This chapter attempts to give a brief overview of nonclassical (-logic) theories of truth. Due to space limitations, we follow a victory-through-sacrifice policy: sacrifice details in exchange for clarity of big-picture ideas. This policy results in our giving all-too-brief treatment to certain topics that have dominated discussion in the non-classical-logic area of truth studies. (This is particularly so of the ‘suitable conditoinal’ issue: §4.3.) Still, we present enough representative ideas that one may fruitfully turn from this essay to (...) the more-detailed cited works for further study. Throughout – again, due to space – we focus only on the most central motivation for standard non-classical-logic-based truth theories: namely, truth-theoretic paradox (specifically, due to space, the liar paradox). (shrink)

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology (...) suffered by at least some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

Theories of Truth provides a clear, critical introduction to one of the most difficult areas of philosophy. It surveys all of the major philosophical theories of truth, presenting the crux of the issues involved at a level accessible to nonexperts yet in a manner sufficiently detailed and original to be of value to professional scholars. Kirkham's systematic treatment and meticulous explanations of terminology ensure that readers will come away from this book with a comprehensive general understanding of one (...) of philosophy's thorniest set of topics. -/- Included are discussions of the correspondence, coherence, pragmatic, semantic, performative, redundancy, appraisal, and truth-as-justification theories. There are also chapters or sections of chapters on the liar paradox, three-valued logic, Field's critique of Tarski, Davidson's program, Dummett's theory of linguistic competence, satisfaction, recursion, the extension/intension distinction, and an explanation of how theories of justification, properly understood, differ from theories of truth. -/- A persistent theme is that philosophers have too often failed to recognize that not all theories of truth are intended to answer the same question. When the various questions are made distinct, it is apparent that many of the "debates" in this field are really cases of philosophers talking past one another. There is much less disagreement within the field than has commonly been thought. (shrink)

The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω-inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing (...) it. Secondly, I show that in second order theories with standard semantics the same procedure yields a theory that doesn’t have models. So, while having an ω- inconsistent theory is a bad thing, having an unsatisfiable theory of truth is actually worse. This casts doubts on whether the predicate in question is, after all, a truthpredicate for that language. Finally, I present some alternatives to prove an inconsistency adding plausible principles to certain theories of truth. (shrink)

At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how (...) the logical results impinge on the philosophical topics related to truth. In particular, he shows that the discussion on topics such as deflationism about truth depends on the solution of the paradoxes. His book is an invaluable survey of the logical background to the philosophical discussion of truth, and will be indispensable reading for any graduate or professional philosopher in theories of truth. (shrink)

Abstract:In the writings of the Chinese Madhyamaka master Jizang (549–623 c.e.), we often read arguments that deduce universal affirmation from universal negation. In previous scholarship, this seemingly paradoxical reasoning was often explained by ascribing to Jizang a type of transcendental realism—the view that reality transcends our ordinary language, logic, and reason—and reading it as his unique way of capturing such a transcendental nature of reality. More recently, an attempt at formalizing this transcendental realist interpretation of Jizang was made by Yasuo (...) Deguchi, who suggests that Jizang could have been tinkering with a type of dialethism. This article challenges the transcendental realist interpretation of Jizang by studying strong anti-realist tendencies found across his writings, and proposes a way to understand his deduction of universal affirmation from universal negation within the boundaries of ordinary reasoning and coherently with his anti-realist philosophy by introducing the modalities of "categorical truth" and "conditional truth.". (shrink)

Gila Sher interviewed by Chen Bo: -/- I. Academic Background and Earlier Research: 1. Sher’s early years. 2. Intellectual influence: Kant, Quine, and Tarski. 3. Origin and main Ideas of The Bounds of Logic. 4. Branching quantifiers and IF logic. 5. Preparation for the next step. -/- II. Foundational Holism and a Post-Quinean Model of Knowledge: 1. General characterization of foundational holism. 2. Circularity, infinite regress, and philosophical arguments. 3. Comparing foundational holism and foundherentism. 4. A post-Quinean model of knowledge. (...) 5. Intellect and figuring out. 6. Comparing foundational holism with Quine’s holism. 7. Evaluation of Quine’s Philosophy -/- III. Substantive Theory of Truth and Relevant Issues: 1. Outline of Sher’s substantive theory of truth. 2. Criticism of deflationism and treatment of the Liar. 3. Comparing Sher’s substantive theory of truth with Tarski’s theory of truth. -/- IV. A New Philosophy of Logic and Comparison with Other Theories: 1. Foundational account of logic. 2. Standard of logicality, set theory and logic. 3. Psychologism, Hanna’s and Maddy’s conceptions of logic. 4. Quine’s theses about the revisability of logic. -/- V. Epilogue. (shrink)

