The Semantic Theory of Truth: Field’s Incompleteness Objection

Alfred Tarski’s semantic conception of truth is arguably the most influential – certainly, most discussed - modern conception of truth. It has provoked many different interpretations and reactions, some thinkers celebrating it for successfully explicating the notion of truth, whereas others have argued that it is no good as a philosophical account of truth. The aim of this work is to offer a systematic and critical investigation of its nature and significance, based on the thorough explanation of its conceptual, technical as well as historical underpinnings. The methodological strategy adopted in the thesis reflects the author’s belief that in order to evaluate the import of Tarski’s conception we need to understand what logical, mathematical and philosophical aspects it has, what role they play in his project of theoretical semantics, which of them hang in together, and which should be kept separate. Chapter 2 therefore starts with a detailed exposition of the conceptual and historical background of Tarski’s semantic conception of truth and his method of truth definition for formalized languages, situating it within his project of theoretical semantics, and Chapter 3 explains the formal machinery of Tarski’s truth definitions for increasingly more complex languages. Chapters 4 - 7 form the core of the thesis, all being concerned with the problem of significance of Tarski’s conception. Chapter 4 explains its logico-mathematical import, connecting it to the related works of Gödel and Carnap. Having explained the seminal ideas of the model-theoretic approach to semantics, Chapter 5 tackles the question to what extent Tarski’s ‘The Concept of Truth in Formalized Languages’ (and related articles from the 1930s) anticipates this approach, and what elements might be missing from it. Chapter 6 then deals with the vexed question of its philosophical import and value as a theory of truth, reviewing a number of objections and arguments that purport to show that the method fails as an explanation (explication) of the ordinary notion of truth, and, in particular, that it is a confusion to think that Tarski’s truth definitions have semantic import. Finally, Chapter 7 is devoted to the question whether Tarski’s theory of truth is a robust or rather a deflationary theory of truth. On the basis of a careful analysis, the thesis aims to substantiate the following view. [A] Tarski’s theory with its associated method of truth definition was primarily designed to serve logico-mathematical purposes. [B] It can be regarded a deflationary theory of a sort, since it completely abstracts from meta- semantical issues concerning the metaphysical or epistemological basis or status of semantic properties. Indeed, [C] this can be interpreted as its laudable feature, since by separating formal (or logico-mathematical) from meta-semantical (or foundational) aspects it usefully divides the theoretical labour to be done in the area of meaning and semantic properties in general. [D] In spite of the fact that Tarski’s conception of truth has this deflationary flavour, the formal structure of its method of truth-definition is quite neutral in that it can be interpreted and employed in several different ways, some of them deflationary, others more robust.

New Essays on Tarski and Philosophy, 2008

In this paper, I want to discuss in some detail the original version of Tarski's condition of adequacy for a definition of truth, his Convention T. I will suggest that Tarski designed Convention T to serve two functions at once. I will then distinguish two possible interpretations of Tarski's work on truth: a standard interpretation and a non-standard, alternative interpretation. On the former, but not on the latter, the very title of Tarski's famous article about the concept of truth harbors a lie. Using the symbol 'Tr' to denote the class of all true sentences, the above postulate can be expressed in the following convention: CONVENTION T. A formally correct definition of the symbol 'Tr', formulated in the metalanguage, will be called an adequate definition of truth if it has the following consequences: (α) all sentences which are obtained from the expression 'x  Tr if and only if p' by substituting for the symbol 'x' a structural-descriptive name of any sentence of the language in question and for the symbol 'p' the expression which forms the translation of this sentence into the metalanguage;

Synthese, 2014

In a recent article, Marian David (2008) distinguishes between two interpretations of Tarski's work on truth. The standard interpretation has it that Tarski gave us a definition of truth in-L within the meta-language; the non-standard interpretation, that Tarski did not give us a definition of true sentence in L, but rather a definition of truth, and Tarski does so for L within the meta-language. The difference is crucial: for on the standard view, there are different concepts of truth, while in the alternative interpretation there is just one concept. In this paper we will have a brief look at the distinction between these two interpretations and at the arguments David gives for each view. We will evaluate one of David's arguments for the alternative view by looking at Tarski's 'On the Concept of Truth in Formalized Languages', and his use of the term 'extension' therein, which, we shall find, yields no conclusive evidence for either position. Then we will look at how Tarski treats 'satisfaction', an essential concept for his definition of 'true sentence'. It will be argued that, in light of how Tarski talks about 'satisfaction' in §4 of 'On the Concept of Truth in Formalized Languages' and his claims in the Postscript, the alternative view is more likely than the standard one.

This dissertation is a philosophical analysis of the concept of truth. It is a development and defense of the “stratified” or “language-level” conception of truth, first advanced in Alfred Tarski’s 1933 monograph The Concept of Truth in Formalized Languages. Although Tarski’s paper had seminal influence both in philosophy and in more technical disciplines, its central philosophical claim has not been generally accepted. This work has two central goals: (a) to give a detailed and analytic presentation of Tarski’s theory and the problems it faces; (b) to offer a solution to these problems and assess the philosophical significance of this solution. The essay is divided in two parts. Part One contains a detailed and analytic presentation and interpretation of the stratified conception of truth. The analysis contains several steps: (a) Crucial basic assumptions, such as the limitation to formalized languages and the requirement of explicit definitions, are stated explicitly, motivated, and their philosophical significance discussed. (b) The main negative result of the stratified conception, the impossibility of semantic closure and of a universal language, is given in detail and interpreted. (c) Tarski’s criterion for adequate truth definitions, known as Convention T, is stated and motivated. (d) The deep structure of Tarski-style truth definitions and the necessary conditions for their availability are analyzed. In particular, the philosophical significance of Tarski’s notion of “essential richness” is discussed. (e) Finally, several problems are raised for the stratified conception, chief among them the unity objection, according to which the stratified conception is not a viable analysis of the concept of truth, since (by (a) above) an analysis should take the form of a definition, and on the stratified conception different languages have different definitions. There is therefore no one analysis of the concept. Part Two is a development of answers to the problems raised at the end of Part One. The crux of the answer to the unity objection is that Convention T, the adequacy criterion, connects the many definitions of truth into a single concept. However, in order to fulfill that role Convention T must apply universally, and a universal language was shown to be impossible ((c) above). The task of Part Two is therefore to develop a mode of expression that allows the universal applicability of Convention T without commitment to a universal metalanguage. The procedure is as follows. (a) Convention T is formalized in order to isolate the place in which universal applicability is required. (b) A new expressive resource of “abstract generality” is developed. To this purpose a digression into the semantics of natural language indexicals is undertaken. David Kaplan’s thesis of the direct reference of indexicals is analyzed and a new formal system is proposed that embodies it. It is shown that this formal system expresses abstract generality. (c) The notion of abstract generality is adapted to languages without indexicals and it isviii shown that Convention T can be expressed without assuming a universal language. (d) A reconstrual of the task of concept analysis is proposed, which is a generalization of the answer to the unity objection. It is often complained against Tarski’s stratified conception of truth that it is of limited philosophical significance. In this work I show that, on the contrary, the problems it faces and the solutions that can be advanced to answer these problems have substantive philosophical consequences. The notion of abstract generality gives rise to a distinction between two fundamentally different modes of discourse: a universal but merely abstract methodological discourse on the one hand, and a concrete but inevitably restricted theoretical discourse on the other. This distinction has many important implications for our understanding of the concepts of truth, meaning and language.

2008