Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals)

By Donald Gillies

© 1982 – Routledge

104 pages

Purchasing Options:
Paperback: 9780415668743
pub: 2012-10-14
US Dollars$46.95
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Hardback: 9780415667098
pub: 2011-04-14
US Dollars$105.00
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e–Inspection Copy

About the Book

First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic.

This historical-critical study provides an excellent introduction to the problems of the philosophy of mathematics - problems which have wide implications for philosophy as a whole. This reissue will appeal to students of both mathematics and philosophy who wish to improve their knowledge of logic.

Table of Contents

1. Kant's Theory of Mathematics 2. Frege's Criticisms of Kant 3. Mill's Theory of Mathematics 4. Frege's Criticisms of Mill 5. The Concept of a Statement of Number is an Assertion About a Concept 6. Frege's Platonism 7. Frege's Logicism 8. Dedekind and Set Theory 9. Dedekind's Development of Arithmetic 10. Peano's Axioms. General Comparison of Frege, Dedekind and Peano 11. Frege's Begriffsschrift 12. Frege's Grundgesetze, and Russell's Paradox

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT004000
MATHEMATICS / Arithmetic
MAT015000
MATHEMATICS / History & Philosophy
MAT018000
MATHEMATICS / Logic
PHI000000
PHILOSOPHY / General
PHI011000
PHILOSOPHY / Logic