This brief note corrects an error in one of the reduction steps in my paper 'Normalisation for Bilateral Classical Logic with some Philosophical Remarks' published in the Journal of Applied Logics 8/2 (2021): 531-556.

G. F. Stout is famous as an early twentieth century proselyte for abstract particulars, or tropes as they are now often called. He advanced his version of trope theory to avoid the excesses of nominalism on the one hand and realism on the other. But his arguments for tropes have been widely misconceived as metaphysical, e.g. by Armstrong. In this paper, I argue that Stout’s fundamental arguments for tropes were ideological and epistemological rather than metaphysical. He moulded his scheme to (...) fit what is actually given to us in perception, arguing that our epistemic practices would break down in an environment where only universals were given to us. (shrink)

The purpose of this paper is to open for investigation a range of phenomena familiar from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the [0, 1] interval. Strange attractors and fractals appear in two dimensions in the graphing of pairs of mutually referential sentences and appear in three dimensions in the graphing of (...) mutually referential triples. (shrink)

In this dissertation, we shall investigate whether Tennant's criterion for paradoxicality(TCP) can be a correct criterion for genuine paradoxes and whether the requirement of a normal derivation(RND) can be a proof-theoretic solution to the paradoxes. Tennant’s criterion has two types of counterexamples. The one is a case which raises the problem of overgeneration that TCP makes a paradoxical derivation non-paradoxical. The other is one which generates the problem of undergeneration that TCP renders a non-paradoxical derivation paradoxical. Chapter 2 deals with (...) the problem of undergeneration and Chapter 3 concerns the problem of overgeneration. Chapter 2 discusses that Tenant’s diagnosis of the counterexample which applies CR−rule and causes the undergeneration problem is not correct and presents a solution to the problem of undergeneration. Chapter 3 argues that Tennant’s diagnosis of the counterexample raising the overgeneration problem is wrong and provides a solution to the problem. Finally, Chapter 4 addresses what should be explicated in order for RND to be a proof-theoretic solution to the paradoxes. (shrink)

The paper explores applications of Kripke's theory of truth to semantics for anti-luck epistemology, that is, to subjunctive theories of knowledge. Subjunctive theories put forward modal or subjunctive conditions to rule out knowledge by mere luck as to be found in Gettier-style counterexamples to the analysis of knowledge as justified true belief. Because of the subjunctive nature of these conditions the resulting semantics turns out to be non-monotone, even if it is based on non-classical evaluation schemes such as strong Kleene (...) or FDE. This blocks the usual road to fixed-point results for Kripke's theory of truth within these semantics and consequently the paper is predominantly an exploration of fixed point results for Kripke's theory of truth within non-monotone semantics. Using the theory of quasi-inductive definitions we show that in case of the subjunctive theories of knowledge the so-called Kripke jump will have fixed points despite the non-monotonicity of the semantics: Kripke's theory of truth can be successfully applied in the framework of subjunctive theories of knowledge. (shrink)

A teoria minimalista da verdade consiste em todas as instâncias do esquema 'φ é verdadeira sse φ' e na afirmação de que nossa aceitação (primitiva) dessas instâncias é suficiente para explicar nossas atitudes em relação a todas sentenças envolvendo ‘verdade’. Filósofos têm apontado que o minimalismo tem dificuldades em explicar nossas atitudes em relação a generalizações envolvendo ‘verdade’ bem como em lidar com instanciações contraditórias do esquema para sentenças paradoxais (ex. paradoxo do mentiroso). Proponentes do minimalismo apresentam soluções para esses (...) problemas. Nesse artigo, argumento que essas soluções entram em conflito, analiso algumas estratégias para resolver esse conflito e concluo que o minimalismo não pode evitar conflitos desse tipo mantendo seu caráter minimalista. ENGLISH: The minimalist theory of truth consists in all the instances of the schema 'φ is true iff φ' and in the claim that our primitive acceptance of these instances explains our attitudes in relation to propositions involving truth. Philosophers point that minimalism has difficulties in explaining our attitudes in relation to generalizations involving truth and with the contradictory instances of the schema for paradoxal sentences (e.g. the liar). Minimalists present solutions to these problems. In this paper, I argue that these solutions conflict with each other. I analyze some strategies to resolve this conflict. I conclude that minimalism cannot avoid the conflict maintaining it minimalist character. (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)

