scheme also schema (plural: schemata), a metalinguistic frame or template used to specify an infinite set of sentences, its instances, by finite means, often taken with a side condition on how its blanks or placeholders are to be filled. The sentence ‘Either Abe argues or it is not the case that Abe argues’ is an instance of the excluded middle scheme for English: ‘Eithe. . . or it is not the case tha. . .’, where the two blanks are to be filled with one and the same (well-formed declarative) English sentence. Since first-order number theory cannot be finitely axiomatized, the mathematical induction scheme is used to effectively specify an infinite set of axioms: ‘If zero is such tha. . . and the successor of every number such tha. . . is also such tha. . . , then every number is such tha. . .’, where the four blanks are to be filled with one and the same arithmetic open sentence, such as ‘it precedes its own successor’ or ‘it is finite’. Among the best-known is Tarski’s scheme T: ‘. . . is a true sentence if and only i. . .’, where the second blank is filled with a sentence and the first blank by a name of the sentence. See also CONVENTION T, LOGICAL FORM, METALANGUAGE , OPEN FORMULA , PHILOSO — PHY OF MATHEMATICS , TARSK. J.Cor.