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  1. Proving Quadratic Reciprocity: Explanation, Disagreement, Transparency and Depth.William D’Alessandro - 2020 - Synthese (9):1-44.
    Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...)
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  • Explanatory Priority Monism.Isaac Wilhelm - 2021 - Philosophical Studies 178 (4):1339-1359.
    Explanations are backed by many different relations: causation, grounding, and arguably others too. But why are these different relations capable of backing explanations? In virtue of what are they explanatory? In this paper, I propose and defend a monistic account of explanation-backing relations. On my account, there is a single relation which backs all cases of explanation, and which explains why those other relations are explanation-backing.
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  • Interview with Paul Égré.Lina M. Lissia - 2021 - The Reasoner 15 (1):1-3.
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  • Explanation in Mathematics: Proofs and Practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11).
    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 (...)
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