Frequencies, Chances and Undefinable Sets

Jan-Willem Romeijn (University of Groningen) gives a talk in the talk series "MCMP & Statistics Department" titled "Frequencies, Chances and Undefinable Sets". Abstract: In this talk I aim to clarify the concept of chance. The talk consists of two parts, concerning the epistemology and metaphysics of chance respectively. In the first part I consider statistical hypothese and their role in inference. I maintain that statistical hypotheses are best explicated along frequentist lines, following the theory of von Mises. I will argue that the well-known problems for frequentism do not apply in the inferential context. In the second part of the talk I ask what relation obtains between these frequentist hypotheses an the world. I will show that we can avoid the problem of the reference class, as well as the closely related conflict between determinism and chance, by means of a formal antireductionist argument: events can be assigned meaningful and nontrivial chances if they correspond to undefinable sets of events in the reducing theory.