Algorithmic Randomness and Probabilistic Laws

We apply recent ideas about complexity and randomness to the philosophy of laws and chances. We develop two ways to use algorithmic randomness to characterize probabilistic laws of nature. The first, a generative chance* law, employs a nonstandard notion of chance. The second, a probabilistic* constraining law, impose relative frequency and randomness constraints that every physically possible world must satisfy. The constraining notion removes a major obstacle to a unified governing account of non-Humean laws, on which laws govern by constraining physical possibilities; it also provides independently motivated solutions to familiar problems for the Humean best-system account (the Big Bad Bug and the zero-fit problem). On either approach, probabilistic laws are tied more tightly to corresponding sets of possible worlds: some histories permitted by traditional probabilistic laws are now ruled out as physically impossible. Consequently, the framework avoids one variety of empirical underdetermination while bringing to light others that are typically overlooked.