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Handbook of the History and Philosophy of Mathematical Practice pp 1–26Cite as

Mathematical Practices Can Be Metaphysically Laden

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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.

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Acknowledgments

I would like to thank Carolin Antos, Neil Barton, Deborah Kant, Juliette Kennedy, Daniel Kuby, Benedikt Löwe, and Deniz Sarikaya for helpful remarks on draft versions of this paper. Research for this paper has been funded by the Centre for Mathematical Cognition at Loughborough University and the Research Foundation - Flanders (FWO), project G056716N.

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Authors and Affiliations

  1. Centre for Mathematical Cognition, Loughborough University, Loughborough, UK

    Colin Jakob Rittberg

  2. Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel, Brussel, UK

    Colin Jakob Rittberg

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  1. Colin Jakob Rittberg
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Correspondence to Colin Jakob Rittberg .

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  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

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  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

  2. Graduate Program for Science & Technology Education, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Michael N. Fried

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Rittberg, C.J. (2020). Mathematical Practices Can Be Metaphysically Laden. In: Sriraman, B. (eds) Handbook of the History and Philosophy of Mathematical Practice. Springer, Cham. https://doi.org/10.1007/978-3-030-19071-2_22-1

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  • DOI: https://doi.org/10.1007/978-3-030-19071-2_22-1

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