Well, all I can say in my own behalf here is that this IS today!
> You see, I believe that Eudoxus was a realist regarding his heavenly
> spheres. But most authors seem to think he was not; instead they think
> that his system was just a mathematical means of calculating the heavenly
> planets' positions. But there is one problem: we don't have any of
> Eudoxus's writings extant. It seems to me that, since we don't have any
> of his writings extant, it would make more sense to me if Eudoxus
> actually also believed that that was the way the heavens was constructed.
> After all, isn't that what the Greek nature philosophers did in general?
> Did they not try to understand nature?
That is true of the "physicists" (Thales, etc.), but Socrates argued
against the physicists that they could not show the reasons why it was good
that things be as they are. Plato argued that physical reality was not
fully intelligible, because matter resisted the ideal forms that were
imposed on it by the demiurge, and that what we really want to understand
is these forms, which can be presented as beautiful theories. He went so
far as to say in the Republic that astronomers should not be interested in
the actual (physical) stars. This, together with the claim (by Simplicius)
that Eudoxus was responding to Plato's challenge to find "hypotheses that
save the phenomena" of the planetary motions, is the positive reason for
thinking Eudoxus was not what you mean by a "realist". (Due to the
vagaries of philosophical terminology, this claim can also be expressed by
saying that Eudoxus WAS a realist--i.e., one who believes that the ideal
forms are real.) The negative part of the reason is that Aristotle, who
was more of a (physical) realist than Plato, modified Eudoxus's theory to
make it more nearly actualizable mechanically (although he was mistaken
that a sphere can be rotated by a force applied to the axis of rotation).
For a good basic discussion, see David Lindberg, The Beginnings of Western
Science, pages 89-96.
Recently I have seen arguments over whether Eudoxus really did this stuff.
My answer to that is that history is not fully intelligible, because it
resists the ideal forms imposed on it by the demiurge, and that what we
really want to understand is these forms, which can be presented as
beautiful theories. One such beautiful theory is this one about Eudoxus.
> The fact that his system is
> described mathematically does not in itself make him a instrumentalist.
> And since that work is not found, and no other work of his is found
> either, I don't understand why would anyone could claim that Eudoxus was
> an instrumentalist instead of a realist. (Aristotle doesn't mention him as
> an instrumentalist, but perhaps Simplicius, in his commentary on de Caelo,
> does?)
>
> Can someone, quickly, give me arguments for why he CANNOT be a realist;
> for why he MUST be a realist; for why he CANNOT be an instrumentalist; and
> why he MUST be an instrumentalist. Sources are most welcome.
>
> Thanks!
>
> Bo Klintberg
>
..............................
Jim Murdock
Mathematics Dept.
Iowa State University
Ames, Iowa 50011