Constructive presence

This morning, I was reading the Georgia Supreme Court’s Simpson v. State (1893) decision on a cross-state shooting, and loved this example, which is exactly the kind of example contemporary analytic philosophers like to give: "a burglary may be committed by inserting into a building a hook, or other contrivance, by means of which goods are withdrawn therefrom; and there can be no doubt that, under these circumstances, the burglar, in legal contemplation, enters the building."

Two attempts at deriving internal time from the causal order of modes

It would be nice to define the internal time of a substance in terms of the causal order of its accidents.

For each mode (i.e., accident or substantial form) α that a finite substance x has, there is the event c_α of α’s being caused. Causal priority provides a strict partial ordering on the events c_α.

Perhaps the simplest theory of the internal time of the substance x is that the moments of internal time just are the events c_α and their order just is the causal priority order.

This has the consequence that internal time need not be totally ordered, since one can have cases where α ≠ β but there is no priority relation between c_α and c_β. This consequence is welcome and unwelcome. It is welcome, as it allows one to give a nice account of bilocation involving the bifurcation of internal time. It is unwelcome, as intuitively time is linear. Let’s see if we can do something to reduce the unwelcome consequence.

Let’s suppose—as per causal finitism—that causal interactions are discrete. Then we can define a fundamental distance between the moments of internal time: d(c_α, c_β) is the length of the longest unidirectional causal priority chain between c_α and c_β. One might reasonably hypothesize that d(c_α, c_β) is something of the order of magnitude of the temporal distance between c_α and c_β in the rest frame of the substance in units of the order of Planck time. (Note that d is not a metric because of the unidirectionality constraint on the chains.)

This lets us have a second way of defining the internal time of a substance x. Let f be x’s substantial form. Then we can define “the start time” of a mode α as d(f, α): the length of the longest internal causal priority chain from c_f to c_α. Now likely some modes will have a simultaneous internal start time—they will have the same distance to c_f.

For this to define an intuitively plausible time sequence, we need the substance to have lots of interconnections between its accidents. Ordinary substances do seem to have that.

And perhaps some accidents won’t have an internal start time—if God turns me blue right now, my blueness won’t have an internal start time. But nonetheless that blueness can be “attached” to my internal temporal sequence by noting that it will be close according to d to some of my near-future accidents. For that miraculous blueness will interact with some of my other accidents to produce new accidents that are properly in my middle age. For instance, it will interact with my memories of observations of things not turning blue to generate the accident of surprise.

A variant of the at-at theory of change

It’s occurred to me that some of the difficulties with the at-at theory of change nicely disappear if the theory is expressed in terms of the internal time of an object: x changes provided that it is F at internal time t₁ and not-F at internal time t₂ such that t₁ < t₂ or t₂ < t₁.

For instance, consider this difficulty: Fred is bilocated and is sitting all day today and he is standing all day today. So at 10 he is not standing (and standing!) and at noon he is standing (and not standing!). On an external-time at-at theory of change, Fred has changed: at one time he is standing and and at another he isn’t. But that doesn’t seem right.

On an internal-time account of bilocation, we need to ask: is an internal time at which Fred is standing earlier or later than an internal time at which Fred is sitting? And what the answer is depends on how the bilocation was arranged. Suppose Fred was sitting all day, and at the end of the day he activated a time machine and went back to the beginning of the day and stood all day. Then he was sitting internally-earlier than he was standing, and so we do have change—just as we should. But suppose that Fred is just leading two parallel bilocated lives, without any time travel involved. Then his internal time splits into two streams when the bilocation begins and rejoins when they reunite. And plauusibly there are no earlier-than or later-than relations between the two parallel streams. And so there is no change.

More on bilocation and movement

It is often said that the four-dimensionalist doesn’t have a good theory of movement beyond the at-at theory which holds that

1. to move is to be at x₁ at one time and at x₂ at a different time, where x₂ ≠ x₁.

However, I am inclined to think the at-at theory is false due to an argument that my son came up with: if an object is bilocated at both x₁ and x₂ at one time and stays unmoved in both locations until a later time, then it is true that the object is at x₁ at one time and at x₂ at another time, and yet has not moved.

It is interesting that this argument also works against the most natural tensed theory of movement, namely that:

2. an object has moved provided that it was at x₁ and is at x₂, where x₂ ≠ x₁.

For imagine that an object was and still is bilocated between x₁ and x₂ and has remained entirely unmoving. Nonetheless, it was at x₁ and is now at x₂, and x₂ ≠ x₁, so according to (2) it has moved.

Thus, my son’s argument against the at-at theory does not seem to confer an advantage on the A-theory of time.

It is tempting to tweak (2) to something like this:

3. an object has moved provided that the set of locations at which it is now present is different from a set of locations at which it was present.

But that fails. For cessation of bilocation is not movement. If an object was bilocated between two locations x₁ and x₂, and then ceased to exist at x₂, while remaining at x₁, the object nonetheless did not move, even though (3) says it did.

Furthermore, space at least could be discrete. So imagine a point particle that was bilocated at two neighboring points x₁ and x₂ in space. The particle then simultaneously moved from x₁ to x₂ and from x₂ to x₁. Yet the set of points occupied by the particle was the same as it is now. So (3) says it did not move, but it did move, twice over.

I suppose one can deny the possibility of bilocation. But that is a big price to pay, I think.

I suspect that any theory of change that the A-theorist comes up with that solves this problem will also solve the problem for the four-dimensionalist.