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Capturing Concepts

45 posts in this topic

Capturing Concepts (1990 – Objectivity V1N1)

Concepts are thoughts. They are thoughts of kinds and sets. They function to indicate and specify kinds and sets of items. They are marked and evoked by words.

Concepts are commonly taken to subsume indefinitely large number of items. One may have concepts, such as the prime numbers among the counting numbers from 1 to 1000, that subsume a definite number of items, but one cannot understand such concepts without first understanding supporting concepts having indefinitely numerous extensions. Directly or indirectly, we engage universals in our concepts.

Since Kant concepts have come to be associated with rules. To possess a concept is to possess the ability to employ the concept’s rules for identification of its referents. Cognitive skills may be implicit or explicit (Dretske 1988, 116–18); employment of a concept’s identification rules may be implicit or explicit. Our first concepts must be held implicitly (Kelley 1984, 348–49, 350). No concepts are plausibly congenital; neither are they genetically determined (Minsky 1985, 115, 310–12; Oyama 1985). Our earliest concepts are constructed or acquired in development, although some are plausibly unlearned (Bennett 1990, 95–99; Macnamara 1986, 72–74, 191–92).

Any serious theory of what concepts are must be answerable to the facts of their employment and to the facts of their acquisition in development. Even if one professes no interest in the psychology of children, “one may have to consider patterns of development to answer questions about the structure of adult knowledge” (Keil 1989, 279; see also Kelley 1984, 346).

Continued below

—Categorical Perception

—Reference and Specification

—Measure and Matter

—Abstraction

—Identity and Definition

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—Categorical Perception

We form perceptual categories before we acquire language. We discriminate before we categorize. The newborn infant is responsive to information from all the senses. She can detect differences in some visual patterns. She can discriminate between the musical notes C and C-sharp and between the spoken syllables pa and ba. Like an adult, but in lesser degree, the young infant can hold different particulars of her environment in active memory. The three-month-old infant can recognize that an object seen from a new orientation is the same old object. She can identify certain qualities across sensory modalities; she correlates a pulsing tone with a broken line, a continuous tone with a continuous line (Kagan 1984, 31–43).

Preverbal infants are able to categorize some of the items in their environments. It has been shown, that, by three months of age, infants have begun to apprehend categories of events and objects. They can sometimes treat an item not seen earlier as an instance of a familiar category while recognizing nonetheless that the item is distinct from ones previously seen. Like adults they apprehend two new contrasting categories, intermixed in presentation, more easily than they apprehend them each alone, in isolation of other categorical stimuli (Quinn 1987). These cognitive developments proceed without vocabulary.

Humans, and some other primates too (Premack 1989, 48–50), are able to categorize perceptually because they are able to perceive directly some of the invariant structural and transformational relations in the world. Consider visual perception. The visual system spontaneously extracts relational invariances in the optical flow across the retina. One result is our ability to see solid objects and their motions in three-dimensional space. An analogy between the visual system and a prism can be drawn. A prism is commonly characterized as a kind of fourier analyzer, a separator of harmonic components of light. Similarly, the visual system can be conceived of as, among other things, an analyzer of projective geometry. Without any measurement of lengths or angles, the visual system sorts out relations in figures that remain invariant under transformations of perspective.

Through evolution we have been constituted such that continuous transformations of perspective result in the appearance of moving objects as having constant sizes and shapes. In experiment subjects shown two spots of light following an elliptical path cannot help but see those two spots as connected by a rigid rod which appears to be rotating in a plane tilted away from or toward them; this despite the subjects’ knowledge, through other perceptions, that there is no such thing there (Johansson 1975, 76–88; see also Kanizsa 1976, 48–52, and Ross 1976, 80–86). In the natural environment, it is generally true that where there is the visual appearance of a figure undergoing continuous perspective transformation, the figure is indeed a moving solid object. The visual system evolved in a natural environment, of course, and situating it in Johansson’s laboratory is like taking a compass down a mineshaft; the indicator no longer indicates what it normally does (Dretske 1988, 57–58, 62–63, 68–69).

It is not only simple objects and motions that we can apprehend by direct perception. Subjects realize, within a tenth of a second, that they are viewing a film of a walking person when all that is visible in the film are a dozen tiny lights that have been attached to (the shoulders, elbows, wrists, hips, knees, and ankles of) the walker. During the initial portion of the film, the actor is motionless; subjects then see just an array of lights, like a constellation. Only when the actor begins to move do subjects “get it” (Johansson 1975, 76–88). We recognize perceptually instances of categories—in this case, an instance of a human and walking—by criteria few of us fathom conceptually. There is much in walking, particularly in the sequence of angular changes at joints, that is used by us, unbeknownst to us, in our visual apprehension of walking (Marr and Vaina 1982).

The human body is a linked lever system. In walking the motions of its segments combine to put the body’s center of mass (belly button area) into a smooth sinusoidal curve (vertically and laterally) distinctive to the biped, upright stride of a human. Variations in this sinusoidal pattern are specific to individual morphological proportions and are fairly reliable indicators of age and gender. From geometric signatures such as this one, we can perceive as walking any instance of that class of events. In vision we can also apprehend categorically skipping, jogging, or sprinting. We can perceive the various kicks of swimmers all as kicks. We can perceive the variations and underlying constancies of these categories directly, sensitively, and without linguistic articulation (McCabe 1986).

Ayn Rand thought that children acquire some concepts before acquiring language. These concepts, she surmised, take a visual form. She pointed to young children’s drawings of humans—relatively large closed figure(s) for head and torso, four sticks for limbs, two small circles high in head for eyes, etc.—as an example of their representation of the essentials of human form (Rand 1990, 13). Marvin Minsky has also argued that such drawings reflect a defining network of relationships among features. He observes further more that young children are very limited in their abilities to draw lines in globally consistent scales and directions. It is expedient, then, to simply follow a procedure that locates each new feature in some recognizable relationship to easily described places which have been depicted at an earlier step in the procedure (Minsky 1985, 135–38).

We should take care, though, not to slip into thinking that a child’s drawing of a human is a standard, imaged for recognition of real humans when they are actually encountered. If a child were to see one of those stick figures really coming toward him, he (and we) would be terrified, notwithstanding his insistence that humans are truly depicted by his stick drawings. Those drawings may or may not fairly reflect the sort of mental image children typically conjure for the human form, but it seems unlikely in any event that children or adults resort to conjured images to accomplish recognitions. We evidently do not generally see objects categorically by comparing them with stereotypical or archetypical instances.

Visual recognition of the human form (but not faces; Young 1989, 80–83) and other form is more plausibly accomplished by activation of three-dimensional models retained in long-term memory. These would be hierarchically decompositional models of objects into parts and parts of parts. Such models for recognition are not devoid of resemblance to the child’s drawing; in recognition models, too, progressively finer structure is based on coarser structure. At the coarsest level of the 3D model, the human form is a single, roughly cylindrical volume. At the next level, it is elaborated into six cylinders; the torso with four limbs and head attached. At the next finer level, an arm becomes elaborated into two cylinders, upper arm and forearm. At the fourth level, the forearm becomes forearm and hand; at fifth, hand becomes palm and fingers; etc. The locations and orientations of all components at a given level are defined in relation to axes of components in the next coarser level. The single cylinder at the coarsest level is the ultimate basis for all spatial relations required in object recognition; the 3D model is object-centered, not viewer-centered (Marr 1982, 295–318).

Models for recognition differ from the child’s drawings in three pertinent respects. First, they are thoroughly volumetric models; objects and their parts are treated as occupying space. Secondly, models can have several levels of description, the finer always embedded in the coarser, through which we may shuffle as we recognize objects. Thirdly, the elements of models are not fully determinate in sizes and configurations at any level; ranges of values appropriate to the modeled object type are permitted, even required (ibid., 318–25).

This third characteristic of 3D models is an important part of what makes them serviceable for registrations of object types. It enables us to perceive objects categorically. It enables us to engage universals, so far as we do, in the course of visual perception. It is the crux of the basic principle Rand took to be operating in all conceptual awareness.

Quite plausibly, 3D models not only enable recognition of objects but also augment language-dependent cognition. We employ 3D models in concert with phonological and syntactic structures in at least some of our reasoning. Knowing the meaning of a word that denotes a physical object or action generally entails knowing what those objects or actions look like. Concepts of functional objects, too, are sustained in part through 3D models. One important characteristic of a chair is its affordance of a place to sit. Our definition of a chair would include the fact that it was something to sit in. Our concept chair relies in part on our 3D model of sitting (Jackendoff 1987, 200–202; see further Shaw and Hazelett 1986).

Acquisition of concepts very much more abstract than those for categories directly available in perception apparently requires the acquisition of language—spoken, signed, or written. William James thought otherwise. He reported in the nineteenth century the case of a deaf-mute, Melville Ballard, who reputedly engaged in fairly abstract thinking without language. Ballard had lost his hearing in infancy but eventually mastered written English. He claimed to have contemplated, in childhood, prior to his acquisition of language, abstract issues such as the origin of life (James 1981, 256–59). Careful reading of Ballard’s testimony, however, strongly suggests that young Ballard had engaged in some sort of mimed linguistic commerce with others. Furthermore, there are evidently significant differences in the cognitive capabilities of children born deaf and those of children who have had some exposure to language before losing their hearing (Heil 1982, 201–5). Assuming that Ballard’s adult memories of his childhood thoughts were accurate, it seems quite possible that in childhood he had possessed a rudimentary and private language, which was later superseded by English.

Words serve to mark and evoke concepts, though not always. Exclamations such as one might utter in a sudden emergency are not likely to express concepts. Demonstratives such as that do not themselves express concepts when they are simply being used rather than considered (as considered in this sentence). Their use by one-year-olds evidently entails only the ability to detect presence and the ability to refer. Proper names and the personal pronoun I (or me) do not themselves express concepts, although they do require the use of unstated concepts to specify their referents (Macnamara 1986, 49–109). For the most part, though, words express concepts.

Continued below

—Reference and Specification

—Measure and Matter

—Abstraction

—Identity and Definition

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—Reference and Specification

At the outset, I asserted that concepts indicate and specify kinds and sets of items. Subsequently, I have tried to make plausible the thesis that some elementary working concepts, not supported by language, are manifest in categorical perception. I shall have puffed up categorical perception too far, though, if it is now thought that all perceptual apprehensions of categories amount to the exercise of concepts. Let us deflate categorical perception somewhat by articulating two crucial characteristics of concepts that do not obtain in all categorical perception. These two characteristics pertain to two aspects of identity: a thing is what it is, and a thing is what it is. A concept must refer to something, and it must specify its referent in the distinctive ways that concepts specify (Peikoff 1990, 105–6).

One case of categorical perception occasioning no corresponding reference, thence no concept, would be the categorical perception of elementary speech sounds. For the perception (or production) of speech to get started, one must apprehend categorically the sounds of various consonants and vowels. We may fairly regard elementary speech sounds as markers of concepts when we are talking about those sounds but not when we are using them simply to speak. The sound of p would not in this statement have been used to mark a concept when used in saying “complete” or “point” or “lips.”

We grant elementary speech sounds the status of being concepts only when they are used as nominals even though they are always, if useful, apprehended categorically. We deny them the status of concepts in their usual, non-nominal role because, although they are themselves perceptible items in the world, they do not, without assimilation into words, refer to items either in the world or in the mind.

Categorical perceptions failing to rise to the level of concepts from weakness of reference also occur in the course of normal visual perception. While focused attention is moving from one location to another in the visual field, information is also being picked up preattentively from the entire field. At the preattentive level, the visual system detects tilted lines (deviations from verticality), curved lines (deviations from straightness), and gaps (deviations from closure). Preattentive pickup has been reported as well for colors, sizes, contrasts, movements, and differences in stereoscopic depth. Focused attention is required in order to conjoin such features at definite locations and to perceive objects in the field (Treisman 1986). At least at the preattentive level, categorical perceptions of features would seem not to exercise concepts.

More needs to be said, though, about what is here meant by “categorical perception of features.” It is not the matter of detecting a curved line as a curved line rather than as a color. Those categorizations presumably occur largely because those different kinds of pickups are handled by distinct visual subsystems. There are evidently three major subsystems: One carries information about borders that are formed by contrasting colors. (This subsystem cannot analyze which colors are present.) A second processes information about color and shades of gray. A third carries information about movement and stereoscopic depth (Livingstone 1988).

Comparisons between these subsystems are somewhat like comparisons between different sensory modalities. Olfaction and vision are separate and quite different systems; it is partially for that reason that odors and colors are radically distinguished. Similarly, lines and color and motion are processed by different visual subsystems and may be deeply distinguished in part for that reason. The categorical perceptions of features in preattention are categorical perceptions within and across each of the three major visual subsystems.

Evidently, such perceptual categorizations are effected at fairly central levels in the process of visual perception. Though they be categorical, preattentive perceptions of features refer too weakly to pass for concepts. It is a different story, of course, when these features are themselves objects of attention rather than simply preattentive elements for objects of attention.

Many categorical perceptions should be discounted as concepts for their shallowness in specification of referents. Pigeons are excellent learners of categories. Laboratory-reared pigeons have been trained to peck at a specific kind of object—say, a tree or truck—in pictures. They can pick the correct object even though the test pictures vary in the parts of the object they display and in distance and angle of view (Gould and Marler 1987, 84). Nevertheless, we should not credit such a laboratory pigeon with having a concept of the pictured object (Dretske 1988, 153–54). The information about the object—a tree, for example—available to such a pigeon is very sparse. These pigeons never experience the motions of trees in the wind, chucking squirrels in branches, insects in the bark, nor fallen fruit on the ground below. There is not enough natural connection of pictured trees to other things for the laboratory pigeon to have a concept of trees. Moreover, pigeons have difficulty using relational rules; apparently they lack the ability to represent relations symbolically (Pearce 1989, 147–51).

Concepts, at least the full-fledged concepts that we exercise, are connected or connectible with other concepts (Keil 1989, 271–72). Through those connections, we trace, in an economical way, the web of relations holding between the kinds of thing there are. In our concepts, we engage not only universals, but multiple layers of identity.

Birds in general may be so limited in the number and experiential mediacy of connections they can maintain that we should not credit them with possession of anything close to concepts (Horn 1989, 298–99). By these criteria, we probably should also not credit the three-month-old infant with concepts. Miniconcepts might be more felicitous. At three months, the infant can recognize objects or their kinds only with frequently repeated exposure. The ability to retrieve the past and hold it in active memory will not begin to blossom until about the eighth month. Just then, for instance, do deaf children learning sign language first use signs to refer to objects in the environment (Kagan 1984, 40–43).

