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IOE, Chapter One
Cognition and Measurement
by David Ross

Date: 26 Jan 1992
Forum: Moderated Discussion of Objectivist Philosophy
Copyright: David Ross

In this chapter, Ayn Rand gives brief discussions of two topics, the forms of human cognition, and the nature and purpose of measurement.

We shall begin, as Rand does, with cognition, and particularly with the statement,

"Consciousness, as a state of awareness, is not a passive state, but an active process that consists of two essentials: differentiation and integration" (Rand, 1990, p.5).

In this chapter Rand presents two examples that are evidence for this claim. The first is that of a percept, "a group of sensations automatically retained and integrated by the brain of a living organism" (Rand,1990). Consider the perception of an object, say a rose. Your eyes respond differently to the light rays from the rose and the light rays from the background: differentiation. However the light rays from the rose that stimulate your eyes are not experienced as an otherwise unrelated group of sensations that are distinct from the sensations of the background. They are experienced as the direct awareness of a single entity, the rose: integration.

The second example of differentiation and integration is the mechanism by which we come to regard entities as units. This is the example of the tables and chairs (Rand,1990,p.6). A child comes to regard the tables and chairs as units by attending to a particular attribute - shape, isolating the objects according to differences in this attribute (differentiation) and integrating them into separate groups according to their similarities (integration).

The processing of sensations to produce percepts occurs automatically. It is accomplished by one's sensory apparatus; one has no choice about whether or how it occurs. By contrast, the mode of attention that allows one to achieve what Peikoff (1991) calls the "unit-perspective" must be volitionally initiated; one chooses to regard things in a certain way. This is why there is a science of logic - to guide our choices at the conceptual level, the level of cognition at which we HAVE choice - but there is no analogous science to guide our perceptions, since at that level we have no choice. Perception is infallible, higher-level cognition is not. This is also why "the base of all man's knowledge is the perceptual stage" (Rand, 1990). It is the base because it comprises precisely those instances of awareness in which we have no choice, which we are given, like it or not.

A detailed discussion of the nature of differentiation and integration as fundamental cognitive operations underlying conceptualization is provided by David Kelley in his paper "A Theory of Abstraction" (Kelley, 1984). Also see Peikoff (1991, p.77). A thorough discussion of the Objectivist theory of perception is given in The Evidence of the Senses; A Realist Theory of Perception (Kelley, 1986). Also see Peikoff (1991, Chap.2).

I'm going to digress here for a moment, to discuss what I found to be a queer passage in Peikoff's discussion of the topics we've been considering. In his section entitled "The Perceptual Level as the Given", he writes "The reason you see an entity is that you have experienced many kinds of sensations from similar objects in the past, and your brain has retained and integrated them: it has put them together to form an indivisible whole." (Peikoff, 1991, p.52). Here Peikoff seems to be saying that the integration that underlies our experiencing the world in the form of entities is one that blends several temporally separated experiences. I'd say that the pertinent integration, the integration to which Rand refers in her definition of "percept", is the blending, in the course of a single experience, of some collection of sensations. There is an element of temporal integration in the experience of an entity - one's direct perceptual awareness of a thing must span some interval of time - but it is integration over the course of a single encounter with the thing; it is not a blending of several different encounters. It seems reasonable to assume that one's prior sensory experiences contribute to the development of the ability of one's perceptual apparatus to perform the integration of sensations into percepts; but I do not think that the integration that goes into forming a percept from sensations is an integration OF those prior experiences, it is an integration of the immediately experienced sensations. (See Kelley (1986,p.47-48)).

Rand discusses two aspects of the development of an individual's conceptual consciousness. One of these is his treatment of sensory data. This develops in three stages, the stage of sensations, the perceptual stage, and the conceptual stage.

The other aspect she discusses is the evolution of the implicit concept 'existent' during a child's development. She also identifies three stages here, one corresponding to each of the implicit concepts 'entity', 'identity', and 'unit'. By saying that a concept is implicit, Rand means that although the child has not formed the concept, he has grasped 'the data which are later to be integrated by that concept' (Rand, 1990, p.6). The stages of evolution of the implicit concept 'existent' span the perceptual level of awareness and the beginning of the conceptual level. One has reached the first stage, the 'entity' stage, as soon as one's sensory organs and brain begin to integrate sense data into percepts, i.e. as soon as one has reached the perceptual level of awareness. When one has reached the final stage, the 'unit' stage, one has entered the conceptual level.

