There Are No Mathematical Explanations

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.

Automated summary

Mathematical explanations are problematic when based on ontic dependence, as the explanatory dependency between mathematical properties and empirical phenomena leads to insurmountable metaphysical and epistemic difficulties. This challenges the core commitments of the counterfactual theory of explanation, with proposed amendments violating its principles. Instead, mathematical explanations are either abstract mechanistic constitutive explanations or reconceptualizations of phenomena, where mathematics itself does not play an explanatory role.