Model-Theoretic Inferentialism; Paraconsistency; Categoricity

Document Type : Scientific-research

Authors

1 . Department of Philosophy, Faculty of Humanities, Tarbiat Modares University, Tehran, Iran.

2 Department of Philosophy, Faculty of Humanities, Tarbiat Modares University, Tehran, Iran.

Abstract

According to model-theoretic inferentialism (and despite proof-theoretic semantics and model-theoretic semantics), both proof-theoretic and model-theoretic notions play a role in the meaning of logical constants. However, proof-theoretic notions have a more fundamental role compared to model-theoretic notions, so that the semantics and its structure are determined by the proof-theoretic notions. In other words, in proof-theoretic inferentialism, we follow a method by which we can read the semantics from the proof theory. This approach is related to the problem of categoricity and Carnap's non-normal models for proof systems. In this paper we investigate this issue for two paraconsistent logics, mbC and LP. We show that while multi-succedent sequent calculi are categorical for mbC, they are not for LP. That latter has non-normal models. We argue that for the latter we cannot easily read the semantics from the proof theory, except at the cost of distorting the notion of logical consequence.

Keywords

References

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The Mirror of Knowledge
Volume 24, Issue 2 - Serial Number 79
September 2024
Pages 52-68

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