The term theory has two broad sets of meanings, one used in the empirical sciences (both natural and social) and the other used in philosophy, mathematics, logic, and across other fields in the humanities. There is considerable difference and even dispute across academic disciplines as to the proper usages of the term. What follows is an attempt to describe how the term is used, not to try to say how it ought to be used.

Although the scientific meaning is by far the more commonly used in academic discourse, it is hardly the only one used, and it would be a mistake to assume from the outset that a given use of the term "theory" in academic literature or discourse is a reference to a scientific or empirically-based theory.

Even so, since the use of the term theory in scientific or empirical inquiry is the more common one, it will be discussed first. (Other usages follow in the section labeled "Theories formally and generally.")

A theory, in the scientific sense of the word, is an analytic structure designed to explain An explanation is a set of statements constructed to describe a set of facts which clarifies the causes, context, and consequences of those facts a set of empirical observations. A scientific theory does two things:

1. it identifies this set of distinct observations as a class of phenomena A phenomenon is any observable occurrence. In popular usage, a phenomenon often refers to an extraordinary event. In scientific usage, a phenomenon is any event that is observable, however commonplace it might be, even if it requires the use of instrumentation to observe it. For example, In physics, a phenomenon may be a feature of matter, energy,, and
2. makes assertions about the underlying reality Reality, in everyday usage, means "the state of things as they actually exist". In a sense it is what is real. The term reality, in its widest sense, includes everything that is, whether or not it is observable or comprehensible. Reality in this sense includes being and sometimes is considered to include nothingness, where existence is that brings about or affects this class.

In the scientific or empirical tradition, the term "theory" is reserved for ideas which meet baseline requirements about the kinds of empirical observations made, the methods of classification used, and the consistency In logic, a consistent theory is one that does not contain a contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if it has a model; this is the sense used in traditional Aristotelian logic, although in contemporary mathematical logic the term of the theory in its application among members of the class to which it pertains. These requirements vary across different scientific fields of knowledge Knowledge is defined by the Oxford English Dictionary as expertise, and skills acquired by a person through experience or education; the theoretical or practical understanding of a subject, (ii) what is known in a particular field or in total; facts and information or (iii) awareness or familiarity gained by experience of a fact or situation, but in general theories are expected to be functional and parsimonious Parsimony is a 'less is better' concept of frugality, economy or caution in arriving at a hypothesis or course of action. The word derives from Middle English parcimony, from Latin parsimonia, from parsus, past participle of parcere: to spare. It is a general principle that has applications from science to philosophy and all related fields: i.e. a theory should be the simplest possible tool that can be used to effectively address the given class of phenomena.

Theories are distinct from theorems In mathematics, a theorem is a statement proved on the basis of previously accepted or established statements such as axioms. In formal mathematical logic, the concept of a theorem may be taken to mean a formula that can be derived according to the derivation rules of a fixed formal system. The statements of a theory as expressed in a formal: theorems are derived A formal proof or derivation is a finite sequence of sentences each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference. The last sentence in the sequence is a theorem of a formal system. The notion of theorem is not in general effective, therefore there may be no method by which we can always find a deductively from theories according to a formal system In formal logic, a formal system consists of a formal language together with a deductive system (also called a deductive apparatus) which consists of a set of inference rules and/or axioms. A formal system is used to derive one expression from one or more other expressions antecedently expressed in the system. These expressions are called axioms, of rules, generally as a first step in testing or applying the theory in a concrete situation. Theories are abstract and conceptual, and to this end they are never considered right or wrong. Instead, they are supported or challenged by observations in the world. They are 'rigorously Rigour or rigor has a number of meanings in relation to intellectual life and discourse. These are separate from public and political applications with their suggestion of laws enforced to the letter, or political absolutism. A religion, too, may be worn lightly, or applied with rigour tentative', meaning that they are proposed as true but expected to satisfy careful examination to account for the possibility of faulty inference or incorrect observation. Sometimes theories are falsified, meaning that an explicit set of observations contradicts some fundamental assumption of the theory, but more often theories are revised to conform to new observations, by restricting the class of phenomena the theory applies to or changing the assertions made. Sometimes a theory is set aside by scholars because there is no way to examine its assertions analytically; these may continue on in the popular imagination until some means of examination is found which either refutes or lends credence to the theory.