Jamin Asay's book offers a fresh and daring perspective on the age-old question 'What is truth?', with a comprehensive articulation and defence of primitivism, the view that truth is a fundamental and indefinable concept. Often associated with Frege and the early Russell and Moore, primitivism has been largely absent from the larger conversation surrounding the nature of truth. Asay defends primitivism by drawing on a range of arguments from metaphysics, philosophy of language and philosophy of logic, and (...) navigates between correspondence theory and deflationism by reviving analytic philosophy's first theory of truth. In its exploration of the role that truth plays in our cognitive and linguistic lives, The Primitivist Theory of Truth offers an account of not just the nature of truth, but the foundational role that truth plays in our conceptual scheme. It will be valuable for students and scholars of philosophy of language and of metaphysics. (shrink)

The Semantic Theory of Truth The semantic theory of truth was developed by Alfred Tarski in the 1930s. The theory has two separate, although interconnected, aspects. First, it is a formal mathematical theory of truth as a central concept of model theory, one of the most important branches of mathematical logic. Second, it … Continue reading Semantic Theory of Truth →.

While Kripke's original paper on the theory of truth used a three-valued logic, we believe a four-valued version is more natural. Its use allows for possible inconsistencies in information about the world, yet contains Kripke's development within it. Moreover, using a four-valued logic makes it possible to work with complete lattices rather than complete semi-lattices, and thus the mathematics is somewhat simplified. But more strikingly, the four-valued version has a wide, natural generalization to the family of interlaced bilattices. (...) Thus, with little more work, the theory is extended to a broad class of settings. Indeed, a result like Theorem 6.2 would not even be possible to state without the interlaced bilattice machinery. We hope the notion of interlaced bilattice will make apparent further such connections. (shrink)

Robert cummins has recently attacked this line of argument: if p is a semantically primitive predicate of a first order language l, then p requires its own clause in the definition of satisfaction integral to a definition of truth of l. thus if l has infinitely many such p, the satisfaction clause cannot be completed and truth for l will remain undefined. against this cummins argues that a single clause in a general base theory for l can (...) specify satisfaction conditions for even infinitely many semantically primitive predicates of l. against cummins we argue that a general base theory contains a primitive expression 'applies to' and that to make his case cummins would need to prove this expression stands for a semantical relation sufficient to a truth definition for l. not only is such a proof lacking but we show the claim to be altogether dubious. (shrink)

In 1920 Łukasiewicz published a two-page article whose title was “On Three-valued Logic”. The paper proposes a semantic characterization for the logic that has been later called Ł3 . In spite of the shortness of the paper, all the important points concerning the semantics of Ł3 are already there and can be naturally generalized to the case of a generic number n of truth-values . The conclusion of the article is quite interesting:The present author is of the opinion that (...) three-valued logic has above all theoretical importance as an endeavour to construct a system of non-aristotelian logic. Whether the new system of logic has any practical importance will be seen only when the logical phenomena, especially those in the deductive sciences, are thoroughly examined, and when the consequences of the indeterministic philosophy, which is the metaphysical substratum of the new logic, can be compared with empirical data. (shrink)

We investigate axiomatizations of Kripke's theory of truth based on the Strong Kleene evaluation scheme for treating sentences lacking a truth value. Feferman's axiomatization KF formulated in classical logic is an indirect approach, because it is not sound with respect to Kripke's semantics in the straightforward sense: only the sentences that can be proved to be true in KF are valid in Kripke's partial models. Reinhardt proposed to focus just on the sentences that can be proved to (...) be true in KF and conjectured that the detour through classical logic in KF is dispensable. We refute Reinhardt's Conjecture, and provide a direct axiomatization PKF of Kripke's theory in partial logic. We argue that any natural axiomatization of Kripke's theory in Strong Kleene logic has the same proof-theoretic strength as PKF, namely the strength of the system RA< ωω ramified analysis or a system of Tarskian ramified truth up to ωω. Thus any such axiomatization is much weaker than Feferman's axiomatization KF in classical logic, which is equivalent to the system RA<ε₀ of ramified analysis up to ε₀. (shrink)

