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 |
| Item ID: | 42201 |
| Date Deposited: | 20. Feb 2018, 07:43 |
| Last Modified: | 04. Nov 2020, 13:17 |
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