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Formalization of Hilbert's geometry of incidence and parallelism

Jan von Plato

Synthese 110 (1):127-141 (1997)

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Constructive geometrical reasoning and diagrams.John Mumma - 2012 - Synthese 186 (1):103-119.details Modern formal accounts of the constructive nature of elementary geometry do not aim to capture the intuitive or concrete character of geometrical construction. In line with the general abstract approach of modern axiomatics, nothing is presumed of the objects that a geometric construction produces. This study explores the possibility of a formal account of geometric construction where the basic geometric objects are understood from the outset to possess certain spatial properties. The discussion is centered around Eu , a recently developed (...) Download Export citation Bookmark 7 citations
On the meaning of Hilbert's consistency problem (paris, 1900).Enrico Moriconi - 2003 - Synthese 137 (1-2):129 - 139.details The theory that ``consistency implies existence'' was put forward by Hilbert on various occasions around the start of the last century, and it was strongly and explicitly emphasized in his correspondence with Frege. Since (Gödel's) completeness theorem, abstractly speaking, forms the basis of this theory, it has become common practice to assume that Hilbert took for granted the semantic completeness of second order logic. In this paper I maintain that this widely held view is untrue to the facts, and that (...) Download Export citation Bookmark 1 citation

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