In this paprer a class of so called mathematically acceptable (shortly MA) languages is introduced First-order formal languages containing natural numbers and numerals belong to that class. MA languages which are contained in a given fully interpreted MA language augmented by a monadic predicate are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of these languages. MTT makes them fully interpreted MA languages which posses their own truth predicates, yielding consequences to philosophy of mathematics. MTT is (...) shown to conform well with the eight norms presented 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. (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)

The aim of this dissertation is to offer and defend a correspondence theory of truth. I begin by critically examining the coherence, pragmatic, simple, redundancy, disquotational, minimal, and prosentential theories of truth. Special attention is paid to several versions of disquotationalism, whose plausibility has led to its fairly constant support since the pioneering work of Alfred Tarski, through that by W. V. Quine, and recently in the work of Paul Horwich. I argue that none of these theories meets the correspondence (...) intuition---that a true sentence or proposition in some way corresponds to reality---despite the explicit claims by each to capture this intuition. I distinguish six versions of the correspondence theory, and defend two against traditional objections, standardly taken as decisive against them, and show, plainly, that these two theories capture the correspondence intuition. Due to the importance of meeting this intuition, only these two theories stands a chance of being a satisfactory theory of truth. I argue that the version of the correspondence theory incorporating a simple semantic representation relation is preferable to its rival, for which the representation relation is complex. I present and argue for a novel version of this correspondence theory according to which truth is a correspondence property sensitive to semantic context. One consequence of this context-sensitivity is that an ungrounded sentence does not express a proposition. In addition to accounting for the similarity between the Liar and Truth-Teller sentences, this theory of truth is immune to the Liar Paradox, including empirical versions. It is argued that the Liar Paradox is devastating to all of the other theories above, and even formal theories of truth designed to solve it, such as the revision and vagueness theories. Customized versions of the Liar Paradox besetting this theory are handled by its context-sensitivity, and by enforcing the distinction between truth and truth value. This same pair of considerations also yields solutions to Lob's Paradox and Grelling's Paradox. Arguments similar to those given to defend this correspondence theory show that with one minor alteration, Kripke's fixed point theory may be used to model this correspondence notion of truth. (shrink)

Ontology is the study of what there is, what kinds of things make up reality. Ontology seems to be a very difficult, rather speculative discipline. However, it is trivial to conclude that there are properties, propositions and numbers, starting from only necessarily true or analytic premises. This gives rise to a puzzle about how hard ontological questions are, and relates to a puzzle about how important they are. And it produces the ontologyobjectivity dilemma: either (certain) ontological questions can be trivially (...) answered using only uncontroversial premises, or the uncertainties of ontology are really a threat to the truth of basically everything we say or believe. The main aim of this dissertation is to resolve these puzzles and to shed some light on the discipline of ontology. I defend a view inspired by Carnap’s internal-external distinction about what there is, but one according to which both internal and external questions are fully factual and meaningful. In particular, I argue that the trivial arguments are valid, but they do not answer any ontological questions. Furthermore, I propose an account of the function of our talk about properties, propositions and natural numbers. According to this account our talk about them has no ontological presuppositions for its literal and objective truth. This avoids the ontology-objectivity dilemma, and solves the puzzles about ontology. To do this I look at quantification and noun phrases in general, and at their relation to ontology. I argue that quantifiers are semantically underspecified in a certain respect, and play two different roles in communication. I discuss the relation between syntactic form and information structure, the function of certain non-referential, non-quantificational noun phrases, the uses of bare number determiners, and how arithmetic truths are learned and taught. The more metaphysical issues discussed include: inexpressible properties, logicism about arithmetic, nominalism, Carnap’s view about ontology, the problem of universals, the relationship between ontology and objectivity, different projects within ontology, non-existent.... (shrink)

