Scientific theory
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A scientific theory is an explanation of an aspect of the natural world that can be or that has been repeatedly tested and has corroborating evidence in accordance with the
scientific method The scientific method is an Empirical evidence, empirical method for acquiring knowledge that has been referred to while doing science since at least the 17th century. Historically, it was developed through the centuries from the ancient and ...
, using accepted protocols of
observation Observation in the natural sciences is an act or instance of noticing or perceiving and the acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the percep ...
, measurement, and evaluation of results. Where possible, theories are tested under controlled conditions in an
experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs whe ...
. In circumstances not amenable to experimental testing, theories are evaluated through principles of
abductive reasoning Abductive reasoning (also called abduction,For example: abductive inference, or retroduction) is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations. It was formulated and advanced by Ameri ...
. Established scientific theories have withstood rigorous scrutiny and embody scientific
knowledge Knowledge is an Declarative knowledge, awareness of facts, a Knowledge by acquaintance, familiarity with individuals and situations, or a Procedural knowledge, practical skill. Knowledge of facts, also called propositional knowledge, is oft ...
. A scientific theory differs from a scientific fact: a fact is an observation and a theory organizes and explains multiple observations. Furthermore, a theory is expected to make predictions which could be confirmed or refuted with addition observations.
Stephen Jay Gould Stephen Jay Gould ( ; September 10, 1941 – May 20, 2002) was an American Paleontology, paleontologist, Evolutionary biology, evolutionary biologist, and History of science, historian of science. He was one of the most influential and widely re ...
wrote that "...facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts." A theory differs from a
scientific law Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow ...
in that a law is an empirical description of a relationship between facts and/or other laws. For example, Newton's Law of Gravity is a mathematical equation that can be used to predict the attraction between bodies, but it is not a theory to explain ''how''
gravity In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...
works. The meaning of the term ''scientific theory'' (often contracted to ''theory'' for brevity) as used in the disciplines of science is significantly different from the common
vernacular Vernacular is the ordinary, informal, spoken language, spoken form of language, particularly when perceptual dialectology, perceived as having lower social status or less Prestige (sociolinguistics), prestige than standard language, which is mor ...
usage of ''theory''. In everyday speech, ''theory'' can imply an explanation that represents an unsubstantiated and speculative
guess Guessing is the act of drawing a swift conclusion, called a guess, from data directly at hand, which is then held as probable or tentative, while the person making the guess (the guesser) admittedly lacks material for a greater degree of certaint ...
, whereas in a scientific context it most often refers to an explanation that has already been tested and is widely accepted as valid. The strength of a scientific theory is related to the diversity of phenomena it can explain and its simplicity. As additional
scientific evidence Scientific evidence is evidence that serves to either support or counter a scientific theory or hypothesis, although scientists also use evidence in other ways, such as when applying theories to practical problems. "Discussions about empirical ev ...
is gathered, a scientific theory may be modified and ultimately rejected if it cannot be made to fit the new findings; in such circumstances, a more accurate theory is then required. Some theories are so well-established that they are unlikely ever to be fundamentally changed (for example, scientific theories such as
evolution Evolution is the change in the heritable Phenotypic trait, characteristics of biological populations over successive generations. It occurs when evolutionary processes such as natural selection and genetic drift act on genetic variation, re ...
, heliocentric theory,
cell theory In biology, cell theory is a scientific theory first formulated in the mid-nineteenth century, that living organisms are made up of cells, that they are the basic structural/organizational unit of all organisms, and that all cells come from pr ...
, theory of plate tectonics,
germ theory of disease The germ theory of disease is the currently accepted scientific theory for many diseases. It states that microorganisms known as pathogens or "germs" can cause disease. These small organisms, which are too small to be seen without magnification, ...
, etc.). In certain cases, a scientific theory or scientific law that fails to fit all data can still be useful (due to its simplicity) as an approximation under specific conditions. An example is
Newton's laws of motion Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body re ...
, which are a highly accurate approximation to
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Ele ...
at velocities that are small relative to the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
. Scientific theories are testable and make verifiable predictions. They describe the causes of a particular natural phenomenon and are used to explain and predict aspects of the physical
universe The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from s ...
or specific areas of inquiry (for example, electricity, chemistry, and astronomy). As with other forms of scientific knowledge, scientific theories are both
deductive Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, th ...
and inductive, aiming for predictive and explanatory power. Scientists use theories to further scientific knowledge, as well as to facilitate advances in
technology Technology is the application of Conceptual model, conceptual knowledge to achieve practical goals, especially in a reproducible way. The word ''technology'' can also mean the products resulting from such efforts, including both tangible too ...
or
medicine Medicine is the science and Praxis (process), practice of caring for patients, managing the Medical diagnosis, diagnosis, prognosis, Preventive medicine, prevention, therapy, treatment, Palliative care, palliation of their injury or disease, ...
. Scientific hypotheses can never be "proven" because scientists are not able to fully confirm that their hypothesis is true. Instead, scientists say that the study "supports" or is consistent with their hypothesis.


