Wednesday, June 13, 2012

A theory of time

This isn't meant to be a very good theory, but it's a start. The primitive notion I want to explicate is this notion of temporal priority between events: A is at least in part earlier than the start of B. I will abbreviate this to "A is earlier than B". And then we say that A is earlier than B if and only if there is a chain of at least partial causation starting at A and ending at B.

A consequence of this theory is that it is not possible to have simultaneous causation: if A causes B, then A is earlier than B. That's a count against it, but perhaps not a fatal one.

Another consequence of this theory is that it gives no account of simultaneity between events. That may not be such a bad thing.

A limitation is that we have no notion of a time, just of temporal ordering of events. That may be fine. But the costs are adding up.

I am more troubled by the fact that this rules out time travel and, more generally, temporally backwards causal influences. This makes me want to reject the theory.

But I can reprise the theory, not as a theory of the temporal priority between events, but of the temporal priority between accidents (or maybe just modes?) of a single substance. Just say that an accident A of a substance S is earlier than an accident B of S if and only if there is a chain of at least partial causation between accidents of S starting at A and ending at B.

We still have to rule the possibility of temporally backwards causation within the life of a single substance. But that's less costly, I think, than ruling out temporally backwards causation between events in general.

We still have the problem of not having simultaneous causation or any account of simultaneity for that matter. And no notion of times.

We can introduce times as follows. In some worlds, it will happen that there are nomic relationships between the accidents of a substance that are simply parametrized in terms of some parameter t such that accident A is earlier than accident B (in the above causal sense) if and only if t(A)<t(B). In such a case, we can call values of this parameter times. In worlds where there is no such neat parametrization, there may be temporal priority, but no times.

We get divine internal atemporality now as a corollary of the claim that God has no accidents.

But there are still a lot of costs. For one, the lack of a notion of simultaneity makes it hard to make sense of the transcendental unity of apperception. Maybe that's just too bad for that unity?

5 comments:

Heath White said...

I would think one would want a theory of time that delivered relations of temporal priority *between* substances (or modes, or events, thereof)?

Alexander R Pruss said...

Well, we can use the same causal kind of story, allowing for some possible backwards-going exceptions, maybe?

Sam said...

It seems to me that all causes and effects must be simultaneous. After all, an effect can't be an effect unless it's the result of a cause, and a cause can't be a cause unless it has brought about an effect. If there were a delay, then you'd have a cause that hasn't caused anything yet, which means it isn't really a cause at all. It's not a cause until it has brought about an effect, so it becomes a cause at exactly the same moment it produces the effect.

Alexander R Pruss said...

That's a neat argument that I haven't run across before.

I think we can say, however, that being a cause is an extrinsic feature of an entity, and whether A is a cause depends on what happens later.

Compare the way that whether x is a murderer can depend on what happens later, namely whether the victim dies.

Sam said...

You have a good point there.