Marina Burik, translation by Vitaliy Pershin and Peter Yitzhakovich
Humanity is constantly faced with contradictions and looking for ways to resolve them. This fact cannot be denied even by the supporters of the unconditional supremacy of the prohibition of contradiction, no matter which formulation of the prohibition they prefer in history. The fact that thinking, if it is consistent, inevitably leads to contradiction, as I noted in the last issue, was carefully studied by Immanuel Kant. He showed that we can prove exactly the opposite statements in the same logical way. Kant derived and demonstrated four antinomies.
Every composite substance in the world is made up of simple parts, and nothing anywhere exists save the simple or what is composed of the simple.
Causality in accordance with laws of nature is not the only causality from which the appearances of the world can one and all be derived.
There belongs to the world, either as its part or as its cause, a being that is absolutely necessary.
The world has a beginning in time, and is also limited as regards space.
Kant was not the first to record and try to understand how thinking comes into conflict with itself. This was already thought about by the ancient Greeks. Zeno of Elea recorded the contradiction in the form of the so-called aporias. Such aporias as “Achilles”, “The Dichotomy”, “The Arrow” have come down to us. Let‘s take a look at “The Arrow”, for example. “If everything is either at rest or moving when it occupies a space equal to itself, while the object moved is always in the instant, a moving arrow is unmoved”.
We also know this aporia in another historical formulation: “The flying arrow is and is not in the same place at the same time”.
Aporias were recorded by Plato and Aristotle. And Eubulid had a lot of fun in this respect. Among others, he formulated the “Liar” aporia. It is still the subject of intense scrutiny in logic. In his time, according to some accounts, this mystery was the cause of some suicides. It goes like this: “I’m lying,” or in other words, “That statement is false”.
Try to answer the question yourself whether a person who says “I am lying” is telling the truth.
A family of omnipotence paradoxes emerged during the Middle Ages, the most famous of which is formulated as follows: “If God, being omnipotent, can make a stone so heavy that it cannot be moved”.
Among the well-known antinomies in history is the set-theoretic paradox, deduced by Bertrand Russell at the very beginning of the twentieth century. This paradox, as Russell himself acknowledged, bears a resemblance to Eubulid’s “Liar”.
By deriving antinomies and reflecting on the nature of thinking, their authors often sought to eliminate the contradiction. But in any case, as in the above cases and others like them, the appearance of a contradiction is not at all the result of sloppy thinking or a breach of the rules of formal logic. On the contrary, it is a contradiction if these rules are followed in their entirety.
Taking thinking seriously therefore obliges philosophy to answer the question of why in thinking contradiction necessarily arises. Moreover, if we go beyond antinomies, that is, specially formulated contradictions, and look at the history of human knowledge in general, we see that in this history opposing mutually exclusive theoretical views on the same subject, taken in the same relation, are constantly reproduced.
And Kant gave his answer to the question of why this is the case. He saw the reason why people are constantly faced with contradictions in strictly following the rules of formal logic, in the defective structure of our “thinking apparatus”. This apparatus according to Kant has a priori, i.e. before any human experience, existing forms of thinking. These forms are paired, opposing, mutually exclusive categories. A person cannot think otherwise than in these categories and therefore falls into contradiction, no matter how hard he tries to avoid it. Consequently, Kant continues, we cannot know the world as it really is. Any theory will eventually either include a contradiction or suggest the emergence of a contradictory theory alongside it. Determining which of these theories is true by thinking, Kant thought, was impossible. This is where the Kantian “thing-in-itself” appears, i.e. the position that the world as it is in itself is incognisable outside and independent of human thinking that cognises it. This position in the theory of knowledge is called agnosticism.
But what led Kant to agnosticism led another representative of German classical philosophy, Hegel, to take a different view of contradiction itself.
Hegel takes the existence of a contradiction as a criterion for the truth of a theory. From his point of view, where there is no contradiction, there is no work of thought. There is only a collection and systematisation of facts, a description of some properties of the subject, but no understanding of the whole subject in its development. The nodal points of the development of science take place where opposite mutually exclusive definitions of the subject of research are fixed, when facts are revealed that cannot be explained, compared with each other and with all the previous understanding of the subject without encountering a contradiction. Next, science, in order to penetrate more deeply into the law of motion of its subject, must find out how this contradiction is actually resolved in reality. This is when the concepts are further developed, deepening the understanding of the case. This is how Hegel saw the history of human knowledge.
