Single Idea 9024

[catalogued under 5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle]

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.


A 'closed sentence' has no free variables in it

Gist of Idea

Excluded middle has three different definitions


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]