Dal Magro, Tamires and García-Pérez, Manuel J. (2019) On Euclidean diagrams and geometrical knowledge. THEORIA. An International Journal for Theory, History and Foundations of Science, 34 (2). pp. 255-276. ISSN 2171-679X
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Abstract
We argue against the claim that the employment of diagrams in Euclidean geometry gives rise to gaps in the proofs. First, we argue that it is a mistake to evaluate its merits through the lenses of Hilbert’s formal reconstruction. Second, we elucidate the abilities employed in diagram-based inferences in the Elements and show that diagrams are mathematically reputable tools. Finally, we complement our analysis with a review of recent experimental results purporting to show that, not only is the Euclidean diagram-based practice strictly regimented, it is rooted in cognitive abilities that are universally shared.
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