Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

Bayesian probability is normally defined over a fixed language or eventspace. But in practice language is susceptible to change, and thequestion naturally arises as to how Bayesian degrees of belief shouldchange as language changes. I argue here that this question poses aserious challenge to Bayesianism. The Bayesian may be able to meet thischallenge however, and I outline a practical method for changing degreesof belief over changes in finite propositional languages.

This paper addresses the problem that Bayesian statistical inference cannot accommodate theory change, and proposes a framework for dealing with such changes. It first presents a scheme for generating predictions from observations by means of hypotheses. An example shows how the hypotheses represent the theoretical structure underlying the scheme. This is followed by an example of a change of hypotheses. The paper then presents a general framework for hypotheses change, and proposes the minimization of the distance between hypotheses as a (...) rationality criterion. Finally the paper discusses the import of this for Bayesian statistical inference. (shrink)