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Introduction To Mathematical Philosophy

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Overview

Not to be confused with the philosophy of mathematics, mathematical philosophy is the structured set of rules that govern all existence. Or, in a word: logic. While this branch of philosophy threatens to be an intimidating and abstract subject, it is one that is surprisingly simple and necessarily sensible, particularly at the pen of writer Bertrand Russell, who infuses this work, first published in 1919, with a palpable and genuine desire to assist the reader in understanding the principles he illustrates.

Anyone interested in logic and its development and application here will find a comprehensive and accessible account of mathematical philosophy, from the idea of what numbers actually are, through the principles of order, limits, and deduction, and on to infinity.

British philosopher and mathematician BERTRAND ARTHUR WILLIAM RUSSELL (1872-1970) won the Nobel Prize for Literature in 1950. Among his many works are Why I Am Not a Christian (1927), Power: A New Social Analysis (1938), and My Philosophical Development (1959).

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Product Details

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