Barton, Neil (2016) Multiversism and Concepts of Set: How much relativism is acceptable? [Preprint]

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Abstract

Multiverse Views in set theory advocate the claim that there are many universes of sets, no-one of which is canonical, and have risen to prominence over the last few years. One motivating factor is that such positions are often argued to account very elegantly for technical practice. While there is much discussion of the technical aspects of these views, in this paper I analyse a radical form of Multiversism on largely philosophical grounds. Of particular importance will be an account of reference on the Multiversist conception, and the relativism that it implies. I argue that analysis of this central issue in the Philosophy of Mathematics indicates that Radical Multiversism must be algebraic, and cannot be viewed as an attempt to provide an account of reference without a softening of the position.

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Item Type:	Preprint
Creators:	Creators Email ORCID Barton, Neil bartonna@gmail.com 0000-0002-3637-1730
Keywords:	Philosophy of mathematics, set theory, foundations of mathematics, multiverse
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics
Depositing User:	Dr. Neil Barton
Date Deposited:	07 May 2018 14:15
Last Modified:	07 May 2018 14:15
Item ID:	14635
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics
Date:	2016
URI:	https://philsci-archive.pitt.edu/id/eprint/14635

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