This chapter contains sections titled: Truth The Liar Tarskian Truth Definition Discussion Conclusion.

Alfred Tarski's work on truth has become a touchstone for a great deal of philosophical work on truth. A good grasp of it is critical for understanding the contemporary literature on truth and semantics. In this paper, I present a fresh interpretation of Tarski's view, one which aims to draw it out more fully in areas of philosophical interest.

Criticism of Soames' understanding of Tarskian theories of truth.

Tarski's theory of truth brings out the question of whether he intended his theory to be a correspondence theory of truth and whether, whatever his intentions, his theory is in fact a correspondence theory. The aim of this paper is to answer both questions. The answer to the first question depends on Tarski's relevant assertions on semantics and his conception of truth. In order to answer the second question Popper's and Davidson's interpretations of Tarski's truth theory (...) are examined; to this end both Tarski's definition of truth in terms of satisfaction and the T-sentences are taken into account. (shrink)

Tarski's theory of truth brings out the question of whether he intended his theory to be a correspondence theory of truth and whether, whatever his intentions, his theory is, in fact, a correspondence theory. The aim of this paper is to answer both questions. The answer to the first question depends on Tarski's relevant assertions on semantics and his conception of truth. In order to answer the second question Popper's and Davidson's interpretations of Tarski's truth theory (...) are examined; to this end both Tarski's definition of truth in terms of satisfaction and the T-sentences are taken into account. (shrink)

Since the publication of Hartry Field’s influential paper “Tarski’s Theory of Truth” there has been an ongoing discussion about the philosophical import of Tarski’s definition. Most of the arguments have aimed to play down that import, starting with that of Field himself. He interpreted Tarski as trying to provide a physicalistic reduction of semantic concepts like truth, and concluded that Tarski had partially failed. Robert Stalnaker and Scott Soames claimed then that Field should have obtained a stronger (...) conclusion, namely that Tarski’s failure in his allegedly intended physicalistic reduction was total. From another front, Hilary Putnam argued for an even more sweeping thesis: “[a]s a philosophical account of truth, Tarski’s theory fails as badly as it is possible for an account to fail.” Scott Soames followed suit also on this count, endorsing Putnam’s argument in section iii of the aforementioned paper; and John Etchemendy used a very similar argument to contend that “a Tarskian definition of truth [...] cannot possibly illuminate the semantic properties of the object language.” The paper argues that these contentions are based on several misunderstandings about the nature of a definition like Tarski’s. Regarding the Putnam-Soames-Etchemendy argument, we must apply a distinction Frege found natural to draw—and is natural to draw anyway—between what he called “constructive” definitions, definitions properly so called, which are mere stipulations, and what he described as “analytic” definitions, definitions which aim to make explicit the meaning of a term already in use. Regarding the Field-Soames-Stalnaker criticism, the paper contends that the true aims of a Tarskian truth definition are perfectly well fulfilled without Field’s amendments. (shrink)

In this paper, I suggest an approach to the alleged problem with the Tarskian formal definition of truth: its enumerative character seems to make it unable to capture our pretheoretic general understanding of truth. For this purpose, after spelling out two requirements for extending an enumerative definition to new cases, I examine to what extent Tarski's Convention T provides what are needed for extending the Tarski's enumerative definition. I conclude that, though not explicitly providing (...) what are needed, Convention T does implicitly suggest something quite promising and provide necessary conceptual resources for its further modifications. Then I suggest a Tarskian explicitly general definition of what it is to be a truth-definition on the basis of some theoretical and conceptual resources within Tarski's semantic theory, and I explain how it would make the Tarskian seemingly enumerative formal definition have a general character in accord with our pretheoretic understanding of truth. Finally, I examine the current proposal in comparison with Davidson's approach and in the light of Hintikka's new perspective. (shrink)

This paper examines the question of the extensional correctness of Tarskian definitions of logical truth and logical consequence. I identify a few different informal properties which are necessary for a sentence to be an informal logical truth and look at whether they are necessary properties of Tarskian logical truths. I examine arguments by John Etchemendy and Vann McGee to the effect that some of those properties are not necessary properties of some Tarskian logical truths, and (...) find them unconvincing. I stress the point that since the hypothesis that Tarski's definitions are extensionally correct is deeply entrenched, the burden of proof is still on the shoulders of Tarski's critics, who have not lifted the burden. (shrink)

