Theory

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For treatment of theories as expressed in formal language as studied in mathematical logic, see Theory (mathematical logic).
For other uses, see Theory (disambiguation).

The word theory has many distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion.

In science a theory is a testable model of the manner of interaction of a set of natural phenomena, capable of predicting future occurrences or observations of the same kind, and capable of being tested through experiment or otherwise verified through empirical observation. For the scientist, "theory" is not in any way an antonym of "fact". For example, it is a fact that an apple dropped on earth has been observed to fall towards the center of the planet, and the theories commonly used to describe and explain this behavior are Newton's theory of universal gravitation (see also gravitation), and the general theory of relativity.

In common usage, the word theory is often used to signify a conjecture, an opinion, a speculation, or a hypothesis. In this usage, a theory is not necessarily based on facts; in other words, it is not required to be consistent with true descriptions of reality. This usage of theory leads to the common incorrect statements. True descriptions of reality are more reflectively understood as statements which would be true independently of what people think about them.

According to the 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 that is supported by many facts gathered over time. Theories also allow scientists to make predictions about as yet unobserved phenomena.[1]

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Contents

[edit] Etymology

English attested since 1592, from Greek theoria (Jerome), Greek "contemplation, speculation", from "spectator", thea - "a view" + horan - "to see.", literally "looking at a show".[2] There is a second possible etymology that traces the word back to to theion (divine things) instead of thea, reflecting the concept of contemplating the divine organisation (Cosmos) of the nature.

[edit] Science

In scientific usage, a theory does not mean an unsubstantiated guess or hunch, as it can in everyday speech. A theory is a logically self-consistent model or framework for describing the behavior of a related set of natural or social phenomena. It originates from or is supported by experimental evidence (see scientific method). In this sense, a theory is a systematic and formalized expression of all previous observations, and is predictive, logical, and testable. In principle, scientific theories are always tentative, and subject to corrections, inclusion in a yet wider theory, or succession. Commonly, many more specific hypotheses may be logically bound together by just one or two theories. As a rule for use of the term, theories tend to deal with much broader sets of universals than do hypotheses, which ordinarily deal with much more specific sets of phenomena or specific applications of a theory.

Of several competing theories, one theory may be superior to another in terms of its approximation of reality. Scientific tests of the quality of a theory include its conformity to known facts and its ability to generate hypotheses with outcomes that would predict further testable facts.

A difference in usage of the word "fact" contributes to confusion in regard to the meaning of "theory." An appreciation of the various meanings of "fact" and "knowledge" can help to clarify an understanding of the meanings of "theory." (See also: relativity of knowledge, under Relativism.)

[edit] The term theoretical

The term theoretical is sometimes informally used in lieu of hypothetical to describe a result which 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 which are later confirmed or proven incorrect by experiment. By inference, a prediction proved incorrect by experiment demonstrates that the hypothesis is invalid. This either means the theory is incorrect or that the experimental conjecture was wrong and the theory did not predict the hypothesis.

[edit] In physics

In physics the term theory is generally used for a mathematical framework—derived from a small set of basic principles (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 the results which can be 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 the fact 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 as yet.

[edit] Currently unverifiable theories

The term theory is regularly stretched to refer to speculation which is currently unverifiable. Examples are string theory and various theories of everything. In the strict sense, the term theory should only be used when describing a model that is derived from experimental evidence and is provable (or disprovable). It is considered sufficient for the model to be in principle testable at some undetermined point in the future.

[edit] Theories as "models"

[edit] Purpose

Theories are constructed in order to explain, predict and master phenomena (e.g. inanimate things, events, or the behaviour 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.

[edit] 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 which 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 which disagrees with the predictions of the theory". The "unprovable by falsifiable" nature of theories is a consequence of the necessity of using inductive logic.

[edit] 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)

[edit] 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 which 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).

[edit] Example: Ptolemy

An example of how theories are models can be seen from theories on the planetary system. The Greeks formulated theories which were recorded by the astronomer Ptolemy. 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 which 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," one which 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 designing bridges and gasoline engines) with his theories of relativity.

[edit] 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 which constrains how scientists theorize and model a phenomenon and thus arrive at testable hypotheses.

In engineering practice, a distinction is made between "mathematical models" and "physical models".

[edit] Characteristics

The difference between science and unscientific nonsense was well caught in Wolfgang Pauli's famous comment on a paper he was shown: "This isn't right. It's not even wrong."

[edit] 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 which makes no predictions which can be observed is not a useful theory. Predictions which are 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. That is, it:

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

[edit] Non-essential criteria

Additionally, a theory is generally only taken seriously if it:

  • is tentative, correctable and dynamic, in allowing for changes to be made as new data are discovered, rather than asserting certainty, and
  • 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.

[edit] Indistinguishable theories

Sometimes it happens that two theories are found to make exactly the same predictions. In this case, they are indistinguishable, and the choice between them reduces to which is the more convenient.

[edit] 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 [3] 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". [4] 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 that we view scientific theories as consisting of 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 that 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.

[edit] 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 which 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 which formalize large bodies of scientific knowledge.

[edit] 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.

[edit] List of notable theories

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[edit] Scientific laws

Main article: Scientific law

Scientific laws are similar to scientific theories in that they are principles which 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.[6] Scientific theories are more overarching explanations of how nature works and why it exhibits certain characteristics.

[edit] Notes

  1. ^ National Academy of Sciences (2005), Science, Evolution, and Creationism, a brochure on the book of the same title.
  2. ^ Frisk; derivation from ?e?? was suggested by Koller Glotta 36, 273ff.
  3. ^ Hempel. C.G. 1951 "Problems and Changes in the Empiricist Criterion of Meaning" in Aspects of Scientific Explanation. Glencoe: the Free Press. Quine, W.V.O 1952 "Two Dogmas of Empiricism" reprinted in From a Logical Point of View. Cambridge: Harvard University Press
  4. ^ Philip Kitcher 1982 Abusing Science: The Case Against Creationism. Page 45 Cambridge: The MIT Press
  5. ^ The theory of plate tectonics is also called the theory of continental drift.
  6. ^ See the article on Physical law, for example.

[edit] References

[edit] See also