Robert E. Haskeil
Claude Levi-Strauss Reconsidered: Cognitive science, epistemology, and the (not so savage) algebraic mind
Reconsidering Levi-Strauss' work - on the eve of his lOOth year of life - that the structure of Cognition is algebraic and analogical as indicated by his analysis of preliterate myths, along with a brief review and analysis of mathematics and Cognition, structuralism, and epistemology, the paper su^ests that critics of his werk (a) were only partially correct, (b) ap- proached his material from an inappropriate epistemology, and (c) while, in applicarion his structural method is problematic, (d) being a pioneer his value is to have posited a novel conceptualization that merits further research. Finally, (e) based on related findings, it is suggested that his no- tion of an algebraic/analogical mind, which allowed him to illustrate a novel mathematical framework in his structuralist project, can be mod- eled and tested.
CORRESPONDENCE Robert E. Haskeil. Dept of Psychology, Univeisity of New Eng- land, Biddefotd, Maine, USA. EMAIL [email protected]
Introduction Reminiscent of a bygone era, Levi-Strauss' anthropology is synoptic in its scope, covering mythology, linguistics, Cognition, philosophy, history, and methodology. More specifically, Levi-Strauss (1963, 1966) saw himself as investigating how the mind works and was thus engaged in cognitive anthro- pology and psychology. With a near singular exception (see Gardner below), however, cognitive psychology has not been disposed to examine Levi-Strauss' work. On the other band, he seems to be held in considerable esteem by some anthropologists, by researchers and theorists outside the discipline's North American boundaries, and by many in the humanities as well as in the field of semiotics.' Why he is so esteemed by non mainstream anthropological factions is not entirely clear as most anthropologists, at least, agree that his structural
1 For a view of Levi-Strauss' relations to the humanities, see Haskeil (2008).
Cognitive Semiotics, Issue 3 (Fall 2008), pp. 65-90 66 R. E. HASKELL
methodology applied to preliterate myths, and his algcbraic formulae applied to kinship systems are, respectively, either problematic, or superfluous.^ Neverthe- less, on this eve of his lOOth year of life, Levi-Strauss continues to be regarded by many as a significant inteUectual figure in the history of ideas.' This paper wül reexamine five major areas of Levi-Strauss' work which continue to be seen as divergent from mainstream frameworks. It is su^ested that his divergence is fivefold: (1) an algebraic basis to the mind, (2) the empirical data used (e.g. myths), (3) a structural epistemology, (4) methodology, and (5) an analogical basis of mind. Each of these divergent areas will be addressed, in order to suggest reconsiderarion of his structural anthropology. In doing so, however, the paper will not address the myriad of related issues in the anthropological literature, e.g. universalism vs. particularism. The final secdon will süßest that his work can be modeled and tested. Levi-Strauss has attracted a host of critics. Most critics - even so-called friendly ones (e.g. Leach 1974) - agree that he does not adequately demonstrate his Claims. I suggest, however, that critiques of Levi-Strauss' method tend to be only partially valid, approaching his material from an inappropriate epistemo- logical framework. Due to Space considerations as well as for convenience, Leach (1974) will be considered the paradigmatic critic. While, in applicaüon, his structural method is problematic, his value is to have posited a novel conceptualizaüon and to have pointed in a new direction, a direction that diverged from the knowledge-base of his time and from Standard empiricist frameworks.'*
For example, even with regard to Levi-Strauss (1969) findings of a kinship algebra in his FJementary Structures of Kinship, which was provided with an imprimatur by renowncd algebraist Andre Weil, others (e.g. Cargal 1996) have maintained it does not add anything to the understanding of kinship relauons. From the perspective of this article, however, the point is his demonstration of an algebraic structure undergirding kinship relations. Levi-Strauss seems to have taken on the negative status in academic anthropology that Freud has in academic psychology and cognitive science. Another parallel berween the rwo is that Freud, like Levi-Strauss, is cited widely and held in high esteem in the humanities and the pop culture. While the term 'empiricist' has merited volumes, for purposes here the two sections below, Verha! Narrative and Empirical Data, and fr.pistemolog/: Empiriast and Structuralist, will serve as shorthand explanations. CLAUDE LEVI-STRAUSSRECONSIDERED | 67
The Mathemadcal and Analogical Mind Mathematics and Cognition It is widely accepted that Levi-Strauss (1954, 1963, 1966) claims an algebraic basis to mind and Cognition. For example, Leach notes that his view of 'algebra corresponds to some deep-rooted organizarional principle in human brains [...]' (Leach 1970: 52); and that it 'is an attribute of human brains everywhere [...]' (Leach 1970: 55). 'Levi-Strauss is endeavoring to establish the rudiments of a semantic algebra' (Leach 1970: 33). Since Levi-Strauss first made this seemingly groundless claim, there has been a growing body of neurological and other research that supports this major claim, e.g. Dehaene (1997). There are, for example, dedicated neurons and entire neurological circuits for various arithmetic Operations (Cohen et al. 2000, Dehaene & Changeux 1993, Stanescu-Cosson et al. 2000). It is thought that these abilities are most likely hard-wired evolutionary mechanisms (Wynn 1998). Also supportive is the work of Marcus (2001). Based on his analysis of connectionism, computational data, and theory, he suggests that the brain inherently functions algebraically. More specifically, research by Hittmair- Delazer, Semenza & Denes (1994) as well as of Hittmair-Delazer, Sailer & Benke (1995) - shows that when people become acalculic they do not necessarily lose their knowledge of algebra, suggesting that there exist neuronal circuits responsible for algebraic functions that are largely independent of those involved in arithmetic calculation. Further, an extensive exposition by Lakoff and Nünez (2000) has advanced the understanding of inherent cognitive bases subserving mathematics. Recently, too, a paper by the Computer scientist and linguist Sheldon Klein (2002), using a binary system (Levi-Strauss also claims the mind works as a binary system), suggests on the basis of a computational model derived from his empirical research that the fmdings can be seen as supporting Levi-Strauss' algebraic model of mind. Klein (2002: 4) finds that "Categorical grammar reformulates phrase structure rules as if they were algebraic equations".^
Though there has been an increasing body of anthropologicaJ research involving mathematics and Cognition, it does not direcdy relate to the thesis of this paper (See Hage 1979, Hoff- mann 1969). Relatedly perünent is Marandas' (2001) crincal analysis of Levi-Strauss' claim of a universal formula of mythopoeic dynamics ffi{(a):fy(b)::fx(b):fa-l(y)] which he refers to as canonical because it apparendy can represent any mythic transformation. For a cridque of Levi-Straussian mathemaucs and group theory, see Almeida (1990) and Turner (1990), see also Barbosa de Almeida (1990). For a positive and forward looking assessment of Levi- 68 I R.LHASKEU.
