IOE, Chapter Two
Concept Formation
by Jimmy (Jimbo) Wales

Date: 5 Feb 1992
Forum: Moderated Discussion of Objectivist Philosophy
Copyright: Jimmy (Jimbo) Wales

Chapter 2 is entitled 'Concept-Formation'. This chapter will cover some of the most essential material in the book. If you wish to understand Objectivist epistemology, it is essential that you understand the fundamental concepts covered in this chapter.

I begin by quoting the following statements from the chapter:

"A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted." (Rand, 1990, 13)

"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." (Rand, 1990, 10)

These two statements say (essentially) the same thing, but from slightly differing perspectives. There are some very important things to note about the specific wording of the two statements.

First, notice that a concept is a mental integration of two or more *units*. Recall that a unit "is an existent regarded as a separate member of a group of two or more similar members." (Rand, 1990, 6) Thus, concept-formation depends critically upon the ability to regard particular entities (existents) in a particular way (as separate members of a group).

Second, notice that the units are isolated based upon specific (distinguishing) characteristics. This is the key link between metaphysics and epistemology. "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..." (Rand, 1990, 10)

Notice that Rand firmly grounds her theory of concept formation in reality. Concepts are not formed by ignoring aspects of reality (per se), but by selective mental focus.

Finally, notice that a concept is a 'mental integration'. The concept is a mental existent. I suspect that future neuroscientists will be able to directly measure a 'concept' as a set of conditions within the human brain. But such direct measurement is not necessary (of course) for a proper theory of concepts.

Leonard Peikoff writes:

"Only concretes exist. If a concept is to exist, therefore, it must exist in some way as a concrete. That is the function of language." (Peikoff, 1991, 78)

It is very important to understand this point. The relationship between words (perceptual symbols used to denote concepts) and concepts is crucial. We might form a perfectly valid concept and retain it for a short time without denoting it with a word. But the existence of such a concept would be very tenuous indeed, without a shorthand perceptual symbol with which we can store and recall the concept. Indeed, it is difficult to imagine how one would go about such a recollection. Try to think of a single concept you have formed for which you _have_ no word (or set of words, as might be appropriate).

Words are not just for communication. Words play a crucial role in our process of cognition, by allowing us to recall previously formed concepts quickly and efficiently.

Finally, after a concept has been formed and denoted with a perceptual symbol (a word), the concept must be defined. The role of definitions in the Objectivist epistemology is quite different from the role which they play in some other epistemologies.

"A definition is a statement that identifies the nature of the units subsumed under a concept." (Rand, 1990, 40).

Definitions will be discussed at length in chapter 5. But you need to have at least a minimal grasp on the role of definitions at this stage. A proper definition will identify the essential characteristics which distinguish the units of a concept from other existents. Thus, a definition does not serve as a 'rule of inclusion and exclusion', except to the degree that the essential characteristics are fundamental in determining the difference between the units integrated and other existents. I will return to this later for a fuller explanation, via an example.

Concept formation is a process of measurement. Measurement is involved in both fundamental processes of concept formation: differentiation and integration.

How do we differentiate? We differentiate based solely upon commensurate characteristics. This is the idea behind the 'Conceptual Common Denominator (CCD)'.

In order to differentiate a group of objects from some other objects, we must first have some basis with which to compare the objects. The objects must have some attributes which allow for comparison. _All_ of the attributes which may be measured in the members of the set of objects from which we are trying to differentiate a subset make up the CCD.

An example will help serve to illustrate. I have written on a piece of paper before me a large circle. Within the circle I have written about 10 or so letters with a pencil. The circle contains 3 As and a variety of other letters, one each. I will illustrate the formation of the concept 'A'.

(Note that this demonstration will be somewhat limited in nature. One does not generally operate in such a microcosmic cognitive context.)

The commensurate characteristics of the group of letters include such things as width, height, shape, color, etc. This group of commensurate characteristics serves as the conceptual common denominator. All of the letters have the characteristics width, height, shape, color, etc. in common. These will serve as the foundation for comparison.

I observe the various letters on the page. I compare them to each other. I am measuring each of the commensurate characteristics in the CCD with my eyes. Notice that a child performing this operation for the first time would NOT have the words to explain what he or she was doing. A child would not be able (generally) to explain that this object has the same shape as the others. But a child would be able to note the differences and similarities.

As I observe the letters, I notice that some of them are more like each other than the others. The 'A's have a pointed top on them; all the other letters are either rounded or flat on top. The A's have a bar across them; the other letters do not.

As I note these similarities (based upon measurement of some of the characteristics in the CCD), I mentally group the objects. I imagine the 'A's together, apart from the group. I have differentiated them from the others. Some characteristics which I could compare turned up a difference between some objects and some others. These characteristics are the 'distinguishing characteristics'.

I could not have separated the 'A's from the others based on color: they are all graphite colored. Of course, I might be able (were my purposes different) to differentiate the letters based on color or any other commensurable attribute. But for the time being, I am working on the concept 'A'. My point is that membership in the concept 'A' will not preclude the 'A's from being members of some other concept.

I have now differentiated the 'A's from the other letters. But such a differentiation will do me little good unless I finish the process. It would be impossible to keep in mind for very long all the objects in the two groups. Because I only have a few letters on the page, I can hold the 'A's separate for quite some time. But if I wish to retain and use my knowledge of the differences between 'A's and other objects, I must finish the job.

