Introduction To Mathematical Philosophy

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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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