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, _it is 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 that the 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 } Some teachers are not-wise } Illustrate the law of identity. Some teachers are unwise } Some teachers are not wise } Some teachers are not not-wise } Illustrate the law of contradiction. 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 A, B and C are not-wise. } destructive.