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  1. Platonism and Intra-mathematical Explanation.Sam Baron - forthcoming - Philosophical Quarterly.
    I introduce an argument for Platonism based on intra-mathematical explanation: the explanation of one mathematical fact by another. The argument is important for two reasons. First, if the argument succeeds then it provides a basis for Platonism that does not proceed via standard indispensability considerations. Second, if the argument fails it can only do so for one of three reasons: either because there are no intra-mathematical explanations, or because not all explanations are backed by dependence relations, or because some form (...)
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  • Do Mathematicians Agree about Mathematical Beauty?Rentuya Sa, Lara Alcock, Matthew Inglis & Fenner Stanley Tanswell - 2024 - Review of Philosophy and Psychology 15 (1):299-325.
    Mathematicians often conduct aesthetic judgements to evaluate mathematical objects such as equations or proofs. But is there a consensus about which mathematical objects are beautiful? We used a comparative judgement technique to measure aesthetic intuitions among British mathematicians, Chinese mathematicians, and British mathematics undergraduates, with the aim of assessing whether judgements of mathematical beauty are influenced by cultural differences or levels of expertise. We found aesthetic agreement both within and across these demographic groups. We conclude that judgements of mathematical beauty (...)
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  • A Noetic Account of Explanation in Mathematics.William D’Alessandro & Ellen Lehet - forthcoming - Philosophical Quarterly.
    We defend a noetic account of intramathematical explanation. On this view, a piece of mathematics is explanatory just in case it produces understanding of an appropriate type. We motivate the view by presenting some appealing features of noeticism. We then discuss and criticize the most prominent extant version of noeticism, due to Inglis and Mejía Ramos, which identifies explanatory understanding with the possession of well-organized cognitive schemas. Finally, we present a novel noetic account. On our view, explanatory understanding arises from (...)
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