My aim in this paper is to amend the Stalnakerian view of context in such a way that it can allow for an adequate treatment of a contextualist position regarding the Liar Paradox. I discuss Glanzberg’s contextualism and the reason why his position cannot be encompassed by the Stalnakerian view, as it is normally construed. Finally, I introduce the phenomenon I call “semantic dissonance”, followed by a mechanism accommodating the Stalnakerian view to the demands of Glanzberg’s contextualism.

This paper revisits a challenge for contextualist approaches to paradoxes such as the Liar paradox and Russell’s paradox. Contextualists argue that these paradoxes are to be resolved by appeal to context dependence. This can offer some nice and effective ways to avoid paradox. But there is a problem. Context dependence is, at least to begin with, a phenomenon in natural language. Is there really such context dependence as the solutions to paradoxes require, and is it really just a familiar (...) linguistic phenomenon at work? Not so clearly. In earlier work, I argued that the required form of context dependence does not look like our most familiar instances of context dependence in natural language. I called this extraordinary context dependence. In this paper, I shall explore, somewhat tentatively, a way that we can see the context dependence needed to address paradoxes as not so extraordinary. Doing so will also allow us to connect thinking about the context dependence of quantifier domains with some interesting ideas about the distinctive semantic properties of certain quantifiers. (shrink)

Contextualist theories of truth appeal to context to solve the liar paradox: different stages of reasoning occur in different contexts, and so the contradiction is dispelled. The word ‘true’ is relativized by the contextualists to contexts of use. This paper shows that contextualist approaches to the liar are committed to a form of semantic relativism: that the truth value of some sentences depends on the context of assessment, as well as the context of use. In particular, it is (...) shown how Simmons’s and Glanzberg’s contextualist approaches entail relativism. In both cases, the liar sentence gets different semantic evaluations as uttered in a fixed context of use but assessed from different contexts. Shift in context of use alone cannot provide the full explanation of the liar. These contextualist approaches, as originally presented, were thus mischaracterised and they should be re-evaluated according to their full implications. (shrink)

The Liar paradox arises when we consider a sentence that says of itself that it is not true. If such self-referential sentences exist? and examples like?This sentence is not true? certainly suggest this?, then our logic and standard notion of truth allow to infer a contradiction: The Liar sentence is true and not true. What has gone wrong? Must we revise our notion of truth and our logic? Or can we dispel the common conviction that there are such (...) self-referential sentences? The present study explores the second path.0After comparing the Liar reasoning in formal and informal logic and showing that there are no Gödelian Liar sentences, the study moves on from the semantics of self-reference to the metaphysics of expressions and proposes a novel solution to the Liar paradox: Meaningful expressions are distinct from their syntactic bases and exist only relative to contexts. Detailed semantico-metaphysical arguments show that in this dynamic setting, an object can be referred to only after it has started to exist. Hence the circular reference needed in the Liar paradox cannot occur, after all. As this solution is contextualist, it evades the expressibility problems of other proposals. (shrink)

Contextualist approaches to the Liar Paradox postulate the occurrence of a context shift in the course of the Liar reasoning. In particular, according to the contextualist proposal advanced by Charles Parsons and Michael Glanzberg, the Liar sentence L doesn’t express a true proposition in the initial context of reasoning c, but expresses a true one in a new, richer context c', where more propositions are available for expression. On the further assumption that Liar sentences involve (...) propositional quantifiers whose domains may vary with context, the Liar reasoning is blocked. But why should context shift? We argue that the paradox involves principles of contextualist reflection that explain, by analogy with well-known reflection principles for arithmetic, why context must shift from c to c' in the course of the Liar reasoning. This provides a diagnosis of the Liar Paradox—one that equally applies to two revenge arguments against contextualist approaches, one recently advanced by Andrew Bacon, the other mentioned by Charles Parsons and more recently revived by Cory Juhl. (shrink)

One recently proposed solution to the Liar paradox is the contextual theory of truth. Tyler Burge (1979) argues that truth is an indexical notion and that the extension of the truth predicate shifts during Liar reasoning. A Liar sentence might be true in one context and false in another. To many, contextualism seems to capture our pre-theoretic intuitions about the semantic paradoxes; this is especially due to its reliance on the so-called Revenge phenomenon. I, however, show that (...) Super-Liar sentences (where a Super-Liar sentence is a sentence which says of itself that it is not true in any context) generate a significant problem for Burge’s contextual theory of truth. (shrink)

