Mathematics and Explanatory Generality

Philosophia Mathematica 25 (2):194-209 (2017)
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Abstract

According to one popular nominalist picture, even when mathematics features indispensably in scientific explanations, this mathematics plays only a purely representational role: physical facts are represented, and these exclusively carry the explanatory load. I think that this view is mistaken, and that there are cases where mathematics itself plays an explanatory role. I distinguish two kinds of explanatory generality: scope generality and topic generality. Using the well-known periodical-cicada example, and also a new case study involving bicycle gears, I argue that what is picked out by the mathematics are structural facts that go beyond any specific physical facts.

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Al Baker
University of Leeds

Citations of this work

Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
Counterfactual Scheming.Sam Baron - 2020 - Mind 129 (514):535-562.
Platonic Relations and Mathematical Explanations.Robert Knowles - 2021 - Philosophical Quarterly 71 (3):623-644.
What could mathematics be for it to function in distinctively mathematical scientific explanations?Marc Lange - 2021 - Studies in History and Philosophy of Science Part A 87 (C):44-53.

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References found in this work

What Makes a Scientific Explanation Distinctively Mathematical?Marc Lange - 2013 - British Journal for the Philosophy of Science 64 (3):485-511.
Mathematics and Reality.Mary Leng - 2010 - Oxford: Oxford University Press.
Mathematical Explanation in Science.Alan Baker - 2009 - British Journal for the Philosophy of Science 60 (3):611-633.

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