Construction of Truth Predicates: Approximation Versus Revision

1998 ◽  
Vol 4 (4) ◽  
pp. 399-417 ◽  
Author(s):  
Juan Barba
Keyword(s):  
Liar Paradox ◽  
Predicate Symbol ◽  
Main Idea ◽  
Truth Predicate ◽  
Order Language ◽  
Fixed Model ◽  
Contextual Dependence ◽  
The Subject ◽  
Concept Of Truth ◽  
The Liar

§1. Introduction. The problem raised by the liar paradox has long been an intriguing challenge for all those interested in the concept of truth. Many “solutions” have been proposed to solve or avoid the paradox, either prescribing some linguistical restriction, or giving up the classical true-false bivalence or assuming some kind of contextual dependence of truth, among other possibilities. We shall not discuss these different approaches to the subject in this paper, but we shall concentrate on a kind of formal construction which was originated by Kripke's paper “Outline of a theory of truth” [11] and which, in different forms, reappears in later papers by various authors.The main idea can be presented as follows: assume a first order language ℒ containing, among other unspecified symbols, a predicate symbol T intended to represent the truth predicate for ℒ. Assume, also, a fixed model M = 〈D, I〉 (the base model)where D contains all sentences of ℒ and I interprets all non-logical symbols of ℒ except T in the usual way. In general, D might contain many objects other than sentences of ℒ but as that would raise the problem of the meaning of sentences in which T is applied to one of these objects, we shall assume that this is not the case.

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.

A theory of properties

1987 ◽  
Vol 52 (2) ◽  
pp. 455-472 ◽  
Author(s):  
Ray Turner
Keyword(s):  
Recent Work ◽  
Set Theory ◽  
Semantic Theory ◽  
Truth Predicate ◽  
Minimal Logic ◽  
History Of ◽  
Concept Of Truth ◽  
Almost All ◽  
The Liar ◽  
Self Reference

Frege's attempts to formulate a theory of properties to serve as a foundation for logic, mathematics and semantics all dissolved under the weight of the logicial paradoxes. The language of Frege's theory permitted the representation of the property which holds of everything which does not hold of itself. Minimal logic, plus Frege's principle of abstraction, leads immediately to a contradiction. The subsequent history of foundational studies was dominated by attempts to formulate theories of properties and sets which would not succumb to the Russell argument. Among such are Russell's simple theory of types and the development of various iterative conceptions of set. All of these theories ban, in one way or another, the self-reference responsible for the paradoxes; in this sense they are all “typed” theories. The semantical paradoxes, involving the concept of truth, induced similar nightmares among philosophers and logicians involved in semantic theory. The early work of Tarski demonstrated that no language that contained enough formal machinery to respresent the various versions of the Liar could contain a truth-predicate satisfying all the Tarski biconditionals. However, recent work in both disciplines has led to a re-evaluation of the limitations imposed by the paradoxes.In the foundations of set theory, the work of Gilmore [1974], Feferman [1975], [1979], [1984], and Aczel [1980] has clearly demonstrated that elegant and useful type-free theories of classes are feasible. Work on the semantic paradoxes was given new life by Kripke's contribution (Kripke [1975]). This inspired the recent work of Gupta [1982] and Herzberger [1982]. These papers demonstrate that much room is available for the development of theories of truth which meet almost all of Tarski's desiderata.

Tarski on the Concept of Truth

2018 ◽  
Author(s):  
Greg Ray
Keyword(s):  
Liar Paradox ◽  
What Is Said ◽  
Truth Definition ◽  
Concept Of Truth ◽  
First Time ◽  
The Liar ◽  
The Liar Paradox

Alfred Tarski’s work on truth has been so central to the discourse on truth that most coming to it for the first time have probably already heard a great deal about what is said there. Unfortunately, since the work is largely technical and Tarski was only tangentially philosophical, a certain incautious assimilation dominates many philosophical discussions of Tarski’s ideas, and so, examining Tarski on the concept of truth is in many ways an act of unlearning. This chapter will focus on key ideas in Tarski’s work that have had a lasting impact: T-sentence, Convention T, Tarskian truth definition, and Tarski’s general limiting theses on the expressibility and definability of truth. Though these ideas are familiar in name, the chapter seeks to uncover and remove certain widespread misunderstandings. Tarski’s name also features prominently in discussions of the liar paradox, so we will discuss Tarski’s misunderstood connection to this ancient puzzle.

scholarly journals The Perceptual-cognitive Foundation of the Subject-predicate Structure

2020 ◽  
Author(s):  
Kaoru Takamatsu
Keyword(s):  
Propositional Logic ◽  
Mental Representations ◽  
Liar Paradox ◽  
Model Structure ◽  
System A ◽  
Logical Connectives ◽  
The Subject ◽  
Grammatical Structures ◽  
The Liar ◽  
The Liar Paradox

This article describes a theoretical attempt to found thesubject predicate structure of declarative sentences on a frameworkof the human perceptual cognitive system. The basis of this studyis the idea that perception and cognition of events in the worldwould form mental representations in the system , a kind of modelsof the events that embody pieces of information about the events.This idea suggests that such models have structures that correspondto grammatical structures of the linguistic expressions thatrepresent the events and express the pieces of informationembodied by the models. The model structure s that correspond tothe subject predicate structure and logical connectives have beenconstructed following the way in which the system should functionto form the models of the events. This construction of thestructures entails propositional logic. Application of the structurest o the liar paradox le ads t o a new solution of this paradox .Keywords:

