This book uses Ludwig Wittgenstein's philosophical methodology to solve a problem that has perplexed thinkers for thousands of years: 'how come (abstract) mathematics applies so wonderfully well to the (concrete, physical) world?' The book is distinctive in several ways. First, it gives the reader a route into understanding important features of Wittgenstein's writings and lectures by using his methodology to tackle this long-standing and seemingly intractable philosophical problem. More than this, though, it offers an outline of important (sometimes little-known) aspects of the development of mathematical thought through the ages, and an engagement of Wittgenstein's philosophy with this and with contemporary philosophy of mathematics on its own terms. A clear overview of all this in the context of Wittgenstein's philosophy of mathematics is interesting in its own right; it is also just what is needed to solve the problem of mathematics and world.
Bob Clark studied maths at Oxford University, UK, and philosophy at the Open University, KCL, and York. He taught maths in Kenya, California, Leeds and Brussels, and philosophy in Brussels and at York. Addicted to teaching though retired from paid work, he still teaches a regular small ad hoc adult seminar in philosophy.
Introduction.- Chapter 1: The Problem Posed.- Chapter 2: Fictionalism, Applicability, and Face Value.- Chapter 3: Infinity and Concept-Determination.- Chapter 4: The Hardness of the Logical 'Must'.- Chapter 5: The Problem Solved.- Appendix 1: Groups, Transformations and Homomorphisms.- Appendix 2: A Representation Theorem.