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

ISBN-13: 9780415668743 / Angielski / Miękka / 2012 / 104 str.

Donald Gillies

Opis

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.

Spis treści

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

O autorze

D. A. Gillies