First, I must regard each A as a separate member of the group of 'A's. This is where the 'unit' idea comes into play. The act of treating each of the 'A's as separate members of the group of 'A's is essential to concept formation.

Then, I must integrate the units into the concept. I do this by omitting the particular measurements of the 'A's which did not go into the formation of the concept, and by omitting the particular measurements of the distinguishing characteristics which were subsumed by the concept.

'Measurement omission' does not mean that we pretend that the measurements do not exist. I mean that we simply allow the measurements to exist in _some_ unspecified quantity within the appropriate range.

I wrote the letters on the page with a pencil. And I did it rather hastily, so that the letters are somewhat sloppy. To form the concept 'A', I must ignore the fact that on that A (I am pointing to one of them) the point isn't very sharp while on that A (I point to another) the cross bar reaches outside the inverted V.

Furthermore, I omit the measurements of all the commensurate characteristics which did NOT distinguish the 'A's from the other letters. If I saw a new 'A' which was written in ink, I would therefore still conclude that it was an 'A' (albeit perhaps of a different sub-type).

Next, to ensure that I can hold the concept in my mind, I designate it with a auditory symbol. 'A' (I am saying A out loud). 'A'. These are 'A's.

Finally, I make up a formal definition. This definition serves a similar purpose to the word 'A'. It ensures that I will be able to recall the concept tomorrow and the next day.

The definition of 'A' is contextual. Within the context as I have described it, the definition of A is: A is the letter with a pointed top. This definition specifies the distinguishing characteristic which best serves to differentiate the letter A from other letters. Recall that one of the differences between the 'A's and the other letters was the cross bar. But one of the other letters written here ('H') has a cross bar as well.

The cross bar served as a distinguishing characteristic. 'A's are different from other letters in many ways, one of which is that 'A's have a cross bar whereas most of the other letters do not.

But none of the other letters I have written has a pointed top like the 'A's do. 'Pointed top' is the characteristic of 'A's which serves to explain the most about the difference between 'A's and other letters.

Thus, my formation of the concept 'A' is complete. Let us review quickly the 7 steps I took. I will bracket the 7 steps which I have identified with the 4 distinct steps identified by Peikoff. (I have gone into more detail about the steps than did Peikoff).

I. "We begin the formation of a concept by isolating a group of concretes." (Peikoff, 1991, 77)

1. We note the commensurate characteristics (the CCD) which may be used for comparison.

2. We measure the concretes via some process. (In my example, direct visual observation was required).

3. We form a group of similars, based on distinguishing characteristics.

II. "But an isolated perceptual group is not yet a concept. If we merely isolated, we could do little or nothing cognitively with the group, nor could we keep the group isolated. To achieve a congitive result, we must proceed to integrate." (Peikoff, 1991, 78)

4. We regard each of the concretes a a separate member of the group.

5. We integrate the units into the concept, omitting the particular measurements as discussed above.

III. "The tool that makes this kind of integration possible is language." (Peikoff, 1991, 79)

6. We assign a word (a perceptual concrete) to the concept.

IV. "The final step in concept-formation is definition." (Peikoff, 1991, 96)

7. We define the concept according the the essential characteristics as will be discussed in chapter 5.

This ends the general discussion of concept-formation. Rand then proceeds to give a (non-exhaustive) catalog of types of concepts. Essentially, Rand briefly explains what measurements are retained and omitted in the formation of some different kinds of concepts.

One omission which I would like to see explained in some future publication is concepts of imagination. Concepts of imagination are a sub-category of concepts of consciousness which provide some particularly interesting issues vis a vis measurement omission.

In this section of the chapter, Rand speaks in an offhand way of certain types of words as being concepts. Be careful not to be confused here. The matter is cleared up in the appendix, which I will quote for those who do not have a copy of the second edition.

"Prof F: On page 16, you refer to words as being themselves concepts. Do you mean that literally? For instance, you say that prepositions are concepts. Do you mean that prepositions stand for concepts? Is this a shorthand way of saying that?

"AR: Oh yes, certainly. I have stated that words are perceptual symbols which stand for these products of the mental integrations.

"And in case this isn't clear, I would like to add one thing. Why did I say 'perceptual'? Because words are available to us either visually or auditorially. They are given to us in sensory, perceptual form....

"So the word is not the concept, but the word is the auditory or visual symbol which stands for a concept." (Rand, 1991, 163)

The chapter finishes with two links between the conceptual and the mathematical fields. A careful reading of this section may help clear up some of the confusion which exists about the definition of mathematics.

First, a concept is much 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." (Rand, 1991, 18) We include in my example concept 'A' all the 'A's which have ever existed or ever will exist, whether I have observed them or not. This is similar to the concept 'integer'. This concept includes every integer which exists, even though I could never have time enough to write down or think about all of them.

Second, "Conceptual awareness is the algebra of cogntion." I find this to be one of the most profound statements in the entire book. Measurement omission in concept formation is very similar to the algebraic 'measurement omission' which allows us to use variables which must stand for some quantity, but which may stand for any quantity.

The final sentence of the chapter illustrates one of the key differences between Objectivist epistemology and any form of instrinsicism. "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." (Rand, 1991, 18)

References

Leonard Peikoff, Objectivism: the philosophy of Ayn Rand, (Penguin Books: New York), 1991.

Ayn Rand, Introduction to Objectivist Epsitemology: Expanded Second Edition, (Penguin Books: New York), 1990.

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