On the ‘Indispensable Explanatory Role’ of Mathematics

Mind 125 (500):1045-1070 (2016)
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Abstract

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.

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Juha Saatsi
University of Leeds

Citations of this work

Explanatory Abstractions.Lina Jansson & Juha Saatsi - 2019 - British Journal for the Philosophy of Science 70 (3):817–844.
Scientific Realism Made Effective.Porter Williams - 2019 - British Journal for the Philosophy of Science 70 (1):209-237.
Mathematical Explanation by Law.Sam Baron - 2019 - British Journal for the Philosophy of Science 70 (3):683-717.
Complements, not competitors: causal and mathematical explanations.Holly Andersen - 2017 - British Journal for the Philosophy of Science 69 (2):485-508.

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References found in this work

Depth: An Account of Scientific Explanation.Michael Strevens - 2008 - Cambridge, Mass.: Harvard University Press.
Science, Perception and Reality.Wilfrid Sellars (ed.) - 1963 - New York,: Humanities Press.
Taking Morality Seriously: A Defense of Robust Realism.David Enoch - 2011 - Oxford, GB: Oxford University Press UK.
True Enough.Catherine Z. Elgin - 2017 - Cambridge: MIT Press.
Realism, Mathematics, and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.

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