Lecture
LAMS Lecture "Physics and Mathematics in Aristotle’s Account of Infinity"
- Date
- Friday 12 May 2023
- Time
- Series
- Past events 2023
- Location
-
Lipsius
Cleveringaplaats 1
2311 BD Leiden - Room
- 1.18
The Leiden Centre for Late Antique and Medieval studies is pleased to announce a lecture by Pieter Sjoerd Hasper.
Physics and Mathematics in Aristotle’s Account of Infinity
Aristotle famously claims in Physics 3.6 that the infinite must be potential, because it cannot be actual, as there cannot be actual infinities, even though there must be infinities to ensure the infinite divisibility of magnitude in physics and mathematics, the infinite extendibility of lines and numbers, and the infinity of time and of the generations of species in time.
But what does Aristotle’s claim that the infinite is potential amount to? Trying to make sense of Aristotle’s analogy for infinity’s existence with the being of the day, scholars typically answer this question in terms of the infinite being potential in that there is always something further to take, without the taking being completable. But then a number of problems arise. What about the complete infinity of the past and the past generations of species, as they are with regard to present time? What about Aristotle’s claims about there being infinitely many possibilities, for example of division or of extension of mathematical lines? What about Aristotle’s claim that the infinite is ‘actual in the way a day is’ (Physics 3.6, 206b13-14)? And why would it then be impossible to have an ever-inflatable universe for the reason Aristotle gives, that it would involve an actual infinity (Physics 3.6, 206b16-26)?
In this paper I will try to solve all these problems by offering a novel interpretation of the analogy of the day as involving a presentist criterion for being actual, and by paying close attention to Aristotle’s use of the distinction between two types of things to which the analogy applies: to things that remains and to things that do not remain. Thus reconstructing the conceptual framework in which Aristotle formulates his claims, I can ascribe to Aristotle a far less restrictive account of infinity than hitherto supposed.
I will also present a preliminary version of a new text of Physica 3.6-8.