The word 'theory' is generally considered to derive from Greek θεωρία theoria Theoria is Greek for contemplation or to view or witness something as a spectator. Within Eastern Orthodox theology it refers to illumination as when one sees and experiences God. It is a particular state of contemplative prayer resulting from the cultivation of watchfulness (Gk: nepsis) achieved by the pure of heart who are no longer subject to (Jerome), Greek "contemplation, speculation", from θεωρός "spectator", θέα thea "a view" + ὁρᾶν horan "to see", literally "looking at a show".^[1] A second possible etymology traces the word back to το θείον to theion "divine things" instead of thea, reflecting the concept of contemplating the divine organisation (Cosmos In its most general sense, a cosmos is an orderly or harmonious system. It originates from a Greek term κόσμος meaning "order, orderly arrangement, ornaments," and is the antithetical concept of chaos. Today the word is generally used as a synonym of the word Universe . The words cosmetics and cosmetology originate from the same) of the nature. The word has been in use in English since at least the late 16th century.^[2]

Theories formally and generally

Theories are analytical tools Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle, though analysis as a formal concept is a relatively recent development for understanding and explaining a given subject matter. There are theories in many different fields of study, and of many different types: from purely syntactic In logic, syntax comprises the rules governing the composition of texts in a formal language that constitute the properly formed formulas of a logical system. In providing an interpretation, it does not make sense to assign a meaning to texts that are not well-formed formulas or 'formal' extrapolations of mathematics or logic, to evidence-driven constructs typical of the physical sciences, to rational/moral analyses found in the social sciences and certain branches of philosophy, and to the interpretive principles found in many arenas of the arts and humanities. Theories are abstract, and may be constructed independently of any semantic Semantics is the study of meaning. The word "semantics" itself denotes a range of ideas, from the popular to the highly technical. It is often used in ordinary language to denote a problem of understanding that comes down to word selection or connotation. This problem of understanding has been the subject of many formal inquiries, over a components, as seen in mathematics, or the syntactic elements may be entirely subordinate the semantic thrust, as is found in post-modernist, post-structuralist, and similar philosophical forms. Theories may be expressed mathematically, symbolically, or in common language, but are generally expected to follow principles of rational thought or logic Logic, from the Greek λογική is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its fundamental place in philosophy. It became part of the classical trivium, a fundamental part of a.

A theory is constructed of a set of sentences which consists entirely of true statements about the subject matter under consideration. However, the truth of any of these statements is always relative to the theory. Therefore the same statement may be true with respect to one theory, and not true with respect to another. This is, in ordinary language, where statements such as "He is a terrible person." cannot be judged to be true or false without reference to some interpretation of who "He" is and for that matter what a "terrible person" is under this theory. ^[3]

Sometimes two theories have exactly the same explanatory power One theory is said to have more explanatory power than another theory about the same subject matter if it can predict and otherwise account for all the facts that the second one does, but also explains the causes of other facts which the second one does not. The opposite of explanatory power is explanatory impotence because they make the same predictions. A pair of such theories is called indistinguishable, and the choice between them reduces to convenience or philosophical preference.

