An indeterminate universe of sets

Synthese 197 (2):545-573 (2020)
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Abstract

In this paper, I develop a view on set-theoretic ontology I call Universe-Indeterminism, according to which there is a unique but indeterminate universe of sets. I argue that Solomon Feferman’s work on semi-constructive set theories can be adapted to this project, and develop a philosophical motivation for a semi-constructive set theory closely based on Feferman’s but tailored to the Universe-Indeterminist’s viewpoint. I also compare the emergent Universe-Indeterminist view to some more familiar views on set-theoretic ontology.

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Chris Scambler
New York University

Citations of this work

Independence Proofs in Non-Classical Set Theories.Sourav Tarafder & Giorgio Venturi - 2023 - Review of Symbolic Logic 16 (4):979-1010.
Arithmetic is Necessary.Zachary Goodsell - 2024 - Journal of Philosophical Logic 53 (4).

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