# Who is Alfred Tarski?

December 13, 2020Alfred Tarski (January 14, 1901 – 1983) is a Polish-born US mathematician and logician known for his contributions to general algebra, measure theory, mathematical logic, set theory and mathematics.

Alfred Tarski formed his semantic method, an important work in logic in the 1930s. This method discusses the connection between the meanings and the symbols represented by the meanings. In the beginning, semantics opened up new possibilities in language studies and offered a natural method in the debates of such object-meaning relations.

Alfred Tarski (1901-1983) is a Polish logician and mathematician. He studied at the University of Warsaw and immigrated to the USA since 1939. He continued his academic studies at the University of California at Berkeley from 1942 until his death. According to some, Tarski is considered to be one of the four greatest logicians ever, along with Aristotle, Gottlob Frege and Kurt Gödel.

He was born on January 4, 1902 in Warsaw. After his secondary education, he studied mathematics at the University of Warsaw in 1924 and earned the title of doctor. He worked as an associate professor in 1926, a lecturer in the USA in 1939, a lecturer at California University in 1942, and a professor of mathematics in 1946. For Tarski, who aimed to establish a method unity between mathematics and logic, what was important was to create a mathematical logic. In order to achieve this, it was first necessary to lay the foundations of a mathematical theory of knowledge. He made use of the “set theory” of logic in this regard.

Tarski adopted the set theory and applied it to his method. According to him, the results of a set of axioms are linked to the smallest set of axioms and their proof rules. In logic, as in mathematics, the relationship between the elements forming a unit or a set is clear. This relationship shows that by proving one, the other is also proven. Tarski thought of applying the set theory, which is valid in logic, to mathematics, providing him with a broader field of knowledge. This theory also shed light on his work on semantics. It has been suggested that this method is particularly useful in the field of language with very complex problems. Another subject that Tarski emphasizes is metamathematics. Metamathematics is a branch of mathematical logic that generally examines formal theories and seeks solutions to problems related to them. According to Tarski, there are certain elements that make up a theory, and these are a set of principles (elements) called formulas and a “result function”. In each set, the set consisting of functions and the set consisting of formulas are found mutually. Here the second set is a new set consisting of the results of the first. The so-called result function is not an arbitrary object, but must be consistent, complementary.

According to Tarski, theories based on “classical propositional logic” have an axiomatic character. For this reason, the inferences obtained by applying the deductive method are important. This importance is due to the fact that it determines the inference function of terms in an invariant set of propositions. Especially in describing systems, a competence should be sought, it is important that a theory is capable of describing all the systems it contains. The aim is to properly describe all the systems that form a unity within themselves.

One of the topics Tarski aims to develop is semantics (semantics). According to this doctrine, the connection between concepts and objects reflected by what happened should be revealed. The accuracy and precision of this connection serves to explain the knowledge of the object that has become a concept. If there is no coherence between the object and its concept, in terms of existence, it cannot be said that the concept reflects reality. If this method is applied especially in the field of language, it becomes easier to put forward correct statements. For the correctness of a proposition stems from the identity, the conformity between the terms and the objects that constitute it. If the concept (term) does not give the object as it is, there is no consistency in the proposition in which it is located. The correctness and consistency of the proposition should not be sought in the harmony between terms, but in the reality of the connection between terms and objects.

works

Crundlegung der wissenschaftlic-hen Semantic, 1935, (“The Foundation of Scientific Semantics”); Der Wahrbeitsbegriff in den formalisierten Sprac-hen, 1935, (“The Concept of Reality in Formalized Languages”); Einfübrung in die Methodologie der Matbematik, 1937, (“Introduction to Mathematical Methodology”); The Semantic Conception of Truth, 1944, (“The Semantic Concept of Reality”), Logis, Semantics, Mathematics, 1956, (“Logic, Semantics, Mathematics”).

– Alfred Tarski’s Definition of Accuracy

Prepared by: Sociologist Ömer YILDIRIM

Source: Ömer YILDIRIM’s Personal Lecture Notes. Atatürk University Department of Sociology 1st Class “Introduction to Philosophy” and 2., 3., 4. Class “History of Philosophy” Lecture Notes (Ömer YILDIRIM); Open Education Philosophy Textbook