Theory

Template:Two other uses The word theory has many distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion. Definitively speaking, a theory is the analysis of a set of facts in their relation to one another. Additionally, in contrast with a theorem the statement of the theory is generally accepted only in some tentative fashion as opposed to regarding it as having been conclusively established. This may merely indicate, as it does in the sciences, that the theory was arrived at using potentially faulty inferences (scientific induction) as opposed to the necessary inferences used in mathematical proofs. In these cases the term theory does not suggest a low confidence in the claim and many uses of the term in the sciences require just the opposite.

Etymology

The word is derived from Greek θεωρία theoria (Jerome), Greek "contemplation, speculation", from θεωρός "spectator", θέα thea "a view" + ὁρᾶν horan "to see", literally "looking at a show". 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) of the nature. It is attested in English since 1592.

Science

Usage

In science, the word theory is used as a plausible general principle or body of principles offered to explain a phenomenon.. For example, it is a fact that an apple dropped on earth has been observed to fall towards the center of the planet but we invoke theories of gravity to explain this occurrence. However, even inside the sciences the word theory picks out several different concepts dependent on the context. In casual speech scientists don't use the term theory in a particularly precise fashion, allowing historical accidents to determine whether a given body of scientific work is called a theory, law, principle or something else. For instance Einstein's relativity is usually called "the theory of relativity" while Newton's theory of gravity often is called "the law of gravity." In this kind of casual use by scientists the word theory can be used flexibly to refer to whatever kind of explanation or prediction is being examined. It is for this instance that a scientific theory is a claim based on a body of evidence.

Philosophical Conception

This is in considerable contrast to the more philosophical context where a scientific theory is understood to be a testable model capable of predicting future occurrences or observations and capable of being tested through experiment or otherwise verified through empirical observation. As with most things in philosophy there is considerable debate as to whether this is really the correct concept to use in describing scientific research. For instance many definitions also add the constrain that a theory describes the natural world, though it is often unclear whether this is a definition of natural world or a constraint on what can be a theory. Note that this concept specifically does not require that a theory be particularly well supported or have any justification whatsoever. A major concern in this philosophical context is the problem of demarcation, i.e., distinguishing those ideas that are properly studied by the sciences and those that are not. Intuitively one might suppose that it doesn't matter where a suggestion came from, when it was made, or if it was ever well supported by the evidence to whether it's the sort of thing that scientists ought to consider (e.g. test or dismiss as already tested). Unsurprisingly, therefore, this concept of a scientific theory tends to apply equally to justified and unjustified predictions . In other words the term theory is used so that it encompasses what might be commonly called a hypothesis.

Pedagogical Definition

Finally, in pedagogical contexts or in official pronouncements by official organizations of scientists one gets a definition like the following.

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,

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.

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 lieu 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.

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.

Theories as "models"

Purpose

Theories are constructed to explain, predict, and master phenomena (e.g., inanimate things, events, or behavior of animals). In many instances we are constructing models of reality. A theory makes generalizations about observations and consists of an interrelated, coherent set of ideas and models.

Description and prediction

According to Stephen Hawking in A Brief History of Time, "A theory is a good theory if it satisfies two requirements: It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations." He goes on to state, "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." The "unprovable but falsifiable" nature of theories is a consequence of the necessity of using inductive logic.

Assumptions to formulate a theory

This is a view shared by Isaac Asimov. In Understanding Physics, Asimov spoke of theories as "arguments" where one deduces a "scheme" or model. Arguments or theories always begin with some premises—"arbitrary elements" as Hawking calls them (see above)—which are here described as "assumptions". An assumption according to Asimov is...

...something accepted without proof, and it is incorrect to speak of an assumption as either true or false, since there is no way of proving it to be either (If there were, it would no longer be an assumption). It is better to consider assumptions as either useful or useless, depending on whether deductions made from them corresponded to reality. ... On the other hand, it seems obvious that assumptions are the weak points in any argument, as they have to be accepted on faith in a philosophy of science that prides itself on its rationalism. Since we must start somewhere, we must have assumptions, but at least let us have as few assumptions as possible.

