The law of the excluded middle is the principle of classical logic stating that for every proposition 
, either 
or its negation is true. Symbolically,
it is
 |
The principle asserts that no third truth value lies between truth and falsehood. It is valid in classical two-valued logic,
but it is not accepted as a general principle in intuitionistic
logic, where a proof of 
must construct either a proof of 
or a proof of 
. It can also fail under the usual interpretations of
three-valued logic and fuzzy
logic.
The law should not be confused with the law of noncontradiction, which states that 
and 
cannot both be true. The two laws are distinct even though both hold in classical
logic.
