On the ‘Indispensable Explanatory Role’ of Mathematics

Mind 125 (500):1045-1070 (2016)
Juha Saatsi
University of Leeds
The literature on the indispensability argument for mathematical realism often refers to the ‘indispensable explanatory role’ of mathematics. I argue that we should examine the notion of explanatory indispensability from the point of view of specific conceptions of scientific explanation. The reason is that explanatory indispensability in and of itself turns out to be insufficient for justifying the ontological conclusions at stake. To show this I introduce a distinction between different kinds of explanatory roles—some ‘thick’ and ontologically committing, others ‘thin’ and ontologically peripheral—and examine this distinction in relation to some notable ‘ontic’ accounts of explanation. I also discuss the issue in the broader context of other ‘explanationist’ realist arguments.
Keywords Indispensability argument  Mathematical explanation  Realism
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DOI 10.1093/mind/fzv175
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Complements, Not Competitors: Causal and Mathematical Explanations.Holly Andersen - 2017 - British Journal for the Philosophy of Science:axw023.
Scientific Realism Made Effective.Porter Williams - forthcoming - British Journal for the Philosophy of Science.
The Because of Because Without Cause†.Daniele Molinini - 2018 - Philosophia Mathematica 26 (2):275-286.
Mathematical Explanation by Law.Sam Baron - 2017 - British Journal for the Philosophy of Science:axx062.

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