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Reason is defined by Ayn Rand as "the faculty that identifies and integrates the material provided by man's senses."

Reason performs this function by means of concepts, and the validity of reason rests on the validity of concepts. But the nature and origin of concepts is a major philosophic problem. If concepts refer to facts, then knowledge has a base in reality, and one can define objective principles to guide man's process of cognition. If concepts are cut off from reality, then so is all human knowledge, and man is helplessly blind.

This is the "problem of universals," on which Western philosophy has foundered.

Plato claimed to find the referent of concepts not in this world, but in a supernatural dimension of essences. The Kantians regard concepts (some or all) as devoid of referents, i.e., as subjective creations of the human mind independent of external facts. Both approaches and all of their variants in the history of philosophy lead to the same essential consequence: the severing of man's tools of cognition from reality, and therefore the undercutting of man's mind. (Although Aristotle's epistemology is far superior, his theory of concepts is intermingled with remnants of Platonism and is untenable.) Recent philosophers have given up the problem and, as a result, have given up philosophy as such.

Ayn Rand challenges and sweeps aside the main bulwark of the anti-mind axis. Her historic feat is to tie man's distinctive form of cognition to reality, i.e., to validate man's reason.

According to Objectivism, concepts are derived from and do refer to the facts of reality.

The mind at birth (as Aristotle first stated) is tabula rasa; there are no innate ideas. The senses are man's primary means of contact with reality; they give him the precondition of all subsequent knowledge, the evidence that something is. What the something is he discovers on the conceptual level of awareness.

Conceptualization is man's method of organizing sensory material. To form a concept, one isolates two or more similar concretes from the rest of one's perceptual field, and integrates them into a single mental unit, symbolized by a word. A concept subsumes an unlimited number of instances: the concretes one isolated, and all others (past, present, and future) which are similar to them.

Similarity is the key to this process. The mind can retain the characteristics of similar concretes without specifying their measurements, which vary from case to case. "A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted." 

The basic principle of concept-formation (which states that the omitted measurements must exist in some quantity, but may exist in any quantity) is the equivalent of the basic principle of algebra, which states that algebraic symbols must be given some numerical value, but may be given any value. In this sense and respect, perceptual awareness is the arithmetic, but conceptual awareness is the algebra of cognition.

Concepts are neither supernatural nor subjective: they refer to facts of this world, as processed by man's means of cognition. (The foregoing is a brief indication; for a full discussion see Introduction to Objectivist Epistemology.)

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The Philosophy of Objectivism: A Brief Summary