What Are Mathematical Coincidences ?

Mind 119 (474):307-340 (2010)
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Abstract

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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Marc Lange
University of North Carolina, Chapel Hill

Citations of this work

What Makes a Scientific Explanation Distinctively Mathematical?Marc Lange - 2013 - British Journal for the Philosophy of Science 64 (3):485-511.
Abstract Explanations in Science.Christopher Pincock - 2014 - British Journal for the Philosophy of Science 66 (4):857-882.
Coincidences and the Grain of Explanation.Harjit Bhogal - 2019 - Philosophy and Phenomenological Research 100 (3):677-694.
Composition as a Kind of Identity.Phillip Bricker - 2016 - Inquiry: An Interdisciplinary Journal of Philosophy 59 (3):264-294.

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References found in this work

The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.
Explanatory unification.Philip Kitcher - 1981 - Philosophy of Science 48 (4):507-531.
Explanatory unification and the causal structure of the world.Philip Kitcher - 1989 - In Philip Kitcher & Wesley Salmon (eds.), Scientific Explanation. Minneapolis: University of Minnesota Press. pp. 410-505.
Natural laws in scientific practice.Marc Lange - 2000 - New York: Oxford University Press.

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