Unificatory Understanding and Explanatory Proofs

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One of the central aims of the philosophical analysis of mathematical explanation is to determine how one can distinguish explanatory proofs from non-explanatory proofs. In this paper, I take a closer look at the current status of the debate, and what the challenges for the philosophical analysis of explanatory proofs are. In order to provide an answer to these challenges, I suggest we start from analysing the concept understanding. More precisely, I will defend four claims: (1) understanding is a condition for explanation, (2) unificatory understanding is a type of explanatory understanding, (3) unificatory understanding is valuable in mathematics, and (4) mathematical proofs can contribute to unificatory understanding. As a result, in a context where the epistemic aim is to unify mathematical results, I argue it is fruitful to make a distinction between proofs based on their explanatory value.
Original languageEnglish
Pages (from-to)1105-1127
Number of pages23
JournalFoundations of Science
Early online date28 Feb 2020
Publication statusPublished - 2 Nov 2021


  • Mathematical explanation
  • Understanding
  • Unification
  • Mathematical proof


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