Wed Feb 8, 2017
234 Moses Hall, 6–7:30 PM
|Working Group in the History and Philosophy of Logic, Mathematics, and Science
Kevin T. Kelly and Konstantin Genin (Carnegie Mellon University)
An Epistemic Justification of Ockham’s Razor in Statistical Inductive Inference
Bayesian statistics allows for inductive inferences beyond the information provided, but it does not provide an epistemic justification in terms of finding the truth better than alternative methods. Frequentist methods come with epistemic guarantees, but the guarantees are too strong to allow for inductive inference. So there is currently no epistemic justification for inductive statistical inference of any kind; much less for Ockham’s razor. We will propose one. The idea is this. Everyone knows that deductive inference is monotonic, meaning that more premises never yield fewer conclusions. Inductive inference is non-monotonic. Everyone allows that deductive (monotonic) inference is better justified epistemically than inductive (non-monotonic) inference. So, presumably, more monotonicity is epistemically better than less. Our thesis is that optimally monotonic inference is necessarily Ockham inference. Before now, we have fully demonstrated that thesis only in the case of qualitative information. In this talk, we extend the result to statistical inference. The development will also illuminate broadly logical (i.e. topological) outlines in frequentist statistics that are crucial, but rarely emphasized.