A metatheory or meta-theory is a

theory A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be ...

whose subject matter is theory itself, aiming to describe existing theory in a systematic way. In mathematics and

mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...

, a metatheory is a mathematical theory about another mathematical theory. Meta-theoretical investigations are part of the

philosophy of science Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ult ...

. A metatheory is not applied directly to practice, but may have applications to the practice of the field it studies. The emerging field of

metascience Metascience (also known as meta-research) is the use of scientific methodology to study science itself. Metascience seeks to increase the quality of scientific research while reducing inefficiency. It is also known as "''research on research''" ...

seeks to use scientific knowledge to improve the practice of science itself.

Examples of metatheories

Metascience

Metascience is the use of scientific methodology to study

science Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earli ...

itself. Metascience seeks to increase the quality of scientific research while reducing waste. It is also known as "''research on research''" and "''the science of science''", as it uses

research methods Research is "creativity, creative and systematic work undertaken to increase the stock of knowledge". It involves the collection, organization and analysis of evidence to increase understanding of a topic, characterized by a particular att ...

to study how

research Research is " creative and systematic work undertaken to increase the stock of knowledge". It involves the collection, organization and analysis of evidence to increase understanding of a topic, characterized by a particular attentiveness ...

is done and where improvements can be made. Metascience concerns itself with all fields of research and has been described as "a bird's eye view of science." In the words of

John Ioannidis John P. A. Ioannidis (; el, Ιωάννης Ιωαννίδης, ; born August 21, 1965) is a Greek-American physician-scientist, writer and Stanford University professor who has made contributions to evidence-based medicine, epidemiology, and cl ...

, "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 Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industria ...

of 295 papers published in ten high-profile 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 in the following decades found many methodological flaws, inefficiencies, and poor practices in research across numerous scientific fields. Many scientific studies could not be reproduced, particularly in

medicine Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pr ...

and the soft sciences. The term "

replication crisis The replication crisis (also called the replicability crisis and the reproducibility crisis) is an ongoing methodological crisis in which the results of many scientific studies are difficult or impossible to reproduce. Because the reproducibi ...

" was coined in the early 2010s as part of a growing 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 __NOTOC__ Consort may refer to: Music * "The Consort" (Rufus Wainwright song), from the 2000 album ''Poses'' * Consort of instruments, term for instrumental ensembles * Consort song (musical), a characteristic English song form, late 16th–earl ...

and the

EQUATOR Network The EQUATOR (Enhancing the QUAlity and Transparency Of health Research) Network is an international initiative aimed at promoting transparent and accurate reporting of health research studies to enhance the value and reliability of medical researc ...

that issue guidelines for methodology and reporting. There are continuing efforts to reduce the

misuse of statistics Statistics, when used in a misleading fashion, can trick the casual observer into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misu ...

, to eliminate

perverse incentives A perverse incentive is an incentive that has an unintended and undesirable result that is contrary to the intentions of its designers. The cobra effect is the most direct kind of perverse incentive, typically because the incentive unintentionall ...

from academia, to improve the

peer review Peer review is the evaluation of work by one or more people with similar competencies as the producers of the work ( peers). It functions as a form of self-regulation by qualified members of a profession within the relevant field. Peer revie ...

process, to combat

bias Bias is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group ...

in scientific literature, and to increase the overall quality and efficiency of the scientific process.

Metamathematics

Introduced in 20th-century philosophy as a result of the work of the

German German(s) may refer to: * Germany (of or related to) ** Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ge ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

David Hilbert, who in 1905 published a proposal for proof of the

consistency In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent ...

and completeness 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, used his

incompleteness theorems Complete may refer to: Logic * Completeness (logic) * Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable Mathematics * The completeness of the real numbers, which implies t ...

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. A

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 metathe ...

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 law or duality principle or by transferring it to another area (from the theory of categories to the theory of groups) or to another context within the same area (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 Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

. Whereas ''logic'' studies how logical systems can be used to construct valid and

sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' b ...

arguments, 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 languages 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 branch of

that is known as model theory, and the study of

deductive system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A for ...

s is the branch 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
/ref> 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-reflective inquiry into the nature, aims, 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 subject 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.

Sociology of sociology

The sociology of sociology is an area of

sociology Sociology is a social science that focuses on society, human social behavior, patterns of social relationships, social interaction, and aspects of culture associated with everyday life. It uses various methods of empirical investigation an ...

that combines social theories with analysis of the effect of socio-historical contexts in sociological intellectual production.

References

External links

*
Meta-theoretical Issues (2003), Lyle Flint
{{Authority control Concepts Concepts in epistemology Concepts in logic Concepts in metaphilosophy Concepts in the philosophy of science Epistemology History of logic History of mathematics History of philosophy History of science Logic Metaphilosophy Metatheory of science Theories