4. THE LAW OF EXCLUDED MIDDLE.
The law of excluded middle may be considered as a combination of identity and contradiction. Identity gives the proposition, “John Doe is honest.” Contradiction, “John Doe is not honest.” Combine the two using either and or and we have the excluded middle proposition, “Either John Doe is honest or he is not honest.”
Excluded middle explains itself. Of the two contradictory notions it must be either the one or the other. There is no “go-between” notion.
The law may be stated in many ways, as will be seen by the following: (1) Everything must either be or not be. (2) Either a given judgment is true or its contradictory is true; there is no middle ground. (3) Of two contradictory judgments one must be true. (4) Every predicate may be affirmed or denied of every subject.
ILLUSTRATIONS:
(1) A man is either mortal or he is not mortal. (2) John Doe is either honest or not-honest. (3) Either you are going or you are not going.
SYMBOLIZATION OF EXCLUDED MIDDLE.
A is either A or not-A
or
A is either B or not-B.