The Law of Identity (A is A) is a rational man’s paramount consideration in the process of determining his interests. He knows that the contradictory is the impossible, that a contradiction cannot be achieved in reality and that the attempt to achieve it can lead only to disaster and destruction. Therefore, he does not permit himself to hold contradictory values, to pursue contradictory goals, or to imagine that the pursuit of a contradiction can ever be to his interest.
A contradiction cannot exist. An atom is itself, and so is the universe; neither can contradict its own identity; nor can a part contradict the whole. No concept man forms is valid unless he integrates it without contradiction into the total sum of his knowledge. To arrive at a contradiction is to confess an error in one’s thinking; to maintain a contradiction is to abdicate one’s mind and to evict oneself from the realm of reality.
[Objectivism agrees with Aristotle’s formulation of the Law of Non-Contradiction]: These truths hold good for everything that is, and not for some special genus apart from others. And all men use them, because they are true of being qua being . . . . For a principle which everyone must have who understands anything that is, is not a hypothesis . . . . Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect.