Reference, paradoxes and truth

Walicki, Michał

doi:10.1007/s11229-008-9392-9

Cited by 17 publications

(7 citation statements)

References 18 publications

(27 reference statements)

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“…is the (object-linguistic term representing the primitive recursive) function g such that: 16 The idea of analysing semantic paradoxes via equations is already found in Wen (2001). Walicki (2009), Dyrkolbotn & Walicki (2014), Walicki (2017) combined this idea with a graphtheoretical analysis of sentences that employs a pointer structure closely related to the one developed by Gaifman (1988Gaifman ( , 1992Gaifman ( , 2000. Their approach differs from the one presented here in several respects.…”

Section: Liar-like Sentencesmentioning

confidence: 99%

“…3 See also Burgess (1986Burgess ( , 1988, Gupta & Belnap (1993), Kremer (2009). 4 See e.g., Davis (1979), Hazen (1981), Barwise & Etchemendy (1987), Gaifman (1988), Gaifman (1992), Yi (1999), Gaifman (2000), Cook (2004), Maudlin (2004), Cook (2006), Schlenker (2007), Walicki (2009), Rabern, Rabern, & Macauley (2013), Cook (2014), Dyrkolbotn & Walicki (2014), Hansen (2015), Walicki (2017), Beringer & Schindler (2017). 5 Consider the treatment of liar and truth-teller sentences in fixed-point and revision theories: in both approaches, several models have to be considered to differentiate liar sentences, truth-teller sentences, and truths or falsities of the base language.…”

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confidence: 99%

“…21 See e.g.,Yablo (1985, p. 130). For analyses of semantic paradoxes that employ graphs (and therefore feature loops as well), see e.g.,Barwise & Etchemendy (1987),Gaifman (1988Gaifman ( , 1992Gaifman ( , 2000,Schlenker (2007),Walicki (2009),Rabern, Rabern, & Macauley (2013),Cook (2014),Beringer & Schindler (2017).…”

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confidence: 99%

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A Unified Theory of Truth and Paradox

Rossi

2019

The Review of Symbolic Logic

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The sentences employed in semantic paradoxes display a wide range of semantic behaviours. However, the main theories of truth currently available either fail to provide a theory of paradox altogether, or can only account for some paradoxical phenomena by resorting to multiple interpretations of the language, as in (Kripke, 1975). In this article, I explore the wide range of semantic behaviours displayed by paradoxical sentences, and I develop a unified theory oftruth and paradox, that is a theory of truth that also provides a unified account of paradoxical sentences. The theory I propose here yields a threefold classification of paradoxical sentences—liar-like sentences, truth-teller–like sentences, and revenge sentences. Unlike existing treatments of semantic paradox, the theory put forward in this article yields a way of interpreting all three kinds of paradoxical sentences, as well as unparadoxical sentences, within a single model.

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Section: Liar-like Sentencesmentioning

confidence: 99%

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confidence: 99%

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A Unified Theory of Truth and Paradox

Rossi

2019

The Review of Symbolic Logic

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“…These sentences contain two features which go beyond standard logic: references to other sentences, and a truth predicate. While it would be possible to make a more refined analysis directly modelling these features, we will not pursue this here, noting that it has been argued extensively and rather compellingly in much of the recent literature on the paradoxes that the essential content is preserved by replacing statements with these features by boolean equations [31,10,30]. For the Liar cycles, we introduce boolean variables x 1 , .…”

Section: Contextuality Logic and Paradoxesmentioning

confidence: 99%

Contextuality, Cohomology and Paradox

Abramsky,

Barbosa,

Kishida

et al. 2015

Preprint

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Contextuality is a key feature of quantum mechanics that provides an important non-classical resource for quantum information and computation. Abramsky and Brandenburger used sheaf theory to give a general treatment of contextuality in quantum theory [New Journal of Physics 13 ( 2011) 113036]. However, contextual phenomena are found in other fields as well, for example database theory. In this paper, we shall develop this unified view of contextuality. We provide two main contributions: first, we expose a remarkable connection between contexuality and logical paradoxes; secondly, we show that an important class of contextuality arguments has a topological origin. More specifically, we show that "All-vs-Nothing" proofs of contextuality are witnessed by cohomological obstructions.

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“…Further notable work in this area includes Bolander[3], Dyrkolbotn and Walicki[8], Gaifman[9], and Walicki[19].…”

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confidence: 99%

A Graph-Theoretic Analysis of the Semantic Paradoxes

Beringer¹,

Schindler²

2017

Bull. symb. log

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We introduce a framework for a graph-theoretic analysis of the semantic paradoxes. Similar frameworks have been recently developed for infinitary propositional languages by Cook [5, 6] and Rabern, Rabern, and Macauley [16]. Our focus, however, will be on the language of first-order arithmetic augmented with a primitive truth predicate. Using Leitgeb’s [14] notion of semantic dependence, we assign reference graphs (rfgs) to the sentences of this language and define a notion of paradoxicality in terms of acceptable decorations of rfgs with truth values. It is shown that this notion of paradoxicality coincides with that of Kripke [13]. In order to track down the structural components of an rfg that are responsible for paradoxicality, we show that any decoration can be obtained in a three-stage process: first, the rfg is unfolded into a tree, second, the tree is decorated with truth values (yielding a dependence tree in the sense of Yablo [21]), and third, the decorated tree is re-collapsed onto the rfg. We show that paradoxicality enters the picture only at stage three. Due to this we can isolate two basic patterns necessary for paradoxicality. Moreover, we conjecture a solution to the characterization problem for dangerous rfgs that amounts to the claim that basically the Liar- and the Yablo graph are the only paradoxical rfgs. Furthermore, we develop signed rfgs that allow us to distinguish between ‘positive’ and ‘negative’ reference and obtain more fine-grained versions of our results for unsigned rfgs.

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Reference, paradoxes and truth

Cited by 17 publications

References 18 publications

A Unified Theory of Truth and Paradox

A Unified Theory of Truth and Paradox

Contextuality, Cohomology and Paradox

A Graph-Theoretic Analysis of the Semantic Paradoxes

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