Let us know examine Rand's theories on concept formation, including the language aspects, to see if she deals satisfactorily with some of the 'difficulties'. Since the majority of this discussion revolves around Rand's ideas, the reader can assume that quotes which do not specify other authors are from Ayn Rand. She expresses that concepts, as universals, is philosophy's central issue: "Since man's knowledge is gained and held in conceptual form, the validity of man's knowledge depends on the validity of concepts. But concepts are abstractions or universals, and everything that man perceives is particular, concrete." Philosophy has been about the business of answering these questions she poses:
|What is the relationship between abstractions and concretes? What is the relationship between abstractions and concretes? To what precisely do concepts refer in reality? Do they refer to something real, something that exists - or are they merely inventions of man's mind, arbitrary constructs or loose approximations that cannot claim to represent knowledge?|
Rand quotes Edward C. Moore to show the importance of how these questions are answered: "All knowledge is in terms of concepts. If these concepts correspond to something that is to be found in reality they are real and man's knowledge has a foundation in fact; if they do not correspond to anything in reality they are not real and man's knowledge is or mere figments of his own imagination." (1, 2) She claims that the validity of scientific induction is at stake here in that we must determine the relationship of concepts to perceptual data. (1, 3) I think that the foundationalists are in error in that they do not see the role of concept formation in building human knowledge, and do not, therefore, understand the role of language in concept formation. The coherentists are in error, in that they see language as merely historical, or cultural, and do not see the real coherence (orderly relationship of parts) of language to the 'given'.
Let us first get an overview of the process of concept formation, and then we will expand on some of the details of this process. It is important to understand that consciousness is an active process. It consists of two essential processes: differentiation and integration. These, in turn, consist of three stages: sensations, perceptual and conceptual. The base of man's knowledge, then, is perceptual, since sensations, per se, are not retained in memory. When we talk of 'direct perception' it is at the perceptual level.(1, 5) The building block of man's knowledge is an "existent" - something that exists (such as a thing, an attribute or an action). A sensation we have is of something - it does not tell us what exists, but only that it exists. We grasp that there are existents implicitly on the perceptual level - i.e. we perceptually grasp the data of the constituents which will later be integrated by concepts.
This implicit concept of "entity" undergoes three stages of development in man's mind. First is a child's awareness of objects, representing the implicit concept entity. Secondly, is the awareness of specific, particular things which he can recognize and distinguish from other things, representing the implicit concept of "identity." The last stage is when the child grasps similarities and differences and comes to grasp the relationships among these entities. This stage transforms the (implicit) concept "entity" into the (implicit) concept "unit." (1, 6) For example, a child observes two objects resemble each other and later learns to call them tables. He sees that these are different from four other objects, chairs, by focusing on a particular attribute, their shape. He is isolating them according to their differences, and integrating them as units into separate groups according to their similarities.
Think about what number of considerations, facts, ideas would man have to have in mind and express when proposing to a woman, if the concept of marriage did not exist. Man's key to conceptual awareness and his distinctive mode of cognition is the ability to regard entities as units. Thus "unit", which is essentially a relation, becomes a bridge between existence and consciousness. Units qua units do not exist in nature as things or parts of things, but when it is formed, a unit is a way of relating one existent to another on the basis of some foundation. An existent being regarded as such-and-such is what the very character of relation is. "A relation does not have a respect to something else but it is, by its very nature, a respect." (qtd. in 13, 13) This is much like Aquinas's view of relations, as Robert W. Schmidt states:
|Quantity serves to refer one thing to another because . . . it is capable of being applied to an external thing as measure. . . . [U]nity, the principle of all number, is a form of quantity. Upon unity are founded various relations. . . . Other relations which are not evidently quantitative are also founded upon numerical unity. The relation of likeness . . . , as Aquinas frequently says, is based upon unity in quality.|
The range of what man can hold in the focus of his conscious awareness at any given moment is limited. "The essence, therefore, of man's incomparable cognitive power is the ability to reduce a vast amount of information to a minimal number of units - which is the task performed by his conceptual faculty. And the principle of unit-economy is one of that faculty's essential guiding principles." Think of the unit-economy in the structure of the decimal system, where one must hold only ten symbols and one simple rule of notation for larger numbers or fractions. We use this constantly when referring to multiple existents, without having to keep each single existent within our conscious awareness (e.g. 250 people, 15 desks, etc.). Whereas mathematics is a science of method, enabling man to perform an unlimited series of integrations, "conceptualization is a method of expanding man's consciousness by reducing the number of its content's units - a systematic means to an unlimited integration of cognitive data." (1, 64)
Words, as concepts, enable us to 'let go' of visual memories. Think how much your mind would have to handle if you had to constantly carry images of concretes or of attributes of concretes. You can treat a total as a single unit through the substitution of words. It is our conceptual ability which enables us to learn and do so much more than animals, where we can substitute one concrete for an unlimited number of concretes.(1, 173) While the visual and auditory form of words are the most efficient and productive means of substitution for concepts, when a person is handicapped, such as Helen Keller, other methods can be employed, such as tactile symbols - but these are still perceptual.