Marxism relies directly on it on this point. Materialist dialectics puts contradiction – the identity of opposites – at the centre of the theory of knowledge. Lenin, who argued that dialectics is the logic and theory of knowledge of modern materialism, and does not need three words for the same thing, drawing on all the preceding tradition, said: “The condition for the knowledge of all processes of the world in their “self-movement,” in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites”.
Development, in dialectical logic, is the “struggle” of opposites. All movement, both change and displacement, is the realisation and resolution of a contradiction.
This state of affairs was recognised as far back as the ancient Greeks. The ancient Greek philosopher Zeno recorded this in the aporia of the flying arrow already mentioned. But while Kant drew his conclusion from the fact of contradiction millennia later in relation to the structure of the human mind, Zeno drew his conclusion in relation to objective reality, comprehended by thinking. The mind for him really penetrates into things, and allows, unlike appearances, to understand them as they are. Therefore, Zeno argued, based on his teacher Parmenides – movement, since it is not conceivable without contradiction, does not really exist. Another Greek philosopher, Heraclitus, on the same basis, did not deny motion, but rather tried to understand it as the interpenetration of opposites.
Note that this is not a purely verbal contradiction, but a very real contradiction in the subject itself. Dialectical contradiction is not ‘speech versus in speech’, but a situation where the same object taken in the same relation has opposite mutually exclusive definitions – is what it is and at the same time, in the same relation, is already something else because it changes. It is very important that we are talking about a subject taken in the same relation, otherwise it would be an opposition of external opposites, where, to use a Russian proverb, one thesis would be about Foma and the other about Yeryoma.
The dialectical position of the identity, or unity of opposites, is the recognition, and requirement for the discovery, of contradictory, mutually exclusive, opposing tendencies in all phenomena and processes of reality: in nature, in society, in the human spirit.
Once again, speaking of dialectical contradiction, we are talking about development, and about the understanding development. There are two main approaches to development. The first is the understanding of development as a quantitative decrease or increase, the complication of structures, systems, and so on. In this approach, the task of thinking is to describe the process of development. Its inner driving forces, its source, are thus left out. The second approach to development is precisely the essence of dialectics – the understanding development as a bifurcation of the one into mutually exclusive opposites, as the unity of opposites in their struggle. This approach also requires a description of development, but it does not allow us to stop at a description, but directs our thinking towards finding the internal, in the object itself, source of development, finding the transitions between opposites.
Dialectics as logic and the theory of knowledge is the science of how opposites are identical, how they pass into each other. And even the very principle of development that underlies it is formulated in dialectics as contradiction: Everything in the world evolves, which means that nothing in the world is eternal, only change is eternal.
But how do we distinguish a valid dialectical contradiction from outright absurdities? In the way they are expressed in speech, they are indistinguishable. Both a dialectical contradiction and some outright nonsense, in form looks like “A is not A”, or “A is both B and not B”. The position of dialectical logic on this point is that it is only possible to distinguish one contradiction from another by examining human knowledge according to its specific subject content. It is necessary each time to specifically understand the essence of the issue that we are studying, to look at how this contradiction appeared, to investigate all the essential facts related to the case. Only this will help us understand what exactly we are dealing with in each individual case and how to act on this contradiction, whether it is a real contradiction and therefore requires an understanding of how it is actually resolved or whether it is simply a contradiction in a statement that has nothing to do with reality.
To use dialectics is to study any phenomenon of nature or social life in development, to understand its place in the universal connection of phenomena, and not to become hysterical when we deal with contradiction, but to record and study it precisely in concepts, because through contradiction, through the unity (identity) of opposites in their struggle, development is realized. Dialectics sees contradiction as a problem that thinking has to solve, that is, to find out how it is really solved in the movement of the object. This would be a move towards understanding a real contradictory world, unlike what post, neo and any logical positivism, however it may call itself, such as critical rationalism, suggest. For positivism, theory is a system of statements which must, in Popper’s words, describe a “consistent possible world”. In his “Logic of Scientific Discovery” he insists on consistency as the most important criterion for the scientific validity of a theory. It is therefore not surprising that such logic, by his own admission, is unsuitable for creating a new theory. It cannot understand how new knowledge is actually born and cannot help in its birth. Popper was honest in this respect. Logic, which is unable to understand the contradiction, and cannot claim to do so, in contrast to dialectics as logic and theory of knowledge, for which the development of the concept is its true subject. Dialectic as logic, therefore, explores opposing categories as stages of concept formation and the movement of categories as a process of this formation.