Truthmaker Gaps and the No-No Paradox

Philosophy and Phenomenological Research 82 (3):547 - 563 (2011)
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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.

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Patrick Greenough
University of St. Andrews

Citations of this work

Ordinal Type Theory.Jan Plate - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
Indeterminate truth.Patrick Greenough - 2008 - Midwest Studies in Philosophy 32 (1):213-241.
A Unified Theory of Truth and Paradox.Lorenzo Rossi - 2019 - Review of Symbolic Logic 12 (2):209-254.
The No-No Paradox Is a Paradox.Roy T. Cook - 2011 - Australasian Journal of Philosophy 89 (3):467-482.

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References found in this work

Vagueness.Timothy Williamson - 1996 - New York: Routledge.
Vagueness.Timothy Williamson - 1995 - British Journal for the Philosophy of Science 46 (4):589-601.
Papers in Metaphysics and Epistemology: Volume 2.David Lewis - 1999 - Cambridge, UK ;: Cambridge University Press.
Vagueness and contradiction.Roy A. Sorensen - 2001 - New York: Oxford University Press.
Truthmaking and difference-making.David Lewis - 2001 - Noûs 35 (4):602–615.

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