In time children learn to express relations among items through predication and attribution (Muma 1986, 129–32; see also), but initially, child language consists of one-word sentences. The one-word stage appears superficially to be a time for simply learning the meaning of words. With close and creative attention, investigators have found that it is also a time for putting sentences together into meaningful groups. What an adult might say in a multiword sentence, a nineteen-month-old child might say in a series of one-word sentences. Verbal predication and attribution are already underway by the time the two-word stage is reached (Moskowitz 1978; see also Macnamara 1986, 144–45). At least implicitly, “every concept stands for a number of propositions” (Rand 1990, 48). That is so even in early stages of conceptual and linguistic development.

Propositions express beliefs. The beliefs held by humans can be about objects, events, or states of affairs substantially remote from what is currently presented to the senses. Such beliefs and the concepts of which they are composed sharply distinguish our thinking from that of other animals (Bennett 1989, 42–86). There are food-storing birds with amazing abilities for remembering locations of their caches; a Clark’s nutcracker can remember (imperfectly, of course) thousands of storage sites for months (Shettleworth 1983). There is insufficient reason, though, to suppose that such animals entertain tensed beliefs along the lines of “now I am going to remote location P where I shall get nuts I stored there some remote time ago” (Heil 1983, 207–10).

Children, we believe, do come to understand quite a lot of the temporal order in their world before they acquire natural language for tensed expression (Macnamara 1986, 100–101; Moskowitz 1978, 96–103). Why are we willing to ascribe tensed but unexpressed beliefs to young children yet deny such beliefs to mute animals? Surely the fact that the children are in the process of gaining expression must figure prominently in the explanation (see further Premack 1989).

We cannot engage universals full force in our concepts until we can prescind from all particular time. An adult’s concept of the kind dog refers to all of them that ever existed or will exist on this planet or any other. We learn the indefinitely large all (as in “all puppies have mommies”) probably by an extrapolation from all in easily surveyable domains (as in “all the puppies in the litter have been given away”) (Macnamara 1986, 163–70). It is unlikely that any nonhuman animals on earth engage universals full force in their thinking, but that is here an issue of secondary importance. The more important issue for us is the nature of our own thinking.

Continued below

—Measure and Matter

—Abstraction

—Identity and Definition

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—Measure and Matter

Ayn Rand endorsed the principle that concepts result from assimilations of items possessing common characteristics that are not possessed by other items. Some version or other of this broad principle has been adopted by many philosophers, notably by Aristotle, by Aquinas, and by Locke. It was cast in a form close to Rand’s by William of Ockham, who regarded concepts as arising from the fact that there are varying degrees of similarity between individual things.

Rand contributed an intriguing specific thesis. She focused on the circumstance that the common distinctive characteristics of instances falling under a concept are possessed to some degree by all those instances but may be possessed to any degree within appropriate limits. Rand saw intellectual suspension of measure as the key to universal concepts: In forming or applying concepts, one disregards the specific magnitudes of the common distinctive characteristics encountered in particular instances, even as one recognizes that every instance possess those characteristics in specific measures. By omitting the specific measurements, one slackens some of what individuates concretes and thereby permits them to fall under a concept (Rand 1990, 5–15). So far as I know, the central and explicit role in abstraction that Rand awards to measurement omission is without precedent.

David Hume did understand something of the importance of measurement omission to abstraction. At least he attempted to discredit received views of our powers of abstraction by denying that we are capable of measurement omission. He contended that we cannot form an idea of a line without any particular length nor as possessing all possible lengths. Moreover, “the mind cannot form any notion of quantity or quality without forming a precise notion of degrees of each” (Hume 1888, 18). Construed ordinarily, these are pretty flashy claims. They are also false. If they were true, we could not comprehend analytic geometry. Some rather pastoral reasoning would also be beyond our ken. “How tall were the trees in the stand on the south forty at their uppermost ascensions yesterday?” We have no trouble understanding that they had heights far more precise than we can estimate without actual measurement. We need not pick hypothetical specific values to understand that they had true values somewhere within (or outside) the margins of our estimations.

Hume’s claims should not be construed so ordinarily. Like Berkeley before him, when Hume says “idea” or “notion,” he really means “image.” Under this translation, Hume’s claims lose their flashiness but gain a modicum of truth.

Hume goes on to say, again following Berkeley, that all ideas (images) are particulars. Our general or abstract ideas (concepts) are just particular ideas (images), “annexed to a certain term, which gives them a more extensive signification, and makes them recall upon occasion other individuals [individual ideas (images)], which are similar to them” (ibid., 17). Similar in what manner? What criteria, more specific that a general similarity, are employed in selecting which individuals may be annexed to the same term? What are the rules of concept construction? Hume does not know (ibid., 20–24; see further Kelley and Krueger 1984, 55, and Kelley 1984, 348–49).

Since we have wandered this far into intellectual history, let us step back an additional 500 years and visit Thomas Aquinas. He understands abstraction in Aristotelian terms. When a material object changes, it may yet remain the same kind of thing it was, or it may be so transformed as to become some other kind(s) of thing(s). In the first case, the essential substance of the object has not changed; in the second case, it has. Yet when an essential substance has changed, there must have been some underlying substrate that endured the change. Underlying all substantial changes of material things is a substrate that is not itself a definite substance. This is prime matter. It is the potential of material substance for specific form but does not exist apart from specific form. That which makes the substance a specific kind is substantial form. Every material substance consists of matter and form.

Form is the universal element in things. Matter renders forms as concretes, instantiating forms in particular individuals. Prime matter has an exigency for quantitative determination which it receives through union with form.

Now in abstracting a universal form from particulars, the mind abstracts from particular individualizing matter but not from matter altogether. Of special interest to us is Aquinas’ view that in abstraction the mind disregards the particular matter of a particular object but not the presence of matter per se, that is, not the pure exigency for quantitative determinations (Aquinas 1947, Pt 1 Q 85, Art 1, Objection 2 and Reply). The shadow of measurement omission passed through the mind of Thomas Aquinas.

Because of the doctrine of substantial forms, Aquinas could not have made measurement omission the central process in abstraction. It was form, not matter or quantity, that made things fundamentally the kinds of thing they are. Furthermore, quantity should not have been given a serious role in individuating substance for, in Aristotle’s scheme, quantity is only an accidental form of substance. Aquinas’ eminent successors, Duns Scotus (1265–1308) and Francis Suarez (1548–1617), resolved the tension by denying to prime matter the role of individuation and by putting quantity entirely back into its Aristotelian place. For Scotus individuation was accomplished by something obscure beneath both matter and form. For Suarez form got most of the job of individualting substance; a natural extension of its basic task of distinguishing classes of substance. The shadow of measurement omission receded.

Continued below

—Abstraction

—Identity and Definition

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—Abstraction

Quantity makes all the difference in the world. Fourteen protons in the nucleus give silicon; fifteen give phosphorous. Modern scientific characterizations of things are quantitative through and through. Quantity is no longer a second-class metaphysical citizen. Neither is matter.

Things are not composed of two metaphysically different constituents, form and matter. There is not immaterial, intellective form in which the true essences of things might reside. There is no inchoate matter partaking form and imparting individuality. That which makes things the kinds of things they are also makes them the particular things they are. The identity of a thing, in both senses, is constituted only of a thing’s determinate characteristics. (This principle would have to be suitably generalized to be applicable in the quantum regime.)

Consider a solid object for example. Solids are distinguished from fluids in virtue of the fact that they have moduli of rigidity that are not (too close to) zero; any solid is capable of withstanding shearing forces up to some particular measure. The particular modulus of rigidity of a particular solid object is part of what constitutes its individual identity, and the fact that its particular modulus is not zero is what qualifies it for the class solid.

In Rand’s theory, concept formation begins with perceptual awareness of some of the network of similarities and differences that exist among particular items. We begin by grouping items in accordance with their similarities with each other. More precisely, items are grouped according to shared contrasts with other items in particular respects (Kelley 1984, 339). Differences in typical shapes are greater between chairs and tables than between chairs and chairs. Differences in typical uses are greater between chairs (used for sitting, rocking, or whirling) and tables (used for keeping various objects off the floor) than between chairs and chairs.

“All concepts are formed by first differentiating two or more existents from other existents. . . . In the process of forming concepts of entities, a child’s mind has to focus on a distinguishing characteristic, i.e., on an attribute in order to isolate one group of entities from another” (Rand 1990, 13–15; see also Dretske 1988, 75–77). Formation of the concept table or chair requires attention to the attributes of shape and function. To detect an attribute, one need not already have formed a concept of it. Indeed, the course of speech development suggests that concepts of entities are formed before concepts of attributes. Perceptual pickup of attributes is sufficient for similarity grouping of objects.

When grouping items by similarity, we may not realize in which respects they are similar. To form a concept, according to Rand, we must discern (some of) those respects. We discern dimensions along which the similar items differ markedly less and contrasting items differ markedly more. Awareness of dimensions underlying similarity groupings must be joined with two other skills, in Rand’s view, to form concepts fully: the ability to treat items in similarity groupings as elements of sets and the ability to see different values along a dimension as a variable.

Having discriminated attributes underlying a similarity group, having recognized those identical attributes among numerically distinct members of the group, having realized that those attributes are possessed by members in magnitudes ranging over a scale, one can form a concept of the group. A single mental item, the concept whose reference is to that group, can be constituted on the principle that members of the group possess the same distinguishing attributes in some measure but may possess them in any measure within appropriate limits. All members are truly members regardless of measure. Then items that have not been actually encountered but, if encountered, would fall into the similarity group and would possess the same distinguishing attributes in some appropriate measure are also truly members.

Acquisition of a concept normally entails attachment of a word, “a single, specific, perceptual concrete,” to facilitate use of the concept as a definite unit of thought. “Words transform concepts into mental entities” (Rand 1990, 10–11).

Words remind us of thoughts. Common nouns are the first conceptual words we learn (Macnamara 1986, 144–45), and they evidently cue us to think of similarity groups (Bauer and Mandler 1989; see also Premack 1989, 52–53). We have another way of grouping things; by spatial-temporal contiguity or neighborhood. Kitchen items and things to take along on vacation are concepts of such groups. These are thematic concepts. They are truly concepts but should be distinguished from taxonomic concepts. The former are grounded in proximities; the latter in similarities of forms and functions. We might bring proximity groups under the heading of similarity groups by saying that members of a proximity group are similar in typical spatial-temporal locations. Subsumption of proximity under similarity seems contrived, though, and I am inclined to resist it.

Children as young as fourteen months form thematic as well as taxonomic categories (Mandler, Fivush, and Reznick 1987). Adults, too, organize their knowledge of the world thematically as well as taxonomically (Mandler and Bauer 1989, 158; Jenkins, Wald, and Pittenger 1986). These perspectives are mutually supporting.

The relation of being a part of is a type of thematic relation and is especially important. Part-whole relations are given in perception along with similarity relations. We learn to form powerful semantic networks from is a part of and is a kind of. “A pear is a kind of fruit which is a part of a tree which is a kind of plant which (with others) is a part of the biosphere.” Parts are natural units of form and natural units of function. Grouping objects according to perceptually salient common parts may engender the child’s transition from classifications (of artifacts, procedures, and biological kinds) according to appearances to classifications according to functions (Tversky 1989, 983–95; see also Keil 1989, 104–9, 111–15, 166–72). Moreover, conceiving of things as systems would surely be impossible without a prior grasp of part-whole relations; similarity relations are not sufficient.

Psychologists and philosophers have given much more attention to the role of similarity in concept formation and organization than to the role of thematic relations. Similarity is the wellspring of conceptual thought. We should note, however, that Rand, for one, was not oblivious to the influence of thematic relations. “The distinguishing characteristics of furniture are a specified range of functions in a specified place (both are measurable characteristics). . . . The concept furniture involves a relationship to another concept . . . which has to be grasped before one can grasp the meaning of furniture: the concept habitation.” (Rand 1990, 22–23; see also 264–67.)

Similarities give rise to taxonomies, but let us not move too casually from the former to the latter. Children one-to-two years old group basic-level classes from different superordinate classes, e.g., dogs v. cars, more easily than basic-level classes from the same superordinate class, e.g., dogs v. horses. They also group superordinate classes, e.g., animals v. vehicles (four-legged walking animals v. street vehicles), more easily than basic-level classes from the same superordinate class. "This is not to say that we should credit children in this age range with having formed superordinate classes in the formal sense, namely, as higher order classes in a hierarchy that dominates subclasses nested under them. If a child responds categorically to the class of animals without distinguishing its subclasses of dogs and horses, it seems more appropriate to speak of the child’s representing a global category rather than a superordinate one" (Mandler and Bauer 1988, 262; see also Macnamara 1986, 157–62; cf. Keil 1989, 195–215 on five-to-ten-year-olds.).

Continued below

—Identity and Definition

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—Identity and Definition

Perceptual groupings and concepts proper trace the web of relations among items. In development these tracings are gradually but radically reformed. Between the ages of about two and five, there is evidently a developmental shift in criteria for perceptual groupings; a shift from relations of overall similarity to those of part (or aspect) identity. During this shift, the child’s perceptual knowledge becomes dimensionally organized (Smith 1989; Evans and Smith 1988). After about five years of age and occurring at different times in different domains of knowledge, there is a similar shift at the level of concepts proper; a shift from conceiving of things in terms of characteristic features to conceiving of things in terms of defining features (Keil 1989).

In imitation tasks reported by Linda Smith, children aged two, three, and four watched one experimenter and then a second experimenter select a pair of objects from among three according to a particular rule. When the experimenters selected objects according to the rule that they be the same along one dimension (e.g., red on color dimension) and different along another (e.g., large and small on size dimension), only about half of the two-year-olds succeeded in imitating the selection; all the three- and four-year-olds succeeded. Not all of the younger children could yet sort out part identities. Another imitation task revealed that the younger children could pair items by whole identity. These are really pairings by overall similarity, with whole identity being regarded simply as a case of overall similarity (Smith 1989, 158–65). Identity, in parts or in wholes, comes with development to be seen not as simply a high degree of similarity but as a distinct and privileged relation. Identity comes to be specially valued, and this apparently leads the child to begin comparing objects by parts in classification tasks (Evans and Smith 1988).

In another portion of the imitation studies, experimenters picked pairs of objects according to dimensional kind. The first experimenter might pick two red balls (of different sizes where a third ball of different color matched one of them in size). The second experimenter might pick two blue balls from another threesome. The child was then to pick two yellow balls from her own threesome. None of the two-year-olds, some of the three-year olds, and all of the four-year-olds succeeded. The youngest children did not preserve the dimensional kind of part identity. If the experimenter had chosen, for example, by sameness of color, “the two-year-olds were equally likely to choose two objects that were same in color or same in size. . . . Many can represent and infer rules about part identities, but they do not have part identities organized into dimensional kinds” (Smith 1989, 161).

