Minimal Truth and Interpretability

Fischer, Martin (2009): Minimal Truth and Interpretability. In: The Review of Symbolic Logic, Vol. 2, No. 4: pp. 799-815

Abstract

In this paper we will investigate different axiomatic theories of truth that are minimal in some sense. One criterion for minimality will be conservativity over Peano Arithmetic. We will then give a more fine-grained characterization by investigating some interpretability relations. We will show that disquotational theories of truth, as well as compositional theories of truth with restricted induction are relatively interpretable in Peano Arithmetic. Furthermore, we will give an example of a theory of truth that is a conservative extension of Peano Arithmetic but not interpretable in it. We will then use stricter versions of interpretations to compare weak theories of truth to subsystems of second-order arithmetic.

• 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 > 100 Philosophy; 100 Philosophy and Psychology > 160 Logic
• ISSN: 1755-0211
• Language: English