Iterative Conceptions of Set
Author:   Neil Barton (Universitetet i Oslo)
Publisher:   Cambridge University Press
ISBN:  

9781009478526


Pages:   104
Publication Date:   13 June 2024
Format:   Hardback
Availability:   Manufactured on demand   Availability explained
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Iterative Conceptions of Set


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Overview

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.

Full Product Details

Author:   Neil Barton (Universitetet i Oslo)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
ISBN:  

9781009478526


ISBN 10:   1009478524
Pages:   104
Publication Date:   13 June 2024
Audience:   General/trade ,  General
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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.

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