- For a more detailed account of theories as expressed in
formal language as they are studied
in mathematical logic see
Theory .
The term
theory has two broad sets of
meanings, one used in the empirical sciences (both natural and
social) and the other used in philosophy, mathematics, logic, and
across other fields in the humanities. There is considerable
difference and even dispute across academic disciplines as to the
proper usages of the term. What follows is an attempt to describe
how the term
is used, not to try to say how it
ought to be used.
Although the scientific meaning is by far the more commonly used in
academic discourse, it is hardly the only one used, and it would be
a mistake to assume from the outset that a given use of the term
"theory" in academic literature or discourse is a reference to a
scientific or empirically-based theory.
Even so, since the use of the term
theory in scientific or
empirical inquiry is the more common one, it will be discussed
first. (Other usages follow in the section labeled "Theories
formally and generally.")
A theory, in the
scientific sense of the word, is an
analytic structure designed to
explain a
set of
empirical observations. A scientific theory does
two things:
- it identifies this set of distinct observations as a class of
phenomena, and
- makes assertions about the underlying reality that brings about or affects this
class.
In the scientific or empirical tradition, the term "theory" is
reserved for ideas which meet baseline requirements about the kinds
of empirical observations made, the methods of classification used,
and the
consistency of the theory in its
application among members of the class to which it pertains. These
requirements vary across different scientific fields of
knowledge, but in general theories are expected to
be functional and
parsimonious: i.e. a
theory should be the simplest possible tool that can be used to
effectively address the given class of phenomena.
Theories are distinct from
theorems:
theorems are
derived deductively from
theories according to a
formal system
of rules, generally as a first step in testing or applying the
theory in a concrete situation. Theories are abstract and
conceptual, and to this end they are never considered right or
wrong. Instead, they are supported or challenged by observations in
the world. They are '
rigorously tentative',
meaning that they are proposed as true but expected to satisfy
careful examination to account for the possibility of faulty
inference or incorrect observation. Sometimes theories are
falsified, meaning that an explicit set of observations contradicts
some fundamental assumption of the theory, but more often theories
are revised to conform to new observations, by restricting the
class of phenomena the theory applies to or changing the assertions
made. Sometimes a theory is set aside by scholars because there is
no way to examine its assertions analytically; these may continue
on in the popular imagination until some means of examination is
found which either refutes or lends credence to the theory.
The word 'theory' is generally considered to derive from Greek
theoria (Jerome), Greek
"contemplation, speculation", from "spectator",
thea "a
view" +
horan "to see", literally "looking at a show". A
second possible etymology traces the word back to
to theion "divine things" instead of
thea,
reflecting the concept of contemplating the divine organisation
(
Cosmos) of the nature. The word has been in
use in English since at least the late 16th century.
Theories formally and generally
Theories are
analytical tools for
understanding,
explaining, and making
predictions about a given
subject matter. There are theories in many
and varied fields of study, including the
arts
and
sciences. A formal theory is
syntactic in nature and is only meaningful
when given a
semantic component by
applying it to some content (i.e.
facts and
relationships of the actual historical world as it is unfolding).
Theories in various fields of study are expressed in
natural language, but are always
constructed in such a way that their general form is identical to a
theory as it is expressed in the
formal
language of
mathematical
logic. Theories may be expressed mathematically, symbolically,
or in common language, but are generally expected to follow
principles of
rational thought or
logic.
Theory is constructed of a set of
sentences which consist entirely of
true
statements about the subject matter
under consideration. However, the truth of any one of these
statements is always relative to the whole theory. Therefore the
same statement may be true with respect to one theory, and not true
with respect to another.
This is, in ordinary language, where statements such as "He is a
terrible person" cannot be judged to be true or false without
reference to some
interpretation of who "He" is and for
that matter what a "terrible person" is under this theory.
Sometimes two theories have exactly the same
explanatory power because they make the
same predictions. A pair of such theories is called
indistinguishable, and the choice between them reduces to
convenience or philosophical preference.