T-biconditionals have often been regarded as insufficient as axioms for truth. This verdict is based on Tarski’s observation that the typed T-sentences suffer from deductive weakness. As indicated by McGee, the situation might change radically if we consider type-free disquotational theories of truth. However, finding a well-motivated set of untyped T-biconditionals that is consistent and recursively enumerable has proven to be very difficult. Moreover, some authors ) have argued that any solution to the semantic paradoxes necessarily involves ‘inflationary’ (...) means, thus spelling doom to deflationist and minimalist truth theories in particular. The situation is indeed worrisome as formal theories of minimalist truth are missing so far. This makes it very hard to properly evaluate the tenets of minimalism. In the present article, we will show how to find safe instances of the T-schema just by relying on syntactic features of the sentences of our language—in particular, we will explore Quine’s idea of stratification. Based on that, we will introduce some disquotational truth theories that are deductively very strong. (shrink)

Definitional and axiomatic theories of truth -- Objects of truth -- Tarski -- Truth and set theory -- Technical preliminaries -- Comparing axiomatic theories of truth -- Disquotation -- Classical compositional truth -- Hierarchies -- Typed and type-free theories of truth -- Reasons against typing -- Axioms and rules -- Axioms for type-free truth -- Classical symmetric truth -- Kripke-Feferman -- Axiomatizing Kripke's theory in partial logic -- Grounded truth (...) -- Alternative evaluation schemata -- Disquotation -- Classical logic -- Deflationism -- Reflection -- Ontological reduction -- Applying theories of truth. (shrink)

Nonclassical theories of truth have in common that they reject principles of classical logic to accommodate an unrestricted truth predicate. However, different nonclassical strategies give up different classical principles. The paper discusses one criterion we might use in theory choice when considering nonclassical rivals: the maxim of minimal mutilation.

We introduce a subclass of Kripke's fixed points in which falsehood is the preferred truth value. In all of these the truthteller evaluates to false, while the liar evaluates to undefined (or overdefined). The mathematical structure of this family of fixed points is investigated and is shown to have many nice features. It is noted that a similar class of fixed points, preferring truth, can also be studied. The notion of intrinsic is shown to relativize to these two (...) subclasses. The mathematical ideas presented here originated in investigations of so-called stable models in the semantics of logic programming. (shrink)

A subtheory of the theory of self-referential truth known as FS is shown to be weak as a theory of truth but equivalent to full FS in its proof-theoretic strength.

This papers deals with the class of axiomatic theories of truth for semantically closed languages, where the theories do not allow for standard models; i.e., those theories cannot be interpreted as referring to the natural number codes of sentences only (for an overview of axiomatic theories of truth in general, see Halbach[6]). We are going to give new proofs for two well-known results in this area, and we also prove a new theorem on the nonstandardness of a certain (...) theory of truth. The results indicate that the proof strategies for all the theorems on the nonstandardness of such theories are "essentially" of the same kind of structure. (shrink)

We investigate how to assign probabilities to sentences that contain a type-free truth predicate. These probability values track how often a sentence is satisfied in transfinite revision sequences, following Gupta and Belnap’s revision theory of truth. This answers an open problem by Leitgeb which asks how one might describe transfinite stages of the revision sequence using such probability functions. We offer a general construction, and explore additional constraints that lead to desirable properties of the resulting probability function. (...) One such property is Leitgeb’s Probabilistic Convention T, which says that the probability of φ equals the probability that φ is true. (shrink)

C i lewis, regarding himself as a pragmatist, repeatedly attempts to identify truth with verification. it is here argued, however, that a correspondence or semantic theory is required by (1) lewis's interpretation of objective judgments in terms of "possible experience" and of possible experience in terms of counterfactual conditions; (2) his distinction between the justification of knowledge and the truth of knowledge; and (3) his logical analysis of truth in terms of the extension (known or (...) unknown) of propositions. it is then argued that verification determines knowledge but reality determines truth, and that lewis himself emphasizes "the transcendence by reality of our present knowledge of it.". (shrink)

The Revision Theory of Truth has been challenged in A. M. Yaqūb's recent book The Liar Speaks the Truth. Yaqūb suggests some non-trivial changes in the original theory - changing the limit rule - to avoid certain artifacts. In this paper it is shown that the proposed changes are not sufficient, i.e., Yaqūb's system also produces artifacts. An alternative solution is proposed and the relation between it and Yaqūb's solution is explored.