Some in the recent literature have claimed that a connection exists between the Liar paradox and _semantic relativism_: the view that the truth values of certain occurrences of sentences depend on the contexts at which they are assessed. Sagi (Erkenntnis 82(4):913–928, 2017) argues that contextualist accounts of the Liar paradox are committed to relativism, and Rudnicki and Łukowski (Synthese 1–20, 2019) propose a new account that they classify as relativist. I argue that a full understanding of how relativism (...) is conceived within theories of natural language shows that neither of the purported connections can be maintained. There is no reason why a solution to the Liar paradox needs to accept relativism. (shrink)

A number of philosophers have argued that the key to understanding the semantic paradoxes is to recognize that truth is essentially relative to context. All of these philosophers have been motivated by the idea that once a liar sentence has been uttered we can 'step back' and, from the point of view of a different context, judge that the liar sentence is true. This paper argues that this 'stepping back' idea is a mistake that results from failing to (...) relativize truth to context in the first place. Moreover, context-relative liar sentences, such as 'This sentence is not true in any context' present a paradox even after truth has been relativized to context. Nonetheless, the relativization of truth to context may offer us the means to avoid paradox, if we can justifiably deny that a sentence about a context can be true in the very context it is about. (shrink)

This paper presents an approach to truth and the Liar paradox which combines elements of context dependence and hierarchy. This approach is developed formally, using the techniques of model theory in admissible sets. Special attention is paid to showing how starting with some ideas about context drawn from linguistics and philosophy of language, we can see the Liar sentence to be context dependent. Once this context dependence is properly understood, it is argued, a hierarchical structure emerges which is (...) neither ad hoc nor unnatural. (shrink)

About twenty-five years ago, Charles Parsons published a paper that began by asking why we still discuss the Liar Paradox. Today, the question seems all the more apt. In the ensuing years we have seen not only Parsons’ work (1974), but seminal work of Saul Kripke (1975), and a huge number of other important papers. Too many to list. Surely, one of them must have solved it! In a way, most of them have. Most papers on the Liar (...) Paradox offer some explanation of the behavior of paradoxical sentences, and most also offer some extension for the predicate ‘true’ that they think is adequate, at least in some restricted setting. But if this is a solution, then the problem we face is far from a lack of solutions; rather, we have an overabundance of conflicting ones. Kripke’s work alone provides us with uncountably many different extensions for the truth predicate. Even if it so happens that one of these is a conclusive solution, we do not seem to know which one, or why. We should also ask, given that we are faced with many technically elegant but contradictory views, if they are really all addressing the same problem. What we lack is not solutions, but a way to compare and evaluate the many ones we have. (shrink)

This paper argues against relativism, focusing on relativism based on the semantics of predicates of personal taste. It presents and defends a contextualist semantics for these predicates, derived from current work on gradable adjectives. It then considers metasemantic questions about the kinds of contextual parameters this semantics requires. It argues they are not metasemantically different from those in other gradable adjectives, and that contextual parameters of this sort are widespread in natural language. Furthermore, this paper shows that if such parameters (...) are rejected, it leads to an unacceptably rampant form of relativism, that relativizes truth to an open-ended list of parameters. (shrink)

Quantification is haunted by the specter of paradoxes. Since Russell, it has been a persistent idea that the paradoxes show what might have appeared to be absolutely unrestricted quantification to be somehow restricted. In the contemporary literature, this theme is taken up by Dummett (1973, 1993) and Parsons (1974a,b). Parsons, in particular, argues that both the Liar and Russell’s paradoxes are to be resolved by construing apparently absolutely unrestricted quantifiers as appropriately restricted.

Lewis argued that ‘there is no way to interpret a conditional connective so that, with sufficient generality, the probabilities of conditionals will equal the appropriate conditional probabilities’. However, as Lewis and others have subsequently recognized, Lewis' triviality results go through only on the assumption that ‘if’ is not context-sensitive. This leaves a question that has not been adequately addressed: what are the prospects of a context-sensitive theory of ‘if’ that complies with Stalnaker's thesis? I offer one interesting constraint on any (...) such theory. I argue that no context-sensitive theory satisfies Stalnaker's thesis if it satisfies three plausible assumptions: first, that the truth of an indicative is determined by the world of evaluation and by the set of worlds in the relevant epistemic context in which the antecedent is true; second, that one can learn an indicative conditional without learning that the antecedent and consequent are both true; third, that belief revision is conservative in the sense that it does not reduce the probabilities to zero unnecessarily. The result gives us a clearer picture of the real costs of a truth-conditional context-sensitive Stalnaker's thesis-compliant semantics. (shrink)