Types

Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
described two different types of scientific theories: "Constructive theories" and "principle theories". Constructive theories are constructive models for phenomena: for example, kinetic theory. Principle theories are empirical generalisations, one such example being
Newton's laws of motion Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body re ...
.


Characteristics


Essential criteria

For any theory to be accepted within most academia there is usually one simple criterion. The essential criterion is that the theory must be observable and repeatable. The aforementioned criterion is essential to prevent fraud and perpetuate science itself. The defining characteristic of all scientific knowledge, including theories, is the ability to make 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 observable predictions is not a scientific theory at all. Predictions not sufficiently specific to be tested are similarly not useful. In both cases, the term "theory" is not applicable. A body of descriptions of
knowledge Knowledge is an Declarative knowledge, awareness of facts, a Knowledge by acquaintance, familiarity with individuals and situations, or a Procedural knowledge, practical skill. Knowledge of facts, also called propositional knowledge, is oft ...
can be called a theory if it fulfills the following criteria: * It makes falsifiable predictions with consistent accuracy across a broad area of scientific inquiry (such as
mechanics Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of ...
). * It is well-supported by many independent strands of evidence, rather than a single foundation. * It is consistent with preexisting experimental results and at least as accurate in its predictions as are any preexisting theories. These qualities are certainly true of such established theories as special and
general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
,
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
,
plate tectonics Plate tectonics (, ) is the scientific theory that the Earth's lithosphere comprises a number of large tectonic plates, which have been slowly moving since 3–4 billion years ago. The model builds on the concept of , an idea developed durin ...
, the modern evolutionary synthesis, etc.


Other criteria

In addition, most scientists prefer to work with a theory that meets the following qualities: * It can be subjected to minor adaptations to account for new data that do not fit it perfectly, as they are discovered, thus increasing its predictive capability over time. * It is among the most parsimonious explanations, economical in the use of proposed entities or explanatory steps as per
Occam's razor In philosophy, Occam's razor (also spelled Ockham's razor or Ocham's razor; ) is the problem-solving principle that recommends searching for explanations constructed with the smallest possible set of elements. It is also known as the principle o ...
. This is because for each accepted explanation of a phenomenon, there may be an extremely large, perhaps even incomprehensible, number of possible and more complex alternatives, because one can always burden failing explanations with ''ad hoc'' hypotheses to prevent them from being falsified; therefore, simpler theories are preferable to more complex ones because they are more testable.Elliott Sober, Let's Razor Occam's Razor, pp. 73–93, from Dudley Knowles (ed.) Explanation and Its Limits, Cambridge University Press (1994).


Definitions from scientific organizations

The
United States National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...
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 some aspect of nature that is 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 does not orbit around the Sun (heliocentric theory), or that living things are not made of cells (cell theory), that matter is not composed of atoms, or that the surface of the Earth is not 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 have not yet been observed.
From the
American Association for the Advancement of Science The American Association for the Advancement of Science (AAAS) is a United States–based international nonprofit with the stated mission of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsib ...
:
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.
Note that the term ''theory'' would not be appropriate for describing untested but intricate hypotheses or even scientific models.


