Alethic undecidability doesn’t solve the Liar

Abstract

Stephen Barker ( 2014 ) presents a novel approach to solving semantic paradoxes, including the Liar and its variants and Curry’s paradox. His approach is based around the concept of alethic undecidability . His approach, if successful, renders futile all attempts to assign semantic properties ( truth , falsity , gap or glut) to the paradoxical sentences, whilst leaving classical logic fully intact. And, according to Barker, even the T-scheme remains valid, for validity is not undermined by undecidable instances. Barker’s approach is innovative and worthy of further consideration, particularly by those of us who aim to find a solution without logical revisionism. As it stands, however, the approach is unsuccessful, as I shall demonstrate below. Barker takes as his starting point a version of the truthmaker principle ( 2014 : 201): ... A non-alethic fact is something like a state of affairs not involving the properties truth or falsity : that students drink is one such fact, whereas that the proposition 〈that students drink〉is true is not, since the latter involves the property being true .