Hilbert's Early Views on Completeness, Categoricity, and ?maximal models

GIOVANNINI, EDUARDO N.; SCHIEMER, GEORG

Prague (Virtual)

Workshop; International Workshop: Intuition and rigor in geometrical thinking from Antiquity to the 19th century.; 2020

Institute of Philosophy of the Czech Academy of Sciences

The aim of this talk is to present a historical analysis and a systematic assessment of Hilbert?s famous ?axiom of completeness? for Euclidean geometry and analysis. This task will be undertaken on the basis of a series of unpublished notes for lecture courses, corresponding to the period 1894?1905. I will argue that this historical and conceptual analysis not only sheds new light on how Hilbert originally conceived the nature of his axiom of completeness, but also it proves relevant for a better understanding of the relation between the axiom and several notions of ?completeness? of an axiomatic system.