ABSTRACT
Two things dominated medieval and Renaissance philosophy in general, and philosophical thought about the infinite in particular: the legacy of the Greeks; and religion. Religion in this context virtually meant Christianity, but not exclusively so. And the legacy of the Greeks was eventually to become, more than anything else, the legacy of Aristotle – albeit tempered and informed by strands of Platonism. Aristotle had denied the possibility of an actual infinity in the world of nature. But this had to be reconciled with belief in God's omnipotence. The thirteenth and fourteenth centuries saw interesting developments and growing sophistication concerning the mathematically infinite. There was general agreement, on Aristotelian grounds, that it was wrong to think of an infinitely divisible quantity a line or solid, say as actually being composed of infinitely many infinitesimal parts.
