IOE, Chapter Three
Abstraction from Abstractions
by Eduardo Chaves
Date: 9 Feb 1992
Forum: Moderated Discussion of Objectivist Philosophy
Copyright: Eduardo Chaves
TABLE OF CONTENTS
I. First-Level and Higher-Level Concepts
II. More Extensive Knowledge: Wider Integrations
III. More Intensive Knowledge: More Precise Differentiations
IV. Psychological and Logical Processes
V. The Importance of First-Level Concepts
VI. Is the Concept of Table a First-Level Concept?
VII. Is the Concept of Man a First-Level Concept?
Chapter 3 of ITOE has the title "Abstraction from Abstractions" and comes right after the all important Chapter 2 on concept- formation. To understand what Rand is doing in Chapter 3 let us assume that a person has formed the concept of table (one of Rand's examples) through the process indicated in Chapter 2, which I here presuppose [1].
I. FIRST-LEVEL AND HIGHER-LEVEL CONCEPTS
All concepts are abstractions.
Some concepts, according to Rand, refer directly to perceptual entities, or identify perceptual concretes. This is the case with the concept of table. She calls these kinds of concepts "first-level concepts" (p23). Rand defines first-level concepts thus: "All the things which you can perceive directly [and conceptualize] without presupposing in that concept some other conceptual material, those are the first-level concepts" (p.214; the passage in brackets is an interpolation by Harry Binswanger) [2].
Other concepts, Rand claims, are not formed directly from perceptual entities and do not identify perceptual concretes: they refer directly to, and identify, other concepts. They are "higher-level concepts", or "abstractions from abstractions", and so logically presuppose other concepts, in the absence of which they could not be formed. "Higher-level concepts", says Peikoff, "cannot be formed directly from perceptual data, but presuppose earlier concepts" [3].
There are two ways of forming higher-level concepts. Taking a first-level concept such as that of table as a point of departure, an individual can move in two directions:
-- Toward more extensive knowledge or wider integrations
-- Toward more intensive knowledge or more precise differentiations
Moving in these two directions an individual can form more abstract concepts, that is, concepts that are abstractions from other concepts and not from perceptual concretes.
Let us examine in some detail these two ways of forming higher- level concepts, or abstractions from abstractions.
II. MORE EXTENSIVE KNOWLEDGE: WIDER INTEGRATIONS
Once an individual has formed the concepts of table, chair, bed, cabinet, etc. he may notice that the objects identified by them have certain similarities. For example:
-- They are all inside a human habitation, a home [integration] - and so are different from things such as lawn-mowers, bushes, fire hydrants, etc., which lie outside a human habitation, and also from things such as heavy machines, which normally lie inside buildings that are not human habitations [differentiation].
-- They are all movable [integration] - and so different from things such as walls, doors, stairways, fireplaces and the like, which are fixed architectural features of the house [differentiation].
-- They can all be used for things such as supporting the human body or supporting and/or storing smaller objects [integration] - and so different from things such as kitchen utensils, pictures, ornamental objects, books, records, ashtrays, etc. [differentiation].
As a result of this process of integration and differentiation, an individual may form the concept of furniture.
The reason why these concepts (of table, chair, bed, cabinet, etc.) can be compared and eventually integrated into a new concept is that they have what Rand calls a "Conceptual Common Denominator" (CCD), a commensurable characteristic [4]. A CCD is not something arbitrary: one would not be able to form a new concept if one chose to select tables and red objects, since they have no commensurable characteristic [5].
It is important to observe that, for Rand, the new concept -- the concept of furniture -- is more extensive than the concept of table and represents a wider integration.
That it is more extensive seems obvious, since it designates not only tables but also chairs, beds, cabinets, etc.
That it represents a wider integration also seems clear, since it incorporates the concept of table and other related concepts into a new concept. The new concept (that of furniture) allows the concepts subsumed under it to be treated as "units", that is, as members of a group (or class) [6].
In the case of the concepts of table, chair, bed, cabinet, etc., since they are all first-level concepts, their meaning can be conveyed ostensively, that is, by pointing to perceptual concretes that are designated by them. The concept of furniture, however, being a higher-level concept, or an abstraction of abstractions, is further removed from reality than any of the abstractions subsumed under it.
