Key ideas: Published in 1966. “As I wrote in For the New Intellectual: ‘To negate man’s mind, it is the conceptual level of his consciousness that has to be invalidated. Under all the tortuous complexities, contradictions, equivocations, rationalizations of the post-Renaissance philosophy—the one consistent line, the fundamental that explains the rest, is: a concerted attack on man’s conceptual faculty…. Most philosophers did not intend to invalidate conceptual knowledge, but its defenders did more to destroy it than did its enemies. They were unable to … define the nature and source of abstractions, to determine the relationship of concepts to perceptual data…’ These are the reasons why I chose to introduce you to Objectivist epistemology by presenting my theory of concepts.” (Ayn Rand)
The building-block of man’s knowledge is the concept of an “existent”—of something that exists, be it a thing, an attribute or an action. Since it is a concept, man cannot grasp it explicitly until he has reached the conceptual stage. But it is implicit in every percept (to perceive a thing is to perceive that it exists) and man grasps it implicitly on the perceptual level—i.e., he grasps the constituents of the concept “existent,” the data which are later to be integrated by that concept. It is this implicit knowledge that permits his consciousness to develop further.
The (implicit) concept “existent” undergoes three stages of development in man’s mind.
The first stage is a child’s awareness of objects, of things—which represents the (implicit) concept “entity.”
The second and closely allied stage is the awareness of specific, particular things which he can recognize and distinguish from the rest of his perceptual field—which represents the (implicit) concept “identity.”
The third stage consists of grasping relationships among these entities by grasping the similarities and differences of their identities. This requires the transformation of the (implicit) concept “entity” into the (implicit) concept “unit.”
When a child observes that two objects (which he will later learn to designate as “tables”) resemble each other, but are different from four other objects (“chairs”), his mind is focusing on a particular attribute of the objects (their shape), then isolating them according to their differences, and integrating them as units into separate groups according to their similarities.
This is the key, the entrance to the conceptual level of man’s consciousness. The ability to regard entities as units is man’s distinctive method of cognition, which other living species are unable to follow.
A unit is an existent regarded as a separate member of a group of two or more similar members. (Two stones are two units; so are two square feet of ground, if regarded as distinct parts of a continuous stretch of ground.) Note that the concept “unit” involves an act of consciousness (a selective focus, a certain way of regarding things), but that it is not an arbitrary creation of consciousness: it is a method of identification or classification according to the attributes which a consciousness observes in reality. …
With the grasp of the (implicit) concept “unit” man reaches the conceptual level of cognition, which consists of two interrelated fields: the conceptual and the mathematical. The process of concept-formation is, in large part, a mathematical process. …
A concept is a mental integration of two or more units which are isolated according to a specific characteristic(s) and united by a specific definition.
The units involved may be any aspect of reality: entities, attributes, actions, qualities, relationships, etc.; they may be perceptual concretes or other, earlier-formed concepts.
The act of isolation involved is a process of abstraction: i.e., a selective mental focus that takes out or separates a certain aspect of reality from all others (e.g., isolates a certain attibute from the entities possessing it, or a certain action from the entities performing it, etc.). The uniting involved is not a mere sum, but an integration, i.e., a blending of the units into a single, new mental entity which is used thereafter as a single unit of thought (but which can be broken into its component units whenever required).
In order to be used as a single unit, the enormous sum integrated by a concept has to be given the form of a single, specific, perceptual concrete, which will differentiate it from all other concretes and from all other concepts. This is the function performed by language.
Language is a code of visual-auditory symbols that serves the psycho-epistemological function of converting concepts into the mental equivalent of concretes. Language is the exclusive domain and tool of concepts. Every word we use (with the exception of proper names) is a symbol that denotes a concept, i.e., that stands for an unlimited number of concretes of a certain kind.
(Proper names are used in order to identify and include particular entities in a conceptual method of cognition. Observe that even proper names, in advanced civilizations, follow the definitional principles of genus and differentia: e.g., John Smith, with “Smith” serving as genus and “John” as differentia— or New York, U.S.A.)
Words transform concepts into (mental) entities; definitions provide them with identity. (Words without definitions are not language but inarticulate sounds.) We shall discuss definitions later and at length.
The above is a general description of the nature of concepts as products of a certain mental process. But the question of epistemology is: what precisely is the nature of that process? To what precisely do concepts refer in reality?
Let us now examine the process of forming the simplest concept, the concept of a single attribute (chronologically, this is not the first concept that a child would grasp; but it is the simplest one epistemologically)—for instance, the concept “length.” If a child considers a match, a pencil and a stick, he observes that length is the attribute they have in common, but their specific lengths differ. The difference is one of measurement.
In order to form the concept “length,” the child’s mind retains the attribute and omits its particular measurements. Or, more precisely, if the process were identified in words, it would consist of the following:
The same principle directs the process of forming concepts of entities—for instance, the concept “table.” The child’s mind isolates two or more tables from other objects, by focusing on their distinctive characteristic: their shape. He observes that their shapes vary, but have one characteristic in common: a flat, level surface and support(s). He forms the concept “table” by retaining that characteristic and omitting all particular measurements, not only the measurements of the shape, but of all the other characteristics of tables (many of which he is not aware of at the time).
An adult definition of “table” would be: “A man-made object consisting of a flat, level surface and support(s), intended to support other, smaller objects.” Observe what is specified and what is omitted in this definition: the distinctive characteristic of the shape is specified and retained; the particular geometrical measurements of the shape (whether the surface is square, round, oblong or triangular, etc., the number and shape of supports, etc.) are omitted; the measurements of size or weight are omitted; the fact that it is a material object is specified, but the material of which it is made is omitted, thus omitting the measurements that differentiate one material from another; etc.
