 A radical solution, which never won big consensus but has been revitalised in recent times (Pleitz 2018), has it that there just cannot be meaningful self-rererential sentences. Various works (notably Martin 1967, van Fraassen 1968, Kripke 1975, Field 2008) have proposed to solve the Liar paradox by dismissing Bivalence, whereby some sentences are neither true nor false, and the Liar is one such truth value ‘gap’. Truth value gaps, and the inclusion of the Liar among them, are differently motivated in the various approaches. But the common core thought is the following: even though the Liar is a sentence such that, if it were true, it would be false, and vice versa, no explicit contradiction according to which it is both true and false need follow. We can avoid the contradiction by rejecting the idea that truth and falsity are the only two options for a sentence: the Liar is neither. For a comparative survey of the two kinds of approach, see Beall and Ripley 2018.