Concepts have a hierarchical structure, i.e., . . . the higher, more complex abstractions are derived from the simpler, basic ones (starting with the concepts of perceptually given concretes).

“Concepts of Consciousness”
Introduction to Objectivist Epistemology, 32

[There is a] long conceptual chain that starts from simple, ostensive definitions and rises to higher and still higher concepts, forming a hierarchical structure of knowledge so complex that no electronic computer could approach it. It is by means of such chains that man has to acquire and retain his knowledge of reality.

Starting from the base of conceptual development — from the concepts that identify perceptual concretes — the process of cognition moves in two interacting directions: toward more extensive and more intensive knowledge, toward wider integrations and more precise differentiations. Following the process and in accordance with cognitive evidence, earlier-formed concepts are integrated into wider ones or subdivided into narrower ones.

“Abstraction from Abstractions”
Introduction to Objectivist Epistemology, 19

Observe that the concept “furniture” is an abstraction one step further removed from perceptual reality than any of its constituent concepts. “Table” is an abstraction, since it designates any table, but its meaning can be conveyed simply by pointing to one or two perceptual objects. There is no such perceptual object as “furniture”; there are only tables, chairs, beds, etc. The meaning of “furniture” cannot be grasped unless one has first grasped the meaning of its constituent concepts; these are its link to reality. (On the lower levels of an unlimited conceptual chain, this is an illustration of the hierarchical structure of concepts.)

“Abstraction from Abstractions”
Introduction to Objectivist Epistemology, 22

The first concepts man forms are concepts of entities — since entities are the only primary existents. (Attributes cannot exist by themselves, they are merely the characteristics of entities; motions are motions of entities; relationships are relationships among entities.)

Since the definition of a concept is formulated in terms of other concepts, it enables man, not only to identify and retain a concept, but also to establish the relationships, the hierarchy, the integration of all his concepts and thus the integration of his knowledge. Definitions preserve, not the chronological order in which a given man may have learned concepts, but the logical order of their hierarchical interdependence.

To know the exact meaning of the concepts one is using, one must know their correct definitions, one must be able to retrace the specific (logical, not chronological) steps by which they were formed, and one must be able to demonstrate their connection to their base in perceptual reality.

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