In each of the three stages, the child is aware of the same existents. What differs is the way in which he regards them. Imagine a child presented with a green ball. In the 'entity' stage, he regards the ball as 'a thing' - he experiences it as an single whole, differentiated from its environment. In the 'identity' stage, he regards it as 'this thing', not just as something that is present to him at the moment, but as something with a specific nature, something that is what it is independent of him. An important aspect of this stage is the child's awareness of persistence through time - he recognizes the ball as the thing he played with yesterday. Rand does not mention this aspect of the 'identity' stage, but Peikoff (1991, p.75) does. In the 'unit' stage, the child regards the ball as 'an instance of this type of thing', he recognizes its similarity to other things - the basketball with which his older brother plays, the beach ball in the swimming pool,...

Rand says virtually nothing about the chronology or psychology of the ascent from the 'undifferentiated chaos' of 'an infant's sensory experience' to the full conceptual functioning of a rational adult. (And for her purpose this is appropriate.) These aspects are discussed in some detail, with many excellent examples and many references to the literature of developmental and cognitive psychology, in Stephen Boydstun's article "Capturing Concepts" (1991). According to Boydstun (citing Kagan (1984, p.31-43)), a newborn infant is already capable of some visual differentiation; such an infant can discriminate between the musical notes C and C#. By the age of three months, an infant can recognize an object viewed from different orientations as a single object. Boydstun's article is a fascinating and well-written survey of psychological and philosophical issues related to conceptual thought from an Objectivist perspective. I recommend it highly.

Those interested in the psychology of cognitive development might also want to look into the work of Jean Piaget. Boydstun (1991) cites some experiments of Piaget (1954) that suggest that the "identity" stage begins around 9 months of age; prior to this age, if a toy in which an infant is interested is hidden by a cloth, the infant will not attempt to remove the cloth to get the toy, but after the age of 9 months, the infant will remove the cloth. Piaget concludes that the infant implicitly regards the toy as 'non-existent' when it's out of sight.

The 'unit' stage brings us to the conceptual level of thought. A 'unit' is "(a thing) viewed by a consciousness in certain existing relationships" (Rand, 1990, p.7). It is in connection with units, at the bottom of page 6 and the top of page 7, that Rand first discusses the nature of objectivity, though she does not use that term. Units qua units do not exist independently of consciousness; to use a popular Aristotelian term, there are no 'units' in rerum natura, in the world as it is, independent of awareness. "The concept 'unit' involves an act of consciousness (... a certain way of regarding things)" (Rand, 1990,p.7). This view of units differentiates the Objectivist approach to concepts from intrinsicist approaches. On the other hand, however, the concept 'unit' "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" (Rand, 1990, p.7). This view differentiates the Objectivist approach from subjectivism. To see that Rand's view of units is objective, let us introduce her definition of the term objectivity; "Metaphysically, it is the recognition of the fact that reality exists independent of any perceiver's consciousness. Epistemologically, it is the recognition of the fact that a perceiver's (man's) consciousness must acquire knowledge of reality by certain means (reason) in accordance with certain rules (logic)" (Rand,1965).

The concept 'unit' is fundamental to both mathematics and conceptualization. One aspect of the relation between these two fields - the measurement omission theory of concept formation - is a central topic of the rest of IOE. The last two pages of Chapter 1 are dedicated to a discussion of the nature and purpose of mathematics.

"Mathematics is the science of measurement". "Measurement is the identification of a relationship- a quantitative relationship established by means of a standard that serves as a unit" (Rand, 1990,p.7). Note that these definitions depend on the concept 'quantity', a concept that is not, to my knowledge, discussed in the Objectivist literature.