The form of theories is studied formally in mathematical logic Mathematical logic is a subfield of mathematics with close connections to computer science and philosophical logic. The field includes the mathematical study of logic and the applications of formal logic to other areas of mathematics. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the, especially in model theory In mathematics, model theory is the study of mathematical structures such as groups, fields, graphs, or even models of set theory, using tools from mathematical logic. Model theory has close ties to algebra and universal algebra. When theories are studied in mathematics, they are usually expressed in some formal language A formal language is a set of words, i.e. finite strings of letters, or symbols. The inventory from which these letters are taken is called the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar. Formal languages are a purely syntactical notion, so there is not necessarily any meaning and their statements are closed In mathematics, a set is said to be closed under some operation if performance of that operation on members of the set always produces a member of the set. For example, the real numbers are closed under subtraction, but the natural numbers are not: 3 and 7 are both natural numbers, but the result of 3 − 7 is not under application of certain procedures called rules of inference In logic, a rule of inference is a function from sets of formulae to formulae. The argument is called the premise set (or simply premises) and the value the conclusion. They can also be viewed as relations holding between premises and conclusions, whereby the conclusion is said to be inferable (or derivable or deducible) from the premises. If the. A special case of this, an axiomatic theory, consists of axioms In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other truths (or axiom schemata) and rules of inference. A theorem In mathematics, a theorem is a statement proved on the basis of previously accepted or established statements such as axioms. In formal mathematical logic, the concept of a theorem may be taken to mean a formula that can be derived according to the derivation rules of a fixed formal system. The statements of a theory as expressed in a formal is a statement that can be derived from those axioms by application of these rules of inference. Theories used in applications are abstractions Abstraction is the process or result of generalization by reducing the information content of a concept or an observable phenomenon, typically in order to retain only information which is relevant for a particular purpose. For example, abstracting a leather soccer ball to a ball retains only the information on general ball attributes and behaviour of observed phenomena and the resulting theorems provide solutions to real-world problems. Obvious examples include arithmetic Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. In common usage, the word refers to a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on (abstracting concepts of number), geometry Geometry is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the third century BC geometry was put into an axiomatic form by Euclid, whose treatment� (concepts of space), and probability Probability, or chance, is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the (concepts of randomness and likelihood).

Gödel's incompleteness theorem In mathematical logic, Gödel's incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. The theorems are of considerable importance to the philosophy of mathematics. They are widely regarded as showing that Hilbert's shows that no consistent, recursively enumerable theory (that is, one whose theorems form a recursively enumerable set) in which the concept of natural numbers In mathematics,there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional definition or the set of non-negative integers {0, 1, 2, ...} according to a formal definition laid in 19th century can be expressed, can include all true The word truth has a variety of meanings, from honesty, good faith, and sincerity in general, to agreement with fact or reality in particular. The term has no single definition about which a majority of professional philosophers and scholars agree, and various theories of truth continue to be debated. There are differing claims on such questions statements about them. As a result, some domains of knowledge cannot be formalized, accurately and completely, as mathematical theories. (Here, formalizing accurately and completely means that all true propositions—and only true propositions—are derivable within the mathematical system.) This limitation, however, in no way precludes the construction of mathematical theories that formalize large bodies of scientific knowledge.

Philosophical theories

Theories whose subject matter consists not in empirical data, but rather in ideas In the most narrow sense, an idea is just whatever is before the mind when one thinks. Very often, ideas are construed as representational images; i.e. images of some object. In other contexts, ideas are taken to be concepts, although abstract concepts do not necessarily appear as images. Many philosophers consider ideas to be a fundamental are in the realm of philosophical theories as contrasted with scientific theories. At least some of the elementary theorems of a philosophical theory are statements whose truth cannot necessarily be scientifically tested through empirical observation In philosophy, empiricism is a theory of knowledge which asserts that knowledge arises from experience. Empiricism is one of several competing views about how we know "things," part of the branch of philosophy called epistemology, or "the Theory of Knowledge". Empiricism emphasizes the role of experience and evidence,.

Metatheory

One form of philosophical theory is a metatheory or meta-theory. A metatheory is a theory whose subject matter is some other theory. In other words it is a theory about a theory. Statements In logic a statement is a declarative sentence that is either true or false. Strawson however advocated the use of the term statement and for it to be such that two declarative sentences make the same statement if they say the same of the same thing. Thus the term "statement" may to refer to a sentence or something made (expressed) by a made in the metatheory about the theory are called metatheorems.

