Giovannini, Eduardo N.
(2013)
Completitud y continuidad en Fundamentos de la geometría
de Hilbert: acerca del Vollständigkeitsaxiom
(Completeness and Continuity in Hilbert’s Foundations of Geometry: on the Vollständigkeitsaxiom).
THEORIA. An International Journal for Theory, History and Foundations of Science, 28 (1).
pp. 139-163.
ISSN 2171-679X
Abstract
El artículo documenta y analiza las vicisitudes en torno a la incorporación de Hilbert de su famoso axioma de completitud, en el sistema axiomático para la geometría euclídea. Esta tarea es emprendida sobre la base del material que aportan sus notas manuscritas para clases, correspondientes al período 1894–1905. Se argumenta que este análisis histórico y conceptual no sólo permite ganar claridad respecto de cómo Hilbert concibió originalmente la naturaleza y función del axioma de completitud en su versión geométrica, sino que además permite disipar equívocos en cuanto a la relación de este axioma con la propiedad metalógica de completitud de un sistema axiomático, tal como fue concebida por Hilbert en esta etapa inicial.
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 This task is undertaken on the basis of his unpublished notes for lecture courses, corresponding to the period 1894–1905.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.
| Item Type: |
Published Article or Volume
|
| Creators: |
| Creators | Email | ORCID  |
|---|
| Giovannini, Eduardo N. | | |
|
| Additional Information: |
ISSN: 0495-4548 (print) |
| Keywords: |
Hilbert, geometría euclídea, axioma de completitud, axiomas de continuidad, método axiomático, filosofía de la geometría; Euclidean geometry, axiom of completeness, continuity axioms, axiomatic method, philosophy of geometry |
| Depositing User: |
Users 15304 not found. |
| Date Deposited: |
09 Jan 2014 21:12 |
| Last Modified: |
09 Jan 2014 21:12 |
| Item ID: |
10192 |
| Journal or Publication Title: |
THEORIA. An International Journal for Theory, History and Foundations of Science |
| Publisher: |
Euskal Herriko Unibertsitatea / Universidad del País Vasco |
| Official URL: |
http://www.ehu.es/ojs/index.php/THEORIA/article/vi... |
| DOI or Unique Handle: |
10.1387/theoria.4544 |
| Date: |
February 2013 |
| Page Range: |
pp. 139-163 |
| Volume: |
28 |
| Number: |
1 |
| ISSN: |
2171-679X |
| URI: |
https://philsci-archive.pitt.edu/id/eprint/10192 |
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