The subject of my article is the principle of characterization – the most controversial principle of Meinong’s Theory of Objects. The aim of this text is twofold. First of all, I would like to show that Russell’s well-known objection to Meinong’s Theory of Objects can be reformulated against a new modal interpretation of Meinongianism that is presented mostly by Graham Priest. Secondly, I would like to propose a strategy which gives uncontroversial restriction to the principle of characterization and which allows (...) to avoid Russell’s argument. The strategy is based on the distinction between object- and metalanguage, and it applies to modal Meinongianism as well as to other so-called Meinongian theories. (shrink)

The Paradox of the Knower was originally presented by Kaplan and Montague [26] as a puzzle about the everyday notion of knowledge in the face of self-reference. The paradox shows that any theory extending Robinson arithmetic with a predicate K satisfying the factivity axiom K → A as well as a few other epistemically plausible principles is inconsistent. After surveying the background of the paradox, we will focus on a recent debate about the role of epistemic closure principles in the (...) Knower. We will suggest this debate sheds new light on the concept of knowledge which is at issue in the paradox – i.e. is it a “thin” notion divorced from concepts such as evidence or justification, or is it a “thick” notion more closely resembling mathematical provability? We will argue that a number of features of the paradox suggest that the latter option is more plausible. Along the way, we will provide a reconstruction of the paradox using a quantified extension of Artemovʼs [2] Logic of Proofs, as well as a series of results linking the original formulation of the paradox to reflection principles for formal arithmetic. On this basis, we will argue that while the Knower can be understood to motivate a distinction between levels of knowledge, it does not provide a rationale for recognizing a uniform hierarchy of knowledge predicates in the manner suggested by Anderson. (shrink)

In this work I argue for the thesis that Grice’s intentional-cooperative analysis of assertion works at three levels: the logical, the epistemological and the normative. I use “conventional implicature” as example. First part shows that other approaches to assertion can’t give an accurate description of semantic content. I point to a general, twofold conclusion: the truth-conditional approach fails by neglecting intentional acts to be the meaning blocks; the rule-oriented approach misses its target by disregarding that all communicative acts are intentional, (...) but many are not conventional. Assertion includes some features of intentional action, the main theme in second part. As rational justification is the basis of intention, the solution of some remaining problems connected to assertion may rest in the justificatory structures underlying intention. Judgment, the epistemic variety of rational acceptability, determines, on one hand, the infelicity in conventional implicature cancellation and, on the other, shows why convention is just a minor component in the theory of meaning. Justification deems a special methodology in which causal explanations of meaning and representation can be replaced by justifications, teleological in character. The rationalist background of Grice’s proposal is thus stressed, as well as his conception of rationality as the body of capacities in charge of identifying and attributing value. Following this interpretation, other problems on meaning and communication, for example the relations between the Cooperative Principle and the conversational maxims, can be dealt with. (shrink)

A novel normal form for propositional theories underlies the logic pdl, which captures some essential features of natural discourse, independent from any particular subject matter and related only to its referential structure. In particular, pdlallows to distinguish vicious circularity from the innocent one, and to reason in the presence of inconsistency using a minimal number of extraneous assumptions, beyond the classical ones. Several, formally equivalent decision problems are identified as potential applications: non-paradoxical character of discourses, admissibility of arguments in argumentation (...) networks, propositional satisfiability, and the existence of kernels of directed graphs. Directed graphs provide the basis for the semantics of pdl and the paper concludes by an overview of relevant graph-theoretical results and their applications in diagnosing paradoxical character of natural discourses. (shrink)

In their (2008) article Liar-Like Paradox and Object Language Features C.S. Jenkins and Daniel Nolan (henceforth, JN) argue that it is possible to construct Liar-like paradox in a metalanguage even though its object language is not semantically closed. I do not take issue with this claim. I find fault though with the following points contained in JN’s article: First, that it is possible to construct Liar-like paradox in a metalanguage, even though this metalanguage is not semantically closed. Second, that the (...) presented examples of Liar-like paradox are supposed to be counterexamples to Tarski’s diagnosis of the classic Liar paradox. Third, that JN fail to notice Tarski’s postulate. And finally, that JN fail to recognize that the world they are pondering is not among the possible worlds. (shrink)

I identify a notion of logical grounding, clarify it, and show how it can be used (i) to characterise various consequence relations, and (ii) to give a precise syntactic account of the notion of “groundedness” at work in the literature on the paradoxes of truth.