This is a collection of eighteen solicited papers on the topics of the title: circularity, definition, and truth. The papers are loosely connected in subject matter, but present a great variety of issues, theories, and approaches. Amongst the many subjects discussed are: the revision theory of truth and applications of revision rules, partiality and fixed point constructions, substitutional quantification, fuzzy logic, negation, belief revision, context dependence, hierarchies, Tarski on truth, deflationism, correspondence theories of truth, and normative aspects of truth. The (...) Liar paradox figures prominently in this collection, but is not alone. Other familiar paradoxes are also discussed, including paradoxes of definability, the Sorites paradox, and the Surprise Exam paradox. So-called paradoxes of rationality, such as the Prisoner’s Dilemma, receive attention as well. (shrink)

This chapter contains sections titled: Nature: Two Conceptions of Truth Background on Logic and Paradox Nature and Logic And Now Revenge References.

The liar paradox in its simplest form is the following argument. Consider the sentence 'this sentence is false'; call that the "liar sentence". Suppose the liar sentence is true. Then, since it says it is false, the liar sentence is false. So our supposition that it is true was mistaken, and the liar sentence must be false. But that's precisely what the liar sentence says, so it is true after all. The liar sentence (...) is, therefore, both true and false---an absurd result. ;Hans Herzberger has argued that several solutions to the Grelling paradox exhibit a common pattern: the very devices we introduce in order to avoid one version of the paradox are integral components of new versions of the paradox. Herzberger suggests that this is typical of semantic paradox in general. Chapters 1, 2, and 3 of this dissertation examine several possible solutions to the liar---especially appeals to language levels and to contexts---and attempt to locate these possible solutions in Herzberger's pattern. ;There is some reason to think that this pattern is inescapable---that is, that the liar paradox is ultimately unsolvable---so the remaining two chapters of this dissertation explore what follows from the claim that it is unsolvable. Chapter 4 develops an argument from the claim that the liar is unsolvable to the claim that we cannot understand ourselves. Chapter 5, then, attempts to make sense of this circumstance by invoking a Nietzschean view of thinking and truth---perspectivalism, which holds that all thinking concerns interpretation and that there are no uninterpreted facts. Given some perspectivalist assumptions, we can see how it is inevitable that we will be unable to understand ourselves---and how we can nevetherless attain a certain limited kind of understanding. Perspectivalism also recommends a certain intellectual humility: if everything is interpretation, then no view of mine can be a comprehensive and accurate view of the way the world really is. This by itself is not a surprising claim; the surprising claim is that the liar paradox is the basis of it. (shrink)

If semantic paradoxes such as the Liar arise because ‘true’ and other metalinguistic expressions can change their reference with changes of linguistic context, is that due to indexicality (they have the same linguistic meaning as reference changes) or ambiguity (their linguistic meaning itself changes)? An argument from communication that appears to favour the indexicality interpretation is not compelling. This paper defends the ambiguity interpretation. It is left open whether its considerations generalize to other kinds of paradox.

In this paper I present a precise version of Stalnaker's thesis and show that it is both consistent and predicts our intuitive judgments about the probabilities of conditionals. The thesis states that someone whose total evidence is E should have the same credence in the proposition expressed by 'if A then B' in a context where E is salient as they have conditional credence in the proposition B expresses given the proposition A expresses in that context. The thesis is formalised (...) rigorously and two models are provided that demonstrate that the new thesis is indeed tenable within a standard possible world semantics based on selection functions. Unlike the Stalnaker-Lewis semantics the selection functions cannot be understood in terms of similarity. A probabilistic account of selection is defended in its place. -/- I end the paper by suggesting that this approach overcomes some of the objections often leveled at accounts of indicatives based on the notion of similarity. (shrink)

Abstract Relativism about knowledge attributions is the view that a single occurrence of ‘S knows [does not know] that p’ may be true as assessed in one context and false as assessed in another context. It has been argued that relativism is equipped to accommodate all the data from speakers’ use of ‘know’ without recourse to an error theory. This is supposed to be relativism’s main advantage over contextualist and invariantist views. This paper argues that relativism does require the attribution (...) of semantic blindness to speakers, viz. to account for sceptical paradoxes and epistemic closure puzzles. To that end, the notion of semantic blindness is clarified by distinguishing between content-blindness and index-blindness, and it is argued that the attribution of index-blindness required by the relativist account is implausible. Along the way, it is shown that error-theoretic objections from speakers’ inter-contextual judgments fail against relativism. Content Type Journal Article Pages 1-19 DOI 10.1007/s11098-011-9783-5 Authors Dirk Kindermann, Arché, University of St Andrews, 17–19 College Street, St Andrews, KY16 9AL UK Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116. (shrink)

