Unfolding the Grammar of Bayesian Confirmation: Likelihood and Antilikelihood Principles

We explore the grammar of Bayesian confirmation by focusing on some likelihood principles, including the Weak Law of Likelihood.We show that none of the likelihood principles proposed so far is satisfied by all incremental measures of confirmation, and we argue that some of these measures indeed obey new, prima facie strange, antilikelihood principles. To prove this, we introduce a new measure that violates the Weak Law of Likelihood while satisfying a strong antilikelihood condition. We conclude by hinting at some relevant links between the likelihood principles considered here and other properties of Bayesian confirmation recently explored in the literature.