IOE, Chapter Three
Abstraction from Abstractions
Date: 5 Mar 1995
Forum: Moderated Discussion of Objectivist Philosophy
All page references taken from the Expanded Second Edition.
Because it may help to understand the context and direction of this discussion, I should like to very briefly comment on what has thus far been introduced. In Chapter 2, Rand details the principles of concept-formation on its base level; the conceptualizing of perceptual entities through the processes of identification, isolation, differentiation, integration and measurement-omission. This is the first stage, and indeed the requisite stage, of conceptual development, for it is here that the fundamental links to reality are made.
In his post, Will Wilkinson expressed the ambiguity of the relationship between words and concepts. Is a word a concept, or a symbol for a concept? Are words necessary in the process of concept-formation? If so, why? Rand offers more insight into this dilemma at the introduction of Chapter 3.
"The process of forming a concept is not complete until its constituent units have been integrated into a single mental unit by means of a specific word." [p. 19]
"Learning consists of... grasping the referents of words, i.e. the kinds of existents that words denote in reality. In this respect, the learning of words is an invaluable accelerator of [man's] cognitive development; but it is not a substitute for the process of concept formation; nothing is." [p. 20]
What I think Rand is saying here (and what it seems we have all agreed upon these past few weeks) is that a word is not the concept itself, nor any part of it, but a necessary *product* of concept-formation--the creation of a mental entity. Merely learning the referent of a word cannot replace the actual process of identifying, isolating, differentiating and integrating. If a child were to simply learn the referents of words, or worse still, merely memorize pronunciation, then any further conceptual development would have no link to the facts of reality. Thus, the importance of concept-formation increases as a child moves further and further away from direct perceptual evidence, i.e. as he begins abstracting from abstractions.
In precisely the same fashion that one identifies, differentiates and integrates perceptual concretes, so one furthers his conceptual development by endeavoring "toward more extensive and more intensive knowledge, toward wider integrations and more precise differentiations." [p.19]. Abstracting from abstractions is this process of conceptualizing beyond the concepts of lowest order, i.e. beyond the concepts that are direct inferences from the entities in reality.
Rand explains the process best; "When concepts are integrated into a wider one, the new concept includes all the characteristics of its constituent units; but their distinguishing characteristics are regarded as omitted measurements, and one of their common characteristics determines the distinguishing characteristic of the new concept."[p. 23]--the Conceptual Common Denominator.
To exemplify this, I will use the concept "man". The distinguishing characteristic of man is his rational consciousness, which only becomes apparent to us if other forms of life with consciousness and locomotion are identified. However, once these other mental entities are identified, and recognized as sharing the commensurable characteristics of consciousness and locomotion, then they can be integrated into a wider concept by omitting the measurement of their respective distinguishing characteristics. Thus, each of the narrower concepts must have *some* form of conscious and locomotion, but *any* form of conscious and locomotion to be integrated into the wider concept, henceforth referred to as "animal".
Rand emphasizes that although "animal" is a new concept, it does not directly refer to a perceptual concrete--there is no perceptual entity "animal". This is why the concepts of first order are so extremely important--
"The meaning of "animal" cannot be grasped unless one has first grasped the meaning of its constituent concepts; these are its link to reality."[p. 22]
In narrowing concepts, the process is simply a reversal of the above.
"When a concept is subdivided into narrower ones, its distinguishing characteristic is taken as their 'Conceptual Common Denominator'--and is given a narrower range of specified measurements or is combined with an additional characteristic(s), to form the individual distinguishing characteristic of the new concepts."[p. 24]
Taking the example of the concept "man" again, the distinguishing characteristic of man is his rational consciousness. To subdivide "man" into narrower concepts based on some measurement, say, profession, we use the Conceptual Common Denominator--rational consciousness--as the standard of integration, then differentiate one man from another according to his distinctive profession. Thus we have the professionals--doctors, engineers, philosophers--each practicing *some* form of profession, but *any* form of profession: and all possessing a rational consciousness.
Through the process of abstracting from abstractions, we are in effect expanding our range of knowledge in two directions. The further one moves away from perceptual concretes the more extensive his knowledge becomes; the further one moves toward identifying specific existents, i.e. perceptual concretes, the more intensive his knowledge becomes. However, each concept is learned within the context of our knowledge at that point in time. When new units are identified in accordance with an existing concept, the original concept is not invalidated, but merely subsumes the new units with the required measurement-omissions. (Rand elucidates this point further in Chapter 5, "Definitions.")
The significance of abstracting from abstractions is indeed the essence of non-contradictory reasoning, because as we move further and further from direct perceptual evidence, there are a myriad of intersections, "cross-classifications and complex conceptual combinations." [p. 28] The degree to which each of us properly conceptualizes beyond direct perceptual concretes determines our ability to understand the world around us.
Coming full circle now to the relationship of words and concepts, it is my understanding that words are absolutely necessary for abstracting from abstractions. My reasoning is this; if we do not have a linguistic mental entity to denote each concept, of what further use can any concept be? We would, basically, have to re-conceptualize every time we encountered a concept, regardless of how many times we encountered it before. As Rand notes, though not specifically in this context, "when he has formed or grasped the concept "man", he does not have to regard every man he meets thereafter as a new phenomenon to be studied from scratch: he identifies him as "man" and applies to him the knowledge he has acquired about man." [p. 27]
If we do not define the concept "man"--or any concept--as a linguistic mental entity, how then would we mentally organize our knowledge as that range of knowledge expands and intensifies? It seems it would be impossible without language, without words. (If you have been following the MDOP discussions, this is precisely what David Axel was referring to when he quoted Rand as saying: "the *automatized* integration of a vast amount of conceptual knowledge.")
Concluding comments; Rand refers to the process of abstracting from abstractions as the hierarchy of concept-formation. This seems to imply that there is a definite, hierarchal order in which everyone abstracts from concepts of lower order. However, Rand also states, "The chronological order in which man forms or learns these concepts is optional."[p. 25] The ambiguities lay in whether the conceptual hierarchy is only a result of an introverted, retrospective process of concept-organization and -validation, or if indeed, narrower concepts must be realized before expanding upon them.
For instance, do each of us need to have a conceptual understanding of "man" (and "bird" and "dog" and so forth...) before we integrate it into the wider concept of "animal"?
I pose this as a topic for discussion, although I am certain you will all find much more to dissect.
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