What do people perceive, think, and know? How do people perceive, think, and know? These questions are of interest to both anthropology and psychology, but whereas psychology emphasizes the second question, the cultural sciences are primarily concerned with the first question. [See Thinking.]
Cultural anthropology in particular has undertaken to describe and catalogue the cognitions typical of the various societies that make up man-kind. An ethnography (the description of a culture) is very largely an account of what the people in a particular society perceive, think, and know. Thus, the large and growing archive of descriptive ethnographic materials is a repository of the information available about man’s cognitions regarding the principal concerns of his existence: working, eating, sleeping, making love, treating illness, performing rituals, fabricating tools, fighting, raising children, and so on, through the outline of cultural categories. Traditional styles of ethno-graphic description have been humanistic rather than formal. But in recent years, as a result of the influence of linguistics on the one hand, and clinical and experimental psychology on the other, formal methods of field work, analysis, and description have been developed which provide more precise, economical, and cross-culturally comparable descriptions of the various kinds of cognition that constitute a culture. Furthermore, there is increased interest in the process of cognition at a level more general, and less conscious, than can be conveniently regarded as appropriate to an ethnographic description of the languages of people in various cultures. These new developments in the formal analysis of culture go beyond the two essential observations that all races or varieties of human beings can perform essentially the same cognitive operations and that what is actually perceived, thought, and known, even in response to the same physical stimuli, varies predictably with culture rather than with physical type.
Although language is conventionally and properly regarded as a fundamental aspect of “culture,” it occupies an ambiguous position in cognitive studies and, as the development of the study of psycholinguistics may suggest, is probably more relevant to psychological than to cultural investigations. Language is employed in many, but by no means all, cognitive processes; there are, for instance, forms of thought in music, painting, and certain of the performing arts that are not linguistic. Language differences are in principle irrelevant to logical and mathematical thinking, which can be reduced from logical or mathematical symbols to linguistic ones in any of dozens of languages. And intraculturally, many of the most interesting individual differences in the cognitive process are observed in dialogues between speakers of the same language whose utterances are equally valid linguistically but not logically. A language provides a small and finite set of elementary signs and symbols, as well as rules for their permissible combination, which permit the construction of a very large number of utterances; but the rules of language do not “contain” the meaning of the utterances any more than the rules for attaching pieces of metal by nuts and bolts, screws, rivets, solder, pins, friction joints, clamps, etc., “contain” the design of an automobile engine. Therefore it would be a mistake to regard the structural description of a language as a description of cognitive process at anything more than a nuts-and-bolts level or for more than a portion of the cognitive operations of its speakers.
Culture as an ideal normative system. Ethnography, although it recognizes the existence of complementary individual variation in role and of individual deviancy from norm, initially describes a culture as an ideal structure that is generated by a group and is an attribute of that group. The formal, sometimes even mathematical, features of a culture thus are to be likened to the geometrical properties of a single object or to the interrelated statements of a highly organized body of knowledge, rather than to the multivariate statistical description of a population. The work of the ethnographer—describing the cognitive processes that have been culturally standardized in a given society —may perhaps best be made clear by an analogy. Let us suppose that a nonmathematician is given the task of describing a new mathematical calculus that is in active use by a group of people who have not formulated their system of calculation in a written text. It has, in other words, been developing informally over the years, is currently being used in its most matured form, and is being taught to new users by example and through oral instruction. The investigator is allowed to interview and observe—that is, he may ask questions during coffee breaks, watch people computing, save scraps of paper from wastebaskets, take photographs of the machines employed, talk a few times with the project director, listen to people teaching one another the right way to do things, and make other such minimally interfering kinds of observations and inquiries. He may even be permitted—and he will certainly be well advised—to join the group as a novice and learn to use the calculus himself.
