This article is a lecture note I wrote for my philosophy of mathematics course. Its main task is to explain the main ideas of Gupta's acceptable model proposed in his paper [J. Philos. Logic 11(1), 1–60, 1982]. I aim to provide detailed information on a result established by Gupta. On the one hand, I hope this explanation can be helpful for those who are learning Gupta's acceptable model, and on the other hand, I also hope to provide a guide for (...) beginners to interpret literature. (shrink)

This paper presents four key results. Firstly, it distinguishes between _partial_ and _consistent_ assertion of a sentence, and introduces the concept of an _equivocal_ sentence, which is both partially asserted and partially denied. Secondly, it proposes a novel definition of truth, stating that _a true sentence is one that is consistently asserted_. This definition is immune from the Liar paradox, does not restrict classical logic, and can be applied to declarative sentences in the language used by any particular person. Thirdly, (...) the paper introduces an epistemic model of language, known as _assertional language_, which is used to formalize the definition of truth. Finally, it provides an argument for the falsity of so-called Liar sentences. The paper also discusses Tarski's solution to the Liar paradox and argues for the abandonment of the Tarski Scheme: _'p' is true if and only if p_, in the context of everyday language. The proposed definition of truth can be viewed as a formal account of the correspondence theory. The epistemic model is a powerful concept on its own that allows for combining different languages in a meaningful way. This model is uniquely capable of reflecting on epistemic inconsistencies, such as logical paradoxes, in a consistent manner. (shrink)

This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. While (...) non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view. (shrink)

In this paper, we extend the expressive power of the logics K3, LP and FDE with anormality operator, which is able to express whether a for-mula is assigned a classical truth value or not. We then establish classical recapture theorems for the resulting logics. Finally, we compare the approach via normality operator with the classical collapse approach devisedby Jc Beall.

In questo capitolo racconto l'articolo classico sulla verità' di Tarski.

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...) of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)

The No-No Paradox consists of a pair of statements, each of which ?says? the other is false. Roy Sorensen claims that the No-No Paradox provides an example of a true statement that has no truthmaker: Given the relevant instances of the T-schema, one of the two statements comprising the ?paradox? must be true (and the other false), but symmetry constraints prevent us from determining which, and thus prevent there being a truthmaker grounding the relevant assignment of truth values. Sorensen's view (...) is mistaken: situated within an appropriate background theory of truth, the statements comprising the No-No Paradox are genuinely paradoxical in the same sense as is the Liar (and thus, on Sorensen's view, must fail to have truth values). This result has consequences beyond Sorensen's semantic framework. In particular, the No-No Paradox, properly understood, is not only a new paradox, but also provides us with a new type of paradox, one which depends upon a general background theory of the truth predicate in a way that the Liar Paradox and similar constructions do not. (shrink)

In (2002) I argued that Gupta and Belnap’s Revision Theory of Truth (1993) has counterintuitive consequences. In particular, the pair of sentences: (S1) At least one of S1 and S2 is false. (S2) Both of S1 and S2 are false.1 is pathological on the Revision account. There is one, and only one, assignment of truth values to {(S1), (S2)} that make the corresponding Tarski..

The majority of disucssions of Benardete’s Paradox conclude that the traveller approaching the infinite series of gods will be mysteriously halted despite none of the gods erecting any barriers. Using a revision-theoretic analysis of Benardete’s puzzle, four distinct possible outcomes that might occur given Benardete’s set-up are distinguished. This analysis provides additional insight into the puzzle at hand, via identifying heretofore unnoticed possible outcomes, but it also serves as an example of how the revision theoretic framework can be used to (...) construct exhaustive taxonomies of potential outcomes in apparently contradictory situations. (shrink)

There is an incompatibility between the deflationist approach to truth, which makes truth transparent on the basis of an antecedent grasp of meaning, and the traditional endeavour, exemplified by Davidson, to explicate meaning through of truth. I suggest that both parties are in the explanatory red: deflationist lack a non-truth-involving theory of meaning and Davidsonians lack a non-deflationary account of truth. My focus is on the attempts of the latter party to resolve their problem. I look in detail at Davidson's (...) more recent work and suggest that it seeks to articulate a primitive notion of truth that may balance between a notion that collapses into deflationism and one that is wholly subsumed under a general theory of interpretation. I conclude that this tightrope walk is ultimately unsuccessful. Equally, however, some reasons are provided for thinking that deflationism might be equally unsuccessful with its problem. 'Truth or meaning?' remains an open question. (shrink)

This paper presents and defends a way to add a transparent truth predicate to classical logic, such that and A are everywhere intersubstitutable, where all T-biconditionals hold, and where truth can be made compositional. A key feature of our framework, called STTT (for Strict-Tolerant Transparent Truth), is that it supports a non-transitive relation of consequence. At the same time, it can be seen that the only failures of transitivity STTT allows for arise in paradoxical cases.

