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 ...
whose
subject matter is theory itself, aiming to describe existing theory in a systematic way. In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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 forma ...
, 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 ultim ...
. 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
Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
Science may be as old as the human species, and some of the earliest archeological evidence ...
to study
science
Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
Science may be as old as the human species, and some of the earliest archeological evidence ...
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 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 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" 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
Clinical trials are prospective biomedical or behavioral research studies on human participants designed to answer specific questions about biomedical or behavioral interventions, including new treatments (such as novel vaccines, drugs, dieta ...
as well as the founding of organizations such as
CONSORT and the
EQUATOR Network that issue guidelines for methodology and reporting. There are continuing efforts to reduce the
misuse of statistics, to eliminate
perverse incentives 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
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many ...
, 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
Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the ter ...
. His hopes for the success of this proof were dashed by the work of
Kurt Gödel
Kurt Friedrich Gödel ( , ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an imm ...
, who in 1931, used his
incompleteness theorems 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
In logic and linguistics, a metalanguage is a language used to describe another language, often called the ''object language''. Expressions in a metalanguage are often distinguished from those in the object language by the use of italics, quota ...
.
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 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 prem ...
. 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'' by ...
argument
An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialecti ...
s, 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
Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, and may be conveyed through a variety of met ...
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
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 forma ...
that is known as
model theory
In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (math ...
, 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
Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Barwise (1978) consists of four corresponding part ...
.
Metaphilosophy
Metaphilosophy is "the investigation of the nature of
philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. ...
".
[ see also the ]Internet Encyclopedia of Philosophy
The ''Internet Encyclopedia of Philosophy'' (''IEP'') is a scholarly online encyclopedia, dealing with philosophy, philosophical topics, and philosophers. The IEP combines open access publication with peer reviewed publication of original p ...
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.
See also
* Meta-emotion
*Metacognition
Metacognition is an awareness of one's thought processes and an understanding of the patterns behind them. The term comes from the root word '' meta'', meaning "beyond", or "on top of".Metcalfe, J., & Shimamura, A. P. (1994). ''Metacognition: knowi ...
* Metahistory (concept)
*Metaknowledge
Meta-knowledge or metaknowledge is knowledge about knowledge.
Some authors divide meta-knowledge into orders:
* ''zero order meta-knowledge'' is knowledge whose domain is not knowledge (and hence zero order meta-knowledge is not meta-knowledge ''p ...
*Metalanguage
In logic and linguistics, a metalanguage is a language used to describe another language, often called the ''object language''. Expressions in a metalanguage are often distinguished from those in the object language by the use of italics, quota ...
*Metalearning
Meta-learning is a branch of metacognition concerned with learning about one's own learning and learning processes.
The term comes from the meta prefix's modern meaning of an abstract recursion, or "X about X", similar to its use in metaknowl ...
* Metamemory
*Meta-ontology
Meta-ontology is the study of the field of inquiry known as Ontology. The goal of meta-ontology is to clarify what ontology is about and how to interpret the meaning of ontological claims. Different meta-ontological theories disagree on what the go ...
*Philosophy of social science
The philosophy of social science is the study of the logic, methods, and foundations of social sciences (psychology, cultural anthropology, sociology, etc...). Philosophers of social science are concerned with the differences and similarities be ...
References
External links
*
Meta-theoretical Issues (2003), Lyle Flint
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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