Explanatory Circles, Induction, and Recursive Structures

Wysocki, Tomasz

doi:10.1002/tht3.229

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2019

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“…For instance, the “downward and upward” proof is more disjunctive than the standard proof, and hence perhaps less explanatory. (For further criticism and discussion, see Baldwin, 2016; Dougherty, 2017; Hoelte, 2013; Lehet, 2019; Salvedra, 2018; Wysocki, 2017. )…”

Section: Particular Proof‐types: Exhaustion Induction Abstraction mentioning

confidence: 99%

Explanation in mathematics: Proofs and practice

D’Alessandro

2019

Philosophy Compass

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Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: What kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do they relate to the sorts of explanation encountered in philosophy of science and metaphysics?

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