Philosophies of Mathematics / Edition 1by Alexander L. George, Daniel Velleman
Pub. Date: 12/11/2001
This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism. See more details below
This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism.
- Publication date:
- Edition description:
- New Edition
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- Product dimensions:
- 6.00(w) x 9.00(h) x 0.68(d)
Table of Contents
3. Set Theory.
5. Intuitionistic Mathematics.
7. The Incompleteness Theorems.
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George and Velleman do an excellent job explaining various schools of thought, with each separate school explained in terms of the historical problems that motivated its foundation. Of particular interest is a chapter on what intuitionist analysis might look like, and a very clear proof of Godel's incompleteness theorem. Each chapter ends with interesting but entirely optional exercises. My one complaint would be that the authors presume a rather peculiar audience: they expect readers to be completely familiar with first-order logic notation, but introduce very basic concepts from analysis to motivate most of the examples in the book. Most math students will be far more comfortable with the latter than the former, I imagine. This suggests that the book is targeted primarily at philosophy students, but if so, why spend so much time on the theorems of intuitionistic mathematics?