Formal and Dialectical Logic as Unity of Opposites
or Development of Classical Philosophy .
By Ilya Stavinsky

Published in magazine
PHILOSOPHICAL RESEARCHES, Moscow 11/2003
and in ECONOMIC GAZETA, Moscow, #40, 10/2003

Until now philosophers interpret formal and dialectical logic as separate logics independent of each other. For this reason some of them state that dialectical logic is more important than formal one, others state vice versa. For example, George Novack wrote:"...dialectics arose out of the criticism of formal logic, overthrew and replaced it as its revolutionary opponent, successor and superior.", and Engels stated that dialectical logic relates to the formal logic as higher mathematics relates to the elementary one (K. Marx, F. Engels p125, vol 5, 1985). But there are some philosophers who completely denied dialectical logic. Even in Russia the latest completely excluded from the main course of study in many colleges and universities including economic faculty of Moscow State University. It is these circumstances forced me to write this article about the relation between formal and dialectical logic.

The logic of the thought process divided itself into formal and dialectical one. They are defined only in relation to each other and only in that relation they have their meaning. They are defined as opposites where each of them conditions the existence of the other. To discover this interconnection is the goal of our further investigation.

The Basics of Dialectical Logic.
Development of the universe surrounding us, is reflected in the laws of dialectical logic which have reached its pinnacle in Hegel's work Objective Logic. According to K. Marx it was Joseph Dietzgen, german philosopher, who have turned upside down the dialectical logic of Hegel and shown that dialectical logic is reflection of development of surrounding us universe but not the spirit as it was according to Hegel.

Any development, in wide sense of this word, consists of the birth of the event, its development, in narrow sense of this word, and its death. So with time the birth of the event transforms into its opposition, the death of the event. Consequently, the birth and the death are opposite meanings and for this reason they constitutes dialectical contradiction. The essence of the dialectical logic consists in the fact that it describes the development of this contradiction i.e. it shows the transition of the event from one stage, the birth, to its opposite stage, death. For this purpose dialectical logic possesses by its system of category and by its abstract laws. By using them dialectical logic can grasp in detail the process of any development independent of its character whether it is social or natural event. Such categories are form, content,essence, quality, quantity, elementary form, particular form, universal form, opposites, real and formal contradiction and so on. Examples of laws: the transformation of content into form, the transformation of quantity into quality, unity of opposites and so on.

Logic of Qualitative Development and Qualitative Constancy.
The subject of the investigation of the formal and dialectical logic is any event in the nature. The dialectical logic analyses the event from the point of view of its qualitative development which include the negation of this event, so it is the logic of qualitative development. But the meaning "development" has sense only in relation to the meaning "constancy" or "rest". So if there is logic of qualitative development then there is logic of qualitative constancy or rest. Such logic is formal logic which analyses the given event as though the later is in the state of rest, in other words, formal logic disregards those quantitative changes that the forms of the event experience during their development, because these quantitative changes do not change their quality and in that sense these forms of the given event are constant. In other words, formal logic try to discover the essence of this event that based on the certain qualitative ground.

Meanwhile dialectical logic shows how behind this qualitative ground hides another qualitative ground which at present moment constitutes the content of the first posited qualitative ground.

From the point of view of knowledge both logic supplement each other, without their mutual condition our knowledge would be one-sided. If we know only the laws of development (dialectical logic) of the given event i.e. its position as a form, negation of this form and as the result the position of its content as a form - in that case it will be not enough, because we would not reveal the content of each posited qualitative ground and vice versa. If by using only formal logic we revealed the essence of the given event then we would miss the hidden content of this posited event.

Formal logic denies contradictive definitions and judgments meanwhile dialectical logic vice versa recognizes them. This difference comes from the fact that the laws of formal logic maintain their power only in relation to the certain qualitative ground where the meanings and judgments are defined simple. Contrary to it, dialectical logic functions on two qualitative levels: form and content. For this reason dialectical logic considers the meanings and judgments not only to the certain qualitative ground (form) but in relation to its content (another qualitative ground which is not posited yet) as well, and because of that it sees and recognizes their contradictory nature.

