Abstraction as Measurement-Omission

From Introduction to Objectivist Epistemology, Expanded Second Edition,

Edited by Harry Binswanger and Leonard Peikoff, Meridian Books, 1990, pp 136-152

 

 

Opening Remarks by Ayn Rand

 

I am very glad to see you all here. I have a definite purpose in mind for these sessions -- namely, to make as clear as possible the nature of the Objectivist theory of concepts. My purpose here will not be to talk about Objec­tivism generally, but to discuss in detail-or, as we call it, to "chew"-this particular book. I regard it as very important; I hope you do too. I think this is a foundation which will help us to understand anything else about Objectivism.

 

I do not want to discuss my Foreword; I assume that everybody here understands what the problem of universals is. The only other issue left open in the Foreword is the question of the validity of sensory data. I indicated that any argument against the validity of sensory data commits what we call the fallacy of the "stolen concept" by relying on the validity of the senses in the attempt to deny them. And I assume that everyone here, if he is in any agreement with us at all, does accept the fact that sensory data are valid.

I also would like to add that the study of sensations as such is much more the province of science than of philoso­phy, since we are not consciously aware of single, isolated sensations. Therefore, we can start where we in fact do start: on the level of percepts.

 

I will ask everyone, to the best of his ability, to consider the subject from scratch-that is, from the beginning, as if we know nothing about concepts. Start from that, as near as one can, and avoid questions based on a different context, on some philosophical theory which is false. In framing your questions, please try to observe whether they are based on and imply some premise improperly accepted as an axiom. Or, in other words, please check your premises.

 

 

 

 

Overview of the Process

 

Prof. A: I want to check my understanding of your theory of concept-formation. What I would like to do is give a brief summary of the process and ask you to comment as to whether I understand it correctly.

 

AR: All right.

 

Prof. A: First of all, I'd like to distinguish the Objectivist position on concept-formation from the Aristotelian posi­tion. According to the Aristotelians, there is some common element, or essence, which is identical in all the concretes of a given kind, and concept-formation is simply the selective awareness of that element. So for Aristotle, the "manness" of men would be something that you would merely focus on selectively; and the "manness" of each man is the same.

 

The Objectivist position is that the "manness" of each man is specific-or not the "manness," but the characteris­tic of rationality. As I understand it, each person's form of rationality has specific measurements, and my rationality or "manness" would not be literally identical to someone else's. But what we do in concept-formation, through a process of measurement-omission, is integrate the concretes according to their common attributes.

 

Now, as I understand it, the measurement-omission is accomplished by means of differentiation. Take the concept of "blue." You begin as a child with two blue objects of different shades perhaps (so their specific color measure­ments differ), and, say, one red object. And then you are able to see that the two blues belong together as opposed to the red; whereas if you just consider the two blues by themselves, you would only be aware of the differences between them; you wouldn't see them as similar until you contrasted them to the red.

 

AR: That's right.

 

Prof. A: Now, the heart of the matter that I want to check on is this. Is it that by means of this differentiation you see blueness as a range or category of measurements within the Conceptual Common Denominator: color? That is the way I understand it. You see the blue of this object and the somewhat different blue of that other object; both have specific measurements, but those measurements fall into one category, as opposed to the measurements of some red object, which fall outside that category. So that the omission of measurements is seeing the measurements as falling within a given range or category of measure­ments.

 

AR: Yes.

 

Prof. A: -within the Conceptual Common Denominator.

 

AR: Yes, that's right. Now, the essential thing there is that you cannot form a concept by integration alone or by differentiation alone. You need both, always. You need to observe similarities in a certain group of objects and differ­ences from some other group of objects within the common standard or kind of measurement. So that you could differ­entiate a red cup from two blue cups, but you couldn't differentiate a blue cup from a heavy stone-there is no Conceptual Common Denominator in that kind of distinc­tion. Does that answer your question?

 

Prof. A: Yes.

 

AR: There is one thing that I want to correct you on, unless it was just foreshortening. You said that "manness" consists of rationality. Don't ever forget the full definition is "rational animal." Otherwise you may give the impression that rationality is the equivalent of the concept "man."

 

Prof. A: No, that was just an offhand way of speaking.

