Friday, April 19, 2019

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:

  1. 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:

  1. 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.


Alexander R Pruss said...

It looks like my son was scooped by Shieva Kleinschmidt:

Red said...

How about if we qualify 3. by adding that new set my acquire locations(at least one) which are not part of original set?

Alexander R Pruss said...


That doesn't take care of the simultaneous x1 to x2 and x2 to x1 motion example. And it's not clear that coming to bilocate is a form of motion.

Alexander R Pruss said...

I am thinking that the best revision of the at-at theory might be to say that the two times mentioned by the at-at theory have to be internal times within a coherent internal timeline.

Bilocation by time travel is now not a problem. Bilocation by miracle -- as in, a saint being in two places at once -- then requires positing that when that happens, there are two parallel internal timelines created.

But the presentist is not going to want to move to internal time.

steve said...

While I'm open to bilocation, do we have verified examples? To establish if bilocation happens, we need evidence from both locations to verify that the individual was in fact at two different places at the same time. A kind of reverse alibi where there are witnesses or other types of evidence to verify that the individual was at one place at the same time the same individual was at another place. By the same token, in order to ID the individual, witnesses must have a comparative frame of reference to recognize the individual in question. Finally, the sighting must distinguish between bilocation and apparitions. Do alleged examples meet those conditions?

Alexander R Pruss said...

The distinction between bilocation and apparitions is a worry, indeed.

Bracketing that, I think one of the particularly well-attested cases was St Alphonsus Ligueri, who is said to have been seen by his servants in an armchair for a number of hours after saying Mass, while at the same time assisting the dying Pope Clement XIV (presumably there would be a lot of witnesses around a dying pope).

It seems that a common feature of a number of cases is that the individual in the original location is not very active -- e.g., is flopped in an armchair -- while being active at a remote location.

I suppose an alternate hypothesis besides bilocation is remote control of some divinely created matter that looks like a body.

Red said...

Bi-location seems kind of incoherent as it appears to involve that there are two distinct yet identical things or that two identical things have some distinct property, their location. Is this possible?

Alexander R Pruss said...

Identical things can have distinct properties: I am tall and I am human. Being tall and being human are distinct properties. Maybe you mean: *incompatible* properties. But whether being at location x and being at a distinct location y are incompatible is far from clear.