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Tarski, in "On the Concept of Truth in Formal Languages" (1935), attempted to formulate a new theory of truth in order to resolve the liar paradox. In the course of this he made several metamathematical discoveries, most notably Tarski's undefinability theorem using the same formal technique Kurt Gödel used in his incompleteness theorems .
The T-schema ("truth schema", not to be confused with "Convention T") is used to check if an inductive definition of truth is valid, which lies at the heart of any realisation of Alfred Tarski's semantic theory of truth. Some authors refer to it as the "Equivalence Schema", a synonym introduced by Michael Dummett. [1]
Alfred Tarski (/ ˈ t ɑːr s k i /; Polish:; born Alfred Teitelbaum; [1] [2] [3] January 14, 1901 – October 26, 1983) was a Polish-American [4] logician and mathematician. [5] A prolific author best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and ...
The main modern approaches to semantics for formal languages are the following: The archetype of model-theoretic semantics is Alfred Tarski's semantic theory of truth, based on his T-schema, and is one of the founding concepts of model theory.
The semantic theory of truth has as its general case for a given language: 'P' is true if and only if P. where 'P' refers to the sentence (the sentence's name), and P is just the sentence itself. Tarski's theory of truth (named after Alfred Tarski) was developed for formal languages, such as formal logic.
This approach to semantics is principally associated with Donald Davidson, and attempts to carry out for the semantics of natural language what Tarski's semantic theory of truth achieves for the semantics of logic. [1] Truth-conditional theories of semantics attempt to define the meaning of a given proposition by explaining when the sentence is ...
Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that "arithmetical truth cannot be defined in arithmetic".
In formal semantics, truth-value semantics is an alternative to Tarskian semantics. It has been primarily championed by Ruth Barcan Marcus, [1] H. Leblanc, and J. Michael Dunn and Nuel Belnap. [2] It is also called the substitution interpretation (of the quantifiers) or substitutional quantification.