Observe, however, that the utilitarian requirements of the table set certain limits on the omitted measurements, in the form of “no larger than and no smaller than” required by its purpose. This rules out a ten-foot tall or a two-inch tall table (though the latter may be sub-classified as a toy or a miniature table) and it rules out unsuitable materials, such as non-solids. …
The first words a child learns are words denoting visual objects, and he retains his first concepts visually. Observe that the visual form he gives them is reduced to those essentials which distinguish the particular kind of entities from all others—for instance, the universal type of a child’s drawing of man in the form of an oval for the torso, a circle for the head, four sticks for extremities, etc. Such drawings are a visual record of the process of abstraction and concept-formation in a mind’s transition from the perceptual level to the full vocabulary of the conceptual level. …
A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted
The element of similarity is crucially involved in the formation of every concept; similarity, in this context, is the relationship between two or more existents which possess the same characteristic(s), but in different measure or degree.
Observe the multiple role of measurements in the process of concept-formation, in both of its two essential parts: differentiation and integration. Concepts cannot be formed at random. All concepts are formed by first differentiating two or more existents from other existents. All conceptual differentiations are made in terms of commensurable characteristics (i.e., characteristics possessing a common unit of measurement). No concept could be formed, for instance, by attempting to distinguish long objects from green objects. Incommensurable characteristics cannot be integrated into one unit.
Tables, for instance, are first differentiated from chairs, beds and other objects by means of the characteristic of shape, which is an attribute possessed by all the objects involved. Then, their particular kind of shape is set as the distinguishing characteristic of tables—i.e., a certain category of geometrical measurements of shape is specified. Then, within that category, the particular measurements of individual table-shapes are omitted. …
Another example of implicit measurement can be seen in the process of forming concepts of colors. Man forms such concepts by observing that the various shades of blue are similar, as against the shades of red, and thus differentiating the range of blue from the range of red, of yellow, etc. Centuries passed before science discovered the unit by which colors could actually be measured: the wavelengths of light—a discovery that supported, in terms of mathematical proof, the differentiations that men were and are making in terms of visual similarities. (Any questions about “borderline cases” will be answered later.)
A commensurable characteristic (such as shape in the case of tables, or hue in the case of colors) is an essential element in the process of concept-formation. I shall designate it as the “Conceptual Common Denominator” and define it as “The characteristic(s) reducible to a unit of measurement, by means of which man differentiates two or more existents from other existents possessing it.”
The distinguishing characteristic(s) of a concept represents a specified category of measurements within the “Conceptual Common Denominator” involved.
New concepts can be formed by integrating earlier-formed concepts into wider categories, or by subdividing them into narrower categories (a process which we shall discuss later). But all concepts are ultimately reducible to their base in perceptual entities, which are the base (the given) of man’s cognitive development.
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.)
In the process of forming concepts of entities, a child’s mind has to focus on a distinguishing characteristic—i.e., on an attribute—in order to isolate one group of entities from all others. He is, therefore, aware of attributes while forming his first concepts, but he is aware of them perceptually, not conceptually. It is only after he has grasped a number of concepts of entities that he can advance to the stage of abstracting attributes from entities and forming separate concepts of attributes. The same is true of concepts of motion: a child is aware of motion perceptually, but cannot conceptualize “motion” until he has formed some concepts of that which moves, i.e., of entities.
(As far as can be ascertained, the perceptual level of a child’s awareness is similar to the awareness of the higher animals: the higher animals are able to perceive entities, motions, attributes, and certain numbers of entities. But what an animal cannot perform is the process of abstraction—of mentally separating attributes, motions or numbers from entities. It has been said that an animal can perceive two oranges or two potatoes, but cannot grasp the concept “two.”)
Concepts of materials are formed by observing the differences in the constituent materials of entities. (Materials exist only in the form of specific entities, such as a nugget of gold, a plank of wood, a drop or an ocean of water.) The concept of “gold,” for instance, is formed by isolating gold objects from all others, then abstracting and retaining the material, the gold, and omitting the measurements of the objects (or of the alloys) in which gold may exist. Thus, the material is the same in all the concrete instances subsumed under the concept, and differs only in quantity. …
Now we can answer the question: 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.)
Two links between the conceptual and the mathematical fields are worth noting at this point, apart from the obvious fact that the concept “unit” is the base and start of both.
A concept is not formed by observing every concrete subsumed under it, and does not specify the number of such concretes. A concept is like an arithmetical sequence 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. An arithmetical sequence extends into infinity, without implying that infinity actually exists; such extension means only that whatever number of units does exist, it is to be included in the same sequence. The same principle applies to concepts: the concept “man” does not (and need not) specify what number of men will ultimately have existed—it specifies only the characteristics of man, and means that any number of entities possessing these characteristics is to be identified as “men.”
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.
The relationship of concepts to their constituent particulars is the same as the relationship of algebraic symbols to numbers. In the equation 2a = a + a, any number may be substituted for the symbol “a” without affecting the truth of the equation. For instance: 2 X 5 = 5 + 5, or: 2 X 5,000,000 = 5,000,000 + 5,000,000. In the same manner, by the same psycho-epistemological method, a concept is used as an algebraic symbol that stands for any of the arithmetical sequence of units it subsumes.
Let those who attempt to invalidate concepts by declaring that they cannot find “manness” in men, try to invalidate algebra by declaring that they cannot find “a-ness” in 5 or in 5,000,000.
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.
… The process of forming a concept is not complete until its constituent units have been integrated into a single mental unit by means of a specific word. …
Learning to speak does not consist of memorizing sounds—that is the process by which a parrot learns to “speak.” Learning consists of grasping meanings, i.e., of grasping the referents of words, the kinds of existents that words denote in reality. In this respect, the learning of words is an invaluable accelerator of a child’s cognitive development, but it is not a substitute for the process of concept-formation; nothing is. …
But the question of how particular men happen to learn concepts and the question of what concepts are, are two different issues. In considering the nature of concepts and the process of abstracting from abstractions, we must assume a mind capable of performing (or of retracing and checking) that process. And we must remember that no matter how many men mouth a concept as a meaningless sound, some man had to originate it at some time.
