Wednesday, July 17, 2019

Knowing how fast to change

Imagine two objects, M and H, where M has the intrinsic causal power of emitting some sort of a pulse once per minute and H has the intrinsic causal power of pulsing once per hour, and suppose M and H are causally separated from the rest of the universe. How do M and H “know” how quickly to pulse?

The problem seems to me to be particularly pressing on Aristotelian theories of time on which time is defined by the changes of objects. Let’s imagine that in addition to M and H there are a thousand identical clocks running in the universe, with all objects causally isolated from each other, and that there is nothing else that is changing besides what I have described. Presumably, then, the changes that define time are the changes in the positions of the clock hands. Then on our Aristotelian theory, to say that H pulses every hour just means that H pulses once per revolution of the minute hand on a typical clock, and to say that H pulses every minute means that H pulses once per revolution of the seconds hand on a typical clock.

But, first, how do M and H know about the movement of the hands of the clocks, so as to keep in sync with them, if all the objects are causally isolated?

And, second, let’s imagine this. God speeds up the clocks one by one by a factor of two: today he speeds up clock C1, tomorrow he speeds up clock C2, and so on, until eventually all the clocks have been sped up. After a week, seven clocks, C1, ..., C7, have been sped up. This doesn’t matter for the definition of time: seven clocks out of a thousand are negligible, and the time standards are set up by C8, ..., C1000. According to C1, ..., C7, M pulses once per two rotations of the seconds hand, and H once per two rotations of the minutes hand. But according to C8, ..., C1000, M pulses once per rotation of the seconds hand and H once per rotation of the minutes hand, since these rotations correspond to real minutes and real hours.

However, after 993 days, clocks C1, ..., C993 are running at the same rate and setting the time standards. The clocks C994, ..., C1000 are the outliers. So, now, M pulses once per rotation of the seconds hands and H once per rotation of the minutes hands of C1, ..., C993. And M pulses twice per rotation of the seconds hands of C994, ..., C1000, and H twice per rotation of their minutes hands. So at some point in the process of speeding up clocks C8, ..., C1000, M’s pulses go from once per two rotations of the seconds hand of C1, ..., C7 to once per rotation, and similarly for H. But how can the speeding up of clocks other than C1, ..., C7 affect the correlations between H and M when everything is causally isolated?

(Note that talk of “speeding up clock Cn” makes sense even if the clocks jointly define time. If n = 1, we can understand it as speeding it up relative to clocks C2, ..., C1000. If n > 1, we can understand it as bringing clock Cn in sync with clock Cn − 1. What may be a bit ambiguous is what “day n” means, but nothing hangs on the details of how to resolve that.)

But even without an Aristotelian theory of time it is puzzling how M and H “know” how quickly to pulse.

I think there is a nice solution that lets one keep a part of the Aristotelian theory of time: (external) time is not just the measure of change, but the measure of change in causally interconnected things. There is no common timeline between M, H and the clocks when there are no causal connections between them. This, I think, requires the rejection of any theory on which there is a metaphysically deep “objective present”.

Another move is to deny that there can be intrinsic causal powers that make reference to metric external time.


Brandon said...

I don't see how this is any kind of problem at all. You've simply stipulated from the beginning that one pulses once per hour and one pulses once per minute; this is not any different from defining 'per hour' as 'in units measurable by the changes of H' and 'per minute' as 'in units measurable by the changes of M'. The pulses then are the clocks; the set-up has already assumed that they function as clocks, so there's no need even to bring in the rest of the clocks. (If you were to stipulate that they pulsed as they do independently of any measure by clock, your set-up would simply have assumed that the Aristotelian account is false, in which case it also would pose no problem for the Aristotelian.)

I do think, though, that Aristotelians are independently committed to the notion that systems completely causally isolated from each other have no temporal connections; there's no way to use a change as a clock for another change if there is no causal context of the sort required for measurement. Historical Aristotelianism, of course, always held that there was a universal change, that of the primum mobile, that guaranteed the causal context and thus made very change relatable to any other change. Modern Aristotelians can't make that assumption.

Alexander R Pruss said...

I think an implicit part of the setup is that M pulses faster than H. But on your stipulative reading, that's impossible.

The setup implies the Aristotelian account is false, but it is nonetheless plausible that the setup is possible. So we have reason to reject the Aristotelian account.

Note, by the way, that the universal change in the historical Aristotelianism also has to be causally connected to the individual changes to get out of my difficulty. Historical Aristotelianism did have such a connection (albeit via final causation).

Brandon said...

If it's an implicit part of the set-up, then it is stipulated by the set-up, and again there is no problem for the Aristotelian -- you are implicitly measuring each change by the other. (It's incoherent to say that one is faster than another unless they can be directly or indirectly used as clocks to measure each other.)

The actual setup doesn't, I think, imply that the Aristotelian account is false, although you are perhaps assuming that it is in your development; it stipulates facts about times that the Aristotelian will explain a certain way, and as far as I can see, that is it.

Michael Gonzalez said...

If "once every minute" has any meaning at all, in the initial stipulation, then the Ms will obviously pulse 60x as often as the Hs. If we (or the Aristotelians) are having trouble figuring out what "once every minute" means in that situation, then, as Brandon has indicated, it's possible the initial question doesn't make sense (or, rather, only makes sense on views the Aristotelian would reject).

Is it intuitively obvious that "M pulses every minute and H pulses every hour" has meaning in total causal isolation? Do we have the right intuitions for total causal isolation? Moreover, if we hold the PSR, one wonders how anything can exist contingently in total causal isolation, and then we're off to the races. It wouldn't be the first time that a robust Aristotelian account leads eventually to God ;-)

Alexander R Pruss said...

Now that I think about it more, I don't have the intuition that "M pulses every minute and H pulses every hour" has meaning in total causal isolation myself. I do have the intuition that "M pulses 60 times faster than H" has meaning in total causal isolation. But I think I could give that up more easily than I initially thought.

If the worry is the PSR, we can weaken total causal isolation to total causal isolation from changing entities.