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)

This paper was written with two aims in mind. A large part of it is just an exposition of Tarski's theory of truth. Philosophers do not agree on how Tarski's theory is related to their investigations. Some of them doubt whether that theory has any relevance to philosophical issues and in particular whether it can be applied in dealing with the problems of philosophy (theory) of science.In this paper I argue that Tarski's chief concern was the following question. Suppose a (...) language L belongs to the class of languages for which, in full accordance with some formal conditions set in advance, we are able to define the class of all the semantic interpretations the language may acquire. Every interpretation of L can be viewed as a certain structure to which the expressions of the language may refer. Suppose that a specific interpretation of the language L was singled out as the intended one. Suppose, moreover, that the intended interpretation can be characterized in a metalanguage L +. If the above assumptions are satisfied, can the notion of truth for L be defined in the metalanguage L + and, if it can, how can this be done? (shrink)

This paper was written with two aims in mind. A large part of it is just an exposition of Tarski’s theory of truth. Philosophers do not agree on how Tarski’s theory is related to their investigations. Some of them doubt whether that theory has any relevance to philosophical issues and in particular whether it can be applied in dealing with the problems of philosophy (theory) of science. In this paper I argue that Tarski’s chief concern was the following question. Suppose (...) a language L belongs to the class of languages for which, in full accordance with some formal conditions set in advance, we are able to define the class of all the semantic interpretations the language may acquire. Every interpretation of L can be viewed as a certain structure to which the expressions of the language may refer. Suppose that a specific interpretation of the language L was singled out as the intended one. Suppose, moreover, that the intended interpretation can be characterized in a metalanguage L +. If the above assumptions are satisfied, can the notion of truth for L be defined in the metalanguage L + and, if it can, how can this be done? Many students of Tarski’s conception will find the above exposition inconsistent with their own views on the essence of Tarski’s conception. On the other hand, as it is argued in this paper, the proposed interpretation of Tarski’s ideas allows one to use Tarski’s theory as a fundamental tool for semantic analyses of various theories, factual theories in particular. More specifically, it is argued that Tarski’s theory of truth allows one to clearly oppose a theory meant to be certain deductive system (a set of accepted sentences, say axioms, and a logical machinery for deducing from them new ones) and a theory meant to be a certain semantic system, i.e a set of sentences that serve to communicate some states of affairs and to use that opposition to explicate and occasionally also define the notion of truth. The opposition in question is of the utmost significance for analyzing some developments in both mathematics and factual sciences. The approach which is concerned with the logical relations between the elements of science such an approach is throughout this paper called analytical is put into question. The growth of science is determined by how well scientific theories are able to account for factual states of affairs. The intuitive notion of truth applied by the scientists does not necessarily correspond in a straightforward way to its Tarskian counterpart. On the other hand, as is claimed in this paper, the Tarskian notion of truth offers as adequate explication of intuitive notion of truth as possible. (shrink)