Formation

The
scientific method The scientific method is an Empirical evidence, empirical method for acquiring knowledge that has been referred to while doing science since at least the 17th century. Historically, it was developed through the centuries from the ancient and ...
involves the proposal and testing of
hypotheses A hypothesis (: hypotheses) is a proposed explanation for a phenomenon. A scientific method, scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educ ...
, by deriving predictions from the hypotheses about the results of future experiments, then performing those experiments to see whether the predictions are valid. This provides evidence either for or against the hypothesis. When enough experimental results have been gathered in a particular area of inquiry, scientists may propose an explanatory framework that accounts for as many of these as possible. This explanation is also tested, and if it fulfills the necessary criteria (see above), then the explanation becomes a theory. This can take many years, as it can be difficult or complicated to gather sufficient evidence. Once all of the criteria have been met, it will be widely accepted by scientists (see
scientific consensus Scientific consensus is the generally held judgment, position, and opinion of the majority or the supermajority of scientists in a particular field of study at any particular time. Consensus is achieved through scholarly communication at confer ...
) as the best available explanation of at least some phenomena. It will have made predictions of phenomena that previous theories could not explain or could not predict accurately, and it will have many repeated bouts of testing. The strength of the evidence is evaluated by the scientific community, and the most important experiments will have been replicated by multiple independent groups. Theories do not have to be perfectly accurate to be scientifically useful. For example, the predictions made by
classical mechanics Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...
are known to be inaccurate in the relativistic realm, but they are almost exactly correct at the comparatively low velocities of common human experience.Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973). ''Gravitation,'' p. 1049. New York: W. H. Freeman and Company. . In
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...
, there are many acid-base theories providing highly divergent explanations of the underlying nature of acidic and basic compounds, but they are very useful for predicting their chemical behavior. Like all knowledge in science, no theory can ever be completely certain, since it is possible that future experiments might conflict with the theory's predictions. However, theories supported by the scientific consensus have the highest level of certainty of any scientific knowledge; for example, that all objects are subject to
gravity In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...
or that life on Earth evolved from a
common ancestor Common descent is a concept in evolutionary biology applicable when one species is the ancestor of two or more species later in time. According to modern evolutionary biology, all living beings could be descendants of a unique ancestor commonl ...
. Acceptance of a theory does not require that all of its major predictions be tested if it is already supported by sufficient evidence. For example, certain tests may be unfeasible or technically difficult. As a result, theories may make predictions that have not yet been confirmed or proven incorrect; in this case, the predicted results may be described informally with the term "theoretical". These predictions can be tested at a later time, and if they are incorrect, this may lead to the revision or rejection of the theory. As
Richard Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist. He is best known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of t ...
puts it:
It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.


Modification and improvement

If experimental results contrary to a theory's predictions are observed, scientists first evaluate whether the experimental design was sound, and if so they confirm the results by independent replication. A search for potential improvements to the theory then begins. Solutions may require minor or major changes to the theory, or none at all if a satisfactory explanation is found within the theory's existing framework. Over time, as successive modifications build on top of each other, theories consistently improve and greater predictive accuracy is achieved. Since each new version of a theory (or a completely new theory) must have more predictive and explanatory power than the last, scientific knowledge consistently becomes more accurate over time. If modifications to the theory or other explanations seem to be insufficient to account for the new results, then a new theory may be required. Since scientific knowledge is usually durable, this occurs much less commonly than modification. Furthermore, until such a theory is proposed and accepted, the previous theory will be retained. This is because it is still the best available explanation for many other phenomena, as verified by its predictive power in other contexts. For example, it has been known since 1859 that the observed perihelion precession of Mercury violates Newtonian mechanics, but the theory remained the best explanation available until relativity was supported by sufficient evidence. Also, while new theories may be proposed by a single person or by many, the cycle of modifications eventually incorporates contributions from many different scientists. After the changes, the accepted theory will explain more phenomena and have greater predictive power (if it did not, the changes would not be adopted); this new explanation will then be open to further replacement or modification. If a theory does not require modification despite repeated tests, this implies that the theory is very accurate. This also means that accepted theories continue to accumulate evidence over time, and the length of time that a theory (or any of its principles) remains accepted often indicates the strength of its supporting evidence.


