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

Busiris
also mentions Pythagoras, who borrowed philosophy (including, naturally, the
mathe¯mata) from the Egyptians, and his followers, Isocrates’ contemporaries,
whom he treats with open irony (28–29). If my suggestion is true, it will, first,
prove that Archytas wrote about the usefulness of all exact sciences, and not
arithmetic only, and second, confirm the dating of his work to the turn of the
fifth century. It does not follow, however, that he was the only one to hold these
views – they may have been shared, for example, by Hippias, who also used to
teach mathematics. As for Plato and his pupils, the dating of
Busiris excludes
the possibility of seeing them among those to whom Isocrates’ irony could
refer.
123
The Academics as adherents and advocates of mathematics appear in two of
Isocrates’ later works. In the
Antidosis (ca. 353) he characterizes his own posi-
tion as intermediate between the majority, who regard
mathe¯mata as empty
talk and hairsplitting with no useful application either to private or to public af-
fairs, and those who praise these sciences, since their words also partake of
truth (261–263). Aware of the inconsistency of his position, Isocrates defends it
by pointing out that mathematics, unlike other sciences, helps us not in life
itself (unless one happens to teach it), but in the very process of learning. Stu-
dying it, a young man exercises and sharpens his mind, strengthens his mem-
ory and acquires the habit of assiduous work, so that later he learns subjects of
greater importance more quickly and easily (263–265).
124
Of course, mathe-
science, accounting for the facts, and a descriptive one, establishing them, nautik3
@strología refers us to the Nautical Astronomy, attributed to Thales (11A 123, A2,
B 1). This work was, of course, of a practical rather than purely descriptive character.
mhcanik2 denoted in Aristotle both a theoretical and a practical science (APo 78b 37,
Mech. 847a 18f.). Anatolius, leaning on Geminus’ classification of sciences, referred
mechanics to the
mathe¯mata, excluding from them tò ômwnúmw~ kaloúmenon
mhcanikón (Ps.-Heron. Def., 164.9f.), i.e., a practical técnh bearing the same name.
120
%n tà~ dunámei~ oî mèn !~ prò~ Énia crhsíma~ ëpainoñsin, oî d’ !~ ple$sta
prò~ @ret3n sumballoména~ @pofaínein ëpiceiroñsin (Bus. 23).
121
Cf.
Antid. 261–268, Panath. 26–28; see further below.
122
Isocrates seems to attribute these views to different people, but since we know that
they were typically both held by the same people (Archytas, Plato), oî mén … oî dé
may have been in this case nothing more than a rhetorical figure.
123
Cf. below, 226f.
124
Cf. Cic.
De orat. 3, 5, 8; De fin. I, 72; Quint. Inst. I, 10, 34: mathematics can be used
to sharpen and to train the intellect of children.

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4. Why is mathematics useful?
75
matics is not yet ‘philosophy’ (i.e., education indispensable for a citizen),
125
but only a ‘gymnastics of the soul’ and ‘preparation for philosophy’, since
learning it does not improve the student’s skill in discussing affairs and making
judgments on them. Isocrates recommends the study of mathematics only to
young people and for a short term, so as not to allow their minds to be dried up
(266–268).
These ideas are repeated and further elaborated in
Panathenaicus, written a
decade later. Within this period Aristotle had published his
Protrepticus, con-
taining, in particular, a positive refutation of Isocrates’ views on philosophy.
126
Having taken certain passages in