A metatheory or meta theory is a theory whose subject matter is some other theory. In other words it is a theory about a theory. Statement logic Statements made in the metatheory about the theory are called metatheorem s. The following is an example of a meta theoretical statement ref Stephen Hawking in A Brief History of Time ref cquote Any physical theory is always provisional, in the sense that it is only a hypothesis you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory. Meta theory belongs to the philosophy philosophical specialty of epistemology and metamathematics , as well as being an object of concern to the area in which the individual theory is conceived. An emerging domain of meta theories is systemics . Taxonomy Examining groups of related theories, a first finding may be to identify classes of theories, thus specifying a taxonomy of theories. A proof engendered by a metatheory is called a metatheorem . History The concept burst upon the scene of 20th century philosophy as a result of the work of the Germany German Mathematics mathematician David Hilbert , who in 1905 published a proposal for proof of the consistency of mathematics, creating the field of metamathematics . His hopes for the success of this proof were dashed by the work of Kurt G del who in 1931 proved this to be unattainable by his G del s incompleteness theorems incompleteness theorems . 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 ... Flint Category Metaphilosophy Category Epistemology Category Theories Category Metatheory cs Metateorie ... more details
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 . Discussion A formal system is determined by a formal language and a deductive system axiom s and rules of inference . The formal system can be used to prove particular sentences of the formal language with that system. Metatheorems, on the other hand, are proved externally to the system in question, in its metatheory. Common metatheories used in logic are set theory especially in model theory and primitive recursive arithmetic especially in proof theory . Rather than demonstrating particular sentences to be provable, metatheorems may show that each of a broad class of sentences can be proved, or show that certain sentences cannot be proved. Examples Examples of metatheorems include The deduction theorem for first order logic says that a sentence of the form &phi &rarr &psi is provable from a set of axioms A if and only if the sentence &psi is provable from the system whose axioms consist of &phi and all the axioms of A . Consistency proof s of systems such as Peano arithmetic See also Metamathematics Use mention distinction References Geoffrey Hunter logician Geoffrey Hunter 1969 , Metalogic . Alasdair Urquhart 2002 , Metatheory , A companion to philosophical logic , Dale Jacquette ed. , p. 307 External links MathWorld urlname Metatheorem title Metatheorem author Barile, Margherita logic Category Metalogic Category Mathematical terminology Category Metatheorems nl Metastelling ... more details
The Law of the Infinite Cornucopia , put forth by Poland Polish philosopher Leszek Ko akowski suggests that for any given doctrine one wants to believe, there is never a shortage of arguments by which one can support it. A history historian s application of this law might be that a plausible cause can be found for any given historical development. A biblical theology theologian s application of this law might be that for any doctrine one wants to believe, there is never a shortage of biblical evidence to support it. See also Niven s Laws No. 17 Category Metatheory Category Principles philo stub ... more details
Unreferenced stub auto yes date December 2009 Inductionism is the Philosophy of science scientific philosophy where laws are induction philosophy induced from sets of data. As an example, one might measure the strength of electrical forces at varying distances from charges and induce the inverse square law of electrostatics . See also Inductive reasoning Category Metatheory of science Category Inductive reasoning Philo stub pl Indukcjonizm sk Indukcionizmus ... more details
Unreferenced stub auto yes date December 2009 Orphan date February 2009 A received view is any world view that is taken for granted or that is assumed to be true without further criticism by the part of the receiver until he or she manages to unhide it, e.g. by getting to know another contrasting worldview. The expression is usually used by other philosophical schools to refer to the logical positivist view see, for instance, the received view of theories . DEFAULTSORT Received View Philo stub Category Philosophical theories Category Metatheory ... more details
