A Quasi-Interventionist Theory Of Mathematical Explanation

Victor Gijsbers

Abstract


Explanations in mathematics are not yet well understood. I discuss Steiner’s theory of mathematical explanation, then attempt to improve it by assimilating its core intuitions to Woodward’s counterfactual theory of explanation. The theory that results deals successfully with many cases, but it fails to handle certain types of explanatory asymmetry. To  fix this, I draw on Woodward’s interventionist theory of causation and develop a quasi-interventionist theory of mathematical explanation. According to this theory, the asymmetry of mathematical explanations is subjective in the sense that it does not depend on the objective structure of mathematics itself; but I argue that this is not a problem, since the same subjectivity can be found in causal explanation.


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