Cristina Sagrafena

The Problem of Old Evidence (POE) states that Bayesian confirmation theory cannot explain why a theory H can be confirmed by a piece of evidence E already known. Different dimensions of POE have been highlighted. Here, I consider the dynamic and static dimension. In the former, we want to explain how the discovery that H accounts for E confirms H. In the latter, we want to understand why E is and will be a reason to prefer H over its competitors. The aim of the paper is twofold. Firstly, I stress that two recent solutions to the dynamic dimension, recently proposed by Eva and Hartmann, can be read in terms of Inference to the Best Explanation (IBE). On this base, I gauge the weaknesses and strengths of the two models. Namely, I show that the two authors endorse a particular IBE’s formulation, and that it is still unsure if it is the one descriptively used. Moreover, I contend that, while one condition of their first model is not expression of this formulation, the only condition of their second model is. Secondly, I focus on the static dimension of POE which, now, has to be expressed in IBE terms. To solve it, I rely on the counterfactual approach, and on a version of IBE in which explanatory considerations help to evaluate the terms in Bayes’ theorem. However, it turns out that the problems of the counterfactual approach recur even when it is used to solve the static POE in IBE terms.

By applying Arrow’s impossibility theorem for social choice to scientific theory choice, Okasha concludes that there is no acceptable theory choice rule. Okasha identifies the only way out of the impossibility in enriching the input for the theory choice rule, following Sen’s work for social choice. However, such a route seems not to be available for ‘large scale’ theory choices—i.e. choices among ‘key theories’ which imply a change of paradigm—based on Kuhn’s criteria, since these criteria cannot provide a richer input. The aim of the paper is to explore two lines of response to this conclusion. The first response proposes an example suggesting that Kuhn’s criteria may, indeed, provide sufficiently rich inputs. The second one proposes to use Kuhn’s criteria to evaluate prior probability and likelihood of the theories, and then take these as elements of the ‘Bayesian theory choice rule’ that avoids the impossibility. I will then argue against an objection to the second response, derived from Stegenga’s observation that a rule that translates the information provided by Kuhn’s criteria into prior probabilities suffers from Arrovian impossibility. Finally, I will answer a separate interesting question suggested by Stegenga’s observation.