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/
