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THE FUZZY BRAIN by Charles Laughlin Carleton University In an article published in the Journal of Anthropological Research (Laughlin 1993), I made the suggestion that fuzzy set theory (FST) offers many useful insights into the nature of natural categories of human thought, culture and communication, especially those related to transpersonal experiences. I noted that ethnologists have been slow to avail themselves of these insights, and that they have upon occasion committed the fallacy of over-crispifying native categories in describing cosmologies and religious systems. I would like to briefly share some thoughts on the possible neurophysiological substrate for fuzziness in natural categories and reason. But first, for those of you not familiar with FST, I will briefly summarize the central insights at the core of the theory. Fuzzy Set Theory FST posits and models the essential fuzziness of natural categories. 1 The central concept in FST is, of course, fuzziness. 2 Fuzziness refers to an easing of the restrictions upon membership in a category -- categories being cognitive classes of objects "which are considered equivalent" (Rosch et al. 1976:383). Fuzzy sets are categories with graded membership, and constraints upon membership in a category are elastic. Instead of an object either belonging to, or not belonging to a category, as is the case in classical set theory, the object may be more or less a member of a category. Examples of fuzzy categories often cited in the literature include "young child," "good person," "tall man" and "beautiful woman." Fuzzy numbers include notions like "lots," "several," "occasional," "a bunch," "a few," etc. By the same token, fuzzy reasoning or logic (Giles 1979, Lakoff 1973) "relates to what might be called approximate reasoning, that is, a type of reasoning which is neither very exact nor very inexact" (Zadeh 1975:1). While propositions in classical logic are 1 Two and a half decades ago, Lotfi Zadeh (1965) published a paper entitled "Fuzzy Sets" in which he described a new theory of membership in conceptual categories. This was the beginning to FST and since then over 5000 papers and books have been written exploring various aspects and applications of FST. 2 Those readers wishing to read more about fuzzy set theory and related issues might wish to consult some of the following sources. The best general introductory textbooks are Zimmermann (1990) and Klir and Folger (1988), but they do not emphasize social science applications. A text that does emphasize the social sciences is Smithson (1987). considered to be either true or false, in fuzzy logic they may be more or less ("sort of," "maybe," "fairly," "pretty much") true, or more or less false. For example, a witness to a crime may make a formal statement of what they saw, and this statement may be considered more or less accurate, more or less true, relative to the statements of other witnesses. Fuzziness is often signalled in natural language by the use of hedges (Lakoff 1973; see also Sapir 1944). Such terms as "sort of," "very," "unlikely," "kind of like," "more or less," "almost," "practically," etc., are commonly used in English to signal fuzzy intent and to modify the meaning of the focal term (see Lakoff 1973:472 for a lengthy list of English hedges). Fuzziness is contrasted with crispness. Crispness refers to precise membership within a category. The crispness of categories we require in scientific theory, description, measurement and discourse is actually abnormal when considered cross-culturally, especially as regards religious knowledge. Indeed, that kind of crispness is rare in each of our own everyday lifeworlds. FST is, by the way, a theoretical approach to crispifying fuzziness. Fuzziness and the Brain A real problem we face is that most theories of human categorization used in ethnology are grounded in cognitive psychology and few give other than passing reference to FST (see Laughlin 1993 for some interesting exceptions). This is unfortunate, because ethnologists utilizing cognitive psychological theories are often uncritical of inherent weaknesses in the cognitive psychological approach. One severe weaknesses is that few cognitive psychology models are grounded in the neurosciences. That means that it is often hard or impossible to map the inferred structures of perception and cognition defined in these theories onto what we have come to know about how the human brain works. This is pretty much the same problem many of us found with Levi-Straus' semiotic structuralism in the 1970s. Moreover, there is considerable controversy in psychology over how categories are learned and whether categorical recognition involves holistic or analytical strategies (see Medin 1984 for a review). Despite these considerations, there does exist a relevant literature on the psychophysiology of natural category construction in the nervous system; see Herrnstein (1982), Kay and McDaniel (1978:617-621), Bieterman (1987). The work of Irving Bieterman (1987) at SUNY-Buffalo is particularly promising. Recognizing that the nervous system is working on abstractions all the way from receptor sites into the central cortical processing structures, he has hypothesized that there