A Logical Foundation for Potentialist Set Theory

Sharon Berry

doi:10.1017/9781108992756

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Himelright, Jack 2023. Applied Mathematics without Numbers. Philosophia Mathematica, Vol. 31, Issue. 2, p. 147.

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Çevik, Ahmet 2023. Hierarchical Multiverse of Sets. Notre Dame Journal of Formal Logic, Vol. 64, Issue. 4,

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Sutto, Davide 2024. A Taxonomy for Set-Theoretic Potentialism. Philosophia Mathematica,

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Berry, Sharon 2024. Potentialist set theory and the nominalist’s dilemma. The Philosophical Quarterly,

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Berry, Sharon 2025. Explanatory indispensability and the set theoretic multiverse. Synthese, Vol. 205, Issue. 6,

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Berry, Sharon 2025. The Palgrave Companion to the Philosophy of Set Theory. p. 205.

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Himelright, Jack 2025. Reassessing the Explanatory Indispensability Argument: A Bayesian Defense of Nominalism. The British Journal for the Philosophy of Science,

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Roberts, Alexander 2025. Necessity in the Highest Degree. Journal of Philosophical Logic, Vol. 54, Issue. 1, p. 51.

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Trueman, Robert and Thunder, Simon 2025. Manyism as mereologicism. Synthese, Vol. 206, Issue. 2,

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Laan, Boaz D 2025. How Should We Understand the Modal Potentialist’s Modality?. Philosophia Mathematica, Vol. 33, Issue. 2, p. 242.

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Warren, Jared 2025. Anti-platonism in the philosophy of mathematics. Philosophical Studies,

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Sharon Berry, Ashoka University, India

Publisher:: Cambridge University Press
Online publication date:: February 2022
Print publication year:: 2022
Online ISBN:: 9781108992756
DOI:: https://doi.org/10.1017/9781108992756

Subjects:: Mathematics, Logic, Categories and Sets, Philosophy of Science, Philosophy

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In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical – as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist (as opposed to actualist) approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends her approach against a number of possible objections, and she shows how a notion of logical possibility that is useful in formulating Potentialist set theory connects in important ways with philosophy of language, metametaphysics and philosophy of science. Her book will appeal to readers with interests in the philosophy of set theory, modal logic, and the role of mathematics in the sciences.

Finalist, 2023 PROSE Philosophy Award, Association of American Publishers

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A Logical Foundation for Potentialist Set Theory

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