Metatheory may also be a study of the truth, validity, coherence, and completeness of a given theory. Every theory may be an object of study for a corresponding metatheory.
Metatheory may include the study of formal, scientific, mathematical, philosophical, political, legal, and social theories.
Examples of formal theories include formal aesthetic, formal ethical, formal epistemological, and formal ontological theories.
Examples of scientific theories include cosmological theories (e.g. the Big Bang theory, multiverse theory, and superstring theory), biological theories (e.g. cell theory, gene theory, and the theory of evolution), and physical theories (e.g. quantum theory, the theory of relativity, and string theory).
Examples of mathematical theories include computability theory, model theory, number theory, and set theory.
Examples of philosophical theories include virtue theory, value theory, critical theory, theory of mind, and theory of truth.
Examples of political theories (or ideologies) include anarchism, socialism, capitalism, communism, and totalitarianism.
Metatheory may be engaged in by a variety of metadisciplines (disciplines involving the study of other disciplines). Every discipline may be an object of study for a corresponding metadiscipline.
Philosophy may be a metadiscipline, insofar as it includes philosophy of science, philosophy of medicine, philosophy of technology, philosophy of religion, philosophy of education, and so on. But philosophy itself may be an object of study for a metadiscipline (metaphilosophy), whose themes and concerns may include the origin, aims, methods, and limits of philosophy.
Nicholas Rescher (2014) distinguishes between descriptive or historical metaphilosophy, which describes how philosophy has historically been conducted, and prescriptive or normative metaphilosophy, which describes how it should be conducted. Rescher says that while these two dimensions of metaphilosophy differ in their priorities and emphasis, they aren't completely separable.2
In addition to having metadisciplinary (or interdisciplinary) branches, philosophy may also be divided into other metadisciplines, such as metalogic, metaethics, meta-aesthetics, metaepistemology, metametaphysics, and metaontology.
Metalogic (or the metatheory of logic) may be the study of the syntax and semantics of the formal languages used to express logical truths, properties, and relations.
Metaethics (or the metatheory of ethics) may be the study of the origin, nature, and meaning of moral attitudes, opinions, or judgments, and the study of the language, methods, and modes of reasoning employed in ethics.
Meta-aesthetics may be the study of the origin, nature, and meaning of aesthetic judgments, and the study of how aesthetic judgments are made.
Metaepistemology may be the study of the origin, nature, and meaning of epistemic judgments, and the study of how epistemic judgments are made.
Metametaphysics may be the study of the language, aims, concerns, and methodology of metaphysics.
Metaontology may be the study of the nature, aims, and concerns of ontology. It may also be an analysis of the nature of ontological commitments, such as what a given ontology says about the kinds of things that exist or do not exist. An example of a metaontological question might be "What are we asking when we ask 'What exists?'"3
Metatheory may include the study of formal, scientific, mathematical, philosophical, political, legal, and social theories.
Examples of formal theories include formal aesthetic, formal ethical, formal epistemological, and formal ontological theories.
Examples of scientific theories include cosmological theories (e.g. the Big Bang theory, multiverse theory, and superstring theory), biological theories (e.g. cell theory, gene theory, and the theory of evolution), and physical theories (e.g. quantum theory, the theory of relativity, and string theory).
Examples of mathematical theories include computability theory, model theory, number theory, and set theory.
Examples of philosophical theories include virtue theory, value theory, critical theory, theory of mind, and theory of truth.
Examples of political theories (or ideologies) include anarchism, socialism, capitalism, communism, and totalitarianism.
Metatheory may be engaged in by a variety of metadisciplines (disciplines involving the study of other disciplines). Every discipline may be an object of study for a corresponding metadiscipline.
Philosophy may be a metadiscipline, insofar as it includes philosophy of science, philosophy of medicine, philosophy of technology, philosophy of religion, philosophy of education, and so on. But philosophy itself may be an object of study for a metadiscipline (metaphilosophy), whose themes and concerns may include the origin, aims, methods, and limits of philosophy.
Nicholas Rescher (2014) distinguishes between descriptive or historical metaphilosophy, which describes how philosophy has historically been conducted, and prescriptive or normative metaphilosophy, which describes how it should be conducted. Rescher says that while these two dimensions of metaphilosophy differ in their priorities and emphasis, they aren't completely separable.2
In addition to having metadisciplinary (or interdisciplinary) branches, philosophy may also be divided into other metadisciplines, such as metalogic, metaethics, meta-aesthetics, metaepistemology, metametaphysics, and metaontology.