This peer-reviewed paper intervenes in debates relating to overarching themes that impact upon mass media studies, communication theory and theories of cognition more generally. In particular, the paper discusses issues involving how our ordinary psychological thinking relates to norms of rationality (and how these latter are conceived). In essence, I argue against a dominant approach taken by Christopher Peacocke, that rationality can be grounded in the possession of certain concepts. The article makes a new contribution to the field by arguing (...) against the dominant approach on two grounds: (a) it fails to distinguish between true and false normative commitments; (b) it is empirically unsound. In response, I briefly offer suggestions towards an alternative, and psychologically tractable, account of rational commitment. Presentations of earlier drafts of the paper were given at a seminar at the Centre for Study of Mind and Nature, Oslo, as well as the conference of the European Society for Philosophy and Psychology. (shrink)

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

This article explores ways in which the Revision Theory of Truth can be expressed in the object language. In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed, and we study different axiomatic systems for the Revision Theory of Truth.

Normative theories can be useful in developing descriptive theories, as when normative subjective expected utility theory is used to develop descriptive rational choice theory and behavioral game theory. “Ought” questions are also the essence of theories of moral reasoning, a domain of higher mental processing that could not survive without normative considerations.

I argue that a new solution to the semantic paradoxes is possible based on truth-making. I show that with an appropriate understanding of what the ultimate truth and falsity makers of sentences are, it can be demonstrated that sentences like the liar are alethically undecidable. That means it cannot be said in principle whether such sentences are true, not true, false, not-false, neither true nor false, both true and false, and so on. I argue that this leads to a solution (...) to the semantic paradoxes that appears to be free of revenge problems, allows us to maintain classical logic and the validity of the T-schema. (shrink)

The Turing Test (TT), the Chinese Room Argument (CRA), and the Symbol Grounding Problem (SGP) are about the question “can machines think?” We propose to look at these approaches to Artificial Intelligence (AI) by showing that they all address the possibility for Artificial Agents (AAs) to generate meaningful information (meanings) as we humans do. The initial question about thinking machines is then reformulated into “can AAs generate meanings like humans do?” We correspondingly present the TT, the CRA and the SGP (...) as being about generation of human-like meanings. We model and address such possibility by using the Meaning Generator System (MGS) where a system submitted to an internal constraint generates a meaning in order to satisfy the constraint. The system approach of the MGS allows comparing meaning generations in animals, humans and AAs. The comparison shows that in order to have AAs capable of generating human-like meanings, we need the AAs to carry human constraints. And transferring human constraints to AAs raises concerns coming from the unknown natures of life and human mind which are at the root of human constraints. Implications for the TT, the CRA and the SGP are highlighted. It is shown that designing AAs capable of thinking like humans needs an understanding about the natures of life and human mind that we do not have today. Following an evolutionary approach, we propose as a first entry point an investigation about the possibility for extending a “stay alive” constraint into AAs. Ethical concerns are raised from the relations between human constraints and human values. Continuations are proposed. (This paper is an extended version of the proceedings of an AISB/IACAP 2012 presentation). (shrink)

In this paper a class of languages which are formal enough for mathematical reasoning is introduced. Its languages are called mathematically agreeable. Languages containing a given MA language L, and being sublanguages of L augmented by a monadic predicate, are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of those languages. MTT makes them fully interpreted MA languages which posses their own truth predicates. MTT is shown to conform well with the eight norms formulated for theories (...) of truth in the paper 'What Theories of Truth Should be Like (but Cannot be)', by Hannes Leitgeb. MTT is also free from infinite regress, providing a proper framework to study the regress problem. Main tools used in proofs are Zermelo-Fraenkel (ZF) set theory and classical logic. (shrink)

Hannes Leitgeb formulated eight norms for theories of truth in his paper [5]: `What Theories of Truth Should be Like (but Cannot be)'. We shall present in this paper a theory of truth for suitably constructed languages which contain the first-order language of set theory, and prove that it satisfies all those norms.

