Coordination and Harmony in Bilateral Logic

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Mind 132 (525):192-207 (2023)
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Abstract

Ian Rumfitt (2000) developed a bilateralist account of logic in which the meaning of the connectives is given by conditions on asserted and rejected sentences. An additional set of inference rules, the coordination principles, determines the interaction of assertion and rejection. Fernando Ferreira (2008) found this account defective, as Rumfitt must state the coordination principles for arbitrary complex sentences. Rumfitt (2008) has a reply, but we argue that the problem runs deeper than he acknowledges and is in fact related to the challenge of establishing proof-theoretic harmony. We motivate a distinctively bilateral criterion for harmony and show how the bilateralist can meet it. This also resolves Ferreira's complaint.

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10.1093/mind/fzac012

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Julian J. Schloeder
University of Connecticut

Citations of this work

A General Schema for Bilateral Proof Rules.Ryan Simonelli - 2024 - Journal of Philosophical Logic (3):1-34.
Harmony and Normalisation in Bilateral Logic.Pedro del Valle-Inclan - 2023 - Bulletin of the Section of Logic 52 (3):377-409.
Introduction: Bilateralism and Proof-Theoretic Semantics (Part II).Sara Ayhan - 2023 - Bulletin of the Section of Logic 52 (3):267-274.

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References found in this work

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Rejection.Timothy Smiley - 1996 - Analysis 56 (1):1–9.

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