It would be profitless (even if it were possible) to catalog every nuance that the word infinity possesses in minor, as well as major, thinkers. Fortunately, the dominant strands are clear. Among these the theistic one is the most important both historically and in terms of contemporary debate.

Greek Philosophy

Anaximander

The first Western philosopher to speculate on infinity was the pre-Socratic Anaximander. By the infinite (to apeiron) he meant a limitless substance from which the limited things that constitute the world have come. This substance is limitless in three respects: It is eternal, not having a beginning or an end; it is inexhaustible; and it lacks internal boundaries and distinctions. But it is not spatially unlimited, for Anaximander (almost certainly) conceived it as a sphere. Also, it is not qualitatively indeterminate, like Aristotle's unformed matter, for it contains nature's...