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Inferences and Metainferences in ST

Abstract

In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences holding in the strict-tolerant logic of transparent truth ST+ and inferences holding in the logic of paradox LP+. They argue that LP+ is ST+’s external logic and they question whether ST+’s solution to the semantic paradoxes is fundamentally different from LP+’s. Here we establish that by parity of reasoning, ST+ can be related to LP+’s dual logic K3+. We clarify the distinction between internal and external logic and argue that while ST+’s nonclassicality can be granted, its self-dual character does not tie it to LP+ more closely than to K3+.

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Acknowledgements

We want to give thanks to two anonymous reviewers of JPL for their helpful comments on earlier versions of this paper. Pablo Cobreros gives thanks to the Humboldt Foundation for a fellowship for twelve months of research at the Munich Center for Mathematical Philosophy. Paul Egré and David Ripley thank the Buenos Aires Logic Group for their hospitality in August 2019. Robert van Rooij was funded by the Dutch Research Council (NWO) via grant ‘From Learning to Meaning’, grant-number 406.18.TW.007. Paul Egré thanks the programs ANR-19-CE28-0004-01 (PROBASEM) and ANR-17-EURE-0017 (FRONTCOG) for research carried out at the Department of Cognitive Studies of ENS. We also received financial support with the project ‘Logic and Substructurality’ Grant no (FFI2017-84805-P), Ministry of Science, Innovation and Universities, Government of Spain. Ripley’s research was partially supported by the Australian Research Council via FT190100147 “Substructural logics for bounded resources”.

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Correspondence to Pablo Cobreros, Paul Egré, David Ripley or Robert van Rooij.

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Cobreros, P., Egré, P., Ripley, D. et al. Inferences and Metainferences in ST. J Philos Logic 49, 1057–1077 (2020). https://doi.org/10.1007/s10992-020-09560-x

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Keywords

  • Strict-tolerant logic
  • Metainferences
  • Proof theory
  • Internal vs external logic
  • Paradoxes