Conceptions of Set and the Foundations of Mathematics

Luca Incurvati (Universiteit van Amsterdam)

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English

Cambridge University Press
23 January 2020

Philosophy: logic; Philosophy of mathematics; Philosophy of science

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.

By: Luca Incurvati (Universiteit van Amsterdam)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 179mm, Spine: 19mm
Weight: 590g
ISBN: 9781108497824
ISBN 10: 1108497829
Pages: 252
Publication Date: 23 January 2020
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Luca Incurvati is Assistant Professor of Philosophy at the Universiteit van Amsterdam.

Reviews for Conceptions of Set and the Foundations of Mathematics

'An indispensable reference work for anyone interested in the philosophy of set theory ... one of the book's virtues is that, for all the information it provides, it shows also how open-ended investigation of the different conceptions remains: almost every paragraph raises further issues for future exploration, and it is bound to generate discussion for years to come.' John Burgess, Philosophia Mathematica