X.5.5 Conclusions

The complementarity in case of the natural distributions requires the existence of an attribute which has values unevenly distributed on a support domain, the reference value being the mean value (the support’s internal reference). By considering this reference value, some values show a property “deficit” while others are characterized by a property “surplus”.

The same situation is found in case of the distribution of the human attributes (qualities) on the set of the individuals belonging to a society; all the qualities of an individual are being evaluated (by himself or by other members of the society) by making a comparison of each quality with a reference value specific to a certain society, and a reference is always existent - that is the mean value of the support attribute⁹7- against which the two segments of the above-mentioned set may be distinguished: with property deficit or with surplus property. Because most of the distributions deployed by these attributes take place as a result of natural processes (self-settle by means of repeated bilateral interactions or by means of the specific individual components of the human genetic code), according to the objectual philosophy, the reference in question (mean value) is referred to as natural reference.

For example, the complementary attributes occur at the moment of the distribution of the instantaneous velocity on the set of gas molecules (either lower speed rates or higher than the average values), the distribution of intellectual abilities (stupid-clever) on the set of the individuals belonging to a social group, esthetic appearance (ugly-beautiful), muscular strength (weak-strong), etc. In most of the cases, the people have assigned different names for the two property types, although the two complementary properties are facets of the same distributed property, but with domains of the support’s quantitative values on both sides of a natural reference. By making a more increased generalization and by extending the dichotomic classification (against a natural reference as well) to all the types of human behavior, we finally reach to the concepts of evil and good, which are certainly determined against a natural reference - an average human behavior, obtained as a result of the mediation between more behaviors of different populations, on periods of time for which stored data are available.

The complementary properties are basic examples of the existence of quality difference of a property, exclusively based on the sign of a quantity difference (against the reference value). If we observe that the Gauss distribution of an attribute has an unique support domain which is dichotomically divided in two sub-domains by the internal reference (natural mean value), in that case we could find that the two opposite qualities are nothing else but the same property, but distributed on adjacent-disjoint support domains.

The complementarity concept which was previously analyzed allows us to operate with new abstract objects (presented in chapter 9), such as the absolute reality as a basis for two complementary abstract objects: the known reality (made-up from the total amount of MS and of the real processes with simultaneous existence for which the mankind owns specific information at a certain moment), and the unknown reality (the rest of MS and of their associated processes, with a simultaneous existence, yet unknown by the mankind).

The non-contradiction principle, exclusively applicable under the conditions of a dichotomic classification of a set of objects with simultaneous existence is a very old principle, accepted without hesitations by the entire scientific community, but yet unreasonably ignored in some cases. A notorious example of non-application of the non-contradiction principle may be found in the classic physics where the simultaneous existence at the same object (for example, a material point) of the position and velocity (or of the impulse) is (still) accepted. But, my dear reader, the velocity implies the variation of the position of that particular point; how can it be possible to simultaneously exist two opposite attributes - an invariant attribute (position) and a variation of the attribute (velocity)? Does it mean that an attribute may be constant and variable at the same moment t? This error of the classic physics comes from another error of a similar kind, but which this time may be found in mathematics - the existence of the derivative in a point (namely, the existence of a variation - derivative - at the same time with the existence of an invariant value - the function value in that particular point (see also the annex X.3).

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INDEX

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