dorsal/arxiv
View SchemaTowards a Coherent Theory of Physics and Mathematics
| Authors | Paul Benioff |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0201093 |
| URL | https://arxiv.org/abs/quant-ph/0201093 |
| Journal | Found.Phys. 32 (2002) 989-1029 |
Abstract
As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently strong, and it must maximally describe its own validity and sufficient strength. The mathematical logical definition of validity is used, and sufficient strength is seen to be a necessary and useful concept. The requirement of maximal description of its own validity and sufficient strength may be useful to reject candidate coherent theories for which the description is less than maximal. Other aspects of a coherent theory discussed include universal applicability, the relation to the anthropic principle, and possible uniqueness. It is suggested that the basic properties of the physical and mathematical universes are entwined with and emerge with a coherent theory. Support for this includes the indirect reality status of properties of very small or very large far away systems compared to moderate sized nearby systems. Discussion of the necessary physical nature of language includes physical models of language and a proof that the meaning content of expressions of any axiomatizable theory seems to be independent of the algorithmic complexity of the theory. G\"{o}del maps seem to be less useful for a coherent theory than for purely mathematical theories because all symbols and words of any language musthave representations as states of physical systems already in the domain of a coherent theory.
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"abstract": "As an approach to a Theory of Everything a framework for developing a\ncoherent theory of mathematics and physics together is described. The main\ncharacteristic of such a theory is discussed: the theory must be valid and and\nsufficiently strong, and it must maximally describe its own validity and\nsufficient strength. The mathematical logical definition of validity is used,\nand sufficient strength is seen to be a necessary and useful concept. The\nrequirement of maximal description of its own validity and sufficient strength\nmay be useful to reject candidate coherent theories for which the description\nis less than maximal. Other aspects of a coherent theory discussed include\nuniversal applicability, the relation to the anthropic principle, and possible\nuniqueness. It is suggested that the basic properties of the physical and\nmathematical universes are entwined with and emerge with a coherent theory.\nSupport for this includes the indirect reality status of properties of very\nsmall or very large far away systems compared to moderate sized nearby systems.\nDiscussion of the necessary physical nature of language includes physical\nmodels of language and a proof that the meaning content of expressions of any\naxiomatizable theory seems to be independent of the algorithmic complexity of\nthe theory. G\\\"{o}del maps seem to be less useful for a coherent theory than\nfor purely mathematical theories because all symbols and words of any language\nmusthave representations as states of physical systems already in the domain of\na coherent theory.",
"arxiv_id": "quant-ph/0201093",
"authors": [
"Paul Benioff"
],
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],
"journal_ref": "Found.Phys. 32 (2002) 989-1029",
"title": "Towards a Coherent Theory of Physics and Mathematics",
"url": "https://arxiv.org/abs/quant-ph/0201093"
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