On the Costs of Classical Logic

Erkenntnis 88 (3):1157-1188 (2021)
  Copy   BIBTEX

Abstract

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, there is a stronger sense in which some variants of and some variants of can be taken to be, truth-theoretically, equivalent. On the other hand, we show that this truth-theoretical equivalence is not preserved by some other variants of and, arguing that the variants are more adequate axiomatisations of the fixed-point semantics than the corresponding variants.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 89,764

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Supervaluation fixed-point logics of truth.Philip Kremer & Alasdair Urquhart - 2008 - Journal of Philosophical Logic 37 (5):407-440.
On the Costs of Nonclassical Logic.Volker Halbach & Carlo Nicolai - 2018 - Journal of Philosophical Logic 47 (2):227-257.
Proof interpretations with truth.Jaime Gaspar & Paulo Oliva - 2010 - Mathematical Logic Quarterly 56 (6):591-610.
Comparing fixed-point and revision theories of truth.Philip Kremer - 2009 - Journal of Philosophical Logic 38 (4):363-403.
Trees for truth.Juan Barba - 2001 - Nordic Journal of Philosophical Logic 6 (1):71-99.
Equivalences for truth predicates.Carlo Nicolai - 2017 - Review of Symbolic Logic 10 (2):322-356.
Axiomatic theories of truth.Volker Halbach - 2008 - Stanford Encyclopedia of Philosophy.
Logic and Truth.Michael Joseph Kremer - 1986 - Dissertation, University of Pittsburgh
Axiomatizing Kripke’s Theory of Truth.Volker Halbach & Leon Horsten - 2006 - Journal of Symbolic Logic 71 (2):677 - 712.
Tarskian and Kripkean truth.Volker Halbach - 1997 - Journal of Philosophical Logic 26 (1):69-80.

Analytics

Added to PP
2021-06-12

Downloads
32 (#426,861)

6 months
3 (#435,693)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Luca Castaldo
University of Warsaw

Citations of this work

Add more citations

References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Saving truth from paradox.Hartry H. Field - 2008 - New York: Oxford University Press.
The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Basic proof theory.A. S. Troelstra - 1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.
Axiomatic Theories of Truth.Volker Halbach - 2010 - Cambridge, England: Cambridge University Press.

View all 39 references / Add more references