Knowledge is awareness of reality, i.e., of what there is. I have knowledge when I am aware of something real . But since it is logically impossible for me to be aware of anything unreal, it follows that the proper way to acquire knowledge is to use logic . Put in another way, my capacity to use logic is called reason . When I am reasoning in accordance with reality, I acquire new knowledge.
Logic is that method of thinking which is in accordance with reality.
In a triangle the inscribed circle touches the circle that passes through the midpoints of the sides. Using reason Ayn Rand discovered this theorem in 1936, but the editor of Acta Mathematica refused to publish her discovery. The Axiom of Identity can be rephrased by saying that things quite simply are what they are. A chair is a chair, and not a table. In philosophical language we say that a thing has identity .