Mathematical pull

Colin J. Rittberg*

*Corresponding author for this work

Research output: Chapter in Book / Report / Conference proceedingChapterAcademicpeer-review

Abstract

In this paper, I show that mathematicians can successfully engage in metaphysical debates by mathematical means. I present the contemporary work of Hugh Woodin and Peter Koellner. Woodin has argued for axiom-candidates which could, when added to our current set-theoretic axiom system, resolve the issue that some fundamental questions of set theory are formally unsolvable. The proposed method to choose between these axioms is to rely on future results in formal set theory. Koellner connects this to a contemporary metaphysical debate on the ontological nature of sets. I argue that Koellner connects mathematics to the philosophical debate in such a way that mathematicians can obtain a new philosophical argument by doing more mathematics. This story reveals an active connectedness between mathematics and philosophy.

Original languageEnglish
Title of host publicationTrends in the History of Science
PublisherSpringer
Pages287-302
Number of pages16
DOIs
Publication statusPublished - 1 Jan 2016
Externally publishedYes

Publication series

NameTrends in the History of Science
ISSN (Print)2297-2951
ISSN (Electronic)2297-296X

Keywords

  • Accessible structure
  • Elementary embedding
  • Measurable cardinal
  • Model programme
  • Structure theory

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