Completeness and continuity in Hilbert's foundations of geometry: On the Vollständigkeitsaxiom

Citation data:

Theoria (Spain), ISSN: 0495-4548, Vol: 28, Issue: 1, Page: 139-163

Publication Year:
Usage 691
Downloads 542
Abstract Views 84
HTML Views 32
PDF Views 30
Link-outs 3
Captures 11
Exports-Saves 9
Readers 2
Repository URL:
Eduardo Nicolás Giovannini
Euskal Herriko Unibertsitatea / Universidad del País Vasco
Arts and Humanities
article description
The paper reports and analyzes the vicissitudes around Hilbert's inclusion of his famous axiom of completeness, into his axiomatic system for Euclidean geometry. This task is undertaken on the basis of his unpublished notes for lecture courses, corresponding to the period 1894-1905. It is argued that this historical and conceptual analysis not only sheds new light on how Hilbert conceived originally the nature of his geometrical axiom of completeness, but also it allows to clarify some misunderstandings regarding this axiom and the metalogical property of completeness of an axiomatic system, as it was understood by Hilbert in this initial stage.

This article has 0 Wikipedia mention.