Ars combinatoria, cybernetics, mimesis & praxis

Henri Lefebvre

In the same way are its intellect and its language, at least virtually. Automatons will ‘speak’ the universal metalanguage, reached by successive approximations (Algol, Syntol, etc., present-day machine languages). Human discourse differs from this by its imperfections: excessive and useless redundancy, spaces between morphemes (words), silences. In the human being, emotion that seems completely personal and draws it into illusions of subjectivity is simply disturbance, hesitation. The automaton also expects: it examines all possible combinations and makes the right choice. It is more intelligent than the human being. Shall we say that it can neither laugh nor cry? But it can; so long as the programmer has well defined laughter and tears, the situation for laughter and the corresponding stimulus. 

Mimesis is double. It reproduces an acquisition and aims at something inaccessible that it incompletely attains. The quality of information gained over the inaccessible that is too complex, chaotic and prolific, can be calculated. This makes it possible to quantify the complexity of any message, and even each new combination of distinct elements (objects, acts, atoms of meaning, etc.). Quantification accompanies the transition from the ‘unstructured’ to the structural. In the name of quality itself, it moves in a dialectic of quality from qualitative data to the quantitative system.

Structuralist activity is thus always bound up with a technology. It combines two fundamental operations: dissection (into discrete units, atoms of meaning) and arrangement [agencement].

What does this reduction bracket out? A good deal. The concrete complexity of praxis, that of man and that of the world. Dialectics. Tragedy. Emotion and passion. The individual, certainly, and perhaps a large part of the social. And then history. All this falls into the residual, which has to bend itself to globalized technicality and disappear.

The source and prototype of intelligibility is situated neither in individual consciousness (the classic Cartesian position, continued in existential philosophy by Sartre), nor in ‘being’ (the classic metaphysical position, continued and transformed by Heidegger), nor again in praxis (the Marxist position). This source and prototype is situated in language. The formal operation of the structuralist intellect is dichotomy. This separates, divides, classifies (into genres and kinds), determines formal differences, paradigms, conjunctions and disjunctions, binary oppositions, questions that it answers by a ‘yes’ or a ‘no’. Leibniz already asserted, building on Llull’s ars combinatoria, that the whole world (numbers and beings) arose from the opposition and combination of zero and unity.

We have to recognize that this conception has received powerful support. In terms of calculating and translation machines, built effectively on the binary principle, structural linguistics, developments in pure and applied logic with games theory, decision theory, operational research, information theory. The definition of the intellect by separation, differences and dichotomy seeks to be functional and operational, which indeed it is. It undoubtedly corresponds to the fundamental activity of technical thought. It thus links up with operationalism: a doctrine of efficacity, a praxeology.

Technocracy, today, needs an ideology that justifies it and makes possible the integration of the society that it seeks to construct. Now the mondialisation of technology and the technocratic conception presupposes a reduction and even a liquidation of the historical (seen as dead weight, residue, more embarrassing than picturesque).

With the reign of pure technicality and technocrats, with the cybernetizing of society, we would no longer have a future in this historical sense, a temporality in the customary sense. We would enter a kind of eternal present, probably very monotonous and boring, that of machines, combinations, arrangements and permutations of given elements. There would be no other events than the introduction of new technologies (which moreover could make great demands). Unless ‘deviants’, who would be pursued with barbaric cruelty, intervene to derail the system. Unless destruction and self-destruction one day put an end to this ‘world’.

Historical thought, on the other hand, maintains that contents have as much importance and interest as forms, if not more. It says that forms and structures are made and unmade, dissolve or break up. It places on the same level, in time, the formation of structures (structuration) and their disappearance (destructuration). It shows, within structuration, the commencing dissolution or inevitable explosion. For it, the historic past is not reduced to a dead weight or a picturesque superfluity. Differences manifest themselves as they have always done within worldwide technology, due to the history of societies, groups, classes, peoples, nations. History continues. The seemingly irrational demands its integration, not into a philosophy or forms that reject it, but into a conception of man as a whole. In the absence of which it rebels. The theory of alienation denounces fetishisms, splits, mutilations of the total human being. It particularly denounces technical, technological, technocratic alienation, recently promoted to the rank of major human alienation.

And time? In the structuralist conception it disappears as becoming, genesis and formation; it is reduced to the order of appearance of more or less probable combinations, with a lower limit in pure repetition and an upper limit in unpredictable combinations involving the most unusual elements. The notion of temporality disappears into that of entropy (measure of the degree of irreversibility), between the lower limit of the immutable and immobile order, absolute cold, and the upper limit, the frenetically disordered agitation of molecules. The aleatory enters into the calculation and is envisaged as such. Along with time, it is history that disappears in the world, or acquires a new aspect, opening onto a kind of technological temporality without history, or with its only history that of combinations between technological operations.

