Explanation by induction?

Abstract

Philosophers of mathematics commonly distinguish between explanatory and non-explanatory proofs. An important subclass of mathematical proofs are proofs by induction. Are they explanatory? This paper addresses the question, based on general principles about explanation. First, a recent argument for a negative answer is discussed and rebutted. Second, a case is made for a qualified positive take on the issue.

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Correspondence to Benjamin Schnieder.

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Hoeltje, M., Schnieder, B. & Steinberg, A. Explanation by induction?. Synthese 190, 509–524 (2013). https://doi.org/10.1007/s11229-011-0045-z

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Keywords

  • Mathematical induction
  • Mathematical explanation
  • Logic of explanation
  • Grounding