There are many books treating various aspects of dialectical logic. However, very few of them are concerned with its specifically logical aspects, while the majority is pondering on the historical issues and trying, for the millionth time, to illustrate dialectical ideas with the same trite examples. The lack of fundamental research comes as a side effect of class struggle in the ideological domain, with dialectics made a slogan of one party and a curse for the other. But dialectical logic was born long before Marx; the elements of dialectics can be found in ancient writers, and it was promoted by philosophical idealism no less than by materialists. As any logic, dialectics is universal and it does not directly reflect the interests of specific social layers. As any logic, it can be used to support quite different ideas, and it is only in practical activity that one way of thought can prevail over another.
For a few thousand years, the humanity developed within the three socioeconomic formations based on expropriation of the products of one's activity by individuals or social groups not involved in the production processes; this phase of human development was necessary to break the primitive syncretism of the earliest communal cultures, but its analytical nature manifested itself in all-penetrating social discrimination, and class antagonism. Classical logic was well suited to reflect such a social organization, commonly known as civilization. Now, when the last formation of this phase of social development, capitalism, is approaching its end, the accents must shift to a more dynamic approach allowing for drastic changes and revolutionary development. Dialectical logic perfectly matches this demand.
Unfortunately, dialectical logic is yet too novel for most thinkers and it may seem hard to grasp. This is especially so for English speaking cultures, which have developed a consumer oriented conceptual system that is not well suited to speak of multiple meaning and mutability. For those brought up to enjoy sharp lines, the diffuse and elusive shapes do not carry much sense; one needs some time to get accustomed to their apparent randomness and perceive the inner regularities. Here, we cannot rely on common sense and language traditions; we need a higher level of abstraction. Even in classical logic, a notion can rarely be expressed in a single word or phrase; the more so in dialectics. Still, dialectical thought is not mere play of words, without any practical importance, as many people are apt to think. The rigid determinism works fine during the periods of cultural stability, and the formal scientific standards are appropriate to systematize the already established relations. In crisis situations, the limitations of the traditional rationality become evident, demanding new logical principles to complement the static (structural) approach of classical logic.
The idea of dialectics
While classical logic stressed the static, structural aspects of reality, dialectics is all about change. Nothing can remain the same in dialectical logic, and there are no clear shapes and rigid boundaries. The adepts of classical logic would find it absolutely illogical—and it is certainly not logical in the classical sense. However, despite its apparently arbitrary and even chaotic look, dialectical logic remains perfectly rational, being controlled by quite definite principles. As the opposite of classical logic, it is as crisp and formal, and the very its arbitrariness is merely an explicit form of the imminent arbitrariness of abstract classical logicality. And, like classical logic, dialectics can be made into scholastics, if no rapport to reality is maintained.
The motion of thought, and the course of any other human activity, must reflect the motion of the world, for the activity to be successful. This means that, in philosophy, dialectical logic is as inseparable from ontology as classical logic, being a reflection of a different aspect of the whole.
Classical logic is perfect for description of quiet things that remain nearly the same for a long time, which is in any case much greater than the duration of discourse. We can observe similarity and repetition, establish firm laws of motion. On the contrary, dialectics is the logic of the transition periods, when nothing is stable and there is no time for contemplation. Of course, this all-embracing mutability is as abstract as the absolute rigidity of the classical world. In reality, some aspects of every activity can well be described classically, while dialectical approach is required in other respects.
Dialectical logic says that even though things cease to be the same and transform into something quite different, these changes are not random or arbitrary, they obey certain fundamental rules, albeit very unusual from the classical viewpoint. This explains the practical significance of dialectics, its heuristic value.
The origin of dialectics
Traditionally, Heraclites is said to be the farther of dialectics in Europe. However, dialectical elements can be found in practically any teaching of Ancient Greece, and, of course, in Aristotle's lectures. It is much later that dialectical and classical logic have become separated and even opposed to each other. In the XIX century, the reverse process of synthesizing the two approaches on a common philosophical basis was initiated, but it is still far from being completed.
Like logic in general, dialectical logic is not an arbitrary construction, and its roots can be discovered in the specific modes of human activity. While classical logic essentially originates from binary discrimination and categorization, dialectical logic is an abstraction of comparison. It is complementary to classical logic in the same sense as considering two distinct things is complemented by considering their common measure, so that the very their difference becomes a manifestation of their unity. This approach is a formal expression of what we usually do in our activities, since drawing the difference between two things is only possible on some common basis. Things cannot differ in an absolute way; they can only be different in some respect. Thus dialectics is implicitly present in classical logic, with its dichotomies being just another aspect of dialectical contradictions inherent in higher-level entities.
