The Expressive Power of Truth (original) (raw)

Notes on Formal Theories of Truth

Mathematical Logic Quarterly, 1989

8 0. Introduction I n this paper we investigate formal systems, which are related to KRIPKE's theory of truth and to its subsequent extensions via four-valued logic (see KRIPKE [22], VISSER [33], WOODRUFF [34]). There are several motivations for an axiomatic study: let us mention a few of them.

On some recently debated issues in the theory of formal truth

As the title suggests, this paper aims at surveying some recent advances in the theory of formal truth. It contains an account of the debate concerning the deflationist approach to truth, according to which truth is a 'thin' notion in that it should involve no assumption of whatsoever nature. We review here the main issues that were comprised by the discussion accompanying the attempts of translating this idea into logical terms. In the second half of the paper, we focus on a recent theory of truth proposed by Hartry Field, a former 'champion' of the deflationary approach. We then discuss it both with respect to the previous conceptual account, and to some further observation concerning the truth-as-revision machinery that this theory can be proved to implicitly make use of.

An Observation about Truth (with Implications for Meaning and Language) [PhD dissertation]

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.

Some Arguments for the Operational Reading of Truth Expressions

Analiza i Egzystencja, 2013

The main question of our article is: What is the logical form of statements containing expressions such as “… is true” and “it is true that …”? We claim that these expressions are generally not used in order to assign a certain property to sentences. We indicate that a predicative interpretation of these expressions was rejected by Frege and adherents to the prosentential conception of truth. We treat these expressions as operators. The main advantage of our operational reading is the fact that it adequately represents how the words “true” and “truth” function in everyday speech. Our approach confirms the intuition that so-called T-equivalences are not contingent truths, and explains why they seem to be—in some sense—necessary sentences. Moreover, our operational reading of truth

A mathematically derived definitional/semantical theory of truth

arXiv (Cornell University), 2017

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

On the Possibility of a Substantive Theory of Truth

Synthese 117: 133-72, 1999

The paper offers a new analysis of the difficulties involved in the construction of a general and substantive correspondence theory of truth and delineates a solution to these difficulties in the form of a new methodology. The central argument is inspired by Kant, and the proposed methodology is explained and justified both in general philosophical terms and by reference to a particular variant of Tarski's theory. The paper begins with general considerations on truth and correspondence and concludes with a brief outlook on the "family" of theories of truth generated by the new methodology.

Some Arguments For the Operational Reading of Truth Expressions (co-author: Jan Wawrzyniak)

The main question of our article is: what is the logical form of statements containing expressions such as “… is true” and “it is true that …”? We claim that these expressions are generally not used in order to assign a certain property to sentences. We indicate that a predicative interpretation of these expressions was rejected by Frege and adherents of the prosentential conception of truth. We treat these expressions as operators. The main advantage of our operational reading is the fact that it adequately represents how words “true” and “truth” function in everyday speech. Our approach confirms the intuition that so-called T-equivalences are not contingent truths and explains why they seem to be – in some sense – necessary sentences. Moreover, our operational reading of truth expressions dissolves problems arising from the belief that there is some specific property – truth. The fact that we reject that truth is a certain property does not mean that we deny that the concept of truth plays a very important role in our language, and hence in our life. We indicate that the concept of truth is inseparable from the concept of sentence and vice versa – it is impossible to explicate one of these concepts without an appeal to the other. Analiza i Egzystencja, 24 (2013), pp. 61-86

The Norm of Truth: An Introduction to the Philosophy of Logic

The Philosophical Quarterly, 1994

This volume accurately reproduces the talks given there. As its title indicates, the conference focused on different varieties of contemporary expressivism, and how they fare in relation to the truth-aptness of utterances with expressive meaning, and the status of knowledge claims. Expressivisms of all kinds share the negative thesis that claims with expressive meaning do not represent states of affairs 1. This semantic characterisation of the negative thesis also permits the pragmatic wording that the business of expressive discourse is something other than describing. Endorsing this negative thesis suffices for an approach to count as expressivist. The negative thesis can applied to all uses of language, and thus be global, or alternatively be restricted to some specific areas of discourse, or to some specific terms and phrases. The first kind of non-global expressivism is local expressivism, and I'll call the second kind term-focused expressivism. In term-focused expressivism, terms with expressive meaning do not contribute a component to what is said, i.e. they are semantically irrelevant. Frápolli's and Price's contributions defend global versions of expressivism, while Bar-On's, Besson's and Osorio and Villanueva's propose local versions, and Chrisman's, Soria and Stojanovic's, and Zalabardo's views are term-focused varieties. Within their respective scopes, all expressivisms stick to the negative thesis. It is the positive thesis, i.e. the thesis that identifies what expressive claims and utterances actually do, where a deeper disagreement between the different approaches lies. And at this point the options multiply. Just to give a hint of the variety, the positive thesis has attributed to expressive claims subjective as well as 1