Ayn Rand

Introduction to Objectivist Epistemology

Expanded Second Edition,Edited by Harry Binswanger and Leonard Peikoff,

Meridian Books, 1990, pp 5-28

Chapters 1-3

 

 

1. Cognition and Measurement

 

Consciousness, as a state of awareness, is not a passive state, but an active process that consists of two essentials: differentiation and integration.

 

Although, chronologically, man's consciousness develops in three stages: the stage of sensations, the perceptual, the conceptual--epistemologically, the base of all of man's knowl­edge is the perceptual stage.

 

Sensations, as such, are not retained in man's memory, nor is man able to experience a pure isolated sensation. As far as can be ascertained, an infant's sensory experience is an undifferentiated chaos. Discriminated awareness begins on the level of percepts.

 

A percept is a group of sensations automatically retained and integrated by the brain of a living organism. It is in the form of percepts that man grasps the evidence of his senses and apprehends reality. When we speak of "direct percep­tion" or "direct awareness," we mean the perceptual level. Percepts, not sensations, are the given, the self-evident. The knowledge of sensations as components of percepts is not direct, it is acquired by man much later: it is a scientific, conceptual discovery.

 

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.

 

(It may be supposed that the concept "existent" is implicit even on the level of sensations-if and to the extent that a consciousness is able to discriminate on that level. A sensa­tion is a sensation of something, as distinguished from the nothing of the preceding and succeeding moments. A sensa­tion does not tell man what exists, but only that it exists.)

 

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. This method permits any number of classifications and cross-classifications: one may classify things according to their shape or color or weight or size or atomic structure; but the criterion of classification is not invented, it is perceived in reality. Thus the concept "unit" is a bridge between metaphysics and epistemology: units do not exist qua units, what exists are things, but units are things viewed by a consciousness in certain existing relationships.

 

With the grasp of the (implicit) concept "unit" man reaches the conceptual level of cognition, which consists of two interrelated fields: Conceptual and the Mathematical. The process of concept-formation is, in large part, a mathemati­cal process.

 

Mathematics is the science of measurement. Before pro­ceeding to the subject of concept-formation, let us first consider the subject of measurement.

 

Measurement is the identification of a relationship-a quantitative relationship established by means of a standard that serves as a unit. Entities (and their actions) are mea­sured by their attributes (length, weight, velocity, etc.) and the standard of measurement is a concretely specified unit representing the appropriate attribute. Thus, one measures length in inches, feet and miles-weight in pounds-velocity by means of a given distance traversed in a given time, etc.

 

It is important to note that while the choice of a given standard is optional, the mathematical rules of using it are not. It makes no difference whether one measures length in terms of feet or meters; the standard provides only the form of notation, not the substance nor the result of the process of measuring. The facts established by measurement will be the same, regardless of the particular standard used; the standard can neither alter nor affect them. The require­ments of a standard of measurement are: that it represent the appropriate attribute, that it be easily perceivable by man and that, once chosen, it remain immutable and abso­lute whenever used. (Please remember this; we will have reason to recall it.)

 

Now what is the purpose of measurement? Observe that measurement consists of relating an easily perceivable unit to larger or smaller quantities, then to infinitely larger or infinitely smaller quantities, which are not directly perceiv­able to man. (The word "infinitely" is used here as a mathe­matical, not a metaphysical, term.) The purpose of measure­ment is to expand the range of man's consciousness, of his knowledge, beyond the perceptual level: beyond the direct power of his senses and the immediate concretes of any given moment. Man can perceive the length of one foot directly; he cannot perceive ten miles. By establishing the relationship of feet to miles, he can grasp and know any distance on earth; by establishing the relationship of miles to light-years, he can know the distances of galaxies.

 

The process of measurement is a process of integrating an unlimited scale of knowledge to man's limited perceptual experience-a process of making the universe knowable by bringing it within the range of man's consciousness, by es­tablishing its relationship to man. It is not an accident that man's earliest attempts at measurement (the evidence of which survives to this day) consisted of relating things to himself-as, for instance, taking the length of his foot as a standard of length, or adopting the decimal system, which is supposed to have its origin in man's ten fingers as units-of counting.

 

It is here that Protagoras' old dictum may be given a new meaning, the opposite of the one he intended: "Man is the measure of all things." Man is the measure, epistemolog­ically-not metaphysically. In regard to human knowledge, man has to be the measure, since he has to bring all things into the realm of the humanly knowable. But, far from leading to subjectivism, the methods which he has to em­ploy require the most rigorous mathematical precision, the most rigorous compliance with objective rules and facts-if the end product is to be knowledge.

