A Dilemma for Dialetheism

The Dualist 15 (Spring):21-31 (2010)
Abstract
Dialetheic accounts of the liar paradox hold that liar sentences are both true and false. One problem that besets accounts of the liar paradox is that of “revenge liars”. A revenge liar is a liar sentence which, while being of the same kind as the liar sentences an account attempts to handle, cannot be handled in the same way they are without generating contradictions that the account in question is powerless to resolve. It might be thought that dialetheic accounts are immune to revenge problems: If one can intelligibly hold that standard liars are both true and false, why not revenge liars as well? However, in this paper it is argued that dialetheism faces a dilemma: Either it cannot express the distinction between those sentences which are both true and false and those which are not, or else it too suffers from revenge problems. I explore a few different ways in which a dialetheist might try to avoid this dilemma. First, I present a variant of the logic called LP, and show both that it is subject to revenge problems and that it is not well suited to a dialetheic interpretation. Second, I develop a means of expressing the exclusive truth or falsity of sentences which can be utilized by any language that has certain features. Unfortunately, it leads straight to trivialism. Finally, I examine the claim that dialetheists can express the exclusive truth or falsity of sentences in the same way a non-dialetheist can, and conclude that they cannot do so. In the end, it seems that dialetheism’s dilemma is inescapable.
Keywords Dialetheism  Logic  Liar Paradox  Logical Paradoxes  Contradiction  Negation
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