There is much evidence to suggest that preschoolers typically contrast objects in terms of holistic, dimensionally nonspecific relations of magnitude. Objects intense in size and color are grouped together and segregated from objects not intense in both size and color. It is moreness and lessness across both dimensions that matter for these young children. They are observed trying to seriate objects on two dimensions at once. Quite possibly, they have not only notions of global magnitude polarities, but notions of dimensionally undifferentiated directions of difference. The preschooler’s understanding of global magnitude, however, does not entail an understanding that greater than and less than are necessarily opposing directions of difference. That understanding comes later, with an understanding of the ordering of values along single dimensions (Smith 1989, 165–72; Halford 1984; Chapman and Lindenberger 1988; Minsky 1985, 99–107, 149, 241).

The formation of concepts according to Rand’s formula of measurement omission requires a dimensional understanding of isolated attributes. The dimensions must be accessible but might be scalable only ordinally (Rand 1990, 31–33, 14–15). A child knows size as a dimension when he regards big and little as attributes of a single kind; part identities have then become organized by dimensional kind. He knows size as an ordinal dimension when he regards bigger and littler as necessarily opposing directions of difference. Preschoolers have only a very incomplete and fragmented understanding of these quantitative relations. They do have the beginnings of such understanding (Smith 1989, 168–72; Gelman and Gallistel 1986, 160–67), and perhaps there is enough in some of the preschooler’s domains of knowledge to begin to form concepts along the lines of Rand’s formula.

It is doubtful, though, that preschoolers could hold the full-blown Randian form of concepts; they cannot yet view numbers algebraically. (Could they nonetheless view different values along some dimensions as variables?) It is doubtful, furthermore, that the preschooler’s concepts engage universals full-force; they do not yet realize that counting numbers are endless (Gelman and Meck 1983, 357–58).

John Macnamara observes that logic is not a method we are always bound to employ (correctly) in our reasoning. He portrays logic instead as a theory of competence in reasoning (Macnamara 1986, 21–42). Similarly, Rand’s theory of concepts might be best seen as a theory of competence in conceptual function. Her model for concept formation should perhaps not be taken as a model of how we must conceive things, but of how we, as adults, can conceive them when we want to clarify our concepts and understanding. Rand supposed that in rendering exact the meaning of one’s concepts one is retracing to some extent the logical steps by which they were formed (Rand 1990, 51, 41). Perhaps we need only trace logical steps by which they could have been formed. I suggest that the model process of concept formation may not be always our way of generating or regenerating conceptual thought, and yet it may be our way of validating those thoughts. (And in validation do we not reform?)

During the first few years of speech, we evidently tend to conceive of things in terms of characteristic features. After about the age of five, there is a profound developmental shift to conceiving things in terms of defining features. The course of this cognitive development has been partially charted in careful empirical studies by Frank Keil and associates.

In one study, children in three grades (K, 2, and 4) were read descriptions and then asked if what had been described could be a certain thing, say, a menu. Two descriptions had been composed for each item included in the study. One description contained characteristic features of the item and one feature contrary to the definition of the item. The other description contained uncharacteristic features of the item along with the defining feature of the item. Descriptions used for island illustrate the pattern:

C/~D There is this place that sticks out of the land like a finger. Coconut trees and palm trees grow there, and the girls sometimes wear flowers in their hair because it’s so warm all the time. There is water on all sides except one. Could that be an island?

~C/D On this piece of land, there are apartment buildings, snow, and no green things growing. This piece of land is surrounded by water on all sides. Could that be an island?

(Keil 1989, 71)

Coming into second grade, children tend to say that C/~D describes an island and ~C/D does not. By end of second grade, their judgment of the matter is reversed.

The characteristic-to-defining shift does not usually occur for the terms news or museum until a little after second grade. The shift occurs for lie and robber sometime in the preschool period. A follow-up study with preschoolers, as young as three years, indicated that in general they rely more than kindergartners on characteristic features. Even the preschoolers, though, did not seem to rely completely on characteristic features for all concepts.

The shift is truly from characteristic to defining features; it is not a shift from idiosyncratic defining features to conventional defining features (ibid. 119–27). “Early on, at least for some terms, children frequently have true probabilistic representations wherein no one feature seems essential but a weighted sum of several is sufficient for describing an instance” (ibid., 127). It should be noted also that the shift is not a shift from visible features to nonvisible features (ibid., 115–16, 107–8, 195–207, 264–65).

Concepts within a given domain tend to undergo a characteristic-to-defining shift at roughly the same time. Keil investigated the shifts for concepts in five domains:

moral acts (lie, steal, cheat, tease)

meals (breakfast, lunch, dinner)

hand tools (screwdriver, hammer, saw, scissors, drill)

kinships (aunt, uncle, cousin, grandmother, grandfather)

cooking (boil, fry, bake).

The characteristic-to-defining shift occurs at different times, ordered as listed above, for these five domains. Leaving aside the moral act concepts, which all children of speaking age handle by defining features, the more coherent the conceptual domain, the more synchronous is the shift among its member concepts. In the most coherent domains, meals and kinships, mastery of the definition of just one of the concepts in the domain reveals almost all the dimensions relevant to defining the other concepts in the domain. The least coherent domain was hand tools; the characteristic-to-defining shifts varied from slightly before kindergarten for drill to between second and fourth grade for saw (ibid., 84–114).

Definition is a technique for keeping different kinds and sets of items distinct as the number of one’s concepts increases (Rand 1990, 40–45, 230–33). Rand supposed that we require verbal definitions to securely grasp any concepts beyond those which are of items plainly demonstrable in perception (ibid., 49–50).

The essence of definition is essence. “A definition must identify the nature of the units [the existents falling under the subject concept], i.e., the essential characteristics without which the units would not be the kind of existents they are” (Rand 1990, 42). When the existents falling under a concept have more than one distinguishing characteristic in common, Rand says that one must observe the relationships among those characteristics and select as defining the one that is most fundamental. “Metaphysically, a fundamental characteristic is that which makes the greatest number of others possible; epistemologically, it is the one that explains the greatest number of others” (ibid., 45; see further 230–33 and Peikoff 1990, 102–3). Essence and explanation are intimately related. I take Rand’s “greatest number” criterion for essence to be of a piece with the “unifying power” criterion for explanation Friedman 1983, 236–50).

It seems that for some concepts the best we can do is select the distinguishing characteristic that most reliably distinguishes. Selecting the deepest distinguishing characteristic is a preferable way of accomplishing that, but such a characteristic is not always available to us. Consider the concept breakfast. The kinds of foods typically consumed for breakfast are only typical; there is no breakfast food by which we might always distinguish breakfast from lunch or dinner. That breakfast is the first meal consumed after a full sleep is a more reliable distinguishing characteristic. What foods are typical might well depend, of course, in some unknown way, on the circadian place of breakfast. Surely our knowledge that the dependence could not be the other way around—that the foods typically consumed could not influence the time of day breakfast is consumed—also inclines us to define breakfast as first meal after full sleep.

The shift from conceiving in terms of characteristic features to conceiving in terms of defining features can be interpreted as a shift from formulation according to relatively atheoretical similarities and conjunctions to formulation according to more theoretical relations. We seek defining features, and we seek theoretical relations, especially causal relations, which yield them (Keil 1989, 34–57, 268–81; on the complexity of essence and causation in biological systems, see Oyama 1985, 10–23, 137–39.)

Reliance upon similarities and identities among relatively accessible surface properties is reasonable in our early conceptual formulations. Surface properties are in fact generated and constrained by deeper properties. The former are diagnostic of the latter. Surface similarities sometimes mislead, and we must regroup (e.g., Sibley and Ahlquist 1986); these are exceptions proving the heuristic (Medin and Ortony 1989, 185–86). We advance our theoretical understanding by reforming our concepts in accordance with ever-deeper similarities and identities.

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References

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Bauer, P., and J.M. Mandler 1989. Taxonomies and Triads: Conceptual Organization in One- to Two-Year-Olds. Cognitive Psychology 21:156–84.

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Dretske, F. 1988. Explaining Behavior. Cambridge, MA: MIT Press.

Evans, P., and L.B. Smith 1988. The Development of Identity as a Privileged Relation in Classification: When Very Similar is Just Not Similar Enough. Cognitive Development 3:265–84.

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Supplements

“Pursuing Similarity”

Merlin Jetton

“Shape, Action, Symbolic Play, and Words”

Linda B. Smith and Alfredo F. Pereira

The Origin of Concepts

Susan Carey

(Oxford 2009)

The Making of Human Concepts

Mareschal, Quinn, and Lea, editors

(Oxford 2010)

Plato’s Camera

How the Physical Brain Captures a Landscape of Abstract Universals

Paul Churchland (MIT 2012)

Edited by Stephen Boydstun
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Remarks

In the introduction to “Capturing Concepts,” I referred to the concept the prime numbers among the counting numbers from 1 to 1000. In the Abstraction section, I referred to the concepts kitchen items and things to take along on vacation.

Allan Gotthelf mentioned to me that he had an exchange with Rand in which she addressed the question of whether such phrases are concepts, that is, whether they designate a concept. Here is the exchange, from the Appendix to ITOE, page 175 [Oops! Page 177 is the one. Thanks, Thom.]:

Gotthelf: I want to get clearer on the distinction between a concept and what you call a qualified instance of a concept [ITOE 23, 71]. How would you classify stationery supplies in that regard?

Rand: That is a qualified instance of a concept; it is used as if it were a concept, but it is a compound concept.

Gotthelf: What would turn it into a concept?

Rand: If we had a special word for it.

Gotthelf: Just as the phrase Conceptual Common Denominator became a concept by reducing it to CCD.

Rand: Yes, that’s right.

Gotthelf: If the phrase stationery supplies became, in effect, one unit—if you hyphenated it, so to speak, then it would become a concept?

Rand: That’s right.

I would add that a factor of reinforcement should figure in whether a phrase, consisting of more than one word, could designate a single concept. As one uses a phrase such as stationery supplies or kitchen items more routinely, one’s attention becomes less drawn to the two concepts in these two-word phrases, followed by this way of joining the concepts. Rather, with routine use, one’s attention goes more directly—or anyway, more swiftly—to the collection of items being described by the phrase.

Rand’s view is ready to assimilate that point. In a discussion with Prof. Nelson, Rand remarked that “when you utter a sentence, you are using concepts which do exist in our minds, and we are able to recognize and hold them for the length of your sentence—particularly if the sentence is grammatical. / The answer to how we are able to understand a whole sentence, let alone a whole book, lies in the nature of concepts. Which part of their nature? Automatization. When a concept automatically stands in your mind for a certain kind of concrete, when you don’t have to take time to remind yourself what you mean by the word table, by the word child, etc., it’s that speed of lightning-like integrations of the referents of your concepts to your words that permits you to understand a sentence.” (ITOE Appendix 182–83)

Let me use one of my longer phrases from the Introduction of “Capturing Concepts” in a sentence. “This computer program selects the prime numbers among the counting numbers from 1 to 1000.” I maintain that the italicized phrase marks a definite concept. It is the particular rule according to which the particular set of numbers is selected. This phrase states the essence of its concept, and its concept is nothing but that essence. Each of these particular primes has other characteristics besides being a prime, but being prime is one of the fundamental characteristics of each. I notice that routine use of the phrase does make use of the concept ever faster; I mean I notice that about mathematics-talk in general.