orphan date August 2009 Contextual empiricism is a theory about validating scientific knowledge. It is the view that scientific knowledge is shaped by contextualism contextual values as well as constitutive ones. ref Janet Kourany, Scientific Knowledge ref See also Scientific theory Helen Longino References reflist DEFAULTSORT Contextual Empiricism Category Empiricism Category Metatheory of science philosophy stub ... more details
strength the metatheory in which the discussion takes places needs to be carefully addressed ... a set theoretic statement A is said to be equiconsistent to another B, what is being claimed is that in the metatheory ... B are equiconsistent. Usually, primitive recursive arithmetic can be adopted as the metatheory in question, but even if the metatheory is ZFC or an extension of it, the notion is meaningful. Thus, the method ... more details
The received view of theories is a position in the philosophy of science that identifies a scientific theory with a set of propositions which are considered to be linguistic objects, such as axiom axioms . Frederick Suppe describes the position of the received view by saying that it identifies scientific theories with an axiomatic calculi in which theoretical terms are given a partial observation interpretation by mean of correspondence rules. ref Suppe, Frederick 1989 , The Semantic Conception of Theories and Scientific Realism. Urbana University of Illinois Press. p. 38 ref The received view is generally associated with the logical positivism logical empiricists . Recently, the received view of theories has been displaced by the semantic view of theories as the dominant position in theory formulation in the philosophy of science. Notes references philosophy of science philo stub Category Metatheory of science Category Logical positivism ... more details
saved book title Logic and Metalogic subtitle cover image cover color Logic and Metalogic Main article Logic History History of logic Topics in logic Term logic Aristotelian logic Propositional calculus Predicate logic Modal logic Informal logic Mathematical logic Algebraic logic Multi valued logic Fuzzy logic Metatheory Metalogic Philosophical logic Logic in computer science Controversies in logic Principle of bivalence Paradoxes of material implication Paraconsistent logic Is logic empirical? Category Wikipedia books on logic Logic Category Wikipedia books on computer science ... more details
for the term as used in computer science Metasyntactic variable In logic , a metavariable also metalinguistic variable ref Geoffrey Hunter logician Geoffrey Hunter , Metalogic An Introduction to the Metatheory of Standard First Order Logic p.13 ref or syntactical variable ref Citation page 7 last1 Shoenfield first1 Joseph R. title Mathematical Logic origyear 1967 publisher A K Peters edition 2nd isbn 978 1 56881 135 2 year 2001 ref is a symbol formal symbol or symbol string which belongs to a metalanguage and stands for elements of some object language . For instance, in the sentence Let A and B be two sentences of a language the symbols A and B are part of the metalanguage in which the statement about the object language is formulated. References Reflist Category Metalogic Category Variables Category Syntax logic ... more details
Na ve empiricism is a term used in several ways in different fields. In the philosophy of science , it is used by opponents to describe the position, associated with some logical positivist s, that knowledge can be clearly learnt through evaluation of the natural world and its substances, and, through empirical means, learn truths . ref cite book author Thomas Ernst Uebel title Overcoming Logical Positivism from Within The Emergence of Neurath s Naturalism in the Vienna Circle s Protocol Sentence Debate pages 205 year 1992 publisher Rodopi ref The term also is used to describe a particular methodology for literary analysis . ref cite book author Michael McKeon title The Origins of the English novel pages 105 109 year 1986 publisher Johns Hopkins University Press ref See also Empiricism Falsifiability especially, Falsifiability Na.C3.AFve falsification Na ve falsification References reflist DEFAULTSORT Naive Empiricism Category Empiricism Category Epistemological theories Category Metatheory of science epistemology stub ... more details
