Tarski on truth and logical consequence

Abstract

Tarski's writings on the concepts of truth and logical consequence rank among the most influential works in both logic and philosophy of the twentieth century. Because of this, it would be impossible to give a careful and accurate account of how far that influence reaches and of the complex route by which it spread. In logic, Tarski's methods of defining satisfaction and truth, as well as his work pioneering general model-theoretic techniques, have been entirely absorbed into the way the subject is presently done; they have become part of the fabric of contemporary logic, material presented in the initial pages of every modern textbook on the subject. In philosophy, the influence has been equally pervasive, extending not only to work in semantics and the philosophies of logic and language, but to less obviously allied areas such as epistemology and the philosophy of science as well.Rather than try to chart the wide-ranging influence of these writings or catalog the important research they have inspired, I will concentrate on various confusions and misunderstandings that continue to surround this work. For in spite of the extensive attention the work has received in the past fifty years, especially in the philosophical literature, misunderstandings of both conceptual and historical sorts are still remarkably widespread. Indeed in the philosophical community, recent reactions to Tarski's work on truth range from Karl Popper's “intense joy and relief” at Tarski's “legitimation” of the notion [1974, p. 399], to Hilary Putnam's assessment that “as a philosophical account of truth, Tarski's theory fails as badly as it is possible for an account to fail” [1985, p. 64]. Opinions have not exactly converged.

Alfred Tarski: Philosophy of Language and Logic

“…Though the conception of consequence is problematic, truth-theoretic semantics has many advantages over the Intuitionistic Formalist account, especially when it is detached from Tarski's definitional project and treated as issuing in axiomatic theories that state the truth conditions of the sentences of a language as recommended in [Davidson, 1990] and [Etchemendy, 1988]. In the place of hand-waving about the association of complex thoughts or thought-constitutents with complex expressions one has a straightforward, genuine account of semantic compositionality in Tarski's recursion on satisfaction.…”

Reflections on Consequence

“…Contingent facts about the shapes of objects in the universe will result in arguments that are declared logically valid, but which do not display the guarantee of truth preservation that seems evident in our chosen example. 12 As I said, this is a controversial example, but it is worth mentioning for a couple of reasons. For one thing, it is not obvious that this example is all that different from the previous argument, which is universally acknowledged to be logically valid.…”

“…1 A partial list is contained in the references at the end of this article. Some of these were reactions to my earlier articles [11] and [12] (plus private correspondence) which covered some of the points discussed at greater length in CLC. I apologize to any authors whose work I have inadvertantly overlooked.…”

The Place of Ontology in Davidson’s Theory of Interpretation

“…and so on ad infinitum, with a disjunct for each of the infinite sentences of the object language. As far as I know, Davidson has never analysed in detail the second strategy, mentioned en passant in (Etchemendy 1988), but he argues that if the object language has normal expressive powers, a theory of truth à la Kripke is materially inadequate, that is, unable to yield all the T-sentences required by Convention T.…”