Keywords
history
philosophy
non-Euclidean geometries
epistemology
How to Cite
Abstract
The path followed to construct a theoretical science, from Euclid to Hilbert, is described. The Aristotelian philosophical intentions to build demostrative sciences, lead necessarily to the exploration of propositions as building blocks of an axiomatic system for geometry, which in turn allowed mathematicians pass from ontological aspects to logical ones. In this process, the attempts to prove the Fifth Postulate of Euclidean geometry, had a crucial role since at the end they lead from "Euclidean truth" to "Hilbertian consistency".
References
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Whiteside, T., Mathematical Papers of I. Newton, Cambridge University Press, 1967.
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Lobachévsky, Nuovi Principii della Geometría, Lombardo-Radice (ed.), Boringhieri, 1974.
Torretti, R., Philosophy of Geometry from Riemann to Poincaré, Reidel, 1978.
Piaget, J., & García, R., Psicogénesis e Historia de la Ciencia, Siglo XXI, 1982.
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