Unification

In some cases, two or more theories may be replaced by a single theory that explains the previous theories as approximations or special cases, analogous to the way a theory is a unifying explanation for many confirmed hypotheses; this is referred to as ''unification'' of theories.Weinberg S (1993). ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature.'' For example,
electricity Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwel ...
and
magnetism Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, ...
are now known to be two aspects of the same phenomenon, referred to as
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...
. When the predictions of different theories appear to contradict each other, this is also resolved by either further evidence or unification. For example, physical theories in the 19th century implied that the Sun could not have been burning long enough to allow certain geological changes as well as the
evolution Evolution is the change in the heritable Phenotypic trait, characteristics of biological populations over successive generations. It occurs when evolutionary processes such as natural selection and genetic drift act on genetic variation, re ...
of life. This was resolved by the discovery of
nuclear fusion Nuclear fusion is a nuclear reaction, reaction in which two or more atomic nuclei combine to form a larger nuclei, nuclei/neutrons, neutron by-products. The difference in mass between the reactants and products is manifested as either the rele ...
, the main energy source of the Sun. Contradictions can also be explained as the result of theories approximating more fundamental (non-contradictory) phenomena. For example, atomic theory is an approximation of
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
. Current theories describe three separate fundamental phenomena of which all other theories are approximations; The potential unification of these is sometimes called the
Theory of Everything A theory of everything (TOE), final theory, ultimate theory, unified field theory, or master theory is a hypothetical singular, all-encompassing, coherent theoretical physics, theoretical framework of physics that fully explains and links togeth ...
.


Example: Relativity

In 1905,
Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
published the theory of
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Ele ...
. He started with a principle known for three hundred years, since the time of
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei ( , , ) or mononymously as Galileo, was an Italian astronomer, physicist and engineer, sometimes described as a poly ...
: the principle of relativity and a prediction from a well established theory for electromagnetism known as
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, Electrical network, electr ...
, the prediction that the speed of light in a vacuum does not depend on relative motion of the source and receiver. Einstein proposed, or hypothesized, that the concept of Galilean relativity should be modified to align mechanical physics with electromagnetism.. In addition to unifying two branches of physics, this modification lead to specific consequences such as
time dilation Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unsp ...
and
length contraction Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald ...
. Careful, repeated experiments have both confirmed Einstein's postulates are valid and that the predictions of the special theory of relativity match experiement. Einstein next sought to generalize the invariance principle to all reference frames, whether inertial or accelerating. Rejecting Newtonian gravitation—a central force acting instantly at a distance—Einstein presumed a gravitational field. In 1907, Einstein's
equivalence principle The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same t ...
implied that a free fall within a uniform gravitational field is equivalent to inertial motion.Roberto Torretti, ''The Philosophy of Physics'' (Cambridge: Cambridge University Press, 1999)
pp. 289–90
By extending special relativity's effects into three dimensions,
general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
extended length contraction into space contraction, conceiving of 4D space-time as the gravitational field that alters geometrically and sets all local objects' pathways. Even massless energy exerts gravitational motion on local objects by "curving" the geometrical "surface" of 4D space-time. Yet unless the energy is vast, its relativistic effects of contracting space and slowing time are negligible when merely predicting motion. Although general relativity is embraced as the more explanatory theory via '' scientific realism'', Newton's theory remains successful as merely a predictive theory via '' instrumentalism''. To calculate trajectories, engineers and NASA still use Newton's equations, which are simpler to operate.


Theories and laws

Both scientific laws and scientific theories are produced from the scientific method through the formation and testing of hypotheses and can predict the behavior of the natural world. Both are also typically well-supported by observations and/or experimental evidence. However, scientific laws are descriptive accounts of how nature will behave under certain conditions. Scientific theories are broader in scope and give overarching explanations of how nature works and why it exhibits certain characteristics. Theories are supported by evidence from many different sources and may contain one or several laws. A common misconception is that scientific theories are rudimentary ideas that will eventually graduate into scientific laws when enough data and evidence have 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. Both theories and laws could potentially be falsified by countervailing evidence.