 

AR: Merely foreshortening. Okay.

 

Prof. A: So the Aristotelians thought there really was an attribute of blueness as such-like a kind of little banner sticking up from blue objects saying "blue." Whereas the Objectivist position is that there is a Conceptual Common Denominator uniting a red and two blues, and that the two blues are close together on the measurement range within. that Conceptual Common Denominator, and that all the different shades of blue can be integrated because they fall within that range.

 

AR: Exactly.

 

 

Similarity and Measurement-Omission

 

Prof. B: In forming the concept "blue," a child would perceive that two blue things, with respect to color, are similar and are different from some red thing. And he places the blues in a range of measurements within the broader category, red being somewhere else on the scale.

 

 AR: Right

.

Prof. B: Now, in fact, he doesn't have a category of measurements explicitly, so what actually goes on, as you indicate, is that he perceives similarities and differences directly.

 

AR: That's right.

 

Prof. B: Then is what enables him to classify the blue things as blue the fact that he experiences them as belonging together, as against the red one?

 

AR: If you are trying to project what his psychological state actually is, I think the better way to say it would be: he would feel "these things are similar and these things are different," rather than "they belong together," because the second is a more sophisticated concept.

 

If you want to know what the nature of the process is, it would be more useful to try to remember how you, as an adult, learn new concepts. Because we learn new concepts constantly-for instance, concepts for new inventions, such as television or radar. Ask yourself how you learned that these objects are called by such-and-such name, and how you learned to distinguish television from radio, or radar from other forms of wireless communication. Observe that you would first have to grasp that there is such an entity, and then you would have to grasp in what way it is different from the class of objects which it resembles most. You would immediately have to establish a relationship of genus and differentia. Now, it never occurred to you to measure television, and it wouldn't be necessary to do so. You sim­ply grasped what it has in common with radio and in what ways it is different.

 

Prof. B: Regarding similarity, is it correct to say that similarity is the form in which we perceive certain quantita­tive differences within a range?

 

AR: That's right.

 

Prof. B: So, "similarity" is an epistemological concept, and a formulation of the metaphysical base of that would be: quantitative differences within a range.

 

AR: That's right.

 

Prof. B: To describe the process of concept-formation on a conscious level, one wouldn't have to refer to omitting measurements. Is the purpose then of discussing it in terms of omitting measurements to stress the metaphysical basis of the process?

 

AR: No, not only to stress the metaphysical basis, but to explain both the metaphysical and the epistemological as­pects. Because, in modern philosophy, they dismiss similar­ity practically as if it were ineffable; the whole nominalist school rests on that in various ways. The nominalists claim that we form concepts on the ground of vague similarities, and then they go into infinite wasted discussions about what we mean by similarity, and they arrive at the conclusion that nobody can define similarity. So that one of the important issues here, and the reason for going into the process in detail, is to indicate the metaphysical base of similarity and the fact that it is grasped perceptually, that it is not a vague, arbitrary abstraction, that similarity is perceptually given, but the understanding of what similarity means has to be arrived at philosophically or scientifically. And similarity, when analyzed, amounts to: measurements omitted.

 

Prof. C: I understand how one grasps similarity on the perceptual level. Aristotle, presumably, was unable to iden­tify how we grasp similarity beyond that point. He held that we grasp the essence of things-namely, how they are similar-intuitively. What in addition to that is the Objectiv­ist theory stating?

 

AR: He didn't say you grasp similarities intuitively. He said you grasp the essence of things intuitively.

 

Prof. C: Yes, the essence as the fundamental similarity.

 

AR: But that isn't the way he saw it. Aristotle proceeded from a certain erroneous metaphysics. He assumed that there are such things as essences-and that's the Platonism in him. But he didn't agree with Plato's theory that essences are in a separate world. He held that essences do exist, but only in concretes. And the process of concept-formation, in his view, is the process of grasping that essence, and there­fore grouping concretes in certain categories because they have that essence in common. It is the same essence, but in different concretes.

 

You see, he approaches the subject from that perspective. He isn't concerned with perceived similarities and differ­ences. And since he can't explain how it is that we grasp these essences, which are not perceived by our senses, he would have to treat that grasp as a direct intuition, a form of direct awareness like percepts, but of a different order and therefore apprehending different objects.

