Comparing Mathematical Explanations

British Journal for the Philosophy of Science 74 (1):269-290 (2023)
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Philosophers have developed several detailed accounts of what makes some mathematical proofs explanatory. Significantly less attention has been paid, however, to what makes some proofs more explanatory than other proofs. That is problematic, since the reasons for thinking that some proofs explain are also reasons for thinking that some proofs are more explanatory than others. So in this paper, I develop an account of comparative explanation in mathematics. I propose a theory of the `at least as explanatory as' relation among mathematical proofs.



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Isaac Wilhelm
National University of Singapore

References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Counterfactuals.David Lewis - 1973 - Philosophy of Science 42 (3):341-344.
Studies in the logic of explanation.Carl Gustav Hempel & Paul Oppenheim - 1948 - Philosophy of Science 15 (2):135-175.
Studies in the Logic of Explanation.Carl Hempel & Paul Oppenheim - 1948 - Journal of Symbolic Logic 14 (2):133-133.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.

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