Semantic interpretations of both natural and formal languages are usually taken to involve the specification of a domain of entities with respect to which the sentences of the language are to be evaluated. A question that has received much attention of late is whether there is unrestricted quantification, quantification over a domain comprising absolutely everything there is. Is there a discourse or inquiry that has absolute generality? After framing the debate, this article provides an overview of the main arguments for (...) and against the possibility of unrestricted quantification, highlighting some of the broader implications of the debate. (shrink)

Carnap’s work was instrumental to the liberalization of empiricism in the 1930s that transformed the logical positivism of the Vienna Circle to what came to be known as logical empiricism. A central feature of this liberalization was the deployment of the Principle of Tolerance, originally introduced in logic, but now invoked in an epistemological context in “Testability and Meaning”. Immediately afterwards, starting with Foundations of Logic and Mathematics, Carnap embraced semantics and turned to interpretation to guide the choice of a (...) theoretical language for science. The first thesis of this paper is that recourse to an intended interpretation led to a partial retrenchment of the conventionalism implied by the Principle of Tolerance. It required that the choice of a language be based on abstraction from a context; this procedure later became a component of the process of explication that was distinctive to Carnap’s mature views. The interpretive origin of formal systems also ensured their likely syntactic consistency, an issue on which Carnap was strongly criticized by figures such as Beth and Gödel. The second thesis of this paper is that this reliance on an intended interpretation enabled constructed formal systems to be relevant to the development of empirical science. (shrink)

Paraconsistent and dialetheist approaches to a theory of truth are faced with a problem: the expressive resources of the logic do not suffice to express that a sentence is just true—i.e., true and not also false—or to express that a sentence is consistent. In his recent book, Spandrels of Truth, Jc Beall proposes a ‘just true’-operator to identify sentences that are true and not also false. Beall suggests seven principles that a ‘just true’-operator must fulfill, and proves that his operator (...) indeed fulfills all of them. He concludes that just true has been expressed in the language. I argue that, while the seven conditions may be necessary for an operator to express just true, they are not jointly sufficient. Specifically, first, I prove that a further plausible desideratum for necessary conditions on ‘just true’ is not fulfilled by Beall's proposal, namely that ‘just true’ ascriptions should themselves be just true, and not also false (or equivalently, that the ‘just true’-operator iterates). Second, I show that Beall's operator does not adequately express just true, but that it merely captures an arbitrary proper subset of the just true sentences. Further, there is no prospect of extending the proposal in order to encompass a more reasonable subset of the just true sentences without presupposing that we have antecedent means to characterize the class of just true sentences. (shrink)

1. For simplicity, let the domain of our first-level quantifiers, ‘∀ x’ and so on, be words, and in particular just those words which are adjectives. And let the adjective ‘heterological’ be abbreviated just to As is well known, one cannot legitimately stipulate that Why not? Well, the obvious answer is that if is supposed to be an adjective, then this alleged stipulation would imply the contradiction But contradictions cannot be true, and it is no use stipulating that they shall (...) be. Do we need to say anything more? Russell would apparently wish to add this: the stipulation is illegitimate because it attempts to define the word by a quantification over all words, and the word is itself taken to be one of the words quantified over. That is how this supposed definition would infringe his vicious-circle principle . 1 It is of course true that if our quantification is taken to range only over words of a certain kind, say first-order adjectives, and if the word is taken to be a word of a different kind, say a second-order adjective, then the contradiction is avoided. For the supposed stipulation then has no implications for whether is or is not true of any second-order words. Russell imagines the stipulation to be strengthened by adding that is to be true only of first-order words, and hence that it is not true of itself. But no contradiction now results from this. However, one must ask: did we need this explanation in terms of the VCP? It may seem helpful, because there is an initial temptation to say that the original stipulation could not be illegitimate. This is because it is thought of as introducing a new word, and explaining what it means, and one is apt to think that we …. (shrink)

The medieval Islamic solutions to the liar paradox can be categorized into three different families. According to the solutions of the first family, the liar sentences are not well-formed truth-apt sentences. The solutions of the second family are based on a violation of the classical principles of logic (e.g. the principle of non-contradiction). Finally, the solutions of the third family render the liar sentences as simply false without any contradiction. In the Islamic tradition, almost all the well-known solutions of the (...) third family are inspired by the solution proposed by At_īr al-Dīn al-Abharī (d. 1265). Providing a logical analysis of his discussion of the liar paradox, I show that his solution is based on a conception of truth according to which every sentence signifies, usually among other things, its own truth. This makes Abharī’s solution of the same spirit as certain solutions that were later developed in the Latin tradition, in particular by John Buridan (d. 1358) and Albert of Saxony (d. 1390). (shrink)

The medieval Islamic solutions to the liar paradox can be categorized into three different families. According to the solutions of the first family, the liar sentences are not well-formed truth-apt...

