Hi Stephen,
> I merely wish to comprehend the ideas of those that take a Pythagorean
> approach to mathematics; e.g. that Mathematics is "more real" than the
> physical world - "All is number".
> One thing that I have learned in my study of philosophy is that no
> single finite model of reality can be complete. Perhaps that
> asymptotic optimum involves the comprehension of how such a disparate
> set of models can obtain in the first place.
I agree with you that no single finite "theory" of reality can be
complete. Actually Godel's incompleteness theorem just proves that in
the case of arithmetical truth. And that was an argument for realism in
math (platonism).
You should not confuse a theory (like Peano Arithmetic, or Zermelo Set
theory) and its intended reality (called model by logician), which by
incompleteness, are not fully describable by finite theory (or by any
machine).
About the idea that math (or just arithmetic) is more real than the
physical worlds is a logical consequence of comp. And comp is testable,
it entails quite strong constraints on the "observable" propositions
(like being necessarily not boolean for example).
Regards,
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Tue Jul 26 2005 - 06:47:02 PDT