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Article

Carnap’s Problem for Intuitionistic Propositional Logic

by
Haotian Tong
1,† and
Dag Westerståhl
2,3,*
1
Department of Philosophy, Tsinghua University, Beijing 100084, China
2
Department of Philosophy, Stockholm University, 106 91 Stockholm, Sweden
3
Tsinghua-UvA Joint Research Center for Logic, Department of Philosophy, Tsinghua University, Beijing 100084, China
*
Author to whom correspondence should be addressed.
†
Current address: Duke-NUS Medical School, Singapore 169857, Singapore.
Logics 2023, 1(4), 163-181; https://doi.org/10.3390/logics1040009
Submission received: 26 December 2022 / Revised: 18 May 2023 / Accepted: 14 August 2023 / Published: 22 September 2023
Review Reports Versions Notes

Abstract

We show that intuitionistic propositional logic is Carnap categorical: the only interpretation of the connectives consistent with the intuitionistic consequence relation is the standard interpretation. This holds with respect to the most well-known semantics relative to which intuitionistic logic is sound and complete; among them Kripke semantics, Beth semantics, Dragalin semantics, topological semantics, and algebraic semantics. These facts turn out to be consequences of an observation about interpretations in Heyting algebras.
Keywords: intuitionistic logic; Carnap’s problem; Heyting algebras; set-based semantics; nuclear semantics; algebraic semantics; logical constants; consequence relations; categoricity intuitionistic logic; Carnap’s problem; Heyting algebras; set-based semantics; nuclear semantics; algebraic semantics; logical constants; consequence relations; categoricity

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MDPI and ACS Style

Tong, H.; Westerståhl, D. Carnap’s Problem for Intuitionistic Propositional Logic. Logics 2023, 1, 163-181. https://doi.org/10.3390/logics1040009

AMA Style

Tong H, Westerståhl D. Carnap’s Problem for Intuitionistic Propositional Logic. Logics. 2023; 1(4):163-181. https://doi.org/10.3390/logics1040009

Chicago/Turabian Style

Tong, Haotian, and Dag Westerståhl. 2023. "Carnap’s Problem for Intuitionistic Propositional Logic" Logics 1, no. 4: 163-181. https://doi.org/10.3390/logics1040009

APA Style

Tong, H., & Westerståhl, D. (2023). Carnap’s Problem for Intuitionistic Propositional Logic. Logics, 1(4), 163-181. https://doi.org/10.3390/logics1040009

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