What is "excluded middle"

Exclude \Ex*clude"\, v. t. [imp. & p. p. Excluded; p. pr. & vb. n. Excluding.] [L. excludere, exclusum; ex out + claudere to shut. See Close.]

1. To shut out; to hinder from entrance or admission; to debar from participation or enjoyment; to deprive of; to except; -- the opposite to admit; as, to exclude a crowd from a room or house; to exclude the light; to exclude one nation from the ports of another; to exclude a taxpayer from the privilege of voting.

   And none but such, from mercy I exclude.
   --Milton.

2. To thrust out or eject; to expel; as, to exclude young animals from the womb or from eggs.

   Excluded middle. (logic) The name given to the third of the ``three logical axioms,'' so-called, namely, to that one which is expressed by the formula: ``Everything is either A or Not-A.'' no third state or condition being involved or allowed. See Principle of contradiction, under Contradiction.