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Title: Mathematical Counterfactuals with Number-Theoretic Antecedents and Extra-Mathematical Explanation
Author(s): TUMP, Lars Arthur
Journal: Logique et Analyse
Volume: 254    Date: 2021   
Pages: 191-213
DOI: 10.2143/LEA.254.0.3289657

Abstract :
A proposal by Baron, Colyvan, and Ripley to extend the counterfactual theory of explanation to include counterfactual reasoning about mathematical explanations of physical facts is discussed. Their suggestion is that the explanatory role of mathematics can best be captured counterfactually. This paper focuses on their example with a number-theoretic antecedent. Incorporating discussions on the structure and de re knowledge of numbers, it is argued that the approach leads to a change in the structure of numbers. As a result, the counterfactual is not about the natural numbers anymore. Linking the antecedent and consequent of the counterfactual also becomes problematic.

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