Ramsey était‐il “deflationniste”? C'est douteux, à lire attentivement le manuscrit “On Truth”. La position de Ramsey a nénmoins quelque chose de curieux, comme Austin l'a fait remarquer: quel est l'intérêt d'éliminer le prédicat de vérité sile problème de la vérité n'est pas en même temps éliminé? En poursuivant ces remarques, je suggére, à titre d'expérience de pensée, de lire autrement les fameuses “équivalencesT”.

We give a survey on truth theories for applicative theories. It comprises Frege structures, universes for Frege structures, and a theory of supervaluation. We present the proof-theoretic results for these theories and show their syntactical expressive power. In particular, we present as a novelty a syntactical interpretation of ID1 in a applicative truth theory based on supervaluation.

We introduce a notion of semantical closure for theories by formalizing Nepeivoda notion of truth. [10]. Tarski theorem on truth definitions is discussed in the light of Kleene's three valued logic (here treated with a formal reinterpretation of logical constants). Connections with Definability Theory are also established.

This paper develops a classical model for our ordinary use of the truth predicate (1) that is able to address the liar's paradox and (2) that satisfies a very strong version of deflationism. Since the model is a classical in the sense that it has no truth value gaps, the model is able to address Tarski's indictment of our ordinary use of the predicate as inconsistent. Moreover, since it is able to address the liar's paradox, it responds to arguments against (...) deflationism based upon that paradox alone. The model is based upon a notion of the complexity of propositions that a fixed set of speakers might express. A context-sensitive definition of the truth predicate is then provided based upon a class of possible worlds defined in terms of these speakers. Reasonable constraints on the memories and lifetimes of ordinary speakers are used to limit the set of propositions that they might express so that deflationist requirements are satisfied. (shrink)

In defense of the minimalist conception of truth, Paul Horwich(2001) has recently argued that our acceptance of the instances of the schema,`the proposition that p is true if and only if p', suffices to explain our acceptanceof truth generalizations, that is, of general claims formulated using the truth predicate.In this paper, I consider the strategy Horwich develops for explaining our acceptance of truth generalizations. As I show, while perhaps workable on its own, the strategy is in conflictwith his response to (...) the liar paradox. Something must give. I consider and reject variousalternatives and emendations to the strategy. In order to resolve the conflict,I propose an alternative approach to the liar, one that supports Horwich's strategywhile leaving minimalism maximally uncompromised. (shrink)

In various theories of truth, people have set forth many definitions to clarify in what sense a set of sentences is paradoxical. But what, exactly, is _a_ paradox per se? It has not yet been realized that there is a gap between ‘being paradoxical’ and ‘being a paradox’. This paper proposes that a paradox is a minimally paradoxical set meeting some closure property. Along this line of thought, we give five tentative definitions based upon the folk notion of paradoxicality implied (...) in Tarski’s undefinability theorem of truth and the dependence relation proposed by Leitgeb (J Philos Log 34(2):155–192, 2005). A definition of ‘being a paradox’ is acceptable if its extension must be sufficiently comprehensive to include all known paradoxes on the one hand, and its standard must also be high enough to exclude those that are evidently not paradoxes on the other hand. It turns out that only the last attempt is acceptable: a set of sentences is a paradox if it is paradoxical and self-dependent, and at the same time, it and any of its paradoxical and self-dependent subsets bisimulate each other. In this way, we articulate in what sense a set of sentences is a paradox, and so establish a connection between the notion of a paradox and the notion of paradoxicality. (shrink)

When are two formal theories of broadly logical concepts, such as truth, equivalent? The paper investigates a case study, involving two well-known variants of Kripke–Feferman truth. The first, \, features a consistent but partial truth predicate. The second, \, an inconsistent but complete truth predicate. It is known that the two truth predicates are dual to each other. We show that this duality reveals a much stricter correspondence between the two theories: they are intertraslatable. Intertranslatability, under natural assumptions, coincides with (...) definitional equivalence, and is arguably the strictest notion of theoretical equivalence different from logical equivalence. The case of \ and \ raises a puzzle: the two theories can be proved to be strictly related, yet they appear to embody remarkably different conceptions of truth. We discuss the significance of the result for the broader debate on formal criteria of conceptual reducibility for theories of truth. (shrink)

