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Conceptions of Set and the Foundations of Mathematics

Conceptions of Set and the Foundations of Mathematics

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  • ISBN:9781108497824
  • Editorial: Cambridge University Press
  • Fecha de la edición:
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  • Nº Pág.:252
  • Idiomas:Ingles,Inglés

Materias:

Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.

The first book-length treatment of conceptions of set
Provides historical background on a variety of competing approaches and explores the mathematical theories with which they are associated
Sets out a novel account and defence of the iterative conception of set

1. Concepts and conceptions
2. The iterative conception
3. Challenges to the iterative conception
4. The naïve conception
5. The limitation of size conception
6. The stratified conception
7. The graph conception.

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