Mathematical Practices Can Be Metaphysically Laden

Colin Jakob Rittberg ()
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Colin Jakob Rittberg: Loughborough University, Centre for Mathematical Cognition

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 109-134 from Springer

Abstract: Abstract In this chapter I explore the reciprocal relationship between the metaphysical views mathematicians hold and their mathematical activity. I focus on the set-theoretic pluralism debate, in which set theorists disagree about the implications of their formal mathematical work. As a first case study, I discuss how Woodin’s monist argument for an Ultimate-L feeds on and is fed by mathematical results and metaphysical beliefs. In a second case study, I present Hamkins’ pluralist proposal and the mathematical research projects it endows with relevance. These case studies support three claims: (1) the metaphysical views of mathematicians can shape what counts as relevant research; (2) mathematical results can shape the metaphysical beliefs of mathematicians; (3) metaphysical thought and mathematical activity develop in tandem in mathematical practices. This makes metaphysical thought an integral part of mathematical practices.

Keywords: Set theory; Set-theoretic pluralism; Metaphysics; Ultimate-L; Mathematical practices; Set-theoretic multiverse (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-40846-5_22

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DOI: 10.1007/978-3-031-40846-5_22

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