Introduction to Mathematical Philosophy

Overview

In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive ...

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Introduction to Mathematical Philosophy (Barnes & Noble Library of Essential Reading)

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Overview

In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy.
In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.

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Product Details

  • ISBN-13: 9780486277240
  • Publisher: Dover Publications
  • Publication date: 9/14/1993
  • Pages: 226
  • Sales rank: 985,760
  • Product dimensions: 5.50 (w) x 8.50 (h) x 0.48 (d)

Table of Contents

Preface; Editor's Note
1. The Series of natural numbers
2. Definition of number
3. Finitude and mathematical induction
4. The definition of order
5. Kinds of relations
6. Similarity of relations
7. Rational, real, and complex numbers
8. Infinite cardinal numbers
9. Infinite series and ordinals
10. Limits and continuity
11. Limits and continuity of functions
12. Selections and the multiplicative axiom
13. The axiom of infinity and logical types
14. Incompatibility and the theory of deduction
15. Propositional functions
16. Descriptions
17. Classes
18. Mathematics and logic
Index
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See All Sort by: Showing 1 – 20 of 22 Customer Reviews
  • Anonymous

    Posted December 20, 2006

    Good introduction to an overlooked but important part of philosophy

    The book explores a much neglected area of philosophy. The Nature of Mathematics and mathematical truth. It also touches briefly on the Ontology of mathematical concepts. Do mathematical concepts exist independently of mathematicians or instead are they invented by them. This is an obscure question to many but could be seen to be as important as asking 'do entities such as numbers and concepts exist independently of the material world. The answer to this question would have very important consequences for materialism as a reigning philosophy. Russell's book is a great intro to this neglected subject.

    7 out of 7 people found this review helpful.

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  • Anonymous

    Posted August 12, 2009

    Why pay for what you can get for free?

    Minus the editor's introduction, you can get this book free in several different formats elsewhere...
    http://people.umass.edu/klement/russell-imp.html

    2 out of 4 people found this review helpful.

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  • Anonymous

    Posted January 9, 2007

    First Class

    The only thing which could possibly make this book better would be if it were written after Godel's work.

    2 out of 2 people found this review helpful.

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