What would one say about those scientists who recognized the existence of a human being only in the form of a man or in the form of a woman, denying the existence of his or her opposite sex, or who recognize the existence of women more important than the existence of men and vice versa. And where would the science of physics be if scientists recognized the existence of positive charge more important than its opposite negative charge and vice versa. Groundlessness of these statements is obvious on these examples, but when these statements are made in philosophy about formal and dialectical logic everyone accept them without deserving critic. Even Hegel, the founder of dialectical logic, recognizing the formal logic, did not notice that formal and dialectical logic are unity of opposites and thus he himself took the bait of dialectical logic. Otherwise he would not severely criticized the four laws of formal logic in his book "Science of Logic".

Up to now we have shown that formal and dialectical logic represent the unity of opposites, proceeding from their formal definitions. But this is only the beginning. The whole beauty of the prove of this statement becomes more obvious when we analyze more closely the laws of formal logic that inevitably bring us to dialectical logic.

Formal Logic.
Everybody is familiar with four fundamental laws of formal logic:


1. Law of identity.
2. Law of contradiction.
3. Law of the excluded middle.
4. Law of Sufficient Ground.Let us consider each of them more closely and show that the first three laws have sense only in relation to the fourth law of formal logic, law of sufficient ground.

Law of identity in general states that each word in our language or each category in science has to have the same meaning. It is very legitimate statement, otherwise people who speak the same language would stop to understand each other. Categorical language of any science is subordinated to this law as well. This is how people by using different examples, interpret law of identity.

But let us take more close analyze of this law. For example, how this law will work if a word has several meanings. In this case we choose the right meaning of the word, basing on the context of the sentence. From here follows that the context of the sentence is that ground which defines the content of the given word. In science that fixes in its categories the development of surrounding us universe we each time come across with categories the content of which is changed all the time as the result of our more profound understanding of nature. For this reason the same category can have several contents and each of them is true in relation to its sufficient ground. For example in Euclidean geometry the sum of angles of triangle is equal 180 degrees at the same time in Non-Euclidean geometry the sum of angles of triangle could be more or less 180 degrees.

In this case how do we establish the identity of the concept, "sum of the angles of triangle", if it has so many definitions ? It all depends on what ground our logic is build whether it is Euclid geometry or Lobachevsky geometry or Riemann geometry. In other words, identity of meanings is always defined and maintained only in relation to the given ground. It is the fourth law of formal logic, law of sufficient ground that makes the law of identity to be complete. So insufficience of old definitions of the law of identity consists in the fact, that they pointed out only to the necessity of existence of this law and lost sight of defining its sufficiency of existence.

Law of contradiction.
The essence of the law of contradiction at the present time is formulated as follows. Two opposite judgments can not be true at the same time, one of them must be false.

Incompleteness of this definition is that it defines only the necessary side of existence of this law and don't point out to its sufficiency which is the ground in relation to which this judgment is true. For example, one can say that "a building is at rest and in motion." According to the law of contradiction the building can not be at rest and at the same time be in motion. But how true is this ? In relation to the earth the building is at rest, but at the same time in relation to the sun the building is in motion. Thus both statements are true but they are true in relation to different grounds.

Consequently, in order to make "the law of contradiction" to work we must add to our statement the certain ground in relation to which one of the opposite judgments will become true. So if we say " the building in relation to earth is at rest and in motion", then the absurd of this statement is obvious. In relation to earth the building can only be at rest, for this reason the second statement, "In relation to earth the building is in motion", is false. So the full definition of the law of contradiction is as follows: two opposite judgments can not be at the same time true in relation to the given ground which is the law of sufficient ground discovered by Leibniz.

The Law of the excluded middle. The law of the excluded middle can be expressed as "two opposite judgments can not be at the same time false: one of them must be true, and there is no third or middle judgment."

The weakness of this definition consists in the fact that it does not demand sufficient ground for one of these judgment. and Hegel took advantage of this weakness of the definition when he asked question with sarcasm. "Which of two judgments is true ? The spirit is green or is not green." None of these statements is true. So the full definition of the law of the excluded middle is as follows: two opposite judgments can not be at the same time false if one of them has sufficient ground; one of them must be true and there is no third or middle judgment.

