**The Law or Principle of Excluded Middle**
Originally proposed by Aristotle: "There is nothing between asserting and denying." Generally given as "`A` is `B` or `A` is not `B`;" i.e., that an object (A) either has or lacks a given property (B). An alternate formulation of this (with propositions instead of objects) is "`p` or not `p`" - but not both. It is not the same as the Law of Bivalence, that everything is either true or false. The excluded middle is a logical argument, while bivalence is a semantic argument involving the idea of "truth." The excluded middle is one of the three Laws or Principles of Thought in Aristotelian logic: Identity (`A` is `A`), Contradiction (`A` is not both `B` and not `B`), and the Excluded Middle.

One problem with the excluded middle is with vague properties such as "bald." If we are to determine whether a person is bald or not bald, where is the line drawn? At 10 hairs, or 10000 hairs? In this situation, the excluded middle is actually more useful than bivalence; one of "`A` is bald" or "`A` is not bald" does not hold for all definitions of bald. However, it is true that for all definitions of bald, one of the two must hold. Intuitionism and many-valued logics also deny the excluded middle, instead preferring a version of bivalence: "No proposition is neither true nor false."