Pertinent to his claim of an algebraic structure to Cognition as derived from the analysis of myths is the recent work of Griffin (2006, 2003). Using mathematical set notation, he found a general underlying pre-algebraic form for many myths and stories. Further, using a set of oral narratives - that in significant ways are analogous and homologous to myths - Haskell (2003a) and Haskell & Badalamenri (2003) have found an algebraic structure undergirding a set of oral narratives containing numeric references.^
Analo^cal Thought A second major cognitive claim by Levi-Strauss is that the 'savage' mind — and by implication the modern mind — inherendy functions analogically. As he observed, "savage thought can be defined as analogical thought" (Levi-Strauss 1966: 263). At the time, there was virtually no scientific support for this claim; with few important exceptions in science (e.g. Oppenheimer 1956, Bertalanffy 1963, Hesse 1963), reasoning by analogy was generally considered — at best - something in which literary types engaged, not logicians and scientists. Hence, his claim that preliterate thought is analogical — even if considered valid at the time - appeared unimpressive. Accordingly, while analogical reasoning had been well researched in the humanities (e.g. Shibles 1971), it was not generally considered to have a cognitive basis; it was to be avoided by "hard" scientists (see Haskell 1968). Since Levi-Strauss made this claim, however, analogical reasoning has been widely recognized by cognitive science as foundational to all thinking (e.g. Beck 1978, Genmer 1983, Gentner, Holyoak & Kokinov 2001, Fernandez 1972, HaskeU 1987a, Haskell 2002, Hoffman 1980, Holyoak & Koh 1987, Holyoak & Thagard 1995, MacCormac 1985). Clearly, like Levi-Strauss' claim of an algebraic basis of mind, he glimpses the analogical basis of mind as well. Interestingly, Vico, Cassirer, and Jaynes mentioned above also considered analogical/metaphorical reasoning as fundamental to all thinking and as based on invariant relations (Haskell 2000, 2002). It should be noted that the terms analogy and metaphor are integrally related by similarity relations (Vosniadou & Ortony 1989) and are unfortunately
Strauss' work and impact in relation to methodolog)', including mathematics see Almeida (1990), Doja P006). This paper will not attempt to define myth. Suffice it to say for purposes here that myth is equated, a la Levi-Strauss, to any spontaneous oral linguistic narrative with an unconsciously generated structure and, arguably, a "message". CLAUDE liVI-STRAUSSRECONSIDERED | 69 often used interchangeably. Analogical reasoning is also considered foundation- al to madiematical - and hence algebraic - reasoning (see English & Sharry 1996, Gentner, Holyoak & Kokinov 2001, Krieger 2003, Polya 1954, Vosnia- dou 1995). For example, it is generally agreed diat much if not most of mathematics, especially algebra and group theory, requires analogical mapping and invariance relations/transformations. Indeed, Levi-Strauss has clearly seen "analogical" reasoning as something more than the use of "analogies". He saw early on (1978: 8) that underlying analogical reasoning was a quest for invariance, for which throughout his life he has had a penchant. Indeed, he notes that, like analogical reasoning, underlying structuralism "is the quest for the invarianf [italics added]. Clearly, he recognizes that analogical reasoning and invariant relations undergird the mapping processes outlined above in "structuralist" narrative and myth analysis.
Epistemology: Empiricist and Structuralist Verbal Narrative and Empirical Data The second way in which Levi-Strauss deviated from Standard empiricist frameworks was his use of mythic narratives for deriving evidence of (an algebraic) cognitive structure. At least within cognitive science, oral narratives are not considered valid data for deriving knowledge about Cognition. Only rarely (see Thorndyke 1977) have oral narratives been used in mainstream psychology and cognitive science as cognitive data,'' despite a major founder of the cognitive revolution, Jerome Bruner (1990: 77) recognizing that "One of the most ubiquitous and powerful discourse forms in human communication is narrative". Mainstream cognitive science has not only tended to ignore narrative data, but especially the oral or verbal aspects of narrative.® Nevertheless, there have long been those who recognized that cognitive structures are reflected in verbal narratives of various kinds in the humanities.