Rand claims that, because the concept of furniture "is an abstraction one step further removed from perceptual reality than any of its constituent concepts" (p.22), "there is no such perceptual object as 'furniture'; there are only tables, chairs, beds, etc." (p.22). According to her, therefore, there is no way that the meaning of the concept of furniture can be conveyed ostensively, by pointing to perceptual concretes. It designates other concepts, not perceptual concretes.
I will come back to this, after I discuss the next two topics.
III. MORE INTENSIVE KNOWLEDGE: MORE PRECISE DIFFERENTIATIONS
Once an individual has formed the concept of table he may also notice that the objects identified by it have certain differences. For example, there are dining tables, coffee tables, end tables, "office tables" (desks), etc.
What is happening here, according to Rand, is "the process of subdividing the concept 'table'" (p.23). The concept of table is differentiated in terms of function and size ("coffee tables are lower and smaller than dining tables; end tables are higher than coffee tables, but lower than dining tables, etc. . . ., a 'desk' is a table that has drawers for storing stationery supplies" [p.23]) and new integrations are made. As a result of this process of differentiation and integration, the individual forms the concepts of dining table, coffee table, end table, desk, etc. The (CCD) among these concepts seems to be size. They are all commensurable in regard to size.
It is important to observe that, for Rand, the new concepts are more intensive than the concept of table and represent a more precise differentiation.
That the new concepts are more intensive seems clear, since they, while preserving all the characteristics of the original concept, have characteristic(s) added to them (p.24).
That the new concepts are more precise also seems clear, since they narrow the range of measurements in relation to the range that prevailed in the case of the concept of table (p.24).
I did not find any explicit discussion of what I going to say now. It could be inferred, from the title of the chapter and from the context, that Rand considers the concepts of dining table, coffee table, end table, desk, etc. as abstractions from abstractions, as concepts formed from the original concept of table by a process of subdivision. However, the abstractions, in this case, do not seem further removed from reality than the original concept, since the meaning of the new concepts apparently can be conveyed ostensively, that is, by pointing to perceptual concretes that are designated by them. How is one to handle this problem?
I think that Rand would say, coherently with what she said regarding the concept of furniture, that the concepts of dining table, etc. presuppose the concept of table and so cannot be understood apart from it. Consequently, she would have to say that the meaning of the concept of dining table (for instance) cannot be conveyed ostensively, by pointing to perceptual concretes, since it presupposes the concept of table, and, consequently, that there is no perceptual object as "dining table": there are only tables (see p.22).
I did not find any place where Rand explicitly says this, and so I am conjecturing here. But I will come back to this issue, after I discuss the next topic.
IV. PSYCHOLOGICAL AND LOGICAL PROCESSES
Although in the last two sections I have used the expression "Once an individual has formed the concept(s) of ...", thereby giving the impression that there is a necessary chronological order in which individuals form concepts, the impression is erroneous. According to Rand, individuals can form concepts in any order, beginning with the less abstract and moving to the more abstract, or vice-versa, or, still, beginning somewhere in the middle and going in both directions. So, there is not, from a psychological point of view, any necessity why an individual would have to form, first, the concept of table, and then go up, so to say, to the concept of furniture, and go down, so to speak, to the concepts of dining table, coffee table, etc.
Rand has no doubt, however, that, from a logical point of view, concepts are hierarchically structured and that it does make a great difference where we place a concept in the hierarchy.
Peikoff in some places does give the impression that there is a necessary order even to the process of concept-formation. When he discusses the concept of culture he says: "Like every concept, 'culture' is an integration of concretes -- in this instance, of certain human products and actions. But the point is that, in this kind of case, the concept cannot be reached ~directly~ from its concretes. It presupposes that they have been conceptualized earlier, usually in several stages, on increasing levels of abstraction. A definite ~order~ of concept-formation is necessary. We begin with those abstractions that are closest to the perceptually given and move gradually away from them" [7]. Peikoff refines his position two pages later, when he speaks of "cognitive options", But even there his position is that "a higher-level item ~is~ dependent on the grasp of a series of earlier items". The "cognitive option" lies in the fact that the series does not have to be the same for everyone [8].
