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".
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References
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