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

This special issue collects together nine new essays on logical consequence :the relation obtaining between the premises and the conclusion of a logically valid argument. The present paper is a partial, and opinionated,introduction to the contemporary debate on the topic. We focus on two influential accounts of consequence, the model-theoretic and the proof-theoretic, and on the seeming platitude that valid arguments necessarilypreserve truth. We briefly discuss the main objections these accounts face, as well as Hartry Field’s contention that such objections (...) show consequenceto be a primitive, indefinable notion, and that we must reject the claim that valid arguments necessarily preserve truth. We suggest that the accountsin question have the resources to meet the objections standardly thought to herald their demise and make two main claims: (i) that consequence, as opposed to logical consequence, is the epistemologically significant relation philosophers should be mainly interested in; and (ii) that consequence is a paradoxical notion if truth is. (shrink)

Three recent books have argued that Keynes’s philosophy, like Wittgenstein’s, underwent a radical foundational shift. It is argued that Keynes, like Wittgenstein, moved from an atomic Cartesian individualism to a more conventionalist, intersubjective philosophy. It is sometimes argued this was caused by Wittgenstein’s concurrent conversion. Further, it is argued that recognising this shift is important for understanding Keynes’s later economics. In this paper I argue that the evidence adduced for these theses is insubstantial, and other available evidence contradicts their claims.

A theory of truth is introduced for a first--order language L of set theory. Fully interpreted metalanguages which contain their truth predicates are constructed for L. The presented theory is free from infinite regress, whence it provides a proper framework to study the regress problem. Only ZF set theory, concepts definable in L and classical two-valued logic are used.

The present paper is concerned with an exposé of the basic general-semantic theses presented in the tract called “De insolubilibus” written by the 14th century British logician Roger Swyneshed. Swyneshed‘s semantics is analysed as a highly specific theory of truth, correspondence and facts . Swyneshed’s theory revises the correspondence theory of truth and rejects the principle of bivalence, while offering the solution to two different types of paradoxes . As it is usual for theories of this kind, Swyneshed’s semantics has (...) to face the specific forms of revenge-arguments, which lead to a specific conception of truthmaking. (shrink)

In this dissertation I examine the NeoFregean metaontology of mathematics. I try to clarify the relationship between what is sometimes called Priority Thesis and Platonism about mathematical entities. I then present three coherent ways in which one might endorse both these stances, also answering some possible objections. Finally I try to show which of these three ways is the most promising.

We argue that it would seem to be a mistake to blame Liar-like paradox on certain features of the object language, since the effect can be created with very minimal object languages that contain none of the usual suspects (truth-like predicates, reference to their own truth-bearers, negation, etc.).

I first discuss Chihara's claim that the presence of Liar-paradoxical sentences presents no problem for our understanding of natural languages, and argue that this cannot be held as easily as he suggests. I then consider the theories advanced by Martin, van Fraassen, Kripke and Burge which attempt to meet some of the problems involved. I argue that the claim in the first two theories that Liar sentences are ill-formed cannot be maintained, and that Burge's theory is methodologically unsound and seriously (...) incomplete. Kripke's theory, though it gives implausible truth-values to some sentences, is more satisfactory. Finally, I discuss Gupta's revision theory, and provide my own alternative which has the following advantages. First, it facilitates our understanding of Kripke's and Gupta's theories, and of their relationship. Second, it provides a third theory in which we can understand how the presence of the Liar does not radically infect a language. (shrink)

This article reveals a tension between a fairly standard response to "liar sentences," of which -/- (L) Sentence (L) -/- is not true is an instance, and some features of our natural language determiners (e.g., 'every,' 'some,' 'no,' etc.) that have been established by formal linguists. The fairly standard response to liar sentences, which has been voiced by a number of philosophers who work directly on the Liar paradox (e.g., Parsons [1974], Kripke [1975], Burge [1979], Goldstein [1985, 2009], Gaifman [1992, (...) 2000]), Glanzberg [2004], Azzouni [2006], and others), but can also be heard from philosophers who do not work directly on that paradox, is that liar sentences do not express propositions. Call this the "No Proposition View" (hereafter NPV). Evidently, the belief that liar sentences do not express propositions is a deeply held intuition. As the previously mentioned tension will reveal, there is reason to worry about whether this deeply held intuition can be sustained. (shrink)