Rand, however, does seem to be more flexible with respect to the order of forming concepts. In answer to the question "might a person form the concept of 'furniture' without having formed the concept of 'table' before?" she says "In a sense, yes. . . . In a loose way, that can be done, but only up to a certain level" (pp.204-205). However, she denies (as we will see) that the concept of furniture can be formed "directly from the perceptual level" (p.215).
In an important passages, Rand explains: "Even if chronologically you may learn those concepts [birds, eagles, penguins, hummingbirds] in different orders, ultimately when you organize your concepts to determine which are basic-level concepts and which are derivative (in both directions, wider integration or narrowqer subdivision), the test will be: which objects you perceive directly in reality and can point to, and which you have to differentiate by means of other concepts" (p.205).
So Rand does admit that one does not need to form the concept of bird (which she regards as a first-level concept) before one forms the concept of eagle, penguin, hummingbird, etc. Peikoff does seem to be more strict. He allows that the series of concretes through which one learns one concept does not have to be identical for everyone. He says, in a passage already quoted: "A definite ~order~ of concept-formation is necessary. We begin with those abstractions that are closest to the perceptually given and move gradually away from them" [9].
I will add, here, that I see no reason, in Rand's arguments, why one could not develop a pedagogical theory, based on well researched empirical data, to show that an individual learns better if he learns, let us say, "top-down", or, conceivably, "bottom-up", or, still, if he learns first-level concepts first and then proceeds, by integration and differentiation, to learn more extensive and more intensive concepts. I don't see Rand committing herself, in terms of theory of learning, to any of these possibilities nor a priori excluding any. But this is another problem, that deals with more deductive or more inductive approaches to learning.
V. THE IMPORTANCE OF FIRST-LEVEL CONCEPTS
The preceding discussion does leave one with the impression that Rand regards first-level concepts as quite important and, in a sense, more basic and fundamental than higher-level concepts. And this impression is quite correct.
The reason why first-level concepts are important in Rand's epistemology is that they allow, in Rand's view, that all our concepts, including the more abstract ones, and all our propositional knowledge, be anchored in reality.
If our higher-level concepts are formed from first-level concepts, through wider integrations and more precise differentiations, they will be anchored in reality since first-level concepts refer to perceptual concretes. If we can reconstruct the logical process by which our concepts are linked to first-level concepts, we will have found their "roots" and will have shown that knowledge is objective. Objectivism's objectivity is to a large extent tied to this issue.
Here is how Peikoff puts the issue: "Reduction is the means of connecting an advanced knowledge to reality by traveling backward through the hierarchical structure involved, i.e., in the reverse order of that required to reach the knowledge. 'Reduction' is the process of identifying in the logical sequence the intermediate steps that relate a cognitive item to perceptual data. Since there are options in the detail of a learning process, one need not always retrace the steps one initially happened to take. What one must retrace is the essential logical structure" [10].
According to Peikoff, this retracing is what makes objectivity possible: it is, therefore, a requirement of objectivity. "Man's only direct contact with reality is the data of sense. These, therefore, are the ~standard~ of objectivity, to which all other cognitive material must be brought back" [11].
The notion of proof is also tied to this issue. Says Peikoff: "'Pooof' is the process of establishing truth by reducing a proposition to axioms, i.e., ultimately, to sensory evidence. Such reduction is the only means man has of discovering the relationship between nonaxiomatic propositions and the facts of reality" [12].
It is possible to somehow move to higher levels of cognition without forming the intermediate concepts. "The most common cause [for this] is intellectual dependence; many men are content to take over the concepts and conclusions ~of other people~ without understanding the steps that led to them" [13]. When this happens, the higher-level concepts have no logical link to perceptual reality, and the result is not knowledge, but confusion [14].
VI. IS THE CONCEPT OF TABLE A FIRST-LEVEL CONCEPT?
I am going to grant, for the sake of the argument, the claim that there are first-level concepts, i.e., concepts the meaning of which can be conveyed ostensively by pointing to the perceptual concretes that they identify.
