Contrary to those who try to disparage logic by tying it to ivory tower types, knowledge is not gained from logic by some exclusively mental process unconnected to reality. Logic is not some isolated conscious process. The rules of logic are applied to man's sensory experience in order to make sense of that experience. Concepts Most assaults on reason begin as an assault on concepts. Almost all of the confusion centers around the difference between a concept and its definition.
First lets consider the role of concepts.
Concepts allow man to subsume vast amounts of information and an extensive reasoning process and fix that information to a word. One of Ayn Rand's greatest achievements had to do with her theory of concepts. She took concepts out of Plato's supernatural world of the forms and restored them as a valuable tool created by man. Mathematics and algebra provide a cogent example of the power of concepts. Numbers as a concept of quantity allows us to manipulate, think and analyze about quantity relationships using mathematics, particularly quantities that are not immediately apprehendable.