Dialetheism and the Problem of the Missing Difference

SATS ◽  
2018 ◽  
Vol 19 (2) ◽  
pp. 89-110
Author(s):  
Gregory Scott Moss
Keyword(s):  
Conceptual Analysis ◽  
Classical Model ◽  
Liar Paradox ◽  
Necessary Condition ◽  
The Subject ◽  
The Liar ◽  
Philosophical Community ◽  
The Liar Paradox ◽  
Self Reference ◽  
Graham Priest

Abstract During the past few decades, Graham Priest has advocated for Dialetheism, the controversial position that some contradictions are true. Dialetheism entails that the Law of Non-Contradiction fails. In recent decades the philosophical community has begun to recognize the significant challenge posed by Priest’s arguments. Priest has primarily appealed to paradoxes of self-reference, such as the Liar Paradox, to support his position. Following Priest’s approach, I offer another argument for Dialetheism, which appeals to a self-referential paradox that has been more or less ignored in the philosophical literature on the subject: the paradox of the missing difference. When we reflect on the question ‘what is a concept?’ from the perspective of a classical model of conceptual analysis, we arrive at the paradox of the missing difference. Although contradictions may be improbable, when we reflect on the question ‘how is the domain of concepts possible?’ we are led to a startling principle: without dialetheia any theory concerning concept formation (from a classical perspective on concepts) would be impossible. Dialetheism is a necessary condition for the existence of a domain of concepts in general. As a result, Dialetheism may even be more central to philosophical reflection than even dialetheists themselves have recognized.

scholarly journals The Subject and the Quest for Truth: Heidegger and Lonergan on Truth

Phronimon ◽  
2020 ◽  
Vol 21 ◽  
Author(s):  
Patrick Owo Aleke
Keyword(s):  
Martin Heidegger ◽  
Linguistic Analysis ◽  
Truth Predicate ◽  
Bernard Lonergan ◽  
Adequate Account ◽  
Philosophical Investigations ◽  
The Subject ◽  
Concept Of Truth ◽  
Logical Semantic

Since the “elimination of the subject” from truth discourse by Frege, by identifying the subject—or rather the subjective—with the private and personal, philosophical investigations of truth have consciously or unconsciously truncated the role of the knowing subject in the quest for truth. The neglect of the subject has turned the exploration of truth into logical, semantic, conceptual or linguistic analysis of the truth predicate. The consequence of this is that some philosophers tend to treat truth as if it does not really matter; as is shown by their deflationary attitude towards truth or even the total denial of truth. Despite the prevalent elimination of the subject from truth discourses, two thinkers that acknowledge the importance of the subject in the exposition of the concept of truth are Martin Heidegger and Bernard Lonergan. In this paper I explore their positions and argue that Heidegger’s situating of the centrality of Dasein in relation to truth in disclosedness—as the basic state of Dasein’s ontological constitution—is inadequate. Following Lonergan, I argue that an adequate account of the centrality of the role of the subject can only be situated in the cognitional acts of the subject within the context of the human quest for knowledge, and that the pivotal cognitional act is the act of judgment.

scholarly journals Not Wanted: On Scharp’s Solution to the Liar

Erkenntnis ◽  
2019 ◽  
Author(s):  
Mark Pinder
Keyword(s):  
Natural Language ◽  
Alternative Treatment ◽  
Liar Paradox ◽  
Adequate Account ◽  
Liar Sentence ◽  
Truth Conditional ◽  
Concept Of Truth ◽  
Resultant Theory ◽  
The Liar ◽  
The Liar Paradox

AbstractKevin Scharp argues that the concept of truth is defective, and is therefore unable to play its intended role in natural language truth-conditional semantics. As such, for this theoretical purpose, Scharp constructs two replacements: ascending truth and descending truth. Scharp applies the resultant theory, AD semantics, to the liar sentence, thereby obtaining a novel solution to the liar paradox. The aim of the present paper is fourfold. First, I show that, contrary to Scharp’s claims, AD semantics in fact yields an inconsistency when applied to standard liar sentences. Second, I diagnose the problem: AD semantics mishandles negation. I propose an alternative treatment, resulting in what I call AD* semantics. Third, I show that AD* semantics gives Scharp the resources required to respond to an alleged revenge paradox that has been raised against his view. Finally, I argue that, these consequences notwithstanding, it remains unclear whether AD* semantics provides an adequate account of alethic paradoxes more generally.

Pluralism and the Liar

2017 ◽  
Author(s):  
Cory Wright ◽  
Bradley Armour-Garb
Keyword(s):  
Alternative Treatment ◽  
Liar Paradox ◽  
Recent Attempt ◽  
In Virtue Of ◽  
The Liar ◽  
The Liar Paradox

Pluralists maintain that there is more than one truth property in virtue of which bearers are true. Unfortunately, it is not yet clear how they diagnose the liar paradox or what resources they have available to treat it. This chapter considers one recent attempt by Cotnoir (2013b) to treat the Liar. It argues that pluralists should reject the version of pluralism that Cotnoir assumes, discourse pluralism, in favor of a more naturalized approach to truth predication in real languages, which should be a desideratum on any successful pluralist conception. Appealing to determination pluralism instead, which focuses on truth properties, it then proposes an alternative treatment to the Liar that shows liar sentences to be undecidable.

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