ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book shows that the natural numbers are numerical properties and humans have empirical, even perceptual, access to numerical attributes. It examines psychological studies of numerical cognition, which support the empirical access thesis. The book provides a naturalistic theory of intuitions, which is then used to respond to Benacerraf's problem. It points out that systems of number words and of numerals should not be treated alike since psychologists have crucial structural differences. The book also examines the relation between external representations and mathematical cognition by drawing on experimental results from cognitive science and mathematics education. It describes the case for the claim that the naturalization project for mathematics can only succeed if psychologists take the method of mathematics to be the analytic method rather than the axiomatic method.
