Conceptions of Set and the Foundations of Mathematics

Incurvati, Luca

Cambridge University Press（2020/01発売）

• 製本 Hardcover:ハードカバー版／ページ数 252 p.
• 言語 ENG
• 商品コード 9781108497824
• DDC分類 511.322

Full 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.

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.