Closely related to unit economy is the concept of automatization. In order to perform its unit-reducing function, the symbol, a word, must become automatized in man's consciousness. "The total sum of referents must be instantly (implicitly) available to his conscious mind whenever he uses that concept, without the need of perceptual visualization or mental summarizing - in the same manner as the concept "5" does not require that he visualize five sticks every time he uses it." For example, in order to use the term justice, one would not have to recite to himself a long treatise on its meaning while he listens to evidence in a court of law. The mere sentence "I must be just" holds that meaning in his mind automatically, leaving his conscious attention free to deal with the factual evidence of the case. However, if he were to doubt, he could (should be able to) perform a conscious recall of the meaning. (1, 64)
We can see that learning to speak involves automatizing the use of concepts, and further, that all learning involves this process. Man first acquires knowledge by fully conscious, focused attention and observation, then he establishes mental connections to make that knowledge automatic, freeing the mind to pursue further, more complex knowledge. (1, 65) The reason we are able to understand whole sentences, indeed even whole books, is due to part of the nature of concepts - automatization. You do not have to take the time to remind yourself what you mean by the word 'table' each time you use it. ". . . it's that speed of lightning-like integration of the referents of your concepts to your words that permits you to understand a sentence." (1, 183)
Dreyfus has a different bias about how one comes to knowledge, particularly in learning skills. Practical understanding, Dreyfus explains, as an 'everyday coping', involves explicit beliefs and hypotheses which "can only be meaningful in specific contexts and against a background of shared practices." He gives an example of a social skill one learns in standing the correct distance from another person, and how we learn this, not by consciously or unconsciously learning rules or beliefs, but by merely being brought up within a culture. (15, 7) I disagree. A child may begin to stand at a certain distance not by any explicit explanation, but those rules are given to him implicitly through his observation. He does not learn things automatically or through some kind of osmosis. Of course, he will naturally pick up the habits and customs of his culture, but he must first learn what these are and how to do them.
On a more general basis, for Dreyfus, these skills "embody a whole cultural interpretation of what it means to be a human being . . . [what Heidegger calls] "primordial truth." Since this background of practices is so pervasive, and because it involves skills, Heidegger, Merleau-Ponty, and Wittgenstein, in a rather a priori manner, argue that this cannot be made into a theory.(15, 7) I think, rather, that what we do, in an 'everyday kind of way' becomes a natural kind of automatization due to a continual interfacing within a culture. Of course that culture has a rich and long history behind it, but how do these philosophers think all of this background stuff gets into one's body and mind? A child, born with a blank slate, must (volitionally) use his conceptual skills to process all the perceptual data he is presented with.
A large part of our conceptual skills has to do with measurements. Entities and their actions are measured by their attributes, e.g. length, weight, velocity, etc. This is done using an standard of measurement appropriate to the attribute - e.g. length using inches, feet, miles, etc. The purpose of measurement, from an epistemological perspective, is to expand the range of man's knowledge beyond the perceptual level, i.e. beyond the direct immediate perception of his senses at 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." This, then, becomes a process of "making the universe knowable by bringing it within the range of man's consciousness, by establishing its relationship to man." (1, 8)
Objectivists have a metaphysical base of similarity in that it is grasped perceptually. It is not a vague, arbitrary abstraction as the nominalists claim, while trying to determine what we mean by similarity. When analyzed, similarity amounts to: measurements omitted. (1, 141) For example, in forming the concept blue, one would perceive that two blue cups, with respect to color, are similar, and yet are different from red cups. Blues are placed within a range of measurements within the broader category, color, with red being placed somewhere else on this scale. While man does not have measurements explicitly built into our bodies per se, he perceives similarities and differences directly. (1, 139) It is in the laboratory where the colors would be measured according to the appropriate standard.