“Gather things to take along on vacation beside the door to the garage.” Here the phrase states the essence of its concept, but that characteristic of the collected items is not part of the fundamental character of those items. In this case, routine use does not seem likely to greatly speed up concept-access. Substituting the phrase vacation-items for the longer phrase surely does.

~~~~~~~~~~~~~~~~~~~~~~~~

Something Rand said in the preceding informal remarks, reminds me of a construction of Rand I made in “Capturing Concepts.” Rand used the phrase “integrations of the referents of your concepts to your words.” This reminded me of certain passages in her essay. Rand wrote of “the feat of grasping the nature of language, the process of symbolizing concepts by means of words” (19). “A word is merely a visual-auditory symbol used to represent a concept; a word has no meaning other than that of the concept it symbolizes, and the meaning of a concept consists of it’s units. It is not words, but concepts that man defines—by specifying their referents” (40).

Talking of words symbolizing or representing concepts can be confusing. The way in which concepts (or words) symbolize referents is more than the way in which words “symbolize” concepts. Words are markers for concepts, and that is the term I usually use: mark. Sometimes that is all one means by symbol, and I think that is all Rand meant by saying that words are symbols for concepts.

Here, a note on the hierarchy of symbolic reference.

Edited by Stephen Boydstun
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Searching for Essence and Definition

Aristotle wrote that "a definition is a phrase signifying a thing's essence" (Top. 101b37). Rand concurred. For Aristotle the essence of a thing might be made plain to the senses or it might be established as a hypothesis (Metaph. 1025b11). Rand did not dispute that.

Fundamentally, "the essence of each thing is what it is said to be in virtue of itself. For being you is not being musical; for you are not musical in virtue of yourself. What, then, you are in virtue of yourself is your essence" (1029b14-16). For Aristotle the essential predicates of a thing say what it is, what it is to be it. To say that man is musical does not say what man is. It says something truly of man, but it does not say what is man. Moreover, for Aristotle the essence of a thing is its characteristic on which its other characteristics depend.

Thus far, Rand concurs: "A definition must identify the nature of the units [subsumed under the concept being defined], i.e., the essential characteristics without which the units would not be the kind of existents they are" (ITOE 42). Moreover, the essential characteristic of a kind under a concept is "the fundamental characteristic without which the others would not be possible. . . . Metaphysically, a fundamental characteristic is that distinctive characteristic which makes the greatest number of others possible; epistemologically, it is the one that explains the greatest number of others" (ITOE 45).

Aristotle held that all natural bodies are a composite of matter and form. Rand rejects this component of his metaphysics (ITOE Appendix 286).] Typically, Aristotle took form, rather than matter, to be what makes a thing the kind of thing it is. Essence is a form. (See further: A, B, C)

"Aristotle held that definitions refer to metaphysical essences, which exist in concretes as a special element or formative power. . . . Aristotle regarded 'essence' as metaphysical; Objectivism regards it as epistemological" (ITOE 52). For Aristotle what makes gold gold or an animal cell an animal cell is a metaphysical essence, a metaphysical form. This metaphysical essence is in contrast to physical essence.

I say that the essence of the chemical element gold, that in virtue of which it is gold, is: having such-and-such numbers of protons and neutrons bound in a nucleus and the electrons about it. That is what makes its further distinctive properties possible. The essence of a living animal cell is that it offsets the potentially catastrophic drive of water inward through its wall by pumping sodium ions out through its wall. That is what makes possible its further distinctive properties (distinctive, say, from a living plant cell). * These essences are physical. The essence of a human being—rationality—is mental. These are all essences in Rand's sense. They are physical or mental, but not metaphysical in the form-sense of Aristotle's essences.

For Rand "an essential characteristic is factual, in the sense that it does exist, does determine other characteristics, and does distinguish a group of existents from all others; it is epistemological in the sense that the classification of 'essential characteristic' is a device of man's method of cognition" (ITOE 52).

Proper definition, in Rand's view, is always based on real essential characteristics. She is not so restrictive as Aristotle as to what counts as an essential characteristic.

I have reported in the section Identity and Definition research showing a general developmental shift from conceiving of things in terms of characteristic features to conceiving things in terms of defining features (cf. ITOE 230–31, 234). Concerning the latter, the mature and desirable way of conceiving things, Rand says that the essential characteristic of a kind under a concept is “the fundamental characteristic without which the others would not be possible. . . . Metaphysically, a fundamental characteristic is that distinctive characteristic which makes the greatest number of others possible; epistemologically, it is the one that explains the greatest number of others” (ITOE 45).

What is the sense of making in “makes the greatest number of others possible”? It would seem to be any sort of objective dependence of one thing on another, not only causal dependencies. The latter are highly desirable, and as we work our way deeper into the identities of things, causal production should eventually be among the kinds of making in what we take for essence. Short of that depth, we can have other kinds of objective dependencies for essence, and these can count as explanatory.

Locke called real essences those essences whose makings were causal. Outward the real essence, Locke would have nominal essence. He would say that gold had a real essence, which was in his day unknown. The real essence would be that inner constitution of gold on which depend its color, weight, fusibility, and so forth. Having no knowledge of that inner constitution, Locke would count the known distinctive qualities of gold its essence. Knowing them to depend on some unknown inner essence, Locke would call them the nominal essence of gold.

When Rand writes of essential characteristics being factual, it means they are real characteristics having real distinguishing power and real dependency relations, however far those dependencies are from inner constitution and deep cause. So on Rand’s view, I see no need for a notion of real essence that is in contrast to nominal essence (contrary). All essences, at each stage of knowledge, are real, and as Leibniz maintained, the alternative to a real essence is a false essence (NEU 293).

Rand offers at least one general dependency relation that is not causal and that should constrain formulation of definitions. That is the dependence of attributes and actions on entities (ITOE 71). Man can be properly defined as a rational animal, but not as animal rationality (contrast with Leibniz in NEU 291–92). The entity-attribute and entity-action relationships are the framework for definitions that explain what a thing is. The role of entity in Rand’s metaphysics is somewhat like the role of substance in Aristotle’s. “Definition is of what a thing is and of substance” (APo. 90b30).

Another constraint to be met in definitions would be recognition of the dependence of absence on presence. A valley is an entity, but it has a dependence on mountains more profound than the dependence of mountains on valleys (ITOE Appendix 273). So we define valley as in American Heritage Dictionary: “An elongated lowland between ranges of mountains or hills, or other uplands, often having a river or stream running along the bottom.” That last feature, a typical feature, touches on the cause of valleys. Turning to the definition of mountain, valleys are not mentioned: “A natural elevation of the earth’s surface having considerable mass, generally steep sides, and a height greater than that of a hill.”

Edited by Stephen Boydstun
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Capturing Concepts (1990 – Objectivity V1N1)

Concepts are thoughts. They are thoughts of kinds and sets. They function to indicate and specify kinds and sets of items. They are marked and evoked by words.

[...]

—Abstraction

[...]

Acquisition of a concept normally entails attachment of a word, “a single, specific, perceptual concrete,” to facilitate use of the concept as a definite unit of thought. “Words transform concepts into mental entities” (Rand 1990, 10–11).

Words remind us of thoughts. Common nouns are the first conceptual words we learn (Macnamara 1986, 144–45), and they evidently cue us to think of similarity groups (Bauer and Mandler 1989; see also Premack 1989, 52–53). [...]

[...]

[...] Similarity is the wellspring of conceptual thought. [...]

[...]

I wonder what your definition of "thought" is. It seems to me that the term is too vague, and too few writers define it for extended discourse. Ayn Rand defines it as "a purposefully directed process of cognition." (ITOE 32a) Is your concept of "thought" the same as this? Do you think the writers you cite (e.g., Horn, Weiskrantz) mean the same units when they use "thought" in referring to "thought without language"?

Within the Objectivist literature, "thought" is still rubbery, Rand's definition notwithstanding. What is a thought? Is "thinking a thought" in your view a valid phrase? Or is it that you "think with a thought"? And when a grammarian says that a sentence expresses a complete thought, is this kind of thought the same as the unit of thought that is a concept?

—Abstraction

[...]

Words remind us of thoughts. Common nouns are the first conceptual words we learn (Macnamara 1986, 144–45), and they evidently cue us to think of similarity groups (Bauer and Mandler 1989; see also Premack 1989, 52–53). We have another way of grouping things; by spatial-temporal contiguity or neighborhood. Kitchen items and things to take along on vacation are concepts of such groups. These are thematic concepts. They are truly concepts but should be distinguished from taxonomic concepts. The former are grounded in proximities; the latter in similarities of forms and functions. We might bring proximity groups under the heading of similarity groups by saying that members of a proximity group are similar in typical spatial-temporal locations. Subsumption of proximity under similarity seems contrived, though, and I am inclined to resist it.

Children as young as fourteen months form thematic as well as taxonomic categories (Mandler, Fivush, and Reznick 1987). Adults, too, organize their knowledge of the world thematically as well as taxonomically (Mandler and Bauer 1989, 158; Jenkins, Wald, and Pittenger 1986). These perspectives are mutually supporting.

The relation of being a part of is a type of thematic relation and is especially important. Part-whole relations are given in perception along with similarity relations. We learn to form powerful semantic networks from is a part of and is a kind of. “A pear is a kind of fruit which is a part of a tree which is a kind of plant which (with others) is a part of the biosphere.” Parts are natural units of form and natural units of function. Grouping objects according to perceptually salient common parts may engender the child’s transition from classifications (of artifacts, procedures, and biological kinds) according to appearances to classifications according to functions (Tversky 1989, 983–95; see also Keil 1989, 104–9, 111–15, 166–72). Moreover, conceiving of things as systems would surely be impossible without a prior grasp of part-whole relations; similarity relations are not sufficient.

Psychologists and philosophers have given much more attention to the role of similarity in concept formation and organization than to the role of thematic relations. Similarity is the wellspring of conceptual thought. We should note, however, that Rand, for one, was not oblivious to the influence of thematic relations. “The distinguishing characteristics of furniture are a specified range of functions in a specified place (both are measurable characteristics). . . . The concept furniture involves a relationship to another concept . . . which has to be grasped before one can grasp the meaning of furniture: the concept habitation.” (Rand 1990, 22–23; see also 264–67.)

[...]

I think "thematic concept" is not a well-defined notion, which may explain why you are resisting it, though it may have some use. An alternative is to consider Ayn Rand's category of concepts of consciousness which she calls composite concepts. (ITOE 37a) Concepts such as "system," "state of affairs," "event," "condition," "context," "domain," etc. are composite concepts. They are concepts not of existents but of conscious POVs of existents; they conceptualize the awareness of facts of existents. Those related collections of things in the so-called thematic concepts--if they are concepts at all--may be classified as concepts of consciousness of this composite type with the element of purpose as the essential characteristic.

A dog can perceive everything going on in a span of time, but it will not see a meteor shower, birthday party, a wedding, a waltz, a battle, or an election.

In the same way that "conceiving of things as systems would surely be impossible without a prior grasp of part-whole relations," so conceiving of men as husbands would be impossible without a prior grasp of marriage relations. This has nothing to do with the part-whole relation being a "thematic" relation--whatever that is. It is a matter of being aware of such relations as facts. That is, it is not the similarity relations among existents per se that are sufficient in forming "system" or "husband," but it is similarity relations among (implicit) facts of existents that are sufficient to form these concepts of consciousness.

—Identity and Definition

[...]

There is much evidence to suggest that preschoolers typically contrast objects in terms of holistic, dimensionally nonspecific relations of magnitude. Objects intense in size and color are grouped together and segregated from objects not intense in both size and color. It is moreness and lessness across both dimensions that matter for these young children. They are observed trying to seriate objects on two dimensions at once. Quite possibly, they have not only notions of global magnitude polarities, but notions of dimensionally undifferentiated directions of difference. The preschooler’s understanding of global magnitude, however, does not entail an understanding that greater than and less than are necessarily opposing directions of difference. That understanding comes later, with an understanding of the ordering of values along single dimensions (Smith 1989, 165–72; Halford 1984; Chapman and Lindenberger 1988; Minsky 1985, 99–107, 149, 241).

The formation of concepts according to Rand’s formula of measurement omission requires a dimensional understanding of isolated attributes. The dimensions must be accessible but might be scalable only ordinally (Rand 1990, 31–33, 14–15). A child knows size as a dimension when he regards big and little as attributes of a single kind; part identities have then become organized by dimensional kind. He knows size as an ordinal dimension when he regards bigger and littler as necessarily opposing directions of difference. Preschoolers have only a very incomplete and fragmented understanding of these quantitative relations. They do have the beginnings of such understanding (Smith 1989, 168–72; Gelman and Gallistel 1986, 160–67), and perhaps there is enough in some of the preschooler’s domains of knowledge to begin to form concepts along the lines of Rand’s formula.

It is doubtful, though, that preschoolers could hold the full-blown Randian form of concepts; they cannot yet view numbers algebraically. (Could they nonetheless view different values along some dimensions as variables?) It is doubtful, furthermore, that the preschooler’s concepts engage universals full-force; they do not yet realize that counting numbers are endless (Gelman and Meck 1983, 357–58).

[...]

I wonder if a sample of preschoolers in a Montessori-like environment would yield different results. The open question is whether it is a neuro-physiological development or else a psycho-epistemological development that enables preschoolers to differentiate dimensional aspects of identity, as corresponded to man's 2nd stage of awareness. (ITOE 6b) From Rand's theory, I would predict that preschoolers with proper sensory training at home or in daycare would shine in their understanding of quantitative relations.

As for their understanding of counting numbers being endless, that too is an open question. A proper understanding of infinity requires a sufficient vocabulary for introspection (ITOE 20c, 76d) It would seem therefore that it is the degree of precision in forming simple concepts that would enable the preschoolers to reach "infinity" as a concept of method. And this development is a matter of psycho-epistemology, specifically, verbal training, and not a matter of neuro-physiological development.

—Identity and Definition

[...]

The shift from conceiving in terms of characteristic features to conceiving in terms of defining features can be interpreted as a shift from formulation according to relatively atheoretical similarities and conjunctions to formulation according to more theoretical relations. We seek defining features, and we seek theoretical relations, especially causal relations, which yield them (Keil 1989, 34–57, 268–81; on the complexity of essence and causation in biological systems, see Oyama 1985, 10–23, 137–39.)

[...]

Why do we seek defining features over and above characteristic features? I would suggest the explanation to be the psycho-epistemological need for efficacy in mental operations. (NB TPOSE2 72d) After all, the standard of mental health is "appropriate mental functioning." (TVOS 40) I think the inner sense of mental chaos is a "painful," albeit volitional, incentive for us to seek conceptual clarity.

Remarks

[...]

Let me use one of my longer phrases from the Introduction of “Capturing Concepts” in a sentence. “This computer program selects the prime numbers among the counting numbers from 1 to 1000.” I maintain that the italicized phrase marks a definite concept. It is the particular rule according to which the particular set of numbers is selected. This phrase states the essence of its concept, and its concept is nothing but that essence. Each of these particular primes has other characteristics besides being a prime, but being prime is one of the fundamental characteristics of each. I notice that routine use of the phrase does make use of the concept ever faster; I mean I notice that about mathematics-talk in general.

“Gather things to take along on vacation beside the door to the garage.” Here the phrase states the essence of its concept, but that characteristic of the collected items is not part of the fundamental character of those items. In this case, routine use does not seem likely to greatly speed up concept-access. Substituting the phrase vacation-items for the longer phrase surely does.

[...]

I side with Ayn Rand here in thinking that the phrase "the prime numbers among the counting numbers from 1 to 1000" is not a concept. It is a qualified instance of a concept. (ITOE 23c) It may form a temporary mental unit, but it is not a concept in accordance with Rand's Razor. (ITOE 72b)

- - -

This article is a good elaboration of the tracing of the development of our human form of cognition that Rand spent all but four sentences on. (ITOE 6b)

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Thom,

Thank you for your reflections on “Capturing Concepts.”

I have noticed that definitions of thought tend to be quickly circular. My good dictionary tells me that thought is: the act or process of thinking; cogitation. Turning to cogitation: thoughtful consideration. Turning to think, I gain a little ground: to exercise the power of reason; to conceive of ideas, draw inferences, and use judgment.

I like Rand’s definition of thought that you noted: a purposefully directed process of cognition (also). Yes, the cited writers on thought without language, such as the cognitive psychologists who investigate thinking in the pre-linguistic child, mean thought in that usual way of Rand’s definition. We can let the genus cognition be as in my dictionary: 1. The mental process or faculty by which knowledge is acquired. 2. That which comes to be known, as through perception, reasoning, or intuition; knowledge. (Well, reservations about that intuition part: A, B.)

