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CHAPTER III
TAXONOMY
Historically, taxonomy goes back to ancient astrologers, to
Aristoteles and Theophrastus. Aristoteles provided the first
classification and description of many animal species, and
Theophrastus developed observation methods and generalizations.
Taxonomy receives a further development in Linne’s botany
philosophy, Lamarck’s zoology philosophy, Lyell’s classification
of rocks, and in Darwin’s Derivative theory of the origin of
species. Logically, taxonomy includes a classification of any
objects: Mendeleev’s periodical system of chemical elements,
Butlerov’s theory of chemical structure, Fedorov’s structural
crystallography and mineralogy, Schwann-Schleiden’s cell theory,
Hertzsprung-Russell’s spectral classification of stars,
Hubble’s classification of the Galaxies, etc. They are all based
on structural determinism of objects.
I. The postulate of structural determinism
All objects in the surrounding world represent different
forms of unified matter. By virtue of the material unity of the
world, the objects are not only different but also similar to
each other. The objects’ similarity is due to the fact that all
of them are built up from unified matter: they are akin by
origin and are interrelated genetically. The diference is that
they are constructed differently and are inimitable
morphologically.
The morphological difference and the genetic similarity of
the objects is reflected in our consciousness via categories:
individual, species, and genus. The ascent from an individual to
a species and from this latter to a genus forms the basis for
the ascent from a single to a special and from this latter to
the universal.
1. The principle of singleness
Each concrete object is individual and inimitable in
another. The category of the individual reflects in our
consciousness the extreme degree of difference between objects:
their singleness and morphological inimitableness, and an
individual – a single something finite in space and transient
with the time, through the combination of which matter exists at
each time instant. Nothing is eternal in the eternal world – all
the concrete is relative.
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2. The principle of speciality
3. The principle of universality
All species of objects represent different links in a
common chain of development of matter: they are akin to each
other. The category of genus reflects the second stage of
genetic similarity of objects - a phylogenetic similarity of
species between themselves. Phylogenetic divergence of species
occurs as a result of the nonuniformity of quantitative and
qualitative changes in the process of ontogenetic
development of individuals and a succession of their generation.
Nomologically, this process is reflected in the law of
nonuniformity of motion and development of matter and in the law
of transition of quantitative to qualitative changes.
The categories of individual, species and genus reflect in
our consciousness the objective presence of morphological stages
in the development of matter and are the initial ones in
cognition of its forms. In accordance with the objective
presence of these stages, regions of the real world do come into
existence, and branches of our knowledge do arise, hence sciences
emerge. On the basis of a morphological difference-similarity of
forms of matter, through Plato’s dichotomy - a successive
dichotomy of higher genera into lower genera and species and
through Aristoteles’ logic of classes – a successive
categorization of individuals under a species and a genus, a
taxonomic classification of these forms is accomplished. On this
same morphological basis an objective differentiation of
branches of Knowledge takes effect. Special sciences ought to be
concerned with the Ooda genera which, according to Aristoteles,
are the first definitions of the existent. Each genus of objects
has its own universality, ought to be treated by its special
science and is described by its own certain class of categories.
This provides the basis for the construction of the genetic
structure of the world and, accordingly, the genetic structure
of sciences. All sciences are divided into genetic and
predicative (see the genetic structure of the world and the
genetic structure of sciences).
CHAPTER IV
ONTOLOGY
Historically, ontology as a science of universal
definitions, goes back to Old-Indian philosophers of two schools
of thought: Vaisheshika and Nyanya, and to Aristoteles’ first
philosophy. Aristoteles, by calling the teaching of the existent
the "first philosophy", thereby determined its role and
significance in philosophy. The first philosophy, according to
Aristoteles, treats, as its subject, the existent as something
universal rather than in some of its parts, i.e. it is not aimed
at examining and explaining the specific features of all
individual genera of the existent and, moreover, the individual
features of each particular existent. Any existent, Aristoteles
posits, is defined in itself - it has a limited number of
attributive predicates; otherwise, when describing it, one would
have to go to infinity of random definitions – the postulate of
predicative determinism.
II. The postulate of predicative determinism
Any concrete object is finite: it is bounded in itself.
Each facet of an object has its specific character and is in
regular coordinationally-subordinative interrelationship with
all the others. Any object exists only so far as the unity of
its facets is conserved - the interrelationship of its facets
and relations. Each objet’s facet is reflected in our
consciousness by its special definition, the predicate, of
categories. Each category, as the object’s facet, has its own
specific character, and for the object to be described
correctly, it must be in the same regular coordinationally-
-subordinative interrelationship with other categories that
reflect this object’s facets.
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1. The principle of specific character
Each category reflects one and only one facet of the
object: form, content, quality, quantity, measure, cause,
effect, etc. The categories, as the object’s facets, are
irreducible one to another and do not substitute for each other.
Each category, as the object’s facet, is an indivisible but
continually ontological unity. This signifies that there cannot
be half a category or some of its parts. Therein lies the basic
difference of an ontological unity from a mathematical unity.
If the object’s facets, since a given object is conserved
as a given something, are inseparably linked with each other,
then the categories can and are usually employed separately.
Thus, the form can be treated independently of the content,
and the quality – independently of the quantity, and vice versa.
Separate use of the categories complicates the
establishment of an interrelationship between them. A simple
listing and even an investigation of separate categories fails
to provide either a comprehensive definition of the object or
its systematic description. If however, there is a regularity in
the interrelationship between the objects’ facets, then it will
also necessarily be present in the interrelationship between the
categories. Logically, links and relations between the
categories may and should correspond to those between the facets
of objects being defined.
