TheT-schema ("truthschema", not to be confused with "Convention T") is used to check if aninductive definition of truth is valid, which lies at the heart of any realisation ofAlfred Tarski'ssemantic theory of truth. Some authors refer to it as the "Equivalence Schema", a synonym introduced byMichael Dummett.^[1]

The T-schema is often expressed innatural language, but it can be formalized inmany-sorted predicate logic ormodal logic; such a formalisation is called a "T-theory."^{[citation needed]} T-theories form the basis of much fundamental work inphilosophical logic, where they are applied in several important controversies inanalytic philosophy.

As expressed in semi-natural language (where 'S' is the name of the sentence abbreviated to S): 'S' is trueif and only if S.

Example: 'snow is white' is true if and only if snow is white.

By using the schema one can give an inductive definition for the truth of compound sentences.Atomic sentences are assignedtruth valuesdisquotationally. For example, the sentence "'Snow is white' is true" becomes materially equivalent with the sentence "snow is white", i.e. 'snow is white' is true if and only if snow is white. Said again, a sentence of the form "A" is true if and only if A is true. 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; seematerial 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 ofx, A(x) is true.
• A sentence of the form "for some x, A(x)" is true if and only if, for some possible value ofx, A(x) is true.

Predicates for truth that meet all of these criteria are called "satisfaction classes", a notion often defined with respect to a fixed language (such as the language ofPeano arithmetic); these classes are considered acceptable definitions for the notion of truth.^[2]

Joseph Heath points out that "the analysis of thetruth predicate provided by Tarski's Schema T is not capable of handling all occurrences of the truth predicate in natural language. In particular, Schema T treats only "freestanding" uses of the predicate—cases when it is applied to complete sentences."^[3] He gives as an "obvious problem" the sentence:

• Everything that Bill believes is true.

Heath argues that analyzing this sentence using T-schema generates thesentence fragment—"everything that Bill believes"—on the righthand side of thelogical biconditional.

• Principle of bivalence
• Law of excluded middle

• Zalta, Edward N. (ed.)."Tarski's Truth Definitions".Stanford Encyclopedia of Philosophy.
• Zalta, Edward N. (ed.)."Consequences of the Semantic Paradoxes".Stanford Encyclopedia of Philosophy.

• Mathematical logic
• Philosophical logic
• Truth
• Logical expressions

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