Theories and facts

A scientific theory does not turn into a fact. Scientific facts are observations that theories organize and explain."And facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts." Gould, S. J. (1981)
Evolution as fact and theory
Discover, 2(5), 34-37.
As new facts appear, a theory may be revised or new theories may emerge that encompass these additional facts. While American vernacular speech uses "theory" as similar to a "guess" in opposition to a "fact", in science the word "theory" means a model that is expected to explain a wide range of facts.


About theories


Theories as axioms

The
logical positivists Logical positivism, also known as logical empiricism or neo-positivism, was a philosophical movement, in the empiricist tradition, that sought to formulate a scientific philosophy in which philosophical discourse would be, in the perception of ...
thought of scientific theories as statements in a
formal language In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet". The alphabet of a formal language consists of symbols that concatenate into strings (also c ...
.
First-order logic First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over ...
is an example of a formal language. The logical positivists envisaged a similar scientific language. In addition to scientific theories, the language also included observation sentences ("the sun rises in the east"), definitions, and mathematical statements. The phenomena explained by the theories, if they could not be directly observed by the senses (for example,
atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...
s and
radio waves Radio waves (formerly called Hertzian waves) are a type of electromagnetic radiation with the lowest frequencies and the longest wavelengths in the electromagnetic spectrum, typically with frequencies below 300 gigahertz (GHz) and wavelengths ...
), were treated as theoretical concepts. In this view, theories function as axioms: predicted observations are derived from the theories much like
theorems In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to esta ...
are derived in
Euclidean geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry, ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set ...
. However, the predictions are then tested against reality to verify the predictions, and the "axioms" can be revised as a direct result. The phrase " the received view of theories" is used to describe this approach. Terms commonly associated with it are "
linguistic Linguistics is the scientific study of language. The areas of linguistic analysis are syntax (rules governing the structure of sentences), semantics (meaning), Morphology (linguistics), morphology (structure of words), phonetics (speech sounds ...
" (because theories are components of a language) and "
syntactic In linguistics, syntax ( ) is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure (constituency ...
" (because a language has rules about how symbols can be strung together). Problems in defining this kind of language precisely, e.g., are objects seen in microscopes observed or are they theoretical objects, led to the effective demise of logical positivism in the 1970s.


Theories as models

The semantic view of theories, which identifies scientific theories with
models A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , . Models can be divided int ...
rather than
proposition A proposition is a statement that can be either true or false. It is a central concept in the philosophy of language, semantics, logic, and related fields. Propositions are the object s denoted by declarative sentences; for example, "The sky ...
s, has replaced the received view as the dominant position in theory formulation in the philosophy of science. 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 that fulfil the necessary criteria (see above). One can use language to describe a model; however, the theory is the model (or a collection of similar models), and not the description of the model. A model of the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...
, for example, might consist of abstract objects that represent the Sun and the planets. These objects have associated properties, e.g., positions, velocities, and masses. The model parameters, e.g., Newton's Law of Gravitation, determine how the positions and velocities change with time. This model can then be tested to see whether it accurately predicts future observations; astronomers can verify that the positions of the model's objects over time match the actual positions of the planets. For most planets, the Newtonian model's predictions are accurate; for Mercury, it is slightly inaccurate and the model of
general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
must be used instead. The word "
semantic Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction betwee ...
" refers to the way that a model represents the real world. The representation (literally, "re-presentation") describes 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 the Solar System is clearly not an actual house or an actual Solar System; the aspects of an actual house or the actual Solar System represented in a scale model are, only in certain limited ways, representative of the actual entity. A scale model of a house is not a house; but to someone who wants to ''learn about'' houses, analogous to a scientist who wants to understand reality, a sufficiently detailed scale model may suffice.