Rand’s differentia for the concept thought is good, although it might be made better with addition of clauses to capture further the distinctive character of the cognition we mean by thought. I should mention that cognition has also been used as synonymous with thought, so not including any other mentality such as perception. Under the usage in which cognition means exactly thought, we can find insight into the latter in explications of the former. I’m thinking of John Haugeland’s 1985 Artificial Intelligence: The Very Idea (MIT).

In this work, Haugeland takes cognition to be “more or less rational manipulations of complex quasi-linguistic symbols” (228). The “more or less” is meant to qualify only the word rational in that definition; rationality comes in degrees. This understood, we may say: cognitions (thoughts) are rational manipulations of complex quasi-linguistic symbols.

I should mention, at the risk of belaboring the full context: To say that an item is a symbol is to make a statement not about the item (the token); whether the item is a symbol is not something that is carried around by, or determined by, the item itself. To say that an item is a symbol is to say something about the interpreter, about the sort of representational work being done by the interpreter using the item. So cognition that is thought requires interpreters. Interpretation is mentality and awareness beyond basic awareness. In my own compositions, I use the word comprehend in connection with conceptualization or thought, where I would be using apprehend in connection with perception. Mention of comprehension brings us to an important point about the distinctive character of thought: it requires understanding.

Returning to Haugeland 1985: “A quasi-linguistic representation must be a legal symbol in a symbolic system: a complex interpreted token, whose meaning about the world is a function of its syntax and the separate meanings of its parts” (265n12). This would be, I notice, a more advanced level of representation than the child makes with her first word (more on this within a later, major post to this thread), and is significantly more narrow than what I (and the researchers of thought without language) would count as thought.

The word rational in Haugeland’s definition qualifies manipulation. So, cognition that is thought sits in rationality.

Haugeland was inclined, at least as of 1985, to adopt the assumption that cognition (thought) and mental imagery are different mental faculties that interact only through a well-defined input/output interface (228). With that same genre of segregation, but with more certainty, he would segregate sensation and cognition (235–36).

He was inclined to also segregate “visceral,” passionate reactions (e.g. fright, rage) from cognition, but under a more subtle pattern of segregation. “It could be that passions are fundamentally compound, with one component rooted in mammalian physiology, another allocated to the faculty of sensation proposed above, and a third being genuinely cognitive. . . . The cognitive and noncognitive components are segregated and interact (bidirectionally) only through suitable input/output channels” (236). Haugeland suggested that a similar component-scheme might apply to emotions (e.g. fear, anger) and for senses of merit. He was unsure whether his component-scheme would work for general, diffuse moods.

Concerning interpersonal feelings (e.g. devotion, friendship, hatred), Haugeland thought that we must bring in also the ego/person of beings having a life to fill and to devote (237). “Actual current [ego-involved] feelings (such as embarrassed twinges, vicarious excitement, and the like) may be essential factors in real-time understanding. People do get involved in what they hear, and their own reactions affect the listening—what they notice, how they conceptualize, what it reminds them of, and so on” (240). He argues “against the segregation of self and intellect on the grounds that real-time ego involvement can be an integral factor in the process of understanding ordinary discourse. . . . Everyday conversation is fraught with life and all its perils; the listener’s involvement goes far beyond common knowledge and self-image” (244).

This is good thinking about thinking. As you will have gathered, I would have the concept cognition be broadened somewhat from Haugeland 1985. Then the concept thought would be broader too. But the elements pondered by Prof. Haugeland are certainly important in the core of our concept of thought; likewise is the merit of my dictionary definition of think above.

I dare not get into it just now, but I will at least leave a teaser from the parallel-distributed-processing researchers. In their Semantic Cognition: A Parallel Distributed Processing Approach (MIT 2004), Timothy Rogers and James McClelland write: “A slightly more general idea is that thinking is a kind of mental simulation, not only encompassing internally formulated propositions or sequences of discrete game-board configurations, but also including a more continuous playing out of imagined experience. This perspective . . . seems to us to be quite a natural way of thinking about thinking in a parallel distributed processing framework” (372–73).

A note about my opening line, “Concepts are thoughts,” then I’ll close this post. In the third paragraph I go on to say “To possess a concept is to possess the ability to employ the concept’s rules for identification of its referents.” In his New Essays on Human Understanding, Leibniz writes: “Thoughts are actions, whereas items of knowledge (or truths), in so far as they are within us even when we do not think of them, are tendencies or dispositions; and we know many things which we scarcely think about.” Concepts are both ways, actions at times, waiting actions at other times.

Thom, I want you to know that I remember your questions that I have yet to answer. I remember—with the help of this written medium—all the questions participants have asked me, which I hope to answer, but have yet to answer. That I remember them, that they are so delicious, and that I want to tackle them, this is my little curse and my big blessing.

Thought

Edited by Stephen Boydstun
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Concerning Childhood Concepts (From Objectivity, after “Capturing Concepts”)

—From “Induction on Identity” (V1N2 38–40)

Jean Piaget (1954) concluded from his investigations that infants first acquire a notion of enduring objects at nine months of age. Until then, if a toy attractive to the infant were covered with a cloth, the infant would make no attempt to lift the cloth and grasp the toy, even though she were capable (after the fifth month) of performing each of these actions. Piaget concluded that, until the ninth month, the infant does not regard the toy as an enduring entity that continues to exist while not in view; only after the ninth month does the infant begin to infer the continued existence of objects.

Piaget’s conclusion was consistent with his view, and that of traditional empiricists (e.g. Helmholtz 1885), that comprehension of a world extending beyond immediate sensory experience is the product of a long process of visual and manual exploration. From the fifth month to sometime in the second year, the infant attempts to manipulate what she sees and to see what she manipulates. These explorations were thought to lead to elementary comprehension of an objective enduring world.

Piaget’s observations have been reconfirmed many times, but Piaget’s interpretation is now widely questioned. Infants younger than nine months may fail to lift the cover and grasp the toy not because by lack a notion of enduring objects, but because they are not yet able to coordinate such a means-ends sequence (Baillargéon 1986, 38–39). It is likely that this inability is due to immaturity of the frontal cortex (Diamond 1989). Recent experiments, not demanding coordination of means-ends-sequences, indicate that infants as young as six months (Baillargéon 1986), even four months (Baillargéon 1987), understand not only that objects continue to exist when not seen, but that moving objects continue along trajectories when not seen and that those trajectories could not be through other solid objects. Perhaps this is the most primitive form in which we grasp the principle of noncontradiction (see also Peikoff 1985).

Infants four months old can determine whether two objects (rings) are connected by a solid (but occluded) link through bimanual grasping and displacement of the two objects They can discriminate visually (without touching) which of two assemblies, linked rigidly or elastically, they previously explored haptically. Object perception, even in the earliest phases of our development, seems to be mediated by relatively central mechanisms; haptic and visual discriminations are coordinated even before the onset of active manual-visual explorations (Streri and Spelke 1988; Spelke 1989). Notice, “counter to the views of Quine (1960) and others, that the organization of the world into objects precedes the development of language and thus does not depend upon it. I suspect, moreover, that language plays no important role in the spontaneous elaboration of physical knowledge” (Spelke 1989, 181).

—From “Induction on Identity” (V1N3 9–10)

By four months the infant has comprehended that solid objects are impenetrable; two cannot occupy the same space at the same time (Baillergéon 1987, 1986). This is part of what we mean in ordinary parlance by the substantiality of an object. The infant soon has experience of the pliability or rigidity of solid objects. She experiences their inertia and their weight (Mounoud and Bower 1974). These are all aspects of substantiality. Surely the idea of substance has taken root once the infant has apprehended the elementary substantialities of objects.

Mention should be made here of another aspect of material substance that seems to be readily available in perception: materiality. One can perceive and contrast solid objects with nonsolid stuff such as clay, sand, or liquids. Evidently, the prelinguistic child makes a categorical distinction between solid objects and nonsolid stuff. These early ontological categories guide the learning, at about two years of age, of count nouns and mass nouns and their appropriate syntax (in a language such as English, which quantifies differently over count nouns, e.g. a table, and mass nouns, e.g. a glass of water. If a speaker seems to be talking about a present solid object, the child concludes that the word refers to individual objects of the type present. If a speaker seems to be talking about some present nonsolid stuff, the child concludes that the word refers to portions of stuff of the type present (Soja, Carey, and Spelke 1991).

The child will be about eight years old before she has a secure concept of materiality. Until then the child will tend to interpret “made out of” as “constructed from” and will rely on the perceptual properties of large-scale chunks of a material in judging kind of material. Until then the child will not typically interpret “made out of’ as “is a constituent of” and will not reason that materials, such as wood, remain the same kind of stuff even when they are ground up (Smith, Carey, and Wiser 1985).

[see also ITOE 16; Li, Dunham, and Carey 2009; Millikan 2000.]

—From “Induction on Identity” (V1N3 12–13)

By the time one were four years old (earlier, by Macnamara 1986, 147–49), one had come to rely on underlying identities of the objects of perception. In identifying kinds of objects, especially natural objects, one had begun to rely not only on properties presently apparent in perception, but to ask about presently unapparent properties. One had begun to seek the kind of thing a thing is and to use knowledge of kind, of categorical identity, to override obvious characteristics on their misleading occasions (Markman 1989, 95–135; Keil 1989, 195–215, 249–53).

Children were taught a property of one object and a different property of a second one. They were shown a third object that looked much like one of the first two but was given the same category label as the other. For example, children saw a tropical fish and were told that it was a fish and that it breathes underwater. They saw a dolphin and were told it was a dolphin and that it pops out of the water to breathe. They then had to decide how a second fish, a shark that looks like a dolphin, breathes. Children relied on the shared category to promote inductions even in this stringent case where perceptual similarity would lead to a different conclusion. Moreover, [studies showed that] children’s inferences are based on common category membership and not just on identity of labels. (Gelman and Markman 1986, 203)

—References—

Baillargéon, R. 1986. Representing the Existence and the Location of Hidden Objects: Object Permanence in 6- and 8-Month-Old Infants. Cognition 23:21–41.

———. 1987. Object Permanence in 3.5- and 4.5-Month-Old Infants. Developmental Psychology 23:655–64.

Diamond, A. 1989. Differences Between Adult and Infant Cognition: Is the Crucial Variable Presence or Absence of Language? In Weiskrantz 1989.

Gelman, S.A., and E.M. Markman 1986. Categories and Induction in Young Children. Cognition 23:186–209.

Helmholtz, H. 1962 [1885]. Treatise on Physiological Optics. J. Southall, translator. New York: Dover.

Keil, F.C. 1989. Concepts, Kinds, and Cognitive Development. Cambridge, MA: MIT.

Macnamara, J. 1986. A Border Dispute: The Role of Logic in Psychology. Cambridge, MA: MIT.

Markman, E.M. 1989. Categorization and Naming in Children. Cambridge, MA: MIT.

Mounoud, P. and T.G.R. Bower 1974. Conservation of Weight in Infants. Cognition 3(1):29–40.

Peikoff, L. 1985. Aristotle’s ‘Intuitive Induction’. The New Scholasticism 59(2):185–99.

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

Quine, W.V.O. 1960. Word and Object. Cambridge, MA: MIT.

Soja, N.N., Carey, S., and E.S. Spelke 1991. Ontological Categories Guide Young Children’s Inductions of Word Meaning: Object Terms and Substance Terms. Cognition 38:179–211.

Spelke, E.S. 1989. The Origins of Physical Knowledge. In Weiskrantz 1989.

Smith, C., Carey, S., and M. Wiser 1985. On Differentiation: A Case Study of the Development of the Concepts of Size, Weight, and Density. Cognition 21:177–237.

Streri, A., and E.S. Spelke 1988. Haptic Perception of Objects in Infancy. Cognitive Psychology 20:1–23.

Weiskrantz, L., editor, 1989. Thought without Language. Oxford: Clarendon.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

On childhood concepts, other writers in Objectivity are these:

Merlin Jetton – Childhood Schemata according to Ecological Psychology

V1N3 71–72

Jay Friedenberg – Development of Object Concept and Awareness of Self

V1N5 32–34

Paul Vanderveen – The Child’s Development of the Concept of Mind

V1N6 1–33

Merlin Jetton – Development of Temporal Concepts

V2N2 83–85

Kathleen Touchstone – Development of the Child’s Concept of Number

V2N4 121–23

Merlin Jetton – Work of Piaget, Vygotsky, and Keil

V2N6 100–124

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Rand on Knowledge

Rand’s definition of knowledge is: “a mental grasp of a fact(s) of reality, reached either by perceptual observation or by a process of reason based on perceptual observation” (ITOE 35).

Perceptual Observation

The following . . . are some capabilities in the typical infant prior to the acquisition of language: By 5 months, she expects that an object endures while the lights are out; she reaches for objects in the dark. By 6 months, she can discriminate an object in the dark by its sound associated in light; she makes the type of reach appropriate for this object. By 9 months, she shows awareness of her movement in a mirror; she turns to locate reflected objects in real space. By 12 months, she uses mechanical aids to extend her reach.

Suppose it is correct to say that this human infant knows that objects of various sorts endure in the dark; that mirrors show particular objects in real space in front of the mirror; and that some objects are beyond her reach and can be reached with a mechanical aid. Then is it also correct to say that the pre-linguistic infant believes those facts?

Do we have perceptions without knowledge? Is knowledge an essential ingredient of human perception? Is belief an essential ingredient of human perception? (See John Heil’s Perception and Cognition, chps. 5-6; David Kelley’s The Evidence of the Senses, pp. 197-228. [also])

I take it that prior to language acquisition any knowledge or beliefs integral to perceptions are held in schematic forms, rather than in conceptual forms. (See, in Objectivity: “Capturing Concepts” V1N1, pp. 16-18; “Imagination and Cognition” V1N3, pp. 69-78.)

There seems to be no viable way to pry apart knowledge and belief even in the non-conceptual comprehension of the world. It seems, indeed, that knowledge entails belief as a part of itself. To use an example of Rand’s: one can experience hunger before becoming capable of identifying the feeling as hunger, as requiring food for satisfaction. Rand’s language in saying that one can have knowledge through a perceptual observation seems right. The experience of hunger is not an observation, but cognizance that what one is experiencing is hunger is a perceptual observation. And it is a belief. (See also Harold Brown’s Observation and Objectivity, chp. 4.)

Reciprocating Perceptions and Conceptions

In the note “Perception and Observation,” I had asked: “Do we have perceptions without knowledge? Is knowledge an essential ingredient of human perception?” Rand had some ideas on that.

“A mind’s cognitive development involves a continual process of automatization. For example, you cannot perceive a table as an infant perceives it—as a mysterious object with four legs. You perceive it as a table, i.e., a man-made piece of furniture, serving a certain purpose belonging to a human habitation, etc.; you cannot separate these attributes from your sight of the table, you experience it as a single, indivisible percept—yet all you see is a four-legged object; the rest is an automatized integration of a vast amount of conceptual knowledge which, at one time, you had to learn bit by bit. The same is true of everything you perceive or experience; as an adult, you cannot perceive or experience in a vacuum, you do it in a certain automatized context—and the efficiency of your mental operations depends on the kind of context your subconscious has automatized.” (“The Comprachicos” 1971)

Critical Belief

Rand wrote that the higher animals “possess the faculty of retaining sensations, which is the faculty of perception. A ‘perception’ is a group of sensations automatically retained and integrated by the brain of a living organism, which gives it the ability to be aware, not of single stimuli, but of entities, of things. An animal is guided, not by immediate sensations, but by percepts. Its actions are not single, discrete responses to single, separate stimuli, but are directed by an integrated awareness of the perceptual reality confronting it. It is able to grasp the perceptual concretes immediately present, and it is able to form automatic perceptual associations” (OE, 1961, 19).

Nathaniel Branden maintained that higher animals can engage in perceptual abstractions (Mortimer Adler’s term), which is recognition of a number of sensible particulars as of the same kind. The animal does not have the further, human conceptual power, which entails “identifying explicitly of what the kind consists” (Psy of S-E 1969, 30).

Leonard Peikoff remarked that perceptual similarities are seen by animals, but humans go beyond that. We isolate similar concretes and form concepts standing for an unlimited number of concretes (Phil of Obj, Lecture 4, 1976).

David Kelley wrote that in judging of an object, which one is perceiving, that it is a such-and-such, one “classifies the object on the basis of similarities that have been explicitly isolated and named” (ES, 1986, 219).

Rand wrote that “an animal has no critical faculty; he has no control over the function of his brain and no power to question its content. To an animal, whatever strikes his awareness is an absolute that corresponds to reality—or rather, it is a distinction he is incapable of making: reality to him is whatever he senses or feels” (FNI, 1961, 17). She remarked orally that “an animal does not have the capacity to isolate critically the fact that there is something and he is conscious of it” (IOE, c.1970, 246). An animal lacks the human ability “to apply introspection to the processes of one’s own consciousness and check them” (256).

In the preceding statements, notice these phrases especially: identifying explicitly /// isolate similar concretes /// explicitly isolated /// isolate critically the fact that there is something.

In their Scientific American article “The Biological Basis of Learning and Individuality” (Sep 1992), Kandel and Hawkins distinguish between two kinds of learning found in animals with nervous systems. Higher animals, including humans, learn in both ways. One kind of learning is called implicit, the other is called explicit.

Habituation, sensitization, and classical conditioning are forms of what is called implicit learning. Such learning “is slow and accumulates through repetition over many trials. It often [viz., classical conditioning] involves association of sequential stimuli and permits storage of information about predictive relations between events” (80). In contrast, “explicit learning is fast and may take place after only one training trial. It often involves association of simultaneous stimuli and permits storage of information about a single event that happens in a particular time and place; it therefore affords a sense of familiarity about previous events” (80). Explicit learning requires consciousness. Explicit learning evidently occurs only in vertebrates; it requires structures in the temporal lobes.