If this is granted, is it possible to contest Rand's claim that the concept of table is a first-level concept? Is it possible to question that, when one is trying to convey the meaning of the concept of table, one can do so ostensively, pointing to objects?
The answer, at first sight, seems to be yes.
One the one hand, one could argue that the concept of table is an abstraction from abstractions, formed by a wider integration of the concepts of dining table, coffee table, end table, desk, etc.. The concept of table, in this case, would be further removed from reality than any of the abstractions subsumed under it, and the only concepts the meaning of which could be conveyed by pointing to perceptual concretes would be the concepts of dining table, etc. The concept of table, if this suggestion is tenable, would be in a position similar to that in which Rand places the concept of furniture.
What is the problem with this suggestion? The main problem is that it is difficult to imagine how, by pointing (for instance) to dining tables, one could form the right concept, if one does not already have the concept of table. After all, a dining table is a table. If this is so, Rand will have to say that the meaning of the concept of dining table (for instance) cannot be conveyed ostensively, by pointing to perceptual concretes, since it presupposes the concept of table, and, consequently, that there is no perceptual object as "dining table": there are only tables.
The concept of table, then, does seem more basic than the concept of dining table, coffee table, etc., since it is presupposed by these concepts. Let us admit, then, that the concept of table is more basic than the concepts subsumed under it, and, therefore, possibly first-level.
On the other hand, one could argue that the meaning of the concept of furniture can be conveyed ostensively, by pointing to perceptual concretes, to tables, chairs, beds, cabinets, etc. and so claim that IT is first-level. The concept of table, in this case, would not be first-level, being a subdivision of the concept of furniture.
Rand firmly denies that this argument is tenable. Here is what she says, during a discussion of her epistemology, in response to the suggestion that someone could form the concept of furniture, defined as "movable man-made objects within a human habitation", "directly from the perceptual level": "Oh, that he couldn't do. That I can say with assurance. Because he couldn't arrive at that kind of definition while by-passing the identification of the objects he means. He could conceivably memorize the definition if he's heard it, but he couldn't form it himself" (p.215). The person who asked the question insists, asking why that is so, and Rand explains: "To separate furniture from architectural features is a much more complex issue of observations and requires a certain subtlety, which is why I say it is not likely [sic] -- if a man has that much subtlety, he would certainly not fail to observe the differences between tables and chairs" (p.215).
In the first passage Rand asserts that it cannot be done. In the second, she says that it is not likely that it will be done. Perhaps the difference can be explained by the fact that this was an extemporaneous discussion and one is not as precise when one is speaking as when one is writing. But perhaps there is here a hint of the difficulties involved. Despite the difficulties, I do think that Rand's claim that the concept of table is a first-level concept is plausible.
I have used until now only one of Rand's favorite examples, the concept of table. It is time to go into the other example, the concept of man.
VII. IS THE CONCEPT OF MAN A FIRST-LEVEL CONCEPT?
Whatever the difficulties that there may be in deciding whether the concept of table is a first-level concept, they are greatly increased when one comes to discuss the concept of man.
In the same way that we started the previous discussing on the assumption that a person has already formed the concept of table through the process discussed in Chapter 2 of ITOE, here we are going to assume that the person has already formed the concept of man.
Starting from the concept of man, one can, as in the previous case, move toward more extensive knowledge or wider integrations or toward more intensive knowledge or more precise differentiations.
The first path (the direction of more extensive knowledge or wider integrations) will bring one, progressively, to the concepts of animal, organism, etc. [15]
The second path (the direction of more intensive knowledge or more precise differentiations) will bring one to several clusters of concepts, depending on the criteria utilized to make the subdivision. If one takes sex (or gender) as the criterion, one will arrive at the concepts of (male) man and woman. If one chooses to take color as the criterion, one could arrive at the concepts of white man, black man, brown man, red man, yellow man. (One always can, of course, deny that color is a relevant or essential criterion to form new concepts, and that the distinctions in question can be easily accounted for descriptively, without need of new concepts). If one chooses criteria that are not physical, but cultural, one could divide the concept of man into the concepts of unmarried man, married man, divorced man, widowed man, etc. There do not seem to be limits to the subdivisions one can make.
