Dialetheism and the Graphic Liar

2012 ◽  
Vol 42 (1) ◽  
pp. 15-27
Author(s):  
Greg Littmann
Keyword(s):  
Classical Logic ◽  
Liar Paradox ◽  
The Other ◽  
Liar Sentence ◽  
Other Hand ◽  
Standard Response ◽  
The Liar ◽  
The Liar Paradox

A Liar sentence is a sentence that, paradoxically, we cannot evaluate for truth in accordance with classical logic and semantics without arriving at a contradiction. For example, consider LL L is falseIf we assume that L is true, then given that what L says is ‘L is false,’ it follows that L is false. On the other hand, if we assume that L is false, then given that what L says is ‘L is false,’ it follows that L is true. Thus, L is an example of a Liar sentence.Several philosophers have proposed that the Liar paradox, and related paradoxes, can be solved by accepting the contradictions that these paradoxes seem to imply (including Priest 2006, Rescher and Brandom 1980). The theory that there are true contradictions is known as ‘dialetheism’ and we may call this the ‘dialethic solution.’ One standard response to the dialethic solution to the Liar paradox and related paradoxes has been to attempt to develop new ‘revenge’ versions of the paradoxes that are not subject to the dialethic solution (e.g. Parsons 1990, Restall 2007, Shapiro 2007).

Jalāl ad-Dīn ad-Dawānī’s Solution to the Liar Paradox and Its Reception in Qāḍī Mubārak and Mullā Mubīn

2018 ◽  
Vol 1 (2) ◽  
pp. 183-220 ◽  
Author(s):  
Hassan John Rezakhany
Keyword(s):  
Liar Paradox ◽  
The Other ◽  
Major Premise ◽  
Present Evidence ◽  
False Self ◽  
Liar Sentence ◽  
Truth Value ◽  
The One ◽  
The Liar ◽  
The Liar Paradox

AbstractI examine the views of Jalāl ad-Dīn ad-Dawānī (d. 1502) on the Liar paradox and their reception in the work of Qāḍī Mubārak (d. 1748) and Mullā Mubīn (d. 1810). Dawānī argues that the Liar sentence is neither true nor false since it is not the kind of utterance that is capable of bearing a truth-value (i.e., it is not truth-apt). In the course of justifying this view, he proposes a criterion for a sentence’s being truth-apt and attempts to counter a number of objections. I address two of these: one involves certain intuitively true or false self-referential sentences and the other is the ‘strengthened Liar.’ I then argue that both Qāḍī Mubārak and Mullā Mubīn present a version of the solution Dawānī gives in his Sharḥ at-Tahdhīb and, moreover, that Dawānī does not endorse this solution in all his other works. Furthermore, the solution they attribute to Dawānī differs slightly from the one he gives in his Sharḥ at-Tahdhīb in terms of how the major premise is justified. I present evidence which shows that this modification was inspired by Mīr Zāhid al-Harawī’s (d. 1689) gloss on Dawānī’s Sharḥ at-Tahdhīb.

Non-Classical Theories of Truth

2018 ◽  
Author(s):  
Jc Beall ◽  
David Ripley
Keyword(s):  
Classical Logic ◽  
Liar Paradox ◽  
Theories Of Truth ◽  
The Liar ◽  
The Liar Paradox

This chapter gives a brief overview of theories of truth based on non-classical logics. It sticks to the most central motivation for such theories—the liar paradox—and focuses on a range of responses that have been made to this paradox. The chapter presents the paradox, and shows how it leads to trouble for classical logic. Then the chapter proceeds to lay out four families of response, which we call “paracomplete,” “paraconsistent,” “nontransitive,” and “noncontractive.” For each kind of theory, the chapter goes on to show how it can block paradoxical derivations, and gives references to sources that develop it more fully.

