What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions. Written by some of the world's leading philosophers of mathematics, psychologists, and mathematicians, Mathematical Knowledge gives a lively sense
of the current state of debate in this fascinating field.
Introduction ; 1. What is the problem of mathematical knowledge? ; 2. Mathematics, memory, and mental arithmetic ; 3. Is there a problem of induction for mathematics? ; 4. The cognitive basis of mathematical knowledge ; 5. What's there to know? A fictionalist account of mathematical knowledge ; 6. Mathematical recreation versus mathematical knowledge ; 7. Scientific Platonism ; 8. On quantifying into predicate position: Steps towards a new(trialist) perspective