In philosophy and particularly political philosophy , theoreticism is the preference for theory over practice or, more broadly, abstract knowledge over concrete action , or a philosophical position which would lead to such a preference. The term is often used pejoratively. In Marxist philosophy , for instance, theoreticism is often identified as a political error, valorizing the efforts of academic Marxism over those of revolutionary struggle. Louis Althusser , for instance, criticized his own early work for theoreticism. In Phenomenology philosophy phenomenology , theoreticism would be something closer to the over valuing of knowledge at the cost of losing a proper appreciation of experience . Martin Heidegger claimed this trend was begun by Plato , and that it continued in an intensification and hardening of theoreticism , the drive toward technical and objectifying modes of knowledge and, with it, the oblivion of any more primordial or more reverential kind of existence. External links http www.morose.fsnet.co.uk reviews Clark Heidegger.htm Heidegger source Category Metatheory Category Philosophical theories Category Political theories Philo stub ... more details
Orphan date February 2009 Refimprove date July 2007 The Domon Group, or Domon Research Group, is an interdisciplinary research Groups of people group founded by former IBM researcher Eduard Domon in 1973. The group is organized in a loose affiliation of scientists, artists, and activists in laboratories and studios around the world. ref DRG Restricted Media, 1984 Vol.2 ref The Domon Group s research is wide ranging, but is generally concerned with issues in artificial intelligence , information theory , self organizing systems and language . The distributed structure of the group has helped maintain the relative anonymity of members, while providing support and community to researchers working at the fringes of established fields. While there is no available master list of members, former members are believed to include Shawn Brixey of DXARTS at University of Washington , Jacque Servin of the Yes Men , and the model and philosopher Lorianna Tuck. ref Distributed Research Models and Postmodern Critical Theory, Metatheory. Summer Quarter 1999 ref It has also been suggested that Domon Group members have a relatively strong presence in the research department of Google . References references Category Working groups ... more details
Structuralism structural theory of the empirical sciences is a theory of science , reconstructing scientific theory empirical theories . Its aim is to comprise all important aspects of an empirical theory in one formal framework. The proponents of this meta theoretic theory are Patrick Suppes , Joseph D. Sneed , Wolfgang Stegm ller , Carlos Ulises Moulines and Wolfgang Balzer . References J.D. Sneed, The Logical Structure of Mathematical Physics . Reidel, Dordrecht, 1971 revised edition 1979 . W. Balzer, C.U. Moulines, J.D. Sneed, An Architectonic for Science the Structuralist Approach . Reidel, Dordrecht, 1987. Frederick Suppe ed., The structure of scientific theories symposium, 1969, Urbana, Ill. outgrowth with a critical introduction and an afterword by Frederick Suppe , University of Illinois Press, 1977. External links http plato.stanford.edu entries physics structuralism Stanford Encyclopedia of Philosophy Structuralism in Physics Category Scientific method Category Metatheory of science Category Structuralism de Strukturalistisches Theorienkonzept ... more details
Definitionism also called the classical theory of concepts ref Cite book title A Brief Introduction to the Philosophy of Mind author Jack S. Crumley publisher Rowman & Littlefield date 2006 page 150 location Lanham, Maryland isbn 0742544966 ref is the school of thought in which it is believed that a proper explanation of a theory consists of all the concept s used by that theory being Well definition well defined . ref Cite book title Philosophy of physics author Mario Augusto Bunge publisher Springer Science & Business date 1973 page 135 location Boston isbn 9027702535 ref This approach has been criticized for its dismissal of the importance of ostensive definition s. ref Cite book title Modern Methods and Materials for Teaching Science author Elwood D. Heiss publisher Read Books date 2007 page 23 isbn 1406738301 ref References reflist Category Definition Category Philosophical theories Category Metatheory philosophy stub ... more details
Hunter logician Hunter, Geoffrey . 1971. Metalogic An Introduction to the Metatheory of Standard First ... math mathcal L math . Metatheories and metatheorems Main Metatheory Main Metatheorem A metatheory ... Statements made in the metatheory about the theory are called metatheorem s. A metatheorem is a truth ... formal system, a metatheorem is proved within a metatheory , and may reference concepts that are present in the metatheory but not the object theory . ref George Ritzer Ritzer, George . 1991. Metatheorizing ... more details
