Workshop in Ancient Philosophy (Thursday - Week 6, TT23)

Workshop in Ancient Philosophy

Many of the interpretative questions about the infinite in Aristotle center around the potentiality/actuality distinction.

(1) I argue that Aristotle’s explanation which contrasts the infinite with a statue (206a18-21) should be taken to mean that the way in which the infinite exists potentially/actually is not the same as the way in which a statue exists potentially/actually, and not that the infinite, unlike a statue, does not exist actually. I criticize scholars (e.g. Bowin 2007) who are perhaps influenced by Hardie & Gaye’s (1930/1984) standard (but imprecise) translation of the passage, ‘something infinite will not be in actuality’ (206a20-21).

(2) I propose interpreting Aristotle’s account of the infinite by analogy with ‘the Olympic games’ (206a24) as implying that, in his view, the infinite is said to exist actually because of the fact that its parts become actual one after another. My contention is that Aristotle understands the infinite by division in actuality as a process of becoming actually divided from being divisible, which can be repeated infinitely, rather than as a process of being divided infinitely in actuality as opposed to in potentiality (pace Hintikka 1966).

(3) It is mistaken or misleading, pace Coope (2012), to explain the incompleteness of infinite division in terms of ‘[being] incomplete while it is going on’, which belongs to a process of change as contrasted with an activity (Metaphysics Θ.6, 1048b18-35). The day and the contest (206a21-22, 206a31, 206b14) as examples of something progressive are, in my view, used to explain what belongs to the infinite by division in so far as it is infinite. I also clarify why Aristotle does not explain the infinite by division by an analogous comparison to a process of a statue’s coming to be, a more familiar Aristotelian example of a process.

Chair: Ursula Coope

Workshop in Ancient Philosophy Convenors: Ursula Coope, Simon Shogry and Alexander Bown