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Cantor Paradoxes, Possible Worlds and Set Theory

Author

Listed:
  • José-Luis Usó-Doménech

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

  • Josué-Antonio Nescolarde-Selva

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

  • Lorena Segura-Abad

    (Department of Mathematics, University of Alicante, 03690 Alicante, Spain)

  • Hugh Gash

    (Institute of Education, Dublin City University, D09 Y18 Dublin, Ireland)

  • Kristian Alonso-Stenberg

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

Abstract

In this paper, we illustrate the paradox concerning maximally consistent sets of propositions, which is contrary to set theory. It has been shown that Cantor paradoxes do not offer particular advantages for any modal theories. The paradox is therefore not a specific difficulty for modal concepts, and it also neither grants advantages nor disadvantages for any modal theory. The underlying problem is quite general, and affects anyone who intends to use the notion of “world” in its ontology.

Suggested Citation

  • José-Luis Usó-Doménech & Josué-Antonio Nescolarde-Selva & Lorena Segura-Abad & Hugh Gash & Kristian Alonso-Stenberg, 2019. "Cantor Paradoxes, Possible Worlds and Set Theory," Mathematics, MDPI, vol. 7(7), pages 1-10, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:628-:d:248531
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