Truth, the liar, and relativism

This essay proposes a theory of the nature and logic of truth on which truth is an inconsistent concept that should be replaced for certain theoretical purposes. The paradoxes associated with truth (for example, the liar) and the pattern of failures in our attempts to deal with them suggest that truth is an inconsistent concept. The first part of the essay describes a pair of replacement concepts, which the essay dubs ascending truth and descending truth, along with an axiomatic theory of them and an empirical interpretation of the theory. The essay shows how to use these replacements in a familiar truth-conditional semantics as well. The second part of the essay offers a descriptive theory of our natural language truth predicate that takes it to be assessment sensitive, which means that it has the same content in every context of utterance, but its extension (that is, the set of things that are true) depends on a context of assessment. Contexts of assessment model situations in which a person interprets someone's utterance. From different contexts of assessment, the truth predicate has different extensions. The descriptive theory employs the concepts of ascending truth and descending truth, and they determine how the extension of the truth predicate varies across contexts of assessment. This assessment-sensitive theory of truth solves the liar and other paradoxes, it is compatible with classical logic and all the expressive resources we have in natural language, and it does not give rise to any new paradoxes.