The Strengthened Liar Problem

Standard liar sentences seem to claim themselves false; strong liar sentences seem to claim themselves untrue. The most popular diagnosis of liar sentences, from ancient to modern times, is that they are neither true nor false. But this doesn't work for strong liars—if strong liar sentences are neither true nor false, then they are not true, but that is what they say, so they are true. This generates the strengthened liar problem for gap theories. This is a philosophical problem, not a formal or technical problem. But despite the continuing popularity of gap theories, there is no consensus resolution of this problem. Here I critically survey the main options, ultimately arguing that the one option that has never been seriously pursued in the literature—that the putative referring terms in strong liar sentences do not refer—is well-motivated by gap theories that see liar sentences as semantically malfunctioning.