 

 

 

 

 

 

Measurement-Omission and Generality

 

Prof. D: This is meant to be a counterexample to a very important part of your thesis: the role of measurement-omission in concept-formation. In general, I agree with what you say, but here is the problem I have. I take it that a concept's generality of reference is achieved by leaving out the specific measurements of the objects referred to.

 

AR: Right.

 

Prof. D: But now take the following case. I have a con­cept of a specific kind of tire, "710-15 tires." This concept specifies all of the significant measurements of the tire (its width and diameter). So what measurements have I left out in forming the concept to achieve the generality?

 

AR: The measurements relevant to the concept "tire." When you say that this is a particular kind of tire, and you specify the measurements, you are talking about a subcate­gory of the wider category "tire." In order to identify it as a 710-15 tire, you first had to know that it is possible to have 620-15 tires (or whatever the figures might be), which you would also subsume under the concept "tire."

 

What you have omitted in classifying a particular group by its measurements is the fact that those measurements may be altered and the object would still be a tire, but not a tire of this subgrouping. You have merely isolated a subcat­egory of the wider concept "tire."

 

I think it is exactly the same process as I described in subdividing "table" into "dining table," "coffee table," etc. [page 23] Those are subcategories, with more restricted measurements, of the wider category, whose measurements are also limited within a certain range.

 

Prof. D: But if it is the omission of the exact measure­ments that provides a generality of reference, then if you reintroduce the exact measurements wouldn't you dissolve the generality?

 

AR: You merely narrow it down. You merely form a subcategory.

 

Prof. D: But I would find that all of these particular tires measure exactly 710 by 15.

 

Prof. E: There would still be many respects in which the measurements of those tires would vary, even if the physical dimensions that you specify remain constant. For instance, they could be whitewall tires or ordinary black ones, pre­sumably they could be made out of somewhat different types of material, etc. Therefore, even though a certain range of measurements was fixed, there would still be varia­tions along other dimensions.

 

AR: But also there is the ultimate variation which you mustn't forget: they are individual tires. Suppose, theoreti­cally, that you could with the finest instruments produce a set of tires of exactly the same measurable aspects in every respect. This wouldn't make them blend into one super-tire. You would still say, "I have one hundred tires of this particular kind."

 

But in order even to make that observation, you first have to have the concept "tire." You first have to know that the issue involved here is the issue of measurements. And if this particular group of tires is identical in all their measure­ments, it is a subgroup; in this respect they are different from other tires, which may have different measurements.

 

Prof. D: But if the essence of generality was the omission of the specific measurement of the individuals, then by reintroducing the specific measurement of individuals the generality would be lost.

 

AR: Except for one very important element that you omit here and that can't be omitted: the Conceptual Common Denominator. Even if all tires, [not just one subgroup], were absolutely alike in every measurement (which is not really possible, but assuming that for the sake of argument), you couldn't form the concept "tire" unless there was some­thing that you could isolate that grouping from. Let us suppose it is the concept of the wheel or some other part of an automobile. Unless you differentiate this particular group­ing from another one with which it has something in com­mon but differs in measurement, you couldn't have a concept. Because you forget there are two aspects of the process -- ­one is integration, but the first one is separation [i.e., differentiation].

 

Prof. D: But does the separation give you the generality, or is it the type of integration that operates that gives you the generality?

 

AR: Both. One is not possible without the other. You could not integrate a given set of concretes unless you could first differentiate it from other concretes. You have to iso­late it first, and then you can integrate it into a particular grouping and form a concept. But if you can't isolate it, you can't abstract.

 

Prof. D: Then you are maintaining that the generality remains in the case of the subcategory where measurements are specified; the generality isn't lost because it was origi­nally obtained in the concept of "tire" by leaving out mea­surements, and bringing back in the measurements now doesn't affect the generality of the notion of tires.