Now, as he analyzes the data collected in these various ways, he does not merely tabulate the frequencies and intercorrelations of various classes of observed behavior in order to arrive at the calculus; if he did this, he would be giving equal weight to misunderstood jokes, learners’ mistakes, slips of the pen, careless work, gibberish produced by broken computers, and competent professional operations. What he does, instead, is to infer the system of rules that these people are attempting to apply. He will gain the assurance that he is on the way to an adequate understanding of these rules from the logical completeness of the system he infers and from his ability, when using it, to produce behavior that an expert will reward by saying, in effect, “That’s right; that’s good; now you’ve got it.” Of course, a sociologist or a psychologist might say, “But it is the behavior that is real, not this abstract system which no one actually applies perfectly and completely and which is merely the asymptote of the real curve of behaviors.” The investigator replies that culture—conceived in this sense as a collection of formal calculi—is just as real as algebra, Euclidean geometry, and set theory, which are the asymptotes of the “real” behavior of fallible students, mathematicians, and machines. Indeed, he will point out, these other calculi are aspects of a culture, and their apparently greater tangibility stems from the incidental circumstance that they have been the object of more intensive study and explicit description than the calculus which he has been investigating.
Certain aspects of cultures that are understood as ideal normative systems have been subjected to formal analysis. The semantic analysis of kinship terminology and other taxonomic systems by such techniques as componential analysis, the reduction of prescriptive marriage and descent rules to the form of permutation matrices (Bush 1963; Kemeny et al. 1957; Weil 1949; White 1963), the treatment of certain status relationship systems as Guttman scales (Goodenough 1963), and the formalization of the Hindu purity-impurity transformation cycle as a product of Galois groups (Wallace 1966) are examples of this effort to delineate in the most economical form the essential structure of limited aspects of culture. To the extent that the cultural structures thus formally delineated require that some or all of the generating population entertain equivalent cognitive structures, these ideal normative systems give information about cognition.
But it would be naive to suppose that all members of a group maintain identical cognitive structures which are, in effect, the single normative structure revealed by ethnography and formal cultural analysis. Not only are there individuals with deviant or incomplete models but also the existence of complementary specialized roles in every human society requires that a model of the ideal normative system not be completely housed in the brain of every, or even any, single individual. Thus the question must be asked, What is the relationship of the ideal normative system to individual cognitions?
Culture as a cognitive system. Linguists, psychiatrists, philosophers, and social scientists have long been concerned with an issue which may be crudely but adequately stated as a pair of questions: Do all human beings, with more or less accuracy and complexity, follow one single neuro-logically founded logical calculus, the system that Boole called “the laws of thought” (i.e., the elementary logical calculus which is the root of all formal logical and mathematical reasoning), or are there many logics, mutually inconsistent, generated by differences in language (as the Sapir-Whorf hypothesis might suggest), by other aspects of culture, or by evolutionary level? The evidence to support the notion of logical pluralism has so far been unconvincing. Some “different” logics appear to be merely variants comparable to contrasts in emphasis on class products as opposed to relative products or preferences for probabilistic versus true-false truth values. And some appear to be based on mistaken assumptions about the primitiveness or irrationality of non-Western or ancient thinking. Although there are great differences in the degree of explicitness, the form, and the complexity of reasoning embedded in different linguistic and cultural traditions, and also differences in the de-termination of situations to which formal reasoning will be applied, it appears that such elementary rational procedures as syllogistic deduction and Mill’s canons of inductive inference are universal. It is probable, furthermore, that the extent of the complexity of rational operations performed without mechanical aid or specialized training by the normal members of any society, regardless of their level of economic and political organization, has an upper limit which is roughly the same for all racial and cultural groups (see Wallace 196la).
Social science studies of cognition tend to emphasize the description of those perceptions, beliefs, and thoughts which are standardized, repetitive, and conventional in a society. Where such cognitions seem to be shared by all mature persons in the society, there may be little need to consider the individual; but where cognitions are not shared by all, the individual becomes important as a unit of analysis. In the general case the individual may be conceived as the site of a large and complexly organized set of perceptions, thoughts, and knowledge. This assemblage has been variously denoted the “image,” the “mazeway,” and so on; the term refers to the entire structure of the individual’s cognition about himself and the surrounding world, including memories, abstract knowledge, and rules of thought. Although the total description of any one person’s mazeway would doubtless be an impracticably large task, portions of any one mazeway can be described as a set of propositions which, in symbolic form, will approximate an internally consistent system. When one considers the group of individuals who compose a community of any size, with regard to a given aspect of behavior, the sum of the propositions with regard to that aspect may or may not yield an approximation of a logically consistent system. If they do sum to a system, then that sum is referred to as an aspect of “their culture.” In general, summing to culture will occur under two conditions: first, and obviously, if the individual mazeways are identical in content and internally consistent in structure; and second, if the individual mazeways, even if not all identical, sum to a consistent system. Anthropologists have traditionally drawn attention to the existence of identical (shared) structures and to a certain kind of sum (the equivalence structure) of nonshared structures. The two sorts of cultural summing of cognitions are represented schematically in Figure 1.
