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:
- x is wholly present in A iff x is located at A and not located outside A.
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:
- x is wholly present in A iff every feature of x is located at A.
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:
- 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.
- 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.
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.