Desde que Tarski publicó su estudio sobreel concepto de verdad en los años 30, hasido una práctica ortodoxa el considerarque t oda i nst anci a del esquema T esverdadera. Sin embargo, algunas instanciasdel esquema son falsas. Éstas incluyen lasi nst anci as paradój i cas ej empl i f i cadaspor la oración del mentiroso. Aquí sedemuestra que un esquema mejor permiteun tratamiento uniforme de la verdad enel que las paradojas semánticas resultanser simplemente falsas.Si nc e Ta r s (...) ki publ i s he d hi s s t udy ofthe concept of truth in the 1930s, it hasbeen orthodox practice to suppose thatevery instance of the T-schema is true.However, some instances of the schemaare false. These include the paradoxicalinstances exemplified by the Liar sentence.It is shown that a better schema allows auniform treatment of truth in which thesemantic paradoxes turn out to be simplyfalse. (shrink)

This thesis is concerned with the challenge truth-value gaps pose to the principle of bivalence. The central question addressed is: are truth-value gaps counterexamples to bivalence and is the supposition of counterexamples coherent? My aim is to examine putative cases of truth-value gaps against an argument by Timothy Williamson, which shows that the supposition of counterexamples to bivalence is contradictory. The upshot of his argument is that either problematic utterances say nothing, or they cannot be neither true nor false. I (...) start by identifying truth-bearers: an utterance, for instance, is a truth-bearer if it says that something is the case. Truth-bearers are evaluable items, with truth- and falsity-conditions statable in corresponding instances of schemas for truth and falsehood. A genuine case of a truth-value gap should be an utterance that is neither true nor false but says something to be the case. But it is inconsistent to accept the schemas for truth and falsehood and the existence of genuine cases of truth-value gaps. Secondly, I expound Williamson’s argument, which explores this inconsistency, and I identify two kinds of strategy to disarm his argument: those that preserve the schemas for truth and falsehood, and those that do not. Neither strategy is found to be persuasive. Thirdly, I argue that cases of reference failure causing truth-value gaps illustrate the upshot of Williamson’s argument. Fourthly, I examine Scott Soames’s account of liar sentences as counterexamples to bivalence. Soames adopts a strategy of the first kind to avoid contradictions. I argue that his solution allows some contradictions to be true, and that he fails to show that liar sentences are truth-bearers. Finally, I examine Charles Travis’s case for isostheneia: an equal balancing of reasons to evaluate a statement as true or as false, in which case a statement is neither. Travis avoids contradictions by adopting a strategy of the second kind. I argue that the schemas for truth and falsehood are immune to Travis’s objections, and that isostheneia fails to identify evaluable items. The cases examined confirm that utterances that are neither true nor false say nothing. My claim is thus that truth-value gaps are not counterexamples to bivalence. (shrink)

This thesis is on the history and philosophy of logic and semantics. Logic can be described as the ‘science of reasoning’, as it deals primarily with correct patterns of reasoning. However, logic as a discipline has undergone dramatic changes in the last two centuries: while for ancient and medieval philosophers it belonged essentially to the realm of language studies, it has currently become a sub-branch of mathematics. This thesis attempts to establish a dialogue between the modern and the medieval traditions (...) in logic, by means of ‘translations’ of the medieval logical theories into the modern framework of symbolic logic, i.e. formalizations. One of its conclusions is that, when properly understood within their own framework, the interest of medieval logical theories for modern investigations go beyond mere historical interest, but that a thorough conceptual analysis of such theories must be undertaken in order to avoid conceptual misprojections. While such translations of medieval into modern logic have been attempted before, the approach presented here is innovative in that attention is paid to the similarities as well as to the dissimilarities between the two traditions, and to what can be learned from the medieval masters for modern investigations in logic and semantics. (shrink)

In this contribution I will examine Cotnoir’s (2013) solution to the problems that alethic pluralism faces when it comes to logical paradoxes. I will argue that his proposal fails to be a viable option and I will put forward an alternative approach, more Tarskian in spirit, but with the same “pluralist” trait of Cotnoir’s solution. Such an alternative approach is based on the idea that each truth predicate can be associated with an index that fully describes its relation with other (...) truth predicates.I will show how such indexes must be constrained in order to avoid logical paradoxes. (shrink)

Che cos'è la verità? A questa domanda le teorie deflazioniste rispondono in modo sorprendente: niente, o quasi. Secondo il deflazionismo la verità, come proprietà, semplicemente non esiste o è priva di qualsiasi sostanza. In questo contributo presenterò tale posizione offrendo un breve resoconto critico dell'evoluzione della proposta e una disamina delle sue tesi centrali.

