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Luca Castaldo
King's College London
  1.  4
    KF, PKF and Reinhardt’s Program.Luca Castaldo & Johannes Stern - 2022 - Review of Symbolic Logic:1-26.
    In “Some Remarks on Extending and Interpreting Theories with a Partial Truth Predicate”, Reinhardt [21] famously proposed an instrumentalist interpretation of the truth theory Kripke–Feferman in analogy to Hilbert’s program. Reinhardt suggested to view $\mathrm {KF}$ as a tool for generating “the significant part of $\mathrm {KF}$ ”, that is, as a tool for deriving sentences of the form $\mathrm{Tr}\ulcorner {\varphi }\urcorner $. The constitutive question of Reinhardt’s program was whether it was possible “to justify the use of nonsignificant sentences (...)
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    Fixed-Point Models for Paradoxical Predicates.Luca Castaldo - 2021 - Australasian Journal of Logic 18 (7):688-723.
    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.
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    On the Costs of Classical Logic.Luca Castaldo - forthcoming - Erkenntnis:1-32.
    This article compares classical and nonclassical axiomatisations of the fixed-point semantics developed by Kripke : 690–716, 1975). Following the line of investigation of Halbach and Nicolai : 227–257, 2018), we do not compare KF and PKF qua theories of truth simpliciter, but rather qua axiomatisations of the Kripkean conception of truth. We strengthen the central results of Halbach and Nicolai and Nicolai : 101–130, 2018), showing that, on the one hand, there is a stronger sense in which some variants of (...)
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