According to the traditional bundle theory, particulars are bundles of compresent universals. I think we should reject the bundle theory for a variety of reasons. But I will argue for the thesis at the core of the bundle theory: that all the facts about particulars are grounded in facts about universals. I begin by showing how to meet the main objection to this thesis (which is also the main objection to the bundle theory): that it is inconsistent with the possibility (...) of distinct qualitative indiscernibles. Here, the key idea appeals to a non-standard theory of haecceities as non-well-founded properties of a certain sort. I will then defend this theory from a number of objections, and finally argue that we should accept it on the basis of considerations of parsimony about the fundamental. (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)

We present a new proposal for what to do at limits in the revision theory. The usual criterion for a limit stage is that it should agree with any definite verdicts that have been brought about before that stage. We suggest that one should not only consider definite verdicts that have been brought about but also more general properties; in fact any closed property can be considered. This more general framework is required if we move to considering revision theories for (...) concepts that are concerned with real numbers, but also has consequences for more traditional revision theories such as the revision theory of truth. (shrink)

I here present and defend what I call the Triviality Theory of Truth, to be understood in analogy with Matti Eklund’s Inconsistency Theory of Truth. A specific formulation of is defended and compared with alternatives found in the literature. A number of objections against the proposed notion of meaning-constitutivity are discussed and held inconclusive. The main focus, however, is on the problem, discussed at length by Gupta and Belnap, that speakers do not accept epistemically neutral conclusions of Curry derivations. I (...) first argue that the facts about speakers’ reactions to such Curry derivations do not constitute a problem for the Triviality Theory specifically. Rather, they follow from independent, uncontroversial facts. I then propose a solution which coheres with the theory as I understand it. Finally, I consider a normative reading of their objection and offer a response. (shrink)

Gupta has proposed a definition of strategic rationality cast in the framework of his revision theory of truth. His analysis, relative to a class of normal form games in which all players have a strict best reply to all other players’ strategy profiles, shows that game-theoretic concepts have revision-theoretic counterparts. We extend Gupta’s approach to deal with normal form games in which players’ may have weak best replies. We do so by adapting intuitions relative to Nash equilibrium refinements to the (...) revision-theoretic framework. We prove that there is a precise equivalence between trembling-hand perfect equilibria in two-player normal games and a revision-theoretic property. We then introduce lexicographic choice of action as a way to represent players’ expectations, which allows our analysis to reach full generality. Finally, we provide an example of the versatility of revision theory as applied to strategic interaction by formalizing a risk-and-compensation procedure of strategic choice in the revision-theoretic framework. (shrink)

This paper introduces theories for arithmetical quasi-inductive definitions (Burgess, 1986) as it has been done for first-order monotone and nonmonotone inductive ones. After displaying the basic axiomatic framework, we provide some initial result in the proof theoretic bounds line of research (the upper one being given in terms of a theory of sets extending Kripke–Platek set theory).

Two semantic paradoxes, the Liar and Curry’s paradox, are analysed using a newly developed conception of procedural semantics (semantics according to which the truth of propositions is determined algorithmically), whose main characteristic is its departure from methodological realism. Rather than determining pre-existing facts, procedures are constitutive of them. Of this semantics, two versions are considered: closed (where the halting of procedures is presumed) and open (without this presumption). To this end, a procedural approach to deductive reasoning is developed, based on (...) the idea of simulation. As is shown, closed semantics supports classical logic, but cannot in any straightforward way accommodate the concept of truth. In open semantics, where paradoxical propositions naturally ‘belong’, they cease to be paradoxical; yet, it is concluded that the natural choice—for logicians and common people alike—is to stick to closed semantics, pragmatically circumventing problematic utterances. (shrink)

