An Analysis of the Liar Paradox

It seems that the most common strategy to solve the liar paradox is to argue that liar sentences are meaningless and, consequently, truth-valueless. The other main option that has grown in recent years is the dialetheist view that treats liar sentences as meaningful, truth-apt and true. In this paper I will offer a new approach that does not belong in either camp. I hope to show that liar sentences can be interpreted as meaningful, truth-apt and false, but without engendering any contradiction. This seemingly impossible task can be accomplished once the semantic structure of the liar sentence is unpacked by a quantified analysis. The paper will be divided in two sections. In the first section, I present the independent reasons that motivate the quantificational strategy and how it works in the liar sentence. In the second section, I explain how this quantificational analysis allows us to explain the truth teller sentence and a counter-example advanced against truthmaker maximalism, and deal with some potential objections.

Russell's paradox shows that the set of all sets does not exist, which gives an example of set theoretical paradox. To resolve a version of this paradox, Russell proposed a theory of types, and then the type hierarchy to infinity appeared in the resolution of the paradox. Victor gave a solution to remove the infinite type hierarchy by proposing his Duality Principle, which not only can solve Russell's paradox, but also can solve the Liar's paradox. In this paper, I contend the completeness of meanings in Duality Principle. Firstly, in solving the Russell's paradox, I assert that the complete meaning of a set should contain Miscellaneous Sets such as A={a,{b}}, in addition to Pure Sets {a,b,c} and Set of Sets {{a},{{b},c}}. And this will require solution of Russel's paradox by Duality principle change its disjunction condition to have 3 conditions. i.e A set is either a Pure Set, or a Set of Sets, or a Miscellaneous Set. Then his original solution can not follow these new conditions of the Duality Principle. Secondly, in resolving the Liar's paradox by Victor's Duality Principle, I argue that the completeness of meaning of a statement, in addition to {a statement, a statement about statements}, there should be also { a statement about (statement about statements) }. It means that the original meaning of a statement is incomplete, there are more meanings of a statement such that it is a complete set of meanings. However, this will push us to Russell's infinite type hierarchy which Victor tried to avoid. Therefore, I myself would like to give the meaning of a statement in Liar's paradox as a Boolean function, which in turn renders the Dialetheism.

In The Philosophy of David Kaplan, Edited by J. Almog and P. Leonardi, Oxford University Press, 2009

2018

SU M M A RY: Our approach to the liar paradox is based on the Wittgensteinian approach to semantic and logical paradoxes. The main aim of this article is to point out that the liar sentence is only seemingly intelligible, and that it has not been given any sense. First, we will present the traditional solutions of the paradox, especially those which we call modificational. Then we will determine what the defects of these solutions are. Our main objection is that the modificational approaches assume that we can express in languages certain senses which are improper. Next, we will explain why we think that the liar sentence is a mere nonsense. This sentence does not have any role in any language game – it is completely useless. We will also respond to several objections to our approach. 1. That it is not consistent with the principle of compositionality of sense. 2. According to the Quineian philosophy of logic, paradoxical sentences can be conceived as false assumptions leading to cr...

Croatian Journal of Philosophy 23 (67): 1-31. 2023., 2020

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions ("the revenge of the Liar"). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical two-valued language. Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fi xed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIF-PSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out.

Rescher 1967 discusses the pros and cons of having hybrid truth-values vis-à-vis triviality and the loss or gain of tautologies and antilogies. We argue that hybrid truth-values are not an option for systems within the scope of the hexagon of oppositions, and try to clarify certain issues of many-valued logics, such as the basic distinction between half-truths and teratologies.

Truth and Paradox, 2004

Reviews the standard semantic paradoxes, and constructs a simple formal language in which the paradoxical reasoning can be reconstructed. Particular attention is paid to Löb's paradox, which allows for the derivation of any sentence in the language as a theorem. The advantages of a natural deduction system over an axiomatic logic is discussed.

Topoi, 2012

Anti-realistic conceptions of truth and falsity are usually epistemic or inferentialist. Truth is regarded as knowability, or provability, or warranted assertability, and the falsity of a statement or formula is identified with the truth of its negation. In this paper, a non-inferentialist but nevertheless anti-realistic conception of logical truth and falsity is developed. According to this conception, a formula (or a declarative sentence) A is logically true if and only if no matter what is told about what is told about the truth or falsity of atomic sentences, A always receives the top-element of a certain partial order on non-ontic semantic values as its value. The ordering in question is a told-true order. Analogously, a formula A is logically false just in case no matter what is told about what is told about the truth or falsity of atomic sentences, A always receives the top-element of a certain told-false order as its value. Here, truth and falsity are pari passu, and it is the treatment of truth and falsity as independent of each other that leads to an informational interpretation of these notions in terms of a certain kind of higher-level information.

2001

On the basis of elementary thinking about language functioning, a solution of truth paradoxes is given and a corresponding semantics of a truth predicate is founded. It is shown that it is precisely the two-valued description of the maximal intrinsic xed point of the strong Kleene threevalued semantics.