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

Nic. 63, Euag. 81, De pace 20.

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5. From ‘progress’ to ‘perfection’
81
conceptions of progress, cognitive as well as social, are of a limited character
and refer to the past and the present rather than to the future. The theory of the
origin of culture that is imbued with these conceptions, most likely created by
Protagoras and further developed by Democritus, exerts profound influence on
a great variety of genres, from history and rhetoric to philosophy and medicine,
and helps to establish new notions of the motive forces in civilization.
Still more popular becomes the Sophistic theory of técnh, used on the de-
scriptive, as well as on the normative level for the realization of any systemati-
cally organized and practically oriented knowledge. It was flexible enough to
allow the interpretation of such sciences as arithmetic, geometry, or astronomy,
traditionally counted among técnai. The formation of the quadrivium of re-
lated mathematical sciences, accomplished by the second half of the fifth cen-
tury, sets the
mathe¯mata apart as a special group of técnai, which best answer
such major criteria of scientific knowledge as exactness and clarity. The further
progress of mathematics turns it into an obvious model for the new theory of
knowledge, in which practical orientation recedes into the background. Among
the prominent features of the old model inherited by the new one is an aware-
ness that science is not just an organized sum total of knowledge, but that it is
founded on the true method, which guarantees the correct results. Another im-
portant element of science is the search for and the transmission of knowledge,
which are explained in terms of the contrasting notions of ‘discovery’ and
‘learning (imitation)’.

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Chapter 3
Science in the Platonic Academy
1. Plato as architect of mathematical sciences?
The previous chapter, devoted to the formation of the notions of science that
later found their reflection in the Peripatetic historiography of science, focused
mainly on three elder contemporaries of Plato: the author of
VM, Isocrates, and
Archytas
. This choice of sources was intended, in particular, to emphasize that
Plato’ role in the development of the new concept of science cannot be ad-
equately defined without a thorough analysis of his predecessors’ views. Not
every idea to be found in his dialogues belongs to Plato himself. Trivial as it
seems, this thesis must be one of the fundamental premises of any research on
‘Plato and the exact sciences’.
In the 19
th
and the early 20
th
centuries, attention was paid predominantly, al-
though not exclusively, to the questions how great Plato’s contribution to spe-
cific mathematical research really was and how reliable our sources are that as-
cribe to him particular discoveries. The general conclusion of these studies was
that Plato himself was not an active scientist and that the scientific discoveries
and hypotheses attributed to him in the ancient tradition are not really his.
1
There do not seem to have been any later serious attempts to debate this con-
clusion,
2
and the discussion has been concerned not with Plato as a scientist,
but rather with science in the Platonic school. Since the late 19
th
century, the
opinion has been established that even if Plato did not achieve any success in
mathematics, he did play a considerable role as an organizer of scientific re-
search and as a methodologist who defined the problems mathematicians and
astronomers studied and the methods they used.
3
I quote only one typical
opinion:
1
See e.g. Blass, C.