Full Idea
The law of excluded middle, or 'tertium non datur', may be pictured variously as 1) Every closed sentence is true or false; or 2) Every closed sentence or its negation is true; or 3) Every closed sentence is true or not true.
Clarification
A 'closed sentence' has no free variables in it
Gist of Idea
Excluded middle has three different definitions
Source
Willard Quine (Philosophy of Logic [1970], Ch.6)
Book Reference
Quine,Willard: 'Philosophy of Logic' [Prentice-Hall 1970], p.83
A Reaction
Unlike many top philosophers, Quine thinks clearly about such things. 1) is the classical bivalent reading of excluded middle; 2) is the purely syntactic version; 3) leaves open how we interpret the 'not-true' option.
Related Ideas
Idea 8709 The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend]
Idea 17924 Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]