Cognition and Measurement
Introduction to Objectivist Epistemology Compilation
by Paul Spunzar
Date: Sun, 20 Nov 1994 22:48:49 -0500
From: Paul Szpunar email@example.com
Subject: ITOE 1
Here is the kickoff essay to our chapter by chapter discussion of Rand's ITOE, written by yours truly. I've included in this summary a discussion of Rand's intended purpose in writing ITOE -- a solution to the problem of universals. Rand discussed the problem in the foreword. Of course, this is in addition to a summary of the first chapter -- "Cognition and Measurement."
All citations refer to ITOE -- 2nd expanded edition, unless otherwise noted.
Rand begins the foreword with a description of the "problem of universals." She equates "the issue of concepts" with the problem of universals, and goes on to ask: ". . . concepts are abstractions or universals, and everything that man perceives is particular, concrete. What is the relationship between abstractions and concretes? To what precisely do concepts refer in reality?" (1)
She also asks "When we refer to three persons as 'men,' what do we designate by that term? [. . .] Where is the 'manness' in men? What, in reality corresponds to the concept 'man' in our mind?" (2)
I think Rand's formulation of the problem of universals is rather sloppy. For one thing, the problem has historically been a metaphysical question. To Plato and Aristotle, for instance, the problem of universals wasn't just the *same* as the issue of concepts, although the two issues may have been closely connected.. Instead, they sought to establish a metaphysical, ontological relationship underlying entities we group together. For Plato, it is the Forms; for Aristotle, essences -- both metaphysical "somethings" in and of themselves -- that united together men, horses, tables, etc. They saw groups such as these to be *metaphysically* united -- our concepts just reflected that. So, it cannot be said that the issue of concepts *is the same as* the problem of universals, at least for Plato and Aristotle. In fact, I would argue (although I won't do so now) that even on Rand's terms, even given her own solution to the problem, the issue of concepts is not quite the same thing as the problem of universals, although they *are* closely related. Furthermore, I'm afraid that in formulating the issue in this way Rand suggests what I view as a false dichotomy -- the issue of whether universals exist in reality or merely in the head.
I think Rand best represents the problem when she asks "Where is the 'manness' in men?" Let me offer a tentative characterization of the problem of universals: The problem of universals is the problem of determining what, if anything, enables us to group certain entities together as being somehow similar in some respect. Now, I don't think this is a perfect formulation of the problem, but I do think it is better than Rand's, and it allows us to consider how her theory of concept formation is supposed to provide an answer.
From here, Rand proceeds to distinguish between five different approaches to a solution of the problem of universals. I won't list them here, because you can just read the book to find out. It is worth noting, however, that subsequent to the publication of ITOE in 1967, another form of realism was put forward by Putnam (1975, 1981, 1987). Kripke (1980) and Burge (1979, for example) have put forward roughly similar theories. According to Putnam, concepts (and, implicitly, universals) have a basis in reality, but -- unlike realists like Plato and Aristotle -- need not, in most cases do not, refer or depend upon internal "essences" or Platonic Forms. It would be interesting to compare and contrast Putnam's views with Rand's.
Finally, we are now ready to discuss Chapter One: "Cognition and Measurement."
Rand begins by stating "Consciousness, as a state of awareness, is not a passive state, but an active process that consists of two essentials: differentiation and integration." (5) I've always found this to be an odd statement.
What exactly is Rand claiming here? Is she claiming that consciousness is the *result* of an active process, or that it *is* this active process, or, perhaps, both? I think the natural interpretation is to conclude that consciousness is both an active process as well as the res ult of this process. This conclusion is supported by her description of the chronological development of consciousness: from sensations to percepts to concepts.
Perception is a nonvolitional activity which integrates sensations into percepts, and it is percepts of which we are normally aware in perception. Concepts, on the other hand, are the result of a volitional process of differentiation and integration (as we shall see in subsequent chapters). Perhaps I'm opening up a can of worms here, but I think it would be interesting to explore exactly what Rand means by "consciousness." I've always been somewhat confused by her characterization of it.
Implicit in every percept is the concept of existent: "something that exists, be it a thing, an attribute or an action." I suppose this is just to restate the standard claim that "To be aware is to be aware of *something*" Another interesting question is to ask if existent is a concept implicit in every percept, but is not acknowledged explicitly until one reaches the conceptual level, can animals that supposedly are unable to form concepts, but are able to form percepts, be said to have acquired the "implicit" concept of existent?
Rand claims that the implicit concept of existent undergoes three stages of development: (6)
1. entity -- awareness of objects
2. identity -- awareness of specific, particular things which can be recognized and distinguished from the rest of the perceptual field.
3. unit -- grasping relationships among entities by grasping the similarities and differences of their identities.Rand also states that "The ability to regard entities as units is man's distinctive method of cognition."(6) Why is this ability so distinctive and important? Rand defines a unit as "an existent regarded as a separate member of a group of two or more similar members." (6) She goes on to state that "'unit' involves an act of consciousness (a selective focus, a certain way of regarding things), but it is *not* an arbitrary creation of consciousness: it is a method of identification or classification according to the attributes which a consciousness observes in reality."
