Peirce and the liar’s logic

Abstract

This paper discusses two treatments given by Charles Sanders Peirce to the Liar paradox, establishing connections with the current debate on the subject. In the Harvard Lectures of 1865, Peirce considers that the Liar proposition is both true and false, which, according to his view of logic, renders the proposition meaningless. This treatment partially anticipates the contemporary dialetheistic position, which considers that the Liar is an evidence that some propositions are both true and false. In later texts, Peirce revises his treatment of the problem, considering that the Liar contradiction is false, in line with the tradition of logic of his time. This paper’s discussion shows that specific logical conceptions presupposed in Peirce’s investigation are responsible for the interpretations he provides for the contradiction involved in the paradox. From this discussion, this paper argues that the treatment given to the Liar depends on the background logical conceptions. Thus, the limitations encountered by Peirce in his approaches to the problem are introduced by traditional logic, which, unlike some contemporary logics, does not offer an apparatus compatible with true contradictions.