Editing T-schema (section)

==The inductive definition==

By using the schema one can give an inductive definition for the truth of compound sentences. [[Atomic sentences]] are assigned [[truth value]]s [[disquotational principle|disquotationally]]. 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; see [[material implication (rule of inference)|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.
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 of [[Peano arithmetic]]); these classes are considered acceptable definitions for the notion of truth.<ref>H. Kotlarski, [https://projecteuclid.org/download/pdf_1/euclid.ndjfl/1093635929 Full Satisfaction Classes: A Survey] (1991, [[Notre Dame Journal of Formal Logic]], p.573). Accessed 9 September 2022.</ref>