On the open-endedness of logical space

On the conception of metaphysical possibility that I prefer, a metaphysical possibility is simply a coherent way for the world to be. That is a substantial view. There are conceptions of metaphysical possibility on which not every coherent way for the world to be counts as a metaphysical possibility. To illustrate this point, consider a conception of metaphysical possibility based on a simplified version of David Lewis’s Humean Supervenience Thesis (Lewis 1986). The picture proceeds by postulating a canonical spacetime structure and a set of “natural” properties, which are assumed to be intrinsic. It is then claimed that a metaphysical possibity is a distribution of pointwise instantiations of natural properties across the canonical spacetime structure. On this conception of metaphysical possibility, there are seemingly coherent ways for the world to be that fail to count as metaphysical possibilities. Here is an example. For each set X of distributions of natural properties across canonical spacetime, consider the result of uniting the distributions in X into single superstructure, which consists of one copy of the canonical spacetime structure, along with its distribution of properties, for each distribution in X . There is nothing obviously incoherent about the world’s instantiating the superstructure generated by X . But Cantor’s Theorem entails there are more superstructures