Vol. 44 No. Especial (2024): Coloquio SADAF 2022: Pasado, presente y futuro del análisis filosófico: A 50 años de la fundación de SADAF
Critical Notes

Implicit Rules and the Difference between Natural Deduction and Sequent Calculi: On “Gentzen y la naturalidad de la deducción” by Alberto Moretti

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  • Paula Teijeiro
Paula Teijeiro
Instituto de Investigaciones Filosóficas - Sociedad Argentina de Análisis Filosófico - Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires, Argentina / Universidad de Buenos Aires, Buenos Aires, Argentina.
DOI: https://doi.org/10.36446/af.e1006

Published 2024-08-27

Keywords

  • Reglas estructurales,
  • Derivabilidad,
  • Admisibilidad,
  • Reglas implícitas
  • Structural Rules,
  • Derivability,
  • Admisibility
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Abstract

The goal of this note is to analyze the ideas presented by Alberto Moretti (1984) in his article “Gentzen y la naturalidad de la deducción” regarding the importance of sequent calculi. My goal is to argue that the difference between these systems and those of natural deduction lies fundamentally in the way in which structural rules can be implicit in them, and that, unlike what Moretti proposes, natural deduction calculi are particularly appropriate for characterizing the notion of consequence.

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References

  1. Beall, J. C., & Restall, G. (2006). Logical pluralism. Oxford University Press.
  2. da Costa, N. C. A. (1974). On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15(4), 497-510. https://doi.org/10.1305/ndjfl/1093891487
  3. Gentzen, G. (1934). Untersuchungen über das logische Schliessen. Mathematische Zeitschirift, 39, 176-210. https://doi.org/10.1007/BF01201353
  4. Moretti, A. (1984). Gentzen y la naturalidad de la deducción. Análisis Filosófico, 4(1), 45-51. https://doi.org/10.36446/af.1984.843
  5. Negri, S. (2002). Varieties of linear calculi. Journal of Philosophical Logic, 31, 569-590. https://doi.org/10.1023/A:1021264102972