3. LAW OF CONTRADICTION.
The law of contradiction underlies all negative propositions. It is the mission of this law to tear down or to be destructive in nature; while the law of identity builds up or is constructive in nature.
The law of contradiction may be stated in this way: It is impossible for the same thing to be and not to be at the same time and in the same place. Or better, itis impossible for the same thing to be itself and its contradictory at the same time. Bringing out a further aspect, no thing can have and not have the same attributes at the same time.
The little word not bisects the universe. All the people in the world are either honest or not honest, virtuous or not virtuous. These are contradictory statements and what is comprehended by the one cannot be comprehended by the other at the same time, any more than a man can shake his head and nod his head at the same time.
If we assert the identity between two notions then we cannot in the same breath deny their identity.
ILLUSTRATIONS:
(1) A red flower cannot be a red flower and not a red flower at the same time.
(2) No man can be guilty and not guilty at the same time.
(3) A boy cannot be working and not working at the same time.
If I assert that the flower is red, then I cannot affirm in the same breath that the flower is not red.
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.
It is easy to use opposite terms in a contradictory sense. This leads to serious error. “Not-guilty” is the contradictory of “guilty,” while “innocent” is the opposite of “guilty.” We could hardly say that the water must either be cold or hot, as it might be warm. “Not-hot” is the only term which contradicts “hot.” The law of contradiction has nothing to do with opposites.
Further, it is dangerous to regard words with the negative prefix as being contradictory of the affirmative form. For example: Valuable and invaluable are not contradictory. There is likewise some doubt as to the contradictory nature of such words as agreeable and disagreeable, though we are sure that agreeable and not-agreeable contradict each other. To use the “not” with a hyphen is safer than to depend upon some prefix which is supposed to mean “not.”
ILLUSTRATIONS OF CONTRADICTORY AND OPPOSITE TERMS.
| Opposite. | Contradictory. | |||
| bad | good | bad | not-bad | |
| soft | hard | soft | not-soft | |
| cold | hot | cold | not-cold | |
| rough | smooth | rough | not-rough | |
| good | evil | good | not-good | |
| warm | cool | warm | not-warm | |
| weak | strong | weak | not-weak | |