The liar paradox is standardly supposed to arise from three conditions: classical bivalent truth value semantics, the Tarskian truth schema, and the formal constructability of a sentence that says of itself that it is not true. Standard solutions to the paradox, beginning most notably with Tarski, try to forestall the paradox by rejecting or weakening one or more of these three conditions. It is argued that all efforts to avoid the liar paradox by watering down any of the three assumptions (...) suffers serious disadvantages that are at least as undesirable as the liar paradox itself. Instead, a new solution is proposed that admits that if the liar sentence is true then it is false, in the first paradox dilemma horn, but denies that the liar sentence is true, but asserting instead that it is false, and refuting the second paradox dilemma horn according to which it is supposed to follow that if the liar sentence is false then it is true. The reasoning for the second paradox dilemma horn is flawed, in that is not only not supported by but actually contradicted by the Tarskian truth schema. We could only infer the second dilemma horn if it were to clasically follow from the assumption that the liar sentence is false, and from the three liar paradox conditions, that therefore it is false that the liar sentence is false. This entire sentence can be shown to be false on the basis of the standard truth schema, thus blocking the paradox. Alternative formulations of the liar sentence are discussed, and the formal proofs and counterproofs for the two paradox dilemma horns, are considered along with the further philosophical implications of maintaining a resolute stance that the liar sentence is simply false. (shrink)

Tarski avoids the liar paradox by relativizing truth and falsehood to particular languages and forbidding the predication to sentences in a language of truth or falsehood by any sentences belonging to the same language. The Tarski truth-schemata stratify an object-language and indefinitely ascending hierarchy of meta-languages in which the truth or falsehood of sentences in a language can only be asserted or denied in a higher-order meta-language. However, Tarski’s statement of the truth-schemata themselves involve general truth functions, and in particular (...) the biconditional, defined in terms of truth conditions involving truth values standardly displayed in a truth table. Consistently with his semantic program, all such truth values should also be relativized to particular languages for Tarski. The objection thus points toward the more interesting problem of Tarski’s concept of the exact status of truth predications in a general logic of sentential connectives. Tarski’s three-part solution to the circularity objection which he anticipates is discussed and refuted in detail. (shrink)

In this paper I respond to Jacquette’s criticisms, in (Jacquette, 2008), of my (Barker, 2008). In so doing, I argue that the Liar paradox is in fact a problem about the disquotational schema, and that nothing in Jacquette’s paper undermines this diagnosis.

In this challenging and provocative analysis, Dale Jacquette argues that contemporary philosophy labours under a number of historically inherited delusions about the nature of logic and the philosophical significance of certain formal properties of specific types of logical constructions. Exposing some of the key misconceptions about formal symbolic logic and its relation to thought, language and the world, Jacquette clears the ground of some very well-entrenched philosophical doctrines about the nature of logic, including some of the most fundamental seldom-questioned parts (...) of elementary propositional and predicate-quantificational logic. Having presented difficulties for conventional ways of thinking about truth functionality, the metaphysics of reference and predication, the role of a concept of truth in a theory of meaning, among others, Jacquette proceeds to reshape the network of ideas about traditional logic that philosophy has acquired along with modern logic itself. In so doing Jacquette is able to offer a new perspective on a number of existing problems in logic and philosophy of logic. (shrink)

In this challenging and provocative analysis, Dale Jacquette argues that contemporary philosophy labours under a number of historically inherited delusions about the nature of logic and the philosophical significance of certain formal properties of specific types of logical constructions. Exposing some of the key misconceptions about formal symbolic logic and its relation to thought, language and the world, Jacquette clears the ground of some very well-entrenched philosophical doctrines about the nature of logic, including some of the most fundamental seldom-questioned parts (...) of elementary propositional and predicate-quantificational logic. Having presented difficulties for conventional ways of thinking about truth functionality, the metaphysics of reference and predication, the role of a concept of truth in a theory of meaning, among others, Jacquette proceeds to reshape the network of ideas about traditional logic that philosophy has acquired along with modern logic itself. In so doing Jacquette is able to offer a new perspective on a number of existing problems in logic and philosophy of logic. (shrink)

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.