Peter Milne; VII*—Tarski, Truth and Model Theory, Proceedings of the Aristotelian Society, Volume 99, Issue 1, 1 June 1999, Pages 141–168, https://doi.org/10.11.

John Etchemendy has argued that it is but "a fortuitous accident" that Tarski's work on truth has any signifance at all for semantics. I argue, in response, that Etchemendy and others, such as Scott Soames and Hilary Putnam, have been misled by Tarski's emphasis on definitions of truth rather than theories of truth and that, once we appreciate how Tarski understood the relation between these, we can answer Etchemendy's implicit and explicit criticisms of neo-Davidsonian semantics.

The first part of the paper traces the history of the relationship between logic and linguistics with particular emphasis on the contributions of Tarski and Ajdukiewicz. In the second part we give a brief review of current work on formal semantics for natural language systems and argue for the need for a richer geometric structure on the semantic model space.

Alfred Tarski’s theory of truth, to which we will also refer as the classical theory,1 has a conspicuous place in mathematics as well as in general philosophy. The place in philosophy appears the more prominent of the two, although it is still somewhat unsettled, and perhaps even controversial.

Published with the aid of a grant from the National Endowment for the Humanities. Contains the only complete English-language text of The Concept of Truth in Formalized Languages. Tarski made extensive corrections and revisions of the original translations for this edition, along with new historical remarks. It includes a new preface and a new analytical index for use by philosophers and linguists as well as by historians of mathematics and philosophy.

As Wilfrid Hodges has observed, there is no mention of the notion truth-in-a-model in Tarski's article 'The Concept of Truth in Formalized Languages'; nor does truth make many appearances in his papers on model theory from the early 1950s. In later papers from the same decade, however, this reticence is cast aside. Why should Tarski, who defined truth for formalized languages and pretty much founded model theory, have been so reluctant to speak of truth in (...) a model? What might explain the change in his practice? The answers, I believe, lie in Tarski's views on truth simpliciter. (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)

Published with the aid of a grant from the National Endowment for the Humanities. Contains the only complete English-language text of The Concept of Truth in Formalized Languages. Tarski made extensive corrections and revisions of the original translations for this edition, along with new historical remarks. It includes a new preface and a new analytical index for use by philosophers and linguists as well as by historians of mathematics and philosophy.

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)

Many commentators on Alfred Tarski have, following Hartry Field, claimed that Tarski's truth-definition was motivated by physicalism—the doctrine that all facts, including semantic facts, must be reducible to physical facts. I claim, instead, that Tarski did not aim to reduce semantic facts to physical ones. Thus, Field's criticism that Tarski's truth-definition fails to fulfill physicalist ambitions does not reveal Tarski to be inconsistent, since Tarski's goal is not to vindicate physicalism. I argue that Tarski's only published remarks that (...) speak approvingly of physicalism were written in unusual circumstances: Tarski was likely attempting to appease an audience of physicalists that he viewed as hostile to his ideas. In later sections I develop positive accounts of: (1) Tarski's reduction of semantic concepts; (2) Tarski's motivation to develop formal semantics in the particular way he does; and (3) the role physicalism plays in Tarski's thought. (shrink)

This chapter contains sections titled: Tarski's Theory of Truth Tarski's Solution to the Liar Paradox Tarski's Method of Defining Truth for Formalized Languages Tarskian Semantics Three Criticisms of Tarski's Theory Kripke's Solution to the Liar Paradox A Reinterpretation of Tarski's Theory Truth Beyond Logic.

This chapter contrasts Alfred Tarski's compositional conception (whereby the truth-values of sentences are explained in terms of the referential characteristics of their component words) unfavorably with minimalism (which relies merely on the schema, ‘(p) is true ↔ p’). First, it argues against Tarski that his approach is: (i) misdirected, insofar as it doesn't elucidate our actual concept of truth, which applies to propositions rather than sentences; (ii) ill-motivated, insofar as it reflects an insistence on explicit definitions; (iii) not (...) generally workable, insofar as those definitions cannot devised for all the multifarious constructions that occur in natural languages; and (iv) pointless, insofar as it addresses no question worth answering. Second, it is shown that minimalism can be the basis for a superior treatment of the liar paradoxes. And, finally, a response is developed to the claim (Tarski, Gupta, Soames, Halbach) that Tarski-style compositional definitions are needed in order to accommodate generalizations about truth (e.g., that all instances of ‘p→p’ are true). (shrink)

