February 08, 2017, 6-7:30 PM in 234 Moses Hall
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.
February 22, 2017, 6-7:30 PM in 234 Moses Hall
Sean Walsh (Department of Logic and Philosophy of Science, UC Irvine)
Interpreting Categorical Grammar in Church’s Intensional Logic
Church’s intensional logic was an attempt to axiomatize the relation which a Fregean sense bears to a referent in the circumstance that there is a linguistic expression which expresses the sense and denotes the referent. In some recent work (), fragments of Church’s intensional logic have been developed which resolve the paradoxes of propositions by weakening comprehension. In this talk, we survey these fragments and assay the extent to which the traditional Montagovian interpretation of categorical grammar into the intensional theory of types can be mirrored by a interpretation of categorical grammar into the fragments of Church’s intensional logic.
References:  S. Walsh. Predicativity, the Russell-Myhill paradox, and Church’s intensional logic. The Journal of Philosophical Logic, 45(3):277–326, 2016.
March 22, 2017, 6-7:30 PM in 470 Stephens Hall
Jeremy Gray (Mathematics and Statistics, The Open University and The Mathematics Institute, University of Warwick, U.K.)
Theory choice: Felix Klein and Galois theory
In the 19th century a handful of short difficult papers about solution methods for polynomial equations grew into a vigorous branch of algebra (Galois theory) and even into a rallying cry for modern structural mathematics. The influential German mathematician Felix Klein’s well-known but little-read book The Icosahedron of 1884 played a significant, and often neglected, role in the controversies that attended the creation of these ideas. The arguments he and his opponents used range over important questions about the organisation of mathematical knowledge and the direction of research.