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Lately, there has been a lot of discussion about the place of IBE in Bayesian reasoning. Niiniluoto (2004, 68) argues that "Bayesianism provides a framework for studying abduction and induction as forms of ampliative reasoning". There is a tension, however, at the outset. Bayesian reasoning does not have rules of acceptance. On a strict Bayesian approach,¹ we can never detach the probability of the conclusion of a probabilistic argument, no matter how high this probability might be. So, strictly speaking, we are never licensed to accept a hypothesis on the basis of the evidence. All we are entitled to do, we are told by strict Bayesians, is (a) to detach a conclusion about a probability, namely, to assert that the posterior probability of a hypothesis is thus and so; and (b) to keep updating the posterior probability of a hypothesis, following Bayesian conditionalisation on fresh evidence. But IBE is a rule of acceptance. In its least controversial form, IBE authorises the acceptance of a hypothesis H, on the basis that it is the best explanation of the evidence. Think of the standard IBE-based argument for the existence of middle-sized material objects. According to this, the best explanation of the systematic, orderly and coherent way we experience the world is that there are stable middle-sized material objects that cause our experiences. Presumably, those who endorse this argument do not just assert a conclusion about a probability; they assert a conclusion, simpliciter. Their claim is not that the probability that material objects exist is high, but rather that it is reasonable to accept that they do exist. Hence, there is a tension between Bayesianism and standard renderings of IBE. This might make us wary of attempts to cast IBE in a Bayesian framework. But this is only the beginning of our worries.

DOI: 10.1057/9780230234666_11

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