Alfred Tarski and His Philosophy
Polish Logician and Philosopher, Famous for The Concept of Truth
Nov 11, 2009
Alfred Tarski is considered as one of the greatest logicians of the 20th century. His work is fundamental to modern philosophy of language and philosophical logic. He is regarded as one of the four greatest logicians of all time, matched only by Aristotle, Kurt Gödel, and Gottlob Frege. He was best known for his work on model theory, algebraic logic and metamathematics.
Brief Biography of Alfred Tarski
Alfred Tarski (1902-1983), was born on January 14, 1902, in Warsaw, Poland, at that time ruled by Russia. He was a logician and mathematician. He emigrated to the US in 1939, but educated in the Warsaw University where he studied mathematics, linguistics, philosophy, and biology.
Early in his career he made a name for himself for his work on the foundations of mathematics. But it is principally for his work in semantics and his definition of truth in formal languages that Tarski’s influence has been greatest.
From 1942 until his death in October 26, 1983, Tarski taught and performed research in mathematics at the University of California, Berkeley.
Alfred Tarski Pursues the Concept of Truth
Philosophy has struggled to find an adequate account of the concept of truth. What exactly is it for a sentence to be true? The most popular answer, since Aristotle, has always been to think that a sentence is true when it somehow corresponds with the facts. However, trying to explicate the idea of “correspondence” without referring to the concept of truth in the definition has proven it difficult.
Tarski solves that problem for formal languages. He was himself pessimistic of applying his solution to natural languages like English or French. Nonetheless, this has not stopped some philosophers from trying to complete such as project.
Alfred Tarski’s Philosophy Rationale
According to Tarski, any proposed definition of truth must entail as a consequence all equivalences of the following form:
1. Some sentence S is true in some language L, if and only if p, where p represents a translation of S in a second-order, or “meta” language.
2. A condition, might have as an instance, for example, “Schnee ist weiss” (in German, meaning, “Snow is white.”) if and only if snow is white.
But also equally:
3. "Snow is white." is true in English, if and only if snow is white.
These examples highlight that what is important for any proposed definitions is the distinction between an “object language” and a “meta language.”
The complete sentences, (1), (2) and (3) are all sentences in a meta-language, which means that they are used to mention and assert something of another sentence.
In the case of (3), it is clear that the object language and meta-language are both English.
Natural languages, such as English or German, are in fact their own meta-languages, a peculiar feature which allows them to both use and mention their own sentences. He further claimed that languages such as those found in logic, mathematics and computer programming, may be “semantically open,” as far as no sentence which mentions another sentence in the same language counts as a well-formed formula.
Semantically Open versus Semantically Close
To Tarski, the distinction between a “semantically open” and “semantically closed” language is important. First, he maintains that only semantically open languages can have a definition of truth. Second, since, as in natural languages, the object language and the meta-language are identical, paradoxes such as the “liar paradox” can be generated which are un-decidable.
In his explanation, this statement is considered: (4) This sentence is false.
(4) is un-decidable because in referring to itself that it is true, it is false; and if it is false, it is true. Accordingly, Tarski insists that truth can only be completely defined for “open” languages, languages where truth is ascribed from “outside” of the language (that is, in a meta-language) under consideration.
This makes him a pessimist, something that has not always been shared by his philosophical descendants, such as Saul Kripke.
Alfred Tarski Contributions
Tarski is regarded as one of the four greatest logicians of all time. Although his account has stimulated much work in an attempt to solve the problem of defining truth in natural or “closed” languages, many philosophers remained convinced that his pessimism was justified.
He was a prolific writer best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, analytic philosophy, and other mathematical areas of discipline.
Works by Alfred Tarski
- The Concept of Truth in Formulated Languages, 1933
- Logic, Semantics andMetamathematics, 1956
Sources:
McGovern, Una, Ed. Biographical Dictionary. Edinburgh: Chambers Harrap Publishers, 2002,
Stokes, Philip. Philosophy, the Great Thinkers. London: Capella, 2007,
 |