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

Three leading philosopher-logicians present a clear and concise overview of formal theories of truth, explaining key logical techniques. Truth is as central topic in philosophy: formal theories study the connections between truth and logic, including the intriguing challenges presented by paradoxes like the Liar.

This is not a research paper. It is just a handout that I prepared for a course some years ago. It is a presentation of Kripke's theory of truth that I intend to be understandable even to people who have had only a first course in logic. Although elementary, it is completely precise. All the terms are defined and all the proofs (except one trivial induction) are given in detail. I am putting this on the web because I (...) think there are probably a lot of people who want to think about truth and who recognize that they need to know something about Kripke's theory but who are not sure whether they have the necessary background to follow the precise presentations that have been published. (shrink)

Kripke’s work on modal logic has been immensely influential. It hardly needs remarking that this is not his only work. Here we address his pioneering applications of fixpoint constructions to the theory of truth, and related work by others. In his fundamental paper on this he explicitly described a modal version, applying a fixpoint construction world by world within a modal frame. This can certainly be carried out, and doubtless has been somewhere. Others have suggested a variety of (...) other extensions such as using the unit interval as the underlying space of truth values, or using a four valued logic instead of three, or various combinations of these. When many similar formal constructions have been proposed, one naturally asks what is the common core. Is there some setting in which things can be proved once and for all, with the various specific proposals seen as applications of this common core. In fact this is the case, with bilattices providing the desired structure. Much of such a development has already appeared in some form or other. It is the purpose of this article to bring everything together, and also add a few things. We present general results that, more or less, have everything currently in the fixpoint literature as special cases. Fortunately this does not make things more complicated, since the underlying proofs are essentially the same as they have always been. It is just that they are being carried out in generality rather than in specificity. (shrink)

The paper develops a precise account of a logic of truth and, in particular, the logic of truth of a given truth theory. On the basis of this account maximality considerations are employed for comparing and evaluating different classical logics of truth. It is argued that, perhaps surprisingly, maximality considerations lead to a fruitful criterion for evaluating logics of truth. The paper provides two different routes for motivating the application of maximality considerations in the (...) truth case. The first route employs the Maxim of Minimum Mutilation and suggests that we should vindicate as much of our basic truth intuition, that is, the transparency intuition, as it is consistently possible. The second route argues that maximality considerations underlie much of our logical theorizing and its application in the truth case is just one particular such instance. On this view maximality considerations do not implicitly depend on the basic truth intuition but rather explain how the intuition arises and why it is not fully reliable. (shrink)

It is often thought that instances of the T-schema such as snow is white is true if and only if snow is white state correspondences between sentences andthe world, and that therefore such sentences play a crucial role in correspondence theories oftruth. I argue that this assumption trivializes the correspondence theory: even a disquotationaltheory of truth would be a correspondence theory on this conception. This discussionallows one to get clearer about what a correspondence theory does claim, (...) and toward the end of thepaper I discuss what a true correspondence theory of truth would involve. (shrink)

In this essay I propose two theories of truth and show how they deal with semantic paradoxes. Their most salient feature is that they are based on a gametheoretic understanding of logic and meaning. “Truth”, therefore, is understood dialogically, as agreement between parts. I compare this proposal with a similar one already existing in the literature —Dutilh Novaes and French 2018—, and highlight the advantages of mine. The theories of truth I present are non-trivial, substructural (in a (...) sense to be clarified) and capture strong intuitions about truth. Some philosophical recommendations in favor of our understanding of Dialogics are delivered along the way. (shrink)

