**Theory** is a contemplative and rational type of abstract or generalising thinking, or the results of such thinking. Depending on the context, the results might for example include generalised explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several different related meanings.

A theory can be *normative* (or prescriptive), meaning a postulation about what ought to be. It provides "goals, norms, and standards". A theory can be a body of knowledge, which might or might not be associated with particular explanatory models. To theorise is to develop this body of knowledge.^{:46}

As already in Aristotle's definitions, theory is quite often contrasted to "practice" (from Greek *praxis*, πρᾶξις) a Greek term for "doing", which is opposed to theory because pure theory involves no doing apart from itself. A classical example of the distinction between "theoretical" and "practical" uses the discipline of medicine: medical theory 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 science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with scientific method, and fulfilling the criteria required by modern science. Such theories are 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. Scientific theories are the most reliable, rigorous, and comprehensive form of scientific knowledge, in contrast to more common uses of the word "theory" that imply that something is unproven or speculative (which is better characterised by the word 'hypothesis'). Scientific theories are distinguished from hypotheses, which are individual empirically testable conjectures, and scientific laws, which are descriptive accounts of how nature will behave under certain conditions.

## Ancient uses

The English word *theory* was derived from a technical term in philosophy in Ancient Greek. As an everyday word, *theoria*, θεωρία, meant "a looking at, viewing, beholding", but in more technical contexts it came to refer to contemplative or speculative understandings of natural things, such as those of natural philosophers, as opposed to more practical ways of knowing things, like that of skilled orators or artisans. The word has been in use in English after at least the late sixteenth century. Modern uses of the word "theory" are derived from the original definition, but have taken on new shades of meaning, still based on the idea that a theory is a thoughtful and rational explanation of the general nature of things.

Although it has more mundane meanings in Greek, the word θεωρία apparently developed special uses early in the recorded history of 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 knowledge, because he considered this intellectual pursuit the way to reach the highest plane of existence. Pythagoras emphasised 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.

In Aristotle's terminology, as has already been mentioned above, theory is contrasted with *praxis* or practice, which remains the case today. For Aristotle, both practise and theory involve thinking, but the aims are different. Theoretical contemplation considers things which humans don't move or change, such as nature, so it has no human aim apart from itself and the knowledge it helps create. On the additional hand, *praxis* involves thinking, but always with an aim to desired actions, whereby humans cause change or movement themselves for their own ends. Any human movement which involves no conscious choice and thinking couldn't be an example of *praxis* or doing.

## Theories formally and scientifically

Theories are analytical tools for understanding, explaining, and making predictions about a given subject matter. There are theories in a large number of 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 a few content (e.g., 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 might 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 consists entirely of true statements about the subject matter under consideration. Notwithstanding the truth of any one of these statements is always relative to the whole theory. Therefore, the same statement might 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" can't be judged to be true or false without reference to a few 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 or observationally equivalent, 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're usually expressed in a few 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, a few domains of knowledge can't be formalized, accurately and completely, as mathematical theories. (Here, formalising 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 formalise large bodies of scientific knowledge.

### Underdetermination

A theory is *underdetermined* (also called *indeterminacy of data to theory*) if a rival, inconsistent theory is at least as consistent with the evidence. Underdetermination is an epistemological issue about the relation of evidence to conclusions.

A theory that lacks supporting evidence is generally, more properly, referred to as a hypothesis.

### Intertheoretic reduction and elimination

If there's a new theory which is better at explaining and predicting phenomena than an older theory (i.e. it has more explanatory power), we're 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 additional are called *intertheoretic identities.* When an old theory and a new one are parallel in this way, we can conclude that we're describing the same reality, only more completely.

In cases where a new theory uses new terms which don't reduce to terms of an older one, but rather replace them entirely because they're 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 objections according to a formal system of rules, at times as an end in itself and at times 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 objections. Theories are abstract and conceptual, and to this end they're always considered true. They are supported or challenged by observations in the world. They are 'rigorously tentative', meaning that they're proposed as true and expected to satisfy careful examination to account for the possibility of faulty inference or incorrect observation. Sometimes theories are incorrect, meaning that an explicit set of observations contradicts a few fundamental objection or application of the theory, but more often theories are corrected to conform to new observations, by restricting the class of phenomena the theory applies to or changing the assertions made. An example of the former is the restriction of Classical mechanics to phenomena involving macroscopic length scales and particle speeds much lower than the speed of light.

"Sometimes a hypothesis never reaches the point of being considered a theory because the answer isn't found to derive its assertions analytically or not applied 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 a few of the elementary theorems of a philosophical theory are statements whose truth can't necessarily be scientifically tested through empirical observation.

