But another argument against perdurantism that I want to get on "paper" before it slips my mind is one I got from David Oderberg's essay, "Hylomorphic Dualism." Oderberg remarks, in a footnote, I believe, that it is incoherent to say a thing's spatiotemporal structure is comprised of spaceless, timeless slices. In other words, offering two trillion totally worthless pennies to the cashier is no better or worse than offering only two. Since perdurantism denies there are substantial wholes which exist as wholes over multiple points of spacetime, it must also deny that any of the time slices "in" an "object" endure over any extended amount of spacetime. Ergo, each time slice is infinitely thin and infinitesimally brief. Unfortunately, however, stacking two trillion infinitely thin plates under your feet gets you no higher than stacking only two infinitely thin plates under them. Likewise, if I give you all my money for an infinitesimal amount of time, it really just means I do not give you my money. There is no coherent natural way to get spatiotemporally extended objects from spatiotemporally non-extended parts.
But I'm willing to admit there might be a supernatural way to do it.
(FWIW, I have touched on endurantism and perdurantism at FCA before: http://veniaminov.blogspot.com/search?q=perdurantism. I am willing to elaborate on the arguments for endurantism and against perdurantism that I mentioned in the first paragraph. Just let me know, O my mighty throng of readers!)