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

Epinomis.
135
Plato seems to have been only peripherally inter-
ested in the history of knowledge; he does not as much as mention the historical
development of mathematics. Gaiser’s attempt to prove that Plato divided the
development of knowledge into clearly defined periods is unsatisfactory.
136
As
a rule, we find only schemes borrowed from Protagoras and Democritus, where
political técnai (or arts) follow the necessary ones. As a result, Plato’s variant
of
Kulturentstehungslehre proved even less historical than that of many of his
predecessors: the invention of arts and sciences is usually represented as the
gift of gods, the story of the invention taking the form of a myth.
137
Turning to Plato’s
theory of science, let us stipulate that it interests us only
insofar as it influenced the formation of the historiography of science, provid-
ing it with indispensable theoretical tools. The first steps in the development of
the theory of exact sciences were made by the Pythagorean school, which was
most closely connected with mathematics. The notion that knowledge is im-
possible without number is found in Philolaus.
138
This notion laid the basis for
133
Pl.
Tim. 22c 1f., 23a 5f., Crit. 109d–110a, Leg. 677a–681e; Festugière, A.-J. La
révélation d’Hermès Trismégiste, Vol. 2, Paris 1949, 99f.
134
See below, 212 n. 225.
135
See below, 112f.
136
Gaiser.
Platons ungeschriebene Lehre, 223ff. On the specific character of Plato’s at-
titude toward history, see Weil, R.
L’ “archéologie” de Platon, Paris 1959, esp. 18f.,
42f.
137
Menex. 238b, Phileb. 16c, Polit. 274e. So the invention of writing and exact sciences
(geometry, astronomy, arithmetic) is ascribed to the Egyptian god Thoth (
Phdr.
274c–d;
Phileb. 18b–d); Plato, however, does not insist on it. See below, 224 ff.
138
“And indeed all the things that are known have number, for it is not possible that any-

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Chapter 3: Science in the Platonic Academy
110
the classification of técnai in Philebus and was embraced with enthusiasm by
the author of
Epinomis.
139
Archytas considered
mathe¯mata, arithmetic in par-
ticular, to be the most exact of the técnai and insisted on its wholesome effect
upon virtue (47 B 3–4). Plato developed both ideas,
140
along with Archytas’
theory of four related sciences (47 B 1).
It is to be emphasized that mathematics, which was not part of Socrates’ leg-
acy, entered the sphere of Plato’s philosophical interests through his contacts
with the Pythagoreans, first of all with Archytas and Theodorus. Plato, how-
ever, treats mathematics in a way substantially different from the Pythagoreans.
Archytas considered
mathe¯mata within the framework of the Sophistic theory
of técnh, which served to account for every systematically organized and prac-
tically oriented kind of knowledge (2.3). This orientation is not to be inter-
preted as purely utilitarian. The practical utility of
mathe¯mata seemed still an-
other argument in favor of their being made part of the técnai. In the further
differentiation of técnai into sciences, arts, and crafts, it is the problem of util-
ity, however, that comes to the fore. While Archytas emphasized the utility of
mathematics, and Socrates and Isocrates tried to refute or downplay it, Plato
offers a radically different solution to the problem. The necessary and the use-
ful (crafts) hold the lowest grade in his hierarchy of activities; mousik2, based
not solely on knowledge but on inspiration as well, is differentiated from the
sphere of the técnai, while mathe¯mata and ëpist4mai do not serve any end but
knowledge itself (
Res. 525c–d). Without denying the applied value of scientific
knowledge, Plato derives his model of science from mathematics, its least utili-
tarian and most thoroughly theoretical branch. His own science, dialectic,
which aims at the knowledge of Forms, was to surpass mathematics in both pu-
rity and exactness, being still further removed from the corporeal world.
The particular attention the Academy paid to mathematics played an import-
ant role in the new approach to science. The exact and irrefutable character of
mathematical knowledge, the transparency of the criteria of mathematical cer-
tainty, the absence of disagreement on essential points, so typical of other
sciences – all these factors concurred to make mathematics an attractive model
for the development of a conception of theoretical knowledge. In this respect,
mathematics proved unrivaled by any other técnh; in time, all other models
sank into the background.
141
At the same time, it would be wrong to take the at-
tractiveness of mathematics for granted: the Sophists and Socrates, e.g., did not
thing whatsoever be understood or known without this.” (44 B 4, transl. by C. Huff-
man).
139