TWO USES OF NOT.
The word not when used with the copula of a given proposition makes that proposition negative, as (1) “Some men are not wise.” But when not is attached to the predicate by a hyphen, the predicate is made negative, not the proposition, as (2) “Some men are not-wise.” Here the predicate not-wise is negative, but the proposition in which it appears is affirmative. It is obvious thatthe proposition “Some men are not wise” illustrates the law of contradiction, since the some men referred to are contradicted of all which is wise. Whereas the proposition “Some men are not-wise” illustrates relative identity, since the subject “some men” is affirmed of a part of the predicate “not-wise.” The student may be led to see these relations by drawing circles, the one to represent the subject, the other the predicate. (See [page 141.])
FURTHER ILLUSTRATIONS:
| Some teachers are wise |  | Illustrate the law of identity. |
| Some teachers are not-wise | ||
| Some teachers are unwise | ||
| Some teachers are not wise | | Illustrate the law of contradiction. |
| Some teachers are not not-wise | ||
| Some teachers are not unwise |
The student must understand that a term and its contradictory destroy each other. If we affirm something of the one, then we must deny it of the other, or we undermine the integrity of both. If it is affirmed of teachers A, B and C that they are wise, then it must be denied that they are not-wise.
ILLUSTRATIONS:
| A, B and C are wise. | | These are mutually destructive. |
| A, B and C are not-wise. | ||
| A, B and C are wise. | | These are not mutually destructive, but virtually mean the same thing. |
| A, B and C are not not-wise. |
SYMBOLIZATION OF THE LAW OF CONTRADICTION.
| A is not not-A. | or | A is not B. |
| (As A is always A it would be absurd to say that A is not A.) | or | |
| A is not not-B. |
CONTRADICTORY AND OPPOSITE TERMS.