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Intuición y método axiomático en la concepción temprana de la geometría de David Hilbert

Keywords: hilbert, axiomatic method, geometry, early view, intuition.

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Abstract:

the paper discusses hilbert's early axiomatic approach to geometry, particularly his notes for lecture courses between 1891 and 1905 are analyzed. it is argued that, although hilbert privileged from early on an abstract axiomatic presentation of geometry, he also maintained in this early period more traditional theses, like the claim that geometry is the most perfect of all natural sciences, which deals with the properties or shapes of things in space. among these, at a first glance, contradictory theses, hilbert also stresses throughout the lecture courses the importance of "spatial" or "geometrical" intuition for the axiomatization of geometry. the role and notion of spatial intuition in hilbert's early axiomatic approach are discussed. finally, this emphasis on the notion of intuition will be used to criticize the standard, formalist view of hilbert's axiomatic approach to geometry, which will be considered as misleading, or at least inadequate, when his notes for lectures courses are taken into account.

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