Plausible principles on truth seem to yield contradictory conclusions about paradoxical sentences such as the Strengthened Liar. Those who take the contextualist approach, such as Parsons and Burge, attempt to justify the seemingly contradictory conclusions by arguing that the natural reasoning that leads to them involves some kind of contextual shift that makes them compatible. This paper argues that one cannot take this approach to give a proper treatment of infinite descending chains of semantic attributions. It also examines a (...) related approach taken by Gaifman and argues that it has the same problem. (shrink)

This dissertation is a study of some recent theories of truth. The theories fall into three groups: The Revision Theories, the context-sensitive theories, and the "Chrysippian theories". ;The "Chrysippian theories" are based on the intuition that pathologicalities arising from the concept of truth can be recognized and acknowledged with the concept of truth itself. Thus, from the pathologicality of the Liar, for example, we can conclude that the Liar is not true. This leads to immediate difficulties since the (...) Liar claims just that--that it is not true--and it would thus seem to be true. The Chrysippian theories are designed to avoid these difficulties while preserving the motivating intuition. Haim Gaifman's Pointer Semantics, and Brian Skyrms' Intensional Fixed-Point Theory of Truth are examples of such theories. They are exposited and criticized. ;The context-sensitive theories dealt with are Tyler Burge's Indexical Theory of Truth and the theory of Jon Barwise and John Etchemendy. These theories claim that an ambiguity due to a contextual parameter is the reason for the difficulties we encounter. Burge offers a theory of Tarskian levels coupled with a pragmatic theory that explains the assignment of levels to occurrences of 'true'. Barwise and Etchemendy make explicit a situational parameter in their account of propositions. They consider the ambiguity with respect to the situation a propositions is about a main source of the paradoxes. ;Finally, the Revision Theories of Truth of Anil Gupta and Nuel Belnap and two variations of this theory are considered. One is due to Aladdin Yaqub, the other, the "fully-varied theory", is due to Gupta and Belnap but remains largely unexplored. Revision theories are put forward as the most promising account of the difficulties. They are based on a definitional reading of all Tarski biconditionals. The circularity implied by such a reading is handled by Gupta's and Belnap's general theory of definitions. ;Yaqub's objections raised against the standard theory are examined, and his proposed solution is shown to be inadequate. The fully-varied Revision Theory is shown to provide a better solution. (shrink)

This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by our concepts of denotation, predicate extension, and truth. The solution makes two main claims. The first is that our semantic expressions 'denotes', 'extension' and 'true' are context-sensitive. The second, inspired by a brief, tantalizing remark of Godel's, is that these expressions are significant everywhere except for certain singularities, in analogy with division by zero. A formal theory of singularities (...) is presented and applied to a wide variety of versions of the definability paradoxes, Russell's paradox, and the Liar paradox. Keith Simmons argues that the singularity theory satisfies the following desiderata: it recognizes that the proper setting of the semantic paradoxes is natural language, not regimented formal languages; it minimizes any revision to our semantic concepts; it respects as far as possible Tarski's intuition that natural languages are universal; it responds adequately to the threat of revenge paradoxes; and it preserves classical logic and semantics. Simmons draws out the consequences of the singularity theory for deflationary views of our semantic concepts, and concludes that if we accept the singularity theory, we must reject deflationism. (shrink)

In epistemology and in philosophy of language there is fierce debate about the role of context in knowledge, understanding, and meaning. Many contemporary epistemologists take seriously the thesis that epistemic vocabulary is context-sensitive. This thesis is of course a semantic claim, so it has brought epistemologists into contact with work on context in semantics by philosophers of language. This volume brings together the debates, in a set of twelve specially written essays representing the latest work by leading figures in the (...) two fields. All future work on contextualism will start here. Contributors: Kent Bach, Herman Cappelen, Andy Egan, Michael Glanzberg, John Hawthorne, Ernest Lepore, Peter Ludlow, Peter Pagin, Georg Peter, Paul M. Pietroski, Gerhard Preyer, Jonathan Schaffer, Jason Stanley, Brian Weatherson, Timothy Williamson. (shrink)

The problem of truth and the liar paradox is one of the most extensive problems of philosophy. The liar paradox can be avoided by assuming a so-called theory of partial truth instead of a classical theory of truth. Theories of partial truth, however, cannot solve the so-called strengthened liar paradox, which is the problem that many semantic statements about the so-called strengthened liar cannot be true in a theory of partial truth. If such semantic statements were (...) true in the theory, another paradox would emerge. To proponents of contextual accounts, which assume that the concept of truth is context-dependent, the strengthened liar paradox is the core of the liar problem. This book provides an overview of current contextual approaches to the strengthened liar paradox. For this purpose, the author investigates formal theories of truth that result from formal reconstructions of such contextual approaches. (shrink)

