I’m about halfway done reading Michael Huemer’s new book Approaching Infinity. It’s a fascinating foray into the philosophy of math, metaphysics, and philosophy of science. Huemer begins by presenting a large number of paradoxes about infinity, plus a number of standard problems in thinking about vicious or virtuous regresses, and then offers a new account of numbers and the concept of infinity meant to solve these problems.

Blurb:

Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters.

The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It discusses the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes.

Fascinating work. Highly recommended.