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

part of fragment B 3 deals with the practical art of calculation does not prove
that Archytas was consistent in drawing a distinction between logismó~ as the
practical part of arithmetic and logistik2 as its theoretical part.
115
Emphasiz-
ing the utility of the art of calculation, he might equally as well have used the
term logistik3 técnh, which, like logismó~, could denote both practical and
theoretical arithmetic. Turning to the traditional subject of the utility of a técnh
does not imply that the técnh itself is regarded as practical. The usefulness of
mathe¯mata for society was acknowledged even by Plato,
116
who saw their main
value elsewhere. Aristotle, ascribing in his
Protrepticus an independent value
to theoretical knowledge, did not, however, fail to point out that philosophy
could well prove useful in practical affairs as well.
117
The fact that mathematics
and philosophy have an applied aspect does not undermine their status as the-
oretical disciplines.
Archytas, of course, could not fail to see the difference between the theor-
etical and the practical aspects of the
mathe¯mata, nor to realize that one and the
same term, for example @strología, denotes both a mathematical science and
applied knowledge used by sailors and farmers. This difference was obvious, at
any rate, even for such a layman in mathematics as Xenophon. Speaking of So-
crates’ attitude toward astronomy, geometry, and arithmetic, he notes that the
latter recommended limiting oneself to the practical part of each of these
sciences, without going deeply into theory (
Mem. IV,7.1–8). Hence, one does
not need different terms to distinguish between a theoretical discipline and its
applied counterpart. Though we do find in Archytas a new term, ârmonik2, de-
noting, unlike mousik2, the science of music,
118
mousik2 is also repeatedly
used in the same treatise for the science of music (B 1–2). Philip of Opus ob-
serves that a theoretical science bears the ‘ridiculous’ name of gewmetría
(
Epin. 990d 2), associating it with measuring land; the new term, gewdaisía,
denoting the practical discipline, appears later in Aristotle’s
Metaphysics (997b
26f.).
119
115
It is contradicted by the usage of Isocrates, Plato, and Aristotle, who referred lo-
gismoí to theoretical arithmetic (see above, 61 n. 65–66).
116
Res. 522c, e, 526d, Leg. 809c–d.
117
Fr. 46, 51, 54 Düring;
EN 1172b 5f., 1177a 32–b 4. Elsewhere he stresses again:
though theoretical sciences like astronomy or geometry may prove to be useful, their
main purpose is knowledge (
EE 1216b 11f.; cf. Isoc. Antid. 262–269, Panath.
30–32). For the same in Proclus, see
In Eucl., 25.18ff.
118
Archytas’ treatise on the theory of music was entitled ˆArmonikó~ (B 1), but
whether it was he who coined the term remains uncertain. In Aristoxenus (
Harm. I,
2, 5, 7 etc.), the word ârmonikoí denotes a trend in the fifth-century harmonics; ac-
cording to the papyrus Hibeh 13 (col. I,4) this was a self-definition.
119
Aristotle also pointed out that different disciplines could bear the same name: sce-
dòn dè sunønumoí eısin Éniai toútwn tõn ëpisthmõn o‰on @strología 6 te
maqhmatik3 kaì 1 nautik2 (APo 78b 39). Though he means here a theoretical

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Chapter 2: Science as técnh: theory and history
74
Isocrates, speaking about Busiris’ invention of philosophy, which included
astronomy, geometry, and arithmetic, observes that some praise the utility of
these sciences, while others attempt to demonstrate that they are conducive in
the highest measure to the attainment of virtue.
120
Though the rhetorician does
not state his attitude toward these views directly, his silence seems to indicate
that he does not share them.
121
Among those who did hold both these views, one
ought, first of all, to cite Archytas, who praised the practical utility of mathe-
matics and its ability to improve moral qualities.
122
It is revealing that