The main thesis of this work is as follows: there are versions of Yablo’s paradox that, if Cook is right about the non-circular character of his version of it, are truly paradoxical and genuinely non-circular, and Cook’s version of Yablo’s paradox is one of them. Here I will not evaluate the"circular" or"non-circular" side to Cook’s proposal. In fact, I think that he is right about it, and that his version of Yablo’s list is non-circular. But is it paradoxical? In order (...) to be so, the principles that lead to (i) the derivation of a contradiction, or (ii) the impossibility to give a stable assignment of truth values to the relevant set of sentences, must be acceptable. I will explore two ways to argue that they are not. I will conclude that these attempts lead to a very narrow conception of a theory of truth, or to deny that a paradigmatic case of paradox, such as the"Old-Fashioned Liar," is truly paradoxical. La tesis principal de este trabajo es la siguiente: hay versiones de la paradoja de Yablo tales que, si Cook está en lo cierto acerca del carácter no-circular de su propia versión de ella, son genuinamente paradójicas y auténticamente no-circulares, y la versión de Cook en cuestión es una de ellas. Aquí no voy a evaluar su carácter circular o no-circular. Creo, de hecho, que Cook está en lo correcto sobre el punto. Pero, ¿es su versión auténticamente paradójica? Para que lo fuera, los principios que llevan a (i) derivar una contradicción, o (ii) la imposibilidad de dar una asignación de valores de verdad estables al conjunto relevante de oraciones, deben ser aceptables. Voy a explorar dos modos de argumentar que no lo son. voy a concluir que estos intentos llevan a una concepción de la teoría de la verdad muy estrecha, o a negar que un caso paradigmático de paradoja, como el"mentiroso Tradicional", sea auténticamente paradójica. (shrink)

Tarski's Undefinability of Truth Theorem comes in two versions: that no consistent theory which interprets Robinson's Arithmetic (Q) can prove all instances of the T-Scheme and hence define truth; and that no such theory, if sound, can even express truth. In this note, I prove corresponding limitative results for validity. While Peano Arithmetic already has the resources to define a predicate expressing logical validity, as Jeff Ketland has recently pointed out (2012, Validity as a primitive. Analysis 72: 421-30), no theory (...) which interprets Q closed under the standard structural rules can define nor express validity, on pain of triviality. The results put pressure on the widespread view that there is an asymmetry between truth and validity, viz. that while the former cannot be defined within the language, the latter can. I argue that Vann McGee's and Hartry Field's arguments for the asymmetry view are problematic. (shrink)

In the sentence “Tom sits,” the name distinguishes Tom from anyone else, whereas the predicate assimilates Tom, Theaetetus, and anyone else to whom the predicate applies. The name marks out its bearer and the predicate groups together what it applies to. On that ground, his name is used to trace back Tom, and the predi- cate is used to describe and classify what it applies to. In both cases, the semantic link is a direct link between expressions and particulars. Here, (...) I will explore the workings of predicative names along the direction just hinted at. The analysis of predication has been less central to philosophical investigation than that of referen- tial expressions. Some problems have concerned the unity of the sentence—what makes us understand “The baby cries” as a sentence rather than a list of words? Other problems have been what a predicate was taken to stand for, properties and relations, and the understanding of either at the ontological level. If a predicate refers to a property or a relation, yet predication, which is central to our understand- ing of predicates, applies it to one or more particulars. On the background hinted at, these problems might be differently viewed. (shrink)

A reply to two responses to an earlier paper, "A Liar Paradox".