The question that can be asked is whether Rand views the concept of man as a first-level concept, as a concept on the same level as the concept of table.
The answer, for Rand, is definitely yes. Peikoff in several places explicitly states that the concept of man is a first- level concept. Here is what he says: "Only when the child has first conceptualized separately the various perceptually given entities is he capable of the more extensive acts of abstraction and integration that identify ~their~ common denominators. These latter are not available on the perceptual level, because only concretes exist: there are no such things as 'organisms' to be seen -- there are only men, dogs, roses. Similarly a child cannot identify distinctions among men -- he cannot grasp ~types of men~, such as doctor or teacher -- until he has first grasped and conceptualized man" [16].
NOTES
1 Rand prefers to say the concept "table" instead of the concept of table. I will use quotation marks only when I refer to the term "table". Cf. Leonard Peikoff's summary of Rand's discussion of the concept of table in Objectivism: The Philosophy of Ayn Rand (Dutton, New York, 1991), pp.83ff. Given the limitations of computer terminals, I will use the tilde to indicate beginning and end of italics in quotations.
2 Peikoff defines a first-level concept as follows: "A first- level concept is one formed directly from perceptual data, without the need of prior conceptualization" (op.cit., p.129). Rand argues that there are first-level concepts "epistemologically, not metaphysically" (p.214). Peikoff explains what this means. "Knowledge has a ~hierarchical~ structure. . . . A hierarchy of knowledge means a body of concepts and conclusions ranked in order of logical dependence, one upon another, according to each item's distance from the base of the structure. The base is the perceptual data with which cognition begins. The concept of 'hierarchy' in this sense is epistemological, not metaphysical. In reality, facts are simultaneous. ... facts themselves exist eternally. But an order of logical dependence among them exists from man's perspective, because man cannot come to know all facts with the same directness" (op.cit., p.131).
3 Cf. Peikoff, op.cit., p.129.
4 Rand sees the CCD of the concept of furniture as being "large objects inside a human habitation". Here is what she says: "The ~distinguishing~ characteristic of the new concept [the concept of furniture] 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" (p.22). Peikoff claims that the CCD that allows us to "differentiate tables from chairs or beds" is shape (op.cit., p.87; cf. p.84). A CCD is defined by Rand (in the Introduction to ITOE) 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" (p.15). Cf. Peikoff, op.cit., p.87.
5 Peikoff explains: "The reason is that the relationships required for concept-formation are established quantitatively, by means of (implicit) measurements -- and there is no unit of measurement common to table-shaped objects and red objects. The attributes of shape and color are ~incommensurable~" (op.cit., p.87).
6 Cf. Peikoff: "A higher-level abstraction, for example, condenses concepts themselves. Thus 'furniture' reduces to a single unit such first-level concepts as 'chair', 'table', and 'bed'" (op.cit., p.108).
7 Peikoff, op.cit., pp.129-130.
8 Peikoff, op.cit., p.132.
9 Peikoff, op.cit., p.130.
10 Peikoff, op.cit., p.133.
11 Peikoff, op.cit., p.133. Cf. also p. 120: "If logic is to be the means of objectivity, a logical conclusion must be derived from reality; it must be warranted by antecedent ~knowledge~, which itself may rest on earlier knowledge, and so on back, until one reaches the self-evident, the data of sense. This kind of chain and nothing less is what Objectivism requires as 'proof' of an idea". I may be wrong, but I think that the early Wittgenstein and the Logical Positivists might well endorse this statement, as it stands, in isolation.
12 Peikoff, op.cit., p.120.
13 Peikoff, op.cit., p.133.
14 Cf. Peikoff, op.cit., pp.129ff, in a section where he discusses the hierarchical nature of knowledge, for a demonstration of how a very high-level concept, such as that of culture, is linked, through a process of reduction, to perceptual concretes.
15 The issue is more complicated than it seems. Why move from the concept of man to the concept of animal, and not to the concept of primate, or to the concept of mammal? Rand discusses the issue but I have not found the arguments very convincing. Why not define man as a rational primate? Or, if one does not want to place man in the same class with other primates, at least, a rational mammal? Cf.
16 Peikoff, op.cit., pp.91. Cf. p.135.
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