Most paradoxes of self-reference have a dual or ‘hypodox’. The Liar paradox (Lr = ‘Lr is false’) has the Truth-Teller (Tt = ‘Tt is true’). Russell’s paradox, which involves the set of sets that are not self-membered, has a dual involving the set of sets which are self-membered, etc. It is widely believed that these duals are not paradoxical or at least not as paradoxical as the paradoxes of which they are duals. In this paper, I argue that some paradox’s (...) duals or hypodoxes are as paradoxical as the paradoxes of which they are duals, and that they raise neglected and interestingly different problems. I first focus on Richard’s paradox (arguably the simplest case of a paradoxical dual), showing both that its dual is as paradoxical as Richard’s paradox itself, and that the classical, Richard-Poincaré solution to the latter does not generalize to the former in any obvious way. I then argue that my argument applies mutatis mutandis to other paradoxes of self-reference as well, the dual of the Liar (the Truth-Teller) proving paradoxical. (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)

After summarizing the essential details of Anil Gupta’s account of perceptual justification in his book _Empiricism and Experience_, I argue for three claims: (1) Gupta’s proposal is closer to rationalism than advertised; (2) there is a major lacuna in Gupta’s account of how convergence in light of experience yields absolute entitlements to form beliefs; and (3) Gupta has not adequately explained how ordinary courses of experience can lead to convergence on a commonsense view of the world.

The first section (§1) of this essay defends reliance on truth values against those who, on nominalistic grounds, would uniformly substitute a truth predicate. I rehearse some practical, Carnapian advantages of working with truth values in logic. In the second section (§2), after introducing the key idea of auxiliary parameters (§2.1), I look at several cases in which logics involve, as part of their semantics, an extra auxiliary parameter to which truth is relativized, a parameter that caters to special kinds (...) of sentences. In many cases, this facility is said to produce truth values for sentences that on the face of it seem neither true nor false. Often enough, in this situation appeal is made to the method of supervaluations, which operate by “quantifying out” auxiliary parameters, and thereby produce something like a truth value. Logics of this kind exhibit striking differences. I first consider the role that Tarski gives to supervaluation in first order logic (§2.2), and then, after an interlude that asks whether neither-true-nor-false is itself a truth value (§2.3), I consider sentences with non-denoting terms (§2.4), vague sentences (§2.5), ambiguous sentences (§2.6), paradoxical sentences (§2.7), and future-tensed sentences in indeterministic tense logic (§2.8). I conclude my survey with a look at alethic modal logic considered as a cousin (§2.9), and finish with a few sentences of “advice to supervaluationists” (2.10), advice that is largely negative. The case for supervaluations as a road to truth is strong only when the auxiliary parameter that is “quantified out” is in fact irrelevant to the sentences of interest—as in Tarski’s definition of truth for classical logic. In all other cases, the best policy when reporting the results of supervaluation is to use only explicit phrases such as “settled true” or “determinately true,” never dropping the qualification. (shrink)

Tim Maudiin’s Truth and Paradox (Maudlin 2004, cited here as T&P), a book that is richly endowed with interesting analyses and original theses, chooses to ignore both the prosentential theory of truth from Grover, Camp and Belnap 1975 and the revision theory in its book form, Gupta and Belnap 1993 (The Revision Theory of Truth, henceforth RTT).1 There is no discussion of either theory, nor even any mention of them in the list of references. I offer a pair of quotes (...) chosen from among a number of T&P generalizations that Maudlin would doubtless have modified if RTT had been on his mind at the time of composition of T&P. (1) "...every acceptable account of truth seems to imply that the Tlnferences must be valid" (p. 15). My response is that the revision theory of truth is built on an explicit denial of this. Rather than taking them as "valid," RTT takes the T—Inferences as stage-of-revision—shifting revision principles in the context of a definitional account of truth. (2) "...most discussions of the Liar paradox and related paradoxes...do not address [such questions as]...where ['l`&P’s] Proof Lambda and Proof Gamma go wrong" (p. 20). In fact, RTT is not open to this criticism. It’s simple natural-deduction calculus C0 addresses exactly such questions. (shrink)

