FOREVER FINITE

An extensively detailed philosophical case against the infinite.

As Sewell notes in his sprawling nonfiction debut, the concept of infinity is ancient and has powerful cultural weight. The notion of an infinite universe, for example, is deeply entrenched in human metaphysics. And yet, Sewell flatly announces that this idea is mistaken, “a logically inconsistent concept that has caused a great deal of confusion for the past 2.5 millennia.” Infinity, which Sewell defines as the state of being “limitless—in quantity, quality, or both,” he considers contradictory in nature and logically inconsistent, and he applies his objections to both the literal and the figurative sense of the infinity concept. Sewell sets out to prove that everything not “void of properties”—that is, everything that exists—is finite. In a series of densely packed chapters with numerous headings, subheadings, graphs, charts, and illustrations, he delves deeply into the realms of mathematics and philosophy to demonstrate that the description of “infinite” is ultimately nonsensical. Given the seriousness of his inquiry and the technical nature of much of his subject matter (“Collections that have a limit, in the sense of a specifiability condition for a range, are those that can be completely enumerated,” reads one of the gentler lines), large sections of the book may be an uphill climb for many readers. Sewell acknowledges this early on, adding a disclaimer that his book is intended for those who already have a fair knowledge of key elements of mathematics and philosophy. In this, however, he underestimates his own skills, as he’s extremely effective at breaking down all but the most abstruse concepts he discusses in these pages. Still, some ideas will still be hard for non-specialists to grasp.

A wide-ranging and comprehensive, if sometimes opaque, challenge to the traditional concept of the endless.