Scientific theory
Encyclopedia
A scientific theory comprises a collection of concept
s, including abstraction
s of observable
phenomena expressed as quantifiable properties, together with rules (called scientific law
s) that express relationships between observation
s 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 inductive 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 idea
s. Such theories are in the realm of philosophical theories
as contrasted with scientific theories. A philosophical theory is not necessarily scientifically testable through experiment
.
– which was prevalent in logical empiricism has in the course of the second half of the 20th century been replaced by the semantic view of theories
which identifies scientific theories with models rather than propositions.
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 axiom
s 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.
, 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.
. 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...
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).
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.
(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."
. 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:
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.
likened a theory to a network:
Michael Polanyi
made a powerful analogy between a theory and a map:
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. Galileo Galilei
spoke of the book of nature being written in the language of mathematics. Perhaps the book about the book of nature is also written with mathematics. And it is this metaphor that the contemporary philosopher of science Ian Hacking
seems to allude to in the following multi-faceted passage:
Scientific theories as networks, maps, and books. A rich array of images, analogies, and metaphors. Add your own.
described the characteristics of a scientific theory as follows:
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:
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.
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 synchrotron
s. 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.
According to the United States National Academy of Sciences
,
According to this definition, a theory must be well supported by evidence. Furthermore, the term theory would not be appropriate for describing untested but intricate hypotheses or even scientific models. Consumers of science may find the above definition useful when evaluating the validity and/or efficacy of a theory.
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.
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.
Concept
The word concept is used in ordinary language as well as in almost all academic disciplines. Particularly in philosophy, psychology and cognitive sciences the term is much used and much discussed. WordNet defines concept: "conception, construct ". However, the meaning of the term concept is much...
s, including abstraction
Abstraction
Abstraction is a process by which higher concepts are derived from the usage and classification of literal concepts, first principles, or other methods....
s of observable
Observable
In physics, particularly in quantum physics, a system observable is a property of the system state that can be determined by some sequence of physical operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value off...
phenomena expressed as quantifiable properties, together with rules (called scientific law
Scientific law
A scientific law is a statement that explains what something does in science just like Newton's law of universal gravitation. A scientific law must always apply under the same conditions, and implies a causal relationship between its elements. The law must be confirmed and broadly agreed upon...
s) that express relationships between observation
Observation
Observation is either an activity of a living being, such as a human, consisting of receiving knowledge of the outside world through the senses, or the recording of data using scientific instruments. The term may also refer to any data collected during this activity...
s of such concepts. A scientific theory is constructed to conform to available empirical data about such observations, and is put forth as a principle
Principle
A principle is a law or rule that has to be, or usually is to be followed, or can be desirably followed, or is an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed...
or body of principles for explaining a class of phenomena.
A scientific theory is a type of inductive theory, in that its content (i.e. empirical data) could be expressed within some formal system of logic
Formal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...
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
Humanities
The humanities are academic disciplines that study the human condition, using methods that are primarily analytical, critical, or speculative, as distinguished from the mainly empirical approaches of the natural sciences....
, one finds theories whose subject matter does not (only) concern empirical data, but rather idea
Idea
In the most narrow sense, an idea is just whatever is before the mind when one thinks. Very often, ideas are construed as representational images; i.e. images of some object. In other contexts, ideas are taken to be concepts, although abstract concepts do not necessarily appear as images...
s. Such theories are in the realm of philosophical theories
Philosophical theory
In the general sense, a philosophical theory is a theory that explains or accounts for a general philosophy or specific branch of philosophy. While any sort of thesis or opinion may be termed a theory, in analytic philosophy it is thought best to reserve the word "theory" for systematic,...
as contrasted with scientific theories. A philosophical theory is not necessarily scientifically testable through experiment
Experiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...
.
Theories as models
The previously dominant position in philosophy of science – the received view of theoriesReceived view of theories
The received view of theories is a position in the philosophy of science that identifies a scientific theory with a set of propositions which are considered to be linguistic objects, such as axioms...
– which was prevalent in logical empiricism has in the course of the second half of the 20th century been replaced by the semantic view of theories
Semantic view of theories
The semantic view of theories is a position in the philosophy of science that holds that a scientific theory can be identified with a collection of models...
which identifies scientific theories with models rather than propositions.
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
Reality
In philosophy, reality is the state of things as they actually exist, rather than as they may appear or might be imagined. In a wider definition, reality includes everything that is and has been, whether or not it is observable or comprehensible...
, and its statements as axiom
Axiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
s of some axiomatic system
Axiomatic system
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A mathematical theory consists of an axiomatic system and all its derived theorems...
. The aim of this construction is to create a formal system
Formal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...
for which reality
Reality
In philosophy, reality is the state of things as they actually exist, rather than as they may appear or might be imagined. In a wider definition, reality includes everything that is and has been, whether or not it is observable or comprehensible...
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 PopperKarl Popper
Sir Karl Raimund Popper, CH FRS FBA was an Austro-British philosopher and a professor at the London School of Economics...
, Stephen Hawking
Stephen Hawking
Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
in A Brief History of Time
A Brief History of Time
A Brief History of Time is a popular science book written by renown physicist Stephen Hawking and first published by the Bantam Dell Publishing Group in 1988. It became a best-seller and has sold more than 10 million copies...
