Barton, Neil (2019) Forcing and the Universe of Sets: Must we lose insight? [Preprint]

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Abstract

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions.

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Item Type:	Preprint
Creators:	Creators Email ORCID Barton, Neil bartonna@gmail.com 0000-0002-3637-1730
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics
Depositing User:	Dr. Neil Barton
Date Deposited:	15 Apr 2019 18:10
Last Modified:	15 Apr 2019 18:10
Item ID:	15907
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics
Date:	2019
URI:	https://philsci-archive.pitt.edu/id/eprint/15907

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