In comparing classical and non-classical solutions to the semantic paradoxes arguments relying on strength have been influential. In this paper I argue that non-classical solutions should preserve the proof-theoretic strength of classical solutions. Leitgeb’s logic of HYPE is then presented as an interesting possibility to strengthen FDE with a suitable conditional. It is shown that HYPE allows for a non-classical Kripkean theory of truth, called KFL, that is strong enough for the relevant purposes and has additional attractive properties.

The notions of belief and truth frequently interact in philosophical discourse but, surprisingly, a coherent semantics for such discourse is still wanting. Indeed, a number of puzzles stand in way of a satisfactory semantic account of the notion of truth in doxastic contexts. In this paper we discuss these puzzles and develop a more satisfactory semantic account that combines ideas from contextualist theories of attitude reports and Awareness semantics for non-idealized belief.

In order to define some interesting consequence relations, certain generalizations have been proposed in a many-valued semantic setting that have been useful for defining what have been called pure, mixed and ordertheoretic consequence relations. But these generalizations are insufficient to capture some other interesting relations, like other intersective mixed relations or relations with a conjunctive interpretation for multiple conclusions. We propose a broader framework to define these cases, and many others, and to set a common background that allows for a (...) direct compared analysis. At the end of the work, we illustrate some of these comparisons. (shrink)

Conditionalization governs how to reallocate credence in light of new evidence. One prominent argument in favor of Conditionalization holds that an agent who violates it is vulnerable to a diachronic Dutch book: a series of acceptable bets offered at multiple times that inflict a sure loss. van Fraassen argues that an agent who violates the Principle of Reflection is likewise vulnerable to a diachronic Dutch book. He concludes that agents should conform to both Conditionalization and Reflection. Some authors reply that (...) Reflection is implausible and hence that there must be something wrong with diachronic Dutch book arguments. Other authors try to isolate a principled difference between the Dutch book argument for Conditionalization and the Dutch book argument for Reflection, such that the former argument may succeed even though the latter fails. I pursue a version of this strategy. I contend that, once we properly elucidate the notion of sure loss, non‐reflectors are not vulnerable to a sure loss. An agent who violates Reflection is not thereby subject to a diachronic Dutch book. Appearances to the contrary result from an unmotivated focus upon an overly narrow set of gambling scenarios. (shrink)

This paper is based on Tarski’s theory of truth. The purpose of this paper is to solve the liar paradox (and its cousins) and keep both of the deductive power of classical logic and the expressive power of the word “true” in natural language. The key of this paper lies in the distinction between the predicate usage and the operator usage of the word “true”. The truth operator is primarily used for characterizing the semantics of the language. Then, we do (...) not need the hierarchy of languages. The truth predicate is mainly used for grammatical function. Tarski’s schema of the truth predicate is not necessary in this proposal. The schema of the word "true" is the schema of the truth operator. The liar paradox (and its cousins) can be solved in this way. In the appendix, I show a consistent model for both of the truth predicate and the truth operator. (shrink)

BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to be extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a couple of (...) its strengthenings. It turns out that obtaining a sensible strengthening is not straightforward. We prove that most strategies commonly used for strengthening non-deterministic logics fail in our case. Nevertheless, we identify one method of extending the system which does not. (shrink)

This anthology of the very latest research on truth features the work of recognized luminaries in the field, put together following a rigorous refereeing process. Along with an introduction outlining the central issues in the field, it provides a unique and unrivaled view of contemporary work on the nature of truth, with papers selected from key conferences in 2011 such as Truth Be Told, Truth at Work, Paradoxes of Truth and Denotation and Axiomatic Theories of Truth. Studying the nature of (...) the concept of ‘truth’ has always been a core role of philosophy, but recent years have been a boom time in the topic. With a wealth of recent conferences examining the subject from various angles, this collection of essays recognizes the pressing need for a volume that brings scholars up to date on the arguments. Offering academics and graduate students alike a much-needed repository of today’s cutting-edge work in this vital topic of philosophy, the volume is required reading for anyone needing to keep abreast of developments, and is certain to act as a catalyst for further innovation and research. (shrink)

