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2018 On the Status of Reflection and Conservativity in Replacement Theories of Truth
Jeffrey R. Schatz
Notre Dame J. Formal Logic 59(3): 437-454 (2018). DOI: 10.1215/00294527-2018-0004


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.


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Jeffrey R. Schatz. "On the Status of Reflection and Conservativity in Replacement Theories of Truth." Notre Dame J. Formal Logic 59 (3) 437 - 454, 2018.


Received: 2 February 2016; Accepted: 11 May 2016; Published: 2018
First available in Project Euclid: 26 June 2018

zbMATH: 06939330
MathSciNet: MR3832091
Digital Object Identifier: 10.1215/00294527-2018-0004

Primary: 03Axx

Keywords: formal theories of truth , liar paradox , philosophical logic , replacement theories , Truth

Rights: Copyright © 2018 University of Notre Dame


Vol.59 • No. 3 • 2018
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