Cantor’s Proof in the Full Definable Universe

  • Laureano Luna I. E. S. Doctor Francisco Marin Philosophy
  • William Taylor Canterbury University, Mathematics and Statistics

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.

Author Biographies

Laureano Luna, I. E. S. Doctor Francisco Marin Philosophy
William Taylor, Canterbury University, Mathematics and Statistics
Published
2010-11-03
How to Cite
LUNA, Laureano; TAYLOR, William. Cantor’s Proof in the Full Definable Universe. The Australasian Journal of Logic, [S.l.], v. 9, nov. 2010. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/1818>. Date accessed: 15 nov. 2019. doi: https://doi.org/10.26686/ajl.v9i0.1818.