The Morphological Genealogy of Structuralism

The Morphological Genealogy of Structuralism

Jean Petitot
(Extracts translated by Daniel Whistler)

The Reference to Naturalism

The second part of Chapter 11 of Claude Lévi-Strauss’ De Près et de Loin (“On Sensible Qualities”) offers a host of very illuminating remarks on the way in which he understood the epistemology of structuralism and its position in the history of ideas. To Didier Eribon’s question concerning the central concept of transformation (“Who did you take it from? From the logicians?”), Lévi-Strauss responds as follows:

“Neither in logic nor linguistics. I found it in a work that played a decisive role for me… On Growth and Form… by D’Arcy Wentworth Thompson… The author… interpreted the visible differences between species or between animal or vegetable organs within the same genera, as transformations. This was an illumination for me, particularly since I was soon to notice that this way of seeing was part of a long tradition: behind Thompson was Goethe’s botany, and behind Goethe, Albrecht Dürer and his Treatise on the Proportions of the Human Body.”*

This testimony is crucial not only, specifically, for the history of anthropology and structural mythology, but also, more generally, for a proper understanding of the theoretical genealogy of structuralism as such. Instead, it is typically thought (it is a received idea) that structuralism is contained within a formalist, logical and linguistic lineage, and so it is conceived as the application of a static, algebraic-combinatory concept—in the best case, a Hilbertian-Bourbakist concept—to the human sciences. However, there also exists an alternative way—“another itinerary”, as Lévi-Strauss puts it—of envisaging it, which is essentially different.

Naturalist and not formalist, it consists in treating structures as dynamic forms in development (“growth and form”), as morphodynamically (self-)organised and (self-)regulated totalities. This “other” tradition is much older and more profound than the formalist perspective, and it is thrilling to see the way in which Lévi-Strauss associates himself with it.

Throughout De Près et de Loin, he makes known his longstanding interest in this type of naturalism:

“The traditional natural sciences—zoology, botany, geology—have always fascinated me, like some sort of promised land I will never have the privilege of entering… From the time I began to write Totemism and The Savage Mind up to the end of the Mythology series, I lived surrounded by books on botany and zoology… my curiosity about such matters dates back to my childhood.”*

And this reference to naturalism is, of course, radicalised by his critique of the formalist paradigm. After having distinguished himself from it (“the nature and importance of my borrowings from linguistics have been misunderstood”*), he continues with an evaluation of the theoretical role of the concept of transformation:

“The notion of transformation is inherent in structural analysis. I would even say that all the errors, all the abuses committed through the notion of structure are a result of the fact that their authors have not understood that it is impossible to conceive of structure separate from the notion of transformation. Structure is not reducible to a system: a group composed of elements and the relations that unite them. In order to be able to speak of structure, it is necessary for there to be invariant relationships between elements and relations among several sets, so that one can move from one set to another by means of a transformation.”*

This belonging together of the concepts of structure and natural form is found everywhere in Lévi-Strauss’ writing, from his epistemology to his aesthetics. […]

Genealogies: The Origin, Essence and Horizon of Structuralism

This assortment of evidence suggests a naturalist genealogy to structuralism, which can determine very precisely its origin, its essence and its scientific horizon. Insofar as I myself have long been engaged in research into morphodynamic structuralism, Lévi-Strauss’ affirmations were an “illumination” to me. From the very beginning of the 70s, I had, indeed, established a link between, on the one side, authentically scientific structuralism (C. Lévi-Strauss, R. Jakobson, L. Hjemslev, A.J. Greimas) and, on the other side, the revolutionary dynamic models for morphogenesis proposed by René Thom. On this basis, I had tried to reconceptualise those philosophical and scientific traditions from which the new models could be considered to descend, and I passed backwards through Waddington and D’Arcy Thompson (Thom’s great biological heroes, alongside Saint-Hilaire and Goethe) to the vitalism and Naturphilosophie of the previous century, then to Kant’s third Critique and finally to Leibniz. Thus, the fact that Lévi-Strauss himself—so often criticised for his formalising abstraction—considered himself to belong to this intellectual family was an astonishing confirmation of this trajectory.

This remarkable convergence proves that there really exists a scientific lineage and a genealogy of ideas from structuralism. In many texts, I have analysed all this in detail. I will return here briefly to this genealogy to give some points of reference. To evaluate them properly, three fundamental givens must be kept in mind:

(i) structuralism raises a general scientific and philosophical problem—that of the relations between form and matter by way of substance and, more precisely that of the systematic organisation of parts in a whole by way of relations of dependence;

(ii) this problematic is evidently manifest in the case of natural forms;

(iii) in the case of cognitive and semiotic structures where matter is not immediately given, and is thus phenomenally absent, form is traditionally thought, because of this very absence, on the basis of the model of logical form.

[…]

After Kant, Romanticism looked to transcend the critical claim that the attainment of knowledge demands the negation of nature’s interiority. In particular, with Naturphilosophie, Schelling opposed the objective mechanical concept of nature with a free intuition of itself, which is the absolute conceived as the proleptic tendency towards unconditioned freedom. In situating “life” at the crossroads of nature and freedom, in thinking it as “freedom in the phenomenon” and as autonomy in sensible existence, he transgressed the Critique of the Power of Judgement’s conclusions and inaugurated vitalism. He admitted the Idea of the system as principle of the formation of organised forms and developed a new principle of entelechy.