The Law of Sufficient Ground.
Everything that exists must have a necessary and sufficient reason for existence - and that reason can be discovered and communicated to others. This conception was formulated in 1646 by Leibniz, the great German logician, mathematician and philosopher , as “the principle of sufficient reason”.

This general definition of the law is needed to be interpreted in more details. First, as we have shown before, all three laws of formal logic, discovered by Aristotle, are based on this law of sufficient ground and only in relation to this ground they have their meaning. Second, sufficient ground according Hegel's apt expression, is not just ground but qualitative ground where the development forms take place. In other words, the qualitative ground is that limit within which the formal logic establishes logical connections between these forms.

If qualitative ground is changed - when certain event is developing itself - then the change of the forms take place and these new forms continue to develop itself on this new qualitative ground. These new forms have completely different logical interconnection. For example, forms B1, B2, B3, and so on are based on the ground A, and between those forms the formal logic established logical connection T1. But with development of the given event its content comes to the surface, in other words, the content turn into a form that becomes new qualitative ground on which the development of another forms takes place. Thus the ground A transforms into the ground A1 to which correspond new forms C1, C2, C3, and so on between which the formal logic establishes another logical connection T2.

Change of the qualitative ground under formal logical investigation takes place not only when certain event develops itself but when our experimental research goes deeper in the subject of investigation. For example, from investigation of behavior of solid body to investigation of its behavior in liquid condition then gaseous condition then to the analysis of the matter on the molecular level, atom level and so on. This is true in relation to any science. When scientists penetrates into new qualitative ground then the first sign of that will be the fact that specific laws discovered on the previous qualitative ground will not work on the new qualitative ground. And this is quit obvious from the point of view of formal logic that states, as we saw early, that all meanings including scientific category maintain their meaning or are true only in relation to its sufficient ground. For example, the laws describing the behavior of solid body completely different from the laws describing the behavior of the same body in liquid or gaseous condition.

Furthermore, a group of Grounds can belong to more general Ground, so the Laws discovered on one ground, can be valid for other grounds. For example the physics law "The amount of energy in a system always remains constant" and so on.

Interconnection of formal and dialectical logic through the law of sufficient ground.
Let us make one step more in our analysis. If we compare qualitative grounds in which the above mentioned body exists, solid state, liquid and gaseous state then it is not difficult to notice that they relate to each other as opposites: solid and liquid state, liquid and gazes state. The body from solid state under certain degree of temperature, transforms itself into liquid state and under more high temperature from the later into gazes state . "Just a minute", one tells me " you are talking already about dialectical logic but not formal one. It is quite right. The rise of the temperature is quantitative changes in the process of heating of the body, which causes, at certain temperature, its transformation into another qualitative state. Already in this example is embodied the whole idea of dialectical logic. "Just a minute," -one says again, -"you just selected very lucky example in order to prove your point about the relation of formal and dialectical logic through the law of sufficient ground." With this in mind I will give you more examples from geometry and economic science.

Euclid geometry is based on assumption that through a given point not on a given line exactly one line can be drawn parallel to a given line. This postulate is qualitative ground on which Euclid geometry was built. Lobachevsky geometry is based on assumption that through a given point not on a given line there are more than two lines can be drawn parallel to this line through this point. More than two lines could mean 10,20,100,..N (where N is any number > than 2). This postulate is qualitative ground on which Lobachevsky geometry was built. In both cases both mathematicians built their geometry by using the same formal logic regarding of the fact that logic of Euclid geometry is different from the logic of Lobachevsky geometry.

If we compare these two qualitative grounds then it is not difficult to notice that they are opposites from the point of view of their qualitative definition. In first case, that through a given point not on a given line exactly one line can be drawn parallel to a given line. In the second case, that through a given point not on a given line there are any numbers of lines can be drawn parallel to this line through this point.

