Language peer sets for Tarski:
Designed 1933 ↑
1930s languages ↑
Genus Symbolic ↑
alternate simple view
Formalisation of language
Alfred Tarski. (1956) Alfred Tarski. The concept of truth in formalized languages. In Logic, Semantics and Metamathematics, pages 152--278. Clarendon Press, 1956.
Dunham, Bradford (1957) Dunham, Bradford "The formalization of scientific languages. I. The work of Woodger and Hull" IBM Journal of Research and Development Volume 1, Number 4, October, 1957 pp341-8
Copy at IBM
Rudnicki, Piotr (1992) Rudnicki, Piotr "An Overview of the MIZAR Project" Department of Computing Science University of Alberta June 30, 1992
History of Mizar
1985, University of California: In Memoriam Alfred Tarski, Mathematics: Berkeley In 1926-28, Tarski held a seminar at Warsaw University on a relatively new topic in logic, called the method of eliminating quantifiers. This seminar was Tarski's beginning work on what 30 years later came to be called the theory of models, the branch of logic in which perhaps his greatest work lies. The studies in the seminar soon began to go in two directions. On the one hand, various new and more difficult "eliminations" were carried out. These led in particular to a well-known result of Presburger (1930) concerning addition of natural numbers. They also led to one of Tarski's most famous results, a decision method for all questions in the elementary theory of the real field and in elementary geometry (announced in 1931, published in full in 1948). He showed that theoretically a machine can be built to answer all such questions. This work has many applications in algebra; a well-known modern graduate textbook on algebra by Nathan Jacobson devotes a chapter to it.
The other direction in which the seminar studies led was this: Tarski saw that, in order to state the results of the seminar precisely, one needed to define the notions of truth and definability. Eventually (in 1933), Tarski published, in a philosophical journal, his famous paper on the theory of truth in formalized languages. He obtained two remarkable results: that truth can be precisely defined for essentially all formalized languages and, using a famous result of Gödel , that the truth for a system cannot be defined within the system itself. Tarski's work on truth is valued highly by mathematicians. It also has been extremely influential in philosophy. The logical positivists had argued that to know the meaning of a sentence is to know the conditions under which it would be true; combining this idea with Tarski's method for defining truth for formalized languages, a number of more recent philosophers have concluded that, to understand the sentences of a language, is, in effect, to have, implicitly or explicitly, a Tarski-like definition of truth for that language. The implications of this view are being explored at the present time in the writings of a number of leading philosophers.