Is There a Gödelian Liar Sentence?

2018 ◽  
pp. 203-232
Keyword(s):  
Liar Sentence

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.

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.

NAIVE TRUTH AND RESTRICTED QUANTIFICATION: SAVING TRUTH A WHOLE LOT BETTER

2013 ◽  
Vol 7 (1) ◽  
pp. 147-191 ◽  
Author(s):  
HARTRY FIELD
Keyword(s):  
Fixed Point ◽  
Truth Theory ◽  
Semantic Paradoxes ◽  
Nonclassical Logic ◽  
Naive Theories ◽  
Liar Sentence ◽  
Nonclassical Logics ◽  
Restricted Quantification ◽  
Definition Of ◽  
Naïve Truth Theory

AbstractRestricted quantification poses a serious and under-appreciated challenge for nonclassical approaches to both vagueness and the semantic paradoxes. It is tempting to explain “All A are B” as “For all x, if x is A then x is B”; but in the nonclassical logics typically used in dealing with vagueness and the semantic paradoxes (even those where ‘if … then’ is a special conditional not definable in terms of negation and disjunction or conjunction), this definition of restricted quantification fails to deliver important principles of restricted quantification that we’d expect. If we’re going to use a nonclassical logic, we need one that handles restricted quantification better.The challenge is especially acute for naive theories of truth—roughly, theories that take True(〈A〉) to be intersubstitutable with A, even when A is a “paradoxical” sentence such as a Liar-sentence. A naive truth theory inevitably involves a somewhat nonclassical logic; the challenge is to get a logic that’s compatible with naive truth and also validates intuitively obvious claims involving restricted quantification (for instance, “If S is a truth stated by Jones, and every truth stated by Jones was also stated by Smith, then S is a truth stated by Smith”). No extant naive truth theory even comes close to meeting this challenge, including the theory I put forth in Saving Truth from Paradox. After reviewing the motivations for naive truth, and elaborating on some of the problems posed by restricted quantification, I will show how to do better. (I take the resulting logic to be appropriate for vagueness too, though that goes beyond the present paper.)In showing that the resulting logic is adequate to naive truth, I will employ a somewhat novel fixed point construction that may prove useful in other contexts.

The Liar without Truth

2017 ◽  
Author(s):  
Ian Rumfitt ◽  
Bradley Armour-Garb
Keyword(s):  
Liar Sentence ◽  
Definition Of ◽  
The Liar

Liar sentences say nothing, according to this chapter—which, it claims, we can, in effect, prove. But extending the proof as the chapter does appears to result in revenge. The solution to this problem is to restrict the laws of logic by distinguishing expressing a falsehood from failing to express a truth. But the question that presses is how we can signify that a given sentence—a liar sentence, for example—fails to express a truth without being mired in paradox. To this end, the chapter revisits the sort of bilateral system that Rumfitt (2000) has discussed. The chapter shows that there is a way of developing Aristotle’s conception of truth into a definition of truth that does not yield a contradiction, even when applied to a semantically closed language. If successful, the proposal will enable us to reject a Strengthened Liar as untrue without asserting its negation.

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.

scholarly journals From Paradox to Judgment: towards a metaphysics of expression

2005 ◽  
Vol 3 ◽  
Author(s):  
Mariam Thalos
Keyword(s):  
Language Use ◽  
Human Judgment ◽  
Liar Sentence ◽  
Important Clue ◽  
The Liar

The Liar sentence is a singularly important piece of philosophical evidence. It is an instrument for investigating the metaphysics of expressing truths and falsehoods. And an instrument too for investigating the varieties of conflict that can give rise to paradox. It shall serve as perhaps the most important clue to the shape of human judgment, as well as to the nature of the dependence of judgment upon language use.

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.

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