Introduction to Mathematical Philosophy

( 22 )

Overview

Bertrand Russell is the most important philosopher of mathematics of the twentieth century. The author of The Principles of Mathematics, and, with Alfred Whitehead, the massive Principia Mathematica, Russell brought together his formidable knowledge of the subject and his skills as a gifted communicator to provide a classic introduction to the philosophy of mathematics. Introduction to Mathematical Philosophy sets out in a lucid and non-technical way the main ideas of Principia Mathematica. It is as inspiring and...
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Introduction to Mathematical Philosophy (Barnes & Noble Library of Essential Reading)

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Overview

Bertrand Russell is the most important philosopher of mathematics of the twentieth century. The author of The Principles of Mathematics, and, with Alfred Whitehead, the massive Principia Mathematica, Russell brought together his formidable knowledge of the subject and his skills as a gifted communicator to provide a classic introduction to the philosophy of mathematics. Introduction to Mathematical Philosophy sets out in a lucid and non-technical way the main ideas of Principia Mathematica. It is as inspiring and useful to the beginner as it was when it was first published in 1919.
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Product Details

  • ISBN-13: 9781313305914
  • Publisher: Hard Press Editions
  • Publication date: 1/28/2013
  • Pages: 224
  • Product dimensions: 6.00 (w) x 9.00 (h) x 0.47 (d)

Meet the Author

Bertrand Arthur William Russell, (1872 - 1970) was a British philosopher, logician, mathematician, historian, social critic and political activist. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these in any profound sense. He was born in Monmouthshire, into one of the most prominent aristocratic families in Britain.

In the early 20th century, Russell led the British "revolt against idealism". He is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege, colleague G. E. Moore, and his protégé Ludwig Wittgenstein. He is widely held to be one of the 20th century's premier logicians. With A. N. Whitehead he wrote Principia Mathematica, an attempt to create a logical basis for mathematics.

His philosophical essay "On Denoting" has been considered a "paradigm of philosophy". His work has had a considerable influence on logic, mathematics, set theory, linguistics, artificial intelligence, cognitive science, computer science (see type theory and type system), and philosophy, especially philosophy of language, epistemology, and metaphysics.

Russell was a prominent anti-war activist; he championed anti-imperialism and went to prison for his pacifism during World War I. Later, he campaigned against Adolf Hitler, then criticised Stalinist totalitarianism, attacked the involvement of the United States in the Vietnam War, and was an outspoken proponent of nuclear disarmament.

In 1950 Russell was awarded the Nobel Prize in Literature "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought".

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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
( 22 )
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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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