Theory





In mathematics, a theory is a set of statements closed under logical
implication. In mathematical logic, "theory" is the term for a set of
well-formed formulae consisting of certain axioms and all theorems provable
from said axioms. Gšdel's incompleteness theorem states that no consistent
theory, with a finite number of axioms (in a language at least as strong as
arithmetic), can include all true statements.

In science, a theory is a model of reality, used for rationalizing,
explaining, predicting, and mastering physical phenomena. There is a
difference between the technical term and its common usage. A theory has to
be something which is in some way testable; for example, one can theorize
that an apple will fall when dropped, and then drop an apple, to see what
happens. Many scientists, but not all, argue that religious beliefs are not
testable, and thus not theories, because they are matters of faith.

According to Stephen Hawking in A Brief History of Time, "a theory is a good
theory if it satisfied 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 thoery 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."

There are two types of theories; a supposition which is not backed by
observation is known as a conjecture, and if backed by observation it is a
hypothesis. A theory is different from a theorem. The former is a model of
physical events and cannot be proved from basic axioms. The latter is a
statement of mathematical fact which logically follows from a set of axioms.
A theory is also different from a physical law in that the former is a model
of reality whereas the latter is a statement of what has been observed.

The word theoretical is derived from theory, and is used to describe that
which has not yet been observed. For example, until recently, black holes
were theoretical.

Theories can become accepted if they are able to make correct predictions
and avoid incorrect ones. Theories which are simplier, and more
mathematically elegant, tend to be accepted over theories which are complex.
Theories are more likely to be accepted if they connect a wide range of
phenonomena. The process of accepting theories is part of the scientific method.

Further explanation of a scientific theory

In common usage a theory is often viewed as little more than a guess or a
hypothesis. But in science, a theory is much more than that. A theory is an
established paradigm that explains all of the data we have and offers valid
predictions that can be tested. In science, a theory can never be proven
true, because we can never assume we know all there is to know. Instead,
theories remain standing until they are disproven, at which point they are
thrown out altogether or modified slightly.

Some theories that have been disproved are those such as Lamarckism and the
geocentric universe theory. Sufficient evidence has risen to declare these
theories false.

Often the statement "Well, it's just a theory," is used to dismiss
controversial theories such as evolution, but in science a theory usually

  1. is supported by many strands of evidence rather than a single
     foundation, ensuring that it probably is a good approximation if not
     totally correct,
  2. has survived many critical tests that could have proven it false,
  3. makes predictions that might someday be used to disprove the theory,
     and
  4. is the best known explanation, in the sense of Occam's Razor, of the
     infinite variety of alternative explanations for the same data.

This is true of such established theories as evolution, special and general
relativity, quantum mechanics (with minimal interpretation), plate
tectonics, etc. Unfortunately the usage is muddled by cases like string
theory and "theories of everything," each probably better characterized at
present as a bundle of competing hypotheses. A hypothesis, however, is still
vastly more reliable than a conjecture, which is at best an untested guess
consistent with selected data, and is often a belief based on non-repeatable
experiments, anecdotes, popular opinion, "wisom of the ancients," commercial
motivation, or mysticism.

A good example of a non-scientific "theory" is Intelligent Design. Likewise,
other claims such as homeopathy are also not theories.