The Liar sentence L, which reads ‘L is not true’, can be used to produce an apparently valid argument proving that L is not true and that L is true. There has been increasing recognition of the appeal of contextualist solutions to the Liar paradox. Contextualist accounts hold that some step in the reasoning induces a context shift that causes the apparently contradictory claims to occur at different contexts. Attempts at identifying the most promising contextualist account often rely (...) on timing arguments, which seek to isolate a step at which the context cannot be claimed to have shifted or must have shifted. The literature contains a number of timing arguments that draw incompatible conclusions about the location of the context shift. I argue that no existing timing arguments succeed. An alternative strategy for assessing contextualist accounts evaluates the plausibility of their explanations of why the context shifts. However, even this strategy yields no clear verdict about which contextualist account is the most promising. I conclude that there are some grounds for optimism and for pessimism about the potential to adequately motivate contextualism. (shrink)

Contextualist theories of knowledge offer a semantic hypothesis to explain the observed contextual variation in what people say they know, and the difficulty people have resolving skeptical paradoxes. Subject or speaker relative versions make the truth conditions of “S knows that p” depend on the standards of either the knower’s context (Hawthorne and Stanley) or those of the speaker’s context (Cohen and DeRose). Speaker contextualism avoids objections to subject contextualism, but is implausible in light of evidence that “know” does not (...) behave like an indexical. I deepen and extend these criticisms in light of recent defenses by contextualists (including Ludlow). Another difficulty is that whether certain standards are salient or intended does not entail that they are the proper standards. A normative form of contextualism on which the truth of a knowledge claim depends on the proper standards for the context is more promising, but still unsatisfactory whether the view is speaker or subject relative. I defend alternative explanations for the observed linguistic and psychological data: a pragmatic account for some cases and a cognitive account for others. 1. (shrink)

Skeptics try to persuade us of our ignorance with arguments like the following: 1. I don’t know that I am not a handless brain-in-a-vat [BIV]. 2. If I don’t know that I am not a handless BIV, then I don’t know that I have hands. Therefore, 3. I don’t know that I have hands. The BIV argument is valid, its premises are intuitively compelling, and yet, its conclusion strikes us as absurd. Something has to go, but what? Contextualists contend that (...) an adequate solution to the skeptical problem must: (i) retain epistemic closure, (ii) explain the intuitive force of skeptical arguments by explaining why their premises initially seem so compelling, and (iii) account for the truth of our commonsense judgment that we do possess lots of ordinary knowledge. Contextualists maintain that the key to such a solution is recognizing that the semantic standards for ‘knows’ vary from context to context such that in skeptical contexts the skeptic’s premises are true and so is her conclusion; but in ordinary contexts, her conclusion is false and so is her first premise. Despite its initial attractiveness, the contextualist solution comes at a significant cost, for contextualism has many counterintuitive results. After presenting the contextualist solution, I identify a number of these costs. I then offer a noncontextualist solution that meets the adequacy constraint identified above, while avoiding the costs associated with contextualism. Hence, one of the principal reasons offered for adopting a contextualist theory of knowledge–its supposedly unique ability to adequately resolve the skeptical problem – is undermined. (shrink)

In this note, we review paradoxes like Russell’s, the Liar, and Curry’s in the context of intuitionistic logic. One may observe that one cannot blame the underlying logic for the paradoxes, but has to take into account the particular concept formations. For proof-theoretic semantics, however, this comes with the challenge to block some forms of direct axiomatizations of the Liar. A proper answer to this challenge might be given by Schroeder-Heister’s definitional freedom.

Epistemic contextualism is a recent and hotly debated topic in philosophy. Contextualists argue that the language we use to attribute knowledge can only be properly understood relative to a specified context. How much can our knowledge depend on context? Is there a limit, and if so, where does it lie? What is the relationship between epistemic contextualism and fundamental topics in philosophy such as objectivity, truth, and relativism? The Routledge Handbook of Epistemic Contextualism is an outstanding reference source to the (...) key topics, problems, and debates in this exciting subject and is the first collection of its kind. Comprising thirty-seven chapters by a team of international contributors the _Handbook_ is divided into eight parts: Data and motivations for contextualism Methodological issues Epistemological implications Doing without contextualism Relativism and disagreement Semantic implementations Contextualism outside ‘knows’ Foundational linguistic issues. Within these sections central issues, debates and problems are examined, including contextualism and thought experiments and paradoxes such as the Gettier problem and the lottery paradox; semantics and pragmatics; the relationship between contextualism, relativism, and disagreement; and contextualism about related topics like ethical judgments and modality. The Routledge Handbook of Epistemic Contextualism is essential reading for students and researchers in epistemology and philosophy of language. It will also be very useful for those in related fields such as linguistics and philosophy of mind. (shrink)