Though there are areas of study in both anthropology and psychology (see
beginning with the long history of the study of rhetoric (Quintilian 1922) in ancient Greece and Rome to modern times. However, such approaches have tended to be considered literary, not scientific. Perhaps the first individual to fundamentally and systemically understand the importance of mythic oral narratives in reflecting cognitive structures was the eighteenth Century Italian philosopher Giambatösta Vico (1948/1727), with whom Levi-Strauss is familiar. Since about the early 1970s there has been a growing interest in Vico's work (see Haskell 1987b, Tagliacozzo & Verene 1976). Vico's claims, like Levi- Strauss', are grounded in an empirical oral narrative data-base of ancient fables, myths and Homeric epic poetry. Vico's method was a linguistic analysis of these fables and ancient epic poems, which he considers to be üteral histories, not fanciful literary tales (lest this latter claim itself sound fanciful, much of modern humanities research has come to the same conclusion as Vico about these classic documents).' Vico saw in these narratives a series of cognitive, structural, and linguistic structures and transformations extending through time, the assumption being that changes observed in the surface linguistic processes of that body of narratives were indices of changing cognitive functions developing over time (see also White 1976). For example, Vico found in the corpus of myths a Progression from not distinguishing between metaphoric naming and literal naming to recognizing a difference between the two. Similarly, fmding over time the introduction of ironic thought indicated to him a change in cognitive processes; indeed, a different level of consciousness. Vico (1948/1727: 78) recognized that "Irony[... requires the sophistication of the reflective mind that can distinguish between truth and falsehood and thus manipulate this distinction to achieve ironic Statement". Such findings indicated to him that a different kind of consciousness/cognition had evolved. A more contemporary philosopher - who was also familiar with Vico - was Ernst Cassirer (1955a, 1955b, 1957), who used language, myths, and a host of other empirical data, to derive evidence of cognitive functions. All of this, of
While this thesis has been around for centuries in one form or another, Milman Parry (1971), considered one of the leading classical scholars of his time in the late 1920s and early 1930s, documentcd that the language in the lliad and the Odyssey was the consequence of memory demands imposed on lengthy oral recitation and thus not poetic in the modern sense. He showed that repeated formulae were mnemonic devices imposed on an oral mode for remembering large stores of Information. CUUDELfVI-STRAUSSRECONSIDERED | 71 course, was prior to what is now known as the cognitive revoludon.'^ Finally, like Cassirer and Vico, the psychologist Julian Jaynes (1976) also used the classic Greek myths, e.g. Iliad, as data to derive evidence of cognitive funcdons. Jaynes (1976a: 69) says of the Iliad, "I propose here to regard the poem as a psychological document of immense importance". While Jaynes' work remains controversial in cognitive science, noted phiJosopher Daniel Dennett has characterized Jaynes work as Software archeology, a phrase that refers to the use of ancient artifacts to reflect cognitive funcdons. Dennett says.
So if you want to find a record of major Software changes in archeologi- cal history, what are you going to have to look at? You are going to have to look at the printouts, but they are very indirect. You are going to have to look at texts (...] and if Jaynes is completely wrong in the details (...] something like what he proposes has to be right (Dennett 1998: 130. Italics add- ed).
The point here is that Software archeology is what Levi-Strauss was attempting to do prior to the cognitive and Computer revolutions.
Epistemologi The third way Levi-Strauss deviates from Standard frameworks is in his epistemology. It will be suggested that much of the critique of Levi-Strauss' method, and therefore most structuralist approaches, are due to his divergent methodology and epistemology (for a similar and more detailed exposition of method, epistemology, and theory, see Haskeil 2003a, 2003b, 2004b). Though empirical in using preliterate myths as data, the structural metho- dology of Levi-Strauss does not fit mainstream cognitive science methods, with the latter being exclusively committed not only to experimental and Statistical
10 In presenting the work of Vico and Cassirer as empirical and cognitive there is a minor semandc problem: Both Vico, from the eighteenth Century, and Cassirer from the twenoeth Century speak a classic philosophical idiom that presents problems for many cognitive scientists. Cassirer, for example, uses the term Spiritual prindpk, which for many cognitive scientists evokes an immediate negative reaction. If one reads-in-translation, however, it becomes clear that Cassirer's Spiritual principle can be considered a theoretical construct that can be read-as a cognitive ordering rule. One cognitive psychologist (Weimer 1973: 435) recognized the importance of Cassirer's work for Cognition, saying that a good phenomenol- ogy (read: cognitive theory) is indispensable to psychology and recommends Cassirer's works as the finest cognitive psychology yet written. 72 I R.LHASKEU.
design but to methods compatible with computaoonal/algorithmic processing as well. While cognitive science is generaUy acknowledged to include andiropology, andiropological findings are seldom cited in the mainstream cognitive science literature, despite Bruner (1990: 2) having noted that "The cognitive revolution as originally conceived virtually required that psychology join Forces with anthropology and linguistics, philosophy, and history, even with the discipline of law". Most of history, anthropology, and law, however, are considered to utilize methods not compatible with current mainstream cognitive science.
Brief Historical Ovemew of Struäuralism and Cognition Though not commonly viewed as structuralist, it is mathematics that optimally exemplifies a structuralist model. Levi-Strauss certainly saw mathematics as structural (see below). As used here, like mathematics, structuralism essentially views phenomena as systems of elements characterized by a set of transforma- tions. Structures of transformations are lavful sets of Operations with the structure of the system maintained and enhanced by the integral character of its set of internal Operations. For example, mathematical groups and sets are exemplifica- tions because they are based on a system of transformations in which each of its subclasses, for example integers, can be reconstructed by reference to any other of its integer elements. An algebraic group is the epitome of mathematical structure with its Opera- tions of identity, reversibility, inversion, closure, associativity, commutativity, and transformation. In this definition, simple structures in the sense of form are excluded from the definition of structural. For example, the typical description of the structure of a building or a society is not a structure in the logico-mathematic sense; nor is a class such as furniture because the properties of its subclasses, for example a table, can neither generate nor lead to the re- construction of other subclasses or to the class fiarniture as a whole as do arithmetic elements. It should also be noted that group theory and algebra are not quantitative, in the sense that they do not involve metric measuring; instead they are based on abstract or conceptual Operations.''
