Synthese 192 (8):2463-2488 (2015)

Authors
Claudio Ternullo
Universitat de Barcelona
Carolin Antos
Universität Konstanz
Abstract
We review different conceptions of the set-theoretic multiverse and evaluate their features and strengths. In Sect. 1, we set the stage by briefly discussing the opposition between the ‘universe view’ and the ‘multiverse view’. Furthermore, we propose to classify multiverse conceptions in terms of their adherence to some form of mathematical realism. In Sect. 2, we use this classification to review four major conceptions. Finally, in Sect. 3, we focus on the distinction between actualism and potentialism with regard to the universe of sets, then we discuss the Zermelian view, featuring a ‘vertical’ multiverse, and give special attention to this multiverse conception in light of the hyperuniverse programme introduced in Arrigoni and Friedman (2013). We argue that the distinctive feature of the multiverse conception chosen for the hyperuniverse programme is its utility for finding new candidates for axioms of set theory.
Keywords Set theory  Universe of sets  Set-theoretic multiverse  Hyperuniverse programme  New axioms of set theory
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Reprint years 2015
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DOI 10.1007/s11229-015-0819-9
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References found in this work BETA

Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford University Press.

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Citations of this work BETA

Universism and Extensions of V.Carolin Antos, Neil Barton & Sy-David Friedman - forthcoming - Review of Symbolic Logic:1-50.
Maximality Principles in Set Theory.Luca Incurvati - 2017 - Philosophia Mathematica 25 (2):159-193.

View all 7 citations / Add more citations

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