McCabe, Gordon (2010) *The non-unique Universe.* [Preprint]

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## Abstract

The purpose of this paper is to elucidate, by means of concepts and theorems drawn from mathematical logic, the conditions under which the existence of a multiverse is a logical necessity in mathematical physics, and the implications of Godel's incompleteness theorem for theories of everything. Three conclusions are obtained in the final section: (i) the theory of the structure of our universe might be an undecidable theory, and this constitutes a potential epistemological limit for mathematical physics, but because such a theory must be complete, there is no ontological barrier to the existence of a final theory of everything; (ii) in terms of mathematical logic, there are two different types of multiverse: classes of non-isomorphic but elementarily equivalent models, and classes of model which are both non-isomorphic and elementarily inequivalent; (iii) for a hypothetical theory of everything to have only one possible model, and to thereby negate the possible existence of a multiverse, that theory must be such that it admits only a finite model.

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Item Type: | Preprint |
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Keywords: | Multiverses; Godel's incompleteness theorem; theories of everything; mathematical logic; model theory |

Subjects: | Specific Sciences > Physics > Cosmology Specific Sciences > Mathematics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics Specific Sciences > Physics > Quantum Field Theory |

Depositing User: | Gordon McCabe |

Date Deposited: | 23 Jan 2010 |

Last Modified: | 07 Oct 2010 11:19 |

Item ID: | 5132 |

URI: | http://philsci-archive.pitt.edu/id/eprint/5132 |

### Available Versions of this Item

- The non-unique Universe. (deposited 02 Jul 2009)
- The non-unique Universe. (deposited 23 Jan 2010)
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- The non-unique Universe. (deposited 23 Jan 2010)

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