Mathematical Explanations Of Empirical Facts, And Mathematical Realism

Australasian Journal of Philosophy 90 (3):559-578 (2012)
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A main thread of the debate over mathematical realism has come down to whether mathematics does explanatory work of its own in some of our best scientific explanations of empirical facts. Realists argue that it does; anti-realists argue that it doesn't. Part of this debate depends on how mathematics might be able to do explanatory work in an explanation. Everyone agrees that it's not enough that there merely be some mathematics in the explanation. Anti-realists claim there is nothing mathematics can do to make an explanation mathematical ; realists think something can be done, but they are not clear about what that something is. I argue that many of the examples of mathematical explanations of empirical facts in the literature can be accounted for in terms of Jackson and Pettit's [1990] notion of program explanation, and that mathematical realists can use the notion of program explanation to support their realism. This is exactly what has happened in a recent thread of the debate over moral realism. I explain how the two debates are analogous and how moves that have been made in the moral realism debate can be made in the mathematical realism debate. However, I conclude that one can be a mathematical realist without having to be a moral realist



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Aidan Lyon
Leiden University

Citations of this work

Explanatory Abstractions.Lina Jansson & Juha Saatsi - 2019 - British Journal for the Philosophy of Science 70 (3):817–844.
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.
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Mind, Language and Reality: Philosophical Papers.Hilary Putnam - 1975 - New York: Cambridge University Press.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.

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