Jan-Willem Romeijn

We present a conservative extension of a Bayesian account of confirmation that can deal with the problem of old evidence and new theories. So-called open-minded Bayesianism challenges the assumption—implicit in standard Bayesianism—that the correct empirical hypothesis is among the ones currently under consideration. It requires the inclusion of a catch-all hypothesis, which is characterized by means of sets of probability assignments. Upon the introduction of a new theory, the former catch-all is decomposed into a new empirical hypothesis and a new catch-all. As will be seen, this motivates a second update rule, besides Bayes’ rule, for updating probabilities in light of a new theory. This rule conserves probability ratios among the old hypotheses. This framework allows for old evidence to confirm a new hypothesis due to a shift in the theoretical context. The result is a version of Bayesianism that, in the words of Earman, “keep[s] an open mind, but not so open that your brain falls out”

In this paper I discuss probabilistic models of experimental intervention, and I show that such models elucidate the intuition that observations during intervention are more informative than observations per se. Because of this success, it seems attractive to also cast other problems addressed by the philosophy of experimentation in terms of such probabilistic models. However, a critical examination of the models reveals that some of the aspects of experimentation are covered up rather than resolved by probabilistic modelling. I end by drawing a number of general lessons on the use of formal methods in the philosophy of science

This paper investigates the viability of the Bayesian model of belief change. Van Benthem (2003) has shown that a particular kind of information change typical for dynamic epistemic logic cannot be modelled by Bayesian conditioning. I argue that the problems described by van Benthem come about because the information change alters the semantics in which the change is supposed to be modelled by conditioning: it induces a shift in meanings. I then show that meaning shifts can be modelled in terms of conditioning by employing a semantics that makes these changes in meaning explicit, and that the appropriate probability kinematics can be described by Dempster’s rule. The new model thereby facilitates a better understanding between probabilistic epistemology and dynamic epistemic logic

This paper develops a probabilistic model of belief change under interpretation shifts, in the context of a problem case from dynamic epistemic logic. Van Benthem [4] has shown that a particular kind of belief change, typical for dynamic epistemic logic, cannot be modelled by standard Bayesian conditioning. I argue that the problems described by van Benthem come about because the belief change alters the semantics in which the change is supposed to be modelled: the new information induces a shift in the interpretation of the sentences. In this paper I show that interpretation shifts can be modeled in terms of updating by conditioning. The model derives from the knowledge structures developed by Fagin et al [8], and hinges on a distinction between the propositional and informational content of sentences. Finally, I show that Dempster-Shafer theory provides the appropriate probability kinematics for the model

An inductive logic is a system of inference that describes the relation between propositions on data, and propositions that extend beyond the data, such as predictions over future data, and general conclusions on all possible data. Statistics, on the other hand, is a mathematical discipline that describes procedures for deriving results about a population from sample data. These results include predictions on future samples, decisions on rejecting or accepting a hypothesis about the population, the determination of probability assignments over such hypotheses, the selection of a statistical model for studying the population, and so on. Both inductive logic and statistics are calculi for getting from the given data to propositions or results that transcend the data

This article argues that time-asymmetric processes in spacetime are enantiomorphs. Subsequently, the Kantian puzzle concerning enantiomorphs in space is reviewed to introduce a number of positions concerning enantiomorphy, and to arrive at a dilemma: one must either reject that orientations of enantiomorphs are determinate, or furnish space or objects with orientation. The discussion on space is then used to derive two problems in the debate on the direction of time. First, it is shown that certain kinds of reductionism about the direction of time are at variance with the claim that orientation of enantiomorphic objects is intrinsic. Second, it is argued that reductive explanations of time-asymmetric processes presuppose that enantiomorphic processes do not have determinate orientation.