Political theories

A political theory is an ethical Ethics is a branch of philosophy which seeks to address questions about morality, such as what the fundamental semantic, ontological, and epistemic nature of ethics or morality is , how moral values should be determined (normative ethics), how a moral outcome can be achieved in specific situations (applied ethics), how moral capacity or moral theory about the law and government. Often the term "political theory" refers to a general view, or specific ethic, political belief or attitude, about politics Politics is a process by which groups of people make decisions. The term is generally applied to behaviour within civil governments, but politics has been observed in all human group interactions, including corporate, academic, and religious institutions. It consists of "social relations involving authority or power" and refers to the.

Scientific theories

In the sciences Science refers to any systematic knowledge-base or prescriptive practice that is capable of resulting in a prediction or predictable type of outcome. In this sense, science may refer to a highly skilled technique or practice generally, theories are constructed from elementary theorems that consist in empirical data about observable phenomena. A scientific theory is used as a plausible general principle or body of principles offered to explain a phenomenon.^[4]

A scientific theory is a deductive theory, in that, its content is based on some formal system of logic In formal logic, a formal system consists of a formal language together with a deductive system (also called a deductive apparatus) which consists of a set of inference rules and/or axioms. A formal system is used to derive one expression from one or more other expressions antecedently expressed in the system. These expressions are called axioms, and that some of its elementary theorems are taken as axioms In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other truths. In a deductive theory, any sentence which is a logical consequence Logical consequence is a fundamental concept in logic. It is the relation that holds between a set of sentences and a sentence (proposition) when the former "entails" the latter. For example, 'Kermit is green' is said to be a logical consequence of 'All frogs are green' and 'Kermit is a frog', because it would be "self-contradictory& of one or more of the axioms is also a sentence of that theory.^[3]

A major concern in construction of scientific theories is the problem of demarcation The demarcation problem in the philosophy of science is about how and where to draw the lines around science. The boundaries are commonly drawn between science and non-science, between science and pseudoscience, and between science and religion. A form of this problem, known as the generalized problem of demarcation subsumes all three cases. The, i.e., distinguishing those ideas that are properly studied by the sciences and those that are not.

Theories are intended to be an accurate, predictive description of the natural world. However, it is sometimes not clear whether the conclusions derived from the theory inform us about the nature of the world, or the nature of the theory.

Theories as models

Theories are constructed to explain, predict, and master phenomena (e.g., inanimate things, events, or behavior of animals). A scientific theory can be thought of as a model Scientific modelling is the process of generating abstract, conceptual, graphical and/or mathematical models. Science offers a growing collection of methods, techniques and theory about all kinds of specialized scientific modelling. Also a way to read elements easily which have been broken down to the simplest form of reality Reality, in everyday usage, means "the state of things as they actually exist". In a sense it is what is real. The term reality, in its widest sense, includes everything that is, whether or not it is observable or comprehensible. Reality in this sense includes being and sometimes is considered to include nothingness, where existence is, and its statements as axioms In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other truths of some axiomatic system In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A mathematical theory consists of an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system; usually though the effort towards. The aim of this construction is to create a formal system for which reality is the only model. The world is an interpretation (or model) of such scientific theories, only insofar as the sciences are true.

Theories in physics

In physics the term theory is generally used for a mathematical framework—derived from a small set of basic postulates (usually symmetries—like equality of locations in space or in time, or identity of electrons, etc.)—which is capable of producing experimental predictions for a given category of physical systems. A good example is classical electromagnetism, which encompasses results derived from gauge symmetry (sometimes called gauge invariance) in a form of a few equations called Maxwell's equations. Note that the specific theoretical aspects of classical electromagnetic theory, which have been consistently and successfully replicated for well over a century, are termed "laws of electromagnetism", reflecting that they are today taken for granted. Within electromagnetic theory generally, there are numerous hypotheses about how electromagnetism applies to specific situations. Many of these hypotheses are already considered to be adequately tested, with new ones always in the making and perhaps untested.

