## Thursday, November 6, 2014

### A funny discrete view of time

A number of my posts are exercises in philosophical imagination rather than serious philosophical theories. These exercises can have several benefits, including: (a) they're fun, (b) they expand the range of possibilities to think about and thus might contribute to a new and actually promising approach, and (c) they potentially contribute to philosophical humility by making us question whether the views that we take more seriously are actually better supported than these. This is one of those posts.

Suppose that time is discrete and made up of instants. However instead of saying that always some instant is present, we now allow for two possibilities. Sometimes an instant is present. But sometimes presently we are between instants. When an instant is present, there is a present moment. When an instant is not present, when we are between instants, there is a present interval, bounded by the last past instant and the first future instant.

Why posit that sometimes we are between instants? Because this lets us get out of Zeno's paradox of the arrow. Zeno notes that at no instant is the arrow moving, because at no instant does it occupy two places, and so the arrow never moves. But now that we have two possibilities, that of an instant being present and of an interval being present, we see that Zeno's inference from

1. At no instant is the arrow moving
to
1. The arrow never moves
uses the implicit assumption that we are always at an instant. But if sometimes instead of being at an instant we are between them, we are at an interval, then the inference fails. And indeed when instead of a present moment we have a present interval, we can say that the arrow really is moving in the present—it is in two places in the present, in one place in the last past instant and in another in the first future instant.

So we have positions when an instant is present and velocities when an interval is present.

Of course there are other ways out of the Zeno paradox of the arrow, the best of which is to adopt the at-at theory of motion. But it's nice to have other solutions besides the usual ones.

Michael Gonzalez said...

If the "intervals" are discrete segments between instants, in what way do they differ from instants?

Alexander R Pruss said...

Objects will routinely be in two different places, have two different shapes, and so on, in one interval. They don't routinely do that at an instant.

William said...

Interestingly, if we allow the intervals to vary, with the quantum superpostions during interval undergoing objective reduction at the two points, this view of time is, if I understand him, compatible with some of Roger Penrose's published interpretations of quantum mechanics.

Michael Gonzalez said...

Pruss: I can't think of anything in the definition of "instant" that precludes having two different shapes or being in two different places, by definition. And even if there were such a prohibition, wouldn't an interval then be identical with a series of instants?

Alexander R Pruss said...

An instant is *instantaneous*. But (barring timetravel, bilocation, etc.) nothing can be in two places at once.

Yes, an interval might be a pair of instants. But it's still a substantive claim that sometimes instead of an instant being present, an interval is.

Dagmara Lizlovs said...

Alex:

Can you explain why the arrow never moves to all the deer we've got hanging here at Mattapany Rod and Gun Club? :-)

Alexander R Pruss said...

Dagmara:

Because you're not using the Android bowsight app that I'm developing? :-)

Dagmara Lizlovs said...

Alex:

I can just picture your android bowsight app in the Cabela's catalogue. :-)

Michael Gonzalez said...

If an interval is a pair of instants, then we don't seem to be doing any better by adding this concept. Why not just say that the thing exists across a pair of instants?

Alexander R Pruss said...

For anti-Zenonian purposes, I think we want the pair of instants to be able to be both present. Otherwise, it's still true that always we're at an instant, and nothing moves at an instant (barring the at-at theory, which I think is the real solution).

Michael Gonzalez said...

I think saying that pairs of instants can coexist does exactly the same work as saying "some pairs of instants are called 'intervals' and therefore can coexist", no?

Personally, I lean toward responding to Zeno by saying that time is not discrete, but continuous. That the world is always becoming; it's not just jumping from discrete states of being. It's artificial to talk about pieces or chunks of time.