Constructive realism is a branch of philosophy , specifically the philosophy of science . It was developed in the late 1980s by Friedrich Wallner also Fritz Wallner in Vienna. In his paper abstract on constructive realism, Wallner describes it as follows Traditional convictions regarding science such as universalism, necessity and eternal validity are currently in doubt. Relativism seems to destroy scientific claims to rationality. This paper shows a way to keep the traditional convictions of scientific knowledge while acknowledging relativism. With reference to the practicing scientist, we replace descriptivism with constructivism we modify relative validity with the claim to understanding and, we offer methodological strategies for acquiring understanding. These strategies we call strangification, which means taking a scientific proposition system out of its context and putting it in another context. We can thus see the implicit presuppositions of the given proposition system by means of the problems arising out of the application of this procedure. Such a change in the understanding of science holds important consequences. External links http www.bu.edu wcp Papers Scie ScieWall.htm top A complete description of constructive realism http homepage.univie.ac.at friedrich.wallner Home page of Friedrich Wallner philosophy stub Category Constructivism Category Realism Category Metatheory of science de Konstruktiver Realismus fi Konstruktiivinen realismi ... more details
A deductive system also called a deductive apparatus of a formal system consists of the axiom s or axiom schema ta and rules of inference that can be used to formal proof derive the theorem s of the system. ref Hunter, Geoffrey, Metalogic An Introduction to the Metatheory of Standard First Order Logic, University of California Pres, 1971 ref Such a deductive system is intended to preserve deductive reasoning deductive qualities in the formula mathematical logic formula s that are expressed in the system. Usually the quality we are concerned with is truth as opposed to falsehood. However, other modal logic modalities , such as Theory of justification justification or belief may be preserved instead. In order to sustain its deductive integrity, a deductive apparatus must be definable without reference to any intended interpretation of the language. The aim is to ensure that each line of a Mathematical proof derivation is merely a syntactic consequence of the lines that precede it. There should be no element of any Interpretation logic interpretation of the language that gets involved with the deductive nature of the system. See also Formal grammar Natural deduction Axiomatic system Proof calculus References reflist logic Category Syntactic entities Category Proof theory Category Deduction Category Formal systems el es Sistema deductivo nl Deductief systeem pt Sistema dedutivo ... more details
In mathematics, constructive nonstandard analysis is a version of Abraham Robinson s non standard analysis , developed by Moerdijk 1995 , Palmgren 1998 , Ruokolainen 2004 . Ruokolainen wrote The possibility of constructivization of nonstandard analysis was studied by Palmgren 1997, 1998, 2001 . The model of constructive nonstandard analysis studied there is an extension of Moerdijk s 1995 model for constructive nonstandard arithmetic. See also Smooth infinitesimal analysis John Lane Bell References Ieke Moerdijk , A model for intuitionistic nonstandard arithmetic , Annals of Pure and Applied Logic, vol. 73 1995 , pp. 37&ndash 51. Abstract This paper provides an explicit description of a model for intuitionistic non standard arithmetic, which can be formalized in a constructive metatheory without the axiom of choice. http www.sciencedirect.com science journal 01680072 Erik Palmgren , Developments in Constructive Nonstandard Analysis , Bull. Symbolic Logic Volume 4, Number 3 1998 , 233&ndash 272. Abstract We develop a constructive version of nonstandard analysis, extending Errett Bishop Bishop s constructive analysis with infinitesimal methods. ... http projecteuclid.org euclid.bsl 1182353577 Juha Ruokolainen 2004, Constructive Nonstandard Analysis Without Actual Infinity https oa.doria.fi bitstream handle 10024 2865 construc.pdf Category Non standard analysis mathlogic stub ... more details