Metalogic (or the metatheory of logic) may be the study of the syntax and semantics of the formal languages used to express logical truths, properties, and relations.
Metaethics (or the metatheory of ethics) may be the study of the origin, nature, and meaning of moral attitudes, opinions, or judgments, and the study of the language, methods, and modes of reasoning employed in ethics.
Meta-aesthetics may be the study of the origin, nature, and meaning of aesthetic judgments, and the study of how aesthetic judgments are made.
Metaepistemology may be the study of the origin, nature, and meaning of epistemic judgments, and the study of how epistemic judgments are made.
Metametaphysics may be the study of the language, aims, concerns, and methodology of metaphysics.
Metaontology may be the study of the nature, aims, and concerns of ontology. It may also be an analysis of the nature of ontological commitments, such as what a given ontology says about the kinds of things that exist or do not exist. An example of a metaontological question might be "What are we asking when we ask 'What exists?'"3
Metamathematics may be the study and analysis of the symbols, conventions, rules, principles, theorems, and proofs of mathematics.
We may be engaging in metatheory whenever we examine the adequacy, consistency, completeness, explanatory potential, or practical applicability of a given theory. Any theorizing we do may thus require us to do some metatheorizing as well.
Are we almost always or only occasionally aware we're thinking about whatever we're thinking about? If the latter is the case, then metathinking may be something we often do without truly being aware we're doing it.
Metacognition may be an object of study for cognitive science, neuroscience, linguistics, and the philosophy of mind. It may be described as awareness, evaluation, and understanding of our own cognitive processes and the cognitive processes of others, or as reasoning about our own reasoning and the reasoning of others. It may also be an awareness of the extent or limits of our own knowledge and of our ability to understand, modify, and control our own cognitive processes.4 Aspects of metacognition include metathinking, metareasoning, metalearning, metaknowing, metamemory, and meta-emotions.
Metaknowledge may include knowing that (what, how, or why) we or others know or don't know something. It may also include knowing about some domain of knowledge, e.g. about its relevance or applicability to solving a particular problem or illuminating a particular field of inquiry.
Metaknowledge may also include knowing what we know that others don't know, and what they know that we don't know. Thus, it may also include knowing how much more or less we know than they know.
It may also include knowing how to access various knowledge domains. Metaknowledge tools or techniques may include tagging sources or references by means of keywords and search terms, using bookmarks, indices, and bibliographies, and doing literature reviews, abstracts, and meta-analyses.
We may be engaging in metatheory whenever we examine the adequacy, consistency, completeness, explanatory potential, or practical applicability of a given theory. Any theorizing we do may thus require us to do some metatheorizing as well.
Are we almost always or only occasionally aware we're thinking about whatever we're thinking about? If the latter is the case, then metathinking may be something we often do without truly being aware we're doing it.
Metacognition may be an object of study for cognitive science, neuroscience, linguistics, and the philosophy of mind. It may be described as awareness, evaluation, and understanding of our own cognitive processes and the cognitive processes of others, or as reasoning about our own reasoning and the reasoning of others. It may also be an awareness of the extent or limits of our own knowledge and of our ability to understand, modify, and control our own cognitive processes.4 Aspects of metacognition include metathinking, metareasoning, metalearning, metaknowing, metamemory, and meta-emotions.
Metaknowledge may include knowing that (what, how, or why) we or others know or don't know something. It may also include knowing about some domain of knowledge, e.g. about its relevance or applicability to solving a particular problem or illuminating a particular field of inquiry.
Metaknowledge may also include knowing what we know that others don't know, and what they know that we don't know. Thus, it may also include knowing how much more or less we know than they know.
It may also include knowing how to access various knowledge domains. Metaknowledge tools or techniques may include tagging sources or references by means of keywords and search terms, using bookmarks, indices, and bibliographies, and doing literature reviews, abstracts, and meta-analyses.
