Abstract
Mathematicians use diagrams in their work all the time, whether they want to make use of Euclid’s fifth postulate, to prove Fermat’s principle, or to extract an algorithm that defines the seemingly chaotic movement of pigeons picking bread crumps from the ground. Using diagrams helps mathematicians identify patterns that solve particular mathematical problems by making the force of necessary reasoning visually given. A mathematical diagram, a paradigmatic use of which is exemplified in Euclid’s Elements, is an individual image that instantiates necessary relations. As an observable entity, it allows a mathematician to experiment upon it and to visually demonstrate the necessity of a given conclusion. At the same time, it represents an abstract mathematical object. We do not use diagrams simply to facilitate our reasoning and then translate those diagrams into a formal calculus in order to make inferences. Diagrams themselves are immediate visualizations of the deductive process as such. The necessary character of deductive arguments is thus internal to the diagrams mathematicians construct (Sloman 2002).
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Kiryushchenko, V. (2019). Diagrams in Mathematics: On Visual Experience in Peirce. In: Danesi, M. (eds) Interdisciplinary Perspectives on Math Cognition. Mathematics in Mind. Springer, Cham. https://doi.org/10.1007/978-3-030-22537-7_8
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