Chance and the Structure of Modal Space

In a probabilistic universe, different possible futures have different chances of occurring. We can think of the chance distribution at t as a probability measure on the class of those metaphysically possible worlds that are compatible with the actual history up to t and with the actual laws of nature. Given this connection between chance and modality, one’s views about modal space can have significant implications for the theory of physical chance, and one’s modal views can be evaluated in part by how plausible these implications are. I apply this methodology to two influential modal theses. The first of these is the view, proposed by Hugh Chandler and Nathan Salmon, that many individuals have their modal features contingently. This thesis can be shown to entail that the present chances of various events are partly determined by the outcomes of future chance processes. As a result, the account yields a cluster of problematic consequences that are usually associated with Humean frequentist accounts of chance and which are known as “the problem of undermining futures.” The second account I consider is the thesis (held by a number of philosophers) that the existence of a possible world w depends on the existence of the contingent individuals that exist at w, and that many possible worlds are therefore contingent existents. The problem of undermining arises for this view as well, although in a milder form.