Michael T. Cox and Anita Raja (2011) formulate a model of reasoning according to which doing is at the ground level, reasoning is at the object level, and metareasoning is at the metalevel. They describe metareasoning as the process of reasoning about the action-perception cycle, whereby doing at the ground level leads by means of perception to reasoning at the object level, and reasoning at the object level leads by means of action selection to doing at the ground level, Thus, metareasoning consists of both the computational control and introspective monitoring of reasoning. According to Cox and Raja, distributed metareasoning requires coordination of metareasoning by multiple agents. Each agent in a multi-agent setting must coordinate their control and monitoring of their own reasoning with other agents' control and monitoring of their own reasoning, if they are to collectively participate in problem solving and decision making and are to successfully engage in a dynamic interaction at the metalevel.5
Meta-emotions may be emotions about our own emotions or the emotions of others. Thus, in some cases we may be remorseful that we were jealous, or we may feel vaguely disquieted that we felt unsympathetic to someone else's being disappointed, or we may even be pleased that someone has been embarrassed or humiliated (schadenfreude may be a meta-emotion). Our own meta-emotions may be concordant or discordant with those of others, depending on whether they feel the same as or different than we do about our emotions and about their own emotions. Meta-emotions may also be integrated into complex emotions whose components may be concordant or discordant with one another.
Other metaphenomena include metajudgments, metacriticisms, metainterpretations, metatexts, metadata (descriptive, administrative, and structural), metacontent, metainformation, meta-analysis, meta-argumentation, and metamodeling.
Language as an object of metatheory may, at the object level, be an object or target language, and at the metalevel, a language about that language (a metalanguage). At the mixed level, it may be both an object language and metalanguage. A metalanguage may have its own syntax (metasyntax), semantics (metasemantics), and pragmatics (metapragmatics).
A metasyntax may be a set of rules or principles that govern the integration of words and phrases into the well-formed sentences of a metalanguage. A metasemantics may be a set of rules or principles that govern the meaning of words and sentences of a metalanguage. A metapragmatics may be a set of rules or principles that govern the use of the words and sentences of a metalanguage in order to fulfill desired social or communicative functions in a given (sociocultural, linguistic, or discursive) context.
Examples of metalinguistic utterances include the sentences: "What I meant to say was 'I wasn't ready.'" "What I thought you meant to say was that you weren't really sure." "Did you say you weren't going to be there?" "What I'm telling you is that you have nothing to worry about." and "That's a very roundabout way of saying something that could be said very straightforwardly."
Meta-emotions may be emotions about our own emotions or the emotions of others. Thus, in some cases we may be remorseful that we were jealous, or we may feel vaguely disquieted that we felt unsympathetic to someone else's being disappointed, or we may even be pleased that someone has been embarrassed or humiliated (schadenfreude may be a meta-emotion). Our own meta-emotions may be concordant or discordant with those of others, depending on whether they feel the same as or different than we do about our emotions and about their own emotions. Meta-emotions may also be integrated into complex emotions whose components may be concordant or discordant with one another.
Other metaphenomena include metajudgments, metacriticisms, metainterpretations, metatexts, metadata (descriptive, administrative, and structural), metacontent, metainformation, meta-analysis, meta-argumentation, and metamodeling.
Language as an object of metatheory may, at the object level, be an object or target language, and at the metalevel, a language about that language (a metalanguage). At the mixed level, it may be both an object language and metalanguage. A metalanguage may have its own syntax (metasyntax), semantics (metasemantics), and pragmatics (metapragmatics).
A metasyntax may be a set of rules or principles that govern the integration of words and phrases into the well-formed sentences of a metalanguage. A metasemantics may be a set of rules or principles that govern the meaning of words and sentences of a metalanguage. A metapragmatics may be a set of rules or principles that govern the use of the words and sentences of a metalanguage in order to fulfill desired social or communicative functions in a given (sociocultural, linguistic, or discursive) context.
Examples of metalinguistic utterances include the sentences: "What I meant to say was 'I wasn't ready.'" "What I thought you meant to say was that you weren't really sure." "Did you say you weren't going to be there?" "What I'm telling you is that you have nothing to worry about." and "That's a very roundabout way of saying something that could be said very straightforwardly."
FOOTNOTES
1"Metatheory," in Wolfram MathWorld (Wolfram Research, Inc., 2019) online at http://mathworld.wolfram.com/Metatheory.html.
2Nicholas Rescher, Metaphilosophy: Philosophy in Philosophical Perspective (Lantham, MD: Lexington Books, 2014), p.xi.
3Peter van Inwagen, "Meta-Ontology," in Erkenntnis, 48 (1998), p. 233.
4Donald Meichenbaum (1985). Teaching thinking: A cognitive-behavioral perspective. In S. F., Chipman, J. W. Segal, & R. Glaser (Eds.), Thinking and learning skills, Vol. 2: Research and open questions. Hillsdale, NJ: Lawrence Erlbaum Associates.
5Michael T. Cox and Anita Raja, Metareasoning: Thinking about Thinking (Cambridge: The MIT Press, 2011), pp. 4-7.
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