 

AR: Not only was the generality present originally, but you are using and introducing it when you say these are 710-15 tires. The generality is present in the classification of these objects as tires. By identifying them in that form you are introducing the issue of measurement-omission by classi­fying them still as tires. If you didn't do that, then you couldn't call them tires. Then they would be sui generis objects; but they are not, they are tires. Why do you classify them as that? Because their submeasurements, which you are now specifying, are different from the measurements of others which you call "tires"; yet you subsume them in the same concept, in the same category. So you are using measurement-omission even in the classification.

 

 

The Conceptual Common Denominator

 

Prof. E: In the process of concept-formation in child­hood, am I correct that it is impossible for a mind to mistakenly choose a Conceptual Common Denominator? That is, if in fact the two groups were incommensurable, the child's mind would just stop. He couldn't actually form a concept in this case mistakenly, could he?

 

AR: I don't think so. Here, frankly, I have not consid­ered it, but as an offhand answer, I don't quite see how that would be possible.

 

Prof. A: On the perceptual level, you wouldn't then be aware of similarities and differences.

AR: Yes. Now in the case of abstractions from abstrac­tions that sort of mistake is unfortunately made constantly. Only the result isn't really a concept. It usually comes out as one of those "anti-concepts." [See page 71.]

 

Prof. D: I can think of some cases that seem to present a difficulty for the statement: "All conceptual differentiations are made in terms of commensurable characteristics." What would you say about the case of distinguishing mental enti­ties from physical entities? You have the concept of "mental entity" vs. the concept of "physical entity," and there you are distinguishing objects which presumably possess no commensurable characteristic.

 

AR: But you don't form those concepts directly. You form the concept "mental entity" only after you have formed the following concepts: the concept "man," the concept "consciousness," then you identify certain mental states or events in your own mind, such as thoughts, let's say, which you call "mental entities." Then you infer that other human beings also possess the ability to have mental entities in their minds. Therefore you have gone through a long conceptual chain, making differentiations as you went along. You didn't start by looking at reality from scratch so to speak, and as a first-level concept form the concept "men­tal entity" as distinguished from "physical entity." That would not be possible. They would be incommensurable.

 

Now remember, I said here that you cannot form a con­cept, a specific concept, by differentiating objects through an incommensurable characteristic. But, [once formed], you can relate such objects in a wider sense. And the commen­surable characteristic between physical objects and conscious­ness is the content of consciousness, as I discuss in Chapter 4. There is a commensurable link [between concepts of con­sciousness and existential concepts], but that link will be found after you have established the fact of consciousness. Then you consider, "What do I have inside my mind?" and you see that it is exclusively made up of content derived from the outside world, from existence. (It may be indirectly derived, such as you may have thoughts about other thoughts, or you may think about your memories. But ultimately the content of your consciousness, since it begins tabula rasa, consists entirely of your awareness of the outside world.) And there you have the commensurable attribute, or one of the commensurable attributes, which is essential in form­ing concepts of consciousness.

 

Prof. A: If you differentiated length and green from man, at a sophisticated level of knowledge, on the basis of the fact that man is an entity, while length and green are both attributes, there you have found a Conceptual Common Denominator, but you couldn't reach that stage without the earlier abstractions.

 

AR: That's right. But between those two, if you were to consider only those two attributes, apart from "man" or any other concepts, just those two, they won't become commen­surable. But when you establish the category "attributes of physical objects," then you see they have that in common.

 

 

Concepts as Open-ended

 

Prof. A: Isn't what is commensurable or incommensura­ble an issue of one's context of knowledge? Between length and color, for instance, there is actually a commensurable characteristic in a wider context of knowledge-both are attributes-but in order to reach that wider characteristic, you have to begin by making differentiations which you can grasp as commensurable. Or else, you would never get to that later stage.

 

AR: That's right. Even in the wider context, however, it isn't that characteristics which appeared at the first level to be incommensurable suddenly become commensurable.

 

Here we are talking particularly about the process of concept-formation. In that process, you cannot form a con­cept to unify concretes into one category except by means of a commensurable characteristic. And two characteristics that appear to you, on the perceptual level, as incommensurable (like length and green) will not be commensurable at any stage. But you will be able to establish certain relationships between them through many other intermediate concepts. But by themselves those two will remain incommensurable. If we take just the referents of the concepts "length" and "green," there is nothing that you can establish as a com­mensurable characteristic between them.