In “Truth – A Traditional Debate Reviewed”, Crispin Wright proposed an inductive definition of “coherence truth” for arithmetic relative to an arithmetic base theory B. Wright’s definition is in fact a notational variant of the usual Tarskian inductive definition, except for the basis clause for atomic sentences. This paper provides a model-theoretic characterization of the resulting sets of sentences "cohering" with a given base theory B. These sets are denoted WB. Roughly, if B satisfies (...) a certain minimal condition, then WB is the Th, where M is the canonical model of the set At of atomic sentences provable in B. The paper also shows that the disquotational T-scheme is provable from Wright’s inductive definition just in case the base theory B is sound and complete for arithmetic atomic sentences. (shrink)

Several writers have assumed that when in “Outline of a Theory of Truth” I wrote that “the orthodox approach” – that is, Tarski’s account of the truth definition – admits descending chains, I was relying on a simple compactness theorem argument, and that non-standard models must result. However, I was actually relying on a paper on ‘pseudo-well-orderings’ by Harrison. The descending hierarchy of languages I define is a standard model. Yablo’s Paradox later emerged as a key to (...) interpreting the result. (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)

Philosopher’s judgements on the philosophical value of Tarski’s contributions to the theory of truth have varied. For example Karl Popper, Rudolf Carnap, and Donald Davidson have, in their different ways, celebrated Tarski’s achievements and have been enthusiastic about their philosophical relevance. Hilary Putnam, on the other hand, pronounces that “[a]s a philosophical account of truth, Tarski’s theory fails as badly as it is possible for an account to fail.” Putnam has several alleged reasons for his dissatisfaction,1 but one (...) of them, the one I call the modal objection (cf. Raatikainen 2003), has been particularly influential. In fact, very similar objections have been presented over and over again in the literature. Already in 1954, Arthur Pap had criticized Tarski’s account with a similar argument (Pap 1954). Moreover, both Scott Soames (1984) and John Etchemendy (1988) use, with an explicit reference to Putnam, similar modal arguments in relation to Tarski. Richard Heck (1997), too, shows some sympathy for such considerations. Simon Blackburn (1984, Ch. 8) has put forward a related argument against Tarski. Recently, Marian David has criticized Tarski’s truth definition with an analogous argument as well (David 2004, p. 389-390).2 This line of argument is thus apparently one of the most influential critiques of Tarski. It is certainly worthy of serious attention. Nevertheless, I shall argue that, given closer scrutiny, it does not present such an acute problem for the Tarskian approach to truth as many philosophers think. But I also believe that it is important to understand clearly why this is so. Moreover, I think that a careful consideration of the issue illuminates certain important but somewhat neglected aspects of the Tarskian approach. (shrink)

Alfred Tarski’s work on truth has played such a central role in the discourse on truth that most coming to it for the first time have probably already heard a great deal about what is said there. Unfortunately, since the work is largely technical and Tarski was only tan- gentially philosophical, a certain incautious assimilation dominates many philosophical discussions of Tarski’s ideas, and so, examining Tarski on the concept of truth is in many ways an act of (...) unlearning. -/- In this paper I focus on those key ideas in Tarski’s work that have made a lasting impact on the philosophical discourse. These are the notions of T-sentence, Convention T, Tarskian truth definition, and Tarski’s general limiting theses on the expressibility and definability of truth. Though these ideas are in name familiar, we will seek in this essay to uncover and remove certain widespread misunderstandings of each. Tarski’s name also features prominently in discussions of the liar paradox, so we will take time out to explain Tarski’s connection to this ancient puzzle. (shrink)

Although philosophers have been concerned with truth since at least the age of Plato, the last thirty years have witnessed a veritable explosion of the philosophical debate on this topic. The touchpaper which lit the fuse for this was undoubtedly the Deflationist Renaissance (half a century after the seminal work of F.P. Ramsey) due, in the Seventies, both to the Quinean disquotational interpretation of the Tarskian truth definitions and to the development of the prosentential theory of (...) class='Hi'>truth by D. Grover, J. Kamp and N. Belnap, and, from the second half of the Eighties onwards, to the forceful defences of deflationary conceptions provided by H. Field and P. Horwich. The philosophical struggle on deflationism has been thought-provoking: by arguing on the merits and shortcomings of such a conception, philosophers have come to broaden and deepen the discussion on truth beyond the boundaries of deflationism. The varieties of problems tackled by the essays in this book highlight how the land of Truth is still far from having been totally explored, and how, in this intellectual endeavour, real progresses can be achieved. (shrink)

