portada hilbert's program: an essay on mathematical instrumentalism (en Inglés)

hilbert's program: an essay on mathematical instrumentalism (en Inglés)

Formato

Libro Físico

Autor

M. Detlefsen

Editorial

Springer

Año

2010

Idioma

Inglés

N° páginas

186

Encuadernación

Tapa Blanda

Dimensiones

22.9x15.2x1.1 cm

Peso

0.28 kg.

ISBN

9048184207

ISBN13

9789048184200

Categorías

Filosofía de las matemáticas
Lógica matemática
Historia de las matemáticas
Filosofía: lógica

hilbert's program: an essay on mathematical instrumentalism (en Inglés)

M. Detlefsen (Autor) · Springer · Tapa Blanda

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Reseña del libro "hilbert's program: an essay on mathematical instrumentalism (en Inglés)"

Hilbert's Program was founded on a concern for the phenomenon of paradox in mathematics. To Hilbert, the paradoxes, which are at once both absurd and irresistible, revealed a deep philosophical truth: namely, that there is a discrepancy between the laws accord- ing to which the mind of homo mathematicus works, and the laws governing objective mathematical fact. Mathematical epistemology is, therefore, to be seen as a struggle between a mind that naturally works in one way and a reality that works in another. Knowledge occurs when the two cooperate. Conceived in this way, there are two basic alternatives for mathematical epistemology: a skeptical position which maintains either that mind and reality seldom or never come to agreement, or that we have no very reliable way of telling when they do; and a non-skeptical position which holds that there is significant agree- ment between mind and reality, and that their potential discrepan- cies can be detected, avoided, and thus kept in check. Of these two, Hilbert clearly embraced the latter, and proposed a program designed to vindicate the epistemological riches represented by our natural, if non-literal, ways of thinking. Brouwer, on the other hand, opted for a position closer (in Hilbert's opinion) to that of the skeptic. Having decided that epistemological purity could come only through sacrifice, he turned his back on his classical heritage to accept a higher calling.