Iterative Conceptions of Set

Neil Barton (Autor)

Buch | Softcover

104 Seiten

2024
Cambridge University Press (Verlag)
978-1-009-22726-1 (ISBN)

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This Element will examine possibilities for articulating this solution. 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.

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.

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.

Erscheinungsdatum	04.06.2024
Reihe/Serie	Elements in the Philosophy of Mathematics
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	152 x 229 mm
Gewicht	163 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	1-009-22726-2 / 1009227262
ISBN-13	978-1-009-22726-1 / 9781009227261
Zustand	Neuware