most exact of material things but we must recognize that
they fall far short of the truth,The meaning of
this sentence is certain, but the expression will no more bear a
matter-of-fact logical analysis than that of Phaedo 69 A-B,
or Rep. 365 C, or many other subtle passages in Plato. No
material object perfectly embodies the ideal and abstract mathematical
relation. These mathematical ideas are designated as the true,ἀληθινῶν, and the real,ὄν. As in the Timaeus(38 C, 40 A-B, 36 D-E)
the abstract and ideal has the primacy and by a reversal of the ordinary
point of view is said to contain or convey the concrete. The visible stars
are in and are carried by their invisible mathematical orbits. By this way
of speaking Plato, it is true, disregards the apparent difficulty that the
movement of the visible stars then ought to be mathematically perfect. But
this interpretation is, I think, more probable for Plato than Adam's attempt
to secure rigid consistency by taking τὸ ὂν
τάχος etc., to represent invisible and ideal planets, and
τὰ ἐνόντα to be the perfect
mathematical realities, which are in them. ἐνόντα would hardly retain the metaphysical meaning of ὄντα. For the interpretation of 529 D cf. also
my “Platonism and the History of Science,”Am.
Philos. Soc, Proc. lxvi. p. 172. the movements, namely,
of real speed and real slowness in true number and in all true figures both in
relation to one another and as vehicles of the things they carry and contain.
These can be apprehended only by reason and thought, but not by sight; or do you
think otherwise?” “By no means,” he said.
“Then,” said I, “we must use the blazonry of the
heavens as patterns to aid in the study of those realities, just as