The first stages of integrating concepts into wider concepts are fairly simple, because they still refer to perceptual concretes. For instance, man observes that the objects which he has identified by the concepts “table,” “chair,” “bed,” “cabinet,” etc. have certain similarities, but are different from the objects he has identified as “door,” “window,” “picture,” “drapes”—and he integrates the former into the wider concept “furniture.” In this process, concepts serve as units and are treated epistemologically as if each were a single (mental) concrete—always remembering that metaphysically (i.e., in reality) each unit stands for an unlimited number of actual concretes of a certain kind. …
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.)
Observe also that the concept “furniture” involves a relationship to another concept which is not one of its constituent units, but which has to be grasped before one can grasp the meaning of “furniture”: the concept “habitation.” This kind of interrelationship among concepts grows progressively more complex as the level of concept-formation grows farther away from perceptual concretes.
Now let us examine the process of subdividing the concept “table.” By observing the differences in the size and function of various tables, man subdivides the concept into: “dining table,” “coffee table,” “end table,” “desk,” etc. In the first three instances, the distinguishing characteristic of “table,” its shape, is retained, and the differentiations are purely a matter of measurement: the range of the shape’s measurements is reduced in accordance with the narrower utilitarian function. (Coffee tables are lower and smaller than dining tables; end tables are higher than coffee tables, but lower than dining tables, etc.)
In the case of “desk,” however, the distinguishing characteristic of “table” is retained, but combined with a new element: a “desk” is a table with drawers for storing stationery supplies. The first three instances are not actually new concepts, but qualified instances of the concept “table.” “Desk,” however, involves a significant difference in its distinguishing characteristic; it involves an additional category of measurements, and is given a new linguistic symbol. (As far as the process of concept-formation is concerned, it would make no difference if “desk” were designated as “office table,” or if a new word were coined for each of the other sub-categories of “table.” There is, however, an epistemological reason for the present designations, which we shall discuss when we discuss definitions.) …
Some concepts of relationships (such as “legal” or “economic”) involve concepts of consciousness. The most complex abstractions (both in regard to wider integrations and narrower subdivisions) are those which involve a combination of concepts of action with concepts of consciousness. (We shall discuss these in the next chapter.)
Two aspects of the cognitive content of abstractions are worth noting at this point.
The formation (or the learning) of wider concepts requires more knowledge (i.e., a wider range of conceptualized evidence) than was required by any one of the constituent concepts which they subsume. For instance, the concept “animal” requires more knowledge than the concept “man” —since it requires knowledge of man and of some of the other species. It requires a sufficient knowledge of man’s characteristics and of the characteristics of other animals to differentiate man from other animals, and to differentiate animals from plants or from inanimate objects.
The formation of a concept provides man with the means of identifying, not only the concretes he has observed, but all the concretes of that kind which he may encounter in the future. Thus, when he has formed or grasped the concept “man,” he does not have to regard every man he meets thereafter as a new phenomenon to be studied from scratch: he identifies him as “man” and applies to him the knowledge he has acquired about man (which leaves him free to study the particular, individual characteristics of the newcomer, i.e., the individual measurements within the categories established by the concept “man”).
This process of conceptual identification (of subsuming a new concrete under an appropriate concept) is learned as one learns to speak, and it becomes automatic in the case of existents given in perceptual awareness, such as “man,” “table,” “blue,” “length,” etc. But it grows progressively more difficult as man’s concepts move farther away from direct perceptual evidence, and involve complex combinations and cross-classifications of many earlier concepts. (Observe the difficulties of identifying a given political system, or of diagnosing a rare disease.)
Thus the process of forming and applying concepts contains the essential pattern of two fundamental methods of cognition: induction and deduction.
The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction. The process of subsuming new instances under a known concept is, in essence, a process of deduction.
Consciousness is the faculty of awareness—the faculty of perceiving that which exists.
Awareness is not a passive state, but an active process. On the lower levels of awareness, a complex neurological process is required to enable man to experience a sensation and to integrate sensations into percepts; that process is automatic and non-volitional: man is aware of its results, but not of the process itself. On the higher, conceptual level, the process is psychological, conscious and volitional. In either case, awareness is achieved and maintained by continuous action. …
It is only in relation to the external world that the various actions of a consciousness can be experienced, grasped, defined or communicated. Awareness is awareness of something. A content-less state of consciousness is a contradiction in terms. ## These two attributes are the fundamental Conceptual Common Denominator of all concepts pertaining to consciousness
Two fundamental attributes are involved in every state, aspect or function of man’s consciousness: content and action—the content of awareness, and the action of consciousness in regard to that content.
These two attributes are the fundamental Conceptual Common Denominator of all concepts pertaining to consciousness.
On the perceptual level of awareness, a child merely experiences and performs various psychological processes; his full conceptual development requires that he learn to conceptualize them (after he has reached a certain stage in his extrospective conceptual development).
To form concepts of consciousness, one must isolate the action from the content of a given state of consciousness, by a process of abstraction. Just as, extrospectively, man can abstract attributes from entities—so, introspectively, he can abstract the actions of his consciousness from its contents, and observe the differences among these various actions.
For instance (on the adult level), when a man sees a woman walking down the street, the action of his consciousness is perception; when he notes that she is beautiful, the action of his consciousness is evaluation; when he experiences an inner state of pleasure and approval, of admiration, the action of his consciousness is emotion; when he stops to watch her and draws conclusions, from the evidence, about her character, age, social position, etc., the action of his consciousness is thought; when, later, he recalls the incident, the action of his consciousness is reminiscence; when he projects that her appearance would be improved if her hair were blond rather than brown, and her dress were blue rather than red, the action of his consciousness is magination.