This thesis comprises three main chapters—each comprising one relatively standalone paper. The unifying theme is fragmentalism about truth, which is the view that the predicate “true” either expresses distinct concepts or expresses distinct properties. -/- In Chapter 1, I provide a formal development of alethic pluralism. Pluralism is the view that there are distinct truth properties associated with distinct domains of subject matter, where a truth property satisfies certain truth-characterizing principles. On behalf of pluralists, I propose an account of logic (...) and semantics that shows how they can answer central conceptual and logical challenges for their view. -/- In Chapter 2, I motivate and develop a modal account of propositions on the basis of an iterative conception of propositions, where the modality is logico-mathematical. The modal account of propositions takes the conception to motivate an inherently potential hierarchy of propositions. I show that the account helps provide satisfying solutions to the intensional paradoxes of Russell-Myhill, Kaplan, and Prior. -/- In Chapter 3, I propose that “true” is polysemous. I suggest that “true” is initially polysemous between correspondence truth and disquotational truth, and further polysemous between the meanings corresponding to the subconcepts of the concept truth generated by the indefinite extensibility of that concept. I show that the proposal provides satisfying solutions to the semantic paradoxes. (shrink)

Revised and reprinted; originally in Dov Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic, Volume IV. Kluwer 133-251. -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in the (...) course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

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

To borrow a colorful phrase from Kant, this dissertation offers a prolegomenon to any future semantic theory. The dissertation investigates Yablo's omega-liar paradox and draws the following consequence. Any semantic theory that accepts the existence of semantic objects must face Yablo's paradox. The dissertation endeavors to position Yablo's omega-liar in a role analogous to that which Russell's paradox has for the foundations of mathematics. Russell's paradox showed that if we wed mathematics to sets, then because of the many different possible (...) restrictions available for blocking the paradox, mathematics fractionates. There would be different mathematics. This is intolerable. It is similarly intolerable to have restrictions on the `objects' of Intentionality. Hence, in the light of Yablo's omega-liar, Intentionality cannot be wed to any theory of semantic objects. We ought, therefore, to think of Yablo's paradox as a natural language paradox, and as such we must accept its implications for the semantics of natural language, namely that those entities which are `meanings' must not be construed as objects. To establish our result, Yablo's paradox is examined in light of the criticisms of Priest. Priest maintains that Yablo's original omega-liar is flawed in its employment of a Tarski-style T-schema for its truth-predicate. Priest argues that the paradox is not formulable unless it employs a "satisfaction" predicate in place of its truth-predicate. Priest is mistaken. However, it will be shown that the omega-liar paradox depends essentially on the assumption of semantic objects. No formulation of the paradox is possible without this assumption. Given this, the dissertation looks at three different sorts of theories of propositions, and argues that two fail to specify a complete syntax for the Yablo sentences. Purely intensional propositions, however, are able to complete the syntax and thus generate the paradox. In the end, however, the restrictions normally associated with purely intensional propositions begin to look surprisingly like the hierarchies that Yablo sought to avoid with his paradox. The result is that while Yablo's paradox is syntactically formable within systems with formal hierarchies, it is not semantically so. (shrink)

In this paper, I explore the possibility of applying the methods and results of Judgement Aggregation to the problem of logical disagreement. I develop and evaluate different ways in which individuals who logically disagree can generate a collective logic. I prove a version of the discursive paradox, where the majority voting of a group of structural logicians can give rise to a substructural logic; then I develop a more general impossibility result. After this, I analyze different ways to avoid the (...) paradox, in particular some methods which appeal to domain restrictions. Finally, I consider the application of these results to the discussion on semantic paradoxes. (shrink)

A survey of logical problems for the concept of omniscience.

