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John Stuart Mill, in his debate with William Whewell on the nature and logic of induction, is regarded as being the first to dismiss the supposed value of successful predictions as merely psychological. I shall argue that this view of the Whewell-Mill debate on predictions misconstrues Mill’s position and argument. From Mill’s point of view, the controversial point was not the question whether predictions ‘count more’ than ex-post explanations but the alleged assertion by Whewell that the successful predictions of the wave theory of light prove the existence of the ether. Mill argued that, on the one hand, the predictions of the wave theory of light do not and cannot provide evidence for the existence of the ether; as evidence for the laws of the theory, on the other hand, the predictions are superfluous, the laws being already well-confirmed. Mill actually endorsed a requirement of independent support closely resembling Whewell’s requirements for hypotheses; the controversy on the value of predictions is a product of the 20th century.

One way to reconstruct the miracle argument for scientific realism is to regard it as a statistical inference: since it is exceedingly unlikely that a false theory makes successful predictions, while it is rather likely that an approximately true theory is predictively successful, it is reasonable to infer that a predictively successful theory is at least approximately true. This reconstruction has led to the objection that the argument embodies a base rate fallacy: by focusing on successful theories one ignores the vast number of false theories some of which will be successful by mere chance. In this paper, I shall argue that the cogency of this objection depends on the explanandum of the miracle argument. It is cogent if what is to be explained is the success of a particular theory. If, however, the explanandum of the argument is the distribution of successful predictions among competing theories, the situation is different. Since the distribution of accidentally successful predictions is independent of the base rate, it is possible to assess the base rate by comparing this distribution to the empirically found distribution of successful predictions among competing theories. (C) 2013 Elsevier Ltd. All rights reserved.