This article examines Kevin Scharp’s formal solution to the alethic paradoxes, ADT, which stands for ascending and descending truth. One of the main supposed benefits of ADT over its competitors is that it alone can validate the uses of truth concepts in theoretical contexts, such as truth-theoretic semantics. The appendixes contain a new consistency proof for ADT, and additionally show that it is conservative. As a result of its conservativity, the article argues that ADT faces a problem in accounting for certain mathematical uses of truth. Thus, Scharp’s theory needs to be amended in order to fulfill its aim of replicating all substantive uses of truth.
"On the Status of Reflection and Conservativity in Replacement Theories of Truth." Notre Dame J. Formal Logic 59 (3) 437 - 454, 2018. https://doi.org/10.1215/00294527-2018-0004