Goethe partly followed Schelling. But, in opposition to the speculative vertigo of interiority, he held fast to the appearing of natural forms. For him, the solidarity between teleology and aesthetics opened up a problematic of the description of appearing which—as has been nicely shown by Filomena Molder—can be considered as a precursor to the phenomenological, structural and semiotic problematics. Goethe limited the entelechial principle to Erscheinung. For him, any understanding of the latter is symbolic. Appearing manifests an expressivity which affects the subject and which must be described in an appropriate symbolic language. Phenomena are not only representations which must be transformed into objects of experience, they are equally signs, presences translatable into symbols. There exists for Goethe a sui generis structure of the visibility of appearing, which in turn expresses, in a play between Bildung and Gestaltung, his entelechial principle of formation. Of course, there is an internal principle of formation, but this is just a matter of understanding it from the description of its “externalisation”. In opposition to what happens in Schelling, in Goethe the entelechial principle is not teleological. The “ground” (the internal organisational principle) is not within or beyond appearing. It is given in appearing, even to the extent that morphologies are like signs which self-interpret. This is why “metamorphosis” is the object of a “new” science, morphology, an autonomous, descriptive, eidetic science—new not in terms of its object, but in terms of its method.

[…]

D’Arcy Thompson was an exceptional man of letters, an eminent naturalist, a pioneer of oceanography, a mathematician, a Hellenist and a poet. Other than Lévi-Strauss, it was he who inspired the greatest specialists of morphogenesis and the theory of evolution, in particular Alan Turing, René Thom and Steve Gould (who wrote a preface to On Growth and Form). Fascinated by the enigma of bio-physical formation in the geometry of the living, he returned to the idea of a plan for species organisation (Buffon, Saint-Hilaire, Goethe) and exploited it to understand specifically how the morphologies of comparable species (like different species of fish or the chimpanzee and homo sapiens) could be geometrically transformed into each other. He can thus be considered as one of the founders of morphometry. The transformations that he deployed are often conformal transformations, less rigid than isometries (isomorphisms of metric structure), but much more rigid than diffeomorphisms (isomorphisms of differential structure) or, a fortiori, homeomorphisms (isomorphisms of topological structure).

Without doubt, René Thom was D’Arcy Thompson’s chief heir insofar as the former realised much of the latter’s dream for a morphological geometry. But Alan Turing must not be forgotten as one of the pioneers of a general physicalist theory of biological morphogenesis, particularly in his key 1952 article, “The Chemical Basis of Morphogenesis”. He was the first to understand how forms could result from instabilities in biochemical processes of reaction-diffusion through the interaction of different morphogenic substances. Instabilities rupture the homogeneity of tissues and, from this nucleation, develop morphological structures. These ideas have been applied with considerable success to the process of the emergence of characteristic spatio-temporal patterns (markings on animal fur, pigmentations on shells, parallel stripes on digital prints, etc).

Turing is equally very important to the extent that he was one of the first to understand technically (and not only speculatively, as his predecessors did) that there exists an essential connection between biological morphogenesis and cognitive structures. In both cases, the “macroscopic” form-structures emerge from “microscopic” interactions in physical nature (chemical, electric, neuronal) and this, in turn, justifies the aim of describing a unitary physicalist theory of biological forms and cognitive structures.

Since these pioneering works, extraordinary progress has been made in understanding the morphological organisation of substrates. We will return to this below. For example, we now understand more and more about how biomineralization is achieved and how the formation of biogenic crystals in tissues with very different forms can be controlled by the organism. In short, we are beginning to explain the way in which, in every domain, morphodynamical structures can be materially achieved.

[…]

Matter, Substance, Form: The Naturalisation of Structuralism

Form is the phenomenon of the organisation of matter, matter organised by form being substance. And from this there is a double destiny for the idea of form. In the case of natural forms, the material substrate is given. Even if for a long time no one understood the physical, biochemical, thermodynamic and systematic processes engendering forms, even if, in order to think them, there was recourse to speculative concepts like that of entelechy, it did not prevent the donation of the substrate from being put into question. Idealisms of form (vitalism, for example) resulted from insurmountable difficulties in theorisation, rather than arising from the phenomena as such. However, in the case of cognitive, semiotic and symbolic structures, everything proceeded differently. Matter is not given in the phenomenon and this is why the objectivization of form occurs, in general, on a formalist model: formalist idealism comes to the fore when forms are decoupled from their matter. Indeed, the matter of cognition, of thought, of consciousness, of spirit and of sense—matter where its structures are self-forming—is neuronal matter.

The scientific actuality of structuralism encompasses two aspects:

(i) the convergence of its two genealogies in the framework of an expanded naturalism that includes a naturalisation of phenomenology;

(ii) the possibility of developing its materialist models to allow for the surpassing of formalist idealism.

[…]