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

There are two different ways to introduce the notion of truthin constructive mathematics. The first one is to use a Tarskian definition of truth in aconstructive (meta)language. According to some authors, (Kreisel, van Dalen, Troelstra ... ),this definition is entirely similar to the Tarskian definition of classical truth (thesis A).The second one, due essentially to Heyting and Kolmogorov, and known as theBrouwer–Heyting–Kolmogorov interpretation, is to explain informally what it means fora mathematical proposition to (...) be constructively proved. According to other authors (Martin-Löfand Shapiro), this interpretation and the Tarskian definition of truth amount to thesame (thesis B). My aim in this paper is to show that thesis A is only reasonable, that thesis Bis false and to answer the following question: what is defined by the Tarskian definition ofconstructive truth? (shrink)

There is a certain view abroad in the land concerning the philosophical problems raised by Tarskian semantics. This view has it that a Tarskian theory of truth in a language accomplishes nothing of interest beyond the definition of truth in terms of satisfaction, and, further, that what is missing — the only thing that would yield a solution to the philosophical problem of truth when added to Tarskian semantics — is a reduction of (...) satisfaction to a non-semantic relation. It seems to me that this view either misidentifies the philosophical problem altogether, or encourages a seriously misleading picture of the nature of the problem.The view I have in mind is nowhere more persuasively at work than in a recent paper by Hartry Field.1 In this paper Field argues that a Tarskian theory of truth for a natural language is impossible if we insist on Tarski's case-by-case elimination of ‘satisfies'. More fundamentally, however, he argues that a Tarskian theory could provide nothing of philosophical interest beyond the admittedly interesting reduction of truth to satisfaction, and his ground for this claim is, roughly, that a Tarskian theory does not reduce its primitive semantic relation — satisfaction — to a non-semantic relation. (shrink)

In this paper, I argue that the cleavage between the theory of reference and the theory of meaning, which under the influence of Quine has dominated a large part of the philosophy of language of the last fifty years, is based on a misrepresentation of Tarski's achievement and on an overestimation of the scope and value of disquotation. In particular, I show that, if we accept Davidson's critique of disquotation, the same kind of reasons that Quine offered in opposition to (...) the Carnapian theory of meaning also apply, mutatis mutandis, to the Tarskian theory of reference. (shrink)

What is the fundamental insight behind truth-functionality ? When is a logic interpretable by way of a truth-functional semantics? To address such questions in a satisfactory way, a formal definition of truth-functionality from the point of view of abstract logics is clearly called for. As a matter of fact, such a definition has been available at least since the 70s, though to this day it still remains not very widely well-known. A clear distinction can be (...) drawn between logics characterizable through: (1) genuinely finite-valued truth-tabular semantics; (2) no finite-valued but only an infinite-valued truthtabular semantics; (3) no truth-tabular semantics at all. Any of those logics, however, can in principle be characterized through non-truth-functional valuation semantics, at least as soon as their associated consequence relations respect the usual tarskian postulates. So, paradoxical as that might seem at first, it turns out that truth-functional logics may be adequately characterized by non-truth-functional semantics . Now, what feature of a given logic would guarantee it to dwell in class (1) or in class (2), irrespective of its circumstantial semantic characterization? (shrink)

We prove that: • if there is a model of I∆₀ + ¬ exp with cofinal Σ₁-definable elements and a Σ₁ truth definition for Σ₁ sentences, then I∆₀ + ¬ exp +¬BΣ₁ is consistent, • there is a model of I∆₀ Ω₁ + ¬ exp with cofinal Σ₁-definable elements, both a Σ₂ and a ∏₂ truth definition for Σ₁ sentences, and for each n > 2, a Σ n truth definition for Σ n sentences. (...) The latter result is obtained by constructing a model with a recursive truth-preserving translation of Σ₁ sentences into boolean combinations of $\exists \sum {\begin{array}{*{20}{c}} h \\ 0 \\ \end{array} } $ sentences. We also present an old but previously unpublished proof of the consistency of I∆₀ + ¬ exp + ¬BΣ₁ under the assumption that the size parameter in Lessan's ∆₀ universal formula is optimal. We then discuss a possible reason why proving the consistency of I∆₀ + ¬ exp + ¬BΣ₁ unconditionally has turned out to be so difficult. (shrink)

§1. The mission of axiomatic set theory. What is set theory needed for in the foundations of mathematics? Why cannot we transact whatever foundational business we have to transact in terms of our ordinary logic without resorting to set theory? There are many possible answers, but most of them are likely to be variations of the same theme. The core area of ordinary logic is by a fairly common consent the received first-order logic. Why cannot it take care of itself? (...) What is it that it cannot do? A large part of every answer is probably that first-order logic cannot handle its own model theory and other metatheory. For instance, a first-order language does not allow the codification of the most important semantical concept, viz. the notion of truth, for that language in that language itself, as shown already in Tarski. In view of such negative results it is generally thought that one of the most important missions of set theory is to provide the wherewithal for a model theory of logic. For instance Gregory H. Moore asserts in his encyclopedia article “Logic and set theory” thatSet theory influenced logic, both through its semantics, by expanding the possible models of various theories and by the formal definition of a model; and through its syntax, by allowing for logical languages in which formulas can be infinite in length or in which the number of symbols is uncountable. (shrink)

