In Mathematics
An effective theory is a formal theory whose set of axioms is recursively enumerable, that is, it is theoretically possible to write a computer program that, if allowed to run forever, would output the axioms of the theory one at a time and not output anything else.
Godel's first incompleteness theorem demonstrates that such a theory cannot at the same time be complete, consistent, and include elementary arithmetic. See also Proof sketch for Gödel's first incompleteness theorem#Hypotheses of the theory.
Read more about this topic: Effective Theory
Famous quotes containing the word mathematics:
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)