 

Prof. A: Concepts are open-ended in the sense that every new concrete of the same type is to be subsumed under the concept. Can you say anything about the process by which a child moves from a limited group from which he forms the concept to making it open-ended? How does he get beyond the concretes from which he starts?

 

AR: In order to grasp a concept he has to grasp that it applies to all entities of that particular kind. If he doesn't, he's merely repeating a word. If you ever watch how a child learns to speak, he may first grasp only that "nose" applies to his own nose and, let's say, his mother's. But he hasn't grasped the concept until he can point to any face and say "nose." And that is what children usually do; that is exactly how they learn words. First they have to grasp the word as standing for a particular concrete, then they begin to apply it to other concretes of that kind. Until they have done that, they haven't got it yet. But once they begin to apply the word to new concretes of the same kind, they've made it open-ended.

 

Prof. A: So to make the classification open-ended is part of the integration itself?

 

AR: Yes.

 

Prof. A: To see that there is a kind of thing.

 

AR: Yes.

 

 

Three "Hard Cases"

 

Prof. D: Here are some concepts that present a difficulty with respect to leaving out differing specific measurements and abstracting a common feature. What measurements of what particulars do we leave out and what common features do we retain in the case of the following three concepts: (1) "God"; (2) "infinity"; (3) "nothing"?

 

AR: What measurements do we omit?

 

Prof. A: Yes. And what common features of particulars are retained in order to get the concept "God"­ --

 

AR: I would have to refer you to a brief passage about invalid concepts [page 49]. This is precisely one, if not the essential one, of the epistemological objections to the con­cept "God." It is not a concept. At best, one could say it is a concept in the sense in which a dramatist uses concepts to create a character. It is an isolation of actual characteristics of man combined with the projection of impossible, irratio­nal characteristics which do not arise from reality-such as omnipotence and omniscience.

 

Besides, God isn't even supposed to be a concept: he is sui generis, so that nothing relevant to man or the rest of nature is supposed, by the proponents of that viewpoint, to apply to God. A concept has to involve two or more similar concretes, and there is nothing like God. He is supposed to be unique. Therefore, by their own terms of setting up the problem, they have taken God out of the conceptual realm. And quite properly, because he is out of reality.

 

The same applies to the concept "infinity," taken meta­physically. The concept of "infinity" has a very definite purpose in mathematical calculation, and there it is a con­cept of method. But that isn't what is meant by the term "infinity" as such. "Infinity" in the metaphysical sense, as something existing in reality, is another invalid concept. The concept "infinity," in that sense, means something without identity, something not limited by anything, not definable.

 

Therefore, the measurements omitted here are all measure­ments and all reality. Now, what was the third one?

 

Prof. A: "Nothing."

 

AR: That is strictly a relative concept. It pertains to the absence of some kind of concrete. The concept "nothing" is not possible except in relation to "something." Therefore, to have the concept "nothing," you mentally specify-in parenthesis, in effect-the absence of a something, and you conceive of "nothing" only in relation to concretes which no longer exist or which do not exist at present.

 

You can say "I have nothing in my pocket." That doesn't mean you have an entity called "nothing" in your pocket. You do not have any of the objects that could conceivably be there, such as handkerchiefs, money, gloves, or what­ever. "Nothing" is strictly a concept relative to some exis­tent concretes whose absence you denote in this form.

 

It is very important to grasp that "nothing" cannot be a primary concept. You cannot start with it in the absence of, or prior to, the existence of some object. That is the great trouble with Existentialism, as I discuss in the book [page 60]. There is no such concept as "nothing," except as a relational concept denoting the absence of some things. The measurements omitted are the measurements of those things.

 

Prof. A: Does the concept of "non-existence" refer only to an absence? Is there no valid concept of sheer non-being, of something that never was and never will be?

 

AR: That's right. Non-existence as such-particularly in the same generalized sense in which I use the term "exis­tence" in saying "existence exists," that is, as the widest abstraction without yet specifying any content, or applying to all content-you cannot have the concept "non-existence" in that same fundamental way. In other words, you can't say: this is something pertaining to the whole universe, to every­thing I know, and I don't say what. In other words, without specifying content.