ABSTRACT Section 1 discusses properties and propositions, and some of the motivation for an account in which property instantiation and propositional truth behave ‘naively’. Section 2 generalizes a standard Kripke construction for naive properties and propositions, in a language with modal operators but no conditionals. Whereas Kripke uses a 3-valued value space, the generalized account allows for a broad array of value spaces, including the unit interval [0,1]. This is put to use in Section 3, where I add to the (...) language a conditional suitable for restricting quantification. The shift from a value space based on the ‘mini-space’ {0,, 1} to one based on the ‘mini-space’ [0,1] leads to more satisfactory results than I was able to achieve in previous work: a vast variety of paradoxical sentences can now be treated very simply. In Section 4 I make a further addition to the language, a conditional modeled on the ordinary English conditional, paying particular attention to how it interacts with the restricted quantifier conditional. This is all done in the [0,1] framework, and two alternatives are considered for how the ordinary conditional is to be handled; one of them results from adding a tweak to a construction by Ross Brady. Section 5 discusses a further alternative, a standard relevance conditional (for the ordinary conditional, perhaps for use with a different quantifier-restricting conditional), but argues that it is not promising. Section 6 discusses the identity conditions of properties and propositions (again in the setting of a value space based on [0,1]); the issue of achieving naivety for coarse-grained properties is seen to be more complicated than some brief remarks in Field [2010] suggested, but a way to get a fair degree of coarse-grainedness is shown. (shrink)

Anti-exceptionalism about logic states that logical theories have no special epistemological status. Such theories are continuous with scientific theories. Contemporary anti-exceptionalists include the semantic paradoxes as a part of the elements to accept a logical theory. Exploring the Buenos Aires Plan, the recent development of the metainferential hierarchy of ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document}-logics shows that there are multiple options to deal with such paradoxes. There is a whole ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} (...) \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document}-based hierarchy, of which LP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {LP}}$$\end{document} and ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document} themselves are only the first steps. This means that the logics in this hierarchy are also options to analyze the inferential patterns allowed in a language that contains its own truth predicate. This paper explores these responses analyzing some reasons to go beyond the first steps. We show that LP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {LP}}$$\end{document}, ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document} and the logics of the ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document}-hierarchy offer different diagnoses for the same evidence: the inferences and metainferences the agents endorse in the presence of the truth-predicate. But even if the data are not enough to adopt one of these logics, there are other elements to evaluate the revision of classical logic. Which is the best explanation for the logical principles to deal with semantic paradoxes? How close should we be to classical logic? And mainly, how could a logic obey the validities it contains? From an anti-exceptionalist perspective, we argue that ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document}-metainferential logics in general—and STTω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {STT}}_{\omega }$$\end{document} in particular—are the best available options to explain the inferential principles involved with the notion of truth. (shrink)

This article compares classical (or -like) and nonclassical (or -like) axiomatisations of the fixed-point semantics developed by Kripke (J Philos 72(19): 690–716, 1975). Following the line of investigation of Halbach and Nicolai (J Philos Logic 47(2): 227–257, 2018), we do not compare and qua theories of truth simpliciter, but rather qua axiomatisations of the Kripkean conception of truth. We strengthen the central results of Halbach and Nicolai (2018) and Nicolai (Stud Log 106(1): 101–130, 2018), showing that, on the one hand, (...) there is a stronger sense in which some variants of and some variants of can be taken to be, truth-theoretically, equivalent. On the other hand, we show that this truth-theoretical equivalence is not preserved by some other variants of and, arguing that the variants are more adequate axiomatisations of the fixed-point semantics than the corresponding variants. (shrink)

In this paper, I argue against present accounts of anti-exceptionalism about logic, while preserving some of their insights. I will do that by offering objections against the anti-exceptionalists’ claims that revisions happen in the same way in sciences and in logic, and that the methodology of logic involves abduction simpliciter. I propose a new account of theory divergence for logic with anti-exceptionalist aspects which also preserves exceptionalism on some level while considering the role of metalogic in the exceptionalist/anti-exceptionalist debate.

