The essays are uniformly thoughtful, careful, and interesting … This collection demonstrates that new avenues of approach can point the way to new insights into philosophical concepts, they can help adjudicate between competing theories, and they can show how various subsets of the population make sense of ideas philosophers and mathematicians take for granted.

Philosophia

Imre Lakatos' call for a renaissance of empiricism in the philosophy of mathematics has at last been answered. This volume shows that deep questions in the philosophy of mathematics and logic can be attacked through empirical studies and non-foundational reasoning. Drawing on philosophy, logic, cognitive science and mathematics education, perennial questions are answered, including the roles of aesthetics and visualisation in proofs, and logic in practical reasoning. This landmark collection will undoubtedly be an indispensable resource for future research in this important field.

Paul Ernest, Emeritus Professor of Philosophy of Mathematics Education, Exeter University, UK

How are natural language terms actually used in technical contexts, and how do people interpret them? The answer is often surprising! This book extols the use of empirical studies to challenge implicit assumptions about the practice of philosophers and mathematicians, and the way that these groups talk about their practice.

John Mason, Emeritus Professor of Mathematics Education, The Open University, UK