Skeptics try to persuade us of our ignorance with arguments like the following: 1. I don't know that I am not a handless brain-in-a-vat [BIV]. 2. If I don't know that I am not a handless BIV, then I don't know that I have hands. Therefore, 3. I don't know that I have hands. The BIV argument is valid, its premises are intuitively compelling, and yet, its conclusion strikes us as a absurd. Something has to go, but what? Contextualists contend (...) that an adequate solution to the skeptical problem must: (i) retain epistemic closure, (ii) explain the intuitive force of skeptical arguments by explaining why their premises initially seem so compelling, and (iii) account for the truth of our commonsense judgment that we do possess lots of ordinary knowledge. Contextualists maintain that the key to such a solution is recognizing that the semantic standards for 'knows' vary from context to context such that in skeptical contexts the skeptic's premises are true and so is her conclusion; but in ordinary contexts, her conclusion is false and so is her first premise. Despite its initial attractiveness, the contextualist solution comes at a significant cost, for contextualism has many counterintuitive results. After presenting the contextualist solution, I identify a number of these costs. I then offer a noncontextualist solution that meets the adequacy constraint identified above, while avoiding the costs associated with contextualism. Hence, one of the principal reasons offered for adopting a contextualist theory of knowledge -- its supposedly unique ability to adequately resolve the skeptical problem -- is undermined. (shrink)

We employ topos quantum theory as a mathematical framework for quantum logic, combining the strengths of two distinct intuitionistic quantum logics proposed by Döring and Coecke respectively. This results in a novel intuitionistic quantum logic that can capture contextuality, express the physical meaning of superposition phenomenon in quantum systems, and handle both measurement and evolution as dynamic operations. We emphasize that superposition is a relative concept dependent on contextuality. Our intention is to find a model from the perspective of quantum (...) theory that accommodates semantic paradoxes. We refine Aerts et al.’s interpretation of the liar paradox using models from quantum mechanics and present a model based on quantum theory, incorporating contextuality and superposition to interpret semantic paradoxes. We associate the truth values of statements in semantic paradoxes with quantum states in a given context, interpreting statements with unclear truth value assignments as superposition states within the current context. Dynamic operations are employed to distinguish the truth value assignments of statements among different times. Unlike the classic interpretation of paradoxes, we accept the reasonable existence of semantic paradoxes and point out the difference between paradoxes and contradictions. (shrink)

The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema “True(A)↔A”, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in “ordinary” contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A (...) within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are “defective”. We can in fact define a hierarchy of “defectiveness” predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (“revenge problems”) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various “levels of defectiveness” can all be made coherent together within a single object language. (shrink)

This paper investigates the relevance of liar sentences, and semantic circularity more generally, to compositional semantic theorizing. The paper begins by explaining our need for a compositional semantics for semantic vocabulary like "true". It then details a distinctive challenge for compositional theories accommodating semantic circularity. The challenge is to explain, consistently with linguistic productivity facts, relatively stable truth-value judgments concerning two classes of virtuous semantic circularities. I argue that we cannot explain the productive speaker judgements concerning the two classes (...) using a theory that gives "true" an extension assignment as part of its semantic value, owing to a special kind of explanatory circularity. After giving this argument, I explain what shape semantic theories would need to take to avoid the circularity. Intriguingly, the theories in question accommodate a very unusual form of context-sensitivity, unlike that found in (say) ordinary indexical pronouns or gradable adjectives. Theories with precisely this unusual form of sensitivity have been exploited to avoid problems arising from the vicious semantic circularity of the liar. Thus, exploring the conditions for accommodating semantic circularity within a compositional framework privileges a particular kind of approach to the liar paradox, notably advocated by Haim Gaifman. (shrink)

The story goes that Epimenides, a Cretan, used to claim that all Cretans are always liars. Whether he knew it or not, this claim is odd. It is easy to see it is odd by asking if it is true or false. If it is true, then all Cretans, including Epimenides, are always liars, in which case what he said must be false. Thus, if what he says is true, it is false. Conversely, suppose what Epimenides said is false. Then (...) some Cretan at some time speaks truly. This might not tell us anything about Epimenides. But if, to make the story simple, he were the only Cretan ever to speak, and this was the only thing he ever said, then indeed, he would have to speak truly. And we would then have shown that if what he said was false, it must be true. (shrink)