This is true of mathematical principles and of the princi­ples by which man forms his concepts. Man's mathematical and conceptual abilities develop simultaneously. A child learns to count when he is learning his first words. And in order to proceed beyond the stage of counting his ten fin­gers, it is the conceptual level of his consciousness that man has to expand.

 

 

 

2. Concept-Formation

 

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 attribute 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 (chronological y, 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: "Length must exist in some quantity but may exist in any quantity.  I shall identify as ‘length’ that attribute of any existent pos­sessing it which can be quantitatively related to a unit of length, without specifying the quantity."

 

The child does not think in such words (he has, as yet, no knowledge of words), but that is the nature of the process which his mind performs wordlessly. And that is the princi­ple which his mind follows, when, having grasped the con­cept "length" by observing the three objects, he uses it to identify the attribute of length in a piece of string, a ribbon, a belt, a corridor or a street.

 

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.

Bear firmly in mind that the term "measurements omit­ted" does not mean, in this context, that measurements are regarded as non-existent; it means that measurements exist, but are not specified. That measurements must exist is an essential part of the process. The principle is: the relevant measurements must exist in some quantity, but may exist in any quantity.

 

A child is not and does not have to be aware of all these complexities when he forms the concept "table." He forms it by differentiating tables from all other objects in the context of his knowledge. As his knowledge grows, the defi­nitions of his concepts grow in complexity. (We shall dis­cuss this when we discuss definitions.) But the principle and pattern of concept-formation remain the same.

 

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 concept­formation in a mind's transition from the perceptual level to the full vocabulary of the conceptual level.

 

There is evidence to suppose that written language origi­nated in the form of drawings-as the pictographic writing of the Oriental peoples seems to indicate. With the growth of man's knowledge and of his power of abstraction, a pictorial representation of concepts could no longer be ade­quate to his conceptual range, and was replaced by a fully symbolic code.

A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s),with their particular measurements omitted.

 

I 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 L 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.

 

Please note the fact that a given shape represents a cer­tain category or set of geometrical measurements. Shape is an attribute; differences of shape-whether cubes, spheres, cones or any complex combinations-are a matter of differ­ing measurements; any shape can be reduced to or ex­pressed by a set of figures in terms of linear measurement. When, in the process of concept-formation, man observes that shape is a commensurable characteristic of certain ob­jects, he does not have to measure all the shapes involved nor even to know how to measure them; he merely has to observe the element of similarity.

 

Similarity is grasped perceptually; in observing it, man is not and does not have to be aware of the fact that it involves a matter of measurement. It is the task of philoso­phy and of science to identify that fact.

 

As to the actual process of measuring shapes, a vast part of higher mathematics, from geometry on up, is devoted to the task of discovering methods by which various shapes an be measure --comp ex methods which consist of reducing the problem to the terms of a simple, primitive method the only one available to man in this ie linear measurement(Integral calculus, used to measure the area of circles, is just one example.

 

In this respect, concept-formation and applied mathemat­ics have a similar task, just as philosophical epistemology and theoretical mathematics have a similar goal: the goal and task of bringing the universe within the range of man's knowledge-by identifying relationships to perceptual data.

 

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 red: the wavelengths of light­a 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 characteristics 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.

Concepts of motion are formed by specifying the distinc­tive nature of the motion and of the entities performing it, and/or of the medium in which it is performed-and omit­ting the particular measurements of any given instance of such motion and of the entities involved. For instance, the concept "walking" denotes a certain kind of motion per­formed by living entities possessing legs, and does not apply to the motion of a snake or of an automobile. The concept "swimming" denotes the motion of any living entity propel­ling itself through water, and does not apply to the motion of a boat. The concept "flying" denotes the motion of any entity propelling itself through the air, whether a bird or an airplane.

 

Adverbs are concepts of the characteristics of motion (or action); they are formed by specifying a characteristic and omitting the measurements of the motion and of the entities involved-e.g., "rapidly," which may be applied to "walk­ing" or "swimming" or "speaking," etc., with the measure­ment of what is "rapid" left open and depending, in any given case, on the type of motion involved.

 

Prepositions are concepts of relationships, predominantly of spatial or temporal relationships, among existents; they are formed by specifying the relationship and omitting the measurements of the existents and of the space or time involved-e.g., "on," "in," "above," "after," etc.

Adjectives are concepts of attributes or of characteristics. Pronouns belong to the category of concepts of entities. Conjunctions are concepts of relationships among thoughts, and belong to the category of concepts of consciousness.

 

As to concepts of consciousness, we shall discuss them later and at length. (To anticipate questions such as: "Can you measure love?"-I shall permit myself the very philo­sophical answer: "And how!")

 

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.

 

1. 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."

