Conceptions of Set and the Foundations of Mathematics

Luca Incurvati

doi:10.1017/9781108596961

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.

‘Incurvati provides a veritable handbook for researchers and practitioners in the domain of logic and the foundations of mathematics … Each chapter raises significant foundational questions, fertile ground for further research.’

R. L. Pour Source: Choice

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Conceptions of Set and the Foundations of Mathematics

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Contents

Frontmatter
pp i-iv

Contents
pp v-vii

List of Figures
pp viii-viii

List of Tables
pp ix-x

Preface
pp xi-xvi

1 - Concepts and Conceptions
pp 1-35

2 - The Iterative Conception
pp 36-69

3 - Challenges to the Iterative Conception
pp 70-100

4 - The Naïve Conception
pp 101-127

5 - The Limitation of Size Conception
pp 128-159

6 - The Stratified Conception
pp 160-183

7 - The Graph Conception
pp 184-217

8 - Concluding Remarks
pp 218-220

Bibliography
pp 221-232

Index
pp 233-238

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