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On the representational role of Euclidean diagrams: representing qua samples

Dal Magro, Tamires and Valente, Matheus (2020) On the representational role of Euclidean diagrams: representing qua samples. [Preprint]

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Abstract

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 – (i) that Euclidean diagrams are used in proofs whose results are wholly general, (ii) that Euclidean diagrams indicate the co-exact features that the geometer is allowed to infer from them and (iii) that Euclidean diagrams play the same role in both direct proofs and indirect proofs by reductio – and argue that our view is the one best suited to account for them. We conclude by illustrating the virtues of our conception of Euclidean diagrams as samples by means of an analysis of Saccheri’s quadrilateral.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Dal Magro, Tamirestamiresdma@gmail.com0000-0001-7423-9223
Valente, Matheusmatheusvalenteleite@gmail.com0000-0001-6380-2623
Additional Information: Forthcoming in Synthese.
Keywords: Euclidean diagrams; reductio ad absurdum; co-exact information; iconicity; samples
Subjects: Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics
Depositing User: Dr. Matheus Valente
Date Deposited: 07 Nov 2020 18:22
Last Modified: 07 Nov 2020 18:22
Item ID: 18362
Subjects: Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics
Date: 2020
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/18362

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