„Every definition implies an axiom, since it asserts the existence of the object defined.“

—  Henri Poincaré, livro Science and Method

Part II. Ch. 2 : Mathematical Definitions and Education, p. 131
Science and Method (1908)
Contexto: Every definition implies an axiom, since it asserts the existence of the object defined. The definition then will not be justified, from the purely logical point of view, until we have proved that it involves no contradiction either in its terms or with the truths previously admitted.

Original

Toute définition implique un axiome, puisqu'elle affirme l'existence de l'objet défini. La définition ne sera donc justifiée, au point de vue purement logique, que quand on aura démontré qu'elle n'entraîne pas de contradiction, ni dans les termes, ni avec les vérités antérieurement admises.

Science and Method (1908)

Última atualização 22 de Maio de 2020. História
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Henri Poincaré15
1854 - 1912

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Proposition 1
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