Appendix: Scrutability, Supervenience, and Grounding

Our central scrutability theses have been epistemological theses, not metaphysical theses. But it is natural ask whether scrutability theses have any metaphysical upshot. For example, does a minimal scrutability base give us some guidance about the fundamental metaphysical strycture of the workd? We can approach question by comparing the epistemological relation of scrutability to two notions that are often thought to do metaphysical work. One notion is supervenience (Kim 19xx): B-properties supervene on A-properties when any two possible worlds that are indiscernible with respect to their A-properties are indiscernible with respect to their B-properties. Another notion is grounding (Schaffer 2009): B-properties are grounded in A-properties when B-properties are instantiated in virtue of A-properties being instantiated. I will start with supervenience. How does the claim that B-truths are scrutable from A-truths relate to the claim that B-properties supervene on A-properties? The most obvious difference here is that the first claim is cast in terms of a priori entailment (an epistemological notion) whereas the second is case in terms of possibility (a modal notion). Apart from this difference, there is also a structural difference in the way the notions are cast. To first address the structural difference, it is useful to abstract away from the modal/epistemological difference by comparing supervenience not to A Priori Scrutability but to Necessary Scrutability: the thesis that all B-truths are necessitated by A-truths. We might put this by saying that in every possible world where all the (actual) A-truths are true, all the (actual) B-truths are true. Let us assume that Aand B-truths always concern the instantiation of Aand B-properties (perhaps using expressions for these properties along with logical expressions). Assume more specifically that there is a class of A-sentences and B-sentences such that the the A-truths in a given world are the A-sentences that are true in that world, and such that two worlds are A-indiscernible or B-indiscernible (i.e. indiscernible with respect to their Aand B-properties) when the same Aand B-sentences hold in them. This structural assumption is neutral on just what indiscernibility