Excluded middle. A is either A or not-A. A is either B or not-B.
Contradiction. A is not not-A. A is not B or A is not not-B.
Excluded middle. A man is either a man or A man is either honest or a not-man. not-honest.
Contradiction. A man is not a not-man. A man is not honest, or a man is not not-honest.
Identity. A man is a man. A man is not-honest, or a man is honest.
The “excluded middle” propositions of the foregoing express alternatives which are mutually contradictory. There is no middle ground. The “contradictory propositions” contradict the identity of the subject with one alternative, while the “identity” propositions affirm the identity of the subject with the other alternative. This is made possible because of the principle, “Of two mutually contradictory terms, if one is true the other must be false.” The foregoing scheme shows how closely “contradictory” and “identity” propositions are related to “excluded middle” propositions. Expressed mathematically: excluded middle = contradiction + identity.
(1) Two fundamental laws. Identity, contradiction.
(2) Law of identity. Absolute――complete, incomplete. Relative.
(3) Law of contradiction. Two uses of _not_. Contradictory and opposite terms.
(1) The elemental forms of evolved thought are the affirmative and negative judgments. This suggests two fundamental laws of thought, the law of identity and the law of contradiction. The former conditions the affirmative judgment, the latter the negative.
(2) The law of identity implies a permanency of being. “Everything remains identical with itself,” is a statement of identity.
Absolute identity may be divided into complete and incomplete identity.
In complete absolute identity the subject is the same as the predicate in both form and meaning. Truisms illustrate this.
In incomplete absolute identity the subject is identical with the predicate in meaning only. Illustrated by definitions.
In relative identity the whole of the subject may be affirmed of a part of the predicate or a part of the subject may be affirmed of a part of the predicate.
(3) “It is impossible for the same thing to be itself and its contradictory at the same time,” is a statement of the law of contradiction. _Identity_ is _con_structive while _contradiction_ is _de_structive in nature. To make the proposition negative the word _not_ must be used with the copula. “_Not_” attached to the predicate with a hyphen makes the _predicate_ negative, but not the _proposition_.