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A Mathematical Prelude to the Philosophy of Mathematics

Stephen Pollard
Publication Date: 
Number of Pages: 
[Reviewed by
Charles Ashbacher
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The value of studying the content of this book is largely independent of what one does after using it. A large amount of the content is very similar to what I studied in the two foundations of mathematics courses that I took while in grad school. Naturally, there is the occasional word more familiar to philosophers than to mathematicians, but these are mere pebbles in the road rather than bumps for the reader that is a mathematician. If you read them carefully the mathematician can also get a bit of insight into the intertwined relationships between mathematics and philosophy.

The chapter titles are:

  • Recursion, induction
  • Peano arithmetic, incompleteness
  • Hereditarily finite lists
  • Zermelian lists
  • The hierarchy of sets
  • Frege arithmetic
  • Intuitionist logic

One of the features that make this book very useful for self-study or as a text in a graduate class in mathematics/philosophy is that exercises are embedded throughout, with solutions to the odd-numbered ones appended at the end of each chapter. The immediate reinforcement and the assessment of the level of (lack of) understanding is a big help in establishing the true level of knowledge.

While the content is targeted at the mathematically oriented philosopher, this book will serve the person on a straight mathematical track as well. 

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.