PDF Ebook Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals), by Donald Gillies
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Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals), by Donald Gillies
PDF Ebook Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals), by Donald Gillies
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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.
- Sales Rank: #4175483 in Books
- Published on: 2012-10-17
- Released on: 2012-10-15
- Original language: English
- Dimensions: 8.50" h x .27" w x 5.43" l, .35 pounds
- Binding: Paperback
- 116 pages
Most helpful customer reviews
2 of 2 people found the following review helpful.
Some good philosophy of math stuff you can't find elsewhere
By Steve L
The highlights of this book are:
--A really good, clear, 16-page summary of Dedekind's views on the Foundations of Mathematics (e.g. his development of arithmetic from set theory)
--A short but also good and clear summary of Peano's views on the Foundations
--Comparisons of the Foundational views of Frege, Dedekind, and Peano with each other
--A really great explanation, which I've only seen in this work and another paper by Gillies, of why people like Frege and Dedekind were so focused on "explaining" the natural numbers. (This comes in the introduction.)
The book is definitely worth reading for the above, if you are into this subject matter.
There is also a nice summary of Frege's criticisms of Kant and Mill from his "Foundations of Arithmetic." More generally, there is a summary of Frege's logicist views about mathematics, but while this is serviceable, you can get this elsewhere. The aforementioned highlights, however, I have never found elsewhere.
(Note: I read the 1982 version, but I assume this version is the same.)
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