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"Introduction to Mathematical Philosophy" by Bertrand Russell

First book we've read and reviewed by Bertand Russell!

With his name mentioned among authors of math books everywhere, it was a matter of time we read a title by the main man himself, Bertrand Russell. You're wondering, "Kris, math and philosophy go hand in hand?" That's exactly what the emphasis is on this book, and Russell simply explains why that is. Sounds like a weird combo, but if you're a mathematician, wouldn't it make sense as to why the numbers and the mathematical operations are what they are? There's no harm in questioning everything.

Being the title of the book contains the word "introduction," it's no joke: Anyone with basic knowledge of math and/or philosophy will be able to grasp this book. Russell writes and explains in a way that's easy to understand, given the philosophy of math can be a little, shall we say, abstruse. Meaning, the more it is explained, the confusing it can get. For that, what is the goal of mathematics? Even when Russell himself asks that very same thing, this book goes through the "baby steps" of it all, such as what a number is, complexity and its mathematical functionality in the philosophical side—translating statements into simple variables. Russell also talked about the importance and the meaning behind symbolism needed in math and philosophy, for their jobs implicate a "computational rationale," if you will, helping the mathematician/logician/student process the calculation(s) such that providing an 'input' ought to generate its 'output' to acquire the answer (i.e. adding or multiplying two numbers to get one definite answer).

Although the style of writing is pretty old fashioned, the reader will still be able to follow through gently. Russell also added a little humor to get some of his points across which is a treat. Besides that, the reader will get a nice introductory explanation to a subject that branches out immediately, especially over to more advanced mathematical disciplines.

In the later chapters, Russell sort of transitions into the philosophical aspect that needs math to consolidate truth and falsity of statements (symbolic logic, anyone?). Given that Logic has ties under philosophy, this was our favorite say from Russell himself:

"Mathematics and logic, historically speaking, have been entirely distinct studies. Mathematics has been connected with science, logic with Greek. But both have developed in modern times: logic has become more mathematical and mathematics has become more logical.

— Bertand Russell, CHAPTER XVIII 'Mathematics and Logic' pg. 194

For those who have majored in Math, or are currently working as a mathematician or professor, would know the importance to doing proofs as you advance your mathematical studies. Makes you wonder if there's a "limit" to how much math is required and/or needed both in academics and the real world. Still, there's no shame in learning as much as you can, and that includes knowing what it is that mathematics is supposed to be.

This copy we got, which is by Dover Publications, ought to be a good recommendation to schools teaching students about the meaning behind math. Oh sure, they'll complain why they won't ever use Geometry in real life, but how about knowing what a "class" is, and what makes a number "imaginary?" Books like these will definitely reduce any kind of anxiety towards math, having to learn and find out what makes the discipline "beautiful," as it's been described. You don't have to like Math, but knowing about it should give you a sense of confidence now that you understand it, and Russell has done a great job with this project.

Simple but excellent book to those wanting to extend their knowledge. Highly recommended! Thank you Mr. Russell and thank you to Dover Publications!





  • Great introduction to a complex subject, hence the title.
  • Written by the man himself Bertrand Russell.
  • Despite the old-style writing, the subject is explained thoroughly and gently.
  • The price.
  • Recommended for schools teaching students about the meaning and functionality behind math (as a means to reduce academic anxiety toward the subject).
  • None.
100% (A+)
Fan Rating
Title Introduction to Mathematical Philosophy
Author(s) Bertrand Russell
Description 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 mannerm requiring neither a knowledge of mathematics nor an apititude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophymeet—a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.
Dedication ???
ISBN 0-486-27724-0
Book Dimensions Width: 5.38″ (5 3/8″)
Height: 8.44″ (8 7/16″)
Depth: 0.44″ (7/16″)
Page Count 224
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
Book / Cover / Jacket Design ???
Author Photograph ???
Bibliographical Note This Dover edition, first published in 1993, is an unabridged and unaltered republication of the second edition (1920) of the work first published in 1919 by George Allen & Unwin, Ltd., London, and The Macmillan Co., New York.
Publisher Dover Publications, Inc. / George Allen & Unwin. Ltd. / The Macmillan Co.
Copyright ???
Manufactured in United States of America
Dover Publications, Inc., 31 East 2nd Street, Mineola, N.Y. 11501
Book Format Paperback, Kindle
Quoted Reviews --
Best Seller's List --
Other Unabridged Dover (1993) republication of the second edition published by Macmillan, New York, 1920. Preface. Editor's note. viii + 208pp. 5 3/8 x 8½. Paperbound.


THE PHILOSOPHY OF MATHEMATICS: AN INTRODUCTORY ESSAY, Stephan Körner. 198pp. 5 3/8 x 8½. 25048-2 Pa. $6.95
FOUNDATIONS OF MATHTHEMATICAL LOGIC, Haskell B. Curry. 416pp. 5 3/8 x 8½. 63462-0 Pa. $9.95
MATHEMATICS AND LOGIC, Mark Kac and Stanislaw M. Ulam. 192pp. 5 3/8 x 8¼. 67085-6 Pa. $6.95

Free Dover Mathematics and Science Catalog (59065-8) available upon request.
Library of Congress
Cataloging-in-Publication Data
1. Mathematics—Philosophy.
I. Title.
CIP Number 93-21477
LC Control Number ????
LC Call Number QA8.4.R87  1993b
DDC Call Number 510′.1—dc20


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