Lange, Marc (2021) Challenges Facing Counterfactual Accounts of Explanation in Mathematics. [Preprint]

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Abstract

Some mathematical proofs explain why the theorems they prove hold. This paper identifies several challenges for any counterfactual account of explanation in mathematics (that is, any account according to which an explanatory proof reveals how the explanandum would have been different, had facts in the explanans been different). The paper presumes that countermathematicals can be nontrivial. It argues that nevertheless, a counterfactual account portrays explanatory power as too easy to achieve, does not capture explanatory asymmetry, and fails to specify why certain proofs are explanatory and others are not. Greater informativeness about counterfactual dependence can even yield less explanatory power.

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Item Type:	Preprint
Creators:	Creators Email ORCID Lange, Marc mlange@email.unc.edu
Keywords:	explanation, mathematics, unification, counterfactual, proof
Subjects:	Specific Sciences > Mathematics > Explanation Specific Sciences > Mathematics > Practice Specific Sciences > Mathematics > Proof Specific Sciences > Mathematics
Depositing User:	Prof. Marc Lange
Date Deposited:	06 Mar 2022 20:25
Last Modified:	06 Mar 2022 20:25
Item ID:	20234
Official URL:	https://doi.org/10.1093/philmat/nkab023
DOI or Unique Handle:	10.1093/philmat/nkab023
Subjects:	Specific Sciences > Mathematics > Explanation Specific Sciences > Mathematics > Practice Specific Sciences > Mathematics > Proof Specific Sciences > Mathematics
Date:	2021
URI:	https://philsci-archive.pitt.edu/id/eprint/20234

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