Impossible, yet not problematic: Making sense of adoption with dialogic type theory

Authors

DOI:

https://doi.org/10.15381/tesis.v14i19.21937

Keywords:

adoption problem, dialogic, constructive type theory, anti-exceptionalism, game-theoretic semantics

Abstract

Logical laws cannot be adopted —so goes Kripke and Padró’s Adoption Problem. Their argument can be seen as an invitation to revisit the way in which we relate Logic and inferential practice. For them, the former does not come before, but after the latter. In this paper I delve into this conclusion by showing how the impossibility of adoption can be naturally associated with some features of Immanent Reasoning, which is a mix between Dialogic and Constructive Type Theory that incorporates the pragmatics of inference at its core. The major insight to be drawn from this approximation is that adoption, although not possible, is no longer needed. Subsequently, the ‘problem’ loses its ‘problematic’ character. This conclusion illustrates some of the advantages of favoring the game-theoretic approach to semantics in philosophical logic.

References

Beall, J. C., Restall, G. (2006). Logical pluralism. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199288403.001.0001

Berger, A. (2011). Kripke on the incoherency of adopting a logic. In A. Berger (Ed.), Saul Kripke (pp. 177-207). Cambridge University Press. https://doi.org/10.1017/CBO9780511780622.009

Blass, A. (1992). A game semantics for linear logic. Annals of Pure and Applied logic, 56(1-3), 183-220. https://doi.org/10.1016/0168-0072(92)90073-9

Clerbout, N. (2014). Finiteness of plays and the dialogical problem of decidability. IfCoLog Journal of Logics and their Applications, 1(1):115-140.

Ferrari, F. and Orlandelli, E. (2021). Proof-theoretic pluralism. Synthese, 198, 4879-4903. https://doi.org/10.1007/s11229-019-02217-6

Finn, S. (2019). The adoption problem and anti-exceptionalism about logic. The Australasian Journal of Logic, [S. I.], 16(7), 231-249. https://doi.org/10.26686/ajl.v16i7.5916

Kamareddine, F. D., Laan, T. and Nederpelt, R. (2004). A modern perspective on type theory: from its origins until today (Vol. 29). Springer Science & Business Media. https://doi.org/10.1007/1-4020-2335-9

Keiff, L. (2007). Le pluralisme dialogique: Approches dynamiques de l’argumentation formelle. [PhD thesis, Université de Lille].

Padró, R. (2015). What the tortoise said to Kripke: The adoption problem and the epistemology of logic. CUNY Academic Works. [PhD thesis, City University of New York]. https://academicworks.cuny.edu/gc_etds/603

Quine, W. (1986). Philosophy of logic. (2nd ed.). Harvard University Press. https://doi.org/10.2307/j.ctvk12scx

Rahman, S., McConaughey, Z., Klev, A. and Clerbout, N. (2018) Immanent reasoning or equality in action. A plaidoyer for the player level. Springer. https://doi.org/10.1007/978-3-319-91149-6

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Published

2021-12-30

How to Cite

Impossible, yet not problematic: Making sense of adoption with dialogic type theory. (2021). Tesis (Lima), 14(19), 677-696. https://doi.org/10.15381/tesis.v14i19.21937