1 The Birth of Science - MSRI

202 8. The Decadence and End of Science
Sextus then gives an argument for the nonexistence of the thing being
taught:
Furthermore, since some somethings are bodies and others are incorporeal,
the things which are taught will, as somethings, have to be page 254
either bodies or incorporeal. . . . Now body would not be a teachable
thing, and especially not according to the Stoics, for things that are
taught must be lekta, but bodies are not lekta and hence not taught. . . .
Nor indeed can the incorporeal [be taught, for] . . . every [incorporeal]
is obviously under investigation. . . , some insisting that they exist,
others that they do not, and others undecided. 2
The lekta (literally “utterables”, which is to say meanings) were for the
Stoics the only possible object of teaching; they are of course conceptual
constructs. In the imperial age, when the notion of theoretical models had
been lost, such entities were conceivable only as real objects: the alternative
between “bodies” and “incorporeal beings” thus became ineluctable.
Some such entities were indeed made corporeal — witness the crystalline
celestial spheres which replaced the spheres of Eudoxus of Cnidus and the
epicycles of Apollonius of Perga. Likewise, the “visual rays” of optics reacquired
the character of physical objects emitted by the eyes, which was
not present in Euclid’s theory. This new interpretation appears already in
a preface to Euclid’s Optics 5 dating perhaps from the fourth century A.D.
and prepended to the work in manuscripts that contain the recension generally
attributed to Theon. 6 Other entities, such as those of geometry, were
given an incorporeal reality. 7 This placed geometry in the realm of Platonic
thought, a position that Hellenistic mathematics had left behind.
(The memory of the function played by theoretical entities in Hellenistic
science did not disappear completely. As late as the fifth century A.D.,
Proclus muses, probably harking back to an ancient epistemological debate:
What shall we say about eccentrics, which are still the subject of talk,
and about epicycles? Are they mere inventions or do they really exist
in the sphere to which they are attached? 7a
2
Sextus Empiricus, Adversus mathematicos, I, 19–20, 28, Blank translation (leaving lekta untranslated:
see subsequent text and also page 195, where the singular, lekton, is discussed).
5
See [Euclid: OO], vol. VII, p. 150, where it is said that if the eyes were to be receivers of something
rather than emitters they would have to be hollow, like the nose and ears.
6
This attribution was made by Heiberg, who also discovered a different version of the work,
which he thinks is original, and which was transmitted by certain other codices. Both versions are
published in [Euclid: OO], vol. VII.
7
For an explicit statement of this position, see for example Iamblichus, De communi mathematica
scientia, xxviii.
7a
Proclus, Hypotyposes astronomicarum positionum, 236, 15 ff.
Revision: 1.4 Date: 2002/07/12 23:34:21