T-schema

The T-schema or truth schema (also known as Convention T) is the inductive definition that lies at the heart of any realisation of Alfred Tarski's semantic theory of truth, expressing the commutation of truth over logical operators.

The T-schema is often expressed in natural language, but it can be formalized in many-sorted predicate logic or modal logic; such a formalisation is called a T-theory. T-theories form the basis of much fundamental work in philosophical logic, where they are applied in several important controversies in analytic philosophy.

The schema

The schema gives an inductive definition for the truth of compound sentences. Atomic sentences are assigned truth values disquotationally. For example, 'Snow is white' is true if and only if snow is actually white. The truth of more complex sentences is defined in terms of the components of the sentence:

• A sentence of the form "A and B" is true if and only if A is true and B is true
• A sentence of the form "A or B" is true if and only if A is true or B is true
• A sentence of the form "if A then B" is true if and only if A is false or B is true; see material implication.
• A sentence of the form "not A" is true if and only if A is false
• A sentence of the form "for all x, A(x)" is true if and only if, for every possible value of x, A(x) is true.
• A sentence of the form "for some x, A(x)" is true if and only if, for some possible value of x, A(x) is true.

See also

• Principle of bivalence
• Law of excluded middle

External links

• Stanford Encyclopedia of Philosophy entry on Tarski's Truth Definitions
• Self-reference:2.1 Consequences of the Semantic Paradoxes in Stanford Encyclopedia of Philosophy

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