Prof. Kevin Kelly, Carnegie Mellon University
(joint work with Konstantin Genin, Carnegie Mellon University)
Date: June 28 (Wednesday) 2017
Time: 18:15 – 19:45
Venue: Large conference room in the basement, Faculty of Letters Main Building, Yoshida Campus, Kyoto University.
Title: Deduction and Induction in Statistics
Abstract: The distinction between inductive and deductive reasoning is among the most basic in philosophy. But where, exactly, should one draw it? The logical positivists drew it in terms of logic—deductive inferences are those in which the conclusion follows by first-order logic from the premises. By that standard, all statistical inference is inductive, because the proposition that a sample was received never logically entails the intended conclusion. We propose, instead, to characterize deductive inference in terms of guaranteed, arbitrarily low chance of error. We present three arguments in favor of the proposal. (1) It reflects the situation of real, as opposed to mathematically formalized, deduction. (2) Unlike the received view, it allows one to transfer logical insights from epistemology and the philosophy of science to issues that arise in advanced statistical data analysis. (3) Finally, it rests on a deep, topological analogy between the logical and statistical cases. Time permitting, we illustrate the idea with a statistical application of tremendous practical and ethical consequence: the inference of causal connections from non-experimental data.