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The Foundations of Mathematics in the Theory of Sets John P. Mayberry

The Foundations of Mathematics in the Theory of Sets By John P. Mayberry

The Foundations of Mathematics in the Theory of Sets by John P. Mayberry


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Summary

This 2001 book presents a unified approach to the foundations of mathematics in the theory of sets, covering conventional and finitary mathematics. It analyses the relation between the concepts of 'natural number' and 'set', and investigates the logic of quantification over the universe of sets. Suitable for both philosophers and mathematicians.

The Foundations of Mathematics in the Theory of Sets Summary

The Foundations of Mathematics in the Theory of Sets by John P. Mayberry

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.

The Foundations of Mathematics in the Theory of Sets Reviews

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

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.

Additional information

NLS9780521172714
9780521172714
0521172713
The Foundations of Mathematics in the Theory of Sets by John P. Mayberry
New
Paperback
Cambridge University Press
2011-10-27
446
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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