Gestalt Shifts in the Liar Or Why KT4M Is the Logic of Semantic Modalities

In Bradley Armour-Garb (ed.), Reflections on the Liar. Oxford University. pp. 71-113 (2017)
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ABSTRACT: This chapter offers a revenge-free solution to the liar paradox (at the centre of which is the notion of Gestalt shift) and presents a formal representation of truth in, or for, a natural language like English, which proposes to show both why -- and how -- truth is coherent and how it appears to be incoherent, while preserving classical logic and most principles that some philosophers have taken to be central to the concept of truth and our use of that notion. The chapter argues that, by using a truth operator rather than truth predicate, it is possible to provide a coherent, model-theoretic representation of truth with various desirable features. After investigating what features of liar sentences are responsible for their paradoxicality, the chapter identifies the logic as the normal modal logic KT4M (= S4M). Drawing on the structure of KT4M (=S4M), the author proposes that, pace deflationism, truth has content, that the content of truth is bivalence, and that the notions of both truth and bivalence are semideterminable.
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A New Introduction to Modal Logic.Cresswell, M. J. & Hughes, G. E.
The Revision Theory of Truth.Gupta, A. & Belnap, N.

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