Differences between theory and model

Several commentators have stated that the distinguishing characteristic of theories is that they are explanatory as well as descriptive, while models are only descriptive (although still predictive in a more limited sense). Philosopher Stephen Pepper also distinguished between theories and models and said in 1948 that general models and theories 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"; the cost of fabricating a physical model can be minimized by first creating a mathematical model using a computer software package, such as a
computer-aided design Computer-aided design (CAD) is the use of computers (or ) to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve c ...
tool. The component parts are each themselves modelled, and the fabrication tolerances are specified. An exploded view drawing is used to lay out the fabrication sequence. Simulation packages for displaying each of the subassemblies allow the parts to be rotated, and magnified, in realistic detail. Software packages for creating the bill of materials for construction allow subcontractors to specialize in assembly processes, which spreads the cost of manufacturing machinery among multiple customers. See: Computer-aided engineering,
Computer-aided manufacturing Computer-aided manufacturing (CAM) also known as computer-aided modeling or computer-aided machining is the use of software to control machine tools in the manufacturing of work pieces. This is not the only definition for CAM, but it is the most ...
, and
3D printing 3D printing, or additive manufacturing, is the construction of a three-dimensional object from a CAD model or a digital 3D model. It can be done in a variety of processes in which material is deposited, joined or solidified under computer ...


Assumptions in formulating theories

An assumption (or
axiom An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or ...
) is a statement that is accepted without evidence. For example, assumptions can be used as premises in a logical argument.
Isaac Asimov Isaac Asimov ( ;  – April 6, 1992) was an Russian-born American writer and professor of biochemistry at Boston University. During his lifetime, Asimov was considered one of the "Big Three" science fiction writers, along with Robert A. H ...
described assumptions as follows:
...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 correspond to reality...Since we must start somewhere, we must have assumptions, but at least let us have as few assumptions as possible.
Certain assumptions are necessary for all empirical claims (e.g. the assumption that
reality Reality is the sum or aggregate of everything in existence; everything that is not imagination, imaginary. Different Culture, cultures and Academic discipline, academic disciplines conceptualize it in various ways. Philosophical questions abo ...
exists). However, theories do not generally make assumptions in the conventional sense (statements accepted without evidence). While assumptions are often incorporated during the formation of new theories, these are either supported by evidence (such as from previously existing theories) or the evidence is produced in the course of validating the theory. This may be as simple as observing that the theory makes accurate predictions, which is evidence that any assumptions made at the outset are correct or approximately correct under the conditions tested. Conventional assumptions, without evidence, may be used if the theory is only intended to apply when the assumption is valid (or approximately valid). For example, the special theory of relativity assumes an
inertial frame of reference In classical physics and special relativity, an inertial frame of reference (also called an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative ...
. The theory makes accurate predictions when the assumption is valid, and does not make accurate predictions when the assumption is not valid. Such assumptions are often the point with which older theories are succeeded by new ones (the general theory of relativity works in non-inertial reference frames as well). The term "assumption" is actually broader than its standard use, etymologically speaking. The Oxford English Dictionary (OED) and online Wiktionary indicate its Latin source as ''assumere'' ("accept, to take to oneself, adopt, usurp"), which is a conjunction of ''ad-'' ("to, towards, at") and ''sumere'' (to take). The root survives, with shifted meanings, in the Italian ''assumere'' and Spanish ''sumir''. The first sense of "assume" in the OED is "to take unto (oneself), receive, accept, adopt". The term was originally employed in religious contexts as in "to receive up into heaven", especially "the reception of the Virgin Mary into heaven, with body preserved from corruption", (1297 CE) but it was also simply used to refer to "receive into association" or "adopt into partnership". Moreover, other senses of assumere included (i) "investing oneself with (an attribute)", (ii) "to undertake" (especially in Law), (iii) "to take to oneself in appearance only, to pretend to possess", and (iv) "to suppose a thing to be" (all senses from OED entry on "assume"; the OED entry for "assumption" is almost perfectly symmetrical in senses). Thus, "assumption" connotes other associations than the contemporary standard sense of "that which is assumed or taken for granted; a supposition, postulate" (only the 11th of 12 senses of "assumption", and the 10th of 11 senses of "assume").


