Mathematics and Explanatory Generality: Nothing but Cognitive Salience

Erkenntnis 86 (5):1119-1137 (2021)
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Abstract

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 explanatory generality is concerned.

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Author Profiles

Robert Knowles
Swansea University
Juha Saatsi
University of Leeds

Citations of this work

Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
An Extra-Mathematical Program Explanation of Color Experience.Nicholas Danne - 2020 - International Studies in the Philosophy of Science 33 (3):153-173.
Unification and mathematical explanation.Robert Knowles - 2021 - Philosophical Studies 178 (12):3923-3943.

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References found in this work

Explanatory Abstractions.Lina Jansson & Juha Saatsi - 2019 - British Journal for the Philosophy of Science 70 (3):817–844.
What Makes a Scientific Explanation Distinctively Mathematical?Marc Lange - 2013 - British Journal for the Philosophy of Science 64 (3):485-511.

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