There is one truth, but many truths: i.e., one unambiguous, non-relative truth-concept, but many and various propositions that are true. One truth-concept: to say that a proposition is true is to say (not that anyone, or everyone, believes it, but) that things are as it says; but many truths: particular empirical claims, scientific theories, historical propositions, mathematical theorems, logical principles, textual interpretations, statements about what a person wants or believes or intends, about grammatical and legal rules, etc., etc. But, as (...) Frank Ramsey once said, “There is no platitude so obvious that eminent philosophers have not denied it”; and as soon as you ask why anyone would deny that there is one truth-concept, or that there are many true propositions, it becomes apparent that my initial, simple formula disguises many complexities. (shrink)

In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A unified treatment of curry paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, the substructure—of the validity relation itself.

Richard Heck has recently drawn attention on a new version of the Liar Paradox, one which relies on logical resources that are so weak as to suggest that it may not admit of any “truly satisfying, consistent solution”. I argue that this conclusion is too strong. Heck's Liar reduces to absurdity principles that are already rejected by consistent paracomplete theories of truth, such as Kripke's and Field's. Moreover, the new Liar gives us no reasons to think that (versions of) these (...) principles cannot be consistently retained once the structural rule of contraction is restricted. I suggest that revisionary logicians have independent reasons for restricting such a rule. (shrink)

We investigate the properties of Yablo sentences and for- mulas in theories of truth. Questions concerning provability of Yablo sentences in various truth systems, their provable equivalence, and their equivalence to the statements of their own untruth are discussed and answered.

Answering a question formulated by Halbach (2009), I show that a disquotational truth theory, which takes as axioms all positive substitutions of the sentential T-schema, together with all instances of induction in the language with the truth predicate, is conservative over its syntactical base.

Is there some large number of very mild hangnail pains, each experienced by a separate person, which would be worse than two years of excruciating torture, experienced by a single person? Many people have the intuition that the answer to this question is No. However, a host of philosophers have argued that, because we have no intuitive grasp of very large numbers, we should not trust such intuitions. I argue that there is decent intuitive support for the No answer, which (...) does not depend on our intuitively grasping or imagining very large numbers. (shrink)

The semantic paradoxes are often associated with self-reference or referential circularity. Yablo (Analysis 53(4):251–252, 1993), however, has shown that there are infinitary versions of the paradoxes that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality. In this essay, we lay the groundwork for a general investigation into the nature of reference structures that support the semantic paradoxes and the semantic hypodoxes. We develop (...) a functionally complete infinitary propositional language endowed with a denotation assignment and extract the reference structural information in terms of graph-theoretic properties. We introduce the new concepts of dangerous and precarious reference graphs, which allows us to rigorously define the task: classify the dangerous and precarious directed graphs purely in terms of their graph-theoretic properties. Ungroundedness will be shown to fully characterize the precarious reference graphs and fully characterize the dangerous finite graphs. We prove that an undirected graph has a dangerous orientation if and only if it contains a cycle, providing some support for the traditional idea that cyclic structure is required for paradoxicality. This leaves the task of classifying danger for infinite acyclic reference graphs. We provide some compactness results, which give further necessary conditions on danger in infinite graphs, which in conjunction with a notion of self-containment allows us to prove that dangerous acyclic graphs must have infinitely many vertices with infinite out-degree. But a full characterization of danger remains an open question. In the appendices we relate our results to the results given in Cook (J Symb Log 69(3):767–774, 2004) and Yablo (2006) with respect to more restricted sentences systems, which we call $\mathcal{F}$ -systems. (shrink)

In this paper I respond to Jacquette’s criticisms, in (Jacquette, 2008), of my (Barker, 2008). In so doing, I argue that the Liar paradox is in fact a problem about the disquotational schema, and that nothing in Jacquette’s paper undermines this diagnosis.

