Metatheory
Encyclopedia
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 metatheorem
s.
The following is an example of a meta-theoretical statement:
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
.
of theories. A proof engendered by a metatheory is called a metatheorem.
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
.
TOGA meta-theory , 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. A general theory is not a meta-theory because its domain D are not theories.
Theory
The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...
whose subject matter
Subject matter
Subject matter, in general, is anything which can be content for some theory.Subject matter may refer to:* Patentable subject matter , defining whether patent protection is available...
is some other theory. In other words it is a theory about a theory. Statements
Statement (logic)
In logic a statement is either a meaningful declarative sentence that is either true or false, or what is asserted or made by the use of a declarative sentence...
made in the metatheory about the theory are called metatheorem
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 but not the object theory.- Discussion :A formal...
s.
The following is an example of a meta-theoretical statement:
Meta-theory belongs to the philosophical
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
specialty of epistemology and metamathematics
Metamathematics
Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories...
, as well as being an object of concern to the area in which the individual theory is conceived. An emerging domain of meta
Meta
Meta- , is a prefix used in English to indicate a concept which is an abstraction from another concept, used to complete or add to the latter....
-theories is systemics
Systemics
In the context of systems science and systems philosophy, the term systemics refers to an initiative to study systems from a holistic point of view...
.
Taxonomy
Examining groups of related theories, a first finding may be to identify classes of theories, thus specifying a taxonomyTaxonomy
Taxonomy is the science of identifying and naming species, and arranging them into a classification. The field of taxonomy, sometimes referred to as "biological taxonomy", revolves around the description and use of taxonomic units, known as taxa...
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 GermanGermany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
mathematician
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
, who in 1905 published a proposal for proof of the consistency of mathematics, creating the field of metamathematics
Metamathematics
Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories...
. His hopes for the success of this proof were dashed by the work of Kurt Gödel
Kurt Gödel
Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...
who in 1931 proved this to be unattainable by his incompleteness theorems
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of...
. 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
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
and its concept of metalanguage
Metalanguage
Broadly, any metalanguage is language or symbols used when language itself is being discussed or examined. In logic and linguistics, a metalanguage is a language used to make statements about statements in another language...
.
TOGA metatheory
According to the systemicSystemics
In the context of systems science and systems philosophy, the term systemics refers to an initiative to study systems from a holistic point of view...
TOGA meta-theory , 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. A general theory is not a meta-theory because its domain D are not theories.
See also
- meta-
- meta-knowledge
- MetalogicMetalogicMetalogic is the study of the metatheory of logic. While logic is the study of the manner in which logical systems can be used to decide the correctness of arguments, metalogic studies the properties of the logical systems themselves...
- MetamathematicsMetamathematicsMetamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories...
- MetahistoryMetahistoryMetahistory: The Historical Imagination in Nineteenth-Century Europe is a historiography book by Hayden White first published in 1973.On the second page of his Introduction Hayden White stated:...
, a book by Hayden WhiteHayden WhiteHayden White is a historian in the tradition of literary criticism, perhaps most famous for his work Metahistory: The Historical Imagination in Nineteenth-Century Europe... - Philosophy of social sciencePhilosophy of social scienceThe philosophy of social science is the study of the logic and method of the social sciences, such as sociology, anthropology and political science...
- Robert T. Craig (scholar)Robert T. Craig (scholar)Robert T. Craig is a communication theorist from the University of Colorado, Boulder who received his B.A. in Speech at the University of Wisconsin–Madison, and his M.A and PhD. in communication from Michigan State University. Craig was on the 1988 founding board of the journal "Research on...