Westphal, Jonathan - An Aristotelian Solution to the Problem of the Measuring of Time

07/31/2009

Unpublished paper

This article starts with a particular problem found in Augustine's Confessions, regarding measurement of time. The idea goes as follows:
-What is past no longer exists, so it can't be measured, what is future has yet to exist, so it too can't be measured. And the present has no extension, so it also can't be measured.
Author points out this is a different problem from Aristotle's, who questions the very existence of time in the first place. Augustine's problem is about both measurement and ontological status. (pg1)

The solution given starts with a Wittgenstein-esque 'diagnosis' of the problem; the problem is that we think that the only kind of measurement is the kind that measures length along a 'traveling band' with a beginning point and and end point, yet all we can see is a small fraction of the middle (the present). The problem, then, is not with time but with our grammatical understanding of 'measurement', that the prototypical kind of measurement, that of length, becomes an essential aspect of measurement. Instead, we should get a 'reminder' of what we do when we do measure time, so that we can get a suitable analysis. (pg2-3)

Author first presents a clarification: we don't measure 'time' but 'a time', a piece of time. Next, we need to look for an event, a happening through time that we want to measure. There are some rules: There needs to be a measurement device that moves at a regular and unchanging rate over a fixed and equal set of units. Now we set the device to '0' and proceed with the measurement. The key here is that a time is used to measure a time, just as a length is used to measure a length. We measure 'over a series of present moments ... rather than at a present moment' (pg4) So there isn't a good answer to the question "how long (time) is it?", but there is a good answer to "how long (time) was it?". In the latter case the measurement is co-extensional with the event in that one dimension (time). (pg4) The temporal measuring device extends through time just as a length-wise measuring device extends through space.