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The non-unique Universe

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
    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

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