Misunderstanding occurs between speakers when they disagree about the meaning of words in use. In the case of truth-values, Frege took these to be referents of sentences which consist of classes of accepted (i.e. “true”) or rejected (i.e. “false”) sentences. From this usual depiction of truth and falsity, a general algebraic framework is proposed to systematize the use of truth-values from a dialogical point of view of logic. A special attention will be paid to two radically opposed (...) pseudo-speakers: Heraclites and Nagarjuna, according to whom truth-values respectively refer to everything or nothing. Finally, dialectical (pseudo-Hegelian) negation will be rendered as a very special function: an ontological object-forming operator, similar to the arithmetic successor-forming operator Sn+1(x) on integers and consistent within our generalized theory of truth-values as variable referents. (shrink)

Epistemic theories of truth, such as those presumed to be typical for anti-realism, can be characterised as saying that what is true can be known in principle: p → ◊Kp. However, with statements of the form “p & ¬Kp”, a contradiction arises if they are both true and known. Analysis of the nature of the paradox shows that such statements refute epistemic theories of truth only if the the anti-realist motivation for epistemic theories of truth is not (...) taken into account. The motivation in a link of understandability ans meaningful- ness suggests to change the above principle and to restrict the theory to logically simple sentences, in which case the paradox does not arise. This suggestion also allows to see the deep philosophical problems for anti-realism those counterexamples are pointing at. (shrink)

In this rigorous investigation into the logic of truth Anil Gupta and Nuel Belnap explain how the concept of truth works in both ordinary and pathological..

In the following paper we propose a model-theoretical way of comparing the “strength” of various truth theories which are conservative over $$ PA $$. Let $${\mathfrak {Th}}$$ denote the class of models of $$ PA $$ which admit an expansion to a model of theory $${ Th}$$. We show (combining some well known results and original ideas) that $$\begin{aligned} {{\mathfrak {PA}}}\supset {\mathfrak {TB}}\supset {{\mathfrak {RS}}}\supset {\mathfrak {UTB}}\supseteq \mathfrak {CT^-}, \end{aligned}$$ where $${\mathfrak {PA}}$$ denotes simply the class of all (...) models of $$ PA $$ and $${\mathfrak {RS}}$$ denotes the class of recursively saturated models of $$ PA $$. Our main original result is that every model of $$ PA $$ which admits an expansion to a model of $$ CT ^-$$, admits also an expansion to a model of $$ UTB $$. Moreover, as a corollary to one of the results (brought to us by Carlo Nicolai) we conclude that $$ UTB $$ is not relatively interpretable in $$ TB $$, thus answering the question from Fujimoto (Bull Symb Log 16:305–344, 2010). (shrink)

Quine argues, in “On the Nature of Moral Values” that a coherence theory of truth is the “lot of ethics”. In this paper, I do a bit of work from within Quinean theory. Specifically, I explore precisely what a coherence theory of truth in ethics might look like and what it might imply for the study of normative value theory generally. The first section of the paper is dedicated to the exposition of a formally (...) correct coherence truth predicate, the possibility of which has been the subject of some skepticism. In the final two sections of the paper, I claim that a coherence theory in ethics does not reduce the practice of moral inquiry to absurdity, in practice as well as in principle. (shrink)

The present article purports to show that the protocol sentence debate, pursued by some leading members of the Vienna Circle in the mid-1930s, was essentially a controversy over the explanation and the real significance of the concept of truth. It is further shown that the fundamental issue underlying the discussions about the concept of truth was the relationship between form and content, as well as between logic/language and the world. R. Carnap was the philosopher who most explicitly and (...) systematically attempted to come to grips with this problem. It is shown that the form-content distinction pervades the three most important phases of Carnap's philosophical development: the structuralist (in Der logische Aufbau der Welt), the syntactical and the semantical. His final semantical stance is essentially determined by the concept of linguistic frameworks. The article purports to demonstrate that this concept cannot be dispensed with in philosophy, but that Carnap failed to work out its ontological implications. Finally, the concept of an internal ontology is briefly delineated. (shrink)

Substructural theories of truth are theories based on logics that do not include the full complement of usual structural rules. Existing substructural approaches fall into two main families: noncontractive approaches and nontransitive approaches. This paper provides a sketch of these families, and argues for two claims: first, that substructural theories are better-positioned than other theories to grapple with the truth-theoretic paradoxes, and second—more tentatively—that nontransitive approaches are in turn better-positioned than noncontractive approaches.

