Mathematical practices can be metaphysically laden

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Samenvatting

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.
Originele taal-2English
TitelHandbook of the History and Philosophy of Mathematical Practice
UitgeverijSpringer
Aantal pagina's26
ISBN van elektronische versie978-3-030-19071-2
ISBN van geprinte versie978-3-030-19071-2
DOI's
StatusPublished - 2020

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