Technological rationality, then, goes a long way. It challenge and undermines many theoretical and practical elements that seemed to form part of the definition of man, whether considered as faber, sapiens or ludens. It attacks time. This is far more than a matter of history considered as science of time, and heralds attacks on real (practical) time and its mutation into technological time, if this is allowed. It is scarcely a caricature of technological and cybernetic rationality (a rationality that, as we see ever more clearly, defines itself as understanding rather than reason) to say that for it, nature or what passes for nature scarcely counts for anything. It is an obstacle. It should be got rid of, the time devoted to these functions reduced or even substitutes found for them. Vital and cosmic rhythms? They are a kind of enemy to pursue in favour of a linear time broken into well-defined atoms (semantemes). Technological and structuralist thought is culturalist. Like culturalism, it deprecates nature. Like structuralism, it brackets it out. Nature is simply residual, and history likewise.

If robots converge with men, and man recognizes himself in this mimetic image, the spontaneity of the automaton, this is because man was already a robot. He did not know this. He is learning it. The nervous system and other biological, physiological ‘systems’ are self-regulating systems. The living body? A network of such systems, a complex homeostatic system of which Ashby’s quadripole offers a simplified model. The brain? A complex and imperfect machine for recording, combining, disjoining and arranging. Thought? A succession of ‘yeses’ and ‘noes’, dichotomies. Action? A series of strategic decisions in a complex play with ‘nature’ and other social groups. If society can subsist, it is because it contains self-regulating systems. It is because it is already a homeostatic system. In the new sciences of information and communications, the combinatory essence of the real, its fundamental structure, is discovered and recognized. As for nature, it does not even exist. It was also just illusion and myth. Still more: a residue. Mimesis turns out to be the essence of praxis; the appearances of appearance or of appearing fall away: those of poiesis, those of transcendence, of subjectivity and subjective freedom, of temporality and historicity, of nature as a whole. The robot is no threat to man, for the excellent reason that individual and social man is already a robot, and the threatening image of the robot is mere illusion. The figure of the monstrous and untameable golem, rebelling against the sorcerer’s apprentice, would be simply a myth of the machine, and the myth of the robotic inhuman a myth of man. The two entities, automaton and human, meet up in a single category: the Cybernanthrope!

SOURCE: Lefebvre, Henri. Metaphilosophy (Métaphilosophie, 1965), translated by David Fernbach, edited with an introduction by Stuart Elden. London; New York: Verso, 2016. Excerpts from Chapter 6: Mimesis and Praxis.

Note: This book is very rich on a number of fronts. I have singled out the key passages related to the ars combinatoria (combinatorial thinking in general), from chapter 6, which has even more to say about cybnernetics (artificial intelligence) and other matters.

Two quotes from chapter 7 are also outstanding. These themes are amplified especially in chapter 6, also in chapter 7. There are stray references to combinatoria elsewhere:

Chapter 1 (Prolegomena: Notice to Readers): Combinatory conception of intelligence (Leibniz, Condillac, etc.);

Chapter 3 (Philosophy in Crisis): Leibniz: harmony in the combinations (among monads);

Chapter 5 (The Search for Heirs): Structuralism analytically proceeds from elements to their combinations.


Introduction: A Study of Productive Tensions by Stuart Elden
1. Prolegomena: Notice to Readers
2. The Superseding of Philosophy
3. Philosophy in Crisis
4. Opening of the Testament: Inventory of the Legacy
5. The Search for Heirs
6. Mimesis and Praxis
7. Philosophy as Message
8. Metamorphosis of Philosophy: Poiesis and Metaphilosophy
Postface: Marxism and Poetry by Georges Labica

Is philosophical creativity combinatorial?
by Henri Lefebvre

Henri Lefebvre on Leibniz & Ars Combinatoria
by Henri Lefebvre

Henri Lefebvre’s Metaphilosophy – First Notes
by Ralph Dumain

Henri Lefebvre on Marx, Religion, Philosophy, Ideology & Politics

Henri Lefebvre on Praxis

On Charlie Chaplin by Henri Lefebvre

On Trends in the Status of Dialectical Logic: A Brief Study of Lefebvre, Ilyenkov and Wald
by Claude M. J. Braun

Badiou and the Bankruptcy of Fashionable French Philosophy
by R. Dumain

Leibniz & Ideology: Selected Bibliography

Hegel on Ars Combinatoria & Characteristica Universalis

Ways of Thinking (artificial intelligence, cognitive science, Hungarian literature)
by László Mérő

Jorge Luis Borges: Selected Study Materials on the Web

Sándor Szathmári (1897-1974): Bibliografio & Retgvidilo / Bibliography & Web Guide

Science Fiction & Utopia Research Resources: A Selective Work in Progress

Ars Combinatoria Study Guide

Cybernetics & Artificial Intelligence: Ideology Critique

Marx and Marxism Web Guide

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