Eudoxus, Callippus and the Astronomy of the Timaeus

Abstract

Whether the astronomy of the Timaeus had any significant influence on Eudoxus' theory of homocentric spheres is a matter of contention. Some commentators deny any such influence.' Here I argue for a view of the Timaeus' astronomy, and of Eudoxus' astronomy, whereby Eudoxus' work was as much a natural development of the Timaeus as Callippus' work was of Eudoxus. I also argue for an important interpretative principle. This is that Plato, Eudoxus and Callippus could not account for all the phenomena they were aware of, and were aware of that fact. If the Timaeus presents a prototype, Eudoxus can then be seen to develop this astronomy, making the model more sophisticated and complex while staying within the cosmological principles, and attempting to solve the key problems which were left unsolved by the Timaeus model. He does this in much the same way as Callippus made Eudoxus' model more complex and sophisticated, and attempted to solve the leading problems in that model. I also consider some further objections to a significant interaction between Plato and Eudoxus, based on supposed philosophical differences, dating, and the evidence of later commentators. I conclude that these provide no significant obstacle to considering there to be a fruitful liaison between Plato and Eudoxus. I The model proposed by the Timaeus was a significant advance on any previous model we are aware of, including Plato's model in the Republic's myth of Er.' Most notably J. Mittelstrass. Die Refrung der Phanomene (Berlin 1963). W. R. Knorr, 'Plato and Eudoxus on the planetary motions', J.Hisr.Astron. 21 (1990) 313-29, L. Zhmud, 'Plato as "architect of science", Phronesis 43/3 (1998)211-44. Ancient approaches to Plato 's 'Timaeus' 5 6 ANCIENT APPROACHES TO PLATO'S TIMAEUS Philolaus.' Republic, myth of Er.3n The basic problem with these models can be put like this. The earth effectively has two motions, a daily rotation and its annual orbit of the sun.4 The axes of those motions are not identical.Earth's axes. The earth's axis of rotation is offset from the plane of its orbit around the ~ i -If we treat the earth as being central and stable, and so transfer these motions to the heavens, there need to be two axes of rotation, one for the fixed stars and one for the sun and the other bodies of the solar system. This, in effect, is what we get for the first time in the Timaeus. See Aristotle, Cael. 293a18ff.. cf. Meraph. A 5 986a10-12. See Plato, Republic 616b ff. Ignoring the motion of the earth's axis of rotation, the effect of which (the precession of the equinoxes) had yet to be discovered. Winter Equinoxes Summer Solstice Solstice 23.5 Due West 23.53 ' One can also have good explanations of the phases of the moon and the periods of the planets, but previous models had managed these as well.

Traditional and Cosmic Gods in Later Plato and the Early Academy

“…On this particular point, I follow Dicks (1970) and Vlastos (1975), who have convincingly showed that the motion of difference is sufficient to account for retrogradation. For a more comprehensive analysis, see the recent assessments of this debate in Cavagnaro (1997), Gregory (2003) and Guetter (2003).…”