The study of truth is often seen as running on two separate paths: the nature path and the logic path. The former concerns metaphysical questions about the ‘nature’, if any, of truth. The latter concerns itself largely with logic, particularly logical issues arising from the truth-theoretic paradoxes. Where, if at all, do these two paths meet? It may seem, and it is all too often assumed, that they do not meet, or at best touch in only incidental ways. It is (...) often assumed that work on the metaphysics of truth need not pay much attention to issues of paradox and logic; and it is likewise assumed that work on paradox is independent of the larger issues of metaphysics. Philosophical work on truth often includes a footnote anticipating some resolution of the paradox, but otherwise tends to take no note of it. Likewise, logical work on truth tends to have little to say about metaphysical presuppositions, and simply articulates formal theories, whose strength may be measured, and whose properties may be discussed. In practice, the paths go their own ways. Our aim in this paper is somewhat modest. We seek to illustrate one point of intersection between the paths. Even so, our aim is not completely modest, as the point of intersection is a notable one that often goes unnoticed. We argue that the ‘nature’ path impacts the logic path in a fairly direct way. What one can and must say about the logic of truth is influenced, or even in some cases determined, by what one says about the metaphysical nature of truth. In particular, when it comes to saying what the well-known Liar paradox teaches us about truth, background conceptions — views on ‘nature’ — play a significant role in constraining what can be said. This paper, in rough outline, first sets out some representative ‘nature’ views, followed by the ‘logic’ issues (viz., paradox), and turns to responses to the Liar paradox. What we hope to illustrate is the fairly direct way in which the background ‘nature’ views constrain — if not dictate — responses to the main problem on the ‘logic’ path.. (shrink)

A theory of truth is usually demanded to be consistent, but -consistency is less frequently requested. Recently, Yatabe has argued in favour of -inconsistent first-order theories of truth, minimising their odd consequences. In view of this fact, in this paper, we present five arguments against -inconsistent theories of truth. In order to bring out this point, we will focus on two very well-known -inconsistent theories of truth: the classical theory of symmetric truth FS and the non-classical theory of naïve truth (...) based on ᴌukasiewicz infinitely valued logic: PAᴌT. (shrink)

ABSTRACTKevin Scharp’s ‘Replacing Truth’ is an ambitious and far reaching account of the semantic paradoxes. In this critical discussion we examine one the books central claims: to have provided a theory of truth that avoids the revenge paradoxes. In the first part we assess this claim, and in the second part we investigate some features of Scharp’s preferred theory of truth, ADT, and compare it with existing theories such as the Kripke–Feferman theory. In the appendix a simple model of Scharp’s (...) theory is presented, and some potential consistent ways to strengthen the theory are suggested. (shrink)

Most work on the semantic paradoxes within classical logic has centered around what this essay calls “linguistic” accounts of the paradoxes: they attribute to sentences or utterances of sentences some property that is supposed to explain their paradoxical or nonparadoxical status. “No proposition” views are paradigm examples of linguistic theories, although practically all accounts of the paradoxes subscribe to some kind of linguistic theory. This essay shows that linguistic accounts of the paradoxes endorsing classical logic are subject to a particularly (...) acute form of the revenge paradox: that there is no exhaustive classification of sentences into “good” and “bad” such that the T-schema holds when restricted to the “good” sentences unless it is also possible to prove some “bad” sentences. The foundations for an alternative classical nonlinguistic approach is outlined that is not subject to the same kinds of problems. Although revenge paradoxes of different strengths can be formulated, they are found to be indeterminate at higher orders and not inconsistent. (shrink)

Theories of truth and vagueness are closely connected; in this article, I draw another connection between these areas of research. Gupta and Belnap’s Revision Theory of Truth is converted into an approach to vagueness. I show how revision sequences from a general theory of definitions can be used to understand the nature of vague predicates. The revision sequences show how the meaning of vague predicates are interconnected with each other. The approach is contrasted with the similar supervaluationist approach.

We address an issue recently discussed by Graham Priest: whether the very nature of truth (understood as in correspondence theories) rules out true contradictions, and hence whether a correspondence-theoretic notion of truth rules against dialetheism. We argue that, notwithstanding appearances to the contrary, objections from within the correspondence theory do not stand in the way of dialetheism. We close by highlighting, but not attempting to resolve, two further challenges for dialetheism which arise out of familiar philosophical theorizing about truth.

