Hilbert's Synthesis on Foundation of Geometry

Andrea Battocchio
2019 Journal of Humanities and Education Development  
The relations between intuition, axiomatic method and formalism in Hilbert's foundational studies has been discussed several times, but geometrical ones still have unclear sides and there is not a commonly held opinion. In this article we try to frame Hilbert's geometrical works within a historical context. The aim is to show that intuition and nature of the axioms in Grundlagen der Geometrie do not derive from a mature philosophical awareness of the author, but from the development of a
more » ... cal path of the idea of geometry and of its foundations. The path begins with the discovery of non-Euclidean geometry and finds in Hilbert's work its final and definitive synthesis for Euclidean geometry.
doi:10.22161/jhed.1.6.3 fatcat:ykinzi2i75bbvkh3uv2rvglvl4