Within the broad category known as explicit learning, there are degrees of explicitness. In Explaining Behavior, Fred Dretske characterizes those degrees: Consider a rat that has learned through operant, or instrumental, conditioning that to obtain food it should press a bar. The rat could reasonably be said to be guided in its behavior by a belief that is relatively implicit. An implicit belief (explicit, but relatively implicit) is applied in fairly narrow circumstances. A fully explicit belief “can enter into combinations with other beliefs to generate a wide range of different actions” (1988, 118).

Prior to the acquisition of language, our beliefs lie in the more implicit zones of explicit learning and belief. Even at the relatively implicit levels of belief guiding a rat’s operantly conditioned behavior, it is possible to err and correct, although it be in a very local way. Nevertheless, I decline to call such beliefs knowledge. I incline to reserve knowledge for beliefs attaining truth where those beliefs are interconnected within and improvable by a critical consciousness holding them. This lies in the more fully explicit zone of explicit belief, a zone not far from linguistically held beliefs of an intact human mind.

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Rand on Knowledge

Rand's definition of knowledge is: "a mental grasp of a fact(s) of reality, reached either by perceptual observation or by a process of reason based on perceptual observation" (ITOE 35).

I find "a mental grasp of a fact(s) of reality" quite abstract. I prefer Korzybski's definition of knowledge which is that the only thing we can know is structure, verbal and non-verbal. We perceive structure and we describe and infer structure verbally.

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Rand wrote that "an animal has no critical faculty; he has no control over the function of his brain and no power to question its content. To an animal, whatever strikes his awareness is an absolute that corresponds to reality—or rather, it is a distinction he is incapable of making: reality to him is whatever he senses or feels" (FNI, 1961, 17). She remarked orally that "an animal does not have the capacity to isolate critically the fact that there is something and he is conscious of it" (IOE, c.1970, 246). An animal lacks the human ability "to apply introspection to the processes of one's own consciousness and check them" (256).

I believe Korzybski said the same thing in different words. He said that man and animals both abstract information but an animal does not and cannot know that it abstracts - ie. it's abstractions are reality. He calls this uniquely human ability consciousness of abstracting and it is the central principle in his theory of sanity.

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Thomas, thanks for your thoughts in #15 and #16.

Some related remarks from Thomas are these:

One

“‘Knowledge’ represents similarity of structure between our language (higher order abstractions) and our perceptions (lower order abstractions).” [See also; responses a, b, c, d, e.]

Two

“I think it would help to make a sharp distinction between ‘concept’ and ‘word’. The concept lives in one's brain, as a visualization or neural net, or something. The word refers to the concept. So repeated pointing at the object (tree) coupled with repeated verbalizing ‘tree’ begins the building of associative structures in the brain that connect the lower order nervous abstractions (concepts) to the higher order verbal abstractions (words).”

Three

“This ‘conceptual faculty’, which I call abstraction process, continues with linguistic abstraction which in turn influences, or sharpens, conceptual abstraction. It is much easier to 'see' something when someone ‘tells’ us what to look for.”

Four

“I keep seeing this confusion between concepts and words. A concept is an imagination, and we can not know what someone is imagining. Words, on the other hand, are things that exist outside our nervous system. Words cause imaginations in other people and, if all goes right, they may imagine the same thing we are.

“Language can be thought of as an extension of the nervous system which enables similar processes to be shared with others possessing the same faculty.”

Five

“We know from science that ‘reality’ is in a constant state of change, at microscopic levels. What we sense as ‘properties’ are merely abstractions produced by our nervous systems, a kind of invariance under transformation of external stimuli to neural stimuli. Scientists go about their business by carefully recording and measuring their abstractions and comparing them to other scientists. They build theories (higher order abstractions) and other scientists can start with these and recreate the lower order abstractions independently and so we begin to get a kind of ‘objectivity’ which really amounts to invariance of abstractions by many individuals.”

Six

“I will admit that ‘reality’ has some structure—at least it seems a reasonable assumption, BUT, we can only learn of this structure through our perceptions—which are always incomplete. In science there is a cycle—we produce a theory which allows us to compare some experimental results with some calculated ones. If there is some discrepancy we know the structure is incorrect and we modify it until it works. At no point do we ever know the ‘true’ structure, we only ever have a working structure. As time goes on new data, which becomes available do to extra-neural devices, will invariably make a working theory not work anymore. These extra-neural devices, like telescopes etc., increase the amount of structure we perceive but it is still, and always will be, incomplete.”

Seven

“I don’t use the word ‘concept’ because I find it ambiguous and I replace it with ‘visualization’ or ‘image’. We cannot sense an electron, its existence is postulated. This does not mean there is no connection between our senses and these postulated things it means the connection is more complicated than for something we can sense, like a pencil. If I try to describe a pencil to you, you could conceivably recognize one from a group of objects but not so with an electron. My description will come from mathematical physics and will not help you to ever recognize one.

“Herein lies the difference between what F. S. C. Northrop describes as ‘concept by intuition’ and ‘concept by postulation’. . . . [note].

“As I said, I prefer ‘visualization by intuition’ and ‘visualization by postulation’ so as to emphasize that this exists in one’s nervous system as some sort of ‘neural network’. When I describe an object which is ‘sensible’ (intuitive) you may take this description and visualize in your nervous system. But with a non-sensible object my description [is] a theoretical construct and only indirectly visualizable and so of a completely different character and needs to be evaluated by different standards.

“For a person who has never looked in a microscope and seen a cell the term ‘cell’ would represent a ‘visualization by postulation’ to them but to a biochemist it would represent a ‘visualization by intuition’. This brings up an interesting point that these formulations can be relative to observer and not absolute, which could explain a good deal of miscommunication.”

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Structuralism in Philosophy of Mathematics

Structural Realism in Science

Rand’s Realism

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Concepts

Debating Concepts

Knowledge

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Third Section of “Universals and Measurment”

(2004 – Journal of Ayn Rand Studies V5N2)

Genesis

Rand takes concepts to be mental products of a mental process "that integrates and organizes the evidence provided by man's senses" (1970, 90). She gives three definitions of concepts. (1) Concepts are mental integrations of "two or more perceptual concretes, which are isolated by a process of abstraction and united by means of a specific definition" (1961, 20). More generally in terms of the data processed, (2) concepts are mental integrations of "two or more units which are isolated according to a specific characteristic(s) and united by a specific definition" (1966, 10). Finally and most deeply, (3) concepts are mental integrations of "two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted" (ibid., 12).

The "two or more perceptual concretes" spoken of in definition (1) are the elementary type of "two or more units" spoken of in (2) and (3). Rand proposes, in a general way, a developmental intellectual ascent from apprehending the world only in terms of perceptual concretes and actions they afford to apprehending that same world in terms of units in classes. That ascent is a refinement and sophistication in our apprehensions of existents: an ascent from apprehending existents as entities to apprehending them as identities to apprehending them as units (1966, 6–7; 1969, 180–81).

Rand's measurement-omission analysis of concepts could be correct even if her account of their genesis were incorrect. In particular, her analysis could be correct even if her proposed developmental intellectual ascent were incorrect. I contend that her general proposed ascent is correct. I shall give a thumbnail sketch of the developments I think should be seen as tracing an entity-identity-unit ascent in the apprehension of existents.

Continued below—

—Elaboration of Identity

—First Words, First Universals

—Analytic Constraint

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—Elaboration of Identity

For the first day or two after birth, existents for us are plausibly only entities. Such would be the occasions of Mother's face or voice [33]. Very soon existents become for us not mere entities, but identities, particular and specific [34].

At 20 days, there is expectation of the reappearance of a visual object gradually occluded by a moving screen; here is rudimentary particular identity of visual objects (Bremner 1994). At 4 weeks, there is some oral tactile-to-visual transfer of object features, without opportunity for associative learning; here is rudimentary specific identity (Meltzoff 1993). At 5 weeks, there is recognition memory of color and form; here is growth of specific identity. At 8 weeks, there is onset of attention toward internal features of patterns and onset of smooth visual tracking, and there is hand tactile-to-visual transfer of object features; here is growth of particular and specific identity. At 10 weeks, there is expectation that one visual solid object cannot move through another (Bremner 1994). By 3 months, visual tracking is becoming anticipatory (Johnson 1990); there is visual fill-in of invisible parts of objects (Bremner 1994); visual objects are being identified as separate using various static-separation and motion traits (Spelke and Van de Walle 1993); there is categorical perception of objects and events (Quinn 1987). At 4 months, haptic apprehensions of shapes can be transferred to the visual mode (Streri and Spelke 1988); visual solid objects are expected to endure and retain size when occluded for a brief period (Bremner 1994); objects are expected to fall if not supported (Needham and Baillargeon 1993).

The infant's world of entities-identities will continue to elaborate. Units are not yet. At 6 months, the infant will have some sensitivity to numerosity; will be able to detect numerical correspondences between disparate collections of items, even correspondences between visible objects and audible events; and will be able to detect the equivalence or nonequivalence of numerical magnitudes of collections (Starkey, Spelke, and Gelman 1990). At 7 months, still without words, the infant distinguishes global categories (e.g., animals v. vehicles) which will later become superordinates of so-called basic-level categories (e.g., dog v. car) yet to be formed (Mandler and Bauer 1988; cf. Rand 1969, 213–15). By 12 months, the infant reliably interprets adult pointing, looking from hand to target (Butterworth and Grover 1988).

Continued below—

—First Words, First Universals

—Analytic Constraint

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—First Words, First Universals

At around 12 months, the infant puts first words, single-word utterances, into her play. Words at this stage are used only in play, not for communication, which is still accomplished with cries, gestures, and gazes (Bremner 1994, 249–51; Nelson 1996, 105, 112). An infant in my family, just past his first birthday, uses the word ba. He says it quietly to himself whenever he sees or is handed a spherical ball; he does not say his word when the ball is a football. We should not suppose too hastily, I should note, that his word ba refers simply to the spherical ball with which he is engaged. At this first-words stage, his utterance may designate the object as component of his whole activities that go with those objects (activities like training the adults to fetch) (Bremner 1994, 251–52; Nelson 1996, 97, 109–10, 115, 227–29; Bloom 2000, 35–39).

By 14 months, the toddler points to indicate items (Butterworth and Grover 1988). By 16 months she spontaneously groups objects of a single category (Bremner 1994, 173). In another month or two comes the naming explosion, naming of objects especially (Nelson 1996, 111–15; Macnamara 1986, 144–45; Bloom 2000, 91–100). (That there really is such a dramatic burst in the rate of word acquisition at this time is disputed; Bloom 2000, 39–43.)

By that time, at 17 or 18 months, the toddler is using single words to refer (Macnamara 1986, 56–57). These words (50 to 100 words) include demonstratives such as that, common nouns such as ball, and proper names such as Star, say, to refer to a particular ball. The use of common nouns and proper names in single-word reference indicates certain competencies of identification, certain representational comprehensions of identities specific and particular. The representational comprehensions of specific and particular identity that are evidently coming into operation at this stage are class-membership relation, individuation within a class, and particular identity over time.

Skillful reference for the utterance ball indicates that the beginning speaker has some working principles for deciding whether a given item qualifies as being in the category ball. Then such a speaker has some operational sense of class-membership relation (ibid., 61–62, 72–74, 124–28, 148–49, 152–56). Ball is a count noun. Although the beginning speaker does not yet possess the principles of counting, not even implicitly, she has some working principles of individuation within a class, some principles for holding in mind individual balls as distinct from one another (ibid., 128–30) [35]. Moreover, ball refers to any individual ball as a distinct individual over time (ibid., 59–60, 130–36, 141–42, 152). Finally, the name Star is attached to a particular one of those individual balls over time (ibid., 55–62, 71–83) [36].

I suggest that even at the single-words stage of language development, the toddler has entered the conceptual level of consciousness in Rand's sense of that level. The utterance ball refers, and marks a concept, already at this stage.

One problem for that conjecture is the following. Rand required that the items falling under a concept be united with a specific definition. [see (1) and (2) above and Rand 1966, 48–50.] But at the single-words stage of development, the toddler cannot yet form two-word expressions. That competence will not be attained for another six months or so, at around 24 months of age [37]. Not yet having two-word expressions, she cannot yet form a sentence, cannot yet use words in assertive sentences. Without propositions one is without defining propositions, hence, without definitions. Then at the single-words stage of development, the items falling under a "concept" cannot be united by a specific definition. Then it would seem one does not yet possess a concept in Rand's sense. I think that conclusion would be an overstatement.

For an older child or an adult, of course, "a concept identifying perceptual concretes stands for some implicit propositions" (Rand 1966, 48, 21). For a single-words toddler, no propositions can be adduced. Actions can be adduced. A ball is something that can be handled and thrown down. It bounces and rolls. These things are clearly known of balls even by the one-year-old whose first and only word is ba. The concept ball is likely held in mind in the form of image and action schemata as well as by the term ball (Rand 1966, 13, 20, 43; 1969, 167–70) [38].

There is something else, something profoundly conceptual, at hand in linguistic competence at least by the time of the naming explosion. John Macnamara concludes that having a word such as ball at this stage means having a logical principle of application. That is a surrogate for definition at this single-words stage. A principle of application is the working principle, spoken of above, for determining whether an item is or is not a ball (Macnamara 1986, 124–28) [39]. A principle of application determines class membership. That is the basic function a definition accomplishes for more advanced language users (Rand 1966, 40; 1969, 231–32).

To have an operational grasp of the class-membership relation is to have a tacit grasp of the notion of unit in the sense of a substitution unit, which is the unit for counting. That does not mean that one has yet grasped the elementary principles of counting (nor that one can put the notion of a substitution unit to work in counting). At 18 months, one has evidently gotten some working hold on the notion of a substitution unit, the notion of a simple member-of-a-class, without yet having the principles of counting. But at this single-words stage, one has taken the first step into the dual realms of the conceptual and the mathematical. With a tacit grasp of the notion of unit in the substitutional sense, "man reaches the conceptual level of cognition, which consists of two interrelated fields: the Conceptual and the Mathematical" (Rand 1966, 7). Rand was correct in thinking that "man's mathematical and conceptual abilities develop simultaneously," even though she was incorrect in thinking that "a child learns to count when he is learning his first words" (1966, 9; 1969, 200) [40].

Having ball, one is getting hold of "ball, any one." That is the membership relation and its requisite principle of application. Having ball, one is also getting hold of "some things of a class, the balls" (Rand 1966, 17–18). That is the individuation-within-class relation and principle (Macnamara 1986, 128–30). Then already at the stage of first concepts, one has beginning working principles of universal quantification (any) and existential quantification (some) [41].

Continued below—

—Analytic Constraint

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—Analytic Constraint

As we have seen, in Rand's view, in the analysis of any concept there can be found a double application for some and any: with respect to substitution units and with respect to measure values. To form our concepts, however, Rand supposes that we do not need to grasp, expressly nor tacitly, the notion of units as measure values. We discern similarities. Where there is similarity, there can be found various measure values along a common dimension, in Rand's view, but we need not know anything about such measure bases.

When we pick up a ball, our sensory systems measure it in several ways. When we perceive a similarity between two items, according to Rand's account, we are perceiving some same characteristic(s) they both possess in different measure or degree (1966, 13–14; 1969, 139–40, 143). They both possess that characteristic in some measure or degree. Items of their class possess that characteristic in some degree, but may possess it in any degree within a range of measure delimiting the class (Rand 1966, 11–12, 25, 31–32).

On which characteristic(s) does the similarity class, thence the concept class, rest? Like Ockham, Rand observed that items in a similarity class are more similar to (and less different from) one another than they are to things not in the class. A ball is more similar in various ways to other balls than it is to sticks, hands, and so forth. As we know, Rand analyzed similarity in terms of measurable dimensions, in terms of measures of dimensional characteristics. The characteristic(s) on which the similarity class and its concept ball rests, analytically and genetically, in Rand's theory, is whichever measurable characteristic(s) makes a ball measurably closer to other balls than to sticks, hands, and so forth (1966, 13–14, 21–23, 41–42; 1969, 144–47, 217, 274–76) [42].

I have addressed the defect and remedy of this measure-theoretic analysis of similarity classes and concepts in the preceding section. It remains to address the genetic aspect, which I cast as: in forming a similarity class and its concept, one is relying on (tacitly using) whichever measurable characteristic(s) makes items in that class and under that concept measurably closer to one another than to opponent items.