11 While not literally mathematical in form, the internal structure of at least structural linguistics resembles mathematical structure in that it is based on systems involving an inferential and lawful set of internal relations and transformations among the elements of Syntax, phonolog)' and - more arguably - semantics. CLAUDE LEVI-STRAUSSRECONSIDERED | 73
For years, a number of methods called structuralist could be found in many disciplines. Indeed, structuralism became an umbrella tenn for numerous related mediods and dieories. Basing in some measure die structural approach on the early tum of the 20th Century linguists Ferdinand Saussure and Roman Jakobson, structuralism in anthropology has perhaps been best exemplified by Levi-Strauss (1963); in contemporary linguistics by Chomsky (1968); and in philosophy by Foucault (1972) - though the latter denied being a structuralist. For a time structuralist approaches were widespread in literary criticism (e.g. Boon 1972, Ehrmann 1966), as well as in other areas (see Gardner 1972, WUden 1972). With the major exception of the Swiss psychologist Jean Piaget (1970, 1971), and rare structural approaches like Mucchielli (1970) and Riegel & Rosenwald (1975), not being experimental or computational, structuralism never gained acceptance in psychology. Despite this, the psychologist Howard Gardner in his history of cognitive science says of Levi-Strauss that:
Most of my colleagues would, I suspect, consign him to the tradition of Rousseau, Montesquieu, and the French Academy (to which he was re- cendy elected) rather than to the ranks of Simon or Chomsky, but I think that this assessment will tum out to be shortsighted. In my own view, despite his conceits and idiosyncrasies, his rather cranky set of interests and obsessions, IJvi-Strauss willprove to he an enduringfigure in the history of cognitive science (Gardner 1985: 241. Italics added).
Despite Gardner's (1972: xü) early recognition that the structural methods of Levi-Strauss and Piaget constituted "the most significant contemporary innovation" in the social and behavioral sciences, structuralism reached a relative dead end in the late 1970s or early 1980s. Aside from a general assigning of Levi-Strauss to the rank of forward look- ing visionary, the specifics of his enduring as a major figure in the history of cognitive science include: Posing questions central to both anthropology and Cognition as to the relationships between culture and mind, and contributing to current notions of classifying and categorizing. But more importandy, for developing a methodology founded on mathematic/algebraic/group theory.
The most strucmralist of psychologists was Piaget. Similar to Levi-Strauss — but independendy and structurally different — Piaget has, arguably, demonstrated a logico-mathematic structure underlying the cognitive development of children's 74 I R.LHASKELL
thought processes, espedally with regard to the concept of number. Seidom mentioned, Piaget believed he had illustrated that the development of cognitive opeiadons of children parallels die three Bourbaki elementary mathemadcal structures: an algebraic group, an order er network structure, and a topological structure.'2 He believed diat his findings indicated that mathemadcal structures are inherent in cognitive development and derive from a primitive sensory- motor action (the veridicality of his sensory-motor origin of number is not important for this paper). While many psychologists generally accepted Piaget's developmental find- ings, his structuralist writings have been virtually ignored and few have taken seriously the füll implications of his genetic epistemology framework as exemplified in what is here considered his three major theoretical works (1970, 1971a, 1971b) that constitute his structuralist thinking (Though Piaget is considered by most a child developmental psychologist, he considered himself first and foremost a genetic epistemologist). Even fewer psychologists seem to have understood the implications of Piaget's genetic epistemology than perhaps anthropologists who understand Levi-Strauss structuralist methodology.
Claude Levi-Strauss' Stmctural Framework and Method
The fourth way Levi-Strauss deviates from Standard frameworks was in the assumptions underlying his methodology. In attempting to demonstrate a logico-mathematic structure to Cognition, Levi-Strauss (e.g. 1963, 1966) worked with preliterate mythologies maintaining that they exhibited a kind of algebraic structure.
Mathematics and the Structure of Myths Levi-Strauss maintains that for any series of cultural myths it should be possible to Order the myths into a series of transformations of the same logical type. He Claims that:
12 Piaget (1971b) describes a conference he once attended on Mental Structures and Mathematical Structures. The conference brought together psychologists and mathematicians from around the world, including the renowned mathematician Jean Alexandre Dieudonne. Dieudonne was known for mistrusting anything psychological. His talk described the three Bourbaki mother structures of mathemadcal thought. Piaget then gave a talk in which he described the three mental structures that he had found in the development of thinking in children. To the astonishment of both Piaget and Dieudonne, they saw that there was a direct parallel between the three mathematical mother structures and the three structures of children's operaüona! thinking. Dieudonne said to Piaget (1971b: 26), "This is the first time that I have taken psychology seriously. It may also be the last, but at any rate it's the first". CLAUDE liVI-SntAUSSRECONSIDERED | 75
By systematically using this kind of structural analysis it becotnes possible to organize all the known variants of a myth into a set fotming a kind of permutation gnup, the two variants placed at the far ends being in a symme- trica!, though inverted, relationship to each other (Levi-Strauss 1963: 223. Italics added).