He can also observe the similarities among the actions of his consciousness on various occasions, by observing the fact that these same actions—in different sequences, combinations and degrees—are, have been or can be applicable to other objects: to a man, a dog, an automobile, or the entire street; to the reading of a book, the learning of a new skill, the choice of a job, or to any object within the scope of his awareness.
Such is the pattern of the process by which (in slower, gradual steps) man learns to form concepts of consciousness. …
In regard to the concepts pertaining to evaluation (“value,” “emotion,” “feeling,” “desire,” etc.), the hierarchy involved is of a different kind and requires an entirely different type of measurement. It is a type applicable only to the psychological process of evaluation, and may be designated as “teleological measurement.”
Measurement is the identification of a relationship—a quantitative relationship established by means of a standard that serves as a unit. Teleological measurement deals, not with cardinal, but with ordinal numbers—and the standard serves to establish a graded relationship of means to end.
For instance, a moral code is a system of teleological measurement which grades the choices and actions open to man, according to the degree to which they achieve or frustrate the code’s standard of value. The standard is the end, to which man’s actions are the means.
A moral code is a set of abstract principles; to practice it, an individual must translate it into the appropriate concretes —he must choose the particular goals and values which he is to pursue. This requires that he define his particular hierarchy of values, in the order of their importance, and that he act accordingly. Thus all his actions have to be guided by a process of teleological measurement. (The degree of uncertainty and contradictions in a man’s hierarchy of values is the degree to which he will be unable to perform such measurements and will fail in his attempts at value calculations or at purposeful action.)
Teleological measurement has to be performed in and against an enormous context: it consists of establishing the relationship of a given choice to all the other possible choices and to one’s hierarchy of values.
The simplest example of this process, which all men practice (with various degrees of precision and success), may be seen in the realm of material values—in the (implicit) principles that guide a man’s spending of money. On any level of income, a man’s money is a limited quantity; in spending it, he weighs the value of his purchase against the value of every other purchase open to him for the same amount of money, he weighs it against the hierarchy of all his other goals, desires and needs, then makes the purchase or not accordingly.
A special sub-category of concepts pertaining to the products of consciousness, is reserved for concepts of method. Concepts of method designate systematic courses of action devised by men for the purpose of achieving certain goals. The course of action may be purely psychological (such as a method of using one’s consciousness) or it may involve a combination of psychological and physical actions (such as a method of drilling for oil), according to the goal to be achieved.
Concepts of method are formed by retaining the distinguishing characteristics of the purposive course of action and of its goal, while omitting the particular measurements of both.
For instance, the fundamental concept of method, the one on which all the others depend, is logic. The distinguishing characteristic of logic (the art of non- contradictory identification) indicates the nature of the actions (actions of consciousness required to achieve a correct identification) and their goal (knowledge)—white omitting the length, complexity or specific steps of the process of logical inference, as well as the nature of the particular cognitive problem involved in any given instance of using logic.
Concepts of method represent a large part of man’s conceptual equipment. Epistemology is a science devoted to the discovery of the proper methods of acquiring and validating knowledge. Ethics is a science devoted to the discovery of the proper methods of living one’s life. Medicine is a science devoted to the discovery of the proper methods of curing disease. All the applied sciences (i.e., technology) are sciences devoted to the discovery of methods.
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.
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.
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.
Just as a concept becomes a unit when integrated with others into a wider concept, so a genus becomes a single unit, a species, when integrated with others into a wider genus. For instance, “table” is a species of the genus “furniture,” which is a species of the genus “household goods,” which is a species of the genus “man-made objects.” “Man” is a species of the genus “animal,” which is a species of the genus “organism,” which is a species of the genus “entity.”
… 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. But 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.
This leads to a crucial question: since a group of existents may possess more than one characteristic distinguishing them from other existents, how does one determine the essential characteristic of an existent and, therefore, the proper defining characteristic of a concept?
The answer is provided by the process of concept-formation.
Concepts are not and cannot be formed in a vacuum; they are formed in a context; the process of conceptualization consists of observing the differences and similarities of the existents within the field of one’s awareness (and organizing them into concepts accordingly). From a child’s grasp of the simplest concept integrating a group of perceptually given concretes, to a scientist’s grasp of the most complex abstractions integrating long conceptual chains—all conceptualization is a contextual process; the context is the entire field of a mind’s awareness or knowledge at any level of its cognitive development.
This does not mean that conceptualization is a subjective process or that the content of concepts depends on an individual’s subjective (i.e., arbitrary) choice. The only issue open to an individual’s choice in this matter is how much knowledge he will seek to acquire and, consequently, what conceptual complexity he will be able to reach.
But so long as and to the extent that his mind deals with concepts (as distinguished from memorized sounds and floating abstractions), the content of his concepts is determined and dictated by the cognitive content of his mind, i.e., by his grasp of the facts of reality. If his grasp is non-contradictory, then even if the scope of his knowledge is modest and the content of his concepts is primitive, it will not contradict the content of the same concepts in the mind of the most advanced scientists.
The same is true of definitions. All definitions are contextual, and a primitive definition does not contradict a more advanced one: the latter merely expands the former.
On the pre-verbal level of awareness, when a child first learns to differentiate men from the rest of his perceptual field, he observes distinguishing characteristics which, if translated into words, would amount to a definition such as: “A thing that moves and makes sounds.” Within the context of his awareness, this is a valid definition: man, in fact, does move and make sounds, and this distinguishes him from the inanimate objects around him.
When the child observes the existence of cats, dogs and automobiles, his definition ceases to be valid: it is still true that man moves and makes sounds, but these characteristics do not distinguish him from other entities in the field of the child’s awareness. The child’s (wordless) definition then changes to some equivalent of: “A living thing that walks on two legs and has no fur,” with the characteristics of “moving and making sounds” remaining implicit, but no longer defining. Again, this definition is valid—within the context of the child’s awareness.
When the child learns to speak and the field of his awareness expands still further, his definition of man expands accordingly. It becomes something like: “A living being that speaks and does things no other living beings can do.”
