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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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  • The role of syntactic representations in set theory.Keith Weber - 2019 - Synthese 198 (Suppl 26):6393-6412.
    In this paper, we explore the role of syntactic representations in set theory. We highlight a common inferential scheme in set theory, which we call the Syntactic Representation Inferential Scheme, in which the set theorist infers information about a concept based on the way that concept can be represented syntactically. However, the actual syntactic representation is only indicated, not explicitly provided. We consider this phenomenon in relation to the derivation indicator position that asserts that the ordinary proofs given in mathematical (...)
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  • Rigour and Intuition.Oliver Tatton-Brown - 2019 - Erkenntnis 86 (6):1757-1781.
    This paper sketches an account of the standard of acceptable proof in mathematics—rigour—arguing that the key requirement of rigour in mathematics is that nontrivial inferences be provable in greater detail. This account is contrasted with a recent perspective put forward by De Toffoli and Giardino, who base their claims on a case study of an argument from knot theory. I argue that De Toffoli and Giardino’s conclusions are not supported by the case study they present, which instead is a very (...)
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  • Rigour and Proof.Oliver Tatton-Brown - 2023 - Review of Symbolic Logic 16 (2):480-508.
    This paper puts forward a new account of rigorous mathematical proof and its epistemology. One novel feature is a focus on how the skill of reading and writing valid proofs is learnt, as a way of understanding what validity itself amounts to. The account is used to address two current questions in the literature: that of how mathematicians are so good at resolving disputes about validity, and that of whether rigorous proofs are necessarily formalizable.
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  • On the Contemporary Practice of Philosophy of Mathematics.Colin Jakob Rittberg - 2019 - Acta Baltica Historiae Et Philosophiae Scientiarum 7 (1):5-26.
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  • On the unreasonable reliability of mathematical inference.Brendan Philip Larvor - 2022 - Synthese 200 (4):1-16.
    In, Jeremy Avigad makes a novel and insightful argument, which he presents as part of a defence of the ‘Standard View’ about the relationship between informal mathematical proofs and their corresponding formal derivations. His argument considers the various strategies by means of which mathematicians can write informal proofs that meet mathematical standards of rigour, in spite of the prodigious length, complexity and conceptual difficulty that some proofs exhibit. He takes it that showing that and how such strategies work is a (...)
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  • The material reasoning of folding paper.Michael Friedman & Colin Jakob Rittberg - 2021 - Synthese 198 (S26):6333-6367.
    This paper inquires the ways in which paper folding constitutes a mathematical practice and may prompt a mathematical culture. To do this, we first present and investigate the common mathematical activities shared by this culture, i.e. we present mathematical paper folding as a material reasoning practice. We show that the patterns of mathematical activity observed in mathematical paper folding are, at least since the end of the nineteenth century, sufficiently stable to be considered as a practice. Moreover, we will argue (...)
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  • On fluidity of the textual transmission in Abraham bar Hiyya’s Ḥibbur ha-Meshiḥah ve-ha-Tishboret.Michael Friedman & David Garber - 2022 - Archive for History of Exact Sciences 77 (2):123-174.
    We examine one of the well-known mathematical works of Abraham bar Ḥiyya: Ḥibbur ha-Meshiḥah ve-ha-Tishboret, written between 1116 and 1145, which is one of the first extant mathematical manuscripts in Hebrew. In the secondary literature about this work, two main theses have been presented: the first is that one Urtext exists; the second is that two recensions were written—a shorter, more practical one, and a longer, more scientific one. Critically comparing the eight known copies of the Ḥibbur, we show that (...)
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  • Who's Afraid of Mathematical Diagrams?Silvia De Toffoli - 2023 - Philosophers' Imprint 23 (1).
    Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show that (...)
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