There seems to be a problem for the conjunction of Special Relativity and perdurantism. Maybe this is a standard problem that has a standard solution?
Let's say that being bent is an intrinsic property. Perdurantists of the sort I am interested in think that Socrates is bent at a time in virtue of an instantaneous temporal part of him being bent (I think the argument can be made to work with thin but not instantaneous parts, but it's a little more complicated). Therefore:
Let's say that being bent is an intrinsic property. Perdurantists of the sort I am interested in think that Socrates is bent at a time in virtue of an instantaneous temporal part of him being bent (I think the argument can be made to work with thin but not instantaneous parts, but it's a little more complicated). Therefore:
- x is bent at t only if the temporal part of x at t is bent simpliciter.
- x is bent simpliciter only if every temporal part of x is bent simpliciter.
- There is a one-to-one correspondence between times and maximal spacelike hypersurfaces such that one exists at a time if and only if one at least partly occupies the corresponding hypersurface.
- P(x,t) is wholly contained within H(t) and if z is a spacetime point in H(t) and within x, then z is within P(x,t)
- If a point within x is within a maximal spacelike hypersurface h, then P(x,T(h)) exists.
- For any point z in spacetime, there are three maximal spacelike hypersurfaces h_{1}, h_{2} and h_{3} whose intersection contains no points other than z.
- No object wholly contained within a single spacetime point is bent simpliciter.
- x is an object that is bent at t.
- x_{1}=P(x,t)
- x_{2}=P(x_{1},T(h_{1}))
- x_{3}=P(x_{2},T(h_{2}))
- x_{4}=P(x_{3},T(h_{3}))
- x_{4} is wholly at z.
- It is not the case that x_{4} is bent simpliciter.
- x_{1} is bent simpliciter. (By 1 and 8)
- x_{2} is bent simpliciter. (By 2 and 11)
- x_{3} is bent simpliciter. (By 2 and 12)
- x_{4} is bent simpliciter. (By 2 and 13)
If I were a perdurantist, I'd deny 2, and maintain that an object can be bent simpliciter despite having temporal parts that are bent and temporal parts that are not bent. But I would not be comfortable with maintaining this. I would take this to increase the cost of perdurantism.
What is ironic here is that it is often thought that endurantism is what has trouble with Relativity.