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

Author/Creator:
Gillies, Donald.
Publication:
London : Taylor & Francis Group, 2011.
Format/Description:
Book
1 online resource (114 pages)
Series:
Routledge Revivals Ser.
Routledge Revivals Ser.
Status/Location:
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Other records:
Subjects:
Frege, Gottlob, -- 1848-1925.
Dedekind, Richard, -- 1831-1916.
Arithmetic -- Foundations.
Form/Genre:
Electronic books.
Summary:
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..
Contents:
Cover
Frege, Dedekind and Peano on the Foundations of Arithmetic
Title Page
Copyright Page
Table of Contents
Preface
Introduction
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 content 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
Appendix I. On Notation
Appendix II. On the Principle of Mathematical, or Complete, Induction
References
Index.
Notes:
Description based on publisher supplied metadata and other sources.
Local notes:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2021. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Other format:
Print version: Gillies, Donald Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals)
ISBN:
9781136721083
9780415667098
OCLC:
829461725