Logical multilateralism

  • In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with multiple sequent arrows satisfying some specific conditions, which we will lay out in this paper. We will unfold our ideas with the help of a case study in logical tetralateralism and present an extension of Almukdad and Nelson’s propositional constructive four-valued logic by unary operations of meaningfulness and nonsensicality. We will argue that in sequent calculi with multiple sequent arrows it is possible to maintain certain features that are desirable if we assume an understanding of the meaning of connectives in the spirit of proof-theoretic semantics. The use of multiple sequent arrows will be justified by the presence of congruentiality-breaking unary connectives.

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Author:Heinrich WansingORCiDGND, Sara AyhanORCiDGND
Parent Title (English):Journal of philosophical logic
Publisher:Springer Nature
Place of publication:Berlin
Document Type:Article
Date of Publication (online):2024/04/12
Date of first Publication:2023/09/25
Publishing Institution:Ruhr-Universität Bochum, Universitätsbibliothek
Tag:ConLog, Projekt ID: 101018280
Bilateralism; Congruentiality; Consequence relations; Multilateralism; Proof-theoretic semantics; Sequent calculus
First Page:1603
Last Page:1636
ConLog, Projekt ID: 101018280
Relation (DC):info:eu-repo/grantAgreement/EC/H2020/101018280
Institutes/Facilities:Institut für Philosophie I
Dewey Decimal Classification:Philosophie und Psychologie / Philosophie
faculties:Fakultät für Philosophie und Erziehungswissenschaft
Licence (German):License LogoCreative Commons - CC BY 4.0 - Namensnennung 4.0 International