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

De. gen. Socr. 579 B–C; Quaest. conv. 718 E–F; Theon. Exp., 2.8–12.
125
The Republic of Plato, ed. by J. Adam, Vol.2, Cambridge 1902, 122; Robins, op. cit.,
370.

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4. Plato on science and scientific directorship
107
gives two reasons for this situation: first, the state does not support these studies
and, being very complex, they develop rather slowly and, second, “the investi-
gators need a director, without whom they will hardly discover anything” (ëpi-
státou te déontai oî zhtoñnte~, Áneu o0 oÿk Àn eÛroien). It is hard to find
a clearer expression of the need for philosophical or even state-philosophical
patronage of science. The passage from Philodemus (@rcitektonoñnto~ mèn
kaì probl2mata didónto~ toñ Plátwno~, zhtoúntwn dè metà spoud4~
aÿtà tõn maqhmatikõn) thus becomes an immediate reflection of Plato’s
words.
The suggestion that Plato designed the role of this ëpistáth~ for himself
126
acquires substance from the following words of Socrates:
It is not easy to find such a director, and then if he could be found, as things are
now, investigators in this field would be too arrogant (megalofronoúmenoi) to
submit to his guidance. But if the state as a whole join in superintending these
studies and honour them, these specialists would accept advice and continuous
and strenuous studies would bring out the true nature of the studied subject.
127
As long as this is not so, mathematicians are prompted exclusively by their in-
tellectual interest in solid geometry and cannot even account for the practical
use of their research.
128
Interpretations taking this ‘director’ as some famous
mathematician of that time, e.g. Archytas or Eudoxus,
129
seem naive and to im-
pute to Plato an unlikely generosity. Obviously what is meant here is not a
specialist but a dialectical philosopher, one who would be obeyed only in the
ideal state and only with the support of this state. Hippocrates, Archytas, and
Eudoxus did not need such support and they definitively would react to the dia-
lectician’s advice with a megalofrosúnh, so characteristic of all specialists.
Earlier in the
Euthydemus (290c), Plato did not yet lay claim to setting prob-
lems to the scientists, but only to a true interpretation of scientific achieve-
ments. Mathematicians and astronomers themselves do not know how to use
their discoveries (cf.
Res. 528c 5), so they have to hand them over to the dia-
lecticians to use properly. This concerns, at least, those mathematicians “who
are not utter blockheads” (m3 pantápasin @nóhtoi). How then were Archytas
and Eudoxus supposed to respond to such advice?
One more line leading to the
Republic is the reference in the Catalogue to a
certain section, which originates from Plato: Eudoxus augmented tà perì t3n
126
Plato’s Republic, ed. by P. Shorey, Vol. 2, Cambridge, Mass. 1935, 177; Cornford,
op. cit., 78.
127
528b 8–c 4, transl. by P. Shorey.
128
528c 5f. It is interesting that Aristotle, who writes in the
Protrepticus about the rapid
progress of mathematics and philosophy in comparison with all other técnai, ex-
plains it by the inner attractiveness of these sciences, rather than by measures of en-
couragement on the part of the state (see above, 70 n. 105–107). Evidently he saw no
need of such measures.
129
See Adam,
op. cit., 123f.; Heath. History 1, 12f.

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Chapter 3: Science in the Platonic Academy
108
tom3n @rc3n labónta parà Plátwno~ (In Eucl., 67.6). The only place
where Plato mentions the geometrical section is the well-known passage about
the division of a line into extreme and mean ratio (golden section): the ratio be-
tween the segments of this line symbolizes the relationship between the materi-
al world and the world of Forms (
Res. 509d–e). Meanwhile, the golden section
was already known to the Pythagoreans,
130
so only someone who was abso-
lutely sure that everything Plato says about mathematics derives from him
could have regarded him as the author of this discovery.
Can we conclude that book VII of the