Aristotle’s Definition of Time: A Modest Proposal

John Thorp (University of Western Ontario)

Aristotle’s definition of time is a real head-scratcher: ‘number of motion with respect to before and after’. The phrase is opaque, to say the least. Moreover, it flirts with danger: it seems to suggest that somehow time is made up of countable instants. And yet nothing could be clearer than that Aristotle would not have made that elementary mistake: he was very clear-headed about the nature of continua, of mathematical density. So what on earth does the definition mean?

The phrase, of course, has puzzled commentators from the get-go. Many have gone poking around in the arcana of ancient mathematics to try to find a meaning of ‘number’ that would make sense here. Some of these proposals have been very ingenious, even acrobatic. Other commentators have said that Aristotle must be using the word ‘number’ metaphorically – but it seems implausible that, in an otherwise sober discussion, he would make such prominent use of a metaphor, without at least flagging it as such. It’s a puzzling business.

This paper is deflationary. Based on some modest philological and grammatical research, as well as a culinary parallel, it shows that the meaning of the phrase is extremely easy and straightforward: for a millennium and a half we have been mishearing it. It’s all so simple – once you see it.