PhilSci Archive

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

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

This is the latest version of this item.

[img]
Preview
Text
2016_06_Countable_models(1).pdf

Download (428kB) | Preview
[img]
Preview
Text
Forcing_and_the_Universe_2.pdf

Download (464kB) | Preview

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.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

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: 15907
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Specific Sciences > Mathematics
Date: 2019
URI: http://philsci-archive.pitt.edu/id/eprint/15907

Available Versions of this Item

  • Forcing and the Universe of Sets: Must we lose insight? (deposited 15 Apr 2019 18:10) [Currently Displayed]

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item