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

The Cambridge com-
panion to the Stoics, ed. by B. Inwood, Cambridge 2003, 328–344.
41
Kühnert,
op. cit., 76f. Zeno’s circle included Aratus, a popularizer of Eudoxus, on
whose poem the Stoic Boethus of Sidon wrote a commentary (Gemin.
Eisag. XVII,
48).
42
Plut.
De facie 923 A; Quaest. conv. 1006 C.
43
D. L. VII, 129 =
SVF III, 739; Procl. In Eucl., 395.13f., Plut. Mor. 1079 D, E – 1080
A = fr. 458, 460 Hülser. Cf. also
SVF II, 365, 482, 489.
44
SVF II, 527, 580, 625, 648–692. The same concerns Zeno (SVF I, 119–120).

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Chapter 8: Historiography of science after Eudemus: a brief outline
288
and Aristotle, the Stoics neither strove to put
mathe¯mata at the service of their
on the whole practically-oriented philosophy, nor regarded them as a model for
imitation.
45
They rather saw such a model in técnh, which, according to Zeno’s
definition, included only knowledge useful for life (fr. 392–397 Hülser).
The adoption of new cognitive ideals transformed the cognitive space as
well. The Aristotelian unified field of theoretical sciences that included maqh-
matik2 along with fusik2 and qeologik2 (4.2) was now out of the question.
Mathematics loses the autonomy it had in the eyes of Aristotle and Eudemus
and turns into philosophy’s maidservant:
But certainly everybody knows that philosophy gave to all individual sciences the
principles and the seeds from which then apparently their theorems arose. For al-
though equilateral and non-equilateral triangles, circles and polygons as well as
the other figures were additionally discovered by geometry, geometry did not dis-
cover the nature of the point, the line, the surface and the body, which are namely
the roots and cornerstones of the mentioned figures … These definitions are left
for philosophy, as the whole topic of the definitions is incumbent upon a philos-
opher.
46
If the point of view exposed here by Philo of Alexandria is indeed that of the
Stoics, the latter must have been completely at variance both with the position
of the Lyceum and the views of the mathematicians themselves.
47
Following his
teacher, Eudemus admitted that mathematics had principles of its own on
which its entire edifice rested; leaving to metaphysics the task of
investigating
some of them was but a natural division of labor.
48
The idea of somebody look-
ing for an alternative definition of line seemed to him ridiculous.
49
The Stoics
did not find it ridiculous in the least.
50
The first Stoic to pursue science seriously was Posidonius; later he was also
considered to have been the best expert in
mathe¯mata among the Stoics.
51
This
45
According to Stoic dogma, ëgkúklia maq2mata belong not to @gaqá, but to @diá-
fora (SVF III, 136). Cf. Mansfeld, J. Intuitionism and formalism: Zeno’s definition
of geometry in a fragment of L. Calventius Taurus,
Phronesis 28 (1983) 59–74.
46
Phil. Alex.
De congr. 146–147 = fr. 416 Hülser; Cambiano. Philosophy, 592f. – Phil-
osophy is the mistress (déspoina) of ëgkúklia maq2mata (Clem. Alex. Strom. I, 5,
30 = fr. 6 Hülser). This metaphor is found already in Aristippus of Cyrene (D. L. II,
79) and the early Stoic Aristo of Chios (
SVF I, 350).
47
See above, 118, 168.
48
Arist.
Met. 1005a 19–29, 1025b 4f., 1061b 19–21; Eud. fr. 32 and esp. 34.
49
“For mathematicians display their own principles and give its definition to every
thing they talk about, so that a person who does not know all this would look ridicu-
lous if he tried to investigate what a line is and every other mathematical object.”
(fr. 34).
50
See above, 287 n. 43 and, in particular, Posid. fr. 195–199 E.-K. with commentary;
for Stoic definitions of line and figure, see also Simpl.