Paraconsistent Metatheory: New Proofs with Old Tools

Journal of Philosophical Logic 51 (4):825-856 (2022)
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Abstract

This paper is a step toward showing what is achievable using non-classical metatheory—particularly, a substructural paraconsistent framework. What standard results, or analogues thereof, from the classical metatheory of first order logic can be obtained? We reconstruct some of the originals proofs for Completeness, Löwenheim-Skolem and Compactness theorems in the context of a substructural logic with the naive comprehension schema. The main result is that paraconsistent metatheory can ‘re-capture’ versions of standard theorems, given suitable restrictions and background assumptions; but the shift to non-classical logic may recast the meanings of these apparently ‘absolute’ theorems.

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Author Profiles

Guillermo Badia
University of Queensland
Patrick Girard
University of Auckland

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References found in this work

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