Undeniably Paradoxical

Abstract

Jacquette’s proposed solution to the Liar paradox—namely, that the paradox can be defused by declaring Liar sentences to be false—is criticized. Specifically, it is argued that the proposed solution rests on misidentifying the condition that a sentence needs to satisfy in order to count as a Liar sentence. If Jacquette’s condition is used, then the resulting “Liar” sentences are indeed straightforwardly false; however, a genuine paradox remains if a more standard formulation is employed. Can we solve the Liar paradox by simply declaring Liar sentences to be false? That is the proposal of Dale Jacquette in (Jacquette 2007). The Liar paradox arises because apparently, we can derive a contradiction from the assumption that the Liar sentence is true, and we can also derive a contradiction from the assumption that it is false. Jacquette argues that the former reasoning (i.e., the derivation of a contradiction from the assumption that the Liar is true) is sound, while the latter reasoning is unsound. Thus, he argues, we can consistently hold Liar sentences to be false, thereby solving the Liar paradox. Unfortunately, Jacquette’s reasoning is flawed. Specifically, it depends on misidentifying the Liar paradox. Jacquette’s proposed solution does indeed solve a puzzle, of sorts; that puzzle just happens not to be the Liar paradox. As is well known, the Liar paradox is an apparent contradiction generated by (1) the Tarskian disquotational schema for the truth predicate, and (2) the fact that sentences can refer to themselves, and in particular, can ascribe falsehood to themselves. Jacqutte chooses the following formalization for the disquotational schema: (TS) ∀p [TRUE(ppq)↔ p] He also adds the following to “formalize commitment to bivalent logic”: