Bilateralism does not provide a proof theoretic treatment of classical logic

Journal of Applied Logic 25:S108-S122 (2017)
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Abstract

In this short paper I note that a key metatheorem does not hold for the bilateralist inferential framework: harmony does not entail consistency. I conclude that the requirement of harmony will not suffice for a bilateralist to maintain a proof theoretic account of classical logic. I conclude that a proof theoretic account of meaning based on the bilateralist framework has no natural way of distinguishing legitimate definitional inference rules from illegitimate ones (such as those for tonk). Finally, as an appendix to the main argument, I propose an alternative non-bilateral formal solution to the problem of providing a proof-theoretic account of classical logic.

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Citations of this work

Logical Multilateralism.Heinrich Wansing & Sara Ayhan - 2023 - Journal of Philosophical Logic 52 (6):1603-1636.
Bilateral Inversion Principles.Nils Kürbis - 2022 - Electronic Proceedings in Theoretical Computer Science 358:202–215.
Introduction: Bilateralism and Proof-Theoretic Semantics (Part I).Sara Ayhan - 2023 - Bulletin of the Section of Logic 52 (2):101-108.

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References found in this work

The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
The runabout inference ticket.Arthur Prior - 1967 - In P. F. Strawson (ed.), Philosophical logic. London,: Oxford University Press. pp. 38-9.
Yes and no.I. Rumfitt - 2000 - Mind 109 (436):781-823.
Rejection.Timothy Smiley - 1996 - Analysis 56 (1):1–9.
Harmony and autonomy in classical logic.Stephen Read - 2000 - Journal of Philosophical Logic 29 (2):123-154.

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