Introduction to Mathematical Philosophy

Two of the very first courses I took in graduate school were in the foundations of mathematics, a decision that I have repeatedly praised myself for since. By learning the basic structure of mathematics, it was much easier to understand what came later. In this book, Bertrand Russell, one of the giants of mathematical philosophy, writes about the subject for a general audience. Russell, known in mathematical circles more for his giant work "Principia Mathematica" co-authored by Alfred North Whitehead, does an excellent job in describing the foundations of mathematics for the non-mathematician. It is a difficult task, as it is hard to describe mathematics without using mathematics. While there are some sections where Russell has no choice but to mention some higher-level mathematics, he does so only when necessary and explains it well. Most people with at least some exposure to mathematics will be able to understand it. There are no proofs in the book. As a primer on many of the basic ideas of mathematics, this book is one of the best. Russell was also a great expository writer and he demonstrates that trait here.

Okay, I have to be honest- I was a little intrepid picking up this book, and it had nothing to do with Russell's math. I had this really dogmatic atheist friend who used to endlessly quote "Why I am not a Christian," and it put me off of Bertrand Russell. This book is a joy. It's easy to read, interesting to think about, and inexpensive. Three virtues of math books that are hard to find in combination!

Bertand Russell's "Introduction to Mathematical Philosophy" provides the reader with a great understanding of mathematical philosophy in a very simple and straightforward manner. Though this is an introductory work it may not be casual reading to all who endeavor to read it. Beginning with definition of numbers and sets it expands to provide definitions of simple and complex and builds to provide a good understanding of the logic behind mathematics. While much of what is spoken about may seem very elementary the logic behind certainly is not. While the book is not nearly as expansive ad "Principia Mathematica" it is a good distillation of the bigger work and provides a great introduction to anyone wishing to explore that work. I recommend this book to anyone interested in formal logic and believe that it should be in the required reading for any formal logic introductory class. Further anyone interested in reading Goedel's work's which expand on Russell's work needs at least to read this work prior to Goedel. I find this book to be very succinct and readable and ultimately very worthy of the effort it takes to read. -- Ted Murena

A magnificent, fantastic and very readable introduction to the highly abstract world of formal logic and the foundations of mathematics. Lord Russell is not only one of the greatest logicians of all time, but he is also an astonishing writer, blessed with an elegant, heavenly precise concision of style and sharpness of argumentation.

An excellent and lucid exposition of what we really mean when we talk about 2 houses, or 1/2 an hour, or square root of 2 meters, or that the counting numbers are infinite. It does not require any prior mathematical knowledge beyond the basics, although it probably will be of interest only to those that care about math at its most abstract. It is fascinating to realize how much we take for granted when we do math and how much ingenuity it takes to pin down the concept of number. Highly recommended.