Erkenntnis:1-19 (forthcoming)

Juha Saatsi
University of Leeds
Robert Knowles
University of Manchester
We demonstrate how real progress can be made in the debate surrounding the enhanced indispensability argument. Drawing on a counterfactual theory of explanation, well-motivated independently of the debate, we provide a novel analysis of ‘explanatory generality’ and how mathematics is involved in its procurement. On our analysis, mathematics’ sole explanatory contribution to the procurement of explanatory generality is to make counterfactual information about physical dependencies easier to grasp and reason with for creatures like us. This gives precise content to key intuitions traded in the debate, regarding mathematics’ procurement of explanatory generality, and adjudicates unambiguously in favour of the nominalist, at least as far as ex- planatory generality is concerned.
Keywords Indispensability  Mathematical explanation  Mathematical platonism  Mathematical realism  Explanatory indispensability  Cognitive salience
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DOI 10.1007/s10670-019-00146-x
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Abstract Objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
Platonic Relations and Mathematical Explanations.Robert Knowles - forthcoming - The Philosophical Quarterly.
Unification and Mathematical Explanation.Robert Knowles - forthcoming - Philosophical Studies.
An Extra-Mathematical Program Explanation of Color Experience.Nicholas Danne - 2021 - International Studies in the Philosophy of Science 33 (3):153-173.

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