Consideraciones filosóficas sobre la teoría de conjuntos II

• Autores: Lorenzo Peña
• Localización: Contextos, ISSN 0212-6192, Nº 12, 1988, págs. 7-44
• Idioma: español
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• Resumen

  • Quine's systems NF and ML are shown to be philosophically motivated -grounded as they are on whatever defensible reasons may buttress the simple theory of types- while keeping clear of such pitfalls as besiege the theory of types. Yet they don't lack difficulties of their own on a number of points: ML cannot be true, while NF not only doesn't yield any sufficiently strong mathematical induction principle but moreover, fails to countenance the existence of anything deserving the label of the extension of predicate "p" for any "p". The alternative way of doing set-theory the paper espouses is the combinatory approach, whose many advantages are highlighted. A paraconsistent combinatory set-theory is put forward and shown to be both extremely powerful and free of the shackles which clog classical set-theories.