Truthmaker Gaps and the No-No Paradox

Consider the following sentences: The neighbouring sentence is not true. The neighbouring sentence is not true. Call these the no-no sentences. Symmetry considerations dictate that the no-no sentences must both possess the same truth-value. Suppose they are both true. Given Tarski’s truth-schema—if a sentence S says that p then S is true iff p—and given what they say, they are both not true. Contradiction! Conclude: they are not both true. Suppose they are both false. Given Tarski’s falsity-schema—if a sentence S (...) says that p then S is false iff not-p—and given what they say, they are both true, and so not false. Contradiction! Conclude: they are not both false. Thus, despite their symmetry, the no-no sentences must differ in truth-value. Such is the no-no paradox.[1] Sorensen (2001, 2005a, 2005b) has argued that: (1) The no-no paradox is not a version of the liar but rather a cousin of the truth-teller paradox. (2) Even so, the no-no paradox is more paradoxical than the truth-teller. (3) The no-no and truth-teller sentences have groundless truthvalues—they are bivalent but give rise to “truthmaker gaps”. (4) It is metaphysically impossible to know these truth-values. (5) A truthmaker gap response to the no-no paradox provides reason to accept a version of epistemicism. In this paper it is shown that a truthmaker gap solution to the no-no and truth-teller paradoxes runs afoul of the dunno-dunno paradox, the strengthened no-no paradox, and the strengthened truth-teller paradox. In consequence, the no-no paradox is best seen as a form of the liar paradox. As such, it cannot provide a case for epistemicism.