Rand thought, rightly I should say, that formation of any concept whatever requires differentiating two or more existents from other existents. She thought also that such differentiation requires comparative degrees of difference, measurable as such on a dimension(s) common to existents in the class and existents outside the class (Rand 1966, 13). What if Rand were right in this second doctrine? What if, in order to form any concept whatever, there had to be a dimension common to the concept class and its opponents and this had to be a dimension along which comparative closeness measurement is possible? What would that imply for metaphysics? It would imply that every concrete can be placed in concept classes whose linear measures are not only ordinal-scale, but interval- or ratio-scale as well [43].

I avoid that extravagant implication as follows: I retain Rand's assumption that formation of any concept requires differentiating two or more existents from other existents and her assumption that all concept classes are similarity classes and her measure-definitions, as amended above, of concepts and similarity. I reject the assumption that differentiation between existents included in and existents excluded from a concept class require comparative degrees of difference (beyond the comparative-difference-degree pretender that merely says a thing is less different from itself than it is different from things not itself).

Such differentiation may sometimes be based at least partly on fairly blunt sameness and difference. Spherical balls are the same with one another in that they roll regularly, and in this they are baldly different from floors. A dimension along which items in a concept class have various measure values need not be a dimension common with items in an opponent concept class.

Differentiation of existents included in or excluded from a concept class may enlist nontrivial comparative degrees of difference (or likeness). I see three forms of these. In one the comparative degrees are along dimensions common to both included and excluded existents, and those dimensions afford either ratio- or interval-scale measures. Along the dimensions of shape, a spherical ball can be distinguished from a football in that way. The sets of pairs of principal curvatures (ratio scaling) over the surfaces of spherical balls are less different from each other, from one ball's set of pairs to another ball's set of pairs, than they are from the sets of pairs of principal curvatures over the surfaces of footballs.

In light of my amendment to the measure-definition of similarity, we should allow also for a second nontrivial variety of comparative similarity. I observed earlier that hardness and tensile strength are two different measurable forms of a same characteristic (resistance to degradation under some sort of stress) that is different from the measurable characteristic (pairs of principal curvatures, which are spatial extension properties) shared by shapes. This second manner of decomposing a comparative similarity permits concepts based on comparative degrees of similarity without requiring that linear measures of the concept dimensions be anything beyond ordinal measures.

A third decomposition of nontrivial comparative similarity does not rely on shared and unshared dimensions of the relata. It relies simply on numbers of shared and unshared features [44]. Perhaps any concept based on this sort of comparative similarity can be recaptured in a more sophisticated way by ascertaining measurable dimensions on which to base the concept (Boydstun 1990, 31–33). I expect that is so. Notice, however, that the metaphysical implication drawn in the present study (uniform topological lattice structure) need not suppose that all concepts can be analyzed in terms of Rand's measurement-omission formula; only that all concretes can be placed under one or more concepts analyzable in those terms.

I have exhibited a way in which a measurement analysis of concepts can constrain theorizing about the genesis of concepts. I do not want to create the impression, however, that theory of the genesis of concepts based on observations and empirical testing cannot rightly constrain one's analysis of concepts. The analytical principles stating that all concretes can be placed in concept classes having a measurement structure and that these structures are of such-and-such characters are conjectures open to restriction through counterexamples. These conjectures of analysis are subject to reform or replacement in the face of contrary analytical and empirical results, somewhat as the General Relativity principle that freely falling bodies follow time-like geodesics of space-time is subject to reform or replacement [45].

One of the avenues for empirical confrontation of our analytical conjectures concerning concepts and concept classes is research on conceptual development. The core task I have undertaken in the present study [sections I and II of “Universals and Measurement”] has been a certain extension of Rand's metaphysics arising from her analysis of concepts (not her theory of their formation). I have not undertaken here a survey of the various ways in which empirical research on conceptual development may challenge Rand's analysis of concepts. But there is one form of challenge that is invalid, and I want to draw attention to this fallacy, which has required a long struggle for me to overcome. That is a fallacy I insinuated in Boydstun (1990, 33–34). It says that because preschoolers do not possess—not even tacitly—mathematical understanding sufficient to be forming their concepts using a principle of measurement-omission, their concepts do not bear analysis in terms of measurement-omission. That is the fallacy of confusing genesis with analysis.

Edited by Stephen Boydstun
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Notes for “Genesis”

[33] – Rand concluded from research literature as of 1966 that the sensory experience of the infant was apparently entirely “an undifferentiated chaos” and did not contain any percepts (1966, 5, 6). Subsequent research has dispelled that old vision of cognition in neonates. See Bremner (1994); Meltzoff (1993); Clifton (1992); Kellman (1995).

[34] – The distinction of particular and specific identity is mine and is as follows. Particular identity answers to that, which, where, or when. Specific identity answers to what. Every existent consists of both a particular and a specific identity (Boydstun 1991, 43–46, and 1995, 110).

[35] – The sense of implicit here is extracted from the relevant cognitive-development research literature (viz., Gelman and Meck 1983, 344). The child is said to have implicit knowledge of the counting principles if she engages in behavior that is systematically governed by those principles, even though she cannot state them. (See Note 40 for the principles.) Gelman and Meck liken this implicitness of the counting principles at this stage of cognitive development to the way in which we are able to conform to certain rules of syntax when speaking correctly without being able to state those rules. That much seems right, but there is a further distinction I want to make. The child’s implicit counting principles are being learned (and taught) as an integral part of learning to properly count aggregations explicitly, expressly. In contrast, we can (or anyway, my preliterate Choctaw ancestors centuries past could) live out our lives, speaking fine in our mother tongue, following right rules of syntax, yet without being able to state those rules; indeed, without even knowing any of the terminology of syntax. Our learning of tacit rules of syntax is not for the sake of becoming able to follow them explicitly, only tacitly.

In the present developmental discussion, I shall reserve the term implicit to indicate that an operative rule is not only tacit, but has become operative as an integral part of becoming explicitly operative. The tacit logical principles, whose acquisition according to Macnamara is traced in the text, are not implicit in my present sense.

There is, of course, another sense of implicit that I am also happy to use. That is the logicomathematical sense, which was pertinent to our analysis section. It is in that sense that we say a certain theorem is implicit in a set of axioms; Hertz’ wave equation for propagation of electromagnetic radiation is implicit in Maxwell’s field equations; an inverse-cube central force law is implicit in a spiral orbit; dimension reductions are implicit in Kolmogorov superposition-based neural networks; certain measure relations are implicit in any similarity discerned in perception; or certain measure relations are implicit in a concept class. Cf. Rand (1969, 159–62); Campbell (2002, 294–96, 300–10); Boydstun (1996, 201–2).

[36] – Drawn out into our adult expression, here is the logic tacitly put to work by the toddler at this stage: There is a unique kind (class) of which Star is a member, and any object is a ball if and only if it is a member of that kind. For any particular ball, there is a unique member of the kind ball, and as long as that member exists, it is identical (totally same) with that particular ball (Macnamara 1986, 137–39). I should say that such working interpretive principles render one’s perceptual knowledge conceptual. One has conceptual knowledge even at the single-words stage of language development.

My example of proper naming of a special ball Star is contrived for convenience of illustrating the tacit logical resource. Toddlers at this stage are likely to restrict proper names to particular (real or make-believe) animate entities possessing mentality (Bloom 2000, 130–31).

[37] – By 24 months the child is using two-word utterances such as “Mommy sit!” and “guy there” and “I know [how to do it]” (Bremner 1994, 252–53; Nelson 1996, 112, 124–25). Up to about this time, when grammar begins to develop, “words learned remain tied to their world models and do not form systems of their own” (Nelson 1996, 128). In terms of Deacon’s iconic, indexical, and symbolic levels of representation (1997, 70–83), I should say that concepts at the single-words stage are indexical representations, and these concepts will become symbolic representations with the onset of grammar. Rand’s conceptual level of representation cuts across Deacon’s indexical and symbolic levels.

All three levels of representational cognition—even the iconic level (e.g., drawing a stick man)—are active, deliberate, and constructive. I take the membership relation, which is essential for concepts, classes, and sets, to require this sort of active generation, from our first concept to our last. In this way, the membership relation is unlike perceptual relations of similarity, proximity, or containment (cf. Rand 1964, 20; Maddy 1997, 90–94, 108–9, 152n30, 172–76, 185–88).

[38] – See further Boydstun (1990, 16–18); Minsky (1974, 111–17); Johnson (1987, 23–30, 102–4); Iverson and Thelen (1999); Nelson (1996, 16–17).

[39] – Cf. Kelley and Krueger (1984, 47, 52). In saying that this tacit logical principle of application is a surrogate for a concept’s definition, I mean to say only that the tacit principle accomplishes the main function that an explicit definition accomplishes. I do not mean to say that the tacit principle is additionally an implicit definition in the developmental sense of implicit (as in Note 35). Macnamara’s tacit logical principle of application is needed just as much for concepts of things in terms of merely characteristic features as it is for concepts of things in terms of defining features (cf. Bloom 2000, 18–19).

During the first few years of speech, we evidently tend to conceive of things in terms of characteristic features. After about age 5, there is a developmental shift to conceiving of things in terms of defining features. The course of this shift, which occurs at different times in different domains of knowledge, has been partially charted by Frank Keil (1989); see Boydstun (1990, 34–37). The shift need never occur for all our concepts. [in a preliterate culture (my Choctaw ancestors again), is the shift so extensive as in our culture? See Olson (1994).] Acquiring a tacit logical principle of application is not for the sake of becoming able to conceive of things in terms of defining features.

[40] – The child has gone far beyond learning first words (roughly months 12 to 18) by the time she is learning to count. By 30 months, the basic linguistic system has become established and is fairly stable (Nelson 1996, 106). Not until around 36 months or beyond does the child have an implicit grasp of the elementary principles of counting: assign one-label-for-one-item, keep stable the order of number labels recited, assign final recited number as the number of items in the counted collection, realize that any sort of items can be counted, and realize that the order in which the items are counted is irrelevant (Gelman and Meck 1983; Butterworth 1999, 109–16).

At 22 months, a child in my family could “say his numbers.” This competence is not essentially different than being able to “say his ABC’s” (Bloom 2000, 215). Rand may have mistaken the onset of recitation of count-word sequences with onset of ability to count.

[41] – Cf. Macnamara (1986, 143); Burgess (1998, 10–11); Boolos (1984, 72).

[42] – For Ockham on comparative similarity, see Maurer (1994, 387, 389). For more on comparative difference and comparative similarity in theory of concept formation, especially in Rand’s theory, see Kelley and Krueger (1984, 52–61) and Kelley (1984, 336–45). See also Jetton (1998, 63–72) and Livingston (1998, 15–21).

[43] – Cf. Armstrong (1997, 64–65) for a related extravagance, which he boldly embraces. The extravagant implication I pose is avoided by me in one way; for another way, consider Jetton (1991).

[44] – Quine (1969, 117–23); Krantz, Luce, Suppes, and Tversky (1989, 207–22); Nosofsky (1992, 38–40).

[45] – The General Relativity principle that freely falling bodies follow time-like geodesics of space-time is subject to analytical challenges (Torretti 1983, 176–81) and to empirical tests, such as whether Earth and Moon have different accelerations towards the sun (Ciufolini and Wheeler 1995, 14, 88, 113–15). Contrast those methods of evaluating conjectures in natural science with the methods of evaluating various candidate axioms for a formal discipline such as set theory (Maddy 1997). We should expect the forms of evaluation appropriate to measurement conjectures for a theory of concepts and concept classes to lie between forms appropriate to natural science and forms appropriate to the formal disciplines of mathematics, set theory, and logic.

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References for “Genesis”

Armstrong, David. 1997. A World of States of Affairs. Cambridge: Cambridge University Press.

Bloom, Paul. 2000. How Children Learn the Meanings of Words. Cambridge: MIT Press.

Boolos, George. 1998. Logic, Logic, and Logic, edited by R. Jeffrey. Cambridge: Harvard University Press.

Boydstun, Stephen. 1990. Capturing concepts. Objectivity 1(1):13–41.

―――. 1991. Induction on Identity (Part 2). Objectivity 1(3):1–56.

―――. 1996. Volitional Synapses (Part 3). Objectivity 2(4):183–204.

Bremner, J. Gavin. 1994. Infancy. 2nd edition. Oxford: Blackwell.

Burgess, John. 1998. Introduction to Part I of Logic, Logic, and Logic, collected essays of George Boolos, edited by R. Jeffrey. Cambridge: Harvard University Press.

Butterworth, Brian. 1999. What Counts: How Every Brain is Hardwired for Math. New York: Free Press.

Butterworth, George, and Lesley Grover. 1988. The Origins of Referential Communication in Human Infancy. In Thought without Language, edited by L. Weiskrantz. Oxford: Clarendon Press.

Campbell, Robert L. 2002. Goals, Values, and the Implicit: Explorations in Psychological Ontology. Journal of Ayn Rand Studies. 3(2):289–327.

Clifton, Rachel. 1992. The Development of Spatial Hearing in Human Infants. In Developmental Psychoacoustics, edited by L.A. Werner and E.W. Rubel, 135–57. Washington, DC: American Psychological Association.

Ciufolini, Ignazio, and John Archibald Wheeler. 1995. Gravitation and Inertia. Princeton: Princeton University Press.

Deacon, Terrence. 1997. The Symbolic Species: The Co-Evolution of Language and the Brain. New York: W.W. Norton & Company.

Gelman, Rochel, and Elizabeth Meck. 1983. Preschoolers’ Counting: Principles before Skill. Cognition 13:343–59.

Iverson, Jana, and Esther Thelen. 1999. Hand, Mouth, and Brain: The Dynamic Emergence of Speech and Gesture. Journal of Consciousness Studies 6(11–12):19–40.

Jetton, Merlin. 1991. Formation of concepts. Objectivity 1(2):95–97.

―――. 1998. Pursuing similarity. Objectivity 2(6):41–130.

Johnson, Mark. 1987. The Body in the Mind. Chicago: University of Chicago Press.

Keil, Frank. 1989. Concepts, Kinds, and Cognitive Development. Cambridge: MIT Press.

Kelley, David. 1984. A Theory of Abstraction. Cognition and Brain Theory 7:329–57.

Kelley, David, and Janet Krueger. 1984. The Psychology of Abstraction.

Journal for the Theory of Social Behaviour 14(1):43–67.

Kellman, Philip. 1995. Ontogenesis of Space and Motion Perception. In Perception of Space and Motion. 2nd edition. Edited by W. Epstein and S. Rogers. New York: Academic Press.

Krantz, D.H., Luce, R.D., Suppes, P., and A. Tversky. 1989. Foundations of Measurement (Vol. 2). New York: Academic Press.

Livingston, Kenneth. 1998. Rationality and the Psychology of Abstraction. Objectivist Studies, no. 1. Poughkeepsie: Institute for Objectivist Studies.

Macnamara, John. 1986. A Border Dispute: The Place of Logic in Psychology. Cambridge: MIT Press.

Maddy, Penelope. 1997. Naturalism in Mathematics. New York: Oxford University Press.

Mandler, Jean, and Patricia Bauer. 1988. The Cradle of Categorization: Is the Basic Level Basic? Cognitive Development 3:247–64.

Maurer, Armand. 1994. William of Ockham. In Individuation in Scholasticism, edited by J.J.E. Gracia. Albany: State University of New York Press.

Meltzoff, Andrew. 1993. Molyneux’s Babies: Cross-Modal Perception, Imitation, and the Mind of the Preverbal Infant. In Spatial Representation, edited by N. Eilan, R. McCarthy, and B. Brewer. Oxford: Blackwell.

Minsky, Marvin [1974] 1997. A Framework for Representing Knowledge. In Mind Design II, edited by J. Haugeland. Cambridge: MIT Press.

Needham, Amy, and Renée Baillargéon. 1993. Intuitions about Support in 4.5-Month-Old Infants. Cognition 47:121–48.

Nelson, Katherine. 1996. Language in Cognitive Development. Cambridge: Cambridge University Press.

Nosofsky, Robert. 1992. Similarity Scaling and Cognitive Process Models. Annual Review of Psychology 43:25–53.

Olson, David. 1994. The World on Paper: The Conceptual and Cognitive Implications of Writing and Reading. Cambridge: Cambridge University Press.

Quine, Willard van Orman. 1969. Natural Kinds. In Ontological Relativity and Other Essays, 114–38. New York: Columbia University Press.

Quinn, Paul. 1987. The Categorical Representation of Visual Pattern Information by Young Infants. Cognition 27(2):145–79.

Rand, Ayn. [1961] 1964. The Objectivist Ethics. In The Virtue of Selfishness. New York: New American Library.

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Questions and Comments on “Genesis”

1 – Daniel Barnes

Here you postulate that the baby’s knowledge of existents is at first only of “entities”. Soon after, they become (to the baby) “identities."

But the Law of Identity, according to Rand, asserts that for a thing to exist, it must have an identity.

So, surely this Law must apply to the baby’s knowledge too; surely it cannot “know” an identity-free entity?

2 – Merlin Jetton

One of the identities of an entity is that it is distinct from anything else in the sensory “field”. Thus it is not an “identity-free entity”, even to the baby.

3 – Daniel Barnes

My very point. “Distinct” simply means it already has differences. Thus for purely logical reasons, we must assume the baby grasps some form of identity right from the start, no doubt due to hard-wired biological expectations (as a side note, it seems very odd for Stephen to describe a mother's face and voice as mere “entities”, not yet at the “identity” stage. Actually as I recall some studies show newborns are exceptionally good at detecting both human faces within minutes of their birth, and their mother's voice fairly quickly too - I will have to check up on how early the voice tests were conducted) If this is what Stephen means to say, he should clarify. Currently it seems that regardless of the other merits of his essay, he has imported Rand's gaffe in the ITOE where she accidentally postulates an entity-without-identity stage in the process of concept formation. This obviously cannot fly, even by Objectivist lights.

4 – Michael Stuart Kelly

Rand is talking about newborns and concepts, . . . Rand has specifically said newborns have no conceptual knowledge.

5 – Merlin Jetton

A . . . reasonable, charitable way to interpret . . . Rand is that the child in the first stage does not conceptually distinguish between an entity and its characteristics (identity).

6 – Daniel Barnes

Does the child's concept of “entity” have identity or not?

