4 found
See also
Luca Castaldo
University of Warsaw
  1.  13
    KF, PKF and Reinhardt’s Program.Luca Castaldo & Johannes Stern - 2022 - Review of Symbolic Logic (1):33-58.
    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 ( $\mathrm {KF}$ ) 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 (...)
    Direct download (2 more)  
    Export citation  
    Bookmark   4 citations  
  2.  30
    On the Costs of Classical Logic.Luca Castaldo - 2021 - Erkenntnis 88 (3):1157-1188.
    This article compares classical (or -like) and nonclassical (or -like) axiomatisations of the fixed-point semantics developed by Kripke (J Philos 72(19): 690–716, 1975). Following the line of investigation of Halbach and Nicolai (J Philos Logic 47(2): 227–257, 2018), we do not compare and qua theories of truth simpliciter, but rather qua axiomatisations of the Kripkean conception of truth. We strengthen the central results of Halbach and Nicolai (2018) and Nicolai (Stud Log 106(1): 101–130, 2018), showing that, on the one hand, (...)
    No categories
    Direct download (3 more)  
    Export citation  
    Bookmark   1 citation  
  3.  9
    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.
    Direct download (3 more)  
    Export citation  
    Bookmark   1 citation  
  4.  19
    Notes on Models of (Partial) Kripke–Feferman Truth.Luca Castaldo - 2023 - Studia Logica 111 (1):83-111.
    This article investigates models of axiomatizations related to the semantic conception of truth presented by Kripke (J Philos 72(19):690–716, 1975), the so-called _fixed-point semantics_. Among the various proof systems devised as a proof-theoretic characterization of the fixed-point semantics, in recent years two alternatives have received particular attention: _classical systems_ (i.e., systems based on classical logic) and _nonclassical systems_ (i.e., systems based on some nonclassical logic). The present article, building on Halbach and Nicolai (J Philos Log 47(2):227–257, 2018), shows that there (...)
    Direct download (3 more)  
    Export citation