Pedagogical definition

In pedagogical contexts or in official pronouncements by official organizations of scientists a definition such as the following may be promulgated.

According to the United States National Academy of Sciences,

Some scientific explanations are so well established that no new evidence is likely to alter them. The explanation becomes a scientific theory. In everyday language a theory means a hunch or speculation. Not so in science. In science, the word theory refers to a comprehensive explanation of an important feature of nature supported by facts gathered over time. Theories also allow scientists to make predictions about as yet unobserved phenomena, ^[5]

A scientific theory is a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment. Such fact-supported theories are not "guesses" but reliable accounts of the real world. The theory of biological evolution is more than "just a theory." It is as factual an explanation of the universe as the atomic theory of matter or the germ theory of disease. Our understanding of gravity is still a work in progress. But the phenomenon of gravity, like evolution, is an accepted fact.^[6]

The primary advantage enjoyed by this definition is that it firmly marks things termed theories as being well supported by evidence. This would be a disadvantage in interpreting real discourse between scientists who often use the word theory to describe untested but intricate hypotheses in addition to repeatedly confirmed models. However, in an educational or mass media setting it is almost certain that everything of the form X theory is an extremely well supported and well tested theory. This causes the theory/non-theory distinction to much more closely follow the distinctions useful for consumers of science (e.g. should I believe something or not?)

The term theoretical

The term theoretical is sometimes informally used in place of hypothetical to describe a result that is predicted by theory but has not yet been adequately tested by observation or experiment. It is not uncommon for a theory to produce predictions that are later confirmed or proven incorrect by experiment. By inference, a prediction proved incorrect by experiment demonstrates the hypothesis is invalid. This either means the theory is incorrect, or the experimental conjecture was wrong and the theory did not predict the hypothesis.

Fields of study called "theories"

Fields of study are sometimes named "theory" because their basis is some initial set of assumptions describing the field's approach to a subject matter. These assumptions are the elementary theorems of the particular theory, and can be thought of as the axioms of that field. Some commonly known examples include set theory, game theory, and number theory; however literary theory, critical theory, and music theory are also of the same form.

Intertheoretic reduction and elimination

If there is a new theory which is better at explaining and predicting phenomena than an older theory (i.e. it has more explanatory power), we are justified in believing that the newer theory describes reality more correctly. This is called an intertheoretic reduction because the terms of the old theory can be reduced to the terms of the new one. For instance, our historical understanding about "sound," "light" and "heat," have today been reduced to "wave compressions and rarefactions," "electromagnetic waves," and "molecular kinetic energy" respectively. These terms which are identified with each other are called intertheoretic identities. When an old theory and a new one are parallel in this way, we can conclude that we are describing the same reality, only more completely.

In cases where a new theory uses new terms which do not reduce to terms of an older one, but rather replace them entirely because they are actually a misrepresentation it is called an intertheoretic elimination. For instance, the obsolete scientific theory that put forward an understanding of heat transfer in terms of the movement of caloric fluid was eliminated when a theory of heat as energy replaced it. Also, the theory that phlogiston is a substance released from burning and rusting material was eliminated with the new understanding of the reactivity of oxygen.

Underdetermination

A theory is underdetermined (also called indeterminacy of data to theory) if, given the available evidence cited to support the theory, there is a rival theory which is inconsistent with it that is at least as consistent with the evidence. Underdetermination is an epistemological issue about the relation of evidence to conclusions.

