## Wednesday, May 2, 2018

### Time as the measure of change?

Aristotle says that time is the measure of change.

Suppose a pool of liquid changes from fragrant to putrid. We can quantify or measure such features as:

• the spatial extent of the change

• the value (in multiple senses) of the change

• the probability of the change

• the temporal extent of the change.

Obviously, when we talk of time as the measure of change, we have in mind the last of these four. But to define time as the temporal measure of change is blatantly circular. So the Aristotelian needs to non-circularly specify the sort of measurement of change that time provides. (I am not saying this can’t be done. But it is a challenge.)

Brandon said...

Aristotle doesn't just say that time is the measure of change; he explicitly says that it is the measure of change by numeration according to before and after. (He thinks that 'before' and 'after' here are abstract and apply to relative place as well as time, and thus that the terms themselves do not presuppose time.) Spatial extent of the change wouldn't, in Aristotle's sense, be measured by a numeration, but by containment; value change doesn't seem to have any obviously consistent before and after that doesn't reduce to temporal before and after; probability is arguably not a measure of the change itself at all, since it is determined, in its simplest form, by counting and weighting abstract possibilities.

Alexander R Pruss said...

Brandon:

Yeah, I missed the before and after. Thanks for bringing it up.

Think of the probability as the objective chance of the change. That's not an abstract thing. And it does seem to have to do with before and after.

We can talk of the (instrumental or non-instrumental) value of the change change according to before and after (did things get better, and if so by how much; did they get worse, and if so by how much).

There is also the worry that prima facie "before" and "after" is already temporal.

Brandon said...

I think the possible temporality of before and after is probably the most obvious potential problem. Aristotle himself does address it. On Aristotle's account of before and after we get the notions from spatial direction (in the case of being in front and being behind) and only extend it to time afterward. (The difference between the spatial and temporal cases would be the kind of measurement, according to number or according to containment. Aristotle, of course, doesn't have a notion of analytical geometry that tries to link the two by a coordinate system. And perhaps this uncovers a set of assumptions that Aristotle is making without realizing it.)

I'm still not convinced either the probability or the value examples work. If we're talking about things getting better we're really dealing with two different measures: one is purely temporal (which came first in time, the better or the worse) and the other is of intensity. I'm not sure there's any obvious sense of before and after in the latter. And similarly with the probability, I'm not sure how the before and after of probability would be different from a temporal measurement.

Perhaps the intensity in the value case does raise something of an issue; the possibility of a numerical value scale suggests that we can identify a linear direction, which seems to allow before and after in some sense. But this is complicated, I think, by the fact that such scales are based on analogy between domains we know to be in fact very different. (Unless we are assuming that you could in principle measure the value by actually counting something in the value itself.)