exists a finite set of generalized component detectors in the retina -- structures he calls "geons" -- that produce information about the properties of objects. Recognition occurs because of a free combination of geons -- the principle he calls "componential recovery." He has shown in experimental research that if two or three geons can be recovered by a subject, they are sufficient for recognition. Additional research confirming the importance of geons in both recognition and access to memory may be found in Biederman and Ju (1988). It is easy to see from this type of psychophysiological research that "fuzziness" of natural categories in both perception and cognition may be due in part from the additive effect of components (geons). A robin will trigger more geons characteristic of "birdliness" than will a bat. I suspect, however, that we will find the picture much more complex than can be modelled by geon theory. I have always argued that adult perceptual and cognitive structures develop from nascent structures ("neurognosis" in biogenetic structural theory; see Laughlin 1991) that are "already there" in the newborn and infant. It may well be that the origins of developed geons are to be found in retinal neurognosis, as well as the deeper neurocognitive structures mediating perceptual and cognitive categories. There is considerable evidence in favor of this view with respect to, say, facial and hand recognition in humans and non-human primates. Experiential Proximity Hypothesis In the 1993 article, I proposed what I call the "Experiential Proximity Hypothesis." The hypothesis states: The more a state of consciousness is oriented on direct experience, the more fuzzy will be the categories informing experience. What was unstated, but implicit in the article was the fact that we now know that virtually all interactions within the nervous system are reciprocal. That is, for every afferent pathway between two areas of nervous tissue, there exists a reciprocal efferent pathway. It used to be thought for example that the thalamus is a passive gateway into higher cortical processes. We now know that the relationship between thalamic nuclei and the cortical areas they innervate is a reciprocal one. The innervation is two-way. Both the nuclei and the cortical areas interact -- they communicate with each other. The same is the case between sensory receptor sites and tissues "higher-up" in the nervous system. The "experiential proximity hypothesis" tacitly recognizes that a state of consciousness may be initiated from the exteroceptor, interoceptor or sensorial structures (a butterfly suddenly appears before my eyes, or I imagine a chocolate milkshake) and propagate toward intentional processes, or it may be initiated from intentional structures and propagate outward (I reason out a problem, and then orient my senses and body to implement the solution). I suspect that fuzziness of natural categories manifests most obviously where the intention is from peripheral (exteroceptive or interoceptive) toward higher cortical processes, and least operative where intention derives from higher cortical processes. Overly crisp categories only naturally operate where reasonable precision is required, as is the case for example in traditional pharmacological systems. Notes References Bieterman, I., 1987, Recognition-by-Components: A Theory of Human Image Understanding. Psychological Review 94(2):115-147. Biederman, I. and G. Ju, 1988, Surface versus Edge-Based Determinants of Visual Recognition. Cognitive Psychology 20: 38-64. Giles, R., 1979, A Formal System for Fuzzy Reasoning. Fuzzy Sets and Systems 2:233-257. Herrnstein, R.J., 1982, Stimuli and the Texture of Experience. Neuroscience and Biobehavioral Reviews 6: 105-117. Kay, P. and C.K. McDaniel, 1978, The Linguistic Significance of the Meanings of Basic Color Terms. Language 54(3):610-646. Klir, G.J. and T.A. Folger, 1988, Fuzzy Sets, Uncertainty, and Information. Englewood Cliffs, NJ: Prentice-Hall. Lakoff, G., 1973, Hedges: A Study in Meaning Criteria and the logic of Fuzzy Concepts. Journal of Philosophical Logic 2:458-508. Laughlin, C.D., 1991, Pre- and Perinatal Brain Development and Enculturation: A Biogenetic Structural Approach." Human Nature 2(3):171-213. Laughlin, C.D., 1993, "Fuzziness and Phenomenology in Ethnological Research: Insights from Fuzzy Set Theory. Journal of Anthropological Research 49(1). Medin, D.L., 1984, Concepts and Concept Formation. Annual Review of Psychology 35:113-138. Rosch, E., C.B. Mervis, W.D. Gray, D.M. Johnson, and P. Boyes-Braem, 1976, Basic Objects in Natural Categories. Cognitive Psychology 8:382-439. Sapir, E., 1944, Grading: A Study in Semantics. Philosophy of Science 11:93-116 [also pp. 122-149 in Selected Writings of Edward Sapir in Lauguage, Culture and Personality (ed. by D.G. Mandelbaum). Berkeley: University of California Press, 1968.] Zadeh, L.A., 1965, Fuzzy Sets. Information and Control 8:338-353 [reprinted in Yager et al. 1987]. Zadeh, L.A., 1975, Calculus of Fuzzy Restrictions. Pp. 1-39 in Fuzzy Sets and Their Applications to Cognitive and Decision Processes (ed. by L.A. Zadeh, K.-S. Fu, K. Tanaka & M. Shimura). New York: Academic Press. Zimmermann, H.-J., 1990, Fuzzy Set Theory and Its Applications. Boston: Kluwer.