Undeniably Paradoxical: Reply to Jacquette

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. Jacquette chooses the following formalization for the disquotational schema: