Mao wrote
The law of contradiction in things, that is, the law of the unity of opposites, is the basic law of materialist dialectics… The fundamental cause of the development of a thing is not external but internal; it lies in the contradictoriness within the thing. There is internal contradiction in every single thing, hence its motion and development. Contradictoriness within a thing is the fundamental cause of its development, while its interrelations and interactions with other things are secondary causes.
As a matter of fact, even mechanical motion under external force occurs through the internal contradictoriness of things. Simple growth in plants and animals, their quantitative development, is likewise chiefly the result of their internal contradictions
Changes in society are due chiefly to the development of the internal contradictions in society, that is, the contradiction between the productive forces and the relations of production, the contradiction between classes and the contradiction between the old and the new; it is the development of these contradictions that pushes society forward and gives the impetus for the supersession of the old society by the new.
The one is victorious either because it is strong or because of its competent generalship, the other is vanquished either because it is weak or because of its incompetent generalship; it is through internal causes that external causes become operative. In China in 1927, the defeat of the proletariat by the big bourgeoisie came about through the opportunism then to be found within the Chinese proletariat itself (inside the Chinese Communist Party). When we liquidated this opportunism, the Chinese revolution resumed its advance.
What are these “contradictions” that are able to account for everything from the growth of plants to the development of societies? If we want to really work with them, to track them, to move with them, to encourage them, we must first of all understand them.
Despite it being such an important concept, Marxist thinking on contradiction is a bit muddy. Mao cites Lenin who gave certain examples.
In mathematics: + and - . Differential and integral.
In mechanics: action and reaction.
In physics: positive and negative electricity.
In chemistry: the combination and dissociation of atoms.
In social science: the class struggle
Certainly various analogies can be drawn between these things: +/- and differentiation/integration are sort of inverse operations to each other (or maybe adjoint…), action/reaction is certainly connected in so far as the force represented by an action is -1 times the force represented by reaction. Positive and negative electricity is more complicated and the connection is far from clear. The last two, combination and dissociation of atoms, and the class struggle seem to both be of a different type from the preceding. And it’s very hard to see what any of this would have to do with the growth of a plant.
In fact the apparent connections are rather shallow between these. If there is a concept that accounts for such disparate things as these, it must be a very weak one. A principle can either be general, but weak, or strong, but more specific.
We have to move past a single word “contradiction” to attempt to encompass all these phenomena.
I propose a set of notions, relatively simple, that can account for at least some of what Marxists mean with “contradiction”. I would call this notion, a contradiction between two material processes.
A contradiction between material processes is a sort of softening of the notion of a logical contradiction.
It is like a logical contradiction, but one which may sustain for some time before exploding. A logical contradiction on the other hand, takes down the whole building at once, since any proposition is implied by a logical contradiction. This is because logic takes place in the moment of eternity: the reconciliation at the end of the universe. The timeless mind of God. A material contradiction takes place in space and time.
It is a conflict between 2 or more ”logics” that are trying to execute themselves, to play themselves out, to run themselves in the world.
This we will try to make more precise in a moment, by giving a mathematical model.
It is helpful as always to look at an example (or maybe 2).
One is the contradiction between our current method of organizing human life – capitalism – and the logics of the biosphere, which have come into particularly stark contradiction as of date. The physical requirements of the one disagree with the physical requirements of the other.
Thus we have entered a state where these 2 logics have come into conflict: if the world is to continue (and of course it will, it can’t help itself), one or the other of these logics is going to start running in an altered manner.
In other words, it is not possible for both of these logics to execute indefinitely according to their current embedding in the universal logic of physical matter, because they demand physical matter be ordered in distinct, incompatible (or contradictory) ways.
This shows that contradiction are ultimately creative. The world can’t help itself but keep running, despite the contradictions among the systems it contains at any given moment. Therefore contradictions are what are responsible for producing new situations. In other words, the passage of time itself (which is nothing but physical change) is the result of the process of contradictions being resolved.
Every logic is in fact in contradiction to some degree with the logic of physical matter. The body decays, a company goes bust, a society collapses, life becomes impossible on Earth, the sun will go dark, etc. This is a way of saying everything dies, but which encompasses non-biological entities. However, a system may be done in by a contradiction with a system other than the physical universe itself.
What constitutes a logic is in the eye of the beholder. It is defined by the mental (or other physical) processes which recognize it, its states, and its evolution in the world. We can however make symbolic/mathematical models which aim to mirror what happens in our minds (or in another physical system), though they must always remain provisional and subject to revision.
Let’s make a mathematical definition as a first step. A material process is modelled by a stochastic process $\{X_t\}_{t \in \mathbb{R}}$ with state set $X$ equipped with a map $x \colon X \to U$ where $U$ is the state set of some stochastic process
$$\{U_t\}_{t \in \mathbb{R}}$$ which is a model for the universe.
$X_t$ is a model process (or “logic”) and we can compare its evolution with its material instantiation $x(U_t)$.
The material contradiction from $X_t$ to $Y_t$ at time $T$ is $$ \mathsf{Pr}[y(U_t) \neq Y_t \mid \forall t \leq T, x(U_t) = X_t] $$
The mutual harmony from $X_t$ to $Y_t$ at time $T$ is $$ \mathsf{Pr}[y(U_t) = Y_t \mid \forall t \leq T, x(U_t) = X_t] $$
A material process $X_t$ contradicts $Y_t$ if the probability that
Two material processes $X_t, Y_t$ are contradictory to an extent measured by their material contradiction.