According to the objectual philosophy,
a modification occurs in the definition of the *elementariness*
concept (of an object or process), which means that the
elementariness as an attribute and abstract object must have the two
components, respectively, the *qualitative* and *quantitative
*component. *Qualitatively* speaking, the elementariness of
an abstract object is provided by means of the existence of a __single__
qualitative property (the set of the distributed attributes contains
a single element). *Quantitatively*, the same elementariness is
provided by the existence of an __indivisible__ quantity
(non-decomposable) from the elementary qualitative attribute. From
the point of view of the distributions, the quantitative
elementariness of an assigned attribute is related to the
*distribution element.*

As for the *primary*
distributions, the distribution element is a __singular value__
(virtual or normal) of the distributed attribute, assigned to a
__singular value__ (a virtual or normal too) of the support
attribute, by means of a __local relation__. Depending on the
distribution class (virtual or realizable), the two values have a non
determination interval (null for the virtual distributions and
DP-type for the realizable ones.

In case of the *derived*
distributions, the distribution element is made-up as a result of an
__elementary variation__ (of a certain rank) of the distributed
attribute, assigned to an __elementary variation__ of the support
attribute, __through a local relation__. Here, the *processual
quantitative* elementariness intervenes, which means that a
non-decomposable variation is imposed (as magnitude) for the two
variations (mostly for the support one) which makes-up the element of
the derived distribution, but which also allows the existence of a
non-null process. The definition manner of this elementary variation
is different for the two distribution types, one currently used by
mathematicians, and the other used by the objectual philosophy. As
for the classic derived distributions (the ones used in mathematics),
the elementary variation is defined as a limit of a process which
implies the amount decrease towards zero, whereas in case of the
systemic derived distributions, the quantitative elementariness is
provided only with the condition that the previous distribution (in
terms of rank) of the dependent attribute on the elementary support
interval to be considered as linear, so that its density to be evenly
distributed.

Due to such a definition of the
elementariness, mostly in case of the processes (whose model abstract
objects are the derived distributions), it is possible the unified
approach of all the vector classes (SEP), including of the position
vectors, which according to a classic quantitative approach, do not
belong to the class of the elementary processes (their variation
being unlimited in terms of magnitude), but which are elementary in
terms of *quality, *due to the fact they have the spatial
density (direction) evenly distributed on the support domain.

Copyright © 2006-2011 Aurel Rusu. All rights reserved.