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)

The Hangman Paradox has a simple solution. The amazing refutation of the judge's decree rests on the axiom of knowledge-conservation. This axiom is false under unfavourable conditions. You can have a perfect piece of knowledge in the ordinary sense, i.e. a true justified conviction, and yet be unable to conserve it. More interesting than its solution is the element of self-reference, connecting the Hangman via Moore's Paradox and Buridan's Epistemic Paradox with the Liar. This one, I think, has also a (...) natural solution, but less simple. The basic idea is given here, but the technical treatment goes far beyond this paper. It requires a strong, but conservative, extension of classical and three-valued logic to a six-valued logic with infinitely many levels of reflection. (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.

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)

Ordinary and transfinite recursion and induction and ZF set theory are used to construct from a fully interpreted object language and from an extra formula a new language. It is fully interpreted under a suitably defined interpretation. This interpretation is equivalent to the interpretation by meanings of sentences if the object language is so interpreted. The added formula provides a truth predicate for the constructed language. The so obtained theory of truth satisfies the norms presented in Hannes Leitgeb's paper 'What (...) Theories of Truth Should be Like (but Cannot be)'. (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)

This paper argues that the Correspondence Theory of Truth is not well- served by Truthmaker Theory and is better developed in a different direction. For there are reasons to believe that the main axiom of that theory (TA) which states that for every truth there is a truthmaker is either unjustified or false. Some of these reasons are already well-known. Negative existentials and universal generalizations present initial difficulties for TM theory as do necessary truths. There is a more serious problem, (...) though which has not hitherto been noticed. (TA) even when restricted to contingent sentences seems to tolerate clear counterexamples. There seem to be, and I argue that there in fact are, true contingent sentences which lack truthmakers. The examples adduced are all truthmaker analogues of semantically pathological sentences. The positive proposal shares with Truthmaker Theory the view that our judgments and sentences are rendered true by the worldly facts but argues for an alternative conception of Ôrendering trueÕ and a novel conception of 'facts'. (shrink)

I justify a non-logician speaking of the liar antinomy by Peano view that semantic antinomies are linguistic issues. The remarks I formulate below follow Alfred Gawroński’s idea, namely, that the liar antinomy is an apparent antinomy.

Professor Barbara Stanosz was a years-long lecturer at the Institute of Philosophy, University of Warsaw. In her work she mainly – but not exclusively – focused on the theory of language, particularly semantics and the issues of logical description of phrases in language. She was an author of renowned textbooks, including the famous Ćwiczenia z logiki [Exercises in logic], a vastly popular exercise book helping students to acquire the material on propositional logic, predicate logic and set theory. It is worth (...) mentioning that besides her academic and teaching activities, she was also a social activist and a great supporter of the state’s worldview neutrality. She died on 7th June 2014. (shrink)

This original and enticing book provides a fresh, unifying perspective on many old and new logico-philosophical conundrums. Its basic thesis is that many concepts central in ordinary and philosophical discourse are inherently circular and thus cannot be fully understood as long as one remains within the confines of a standard theory of definitions. As an alternative, the authors develop a revision theory of definitions, which allows definitions to be circular without this giving rise to contradiction (but, at worst, to “vacuous” (...) uses of definienda). The theory is applied with varying levels of detail to a circular analysis of concepts as diverse as truth, predication, necessity, physical object, etc. The focus is on truth, and hope is expressed that a deeper understanding of the Liar and related paradoxes has been provided: “We have tried to show that once the circularity of truth is recognized, a great deal of its behavior begins to make sense. In particular, from this viewpoint, the existence of the paradoxes seems as natural as the existence of the eclipses” (p. 142). We think that this hope is fully justified, although some problems remain that future research in this field should take into account. (shrink)

Philip Kremer, Department of Philosophy, McMaster University Note: The following version of this paper does not contain the proofs of the stated theorems. A longer version, complete with proofs, is forthcoming. §1. Introduction. In "The truth is never simple" and its addendum, Burgess conducts a breathtakingly comprehensive survey of the complexity of the set of truths which arise when you add a truth predicate to arithmetic, and interpret that predicate according to the fixed point semantics or the revision-theoretic semantics for (...) languages expressing their own truth concepts. Burgess considers various sets that can be said to represent truth in this context, and shows that their complexity ranges from Π11 or Σ11 to Π12 or Σ12. Thus, enriching arithmetic with a truth predicate increases its complexity, which is otherwise only ∆11. (shrink)