A concept is a mental integration of two or more units which are isolated by a process of abstraction and united by a specific definition. By organizing his perceptual material into concepts, and his concepts into wider and still wider concepts, man is able to grasp and retain, to identify and integrate an unlimited amount of knowledge, a knowledge extending beyond the immediate concretes of any given, immediate moment.
In any given moment, concepts enable man to hold in the focus of his conscious awareness much more than his purely perceptual capacity would permit. The range of man’s perceptual awareness—the number of percepts he can deal with at any one time—is limited. He may be able to visualize four or five units—as, for instance, five trees. He cannot visualize a hundred trees or a distance of ten light-years. It is only his conceptual faculty that makes it possible for him to deal with knowledge of that kind.
Man retains his concepts by means of language. With the exception of proper names, every word we use is a concept that stands for an unlimited number of concretes of a certain kind. A concept is like a mathematical series of specifically defined units, going off in both directions, open at both ends and including all units of that particular kind. For instance, the concept “man” includes all men who live at present, who have ever lived or will ever live—a number of men so great that one would not be able to perceive them all visually, let alone to study them or discover anything about them.
To what precisely do we refer when we designate three persons as “men”? We refer to the fact that they are living beings who possess the same characteristic distinguishing them from all other living species: a rational faculty—though the specific measurements of their distinguishing characteristic qua men, as well as of all their other characteristics qua living beings, are different. (As living beings of a certain kind, they possess innumerable characteristics in common: the same shape, the same range of size, the same facial features, the same vital organs, the same fingerprints, etc., and all these characteristics differ only in their measurements.)
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.
None of [the traditional theories of concepts] regards concepts as objective, i.e., as neither revealed nor invented, but as produced by man’s consciousness in accordance with the facts of reality, as mental integrations of factual data computed by man—as the products of a cognitive method of classification whose processes must be performed by man, but whose content is dictated by reality.
Concepts represent condensations of knowledge, which make further study and the division of cognitive labor possible.
Conceptualization is a method of expanding man’s consciousness by reducing the number of its content’s units—a systematic means to an unlimited integration of cognitive data.
It is crucially important to grasp the fact that a concept is an “open-end” classification which includes the yet-to-be-discovered characteristics of a given group of existents. All of man’s knowledge rests on that fact.
Concepts and, therefore, language are primarily a tool of cognition—not of communication, as is usually assumed. Communication is merely the consequence, not the cause nor the primary purpose of concept-formation—a crucial consequence, of invaluable importance to men, but still only a consequence. Cognition precedes communication; the necessary precondition of communication is that one have something to communicate . . . .
The primary purpose of concepts and of language is to provide man with a system of cognitive classification and organization, which enables him to acquire knowledge on an unlimited scale; this means: to keep order in man’s mind and enable him to think.
Abstract ideas are conceptual integrations which subsume an incalculable number of concretes—and . . . without abstract ideas you would not be able to deal with concrete, particular, real-life problems. You would be in the position of a newborn infant, to whom every object is a unique, unprecedented phenomenon. The difference between his mental state and yours lies in the number of conceptual integrations your mind has performed.
Conceptual awareness is the only type of awareness capable of integrating past, present and future. Sensations are merely an awareness of the present and cannot be retained beyond the immediate moment; percepts are retained and, through automatic memory, provide a certain rudimentary link to the past, but cannot project the future. It is only conceptual awareness that can grasp and hold the total of its experience—extrospectively, the continuity of existence; introspectively, the continuity of consciousness—and thus enable its possessor to project his course long-range.
There are many special or “cross-filed” chains of abstractions (of interconnected concepts) in man’s mind. Cognitive abstractions are the fundamental chain, on which all the others depend. Such chains are mental integrations, serving a special purpose and formed accordingly by a special criterion.
Cognitive abstractions are formed by the criterion of: what is essential? (epistemologically essential to distinguish one class of existents from all others). Normative abstractions are formed by the criterion of: what is good? Esthetic abstractions are formed by the criterion of: what is important?