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Mathematical counterfactuals with number-theoretic antecedents and extra-mathematical explanation

Tump, Lars Arthur (2021) Mathematical counterfactuals with number-theoretic antecedents and extra-mathematical explanation. [Preprint]

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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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Item Type: Preprint
Creators:
CreatorsEmailORCID
Tump, Lars Arthurlarsarthur.tump@kuleuven.be0000-0002-2790-3045
Additional Information: Accepted by Logique & Analyse
Keywords: mathematical explanation; counterfactual theory of explanation; empirical phenomena; Peano numerals; number-theory; counterpossibles
Subjects: Specific Sciences > Mathematics > Ontology
Depositing User: Dr. Lars Arthur Tump
Date Deposited: 28 Sep 2021 15:26
Last Modified: 28 Sep 2021 15:26
Item ID: 19619
Subjects: Specific Sciences > Mathematics > Ontology
Date: 2021
URI: http://philsci-archive.pitt.edu/id/eprint/19619

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