Fields of study are at times named "theory" because their basis is a few initial set of objections 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 additionally 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 a few additional theory. In additional 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 science, the term "theory" refers to "a well-substantiated explanation of a few aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment." Theories must additionally meet further requirements, such as the ability to make falsifiable predictions with consistent accuracy across a broad area of scientific inquiry, and production of strong evidence in favour of the theory from multiple independent sources.

The strength of a scientific theory is related to the diversity of phenomena it can explain, which is measured by its ability to make falsifiable predictions with respect to those phenomena. Theories are improved (or replaced by better theories) as more evidence is gathered, so that accuracy in prediction improves over time; this increased accuracy corresponds to an increase in scientific knowledge. Scientists use theories as a foundation to gain further scientific knowledge, as well as to achieve goals such as inventing technology or curing disease.

### Definitions from scientific organizations

The United States National Academy of Sciences defines scientific theories as follows:

The formal scientific definition of "theory" is quite different from the everyday meaning of the word. It refers to a comprehensive explanation of a few aspect of nature that's supported by a vast body of evidence. Many scientific theories are so well established that no new evidence is likely to alter them substantially. For example, no new evidence will demonstrate that the Earth doesn't orbit around the sun (heliocentric theory), or that living things aren't made of cells (cell theory), that matter isn't composed of atoms, or that the surface of the Earth isn't divided into solid plates that have moved over geological timescales (the theory of plate tectonics)...One of the most useful properties of scientific theories is that they can be used to make predictions about natural events or phenomena that haven't yet been observed.

From the American Association for the Advancement of Science:

A scientific theory is a well-substantiated explanation of a few aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment. Such fact-supported theories aren't "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.

Note that the term *theory* wouldn't be appropriate for describing untested but intricate hypotheses or even scientific models.

### Philosophical views

The logical positivists thought of scientific theories as *deductive theories* — that a theory's content is based on a few 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 additionally a sentence of that theory. This is called the received view of theories.

In the semantic view of theories, which has largely replaced the received view, theories are viewed as scientific models. A model is a logical framework intended to represent reality (a "model of reality"), similar to the way that a map is a graphical model that represents the territory of a city or country. In this approach, theories are a specific category of models which fulfil the necessary criteria. (See Theories as models for further discussion.)

### 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. The specific mathematical aspects of classical electromagnetic theory are termed "laws of electromagnetism", reflecting the level of consistent and reproducible evidence that supports them. 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.

### The term *theoretical*

Acceptance of a theory doesn't require that all of its major predictions be tested, if it is already supported by sufficiently strong evidence. For example, certain tests might be unfeasible or technically difficult. As a result, theories might make predictions that haven't yet been confirmed or proven incorrect; in this case, the predicted results might be described informally with the term "theoretical." These predictions can be tested at a later time, and if they're incorrect, this might lead to revision or rejection of the theory.

## List of notable theories

Most of the following are scientific theories; a few are not, but rather encompass a body of knowledge or art, such as Music theory and Visual Arts Theories.

**Anthropology**: Carneiro's circumscription theory**Astronomy**: Alpher–Bethe–Gamow theory — B^{2}FH Theory — Copernican theory — Giant impact hypothesis — Newton's theory of gravitation — Hubble's Law — Kepler's laws of planetary motion — Nebular hypothesis — Ptolemaic theory**Cosmology**: Big Bang Theory — Cosmic inflation — Loop quantum gravity — Superstring theory — Supergravity — Supersymmetric theory — Multiverse theory — Holographic principle — Quantum gravity — M-theory**Biology**: Cell theory — Evolution — Germ theory**Chemistry**: 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 (successor to 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 — Ligand field theory (successor to Crystal field theory) — Variational Transition State Theory — Benson group increment theory — Specific ion interaction theory**Climatology**: Climate change theory (general study of climate changes) and anthropogenic climate change (ACC)/ global warming (AGW) theories (due to human activity)**Economics**: Macroeconomic theory — Microeconomic theory — Law of Supply and demand**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**Linguistics**: X-bar theory — Government and Binding — Principles and parameters — Universal grammar**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 — Computability theory — Computational complexity 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 — Atomic theory — BCS theory — Dirac hole theory — Dynamo theory — Landau theory — M-theory — Perturbation theory — Theory of relativity (successor to classical mechanics) — Quantum field theory — Scattering theory — String theory — Quantum information theory**Psychology**: Theory of mind — Cognitive dissonance theory — Attachment theory — Object permanence — Poverty of stimulus — Attribution theory — Self-fulfilling prophecy — Stockholm syndrome**Semiotics**: -**Sociology**: Critical theory — Engaged theory — Social theory — Sociological theory**Statistics**: Extreme value theory**Theatre**: Performance theory**Visual Art**: Aesthetics — Art Educational theory — Architecture — Composition — Anatomy — Color theory — Perspective — Visual perception — Geometry — Manifolds**Other**: Obsolete scientific theories