List of notable theories

Textbooks from Wikibooks Quotations from Wikiquote Source texts from Wikisource Images and media from Commons News stories from Wikinews

• Astronomy: Big Bang Theory
• Biology: Cell theory — Evolution
• Chemistry: Atomic theory — Kinetic theory of gases
• Climatology: Theory of Global Climate Change (due to anthropogenic activity)
• Computer science: Algorithmic information theory — Computation theory
• Economics: Decision theory
• Education: Constructivist theory — Critical pedagogy theory — Education theory — Multiple intelligence theory — Progressive education theory
• Engineering: Circuit theory — Control theory — Signal theory — Systems theory
• Film: Film Theory
• Games: Combinatorial game theory — Game theory — Rational choice theory
• Geology: Plate tectonics
• Humanities: Critical theory
• Literature: Literary theory
• Mathematics: Catastrophe theory — Category theory — Chaos theory — Graph theory — Knot theory — Number theory — Probability theory — Set theory
• Music: Music theory
• Philosophy: Proof theory — Speculative reason — Theory of truth — Type theory — Value theory — Virtue theory
• Physics: Acoustic theory — Antenna theory — BCS theory — Landau theory — Theory of relativity — Quantum field theory
• Planetary science: Giant impact theory
• Visual Art: Aesthetics — Art Educational theory — Architecture — Composition — Anatomy — Color theory — Perspective — Visual perception — Geometry — Manifolds
• Sociology: Sociological theory — Social theory — Critical theory
• Sports: Chess theory
• Statistics : Extreme value theory
• Theatre : Theory relating to theatrical performance.
• Other: Obsolete scientific theories — Phlogiston theory

See also

• List of theories
• Falsifiability
• Formal language
• Formal system
• Hypothesis
• Hypothesis testing
• Model
• Predictive power
• Scientific method
• Testability

Notes

1. ^ Frisk; derivation from θεός was suggested by Koller Glotta 36, 273ff.
2. ^ Harper, Douglas. "theory". Online Etymology Dictionary. http://www.etymonline.com/index.php?term=theory. Retrieved on 2008-07-18.
3. ^ ^{a b} Curry, Haskell, Foundations of Mathematical Logic
4. ^ Merriam-Webster.com Merriam-Webster Dictionary: Theory in Science
5. ^ National Academy of Sciences (2005), Science, Evolution, and Creationism, a brochure on the book of the same title.
6. ^ AAAS Evolution Resources

References

• Popper, Karl (1963), Conjectures and Refutations, Routledge and Kegan Paul, London, UK, pp. 33–39. Reprinted in Theodore Schick (ed., 2000), Readings in the Philosophy of Science, Mayfield Publishing Company, Mountain View, Calif., pp. 9–13.
• Chairman of Biology and Kennesaw State Ronald Matson's webpage comparing scientific laws and theories
• Hawking, Stephen (1996). "The Illustrated A Brief History of Time" (Updated and expanded ed.). New York: Bantam Books, p. 15.
• Mohr, Johnathon (2008). "Revelations and Implications of the Failure of Pragmatism: The Hijacking of Knowledge Creation by the Ivory Tower". New York: Ballantine Books. pp. 87–192.

Categories: Mathematical terminology | Mental structures | Philosophy of science | Scientific method | Theories | Greek loanwords

See Also:

• Theory
• Trait Theory
• Theoretical Physicist
• Psychoanalytic Theory
• Theories of Aesthetics

What Links Here:

Recently Viewed Pages:

• Trait Theory: Encyclopedia
• Idea: Encyclopedia
• Creativeness: Dictionary
• Design Research: Encyclopedia
• Art: Encyclopedia
• Creativity Techniques: Encyclopedia
• Encyclopedia: NetBSD
• Henry Moore: Blogs

Most Popular Pages:

• Henry Moore: Blogs
• Creativity Techniques: Encyclopedia
• Creativeness: Dictionary
• Art: Encyclopedia
• Design Research: Encyclopedia
• Idea: Encyclopedia
• Trait Theory: Encyclopedia
• Theory: Encyclopedia

Related 'Theory' Searches: