Back to Search Start Over

Challenges Facing Counterfactual Accounts of Explanation in Mathematics

Authors :
Marc Lange
Source :
Philosophia Mathematica. 30:32-58
Publication Year :
2021
Publisher :
Oxford University Press (OUP), 2021.

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.

Details

ISSN :
17446406 and 00318019
Volume :
30
Database :
OpenAIRE
Journal :
Philosophia Mathematica
Accession number :
edsair.doi...........9a74a4690387c8a0d60967d994988171
Full Text :
https://doi.org/10.1093/philmat/nkab023