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Tarski
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This chapter offers a simplified account of the most basic features of Alfred Tarski's model theory. Tarski foresaw important applications for a notion of truth in mathematics, but also saw that mathematicians were suspicious of that notion, and rightly so given the state of understanding of it circa 1930. In a series of papers in Polish, German, French, and English from the 1930s onward, Tarski attempted to rehabilitate the notion for use in mathematics, and his efforts had by the 1950s resulted in the creation of a branch of mathematical logic known as model theory. The chapter first considers Tarski's notion of truth, which he calls “semantic” truth, before discussing his views on object language and metalanguage, recursive versus direct definition of the truth predicate, and self-reference.
Title: Tarski
Description:
This chapter offers a simplified account of the most basic features of Alfred Tarski's model theory.
Tarski foresaw important applications for a notion of truth in mathematics, but also saw that mathematicians were suspicious of that notion, and rightly so given the state of understanding of it circa 1930.
In a series of papers in Polish, German, French, and English from the 1930s onward, Tarski attempted to rehabilitate the notion for use in mathematics, and his efforts had by the 1950s resulted in the creation of a branch of mathematical logic known as model theory.
The chapter first considers Tarski's notion of truth, which he calls “semantic” truth, before discussing his views on object language and metalanguage, recursive versus direct definition of the truth predicate, and self-reference.
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