Abstract

This book must have been a joy "to write": the author relishes playing with variations of Zeno's 'bisection' paradox to vindicate the reality of an Actual Infinite. The Infinite is a "lush" concept and though mathematical rigor forbids it, the world demands it. Benardete traces the development of mathematics through Aristotle, Leibniz, Gauss, Cantor, and Brouwer, and he examines recent developments in hyper-mathematics. Siding with Cantor, he argues that mathematics is no longer a formal discipline. It is teleological and it requires a rich ontology of the Infinite. He criticizes modern philosophy, particularly Kant and the later Wittgenstein, for rejecting the "cosmological horizon," for ruling out the Actual Infinite. Even a non-mathematician will understand his lively discussions of "random numbers," the "long run," nondenumerable and denumerable infinites, and the significance of the Lowenheim-Skolem theorem.—A. B. D.