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2014 Set Theory, Topology, and the Possibility of Junky Worlds
Thomas Mormann
Notre Dame J. Formal Logic 55(1): 79-90 (2014). DOI: 10.1215/00294527-1960497

Abstract

A possible world is a junky world if and only if each thing in it is a proper part. The possibility of junky worlds contradicts the principle of general fusion. Bohn (2009) argues for the possibility of junky worlds; Watson (2010) suggests that Bohn’s arguments are flawed. This paper shows that the arguments of both authors leave much to be desired. First, relying on the classical results of Cantor, Zermelo, Fraenkel, and von Neumann, this paper proves the possibility of junky worlds for certain weak set theories. Second, the paradox of Burali-Forti shows that according to the Zermelo–Fraenkel set theory ZF, junky worlds are possible. Finally, it is shown that set theories are not the only sources for designing plausible models of junky worlds: topology (and possibly other “algebraic” mathematical theories) may be used to construct models of junky worlds. In sum, junkyness is a relatively widespread feature among possible worlds.

Citation

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Thomas Mormann. "Set Theory, Topology, and the Possibility of Junky Worlds." Notre Dame J. Formal Logic 55 (1) 79 - 90, 2014. https://doi.org/10.1215/00294527-1960497

Information

Published: 2014
First available in Project Euclid: 20 January 2014

zbMATH: 1345.03011
MathSciNet: MR3161414
Digital Object Identifier: 10.1215/00294527-1960497

Subjects:
Primary: 03A99
Secondary: 03E10, 03E30

Rights: Copyright © 2014 University of Notre Dame

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