Abstraction is mainly a process of measurement, "of treating an aspect of reality as a unit of a group sharing the same characteristic(s) but possessed in different degree." (13, 15) Once man has grasped the implicit concept of unit, he has reached the level of cognition consisting of two interrelated fields; the conceptual and mathematical. There are two links between the conceptual and mathematical fields: (1) "A concept is like an arithmetical sequence of specifically define 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." (2) The principle of concept-formation in which omitted measurements must exist in some quantity, but may exist in any quantity, is the equivalent in a basic principle of algebra, which states that algebraic symbols must be given some numeric 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." (1, ?)
As indicated earlier, consciousness is fundamentally about relationships. The identification of a relationship, in numerical terms, is measurement, and the more complex the relationship, the more complex will be the corresponding science of measurement. There are some areas of knowledge which man has just begun to explore, and for which he has yet to find appropriate standards and methods of measurement. Rand explains why everything must be measurable: "If anything were actually "immeasurable," it would bear no relationship of any kind to the rest of the universe, it would not affect nor be affected by anything else in any manner whatever, it would enact no causes and bear no consequences - in short, it would not exist." (1, 39) Measurement requires an appropriate standard: one does not measure length in pounds, or weight in inches. (1, 38)
We can see how this applies to material things of one's perceptions, but what about things of the inner consciousness - e.g., how do we measure love? While Rand does have constructive things to say about measuring such things as 'love', she acknowledges a fundamental difference from measuring, e.g., physical entities. She responds to a criticism and challenges the "extensive" vs. "intensive" distinction:
|I object in principle to the idea of making metaphysical distinctions of any kind on the basis of our ignorance. The fact that we can measure certain attributes but cannot be as precise in regard to others does not justify the idea of saying that entities possess two different categories of attributes, some of which are "extensive," others "intensive." [Norman] Campbell's standard here is not the nature of the entities but our capacity to measure - which means our state of knowledge, which is greater in one case than in another. That is what I mean by taking our ignorance as a metaphysical standard.|
In a discussion about this, a professor suggested that all material measurements may ultimately be reduced to a small list of measurements. Rand countered that this idea about whether nature was reducible to subatomic particles and, therefore, whether measurement was reducible to counting these particles was a matter pertaining to science, not philosophy,. While she insists that all existents are measurable, she never claimed that all standards of measurement are reducible, and says that no one has had any evidence for this. (1, 189)
Another non-philosophical issue to Objectivists is Dreyfus' thematic question, about whether there is any difference between the natural and human sciences. (15) It is rather a matter of methods of study which should be properly applied to what it is that one wishes to gain more knowledge about. Rorty thinks that the reason we make a distinction between the human and non-human is only because of the fields of inquiry where we currently happen to have the "right vocabulary at hand," which may be only a mere coincidence that where we feel uncertain compared to where we feel certain "roughly coincides with the distinction between the fields of the Geistes and the Naturwissenschaften." (15, 5) I do not think this is mere coincidence, nor a matter of vocabulary per se, but rather, a matter of measurement.
