Conceptions of set and the foundations of mathematics / Luca Incurvati.

Format:

Book

Author/Creator:

Incurvati, Luca, author.

Language:

English

Subjects (All):

Set theory.

Physical Description:

1 online resource (xv, 238 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2020.

Summary:

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 naive 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.

Contents:

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

8 - Concluding Remarks

Bibliography

Index.

Notes:

Title from publisher's bibliographic system (viewed on 15 Jan 2020).

Includes bibliographical references and index.

Other Format:

Print version: Incurvati, Luca. Conceptions of set and the foundations of mathematics

ISBN:

1-108-75835-5

1-108-61537-6

1-108-59696-7