Vol. 40 No. 1 (2020)
Articles

The substructural solution to paradoxes and the problem of the dependence

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  • Bruno Da Ré
Bruno Da Ré
IIF-SADAF-CONICET / Universidad de Buenos Aires, Argentina
DOI: https://doi.org/10.36446/af.2020.337

Published 2020-05-01

Keywords

  • Lógicas subestructurales,
  • Teorías de la verdad,
  • Reglas estructurales,
  • Reglas operacionales
  • Substructural Logics,
  • Theories of Truth,
  • Structural Rules,
  • Operational Rules
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Abstract

In past years, several substructural solutions to semantical paradoxes have been developed. In particular, nontransitive, nocontractive, nonmonotonic and nonreflexive theories have been proposed. However, when such a solutions are presented using sequent-calculi it emerges what I call the problem of the dependence. In a nutshell, this problem consists in that it’s not easy (or sometimes even possible) to distinguish between the structural rules and the other rules of the calculus. In this article, I will present in detail this problem and I show that even worst there is a calculus such that doesn’t contain any structural rule but cannot nontrivially handle semantical vocabulary. Finally, I will delimit this problem and I will conclude that the correct methodology for preferring one specific substructural theory should be based on philosophical arguments (or in some case, on empirical bases), but not in the comparison between calculi.

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