This type of definition will suffice for a long time (a great many men, some modern scientists among them, never progress beyond some variant of this definition). But this ceases to be valid at about the time of the child’s adolescence, when he observes (if his conceptual development continues) that his knowledge of the “things no other living beings can do” has grown to an enormous, incoherent, unexplained collection of activities, some of which are performed by all men, but some are not, some of which are even performed by animals (such as building shelters), but in some significantly different manner, etc. He realizes that his definition is neither applicable equally to all men, nor does it serve to distinguish men from all other living beings.
It is at this stage that he asks himself: What is the common characteristic of all of man’s varied activities? What is their root? What capacity enables man to perform them and thus distinguishes him from all other animals? When he grasps that man’s distinctive characteristic is his type of consciousness—a consciousness able to abstract, to form concepts, to apprehend reality by a process of reason—he reaches the one and only valid definition of man, within the context of his knowledge and of all of mankind’s knowledge to date: “A rational animal.”
(“Rational,” in this context, does not mean “acting invariably in accordance with reason”; it means “possessing the faculty of reason.” A full biological definition of man would include many sub-categories of “animal,” but the general category and the ultimate definition remain the same.) …
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.
Every concept stands for a number of propositions. A concept identifying perceptual concretes stands for some implicit propositions; but on the higher levels of abstraction, a concept stands for chains and paragraphs and pages of explicit propositions referring to complex factual data. A definition is the condensation of a vast body of observations—and stands or falls with the truth or falsehood of these observations. Let me repeat: a definition is a condensation. As a legal preamble (referring here to epistemological law), every definition begins with the implicit proposition: “After full consideration of all the known facts pertaining to this group of existents, the following has been demonstrated to be their essential, therefore defining, characteristic …”
The truth or falsehood of all of man’s conclusions, inferences, thought and knowledge rests on the truth or falsehood of his definitions.
(The above applies only to valid concepts. There are such things as invalid concepts, i.e., words that represent attempts to integrate errors, contradictions or false propositions, such as concepts originating in mysticism—or words without specific definitions, without referents, which can mean anything to anyone, such as modern “anti-concepts.” Invalid concepts appear occasionally in men’s languages, but are usually—though not necessarily—short—lived, since they lead to cognitive dead-ends. An invalid concept invalidates every proposition or process of thought in which it is used as a cognitive assertion.)
Above the level of conceptualized sensations and metaphysical axioms, every concept requires a verbal definition. Paradoxically enough, it is the simplest concepts that most people find it hardest to define—the concepts of the perceptual concretes with which they deal daily, such as “table,” “house,” “man,” “walking,” “tall,” “number,” etc. There is a good reason for it: such concepts are, chronologically, the first concepts man forms or grasps, and can be defined verbally only by means of later concepts—as, for instance, one grasps the concept “table” long before one can grasp such concepts as “flat,” “level,” “surface,” “supports.” Most people, therefore, regard formal definitions as unnecessary and treat simple concepts as if they were pure sense data, to be identified by means of ostensive definitions, i.e., simply by pointing.
There is a certain psychological justification for this policy. Man’s discriminated awareness begins with percepts; the conceptual identifications of daily-observed percepts have become so thoroughly automatized in men’s minds that they seem to require no definitions—and men have no difficulty in identifying the referents of such concepts ostensively.
(This, incidentally, is one instance demonstrating the grotesque inversions of Linguistic Analysis: the stock-in-trade of linguistic analysts consists of reducing people to stammering helplessness by demanding that they define “house” or “which” or “but,” then proclaiming that since people cannot define even such simple words, they cannot be expected to define more complex ones, and, therefore, there can be no such things as definitions—or concepts.)
In fact and in practice, so long as men are able to identify with full certainty the perceptual referents of simple concepts, it is not necessary for them to devise or memorize the verbal definitions of such concepts. What is necessary is a knowledge of the rules by which the definitions can be formulated; and what is urgently necessary is a clear grasp of that dividing line beyond which ostensive definitions are no longer sufficient. (That dividing line begins at the point where a man uses words with the feeling “I kinda know what I mean.”) Most people have no grasp of that line and no inkling of the necessity to grasp it—and the disastrous, paralyzing, stultifying consequences are the greatest single cause of mankind’s intellectual erosion.
(As an illustration, observe what Bertrand Russell was able to perpetrate because people thought they “kinda knew” the meaning of the concept “number”—and what the collectivists were able to perpetrate because people did not even pretend to know the meaning of the concept “man.”)
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?
For instance: what fact of reality gave rise to the concept “justice”?
The fact that man must draw conclusions about the things, people and events around him, i.e., must judge and evaluate them. Is his judgment automatically right? No. What causes his judgment to be wrong? The lack of sufficient evidence, or his evasion of the evidence, or his inclusion of considerations other than the facts of the case.
How, then, is he to arrive at the right judgment?
By basing it exclusively on the factual evidence and by considering all the relevant evidence available.
But isn’t this a description of “objectivity”? Yes, “objective judgment” is one of the wider categories to which the concept “justice” belongs. What distinguishes “justice” from other instances of objective judgment? When one evaluates the nature or actions of inanimate objects, the criterion of judgment is determined by the particular purpose for which one evaluates them.
But how does one determine a criterion for evaluating the character and actions of men, in view of the fact that men possess the faculty of volition? What science can provide an objective criterion of evaluation in regard to volitional matters? Ethics.
Now, do I need a concept to designate the act of judging a man’s character and/or actions exclusively on the basis of all the factual evidence available, and of evaluating it by means of an objective moral criterion? Yes. That concept is “justice.”
Note what a long chain of considerations and observations is condensed into a single concept. And the chain is much longer than the abbreviated pattern presented here—because every concept used in this example stands for similar chains….
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 man’s knowledge. Thus the essence of a concept is determined contextually and may be altered with the growth of man’s knowledge….