this is being done in the language of the metatheory see below Given the system O, , O , , , , , , ..., sup ... in the metatheory. Kurt Godel 1931 virtually constructed the entire proof of his incompleteness ... of genetic versus axiomatic methods clears this up these are issues to be discussed in the metatheory ... of the axioms and or propositions to another proposition. Informal theory, object theory, and metatheory A metatheory exists outside the formalized object theory the meaningless symbols and relations and well formed strings of symbols. The metatheory comments on describes, interprets, illustrates these meaningless objects using intuitive notions and ordinary language . Like the object theory, the metatheory ... of objects and rules are intuitive rather than formal. Kleene requires that the methods of a metatheory ... b the formal system or object theory , and c the metatheory, in which the formal system ... more details
refimprove date January 2012 Wikify date December 2009 Scientific essentialism , a view espoused by Saul Kripke and Hilary Putnam , ref Cite jstor 2653754 ref maintains that there exist essential properties that objects possess or instantiate necessarily. In other words, having such and such essential properties is a necessary condition for membership in a given natural kind. For example, tigers are tigers in virtue of possessing a particular set of genetic properties, but identifying or appearance based properties are nonessential properties. If a tiger lost a leg, or didn t possess stripes, we would still call it a tiger. They are not necessary for being a member of the class of tigers. It is important, however, that the set of essential properties of an object not be used to identify or be identified with that object because they are not necessary and sufficient , but only necessary. Having such and such a genetic code does not suffice for being a tiger. We wouldn t call a piece of tiger fur a tiger, even though a piece of tiger fur contains the genetic information essential to being a tiger. Other advocates of scientific essentialism include Brian David Ellis Brian Ellis , ref Citation publisher Cambridge University Press isbn 9780521037747 title Scientific Essentialism Cambridge Studies in Philosophy url http openlibrary.org books OL7715358M Scientific Essentialism Cambridge Studies in Philosophy author Brian Ellis publication date July 23, 2007 oclc 124025546 id 0521037743 ref Caroline Lierse , ref name BJPoS1992 Cite jstor 687764 ref John Bigelow , ref name BJPoS1992 and Alexander Bird . ref Citation publisher Oxford University Press, USA isbn 9780199227013 title Nature s Metaphysics url http openlibrary.org books OL10145956M Nature s Metaphysics author Alexander Bird publication date August 31, 2007 id 0199227012 ref References Reflist DEFAULTSORT Scientific Essentialism Category Metatheory of science Category Contemporary philosophy Category Essentialism ... more details
Multiple issues one source November 2008 cleanup November 2008 refimprove November 2008 Metaknowledge or meta knowledge is knowledge about a preselected knowledge. For the reason of different definitions of knowledge in the subject matter literature, meta information is or is not included in meta knowledge. Detailed cognitive, systemic and epistemology epistemic study of human knowledge requires a distinguishing of these concepts. but in the common language knowledge includes information, and, for example, bibliographic data are considered as a meta knowledge. Meta knowledge is a fundamental conceptual instrument in such research and scientific domains as, knowledge engineering , knowledge management , and others dealing with study and operations on knowledge, seen as a unified object philosophy object entities, abstracted from local conceptualizations and terminologies. Examples of the first level individual meta knowledge are methods of planning, modeling, knowledge tags tagging , learning and every modification of a domain knowledge . Of course, universal meta knowledge frameworks have to be valid for the organization of meta levels of individual meta knowledge. Put simpler, metaknowledge may be linked to knowledge you need but you don t yet possess it is a cluster of definitions and methods aiming to guide you in gathering the pertinent knowledge with regard to your activity. See also Epistemic logic Knowledge Meta Metaprogramming in Computer Science Metahistory , a book by Hayden White Meta philosophy Meta epistemology Metalogic Metamathematics Metaphysics Meta ethics Meta ontology Metatheory meta theory Metadata No footnotes date December 2009 Reflist External links http logic.stanford.edu kif metaknowledge.html Knowledge Interchange Format Reference Manual Chapter 7 Metaknowledge, Stanford University http ai.eecs.umich.edu cogarch0 common prop metaknow.html A Survey of Cognitive and Agent Architectures Meta knowledge, University of Michigan Category Knowledge ... more details
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