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
Hypothesis
A hypothesis is a proposed explanation for a phenomenon. The term derives from the Greek, ὑποτιθέναι – hypotithenai meaning "to put under" or "to suppose". For a hypothesis to be put forward as a scientific hypothesis, the scientific method requires that one can test it...
; 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 AsimovIsaac Asimov
Isaac Asimov was an American author and professor of biochemistry at Boston University, best known for his works of science fiction and for his popular science books. Asimov was one of the most prolific writers of all time, having written or edited more than 500 books and an estimated 90,000...
. 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 philosophyPhilosophyPhilosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
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 EinsteinAlbert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
put forth his Special Theory of Relativity. He took two phenomena that had been observed — that the "addition of velocities" is valid (Galilean transformation
Galilean transformation
The Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. This is the passive transformation point of view...
), and that light did not appear to have an "addition of velocities" (Michelson-Morley experiment
Michelson-Morley experiment
The Michelson–Morley experiment was performed in 1887 by Albert Michelson and Edward Morley at what is now Case Western Reserve University in Cleveland, Ohio. Its results are generally considered to be the first strong evidence against the theory of a luminiferous ether and in favor of special...
). 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 PtolemyPtolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
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 PepperStephen Pepper
Stephen C. Pepper was an American philosopher.-References:*http://people.sunyit.edu/~harrell/Pepper/Index.htm*http://people.sunyit.edu/~harrell/Pepper/pep_efron.htm-External Links:...
(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 predictionsPredictive power
The predictive power of a scientific theory refers to its ability to generate testable predictions. Theories with strong predictive power are highly valued, because the predictions can often encourage the falsification of the theory...
. 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
Knowledge
Knowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...
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 among the most parsimonious explanations, sparing in proposed entities or explanations—commonly referred to as passing the Occam's razorOccam's razorOccam's razor, also known as Ockham's razor, and sometimes expressed in Latin as lex parsimoniae , is a principle that generally recommends from among competing hypotheses selecting the one that makes the fewest new assumptions.-Overview:The principle is often summarized as "simpler explanations...
test. (Since there is no generally accepted objective definition of parsimony, this is not a strict criteria, but some theories are much less economical than others.)
This is true of such established theories as special
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
and general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, plate tectonics
Plate tectonics
Plate tectonics is a scientific theory that describes the large scale motions of Earth's lithosphere...
, evolution
Evolution
Evolution is any change across successive generations in the heritable characteristics of biological populations. Evolutionary processes give rise to diversity at every level of biological organisation, including species, individual organisms and molecules such as DNA and proteins.Life on Earth...
, 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 mechanicsClassical mechanicsIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
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 chemistryChemistryChemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, 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.
Images, Analogies, and Metaphors of Theory
Sometimes images, analogies, and metaphors are more powerful for motivating our understanding of a highly abstract topic than rigid and detached philosophical analysis. Philosophers realize this, and capitalize on it. For instance, regarding the structure of scientific theory, the influential logical empiricist Carl Gustav HempelCarl Gustav Hempel
Carl Gustav "Peter" Hempel was a philosopher of science and a major figure in 20th-century logical empiricism...
likened a theory to a network:
A scientific theory might therefore be likened 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
Michael Polanyi
Michael Polanyi, FRS was a Hungarian–British polymath, who made important theoretical contributions to physical chemistry, economics, and the theory of knowledge...
made a powerful 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. Galileo Galilei
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...
spoke of the book of nature being written in the language of mathematics. Perhaps the book about the book of nature is also written with mathematics. And it is this metaphor that the contemporary philosopher of science Ian Hacking
Ian Hacking
Ian Hacking, CC, FRSC, FBA is a Canadian philosopher, specializing in the philosophy of science.- Life and works :...
seems to allude to in the following multi-faceted passage:
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. Far from being untidy, this is New World Leibnizianism. 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.
Scientific theories as networks, maps, and books. A rich array of images, analogies, and metaphors. Add your own.
Criteria for scientific status
Karl PopperKarl Popper
Sir Karl Raimund Popper, CH FRS FBA was an Austro-British philosopher and a professor at the London School of Economics...
described the characteristics of a scientific theory as follows:
- 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 to happen. 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, 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:
- 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).
- 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).
- 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 physicsPhysics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
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
Classical electromagnetism
Classical electromagnetism is a branch of theoretical physics that studies consequences of the electromagnetic forces between electric charges and currents...
, 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
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.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 synchrotron
Synchrotron
A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field and the electric field are carefully synchronised with the travelling particle beam. The proton synchrotron was originally conceived by Sir Marcus Oliphant...
s. 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 scientific organizations a definition such as the following may be promulgated.According to the United States National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
,
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.
According to this definition, a theory must be well supported by evidence. Furthermore, the term theory would not be appropriate for describing untested but intricate hypotheses or even scientific models. Consumers of science may find the above definition useful when evaluating the validity and/or efficacy of a theory.
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 observationObservation
Observation is either an activity of a living being, such as a human, consisting of receiving knowledge of the outside world through the senses, or the recording of data using scientific instruments. The term may also refer to any data collected during this activity...
or experiment
Experiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...
. 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
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.