Now let us look at a conceptual error, in the guise of a philosophical problem. Bergson maintained that reality is continuous. If he is right, one professor (designated as Professor 'D', in a workshop group discussion with Ayn Rand) claimed, then there is a gap between any numerical system and reality. I.e., under that paradigm, you could not obtain exact measurement, because your discrete units would not be able to handle this continuum - "You would always have those little infinitesimals left over." Rand pointed out that this was also Zeno's argument, and she challenged Professor D to answer how it was possible for us to get to the moon. Professor D did not deny the practicality of measurement. Rand rejoins: "What is the distinction between the practical and the theoretical? That's a distinction which I do not recognize. "Practical" means acting in this world, in reality. If what we do works, how is that possible if it doesn't correspond to reality?" (1, 191) Moreover, Rand wants someone to explain to her what Bergson means by "a continuous reality:"
|. . . does it mean that, if you then proceed to measure a mile by means of that ruler, there is some kind of "discontinuity" in the mere fact that you have to move that ruler over and over and take your measurement in installments? . . . 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. The mere fact that we cannot encompass the whole of the universe at a glance does not mean that, when we attempt to measure it or to establish relationships one step at a time, we somehow destroy the "continuity of existence."|
Just the very fact that you understood that you could not obtain precision of measurement down to some milli-milli-parts of a millimeter indicates that your concept is correct in that it does correspond to reality, and that it is reality that you are consulting when you discover that you cannot measure submicroscopic quantities. Professor E explains that you cannot have infinity in precision, because you are basing your measurement using some measuring instrument. There will always be a 'plus' or 'minus' within the calibrated accuracy of that instrument. No measurement could be exact if the criterion for exactness is defined such that you have to get the last decimal of an infinite series. But there is a way out of this so-called dilemma, as Rand points out: ". . . in the finite you can always be absolutely precise simply by saying, for instance: "its length is no less than one millimeter and no more than two millimeters." (1, 193)
"A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted." Concepts are formed by first differentiating two or more existents from other existents. Conceptual differentiations are made in terms of commensurable characteristics, i.e. possessing a common unit of measurement. We could not form a concept by attempting to distinguish long objects from green objects. "Incommensurable characteristics cannot be integrated into one unit." For example, tables are differentiated from chairs, beds, etc., by means of the characteristic of their shape, which is an attribute possessed by all the objects involved. Centuries before science discovered how color could actually be measured, man was able to use the concepts blue and orange based on visual similarities and differences. Rand's name for the commensurable characteristic is the "Conceptual Common Denominator" (CCD) and defines 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." (1, 15)
You must always employ both integration and differentiation in order to form concepts. Using a common standard of measurement, you observe similarities in one group of objects and differences from some other group of objects. For example, you could differentiate a red cup from two blue cups, but you couldn't differentiate a blue cup from a heavy stone. (1, 138) Think of defining man as 'a rational animal.' Men possess the same characteristic distinguishing them from all other living species: a rational faculty. The individual measurements of their distinguishing characteristic, rationality, as well as of their other characteristics which make them animals, are different. As living beings of a certain kind, they have many characteristics in common, such as the same shape, the same vital organs, etc. (1, 17) However, it is necessary that definitions be in terms of essential characteristics of existents. Consider the fact that thumbs are unique features of man in addition to his rationality. "For example, if [one] 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." (1, 65)
Concepts are integrated into wider concepts. The first stage of doing this still refers to perceptual concretes. For example the wider concept of furniture subsumes the individual concepts of bed, chair, cabinet, table, etc. Furniture is treated epistemologically as a single mental concrete, but metaphysically each unit stands for an unlimited number of actual concretes of a certain kind. The distinguishing characteristic of the new concept, furniture, is derived from the nature of the individual entities from which they are being differentiated, i.e., from their "Conceptual Common Denominator," which, in this case, is: "large objects inside a human habitation." The 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." Furniture is thus differentiated from other architectural features such as doors, or windows, etc. Note that furniture is an abstraction one step further removed from perceptual reality than any of its constituent concepts - one must first grasp the meaning of the constituent concepts, bed, etc., which are furniture's link to reality. Also, there is a relationship to another concept, habitation, which is not one of furniture's constituents. It should seem obvious that these interrelationships among concepts grow progressively more complex the further away they are from perceptual concretes. (1, 22)
