Science-Driven Mathematical Explanation

Mind 121 (482):243-267 (2012)
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Abstract

Philosophers of mathematics have become increasingly interested in the explanatory role of mathematics in empirical science, in the context of new versions of the Quinean ‘Indispensability Argument’ which employ inference to the best explanation for the existence of abstract mathematical objects. However, little attention has been paid to analysing the nature of the explanatory relation involved in these mathematical explanations in science (MES). In this paper, I attack the only articulated account of MES in the literature (an account sketched by Mark Steiner), according to which a genuine MES incorporates an explanatory proof of the mathematical result being used. The central case study involves an explanation for why bees build the cells of their honeycombs in the shape of hexagons. I make a distinction between two kinds of MES, mathematics-driven explanation in science and science-driven mathematical explanation, and argue that it is the second category which is both scientifically and philosophical more central. I conclude that the explanatory relation involved in MES is genuinely scientific and hence that the phenomenon of MES poses a challenge to general accounts of scientific explanation.

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Al Baker
University of Leeds

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.
The Narrow Ontic Counterfactual Account of Distinctively Mathematical Explanation.Mark Povich - 2021 - British Journal for the Philosophy of Science 72 (2):511-543.
Abstract Explanations in Science.Christopher Pincock - 2014 - British Journal for the Philosophy of Science 66 (4):857-882.
Mathematical Explanations Of Empirical Facts, And Mathematical Realism.Aidan Lyon - 2012 - Australasian Journal of Philosophy 90 (3):559-578.

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