Axioms are usually considered to be propositions identifying a fundamental, self- evident truth. But explicit propositions as such are not primaries: they are made of concepts. The base of man’s knowledge—of all other concepts, all axioms, propositions and thought—consists of axiomatic concepts.
An axiomatic concept is the identification of a primary fact of reality, which cannot be analyzed, i.e., reduced to other facts or broken into component parts. It is implicit in all facts and in all knowledge. It is the fundamentally given and directly perceived or experienced, which requires no proof or explanation, but on which all proofs and explanations rest.
The first and primary axiomatic concepts are “existence,” “identity” (which is a corollary of “existence”) and “consciousness.” One can study what exists and how consciousness functions; but one cannot analyze (or “prove”) existence as such, or consciousness as such. These are irreducible primaries. (An attempt to “prove” them is self-contradictory: it is an attempt to “prove” existence by means of nonexistence, and consciousness by means of unconsciousness.)
Existence, identity and consciousness are concepts in that they require identification in conceptual form. Their peculiarity lies in the fact that they are perceived or experienced directly, but grasped conceptually. …
Epistemologically, the formation of axiomatic concepts is an act of abstraction, a selective focusing on and mental isolation of metaphysical fundamentals; but metaphysically, it is an act of integration—the widest integration possible to man: it unites and embraces the total of his experience.
The units of the concepts “existence” and “identity” are every entity, attribute, action, event or phenomenon (including consciousness) that exists, has ever existed or will ever exist.
The units of the concept “consciousness” are every state or process of awareness that one experiences, has ever experienced or will ever experience (as well as similar units, a similar faculty, which one infers in other living entities).
The measurements omitted from axiomatic concepts are all the measurements of all the existents they subsume; what is retained, metaphysically, is only a fundamental fact; what is retained, epistemologically, is only one category of measurement, omitting its particulars: time—i.e., the fundamental fact is retained independent of any particular moment of awareness. …
It must be remembered that 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.
It is by means of axiomatic concepts that man grasps and holds this continuity, bringing it into his conscious awareness and knowledge. It is axiomatic concepts that identify the precondition of knowledge: the distinction between existence and consciousness, between reality and the awareness of reality, between the object and the subject of cognition. Axiomatic concepts are the foundation of objectivity. …
If the state of an animal’s perceptual awareness could be translated into words, it would amount to a disconnected succession of random moments such as “Here now table—here now tree—here now man—I now see—I now feel,” etc.—with the next day or hour starting the succession all over again, with only a few strands of memory in the form of “This now food” or “This now master.” What a man’s consciousness does with the same material, by means of axiomatic concepts, is: “The table exists—the tree exists—man exists—I am conscious.”
(The above projection of an animal’s awareness is what certain modern philosophers, such as logical positivists and logical atomists, ascribe to man, as his start and his only contact with reality—except that they reject the concept “reality,” substitute sensations for percepts, and regard everything above this sub- animal level as an arbitrary human “construct.”) …
The concept “existence” does not indicate what existents it subsumes: it merely underscores the primary fact that they exist. The concept “identity” does not indicate the particular natures of the existents it subsumes: it merely underscores the primary fact that they are what they are. The concept “consciousness” does not indicate what existents one is conscious of: it merely underscores the primary fact that one is conscious.
This underscoring of primary facts is one of the crucial epistemological functions of axiomatic concepts. It is also the reason why they can be translated into a statement only in the form of a repetition (as a base and a reminder): Existence exists—Consciousness is conscious—A is A. (This converts axiomatic concepts into formal axioms.)
That special underscoring, which is of no concern to animals, is a matter of life or death for man—as witness, modern philosophy, which is a monument to the results of the attempt to evade or bypass such reminders.
Since axiomatic concepts refer to facts of reality and are not a matter of “faith” or of man’s arbitrary choice, there is a way to ascertain whether a given concept is axiomatic or not: one ascertains it by observing the fact that an axiomatic concept cannot be escaped, that it is implicit in all knowledge, that it has to be accepted and used even in the process of any attempt to deny it.
For instance, when modern philosophers declare that axioms are a matter of arbitrary choice, and proceed to choose complex, derivative concepts as the alleged axioms of their alleged reasoning, one can observe that their statements imply and depend on “existence,” “consciousness,” “identity,” which they profess to negate, but which are smuggled into their arguments in the form of unacknowledged, “stolen” concepts.
It is worth noting, at this point, that what the enemies of reason seem to know, but its alleged defenders have not discovered, is the fact that axiomatic concepts are the guardians of man’s mind and the foundation of reason—the key-stone, touchstone and hallmark of reason—and if reason is to be destroyed, it is axiomatic concepts that have to be destroyed.
Observe the fact that in the writings of every school of mysticism and irrationalism, amidst all the ponderously unintelligible verbiage of obfuscations, rationalizations and equivocations (which include protestations of fidelity to reason, and claims to some “higher” form of rationality), one finds, sooner or later, a clear, simple, explicit denial of the validity (of the metaphysical or ontological status) of axiomatic concepts, most frequently of “identity.” (For example, see the works of Kant and Hegel. ) You do not have to guess, infer or interpret: they tell you. But what you do have to know is the full meaning, implications and consequences of such denials—which, in the history of philosophy, seem to be better understood by the enemies of reason than by its defenders.
The story of the following experiment was told in a university classroom by a professor of psychology. I cannot vouch for the validity of the specific numerical conclusions drawn from it, since I could not check it first-hand. But I shall cite it here, because it is the most illuminating way to illustrate a certain fundamental aspect of consciousness—of any consciousness, animal or human.
