Conceptions of Set and the Foundations of Mathematics

by Luca Incurvati

Overview

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.

Product Details

ISBN-13:	9781108497824
Publisher:	Cambridge University Press
Publication date:	01/23/2020
Pages:	252
Product dimensions:	7.05(w) x 10.00(h) x 0.75(d)

About the Author

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

Table of 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.

Editorial Reviews

‘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

‘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, Choice

From the Publisher