Monday, August 10, 2015

An argument against pointy continuous time

Suppose time is made of points, and suppose it's continuous. Suppose Sam suffers pain from noon to 1 pm and Sally suffers an equally intense pain from noon to 2 pm. Then Sam and Sally suffer the same number of equally painful points of time. So, it seems, we cannot say that Sally is worse off than Sam. But of course she is worse off than Sam. Hence we should either reject the continuity of time or reject the pointiness of time.

I think there is one gap in this argument. Even if time is a continuum made of points, it doesn't follow that our temporal experience is made of the same points. It could be that the basic perceptual units of time and pain are short intervals, let's say approximately ten milliseconds long (they may vary, too: sometimes time seems to be going faster, after all). And then Sally will have twice as many painful intervals, and the problem disappears. Maybe this works, but I think it's somewhat paradoxical. For this story to solve the problem, it seems that pain has to be suffered not at points of time, but at these short intervals of time. We cannot say Sam is suffering a pain exactly at 1:30 pm, it seems. In other words, we have something like Zeno's paradox of the arrow: at no time are Sam and Sally suffering, yet they are suffering.

But maybe one can respond in the same way that people have responded to the arrow. When we say that the arrow is moving at 1:30 pm, the truth of that statement is not grounded in what is happening exactly at 1:30 pm, but rather in the differences of arrow position between 1:30 pm and slightly earlier. Perhaps, then, we can say that Sam suffers at 1:30 pm, but his suffering at 1:30 pm is grounded not just in what happens at 1:30 pm, but in what happens over the basic perceptual interval that contains 1:30 pm?

Perhaps we can. But it's not quite so simple. For it is deeply implausible that Sam's being in pain at 1:30 pm is grounded in part in what happens after 1:30 pm. Yet a typical time t will be within one of the basic perceptual intervals of time, and hence some of that interval will come after t. So perhaps we should say that Sam's being in pain at 1:30 pm is grounded by the painfulness of the then-past part of the basic perceptual interval. Maybe 6 ms of the interval have passed, and those painful 6 ms is what makes Sam hurt. But then the basic perceptual interval of time isn't 10 ms, because it seems that a mere 6 ms of pain suffices (and if 6 ms, then by the same token 3 ms, and so on). So this is problematic.

A different move would be to say that although time is continuous, pain perception consists of discrete instants of pain. There are infinitely many instants of time between noon and 1 pm, but Sam only suffers at finitely many of them, and Sally has approximately twice as many instants to suffer at. My argument doesn't rule out this possibility, and it does indeed solve the problem. But it does it at the cost of positing a deceptive phenomenology. For a pain can feel temporally unbroken, and yet on this theory it occurs only at an infinitesimal fraction of the instants of time during an interval.

All in all, I think my basic argument and our experience of pain does provide some evidence against pointy continuous time. How much depends on how much we can rely on our phenomenology.


Heath White said...

I think there is a missing step in the argument, namely that if time is pointy then A being worse off than B is a matter of A suffering a larger number of painful time points than B. But since the numbers in question are almost always going to be infinity, this is not very plausible. Perhaps that shows the falsity of the pointiness of time, or perhaps it shows the falsity of the hidden assumption.

Compare: might space be both pointlike and continuous? If so, then volume would be a matter of occupying space points. But both I, and planet Earth, occupy the same number of space points (infinite). Therefore I and planet Earth occupy the same volume? Preposterous.

But we should not conclude that space is not both pointy and continuous (I think) but rather that volume is not well-measured by counting space points.

I am not sure what is at stake in claiming that time, or space, consists of points. In geometry, “point” seems to be what you need to call the intersection of two lines. Nothing similar goes on when talking about space or time other than maybe simultaneity or coincidence.

Alexander R Pruss said...

Maybe the implicit premise is that the badness of temporally extended pain is a sum of the badnesses of the fundamental component pains?

Alexander R Pruss said...

Here's another interesting thought experiment. Suppose we temporally compress Sally's experience into the same 12:00-1:00 slot by making Sally function twice as fast mentally.

At each time t between 12:00 and 1:00, Sally experiences the same intensity of pain as Sam does. Temporal compression doesn't change the subjective feel of the pain at any given time. So she feels the same pain at the same (external) times as Sam does. But obviously her situation is worse, presumably because her pain has greater subjective length. I am not sure what to make of this variant.

ChoirOfAngles said...

I wonder why Sally would suffer the same number of points in the tirst example.

Alexander R Pruss said...

Because the number of points in time between 12 and 1 equals the number of points in time between 12 and 2. At least, there is a one-to-one correspondence between them. The point in time at 12+x corresponds to the point in time at 12+2x (thus, 12:15 corresponds to 12:30, etc.)

IanS said...

Sally’s experience of pain “dominates” Sam’s in the sense that her pain is always at least as bad as Sam’s and sometimes worse (i.e. from 1:00pm to 2:00 pm). There is no need to count points to say that she is worse off. Nor does it make sense to count points, for this would lead us to say that any non-instananeous pain is infinitely bad.

Alexander R Pruss said...

That's true, of course, and helpful. But suppose I didn't foolishly make the two time intervals overlap? And what about my speedup version?

IanS said...

Pain is experienced directly. Cumulative pain – the “badness” of an episode – is not. We have to take pain as it comes, always in the subjective “now” (however that may work). But we judge “badness” in retrospect, or in hypothetical prospect, or as it applies to someone else. How we make these judgements is an interesting question, but probably one for psychologists rather than philosophers. (I’m imagining surveys and experiments along these lines: would you prefer 2 continuous hours of pain or 2 separate hours with a 1 hour break? How much would you pay to have 1 hour of intensity 2 pain reduced to 1 hour of intensity 1 pain? etc.). The link between the experience of pain and our judgement about it is not straightforward, certainly not simply a matter of counting points.

Alexander R Pruss said...

It may be for the psychologists to figure out how we make the judgments, but it's for the philosophers to figure out which of the judgments are true, though.