Critical rationalists cannot reconcile their falibilism with the demand of logic for universality. Popper tried, but failed, to achieve universality in logic without proof. Attempts to find a limited approach to logic as ‘logics of’ have failed to find a coherent critical rationalist alternative. Critical rationalists take Tarski’s logic to be the best of logic today. But Tarski renders logic as close to justification, and thereby universality, as possible. A fallibilist version of Tarskian logic can yield a critical rationalist alternative: (...) It provides rules for solving problems in linguistic contexts, but also discovers mistakes by discovering errors in logical inference. (shrink)

Many papers have been devoted to the semantic turn Carnap took in the late 1930s after Tarski had explained to him his method for defining truth and his work on the establishment of scientific semantics. Commentators have often argued that the major turn in Carnap’s approach to languages had already been taken in the Logical Syntax of Language, but they have usually assumed that Carnap was happy to subsequently follow Tarski and adopt Tarskian semantics. In this paper, it is argued (...) that this assumption needs to be qualified and that Carnap was actually far from following Tarski when he decided to complement his syntactic method with a semantic one. Carnap and Tarski had different goals, divergent programs, and dissenting views on truth and semantics. After exploring several possible methods for the explication of logical concepts such as L-truth and L-implication, Carnap opted for definitions based on concepts he had found in Wittgenstein’s Tractatus and Waismann’s work on a logical interpretation of probability. Carnap’s reasons for taking a semantic turn are to be understood in the context of his principle of tolerance. He first hoped he could use Tarski’s technique to recover in the semantic setting the completeness result he had tried to establish in the Logical Syntax. His eventual adoption of non-Tarskian semantics can be accounted for by his program of a logical analysis of science—including empirical science—and his ambition to elaborate a unified logical framework for deductive, inductive, and modal logic, and for explicating analyticity. (shrink)

In his paper "Undecidability without arithmetization," Andrzej Grzegorczyk introduces a theory of concatenation $\mathsf{TC}$. We show that pairing is not definable in $\mathsf{TC}$. We determine a reasonable extension of $\mathsf{TC}$ that is sequential, that is, has a good sequence coding.

The denitional feature of Tarski's theory of truth will be the subject of this paper. In fact, addition, multiplication and divisibility were well-known mathematical concepts before the accurate Peano formalization. Analogously, the Tarski's metatheory could be an accurate formalization of ‘ x is a formula’, ‘x is the reference/sense of y’ and ‘x is a true sentence’, all them introduced by definition. However, ‘x is a true sentence’, because of the paradoxes, cannot be an accurate formalization of truth predicate of (...) ordinary language. The question is: which concept of truth does the tarskian ‘x is a true sentence’ formalize? The answer is simple and not new, but its meanders are informative and enlightening. (shrink)

I will be concerned with the following question: are there compelling arguments for postulating a distinction between the truth of a statement and the recognition of its truth, when truth is conceived along the lines of a suitable generalization of the intuitionistic idea that it should be characterized as the existence of a proof? I will argue that the distinction is not necessary within the conceptual framework of intuitionism by replying to two arguments to the contrary, one based on the (...) paradox of inference, the other on considerations concerning the content of a statement. (shrink)

The article is part of a symposium on Hartry Field’s “Saving truth from paradox”. The book is one of the most significant intellectual achievements of the past decades, but it is not clear what, exactly, it accomplishes. I explore some alternatives, relating the developed view to the intuitive, pre-theoretic notion of truth.

