Progressive evolution as self-regulation of the World (inductive and deductive description of natural and social development) Прогрессивная эволюция как самоупорядочивание мира (индуктивное и дедуктивное описание естественного и социального развития).

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article 2

Henry L. Zaltsman

(Scientific axiomatic-deductive description)

Keywords: Proctologic – metalogic, contracategories, principles - contraprinciples, Parts – Whole, tetradic periodity.

Neither disciplinary, nor interdisciplinary sciences can represent the general picture of self-regulation of the world. This article is an attempt of axiomatic-deductive description of such self-regulation. We select contrastive spatio-temporal objects to reconstruct the formal model of self-regulation of the world by means of mathematics and the new meta-logic. Such interpretation is aimed at forming an evolutionary picture of the Universe, from the Big Bang to manifestations of human thought (with systematic inter-object relations of the results).

Resources of interdisciplinary scientific cognition.
This kind of speculation has become an answer to further differentiation and specification of disciplinary sciences, which led to a greater distance from understanding world as a whole. The answer may be interdisciplinary integration and consolidation of sciences manifested in interdisciplinary approaches. It started with integration of methods and independent sciences (astrophysics, bio-chemistry, zoo-psychology, etc.) and developed into general integrated approach. Thus, the evolutionary approach produced in biology was later spread onto other sciences dealing with objects in aspects of cosmogenesis, geogenesis, biogenesis, embryogenesis, psychogenesis, sociogenesis, gnoseogenesis, etc. These evolutionary approaches are united under the principle of "evolutionism". Another system principle covers element-system relations which are characteristic for objects on various stages of development. It means that all known objects are ranged in time as evolutionary objects and in space as systematic objects. Disciplinary sciences consider separate objects, while it is necessary to consider generalized generic systems: atom in abstracto, cell in abstracto, brain in abstracto, etc.
My next step was to combine separate generic objects into the general evolutionary system. Its units were characteristics of temporal transitions from the initial to the derivative, and of spatial transitions within element-system hierarchies. It took decades to work out strict rules for such transitions and to use them as an inductive basis for the general evolutionary system. The system covers generalized (generic) objects, from early universe to human cognition, arranged in parallel element-system and system-element series [1, 2]. However, selecting each initial evolutionary object has faced overwhelming difficulties. Multiple choices cannot be but disputable, which puts the system in a disputable rank. With all this, the system has been worked out. Its pivot is a set tetradic periodicity of the evolution; the world evolves as a sequence of four specific worlds: physical (cosmos), biological (life), animal (behavior), and human (cognition). Each of these worlds, in its turn, develops through four successive stages of evolution, and so on. Their regulation has the form of a tetradic tree of fission. On these grounds, we can figure out the fundamental (quantitative) characteristic of the world - the hierarchical tetradic periodicity of its development.
The question is whether periodicity of the world is the limit of cognition? Can we cognize the bearer of periodicity?
These questions aimed at the terminal axiomatic-deductive description of the world. (Such a description is only possible due to accumulated systematic concepts of matter that, in particular, require certain modifications of the ideas about space and time.)


The fundamentals of time and space:
1. The world and its components are based on two counterprinciples. They include:
- principle Whole - a continual state of the world, medium of interior spatial relations;
- counterprinciple Part - the limited (discrete) state of the world, medium of exterior spatial relations.
2. Self-motion, genesis of counter-principles is counterpointed:
- each derivative principle Whole is disabled in the initial - the motion of disabling;
- each initial counterprinciple Part is enabled in the derivative: the motion of enabling.
3. Repeated self-motions of counter-principles form parallel four-stage series: the way "from chaos to order". Thus is realized the successive regular-spatial regulation of relations.

4. Final series of regulation of counter-principles are integrated. Their main characteristic is tetradic periodicity, however, a tetradic series of Parts develops within a specific Whole. A series of Wholes corresponds with a tetradic repetition of Parts. Such sophisticated models (see The Appendix) require a symbolic language. Unfortunately, gnoseologically adequate symbols for world-correlated logic do not exist. We use the language of subject logic.


