This paper has two main goals: first, it reconstructs Aristotle’s account of measurement in the Metaphysics and shows how it connects to modern notions of measurement. Second, it demonstrates that Aristotle’s notion of measurement works only for simple measures, and leads him into a dilemma once it comes to measuring complex phenomena, such as motion, where two or more different aspects, such as time and space, have to be taken into account. This is shown with the help of Aristotle’s reaction to one of the problems that Zeno’s dichotomy paradox raises: Aristotle implicitly employs a complex measure of motion when solving this problem, while he explicitly characterizes the measure of motion as a simple measure in the Physics.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.