Formal theories, as in logic and mathematics, are sets of sentences closed under logical consequence. Philosophical theories, like scientific theories, are often far less formal. There are many axiomatic theories of the truth predicate for certain formal languages; on analogy with these, some philosophers (most notably Paul Horwich) have proposed axiomatic theories of the property of truth. Though in many ways similar to logical theories, axiomatic theories of truth must be different in several nontrivial ways. (...) I explore what an axiomatic theory of truth would look like. Because Horwich’s is the most prominent, I examine his theory and argue that it fails as a theory of truth. Such a theory is adequate if, given a suitable base theory, every fact about truth is a consequence of the axioms of the theory. I show, using an argument analogous to Gödel’s incompleteness proofs, that no axiomatic theory of truth could ever be adequate. I also argue that a certain class of generalizations cannot be consequences of the theory. (shrink)

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. In this paper, I explore the wide range of semantic behaviours displayed by paradoxical sentences, and I develop a unified theory of truth 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 paper yields a way of interpreting all three kinds of paradoxical sentences, as well as unparadoxical sentences, within a single model. (shrink)

The liar and kindred paradoxes show that we can derive contradictions if our language possesses sentences lending themselves to paradox and we reason classically from schema about truth: Sis true iffp, where the letter p is to be replaced with a sentence and the letter S with a name of that sentence. This article presents a theory of truth that keeps at the expense of classical logic. The theory is couched in a language that possesses paradoxical (...) sentences. It incorporates all the instances of the analogue of for that language and also includes other platitudes about truth. The theory avoids contradiction because its logical framework is an appropriately constructed nonclassical propositional logic. The logic and the theory are different from others that have been proposed for keeping, and the methods used in the main proofs are novel. (shrink)

In this second and last paper of the two part investigation on "Modality and Axiomatic Theories of Truth" we apply a general strategy for constructing modal theories over axiomatic theories of truth to the theory Kripke-Feferman. This general strategy was developed in the first part of our investigation. Applying the strategy to Kripke-Feferman leads to the theory Modal Kripke-Feferman which we discuss from the three perspectives that we had already considered in the first paper, where we (...) discussed the theory Modal Friedman-Sheard. That is, we first show that Modal Kripke-Feferman preserves theoremhood modulo translation with respect to modal operator logic. Second, we develop a modal semantics fitting the newly developed theory. Third, we investigate whether the modal predicate of Modal Kripke-Feferman can be understood along the lines of a proposal of Kripke, namely as a truth predicate modified by a modal operator. (shrink)

In this book, Yaqub describes a simple conception of truth and shows that it yields a semantical theory that accommodates the whole range of our seemingly conflicting intuitions about truth. This conception takes the Tarskian biconditionals as correctly and completely defining the notion of truth. The semantical theory, which is called the revision theory, that emerges from this conception paints a metaphysical picture of truth as a property whose applicability is given by a (...) revision process rather than by a fixed extension. The main advantage of this revision process is its ability to explain why truth seems in many cases almost redundant, in others substantial, and yet in others paradoxical. Yaub offers a comprehensive defense of the revision theory of truth by developing consistent and adequate formal semantics for languages in which all sorts of problematic sentences can be constructed. Yaqub concludes by introducing a logic of truth that further demonstrates the adequacy of the revision theory. (shrink)

The paradoxes about truth are the subject of extensive research. Developing an original approach, this book argues that we should diverge from classical logic and presents a number of formal theories of truth. Also included is a beginner-friendly introduction to semantic paradoxes, and a discussion of alternative non-classical theories.

Donald Davidson has claimed that for every logical truth 5 of a language L, a theory of meaning for L will entail that S is a logical truth of L. Jim Edwards has argued (2002) that this claim is false if we take 'entails' to mean 'has as a logical consequence. In this paper, I first show that, pace Edwards, Davidson's claim is correct even under this strong reading. I then discuss the argument given (...) by Edwards and offer a diagnosis of where he went wrong. (shrink)

The paper offers a new analysis of the difficulties involved in the construction of a general and substantive correspondence theory of truth and delineates a solution to these difficulties in the form of a new methodology. The central argument is inspired by Kant, and the proposed methodology is explained and justified both in general philosophical terms and by reference to a particular variant of Tarski's theory. The paper begins with general considerations on truth and correspondence and (...) concludes with a brief outlook on the "family" of theories of truth generated by the new methodology. (shrink)