The object of cognition - world as a whole - is thought of as an axiomatic scheme. The subject of cognition is thought of as logical forms of cognition considered in retrospective. Let us make use of formal binomial logic (object - feature). Supposedly, the primitive society is characterized by the so-called "pre-logical" thinking. Yet, there is no way of agreeing with this concept, so far as names are the basis for both the volume of the notion (a number of named objects) and its meaning (a number of named features). So we shall use the term "proto-logic" for the logic of naming and associate with it "post hoc, ergo proper hoc" thinking. The term "pre-logic" will mean randomly regulated thinking of the savage society (and pre-verbal thinking of the child).
This differentiation is objective: it reflects the relationship between each form of logic and its prototype. Thus, pre-logic is free individual thinking of man since his early childhood. Proto-logic is a conventional social product, which means relations between man and socium. Formal logic is object-correlated. In thought an object is determined by its features (man is also an object). By further generalizing prototypes we shall come to nature-correlated meta-logic.
These types of logic are characterized by univocal hierarchical four-stage form of thought, i.e., random unregulated propositions, simple regulated propositions, their combinations in basic propositions, and their consecution in complex propositions. (The initial stages of the first two forms of thinking "are rooted" in the indeterminacy of the subconscious). For example, segmenting the logic of human thought, the simply regulated proposition is a monomial; its first derivative, the basic proposition, is a binomial, and its second derivative, the complex proposition, is a quadrinomial.
On the basis of these propositions, we can construct a gnostic field, according to the coordinates: object relations for different types of logic, and subject relations for logical segmenting of thoughts. (Fig. 1).


We shall use the term "meta-logic" for nature-correlated logic.
Meta-logic is formed according to its position in the comparative gnoseological series. Specifically, the form of the binomial basic proposition (substantive / subject + attributive / characteristic) is related to the elementary meta-logical proposition (principle / Whole + counterprinciple Part).
Elementary propositions. Counter-categories of substantives [A : Ā] form a contraposition Whole : Part. Counter-categories of attributives [a : ā] form an opposition totalization (integration) : partialization (differentiation). They form elementary propositions [A/ā] - Whole partializes (divides) and [Ā a] - Part totalizes (integrates).
Basic proposition - tetra-countercategory - unity of countercategories:
[(А/ā) (Ā а)]. A principle divides while a counterprinciple integrates. Tetra-countercategory is a complete form of meta-logic thought. Each real prototype for substantive counter-principles is always a point of their integration taken at certain values of their attributes. All propositions of meta-logic must have a tetra-categorial form of thought.
Complex propositions form series of counter-categories and effect through consecutive
iterative attributes, i.e., through regulation of principles and counter-principles:

The Whole principle divides triply, while the Part principle integrates. Meta-logic of negation has three dimensions, which corresponds to the four-stage motion from "chaos to order". Regulation of counterprinciples proceeds as an integral process. As stated above, each Whole principle correlates with a developing series of a Part principle. The integral series correlates with the spiral tetrad of part series. Such spiral blocks of complex propositions form further meta-logic schemes. Thus, "within a pattern", the spiral block forms a secondary derivative spiral, the primary circuit of which is the block itself. Following the double spiral trajectory, the meta-logic figure (2) correlates with genetic transitions of self-regulated world.


The method is based on correlation between meta-logic transformations of formal objects and spatial-terminal genetic transitions of real scientific objects. The fundamentals of such interpretation were set forth in the empirical evolutionary method formulated in earlier works [1, 2]. The results are presented by large-scale progressive evolution objects in Figure 3. (Comparative correlation of particular objects on the vertical line is presented in Figure 2).
According to the method, each evolutionary object takes its own place. This place is the node of its horizontal coordinate (a stage of regulation of Parts) and its vertical coordinate (a stage of regulation of Whole). Each coordinate point of genesis allows fixing and realizing how all precedent particular objects transformed into interior structures of this or that Part, and what path of development (and its potentials) is determined for the future. We can also determine the relationship between the object and all Whole exterior worlds that effect it. Thus, every man consists of molecules and complies with laws of physical world. He consists of cells and complies with laws of biological world. His functioning organs are consistent with animal world laws, and, if not a Maugly, he is consistent with gnoseo-social relations.
The main point is that both the process (operation) and substance of every genetic transition of objects from one stage to another are determined. Thus, this scheme offers a deductive knowledge of natural self-regulation of the world as a whole and of its constituent parts.

The axiomatic-deductive approach for description of the world self-regulation is necessary because no empirical, inductive methods provide admissible accuracy. In contrast to conventional views on mono-principle space, the fundamental idea is that of counterprinciples - Whole (structure of interior spatial relations) and Part (structure of exterior spatial relations), as well as their mutual regulation (series formation). The logic of deductive development was based on: gnoseological appraisal of various forms of thought, formation of nature-correlated tetra-countercategorial meta-logic, and mathematic model of world self-regulation. Interpreting the model, we can come to deductive determinate knowledge of the evolving, self-regulating world. According to this scheme of real self-regulation, every object is positioned on its own node of the horizontal coordinate (a series of direct genesis of Parts) and vertical coordinate (a series of indirect genesis of Whole worlds, general or particular). As a result, we can observe bi-principle past and future of every natural or social object and paths of their advance.
To sum up, the scheme presents (1-4)x(1-4)x(1-4) days of (self-)formation of world in the form of accessible information.


1. H.L. Zaltsman. Sovremennoye miroponimaniye. - S. Petersburg.: Nauka, 2004

2. H.L. Zaltsman. Towards a theory of progressive evolution. The Journal of General evolution.V65, № 3, April 2009

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