Hi Stephen,

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I merely wish to comprehend the ideas of those that take a Pythagoreanapproach to mathematics; e.g. that Mathematics is "more real" than thephysical world - "All is number".One thing that I have learned in my study of philosophy is that nosingle finite model of reality can be complete. Perhaps thatasymptotic optimum involves the comprehension of how such a disparateset 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/