This is likely equivalent to Merricks' proposal—I still need to think about whether it is—but I like it. Question: When is it the case that the same person is located at spatiotemporal location y and at spatiotemporal location z? Answer: When and only when there exists an x such that (a) x is a person, (b) x is located at y, and (c) x is located at z. Note that the answer does not use the concept of identity, and all the concepts it uses are ones that substantive theories of personal identity also presuppose.
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At first I thought this was just funny.
Then it occurred to me that it is not a consequence of the definition that "x is located at both y and z" is transitive. That is, so far as the criterion is concerned, x1 could be located at y and z, x2 be at z and w, but no x located at both y and w.
So, a puzzle: _should_ transitivity be a consequence of this kind of criterion? I'm not sure.
Well, the relation "a person located at y is also located at z" is not transitive. The relation "the person located at y is the person located at z" is transitive.
Here's another version, more direct. Let I(x,x',t) be synchronic identity at t. The folks who give substantive theories of diachronic identity don't give accounts of synchronic identity, so it's perfectly fair to use it.
Now, my analysis of x at t is identical with x' at t' is:
There is a y such that: y has spatiotemporal location within t & y has spatiotemporal location within t' & I(y,x,t) & I(y,x',t').
What makes a thing a person? Isn't that part of what is in question when thinking about continuity through time?
It needn't be part of the question. The memory theorists, animalists, soul theorists and bodily-continuity theorists don't have to answer what makes one a person. Some non-persons have memories; some non-persons are animals; some non-persons have souls (this is controversial, but I do think animals have (non-eternal) souls); some non-persons have bodies. So these folks aren't giving an account of what makes one a person.
Even simpler, without quantification.
x at t is identical with x' at t' iff x has spatiotemporal location within t' & I(x,x',t').
All of this is reminiscent to the Wittgensteinian point that two things are never identical, and one thing always is. :-)
Isn't this compatible with multiple occupancy? If so, I take that to be a problem (of course, if you think multiple occupancy is OK then it's not a problem).
By multiple occupancy, do you mean: of one body or of one place?
I meant one body (Lewis style), but I don't see why one place would be a problematic amendment for someone who is sympathetic to multiple occupancy.
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