Conceptions of Set and the Foundations of Mathematics

Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.

Luca Incurvati (Author)

9781108497824, Cambridge University Press

Hardback, published 23 January 2020

252 pages, 11 b/w illus. 4 tables
25.4 x 17.9 x 1.9 cm, 0.59 kg

'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

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.

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.

Subject Areas: Philosophy of science [PDA], Philosophy [HP], Humanities [H]