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Interdisciplinary Perspectives on Math CognitionDiagrams in Mathematics: On Visual Experience in Peirce

Interdisciplinary Perspectives on Math Cognition: Diagrams in Mathematics: On Visual Experience... [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).] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Interdisciplinary Perspectives on Math CognitionDiagrams in Mathematics: On Visual Experience in Peirce

Part of the Mathematics in Mind Book Series
Editors: Danesi, Marcel
Kiryushchenko, Vitaly
Interdisciplinary Perspectives on Math Cognition — Sep 15, 2019
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References (27)

Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2019
ISBN
978-3-030-22536-0
Pages
155 –169
DOI
10.1007/978-3-030-22537-7_8
Publisher site
See Chapter on Publisher Site

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).]

Published: Sep 15, 2019

Keywords: Signs; Diagrams; Existential graphs; Iconicity; Habitual action; Continuity; Dynamic totality

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