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  1. What are mathematical diagrams?Silvia De Toffoli - 2022 - Synthese 200 (2):1-29.
    Although traditionally neglected, mathematical diagrams have recently begun to attract attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and justification. Certain preliminary questions have, however, been mostly bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term “mathematical diagram” is used in diverse ways. I propose a working definition that carves out the phenomena that are of most importance for a (...)
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  • What mathematical explanation need not be.Elijah Chudnoff & Silvia De Toffoli - 2025 - Journal of Mathematical Behavior 79 (101255):1-12.
    Recent works in the philosophy of mathematical practice and mathematical education have challenged orthodox views of mathematical explanation by developing Understanding-first accounts according to which mathematical explanation should be cashed out in terms of understanding. In this article, we explore two arguments that might have motivated this move, (i) the context-sensitivity argument and (ii) the inadequacy of knowing why argument. We show that although these arguments are derived from compelling observations, they ultimately rest on a misunderstanding of what Explanation-first accounts (...)
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  • The Role of Gestures in Logic.Andrea Reichenberger, Jens Lemanski & Reetu Bhattacharjee - forthcoming - Multimodal Communication.
    Gestures are usually regarded as a casual element of communication processes between logicians. By contrast, we aim to show that gestures have played a significant role in logic. We argue that the development of communication techniques and their standardization have led to the rise of formal notation systems commonly used in logic today. In order to substantiate this claim, the historical development of the use of gestures in (early) modern logic is investigated. This investigation uncovers exemplary communication and proof techniques (...)
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  • The Epistemological Subject(s) of Mathematics.Silvia De Toffoli - 2024 - In Bharath Sriraman, Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer. pp. 2880-2904.
    Paying attention to the inner workings of mathematicians has led to a proliferation of new themes in the philosophy of mathematics. Several of these have to do with epistemology. Philosophers of mathematical practice, however, have not (yet) systematically engaged with general (analytic) epistemology. To be sure, there are some exceptions, but they are few and far between. In this chapter, I offer an explanation of why this might be the case and show how the situation could be remedied. I contend (...)
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  • The Epistemic Roles of Diagrams.Silvia De Toffoli - forthcoming - In Kurt Sylvan, Ernest Sosa, Jonathan Dancy & Matthias Steup, The Blackwell Companion to Epistemology, 3rd edition. Wiley Blackwell.
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