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According to a defense of scientific realism known as the “divide et impera move”, mature scientific theories enjoying predictive success are partially true. This paper investigates a paradigmatic historical case: the prediction, based on Fresnel’s wave theory of light, that a bright spot should figure in the shadow of a disc. Two different derivations of this prediction have been given by both Poisson and Fresnel. I argue that the details of these derivations highlight two problems of indispensability arguments, which state that only the indispensable constituents of this success are worthy of belief and retained through theory-change. The first problem is that, contrary to a common claim, Fresnel’s integrals are not needed to predict the bright spot phenomenon. The second problem is that the hypotheses shared by to these two derivations include problematic idealizations. I claim that this example leads us to be skeptical about which aspects of our current theories are worthy of belief.

DOI: 10.1007/s11229-016-1305-8

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