Introduction

Anaximander proposed ‘the unlimited’ as the foundation of all being, a substance with no analogues in the world of our experience. He understood change as the constant conflict of opposites, the hot and the cold, the wet and dry, which separate out from the unlimited. Heraclitus chose fire as the foundation of being to capture the idea that everything is forever in flux, as illustrated in his famous declaration that one cannot step into the same river twice. The early philosophers struggled to give a rational account of the world that did not resort to myths involving personal gods possessing super-human powers. The achievements of Greek philosophers stand in various relations to knowledge of today. Their achievements in logic and mathematics can be recognized as such and find a place in contemporary knowledge. Pythagoras’s theorem still forms a part of Euclidean geometry and the Pythagorian proof of it remains a proof, whilst it appears that Archimedes anticipated the infinitesimal calculus.