Abstract

The liar paradox results from a line of reasoning that starts with the liar sentence, ‘This sentence is false’ and ends with a contradictory conclusion, ‘The liar sentence is both true and false’. There have been solutions to the paradox that preserve the standard conception of truth and the classical notion of logical validity. In this paper, I explore nonstandard solutions to it. In particular, I focus on two non-classical solutions to the liar paradox; viz., the gappy and the glutty solutions. According to the gappy solution, the liar sentence is neither true nor false, and the reasoning that leads to the paradoxical conclusion is unsound. On the other hand, according to the glutty solution, the paradoxical conclusion is correct, but any subsequent reasoning from it is invalid. I show some ways of motivating each of these solutions. Next, I show what each implies about the notions of truth and validity, and how each solves the paradox. Finally, I highlight some of the more recent problems that could be pitted against each of these solutions.