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There Are No Mathematical Explanations

Published online by Cambridge University Press:  01 January 2022

Jaakko Kuorikoski
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Abstract

If ontic dependence is the basis of explanation, there cannot be mathematical explanations. Accounting for the explanatory dependency between mathematical properties and empirical phenomena poses insurmountable metaphysical and epistemic difficulties, and the proposed amendments to the counterfactual theory of explanation invariably violate core commitments of the theory. Instead, mathematical explanations are either abstract mechanistic constitutive explanations or reconceptualizations of the explanandum phenomenon in which mathematics as such does not have an explanatory role. Explanation-like reasoning within mathematics, distinction between explanatory and nonexplanatory proofs, and comparative judgments of mathematical depth can be fully accounted for by a concept of formal understanding.

Type
Research Article
Information
Philosophy of Science , Volume 88 , Issue 2 , April 2021 , pp. 189 - 212
Copyright
Copyright © The Philosophy of Science Association

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