A note on the introduction of Hilbert’s Grundlagen der Geometrie

Autores

  • Giorgio Venturi Universidade Estadual de Campinas

Palavras-chave:

Hilbert. Geometry. Independence. Simplicity. Grundlagen der Geometrie.

Resumo

We present and discuss a change in the introduction of Hilbert’s Grundl agender Geometrie between the first and the subsequente ditions: the disappearance of the reference to the independence of the axioms. We briefly outline the theoretical relevance of the notion of independence in Hilbert’s work and we suggest that a possible reason for this disappearance is the discovery that Hilbert’s axioms were not, in fact, independent. In the end we show how this change gives textual evidence for the connection between the notions of independence and simplicity.

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Biografia do Autor

Giorgio Venturi, Universidade Estadual de Campinas

Bachelor degree in philosophy from from the Università degli Studi di Torino (2005), bachelor in mathemaitcs from the Università degli Studi di Torino (2007) and master in mathematics from Università degli Studi di Torino (2009). PhD thesis in philosophy (2014) Scuola Normale Superiore di Pisa (under the supervision of Profesor Gabriele Lolli). PhD in mathematics (2014) Université Paris Diderot (under the supervision of Professor Boban Velickovic). Since March 2014 post-doc at Unicamp (CLE) with a projected founded by FAPESP.

Referências

Hallett, M. and Majer, U. eds. 2004. David Hilbert’s lectures on the foundations of geometry, 1891-1902, Berlin Heidelberg: Springer-Verlag.

Hilbert, H. 1894. ‘Die Grundlagen der Geometrie’, in: Hallett, M. and Majer, U. eds. David Hilbert’s lectures on the foundations of geometry, 1891-1902, Berlin Heidelberg: Springer-Verlag, pp. 72–123.

Hilbert, H. 1899. Grundlagen der Geometrie, Leipzig : Verlag von B. G.

Teubner.

Hilbert, H. 1900. [translated by L. Laugel] Les principes fondamentaux de la geometrie, Paris: Gauthier-Villars.

Hilbert, H. 1902a. [translated by E. J. Townsend] The foundations of geometry, Chicago: The Open Court Publishing Company.

Hilbert, H. 1902b. ‘Grundlagen der Geometrie’, in: Hallett, M. and Majer,

U. eds. David Hilbert’s lectures on the foundations of geometry, 1891-1902, Berlin Heidelberg: Springer-Verlag, pp. 540–602.

Hilbert, H. 1902/1903. ‘U¨ ber den Satz von der Gleichheit der Basiswinkel im gleichschenkligen Dreieck’, Proceedings of the London Mathematical Society, 35, 50–68.

Hilbert, H. 1903. Grundlagen der Geometrie, 2nd ed., Leipzig: Verlag von

B. G. Teubner.

Hilbert, H. 1919. ‘Natur und mathematisches Erkennen’, in: Rowe, D. ed.

Natur und Mathematisches Erkennen: Vorlesungen, gehalten 1919-1920 in Gottingen., Basel Boston: Birkhauser.

Hilbert, H. 1968. Grundlagen der Geometrie, 10th ed., Stuttgart: Verlag von B. G. Teubner.

Hilbert, H. 1971a. [translated by L. Unger] The foundations of geometry, 2nd ed., Chicago: The Open Court Publishing Company.

Hilbert, H. 1971b. Les principes fondamentaux de la geometrie. Edition critique avec introduction et complements preparee par Paul Rossier, Paris: Dunod.

Hilbert, H. 1999. Grundlagen der Geometrie, 14th ed., Stuttgart Leipzig:

Verlag von B. G. Teubner.

Majer, U. 2006. ‘The relation of logic and intuition in Kant’s philosophy of

science, particularly geometry’, in: Carson, E. and Huber, R. eds. Intuition

and the Axiomatic Method, Dordrecht: Springer-Verlag, pp. 47–66.

Moore, E. H. 1902. ‘On the projective axioms of geometry’, Transactions of the American Mathematical Society, 3, 142–158.

Peckhaus, V. 1990. Hilbertprogramm und Kritische Philosophie, Gottingen,

Vandenhoeck & Ruprecht.

Peckhaus,V. 2002. ‘Regressive analysis’, Logical Analysis and History of Philosophy, 5, 97–110.

Shur, F. 1901. ‘U¨ ber die Grundlagen der Geometrie’, Mathematiche Annalen, 55, 256.

Sommer, J. 1900. ‘Hilbert’s foundations of geometry’, Bulletin of the American Mathematical Society, 6, 287–299.

Thiele, R. 2003. ‘Hilbert’s twenty-fourth problem’, American Mathematical Monthly, 110, 1–24.

Veblen, O. 1903. ‘Hilbert’s foundation of geometry’, The Monist, 13, 303–309.

Veblen, O. 1904. ‘A system of axioms for geometry’, Transaction of the American Mathematical Society, 5, 439–441.

Venturi, G. 2011. ‘Hilbert, completeness and geometry’, Rivista di Filosofia Analitica Junior, 2, 80–102.

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Publicado

2017-07-11

Como Citar

VENTURI, G. A note on the introduction of Hilbert’s Grundlagen der Geometrie. Manuscrito: Revista Internacional de Filosofia, Campinas, SP, v. 40, n. 2, p. 5–17, 2017. Disponível em: https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8649850. Acesso em: 4 out. 2022.

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