 

You see, the concept of "existence" integrates all of the existents that you have perceived, without knowing all their characteristics. Whereas the concept of "non-existence" in that same psycho-epistemological position would be literally a blank. Non-existence-apart from what it is that doesn't exist-is an impossible concept. It's a hole-a literal blank, a zero.

 

It is precisely on the fundamental level of equating exis­tence and non-existence as some kind of opposites that the greatest mistakes occur, as in Existentialism.

 

 

Abstraction as Volitional

 

Prof. A: Abstraction is a volitional act. Is that right?

 

AR: Oh yes.

 

Prof. D: Then how do I go about abstracting the very first time? How do I know what to do, volitionally? Unless I first had the idea of abstraction, how could I proceed to will to abstract?

 

AR: No, you do something else volitionally. That is, you abstract volitionally, but you don't will it directly the first time. Do you know what you will? You will to observe. You use your senses, you look around, and your will is to grasp, to understand. And you observe similarities. Now, you don't know yet that this is the process of abstraction, and a great many people never grasp consciously that that's what the process is. But you are engaged in it once you begin to observe similarities.

 

And although I hesitate to talk about volition on the preconceptual level-because the subject isn't aware of it in those terms-even a preconceptual infant has the power to look around or not look, to listen or not listen. He has a certain minimal, primitive form of volition over the function of his senses. But volition in the full sense of a conscious choice, and a choice which he can observe by introspection, begins when he forms concepts-at the stage where he has a sufficient conceptual vocabulary to begin to form sentences and draw conclusions, when he can say consciously, in ef­fect, "This table is larger than that one"-that he has to do volitionally. If he doesn't want to, he can skip that neces­sity, and you can observe empirically that too many people do, on too wide a scale.

 

Prof. D: This very first time, or these first times, the child makes observations, and then he finds he has done some­thing which is fait accompli, as it were. And what he was doing, although he didn't have a name or concept for it, was abstracting.

 

AR: That's right. He was talking prose and he didn't know it. That joke [from Moliere] really is very important. In a certain sense, it names a great many psychological processes.

 

Assuming we give words to what goes on in his preverbal consciousness, all he has to will is: "I will look. I will see what things are like." And in that process he makes a discovery: some things have similarities with others and are different from still other things. Now that is a discovery. He doesn't will it at first. Later the process becomes more conscious, but at first it is a discovery. What does he use? His senses. His sensory apparatus at that stage functions automatically. As he discovers certain things, he begins to direct his sensory apparatus, and that is volitional.

 

Prof. D: So he doesn't will to abstract; he looks and then he finds he has done something that is useful to him. Then he does it again and again, but how does he get to the fully conceptual stage?

 

AR: He expands the process. He would say, "By observ­ing, I have seen differences between papers, cups, and ta­bles." Now some strange, nasty relatives enter the room, and he could say, "I will now direct my attention to learning what the difference is between them and my parents." That he would have to do consciously.

 

What would be the subverbal process? It would be as follows: "By observing distinctions and similarities, I have learned a great many things about inanimate objects in my room. I can handle them better because I have observed them. I know that I can drink from a cup but I can't drink from the table. I can deal with these objects if I observe their characteristics-what they have in common and in what ways they are different from each other. Now, I am up against a bewildering experience-people-and there are differences among people, differences which are not so easy to perceive. If I merely look at my mother and my aunt, I won't see differences-at least none that tell me something about the two entities. I have to do something else. I have to consciously direct my attention to observe. If I don't like this aunt, what is it about her? But I like my mother. Why do I? In what respects are they similar? They are both women. In what respects are they different, since I like one and not the other?

 

And then he might observe: "My mother is gentle and understanding, but this new creature yells at me or talks baby talk, and I don't like it." He might observe that much; but his senses won't do it automatically. Here he had to decide: "I want to understand the difference." All his senses gave him is a generalized impression. To differentiate it, he has to do something by conscious decision.

 

And you can observe that, unfortunately, very few people carry that method through life-particularly with regard to such a complex subject as human character. They do not conceptualize why they like one person and not another­ what the meaning is of their own reaction. It is in that field, particularly, that they stop-and stop very early. And that is very unfortunate.