Introduction

Abstract

The purpose of this chapter is to provide a framework within which the whole book will eventually become comprehensible. We must try to understand the relationship of logic and proof to reality, and also the internal structure of mathematical reasoning. These matters have been the subject of sophisticated philosophical debate since Plato. The view we present is highly simplified; it is also just an opinion. As we shall see, there is a very definite sense in which mathematics (which is the concern of the rest of the book) is not ‘just an opinion’; this is the only chapter which permits the reader the luxury of intellectual rebellion.