Synopses & Reviews
In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy.
In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.
Synopsis
Seminal work focuses on concepts of number, order, relations, limits and continuity, propositional functions, descriptions and classes, more. Clear, accessible excursion into realm where mathematics and philosophy meet.
Synopsis
Seminal work focuses on concepts of number, order, relations, limits and continuity, propositional functions, descriptions and classes, more. Clear, accessible excursion into realm where mathematics and philosophy meet.
Synopsis
Seminal work by great modern philosopher and mathematician focuses on certain issues of mathematical logic that Russell believed invalidated much traditional and contemporary philosophy. Topics include number, order, relations, limits and continuity, propositional functions, descriptions and classes, more. Clear, accessible excursion into the realm where mathematics and philosophy meet.
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