What requirements must deflationary formal theories of truth satisfy? This chapter argues against the widely accepted view that compositional and Tarskian theories of truth are substantial or otherwise unacceptable to deflationists. First, two purposes that a formal truth theory can serve are distinguished: one descriptive, the other logical (i.e., to characterise the correctness of inferences involving ‘true’). The chapter argues that the most compelling arguments for the incompatibility of compositional and Tarskian theories concern descriptive theories (...) only. -/- Second, two requirements that any deflationist truth theory intended to serve a logical purpose must satisfy are put forward. These requirements, it is argued, suggest that (i) many well-known compositional and Tarskian theories are acceptable from a deflationist standpoint (including CT); (ii) certain other popular theories of truth (including KF and FS) are not similarly acceptable; (iii) there are no conclusive reasons to impose a conservativeness requirement on deflationary theories of truth. (shrink)

This chapter contains sections titled: References.

Timothy Williamson famously offered an argument from these Tarskian principles in favor of bivalence. I show, dwelling on (Andjelkovic & Williamson, 2000), that the argument depends on a contentious formulation of the Tarskian principles about truth (and falsity), which the supervaluationist can reject without jeopardizing the Tarskian insight. In the mentioned paper, Adjelkovic and Williamson argue that, even if the appropriate formulation seems to make room for failure of bivalence in borderline cases, this appearance is illusory, (...) once one grants an independent further principle involving biconditionals. I finally argue that the formulation of this is, however, contentious in a similar manner. (shrink)

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established (...) to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. -/- Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. -/- However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. -/- The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion. (shrink)

The paper discusses the notion of finite model truth definitions (or FM-truth definitions), introduced by M. Mostowski as a finite model analogue of Tarski's classical notion of truth definition. We compare FM-truth definitions with Vardi's concept of the combined complexity of logics, noting an important difference: the difficulty of defining FM-truth for a logic ᵍ does not depend on the syntax of L, as long as it is decidable. It follows that for a natural (...) ᵍ there exist FM-truth definitions whose evaluation is much easier than the combined complexiy of ᵍ would suggest. We apply the general theory to give a complexity-theoretical characterization of the logics for which the $\Sigma_{m}^{d}$ classes (prenex classes of higher order logics) define FM-truth. For any $d \geq 2.m \geq 1$ we construct a family $\{[\Sigma_{m}^{d}]^{\leg\kappa}\}\kappa\in\omega$ of syntactically defined fragments of $\Sigma_{m}^{d}$ which satisfy this characterization. We also use the $[\Sigma_{m}^{d}]\leg\kappa$ classes to give a refinement of known results on the complexity classes captured by $\Sigma_{m}^{d}$ . We close with a few simple corollaries, one of which gives a sufficient condition for the existence, given a vocabulary $\sigma$ , of a fixed number $\kappa$ such that model checking for all first order sentences over $\sigma$ can be done in deterministic time $n^{\kappa}$. (shrink)

This paper argues that if a person's beliefs are idealized as a set of sentences (theoretical, observational, and mixed) then the device of Ramsey sentences provides a treatment, of the mind-brain problem, that has at least four noteworthy characteristics. First, sentences asserting correlations between one's own brain state and one's own "private" experiences are, on such treatment, reconstrued as neither causal, coreferential, nor as meaning postulates, but as clauses in an overall hypothesis (Ramsey sentence) whose only nonlogical constants have "private" (...) meanings. Second, sentences asserting psycho-physical correlations in general, or in other individuals, remain theoretical and susceptible to scientific reduction, though not prejudged to be so. Third, communication between persons having mutually exclusive, "private," observational vocabularies can be made intelligible. Fourth, it becomes possible in principle (though not necessary) that the world could ultimately be given a total description in a scientific language, $L_{\varnothing}$ , without mental primitives. However, such a language would be susceptible to interpretation by a given individual using a metalanguage whose primitives (not among those of $L_{\varnothing}$ ) were privately observational to that individual. His procedure in accomplishing such an interpretation would be to construct a Tarskian truth definition in a metalanguage $ML_{\varnothing}$ and then to incorporate it, by Ramsifying its descriptive terms, in his own overall Ramsey sentence. The physical language, $L_{\varnothing}$ , while not containing a person's primitives, would, of course, be able to define their physical correlates, thus providing a certain sort of mutual mirroring, and a certain sort of relativity. (shrink)

