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Reinterpreting the universe-multiverse debate in light of inter-model inconsistency in set theory

Kuby, Daniel (2021) Reinterpreting the universe-multiverse debate in light of inter-model inconsistency in set theory. [Preprint]

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Abstract

In this paper I apply the concept of \emph{inter-Model Inconsistency in Set Theory} (MIST), introduced by Carolin Antos (this volume), to select positions in the current universe-multiverse debate in philosophy of set theory: I reinterpret H. Woodin’s _Ultimate $L$_, J. D. Hamkins’ multiverse, S.-D. Friedman’s hyperuniverse and the algebraic multiverse as normative strategies to deal with the situation of de facto inconsistency toleration in set theory as described by MIST. In particular, my aim is to situate these positions on the spectrum from inconsistency avoidance to inconsistency toleration. By doing so, I connect a debate in philosophy of set theory with a debate in philosophy of science about the role of inconsistencies in the natural sciences. While there are important differences, like the lack of threatening explosive inferences, I show how specific philosophical positions in the philosophy of set theory can be interpreted as reactions to a state of inconsistency similar to analogous reactions studied in the philosophy of science literature. My hope is that this transfer operation from philosophy of science to mathematics sheds a new light on the current discussion in philosophy of set theory; and that it can help to bring philosophy of mathematics and philosophy of science closer together.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Kuby, Daniel0000-0002-7779-7500
Additional Information: Draft currently under review, please do not cite without permission. Feedback very welcome!
Keywords: Inconsistency in science, universe-multiverse debate, mathematical practice, set theory, independence
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics
Depositing User: Dr. Daniel Kuby
Date Deposited: 17 Dec 2021 21:36
Last Modified: 17 Dec 2021 21:36
Item ID: 20037
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics
Date: December 2021
URI: http://philsci-archive.pitt.edu/id/eprint/20037

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