Australasian Journal of Logic 18 (7):688-723 (2021)

Luca Castaldo
King's College London
This paper introduces a new kind of fixed-point semantics, filling a gap within approaches to Liar-like paradoxes involving fixed-point models à la Kripke (1975). The four-valued models presented below, (i) unlike the three-valued, consistent fixed-point models defined in Kripke (1975), are able to differentiate between paradoxical and pathological-but-unparadoxical sentences, and (ii) unlike the four-valued, paraconsistent fixed-point models first studied in Visser (1984) and Woodruff (1984), preserve consistency and groundedness of truth.
Keywords Semantic Paradoxes  Fixed-point semantics  Many-valued logic  Kripke’s theory of truth
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