Enduring by time-travelling
Well, what do I mean by "extended"? If "extended" means "having parts", nobody thinks that extended things lack parts. I guess what I mean is "existing at several different (space-, time- or spacetime-) coordinates". For instance, I find it hard to understand how something could cover all of Berlin without having any part that covers Kreuzberg. I see that this is precisely how immanent universals are supposed to exist, but that doesn't help me much, because I find it equally puzzling here.
Now intuitively there are two ways for a thing to exist at different space coordinates. The first is the way in which Russia is both in Europe and in Asia: by having spatial parts. The second is the way in which Russell was both in Europe and in Asia: not by having spatial parts, but by travelling. Could something similar be said about time coordinates? Maybe one way to exist at different times is to have temporal parts, and another way is to -- travel? What kind of travel is this? Not the kind of travel whereby things occupy different places at different times. Rather, the kind of travel whereby they occupy different times at different times. Sounds like time travel. One way to make sense of time travel is to introduce a second time axis. To travel backwards in time then is to go forward on one axis, but backwards on the other. Now what did Russell do? He somehow managed to be at two different places entirely, with all his spatial parts, by there being at different times. (Okay, he didn't, he exchanged many of his parts during the journey. I'm considering some possible Russell who did.) Correspondingly, the time-travelling endurer would have to be at two different times_1 entirely, with all his (zero) proper temporal_1 parts, by there being at different times_2. All he needs to do is to move along the time_2 axis without moving along the time_1 axis. This seems possible. So after all, it makes sense to say that something could be distributed along a dimension in which it doesn't have proper parts! Strange. (Unfortunately, we can't model a more familiar 4D world with endurers as some 4D slice of a (5D) world with two time dimensions. If we cut across time_2, the result corresponds to a time-slice of our world, and we won't find anything traveling in such a time slice. Similarly if we cut across time_1, what we get corresponds to a space-slice of our world, and again there are no travelers in space-slices.)