Notes on ω-inconsistent theories of truth in second-order languages

Review of Symbolic Logic 6 (4):733-741 (2013)
Lavinia Maria Picollo
Universidad de Buenos Aires (UBA)
Eduardo Alejandro Barrio
University of Buenos Aires
It is widely accepted that a theory of truth for arithmetic should be consistent, but -consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adopting -inconsistent theories of truth are considered: the revision theory of nearly stable truth T # and the classical theory of symmetric truth FS. Briefly, we present some conceptual problems with ω-inconsistent theories, and demonstrate some technical results that support our criticisms of such theories.
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DOI 10.1017/S1755020313000269
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References found in this work BETA

Truth and Paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.
Notes on Naive Semantics.Hans G. Herzberger - 1982 - Journal of Philosophical Logic 11 (1):61 - 102.
A System of Complete and Consistent Truth.Volker Halbach - 1994 - Notre Dame Journal of Formal Logic 35 (1):311--27.

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Truth Without Standard Models: Some Conceptual Problems Reloaded.Eduardo Barrio & Bruno Da Ré - 2018 - Journal of Applied Non-Classical Logics 28 (1):122-139.

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