The Question is what is the opposite definition of the qualitative ground of Lobachevsky geometry ? It will be obviously statement that through a given point not on a given line there are no lines can be drawn parallel to this line through this point. That is how the Riemann geometry came into existence. Its logic completely different from the logic of Lobachevsky geometry although Riemann used the same formal logic as the previous above mentioned mathematicians. From here follows that Reimann geometry is universal form of existence of space, because it more profound describes our space. Euclid and Lobachevsky geometry represent by itself something Elementary and Particular accordingly in relation to Universal form of Reimann geometry. Mathematically the relation between Elementary form and Particular one expressed in the fact that Euclid geometry is particular case of Lobachevsky geometry. About this Lobachevsky wrote himself that created by him Non-Euclid geometry in infinitesimal coincides with Euclid geometry.

But Reimann geometry includes in itself not only Lobachevsky geometry but Euclid geometry as well and for this reason it becomes universal form. When we deal with small distances (within our solar system), the Euclid geometry satisfies our needs, because the curved space is so little that it does not matter for our practical use. When we deal with large distances,( for example traveling between stars of our galaxy) then we can not ignore the curved space, and Lobachevsky space will come into existence meanwhile Euclid geometry will lose its sense and become impractical for this purpose. When we will travel between galaxies most likely we will use Reimann geometry. So our idea about qualitative space is changed depending on the distance between objects.

But this is one of the fundamental law of dialectical logic, the transformation of quantity into quality, which is reflected in changing of qualitative ground on which the geometries of Euclid, Lobachevsky and Reimann are built. It is interesting to note that in 1902 Poincare ,french mathematician, stated that "none of the geometry is more true than the other, either geometry can be only convenient." Weakness of this statement is obvious, because it does not reflect the development of our knowledge about the space.

But our presentation about the development of the space is not limited by Reimann Geometry regarding to the fact that we defined it as Universal form of existence of space. As such it defined only in relation to Euclid and Lobachevsky space. In other words the development of these three forms of space take place on one general ground e.i. that they are rigid, stiff space. For this reason if we change this ground for its opposite, lively space which expands and shrinks itself then we come to more profound understanding of space than it was described by Euclid, Lobachevsky and Reimann geometry. That is how Minkovski geometry about lively breathing space, came into existence. This geometry gives us undoubtedly more real idea about space of universe. Will our civilization reach such technological level when this geometry will have practical meaning ? The Future will show.

Example from economic science. So far contemporary capitalist society is based on capitalist commodity production that is posited in the form of private capitals. This capitalist commodity production is unsocialized production and represents that qualitative ground on which classical school of political economy using formal logic, created the whole system of economic categories which logically connected between themselves, and explained quite logically mechanism of its functioning: production of profit in different form, reproduction of all private capitals, causes of economic crisis, unemployment, inflation and so on.

According to the dialectical laws a private capital under certain economic conditions must transform into its opposite, social capital which will be based on socialized capitalist production and which will be new qualitative ground. By using the same formal logic, I explained in my books the function of the future capitalism in the form of social capital based on this new qualitative ground, socialised production. The logic of the function of the social capital is quite different than the logic of function of the private capitals: there will be no unemployment, economic crises, inflation,but there will be reach and poor, healthy environment and absence of many social contradictions which dominate right now.

When I published my articles in "Economic Gazeta" in Russia, Moscow, about the development of categories in an economics by using as example "Social capital", one of the professors in economics said:" there are as much ideas as people." His statement shows only one side of the coin and keeps silent about the other, that among all existing ideas about future society only one idea is true that based on dialectical logic. His statement is based on the formal logic which can consider the same event from the different grounds. For this reason every person can invent his own ground and built his logic according to it. This well-known approach is used by politicians, lawyers, prosecutors and some scientists in economics and philosophy in order to achieve their goal and to hide their real interests. But a whole beauty of dialectical logic consists in the fact that dialectical logic uniquely defines the sufficient ground in science, when we deal with the development of any event in nature, and thus eliminate all other invented theory that are not based on this sufficient ground.

It is not difficult to note, from above mentioned examples, that private (individual) capital and social capital are in the same relation to each other as Euclid and Lobachevsky geometry or Lobachevsky and Reimann geometry. In other words they all are based on the qualitative ground that eventually transforms into its opposite. And this is quite understandable because the development of any science is based on the Laws of formal and dialectical logic. Keeping this in mind one can say that the philosophy is Queen of sciences.
P.S. For more understanding of formal logic read my article "The Development of Laws of Formal Logic of Aristotle"