Examples of shared cultural cognitive elements in the United States, for instance, would be a speaking knowledge of basic English phonemes, vocabulary, and syntax; familiarity with the currency; and recognition of the American flag. Not all normal adult persons born and residing in the United States share even these minimal cognitions, but universality is closely approximated in most communities. Nonshared but complementary cognitions are just as readily discovered in division-of-labor systems: for instance, in household management, the wife’s knowledge of how to buy, cook, and serve food is usually complementary to the husband’s knowledge of how to secure enough money to provide the necessary transportation, cooking and sanitary appliances, and eating equip-
ment; the professional pianist’s skills are complementary to the skills of the piano manufacturer and the tuner; and so on. In some areas of behavior, it may be considered improper for complementary specialists to know each others’ specialties, and in some situations (e.g., religious or military operations) it may be impious or illegal for persons with one role even to know, let alone practice, the role of the other. The analysis and classification of cultural structures in terms of the individual cognitive components of which they are the sum has not yet advanced very far.
At the present stage of research into these matters, however, there are technical and semantic difficulties in analyzing the relationship between individual cognitive structures and those cognitive sums that we have here called a “culture.” Obviously, except in the special case of all members of the society sharing the same cognitive structure, culture cannot be considered to be embodied in any one individual even though it is a product of individual cognitions. Thus, ascribing the contents of ethnographic monographs to each and every, and sometimes even any, individual in the society cannot legitimately be done. Furthermore, even in the case of perfectly shared cognitions, the cultural sum may be ethnographically described in a logical transformation of individual cognitive contents and/or cultural sums which is empirically predictive of behavior and elegant in formulation but not descriptive of cognitive content in anybody at all. In what sense are such logical transformations of the cultural sums themselves descriptive of cognitive content or structure of the individual mazeways from which the observed behavior was originally produced? The status of such transformations is precisely like that of newly formulated and proven theorems which were implicit in the axioms formulated by a mathematician but never anticipated by him. No doubt the possibility of performing such transformations has much to do with the generative power of culture; but it is necessary to keep firmly in mind that the actual cognitions of individuals may be different from these transformations and should be described in their own terms. Indeed, the possibility of understanding the dynamics of culture change would seem very largely to lie in the prospect of unraveling this relationship between individual cognition and unrealized summative implications.
Anthony F. C. Wallace
[Directly related are the entries Culture, article onthe concept of culture; Componential analysis; Ethnography; Language, article onlanguage and culture; Linguistics, article on The field; and the biographies of Sapirand Whorf.]
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Colby, B. N. 1966 Ethnographic Semantics: A Preliminary Survey. Current Anthropology 7:3–32.
Goodenough, Ward H. 1963 Some Applications of Guttman Scale Analysis to Ethnography and Culture Theory. Southwestern Journal of Anthropology 19:235–250.
Hallowell, A. Irving 1955 Culture and Experience. Philadelphia: Univ. of Pennsylvania Press.
Hammel, E. A. (editor) 1965 Formal Semantic Analysis. American Anthropologist New Series 67, no. 5, part 2.
Kemeny, John G. et al. (1957) 1962 Introduction to Finite Mathematics. Englewood Cliffs, N.J.: Prentice-Hall.
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Wallace, Anthony F. C. 1961a On Being Just Complicated Enough. National Academy of Sciences, Proceedings 47:458–464.
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Wallace, Anthony F. C. 1966 Religion: An Anthropological Study. New York: Random House.
Weil, AndrÉ (1949) 1963 On the Algebraic Study of Certain Types of Marriage Laws. Pages 151–157 in Harrison C. White, An Anatomy of Kinship: Mathematical Models for Structures of Cumulated Roles. Englewood Cliffs, N.J.: Prentice-Hall. → An analysis of the Murngin marriage structure. First published in Claude Lévi-Strauss (editor), Les structures élémentaires de la parenté.
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