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Frege’s horizontal and the liar-paradox


Frege’s Horizontal. Liar-paradox. Truth. The True. Undefinability of truth

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GREIMANN, Dirk. Frege’s horizontal and the liar-paradox. Manuscrito: Revista Internacional de Filosofia, Campinas, SP, v. 26, n. 2, p. 359–387, 2016. Disponível em: Acesso em: 30 maio. 2024.


According to Peter Aczel, the inconsistency of Frege’s system in Grundgesetze is due, not to the introduction of sets, as is usually thought, but to the introduction of the Horizontal. His argument is that the principles governing sets are intuitively correct and therefore consistent, while the scheme introducing the Horizontal amounts to an internal definition of truth conflicting with Tarski’s classic result on the undefinability of truth in the object language. The aim of this paper is to show that the Horizontal is innocent: Aczel’s diagnosis is based on a mistaken view of the structure underlying Frege’s ideal language.


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