The starting point of this paper is a claim defended most famously by Graham Priest: that given certain observed similarities between the set-theoretic and the semantic paradoxes, we should be looking for a ‘uniform solution’ to the members of both families. Despite its indisputable surface attractiveness, I argue that this claim hinges on a problematic reasoning move. This is seen most clearly, I suggest, when the claim and its underlying assumptions are examined by the lights of a novel, quite general (...) and, I contend, promising take on inter-theoretic analogy. The ensuing discussion is intended to serve as both a possible case study and a first step towards the broader aim of the paper: namely, to initiate a wider conversation on the methodology of paradox-solving on the one hand, and the use of inter-theoretic analogies on the other. (shrink)

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 framework. I suggest that the paradox arises as a failure of synchronization between (...) two ways of generating the liar situation in two different 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. (shrink)

The main goal of this paper is to provide an abstract framework for constructing proof systems for various many-valued logics. Using the framework it is possible to generate strongly complete proof systems with respect to any finitely valued deterministic and non-deterministic logic. I provide a couple of examples of proof systems for well-known many-valued logics and prove the completeness of proof systems generated by the framework.

The aim of my paper is to compare three alternative formal reconstructions of van Inwagen’s famous argument for incompatibilism. In the first part of my paper, I examine van Inwagen’s own reconstruction within a propositional modal logic. I point out that, due to the expressive limitations of his propositional modal logic, van Inwagen is unable to argue directly (that is, within his formal framework) for incompatibilism. In the second part of my paper, I suggest to reconstruct van Inwagen’s argument within (...) a first-order predicate logic. I show, however, that even though this reconstruction is not susceptible to the same objection, this reconstruction can be shown to be inconsistent (given van Inwagen’s own assumptions). At the end of my paper, I suggest to reconstruct van Inwagen’s argument within a quantified counterfactual logic with propositional quantifiers. I show that within this formal framework van Inwagen would not only be able to argue directly for incompatibilism, he would also be able to argue for crucial assumptions of his argument. (shrink)

The Embracing Revenge account of semantic paradox avoids the expressive limitations of previous approaches based on the Kripkean fixed point construction by replacing a single language with an indefinitely extensible sequence of languages, each of which contains the resources to fully characterize the semantics of the previous languages. In this paper we extend the account developed in Cook (2008), Cook (2009), Schlenker (2010), and Tourville and Cook (2016) via the addition of intensional operators such as ``is paradoxical''. In this extended (...) framework we are able to characterize the difference between sentences, such as the Liar and the Truth-teller, that receive the same semantic value in minimal fixed points yet seem to involve distinct semantic phenomena. (shrink)

In this paper, we use a ‘normality operator’ in order to generate logics of formal inconsistency and logics of formal undeterminedness from any subclassical many-valued logic that enjoys a truth-functional semantics. Normality operators express, in any many-valued logic, that a given formula has a classical truth value. In the first part of the paper we provide some setup and focus on many-valued logics that satisfy some of the three properties, namely subclassicality and two properties that we call fixed-point negation property (...) and conservativeness. In the second part of the paper, we introduce normality operators and explore their formal behaviour. In the third and final part of the paper, we establish a number of classical recapture results for systems of formal inconsistency and formal undeterminedness that satisfy some or all the properties above. These are the main formal results of the paper. Also, we illustrate concrete cases of recapture by discussing the logics $\mathsf{K}^{\circledast }_{3}$, $\mathsf{LP}^{\circledast }$, $\mathsf{K}^{w\circledast }_{3}$, $\mathsf{PWK}^{\circledast }$ and $\mathsf{E_{fde}}^{\circledast }$, that are in turn extensions of $\mathsf{{K}_{3}}$, $\mathsf{LP}$, $\mathsf{K}^{w}_{3}$, $\mathsf{PWK}$ and $\mathsf{E_{fde}}$, respectively. (shrink)

