Consideraciones filosóficas sobre la Teoría de Conjuntos (I)

• Autores: Lorenzo Peña
• Localización: Contextos, ISSN 0212-6192, Nº 11, 1988, págs. 33-62
• Idioma: español
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• Resumen

  • The paper goes into Russell's theory of types regarded as the historical and conceptual background of Quine's set-theories. Russell's approach is examined in its relationshig to Frege's system. While the simple theory of types draws its philosophical justification from Frege's ideas on how language relates to reality, the ramified theory of types enjoys a more powerful motivation, namely a constructivistic view of things, which Russell borrowed from Poincaré. However every theory of types labours under insurmountable difficutties, such as ineffability, unbelievability and unremovable obscurity, Nevertheless, Russell's course in the 2d, edition of PP.MM. is shown to be all in all worthier of choice, thus being the best set-theory compatible with the underlying constructivism. Most of all, it allows one to avoid Russell's and Cantor's paradoxes in an equal way, ensuing on how it blocks the proof of Cantor's theorem.