Aristotelian Infinity (original) (raw)

 begins his treatment of the infinite in book 3 of the Physics in an overtly systematic fashion. The Physics, he says, is a study of nature, and nature has been defined as a principle of change and rest. Change, in turn, is thought to be something continuous, and what is continuous is thought to be infinitely divisible. So the topic of the infinite falls neatly out of the topic of nature. It follows, then, that the student of nature must first investigate whether the infinite exists or not, and then, if it exists, enquire how it exists. It is clear that the infinite must exist in some sense, because if it did not, 'many impossible consequences' would result, such as a beginning and an end of time, and the existence of indivisible lines. It remains, then, to determine in what sense the infinite does exist, and in what sense it does not. Aristotle reminds us, at the beginning of his positive account of infinity in chapter 6, that to exist means either to exist actually or to exist potentially, so if the infinite exists, it must exist in one of these senses. The previous two chapters have established that the infinite cannot exist actually, so, by disjunctive syllogism, the infinite must exist potentially. In Aristotle's words, 'The alternative then remains that the infinite has a potential existence' (Phys. 3. 6, 206A18-19). Jonathan Lear is right to point out that what is at stake, for Aristotle, in the rejection of the actual infinite is 'the possibility of philosophy-of man's ability to comprehend the world-[which] depends on the fact that the world is a finite place containing objects that are themselves finite'. In Aristotle's view, our ability to understand the world amounts to our ability to comprehend substances or actualities, and we could not do this if the definitions of ã John Bowin 2007 I would like to thank R.