## Wednesday, April 4, 2012

### "Wholly present"

Here's something I've been thinking about. I want to start with the technical notion of being located at a region. This notion allows for partial location. If I have one leg in Arkansas and one in Texas, then I count as located in Arkansas and located in Texas. If regions have points, then I am located at a region if and only if I located at some point in the region (maybe that's a more primitive notion).

I'd like to move from the notion of being located at a region to the notion of being wholly present in a region. I am now wholly located in Texas, but if I had a leg in Arkansas and a leg in Texas, I would be wholly located in neither.

I could take the notion of being wholly present as primitive. But I don't want to do because it's a three-dimensional notion, while I think I am a four-dimensional entity, so to me it's a derivative notion.

One obvious thing to say is:

1. x is wholly present in A iff x is located at A and not located outside A.
This rules out multilocation—being wholly present at two distinct regions—by fiat. In so doing, it rules out both my view of the doctrine of transsubstantiation (since on my view, it is literally true that Christ is wholly spatially present in different places[note 1]) and the possibility of backwards time travel (since if you can travel back in time, you could be wholly present in two places, and shake hands with yourself).

A plausible move is to introduce parts or, more generally, features (the blueness of my eyes is a feature but not a part) and their locations (I stipulate that every part, proper or not, is a feature). Maybe, then:

1. x is wholly present in A iff every feature of x is located at A.
While this works for transsubstantiation, it doesn't work for time travel. For suppose that tomorrow I lose a leg, and I travel back to today, so that I am in another room in addition to this one. Then it is false that every part of me is located in that other room, since the lost leg isn't there.

There is another interesting problem with (2) and time travel. Suppose that in ten seconds I travel back to the present, so that I am wholly present in two disconnected rooms, and suppose that in the ten seconds I have neither lost nor gained any features. Let AL be the left half of the space occupied by me in one of the rooms and BR be the right half (including the cut line—don't put the cut line in AL) of the space occupied by me in the other room. Let C be the disconnected region that is the union of AL and BR. Then by (2) I am wholly present at C as every one of my features is in either AL or in BR or in both. But surely I am not wholly located in the messy region C.

At this point things get difficult. My best solution today is moderately complex (but not as complex as my best solution yesterday). It requires the introduction of two sets of times for a persisting substance. There are internal times, which correspond to the internal development of the substance, and there are external times, which correspond to what goes on in the external world. Normally, the two are nicely correlated. But time travel discombobulates things. If in one minute I travel 24 hours into the future, then in one internal minute I will be 24 external hours forward. And if in a minute I travel 24 hours into the past, then in one internal minute it will be externally yesterday.

Now, take the case where I am right now in room A in the normal way, but in room B due to having time-traveled back to that room after losing a leg. Let T be the present external time. There are two internal times associated with t. At internal time t1, I am in room A, and at internal time t2, I am in room B. Moreover, at t1, I have two legs, though at t2 I only have one. I guess at the external time T, I have two legs. My being wholly present in B does not require that I have both of my legs in B. It only requires that I have in B all the legs that I have at the internal time t2.

This yields the following pair of definitions:

1. x is wholly present in A at its internal time t iff every feature that x has at t is located at A at t.
2. x is wholly present in A at external time T iff there is an internal time t of x such that (a) x's internal time t is externally at T and (b) x is wholly present in A at t.
This gives the right answers with respect to (a) transsubstantiation, (b) time-travel and loss/gain of parts, and (c) time-travel and the union of the AL and BR regions.

The account does, however, have the consequence that if x is an extended simple with all features spread over all of x (so, x is the same color all over, etc.), then it counts as wholly present at every point at which it is located. This consequence is perhaps not so plausible, but I can live with it.

Andrew Jaeger said...
This comment has been removed by the author.
Andrew Jaeger said...

Alex - regarding the comment at the end:
It does not seem like an implausible consequence, since it is likely one a believer in the doctrine of the Eucharist will have to accept, regardless. (Perhaps a necessary condition for the doctrine of the Eucharist to be true.) It is something that the Catholic goes into metaphysics wanting to accommodate, as opposed to a bullet to bite as a result from doing metaphysics.

