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Forcing and the Universe of Sets: Must we lose insight?

Barton, Neil (2018) 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 argue that while tradeoffs in naturality have to be made, they are not too severe.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Barton, Neilbartonna@gmail.com0000-0002-3637-1730
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: 15905
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Specific Sciences > Mathematics
Date: 2018
URI: http://philsci-archive.pitt.edu/id/eprint/15905

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