Metatheory

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A metatheory or meta-theory is a theory on a subject matter that is a theory in itself. [1] Analyses or descriptions of an existing theory would be considered meta-theories. [2] If the subject matter of a theoretical statement consists of one or multiple theories, it would also be called a meta-theory. [3] For mathematics and mathematical logic, a metatheory is a mathematical theory about another mathematical theory. [4] Meta-theoretical investigations are part of the philosophy of science. [5] The topic of metascience is an attempt to use scientific knowledge to improve the practice of science itself.

Contents

The study of metatheory became widespread during the 20th century after its application to various topics, including scientific 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". [6] In the words of John Ioannidis, "Science is the best thing that has happened to human beings ... but we can do it better." [7]

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 reproduced, 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. [8]

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.

Metamathematics

Introduced in 20th-century philosophy as a result of the work of the German 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). [9]

Metalogic

Metalogic is the study of the metatheory of logic. Whereas logic is the study of how logical systems can be used to construct valid and sound 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 type of mathematical logic that is known as model theory, and the study of deductive systems is the type that is known as proof theory.

Metaphilosophy

Metaphilosophy is "the investigation of the nature of philosophy". [10] Its subject matter includes the aims of philosophy, the boundaries of philosophy, and its methods. [11] [12] 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-referential 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, [13] while others see it as inherently a part of philosophy, [14] or automatically a part of philosophy [15] while others adopt some combination of these views. [11]

Sociology of sociology

The 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.[ citation needed ]

See also

Related Research Articles

Metaphilosophy, sometimes called the philosophy of philosophy, is "the investigation of the nature of philosophy". 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, while others see it as inherently a part of philosophy, or automatically a part of philosophy while others adopt some combination of these views.

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 systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.

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 scientific, belong to a non-scientific discipline, or no discipline at all. Depending on the context, a theory's assertions might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.

<span class="mw-page-title-main">Theorem</span> In mathematics, a statement that has been proved

In mathematics, a theorem is a statement that has been proved, or can be proved. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.

Philosophy of science is the branch of philosophy concerned with the foundations, methods, and implications of science. Amongst its central questions are the difference between science and non-science, the reliability of scientific theories, and the ultimate purpose and meaning of science as a human endeavour. Philosophy of science focuses on metaphysical, epistemic and semantic aspects of scientific practice, and overlaps with metaphysics, ontology, logic, and epistemology, for example, when it explores the relationship between science and the concept of truth. Philosophy of science is both a theoretical and empirical discipline, relying on philosophical theorising as well as meta-studies of scientific practice. Ethical issues such as bioethics and scientific misconduct are often considered ethics or science studies rather than the philosophy of science.

The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia. The Stoics, especially Chrysippus, began the development of predicate logic.

Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature.

<span class="mw-page-title-main">Metamathematics</span> Study of mathematics itself

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 owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of the 20th century. Metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic". An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system. An informal illustration of this is categorizing the proposition "2+2=4" as belonging to mathematics while categorizing the proposition "'2+2=4' is valid" as belonging to metamathematics.

Metalogic is the study of the metatheory of logic. Whereas logic studies how logical systems can be used to construct valid and sound 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.

A formal system is an abstract structure and formalization of an axiomatic system used for inferring theorems from axioms by a set of inference rules.

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, quotation marks, or writing on a separate line. The structure of sentences and phrases in a metalanguage can be described by a metasyntax. For example, to say that the word "noun" can be used as a noun in a sentence, one could write "noun" is a <noun>.

<span class="mw-page-title-main">Syntax (logic)</span> Rules used for constructing, or transforming the symbols and words of a language

In logic, syntax is anything having to do with formal languages or formal systems without regard to any interpretation or meaning given to them. Syntax is concerned with the rules used for constructing, or transforming the symbols and words of a language, as contrasted with the semantics of a language which is concerned with its meaning.

Meta is an adjective meaning 'more comprehensive' or 'transcending'.

Formal science is a branch of science studying disciplines concerned with abstract structures described by formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, game theory, systems theory, decision theory, and theoretical linguistics. Whereas the natural sciences and social sciences seek to characterize physical systems and social systems, respectively, using empirical methods, the formal sciences use language tools concerned with characterizing abstract structures described by formal systems. The formal sciences aid the natural and social sciences by providing information about the structures used to describe the physical world, and what inferences may be made about them.

