.
The first indication here is the term próblhma, which we came across in the
quotations from Philodemus and Sosigenes: Plato sets the problems to the
specialists.
121
This is the approach insistently put forward in the
 Republic.
When discussing astronomy, Socrates proposes:
probl2masin
Ára … crø-
menoi turns to this when discussing harmonics, reprimanding the Pythagoreans:
zhtoñsin, @ll’ oÿk eı~
probl2mata
@níasin, ëpiskope$n tíne~ xúmfwnoi
@riqmoì kaì tíne~ oÚ (531c 3). Whatever Plato meant by these appeals,
122
the
appeals themselves, urging the necessity to study the
real problems of a true
science, have to remain in the memories of the readers of the
 Republic.
123
The
resemblances become even greater if one compares Plato’s reprimands for the
contempt of geometry, known from the legend about the Delian problem,
124
with Socrates’ description of the situation in solid geometry (528b–c). His defi-
nition of solid geometry, Ésti dé pou toñto perì t3n tõn
kúbwn aÚxhn
kaì
tò báqou~ metécon, contains, as was noted long ago, a clear reference to the
problem of the duplication of the cube.
125
Glaucon agrees with this definition
and remarks that this field has not yet been properly investigated. Socrates
120
See Lloyd, G.E.R. Plato on mathematics and nature, myth and science,
Methods and
problems, 333–351; Hetherington, N. S. Plato and Eudoxus: instrumentalists, real-
ists, or prisoners of themata?,
SHPS 27 (1996) 278.
121
Plutarch (
Marc. 14.9–11) also mentions the ‘problems’, but here the term has a
special mathematical meaning; Philodemus’ passage and Sosigenes use it in a wider
sense.
122
“It seems … that for Plato to proceed in geometry, astronomy, and harmonics by
means of the problems meant to formulate the questions and to find the cause or ex-
planation of certain phenomena in an abstract way.” (Tarán. Proclus, 237 n. 36).
123
One of these readers might have been Sosigenes; he was the first to step up from ge-
ometry to astronomy (see above, 86f.). Knorr. Plato and Eudoxus, 324f.
124
Plut.