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Mathematical Pictures

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Diagrammatic Representation and Inference (Diagrams 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10871))

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Abstract

There is still debate as to whether Euclidean diagrams are symbols, indexes or icons, and of what sort. I hold them to be pictorial icons that reproduce at least some visual features of their objects. This hypothesis has been directly challenged by Sherry [36] and Panza [29] among others. My aim on this paper is defending this thesis against Macbeth’s [24,25,26] claim that if diagrams were pictures their content could not shift the way it does in Euclidean proof. To this goal I will present a broadly Gricean account of pictorial representation, where visual resemblance constraints but no fully determines reference, and then show how this account ratifies Macbeth’s insights about the importance of the author’s intentions in determining a diagram’s content, in a way that allows for the sort of content-shifting that she has identified as key to understanding the role of diagrams in Euclidean proof.

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Acknowledgements

This research was possible thanks to funds from PAPIIT IG400718 “Medio y especie: ecología y evolución desde la filosofía natural” and to helpful input from the “Tecuemepe” research group.

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Authors and Affiliations

  1. Instituto de Investigaciones Filosóficas, UNAM, Mexico City, Mexico

    Axel Arturo Barceló Aspeitia

Authors
  1. Axel Arturo Barceló Aspeitia
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Correspondence to Axel Arturo Barceló Aspeitia .

Editor information

Editors and Affiliations

  1. Edinburgh Napier University, Edinburgh, UK

    Peter Chapman

  2. University of Brighton, Brighton, UK

    Gem Stapleton

  3. Tallinn University of Technology, Tallinn, Estonia

    Amirouche Moktefi

  4. Mitre Corporation, McLean, VA, USA

    Sarah Perez-Kriz

  5. University of Bologna, Bologna, Italy

    Francesco Bellucci

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Barceló Aspeitia, A.A. (2018). Mathematical Pictures. In: Chapman, P., Stapleton, G., Moktefi, A., Perez-Kriz, S., Bellucci, F. (eds) Diagrammatic Representation and Inference. Diagrams 2018. Lecture Notes in Computer Science(), vol 10871. Springer, Cham. https://doi.org/10.1007/978-3-319-91376-6_15

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  • DOI: https://doi.org/10.1007/978-3-319-91376-6_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91375-9

  • Online ISBN: 978-3-319-91376-6

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