Metalog
Logic and Metalogic

Metalogics is the formalized study of logics using a metalanguage.

Although questions of metalogy have been raised since the time of Aristotle (384-322 B.C.), it was not until the development of formal languages around 1900 (Frege, 1893, 1903) that studies of the foundations of logic emerged.

Whereas logic studies how logical systems can be used to construct valid and correct reasoning (and thus arguments), metalogics concerns the validities that can be derived from formal languages and logical systems. Whereas logic deals with demonstrations within a logical system, expressed in a formal language, metalogics deals with demonstrations about a logical system. Thus, the essential nature of metalogics is the differentiation between...