EQUIVALENCES FOR TRUTH PREDICATES

作者：Nicolai Carlo^*

来源：Review of Symbolic Logic, 2017, 10(2): 322-356.

DOI：10.1017/S1755020316000435

• Formal Theories of Truth
• interpretability
• sameness of theories
• arithmetical comprehension

One way to study and understand the notion of truth is to examine principles that we are willing to associate with truth, often because they conform to a pre-theoretical or to a semiformal characterization of this concept. In comparing different collections of such principles, one requires formally precise notions of inter-theoretic reduction that are also adequate to compare these conceptual aspects. In this work I study possible ways to make precise the relation of conceptual equivalence between notions of truth associated with collections of principles of truth. In doing so, I will consider refinements and strengthenings of the notion of relative truth-definability proposed by Fujimoto (2010): in particular I employ suitable variants of notions of equivalence of theories considered in Visser (2006) and Friedman & Visser (2014) to show that there are better candidates than mutual truth-definability for the role of sufficient condition for conceptual equivalence between the semantic notions associated with the theories. In the concluding part of the paper, I extend the techniques introduced in the first and show that there is a precise sense in which ramified truth (either disquotational or compositional) does not correspond to iterations of comprehension.

• 出版日期2017-6