 

2. 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.

3. Abstraction from Abstractions

 

 

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 role of language (which we shall discuss at length when we discuss definitions) must be mentioned briefly at this point. 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. The first concepts a child forms are concepts of perceptual entities; the first words he learns are words designating them. Even though a child does not have to perform the feat of genius performed by some mind or minds in the prehistorical infancy of the human race: the invention of language-every child has to perform independently the feat of grasping the nature of language, the process of symbolizing concepts by means of words.

 

Even though a child does not (and need not) originate and form every concept on his own, by observing every aspect of reality confronting him, he has to perform the process of differentiating and integrating perceptual con­cretes, in order to grasp the meaning of words. If a child's brain is physically damaged and unable to perform that process, he does not learn to speak.

 

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.

 

After the first stage of learning certain fundamentals, there is no particular order in which a child learns new concepts; there is, for a while, a broad area of the optional, where he may learn simple, primary concepts and complex, derivative ones almost concurrently, depending on his own mental initiative and on the random influences of his environment. The particular order in which he learns new words is of no significance, at this stage, provided he understands their meanings. His full, independent conceptual development does not begin until he has acquired a sufficient vocabulary to be able to form sentences-i.e., to be able to think (at which time he can gradually bring order to his haphazard conceptual equipment). Up to that time, he is able to retain the referents of his concepts by perceptual, predominantly visual means; as his conceptual chain moves farther and farther away from perceptual concretes, the issue of verbal definitions becomes crucial. It is at this point that all hell breaks loose.

 

Apart from the fact that the educational methods of most of his elders are such that, instead of helping him, they tend to cripple his further development, a child's own choice and motivation are crucial at this point. There are many different ways in which children proceed to learn new words thereaf­ter. Some (a very small minority) proceed straight on, by the same method as before, i.e., by treating words as con­cepts, by requiring a clear, first-hand understanding (within the context of their knowledge) of the exact meaning of every word they learn, never allowing a break in the chain linking their concepts to the facts of reality. Some proceed by the road of approximations, where the fog deepens with every step, where the use of words is guided by the feeling: "I kinda know what I mean." Some switch from cognition to imitation, substituting memorizing for understanding, and adopt something as close to a parrot's psycho-epistemology as a human brain can come-learning, not concepts nor words, but strings of sounds whose referents are not the facts of reality, but the facial expressions and emotional vibrations of their elders. And some (the overwhelming majority) adopt a precarious mixture of different degrees of all three methods.

 

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.

 

The distinguishing characteristics of these units are speci­fied categories of measurements of shape, such as "a flat, level surface and support(s)" in the case of tables. In rela­tion to the new concept, these distinguishing characteristics are now regarded in the same manner as the measurements of individual table-shapes were regarded in forming the concept "table": they are omitted, on the principle that a piece of furniture must have some shape, but may have any of the shapes characterizing the various units subsumed un­der the new concept.

 

The distinguishing characteristic of the new concept is determined by the nature of the objects from which its constituent units are being differentiated, i.e., by their "Con­ceptual Common Denominator," which, in this case, is: large objects inside a human habitation. The adult definition of "furniture" would be: "Movable man-made objects in­tended to be used in a human habitation, which can support the weight of the human body or support and/or store other, smaller objects." This differentiates "furniture" from archi­tectural features, such as doors or windows, from ornamen­tal objects, such as pictures or drapes, and from a variety of smaller objects that may be used inside a habitation, such as ashtrays, bric-a-brac, dishes, etc.

 

The distinguishing characteristics of "furniture" are a spec­ified range of functions in a specified place (both are mea­surable characteristics): "furniture" must be no larger than can be placed inside a human habitation, no smaller than can perform the specified functions, etc.

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.)

 

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 determines the distinguishing characteristic of the new concept: the one representing their "Conceptual Common Denominator" with the existents from which they are being differentiated.

 

When a concept is subdivided into narrower ones, its distinguishing characteristic is taken as their "Conceptual Common Denominator"-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.

 

Let us observe these two principles on another example: the ramifications of the concept "man."

Man's particular type of consciousness is the distinguishing characteristic by which a child (at a certain level of develop­ment) differentiates him from all other entities. By observ­ing the similarities among "cat," "dog," "horse," "bird," and by differentiating them from other entities, he integrates them into the wider concept "animal"-and, later, includes "man" in this wider concept. The definition of "animal" (in general terms) would be: "A living entity possessing the faculties of consciousness and locomotion."

 

Man's distinguishing characteristic, his rational faculty, is omitted from the definition of "animal"-on the principle that an animal must possess some type of consciousness, but may possess any of the types characterizing the various units subsumed under the new concept. (The standard of mea­surement that differentiates one type of consciousness from another is its range.)

