A metatheory or meta-theory is a theory on a that is a theory in itself.[Merriam-Webster, Definition of metatheory] Analyses or descriptions of an existing theory would be considered meta-theories.[Walter L. Wallace, Metatheory. In: Encyclopedia of Sociology, Encyclopedia.com] For mathematics and mathematical logic, a metatheory is a mathematical theory about another mathematical theory.
The study of metatheory became widespread during the 20th century after its application to various topics, including Linguistics and its concept of metalanguage.
Examples of metatheories
Metascience
Metascience is the use of scientific method to study
science itself. Metascience is an attempt to increase the quality of scientific research while reducing wasted activity; it uses
research methods to study how
research is done or can be improved. It has been described as "
research on research", "
the science of science", and "a bird's eye view of science".
As stated by
John Ioannidis, "Science is the best thing that has happened to human beings ... but we can do it better."
In 1966, an early meta-research paper examined the statistical methods of 295 papers published in ten well-known medical journals. It found that, "in almost 73% of the reports read ... conclusions were drawn when the justification for these conclusions was invalid". Meta-research during the ensuing decades found many methodological flaws, inefficiencies, and bad practices in the research of numerous scientific topics. Many scientific studies could not be reproducibility, particularly those involving medicine and the so-called soft sciences. The term "replication crisis" was invented during the early 2010s as part of an increasing awareness of the problem.
Measures have been implemented to address the issues revealed by metascience. These measures include the pre-registration of scientific studies and clinical trials as well as the founding of organizations such as CONSORT and the EQUATOR Network that issue guidelines for methods and reporting. There are continuing efforts to reduce the misuse of statistics, to eliminate perverse incentives from academia, to improve the peer review process, to reduce bias in scientific literature, and to increase the overall quality and efficiency of the scientific process.
A major criticism of metatheory is that it is theory based on other theory.
Computational Metatheory
Computational metatheory is a conceptual and formal framework based on Theoretical Computer Science to reason about how theories in the sciences can emerge out of theoretical and empirical work.
It is a computation-centered approach to problems such as which properties theories should have, what empirical evidence is relevant in a given scientific problem situation, and how discoveries affect the problem space. As such, it complements prevailing approaches to metatheorizing with a focus on the analysis of computational problems.
Metamathematics
Introduced in 20th-century philosophy as a result of the work of the
Germany mathematician David Hilbert, who in 1905 published a proposal for proof of the
consistency and completeness of mathematics, creating the topic of
metamathematics. His hopes for the success of this proof were disappointed by the work of Kurt Gödel, who in 1931, used his incompleteness theorems to prove the goal of consistency and completeness to be unattainable. Nevertheless, his program of unsolved mathematical problems influenced mathematics for the rest of the 20th century.
A metatheorem is defined as: "a statement about theorems. It usually gives a criterion for getting a new theorem from an old one, either by changing its objects according to a rule" known as the duality principle, or by transferring it to another topic (e.g., from the theory of categories to the theory of groups) or to another context of the same topic (e.g., from linear transformations to matrices).[Barile, Margherita. "Metatheorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/Metatheorem.html]
Metalogic
Metalogic is the study of the metatheory of
logic. Whereas
logic is the study of how
Formal system can be used to construct valid and
Soundness , metalogic studies the properties of logical systems. Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived
about the
Formal language and systems that are used to express truths. The basic objects of metalogical study are formal languages, formal systems, and their interpretations. The study of interpretation of formal systems is the type of mathematical logic that is known as
model theory, and the study of
is the type that is known as
proof theory.
Metaphilosophy
Metaphilosophy is "the investigation of the nature of
philosophy".
[ see also the Internet Encyclopedia of Philosophy article by Nicholas Joll: Contemporary Metaphilosophy] Its subject matter includes the aims of philosophy, the boundaries of philosophy, and its methods.
Thus, while philosophy characteristically inquires into the nature of being, the reality of objects, the possibility of knowledge, the nature of truth, and so on, metaphilosophy is the
self-reference inquiry into the nature, purposes, and methods of the activity that makes these kinds of inquiries, by asking what
is philosophy itself, what sorts of questions it should ask, how it might pose and answer them, and what it can achieve in doing so. It is considered by some to be a topic prior and preparatory to philosophy,
[See for example, ] while others see it as inherently a part of philosophy,
or automatically a part of philosophy
while others adopt some combination of these views.
[
]
Metasociology
Metasociology, or sociology of sociology, is a topic of sociology that combines social theories with analysis of the effect of socio-historical contexts in sociological intellectual production.
See also
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