In statistics, there are two main paradigms: classical and Bayesian statistics. The purpose of this article is to investigate the extent to which classicists and Bayesians can (in some suitable sense of the word) agree. My conclusion is that, in certain situations, they cannot. The upshot is that, if we assume that the classicist is not allowed to have a higher degree of belief (credence) in a null hypothesis after he has rejected it than before, then (in certain situations) he has to either have trivial or incoherent credences to begin with or fail to update his credences by conditionalization.