Early Greek thought

Greek mathematics embraced the infinite in an indirect way, a way that has become an important model for subsequent mathematics. Along with many other aspects of early Greek mathematics the author showed that, even at a technical level, there is an element of truth in the common, though admittedly oversimplified, adage: the Greeks abhorred the mathematically infinite. To Plato’s apeiron made its first significant appearance in early Greek thought with Anaximander of Miletus. Its role was very different from that which it tends to play in modern thought. It was introduced in response to what was then and has remained a basic intellectual challenge: to identify the stuff of which all things are made. In line with Anaximander Plato recognized the problem of conflict between opposites. His solution, however, was Pythagorean. And the attendant metaphysics was in many respects Eleatic.