Internal space

As David Lewis taught us, time travel calls for a notion of internal time. If I am about to travel to the time of the dinosaurs, then maybe in an hour I will meet a dinosaur. But that's an internal time hour. If I am going to spend the rest of my life in the Mesozoic, then—assuming nothing kills me—I will grow old before I am born, but this "before" is tied to external time, since of course in internal time, I grow old after being born.

Perhaps ordinary travel calls for a notion of internal space. Let's say today I am in room 304 of the hospital, and yesterday I was in room 200. The doctor comes and asks: "Does it still hurt in the same place as it did yesterday?" I tell her: "No, because yesterday it hurt in room 200, and today it hurts in room 304." But that's external place, and the doctor was asking about internal place.

Internal place is moved relative to external place while the body as a whole is locomoting. But it can also be moved when only parts of the body are moving. If my hands are hurting, and I clasp my hands to each other, I thereby make the internal places where it hurts be very close externally, but they are still as distant internally as they would be were I to hold my arms wide. If, on the other hand, my two hands grew together into a new super-hand, the two places would come to be close together.

I wonder: If I grow, does my head come to be internally further from my feet? I think so: There are more cells in between, for instance.

Rob Koons has suggested to me that the notion of internal place can help with Brentano's notion of "coincident boundaries": Suppose we have two perfect cubes, with the red one on top of the green one. Then it seems that the red cube's bottom boundary is in the same place as the green cube's top boundary. (Sextus Empiricus used basically this as an argument against rigid objects.) Question: But how can there two boundaries in the same place? Answer: There are two internal places in one external place here.