The form of theories is studied formally in
mathematical logic, especially in
model theory. When theories are studied
in mathematics, they are usually expressed in some
formal language and their statements are
closed under application of
certain procedures called
rules of
inference. A special case of this, an axiomatic theory,
consists of
axioms (or axiom schemata) and
rules of inference. A
theorem is a statement
that can be derived from those axioms by application of these rules
of inference. Theories used in applications are
abstractions of observed phenomena and the
resulting theorems provide solutions to real-world problems.
Obvious examples include
arithmetic
(abstracting concepts of number),
geometry
(concepts of space), and
probability
(concepts of randomness and likelihood).
Gödel's
incompleteness theorem shows that no consistent,
recursively enumerable theory (that
is, one whose theorems form a recursively enumerable set) in which
the concept of
natural numbers can
be expressed, can include all
true statements
about them. As a result, some domains of knowledge cannot be
formalized, accurately and completely, as mathematical theories.
(Here, formalizing accurately and completely means that all true
propositions—and only true propositions—are derivable within the
mathematical system.) This limitation, however, in no way precludes
the construction of mathematical theories that formalize large
bodies of scientific knowledge.
Philosophical theories
Theories whose subject matter consists not in empirical data, but
rather in
ideas are in the realm of
philosophical theories as contrasted with
scientific
theories. At least some of the elementary theorems of a
philosophical theory are statements whose truth cannot necessarily
be scientifically tested through
empirical
observation.
Metatheory
One form of philosophical theory is a
metatheory or
meta-theory. A metatheory is a theory whose
subject matter is some other theory. In other
words it is a theory about a theory.
Statements made in the metatheory about
the theory are called
metatheorems.
Political theories
A political theory is an
ethical theory about
the law and government. Often the term "political theory" refers to
a general view, or specific ethic, political belief or attitude,
about
politics.
Scientific theories
In
science, generally, theories are
constructed from elementary theorems that consist in empirical data
about observable phenomena. A scientific theory is used as a
plausible general principle or body of principles offered to
explain a phenomenon.
A scientific theory is a
deductive theory, in that, its
content is based on some
formal system of
logic and that some of its elementary theorems 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.
A major concern in construction of scientific theories is the
problem of demarcation, i.e.,
distinguishing those ideas that are properly studied by the
sciences and those that are not.
Theories are intended to be an accurate, predictive description of
the
natural world.
Theories as models
Theories are constructed to explain, predict, and master phenomena
(e.g., inanimate things, events, or behavior of animals). A
scientific theory can be thought of as a
model of
reality,
and its statements as
axioms of some
axiomatic system. The aim of this
construction is to create a
formal
system for which
reality is the only
model. The world is an interpretation (or model) of such scientific
theories, only insofar as the sciences are true.
Theories in physics
In
physics the term
theory is
generally used for a mathematical framework—derived from a small
set of basic
postulates (usually
symmetries—like equality of locations in space or in time, or
identity of electrons, etc.)—which is capable of producing
experimental predictions for a given category of physical systems.
A good example is
classical
electromagnetism, which encompasses results derived from
gauge symmetry (sometimes called
gauge invariance) in a form of a
few equations called
Maxwell's
equations. Note that the specific theoretical aspects of
classical electromagnetic theory, which have been consistently and
successfully replicated for well over a century, are termed "laws
of electromagnetism", reflecting that they are today taken for
granted. Within electromagnetic theory generally, there are
numerous hypotheses about how electromagnetism applies to specific
situations. Many of these hypotheses are already considered to be
adequately tested, with new ones always in the making and perhaps
untested.
Pedagogical definition
In pedagogical contexts or in official pronouncements by official
organizations of scientists a definition such as the following may
be promulgated.
According
to the United States National Academy of
Sciences
,
Some scientific explanations are so well established
that no new evidence is likely to alter them.
The explanation becomes a scientific
theory.
In everyday language a theory means a hunch or
speculation.
Not so in science.
In science, the word theory refers to a comprehensive
explanation of an important feature of nature supported by facts
gathered over time.
