On an assumption of geometric foundation of numbers
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[1] Università degli studi di Napoli “Federico II
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[2] Università di Salerno
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- Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 47, Nº. 3, 2016, págs. 395-407
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
In line with the latest positions of Gottlob Frege, this article puts forward the hypothesis that the cognitive bases of mathematics are geometric in nature. Starting from the geometry axioms of the Elementsof Euclid, we introduce a geometric theory of proportions along the lines of the one introduced by Grassmann in Ausdehnungslehrein 1844. Assuming as axioms, the cognitive contents of the theorems of Pappus and Desargues, through their configurations, in an Euclidean plane a natural field structure can be identified that reveals the purely geometric nature of complex numbers. Reasoning based on figures is becoming a growing interdisciplinary field in logic, philosophy and cognitive sciences, and is also of considerable interest in the field of education, moreover, recently, it has been emphasized that the mutual assistance that geometry and complex numbers give is poorly pointed out in teaching and that a unitary vision of geometrical aspects and calculation can be clarifying.
