Iterative Conceptions of Set

Neil Barton (Universitetet i Oslo)

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English

Cambridge University Press
13 June 2024

Philosophy of mathematics; Set theory

Series: Elements in the Philosophy of Mathematics

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.

By: Neil Barton (Universitetet i Oslo)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 152mm, Spine: 8mm
Weight: 290g
ISBN: 9781009478526
ISBN 10: 1009478524
Series: Elements in the Philosophy of Mathematics
Pages: 104
Publication Date: 13 June 2024
Audience: General/trade , ELT Advanced
Format: Hardback
Publisher's Status: Active

1. Introduction; 2. Why set theory?; 3. The naive conception of set and the classic paradoxes; 4. The logical and combinatorial conceptions of set; 5. Iterative conceptions: first examples; 6. Forcing as a construction method; 7. A 'new' kind of paradox?; 8. Countabilist conceptions of iterative set; 9. Mathematics and philosophy under the different conceptions; 10. Conclusions, open questions, and the future; References.