On the representational role of Euclidean diagrams: representing qua samples
| Autor: | Matheus Valente, Tamires Dal Magro |
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| Rok vydání: | 2021 |
| Předmět: |
Philosophy of science
Quadrilateral 05 social sciences General Social Sciences Metaphysics Contrast (statistics) 06 humanities and the arts 0603 philosophy ethics and religion Mathematical proof 050105 experimental psychology Philosophy of language Algebra Philosophy Diagrammatic reasoning 060302 philosophy Euclidean geometry Mathematics::Metric Geometry 0501 psychology and cognitive sciences Mathematics |
| Zdroj: | Synthese. 199:3739-3760 |
| ISSN: | 1573-0964 0039-7857 |
| DOI: | 10.1007/s11229-020-02953-0 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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