The supervenience principle (a central principle of minimal materialism) says there is no difference between possible worlds without a physical difference. But it seems to me that the world could be physically identical to this one, but the person in it who is the psychological center of it, the "me", as it were, could be living in the White House instead of in Glendale, Arizona. Or indeed, I could have lived 1000 years ago and be dead by now. There is a contingent truth that I am Victor Reppert and not some other person. For every person there seems to be a contingent fact that they happen to be in that inner world and not some other inner world. And if that is the case, then it looks to be as if there are truths about the world that are not explained by the set of physical truths.
This does seem explicable if what is at the base of reality is more like a mind than anything else. But if what is at the base of reality is more like a rock than anything else, how do these contingent facts emerge? It looks logically impossible to me.