Published online by Cambridge University Press: 01 January 2022
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.
We would like to thank Vincenzo Crupi, Theo Kuipers, and Luca Tambolo for helpful comments on a previous draft of this article. Financial support from the PRIN grant Models and Inferences in Science (20122T3PTZ), from the FIRB project Structures and Dynamics of Knowledge and Cognition (Turin unit: D11J12000470001), and from the University of Turin and the Compagnia San Paolo project Assessing Information Models: Exploring Theories and Applications of Optimal Information Search (D16D15000190005) is gratefully acknowledged.