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

  • EDUARDO BARRIO (a1) and LAVINIA PICOLLO (a1)
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.

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Corresponding author
*INSTITUTO DE FILOSOFÍA (UBA) 480 PUAN ST., CITY OF BUENOS AIRES ARGENTINA E-mail: eabarrio@gmail.com and lavipicollo@gmail.com
References
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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