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  1. Truth diagrams for some non-classical and modal logics.Can Başkent - 2024 - Journal of Applied Non-Classical Logics 34 (4):527-560.
    This paper examines truth diagrams for some non-classical, modal and dynamic logics. Truth diagrams are diagrammatic and visual ways to represent logical truth akin to truth tables, developed by Peter C.-H. Cheng. Currently, it is only given for classical propositional logic. In this paper, we establish truth diagrams for Priest's Logic of Paradox, Belnap–Dunn's Four-Valued Logic, MacColl's Connexive Logic, Bochvar–Halldén's Logic of Non-Sense, Carnielli–Coniglio's logic of formal inconsistency as well as classical modal logic and its dynamic extension to shed light (...)
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  • The Epistemological Subject(s) of Mathematics.Silvia De Toffoli - 2024 - In Bharath Sriraman (ed.), 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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  • On the heuristic power of mathematical representations.Emiliano Ippoliti - 2022 - Synthese 200 (5):1-28.
    I argue that mathematical representations can have heuristic power since their construction can be ampliative. To this end, I examine how a representation introduces elements and properties into the represented object that it does not contain at the beginning of its construction, and how it guides the manipulations of the represented object in ways that restructure its components by gradually adding new pieces of information to produce a hypothesis in order to solve a problem.In addition, I defend an ‘inferential’ approach (...)
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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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  • 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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  • Virtue theory of mathematical practices: an introduction.Andrew Aberdein, Colin Jakob Rittberg & Fenner Stanley Tanswell - 2021 - Synthese 199 (3-4):10167-10180.
    Until recently, discussion of virtues in the philosophy of mathematics has been fleeting and fragmentary at best. But in the last few years this has begun to change. As virtue theory has grown ever more influential, not just in ethics where virtues may seem most at home, but particularly in epistemology and the philosophy of science, some philosophers have sought to push virtues out into unexpected areas, including mathematics and its philosophy. But there are some mathematicians already there, ready to (...)
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  • On the representational role of Euclidean diagrams: representing qua samples.Tamires Dal Magro & Matheus Valente - 2021 - Synthese 199 (1-2):3739-3760.
    We advance a theory of the representational role of Euclidean diagrams according to which they are samples of co-exact features. We contrast our theory with two other conceptions, the instantial conception and Macbeth’s iconic view, with respect to how well they accommodate three fundamental constraints on theories of the Euclidean diagrammatic practice— that Euclidean diagrams are used in proofs whose results are wholly general, that Euclidean diagrams indicate the co-exact features that the geometer is allowed to infer from them and (...)
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  • A fresh look at research strategies in computational cognitive science: The case of enculturated mathematical problem solving.Regina E. Fabry & Markus Pantsar - 2019 - Synthese 198 (4):3221-3263.
    Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies methods from (...)
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  • Truth diagrams for some non-classical and modal logics.Can Başkent - 2024 - Journal of Applied Non-Classical Logics 34 (4).
    This paper examines truth diagrams for some non-classical, modal and dynamic logics. Truth diagrams are diagrammatic and visual ways to represent logical truth akin to truth tables, developed by Peter C.-H. Cheng. Currently, it is only given for classical propositional logic. In this paper, we establish truth diagrams for Priest's Logic of Paradox, Belnap–Dunn's Four-Valued Logic, MacColl's Connexive Logic, Bochvar–Halldén's Logic of Non-Sense, Carnielli–Coniglio's logic of formal inconsistency as well as classical modal logic and its dynamic extension to shed light (...)
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  • Diagrams in Mathematics.Carlo Cellucci - 2019 - Foundations of Science 24 (3):583-604.
    In the last few decades there has been a revival of interest in diagrams in mathematics. But the revival, at least at its origin, has been motivated by adherence to the view that the method of mathematics is the axiomatic method, and specifically by the attempt to fit diagrams into the axiomatic method, translating particular diagrams into statements and inference rules of a formal system. This approach does not deal with diagrams qua diagrams, and is incapable of accounting for the (...)
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  • Textual materiality and abstraction in mathematics.Anna Kiel Steensen, Mikkel Willum Johansen & Morten Misfeldt - 2022 - Science in Context 35 (1):81-101.
    In this paper, we wish to explore the role that textual representations play in the creation of new mathematical objects. We do so by analyzing texts by Joseph-Louis Lagrange (1736–1813) and Évariste Galois (1811–1832), which are seen as central to the historical development of the mathematical concept of groups. In our analysis, we consider how the material features of representations relate to the changes in conceptualization that we see in the texts.Against this backdrop, we discuss the idea that new mathematical (...)
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  • Truth diagrams for some non-classical and modal logics.Can Başkent - 2024 - Journal of Applied Non-Classical Logics 34 (4):527-560.
    This paper examines truth diagrams for some non-classical, modal and dynamic logics. Truth diagrams are diagrammatic and visual ways to represent logical truth akin to truth tables, developed by Peter C.-H. Cheng. Currently, it is only given for classical propositional logic. In this paper, we establish truth diagrams for Priest's Logic of Paradox, Belnap–Dunn's Four-Valued Logic, MacColl's Connexive Logic, Bochvar–Halldén's Logic of Non-Sense, Carnielli–Coniglio's logic of formal inconsistency as well as classical modal logic and its dynamic extension to shed light (...)
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  • The Logos Categorical Approach to QM: II. Quantum Superpositions.Christian de Ronde & Cesar Massri - unknown
    In this paper we attempt to consider quantum superpositions from the perspective of the logos categorical approach presented in [26]. We will argue that our approach allows us not only to better visualize the structural features of quantum superpositions providing an anschaulich content to all terms, but also to restore —through the intensive valuation of graphs and the notion of immanent power— an objective representation of what QM is really talking about. In particular, we will discuss how superpositions relate to (...)
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