What Are Mathematical Coincidences ?

Mind 119 (474):307-340 (2010)
Although all mathematical truths are necessary, mathematicians take certain combinations of mathematical truths to be ‘coincidental’, ‘accidental’, or ‘fortuitous’. The notion of a ‘ mathematical coincidence’ has so far failed to receive sufficient attention from philosophers. I argue that a mathematical coincidence is not merely an unforeseen or surprising mathematical result, and that being a misleading combination of mathematical facts is neither necessary nor sufficient for qualifying as a mathematical coincidence. I argue that although the components of a mathematical coincidence may possess a common explainer, they have no common explanation ; that two mathematical facts have a unified explanation makes their truth non-coincidental. I suggest that any motivation we may have for thinking that there are mathematical coincidences should also motivate us to think that there are mathematical explanations, since the notion of a mathematical coincidence can be understood only in terms of the notion of a mathematical explanation. I also argue that the notion of a mathematical coincidence plays an important role in scientific explanation. When two phenomenological laws of nature are similar, despite concerning physically distinct processes, it may be that any correct scientific explanation of their similarity proceeds by revealing their similarity to be no mathematical coincidence
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DOI 10.1093/mind/fzq013
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References found in this work BETA
Philip Kitcher (1981). Explanatory Unification. Philosophy of Science 48 (4):507-531.

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Citations of this work BETA
Marc Lange (2013). What Makes a Scientific Explanation Distinctively Mathematical? British Journal for the Philosophy of Science 64 (3):485-511.
Christopher Pincock (2015). Abstract Explanations in Science. British Journal for the Philosophy of Science 66 (4):857-882.

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