(See Occam's Razor)

Example: Special Theory of Relativity

As an example of the use of assumptions to formulate a theory, consider how Albert Einstein put forth his Special Theory of Relativity. He took two phenomena that had been observed — that the "addition of velocities" is valid (Galilean transformation), and that light did not appear to have an "addition of velocities" (Michelson-Morley experiment). He assumed both observations to be correct, and formulated his theory, based on these assumptions, by simply altering the Galilean transformation to accommodate the lack of addition of velocities with regard to the speed of light. The model created in his theory is, therefore, based on the assumption that light maintains a constant velocity (or more commonly: the speed of light is a constant).

Example: Ptolemy

An example of how theories are models can be seen from theories on the planetary system. The Greeks formulated theories, which the astronomer Ptolemy recorded. In Ptolemy's planetary model, the earth was at the center, the planets and the sun made circular orbits around the earth, and the stars were on a sphere outside of the orbits of the planet and the earth. Retrograde motion of the planets was explained by smaller circular orbits of individual planets. This could be illustrated as a model, and could even be built into a literal model. Mathematical calculations could be made that predicted, to a great degree of accuracy, where the planets would be. His model of the planetary system survived for over 1500 years until the time of Copernicus. So one can see that a theory is a "model of reality" that explains certain scientific facts; yet the theory may not be a satisfactory picture of reality. Another, more acceptable, theory can later replace the previous model, as when the Copernican theory replaced the Ptolemaic theory. Or a new theory can be used to modify an older theory as when Einstein modified Newtonian mechanics (which is still used for computing planetary orbits or modeling spacecraft trajectories) with his theories of relativity.

Differences between theory and model

Central to the nature of models, from general models to scale models, is the employment of representation (literally, "re-presentation") to describe particular aspects of a phenomenon or the manner of interaction among a set of phenomena. For instance, a scale model of a house or of a solar system is clearly not an actual house or an actual solar system; the aspects of an actual house or an actual solar system represented in a scale model are, only in certain limited ways, representative of the actual entity. In most ways that matter, the scale model of a house is not a house. Several commentators (e.g., Reese & Overton 1970; Lerner, 1998; Lerner & Teti, 2005, in the context of modeling human behavior) have stated that the important difference between theories and models is that the first is explanatory as well as descriptive, while the second is only descriptive (although still predictive in a more limited sense). General models and theories, according to philosopher Stephen Pepper (1948)—who also distinguishes between theories and models—are predicated on a "root" metaphor that constrains how scientists theorize and model a phenomenon and thus arrive at testable hypotheses.

Engineering practice makes a distinction between "mathematical models" and "physical models."

Characteristics

In a famous comment on a paper someone showed him, Wolfgang Pauli captured the difference between scientific and unscientific thought by saying, "This isn't right. It's not even wrong."

Essential criteria

The defining characteristic of a scientific theory is that it makes falsifiable or testable predictions. The relevance and specificity of those predictions determine how potentially useful the theory is. A would-be theory that makes no predictions that can be observed is not a useful theory. Predictions not sufficiently specific to be tested are similarly not useful. In both cases, the term "theory" is inapplicable.

In practice a body of descriptions of knowledge is usually only called a theory once it has a minimum empirical basis, according to certain criteria:

• It is consistent with pre-existing theory, to the extent the pre-existing theory was experimentally verified, though it will often show pre-existing theory to be wrong in an exact sense.
• It is supported by many strands of evidence, rather than a single foundation, ensuring it is probably a good approximation, if not totally correct.

Non-essential criteria

Additionally, a theory is generally only taken seriously if:

• It is tentative, correctable, and dynamic in allowing for changes as new facts are discovered, rather than asserting certainty.
• It is the most parsimonious explanation, sparing in proposed entities or explanations—commonly referred to as passing the Occam's razor test.

This is true of such established theories as special and general relativity, quantum mechanics, plate tectonics, evolution, etc. Theories considered scientific meet at least most, but ideally all, of these extra criteria.

Theories do not have to be perfectly accurate to be scientifically useful. The predictions made by Classical mechanics are known to be inaccurate, but they are sufficiently good approximations in most circumstances that they are still very useful and widely used in place of more accurate but mathematically difficult theories.

Indistinguishable theories

Sometimes two theories make exactly the same predictions. A pair of such theories is called indistinguishable, and the choice between them reduces to convenience or philosophical preference.

