zbMATH — the first resource for mathematics

Alfred Tarski. Philosophy of language and logic. (English) Zbl 1337.03004
History of Analytic Philosophy. New York, NY: Palgrave Macmillan (ISBN 978-0-230-22121-5/hbk; 978-0-230-36722-7/ebook). x, 262 p. (2012).
The book is devoted to the analysis of Tarski’s philosophy of language and logic. The development of truth-conditional, representational semantics by Tarski from the late 1920s until the mid-1930s is examined. The author’s goal is to explain where Tarski’s views came from, not to defend them. It is shown that Tarski’s views were more complex than is usually taken to be. The author argues that Tarski’s results were in fact motivated by the expressive conception of meaning inherited from his teacher Stanisław Leśniewski and referred to as “intuitionistic formalism.” This doctrine is the subject of Chapter 1 of the book.
Chapter 2 tells about Tarski as intuitionistic formalist, in particular about his attempts to express the discourse about a deductive theory in a deductive theory. This resulted in several papers on axioms for the consequence relation analyzed in the book. Next Tarski’s investigations concerning definability and the completeness of concepts are considered.
Chapter 3 “Semantics” tells about philosophical resistance towards semantic notions (e.g. the Vienna Circle) as well as about the opposite trend, the developments in mathematical logic that involved the treatment of semantic concepts (e.g. algebraic logicians, in particular Pierce, Skolem, American postulate theorists).
Chapter 4 is devoted to truth. The author discusses convention T (truth in the Lvov-Warsaw school, semantic concepts in a mathematical theory, T-sentences), Tarski’s definition and evaluates Tarski’s account (Tarskian definitions and Tarski’s “theory,” reduction and physicalism, correspondence and deflationism).
Chapter 5 discusses indefinability and inconsistency in everyday language. The author first examines indefinability before 1931, then he analyzes Tarski’s theorem on indefinability and its relations to intuitionistic formalism as well as Tarski’s attempts at axiomatic semantics. In connection with the problem of inconsistencies, views of Kotarbiński are considered.
In Chapter 6 “Transitions: 1933 –1935”, the 1935 Postscript to the German translation of Tarski’s fundamental paper on truth is analyzed. Carnap’s views on analyticity and truth are also considered.
The last chapter of the book, Chapter 7, is devoted to logical consequence. The following problems are considered here: Tarski’s definition, consequence in logical syntax, the overgeneration problem and domain variation, the modality problem and “Tarski’s fallacy,” the formality problem and the logical constants as well as the evolution of Tarski’s account.
The book ends with “Conclusions”, which discusses the Unity of Science Congress held in Paris in 1935 and the reception of semantics. Patterson holds that Tarski seems to have been convinced by the episodes there and that to him the attitude of Warsaw logicians to separate philosophical views from the scientific work in logic was the right one.
The book was published in a careful and nice way in the series “History of Analytic Philosophy”.

03-03 History of mathematical logic and foundations
03A05 Philosophical and critical aspects of logic and foundations
00A30 Philosophy of mathematics
01A70 Biographies, obituaries, personalia, bibliographies
01A60 History of mathematics in the 20th century
Biographic References:
Tarski, Alfred