Theories also allow scientists to make predictions
about as yet unobserved phenomena,
According to the American Association for the Advancement of
Science,
A scientific theory is a well-substantiated explanation
of some aspect of the natural world, based on a body of facts that
have been repeatedly confirmed through observation and experiment.
Such fact-supported theories are not "guesses" but reliable
accounts of the real world. The theory of biological evolution is
more than "just a theory." It is as factual an explanation of the
universe as the atomic theory of matter or the germ theory of
disease. Our understanding of gravity is still a work in progress.
But the phenomenon of gravity, like evolution, is an accepted
fact.
The primary advantage enjoyed by this definition is that it firmly
marks things termed theories as being well supported by evidence.
This would be a disadvantage in interpreting real discourse between
scientists who often use the word theory to describe untested but
intricate hypotheses in addition to repeatedly confirmed models.
However, in an educational or mass media setting it is almost
certain that everything of the form X theory is an extremely well
supported and well tested theory. This causes the theory/non-theory
distinction to much more closely follow the distinctions useful for
consumers of science (e.g. should I believe something or
not?)
The term theoretical
The term
theoretical is sometimes informally used in place
of
hypothetical to describe a result that is predicted by
theory but has not yet been adequately tested by
observation or
experiment. It is not uncommon for a theory to
produce predictions that are later confirmed or proven incorrect by
experiment. By inference, a prediction proved incorrect by
experiment demonstrates the hypothesis is invalid. This either
means the theory is incorrect, or the experimental conjecture was
wrong and the theory did not predict the hypothesis.
Fields of study called "theories"
Fields of study are sometimes named "theory" because their basis is
some initial set of assumptions describing the field's approach to
a subject matter. These assumptions are the elementary theorems of
the particular theory, and can be thought of as the axioms of that
field. Some commonly known examples include
set theory,
game
theory, and
number theory; however
literary theory,
critical theory, and
music theory are also of the same form.
Intertheoretic reduction and elimination
If there is a new theory which is better at explaining and
predicting phenomena than an older theory (i.e. it has more
explanatory power), we are
justified in believing that
the newer theory describes reality more correctly. This is called
an
intertheoretic reduction because the terms of the old
theory can be reduced to the terms of the new one. For instance,
our historical understanding about "sound," "light" and "heat,"
have today been reduced to "wave compressions and rarefactions,"
"electromagnetic waves," and "molecular kinetic energy"
respectively. These terms which are identified with each other are
called
intertheoretic identities. When an old theory and a
new one are parallel in this way, we can conclude that we are
describing the same reality, only more completely.
In cases where a new theory uses new terms which do not reduce to
terms of an older one, but rather replace them entirely because
they are actually a misrepresentation it is called an
intertheoretic elimination. For instance, the obsolete
scientific theory that put forward an understanding of heat
transfer in terms of the movement of
caloric fluid was eliminated when a theory of
heat as energy replaced it. Also, the theory that
phlogiston is a substance released from burning
and rusting material was eliminated with the new understanding of
the reactivity of oxygen.
Underdetermination
A theory is
underdetermined (also called
indeterminacy
of data to theory) if, given the available evidence cited to
support the theory, there is a rival theory which is inconsistent
with it that is at least as consistent with the evidence.
Underdetermination is an
epistemological issue about the relation of
evidence to conclusions.
List of notable theories
See also
Notes
References
- Popper, Karl (1963), Conjectures
and Refutations, Routledge and Kegan Paul, London, UK, pp.
33–39. Reprinted in Theodore Schick
(ed., 2000), Readings in the Philosophy of Science,
Mayfield Publishing Company, Mountain View, Calif., pp. 9–13.
- Chairman of Biology and Kennesaw State Ronald
Matson's webpage comparing scientific laws and theories
- Hawking, Stephen (1996). "The Illustrated A Brief History of
Time" (Updated and expanded ed.). New York: Bantam Books, p.
15.
- Mohr, Johnathon (2008). "Revelations and Implications of the
Failure of Pragmatism: The Hijacking of Knowledge Creation by the
Ivory Tower". New York: Ballantine Books. pp. 87–192.