Logic & Philosophy of Science Colloquium

Abstract: When the conjunction of a hypothesis (H1) and a set of auxiliary assumptions (A1) generates an observational prediction that fails to come true, how does the disconfirmation of the conjunction affect the status of the separate conjuncts? Most previous attempts to address this problem probabilistically have been Bayesian, in that they compare the observation�s impact on the probability of H1 with its impact on the probability of A1. The present paper describes two other approaches. The first draws on a resource that Bayesians have available. If the hypothesis and the auxiliary assumptions each have alternatives (H2 and A2, respectively) such that the four conjunctions of the form (Hi & Aj) (i,j = 1,2) are simple (in the technical statistical sense of that term), then a likelihood analysis can identify asymmetries between the observation�s impact on the hypotheses and its impact on the auxiliary assumptions; this analysis does not invoke prior or posterior probabilities. A similar pattern can arise when some or all of the four conjunctions are models that contain adjustable parameters (and so are statistically composite, not simple); here a nonBayesian model selection criterion such as AIC can indicate that the observations have an impact on the hypotheses that differs fundamentally from the impact they have on the auxiliary assumptions. The likelihood approach is developed in terms of a simple example concerning medical diagnosis; the model selection approach is described in the context of the problem of phylogenetic inference.