Over the past 25 years, Graham Priest has ably presented and defended dialetheism, the view that certain sentences are properly characterized as true with true negations. Our goal here is neither to quibble with the tenability of true, assertable contradictions nor, really, with the arguments for dialetheism. Rather, we wish to address the dialetheist's treatment of cases of semantic pathology and to pose a worry for dialetheism that has not been adequately considered. The problem that we present seems to have (...) broader bite, afflicting both consistent and inconsistent proposals for resolving semantic pathology. Thus, while our primary goal is to uncover some important connections between dialetheism, semantic pathology, and other, more general issues, the problem that we pose might be a worry for anyone who aims to resolve semantic pathology - consistently or not. (shrink)

Philosophical work on truth covers two streams of inquiry, one concerning the nature (if any) of truth, the other concerning truth-related paradox, especially the Liar. For the most part these streams have proceeded fairly independently of each other. In his "Deflationary Truth and the Liar" (JPL 28:455-488, 1999) Keith Simmons argues that the two streams bear on one another in an important way; specifically, the Liar poses a greater problem for deflationary conceptions of truth than it does for inflationist conceptions. (...) We agree with Simmons on this point; however, we disagree with his main conclusion. In a nutshell, Simmons' main conclusion is that deflationists can solve the Liar only by compromising deflationism. If Simmons is right, then deflationists cannot solve the Liar paradox. In this paper we argue that, pace Simmons, there is an approach to the Liar that is available to deflationists, namely dialetheism. (shrink)

In this paper we argue that Revision Rules, introduced by Anil Gupta and Nuel Belnap as a tool for the analysis of the concept of truth, also provide a useful tool for defining computable functions. This also makes good on Gupta's and Belnap's claim that Revision Rules provide a general theory of definition, a claim for which they supply only the example of truth. In particular we show how Revision Rules arise naturally from relaxing and generalizing a classical construction due (...) to Kleene, and indicate how they can be employed to reconstruct the class of the general recursive functions. We also point at how Revision Rules can be employed to access non-minimal fixed points of partially defined computing procedures. (shrink)

The ecological approach to perception-action is unlike the standard approach in several respects. It takes the animal-in-its-environment as the proper scale for the theory and analysis of perception-action, it eschews symbol based accounts of perception-action, it promotes self-organization as the theory-constitutive metaphor for perception-action, and it employs self-referring, non-predicative definitions in explaining perception-action. The present article details the complexity issues confronted by the ecological approach in terms suggested by Rosen and introduces non-well-founded set theory as a potentially useful tool for (...) expressing them. The issues and the tool are brought to focus in the concept of affordance that is the basis for explanation of prospective control of action in the ecological approach. (shrink)

I defend the hypothesis that the semantic paradoxes, the paradoxes about collections, and the sorites paradoxes, are all paradoxes of reference fixing: they show that certain conventionally adopted and otherwise functional reference-fixing principles cannot provide consistent assignments of reference to certain relevant expressions in paradoxical cases. I note that the hypothesis has interesting implications concerning the idea of a unified account of the semantic, collection and sorites paradoxes, as well as about the explanation of their “recalcitrance”. I also note that (...) it does not necessarily imply that one should not expect the sometimes hoped for “unique” solution to a paradox of these kinds. (shrink)

This comprehensive volume features the proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, held in Hangzhou, China on September 8-9 and 11-12, 2023. The collection offers a diverse range of papers that explore the intersection of logic, artificial intelligence, and law. With contributions from some of the leading experts in the field, this volume provides insights into the latest research and developments in the applications of logic in (...) these areas. It is an essential resource for researchers, practitioners, and students interested in the latest advancements in logic and its applications to artificial intelligence and law. (shrink)

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.

The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This (...) yields a general soundness and completeness result for a variety of (positive) substructural logics with respect to multimodal Kripke frames with binary accessibility relations. In addition, an epistemic interpretation of pair models is provided. (shrink)

Jamie Tappenden was one of the first authors to entertain the possibility of a common treatment for the Liar and the Sorites paradoxes. In order to deal with these two paradoxes he proposed using the Strong Kleene semantic scheme. This strategy left unexplained our tendency to regard as true certain sentences which, according to this semantic scheme, should lack truth value. Tappenden tried to solve this problem by using a new speech act, articulation. Unlike assertion, which implies truth, articulation only (...) implies non-falsity. In this paper I argue that Tappenden’s strategy cannot be successfully applied to truth and the Liar. (shrink)

It is argued that a certain form of the view that the semantic paradoxes show that natural languages are "inconsistent" provides the best response to the semantic paradoxes. After extended discussions of the views of Kirk Ludwig and Matti Eklund, it is argued that in its strongest formulation the view maintains that understanding a natural language is sharing cognition of an inconsistent semantic theory for that language with other speakers. A number of aspects of this approach are discussed and a (...) few objections are entertained. (shrink)