Notes On ω-inconsistent Theories of Truth in Second-Order Languages

Barrio, Eduardo; Picollo, Lavinia (28. October 2013): Notes On ω-inconsistent Theories of Truth in Second-Order Languages. In: The Review of Symbolic Logic, Vol. 6, No. 4: pp. 733-741

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.

• Item Type: Journal article
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP); Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Logic
• Subjects: 100 Philosophy and Psychology > 160 Logic
• Language: English