Theory

The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria,, meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action. Theory is especially often contrasted to "practice" (from Greek praxis, πρᾶξις) an Aristotelian concept which is used in a broad way to refer to any activity done for the sake of action, in contrast with theory, which does not need an aim which is an action. By extension of the philosophical meaning, "theoria" is also a word still used in theological contexts.

A classical example of the distinction between theoretical and practical uses the discipline of medicine: Medical theory and theorizing involves trying to understand the causes and nature of health and sickness, while the practical side of medicine is trying to make people healthy. These two things are related but can be independent, because it is possible to research health and sickness without curing specific patients, and it is possible to cure a patient without knowing how the cure worked.

In modern contexts, while theories in the arts and philosophy may address ideas and empirical phenomena which are not easily measurable, in modern science the term "theory", or "scientific theory" is generally understood to refer to a proposed explanation of empirical phenomena, made in a way consistent with scientific method. Such theories are preferably described in such a way that any scientist in the field is in a position to understand and either provide empirical support ("verify") or empirically contradict ("falsify") it. In this modern scientific context the distinction between theory and practice corresponds roughly to the distinction between theoretical science and technology or applied science. A common distinction sometimes made in science is between theories and hypotheses, with the former being considered as satisfactorily tested or proven and the latter used to denote conjectures or proposed descriptions or models which have not yet been tested or proven to the same standard.

Other ancient uses
The word apparently developed special uses early in the Greek language. In the book, From Religion to Philosophy, Francis Cornford suggests that the Orphics used the word "theory" to mean 'passionate sympathetic contemplation'. Pythagoras changed the word to mean a passionate sympathetic contemplation of mathematical and scientific knowledge. This was because Pythagoras considered such intellectual pursuits the way to reach the highest plane of existence. Pythagoras emphasized subduing emotions and bodily desires in order to enable the intellect to function at the higher plane of theory. Thus it was Pythagoras who gave the word "theory" the specific meaning which leads to the classical and modern concept of a distinction between theory as uninvolved, neutral thinking, and practice.

Theories formally and scientifically
Theories are analytical tools for understanding, explaining, and making predictions about a given subject matter. There are theories in many and varied fields of study, including the arts and sciences. A formal theory is syntactic in nature and is only meaningful when given a semantic component by applying it to some content (i.e. facts and relationships of the actual historical world as it is unfolding). Theories in various fields of study are expressed in natural language, but are always constructed in such a way that their general form is identical to a theory as it is expressed in the formal language of mathematical logic. Theories may be expressed mathematically, symbolically, or in common language, but are generally expected to follow principles of rational thought or logic.

Theory is constructed of a set of sentences which consist entirely of true statements about the subject matter under consideration. However, the truth of any one of these statements is always relative to the whole 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 the theory.

Sometimes two theories have exactly the same explanatory power 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, especially in model theory. When theories are studied in mathematics, they are usually expressed in some formal language and their statements are closed under application of certain procedures called rules of inference. A special case of this, an axiomatic theory, consists of axioms (or axiom schemata) and rules of inference. A theorem is a statement that can be derived from those axioms by application of these rules of inference. Theories used in applications are abstractions of observed phenomena and the resulting theorems provide solutions to real-world problems. Obvious examples include arithmetic (abstracting concepts of number), geometry (concepts of space), and probability (concepts of randomness and likelihood).

Gödel's incompleteness theorem shows that no consistent, recursively enumerable theory (that is, one whose theorems form a recursively enumerable set) in which the concept of natural numbers can be expressed, can include all true 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.

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.

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.

Theories vs. theorems
Theories are distinct from theorems. Theorems are derived deductively from assumptions according to a formal system of rules, sometimes as an end in itself and sometimes as a first step in testing or applying a theory in a concrete situation; theorems are said to be true in the sense that the conclusions of a theorem are logical consequences of the assumptions. Theories are abstract and conceptual, and to this end they are never considered true. Instead, they are supported or challenged by observations in the world. They are 'rigorously 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 or prediction 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 hypothesis never reaches the point of being considered a theory because there is no way to derive its assertions analytically or no way to test them empirically.