Descriptions


From philosophers of science

Karl Popper Sir Karl Raimund Popper (28 July 1902 – 17 September 1994) was an Austrian–British philosopher, academic and social commentator. One of the 20th century's most influential philosophers of science, Popper is known for his rejection of the ...
described the characteristics of a scientific theory as follows: Popper, Karl (1963), ''Conjectures and Refutations'', Routledge and Kegan Paul, London, UK. Reprinted in Theodore Schick (ed., 2000), ''Readings in the Philosophy of Science'', Mayfield Publishing Company, Mountain View, Calif. # It is easy to obtain confirmations, or verifications, for nearly every theory—if we look for confirmations. # 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. # Every "good" scientific theory is a prohibition: it forbids certain things from happening. The more a theory forbids, the better it is. # 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. # 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. # 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".) # Some genuinely testable theories, when found to be false, might still be upheld by their admirers—for example by introducing post hoc (after the fact) some auxiliary hypothesis or assumption, or by reinterpreting the theory post 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, by
tampering with evidence Tampering with evidence, or evidence tampering, is an act in which a person alters, conceals, falsifies, or destroys evidence with the intent to interfere with an investigation (usually) by a law-enforcement, governmental, or regulatory authority. ...
. The temptation to tamper can be minimized by first taking the time to write down the testing protocol before embarking on the scientific work. Popper summarized these statements by saying that the central criterion of the scientific status of a theory is its "falsifiability, or refutability, or testability". Echoing this,
Stephen Hawking Stephen William Hawking (8January 194214March 2018) was an English theoretical physics, theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between ...
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 also discusses the "unprovable but falsifiable" nature of theories, which is a necessary consequence of inductive logic, and that "you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory". 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."Philip Kitcher 1982 ''Abusing Science: The Case Against Creationism'', pp. 45–48. Cambridge: The MIT Press He also says that scientific theories include statements that cannot be falsified, and 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: # 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." # 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." # 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." (For example, 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 theory must include statements that have 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 result.


Analogies and metaphors

The concept of a scientific theory has also been described using analogies and metaphors. For example, the logical empiricist
Carl Gustav Hempel Carl Gustav "Peter" Hempel (; ; January 8, 1905 – November 9, 1997) was a German writer, philosopher, logician, and epistemologist. He was a major figure in Logical positivism, logical empiricism, a 20th-century movement in the philosophy ...
likened the structure of a scientific theory to a "complex spatial network:"
Its terms are represented by the knots, while the threads connecting the latter correspond, in part, to the definitions and, in part, to the fundamental and derivative hypotheses included in the theory. The whole system floats, as it were, above the plane of observation and is anchored to it by the rules of interpretation. These might be viewed as strings which are not part of the network but link certain points of the latter with specific places in the plane of observation. By virtue of these interpretive connections, the network can function as a scientific theory: From certain observational data, we may ascend, via an interpretive string, to some point in the theoretical network, thence proceed, via definitions and hypotheses, to other points, from which another interpretive string permits a descent to the plane of observation.
Michael Polanyi made an analogy between a theory and a map:
A theory is something other than myself. It may be set out on paper as a system of rules, and it is the more truly a theory the more completely it can be put down in such terms. Mathematical theory reaches the highest perfection in this respect. But even a geographical map fully embodies in itself a set of strict rules for finding one's way through a region of otherwise uncharted experience. Indeed, all theory may be regarded as a kind of map extended over space and time.
A scientific theory can also be thought of as a book that captures the fundamental information about the world, a book that must be researched, written, and shared. In 1623,
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei ( , , ) or mononymously as Galileo, was an Italian astronomer, physicist and engineer, sometimes described as a poly ...
wrote:
Philosophy .e. physicsis written in this grand book—I mean the universe—which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.
The book metaphor could also be applied in the following passage, by the contemporary philosopher of science
Ian Hacking Ian MacDougall Hacking (February 18, 1936 – May 10, 2023) was a Canadian philosopher specializing in the philosophy of science. Throughout his career, he won numerous awards, such as the Killam Prize for the Humanities and the Balzan Prize, ...
:
I myself prefer an Argentine fantasy. God did not write a Book of Nature of the sort that the old Europeans imagined. He wrote a Borgesian library, each book of which is as brief as possible, yet each book of which is inconsistent with every other. No book is redundant. For every book there is some humanly accessible bit of Nature such that that book, and no other, makes possible the comprehension, prediction and influencing of what is going on...Leibniz said that God chose a world which maximized the variety of phenomena while choosing the simplest laws. Exactly so: but the best way to maximize phenomena and have simplest laws is to have the laws inconsistent with each other, each applying to this or that but none applying to all.


In physics

In
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
, 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.)—that 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 Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, Electrical network, electr ...
. 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. An example of the latter might be the radiation reaction force. As of 2009, its effects on the periodic motion of charges are detectable in synchrotrons, but only as ''averaged'' effects over time. Some researchers are now considering experiments that could observe these effects at the instantaneous level (i.e. not averaged over time).


Examples

Note that many fields of inquiry do not have specific named theories, e.g.
developmental biology Developmental biology is the study of the process by which animals and plants grow and develop. Developmental biology also encompasses the biology of Regeneration (biology), regeneration, asexual reproduction, metamorphosis, and the growth and di ...
. Scientific knowledge outside a named theory can still have a high level of certainty, depending on the amount of evidence supporting it. Also note that since theories draw evidence from many fields, the categorization is not absolute. * ''
Biology Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and ...
'':
cell theory In biology, cell theory is a scientific theory first formulated in the mid-nineteenth century, that living organisms are made up of cells, that they are the basic structural/organizational unit of all organisms, and that all cells come from pr ...
, theory of evolution ( modern evolutionary synthesis), abiogenesis, germ theory, particulate inheritance theory,
dual inheritance theory Dual inheritance theory (DIT), also known as gene–culture coevolution or biocultural evolution, was developed in the 1960s through early 1980s to explain how human behavior is a product of two different and interacting evolutionary processes: g ...
,
Young–Helmholtz theory The Young–Helmholtz theory (based on the work of Thomas Young and Hermann von Helmholtz in the 19th century), also known as the trichromatic theory, is a theory of trichromatic color vision – the manner in which the visual system gives rise ...
, opponent process, cohesion-tension theory * ''
Chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...
'':
collision theory Collision theory is a principle of chemistry used to predict the rates of chemical reactions. It states that when suitable particles of the Reagent, reactant hit each other with the correct orientation, only a certain amount of collisions result ...
, kinetic theory of gases, Lewis theory, molecular theory, molecular orbital theory, transition state theory,
valence bond theory In chemistry, valence bond (VB) theory is one of the two basic theories, along with molecular orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of ...
* ''
Physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
'': atomic theory, Big Bang theory,
Dynamo theory In physics, the dynamo theory proposes a mechanism by which a celestial body such as Earth or a star generates a magnetic field. The dynamo theory describes the process through which a rotating, convection, convecting, and electrically conductin ...
,
perturbation theory In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle ...
,
theory of relativity The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical ph ...
(successor to
classical mechanics Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...
),
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
* ''
Earth science Earth science or geoscience includes all fields of natural science related to the planet Earth. This is a branch of science dealing with the physical, chemical, and biological complex constitutions and synergistic linkages of Earth's four spheres ...
'': Climate change theory (from
climatology Climatology (from Greek , ''klima'', "slope"; and , '' -logia'') or climate science is the scientific study of Earth's climate, typically defined as weather conditions averaged over a period of at least 30 years. Climate concerns the atmospher ...
), Plass, G.N., 1956, The Carbon Dioxide Theory of Climatic Change, '' Tellus'' VIII, 2. (1956), pp. 140–54. plate tectonics theory (from
geology Geology (). is a branch of natural science concerned with the Earth and other astronomical objects, the rocks of which they are composed, and the processes by which they change over time. Modern geology significantly overlaps all other Earth ...
), theories of the origin of the Moon, theories for the Moon illusion * ''
Astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
'': Self-gravitating system,
Stellar evolution Stellar evolution is the process by which a star changes over the course of time. Depending on the mass of the star, its lifetime can range from a few million years for the most massive to trillions of years for the least massive, which is consi ...
, solar nebular model,
stellar nucleosynthesis In astrophysics, stellar nucleosynthesis is the creation of chemical elements by nuclear fusion reactions within stars. Stellar nucleosynthesis has occurred since the original creation of hydrogen, helium and lithium during the Big Bang. As a ...


Explanatory notes


References


Further reading

* Essay by a British/American meteorologist and NASA astronaut on anthopogenic global warming and "theory". {{Philosophy of science Epistemology of science Scientific method