Dialectical essence of information
Analyzing the concept of information taking into account the measures introduced, A. A. Denisov shows that information does not satisfy the logical law of the excluded third, does not allow the existence of several contradictory but equally true values, judgments, and concludes that information is a concept that does not yield analysis by means of formal logic and requiring the application of dialectical logic to it, which provides the possibility of analysis not only absolutely, but also with respect to true statements [1, p. 243].
According to Denisov, matter appears as a dialectical synthesis of substance and reflection (information), where information is the structure of matter. So matter, on the one hand, is a substance, but, on the other hand, it contains information.
All this applies to information that circulates both between material objects in the process of their interaction, and within the continuum, realizing the material unity of the world. This information, on the one hand, is quite objective because it does not depend on our will, but, on the other hand, even within the material continuum, the dissemination of information is accompanied by interference and distortion, so that its recipients really do not deal with information "in themselves" , but with the information "for them" similar to the information "for us", which are also objectively real, in the same way as the matter itself. At the same time, neither information can exist without a material carrier, nor matter can not be structureless; meaningless.
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Thus, the main question of philosophy about the primacy of matter or consciousness (information) loses its meaning and becomes an attribute of the history of philosophy, for there is and never was no matter without information, as there is no information without matter.
As noted above, information is measured not by a number in the understanding of classical logic. Classical logic is the logic of numbers, and dialectics is the logic of words and the concepts they express.
Constructing the essence of the concept H, AA Denisov first used the analogies of the theory of chains, and then made a presentation at the seminar B. S. Tyukhtin at the Institute of Philosophy of the Academy of Sciences of the USSR, and Victor Stepanovich saw in the model A. A. Denisov the possibility of deducing his symbolic representations from the sequence of requirements imposed by the laws of dialectics as applied to judgment.
The result is a model that reflects the process of reflection, perception and comprehension of information, taking into account the reaction time and the rigidity (resistance of new information) of the perceiving subject.
In the process of constructing the essence of the concept H in its symbolic representation, the requirements imposed by the laws of dialectics as applied to judgment are consistently taken into account.
The first to introduce a measure of logical information was applied the so-called "basic law of logic", which is valid for both classical logic and dialectics. According to this law, the essence of the self of the concept is inverse to its volume n (1.15).
Here, by the volume of a concept, is meant the total number of homogeneous objects or phenomena, the information J about which was the basis of the concept. In this case, the more objects, the less one of them tracks of information J k, inherent in only one or a few objects. And as a result, with n → ∞, nothing remains of them (as happened with the concept of matter).
On the contrary, for n = 0, i.e. in the case of an ideal (non-existent) object, the essence of information about it is infinite, but it is about nothing. Therefore, philosophy, the concepts of which embrace all that exists, have the right to judge everything, but such judgments are inevitably unaddressed, vague.
On the contrary, the mathematics of ideal numbers is absolutely concrete in its conclusions, which, strictly speaking, are not relevant to real objects.
But, with n = 1, i.e. applied to a single object, the concept coincides with the complete information J about it, preserving all the individual wealth of colors and shades. Therefore, for example, the concept of a specific Ivanov is immeasurably richer than the concept of a man, and even more so of a man in general, for we can accurately indicate his height, weight, color of eyes and even the number of scars on his body, whereas a person in general can be said much less, and even then on average.
Second law in the number of laws that form logical information is the law of development, or the law of variability ("Everything flows and everything changes"). This is a purely dialectical law, since in the classical logic A there is always A and 1 is 1, while in dialectics the formation of truth is continuous and never ends, firstly , because reality changes, and secondly, knowledge itself is improved, so that no one can claim to know the truth in the last resort.
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As shown above, information reflects relative truth and can change in the process of cognition and practice. To describe the process of becoming a concept, the symbol (operator) d/d t, is introduced where the numerator means a partial change, and the denominator indicates that this change occurs in time, so, for example, dJ/dt means changing the information in time. In this case, the accumulation or decrease of information can be reflected by the signs + and - respectively.