In the early 20th century, scepticism was common among philosophers about the very meaningfulness of the notion of truth – and of the related notions of denotation, definition etc. (i.e., what Tarski called semantical concepts). Awareness was growing of the various logical paradoxes and anomalies arising from these concepts. In addition, more philosophical reasons were being given for this aversion.1 The atmosphere changed dramatically with Alfred Tarski’s path-breaking contribution. What Tarski did was to show that, assuming that the syntax (...) of the object language is specified exactly enough, and that the metatheory has a certain amount of set theoretic power,2 one can explicitly define truth in the object language. And what can be explicitly defined can be eliminated. It follows that the defined concept cannot give rise to any inconsistencies (that is, paradoxes). This gave new respectability to the concept of truth and related notions. Nevertheless, philosophers’ judgements on the nature and philosophical relevance of Tarski’s work have varied. It is my aim here to review and evaluate some threads in this debate. (shrink)

Alfred Tarski seems to endorse a partial conception of truth, the T-schema, which he believes might be clarified by the application of empirical methods, specifically citing the experimental results of Arne Næss (1938a). The aim of this paper is to argue that Næss’ empirical work confirmed Tarski’s semantic conception of truth, among others. In the first part, I lay out the case for believing that Tarski’s T-schema, while not the formal and generalizable Convention-T, provides a partial account of (...) truth that may be buttressed by an examination of the ordinary person’s views of truth. Then, I address a concern raised by Tarski’s contemporaries who saw Næss’ results as refuting Tarski’s semantic conception. Following that, I summarize Næss’ results. Finally, I will contend with a few objections that suggest a strict interpretation of Næss’ results might recommend an overturning of Tarski’s theory. (shrink)

Tarski's definition of truth has rehabilitated the application of the word "true" to sentences of formalized languages. But a correspondence theory according to which a sentence is true if, And only if, It is related in the peculiar way of correspondence to the facts, Is incompatible with tarski's definition. Actually no theory of truth, Which claims to make proper assertions about sentences when calling them true, Is compatible with tarski's definition. Hence they all have to find their own (...) solution to the problem of the semantical antinomies and have to explain what it means to say that sentences are true. (shrink)

Tarski’s pioneering work on truth has been thought by some to motivate a robust, correspondence-style theory of truth, and by others to motivate a deflationary attitude toward truth. I argue that Tarski’s work suggests neither; if it motivates any contemporary theory of truth, it motivates conceptual primitivism, the view that truth is a fundamental, indefinable concept. After outlining conceptual primitivism and Tarski’s theory of truth, I show how the two approaches to truth share (...) much in common. While Tarski does not explicitly accept primitivism, the view is open to him, and fits better with his formal work on truth than do correspondence or deflationary theories. Primitivists, in turn, may rely on Tarski’s insights in motivating their own perspective on truth. I conclude by showing how viewing Tarski through the primitivist lens provides a fresh response to some familiar charges from Putnam and Etchemendy. (shrink)

Tarski avoids the liar paradox by relativizing truth and falsehood to particular languages and forbidding the predication to sentences in a language of truth or falsehood by any sentences belonging to the same language. The Tarski truth-schemata stratify an object-language and indefinitely ascending hierarchy of meta-languages in which the truth or falsehood of sentences in a language can only be asserted or denied in a higher-order meta-language. However, Tarski’s statement of the truth-schemata themselves involve general (...) truth functions, and in particular the biconditional, defined in terms of truth conditions involving truth values standardly displayed in a truth table. Consistently with his semantic program, all such truth values should also be relativized to particular languages for Tarski. The objection thus points toward the more interesting problem of Tarski’s concept of the exact status of truth predications in a general logic of sentential connectives. Tarski’s three-part solution to the circularity objection which he anticipates is discussed and refuted in detail. (shrink)

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.

Of his numerous investigations ... Tarski was most proud of two: his work on truth and his design of an algorithm in 1930 to decide the truth or falsity of any sentence of the elementary theory of the high school Euclidean geometry. [...] His mathematical treatment of the semantics of languages and the concept of truth has had revolutionary consequences for mathematics, linguistics, and philosophy, and Tarski is widely thought of as the man who "defined truth". (...) The seeming simplicity of his famous example that the sentence "Snow is white" is true just in case snow is white belies the depth and complexity of the consequences which can be drawn from the possibility of giving a general treatment of the concept of truth in formal mathematical languages in a rigorous mathematical way. (J.W. Addison). (shrink)

