Vol. 40 No. Especial (2020): Lógica, lenguaje y representación. Homenaje a Alberto Moretti
Articles

On Carroll's Regress, Conventionalism and the Foundations of Logic

Mario Gomez Torrente
Instituto de Investigaciones Filosóficas, UNAM, Ciudad de México, México

Published 2020-12-15

Keywords

  • Conventionalism,
  • Adoption of rules,
  • Rule-following,
  • Inferentialism
  • Convencionalismo,
  • Adopción de reglas,
  • Seguimiento de reglas,
  • Inferencialismo

Abstract

I propose that Quine’s Carrollian argument in “Truth by Convention” does not refute an especially genuine variety of conventionalism about logic. I also argue that the basic Carrollian lesson about conventionalism is that the introduction of accepted conventions or theses about what is logically correct cannot by itself create the corresponding inferential dispositions. Based on my discussion of the Carrollian regress, I finally indicate that there are at least certain Carrollian limits to the way in which the “logical laws” could be “replaced” and, contrary to some of Alberto Moretti’s considerations, that there are also other not strictly Carrollian limits to the replaceability of logical laws.

References

  1. Berger, A. (2011). Kripke on the incoherency of adopting a logic. En A. Berger (Comp.), Saul Kripke (pp. 177-207). Cambridge University Press.
  2. Carnap, R. (1937). The logical syntax of language. Kegan Paul, Trench, Trubner & Co.
  3. Carnap, R. (1939). Foundations of logic and mathematics. Encyclopedia of Unified Science, 1(3).
  4. Carnap, R. (1942). Introduction to semantics. Harvard University Press.
  5. Carnap, R. (1947). Meaning and necessity. University of Chicago Press.
  6. Carroll, L. (1895). What the tortoise said to Achilles. Mind 4, 278-280.
  7. Ebbs, G. (2011). Carnap and Quine on truth by convention. Mind 120 (478), 193-237.
  8. Gómez-Torrente, M. (2019). Soames on the logical empiricists on truth, meaning, convention, and logical truth. Philosophical Studies 176, 1357-1365.
  9. Moretti, A. (2010). Concepciones de la lógica. Páginas de Filosofía 11 (13), 162-185.
  10. Moretti, A. (2016). La lógica y la trama de las cosas. Ideas y Valores 65, 5-22.
  11. Padró, R. (2015). What the tortoise said to Kripke: the adoption problem and the epistemology of logic (tesis doctoral). City University of New York.
  12. Quine, W. V. (1935). Truth by convention. En W. V. Quine, The ways of paradox and other essays (1966, pp. 70-99). Harvard University Press.
  13. Quine, W. V. (1954). Carnap and logical truth. En W. V. Quine, The ways of paradox and other essays (1966, pp. 100-125). Harvard University Press.
  14. Quine, W. V. (1970). Philosophy of logic. Prentice-Hall.
  15. Stairs, A. (1978). Quantum mechanics, logic and reality (tesis doctoral). University of Western Ontario.
  16. Stairs, A. (2006). Kriske, Tupman and quantum logic: the quantum logician’s conundrum. En W. Demopoulos e I. Pitowsky (Comps.), Physical theory and its interpretation. Essays in honor of Jeffrey Bub (pp. 253-272). Springer.
  17. Stairs, A. (2016). Could logic be empirical?. En J. Chubb, A. Eskandarian y V. Herizanov (Comps.), Logic and algebraic structures in quantum computing (pp. 23-41). Cambridge University Press.