What makes this ability so unique, and why Rand considers it to be unique to humans, is that it is volitional. It involves a selective focus upon similarities shared by members of a group. It is this grasp of the concept of "unit" that marks the beginning of a conceptual level of cognition. Units, Rand writes, are the "bridge between metaphysics and epistemology," i.e., the bridge between particulars and concepts.
Perhaps the most important point Rand makes about concept formation in this chapter is that it is largely a mathematical process. She defines mathematics as "the science of measurement," and measurement as "the identification of a relationship -- a quantitative relationship established by means of a standard that serves as a unit." Entities, she says, are measured by their attributes, the standard of measurement being a "concretely specified unit representing the appropriate attribute." (7)
Rand requires three things of a standard of measurement: That it represent the appropriate attribute, that it be easily perceivable by man, and that once chosen it remain immutable and absolute whenever used. The purpose of measurement, she says, is "to expand the range of man's consciousness, of his knowledge, beyond the perceptual level: beyond the direct power of his senses and the immediate concretes of any given moment." (8)
As an example, she points out that man can perceive the length of one foot directly, but cannot do so with ten miles. In sum, measurement "consists of relating an easily perceivable unit to larger or smaller quantities, then to infinitely larger or infinitely smaller quantities, which are not directly perceivable." (8)
I have raised several issues for discussion in this summary, but let me list those I consider to be most important.
1. What is the problem of universals? Throughout our discussion of each chapter, we should take time to consider how Rand is proposing to solve this problem.
2. What does Rand mean by the term "consciousness"? What role does it play in her theory of concept formation?
And, 3. What role does measurement play in Rand's theory?
No doubt there are many more questions that can be raised (and I encourage people to do so), but I believe that these are especially important and will need to be addressed continuously as we discuss each chapter of ITOE.
ReferencesBurge, T. (1979) "Individualism and the Mental," Midwest Studies in Philosophy 4.
Krikpe, S. (1980) "Naming and Necessity."
Putnam, H. (1975) "The Meaning of Meaning," Mind, Language, and Reality.
Putnam, H.(1981) Reason, Truth, and History.
Putnam, H. (1987) Representation and Reality.
Rand, A. (1990 ) Introduction to Objectivist Epistemology.
Introduction to Objectivist Epistemology Compilation
by Will Wilkinson
Date: Fri, 17 Feb 1995 14:14:07 -0400
From: WILL WILKINSON WILKINW3253@cobra.uni.edu
Subject: ITOE 2
(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.
Abstraction from Abstractions
Introduction to Objectivist Epistemology Compilation
by Jeremy Spray
Date: Sun, 5 Mar 1995 20:51:06 -0400
From: jeremy michael spray firstname.lastname@example.org
Subject: ITOE 3
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] and, "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.
Concepts of Consciousness
Introduction to Objectivist Epistemology Compilation
by Diana Mertz Brickell
Date: Mon, 27 Mar 1995 22:18:11 -0600 (CST)
From: D.M. Brickell email@example.com
Subject: ITOE 4
-=- Introduction: Why is this subject important? -=-
In this chapter, Rand delves into concepts of consciousness, concepts whose referents are based in the mind rather than directly in external reality. Before I discuss the chapter itself, I'd like to indicate why I think that the subject matter is important. What relevance does epistemology, particularly concerning the formation of concepts of consciousness, have to an individual's life?
I believe that conceptualizing on a second-order level, i.e. about the actions of our consciousness in grasping reality, is crucially important if we expect to properly "carve nature at her joints." As far as I can tell from my plush philosophical armchair, one of the functions of free will is to provide consciousness another level of self-regulation, because of the complexities that naturally arise when the primary means of understanding reality is on a complex conceptual level. "[The ability to conceptualize mental processes as such] gives man an entirely new level of self-regulation: the ability to regulate, within limits, the actions of his consciousness, which in turn regulate his existential actions." (Binswanger, 156)
Since it is only by means of self-reflection that choosing values becomes possible, we must self-reflect well in order to gain clear, objective knowledge of values themselves. Rand only briefly addresses the overall need for study of the concepts of consciousness, although she does provide mini-reasons for its importance throughout the chapter. I hope that my motivational explanation provides a broader view of the importance of the subject.
Just as a warning, this chapter is so packed with interrelated information and interesting ideas that I found it difficult to omit discussions of all but a few sections. I just couldn't restrain myself!
-=- Awareness -=-
Rand begins this chapter with a short discussion of awareness as an active state and as necessarily derived from the external world. These two aspects of consciousness are crucial -- action and content -- since they will serve as the Conceptual Common Denominators for all concepts of consciousness.
Rand makes an interesting observation about perception in this first section, that "man is aware of the results [of perception] but not of the process." (Rand, 29) David Kelley expanded upon this idea in his tape series on epistemology. (Kelley, "The Primacy of Existence") If my notes and memory are to be trusted, Kelley said that there are two distinct perspectives on perception, one external and one internal, and that the facts available in each perspective are unavailable in the other. From the external, scientific perspective, one isn't aware of what the experience of perception is like, and from just the internal, "subjective" perspective, one isn't aware of how the causal mechanisms of perception work. Kelley indicates how this separation between internal and external perspectives has lead to the diaphanous model of consciousness, and thus to (wrong) indirect theories of perception.
I find this progression from a single sentence of Rand's to (through a whole lot of work) an answer to the fundamental problems in the philosophy of perception fascinating. I think that Rand has many such short, yet "pregnant" passages which can serve as a jumping off point for the solution to many traditional philosophical problems.