The Liar Parody

Philosophy ◽  
1988 ◽  
Vol 63 (243) ◽  
pp. 43-62
Author(s):  
Don S. Levi
Keyword(s):  
Liar Paradox ◽  
Liar Sentence ◽  
The Liar ◽  
The Liar Paradox

The Liar Paradox is a philosophical bogyman. It refuses to die, despite everything that philosophers have done to kill it. Sometimes the attacks on it seem little more than expressions of positivist petulance, as when the Liar sentence is said to be nonsense or meaningless. Sometimes the attacks are based on administering to the Liar sentence arbitrary if not unfair tests for admitting of truth or falsity that seem designed expressly to keep it from qualifying. Some philosophers have despaired of ever beating the Liar; so concerned have they been about the threat posed by the Liar that they have introduced legislation to exclude the Liar sentence and anything like it.

Paradoxes of Definability, Russell’s Paradox, the Liar

2018 ◽  
Author(s):  
Keith Simmons
Keyword(s):  
Liar Paradox ◽  
The Other ◽  
Mathematical Notion ◽  
Russell’S Paradox ◽  
Semantic Notion ◽  
Russell's Paradox ◽  
The Liar ◽  
The Liar Paradox

Chapter 5 moves beyond the simple paradoxes discussed in Chapters 2-4. The chapter applies the singularity approach to the traditional paradoxes of definability (or denotation), associated with Berry, Richard, and König. The chapter goes on to argue that there are two settings for Russell’s paradox, one in terms of the mathematical notion of set, and the other in terms of the logico-semantic notion of extension. The chapter then applies the singularity approach to Russell’s paradox for extensions. The chapter moves on to the case of truth, and applies the singularity approach to various versions of the Liar paradox, paying particular attention to the so-called strengthened Liar.

Thinking about the Liar, Fast and Slow

2017 ◽  
Author(s):  
Robert Barnard ◽  
Joseph Ulatowski ◽  
Jonathan M. Weinberg ◽  
Bradley Armour-Garb
Keyword(s):  
Moral Responsibility ◽  
Free Will ◽  
Liar Paradox ◽  
The Past ◽  
Liar Sentence ◽  
The Status ◽  
The Liar ◽  
The Liar Paradox

In the past, experimental philosophers have explored the psychological underpinning of a number of notions in philosophy, including free will, moral responsibility, and more. But prior to this chapter, although a number of philosophers have speculated on how ordinary folks might, or should, think about the liar paradox, no one had systematically explored the psychological underpinnings of the Liar itself. The authors take on this task. In particular, the chapter investigates the status of a liar sentence, L = ‘Sentence L is false’. The thesis, arrived at by interpreting the data the authors have accrued, is that reflective thinkers (some of whom possess a modicum of philosophical expertise) judge L to be neither true nor false (as opposed to false or true), and the authors see this as some evidence for the claim that L is neither true nor false.

The liar paradox in the predictive mind

2020 ◽  
Vol 26 (2-3) ◽  
Author(s):  
Unknown / not yet matched
Keyword(s):  
Language Processing ◽  
Conceptual Knowledge ◽  
Liar Paradox ◽  
Predictive Processing ◽  
World Knowledge ◽  
Psychological Issues ◽  
Liar Sentence ◽  
The Liar ◽  
The Liar Paradox ◽  
Conceptual Competence

Abstract Most discussions frame the Liar Paradox as a formal logical-linguistic puzzle. Attempts to resolve the paradox have focused very little so far on aspects of cognitive psychology and processing, because semantic and cognitive-psychological issues are generally assumed to be disjunct. I provide a motivation and carry out a cognitive-computational treatment of the liar paradox based on a cognitive-computational model of language and conceptual knowledge within the Predictive Processing (PP) framework. I suggest that the paradox arises as a failure of synchronization between two ways of generating the liar situation in two different (idealized) PP sub-models, one corresponding to language processing and the other to the processing of meaning and world-knowledge. In this way, I put forward the claim that the liar sentence is meaningless but has an air of meaningfulness. I address the possible objection that the proposal violates the Principle of Unrestricted Compositionality, which purportedly regulates the conceptual competence of thinkers.

