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NOTES ON ω-INCONSISTENT THEORIES OF TRUTH IN SECOND-ORDER LANGUAGES

Published online by Cambridge University Press:  28 October 2013

EDUARDO BARRIO  and
LAVINIA PICOLLO
EDUARDO BARRIO*
Affiliation:
University of Buenos Aires - conicet
LAVINIA PICOLLO*
Affiliation:
University of Buenos Aires - conicet
*
*INSTITUTO DE FILOSOFÍA (UBA) 480 PUAN ST., CITY OF BUENOS AIRES ARGENTINA E-mail: [email protected] and [email protected]
*INSTITUTO DE FILOSOFÍA (UBA) 480 PUAN ST., CITY OF BUENOS AIRES ARGENTINA E-mail: [email protected] and [email protected]
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Abstract

It is widely accepted that a theory of truth for arithmetic should be consistent, but ω-consistency is less frequently required. This paper argues that ω-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 ω-inconsistent truth theories for arithmetic is unsatisfiability. In order to bring out this point, well known ω-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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 4 , December 2013 , pp. 733 - 741
Copyright
Copyright © Association for Symbolic Logic 2013 

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