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*metatheory*

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metatheory

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**metatheory**or

**meta-theory**is a theory whose (wikt:subject matter|subject matter) is some theory. All fields of research share some meta-theory, regardless whether this is explicit or correct. In a more restricted and specific sense, in mathematics and mathematical logic,

*metatheory*means a

*mathematical theory about another mathematical theory*.The following is an example of a meta-theoretical statement:{{according to whom|date=April 2017}}Meta-theoretical investigations are generally part of the philosophy of science. Also a metatheory is an object of concern to the area in which the individual theory is conceived.

## Taxonomy

Examining groups of related theories, a first finding may be to identify classes of theories, thus specifying a taxonomy of theories.## In mathematics

The concept burst upon the scene of 20th-century philosophy as a result of the work of the German mathematician David Hilbert, who in 1905 published a proposal for proof of the consistency and completeness of mathematics, creating the field of metamathematics. His hopes for the success of this proof were dashed by the work of Kurt GÃ¶del, who in 1931, used his incompleteness theorems to prove this goal of consistency and completeness to be unattainable. 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 20th century.The study of metatheory became widespread during the rest of that century by its application in other fields, notably scientific linguistics and its concept of metalanguage.## See also

- Mapâ€“territory relation
- Metahistory (concept)
*Metahistory*, a book by Hayden White- Metaknowledge
- Metalogic
- Metamathematics
- Object theory
- Philosophy of social science
- Robert T. Craig

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- time: 12:29pm EDT - Sun, Sep 23 2018

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