I am slightly uncomfortable with the way in which Rand formulates the idea that any state of awareness, perceptual or conceptual, is "achieved and maintained by continuous action." (Rand, 29) I fear that this formulation blurs the distinction between consciousness as *metaphysically active* and consciousness as *epistemologically active.* Asserting metaphysical activity commits us to the view that consciousness is, at least in part, the creator of reality, i.e. to the primacy of consciousness. Of course, Rand would not take this position, although she would agree that consciousness is epistemologically active, that the act of grasping reality requires action on the part of the subject, and even conscious effort where conceptual knowledge is sought.
Interestingly, taking consciousness as metaphysically active commits one to subjectivism, while denying that consciousness is epistemologically active inevitably leads to intrinsicism. Only denying the former and asserting the latter leads to an objective view of the relationship between consciousness and reality.
-=- Forming Concepts of Consciousness -=-As I indicated earlier, the content of awareness and the action of consciousness in regard to that content serve as the "fundamental Conceptual Common Denominator for all concepts pertaining to consciousness," because conscious activity can neither be passive nor contentless. (Rand, 30) According to Rand, in the process of forming concepts of consciousness one abstracts "the actions of consciousness from its contents and observe the *differences* among these various actions." (Rand, 30) One way to illustrate how to conceptually separate the action and content of consciousness is by considering only a specific action or content, while varying the other.
So, for example, I can solely consider the mental content of the philosophy of perception, and consider what sort of actions are possible with regard to the subject. I can IDENTIFY a particular theory as belonging to the philosophy of perception; I can EVALUATE the validity of a claim about representations; I can RECALL some empirical evidence in an article; I can INTEGRATE some of Gibson's ideas about perceptual error with Kelley's.
Now although Rand doesn't ever talk about omitting the measurements of the action of consciousness, while retaining the content (within a certain range), I do suspect that such is possible. In fact, I think that this is how we divide up fields of study, like physics, history, and child psychology. To illustrate, I can suppose that my mental action is solely "evaluation," and consider different areas of knowledge in which I can evaluate truth claims. I can evaluate the OBJECTIVIST METAPHYSICS; I can evaluate SPECIAL RELATIVITY (yeah right); I can evaluate the GRAMMAR of a particular sentence.
If it isn't the case that we conceptualize fields of study based on content of mental entities, I wonder whether there are any concepts of consciousness that are conceptualized along the lines of content at all.
Rand goes on to emphasize that "in the realm of introspection, the concretes, the *units* which are integrated into a single concept are the specific instances of a given psychological process" and that the "measurable attributes of a psychological process are its object or *content* and its *intensity*." (Rand, 31)
The content, because it must eventually refer to some aspect of reality, can be measured by the same means by which external existents are. But the intensity (which involves scope, clarity, mental effort, etc.) can only be measured approximately, using a comparative scale. But intensity cannot be completely separated from content, since intensity necessarily depends upon content (or the *scope* of the content, as Rand puts it), as well other facts about consciousness (e.g. values and previous knowledge). To take an extreme example, the level of focus required to grasp the implications of the double-slit experiment is much higher than that required to identify an object as a chair, because of (the scope of) the content of each idea.
-=- Scope and Hierarchy as Means to Measure Intensity -=-In order to more precisely measure intensity, Rand introduces the concepts of "scope" and "hierarchy." Each is applicable to a different type of concepts of consciousness; scope applies to concepts of *cognition*, while hierarchy applies to concepts of *evaluation*.
Concepts of cognition (e.g. "thought," "observation," learning") are measured by scope, which can be "gauged by two interrelated aspects: by the scope of the factual material involved in a given cognitive process, and by the length of the conceptual chain required to deal with the material." (Rand, 32) Of course, in order to gauge the length of conceptual chain, it is necessary to have a clear foundation of "perceptually given concretes," but what exactly constitutes this foundation is a bit controversial. In the workshop section, Rand does say that there is "a certain element of the optional" about what concepts are on the bottom of the hierarchy. (Rand, 204) I think that it is an interesting question what sort of concepts (if any) *must* serve as the foundation of the hierarchy of concepts.
Concepts of evaluation (e.g. "value," "feel," "desire") necessitate an entirely new type of measurement:
teleological measurement. Teleological measurement "serves to establish a graded relationship of means to end" using ordinal ranking. Rand illustrates the importance of having a clear hierarchy of values in her discussion of the relation between ethics and teleological measurement. (See Rand, 33)
-=- Unit of Teleological Measurement? -=-There is an interesting issue which I would like to raise surrounding teleological measurement and the unit of measurement. Rand defines measurement as "the identification of a . . . quantitative relationship established by means of a standard that serves as a unit," but it is unclear if there is actually a unit of measurement in teleological measurement, since the standard in teleological measurement "serves to establish a *graded* relationship of means to end." (Rand, 7; Rand 33, emphasis added) I would not hesitate to say that there is no unit in teleological measurement except for the existence of the following passage: "in the spiritual realm, the currency--which exists in limited quantity and must be teleologically measured in the pursuit of any value--is *time*, i.e. *one's life*." (Rand, 34) (This statement might be confusing in isolation, so you might want to look up the specific passage.) Is it possible that the unit is *time* for the standard of life?
