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.

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.

Holisme et homophonie

Dialogue ◽  
2000 ◽  
Vol 39 (1) ◽  
pp. 123-128
Author(s):  
Madeleine Arseneault ◽  
Robert Stainton
Keyword(s):  
Object Language ◽  
Right Hand ◽  
Left And Right ◽  
The Difference ◽  
Definition Of ◽  
The Liar

AbstractWe believe that, granting radical holism, a homophonie (or disquotational) definition of truth for a language achieves no progress towards guaranteeing the material equivalence of the left- and right-hand-side sentences for T-sentences. In order to avoid paradoxes such as the antinomy of the liar, Tarski requires that the metalanguage be semantically richer than the object language. For a radical holist, the difference in semantic powers of the meta- and object languages means that homophony is no guarantee of synonymy; therefore, worries about the indeterminacy of translation still apply.

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.

Lying and Certainty

2018 ◽  
pp. 169-182
Author(s):  
Neri Marsili
Keyword(s):  
Epistemic Modals ◽  
Philosophical Literature ◽  
Absolute Certainty ◽  
Definition Of ◽  
The Liar

In the philosophical literature on the definition of lying, the analysis is generally restricted to cases of flat-out belief. This chapter considers lies involving partial beliefs (beliefs ranging from mere uncertainty to absolute certainty). The first section analyses graded-belief lies: lies uttered while holding a graded belief in the falsity of the assertion. A revised insincerity condition is introduced to deal with these cases, requiring that the liar believes the assertion to be more likely to be false than true. The second section analyses assertions that express graded beliefs, exploring how epistemic modals affect the insincerity conditions of a given utterance. The last section considers the case of lies that attack certainty (knowledge lies), understood as attempts to alter the hearer’s graded beliefs.

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.

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 Scepsis and paradox: the problem of skepticism in Plato and the ancient tradition of paradoxes

2019 ◽  
Vol 13 (2) ◽  
pp. 683-694
Author(s):  
Roman Svetlov ◽  
Konstantin Shevtsov
Keyword(s):  
Specific Aspect ◽  
The Future ◽  
The Subject ◽  
Logical Paradoxes ◽  
Definition Of ◽  
The Liar

The subject of the research is the question of what texts of Plato could become a stimulus for the formation of skeptical ideas in the Academy. Can we, in particular, raise the question of the presence in the texts of Plato of something similar to the principle of the “epoche”, which is the most important methodological sign of skepticism? Can be compared with skepticism the elenchic strategy of Socrates? In our opinion, there are a number of moments in the works of Plato, which brings him closer to skeptical discourse (although this does not make him a skeptic). We dwell only on two of them. The first is the ability of the protagonists of his dialogues to hold in their arguments the two opposite sides of the subject in their undoubted difference and, at the same time, in mutual necessity. This is the Platonic dialectic in its true expression, examples of which we see in the Sophistes and the Parmenides. The second specific aspect of Plato's thought is in the formulation by Plato of a number of logical paradoxes. In its classic version, it became known, however, a little later, in the works of representatives of the Megarian school. We shall deal in more detail with the paradox of the liar, or “the thesis of Epimenides”, which is often seen as a classic example of a self-referential statement. The article will show analogies to the paradox of the liar in Plato's texts. The key point is the last argument from the Theaetetus, where Socrates examines the definition of knowledge as a true opinion with the addition of a specifying attribute (Thaet 201c-208d), as well as the 7th and 8th hypotheses of the Parmenides (Parm. 164b-166c). It seems to us that this moment of the Platonic dialectic also turns out to be a definite resource for the future “skeptical turn” in the Academy. Especially in the situation when the dialogues of Plato were discussed in terms of interest in the arguments of Pyrrho and the Megarians, for whom paradoxes were one of the important methodological tools.

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