Bridging the gap between analytic and synthetic geometry: Hilbert's axiomatic approach

DOI10.1007/s11229-015-0743-zzbMath1384.03007OpenAlexW2048540134MaRDI QIDQ514037

Eduardo N. Giovannini

Publication date: 8 March 2017

Published in: Synthese (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11229-015-0743-z

zbMATH Keywords

continuityHilbertEuclidean geometryaxiomatic methodarithmetization

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) History of mathematical logic and foundations (03-03) History of mathematics in the 19th century (01A55) Euclidean geometries (general) and generalizations (51M05)

Related Items (5)

H.S.M. Coxeter's theory of accessibility: from Mario Pieri to Marvin Greenberg ⋮ A competent translation/a pitiful bungle: \textit{The foundations of geometry} ⋮ HILBERT, DUALITY, AND THE GEOMETRICAL ROOTS OF MODEL THEORY ⋮ Unnamed Item ⋮ David Hilbert and the foundations of the theory of plane area

Cites Work

• Local axioms in disguise: Hilbert on Minkowski diagrams
• Geometry and arithmetic in the medieval traditions of Euclid's \textit{Elements}: a view from Book II
• Rethinking geometrical exactness
• von Staudt`s theory of ``Würfe`` (jets) -- an irruption of algebra in pure geometry
• The fundamental theorem of projective geometry: evolution of its proof between 1847 and 1900
• Hilbert, logicism, and mathematical existence
• Mechanism, mentalism, and metamathematics. An essay on finitism
• Von Pasch zu Hilbert
• From completeness to Archimedean completeness. An essay in the foundations of Euclidean geometry
• David Hilbert and the axiomatization of physics (1898--1918). From Grundlagen der Geometrie to Grundlagen der Physik.
• ON THE RELATIONSHIP BETWEEN PLANE AND SOLID GEOMETRY
• David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933
• PASCH’S PHILOSOPHY OF MATHEMATICS
• Euclidean and Non-Euclidean Geometries Without Continuity
• ‘Metamathematics’ in Transition
• FORMALIZATION, PRIMITIVE CONCEPTS, AND PURITY
• Axiomatizing Changing Conceptions of the Geometric Continuum I: Euclid-Hilbert†
• DAVID HILBERT. David Hilbert's lectures on the foundations of geometry, 1891-1902. Michael Hallett and Ulrich Majer, eds. David Hilbert's Foundational Lectures; 1. Berlin: Springer-Verlag, 2004. ISBN 3-540-64373-7. Pp. xxviii + 661
• Worlds Out of Nothing
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Bridging the gap between analytic and synthetic geometry: Hilbert's axiomatic approach