-=- Concepts of Products of Psychological Action -=-After her great discussion of whether love can be measured, Rand delves into concepts that refer to products of psychological action (e.g. "truth," "knowledge," "concept"). In the formation of these concepts their content is omitted, while their distinguishing characteristic is retained. Although Rand doesn't say explicitly, it seems that the distinguishing characteristic is the both the actual product of conscious activity, as well as the action that yields the product. So knowledge is "a mental grasp of the fact(s) of reality [product], reached either by perceptual observation or by a process of reason based on perceptual observation [process]" (Rand, 35)
Concepts of method, which are a species of the concepts of products, deserve special consideration, because of their importance in human life. Rand defines methods as "systematic courses of action devised by men for the purpose of achieving certain goals," in which the action can either be purely psychological or existential. (Rand 35-36)
Obviously, methods which designate existential method are extremely important to human life -- survival would be impossible without means to automatize certain actions (like shoelace tying) through learned methods. Methods pertaining to psychological action are no less important, since they will govern the proper use of an individual's mind in grasping reality.
-=- Logic as the Fundamental Concept of Method -=-Rand identifies logic as "*the* fundamental concept of method, the one on which all others depend." (Rand, 36)
With respect to logic, the action is "the actions of consciousness required to achieve a correct identification" and the goal is knowledge. Of course, this doesn't tell us what actions actually *are* required for correct identification, which is why the concept of logic needs to be broken down into components in order to really serve as a guide to thinking.
If I recall correctly, Peikoff breaks down logic into "reduction" and "integration" in his "Objectivism: State of the Art" tape series, but because I disagree with a good part of his discussion on these issues, I don't think that it is all that helpful to explicate his views. (I'd be very interested in a discussion of Peikoff's views, and would be willing to post a summary of his position for those who haven't heard the tapes if others are interested as well.)
-=- Conclusion -=-
One final point about this chapter: in her closing passages Rand emphasizes that "*measurement requires an appropriate standard.*" (Rand, 38) I think that this idea is crucial for giving an Objectivist answer to many traditional philosophical problems. For example, the possibility of certainty is often denied on the grounds that humans are capable of error, in other words because we are fallible. But omniscience is only an appropriate standard for a being for whom such a state of awareness is possible; the fact that humans are fallible must be integrated into any human epistemological theory.
I thank anyone who has slogged all the way through this essay. Let the discussion begin!
-=- References -=-
Binswanger, Harry. "Volition as Cognitive Self-Regulation." Organizational Behavior and Human Decision Processes. 1991. 154-178.
Kelley, David. "Primacy of Existence I."
Rand, Ayn. Introduction to Objectivist Epistemology. 1990.
-=- Diana Mertz Brickell -=- Washington University -=- St-Louis, MO -=-Yet persistently a few men awaken -- men who look back at greatness, areencouraged by reflecting on it, and feel themselves blessed, as thoughhuman life were a splendid thing, as though the loveliest fruit of thisbitter plant were the knowledge that before them one man lived his lifewith pride and strength, another profoundly, and a third with compassionand benevolence -- but all bequeathed the same lesson: the man who isready to risk his existence lives most beautifully. -- Nietzsche
Introduction to Objectivist Epistemology Compilation
by Bryan Register
Date: Mon, 10 Apr 1995 23:39:28 -0500
From: Bryan Register firstname.lastname@example.org
Subject: ITOE 3
'A definition is a statement that identifies the nature of the units subsumed under a concept.' Upon re-reading chapter five of ITOE, I found it to have a few pages of substantive work at the beginning, followed by several pages of wandering criticism and discussion of a number of faintly related issues. I plan to integrate the relatively disconnected bits as well as I can with the main themes and ignore any material which I can't connect with the essence of the chapter, and end up with a problem and a couple of questions that I think may pose challenges to Rand's scheme here.
For Rand, definitions serve to differentiate different concepts by identifying the essential characteristics of given concepts. Some concepts, axiomatic and sensual, are undefinable in terms of words. To define existence or red, one points at an existent or some red. But for all more abstract concepts, definitions are possible though not always necessary. It may be unnecessary to define very simple concepts like table, because one can point easily enough at a table and one knows what one means when one says 'table', so a definition probably will serve no cognitive purpose. All this matter of defining something by direct reference to reality is called ostensive definition.
What is the purpose of definitions in those concepts that do require or at least allow for them? Definitions consist of words, and words, as we know, refer us to concepts. So the definition of a concept is a reference to other concepts. Ultimately, our definitions will always point back to the percepts the integration of which are the concepts. This allows us to have the full structure of our conceptual system at hand, and know the connections of this system to reality. This would seem to be where deductive logic comes from: our concepts subsume one another and refer to each other allowing us to form syllogisms and other logical statements.
How then are valid definitions formed? A definition consists of a genus and a differentia, as Aristotle stated.
(These next few paragraphs of ITOE are very unclear to me, so this is one of the bits that are more likely to be criticized). The genus is a concept from which the concept in question was differentiated. The differentia is the line along which the concept in question was differentiated; it seems to me that the differentia states the CCD of the concept.
For example, life is a process of self-sustaining and self-generating action. Animal is a kind of life which employs locomotion. Man is a rational animal. The genus here of animal is 'life', the differentia is 'kind which employs locomotion.' The genus of man is animal, the differentia is rationality. (This example poses one of the questions with which I intend to end the discussion.)