We cast doubts on the suggestion, recently made by Graham Priest, that glut theorists may express disagreement with the assertion of A by denying A. We show that, if denial is to serve as a means to express disagreement, it must be exclusive, in the sense of being correct only if what is denied is false only. Hence, it can’t be expressed in the glut theorist’s language, essentially for the same reasons why Boolean negation can’t be expressed in such a (...) language either. We then turn to an alternative proposal, recently defended by Beall (in Analysis 73(3):438–445, 2013; Rev Symb Log, 2014), for expressing truth and falsity only, and hence disagreement. According to this, the exclusive semantic status of A, that A is either true or false only, can be conveyed by adding to one’s theory a shrieking rule of the form A & ~A |- \bot, where \bot entails triviality. We argue, however, that the proposal doesn’t work either. The upshot is that glut theorists face a dilemma: they can either express denial, or disagreement, but not both. Along the way, we offer a bilateral logic of exclusive denial for glut theorists—an extension of the logic commonly called LP. (shrink)

According to truthmaker maximalism, each truth has a truthmaker. Peter Milne has attempted to refute truthmaker maximalism on mere logical grounds via the construction of a self-referential truthmaker sentence M “saying” of itself that it doesn’t have a truthmaker. Milne argues that M turns out to be a true sentence without a truthmaker and thus provides a counterexample to truthmaker maximalism. In this paper, I show that Milne’s refutation of truthmaker maximalism does not succeed. In particular, I argue that the (...) notion of truthmaker meets two structural principles which, if added to a formal language of a theory, are already sufficient to produce a provable contradiction—a contradiction that gives rise to a socalled “Truthmaker paradox”. I also address the question of how to possibly resolve the Truthmaker paradox. I thereby show that the Truthmaker paradox, just as the strengthened Liar paradox, yields a “revenge problem” for paracomplete theories and might lead to triviality for Priest’s dialetheist account LP if the notion of truthmaker is defined as a certain semantic predicate within LP. But regardless of how one tries to cope with the Truthmaker paradox, this paradox is surely interesting in its own right. However, its significance is completely orthogonal to the question of whether truthmaker maximalism is a philosophically sound view. (shrink)

This piece continues the tradition of arguments by John Lucas, Roger Penrose and others to the effect that the human mind is not a machine. Kurt Gödel thought that the intensional paradoxes stand in the way of proving that the mind is not a machine. According to Gödel, a successful proof that the mind is not a machine would require a solution to the intensional paradoxes. We provide what might seem to be a partial vindication of Gödel and show that (...) if a particular solution to the intensional paradoxes is adopted, one can indeed give an argument to the effect that the mind is not a machine. (shrink)

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 and Rabern, Rabern, and Macauley. Our focus, however, will be on the language of first-order arithmetic augmented with a primitive truth predicate. Using Leitgeb’s 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. 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), 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. (shrink)

We study the relationships between two clusters of axiomatizations of Kripke’s fixed-point models for languages containing a self-applicable truth predicate. The first cluster is represented by what we will call ‘\-like’ theories, originating in recent work by Halbach and Horsten, whose axioms and rules are all valid in fixed-point models; the second by ‘\-like’ theories first introduced by Solomon Feferman, that lose this property but reflect the classicality of the metatheory in which Kripke’s construction is carried out. We show that (...) to any natural system in one cluster—corresponding to natural variations on induction schemata—there is a corresponding system in the other proving the same sentences true, addressing a problem left open by Halbach and Horsten and accomplishing a suitably modified version of the project sketched by Reinhardt aiming at an instrumental reading of classical theories of self-applicable truth. (shrink)