In defense of his methodology, he maintains that:
[structural methods] are, in the social sciences, the indirect outcome of modern developments in mathematics which have given increasing im- portance to the qualitative point of view in contradistinction to the quan- titative point of view of traditional mathematics. It has become possible, therefore, in fields such as mathematical lo^, set theoiy, group theoiy, and topolo- gf, to develop a rigorous approach to problems which do not admit of a metrical Solution (Levi-Strauss 1963: 26. Italics added).
At the time, claims like these were seen to be grandiose and unsupported.
It should be noted that structuralist methods legitimately involve a non- quantitative btanch of mathematics. As Levi-Strauss (1963: 283) emphasi2es, "One should keep in mind that there is no necessaty connection between measun and struäure" (italics added). Indeed, Kurt Lewin (1931: 150), considered the founder of social psychology, in his classic but seldom cited article, observed: "The propositions of modern physics, which are often considered to be 'anti- speculadve' and 'empirical' unquestionably have in comparison with Aristote- lian empiricism a much less empirical, and a much mon constructive character". (italics added). Along with a non metric lawful structure, it is this constructive character — in contradistinction to the perceptually given character of most empirical psychology and anthropology - that defines Levi-Strauss' structural- ism. Further, though separated by nearly sixty years from Lewin, the well-known psychologist, Roger Shepard su^ests that psychological science need not limit itself to descriptions of observed empirical regularities (e.g. frequency based and phenomenological data), but can
aspire to a science of mind that, by virtue of the evolutionary intemaliza- tion of universal regularities in the -^otXA, pariakes of some of the mathematical ekgance and generaüty of theories of that world. The principles that have been most deeply internalized may reflect quite abstract features of the 76 R. E. HASKEli
World, based as much (or possibly more) in geometr\', probability, and ffvup theoiy as in specific, physical facts about concrete, material objects (Shepard 1987, 1994: 26. Italics added).
Granted, Shepard's work belongs largely to sensory psychology and psycho- physics. Nevertheless, he suggests a search for (non starisdcal) mathemadcal structures undergirding thought and behavior. More recendy, the Computer scientist and linguist Klein wriong on the analogical foundations of language and culture concludes that:
The post-StructuraUst wing of the post-Modem movement in anthropological & archaeological tbeory rejected the Structuralism of the 1960s for a number of reasons, among which was its apparent static nature. The theory I have proposed uses the techniques of structuralist analysis for the coUection and analysis of data, but makes use of implied logical rela- dons as data for dynamic models of complex social behavior and change. The result is that a structuralist methodology is used to derive the conclu- sions of post-structuralist theory, and that the structuralist models of Claude IJvi-Strauss appear to have an empiricalfoundation (Klein 2002: 19. Italics add- ed).
Finally, Haskell & Badalamenti süßest evidence of an algebraic structure in a set of oral narratives with numeric references:
There are many possible uses of generalizing the possible fact that Cogni- tion itself operates via the mathemadcal concepts that have been taken to be the end products of Cognition rather than their progenitors. That is, the narrative that one uses to define the idea of a semi group is itself formed by Operations that presuppose the concept itself as a principle of Operation. [...] If the present inference that some of mathematics is itself the organizing principle of Cognition is correct, then a blueprint for dee- per and more functional mind maps presents itself (Haskell & Badala- menti 2003: 10).
The problem remains, however, that Levi-Strauss' methodological procedures - as practiced - seems to be resistant to replication by others. Finding (mathemadcal) laws undergirding human behavior has been, and conünues to be - albeit not without considerable ambivalence - the Holy Grail CLAUDE IfVl-STRAUSSRECONSIDERED | 77 of behavioral science. Levi-Strauss' stxuctural anthropology was in search of such a Holy Grail.
Invariance and Variation According to Levi-Strauss, myths are permuted into variant myths, with each myth containing slightly different infonnation. Variations form a matrix, constituting a kind of lattice structure. Together, these variations fonn a permutation group constituting one mythic structure. There are, he says, transformation rules rendering the entire series invariant. A basic matrix resulting from his structural analyses of a series of myths is diagramed as foUows:
Myth Matrix Myth #1 ab_d g Myth #2 _bc_e_g Myth #3 a __ d e f_ Myth #4 ab fg Myth #5 __cdefg
Each letter in a matrix represents one element and/or message within the given myth, with each blank Space representing a missing component. Taken collectively, and coUapsed into a single structure, the myth matrix yields a complete message, i.e. a, b, c, d, e, f, g. It should be noted that to construct such a matrix, Levi-Strauss works with abstract relations found within mythic content and with Operations performed on that content, not with the content per se (see more below). So misunderstood and controversial — and admittedly, inadequate — has Levi-Strauss' method been that it has led to characterizing him as "Playing tic- tac-toe with topological diagrams" (see Leach 1974: 54); and as engaging in "intellectual gymnastics" (Leach 1974: 27). Such widespread reactions and dismissals either lead to the conclusion that Levi-Strauss is completely fiazzy headed, or that the critiques point to something unfamiliar being afoot that simply does not fit with historically Standard empiricist ways of knowing. In further Support, the following will suggest the latter is in fact more likely the case. 78 I R.E.HASKEII
