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  3. Conceptions of Set and the Foundations of Mathematics
  • Cited by 25
Publisher:
Cambridge University Press
Online publication date:
January 2020
Print publication year:
2020
Online ISBN:
9781108596961
DOI:
https://doi.org/10.1017/9781108596961
Subjects:
Mathematics (general), Mathematics, Philosophy of Science, Philosophy
Information

Book description

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.

Reviews

‘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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