A metatheory or meta-theory is a theory which concerns itself with another theory or theories. As such its generalization may be called a theory of theories. In Encyclopædia Britannica, metatheory is theory the subject matter of which is another theory. A finding proved in the former that deals with the latter is known as a metatheorem ^[1].

According to the systemic TOGA meta-theory ^[2], a meta-theory may refer to the specific point of view on a theory and to its subjective meta-properties, but not to its application domain. In the above sense, a theory T of the domain D is a meta-theory if D is a theory or a set of theories. We should notice, a general theory is not a meta-theory because its domain D are not theories.

The following is an example of a meta-theoretical statement:^[3]

Meta-theory belongs to the philosophical specialty of epistemology and metamathematics, as well as being an object of concern to the area in which the individual theory is conceived. An emerging domain of meta-theories is systemics.

Taxonomy

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

History

The concept burst upon the scene of twentieth-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 of mathematics, creating the field of metamathematics. His hopes for the success of this proof were dashed by the work of Kurt Gödel who in 1931 proved this to be unattainable by his incompleteness 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, notably scientific linguistics and its concept of metalanguage.

References

1. ↑
   • Metatheory -Encyclopædia Britannica Online
2. ↑
   • Meta-Knowledge Unified Framework - the TOGA meta-theory
3. ↑ Stephen Hawking in A Brief History of Time

See also

• meta-
• meta-knowledge
• Metalogic
• Metamathematics

External links

• Meta-theoretical Issues (2003), Lyle Flint

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