A famous theorem from Gödel entails that if our thinking capacities do not go beyond what an electronic computer is capable of, then there are indeed absolutely unsolvable mathematical problems. Within this context, the contributions to this book critically examine positions about the scope and limits of human mathematical knowledge.

The contributions in this volume have been written by world leading experts in the field. Cutting edge research on scope and limits of mathematical knowledge. Extended introduction to key problems, arguments, and positions. Clear structure through the whole collection of articles.

Leon Horsten is a philosophical logician and philosopher of mathematics, working at the University of Bristol since 2007. His research is concentrated chiefly on bringing formal methods to bear on philosophical problems in the philosophy of science, the philosophy of mathematics, the philosophy of language, epistemology and metaphysics. Formal methods are meant to include not only logical methods, but also methods from other areas of mathematics and computer science (graph theory, probability theory, complexity theory, ...). Philip Welch is a set theorist and mathematical logician, working in Bristol since 1986. For the period 1997-2000 he was at Kobe University Graduate School setting up a research group in Set Theory. He is the author of some 75 papers in set theory, logic, theories of truth, and transfinite models of computation. He is a subject Co-editor for the Stanford Encyclopaedia of Philosophy for philosophy of mathematics, and is an Editor for set theory of the Journal of Symbolic Logic. His doctoral `grandfather' is Alan Turing, his supervisor at Oxford (1975-78) Robin Gandy, being Turing's only PhD student.

The contributions in this volume have been written by world leading experts in the field. Cutting edge research on scope and limits of mathematical knowledge. Extended introduction to key problems, arguments, and positions. Clear structure through the whole collection of articles.