The Foundations of Mathematics in the Theory of Sets
The Foundations of Mathematics in the Theory of Sets
This 2001 book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. This leads to an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. The subject matter of the book falls on the borderline between philosophy and mathematics, and should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics.
- Written by a leading researcher in the field
- Of interest to philosophers as well as mathematicians
- At the time of publication, there were no other books that deal with the foundations of mathematics in such detail
Reviews & endorsements
Review of the hardback: ' … this book is thought-provoking … distinctive approach to the twin issues of mathematical ontology and mathematical foundations'. Australasian Journal of Philosophy
Product details
March 2001Hardback
9780521770347
446 pages
237 × 163 × 27 mm
0.8kg
Available
Table of Contents
- Preface
- Part I. Preliminaries:
- 1. The idea of foundations of mathematics
- 2. Simple arithmetic
- Part II. Basic Set Theory:
- 3. Semantics, ontology and logic
- 4. The principal axioms and definitions of set theory
- Part III. Cantorian Set Theory:
- 5. Cantorian finitism
- 6. The axiomatic method
- 7. Axiomatic set theory
- Part IV. Euclidean Set Theory:
- 8. Euclidian finitism
- 9. The Euclidean theory of cardinality
- 10. The theory of simply infinite systems
- 11. Euclidean set theory from the Cantorian standpoint
- 12. Envoi
- Appendices
- Bibliography
- Index.