The experiment was conducted to ascertain the extent of the ability of birds to deal with numbers. A hidden observer watched the behavior of a flock of crows gathered in a clearing of the woods. When a man came into the clearing and went on into the woods, the crows hid in the tree tops and would not come out until he returned and left the way he had come. When three men went into the woods and only two returned, the crows would not come out: they waited until the third one had left. But when five men went into the woods and only four returned, the crows came out of hiding. Apparently, their power of discrimination did not extend beyond three units—and their perceptual-mathematical ability consisted of a sequence such as: one-two-three-many.
Whether this particular experiment is accurate or not, the truth of the principle it illustrates can be ascertained introspectively: if we omit all conceptual knowledge, including the ability to count in terms of numbers, and attempt to see how many units (or existents of a given kind) we can discriminate, remember and deal with by purely perceptual means (e.g., visually or auditorially, but without counting), we will discover that the range of man’s perceptual ability may be greater, but not much greater, than that of the crow: we may grasp and hold five or six units at most.
This fact is the best demonstration of the cognitive role of concepts. …
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 characterstic(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.
This leads us to a crucial aspect of the cognitive role of concepts: concepts represent condensations of knowledge, which make further study and the division of cognitive labor possible.
Remember that the perceptual level of awareness is the base of man’s conceptual development. Man forms concepts, as a system of classification, whenever the scope of perceptual data becomes too great for his mind to handle. Concepts stand for specific kinds of existents, including all the characteristics of these existents, observed and not-yet-observed, known and unknown.
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.
The pattern is as follows: when a child grasps the concept “man,” the knowledge represented by that concept in his mind consists of perceptual data, such as man’s visual appearance, the sound of his voice, etc. When the child learns to differentiate between living entities and inanimate matter, he ascribes a new characteristic, “living,” to the entity he designates as “man.” When the child learns to differentiate among various types of consciousness, he includes a new characteristic in his concept of man, “rational”—and so on. The implicit principle guiding this process, is: “I know that there exists such an entity as man; I know many of his characteristics, but he has many others which I do not know and must discover.” The same principle directs the study of every other kind of perceptually isolated and conceptualized existents….
Concepts represent a system of mental filing and cross-filing, so complex that the largest electronic computer is a child’s toy by comparison. This system serves as the context, the frame-of-reference, by means of which man grasps and classifies (and studies further) every existent he encounters and every aspect of reality. Language is the physical (visual-auditory) implementation of this system.
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.
Since concepts, in the field of cognition, perform a function similar to that of numbers in the field of mathematics, the function of a proposition is similar to that of an equation: it applies conceptual abstractions to a specific problem.
A proposition, however, can perform this function only if the concepts of which it is composed have precisely defined meanings. If, in the field of mathematics, numbers had no fixed, firm values, if they were mere approximations determined by the mood of their users—so that “5,” for instance, could mean five in some calculations, but six-and-a-half or four-and-three-quarters in others, according to the users’ “convenience”—there would be no such thing as the science of mathematics.
Yet this is the manner in which most people use concepts, and are taught to do so.
Above the first-level abstractions of perceptual concretes, most people hold concepts as loose approximations, without firm definitions, clear meanings or specific referents; and the greater a concept’s distance from the perceptual level, the vaguer its content. Starting from the mental habit of learning words without grasping their meanings, people find it impossible to grasp higher abstractions, and their conceptual development consists of condensing fog into fog into thicker fog—until the hierarchical structure of concepts breaks down in their minds, losing all ties to reality; and, as they lose the capacity to understand, their education becomes a process of memorizing and imitating. This process is encouraged and, at times, demanded by many modern teachers who purvey snatches of random, out-of-context information in undefined, unintelligible, contradictory terms.
To grasp and reclaim the power of philosophy, one must begin by grasping why concepts and definitions cannot and may not be arbitrary. To grasp that fully, one must begin by grasping the reason why man needs such a science as epistemology.
Man is neither infallible nor omniscient; if he were, a discipline such as epistemology—the theory of knowledge—would not be necessary nor possible: his knowledge would be automatic, unquestionable and total. But such is not man’s nature. Man is a being of volitional consciousness: beyond the level of percepts—a level inadequate to the cognitive requirements of his survival—man has to acquire knowledge by his own effort, which he may exercise or not, and by a process of reason, which he may apply correctly or not.
Nature gives him no automatic guarantee of his mental efficacy; he is capable of error, of evasion, of psychological distortion. He needs a method of cognition, which he himself has to discover: he must discover how to use his rational faculty, how to validate his conclusions, how to distinguish truth from falsehood, how to set the criteria of what he may accept as knowledge. Two questions are involved in his every conclusion, conviction, decision, choice or claim: What do I know?—and: How do I know it?
It is the task of epistemology to provide the answer to the “How?”—which then enables the special sciences to provide the answers to the “What?”
In the history of philosophy—with some very rare exceptions—epistemological theories have consisted of attempts to escape one or the other of the two fundamental questions which cannot be escaped. Men have been taught either that knowledge is impossible (skepticism) or that it is available without effort (mysticism). …
Cognition and Measurement. The base of all of man’s knowledge is the perceptual level of awareness. It is in the form of percepts that man grasps the evidence of his senses and apprehends reality. The building- block of man’s knowledge is the concept of “existent” which is implicit in every percept. The (implicit) concept “existent” undergoes three stages of development in man’s mind: entity-identity-unit. The ability to regard entities as units is man’s distinctive method of cognition. A unit is an existent regarded as a separate member of a group of two or more similar members. Measurement is the identification of a quantitative relationship, by means of a standard that serves as a unit. The purpose of measurement is to expand the range of man’s knowledge beyond the directly perceivable concretes.
Concept-Formation. Similarity is the relationship between two or more existents which possess the same characteristic (s), but in different measure or degree. The process of concept-formation consists of mentally isolating two or more existents by means of their distinguishing characteristic, and retaining this characteristic while omitting their particular measurements—on the principle that these measurements must exist in some quantity, but may exist in any quantity. A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted.