Empiricist Epistomethodolo^ In Order to see Levi-Stxauss' current relevance, one must understand his basic epistemological insight, which, while constructivist, is strongly empirical. As briefly mendoned above, the criocisms of Levi-Strauss often stem from basic mediodological and epistemological conflicts. It is increasingly clear that there exist fundamental differences between structuralist and empiricist approaches to (a) the use of data and (b) the methods of analyzing those data, differences that seem to defy accommodation. Without engaging in a lengthy definiüon of empiricism, suffice it here to cite Leach's (1974: 43) brief Observation: "Empiricism here seems to mean that truth must be verifiable by reference to observable facts; it stands opposed to rationalism which reaches to a deeper form of truth by means of Operations of the intellect". This dichotomous view is too simple. First, Levi-Strauss does attend, in empiricist terms, to observable facts. The observable facts are the mythological stories as well as the contextual anthropological data pertinent to their analysis. Second, he engages in Classification of those facts. Thus, he is not simply a rationalist in the philosophical sense. Just as empiricist methods subject facts to procedures (Statistical, comparative analysis, etc), Levi-Strauss also subjects the facts (i.e. myths) to procedures. However, he uses a different set of procedures to categorize and control his data. This is where problems arise from a Standard empiricist perspective. It is important to note that for Levi-Strauss scientific reality does not derive from the phenomenal or empirically given surface facts (again, myths). In contrast to Standard empiricist methods, his structural approach sees scientific reality as a constructive process. This means that scientific reality is that which is derived from Operations performed on phenomenological (read: surface) fijcts or data. As such, the derivations may not bear any immediate similarity to the original phenomenal character of the facts or data. Again, many concepts in physics such as the gravitational constant, black holes, strings and other (seemingly bizarre) mathematically derived structures are exemplifications of constructed (non phenomenological) knowledge - though, admittedly, such realities are tied by a chain of linkages to the empirical observational data. Clearly, though, findings based on Statistical correlations result from Opera- tions performed on data and thus are derived structures, they are not of the same logical type as those derived strucmres from mathematical physics where Operations performed on data suggest that time may be reversible, or that there is a gravitational constant yielding the rate of acceleradon of bodies of lesser CLAUDE LEVI-STRAUSSRECONSIDEREO | 79 mass toward a more massive body. These latter scientific realities are neither phenomenally given, nor are they the consequence of a simple superimposing of arithmetic concepts and procedures on to data, e.g. mapping of / + / = 2 onto any set of entities, or applying Statistical analysis of variance procedures to data. They are instead constructive. Most importandy, unlike contemporary empiricist methods, structural methods do not require Statistical sampling of data. Just as physicists do not work with a sampling of falling bodies, but instead carefuUy examine a specific case, so too Levi-Strauss' work with myths does not require sampling proce- dures. Sampling procedures are not relevant in a structural methodology because the purpose is not necessarily to claim that all or most myths exhibit an algebraic structure, but rather that the form some myths take exhibits a structural lawfulness.'^ In this sense Validation procedures are not only similar to those in mathematics, but to linguistic analysis as well: Linguists do not work with random or representative samples of language. The parts of speech and their combinations such as nouns, verbs, adverbs and so on are regarded as neither random nor merely probable but as lawfid to language. In like manner, the internal structure of myths is considered lawfiil just as mathematic or linguistic systems. Validation in structural systems, then, is in large measure based on consistent internal, systemic order relations and transformations (see HaskeU 2003a). But unlike pure mathematical systems where the extemal realities to which they are applied are irrelevant, structural systems as applied to human behavior must have a correspondence with an extemal reality, otherwise they would just refer to themselves. But even in "pure" mathematics, pragmatic proof is judged by the application to empirical realities. For example, exponential equations, while not required to correspond to any extemal reality in fact do so; they correspond to the growth of Compound interest in bank accounts and to the increase in egg production. Ideally, if not in actuality, a developed structural method - and hence Levi- Strauss' method - adheres to what can be generally considered the five essential characteristics of any scientific methodology: (1) the systematic gathering, and
13 Classically, as Nagel (1961) clearly shows, a scientific theory or law is State dependent. That is, it is ahvays stated within a description of its surrounding conditions. E.g. that water boils at 212degrees Fahrenheit is State dependent on being at sea level. In logico-mathemadc method terms, State dependent translates to a description of the contextual conditions under which a given operation will occur. 80 I R.EHASKEU
(2) manipuJarion of empirical data, with (3) rigorous procedures for the ccjntrol of that data, and (4) the testing of hypotheses, (5) all of which revolve around falsification criteria. These goals, however, may be achieved in a variet)' of ways, e.g. experimentally, statistically, or structurally. While few researchers would deny the power of rigorous design, there is growing recognition and dissadsfac- tion, among otherwise hardnosed researchers, with cognitive science research almost exclusively to experimental, statistical/quantitative, especially for computational and other algorithmic-compatible methods (e.g. Brooks 2001, 2002, Bruner 1990, Fodor 1980, Edelman 1992).""
