The Beginning of Infinity: Explanations That Transform the World

by David Deutsch

Mathematicians realized centuries ago that it is possible to work consistently and usefully with infinity. Infinite sets, infinitely large quantities and also infinitesimal quantities all make sense. Many of their properties are counter-intuitive, and the introduction of theories about infinities has always been controversial; but many facts about finite things are just as counter-intuitive. What Dawkins calls the ‘argument from personal incredulity’ is no argument: it represents nothing but a preference for parochial misconceptions over universal truths. In physics, too, infinity has been contemplated since antiquity. Euclidean space was infinite; and, in any case, space was usually regarded as a continuum: even a finite line was composed of infinitely many points. There were also infinitely many instants between any two times.