ISBN : 9780199605057
Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics. The chapters are written by some of the world's finest mathematicians, mathematical physicists and philosophers of mathematics, each giving their perspective on this fascinating debate. Every chapter is followed by a short response from another member of the author team, reinforcing the main theme and raising further questions. Accessible to anyone interested in what mathematics really means, and useful for mathematicians and philosophers of science at all levels, Meaning in Mathematics offers deep new insights into a subject many people take for granted.
1. Is Mathematics Discovered or Invented?
2. Exploring the Mathematical Library of Babel
3. Mathematical Reality
4. Mathematics, the Mind, and the Physical World
5. Mathematical Understanding
6. Creation and Discovery in Mathematics
7. Discovery, Invention and Realism: Godel and others on the Reality of Concepts
8. Mathematics and Objectivity
9. The Reality of Mathematical Objects
10. Getting More out of Mathematics than What We Put In