In this article, I suggest an original solution to the Liar Paradox, based on the pragmatic theory of speech acts. This solution implies making a distinction between two concepts of truth: the intentional truth of a speaker’s utterances directed toward an addressee with the objective of obtaining a consensual agreement; the effective truth objectively recognized by the addressee in the speaker’s utterances. In view of reaching this new solution to the classic paradox, I conduct a critical review of solutions put (...) forward by Tarski, Kripke and Strawson. (shrink)

The article explores the relationship between Tarski’s theory oftruth and modern deflationary or minimalist accounts of truth. The authornotes many similarites, but he also identifies an important difference betweenTarski’s theory and the various approaches of his modern followers: Tarskithought of his theory of truth as an elaboration of the classical correspondence notion. The heart of his theory is the definition of truth in terms ofsatisfaction. Truth is explicated in terms of a relation between language andaspects of external reality. It is (...) just this central component of his theorywhich is rejected by modern deflationism and minimalism. (shrink)

The Ontological Square is a categorial scheme that combines two metaphysical distinctions: that between types (or universals ) and tokens (or particulars ) on the one hand, and that between characters (or features ) and their substrates (or bearers ) on the other hand. The resulting four-fold classification of things comprises particular substrates, called substances , universal substrates, called kinds , particular characters, called modes or moments , and universal characters, called attributes . Things are joined together in facts by (...) primitive ontological ties or nexus . This article describes a logic that is meant to capture the basic intuitions behind the Ontological Square. Given a minimal correspondence between atomic logical form and ontological structure, the commitment to nexus as a distinct ontological category entails a rehabilitation of copulae as ties of predication. Thus, the Logic of the Ontological Square is a copula calculus rather than a predicate calculus; its soundness and completeness can be established with respect to a model akin to a so-called first-order semantics for standard second-order logic. (shrink)

In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style of Principia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early attempts to develop the semantics (...) of axiomatic theories in the 1930s, by two proponents of the type-theoretic tradition and two proponents of the first-order tradition, we argue that, instead, the move from type theory to first-order logic is better understood as a gradual transformation, and further, that the contributions to semantics made in the type-theoretic tradition should be seen as central to the evolution of model theory. (shrink)

In Untersuchungen zur allgemeinen Axiomatik and Abriss der Logistik, Carnap attempted to formulate the metatheory of axiomatic theories within a single, fully interpreted type-theoretic framework and to investigate a number of meta-logical notions in it, such as those of model, consequence, consistency, completeness, and decidability. These attempts were largely unsuccessful, also in his own considered judgment. A detailed assessment of Carnap’s attempt shows, nevertheless, that his approach is much less confused and hopeless than it has often been made out to (...) be. By providing such a reassessment, the paper contributes to a reevaluation of Carnap’s contributions to the development of modern logic. (shrink)

Anaphoric deflationism is a kind of prosententialist account of the use of “true.” It holds that “true” is an expressive operator and not a predicate. In particular, “is true” is explained as a “prosentence.” Prosentences are, for sentences, the equivalent of what pronouns are for nouns: As pronouns refer to previously introduced nouns, so prosentences like “that’s true” inherit their semantic content from previously introduced sentences. So, if Jim says, “The candidate is going to win the election,” and Bill replies (...) “that’s true,” the real meaning of Bill’s statement is “It is true that the candidate is going to win the election.” This kind of prosententialist deflationism around the use of “true,” especially in Robert Brandom’s version, is an explanation given in terms of anaphora. The prosentence is an anaphoric dependent of the sentence providing its content. Båve (Philosophical Studies, 145, 297-310. 2009) argued that the anaphoric account is not as general as prosententialists claim, and that the analogy between prosentences and pronouns is explanatorily idle because it does not do any real explanatory work. The two criticisms are connected: The lack of unity within the anaphoric theory can be used to show its poor explanatory value. The plurality of uses of “is true” exceeds the anaphoric account indeed. Therefore, prosententialism is just a superficial re-description and the real work is done by means of more general semantic terms, namely “semantic equivalence and consequence” between “p” and ““p” is true.” I analyze Båve’s arguments and highlight that he fails to acknowledge the importance of a pragmatic and expressive dimension explained by the anaphoric account, a dimension that semantic “equivalence” and “consequence” are not capable of explaining. I then show that the anaphoric account can actually explain semantic equivalence and consequence, and this is crucial because equivalence and consequence do not explain anaphoric dependence. This reverses the allegation of generality: The anaphoric account is more general. Again, the cases typically used to defend prosententialism, if correctly described, show a unitary structure: They are all versions of lazy anaphoric dependence. Therefore, the unifying principle performing the explanation here is lazy anaphora. (shrink)