Philosophical theories
Theories whose subject matter consists not in empirical data, but rather in ideas 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.

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 and number theory; however literary theory, critical theory, and music theory are also of the same form.

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 made in the metatheory about the theory are called metatheorems.

Political theories
A political theory is an ethical 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.

Scientific theories
In scientific usage, the term "theory" is reserved for explanations of phenomena which meet basic requirements about the kinds of empirical observations made, the methods of classification used, and the consistency of the theory in its application among members of the class to which it pertains. These requirements vary across different scientific fields of knowledge, but in general theories are expected to be functional and parsimonious: i.e. a theory should be the simplest possible tool that can be used to effectively address the given class of phenomena. Such theories are constructed from elementary assumptions that are motivated by empirical data about observable phenomena. A scientific theory is used as a plausible general principle or body of principles offered to explain a phenomenon.

A scientific theory is a deductive theory, in that its content is based on some formal system of logic and on basic axioms. In a deductive theory, any sentence which is a logical consequence of one or more of the axioms is also a sentence of that theory.

A major concern in construction of scientific theories is the problem of demarcation, 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.

Theories as models
Scientific theories are constructed to explain and predict phenomena (e.g., inanimate things, events, or behavior of animals). A scientific theory can be thought of as a model of reality.

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. One 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,"

According to the American Association for the Advancement of Science, 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.

These definitions firmly mark things termed "theories" as being well supported by evidence, although scientists sometimes also use the word "theory" to describe untested but intricate hypotheses.

The term theoretical
The term theoretical is sometimes informally used in place of hypothetical to describe a result that is predicted, but has not yet been adequately tested by observation or experiment. A hypothesis is a prediction which has yet to be tested, while a theory is a prediction-making conceptual framework that is consistent with data.

List of notable theories

 * Astronomy: Big Bang Theory
 * Biology: Cell theory — Evolution — Germ theory
 * Chemistry: Atomic theory — Molecular theory — Kinetic theory of gases — Molecular orbital theory — Valence bond theory — Transition state theory — RRKM theory — Chemical graph theory — Flory-Huggins solution theory — Marcus theory — Lewis theory — Brønsted–Lowry acid–base theory — HSAB theory — Debye–Hückel theory — Thermodynamic theory of polymer elasticity — Reptation theory — Polymer field theory — Møller–Plesset perturbation theory — Density Functional Theory — Frontier molecular orbital theory — Polyhedral skeletal electron pair theory — Baeyer strain theory — Quantum theory of atoms in molecules — Collision theory — Crystal field theory — Variational Transition State Theory — Benson group increment theory — Specific ion interaction theory
 * Climatology: Climate change theory (due to anthropogenic activity)
 * Economics: Macroeconomic theory — Microeconomic theory
 * Education: Constructivist theory — Critical pedagogy theory — Education theory — Multiple intelligence theory — Progressive education theory
 * Engineering: Circuit theory — Control theory — Signal theory — Systems theory — Information theory
 * Film: Film Theory
 * Geology: Plate tectonics
 * Humanities: Critical theory
 * Literature: Literary theory
 * Mathematics: Approximation theory — Arakelov theory — Asymptotic theory — Bifurcation theory — Catastrophe theory — Category theory — Chaos theory — Choquet theory — Coding theory — Combinatorial game theory — Deformation theory — Dimension theory — Ergodic theory — Field theory — Galois theory — Game theory — Graph theory — Group theory — Hodge theory — Homology theory — Homotopy theory — Ideal theory — Intersection theory — Invariant theory — Iwasawa theory — K-theory — KK-theory — Knot theory — L-theory — Lie theory — Littlewood–Paley theory — Matrix theory — Measure theory — Model theory — Morse theory — Nevanlinna theory — Number theory — Obstruction theory — Operator theory — PCF theory — Perturbation theory — Potential theory — Probability theory — Ramsey theory — Rational choice theory — Representation theory — Ring theory — Set theory — Shape theory — Small cancellation theory — Spectral theory — Stability theory — Stable theory — Sturm–Liouville theory — Twistor 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 — M-theory — Perturbation theory — Theory of relativity — Quantum field theory — Scattering theory — String 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