Abstract
I argue for a version of logical pluralism based on the plurality of legitimate formalizations of the logical vocabulary. In particular, I argue that the apparent rivalry between classical and relevant logic can be resolved, given that both logics capture and formalize normative and legitimate senses of logical consequence: classical logic encodes “follows from” as truth preservation and captures the truth conditions of the logical constants, while relevant logic encodes a notion of “follows from” which, apart from preserving truth, avoids the violation of certain Gricean maxims and captures a different inferential role for the same logical constants, enriching their meaning pragmatically.
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Notes
For simplification I will use \(\vdash\) both for \(\vdash _{LK}\) and \(\vdash _{LR}\) in those cases in which the rest of the symbols help to disambiguate.
Notice that \(\vdash\) refers to \(\vdash _{LR}\), and hence (c) expresses a relation between A and B in which B is derived from Arelevantly.
“Dutchman conditional” refers to those expressions in which the consequent is clearly false (“pigs can fly”, “I am a Dutchman”) to imply that the antecedent is false too, but in which there is no connection between them.
Similar examples on Grice (1989a).
One might think of cases in which one seems to be legitimized to use MP with a conditional asserted on grounds of (a), (b). For instance, if someone asserts 12 and another player discovers that the speaker has a black card, she will correctly derive that she also has a red card—and there seems to be nothing wrong with it. We will come back to this in Sect. 4.
Similar examples on Girard (1995).
Notation modified.
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Acknowledgements
Earlier versions of this paper were presented at the Pluralism Workshop 2: Pluralism and Normativity (Cogito Research Centre, University of Bologna) and at the Pluralism Week (Veritas Research Center, Yonsei University). I would like to thank the audiences of both workshops for their comments and discussions. Special thanks to José Martínez, who carefully read different versions of this paper, making helpful comments and corrections, to Ole Hjortland for providing valuable comments on an earlier draft of the manuscript, to Josep Macià, Genoveva Martí, Francesco Paoli and Elia Zardini for helpful discussions on its content, and to two anonymous reviewers of this journal for their remarks and suggestions. This work was supported by the project FFI2015-70707P of the Spanish Ministry de Economy and Competitiveness on Localism and Globalism in Logic and Semantics, and by the grant BES 2012-056627 of the Spanish Ministry de Economy and Competitiveness.
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Terrés Villalonga, P. From Natural to Formal Language: A Case for Logical Pluralism. Topoi 38, 333–345 (2019). https://doi.org/10.1007/s11245-017-9490-8
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DOI: https://doi.org/10.1007/s11245-017-9490-8