Confirmation and reduction

a bayesian account

F. Dizadji-Bahmani

Roman Frigg

Stephan Hartmann

pp. 321-338

in: Johan van Benthem, Theo A. Kuipers, Henk Visser (eds), Logic and philosophy of science in the footsteps of E. W. Beth, Synthese 179 (2), 2011.

Abstract

Various scientific theories stand in a reductive relation to each other. In a recent article, we have argued that a generalized version of the Nagel-Schaffner model (GNS) is the right account of this relation. In this article, we present a Bayesian analysis of how GNS impacts on confirmation. We formalize the relation between the reducing and the reduced theory before and after the reduction using Bayesian networks, and thereby show that, post-reduction, the two theories are confirmatory of each other. We then ask when a purported reduction should be accepted on epistemic grounds. To do so, we compare the prior and posterior probabilities of the conjunction of both theories before and after the reduction and ask how well each is confirmed by the available evidence.