## Encyclopedia > Law of the excluded middle

Article Content

# Law of excluded middle

Redirected from Law of the excluded middle

The law of excluded middle states that for any proposition P, it is true that (P or not-P).

For example, if P is

Joe is bald

then the disjunction

Joe is bald, or Joe is not bald

is true.

This is not quite the same as the principle of bivalence, which states that P must be either true or false. The law of excluded middle only says that (P or not-P) is true, but does not comment on what truth values P itself may take.

This leaves open the possibility that certain systems of logic may reject bivalence (by allowing more than 2 truth values) but accept the law of excluded middle, by accepting that (P or not-P) is always true, even when P itself is neither true nor false.

The distinction is far less important in traditional logic, however, where bivalence is accepted.

The page bivalence and related laws discusses this issue in greater detail.

The law of excluded middle holds for any bivalent truth system. If we remove the law of excluded middle from a formal logical system, the result will be a system called intuitionistic logic, which is the logic of mathematical intuitionism.

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia
 Search over one million articles, find something about almost anything!

Featured Article
 Springs, New York ... are married couples living together, 8.9% have a female householder with no husband present, and 34.9% are non-families. 26.1% of all households are made up of ...