If two people are exactly alike in physical and functional respects, does it follow that they are also alike in phenomenal respects? If two worlds are exactly alike with respect to the instantiation of
categorical properties, does it follow that they have the same laws of nature, or the same chances? Conceivability intuitions, as well as the failure of reductive analyses, suggest that the answer is no: there are basic respects of similarity and difference beyond the physical and functional, or the categorical. But if these further dimensions of reality are independent of the others, then the pervasive "fit" between phenomenal and non-phenomenal properties, or between the nomic and the categorical, becomes an inexplicable coincidence. Can one deny that the dimensions of reality are independent?