Solutions to semantic paradoxes often involve restrictions of classical logic for semantic vocabulary. In the paper we investigate the costs of these restrictions in a model case. In particular, we fix two systems of truth capturing the same conception of truth: of the system KF of Feferman formulated in classical logic, and the system PKF of Halbach and Horsten, formulated in basic De Morgan logic. The classical system is known to be much stronger than the nonclassical one. We assess the (...) reasons for this asymmetry by showing that the truth theoretic principles of PKF cannot be blamed: PKF with induction restricted to non-semantic vocabulary coincides in fact with what the restricted version of KF proves true. (shrink)

To get to grips with what Shapiro does and can say about higher-order vagueness, it is first necessary to thoroughly review and evaluate his conception of (first-order) vagueness, a conception which is both rich and suggestive but, as it turns out, not so easy to stabilise. In Sections I–IV, his basic position on vagueness (see Shapiro [2003]) is outlined and assessed. As we go along, I offer some suggestions for improvement. In Sections V–VI, I review two key paradoxes of higher-order (...) vagueness, while in Section VII, I explore a possible line of response to such paradoxes given by Keefe [2000]. In Section VIII, I assess whether which Shapiro might adapt Keefe's response to combat both paradoxes. (shrink)

In this paper we develop what we can describe as a “dual two-sided” cut-free sequent calculus system for the non-classical logics of truth lp, k3, stt and a non-reflexive logic ts which is, arguably, more elegant than the three-sided sequent calculus developed by Ripley for the same logics. Its elegance stems from how it employs more or less the standard sequent calculus rules for the various connectives and truth, and the fact that it offers a rather neat connection between derivable (...) sequents and validity in comparison to the calculus developed by Ripley. (shrink)

Tarski's theorem essentially says that the Liar paradox is paradoxical in the minimal reflexive frame. We generalise this result to the Liar-like paradox $\lambda^\alpha$ for all ordinal $\alpha\geq 1$. The main result is that for any positive integer $n = 2^i(2j+1)$, the paradox $\lambda^n$ is paradoxical in a frame iff this frame contains at least a cycle the depth of which is not divisible by $2^{i+1}$; and for any ordinal $\alpha \geq \omega$, the paradox $\lambda^\alpha$ is paradoxical in a frame (...) iff this frame contains at least an infinite walk which has an arbitrarily large depth. We thus get that $\lambda^n$ has a degree of paradoxicality no more than $\lambda^m$ iff the multiplicity of 2 in the (unique) prime factorisation of $n$ is no more than that in the prime factorisation of $m$; and all tranfinite $\lambda^\alpha$ has the same degree of paradoxcality but has a higher degree of paradoxicality than any $\lambda^n$. (shrink)

We provide a systematic recipe for eliminating self-reference from a simple language in which semantic paradoxes (whether purely logical or empirical) can be expressed. We start from a non-quantificational language L which contains a truth predicate and sentence names, and we associate to each sentence F of L an infinite series of translations h 0(F), h 1(F), ..., stated in a quantificational language L *. Under certain conditions, we show that none of the translations is self-referential, but that any one (...) of them perfectly mirrors the semantic behavior of the original. The result, which can be seen as a generalization of recent work by Yablo (1993, Analysis, 53, 251–252; 2004, Self-reference, CSLI) and Cook (2004, Journal of Symbolic Logic, 69(3), 767–774), shows that under certain conditions self-reference is not essential to any of the semantic phenomena that can be obtained in a simple language. (shrink)

The aim of the paper is to formulate rules of inference for the predicate 'is true' applied to sentences. A distinction is recognised between (ordinary) truth and definite truth and consequently between two notions of validity, depending on whether truth or definite truth is the property preserved in valid arguments. Appropriate sets of rules of inference governing the two predicates are devised. In each case the consequence relation is in harmony with the respective predicate. Particularly appealing is a set of (...) ND rules for ordinary truth in which premises and assumptions play different roles, premises being taken to assert definite truth, assumptions to suppose truth. This set of rules can be said to capture everyday reasoning with truth. Also presented are formal characterisations, in the meta-language and in the object language, of paradoxical and 'truth teller'-like sentences. (shrink)

