Liar Paradox and Substitution into Intensional Contexts

John Barker, in two recent essays, raises a variety of intriguing criticisms to challenge my interpretation of the liar paradox and the type of solution I propose in ‘Denying the Liar’ and ‘Denying the Liar Reaffirmed.’ Barker continues to believe that I have misunderstood the logical structure of the liar sentence and its expression, and that as a result my solution misfires. I shall try to show that on the contrary my analysis is correct, and that Barker does not properly grasp what my solution to the liar paradox involves. Additionally, I argue that Barker makes fundamental errors in the explanation of liar sentence formulations in intensional contexts and in the classical metatheory he invokes to support his criticisms. 1. Liar Paradox Redux One cannot exhaust the logical and philosophical interest in the liar paradox, even when to some it seems through a variety of methods to have been finally resolved. In ‘Disquotation, Conditionals, and the Liar’ (Barker, 2009), John Barker takes a second stab at criticizing my solution to the liar in my essay, ‘Denying the Liar’ (Jacquette, 2007), which he first attacks in, ‘Undeniably Paradoxical: Reply to Jacquette’ (Barker, 2008), and again in my reply, ‘Denying the Liar Reaffirmed’ (Jacquette, 2008). Barker in his more recent essay has tightened up his arguments considerably, but I find the new formulations in which he purports to pay careful attention to the intensional contexts in which the liar sentence is expressed, together with his appeal to Gödel’s incompleteness results, to be logically inconclusive when they are not simply mistaken. Barker avoids reacting to the individual countercriticisms I offered in defense of my original solution to the liar paradox in (Jacquette, 2008), when he writes that: ‘Jacquette has offered a veritable laundry-list of complaints about my original paper. It would be easy enough to respond point-by-point, but such a response would try my reader’s patience’ (Barker, 2009). My intention, I should mention, was not to take Barker to the cleaners, but rather to answer systematically the separate components of the criticism he made in his (2008), and I wish he had done the same here in response. Would it really try the patience of readers already interested in the