Introduction to Mathematical Philosophy

by Bertrand Russell Earl

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.

Product Details

ISBN-13:	9781420938401
Publisher:	Digireads.com
Publication date:	01/01/2010
Pages:	116
Product dimensions:	5.90(w) x 8.80(h) x 0.40(d)

About 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".

Table of Contents

Preface; Editor's Note
1. The Series of natural numbers
2. Definition of number
3. Finitude and mathematical induction
4. The definition of order
5. Kinds of relations
6. Similarity of relations
7. Rational, real, and complex numbers
8. Infinite cardinal numbers
9. Infinite series and ordinals
10. Limits and continuity
11. Limits and continuity of functions
12. Selections and the multiplicative axiom
13. The axiom of infinity and logical types
14. Incompatibility and the theory of deduction
15. Propositional functions
16. Descriptions
17. Classes
18. Mathematics and logic
Index