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

Meta-
physics (981b 13–30), goes back to Protrepticus and On Philosophy, two early
works written while Aristotle was still in the Academy.
154
It means that, against
Tarán, we cannot rule out Aristotle’s possible influence on Philip.
155
Both of
them discussed the development of crafts, arts, and sciences according to the
degree to which they participate in sofía. Unlike Philip, who denied wisdom
to all kinds of knowledge except the science of number, Aristotle believed that
while in olden times wisdom had been accorded even to the inventors of useful
técnai, later it was only granted to the inventors of arts and, finally, the notion
of sofía came to be associated with theoretical science, ëpist2mh.
156
Interest-
151
Cf. Pl.
Tim. 24b 7–c 3, Leg. 747b–e.
152
Tarán.
Academica, 69ff.
153
See above, 52 n. 34.
154
Spoerri,
op. cit., 54 n. 19. Book I of Aristotle’s On Philosophy combined the theory
of the origin of culture (as well as its fall as a result of catastrophes) with the history
of philosophy, which ends with Plato (Wilpert, P. Die aristotelische Schrift “Über die
Philosophie”,
Autour d’Aristote, Louvain 1955, 99–118; Effe, B. Studien zur Kos-
mologie und Theologie der Aristotelischen Schrift “Über die Philosophie”, Munich
1970, 62ff.).
155
Tarán.
Academica, 140ff. Gaiser, on the contrary, does not deny the connection of
the
Epinomis with the Protrepticus, but believes that the influence of Plato can ac-
count for their similarities (
Platons ungeschriebene Lehre, 244f.).
156
Note the parallelism with a fragment of Archytas (47 B 4) comparing different téc-
nai from the point of view of sofía they participate in (see above, 61f.). The ‘wi-

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Chapter 3: Science in the Platonic Academy
114
ingly, the passage from the
Metaphysics ends with the invention of geometry in
Egypt, and Philip’s survey of sciences with the invention of astronomy in Egypt
and Syria (whether this subject was touched upon in the
Protrepticus, remains
unknown). On the whole, Aristotle’s theory looks more logical and less sche-
matic; besides, it is closely linked with his theory of science. Considering that
the
Epinomis was written later than the Protrepticus and On Philosophy, Philip
could have drawn the historical part of his scheme largely from Aristotle.
Unlike the theories of Aristotle and Philip, the Academic treatise on Plato
places the exact sciences in a much more topical context. It deals with contem-
porary mathematical sciences, considers actual, rather then reconstructed, dis-
coveries, and mentions such real historical figures as Hippocrates of Chios,
Plato, and Eudoxus. Here we meet a number of elements familiar to us, in this
form or another, from Aristotle and Eudemus, such as the rapid progress made
recently in the exact sciences (which already include optics and mechanics),
further, the rapid progress in geometry, which found expression in the substitu-
tion of new theories for old ones as well as in the emergence of such new
methods as analysis and diorism, and, finally, the completion of the general the-
ory of proportions (tà perì metrologían 7lqen ëpì koruf2n).
The notion of the rapid progress of different branches of knowledge and
their approaching perfection dates back to the late fifth – early fourth cen-
turies.
157
Was the author of the Academic treatise the first to apply it to mathe-
matics? Though we do not know when the treatise was written, we can safely
date it after Plato’s death.
158
Meanwhile, in the
Protrepticus, written still in the
350s, Aristotle notes rapid progress in mathematics – without, of course, men-
tioning Plato.
159
According to Philip, the Greeks will bring to perfection the as-
tronomical knowledge they borrowed in the Orient (
Epin. 987d–e). Thus we
have to admit that the progress and perfection of exact sciences and the devel-
opment of new methods were discussed in the Academy, though they did not
become a subject of special studies, as they were later in the Lyceum.
That Eudemus could have known the treatise quoted by Philodemus and
shared some of its ideas is hard to test, ignorant as we are of both its author and
sest’, i.e., the most exact among them appeared to be arithmetic, surpassing in this
respect geometry as well as all other técnai. Aristotle also considered arithmetic
more exact than geometry (
APo 87a 34f.; Met. 982a 26f.). The comparison made by
Archytas is systematic rather than historical. But considering Aristotle’s interest in
his philosophy (see above, 71 n. 110), it might well have drawn the latter’s attention.
157
See above, 58f., 70f., 77f.
158
This agrees with the mention of Eudoxus, as well as of optics and mechanics (see
above, 47 n. 11).
159
ën ölígœ crónœ tosaúthn ëpídosin t3n tõn maqhmátwn qewrían labe$n (fr. 5
Ross = fr. C 52:2 Düring); tosoñton dè nñn proelhlúqasin ëk mikrõn
@formõn ën ëlacístœ crónœ zhtoñnte~ oΠte perì t3n gewmetrían kaì toù~
lógou~ kaì tà~ Álla~ paideía~, Ôson oÿdèn Êteron géno~ ën oÿdemi* tõn
tecnõn (fr. 8 Ross = fr. C 55:2 Düring). See above, 70 n. 105–107.

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5. The theory and history of science in the Academy
115
the time of its appearance. Eudemus’ works on the history of science most
probably date from the period between the foundation of the Lyceum and the
death of Aristotle, i.e., between 335/4 and 322/1 (5.1). Speusippus, the oldest
of the possible authors of the book on Plato, died in 338, while Xenocrates, who
was ten years older than Philip, lived until 314; Hermodorus’ chronology and
the date of Philip’s death remain unknown. Hence, we have no conclusive evi-
dence that the Academic work was written before Eudemus’
 History of Ge-
ometry. Even if we accept this dating for purposes of argument, the place of this
work in the historiography of science presents a problem.
In spite of the similarities between the papyrus passage and the part of Eude-
mus’
Catalogue devoted to mathematics in the time of Plato,
160
the differences
between them – in general approach as well as in details – remain obvious.
161
The main difference is that the
Catalogue focuses on the history of geometry,
whereas the treatise quoted by Philodemus is primarily concerned with Plato.
The scope of the second part of the
Catalogue, let alone the first, is much
broader than that of the passage from Philodemus, which ends in polemics
against some disciples of Plato who made the ‘fruits of knowledge’ serve their
own ends. The end of column Y (after the words ‘optics and mechanics’) is
seriously damaged, and Gaiser’s reconstruction is only tentative.
162
Yet nothing
of what remains legible points to a work on the history of science as a possible
source of this quotation. The text quoted by Philodemus is clearly related to
Plato, while the passage concerning progress in mathematics seems to be a di-
gression,
163
intended to show that his influence extended to this science as well.