This essay assesses the account of truth presented in Wiggins's 2002 paper ‘An indefinibilist cum normative view of truth and the marks of truth'. I agree with Wiggins that we should seek, not to define truth, but to elucidate it by unfolding its connections with other basic notions. However, I give reasons for preferring an elucidation based on Ramsey's account of truth to Wiggins's Tarski-inspired approach. I also cast doubt on Wiggins's thesis that convergence is a mark of truth, arguing (...) instead that a claim which is up for assessment as true or false must be one to which different speakers/hearers can attach, and know that they are attaching, the same sense. I use this principle to rule out an account of indicative conditionals, and bring some considerations to bear on the question of whether those conditionals have truth values. An appendix revisits a debate about the determinateness of distinctness. (shrink)

I advance arguments in favour of PKF as an articulation of a central sense of the predicate ‘true’, and show how it illuminates the relationship between that sense and the ‘external’ notion of truth found in such claims as ‘An utterance of the Liar Sentence does not say anything, and so is not true’.

Revenge arguments purport to show that any proposed solution to the semantic paradoxes generates new paradoxes that prove that solution to be inadequate. In this paper, I focus on revenge arguments that employ the model-theoretic semantics of a target theory and I argue, contra the current revenge-theoretic wisdom, that they can constitute genuine expressive limitations. I consider the anti-revenge strategy elaborated by Field and argue that it does not offer a way out of the revenge problem. More generally, I argue (...) that the difference between ‘standard’ and ‘revenge’ paradoxes is ill-conceived and should be abandoned. This will contribute to show that the theories that provide a uniform account of truth and other semantic notions are the ones best equipped to avoid the paradoxes altogether—‘standard’ and ‘revenge’ alike. (shrink)

The axiom of canonicity was introduced by the famous Polish logician Roman Suszko in 1951 as an explication of Skolem's Paradox and a precise representation of the axiom of restriction in set theory proposed much earlier by Abraham Fraenkel. We discuss the main features of Suszko's contribution and hint at its possible further applications.

Recent years have witnessed a revival of interest in the method of explication as a procedure for conceptual engineering in philosophy and in science. In the philosophical literature, there has been a lively debate about the different desiderata that a good explicatum has to satisfy. In comparison, the goal of explicating the concept of explication itself has not been central to the philosophical debate. The main aim of this work is to suggest a way of filling this gap by explicating (...) ‘explication’ by means of conceptual spaces theory. Specifically, I show how different, strictly-conceptual readings of explication desiderata can be made precise as geometrical or topological constraints over the conceptual spaces related to the explicandum and the explicatum. Moreover, I show also how the richness of the geometrical representation of concepts in conceptual spaces theory allows us to achieve more fine-grained readings of explication desiderata, thereby overcoming some alleged limitations of explication as a procedure of conceptual engineering. (shrink)

Alfred Tarski (1944) wrote that "the condition of the 'essential richness' of the metalanguage proves to be, not only necessary, but also sufficient for the construction of a satisfactory definition of truth." But it has remained unclear what Tarski meant by an 'essentially richer' metalanguage. Moreover, DeVidi and Solomon (1999) have argued in this Journal that there is nothing that Tarski could have meant by that phrase which would make his pronouncement true. We develop an answer to the historical question (...) of what Tarski meant by 'essentially richer' and pinpoint the general result that stands behind his essential richness claim. In defense of Tarski, we then show that each of the several arguments of DeVidi and Solomon are either moot or mistaken. One of the fruits of our investigation is the reclamation of what Tarski took to be his central result on truth. This is a reclamation since: (i) if one does not understand 'essential richness', one does not know what that result is, and (ii) we must unearth a heretofore unrecognized change that occurs in Tarski's view - an alteration of his main thesis in light of a failing he discovered in it. (shrink)

Self-reference has played a prominent role in the development of metamathematics in the past century, starting with Gödel’s first incompleteness theorem. Given the nature of this and other results in the area, the informal understanding of self-reference in arithmetic has sufficed so far. Recently, however, it has been argued that for other related issues in metamathematics and philosophical logic a precise notion of self-reference and, more generally, reference is actually required. These notions have been so far elusive and are surrounded (...) by an aura of scepticism that has kept most philosophers away. In this paper I suggest we shouldn’t give up all hope. First, I introduce the reader to these issues. Second, I discuss the conditions a good notion of reference in arithmetic must satisfy. Accordingly, I then introduce adequate notions of reference for the language of first-order arithmetic, which I show to be fruitful for addressing the aforementioned issues in metamathematics. (shrink)