Criterion for scientific status

Karl Popper described the characteristics of a scientific theory as follows:

1. It is easy to obtain confirmations, or verifications, for nearly every theory—if we look for confirmations.
2. Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory—an event which would have refuted the theory.
3. Every "good" scientific theory is a prohibition: it forbids certain things to happen. The more a theory forbids, the better it is.
4. A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice.
5. Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability; but there are degrees of testability: some theories are more testable, more exposed to refutation, than others; they take, as it were, greater risks.
6. Confirming evidence should not count except when it is the result of a genuine test of the theory; and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory. (I now speak in such cases of "corroborating evidence".)
7. Some genuinely testable theories, when found to be false, are still upheld by their admirers—for example by introducing ad hoc some auxiliary assumption, or by reinterpreting the theory ad hoc in such a way that it escapes refutation. Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering, its scientific status. (I later describe such a rescuing operation as a "conventionalist twist" or a "conventionalist stratagem".)

One can sum up all this by saying that according to Popper, the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability.

Several philosophers and historians of science have, however, argued that Popper's definition of theory as a set of falsifiable statements is wrong because, as Philip Kitcher has pointed out, if one took a strictly Popperian view of "theory", observations of Uranus when first discovered in 1781 would have "falsified" Newton's celestial mechanics. Rather, people suggested that another planet influenced Uranus' orbit—and this prediction was indeed eventually confirmed.

Kitcher agrees with Popper that "There is surely something right in the idea that a science can succeed only if it can fail." He also takes into account Hempel and Quine's critiques of Popper, to the effect that scientific theories include statements that cannot be falsified (presumably what Hawking alluded to as arbitrary elements), and the point that good theories must also be creative. He insists we view scientific theories as an "elaborate collection of statements", some of which are not falsifiable, while others—those he calls "auxiliary hypotheses", are.

According to Kitcher, good scientific theories must have three features:

1. Unity: "A science should be unified…. Good theories consist of just one problem-solving strategy, or a small family of problem-solving strategies, that can be applied to a wide range of problems" (1982: 47).
2. Fecundity: "A great scientific theory, like Newton's, opens up new areas of research…. Because a theory presents a new way of looking at the world, it can lead us to ask new questions, and so to embark on new and fruitful lines of inquiry…. Typically, a flourishing science is incomplete. At any time, it raised more questions than it can currently answer. But incompleteness is not vice. On the contrary, incompleteness is the mother of fecundity…. A good theory should be productive; it should raise new questions and presume those questions can be answered without giving up its problem-solving strategies" (1982: 47–48).
3. Auxiliary hypotheses that are independently testable: "An auxiliary hypothesis ought to be testable independently of the particular problem it is introduced to solve, independently of the theory it is designed to save" (1982: 46) (e.g. the evidence for the existence of Neptune is independent of the anomalies in Uranus's orbit).

Like other definitions of theories, including Popper's, Kitcher makes it clear that a good theory includes statements that have (in his terms) "observational consequences". But, like the observation of irregularities in the orbit of Uranus, falsification is only one possible consequence of observation. The production of new hypotheses is another possible—and equally important—observational consequence.

Mathematics

In mathematics, the word theory is used informally to refer to certain distinct bodies of knowledge about mathematics. This knowledge consists of axioms, definitions, theorems and computational techniques, all related in some way by tradition or practice. Examples include group theory, set theory, Lebesgue integration theory and field theory.

The term theory also has a precise technical usage in mathematics, particularly in mathematical logic and model theory. A theory in this sense is a set of statements in a formal language, which is 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.

Other fields

Theories exist not only in the so-called hard sciences, but in all fields of academic study, from philosophy to music to literature.

In the humanities, theory is often used as an abbreviation for critical theory or literary theory.

List of notable theories

• 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: 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 — General relativity — Special relativity — 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
• Statistics : Extreme value theory
• Theatre : Theory relating to theatrical performance.
• Other: Obsolete scientific theories — Phlogiston theory

Scientific laws

Main article: Scientific law

Scientific laws are similar to scientific theories in that they are principles that can be used to predict the behavior of the natural world. Both scientific laws and scientific theories are typically well-supported by observations and/or experimental evidence. Usually scientific laws refer to rules for how nature will behave under certain conditions. Scientific theories are more overarching explanations of how nature works and why it exhibits certain characteristics.

A common misconception is that scientific theories are rudimentary ideas that will eventually graduate into scientific laws when enough data and evidence has been accumulated. A theory does not change into a scientific law with the accumulation of new or better evidence. A theory will always remain a theory, a law will always remain a law.

See also

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

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.