Challenges Facing Counterfactual Accounts of Explanation in Mathematics. Issue 1 (21st September 2021)

• Record Type: Journal Article
• Authors: Lange, Marc
• Is Part Of: Philosophia Mathematica. Volume 30:Issue 1(2022)
• Page Start: 32
• Page End: 58
• Publication Date: 2021-09-21
• Subjects: Mathematics -- Philosophy -- Periodicals; Wiskunde; Filosofische aspecten; Mathematics -- Philosophy; Periodicals; 510.105
• DOI: 10.1093/philmat/nkab023
• Languages: English
• ISSNs: 0031-8019

Abstract

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.