The book offers a proposal on how to define truth in all its complexity, without reductionism, showing at the same time which questions a theory of truth has to answer and which questions, although related to truth, do not belong within the scope of such a theory. Just like any other theory, a theory of truth has its structure and limits. The semantic core of the position is that truth-ascriptions are pro-forms, i.e. natural language propositional variables. The book also offers (...) an explanation of the syntactic behaviour of truth-terms, and the pragmatic roles of truth-acts. The theory of truth we present is a technical proposal, relatively uncontaminated by radical philosophical discussion. It makes indeed philosophical points, but it is intended to be a conceptual analysis, as neutral as possible, of the aspects that may serve as a point of departure for more philosophically-laden destinations. Like the Fregean account of quantifiers, which is prior to and, to a large extent, independent of the metaphysical debate about existence and its forms, or the Kaplanian view on demonstratives, that is neutral regarding the debate about individuals and the possibilities we have to actually “reach” them in a referring act, we intend our proposal about truth to be a sophisticated and explicative setting that helps to situate other debates about truth accurately, far from the distorted and sometimes strongly ideological discussions that have turned the topic into a paradigm of philosophical impasse. (shrink)

This note motivates a logic for a theory that can express its own notion of logical consequence—a ‘syntactically closed’ theory of naive validity. The main issue for such a logic is Curry’s paradox, which is averted by the failure of contraction. The logic features two related, but different, implication connectives. A Hilbert system is proposed that is complete and non-trivial.

Logical orthodoxy has it that classical first-order logic, or some extension thereof, provides the right extension of the logical consequence relation. However, together with naïve but intuitive principles about semantic notions such as truth, denotation, satisfaction, and possibly validity and other naïve logical properties, classical logic quickly leads to inconsistency, and indeed triviality. At least since the publication of Kripke’s Outline of a theory of truth , an increasingly popular diagnosis has been to restore consistency, or at least non-triviality, by (...) restricting some classical rules. Our modest aim in this note is to briefly introduce the main strands of the current debate on paradox and logical revision, and point to some of the potential challenges revisionary approaches might face, with reference to the nine contributions to the present volume.For a recent introduction to non-classical theories of truth and other semantic notions, see the excellent Beall a .. (shrink)

One well known approach to the soritical paradoxes is epistemicism, the view that propositions involving vague notions have definite truth values, though it is impossible in principle to know what they are. Recently, Paul Horwich has extended this approach to the liar paradox, arguing that the liar proposition has a truth value, though it is impossible to know which one it is. The main virtue of the epistemicist approach is that it need not reject classical logic, and in particular the (...) unrestricted acceptance of the principle of bivalence and law of excluded middle. Regardless of its success in solving the soritical paradoxes, the epistemicist approach faces a number of independent objections when it is applied to the liar paradox. I argue that the approach does not offer a satisfying, stable response to the paradoxes—not in general, and not for a minimalist about truth like Horwich. (shrink)

outrageous remarks about contradictions. Perhaps the most striking remark he makes is that they are not false. This claim first appears in his early notebooks (Wittgenstein 1960, p.108). In the Tractatus, Wittgenstein argued that contradictions (like tautologies) are not statements (Sätze) and hence are not false (or true). This is a consequence of his theory that genuine statements are pictures.

I will discuss Fields Outline of a Theory of Truth. I will point out important properties of Kripkeleast fixed points constructions and theory. I do this not to demean Field’s superb work on truth but rather to suggest that there may be no really satisfactory conditional connective for languages containing their own truth predicates.

Probabilism is the view that a rational agent's credences should always be probabilistically coherent. It has been argued that Probabilism follows, given the assumption that an epistemically rational agent ought to try to have credences that represent the world as accurately as possible. The key claim in this argument is that the goal of representing the world as accurately as possible is best served by having credences that are probabilistically coherent. This essay shows that this claim is false. In certain (...) cases, the goal of having accurate credences is best served by being probabilistically incoherent. Assuming that an epistemically rational agent ought to try to have credences that are as accurate as possible, it follows that in certain cases a rational agent ought to have probabilistically incoherent credences. (shrink)