Bilateralism does not provide a proof theoretic treatment of classical logic (for technical reasons)

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...

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Bibliographic Details
Published in:Journal of applied logic 2017-12, Vol.25, p.S108-S122
Main Author: Gabbay, Michael
Format: Article
Language:English
Subjects:
Bilateralism
Harmony
Logic
Normalisation
Proof theoretic justification
Proof theory
Validity
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Summary: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.
ISSN:1570-8683
1570-8691
DOI:10.1016/j.jal.2017.11.001