The Early Arabic Liar: The Liar Paradox in the Islamic World from the Mid-Ninth to the Mid-Thirteenth Centuries CE

Vivarium ◽  
2009 ◽  
Vol 47 (1) ◽  
pp. 97-127 ◽  
Author(s):  
Ahmed Alwishah ◽  
David Sanson
Keyword(s):  
Liar Paradox ◽  
Truth Condition ◽  
Correspondence Theory ◽  
Islamic World ◽  
Liar Sentence ◽  
Correspondence Theory Of Truth ◽  
The Liar ◽  
Plural Subjects ◽  
The Liar Paradox

AbstractWe describe the earliest occurrences of the Liar Paradox in the Arabic tradition. The early Mutakallimūn claim the Liar Sentence is both true and false; they also associate the Liar with problems concerning plural subjects, which is somewhat puzzling. Abharī (1200-1265) ascribes an unsatisfiable truth condition to the Liar Sentence—as he puts it, its being true is the conjunction of its being true and false—and so concludes that the sentence is not true. Tūsī (1201-1274) argues that self-referential sen-tences, like the Liar, are not truth-apt, and defends this claim by appealing to a correspondence theory of truth. Translations of the texts are provided as an appendix.

Unsettled Problems with Vague Truth

1995 ◽  
Vol 25 (1) ◽  
pp. 103-117
Author(s):  
Andrew P. Mills
Keyword(s):  
Liar Paradox ◽  
Borderline Case ◽  
List Type ◽  
Type Number ◽  
Natural Reaction ◽  
Liar Sentence ◽  
Truth Value ◽  
The Liar ◽  
The Liar Paradox

A tempting solution to problems of semantic vagueness and to the Liar Paradox is an appeal to truth-value gaps. It is tempting to say, for example, that, where Harry is a borderline case of bald, the sentence(1)Harry is baldis neither true nor false: it is in the ‘gap’ between these two values, and perhaps deserves a third truth-value. Similarly with the Liar Paradox. Consider the following Liar sentence:(2)(2) is false.That is, sentence (2) says of itself that it is false. If we accept the Tarskian schema(T) S is true iff pwhere ‘S’ is a name of a sentence ‘p,’ we are led into paradox. Both the assumption that (2) is true, and the assumption that (2) is false lead us, via (T), to(3)(2) is true if and only if (2) is false.Given this result, a natural reaction is to place (2) in a ‘gap’ between true and false.

scholarly journals A Tale of Excluding the Middle

2021 ◽  
Vol 27 (1) ◽  
pp. 20-30
Author(s):  
Jc Beall ◽  
Graham Priest
Keyword(s):  
Liar Paradox ◽  
Liar Sentence ◽  
The Liar ◽  
The Liar Paradox ◽  
Excluded Middle

he paper discusses a number of interconnected points concerning negation, truth, validity and the liar paradox. In particular, it discusses an argument for the dialetheic nature of the liar sentence which draws on Dummett’s teleological account of truth. Though one way of formulating this fails, a different way succeeds. The paper then discusses the role of the Principle of Excluded Middle in the argument, and of the thought that truth in a model should be a model of truth.

scholarly journals Gestalt Shifts in the Liar orWhy KT4M Is the Logic of Semantic Modalities

2017 ◽  
Author(s):  
Susanne Bobzien ◽  
Bradley Armour-Garb ◽  
Bradley Armour-Garb
Keyword(s):  
Modal Logic ◽  
Classical Logic ◽  
Liar Paradox ◽  
Truth Predicate ◽  
Free Solution ◽  
Formal Representation ◽  
Concept Of Truth ◽  
The Liar ◽  
The Liar Paradox ◽  
Truth Operator

This chapter offers a revenge-free solution to the liar paradox and presents a formal representation of truth in, or for, a natural language like English, which proposes to show both why (and how) truth is coherent and how it appears to be incoherent, while preserving classical logic and most principles that some philosophers have taken to be central to the concept of truth and our use of that notion. The chapter argues that, by using a truth operator rather than truth predicate, it is possible to provide a coherent, model-theoretic representation of truth with various desirable features. After investigating what features of liar sentences are responsible for their paradoxicality, the chapter identifies the logic as the normal modal logic KT4M. Drawing on the structure of KT4M, the author proposes that, pace deflationism, truth has content, that the content of truth is bivalence, and that the notions of both truth and bivalence are semideterminable.

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