The Problem ofReplication Given that Levi-Strauss' definition of structuralism as essenrially mathematical in structure and Operation - and often algebraic in form - his structuralist procedures should, in principle and conceptuaUy, like mathemarics, have been relatively straightforward and unproblematic. But they were not. Problems arose in applying his procedures for demonstrating that a series of myths conform to an algebraic structure and in replicating his transformations responsible for the structures he found. To derive equivalence to a set of myths, his transformations were all too often based on interpretive analyses of semantic content. In addition, cognitive Operations like the algebraic reversal Operation were said to be exemplified by the notion of reciprocity. Maybe so, but it left a lot of researchers unconvinced. As in all of science and mathematics, researchers must be able to replicate Operations performed on a set of data and to derive the same findings. If the structures undergirding myths and their transformations reflect a permutation group as Levi-Strauss claims, then just as in mathematics or linguistics his findings should be replicable. The historical fact is, however, that his findings were considered - and not without some justification - not only problematic but, arguably, irreparably so: Other researchers frequentiy failed to agree on what constituted a transformation of a myth and failed to derive the same structures that he claimed existed between different myths and their variants or permutations. The same problem arose when applying structuralist methods to
14 Rodney Brooks is Professor of Robotics in the Electrical Engineering & Computer Science Department (EECS) at the Massachusetts Institute of Technologe'. Jerome Bruner is one of the founders of what has come to be known as the cognitive revolution. Gerald Edelman is a Nobel Laureate in immunology; he calls the mainstream computational approach to model- ing Cognition 'scandalous'. CLAUDE LEVI-STRAUSSRECONSIDERED | 81 literary works. Using a set of Greek myths as exemplars, Leach correctly identified die problem. He says (1974: 87) diat "for almost any story drawn from the general complex of classic Greek mythology tums out to be a variant in one way or anodier". While cleariy a problem — though not in theory an impossible one - the problem is neither unique to Levi-Strauss, nor to structural analysis in general. Establishing an equivalence or transformation is a problem involved in all categorization and Classification - and thus in how a given entity is said to belong to a given class or category. Any set of data can be carved up in numerous ways. In biology, for example, the very core notion of what constitutes a species continues to be problematic (see Gould 1983) as do many everyday categories, e.g. chair. Does a chair have to have a back, does it have to have four legs, or any legs at all; what of a beanbag chair? The absence of clarity around the core notion of species, however, does not invalidate biological taxonomies involving the concept of species. In addition to the various taxonomic systems, e.g. cladists and the pheneticists, there is the more cognitive problem of establishing and agreeing on the similarities and differences between two organisms (read: myths) that then put them either into one or another category. Once one leaves the agreed upon categories, establishing what belongs with what becomes open to debate. The problem of establishing invariance, then, is an endemic one in everyday settings, cognitive science, and natural science (see Haskell 2000, 2004a). That Levi-Strauss is aware of this problem can be seen in the tides of his chapters in The Savage Mind (1966: 161): "Elements, Species, Numbers"; and "Universalization and Particularization", in which he lays before the reader the very problem of categorization just discussed.'^ The fundamental reason Levi-Strauss structuralist methodology and findings are not as straight forward as the mathematical model he assumed undergirded them was that he was working with interpreted semantic structures in his analysis of myths and their elements, which are inherendy ambiguous. This is perhaps the most serious problem in Levi-Strauss' method. In faimess, it should be said, however, that Levi-Strauss certainly considers his approach only a work in
15 A cladist system of Classification is based on phylogenedc relationships and the evolutionary history of groups of organisms; a phenetic system of Classification based on Overall observa- ble similarities rather than on phylogenetic or evolutionary relationships. 16 The particular vs. the universal is an cid and continuing and unsolved conceptual problem (see Hoffding 1905). 82 R. E HASKEli
progress. As he made clear (1966: 13), "I shall no doubt be accused of over interpretation and oversimplificarion in my use of this method. Let me say again diat all the soludons put forward are not presented as being of equal value, since I tr^self have made a point of emphasi^ng the uncertainty of some of them". And again, he notes (1966: 210), "The only method we can suggest at this stage is toproceed tentatively, by trial and error" (italics added). But what if Levi-Strauss' iniaal demonstrations were taken as only pointers to a new approach and set of tentative procedures rather than being seen as evidence for dismissing his approach as irreparably invalid? And what if a Levi- Straussian analysis did not have to work with semantic structures and interpreta- tions? And further, what if laboratory designs could be developed to model mythic narratives? The following section will suggest that Levi-Strauss' ideas can be modeled and tested in such settings.
The (Modem) Savage Mind Revisited Leach (1974: 59) maintained that "If we are to get at the primitive universal logic in its uncontaminated form, we need to examine the thought processes of very primitive technologically unsophisticated peoples". But I^vi-Strauss hints that one should be able to fmd evidence of the savage mind in modern Cognition. His claim, however, was an in-principle one only, and neither he nor anyone eise has demonstrated the primitive universal structure of Cognition in modern thought. If Levi-Strauss' claim of a universal set of cognitive Opera- tions is correct, then similar cognitive Operations to The Savage Mind should still be vestigially evident in contemporary language and Cognition. Indeed, applying a specifically developed logico-mathematic methodology on data gathered under laboratory conditions, Haskeil (2003a) has found contemporary oral narratives comparable to Levi-Straussian mythic and other semiotic structures (Haskeil 1985), including a set of numeric references with an algebraic undergirding (Haskell & Badalamenti 2003).i'' These findings offer, at least, the possibility of designing laboratory models of mythic narrative analysis, a kind of laboratory for investigating Levi-Straussian claims and findings.
17 The empirical oral narrative data-base was gathered in a small group dynamics laboratorv', where ten to fifteen members engaged in unstructured and spontaneous verbal discourse, similar to everyday occurrences. The narratives are considered the cognitive equivaknt of preliterate myths. However, it should be emphasi7.ed that the term "cognitive equivalency" does not imply identity; there are differences between preliterate myths and verbal narrative. For example, myths issue from an oral culture and the verbal narratives from a literate one (see again Goody 1977, Chemigovskaya 1994, Luria 1976, Ong 1982). CLAUDE LEVI-STRAUSSRECONSIDEREO | 83
I^st a Levi-Straussian laboratory seem inappropriate (as not a few have reflexively suggested), consider Levi-Strauss' view on diis matter. In a different - but structurally equivalent/analogous - context he explained:
What is the virtue of reduction either of scale or in the number of proper- ties? It seems to result from a sort of reversal in the process of under- standing. To understand a real object in its totality we ahvays tend to work from its parts. The resistance it offers us is overcome by dividing it. Reduction in scale reverses this Situation. Being smaller, the object as a whole seems less formidable. By being quantitatively diminished, it seems to US qualitatively simplified. More exacdy, this quantitative transposition ex- tends and diversifies our power over a homologue of the thing, and by means of it the latter can be grasped, assessed and apprehended at a glance (I^vi- Strauss 1966: 23-24. Italics added).