A hallmark of correspondence theories of truth is the principle that sentences are made true by some truth-makers. A well-known objection to treating Tarski’s definition of truth as a correspondence theory has been put forward by Donald Davidson. He argued that Tarski’s approach does not relate sentences to any entities (like facts) to which true sentences might correspond. From the historical viewpoint, it is interesting to observe that Tarski’s philosophical teacher Tadeusz Kotarbinski advocated an ontological doctrine of (...) reism which accepted only concrete individuals and rejected all such abstract entities as facts, states of affairs, properties, and sets. Kotarbinski’s physicalism influenced Tarski who also avoided concepts like “fact” and “property” in his theory of truth, but—unlike Kotarbinski—he used freely set-theoretical terminology. In his mature work in model theory in the 1950s, Tarski used systematically the notion of a relational system (i.e., a domain of objects with designated elements, subsets, and relations). Wilfrid Hodges has argued that the notions of “structure” and “truth in a structure” appeared in Tarski’s work only in 1950. In my view, one can find the main ingredients of the model-theoretic account of truth already in the 1930s. These considerations suggest, against Davidson, that Tarski’s definition presupposes that material truth is always related to some kind of truth-maker. Further, facts as truth-makers can be reconstructed by employing the resources of model theory. (shrink)

I start from Hans Sluga's paper “Truth before Tarski”, in which he argues that the establishing of Tarski's approach to truth brought loss as well as gain to analytic philosophy: what was lost was our understanding of the problem of truth. To recover what was lost, he says, we must examine the variety of pre‐Tarskian views. My paper picks up that task and focuses on Wittgenstein's Tractatus. I interweave ideas borrowed from Thomas Ricketts, P. T. Geach, Warren (...) Goldfarb, Peter Hylton, and Juliet Floyd, and thereby try to explain the relation between Wittgenstein's conception of sense and his view of truth. (shrink)

SummaryIn developing his claim that meaning cannot be understood independently of truth, Donald Davidson argues that a theory of meaning will take the form of a Tarskian theory of truth. In this essay I seek to describe more fully the structure of a Davidsonian theory of meaning and the extent to which Davidson modifies Tarski's account. 1 consider and reject John Foster's claim that Davidson takes, or should take, truth as a formal primitive, and argue that it (...) is Davidson's principle of charity which plays the essential role in giving theories of truth empirical application. (shrink)

This chapter provides a detailed explanation of Tarski's definition of truth for formalized languages. It begins by indicating how he conceived the problem, how his criterion of adequacy guarantees that any definition satisfying it introduces a predicate that applies to all and only object‐language truths, and how he approached the technical problem of formulating a definition that would allow him to derive what he regarded as a “partial definition” of truth for each sentence of the object language. Next, (...) the formal techniques employed in his inductive definitions are explained, along with the method of turning those definitions into explicit definitions, and the way in which his definitions can be shown to be materially adequate. The explication concludes with a discussion of the relationship between truth and proof in the language of arithmetic, and the outlines of Tarski's theorem of the arithmetic indefinability of arithmetical truth. (shrink)

Until Tarski’s semantic truth definition, the concept of truth was used informally in metalogic (metamathematics) or even proposed to be eliminated in favour of syntactic concepts, as in Rudolf Carnap’s early programme of philosophy via logical syntax. Tarski demonstrated that the concept of truth can be defined using precise mathematical devices. If L is a language for which the truth definition is given, it must be done in the metalanguage ML. According to this construction, semantics for (...) L must be performed in ML. The most important example concerns the arithmetic of natural numbers. According to Tarski’s theorem of undefinability, the set of truths of this theory cannot be defined in it – such a definition can be formulated in the metatheory. This fact illuminates the relation between syntax and semantics. If Th is a rich theory and presented as a syntactic theory (a calculus), its semantics is not reducible to its syntax. According to Tarski’s view, related to his work in the simple theory of types, semantics for L can be always constructed in the morphology of ML, provided that L is of the finite order. Two problems arise: what does the word “morphology” mean and how to formulate these ideas, when the framework is based on the distinction between first‑order logic and higher‑order logic. As far as the issue concerns morphology, it is possible to consider it as an extended syntax, i.e. vocabulary which does not refer to semantic concepts or defines such notions by not‑semantic, e.g. set‑theoretical, categories. If the hierarchy of logical types is replaced by the distinction of logics of various orders, in particular between first‑order and higher‑order (it is sufficient to use second‑order), it is possible to show that semantics of first‑order rich theories cannot be defined inside them. (shrink)

