The notion of infinity, and the problems, both philosophical and mathematical, that arise from it have been a central concern for over two millennia. Any serious thought about the nature of space, time, God (or gods), mathematics, and motion quickly leads to more general concerns regarding the notion, or notions, of infinity intimately tied up with such issues. As a result, it is unsurprising that philosophers throughout history have thought deeply about what infinity is, whether the notion is coherent, whether there are infinite entities (or infinitely many entities), and how we can know about such entities if they exist.

This entry focuses on two aspects of the infinite. The first is infinite divisibility, the idea that an object can, in some sense (and perhaps only ideally), be divided into an infinite collection of smaller and smaller parts. The puzzles...