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.

Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.

The branches of science, also referred to as sciences, scientific fields or scientific disciplines, are commonly divided into three major groups:

In mathematical logic, a judgment or assertion is a statement or enunciation in a metalanguage. For example, typical judgments in first-order logic would be that a string is a well-formed formula, or that a proposition is true. Similarly, a judgment may assert the occurrence of a free variable in an expression of the object language, or the provability of a proposition. In general, a judgment may be any inductively definable assertion in the metatheory.

Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application. This involves questions about how logic is to be defined and how different logical systems are connected to each other. It includes the study of the nature of the fundamental concepts used by logic and the relation of logic to other disciplines. According to a common characterisation, philosophical logic is the part of the philosophy of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. But other theorists draw the distinction between the philosophy of logic and philosophical logic differently or not at all. Metalogic is closely related to the philosophy of logic as the discipline investigating the properties of formal logical systems, like consistency and completeness.

References

  1. ↑ Merriam-Webster, Definition of metatheory
  2. ↑ Walter L. Wallace, Metatheory. In: Encyclopedia of Sociology, Encyclopedia.com
  3. ↑ Ch. Mahmood Anwar, What is Metatheory? An easy explanation with example of Self determination theory,
  4. ↑ Baker, W. J.; Mos, Leendert P.; Rappard, Hans V.; Stam, Henderikus J. (2012). Recent Trends in Theoretical Psychology: Proceedings of the Second Biannual Conference of the International Society for Theoretical Psychology, April 20–25, 1987, Banff, Alberta, Canada. New York: Springer-Verlag. ISBN   9780387967578.
  5. ↑ Haas, Emily J.; Mattson, Marifran (2015). Metatheory and Interviewing: Harm Reduction and Motorcycle Safety in Practice. Lanham, MD: Lexington Books. p. 11. ISBN   978-0-7391-8057-0.
  6. ↑ Ioannidis, John P. A.; Fanelli, Daniele; Dunne, Debbie Drake; Goodman, Steven N. (2015-10-02). "Meta-research: Evaluation and Improvement of Research Methods and Practices". PLOS Biology. 13 (10): –1002264. doi: 10.1371/journal.pbio.1002264 . ISSN   1545-7885. PMC   4592065 . PMID   26431313.
  7. ↑ Bach, Author Becky (8 December 2015). "On communicating science and uncertainty: A podcast with John Ioannidis". Scope. Retrieved 20 May 2019.{{cite web}}: |first1= has generic name (help)
  8. ↑ Pashler, Harold; Wagenmakers, Eric Jan (2012). "Editors' Introduction to the Special Section on Replicability in Psychological Science: A Crisis of Confidence?". Perspectives on Psychological Science. 7 (6): 528–530. doi:10.1177/1745691612465253. PMID   26168108. S2CID   26361121.
  9. ↑ Barile, Margherita. "Metatheorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/Metatheorem.html
  10. ↑ Lazerowitz, M. (1970). "A note on "metaphilosophy"". Metaphilosophy. 1 (1): 91. doi:10.1111/j.1467-9973.1970.tb00792.x. see also the Internet Encyclopedia of Philosophy article by Nicholas Joll: Contemporary Metaphilosophy
  11. 1 2 Nicholas Joll (November 18, 2010). "Contemporary Metaphilosophy". Internet Encyclopedia of Philosophy (IEP).
  12. ↑ Armen T Marsoobian (2004). "Metaphilosophy". In John Lachs; Robert Talisse (eds.). American Philosophy: An Encyclopedia. Taylor & Francis. pp. 500–501. ISBN   978-0203492796. Its primary question is "What is philosophy?"
  13. ↑ See for example, Charles L. Griswold Jr. (2010). Platonic Writings/Platonic Readings. Penn State Press. pp. 144–146. ISBN   978-0271044811.
  14. ↑ Martin Heidegger (1956). Was Ist Das – die Philosophie?. Rowman & Littlefield. p. 21. ISBN   978-0808403197.
  15. ↑ Timothy Williamson (2008). "Preface". The Philosophy of Philosophy. John Wiley & Sons. p. ix. ISBN   978-0470695913. The philosophy of philosophy is automatically part of philosophy, just as the philosophy of anything else is...
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