Resumen de Alethic undecidability doesn’t solve the Liar
1. Introduction 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.
2. Barker’s account 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.
Truth or falsity requires a sentence to connect, eventually, to non-alethic facts. Barker (2014: 202) offers two examples of this connection failing. Consider the following infinite sequence of sentences:
Or, consider the truth-teller sentence:
In each case, no sentence has the right kind of connection to non-alethic facts. They are ground-unspecifiable (Barker 2014: 203). Notice that there’s nothing paradoxical about such cases: we can consistently assign them all the value true or all the value false. But Barker claims, based on …
