Introduction to Mathematical Philosophy

Introduction to Mathematical Philosophy

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by Bertrand Russell
     
 

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… See more details below

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.

Product Details

ISBN-13:
9781408681664
Publisher:
Malinowski Press
Publication date:
02/28/2008
Pages:
216
Product dimensions:
5.50(w) x 8.50(h) x 0.49(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
1The Series of Natural Numbers1
2Definition of Number11
3Finitude and Mathematical Induction20
4The Definition of Order29
5Kinds of Relations52
6Similarity of Relations52
7Rational, Real, and Complex Numbers63
8Infinite Cardinal Numbers77
9Infinite Series and Ordinals89
10Limits and Continuity97
11Limits and Continuity of Functions107
12Selections and Multiplicative Axiom117
13The Axiom of Infinity and Logical Types131
14Incompatibility and the Theory of Deduction144
15Propositional Functions155
16Descriptions167
17Classes181
18Mathematics and Logic194
Index207

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