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  1. Mathematicians’ Assessments of the Explanatory Value of Proofs.Juan Pablo Mejía Ramos, Tanya Evans, Colin Rittberg & Matthew Inglis - forthcoming - Axiomathes:1-25.
    The literature on mathematical explanation contains numerous examples of explanatory, and not so explanatory proofs. In this paper we report results of an empirical study aimed at investigating mathematicians’ notion of explanatoriness, and its relationship to accounts of mathematical explanation. Using a Comparative Judgement approach, we asked 38 mathematicians to assess the explanatory value of several proofs of the same proposition. We found an extremely high level of agreement among mathematicians, and some inconsistencies between their assessments and claims in the (...)
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  • The Mark of Understanding: In Defense of an Ability Account.Sven Delarivière & Bart Van Kerkhove - forthcoming - Axiomathes:1-30.
    Understanding is a valued trait in any epistemic practice, scientific or not. Yet, when it comes to characterizing its nature, the notion has not received the philosophical attention it deserves. We have set ourselves three tasks in this paper. First, we defend the importance of this endeavor. Second, we consider and criticize a number of proposals to this effect. Third, we defend an alternative account, focusing on abilities as the proper mark of understanding.
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  • Unificatory Understanding and Explanatory Proofs.Joachim Frans - forthcoming - Foundations of Science:1-23.
    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: understanding is a condition for (...)
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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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