by Henri Lefebvre, from Logique formelle, logique dialectique, 1982
1
Neither logic nor the dialectic can be defined as superstructures of this or that society, this or that mode of production. Nor can they be attached to religious or philosophical ideologies. Linked in their discovery and elaboration with ideologies and even with institutions, at some point in the course of historical time they became detached from them, without being reduced to pure, abstract, timeless forms persisting over centuries. Nor can they be reduced to a simple methodology, gnoseology or pure theory of knowledge. On the one hand they are related to practice and on the other, to theory (concepts) and thought that seeks itself, and believes it finds or recognizes itself in a system, which sooner or later collapses.
2
Dialectical thinking emerges in Heraclitus through direct, immediate contact with the world. His poetical language proclaims his perceptions about fire, the river, the rainbow, etc., that is, Becoming, conflicts, oppositions, creation and destruction. This introduction to the dialectic still preserves its meaning and flavour. And that raises a question: ‘Having passed through all the mediating processes that he has himself produced, that he has managed to turn against himself (alienation), of which the latest is technology, does not the social, thinking, acting man rediscover a relationship with the world in immediacy?' ‘Man here does not refer to any essence, any defined subject, any more than it does to a humanist ideology. The question of the rediscovery of immediacy with the world is raised in terms of contemporary ‘universality,’ interrogation of what is possible or impossible, contradictions within societies, exploration of nature and the universe, etc. It should be pointed out that the dialectic cannot be conceived of only as deriving from Heraclitus but also from his confrontation with Parmenides; the conflict between them marked the inception and the source of the great philosophical questions that have been asked through the centuries; ‘The Same and the Other - repetition and Becoming - positivity and negativity - order and disorder - life and death ..’
3
Logic and its problems are not only problems of form, but ontological, cosmo-logical, anthropo-logical questions. The theory of forms cannot forget that every form presents itself first as a content that is worked up, developed and thus becomes form, in such a way that it eventually appears to pre-date the content. Was this not true of the Greek conception of the universe, developed by Aristotle as the concept of order and necessity, translated into formal deduction?
4
Logic is first considered formally, but its form cannot be separated from a content that it seizes or receives from facts, from practice and sooner or later, from Becoming. The formal refers to 'something’, which it appropriates but which nevertheless escapes it. Is this relationship not doubly dialectical: the relationship of form with content and of content with temporality, i.e. Becoming? At the same time, the dialectic - the dialectical movement of knowledge and thought - has first to be studied formally. Dialectical thought also is defined by a form, by rules and laws. It contradicts logic, but does not abolish it; it does not fall into absurdity. The dialectic does not permit us to make contradictory statements, at the same time, about the same subject; it does not allow us to say this sheet of paper is both black and white. Hence an axiom: ‘The theory of contradictions cannot be contradictory.’ However, formal analysis reveals the defining characteristics of dialectical thought, which fundamentally distinguish it from logic. Logic tries to confine itself to one term: identity and its implications. In order not to be tautological, its relationship with content forces logical thinking to introduce differences, i.e. a second term. This is not without its difficulties. A = A; that’s obvious, but not very useful. A is B; that’s much more complex and harder to define logically. We’re in the mediating area between logic and dialectics, and sooner or later, dialectic introduces three terms. Dialectic resolves itself into neither a single term nor two different terms. The introduction of the third term reveals a transformation in thought, its evolution in the world that is in process of Becoming. The third term indicates both the contradictory complexity of the real and the movement that springs from contradiction and moves towards going beyond it. (An illustration of this idea: in Marx, the triad ‘work/capital/profits-from-the-earth’s-products.’ In music, the triad, ‘rhythm/melody/harmony,’ etc.)
5
The logical form detaches itself and is studied as such. It is not only joined with external contents, but is product and producer. It produces abstractions that join up and tend towards the concrete via the logico-mathematical route. These abstractions, linked together, serve as mediation between the form and the real. Active, these mediations help to create the real, that is, not only to define it as such, in and through science, but actually to make it, to produce it. Philosophy has long attributed this production to the activity of the 'subject’ or 'subjects.’ Logic, or the logical, invests itself in the real and its production, while the dialectical Becoming removes this reality - the reality of the Same - by dissolving it. Logic becomes part of practice: projects and coherent strategies, operational logic, operating systems, and nowadays, ‘software,’ i.e. logical machines, etc. The logical form is thus connected with its effects: consistency, stability, coherence, systematization, etc. Logic thus sets up its empire both in the area of knowledge, as a theory that is stable in terms of rigour, proof, truth and reality, and in practice. It provides and ensures homogeneity in knowledge and practice. Its tendency is to totalize, but it never succeeds in this, either in applied forms of logic or in so-called systems analysis or epistemology. Within the empire it tries to establish, logic starts out as a tool, then becomes a machine and even a machine for producing machines.