Tarski's model-theoretic truth definition of the 1950s differs from his 1930s truth definition by allowing the language to have a set of parameters that are interpreted by means of structures. The paper traces how the model-theoretic theorems that Tarski and others were proving in the period between these two truth definitions became increasingly difficult to fit into the framework of the earlier truth definition, making the later one more or less inevitable. The paper (...) also maintains that neither recursiveness nor satisfaction are essential features of the truth definition . The recursive form was a ‘practical’ step towards the explicit definition that was Tarski's target. There are model-theoretic languages for which satisfaction is provably too crude a notion for expressing those properties of formulas that are needed for determining the truth of sentences. (shrink)

In this paper we show that first-order languages extended with partially ordered connectives and partially ordered quantifiers define, under a certain interpretation, their own truth-predicate. The interpretation in question is in terms of games of imperfect information. This result is compared with those of Kripke and Feferman.

In the present paper, we return to one of the main theses we already defended concerning the role of the tarskian truth notion within the semantic approach (CARNIER, 2022). As it was argued, this truth notion proves to be insufficient to be applied to scientific theories as they are conceived by this approach, i.e., as extralinguistic entities, because it is a property of sentences and because the tarskian truth of a sentence doesn't necessarily mean the (...) world is as it describes, which results in the fact that other truth conceptions more appropriate need to be articulated within the several members of the semanticist family, in order to characterize the relationship between theory and phenomenon. Our argument in this regard was based in a case study applied to constructive empiricism and quasi-realism, but in this paper we extend our analysis to structuralism, assuming and endorsing the position according to which this proposal may be considered a member of the semantic approach. (shrink)

Tarski's manner of defining truth is generally considered highly significant. About why, there is less consensus. I argue first, that in his truth-definitions Tarski was trying to solve a set of philosophical problems; second, that he solved them successfully; third, that all of these that are simply problems about defining truth are as well or better solved by a simpler account of truth. But one of his crucial problems remains: to give an account of validity, one (...) requires an account not just of truth but of truth under varying interpretations. Tarski's account has the merit of generalizing to this, to model theory and to abstract algebra. (shrink)

We study the structure of the partial order induced by the definability relation on definitions of truth for the language of arithmetic. Formally, a definition of truth is any sentence \(\alpha \) which extends a weak arithmetical theory (which we take to be \({{\,\mathrm{I\Delta _{0}+\exp }\,}}\) ) such that for some formula \(\Theta \) and any arithmetical sentence \(\varphi \), \(\Theta (\ulcorner \varphi \urcorner )\equiv \varphi \) is provable in \(\alpha \). We say that a sentence \(\beta (...) \) is definable in a sentence \(\alpha \), if there exists an unrelativized translation from the language of \(\beta \) to the language of \(\alpha \) which is identity on the arithmetical symbols and such that the translation of \(\beta \) is provable in \(\alpha \). Our main result is that the structure consisting of truth definitions which are conservative over the basic arithmetical theory forms a countable universal distributive lattice. Additionally, we generalize the result of Pakhomov and Visser showing that the set of (Gödel codes of) definitions of truth is not \(\Sigma _2\) -definable in the standard model of arithmetic. We conclude by remarking that no \(\Sigma _2\) -sentence, satisfying certain further natural conditions, can be a definition of truth for the language of arithmetic. (shrink)

In 'A Nice Derangement of Epitaphs' Donald Davidson attacks a picture of language which, he says, is prevalent among philosophers and linguists. Davidson's criticism, even if correct, is not radical enough. The common irregularities of everyday language, such as malapropisms, nicknames, and slips of the tongue, not only imply that linguistic meanings are not governed by conventions that are learned in advance of occasions of interpretation, but undermine the very idea that linguistic meaning can be accounted for in terms of (...) systematic meaning-theories. Davidson continues to hold that Tarskian truth-definitions should play a central role in philosophical accounts of language, but if the goal is to describe rather than to improve or otherwise change language, we must give up the aspiration towards theoretical systematicity altogether. In this connection, Davidson's approach is compared with those of Quine and Wittgenstein. It is argued that Davidson's unwillingness to give up the notion that meaning is systematic is best explained in terms of his vacillating between treating meaning-theories as mere representations of the linguistic abilities of a speaker and seeing them as playing a more substantial role in communication. (shrink)

The work of mathematician and logician Alfred Tarski (1901--1983) marks the transition from substantial to deflationary views about truth.