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TWO ARGUMENTS AGAINST THE GENERIC MULTIVERSE

Part of: General and miscellaneous specific topics Philosophical aspects of logic and foundations Set theory

Published online by Cambridge University Press:  02 December 2020

TOBY MEADOWS
TOBY MEADOWS*
Affiliation:
DEPARTMENT OF LOGIC AND PHILOSOPHY OF SCIENCE UNIVERSITY OF CALIFORNIA, IRVINE
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Abstract

This paper critically examines two arguments against the generic multiverse, both of which are due to W. Hugh Woodin. Versions of the first argument have appeared a number of times in print, while the second argument is relatively novel. We shall investigate these arguments through the lens of two different attitudes one may take toward the methodology and metaphysics of set theory; and we shall observe that the impact of these arguments depends significantly on which of these attitudes is upheld. Our examination of the second argument involves the development of a new (inner) model for Steel’s multiverse theory, which is delivered in the Appendix.

Keywords

philosophy of set theoryphilosophy of mathematicsset theoryforcing

MSC classification

Primary: 03A05: Philosophical and critical
Secondary: 00A30: Philosophy of mathematics 03E40: Other aspects of forcing and Boolean-valued models
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 2 , June 2021 , pp. 347 - 379
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Copyright
© Association for Symbolic Logic, 2020

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