A wider concept, then, includes all the characteristics of its constituent units, but all measurements of their distinguishing characteristics are omitted, and the distinguishing characteristic of the new, wider, concept represents the "Conceptual Common Denominator" - one of the common characteristics of the unit existents from which the new concept is derived. When it is subdivided into narrower ones, a concept's distinguishing characteristic is taken as their CCD, and in this process a narrower range of specified measurements are applied, or else the CCD characteristic is combined with an additional characteristic(s), in order to obtain the distinguishing characteristics of the new concepts. For example man can be subdivided into the sub-categories of child, adolescent, adult, according to the measurement of age; or can be subdivided according to special characteristics such as racial (anatomical) descent, such as Caucasian, Negro, Mongolian, etc. There are many such sub-categories we could devise. (1, 24, 25)
Learning and forming wider concepts requires more knowledge. A widespread erroneous view holds that a wider concept has less cognitive content because its distinguishing characteristic is more generalized than those of its constituents. The error is in assuming that a concept consists of nothing but its distinguishing characteristic. But one cannot know what is a distinguishing characteristic unless one has observed other characteristics of the units involved. Man does not consist merely of rational faculty, else the two would be equivalent and interchangeable, which they are not. This error results in an assumption that man learns concepts by memorizing their definitions. To grasp a concept is to grasp at least some of the units which it subsumes, and this, therefore, links one's understanding with the actual apprehension - i.e., to the facts of reality. Concepts are also subdivided. We would subdivide table into e.g. 'dining table', 'coffee table', 'end table', etc., based on their shape, size and functions. While wider integrations of concepts requires a more extensive knowledge, narrower subdivisions require a more intensive knowledge. (1, 27)
Concepts of method are linked with the vast and complex category of concepts integrating existential concepts with concepts of consciousness. These include most concepts pertaining to man's actions. Although they include perceptual aspects, these complex concepts have no direct perceptual referents and require a long antecedent chain of concepts in order to be grasped. For example, as Rand describes, marriage "denotes a certain moral-legal relationship between a man and a woman, which entails a certain pattern of behaviour, based on a mutual agreement and sanctioned by law." One could not form or grasp the concept "marriage" merely by observing a couple's behavior. Rather, one must integrate their actions with a number of other complex concepts of consciousness, such as "contractual agreement," "morality" and "law." (1, 36)
Abstraction is volitional. For example, a child may observe that his mother is gentle and understanding, and that his aunt is silly and talks baby talk. His senses have given him general impressions. He may decide that he does not like his aunt; his senses will not do that for him automatically. He must make a decision to try to understand the differences between his mother and his aunt, to form abstract concepts of the kinds of characteristics that he likes or dislikes. Unfortunately, many people do not act, and therefore do not conceptualize what the meanings are of their own reactions to other people. (1, 152)
We have seen how Rand ties concepts to units in the real world. She continually refers to "the facts of reality," and "factual data." In spite of this, Matson has found what might be "the seeds of subjectivism" within Rand's theory of concepts. These seeds are contained within Rand's definition of a concept as being "a mental integration . . . produced by man's consciousness . . .". He claims that she does not clarify what she means by mental, and he assumes Rand to mean that "a concept is something whose habitat is the mind, something not itself a bit of the objective reality, but at best "corresponding" to it." This, of course, is much like a Cartesian or Lockean "idea". Matson questions what is produced, when she maintains that concepts are "neither revealed nor invented, but . . . produced." Matson assumes that what Rand claims is a "product of a cognitive method of classification" is some "state of mind" and he compares this to her definition of knowledge as "a mental grasp of a fact(s) of reality." (13, 29)
I think that Matson probably read an earlier edition of Introduction to Objectivist Epistemology, one which does not have the benefit of Rand's discussions made during workshops about her theories of knowledge, which were conducted after the original publishing of IOE. In these discussions, she clarifies this 'problem'. Rand explains that concepts are mental concretes and that the referents of the concept of "concept" are all the concepts you have ever learned, and will ever learn. An individual concept is a concrete in relation to the wider abstraction of the concept of "concept." It is a mental entity "bearing a certain specific relationship to the physical concretes." She calls them "mental entities" only metaphorically or for convenience:
|It is a "something." For instance, before you have a certain concept, that particular something doesn't exist in your mind. When you have formed the concept of "concept," that is a mental something; it isn't a nothing. But anything pertaining to the content of a mind always has to be treated metaphysically not as a separate existent, but only with this precondition, in effect: that it is a mental state, a mental concrete, a mental something. Actually, "mental something" is the nearest to an exact identification. Because "entity" does imply a physical thing. . . . We have to agree here on the terminology, because we are dealing with a very difficult subject for which no clear definitions have been established. I personally would like to have a new word for it, but I am against neologisms.|