Mathematical Practices Can Be Metaphysically Laden

In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer. pp. 109-134 (2024)
  Copy   BIBTEX


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.



    Upload a copy of this work     Papers currently archived: 92,923

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Intellectual humility in mathematics.Colin Jakob Rittberg - unknown - Synthese 199 (3-4):5571-5601.
Justified Epistemic Exclusions in Mathematics.Colin Jakob Rittberg - 2023 - Philosophia Mathematica 31 (3):330-359.
Can Mathematical Objects Be Causally Efficacious?Seungbae Park - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (3):247–255.
Hippocratic Oaths for Mathematicians?Colin Jakob Rittberg - 2022 - Philosophia 51 (3):1579-1603.
Mathematical Progress — On Maddy and Beyond.Simon Weisgerber - 2023 - Philosophia Mathematica 31 (1):1-28.
Structuralism reconsidered.Fraser MacBride - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. pp. 563--589.


Added to PP

3 (#1,725,832)

6 months
3 (#1,042,169)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references