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).