6
The logical form (identity) produces repetition: A is A. With everything it engenders, the logical form is connected with the dogmatic assertion of the Being and the real, and consequently with the philosophical questioning of the Same and the Other: ‘What is the Same, i.e. that which persists, is repeated, continues? What is the Other, which changes the Same and makes it a world [qui modifie et qui mondifie le Mime]? And what is Becoming? How can there be repetition and Becoming, continuity and discontinuity, appearances and disappearances? Which is appearance, the Same or the Other? Could the Same be mechanism? The substantial or the Essential? Law? Or Being?
7
Classical philosophy from Plato to Hegel, and its overcoming today, turn on these central questions, to which Hegel provided only incomplete answers: ‘What is identity, or the identical? Being or void? Substance or tautology? Why such questions if identity is obvious, intelligible, true and the image of Truth itself?’ It is a question all the more disquieting in that identity is connected with the repetition, equivalency and ambiguity of the word ‘Being’ (sometimes copula, sometimes substance). But we can safely say that identity is triple or triadic:
a) Logical identity, A is A, repetitive, long taken as the criterion or model of absolute truth (the transcendent deity of the theologians and metaphysicians declares and defines himself in a neat phrase: ‘I am that I am.’)
b) Concrete identity, of the Same that maintains itself against Becoming: the ‘being [étant],’ defined objects, consciousness, concepts, ‘I am myself’ ... Groups of human beings seek, find and lose their identity. This identity persists, and seeks to persist, even though it is relative.
c) Dialectical identity: ‘I is an other’… ‘I only see, and am, in relation to the other ... All that is becomes other.’ This is the figure of the relative, found in relationships, in the world, in Becoming; it is the Same in thrall to the Other, defining itself by it, carried by it, that is, by contradictions.
8
While logic believes it is relegating logical identity to the absurd, dialectical contradiction penetrates its very heart; it installs itself there as becoming stable, difference within the indifferent. Becoming removes all that resists it by using repetition and equivalence. So that what is non-equivalent in equivalence responds to and corresponds with what is non-identical in identity (as it is in the world of exchanges and merchandise). And furthermore, logic or the logical cannot be conceived of without recourse to the dialectic(al). The attempt fails because logic can only be theorized via its other. Logic is not yet thought, but the form and rules of speech and actions through which thought seeks itself. The dialectic is the fertilization of the logical, at the heart of logic. The logic-dialectic nexus brings with it conflicts in the course of which logic tends to eliminate dialectic, but it does not succeed, or succeeds only partially, although logicians think it is for ever - for all eternity! The relationship of logic and dialectic is thus itself dialectical.
9
The contradiction that goes unnoticed, unstated as such, is called a paradox. Thought in search of itself has been both stimulated and blocked by paradoxes, from Epimenides’s paradox of the liar to more recent examples: the paradoxes of set theory, or Godel’s theorem. The terms ‘paradox’ and ‘paradoxical’ occur ever more frequently in contemporary writing. What is not paradoxical? Our contemporaries have lost the sense of the dialectic and thus that of logic. Specialized branches of logic proliferate — down to the ‘logic of the unconscious’ - as do paradoxes and situations described as paradoxical. In this way, the work of the negative continues, in turmoil and confusion. The negative and the dialectic are denied, but return to the scene as the paradoxical.
10
The negative carries on its work in the modern world, with paradoxes and crises, risks and threats. Might it not be the negative that constitutes a totality of the various elements and fragments of today’s world?
11
Logic has established its empire within the world of capitalist production. The use of this theoretical and practical tool has played an important part in the unexpected flexibility of this mode of production and particularly its capacity for technological initiative, including cybernetics and computing. The empire of logic is circumscribed by and in the capitalist mode of production. Logical empiricism [L’empirisme logique] (pun intentional) is therefore coming into its own as the philosophy of this mode of production, as the theorization of a truth that is both factual and propositional. Its success is in direct proportion to the triumph and pressures of the world market - an immense network of equivalences (monetary, etc.) and non-equivalences (inequalities).
12
Contradictions - ancient and modern, cumulative or specific - gnaw away at this empire and the societies that make it up. The dialectic, both theory and practice, continues its work [oeuvre]. It is important to note, however, that dialectical thinking remains at the level of ideas as long as there is no living force to carry through the work of the negative and resolve contradictions by overcoming them. Today these forces manifest themselves on a world scale. Might it not be in this sense that the relationship of thought with the world returns to the foreground, thus overcoming classical philosophy, in which reflexive thought related mainly to itself, its cumulative experience and its history? This does not abolish any specific moment - the national, for example - but subordinates every such moment to the world dialectic. The struggle of logic and dialectic is thus, at the theoretical level, a higher form of ‘classic’ struggles in thought and society.