Tarski and the Semantic Conception of Truth

Tarski showed how to define truth rigorously for a formalized language, anchoring the definition to the requirement that 'snow is white' is true iff snow is white.

Definition

On the semantic conception, an adequate definition of truth for a language must entail every instance of the T-schema ''p' is true iff p', and Tarski supplies such a definition recursively in terms of the satisfaction of formulas by sequences of objects.

Scope

This topic covers Tarski's formal definition of truth and its philosophical interpretation. It treats the object-language/metalanguage distinction, Convention T and the T-schema, the recursive definition of truth via satisfaction, the indefinability of truth for a language within itself (a route to the Liar), and Davidson's use of a Tarski-style truth theory as the core of a theory of meaning for natural language.

Core questions

• What makes a definition of truth materially adequate?
• Why must truth be defined in a metalanguage richer than the object language?
• Is the semantic conception a substantive theory of truth or neutral between them?
• Can a Tarskian truth theory serve as a theory of meaning?

Key concepts

• Convention T and the T-schema
• object language vs. metalanguage
• satisfaction
• material adequacy
• indefinability of truth
• truth-conditional meaning

Key theories

Recursive truth definition via satisfaction

Tarski defines truth for a formal language by first defining satisfaction of open formulas by sequences and then identifying truth with satisfaction by all sequences, securing material adequacy through Convention T.

Truth-conditional semantics

Davidson proposes that a Tarskian theory of truth for a natural language, by entailing the truth conditions of every sentence, can do duty as a theory of meaning for that language.

History

Tarski's 1933 monograph and its 1944 popular presentation gave the first rigorous definition of truth for formalized languages and proved truth indefinable within a sufficiently rich language. Davidson in 1967 turned the apparatus toward natural-language semantics, and Field later debated whether Tarski's definition is philosophically reductive.

Debates

Does Tarski reduce or merely codify truth?

Whether Tarski's definition provides a substantive, reductive account of what truth is, or only a formally adequate codification that, as deflationists claim, is neutral on truth's nature; Field argued it leaves the key semantic notions unexplained.

Key figures

• Alfred Tarski
• Donald Davidson
• Rudolf Carnap
• Hartry Field

Seminal works

• tarski1933
• tarski1944
• davidson1967

Frequently asked questions

Why does Tarski need an object language and a metalanguage?

To avoid the Liar paradox, no sufficiently rich language can consistently contain its own truth predicate. Tarski therefore defines 'true-in-L' for an object language L within a more expressive metalanguage, keeping the truth predicate outside the language it applies to.