met·a·the·o·ry (mĕtʹə-thē'ə-rē, -thîr'ē) n.
A theory devised to analyze theoretical systems.

* * *

      a 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.

      The most notable example of a metatheory was provided by David Hilbert (Hilbert, David), a German mathematician, who in 1905 set out to construct an elementary proof of the consistency of mathematics. For this purpose he needed a theory that studies mathematics and has mathematical proofs as the objects to be investigated. Although theorems proved in 1931 by Kurt Gödel, a Moravian–U.S. mathematical logician, made it unlikely that Hilbert's program could succeed, his metamathematics became the forerunner of much fruitful research. From the late 1920s Rudolf Carnap, a leading philosopher of science and of language, extended this inquiry, under the headings metalogic and logical syntax, to the study of formalized languages in general.

      In discussing a formalized language it is usually necessary to employ a second, more powerful language. The former is then known as the object language, whereas the second is its metalanguage.

* * *

Universalium. 2010.

Look at other dictionaries:

  • metatheory — metatheory, metatheoretical beliefs See axiom …   Dictionary of sociology

  • Metatheory — A metatheory or meta theory is a theory whose subject matter is some other theory. In other words it is a theory about a theory. Statements made in the metatheory about the theory are called metatheorems. The following is an example of a meta… …   Wikipedia

  • metatheory — “+ noun Etymology: meta + theory : a theory concerned with the investigation, analysis, or description of theory itself if we investigate, analyze, and describe a language L1 … the sum total of what can be known about L1 and said in L2 may be… …   Useful english dictionary

  • metatheory — meta·theory …   English syllables

  • МЕТАТЕОРИЯ — (metatheory) все или какие либо оценки второго порядка теорий или теории второго порядка о теориях …   Большой толковый социологический словарь

  • Object theory — For the concept of objects in philosophy, see Object (philosophy). Object theory is a theory in philosophy and mathematical logic concerning objects and the statements that can be made about objects. Contents 1 An informal theory 2 Objects 3 A… …   Wikipedia

  • Metalanguage — For the programming language, see ML (programming language). Broadly, any metalanguage is language or symbols used when language itself is being discussed or examined.[1] In logic and linguistics, a metalanguage is a language used to make… …   Wikipedia

  • New Foundations — In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled New Foundations for …   Wikipedia

  • Equiconsistency — In mathematical logic, two theories are equiconsistent if, roughly speaking, they are as consistent as each other . It is not in general possible to prove the absolute consistency of a theory T. Instead we usually take a theory S, believed to be… …   Wikipedia

  • Metatheorem — In logic, a metatheorem is a statement about a formal system proven in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved within a metatheory, and may reference concepts that are present in the metatheory …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”