Since any change negates stability, i.e. the law of negation, where the symbol d/d t is a synonym for partial negation and corresponds to the verbal to some extent not .
With regard to the law under consideration, the essence H τ of the process of the concept's evolution (evolution) should be inversely proportional to the volume of the notion n, dt = 1/τ, so that
Hz = τ dJ/dt. (1.19)
In the future t is called the information resistance and characterizes the delay in the perception of new information in the process of formation and evolution of the concept.
The third law of dialectics - the law of negating negation - without formalization is the most difficult to understand.
So J is the thesis, Δ1 J is the antithesis, i.e. the negation J, and Δ2 J is the antithesis, the negation of the negation J. In other words, if J is A, then Δ1 J is notA & quot ;, and Δ2 J is & quot ;, i.e. a definite, albeit incomplete, unlike classical logic, a return to A.
This is the famous development in a spiral, fraught with cyclical returns to the original forms, but with a different content.
Since the law of variability is inherently the law of negation, the law of negating negation should be interpreted as a double application of the law of variability, i.e. as the application of the law of variability to the very law of variability. From the formal symbolic point of view, this means applying the operator d /dt to the operator d/d itself (that is, d (d/dt)/dt or d2/d t 2, so, for example, d2 J/dt 2 means changing the evolution of information over time.The essence of the evolution of the concept evolution must in this case be inversely proportional to the change in the evolution of the volume of the concept d2/d t 2 = 1 /L, so that
where L will be called rigidity (inflexibility) of the concept, resistance to change.
The law of negation could be applied again, i.e. to the law of negation of negation, which would lead to the law of negating the negation of negation, symbolically displayed d 3 J/dt 3. It would be possible to talk about the further application of the law of negation. However, apparently, dialectics does not in vain not contain the laws of triple and more negations, since it would be too cumbersome and burdensome for thinking. Our thinking operates sparingly, and all phenomena that go beyond the law of negation break up into transitive forms, etc., which collectively transmit arbitrarily complex processes.
The fourth law of dialectics, the requirements of which must be taken into account - the law of unity of opposites - requires to avoid the absolutization of both the moment of struggle and the moment of solidarity of opposites, subjective dismemberment of a single whole for the sake of facilitating knowledge of the contradictory parts of it.Opposites in our case are the moment of relative stability of the concept, the relation (1.15) is the thesis, the moment of relative variability (1.19) is the antithesis mediated by the negation of the negation (1.20), which in accordance with the applicable law should be considered in indissoluble unity
and in the particular case, a linear approximation is possible
where n is the scope of the concept; τ - information resistance, characterizing the delay in the perception of new information in the process of formation and evolution of the concept; L - rigidity (inflexibility) of the concept, resistance to change.
Thus, the result is the ratio
This means that the true essence of H of objective reality is composed at each moment of time from the memory contents H n (reflected essence) formed at that moment, from that logical information H τ, which is in the process of transmitting sense organs to memory, and from that logical information H L, which is impeded by habits and prejudices.
The fifth dialectical law - the universal interconnection and interdependence of phenomena requires the consideration of all the factors that determine the process under investigation, and not just those that seem to be dominant.
Taking into account the law of universal interrelation and interdependence of phenomena, the relation (1.15) is supplemented with components reflecting the interaction of the original concept with other concepts entering the system by introducing appropriate notations in order to distinguish these components from each other. Then
where H ni - the system is the essence of the concept; the first index with symbols denotes the number of the concept that is taken into account when the system is mapped, and the second is the number of the concept with which the given one interacts, so that n ii means the own volume of the i -th concept; n ij - the mutual volume of the i and j concepts.
The resulting relation (1.23) corresponds to the usual rule of formal logic, according to which in any definition H n1, first, its generic membership J 1 a, in -second, specific differences J 2, J 3, etc.
Similarly, the relation (1.19) is transformed to the form
where H τi is the systemic essence of the evolution of the i -th concept; τii - own information resistance; τij - mutual information resistance i -th and j -th notion.