This paper explores the relationship borne by the traditional paradoxes of set theory and semantics to formal incompleteness phenomena. A central tool is the application of the Arithmetized Completeness Theorem to systems of second-order arithmetic and set theory in which various “paradoxical notions” for first-order languages can be formalized. I will first discuss the setting in which this result was originally presented by Hilbert & Bernays (1939) and also how it was later adapted by Kreisel (1950) and Wang (1955) in (...) order to obtain formal undecidability results. A generalization of this method will then be presented whereby Russell’s paradox, a variant of Mirimanoff’s paradox, the Liar, and the Grelling–Nelson paradox may be uniformly transformed into incompleteness theorems. Some additional observations are then framed relating these results to the unification of the set theoretic and semantic paradoxes, the intensionality of arithmetization (in the sense of Feferman, 1960), and axiomatic theories of truth. (shrink)

Explication is the conceptual cornerstone of Carnap’s approach to the methodology of scientific analysis. From a philosophical point of view, it gives rise to a number of questions that need to be addressed, but which do not seem to have been fully addressed by Carnap himself. This paper reconsiders Carnapian explication by comparing it to a different approach: the ‘formalisms as cognitive tools’ conception. The comparison allows us to discuss a number of aspects of the Carnapian methodology, as well as (...) issues pertaining to formalization in general. We start by introducing Carnap’s conception of explication, arguing that there is a tension between his proposed criteria of fruitfulness and similarity; we also argue that his further desideratum of exactness is less crucial than might appear at first. We then bring in the general idea of formalisms as cognitive tools, mainly by discussing the reliability of so-called statistical prediction rules, i.e. simple algorithms used to make predictions across a range of areas. SPRs allow for a concrete instantiation of Carnap’s fruitfulness desideratum, which is arguably the most important desideratum for him. Finally, we elaborate on what we call the ‘paradox of adequate formalization’, which for the Carnapian corresponds to the tension between similarity and fruitfulness. We conclude by noting that formalization is an inherently paradoxical enterprise in general, but one worth engaging in given the ‘cognitive boost’ it affords as a tool for discovery. (shrink)

This paper consists of three sections. In the first one, some of the main developments in the philosophy of science through the xx century up to the present will be pointed out, and inserted them in the frame of some more general philosophical transformations, such as the so-called “linguistic turn” and “pragmatic turn”, respectively. In the second one, the established connection will be nuanced, from a revision of the work of a “classical” author such as Carnap. Finally, it will be (...) intended a kind of “balance and future perspectives”. (shrink)

What kinds of sentences with truth predicate may be inserted plausibly and consistently into the T-scheme? We state an answer in terms of dependence: those sentences which depend directly or indirectly on non-semantic states of affairs (only). In order to make this precise we introduce a theory of dependence according to which a sentence φ is said to depend on a set Φ of sentences iff the truth value of φ supervenes on the presence or absence of the sentences of (...) Φ in/from the extension of the truth predicate. Both φ and the members of Φ are allowed to contain the truth predicate. On that basis we are able define notions such as ungroundedness or self-referentiality within a classical semantics, and we can show that there is an adequate definition of truth for the class of sentences which depend on non-semantic states of affairs. (shrink)

Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.

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

Deflationists about truth embrace the positive thesis that the notion of truth is useful as a logical device, for such purposes as blanket endorsement, and the negative thesis that the notion doesn’t have any legitimate applications beyond its logical uses, so it cannot play a significant theoretical role in scientific inquiry or causal explanation. Focusing on Christopher Hill as exemplary deflationist, the present paper takes issue with the negative thesis, arguing that, without making use of the notion of truth conditions, (...) we have little hope for a scientific understanding of human speech, thought, and action. For the reference relation, the situation is different. Inscrutability arguments give reason to think that a more-than-deflationary theory of reference is unattainable. With respect to reference, deflationism is the only game in town. (shrink)

The author considers the discussion of designation and truth by black and geach. Geach had pointed out a flaw in black's position and attempted to correct it. The author concludes that geach has not even "described the concepts in terms of which" he is to correct black.

