Scientific theory

For a treatment of theories in general, see Theory.

In the sciences, a scientific theory (also called an empirical theory) comprises a collection of concepts, including abstractions of observable phenomena expressed as quantifiable properties, together with rules (called scientific laws) that express relationships between observations of such concepts. A scientific theory is constructed to conform to available empirical data about such observations, and is put forth as a principle or body of principles for explaining a class of phenomena.

A scientific theory is a type of deductive theory, in that its content (i.e. empirical data) could be expressed within some formal system of logic whose elementary rules (i.e. scientific laws) are taken as 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.

In the humanities, one finds theories whose subject matter does not (only) concern empirical data, but rather ideas. Such theories are in the realm of philosophical theories as contrasted with scientific theories. A philosophical theory is not necessarily scientifically testable through experiment.

Theories as models

Main article: Scientific model

Theories are mostly constructed to explain, predict, and to master phenomena (e.g., inanimate things, events, or behavior of animals). A scientific theory can be thought of as a model of reality, and its statements as axioms of some axiomatic system. 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.

Description and prediction

Echoing the scientific philosopher Karl Popper, Stephen Hawking in A Brief History of Time states, "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 necessary consequence 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.

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."

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 hardly applicable.

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.
• In chemistry, there are many acid-base theories which, while providing highly divergent explanations of what "really" makes acids acids and bases bases, they are very useful for describing the phenomenology of certain chemical reactions which fall under the concept of "acid-base reaction". In a sense, the notion of generalized acid-base reaction is not precisely defined, and therefore theories about what gives rise to acid-base chemistry are "inexact"; nonetheless, they are useful scientific theories.

Criteria 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 raises 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.

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. An example of the latter might be the radiation reaction force. As of 2009, it has never been observed directly, but its effects on periodic motion of charges in a time-averaged sense is detectable in synchrotrons. Some researchers are now considering the possibility of experiments that could observe the effects of this force at the instantaneous (i.e. not averaged over periods of cyclical motion) level

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,

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.

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

• Occam's Razor
• Theorem

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.