The distinguishing characteristics of the new concept are characteristics possessed by all its constituent units: the at­tribute "living" and the faculties "consciousness and loco­motion."

 

With further knowledge, by observing the similarities among animals, plants and certain sub-microscopic entities (and their differences from inanimate objects), man integrates them into the concept "organism." The definition of "or­ganism" (in general terms) would be: "An entity possessing the capacities of internally generated action, of growth through metabolism, and of reproduction."

 

These distinguishing characteristics of the new concept are possessed by all its constituent units. The distinguishing characteristics of "animal" are omitted from the definition-on the principle that the "internally generated actions" must exist in some form (including "consciousness and locomo­tion"), but may exist in any of the forms characterizing the various units subsumed under the new concept.

 

With the growth of man's knowledge, a very broad con­cept, such as "animal," is subdivided into new concepts, such as: "mammal," "amphibian," "fish," "bird," etc. Each of these is then subdivided further and further into narrower sub-categories. The principle of concept-formation remains the same: the distinguishing characteristics of the concept "animal" (the faculties of "consciousness and locomotion") are the "Conceptual Common Denominator" of these sub­divisions, and are retained but qualified by the addition of other (anatomical and physiological) characteristics to form the distinguishing characteristics of the new concepts.

 

(The chronological order in which man forms or learns these concepts is optional. A child, for instance, may first integrate the appropriate concretes into the concepts "ani­mal," "bird," "fish," then later integrate them into a wider concept by expanding his concept of "animal." The princi­ples involved and the ultimate choice of distinguishing char­acteristics will be the same, granting he reaches the same level of knowledge.)

 

Turning now to the process of conceptual subdivision, the concept "man" can be subdivided into innumerable sub­categories, according to various aspects or attributes. For instance, such concepts as "child," "adolescent," "youth," "adult" are formed according to measurements of time, i.e., according to the number of years lived. These concepts retain the distinguishing characteristic of "rational animal" but narrowed by a specified range of years.

 

The concept "man" can be subdivided according to spe­cial characteristics, such as racial (anatomical) descent: "Cau­casian," "Negro," "Mongolian," etc.-or national (politico­geographical) origin: "American," "Englishman," "French­man," etc.-or professional activity: "Engineer," "Doctor," "Artist," etc. (which involve concepts of consciousness)--or even according to such characteristics as the color of hair: "Blonde," "Brunette," "Redhead." In all such cases, the distinguishing characteristic of "rational animal" is retained but narrowed by specified characteristics which represent specified categories of measurements.

 

The concept "man" can be subdivided according to spe­cial relationships-for instance, according to a biological relationship ("Father," "Son," "Brother"), or a legal rela­tionship ("Husband," "Wife"), or an economic relationship ("Employer," "Employee"), etc. In all such cases, the char­acteristic of "rational animal" is retained but combined with a specified relationship.

 

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.

 

1. 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.

 

A widespread error, in this context, holds that the wider the concept, the less its cognitive content-on the ground that its distinguishing characteristic is more generalized than the distinguishing characteristics of its constituent concepts. The error lies in assuming that a concept consists of nothing but its distinguishing characteristic. But the fact is that in

the process of abstracting from abstractions, one cannot know what is a distinguishing characteristic unless one has observed other characteristics of the units involved and of the existents from which they are differentiated.

 

Just as the concept "man" does not consist merely of "rational faculty" (if it did, the two would be equivalent and interchangeable, which they are not), but includes all the characteristics of "man," with "rational faculty" serving as the distinguishing characteristic-so, in the case of wider concepts, the concept "animal" does not consist merely of "consciousness and locomotion," but subsumes all the char­acteristics of all the animal species, with "consciousness and locomotion" serving as the distinguishing characteristic. (We shall discuss this further when we discuss definitions.)

 

An error of that kind is possible only on the basis of assuming that man learns concepts by memorizing their definitions, i.e., on the basis of studying the epistemology of a parrot. But that is not what we are here studying. To grasp a concept is to grasp and, in part, to retrace the process by which it was formed. To retrace that process is to grasp at least some of the units which it subsumes (and thus to link one's understanding of the concept to the facts of reality).

Just as wider integrations of concepts require a more extensive knowledge, so narrower subdivisions of concepts require a more intensive knowledge. For instance, the con­cept "father" requires more knowledge than the concept "man"-since it requires knowledge of man, of the act of reproduction, and of the consequent relationship.

 

2. 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.) In such cases, the knowl­edge of whether a concrete is or is not to be subsumed under a certain concept does not come automatically, but requires a new cognitive effort.

 

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.