Why Bayesians Needn’t Be Afraid of Observing Many Non-black Non-ravens

According to Hempel’s raven paradox, the observation of one non-black non-raven confirms the hypothesis that all ravens are black. Bayesians such as Howson and Urbach (Scientific reasoning: the Bayesian approach, 2nd edn. Open Court, Chicago, 1993) claim that the raven paradox can be solved by spelling out the concept of confirmation in the sense of the relevance criterion. Siebel (J Gen Philos Sci 35:313–329, 2004) disputes the adequacy of this Bayesian solution. He claims that spelling out the concept of confirmation in the relevance sense lets the raven paradox reappear as soon as numerous non-black non-ravens are observed. It is shown in this paper that Siebel’s objection to the Bayesian solution is flawed. Nevertheless, the objection made by Siebel may give us an idea of how Bayesians can successfully handle situations in which we observe more than one non-black non-raven.