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TWO ARGUMENTS AGAINST THE GENERIC MULTIVERSE

Published online by Cambridge University Press:  02 December 2020

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

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.

Type
Research Article
Copyright
© Association for Symbolic Logic, 2020

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