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Series:   Elements in the Philosophy of Mathematics

Iterative Conceptions of Set

Published online by Cambridge University Press:  15 May 2024

Neil Barton
Neil Barton
Affiliation:
Universitetet i Oslo

Summary

Many philosophers are aware of the paradoxes of set theory (e.g. Russell's paradox). For many people, these were solved by the iterative conception of set which holds that sets are formed in stages by collecting sets available at previous stages. This Element will examine possibilities for articulating this solution. In particular, the author argues that there are different kinds of iterative conception, and it's open which of them (if any) is the best. Along the way, the author hopes to make some of the underlying mathematical and philosophical ideas behind tricky bits of the philosophy of set theory clear for philosophers more widely and make their relationships to some other questions in philosophy perspicuous.
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Keywords

set theoryiterative conceptionuncountable setsfoundations of mathematicsinfinity
Type
Element
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Series: Elements in the Philosophy of Mathematics
Online ISBN: 9781009227223
Publisher: Cambridge University Press
Print publication: 13 June 2024

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Iterative Conceptions of Set
  • Neil Barton, Universitetet i Oslo
  • Online ISBN: 9781009227223
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Iterative Conceptions of Set
  • Neil Barton, Universitetet i Oslo
  • Online ISBN: 9781009227223
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Iterative Conceptions of Set
  • Neil Barton, Universitetet i Oslo
  • Online ISBN: 9781009227223
Available formats
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