Introduction To Mathematical Philosophy

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More About This Textbook

Overview

As a mathematician, philosopher, logician, historian, socialist, pacifist and social critic, Bertrand Russell is noted for his "revolt against idealism" in Britain in the early 20th century, as well as his pacifist activism during WWI, a campaign against Adolf Hitler and later the United States' involvement in the Vietnam War. In addition to his political activism, he is considered to be one of the founders of analytic philosophy, receiving the Nobel Prize in Literature in 1950 for his various humanitarian and philosophical works. He wrote his "Introduction to Mathematical Philosophy" (1919) in order to elucidate in a less technical way the main ideas of his and N.A. Whitehead's earlier "Principia Mathematica". The work focuses on mathematical logic as related to traditional and contemporary philosophy, of which Russell remarks, "logic is the youth of mathematics and mathematics is the manhood of logic." It is regarded today as a lucid, accessible exploration of the gray area where mathematics and philosophy meet.
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Product Details

  • ISBN-13: 9781602062917
  • Publisher: Cosimo Classics
  • Publication date: 4/1/2007
  • Pages: 220
  • Product dimensions: 0.50 (w) x 5.50 (h) x 8.50 (d)

Table of Contents

Introduction
Preface
Editor's Note
1 The Series of Natural Numbers 1
2 Definition of Number 11
3 Finitude and Mathematical Induction 20
4 The Definition of Order 29
5 Kinds of Relations 52
6 Similarity of Relations 52
7 Rational, Real, and Complex Numbers 63
8 Infinite Cardinal Numbers 77
9 Infinite Series and Ordinals 89
10 Limits and Continuity 97
11 Limits and Continuity of Functions 107
12 Selections and Multiplicative Axiom 117
13 The Axiom of Infinity and Logical Types 131
14 Incompatibility and the Theory of Deduction 144
15 Propositional Functions 155
16 Descriptions 167
17 Classes 181
18 Mathematics and Logic 194
Index 207
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Customer Reviews

Average Rating 3.5
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See All Sort by: Showing 1 – 20 of 21 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.

    1 out of 1 people found this review helpful.

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