What is Tarski's Theory of Truth?

What is Tarski’s Theory of Truth? 1. Interpretation as generalization In “On the Concept of Truth in Formalized Languages”, Tarski (1933) describes his project as follows: For an extensive group of formalized languages it is possible to give a method by which a correct definition of truth can be con- structed for each of them. The general abstract description of this method and of the languages to which it is applicable would be troublesome and not at all perspicuous. I prefer therefore to intro- duce the reader to this method in another way. I shall construct a definition of this kind in connection with a particular concrete language and show some of its most important consequences. The indications which I shall then give in §4 of this article will, I hope, be sufficient to show how the method illustrated by this example can be applied to other languages of similar logical construction.  Tarski conceived of his theory as a general method for defining truth for a broad, if well defined, range of languages, but he chose to expound it through a single, simple example. This example, however, does not uniquely determine his general method, and the question arises as to how to generalize Tarski’s example. Tarski clarified one aspect of this question, namely, how to extend his example to languages with indefinitely high order of variables, but many other fundamental issues were not addressed either in his original (1933) paper, or, indeed, in his later (informal) papers (1944 and 1969). The fact that Tarski did not address these ques- tions is, of course, indicative of his attitude: Tarski was either unaware of these questions, or uninterested, or believed the answers were obvious and no further explanation was required. Today, however, the philo- sophical discussion has veered away from the technical matters that occupied Tarski in the 30’s (partly, no doubt, due to his own thorough and successful treatment of these matters), and differences in attitude towards Tarski’s theory are often grounded in differences in answers to the open questions. Even general attitudes towards the theory of truth (e.g., towards the possibility Topoi 18: 149–166, 1999.  can be traced to implicit generalizations of Tarski’s example. In this paper I will study Tarski’s theory through a few of its open questions and some of its generaliza- tions. I will concentrate on the “reductionist approach” to Tarski’s theory, exemplified by two generalizations due to Field. My critical investigation of these gener- alizations will not be directed at their exegetical virtues; rather, I will be interested in their viability as philo- sophical theories and in some of the challenges they face. I will begin with a brief introduction to the original goals of Tarski’s theory. 1 2. Aims of theory We can distinguish three aims of Tarski’s theory: a philosophical aim, a methodological aim and a logical aim. 1. The Philosophical Aim. 2 Tarski described his goal in constructing a theory of truth as philosophical in nature. The goal is to construct a materially accurate and formally consistent definition of the classical notion of truth: The present article is almost wholly devoted to a single problem – the definition of truth. Its task is to construct . . . a materially adequate and formally correct definition of the term ‘true sentence’. This problem . . . belongs to the classical questions of philosophy .  See also pp. 266–267] By the ‘classical question’ of truth Tarski means the question of how to define the “classical”, correspon- dence notion of truth: [T]hroughout this work I shall be concerned exclusively with grasping the intentions which are contained in the so-called clas- sical conception truth (‘true – corresponding with reality’) . . . .