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Principles of Mathematics 3rd Edition

3.6 out of 5 stars 21 customer reviews
ISBN-13: 978-0415082990
ISBN-10: 0415082994
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Editorial Reviews

Review

`Unless we are very much mistaken, its lucid application and development of the great discoveries of Peano and Cantor mark the opening of a new epoch in both philosophical and mathematical thought.' - The Spectator

`It is impossible in a short review to do justice to the subtlety and originality.' - TLS

About the Author

Bertrand Russell (1872-1970) was born in England and educated at Trinity College, Cambridge. His long career established him as one of the most influential philosophers, mathematicians, and social reformers of the twentieth century.
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Product Details

  • Paperback: 576 pages
  • Publisher: Routledge; 3 edition (May 21, 1992)
  • Language: English
  • ISBN-10: 0415082994
  • ISBN-13: 978-0415082990
  • Product Dimensions: 1.2 x 6.2 x 9.2 inches
  • Shipping Weight: 2 pounds (View shipping rates and policies)
  • Average Customer Review: 3.6 out of 5 stars  See all reviews (21 customer reviews)
  • Amazon Best Sellers Rank: #6,577,613 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Paperback
Bertrand Russell's greatest pieces of philosophical writing could probably be said to be "The Principles of Mathematics", "On Denoting" and with Alfred North Whitehead "Principia Mathematica". There is however one sense in which it could be said that the russellian magnum opus is The Principles of Mathematics, from here on TPM.

TPM is, arguably, the culmination in print of a long process of thought and concern, philosophically speaking, of Russell's intellectual preoccupations from his adolescence, youth and maturity with questions relating to the foundations of mathematics. Ever since Russell read Mill in his adolescence he had thought there was something suspect with the Millian view that mathematical knowledge is in some sense empirical & that mathematics is, so to speak, the most abstract of empirical sciences, but empirical nonetheless. Though he lacked the sophistication at the time to propose a different philosophy of mathematics, his concerns with these topics remained with him well into the completion of Principia Mathematica. Logic and Mathematics were, by that time, seen as separate subjects dealing with distinct subject-matters; it came to be, however, the intuition of Russell (an intuition shared, and indeed, anticipated by Frege) that mathematics was nothing more than the later stages of logic. He did not come into this view easily; after a long period of Hegelianism and Kantianism in philosophy, in which Russell sought to overcome the so called antinomies of the infinite and the infinitesimal, etc; Russell saw light coming, not from the works of philosophers, but from the work of mathematicians working to introduce rigour into mathematics.
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Format: Paperback
10-Point Rating: (8.75)
One of the claims of the analytical school of western philosophy is that math is reducible to logic, specifically the logic of groups, classes, or sets. In this vein, I can think of no better introduction than Russell's Principles of Mathematics. Although many of the ideas he proposes are intellectually outdated, Russell's method is rigorous and his presentation is lucid. While this book is not for everyone, no serious student of mathematical foundations should be without it. The chapters on zero and the concept of continuity are especially insightful.
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Format: Paperback
This is an excellent introduction to the fundamental principles and the core concepts of mathematics. There is no need to be mathematically inclined or a mathematical specialist to gain significantly from reading this book. Serious students of mathematics, logic, intellectual history, or philosophy will also gain significantly from its lucid and sharp explanations, and Bertrand's ability to question and challenge and manipulate even the most presumed unchangeable fundamental categories of mathematics.

This book is cogently written and is for the serious student and reader (yet there is no new mathematical or logical symbol system that needs to be learned, like in his and A.N. Whitehead's Principia Mathematica). A consistent theme throughout is on the philosophical nature of mathematical knowledge.

Since you cannot really get a sense of this book because there is no listing of table of contents or excerpt, etc.
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Format: Paperback
He doesn't do much theorem proving, but he tackles
head on all the basic problem of mathematics that were known
a hundred years ago. It was how well he did everything
that makes this still a must read if you love mathematics.
There is actually only one equation in his book that I can think of:
and it is of a Clifford geometry measure! This man was a mathematician's
mathematician and a metamathematics master in the language of
philosophy as well! The pages are falling out and I still
go to this and Sommerville when I want inspiration or understanding of really hard issues.
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Format: Paperback
Russell is undoubtedly a brilliant mind and this sometimes goes with a cryptic expression... But here, the "sometimes" turns into "a lot".

If you are both patient and ready to skip the convoluted, if not indigestible sections, then you might safely reach the last page of this monumental work.

If not, then a better route is to use Russell's later "Introduction to Mathematical Philosophy", where he tried and succeeded in clarifying and correcting his thoughts in just 200 pages.

This is not to say that PM doesn't contain illuminating sections, it does but they are gems, lost in dense magma.
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