~~~~~~~~~~~~~~~~

Before forming my answer, I would like to give a more complete picture of the competencies of the human infant from day of birth to three weeks. Prior to birth, one had the grasp reflex, responsiveness to sounds, and the gustofacial reflex. One’s eyelids were opening, the retinal layers of the visual system were complete, and one was responsive to light intensity.

By day of birth, one had the additional reflexes of pupil dilation, kneejerk, and startle. On that day, one had visual preference for 3-dimensional objects (one perceived something of the 3D of objects), visual discriminations of different static line orientations, visual correction for 3D size constancy under variation of distance and correction for shape constancy under variation of object orientation. One was unable to detect boundaries and unable to fill in invisible parts of objects. One’s visual acuity was poor (probably due to immaturity of both the retina and the visual cortex), and one’s contrast sensitivity was poor.

One’s significant body motions were in alternation with visual attending. One was capable of rough, saccadic tracking, which was not only not smooth, but not anticipatory. One fixed on interesting objects, and perhaps one had some slight control in this; perhaps it was not entirely passive capture. One may have had an early visual preference for faces in tracking. One could imitate two facial movements and one head turn; one could perform these imitations when forced to delay until the model movement was absent.

One’s auditory resolution of pitches and volumes was already pretty good. One had a preference for Mother’s voice over the voice of a stranger, and one could distinguish human language from other auditory input. One was engaged in early head-turning, in the horizontal plane, towards sound sources. As of the time I compiled—a dozen years ago—the developmental time line from which the items here are taken, it was unknown whether the sound source is experienced as outside the head; head-turning had been evoked also by earphones.

Let’s wrap up the first day. One cried when other infants cried. One had auditory recognition memory; retention was for days under conditioning, for 24 hours under habituation. One was sensitive to pain, to touch (coetaneous and active), and to changes in bodily position.

By the end of the second day, one could discriminate Mother’s face from a stranger’s face. One had a preference for infant-directed speech (motherese) over adult-directed speech.

By five days, one engaged in early reaching towards an object in the visual field, reaching that included a preparation for grasping. This reaching and visual detection may be an undifferentiated attention system.

By twelve days, one could imitate three facial (oral) movements and one set of sequential finger movements. By fourteen days, one had a preference for Father’s voice over that of other males. By three weeks, one expected the reappearance of visual objects that were gradually occluded by a moving screen, provided the occlusion time was short.

~~~~~~~~~~~~~~~

My Reply

I had proposed in the subsection Elaboration of Identity that in the first couple of days after birth, the sensory experience of the infant is for him only of entities, not of any identities. Daniel took me to be saying that during those days the baby’s knowledge of existents is at first only as entities, not yet as identities.

I don’t know if Daniel meant the word knowledge strictly here or if he meant it very loosely such that mere sensory apprehension might be included under it. When the essay was written, I would have rejected the idea that the newborn has any knowledge in the strict sense, and I would reject that idea even more emphatically today. In the endnote [33], I had pointed out that research subsequent to Rand’s composition had disproven the idea that the sensory experience of the neonate was an undifferentiated chaos. That is correct. But I went on in that note to insinuate the false alternative that either the sensory experience of the neonate was an undifferentiated chaos or it contained some percepts. That is incorrect. I do not think now, if ever I did, that the sensory experience of the neonate, as reported in the sources cited, shows either alternative to be the case.

In fact, looking over the preceding recitation, in this post, of the competencies of the infant through the third week, I don’t think the infant has yet had a percept. He is not yet able to engage in explorations sufficiently controlled, and with enough memory, to have what we would call a percept. Sensory experience, discriminations, detections, responses—but no percepts. If no percepts, then no knowledge in the strict sense.

Daniel went on in 1 to say that, according to Rand, for a thing to exist, it must have an identity. That much is right, but he goes on to say that surely a baby cannot “know” (let us say apprehend) an entity (which is an existent) free of identity. This is a point not just about babies, but about anyone at all. Let me try to fill in an argument along Randian lines concluding in this point posed by Daniel: If one is conscious of something truly, then it exists. Consciousness is identification. Therefore, if one is conscious of an existent, one has identified it. But there can be no true identifications without identities. Therefore, if one is conscious of an existent, one is conscious of (some of) its identity.

That sounds pretty good to me. I don’t recall why (if I indeed had a reason) I was referring to occasions of Mother’s face or voice as entities. Occasions are events, not entities. Daniel’s general point still arises. How in those first couple of days could the infant be apprehending an event without apprehending any of the identities of the event? That what the infant is apprehending are various events is something known to us, or anyway, is something that could become known to us. That fact cannot be perceived by the infant. The infant can make sensory discriminations, but it is not plausible that he discriminates between events and entities, or between existents and identities.

Merlin made the point that when the infant discriminates or detects something in his sensory field, he is apprehending some of the identity of an entity. He is not apprehending an identity-free existent. Yes.

If the infant in the first couple of days, and even in the first three weeks, has yet to have a percept, do his sensory registrations and preferences, his reaches, and his expectations amount to identifications? Well, yes, he does seem bent on singling things out, especially Mother. It’s just that the strivings and discriminations do not yet coalesce into a percept.

Michael pointed out that Rand denied that infants at this early stage had any concepts of anything. That is correct.

“The (implicit) concept ‘existent’ undergoes three stages of development in man’s mind. The first stage is a child’s awareness of objects, of things—which represents the (implicit) concept ‘entity’. The second and closely allied sage is the awareness of specific, particular things which he can distinguish from the rest of his perceptual field—which represents the (implicit) concept ‘identity’”(ITOE 6). Only at a third stage are concepts attained, in Rand’s cameo portrait. The period Rand was taking for first stage was definitely after the first couple of days; to her knowledge, any of the waking periods in the first couple of days were times of undifferentiated chaos. As folk, we naturally see the infant as going through a “that, that, that, . . .” stage before a “this-type-of-that, this-other-type-of-that, . . .” stage. It is true that the ability to make discriminations increases with development. But Rand’s cashing of that pattern in terms of implicit concepts does not square with detail of development we have from modern research, and it does not square with her metaphysics. I, too, was in similar error in my similar cashing of the detail of earliest development.

We should notice that Rand had expressed already in 1957, how she thought about the beginning of the infant’s mind in his first days after delivery. She interpreted the baby as having not yet grasped that A is A. This is the stage “ when a consciousness acquires its initial sensory perceptions and has not learned to distinguish solid objects.” To a baby at this stage, “the world appears as a blur of motion, without things that move—and the birth of his mind is the day when he grasps that the streak that keeps flickering past him is his mother and the whirl beyond her is the curtain, that the two are solid entities and neither can turn into the other . . .” (AS 1040–41) Her remark on the topic in ITOE in 1966 was an additional interpretation.

Merlin mentioned that Rand’s existent-before-identity idea for the early stages of development could be seen as reasonable at least in its entailment of the idea that the infant has no concept of the distinction between an entity and its characteristics. Yes, the latter was Rand’s view. The distinction between existence and identity is a conceptual one concerning a single fact (ITOE Appendix 240–41; note).

Edited by Stephen Boydstun
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I am at a loss as to why so much analysis is required to differentiate between 'existent', 'entity', and 'identity' as I do not see the value in such distinctions. It is clear that the infant (or even the fetus) abstracts something, and this something is not available to anyone else to directly observe. As the nervous system matures we teach the child to associate certain of their private lower order abstractions with certain higher order abstractions (words). One can infer that the lower order abstractions are similar to our own when the child learns and uses our language properly.

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