But, the point remains, anyone who doesn't like the doctrine of the Eucharist will likely find the consequence implausible.

Also, regarding the final account, the complexity of the account will only manifest itself in cases where internal and external times come apart (i.e., time-travel). So, there is a way of putting it so that it doesn't seem so complex for everyday/normal cases (where the external and internal times are the same), yet it still has the machinery to handle the complex cases.

Heath White said...

Minor issue: a region A can move over time (the boundaries of Texas can shift, for example). So A needs to be indexed to external times not internal times.

Alexander R Pruss said...

Heath:

I was thinking of regions of space--the geographical ones were just stand-ins. But it would be nicer if shifty regions can be handled.

Can you generate a counterexample to 3 or 4 using shifty regions? I can't off-hand.

Alexander R Pruss said...

Andrew:

I am not sure why the doctrine of the Eucharist requires that a uniform simple object be wholly present wherever it is present.

Andrew Jaeger said...

Alex:

If I am understanding the doctrine right (which I very well might not be, please tell me if I don't think I am!), the Eucharist is a uniform simple substance (i.e., Christ), who, as Augustine says, "is entire under every morsel."

As Aquinas say's: "...the entire Christ is under every part of the species of the bread, even while the host remains entire..." [ST III,q.76,a.3: http://www.newadvent.org/summa/4076.htm#article3]

I took this to basically amount to "Christ is *wholly present* under every part of the consecrated host even when the host is not broken."

If that is right, then it seems to be an instance of the consequence you mentioned in your post: that there is a substance that is wholly present wherever it is present (i.e., wherever a morsel of consecrated host is present there Christ is wholly present).

But there is a very good chance I am completely botching the proper interpretation of this passage in Aquinas.

Heath White said...

I think my issue was that the phrase in (3) “every feature that x has at t is located at A at t” is not well-defined. Let’s suppose I am standing in West Virginia in 1865, at internal time t1. Then I time-travel back to the same spot in 1860 (before WV’s secession from Virginia), at internal time t2. Uncontroversially I am wholly located in West Virginia in 1865 and wholly not-located in WV in 1860 (there is no such place). But I do not know what to say about whether I am located in WV at t1 or t2. Unless we are just taking t1=1865 and t2=1860, in which case these are really external times not internal ones.

Alexander R Pruss said...

I am thinking that at t2 none of your features are in West Virginia, since at t2 there is no West Virginia.

For at t2, it is 1860, and in 1860 there is no West Virginia.

There are two kinds of locations you can apply my account to. There are locations in four-dimensional space. These locations may be things like West Virginia worms or slices of them. There, there is no ambiguity.

But maybe there are also three-dimensional locations. And maybe West Virginia is such.

So, maybe, my account would benefit from extra explicitness:

x is wholly present in A at its internal time t iff there is an external T such that (a) x is at T at t, and (b) every feature that x has at t is located at A at T

This was implicit in the original version, because what it is to be located at a 3D location A at internal t is to be located at t at A at T, where T is the external time that corresponds to t. My this gets messy.

Andrew Jaeger said...

Let me see if I am following this:

Take the case you gave: You (with 2 legs) are in room A at internal time t1 at external time T1. Due to having time travelled back after losing your leg, you (with 1 leg) are also in room B, at internal time t2 at T1.

Am I right in thinking all following claims are true according to the analysis,
“x is wholly present in A at its internal time t iff there is an external T such that (a) x is at T at t, and (b) every feature that x has at t is located at A at T”:

(A) At T1, you are in both rooms A and B. (kinda just a given)
(B) You are wholly present in room A at t1.
(C) You are not wholly present in room B at t1.
-Because at t1, you are not even in room B!
(D) You are wholly present in room B at t2.
(E) You are not wholly present in room A at t2.
-Because at t2, you are not even in room A!
(F) You are wholly present in room A at T1.
(G) You are wholly present in room B at T1.

Is that correct?

Alexander R Pruss said...

A serious problem with the post is that (3) needs to specify that x exists at t. Otherwise I am wholly present in Rome in 45 BC.

Alexander R Pruss said...

The account in this post is worked out in print here.