Truthmaker Gaps and the No-No Paradox

Abstract
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.
Keywords Analytic Philosophy  Contemporary Philosophy  Philosophy of Mind
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ISBN(s) 0031-8205
DOI 10.1111/j.1933-1592.2011.00491.x
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References found in this work BETA
Vagueness.Timothy Williamson - 1994 - Routledge.
Papers in Metaphysics and Epistemology.David K. Lewis - 1999 - Cambridge: Uk ;Cambridge University Press.
Vagueness and Contradiction.Roy A. Sorensen - 2001 - Oxford University Press.
Truthmaking and Difference-Making.David Lewis - 2001 - Noûs 35 (4):602–615.
Truthmaking Without Truthmakers.Joseph Melia - 2005 - In Helen Beebee & Julian Dodd (eds.), Truthmakers: The Contemporary Debate. Clarendon Press. pp. 67.

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Citations of this work BETA
Indeterminate Truth.Patrick Greenough - 2008 - Midwest Studies in Philosophy 32 (1):213-241.
The No-No Paradox Is a Paradox.Roy T. Cook - 2011 - Australasian Journal of Philosophy 89 (3):467-482.

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