The Labours of Zeno – a Supertask indeed?

Abstract

It is usually supposed that, with his dichotomy paradox, Zeno gave birth to the modern so-called supertask debate – the debate of whether carrying out an infinite sequence of actions or operations in a finite interval of time is physically or even logically possible. I argue that in fact this is not a problem raised by Zeno's dichotomy paradox, and that an account of the dichotomy paradox as a supertask (often implicitly offered also by scholars of ancient philosophy) seriously misconstrues the problems Zeno raises therein. However, comparing Zeno's paradox with a paradigmatic supertask can nevertheless be instructive, since it forces us to make explicit the pre-conditions on which the supertask debate rests and to examine whether these conditions do indeed obtain in the case of a continuous run. I will suggest in the end that the requirements for supertasks and for continuous finite runs are genuinely different.