"The claim for minimum contradictions" derives from the basic philosophical dilemma:
"If the next moment is a causative result of the previous one, then:
either there isn't free will or causality breaks ".
In order to give an answer to this dilemma we will use Gödel theorem and specifically the analysis prior to this theorem. The dependable context which is based on the proof of Gödel's theorems is the Aristotelian logic part of which is the propositional logic and Peanno's Arithmetic Axioms (PA). A basic statement for Gödel's Theorem proof is:
Gödel's Basic Statement: "If formula G (Gödel's formula) can be proved, then its negation (~G) can be proved as well".
This implies that Peanno's Axioms (PA), are inconsistent; the opposite statement is not always valid and this implies that (PA) is simply w-non consistent.
However J. B. Rosser proved that if Theory T is an extension of (PA) (that is T can prove all theorems of (PA)), then there is a formula R T so that the following theorem is valid:
Rosser's Theorem: "If formula RT can be proved, then its negation (~RT) can be proved as well and vice versa".
The basic communication system through which any theory is stated includes classical logic. Beyond it if we claim that syllogisms exist, it does imply that they can be found within space and time. As long as notions of space and time correspond to something measurable they imply arithmetic's validity. This is compatible with Peanno's Axioms (PA). This means that the basic communication system includes Aristotelian Logic and Peanno's Axioms. Thereafter, by Rosser's Theorem we have the following Statement of Inconsistent Communications:
Statement of Inconsistent Communication: "The basic communication system that is based on classic logic and that calls for arithmetic operation is inconsistent".
We notice that the answer to the basic philosophical dilemma mentioned initially has no meaning because this dilemma is logically phrased through the basic communication system that is inconsistent. Therefore the intellectual coherent attitude initially seems to be silence. The condition "initially" is cited because both " Gödel's Basic Statement" and Rosser's Theorem are based on the Gödel hypothesis:
Gödel's Hypothesis: "There is an algorithm that permits the derivation of only true statements".
Besides the trials realized it was impossible to prove this hypothesis, as noticed by H. Putnam and R. Penrose. This makes clear the reason why case studies C are necessary so that "The Claim for Minimum Contradictions" can be better reasoned.
On condition that Gödel's Hypothesis is valid the disengagement of silence, supported on the knowledge that the basic communication system is inconsistent, constitutes something that happens regardless if communication has been determined. In order for the above mentioned to have meaning it needs a claim:
"The claim for minimum contradictions": "We accept as valid what includes the minimum possible contradictions (since contradictions are never vanished)".
On this basis physical laws ought to include contradictions as being formulated through a contradictory communication system. Thereby in the category A case studies, we can notice that what we could call " Fragment Law" , i.e. a law including contradictions. Fragment Law is what is evident from the unification of physical meanings that are produced either from general relativity or through quantum mechanics. It is stressed that the unification of general relativity with quantum mechanics is possible with the following means:
1) Through a new privileged principle. Something along these lines will be mentioned in case studies type C.
2) Through a mathematical process of already existing principles but also on the basis of some other concepts. This is how the super-string theories result.
The other concepts that were mentioned are related with the demand of renormalization, as also the replacement of punctual particles with the notion of a chord that during its movement creates a surface and not a curve.
It is obvious that something like that can not be proven and requires a priori. Over and above, since we are mentioning probability density, this ought to relate with the notion of probability which fulfills the clause for self-normalization. Otherwise we will have a mathematical process, where mathematics will try a posteriori to give a probability meaning to something that a priori does not reflect.
3) With the unification of physical meanings as already mentioned.
By the unification of this type we have the following:
As with the general theory of relativity as with quantum mechanics through familiar principles that ruled, condense already revealed experience. For example these principles are not provable but were formulated in order for nature's laws to be compatible with experimental results.
Due to experience from general relativity a punctual matter is surrounded by a space-time continuum.
Due to experience from quantum mechanics any element of a field is described by a matter wave.
As long as we wish the unification that was mentioned the following IA and II Á principles must apply:
Principle ÉÁ: "Any infinitesimal space-time element can be regarded as a matter wave"
Principle II Á : "The energy of an infinitesimal space-time is equivalent to its internal time"
Internal time is the comparable time as noted in detail in relative case studies.
Type A case studies have as a result the existence of stochastic space-time as recommend by "fragment law".
Basis for the study of unification of this type was initially the Image Field.
As Image Field is defined a hypothetical field, which consists of a Euclidean space-time reference, in which at every point Á 0 the real characteristics of the corresponding - through deformity transformations - point A of the real field exist.
Category A case studies are the following:
Á.1 A.A.Nassikas,1994. The Hypothesis of the Unified Field and the Principle of its Dual Interpretation. III International Conference: "Problems of Space, Time, Gravitation". Russian Academy of Sciences.
Á.2 A.A.Nassikas, 1997. The Hypothesis and the Equations of the Unified Matter Field. a) Infinite Energy - Cold Fusion Technology, Inc. Vol.3, No.13&No.14, b) 1996. International Conference "New Ideas in Natural Sciences" St. Petersbourg's Physical Society. St. Petersbourg , Russia , Ed. A. Smirnov and J. Klyushin.
Á.3 A.A.Nassikas, 1998. The Hypothesis of the Quantum Space Time - Aether. a) Congress-98 Fundamental Problems of Natural Sciences, Russian Academy of Science. St. Petersburg , Russia. b) Galilean Electrodynamics, Special Issues 2, 2000.
This paper is published here by the permission of Dr C. Whitney editor of "Gallilean Electrodynamics"
Results of these case studies are:
a) The induction of a general formula for gravity that is valid everywhere. This formula with certain simplifications is compatible with Newton 's law of gravity.
b) The formulation of space-time operators and the complete geometrization of a unified field. The geometry of a unified field is determined by the basis of the wave function Ø.
c) The stochastic - quantum space-time which is matter itself. In the stochastic space-time, the "geometry distribution" is based on a function that is self-normalized and because of this fulfills the demand to reflect probability. This probability is not always positive and as for this there is epistemological basis from "The claim for minimum contradictions" by which contradictions are never vanished.
d) The unified filed equations are formulated and are valid everywhere. Since space-time is matter itself and does not consist of something empty in which the field can act we can state:
"there is no potential acting at a distance"
This statement facilitates the formulation of equations mentioned.
e) As a result the 2 nd thermodynamic law is formulated. With the unification of this type in a closed expanding matter-space-time system entropy change is always positive. It has been noted that the 2 nd thermodynamic law was formulated as a concept and not as something that can be proven.
f) The property of self-similarity in a material system is proven; this is compatible with the Fractal geometry of nature. It is noted that Fractal geometry as formulated by Mandelbrot uses the property of self-similarity as a principle, meaning something that can be applied for but not proven.
g) The Casimir phenomenon explanation is possible.
In case study A.3 the term "Image Field" is substituted by the successful Hypothetical Measuring Field (HMF) after P.F. Parshin's recommendation. This case study was included in the 2 nd Koryzev Issue in the "Gallilean Electrodynamics-East", since the described space-time has material-active properties, state compatible with Kozyrev's aspects.