A definition is a statement that identifies the nature of the units subsumed under a concept.
It is often said that definitions state the meaning of words. This is true, but it is not exact. A word is merely a visual-auditory symbol used to represent a concept; a word has no meaning other than that of the concept it symbolizes, and the meaning of a concept consists of its units. It is not words, but concepts that man defines — by specifying their referents.
The purpose of a definition is to distinguish a concept from all other concepts and thus to keep its units differentiated from all other existents.
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.
With certain significant exceptions, every concept can be defined and communicated in terms of other concepts. The exceptions are concepts referring to sensations, and metaphysical axioms.
All definitions are contextual, and a primitive definition does not contradict a more advanced one: the latter merely expands the former.
The truth or falsehood of all of man’s conclusions, inferences, thought and knowledge rests on the truth or falsehood of his definitions.
Definitions are the guardians of rationality, the first line of defense against the chaos of mental disintegration.
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.
When in doubt about the meaning or the definition of a concept, the best method of clarification is to look for its referents — i.e., to ask oneself: What fact or facts of reality gave rise to this concept? What distinguishes it from all other concepts?
It is important to remember that a definition implies all the characteristics of the units, since it identifies their essential, not their exhaustive, characteristics; since it designates existents, not their isolated aspects; and since it is a condensation of, not a substitute for, a wider knowledge of the existents involved.
When “rational animal” is selected as the definition of “man,” this does not mean that the concept “man” becomes a shorthand tag for “anything whatever that has rationality and animality.” It does not mean that the concept “man” is interchangeable with the phrase “rational animal,” and that all of man’s other characteristics are excluded from the concept. It means: A certain type of entity, including all its characteristics, is, in the present context of knowledge, most fundamentally distinguished from all other entities by the fact that it is a rational animal. All the presently available knowledge of man’s other characteristics is required to validate this definition, and is implied by it. All these other characteristics remain part of the content of the concept “man.”
The rules of correct definition are derived from the process of concept-formation. The units of a concept were differentiated — by means of a distinguishing characteristic(s) — from other existents possessing a commensurable characteristic, a Conceptual Common Denominator. A definition follows the same principle: it specifies the distinguishing characteristic(s) of the units, and indicates the category of existents from which they were differentiated.
The distinguishing characteristic(s) of the units becomes the differentia of the concept’s definition; the existents possessing a Conceptual Common Denominator become the genus.
Thus a definition complies with the two essential functions of consciousness: differentiation and integration. The differentia isolates the units of a concept from all other existents; the genus indicates their connection to a wider group of existents.
For instance, in the definition of table (“An item of furniture, consisting of a flat, level surface and supports, intended to support other, smaller objects”), the specified shape is the differentia, which distinguishes tables from the other entities belonging to the same genus: furniture. In the definition of man (“A rational animal”), “rational” is the differentia, “animal” is the genus.
A definition must identify the nature of the units, i.e., the essential characteristics without which the units would not be the kind of existents they are.
It is the principle of unit-economy that necessitates the definition of concepts in terms of essential characteristics. If, when in doubt, a man recalls a concept’s definition, the essential characteristic(s) will give him an instantaneous grasp of the concept’s meaning, i.e., of the nature of its referents. For example, if he is considering some social theory and recalls that “man is a rational animal,” he will evaluate the validity of the theory accordingly; but if, instead, he recalls that “man is an animal possessing a thumb,” his evaluation and conclusion will be quite different.
Now observe . . . the process of determining an essential characteristic: the rule of fundamentality. When a given group of existents has more than one characteristic distinguishing it from other existents, man must observe the relationships among these various characteristics and discover the one on which all the others (or the greatest number of others) depend, i.e., the fundamental characteristic without which the others would not be possible. This fundamental characteristic is the essential distinguishing characteristic of the existents involved, and the proper defining characteristic of the concept.
Metaphysically, a fundamental characteristic is that distinctive characteristic which makes the greatest number of others possible; epistemologically, it is the one that explains the greatest number of others.
Since man is not omniscient, a definition cannot be changelessly absolute, because it cannot establish the relationship of a given group of existents to everything else in the universe, including the undiscovered and unknown. And for the very same reasons, a definition is false and worthless if it is not contextually absolute — if it does not specify the known relationships among existents (in terms of the known essential characteristics) or if it contradicts the known (by omission or evasion).
An objective definition, valid for all men, is one that designates the essential distinguishing characteristic(s) and genus of the existents subsumed under a given concept — according to all the relevant knowledge available at that stage of mankind’s development.
Truth is the product of the recognition (i.e., identification) of the facts of reality. Man identifies and integrates the facts of reality by means of concepts. He retains concepts in his mind by means of definitions. He organizes concepts into propositions — and the truth or falsehood of his propositions rests, not only on their relation to the facts he asserts, but also on the truth or falsehood of the definitions of the concepts he uses to assert them, which rests on the truth or falsehood of his designations of essential characteristics.
Let us note, at this point, the radical difference between Aristotle’s view of concepts and the Objectivist view, particularly in regard to the issue of essential characteristics.
It is Aristotle who first formulated the principles of correct definition. It is Aristotle who identified the fact that only concretes exist. But Aristotle held that definitions refer to metaphysical essences, which exist in concretes as a special element or formative power, and he held that the process of concept-formation depends on a kind of direct intuition by which man’s mind grasps these essences and forms concepts accordingly.
Aristotle regarded “essence” as metaphysical; Objectivism regards it as epistemological.
Objectivism holds that the essence of a concept is that fundamental characteristic(s) of its units on which the greatest number of other characteristics depend, and which distinguishes these units from all other existents within the field of a man’s knowledge. Thus the essence of a concept is determined contextually and may be altered with the growth of man’s knowledge. The metaphysical referent of man’s concepts is not a special, separate metaphysical essence, but the total of the facts of reality he has observed, and this total determines which characteristics of a given group of existents he designates as essential. An essential characteristic is factual, in the sense that it does exist, does determine other characteristics and does distinguish a group of existents from all others; it is epistemological in the sense that the classification of “essential characteristic” is a device of man’s method of cognition — a means of classifying, condensing and integrating an ever-growing body of knowledge.