The paper is divided into the following sections: In the first section a short historical survey is given which presents precursors of both Tarski’s truth-condition and Tarski’s truth definition . Secondly some purported objections against Tarski’s truth condition are stated and two important presuppositions of Tarski’s truth condition are analyzed. Thirdly TTC is enlarged in different ways as to incorporate the preconditions explicitly. Finally in the fourth section it will be shown how the revised T-conditions solve (...) different versions of the Liar. All of these topics are discussed in much more detail in my forthcoming book, Chapter 7. (shrink)

Can Tarski's definition of truth be taken to be an analysis of truth – i.e., a method of defining formal truth predicates that are capable of playing the role of truth in all theoretical contexts in which that notion is needed? It is argued that although Tarski's truth predicates can play many of the roles demanded of truth, they cannot play the role of truth in theories of meaning and interpretation. Crucial to the (...) argument is the observation that there is a conceptual connection between our ordinary notions of truth and meaning, in virtue of which statements of the truth conditions of sentences provide some information about their meanings. Since there is no corresponding connection between Tarski's notion of truth and the notion of meaning, statements of the Tarski‐truth conditions of sentences provide no information about meaning. The chapter closes with a detailed defense of Tarski's model‐theoretic analysis of logical truth and logical consequence against John Etchemendy's objections to it. (shrink)

This book provides a detailed commentary on the classic monograph by Alfred Tarski, and offers a reinterpretation and retranslation of the work using the original Polish text and the English and German translations. In the original work, Tarski presents a method for constructing definitions of truth for classical, quantificational formal languages. Furthermore, using the defined notion of truth, he demonstrates that it is possible to provide intuitively adequate definitions of the semantic notions of definability and denotation and that (...) the notion in a structure can be defined in a way that is analogous to that used to define truth. Tarski’s piece is considered to be one of the major contributions to logic, semantics, and epistemology in the 20th century. However, the author points out that some mistakes were introduced into the text when it was translated into German in 1935. As the 1956 English version of the work was translated from the German text, those discrepancies were carried over in addition to new mistakes. The author has painstakingly compared the three texts, sentence-by-sentence, highlighting the inaccurate translations, offering explanations as to how they came about, and commenting on how they have influenced the content and suggesting a correct interpretation of certain passages. Furthermore, the author thoroughly examines Tarski’s article, offering interpretations and comments on the work. (shrink)

This article is a translation of the paper in Polish (Alfred Tarski - człowiek, który zdefiniował prawdę) published in Ruch Filozoficzny 4 (4) (2007). It is a personal Alfred Tarski memories based on my stay in Berkeley and visit the Alfred Tarski house for the invitation of Janusz Tarski.

According to Plato, thinking is the communicating of the mind with itself.1 This is also my view, not because this was asserted by Plato, but since this is part of my own experience.

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 discuss misinformation about “the liar antinomy” with special reference to Tarski’s 1933 truth-definition paper [1]. Lies are speech-acts, not merely sentences or propositions. Roughly, lies are statements of propositions not believed by their speakers. Speakers who state their false beliefs are often not lying. And speakers who state true propositions that they don’t believe are often lying—regardless of whether the non-belief is disbelief. Persons who state propositions on which they have no opinion are lying as much as those (...) who state propositions they believe to be false. Not all lies are statements of false propositions—some lies are true; some have no truth-value. People who only occasionally lie are not liars: roughly, liars repeatedly and habitually lie. Some half-truths are statements intended to mislead even though the speakers “interpret” the sentences used as expressing true propositions. Others are statements of propositions believed by the speakers to be questionable but without revealing their supposed problematic nature. The two “formulations” of “the antinomy of the liar” in [1], pp.157–8 and 161–2, have nothing to do with lying or liars. The first focuses on an “expression” Tarski calls ‘c’, namely the following. -/- c is not a true sentence -/- The second focuses on another “expression”, also called ‘c’, namely the following. -/- for all p, if c is identical with the sentence ‘p’, then not p -/- Without argumentation or even discussion, Tarski implies that these strange “expressions” are English sentences. [1] Alfred Tarski, The concept of truth in formalized languages, pp. 152–278, Logic, Semantics, Metamathematics, papers from 1923 to 1938, ed. John Corcoran, Hackett, Indianapolis 1983. -/- https://www.academia.edu/12525833/Sentence_Proposition_Judgment_Statement_and_Fact_Speaking_about_th e_Written_English_Used_in_Logic. (shrink)