Abstraction from Abstractions. When concepts are integrated into a wider concept, they serve as units and are treated epistemologically as if each were a single (mental) concrete—always remembering that metaphysically (i.e., in reality) each unit stands for an unlimited number of concretes of a certain kind. When concepts are integrated into a wider one, the new concept includes all the characteristics of its constituent units; but their distinguishing characteristics are regarded as omitted measurements, and one of their common characteristics becomes the distinguishing characteristic of the new concept. When a concept is subdivided into narrower ones, its distinguishing characteristic is retained and is given a narrower range of specified measurements or is combined with an additional characteristic(s) to form the individual distinguishing characteristics of the new concepts.
Concepts of Consciousness. Every state of consciousness involves two fundamental attributes: the content (or object) of awareness, and the action (or process) of consciousness in regard to that content. A concept pertaining to consciousness is a mental integration of two or more instances of a psychological process possessing the same distinguishing characteristic(s), with the particular contents and the measurements of the action’s intensity omitted. The intensity of a psychological process is measured on a comparative scale. Concepts pertaining to cognition are measured by the scope of their factual content and by the length of the conceptual chain required to grasp it. Concepts pertaining to evaluation are measured by reference to a person’s hierarchy of values; this involves a process of “teleological measurement” which deals, not with cardinal, but with ordinal numbers, establishing a graded relationship of means to ends, i.e., of actions to a standard of value. A special category of concepts of consciousness consists of concepts pertaining to the products of consciousness (e.g., “knowledge”), and concepts of method (e.g., “logic”).
Definitions. A definition is a statement that identifies the nature of a concept’s units. A correct definition must specify the distinguishing characteristic(s) of the units (the differentia), and indicate the category of existents from which they were differentiated (the genus). The essential distinguishing characteristic(s) of the units and the proper defining characteristic(s) of the concept must be a fundamental charactcristic(s)—i.e., that distinctive characteristic(s) which, metaphysically, makes the greatest number of other distinctive characteristics possible and which, epistemologically, explains the greatest number of others. Just as the process of concept-formation is contextual, so all definitions are contextual. The designation of an essential characteristic depends on the context of man’s knowledge; a primitive definition, if correct, does not contradict a more advanced one: the latter merely expands the former. An objective definition, valid for all men, is determined according to all the relevant knowledge available at that stage of mankind’s development. Definitions are not changelessly absolute, but they are contextually absolute. A definition is false if it does not specify the known relationships among existents (in terms of the known essential characteristics) or if it contradicts the known. (Every concept stands for a number of implicit propositions. A definition is the condensation of a vast body of observations—and its validity depends on the truth or falsehood of these observations, as represented and summed up by the designation of a concept’s essential, defining characteristic (s). The truth or falsehood of all of man’s conclusions, inferences and knowledge rests on the truth or falsehood of his definitions. The radical difference between the Aristotelian view of concepts and the Objectivist view lies in the fact that Aristotle regarded “essence” as metaphysical; Objectivism regards it as epistemological.)
Axiomatic Concepts. An axiomatic concept is the identification of a primary fact of reality, which is implicit in all facts and in all knowledge. It is perceived or experienced directly, but grasped conceptually. The first and primary axiomatic concepts are “existence,” “identity” and “consciousness.” They identify explicitly the omission of psychological time measurements, which is implicit in all concepts—and serve as constants, as cognitive integrators and epistemological guidelines. They embrace the entire field of man’s awareness, delimiting it from the void of unreality to which conceptual errors can lead. Axiomatic concepts are not a matter of arbitrary choice; one ascertains whether a given concept is axiomatic or not by observing the fact that an axiomatic concept has to be accepted and used even in the process of any attempt to deny it. Axiomatic concepts are the foundation of objectivity.
The Cognitive Role of Concepts. The range of what man can hold in the focus of his conscious awareness at any given moment is limited. The essence of his cognitive power is the ability to reduce a vast amount of information to a minimal number of units; this is the task performed by his conceptual faculty. Concepts represent condensations of knowledge, “open-end” classifications that subsume all the characteristics of their referents, the known and the yet-to-be-discovered; this permits further study and the division of cognitive labor. The requirements of cognition control the formation of new concepts, and forbid arbitrary conceptual groupings. In the process of determining conceptual classifications, neither the essential differences nor the essential similarities among existents may be ignored once they have been observed. To sum up in the form of an epistemological “razor”: concepts are not to be multiplied beyond necessity, nor are they to be integrated in disregard of necessity.
Consciousness and Identity. The assault on man’s conceptual faculty has been accelerating since Kant, widening the breach between man’s mind and reality. To reclaim the power of philosophy, one must grasp the reason why man needs epistemology. Since man is neither infallible nor omniscient, he has to discover a valid method of cognition. Two questions are involved in his every conclusion or decision: What do I know?—and: How do I know it? It is the task of epistemology to provide the answer to the “How?” —which then enables the special sciences to provide the answer to the “What?” In the history of philosophy, epistemological theories have consisted predominantly of attempts to escape one or the other of these two questions—by means of skepticism or mysticism. The motive of all the attacks on man’s rational faculty, is a single basic premise: the desire to exempt consciousness from the law of identity. The implicit, but unadmitted premise of modern philosophy is the notion that “true” knowledge must be acquired without any means of cognition, and that identity is the disqualifying element of consciousness. This is the essence of Kant’s doctrine, which represents the negation of any consciousness, of consciousness as such. Objectivity begins with the realization that man (including his consciousness) is an entity of a specific nature who must act accordingly; that there is no escape from the law of identity; that there is no room for the arbitrary in any activity of man, least of all in his method of cognition—and that he must be guided by objective criteria in forming his tools of cognition: his concepts. Just as man’s physical existence was liberated when he grasped that “nature, to be commanded, must be obeyed,” so his consciousness will be liberated when he grasps that nature, to be apprehended, must be obeyed—that the rules of cognition must be derived from the nature of existence and the nature, the identity, of his cognitive faculty.