It was quite natural to express the ideas contrary to the classical approach in the paradoxical form. Zeno's paradoxes have long since become a standard example. However, dialectics is not mere paradoxes; it can be developed in a positive way, like classical logic. In particular, it has its own logical forms and follows definite principles.
In classical logic, we consider notions, statements and inferences as the different levels of the same hierarchy. In dialectical logic, these forms cannot be considered as definite enough, since notions or inferences can become statements, statements become notions etc, within the same activity. However, dialectical logic has its own logical forms that are, quite logically, expected to refer to the general regularities of change.
Indeed, in the idea of change, one always finds three complementary aspects: first of all, there is something to changes (thesis); then, there is something that could be considered as the result of the change (antithesis); and, finally, the transforming proceeds in a definite manner preserving the integrity of the world during the change (synthesis); in other words, there is something that unites the thesis and the antithesis. These are the fundamental logical forms in dialectical logic.
Anything can change, and hence become a thesis. The very possibility of determining the thesis implies its relative stability, which makes classical logic widely applicable to its primary description. Notions, statements and inferences are equally admissible to formulate (formalize) the thesis. However the formulation of the thesis does not necessarily require any language, natural or formal. In most cases the thesis is objectively present as a specific aspect of some activity, a historically formed cultural phenomenon. Quite often, the objective necessity of some activity can be considered as its thesis; there is something that must be changed in the course of that activity; otherwise, why should it start?
As the opposite of the thesis, the antithesis is as abstract and as distinct from anything else; hence classical logic can be used to describe the antithesis as well. The antithesis is a specific thing essentially different from the thesis in some respect, being its dialectical negation. The transformation of the thesis into the antithesis necessarily looks like a leap, a jump from one side of a crevasse to another, something unexplainable (and even impossible) from the classical standpoint. Quite often, the motive of activity plays the role of the antitheses to its objective circumstances as the thesis. Any activity is, in this sense, directed from the thesis to the antithesis, and this is reflected in negation as a standard logical operation.
The important point in any act of dialectical thought is that both thesis and antithesis are the states, phases or aspects of the same thing, which hence must be able to manifest itself in the opposite ways recognizable as thesis and antithesis. Otherwise, this is an as plain thing, which can be described in a classical manner as long as its relation to thesis and antithesis is not considered. However, in dialectics, the presence of both thesis and antithesis in the synthetic whole is pictured as its inherent contradiction. That is, to grasp the synthesis, one must first clearly observe the two opposites, thesis and antithesis, to develop them in full as separate entities (the actualization of contradiction). As soon as this analytical work is over, one is ready to connect the opposites to each other and bring them to unity. However, such a synthesis is not yet stable: its inner contradiction requires further development, and a new cycle of analysis and synthesis. The dialectical process is essentially infinite, which often irritates scientists, who are reluctant to admit that scientific truths are always relative, and every formal model has its limits of applicability.
While the laws of classical logic have been formulated millennia ago, the principles of dialectical logic did not receive an explicit expression until the beginning of XIX century marked by the works of Hegel and Marx. However, Hegel's concerns were mainly about his new, speculative logic, and he treated the issues of dialectics in an offhand manner. Marx did not pay much attention to the foundations of logic, being rather engaged in applying Hegel's method to practical matters. The lack of logical theory is felt up to now. The norms of dialectical thought are yet too young to become commonly accepted, or even widely known. The existing formulations are too vague, there is no consistent development. Of course, the bulk of literature eventually accumulates to something resembling a general idea, but an efficient way to learn dialectics is yet to be found. The present exposition is only one more step in this direction.
The principle of integrity
Dialectics cannot rely on the identity of a thing, since each thing can turn into its opposite under certain conditions. There is a more general principle stating that every definite thing is the unity of its opposite aspects, and that it remains the same despite all the transformations. On the other hand, its internal complexity will drive it to exhibiting its opposite sides to the rest of the world, and each thing must develop all its possible forms in full until it can cease to exit. Sometimes, the presence of the opposite aspects in the same thing may take the form of internal struggle, when two opposite tendencies shape the final appearance of the thing, one of them dominating over another. This is why, in Marxist literature, the principle of integrity is known as the law of the unity and struggle of the opposites.