I don't know how well the interpretation I just gave jives with Rand's second paragraph here: 'The distinguishing characteristic(s) of the units becomes the differentia of the concept's definition; the existents possessing a 'Conceptual Common Denominator' become the genus.' However, I think my interpretation is definitely right given the next paragraph: 'Thus a definition complies with the two essential functions of consciousness: differentiation and integration. The differentia isolates the units of a concept from all other existents; the genus indicates their connection to a wider group of existents.' (Both paragraphs on page 41, these two and the paragraph before seem to comprise the discussion of the form of definitions. The first and last of these are very clear, but the middle one doesn't make much sense to me. Do not all the existents possessing a CCD become the whole concept? and is not the distinguishing characteristic the CCD? Or am I hopelessly confused on the nature of the CCD?)
A definition is not a list. The point being made on page 42 which leads into the discussion of valid definitions would, I think, be made stronger by pointing out the consequences of the crow again. A definition can be only so long before we can no longer hold it in mind at once. Thus a list will not serve. So there must be a single (or very few) characteristic taken out of the mass of qualities of the existents referred to by the concept; a DEFINING characteristic. However, in order to define the CONCEPT, the definition must imply all the rest of the qualities of the existents subsumed by the concept. This characteristic (or very small group thereof) is the ESSENTIAL characteristic of the many existents.
Later in the chapter, Rand contrasts her view with that of Plato and Aristotle; this seem the most reasonable place to bring that in. For Plato, the essential characteristic of an entity was (this is very rough) the fact that it is an instance of a form -- its essence was that form, with the form being transcendent and immaterial. For Aristotle, all entities in a class are united by an essence which is non-transcendent, but still inherent in the entity. For Rand, all entities in a class are united by an essence which is a product of the human mode of understanding. This is her claim to objectivity, rather than intrinsicism (usually known -- by everyone other than Rand, so far as I can see -- as essentialism), that she bears in mind both the context of the observer and the independent reality which he observes. But I get ahead of myself.
Because the essence of a group of entities is that fact about them which implies all facts about them, definitions are open-ended and open to revision -- but not to 'correction', unless an error has been made. (By correction, I mean here a change which contradicts an earlier definition. It is likely that there is a better word for this.) One can form a definition based on a very limited amount of information which will be valid, but once one has more information one must revise one's definition.
For instance, take the atom. Once upon a time, an atom could be reasonably defined as 'the smallest instance of an element which retains the qualities of that element.' Then it was discovered that there were nuclei in atoms and variously charged particles. So the definition might become 'a particle which possesses a dense, positively charged center surrounded by negative charges.' Then it was discovered that electrons have specific orbits, so the definition might have 'which circle in specific orbits about the nucleus' added to the end.
Now, none of those definitions were false. A modern physicist thinking in terms of an atom as defined by being the smallest instance of an element which retains the qualities of that element would not be wrong, per se. But he would be horribly lacking in ability to connect 'atom' to other concepts; would not know the true defining essence of atoms at his level of knowledge.
(If I may put in an aside: I think the problem Kuhn raised in The Structure of Scientific Revolutions might be impacted by Rand's open-ended concepts. Kuhn asserts that scientific revolutions are non-rational gestalt switches between different conceptual orderings, but if concepts aren't the set-in-stone dogma which Kuhn viewed them as, then no such non-rational switches are necessary.)
So the essence of a group of entities is that fact about them which implies all other qualities which they possess.
This essence is epistemological, being formed not only by the means and limitations (finite carrying capacity, the crow again) of human cognition but also by the limits of an individual's context of knowledge -- and, equally or more importantly, by the inherent metaphysical similarities of the entities in question.
Rand maintains that concepts can be true and false. It is at this point (p 48) that I think what may be a very serious problem arises. 'Truth is the product of the recognition... of the facts of reality.... He organizes concepts into propositions -- and the truth or falsehood of his propositions rests, not only on their relation to the facts he asserts but also on the truth or falsehood of the definitions of the concepts he uses to assert them, which rests on the truth or falsity of his designations of essential characteristics. 'Every concept stands for a number of propositions.... A definition is the condensation of a vast body of observations -- and stands or falls with the truth of these observations.' Truth is the correspondence of a proposition to reality; a proposition is true of it accurately describes reality, false if inaccurate. A definition can be true or false only if it is a proposition, and Rand claims that it is. But how does this work? A definition states something like 'man is a rational animal.' This proposition is true if man is indeed the rational animal. But how could one check the truth of this proposition? By pointing at men and claiming that they have all kinds of characteristics of which the essential is rationality. But since 'man' does not exist save as that which is defined as the rational animal, one can't refer to the entities and actually hit men with one's reference except by going by the definition which is exactly what one is checking in the first place.
My point here is also illustrated, I think, by the actual way we form concepts. We do not start with 'man' and figure out what defines him. We start with men and figure out that they need to be mentally integrated and how. We start, then, with rational animals, proceed to 'rational animal', and finish off with 'man.' (Or am I hopelessly confused? I do not rule out the possibility.) With the process running this way, the 'propositions' of definitions will always be vacuously true.