The first sentence in this essay is a lie. There is something odd about saying so, as has been known since ancient times. To see why, remember that all lies are untrue. Is the first sentence true? If it is, then it is a lie, and so it is not true. Conversely, suppose that it is not true. As we (viz., the authors) have said it, presumably with the intention of you believing it when it is not true, it is (...) a lie. But then it is true! (shrink)

This paper concerns the semantics of belief-sentences. I pass over ontologically lavish theories which appeal to impossible worlds, or other points of reference which contain more than possible worlds. I then refute ontologically stingy, quotational theories. My own theory employs the techniques of possible worlds semantics to elaborate a Fregean analysis of belief-sentences. In a belief-sentence, the embedded clause does not have its usual reference, but refers rather to its own semantic structure. I show how this theory can accommodate quantification (...) into belief-contexts. I close with skirmishes against the threat posed by the Liar Paradox. (shrink)

This paper offers an analysis of a hitherto neglected text on insoluble propositions dating from the late XiVth century and puts it into perspective within the context of the contemporary debate concerning semantic paradoxes. The author of the text is the italian logician Peter of Mantua (d. 1399/1400). The treatise is relevant both from a theoretical and from a historical standpoint. By appealing to a distinction between two senses in which propositions are said to be true, it offers an unusual (...) solution to the paradox, but in a traditional spirit that contrasts a number of trends prevailing in the XiVth century. It also counts as a remarkable piece of evidence for the reconstruction of the reception of English logic in italy, as it is inspired by the views of John Wyclif. Three approaches addressing the Liar paradox (Albert of Saxony, William Heytesbury and a version of strong restrictionism) are first criticised by Peter of Mantua, before he presents his own alternative solution. The latter seems to have a prima facie intuitive justification, but is in fact acceptable only on a very restricted understanding, since its generalisation is subject to the so-called revenge problem. (shrink)

Ttler=‘Ttler is true’ says of itself that it is true. It is a truth-teller. I argue that we have equally telling arguments (i) to the effect that all truth-tellers must have the same truth-value (ii) and the effect that truth-tellers differ in truth-value. This is what I call the Truth-Tellers paradox. This paradox stems from the fact that the truth-value of a truth-teller like Ttler should be determined by the fact that it says of itself that it is true (which (...) entails (i)) but that it cannot be determined by that fact (as witnessed by (ii)). The Truth-Tellers paradox resem- bles the classical semantic paradoxes like the Liar. In both cases, a form of self-reference allows us to derive a contradiction from oth- erwise plausible semantic and logical principles. Furthermore the Truth-Tellers paradox can be formulated without using sentences which are in an intuitive sense ungrounded, it thus severs the link, almost universally taken for granted, between the semantic para- doxes and ungroundedness. Finally, some classical solutions to the Liar do not generalize to the Truth-Tellers paradox. (shrink)

In this essay we introduce a new tool for studying the patterns of sentential reference within the framework introduced in [2] and known as the language of paradox $\mathcal {L}_{\mathsf {P}}$ : strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms. In particular, we show that (i) strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms between $\mathcal {L}_{\mathsf {P}}$ constructions preserve paradoxicality, (ii) many (but not all) earlier results regarding the paradoxicality of $\mathcal {L}_{\mathsf {P}}$ constructions can be recast as special cases of our central result regarding (...) strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms, and (iii) that we can use strong $\mathcal {L}_{\mathsf { P}}$ -homomorphisms to provide a simple demonstration of the paradoxical nature of a well-known paradox that has not received much attention in this context: the McGee paradox. In addition, along the way we will highlight how strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms highlight novel connections between the graph-theoretic analyses of paradoxes mobilized in the $\mathcal {L}_{\mathsf {P}}$ framework and the methods and tools of category theory. (shrink)

In the 1330s Roger Swyneshed formulated a solution to semantic paradoxes based on the distinction between correspondence with reality and self-falsification as truth-making factors. Since Swyneshed states that some valid inferences are not truth-preserving, his view implies the question of the general definition of validity which he does not address explicitly. Logical works attributed to Paul of Venice contain developments of Swyneshed's contextualist semantics substantially modified by the assumption that sentential meanings are objective propositional entities. The main goals of this (...) paper are to show the correlations between the ontological and logical developments of Swyneshed's semantics in the works of Paul of Venice and to outline a context-sensitive formal semantics that could serve as a model of this family of semantic theories. (shrink)