From the classical viewpoint, the internal complexity of individual things looks like contradictory definition ascribing opposite attributes to the same notion. In other words, the first principle of dialectical logic says that every thesis is contradictory. Applied to the classical logical forms, it implies that no notion statement of inference can be specified in full, and hence any construction based on classical logic is essentially incomplete. Denying the identity of any notion, the principle of integrity is sometimes referred to as the law of contradiction, compared with the law of non-contradiction in classical logic. The idea of dialectical contradiction is a core of dialectics as such.
In the practical aspect, the principle of integrity demands that every change were based on the properties of the real things, rather than abstract manipulations. To make anything out of something, one has to use that something according to its inherent trends (albeit hidden and non-trivial) instead of raping the world to make things be what they cannot be (the ideological position known as voluntarism).
The principle of negation
While the internal definiteness of a thing is determined by the principle of integrity, the succession of the apparent manifestations of the thing is determined by the principle demanding that every next development phase should be a negation of the original state. In other words, every thesis can (and will) transform into its antithesis under appropriate conditions.
The idea of dialectical negation is quite simple: to produce the antithesis, we have to add something to the thesis that was not originally present there, and, conversely, remove something that should not be present in the result. Adding new features can be considered as removing (negating) their absence. However, in dialectical logic, the changes must be small enough, to preserve the thing's integrity, and there is no absolute change in every respect (which is more like the complement operation in classical logic).
The principle of negation is important to prevent dogmatism. It puts stress on a well-known, but often overlooked, fact that every act is only appropriate in a definite context, and there are no absolute laws, truths, or attitudes.
Dialectical negation is different from negation in classical logic. While the latter leads to an entirely different idea, the former leaves the thing the same, only making it apparently (or functionally) different; it merely shows how the internal opposites of the thing can manifest themselves in the thing's relation to the world. In classical logic, the negation of negation restores the original thing; in dialectical logic, the negation of negation is opposite not only to the antithesis negated, but also to the original thesis, as negated by the primary negation.
The negation of negation was often said to lead to the thing or situation resembling the original that existed before the primary negation. However, such a view is too simplified to be correct. To return to some features of the original thesis, one must negate the antithesis in the same respect, which is not always possible; rather, the negation of negation will result in yet another manifestation of the same thing, which will be different from both thesis and antithesis, retaining them both as its history, and resembling them both, in different aspects. The negation of negation is a synthesis of the thesis and antithesis. Any circularity, terminating the sequence of negations, also terminates dialectics, leading to a zone of relative stability, where classical logic should be applied.
The principle of measure
The fundamental principle that relates the internal complexity of a thing to its apparent motion via a series of negations says that every definite thing has its measure, a unique balance of its internal definiteness (quality) and possible external manifestations (quantity). The category of quality conveys the idea of a thing as it is, as that very thing, and not another. The philosophical category of quantity cannot be reduced to mere numerical value; it also includes any structural aspects, systemic behavior, or other external manifestations of internal complexity; this is how things of the same quality differ from each other.
Everybody knows that most things can be slightly modified without ceasing to be the same things. Such changes, irrelevant to the quality of the thing, are called quantitative. However, the principle of measure states that quantitative changes can reach a threshold, beyond which the quality of the thing would change anyway, producing something quite different from the original. This is the mechanism of dialectical negation.
The other side of the same principle is that the quality of the thing determines when its quantitative changes will put the end to the existence of the thing as such: everything is the cause of its own death.
It should be noted that, since dialectical negation does not entirely annihilate the negated thing, but rather retains it within its negation, qualitative changes do not produce anything from nothing, merely transforming the already existing things, but never annihilating them. A change in quality is still a change, which implies the retention of something that undergoes the change. This something is reflected in the category of measure.
While the principle of negation says that each thing has its limits, the principle of measure states that the limits of a thing are intrinsically determined. This statement is crucial for methodology of science; it demands that, for every scientific model, its limits of its applicability should be expressible in terms of that very model. One does not need to explain how important the idea of measure is in the arts: it is enough to indicate that, for an artist, the feeling of measure is the principal criterion of achieving the desired result. Also, the principle of measure is a cornerstone of any philosophy, since it is concerned with the very ability to express the infinite and universal in finite and partial philosophies.