Dal Magro, Tamires and Valente, Matheus (2020) On the representational role of Euclidean diagrams: representing qua samples. [Preprint]
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Tamires Dal Magro & Matheus Valente - On the representational role of Euclidean diagrams - representing qua sample.docx - Accepted Version Download (188kB) |
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 | |||||||||
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| Additional Information: | Forthcoming in Synthese. | |||||||||
| Keywords: | Euclidean diagrams; reductio ad absurdum; co-exact information; iconicity; samples | |||||||||
| Subjects: | Specific Sciences > Mathematics > Practice Specific Sciences > Mathematics |
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| 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 |
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| Date: | 2020 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/18362 |
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