Logical pluralism has been in vogue since JC Beall and Greg Restall 2006 articulated and defended a new pluralist thesis. Recent criticisms such as Priest 2006a and Field 2009 have suggested that there is a relationship between their type of logical pluralism and the meaning-variance thesis for logic. This is the claim, often associated with Quine 1970, that a change of logic entails a change of meaning. Here we explore the connection between logical pluralism and meaning-variance, both in general and (...) for Beall and Restall's theory specifically. We argue that contrary to what Beall and Restall claim, their type of pluralism is wedded to meaning-variance. We then develop an alternative form of logical pluralism that circumvents at least some forms of meaning-variance. (shrink)

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends classical (...) logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered. (shrink)

In J Philos Logic 34:155–192, 2005, Leitgeb provides a theory of truth which is based on a theory of semantic dependence. We argue here that the conceptual thrust of this approach provides us with the best way of dealing with semantic paradoxes in a manner that is acceptable to a classical logician. However, in investigating a problem that was raised at the end of J Philos Logic 34:155–192, 2005, we discover that something is missing from Leitgeb’s original definition. Moreover, we (...) show that once the appropriate repairs have been made, the resultant definition is equivalent to a version of the supervaluation definition suggested in J Philos 72:690–716, 1975 and discussed in detail in J Symb Log 51(3):663–681, 1986. The upshot of this is a philosophical justification for the simple supervaluation approach and fresh insight into its workings. (shrink)

This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.

An attractive approach to the semantic paradoxes holds that cases of semantic pathology give rise to indeterminacy. What attitude should a rational agent have toward a proposition that it takes to be indeterminate in this sense? Orthodoxy holds that rationality requires that an agent disbelieve such a proposition. I argue that a rational agent should be such that it is indeterminate whether it believes the proposition in question. For rational agents, indeterminacy in the objects of their attitudes will filter up (...) to the attitudes themselves. (shrink)

I argue that on very weak assumptions about truth (in particular, that there are coherent norms governing the use of "true"), there is a proposition absolutely inexpressible with conventional language, or something very close. I argue for this claim "constructively": I use a variant of the Berry Paradox to reveal a particular thought for my readership to entertain that very strongly resists conventional expression. I gauge the severity of this expressive limitation within a taxonomy of expressive failures, and argue that (...) despite its strength there is nothing incoherent about admitting its existence. The argument forms part of a project of clarifying precisely what trade-offs are required to secure the kinds of expressive power truth theorists typically want, in the process showing that the admission of very strong expressive limitations may ultimately prove to be the lesser of two evils. (shrink)

A tempting solution to problems of semantic vagueness and to the Liar Paradox is an appeal to truth-value gaps. It is tempting to say, for example, that, where Harry is a borderline case of bald, the sentenceHarry is baldis neither true nor false: it is in the ‘gap’ between these two values, and perhaps deserves a third truth-value. Similarly with the Liar Paradox. Consider the following Liar sentence: is false.That is, sentence says of itself that it is false. If we (...) accept the Tarskian schema S is true iff pwhere ‘S’ is a name of a sentence ‘p,’ we are led into paradox. Both the assumption that is true, and the assumption that is false lead us, via, to is true if and only if is false.Given this result, a natural reaction is to place in a ‘gap’ between true and false. (shrink)

In this paper, I investigate the prospects for using the distinction between rejection and denial to resolve Saul Kripke’s puzzle about belief. One puzzle Kripke presents in A Puzzle About Belief poses what would have seemed a fairly straightforward question about the beliefs of the bilingual Pierre, who is disposed to sincerely and reflectively assent to the French sentence Londres est jolie, but not to the English sentence London is pretty, both of which he understands perfectly well. The question to (...) be answered is whether Pierre believes that London is pretty, and Kripke argues, of each answer, that it is unacceptable. On my proposal, either answer to the question is to be rejected, but neither answer is to be denied, using the resource of partially-defined predicates. After demonstrating how this serves as a solution to the puzzle, I illustrate some philosophical motivations—independent of Kripke’s puzzle —for adopting a view on which belief is a partially defined predicate. I conclude that there are decent prospects for the proposed response to Kripke’s puzzle. (shrink)

