The Foundations of Mathematics in the Theory of Sets
The Foundations of Mathematics in the Theory of Sets
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This unified approach to the foundations of mathematics in the theory of sets covers 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". The book contains an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, and the analysis of proof by induction and definition by recursion. The book 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
"...an invigorating call to foundational arms..." Notre Dame Journal of Formal Logic
"...this book is thought provoking...a distinctive approach to the twin issues of mathematical ontology and mathematical foundations..." Australasian Journal of Philosophy
"...I also think that it is one of the more philosophically significant books to have been written on this topic in some time. It provides much food for thought... this should certainly be acknowledged as an important piece of conceptual analysis, one which suggests interesting avenues for further exploration." Mary Tiles, Philosophia Mathematica
"...a very lively book, filled with striking theses..." The Bulletin of Symbolic Logic
Product details
April 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.
