[atheist]

Brief characteristics of general materiology (GM):
It is a radical new alternative theory of sets which has following properties:

Its fundamental concept is of course a set, as the most universal concept that includes absolutely all structures. However, this concept is defined differently than in the classic Zermelo-Fraenkel theory(ZF) of sets or in the von Neumann-Gödel-Bernays theory of sets (NGB), namely because it fully complies to the delimitation principle; moreover there exists no structure that could not be included within this concept, nor can any such structure be conceived (!!!). One of the interesting characteristics of this theory is that unlike the latter theory (NGB) it can do without the concept of a class.

Although it is trivially contradicting to the ZF and NGB theories, it does not have a problem to support the creation of any other arbitrary theories of sets, including those mentioned and other theories trivially contradicting to it, because our theory is able to process them with a positive cognitive result. Two indications should make it clear: 1. Human brain is a system with a non-monotonous logic (thus it is able to model contradicting systems of statements!). 2. Even a theory contradicting reality can have a monumental practical relevance (e.g. infinitesimal calculus in our discrete world).

Our theory is based upon the axiomatic principle. Its fundamental formulation thus contains only pseudodefinitions and definitions of terms and relations and a system of axioms. The first axiom expresses a necessary and sufficient condition for the existence of a set, all following axioms express only the necessary condition for the existence of a set, even if after their fusion in any arbitrary combinations. All other more specialized sub-theories of GM strictly use only the information from the axioms, which makes this axiomatic system independent.

Due to the original definition of a set, a structure that could not be processed by this theory never existed, does not and never will exist, nor is such a structure conceivable. Thus it is absolutely universal!!! This is not true about any theory that I know of, mathematical or otherwise!

The sole necessary relation of GM among the sets is the relation of „is an element of“ and its negation – “is not an element of”, all other conceivable relations are derived from these two. There is an interesting fact, that also in the fundamental formulation of GM each of the two must appear at least twice (in the definition of a contradiction and in the first axiom). Due to the original definition of a set, the delimitation principle is valid, and the relations „is an element of“ and “has property” and relations „is not an element of“ and “does not have the property” are considered to be identical!!!

It is strictly a theory of discrete sets, thus accepting the principle of matter quantization known from the Physics with all its radical consequences. Among such consequences are e.g. so-called elementary particle paradox, and the resultant principles of imperceptibility and indeterminateness of matter. Heisenberg’s principle is “only” a special case of the principle of indeterminateness of matter!

It includes concepts such as elementary particle, quantitative property, measure, metrics, topological space, well ordered set, probability … These concepts enable the theory to process also the properties of physical objects, and thus construct its own fundamental physical theory. This point is important because it unites extreme mathematical abstractness of the theory of sets with our surrounding physical, biological, psychological and social reality with all its phenomena!

It is contradicting (in the sense that a set of contradictions is a necessary part of its internal structure). The theory not only defines contradiction as a set, but since it also defines its properties, it turned contradiction into one of its key decision tools. Simply said, even if a set is found contradictive, it does not mean that it is out of consideration in our theory! This is also an argument why this theory radically changes the outlook on the meaning of Gödel’s sentences about incompleteness and other similar sentences, and why it has definitely and mathematically correctly solved the paradoxes of the ZF theory of sets (!!!).

The semantic content of the theory’s axioms is sufficiently broad to implicitly lead to extensive and profuse theories. The four basic ones are: Universal Model of Dynamic Systems(UMDS), the Theory of Existing Numbers and Functions(TENF), the Physical Model of Matter(PMM) and the Theory of Models(TM). These theories of course overlap and do not have precisely set boundaries.

UMDS is a mathematically causal (!) model of the evolution of material systems. Including inorganic systems!!! It works with the terms such as the probability of a set, objectiveness of a set, rational numbers (simply constructed from the set of natural numbers), system-individual … It is based on a stochastic approach and among its results are e. g. mathematically formulated laws of the evolutional process and its attractors (of unstable value!) towards which material systems tend to incline in course of time. The most interesting consequences: Matter fulfils the fundamental qualities of auto-organization!!! There is no difference in quality between the so-called organic and inorganic matter!!! This is the main reason why we are still not able to determine whether viruses and prions are living beings, and why we cannot determine what was the first living organism – the boundaries simply do not exist!!! Practically the whole biology is implicitly derived from UMDS, including the detailed explanation of morphological, anatomical, physiological, ecological and other schemes of “living” organisms. And the most beautiful aspect of it all is that UMDS not only supports Darwinism, it is its causal model, thus placing it in a position of a mathematically proven science!!! Wow!!!

TENF is a theory of the values of all quantities, thus including values of the properties of physical objects. It can do with just the set of natural numbers! The most interesting consequence: Even non-existent structures are attractors which attract the behavior of material systems through the l.i.m. mechanism (e.g. fractals, transcendental numbers such as Ludolf, Euler, the golden number, Feigenbaum’s constant…)!

PMM is more or less a theory of elementary particle. It deals with the question of the fundamental interaction among the elements of matter, space-time in-/finity of the universe, the phenomenon of gravity… It is “tributary” to the results of the so-called paradox of the elementary particle, thus leading to one of its most bizarre positions: There cannot exist a field-type interaction among the elements of matter, thus elements of matter cannot exert a “distance” influence upon each other without a direct mutual contact!!! This part of the theory utilizes terms such as the mass of the set, org (a set with a non-zero mass), triangular inequality (utilized precisely to indicate sets with non-zero mass!), point … Interesting results: This model can do with just the discrete linear spaces of the Euclidean type. This results in a “detail” – the theory had to reformulate Relativistics since this is based on the mathematics of continuous structures. Most material objects have zero total mass and therefore are physically absolutely unobservable!!! Volume and surface of matter is zero, its mass is approaching zero value and will eventually achieve it!!! Juicy bite: According to this theory, too, the universe is constantly expanding (the average absolute value of the measure presenting the physical distance among the physical objects is spontaneously increasing), there occur the phenomena of the increase of mass of objects, and of their shortening (the equivalent of the contraction of length from the Relativistics) when increasing their speed (but absolutely in relationship to the Euclidean space in which they move!).

TM analyzes the relationship between the information and its material medium. Moreover, it also means that it deals with the relationship of a thought to the mirrored reality, as well as to the structures that “think” the thought!!!

All other specialized theories are derived from the four above mentioned ones. For example, the theory of the functions of control systems (structures which include animal brain) can be practically completely derived from TM and UMDS. Yes, practically the whole “secret” of our thinking process rests on a few “ridiculously simple” rules!!! For all that, it explains the problem by the dialectical unity of its basic aspects – brain as a logical net (anatomical and physiological aspects), the essence of creative thinking (informational aspect) and subjective experience of the individual (psychological aspect – consciousness, conscience, humor, love, faith…(!!!))! Interesting results: Freedom of thought does not exist, and creativity of our thinking does not lie in creating new information, only in combining the old ones in new, interesting ways! Please, remember the stochastic nature of the UMDS! It implies that the process of human thinking is no different from the evolution process of any ecosystem. It only progresses quantitatively faster (and therefore with quantitatively greater error rate!!!) thanks to certain mathematical evolutionary “tricks” of nature! It’s no go, who wants to read on further has to begin to tame his or her anthropocentrism.

The theory does not contain any “Bulgarian” constants or “higher” principles.

It is fully “aware” of questions that are known to be “satisfactorily” insoluble. It is thus not, and neither it purports to be an omniscient theory.

This preview is an offer. Because GM is a huge theory, we can realize detailed explanation of GM, but only in case of at least one hundred chalenges to us.