This definition deserves some comment. Other mathematicians with whom I've discussed it have generally disagreed with it. None of those in disagreement has provided an alternative definition. (I only know of two other definitions of math, one given by the mathematician Lipman Bers; "a collection of bad jokes and cheap tricks" and one given by Bertrand Russell "the field in which we don't know what we're talking about, nor whether what we say is true". Bers, at least, was kidding. Both quotes are really paraphrases from memory). Even I, as a young math student reading IOE for the first time, found this definition hard to swallow; surely there was more to this vast, elaborately developed and extensively detailed subject than measurement! There is not. Not only is 'the science of measurement' what mathematics ought to be, it is a correct description of what virtually every person who calls himself a mathematician is engaged in. The only exception I can think of is most people who are specialists in mathematical logic, who, qua experts in this field, should be called logicians, or philosophers of mathematics (or worse). This is not the place to survey all branches of mathematics and establish their connections to measurement, so I'll just provide two currently popular examples: fractal geometry, which comprises methods (Hausdorff dimension) for measuring the irregularity of certain shapes, and chaos theory, which includes methods (Liapunov exponents) for measuring the rates of divergence of once-close trajectories of dynamical systems.

Only attributes can be measured directly. Entities and their actions are measured via their attributes. Thus, we must bear in mind that an entity's being a 'unit', in the sense of being an instance of a type, does not make it a measurement unit. Thus we can't, for example, choose Rochester as the unit of citiness, and determine that Des Moines is 3.2 Rochesters. There are, however, attributes of Rochester that could be used as the standard to measure the same attributes of other cities. We might call the land area occupied by Rochester '1 Rochester', and determine that New York occupies 27 Rochesters.

Rand explains that "the purpose of measurement is to expand the range of man's consciousness,...beyond the perceptual level". This process of "integrating an unlimited scale of knowledge to man's limited perceptual experience" proceeds by "relating an easily perceivable unit to larger or smaller quantities" (Rand, 1990,p.8). In his discussion of this point Peikoff (1991, p.90) presents an interesting contrast, which I'll word in my own way. Mathematics has always been admired as the model of logical perfection because of its deductive methodology. But the purpose of mathematics is inductive, it is used in reasoning from particulars to generalizations, from cases encountered to cases not yet encountered. The simplest example of this is just using decimal system arithmetic, which allows us to deal with quantities vastly greater than we could handle perceptually (see the crow example, (Rand, 1990,p.62). Another (chosen at random) is my own work; given, say, the rates of a variety chemical reactions, I determine and solve mathematical equations to predict the equilibrium concentrations for as-yet-untried combinations of chemicals.

In connection with mathematics and induction, we should note that Rand (1990, p.7) specifies that a standard of measurement must "be easily perceivable by man". (Her other requirements are that it represent the attribute it's intended to measure, and that it be immutable). This brings us back, in a rather concrete way, to her statement that "epistemologically, the base of all of man's knowledge is the perceptual stage" (1990,p.5). Rand summarizes this with the words (but not the meaning) of Protagoras (an early sophist who applied the Heraclitean flux theory to perception, and ended up with subjectivism (Jones,1970)): 'Man is the measure of all things'.


Boydstun, S. Capturing Concepts. Objectivity, 1990, 1(1).(Available from Objectivity, 3023 N. Clark Street, Suite 238, Chicago, IL,60657)

Boydstun, S. Induction on Identity. Objectivity, 1991, 1(2).

Jones, R.T. A History of Western Philosophy I: The Classical Mind, San Diego, Harcourt, Brace, Jovanovich, 1970,

Kelley, D. "A Theory of Abstraction." Cognition and Brain Theory, 1984, 7(3&4).

Kelley, D. The Evidence of the Senses: A Realist Theory of Perception, Baton Rouge, Louisiana State University Press, 1986.

Peikoff, L. Objectivism: The Philosophy of Ayn Rand. New York, Dutton, 1991.

Piaget, J. The Construction of Reality in the Child. New York, Basic Books, 1954.

Rand, A. Introduction to Objectivist Epistemology. New York, Meridian, 1990.

Rand, A. "Who Is the Final Authority in Ethics?" The Objectivist Newsletter. 1965, 7.

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