Deterministic Chance?

Can there be deterministic chance? That is, can there be objective chance values other than 0 or 1, in a deterministic world? I will argue that the answer is no. In a deterministic world, the only function that can play the role of chance is one that outputs just 0s and 1s. The role of chance involves connections from chance to credence, possibility, time, intrinsicness, lawhood, and causation. These connections do not allow for deterministic chance. 1 Overview 2 Four Arguments for Deterministic Chance 3 Four Conceptions of Deterministic Chance 4 The Role of Chance 5 The Case against Posterior Deterministic Chance 6 The Case against Initial Deterministic Chance 7 Epistemic Chance Can there be deterministic chance? That is, can there be objective chance values other than 0 or 1, in a deterministic world? I will argue that the answer is no. In a deterministic world, the only function that can play the role of chance is one that outputs just 0s and 1s. 1 Overview It was once widely assumed that determinism and chance were incompatible. That is, it was once widely assumed that deterministic worlds could only have extremal (0 or 1) objective chances. Thus Popper declares: Today I can see why so many determinists, . . . believe in a subjectivist interpretation of probability: it is, in a way, the only reasonable possibility which they can accept; for objective physical probabilities are incompatible with determinism; . . . ([1982], p. 105)