He goes on to explain:
miniatures have a fiirther feature. They are man made[...].TAgi an therrfore not just projections or passive homotogues of the oiject: th^ constitute a real experiment with it. Now the model being an artefact, it is possible to under- stand how it is made and this understanding of the method of construc- tion adds a supplementary dimension (italics added).
Levi-Strauss clearly understands the value of modeling. Multiple models of both field and laboratory-generated narratives could be developed for analyzing Levi-Straussian (and other) claitns. Two basic approaches to such modeling might include: First, a Standard (empiricist) laboratory experimental design with independent and dependent variables could be conducted with a group of participants generating a series of oral narratives hypothesized to have been stimulated by an independent variable, say the introduction of three confederate members whose role would be to dominate the group. Transcripts of the oral narradve series would then be systemically analyzed for their Levi-Straussian (and other) structural properties. It is at this point that the empiricist method requires further procedures/ methods for analy^ng the complex linguistic and structural Operations in the narratives. Second, other research models could include cultural myths and/or other oral narratives gathered from field work or from the vast anthropological archives of such oral data, which could be analyzed using either the methods 84 R. E HASKEll
oudined below by Haskeil (2003a), those of Griffin (e.g. 2006, 2003) or complementary field models developed from more specific anthropological expertise in preliterate mythology. The logico-mathemadc, stxuctural and linguistic method developed by Haskell (2003a) will be illustrative of the first method. In particular, one set of narratives containing numeric references will serve as an attenuated example. In keeping with the above suggested experimental model, the independent variable of three members, whose role was to dominate the group, generated a series of spontaneous narratives with each containing references to "three people" in various and different situations was found. As with most social situations where people are verbally dominating, there is underlying affective Schemata about being dominated. Further the subgroup triad was composed of one female and two males.'8 Each narrative containing a numeric reference to "three people" forms one tier of a matrix, similar to the Levi-Straussian matrix noted earlier. Together, the tiers constitute a kind of lattice structure forming one multilayered mythic structure with transformation procedures rendering the series invariant. For example, each narrative contained a different attribute of the three dominant members. One narrative describing three people in a bar corresponded exactly to the numeric and gender composition of the three dominant members in the group, i.e. one female and two males. Each narrative within the lattice matrix, like a Levi-Straussian myth matrix, contains only partial information. Taken together, when the multiple narratives are collapsed into a single matrix, they constitute a complete "message" (for a füll discussion of the structural Operations active in this semiotic matrix, please see Haskell 2003a). The modern mind - under certain conditions — then, seems not so significandy different from the Savage Mind described by Levi-Strauss. Still, it is significant to mention that in order for the above set of structurally integral numeric topics to be consistentlj generated, with each representation and its associated attribute description, as well as their corresponding isomorphic meanings across the various transformations they must somehow be cognitively (a) mapped, (b) tracked, and (c) stacked systemically throughout multiple levels of meaning and
18 It should be noted that a tape-recording of the entire eight>-minute narrative Session provided a verbatim transcript. It was therefore possihle to ^stematically account for each numeric reference in a narrative during the entire session, thereby virtually eliminating selection hias. it is methodo- logically noteworthy to note that numeric findings have been found across multiple proto- cols, and that numeric topics also consistendy and systemically corresponded to other facdons within the discourse Situation (for a complete explication see Haskell 2003a: 15-25). ClAUDELEVI-STRAUSSRECONSIDERED | 85 through the various narrative permutations, all remaining invariant with respect to the specific set of characteristics and meanings." Undergirding this series of numeric narrarives - as Levi-Strauss attempts to show with myths - is an algebraic group (Haskell & Badalamenti 2003). As briefly mentioned earlier, the problem with demonstrating an algebraic structure in myths has been that virtually all structuralist research claiming to find (or not to find) one has been conducted on semantic data as constituted in myths and literary stories, etc. In contrast, numeric references being cleariy bounded and concrete can more predsely and systemically be mapped and tracked throughout an entire mythic/narrative protocol than can semantic references. Accordingly, when possible models should analyze protocols containing numeric references. It is methodologically noteworthy to point out that the isomorphic corres- pondences between literal narrative numeric references and the membership subgroup factions in Haskell's (2003a) findings mentioned above are arrived at independent of the complex methodology: No special procedures, methods, Operations, interpretations, or analyses are required to establish such simple mapping correspondences. Very broadly, the procedure used in analyzing the narratives is a straightforward structure mapping process similar to that now currendy found in analogical reasoning research (e.g. Genmer 1983, Haskell 1982) — an area in which, as shown above, Levi-Strauss had early insight.
Conclusion
To conclude where diis article began, a quote by Alfred North Whitehead (1929: 16) seems appropriate: "Every science must devise its own instruments". A quote by Giambattista Vico from his New Säence (1948/1727: 49) argued similarly that "Doctrines must take their beginnings from that of the matters of which they treat", by which he meant — for example — that to understand poetry, methods appropriate to that subject matter must be developed. Based on his Observation and analysis of preliterate myths, Levi-Strauss has developed a methodology and an undergirding epistemology consistent with his (myth) subject matter.
19 Like unconscious numeric referencing, numeric tracking raises the question of what purpose it might serve. It is suggested that it serves to track group membership. It is well established that nonhuman animals possess the ability for tracking. For an initial evoluüonary perspective on this group tracking issue; see Haskell (2004). 86 I R.LHASKELL
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