This essay attempts to give substance to the claim that the liar''sparadox shows the truth predicate to be context sensitive. The aim ismodest: to provide an account of the truth predicate''s contextsensitivity (1) that derives from a more general understanding ofcontext sensitivity, (2) that does not depend upon a hierarchy ofpredicates and (3) that is able to address the liar''s paradox. Theconsequences of achieving this goal are not modest, though. Perhapssurprisingly, for reasons that will be discussed in the (...) last section ofthis essay, a natural account of the truth predicate''s contextsensitivity appears to lead naturally to a version of the correspondencetheory of truth according to which the truth predicate can be understoodas a relation holding between a sentence and a salient set of contexts.The plan of this essay is as follows. Section 1 contains a generalaccount of context sensitivity. The purpose of this section is toisolate certain features of context sensitivity and formal methods oftreating them, which we will then apply to the truth predicate. Section 2then outlines two minimal conditions to be satisfied by a truthpredicate. In Section 3, I present a version of the liar paradoxthat results from these conditions and the assumption that the truthpredicate is not context sensitive in the sense described in sectionone. Finally, in section four, I provide what appear to be naturalconsequences of a truth predicate''s context sensitivity. Section 4 isadmittedly speculative and points in the direction for future research. (shrink)

The Stoic philosopher Chrysippus wrote extensively on the liar paradox, but unfortunately the extant testimony on his response to the paradox is meager and mainly hostile. Modern scholars, beginning with Alexander Rüstow in the first decade of the twentieth century, have attempted to reconstruct Chrysippus? solution. Rüstow argued that Chrysippus advanced a cassationist solution, that is, one in which sentences such as ?I am speaking falsely? do not express propositions. Two more recent scholars, Walter Cavini and Mario Mignucci, have (...) rejected Rüstow's thesis that Chrysippus used a cassationist approach. Each has proposed his own thesis about Chrysippus? solution. I argue that Rüstow's view is fundamentally correct, and that the cassationist thesis gains greater plausibility when viewed in light of a passage in Sextus Empiricus? Adversus mathematicos that the previous commentators have ignored, and when understood within the broader context of Stoic logical theory and philosophy of language. I close with a brief remark on the significance of Chrysippus? work for the modern debate on the semantic paradoxes. (shrink)

Read as a comment on Crispin Wright's \"Vagueness: A Fifth Column Approach\", this paper defends a form of supervaluationism against Wright's criticisms. Along the way, however, it takes up the question what is really wrong with Epistemicism, how the appeal of the Sorities ought properly to be understood, and why Contextualist accounts of vagueness won't do.

Written as a comment on Crispin Wright's "Vagueness: A Fifth Column Approach", this paper defends a form of supervaluationism against Wright's criticisms. Along the way, however, it takes up the question what is really wrong with Epistemicism, how the appeal of the Sorities ought properly to be understood, and why Contextualist accounts of vagueness won't do.

This paper reviews the claim that certain predicates, including what are called predicates of personal taste, have a sometimes-hidden element for a judge or experiencer. This claim was advanced in my own earlier work, as well as a number of other papers. My main goal here is to review some of the arguments in favor of this claim, and along the way, to present some of my earlier unpublished work on the matter. In much of the earlier literature, this claim (...) was part of a debate between relativists, contextualists, and others about the semantics of ‘subjective’ or ‘perspectival’ predicates. I shall argue here that these issues are independent. Whether we opt for experiencer or judge parameters is independent of whether we prefer relativist semantics to any other kind. (shrink)

This paper argues against minimalism about truth. It does so by way of a comparison of the theory of truth with the theory of sets, and consideration of where paradoxes may arise in each. The paper proceeds by asking two seemingly unrelated questions. First, what is the theory of truth about? Answering this question shows that minimalism bears important similarities to naive set theory. Second, why is there no strengthened version of Russell's paradox, as there is a strengthened Liar (...) paradox? Answering this question shows that like naive set theory, minimalism is unable to make adequate progress in resolving the paradoxes, and must be replaced by a drastically different sort of theory. Such a theory, it is shown, must be fundamentally non-minimalist. (shrink)

This is a discussion of Delia Fara’s theory of vagueness, and of its solution to the Sorites paradox, criticizing some of the details of the account, but agreeing that its central insight will be a part of any solution to the problem. I also consider a wider range of philosophical puzzles that involve arguments that are structurally similar to the argument of the Sorites paradox, and argue that the main ideas of her account of vagueness helps to respond to some (...) of those puzzles. (shrink)