I think this can be solved by backing down from the claim that definitions are propositions that can be true and false. Definitions are something other than propositions (what? definitions, I think, and nothing else) and cannot be true or false. They can be valid or invalid, with validity being the quality of maximizing unit-economy by being that definition which implies the most other qualities of the entity-grouping in question, and invalidity being an identification of essential characteristics which does not in the least unify the entities in question. (Note my appeal to the crow again.) This does the same job Rand wants her truth/falsity to do (beat up on defenseless nominalists) without involving her in the rather painful circles of vacuous truth I think I showed above.
I will skip the discussion of essentialists dropping consciousness and subjectivists dropping existence, as we have all heard it before.
So just a couple more questions are these:
1. Justice is classically defined as 'giving each man his due.' No genus, no species that I can see. Is justice being poorly defined here, or is this an exception, or is there a genus and species that I'm not seeing?
2. In an earlier example, I derived man from animal from life. Like justice, life seemed to have no genus and species. It also doesn't seem to be something which can be traced back to a larger-scale concept (explaining the lack of genus.) Same question as for justice, but with the additional: is life a primitive concept, despite being defined? Do such things exist? (I would have asked for justice, but I think it's pretty clearly not primitive.)
Introduction to Objectivist Epistemology Compilation
by Thomas Ryan Stone
Date: Wed, 10 May 1995 20:35:43 -0400 (EDT)
From: Thomas Ryan Stone email@example.com
Subject: ITOE 3
Ayn Rand indicates the importance of axiomatic concepts in the first paragraph of the chapter: "The base of man's knowledge - of all other concepts, all axioms, propositions, and thought - consists of axiomatic concepts"(p55). She does so again at the end of the chapter as she states: "Do you want to assess the rationality of a person, a theory or a philosophical system? Do not inquire about his stand on the validity of reason. Look for the stand on axiomatic concepts. It will tell the whole story."(p61) In properly treating any topic, it is necessary to have a guiding principle or set of such principles. Regarding axiomatic concepts, I see four main questions that I will use as my guide in this essay: What are they?, How are they formed?, What are their functions?, and Why do we need them?
I. WHAT ARE AXIOMATIC CONCEPTS?Ayn Rand notes that *axioms* are typically considered to be propositions identifying self-evident truths. As such they are not "primaries". This is because mental "primaries" are in the form of concepts, from which propositions are later built. The concepts that produce *axioms* when put into propositional form are the *axiomatic concepts*.
Ayn Rand defines *axiomatic concept* as an "identification of a primary fact of reality, which cannot be analyzed, i.e. reduced to other facts or broken into component parts"(p55), and are
1. implicit in all facts
2. implicit in (alternately, the "base of") all knowledge
3. the fundamentally given
4. the directly perceived or experienced
5. that which requires no proof or explanation
6. that upon which all proofs and explanation rest
7. the base of all other concepts, axioms, propositions, thought
Axiomatic concepts are those and only those concepts that fit the definition given above with all of its aspects.
She states that the first and primary axiomatic concepts are "existence", "identity" (called a corollary of "existence"), and "consciousness". She then proceeds to discuss in what way these three examples are "axiomatic" and in what way they are "concepts". They are axiomatic because they display the above listed properties. An interesting question arises, however, when we ask "In what sense are they *concepts*?" Miss Rand's answer is that they are concepts because they require identification in conceptual form. This seems clear:
take an animal who is not above the conceptual threshold, and consider whether it could explicitly grasp existence qua existence, identity qua identity, or consciousness qua consciousness. They are perceived or experienced directly, but grasped conceptually.
1. The genus of axiomatic concept should be the same as that given for concept, shouldn't it? That was given as "mental integration" (p13), but no where is it found in our definition of "axiomatic concept". If axiomatic concepts are *concepts*, which they are, then they should have the same genus. We need to formulate the definition of the concept so as to include the genus.
2. Is Ayn Rand being redundant when she says "first and primary axiomatic concepts"? How are these words different from "fundamental", which she also uses?
3. What exactly is meant by "implicit" in "implicit in every state of awareness"?
4. What exactly is meant by "corollary" in "[identity] is a corollary of existence"?
5. After admitting that they can't be "proven", can't we make a stronger claim than attribute 5, replacing "requires no" with something stronger?
6. An on-going project: after making sure that the list of attributes given above is complete (is it?), it would be interesting to detail other concepts that fail to be axiomatic concepts, even while they are "identifications of a primary fact of reality, which cannot be analyzed". It would be interesting to see a conceptual web develop that would detail which attributes are missing from these near-axiomatic concepts. Some possible candidates include perceptual and introspective-experiential concepts (e.g. desire, urge, anxiety, pleasure/pain), time, space/place, volition, direction, entity, unit, life, motion, change, being, substance, quantity, quality, shape, relation, faculty, function, event, action, phenomenon, cause/effect, equal, matter, intention, awareness, state, position, modality, similarity/ difference, ...
II. HOW ARE AXIOMATIC CONCEPTS FORMED?Ayn Rand notes that these concepts involve an abstraction of a very special sort: "...not the abstraction of an attribute from a group of existents, but of a basic fact from all facts. Existence and identity are *not attributes* of existents, they *are* the existents. Consciousness is an attribute of certain living entities, but it is not an attribute of a given state of awareness, it *is* that state"(p56). The units for these concepts are every entity, attribute, action, event or phenomenon that exists (for "existence" and "identity") and every state or process of awareness that one experiences, has ever experienced or will ever experience.
