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Document Details : 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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