Aristotle’s Measurement Dilemma

Abstract

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.

Representational measurement theory: Is its number up?

“…Measurement is a primeval concept and probably there never was a time when humans did not measure (Morley & Renfrew, 2010). In early Greek thought, μέτρον (measure) was a pivotal concept (Prier, 1976) and profound insights into the logic of measurement appear in Aristotle’s Metaphysics (McKeon, 1941; Sattler, 2017) and Book V of Euclid’s Elements (Bostock, 1979; Heath, 1908; Stein, 1990). These spawned the traditional paradigm of measurement, which guided quantitative science from ancient times to the 20th century and culminated in the brilliant work of Otto Hölder (1901).…”

Three Ones and Aristotle’s Metaphysics

“…The theory is discussed at much greater length inSattler (2017). Our two interpretations of the theory harmonize well-though there are differences on details, and some pronounced differences in emphasis (unsurprising given her focus on how the theory connects to issues in natural philosophy, and mine on how it connects to issues in metaphysics).…”