There *is* a process of measurement omission: that which is omitted from axiomatic concepts "are all the measurements of all the existents they subsume; what is retained metaphysically is only a fundamental fact, epistemologically only one category of measurement, omitting its particulars: *time*, i.e. the fundamental fact is retained independent of any particular moment of awareness."(p56)
1. Ayn Rand's position seems to be that existence (and identity) is not an attribute of an object. This is a common question amongst philosophers and is usually raised as "Is existence a predicate?". Why then does she say "The units of the concepts "existence" are every entity, ..., *that exists*..."? This seems to be acknowledging existence as an attribute of entities. This raises a favorite topic of mine: modes of existence. This doesn't just apply to questions of ontological categories (e.g., in what way do relations "exist"), but also questions concerning "fictional existence" (i.e. is it reasonable to have such a concept).
2. Regarding the measurement-omission: What is left when we omit "all the measurements"? Miss Rand's answer is "a fundamental fact"; but what does this mean? What is the fundamental fact that remains?
Regarding the one category of measurements that remains, that of *time*: why isn't this considered a part of "all the measurements"? Did she mean "all...except its temporal measurement"? Later she mentions "implicit psychological time measurements"(p56-7): is this what she means here? If so, this seems to be the answer, for it isn't an attribute of the object but rather of the awareness of the object. I found this section (on p56-7) to be very confusing.
III. WHAT ARE THE FUNCTIONS OF AXIOMATIC CONCEPTS?Miss Rand states that axiomatic concepts are the *constants* of man's consciousness. They are the *cognitive integrators* that identify and thus serve to protect its continuity. She relates this back to the fact stated earlier that axiomatic concepts have as their omitted measurement the implicit psychological time measurements (p56-7).
Axiomatic concepts have a second function: they "identify the precondition of knowledge: the distinction between existence and consciousness, between reality and the awareness of reality, between the object and the subject of cognition. Axiomatic concepts are the foundation of *objectivity*."(p57) Later they are described as the "foundation of reason" (p.60) [NOTE: perhaps it is more accurate to say that *man* identifies the precondition of knowledge..., *by way* of axiomatic concepts].
A third function of axiomatic concepts is the underscoring of primary facts of reality: that something *exists*, that *something* exists, and that I am conscious.
1. Wouldn't it be great to see an essay entitled "Axiomatic Concepts as the Foundations of Objectivity"? Yet another example of why this treatise is only an "Introduction".
2. See Question #2 in section II.
3. Can somebody explain to me in what way the axiomatic concepts are constants of man's consciousness? As concepts they must be open-ended, right? Are they only "constants" in an attenuated sense? If so, in what context and what is meant by that description?
IV. WHY DOES MAN NEED AXIOMATIC CONCEPTS?Axiomatic concepts each designate a fundamental fact. While this is so, Miss Rand states that "axiomatic concepts are the products of an *epistemological* need - the need of a volitional, conceptual consciousness which is capable of error and doubt."(p.58) For this reason man's consciousness needs axiomatic concepts to embrace and delimit the entire field of its awareness - to delimit it from the void of unreality to which conceptual errors can lead. They are epistemological guidelines that sum up the essence of all human cognition:
"something *exists* of which I am *conscious*; I must discover its *identity*.(p.58-9)
1. Wouldn't it be interesting to hear discussion on the topic of "Axiomatic concepts as necessary conditions of human survival", one that would take an evolutionary biology slant (tying in the discussion of Miss Rand's assertion concerning animals, pg. 58)?
This chapter had its share of unsupported assertions. Many involve assertions about "animals", which is typical of Ayn Rand. I almost always agree with the essence of her points, but I would like to see empirical evidence so we know how to chop up the animal kingdom, i.e. is it really man and non-man? Others involve "logical positivists", "logical atomists", "modern philosophy", "modern philosophers", "the works of Kant and Hegel", and various existentialists (judging by her tone, these folks often seem to be the aforementioned "animals"!).
All of these assertions, while simply assertions as found in the chapter, would make for very interesting essays/articles indeed! So get cracking everyone! Please bring up any other questions you have about this chapter; don't feel restricted to the many I have raised.
Note: all citations are from the 2nd edition.
The Cognitive Role of Concepts
Introduction to Objectivist Epistemology Compilation
by Andrew Breese
Date: Mon, 19 Jun 1995 17:45:06 -0500
From: N. ANDREW BREESE ST547@Jetson.UH.EDU
To: Multiple recipients of list AYN-RAND AYN-RAND@IUBVM.UCS.INDIANA.EDU
Subject: IOE 7
Earning its place in ItOE, this chapter is the most concerned with the value of concepts. It is a wide-ranging discussion of the ways our minds *use* concepts, with many suggestions for improving that utility. Indicating the fundamentality of concepts within O'ist epistemology, Rand stated, "The issue of concepts...is philosophy's central issue. Since man's knowledge is gained and held in conceptual form, the validity of man's knowledge depends on the validity of concepts." (1, Expanded Second Edition, Meridian)
Overview of the Summary:
Chapter seven treats crow epistemology (unit-economy), the relation of mathematics to conceptualization, definition by essentials, learning as automatizing, concepts as including "yet-to-be-discovered characteristics of a given group of existents," language as "primarily a tool of cognition--not of communication," the categories of existents for which individual concepts must be formed, Rand's Razor, "Borderline Case" problems as evading cognition's purpose, and the precise tasks of epistemology.
