IOE, Chapter Two
Concept Formation
by Will Wilkinson
Date: 17 Feb 1995
Forum: Moderated Discussion of Objectivist Philosophy
Copyright: Will Wilkinson
(All page references are from ITOE 2nd expanded edition.)
What I'm going to try to do here is to provide a review of the important ideas of Chapter 2 in, more or less, my own words. I'm expecting that most keeping up with the discussion will have read at least this far in ITOE, so I'll try not to merely repeat it. I'll try to get at the main points from a slightly different vantage. However, if you have not read Chapter 2 you should still be able to get Rand's gist if my treatment is up to par. This is more of an outline than anything, and I hope part of the discussion will have to do with fleshing out and exploring the process of concept formation in greater detail. Additionally, this was written in something of a rush, so please bring up any errors you spot and make any comments that you think are important. This is Moderated Discussion of Objectivist Philosophy, not Moderated Dissertations, so pick the following apart and let's discuss.
"A concept is," as defined on page 13, "a mental integration of two or more units posessing the same distinguishing characteristic(s), with their particular measurements omitted."
Packed into the definition we have a scad of important ideas that we shall want to get intimate with; "integration," "unit," "distinguishing characteristic(s)," and "omitted measurements" are all crucial. "Mental" is too for that matter. Hopefully we'll get to each in due course.
We'll begin at the beginning and go chronologically through the actual steps of concept formation, as far as is possible, and chew on each important idea as it comes up.
In the chapter Rand fires right away into talk of units, abstraction, integration and mental entities. Let us start at the rudiments of abstraction. For the whole poop on the Objectivist theory of abstraction all noble souls will find and peruse David Kelley's aptly titled paper "A Theory of Abstraction." We'll just gloss the basics here.
As we (hopefully) eschew all sorts of apriorism and innate ideas, we have to be able to get from our perceptual awareness of the world to a conceptual grasp of it. For that abstraction is the thing.
The first step is *differentiation.* "All concepts are formed by first differentiating two or more existents from other existents" (p 13). To do that we must pay special attention to two or more things (differentiation also applies to focusing on just one thing, but that doesn't get us far in concept formation, unless we somehow remember a thing when we see something else like it), selectively focus our perceptual faculties, and draw out a group from the background of other things. This is a volitional, self-directed process. But how do we go about picking some things out and grouping them up while leaving others behind? What is it about the things and about us that makes this possible?
It is similarity. "Similarity... is the relationship between two or more existents which posess the same characteristic(s), but in different measure or degree" (p 13). So there we have what it is about the thing; they have a *commensurable characteristic*, which Rand calls a "Conceptual Common Denominator" or "CCD". The commensurable characteristic that binds the individuals into a group, in our minds, is at the same time the *distinguishing characteristic* that serves to segregate these particular things from other possible objects of awareness. The commensurable characteristic might the be shape for a group of chairs, or a certain hue for a grouping of colors. Still, each individual in the group is different, but the difference is one of *measurement*. A crucial point of Rand's theory is this: "The relevant measurments must exist in *some* quantity, but may exist in *any* quantity" (p 12). Here we begin to see the mathematical element of the theory emerging.
This cat can be black, that speckled, and the other fat, but they all have dimensions along which they are similar (size, texture, shape, sound) or not-completely-different. Focusing on the cats, the similarities are given perceptually, and directly evident to us. Our recognition of similarity is accounted for by an implicit, pre-conceptual process of measurement whereby we quantify certain characteristics in an ordinal "more than, less then" sort of way. If the quantitative values of the relevant dimensions fall within a certain range we see those things as similar and can focus on them as abstract *units*, once we drop from attention their specific measurements. We *omit the measurements* to achieve unit-perspective. "...'Measurements omitted' does not mean that measurements are regarded as non-existent; it means that *measurements exist but are not specified" (p12). We are left with a certain way of regarding the individuals through their integration into a single group. They have now become *units* in an abstract class of things and a concept is about ready to happen.
"The uniting involved is not a mere sum, but an *integration*, i.e., a blending of the units into a *single*, new *mental* entity..." (p. 10). This mental entity, "unit" serves as the bridge between existence and consciousness. A unit perspective is not achieved by passively grasping some automatically manifest essences that are inherent in the objects of experience, but by achieving a certain intentional relationship between our awareness and the way the objects of our awareness relate to each other.
So we've been looking at these cats and we're to the point of seeing each as an abstract unit by retaining the unifying distinctive characteristics and dropping all the particular measurements of the cats. Do we have a concept? Not quite. "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 concepts" (p. 10). We need a word. If we can slap the sound "cat" (or whatever) onto this particular unit, we can carry the abstraction around and summon it up at will by invoking the perceptual concrete we tie to it. This way, we have more than a vague resolve to treat these particulars in our memory as one sort of thing. We have an actual percept that represents the mental integration.
I've been confused by the exact relation between words and concepts in the past. Sometimes "word" and "concept" seem to get conflated, sometimes differentiated. When it is said that "Every word we use.. is a symbol that denotes a concept" (p. 10), and then "words transform concepts into (mental) entities" (p. 11), it seems as though one can have a concept before one has a word, and that concept formation can be done without words. But it is stressed that to be used as a unit, what is integrated must be given a word (or other perceptual concrete), and that concept formation is only completed when a word has been assigned to the integration. Comments?
Now, what the word "cat" refers to is the concept (the distinctive characteristics of cats, with the particular measurements of particular cats omitted), which becomes a particular, lasting mental identity by the assignment of the word. The concept then refers to all the particular things in the world, past and future, that fits into the class delimited by the abstract mental content of the concept "cat", i.e., all actual cats living, dead and yet to be.
The first concepts we form are of this type, concepts of entities. From there we can go on to concepts of materials, concepts of motion. Grammatical word forms are specific types of concepts that refer to distinctive aspects of experience, Rand notes. I'm running long, so I won't discuss the different types of concepts that Rand sets out on pages 15 and 16. However, It should be taken up in the discussion, and a comparison to how these relate to, say, Aristotle's categories would be interesting.
At the end of Chapter 2, Rand stresses the mathematical nature of concept formation. The concept "unit" is obviously at the base of both, but there is more in common. "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... 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."
That about sums it up, I suppose.
I've already suggested for discussion the exact relation of words to concepts and the conceptual basis of grammatical forms. Other topics might have to do with how similarity is perceived and the process of measurement, the relationship of Rand's theory to those of other philosophers and the tradition (how she relates to some of the analysts might be interesting), the assumptions about the nature of human consciousness necessary to make Rand's case, or anything that relates to the issues of chapter 2 of ItOE.
Discuss away.
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