In this article I describe and evaluate the debate that surrounds the proper interpretation of Tarski’s account of logical consequence given in his classic 1936 article ‘On the concept of logical consequence’. In the late 1980s Etchemendy argued that the familiar model theoretic account of logical consequence is not to be found in Tarski’s original article. Whereas the contemporary account of logical consequence is a variable‐domain conception – in that it calls for a reinterpretation of the domain of variation of (...) the quantifiers when evaluating logical consequence –, no such reinterpretation is found in Tarski’s original account, which was rather based on a ‘fixed‐domain’ conception. Etchemendy’s claims have sparked a debate on Tarski’s conception of logical consequence with important contributions by, among others, Bach, Bays, Corcoran, Gómez‐Torrente, Mancosu, Ray, Sagüillo, and Sher. (shrink)

We shift attention from the development of model theory for demarcated languages to the development of this theory for fragments of a language. Although it is often assumed that model theory for demarcated languages is not compatible with a universalist conception of logic, no one has denied that model theory for fragments of a language can be compatible with that conception. It thus seems unwarranted to ignore the universalist tradition in the search for the origins and development of model theory. (...) This point is illustrated by Carnap’s early semantics and model theory, which he developed within a type theoretical framework and which stand out both for their universalistic treatment and for certain idiosyncratic technicalities by which the construction is supported. One special property is that individuals are context relative in Carnap’s system. This leads to a model theory in which the model domains are more flexible than has been suggested in the literature. (shrink)

G. Schiemer has recently ascribed to Carnap the so-called domains-as-fields conception of models, which he subsequently used to defend Carnap’s treatment of extremal axioms against J. Hintikka’s criticism that the number of tuples in a relation, and not the domain of discourse, is optimised in Carnap’s treatment. We will argue by a careful textual analysis, however, that this domains-as-fields conception cannot be applied to Carnap’s early semantics, because it includes a notion of submodel and subrelation that is not only absent (...) from Carnap’s work at that time, but even contradicts it. As a consequence, Schiemer’s defense of Carnap’s extremal axioms against Hintikka’s criticism fails. We will reconcile Carnap’s treatment of extremal axioms and Hintikka’s observation by taking into account the practice of axiomatics in the early twentieth century. If one realises that, in Carnap’s time, a predicate for the domain of discourse was often introduced in the formal theory, and that Carnap defined such predicates from the basic relations of an axiom system, the apparent disagreement between optimising relations and optimising domains disappears. (shrink)

We give some information about new proofs of the incompleteness theorems, found in 1990s. Some of them do not require the diagonal lemma as a method of construction of an independent statement.

Des philosophes de la logique comme Prior et Mulligan considèrent le connecteur de vérité ‘Il est vrai que ’ comme étant plus fondamental que le prédicat de vérité ‘ est vrai’. Des philosophes comme Bolzano et Horwich ont adopté l’ordre inverse de priorités et je me suis rallié à eux dans Conceptions of Truth. Je continue à penser que le prédicat « porte la culotte » et vais tenter de désamorcer les arguments contre cette conception, mais je vais aussi rejeter (...) un de mes arguments antérieurs en faveur de celle-ci.Logical Philosophers like Prior and Mulligan regard the truth connective ‘It is true that ’ as more basic than the truth predicate ‘ is true’. Philosophers like Bolzano and Horwich have adopted the opposite priority setting, and in Conceptions of Truth I joined them. I still think that the predicate ‘wears the trousers’, and I shall try to defuse the arguments against this view, but I shall also reject one of my earlier arguments for it. (shrink)

At some step in proving the Liar Paradox in natural language, a sentence is derived that seems overdetermined with respect to its semantic value. This is complemented by Tarski’s Theorem that a formal language cannot consistently contain a naive truth predicate given the laws of logic used in proving the Liar paradox. I argue that proofs of the Eubulidean Liar either use a principle of truth with non-canonical names in a fallacious way or make a fallacious use of substitution of (...) identicals. Tarski never committed the first fallacy and may have himself considered it fallacious. Nevertheless, I clarify that it is fallacious. I then argue substitution of identicals needs to be restricted within the scope of the truth predicate. A logic for truth implementing this restriction is a monotonic extension of a classical first order logic, or indeed a formalizable fragment of natural language. Proofs of Tarski’s Indefinability of Truth theorem are invalid in this logic. This approach generalizes to invalidate proofs of Liar-like paradoxes, particularly the predicate form of the Knower paradox. Consequently, such a logic can be further extended in a way that avoids Montague’s theorem for such a system. Yet, the semantic status of a Liar sentence is not fully resolved. It is no longer overdetermined; it is now underdetermined. (shrink)