This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for Cut—elimination, but the (...) other does not.). (shrink)

The ideas of fixed points (Kripke in Recent essays on truth and the liar paradox. Clarendon Press, London, pp 53–81, 1975; Martin and Woodruff in Recent essays on truth and the liar paradox. Clarendon Press, London, pp 47–51, 1984) and revision sequences (Gupta and Belnap in The revision theory of truth. MIT, London, 1993; Gupta in The Blackwell guide to philosophical logic. Blackwell, London, pp 90–114, 2001) have been exploited to provide solutions to the semantic paradox and have achieved admirable (...) success. This happy situation naturally encourages one to look for other philosophical areas of their further applications where paradoxical results seem to follow from intuitively acceptable principles. In this paper, I propose to extend the use of these ideas to give two new treatments of abstract objects. Sections 1 and 2 below check several abstractionist theories and their main defects. Section 3 shows how the two ideas can be applied to generate consistent theories of abstract objects without any ad hoc restriction on any principle. (shrink)

Dans la première partie de cet article, je presente une thèse parapluie — la thèse de l'«exhaustion» — qui cerne bien l'élément central des diverses positions déflationnistes au sujet de la vérité : l'idée que le contenu du prédicat de vérité s'épuise entièrement dans le contenu de ce à quoi le prédicats'applique. Je soutiens que cette thèse n'est supportée que d'une manière triviale par l'idée courante que la vérite résiste à une analyse substantielle, car les prédicats en général ne se (...) prêtent guere à ce genre d'analyse. J'examine ensuite deux élaborations positives de la thèse de l'exhaustion; et je soutiens que ni l'une ni l'autre ne commence même à montrer que la thèse en question soit explicativement adéquate. (shrink)

Depuis 1967, Donald Davidson defend l'idée qu'une théorie de la signification pour une langue naturelle doit prendre la forme d'une théorie tarskienne de la vérité. Je me propose ici d'exposer les grandes lignes de l a conception davidsonienne de la sémantique des langues naturelles et de chercher à préciser en quel sens une theorie tarskienne de la vérité pour une langue L constitue, selon Davidson, une théorié de la signification pour L. Je ferai pour cela abstraction des obstacles qu'il pourrait (...) y avoir à la réalisation du programme de Davidson. (shrink)

We present $\in_I$-Logic (Epsilon-I-Logic), a non-Fregean intuitionistic logic with a truth predicate and a falsity predicate as intuitionistic negation. $\in_I$ is an extension and intuitionistic generalization of the classical logic $\in_T$ (without quantifiers) designed by Sträter as a theory of truth with propositional self-reference. The intensional semantics of $\in_T$ offers a new solution to semantic paradoxes. In the present paper we introduce an intuitionistic semantics and study some semantic notions in this broader context. Also we enrich the quantifier-free language by (...) the new connective < that expresses reference between statements and yields a finer characterization of intensional models. Our results in the intuitionistic setting lead to a clear distinction between the notion of denotation of a sentence and the here-proposed notion of extension of a sentence (both concepts are equivalent in the classical context). We generalize the Fregean Axiom to an intuitionistic version not valid in $\in_I$. A main result of the paper is the development of several model constructions. We construct intensional models and present a method for the construction of standard models which contain specific (self-)referential propositions. (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)

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)

The present work, which was inspired by Kripke and McCarthy, is about a non-classical predicate logic system containing a truth predicate symbol. In this system, each sentence A is referred to not by a Gödel number but by its quotation name 'A'.

This chapter introduces Kripke's work to advanced undergraduates, mainly focussing on his "A Puzzle About Belief" and "Wittgenstein on Rules and Private Language".