And the relation (1.20) takes a form analogous to relations (1.23) and (1.24), that is,
where H Li - the systemic essence of the evolution of the concept; L ii - the inherent rigidity of the given concept; Lij - mutual rigidity of the i -th and j concepts.
As a result, taking into account the law of universal interrelation and interdependence, we obtain a system of relations:
or in the case of linear approximation and some permutations of components, which is more convenient for a number of applications, we get:
(1.27)The system of diffuse relatively true (dialectical) judgments of the type (1.27) allows us to make a symbolic fuzzy reasoning by solving this system according to rules that differ from mathematical ones insofar as dialectic logic differs from the classical one, i.e. to the extent of the influence of the laws of identity and the excluded third. The absence of these laws in classical logic, their actual replacement by the law of the unity of opposites, leads to the fact that, on the one hand, judgments of the type (1.27) are always compatible, unlike mathematics, because they dilute the area of their existence, they can always be partially combined, and with another hand, the linear combinations of these judgments are not tautologies, because they are not quite reducible to each other because of the fuzziness.
In particular cases (as determined on the basis of justifying the model of a particular problem situation), relation (1.22) can be regarded as an ordinary differential equation, and the system of equations (1.27) can be solved in accordance with the procedure of transformation and solving differential equations in mathematics logical law of sufficient reason (in accordance with which the number of judgments must be not less than the number of objects about which inference must be obtained), the logical laws of the contradiction (mp (compatibility of judgments) and identities (requiring to represent synonyms with the same symbol).
The sixth law of dialectics - the law of transition of quantitative changes to fundamental qualitative - emphasizes the need to avoid the absolutization of the development tendencies revealed at the beginning of the process, because in the future they can change up to to its opposite, and precisely because of development.
From this law it also follows that the sum of the properties of parts is not a property of the whole, and the negation of the whole does not necessarily mean the negation of parts, for it can refer to the negation of only that new property that has arisen due to the synthesis of parts.
This law requires understanding that the characteristic constants n, m and L are constants only in a limited range of evolutionary changes in the concept. In the general case, with large changes, these constants may not retain their values, which will lead to a radical (revolutionary) change in the essence of the concept, violating the smooth evolutionary course of development. From the formal point of view this means that in the general case n, τ and L are functions H , _ J , dJ/dt, d 2 J/dt 2.
Note that although the parameters n , τ and L are named above respectively by capacity (memory capacity), information resistance and rigidity of the concept, but since the latter is formed in the consciousness of one person (or in the future - in the memory of a specific system of perception and storage of information using computers), then these parameters, in essence, characterize the memory, capacity and rigidity of the psyche of a particular person (or automated information system) and can be measured experimentally, iodically to repeat taking into account the last of the considered laws.
If we periodically refine n, τ and L, then expression (1.27) will retain unlimited universality in describing any phenomena; and, describing the complex phenomenon element by element, it preserves the integrity inherent in the relation (1.26).
A more detailed exposition of the application of the laws of dialectics to obtain models of information processes taking into account their kinematics and dynamics can be found in  and the works of AA Denisov [1, 19, 22].
The laws of classical logic and dialectics differ in that in the first case, any deformations of the initial judgments can only be abrupt (either true or false), and in the second case all transitions are smooth and continuous with an infinite set of states between truth and falsehood. Therefore classical logic is binary, two-valued, and dialectic is infinite-valued.
It should be borne in mind here that the marked differences between dialectical logic and the classical are deeply fundamental and lead to ambiguity, multiplicity of inferences based on the same system of judgments.
This allows, in particular, to raise the question of choosing among them the best management or project solution, i.e. formulate the optimization problem, which in this formulation reduces to the search for a solution of a system of relations of the type (1.27), in which a combination of Δ A i chosen as an optimality criterion would be minimal. This means, in essence, the search for the least diffuse solution of the system from all possible.
The considered laws of dialectical logic and their application for explaining the process of the formation of the notion of logical information are not yet sufficiently used at present. At the same time, their accounting seems promising for the development of the theory of information processes and systems.
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