Fixed-point models for paradoxical predicates
Luca Castaldo · The Australasian Journal of Logic · 2021
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 oftruth