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Metatheory

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metatheory is a theory which concerns itself with another theory, or theories. As such it may be called a theory of theories. It belongs to the philosophical specialty of epistemology, as well as being an object of concern to the area in which the individual theory is conceived.

Examining groups of related theories, its first finding may be to identify classes of theories, thus specifying ataxonomy of theories. A proof engendered by a metatheory is called a metatheorem.

The concept burst upon the scene of twentieth-century philosophy as a result of the work of the Germanmathematician David Hilbert, who in 1905 published a proposal for proof of the consistency of mathematics, creating the field of metamathematics. His hopes for the success of this proof were dashed by the work of Kurt Gödel who in1931 proved this to be unattainable by his inconsistency theorems. Nevertheless, his program of unsolved mathematical problems, out of which grew this metamathematical proposal, continued to influence the direction of mathematics for the rest of the twentieth century.

The study of metatheory became widespread during the rest of that century by its application in other fields, notablyscientific linguistics and its concept of metalanguage.

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