Rand points out that a mind can only focus on so much at any given time. Crows apparently can discriminate between one man, two men, three men, and more-than-three men--but not between four men and five men (in their short-term memory). Humans have a slightly greater perceptual comparative ability; the oft-cited cognitive psychology result is seven plus or minus two units. Concepts, though, allow us to keep track of any number of perceptual events. It is possible for us to accurately remember and analyze any event without ever holding more than a few concepts in focus at once. If I were counting crows (up to a ten digit number, say-- I know I can remember a phone number), I would just have to keep track of one number at any point and be able to add one to it. "The essence, therefore, of man's incomparable cognitive power is the ability to reduce a vast amount of information to a minimal number of units--which is the task performed by his conceptual faculty."
(63) Rand calls this reduction to a minimal number of units: unit-economy.
"Mathematics is a science of *method* (the science of measurement, i.e., of establishing quantitative relationships), a cognitive method that enables man to perform an unlimited series of integrations...
Conceptualization is a *method* of expanding man's consciousness by reducing the number of its content's units--a systematic means to an unlimited number of integrations." (64) Mathematics is based on the idea that some existents are commensurable-- that it is meaningful and useful to compare those existents.
Conceptualizing is based on the fact that it is meaningful and useful to treat some existents in exactly the same way in certain situations--that some existents are not just commensurable, but practically equivalent.
Mathematics requires conceptualizing.
"It is the principle of unit-economy that necessitates the definition of concepts in terms of *essential* characteristics." (65) If one is to later focus only on the definition of a concept (which is the most precise way of applying the concept while still keeping the number of units minimal), that definition should be carefully selected.
More generally, because we each automatically rely on our previous reasoning, all new understanding should be carefully reached. "[A]ll learning involves a process of automatizing, i.e., of first acquiring knowledge by fully conscious, focused attention and observation, then of establishing mental connections which make that knowledge automatic (instantly available as a context), thus freeing man's mind to pursue further, more complex knowledge." (65)
This chapter's most complex point is, "Concepts stand for specific kinds of existents, including *all* the characteristics of these existents, observed and not-yet-observed, known and unknown." (65) Rand further clarifies in her summary at ItOE's end, "Concepts represent condensations of knowledge, 'open-end' classifications that subsume *all* the characteristics of their referents, the known and the yet- to-be-discovered; this permits further study and the division of cognitive labor." (86) This is puzzling on its face because Rand also defines a concept as "a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted." (13) We are left to reconcile "including *all* the characteristics" with "particular measurements omitted." My thought is that "*all* the characteristics" refers only to those characteristics possessed by all of the existents subsumed by a concept, which Rand elsewhere calls distinguishing characteristics. "Particular measurements," on the other hand, refers to those characteristics of one or some, but not all, of the subsumed existents. For example, "able to use reason" is included in the concept of man, while "open to rational argument regarding the existence of God" is not.
On the purpose of language, Rand writes, "Concepts and, therefore, language are *primarily* a tool of cognition--*not* of communication, as is usually assumed...*Cognition precedes communication;* the necessary precondition of communication is that one have something to communicate." (69) An understanding does not become a concept and a unit until a word or other perceptual symbol is tied to it. Language is therefore vital for unit-economy and thus for thought of any complexity.
Rand provides a list of categories of existents for which concepts should definitely be formed, then ties them together with, "These [categories] represent existents with which men have to deal constantly, in many different contexts, from many different aspects, either in daily physical action or, more crucially, in mental action and further study." (70) This clearly ties concept-formation to its later use and is a great example of the ethics buried in epistemology.
Emphasizing that each concept should have an important CCD, "[N]either the essential similarities nor the essential differences among existents may be ignored, evaded or omitted once they have been observed. Just as the requirements of cognition forbid the arbitrary subdivision of concepts, so they forbid the arbitrary integration of concepts into a wider concept by means of obliterating their *essential* differences." (71) Rand then rephrases this in terms of a double-edged demand for "necessity" in concept- formation, as her epistemological "razor." (72) Presumably, "necessity" is tested for by weighing "[t]he descriptive complexity of a given group of existents, the frequency of their use, and the requirements of [further study]." (70) It is interesting that concept formation (an action studied at the base of epistemology) properly rests on value judgments.
Rand shows that borderline cases do not threaten her theory of concepts, by arguing that only "traditional-realist theories of universals, which claim that concepts are determined by and refer to archetypes or metaphysical essences" are refuted by such puzzlers. (74) Applying the doctrine of necessity based mostly on the requirements of further study, one can objectively determine how to classify each borderline case; in the absence of necessity either way, one has classification options, none of which challenge the objectivity of the concepts which *are* formed by cognitive necessity.
This chapter closes with a concise list of the tasks of epistemology, pointing the way toward future work: "to keep order in the organization of man's conceptual vocabulary, suggest the changes or expansions of definitions, formulate the principles of cognition and the criteria of science, protect the objectivity of methods and of communications within and among the special sciences, and provide the guidelines for the integration of mankind's knowledge." (74) Rand further distills these tasks as the integration and guardianship of man's knowledge.
N. Andrew Breese
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