Cantor’s Proof in the Full Definable Universe

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Australasian Journal of Logic 9:10-25 (2010)
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Abstract

Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on the scope of quantifiers reveals a natural way out.

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2011

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10.26686/ajl.v9i0.1818

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Laureano Luna
Universidad Nacional de Educación a Distancia (PhD)

Citations of this work

Rescuing Poincaré from Richard’s Paradox.Laureano Luna - 2017 - History and Philosophy of Logic 38 (1):57-71.
Taming the Indefinitely Extensible Definable Universe.L. Luna & W. Taylor - 2014 - Philosophia Mathematica 22 (2):198-208.

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References found in this work

On some difficulties in the theory of transfinite numbers and order types.Bertrand Russell - 1905 - Proceedings of the London Mathematical Society 4 (14):29-53.
On Some Difficulties in the Theory of Transfinite Numbers and Order Types. [REVIEW]Harold Chapman Brown - 1906 - Journal of Philosophy, Psychology and Scientific Methods 3 (14):388-390.

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