Abstract
The strict-tolerant (ST) approach to paradox promises to erect theories of naïve truth and tolerant vagueness on the firm bedrock of classical logic. We assess the extent to which this claim is founded. Building on some results by Girard (Diss Math 136, 1976) we show that the usual proof-theoretic formulation of propositional ST in terms of the classical sequent calculus without primitive Cut is incomplete with respect to ST-valid metainferences, and exhibit a complete calculus for the same class of metainferences. We also argue that the latter calculus, far from coinciding with classical logic, is a close kin of Priest’s LP.
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Acknowledgements
The authors gratefully acknowledge the support of Regione Autonoma Sardegna, within the Project CRP-78705 (L.R. 7/2007), “Metaphor and argumentation”. Versions of this paper have been presented at the Navarra Workshop on Logical Consequence (Pamplona, May 2016), the Prague Workshop on Nonclassical Logics (December 2016) and at the Workshop on Consequence and Paradox: Between Truth and Proof (Tübingen, March 2017). We thank Pablo Cobreros, Petr Cintula and the other participants to these events for their precious remarks. We thank Eduardo Barrio, Nissim Francez, Rohan French, Dave Ripley and two anonymous reviewers for their insightful comments. Finally, we are extremely grateful to Kazushige Terui for his invaluable pointers to the literature on Girard’s three-valued interpretation of the sequent calculus.
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Dicher, B., Paoli, F. (2019). ST, LP and Tolerant Metainferences. In: Başkent, C., Ferguson, T. (eds) Graham Priest on Dialetheism and Paraconsistency. Outstanding Contributions to Logic, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-030-25365-3_18
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