2. The principle of coordination
Each part of an object has one and only one polarly
correlative facet: top and bottom, front and rear, right- and
left-hand sides; opposite points in a sphere; banks in a river;
the poles of the Earth, etc. Accordingly, each category also has
one and only one correlative opposite. This regularity is
embodied in the twoness - the dialectical symmetry of the
categories: form and content, quality and quantity, essence and
phenomenon, cause and effect, etc.
Pairs-dyads of the categories have long been known in
philosophy. But they had been considered in isolation not only
from each other but also in isolation from the subject, the
carrier of definitions. Dyads of definitions, taken without the
definiendum, become devoid of their gnostic meaning, are
rendered aimless and detached from each other, and turn into a
heap of uncoordinated links of a noncreated system of categories
aimed at modeling the object in its many-sidedness.
Investigation of isolated pairs of categories is almost so
unproductive as is investigation of separate categories.
The opposites in a contradiction can not only be
coordinationally correlated but they also are correlated
subordinatively.
3. The principle of subordination
Each correlative pair of facets of an object is
collaterally subordinated through a third facet. Accordingly,
also pairs of categories must be collaterally subordinated in a
new, third, category: form and content in a subject, quality and
quantity in the measure, cause and effect in a phenomenon, etc.
Without merging of the opposites into something third, no onward
march is possible in the development of matter and cognition of
its forms.
At the same time, dialectical merging of two opposite
facets is only one aspect of dialectical motion. If there is
merging of the opposites into a single whole, then there must of
necessity be also a dichotomy of a single whole into the
opposites.
Dialectical analysis through a dichotomy of a single
whole into the opposites, as dialectical synthesis through
merging of the opposites into a single whole, is a mandatory
element of cognition. "Everything, - Heraclides says, - is a
transition to something different, from dichotomy to unity,
and from unity to dichotomy".
Dialectical unity and struggle, joining and division of the
opposites reflects the essence of dialectical motion in Nature,
thinking and practice – in the world as a whole.
a. The triple law
Any contradiction represents a certain structure of three
elements: two opposites (thesis and antithesis), and a single
whole (synthesis). "A single whole, – Heraclides says, – is that
which consists of two opposites". Plato names such a structure
the single-separate and maintains that, with the ability to
think dialectically, a knowledge becomes at most true.
Dialectical thinking, Plato states, imparts a structural
character to cognition. Proclus interpreted the structural
dependence between the facets in a contradiction as the
overwhelming universal law of development and referred to it as
the triple dialectical law. Fichte endowed the triple law with a
structural form of the logical triad:
thesis-antithesis-synthesis. Kant argued that the triple
correlation of notions is rooted in the character of human
reason. Hegel claimed that the process of dialectical motion of
thought implies a sequential ascent from thesis through
antithesis to synthesis. Constructively, the triple law is
modeled in the form of a heuristic triad:
thesis
\ synthesis
antithesis/
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The triad represents a logical figure that reflects the
coordinationally-subordinative interrelation between the
opposites in a contradiction.
The triad forms the basis for constructing any logical
deduction and any mathematical equation. This means that
dialectics and mathematics operate on the basis of the same
algorithm. But there is an intrinsic difference between
equations in mathematics and triads in dialectics.
Relations between terms involved in a mathematical equation
lack any strict coordination and subordination and are mobile -
labile. Mathematics abstracts itself from qualitative
differences between coordinational and subordinational
interrelationships in an equation. Hence it is prevented from
constructing a "rigorous" system of definitions. Mathematical
equations are too fluctuating to do so; they reflect merely a
quantitative definiteness of interrelationships of the subject
with the predicates.
Relations between the members of dialectical triads,
however,are tight-stable, strictly coordinated and subordinated
between themselves. It is this constitutes the preise of
categorial-dialectical structuring in thinking and cognition,
thus opening up new vistas for a constructive modeling of
objects in their unified separatness, – an avenue for
constructing systems of categories that adequately reflect and
describe objects under investigation.
When intercomparing stable and labile triads, it is easy to
notice a disproportion in the development of dialectics and
mathematics. While mathematics has achieved much success,
dialectics as a science is still in its infancy. This is because
dialectics requires greater abstraction force then does
mathematics.
b. Law of dual division.
Dialectical dichotomy is dual. This statement is modeled in
the following form :
Thesis Thesis’
\ /
SYNTHESIS
/ \
Antithesis Antithesis’
The law of dual division is a logical algorithm of the law
of unity and interaction of opposites.
All premises of dialectical-materialist monism are
logically enclosed intj a unified formula in the law of dual
division. The material unity and the objective diversity of the
World, conservation and circulation of matter, substantial
dimorphism of matter, and the structural determinism of its
complex forms.
III. Dialectics of the concrete and the abstract.
Dialectics of the concrete and the abstract is the
principal gnosiological contradiction. We always consider any
object in two ways, in two opposite aspects : concrete and
abstract, as a concrete and abstract definitness.
In the former case the object is regarded as "it" in its
individual immediatness, such as it is given in our sensual
perception.
In the latter case the object is regarded as "the same", as
some individual abstract unit, identical to any other object of
a given genus or a given commonalty.
The dialectical opposite (antithesis) between the concrete
and abstract definitenesses reflects the contradictory nature of
the object.
In accordance with the principle of dichotomy, the object
in both the concrete and abstract aspects must also be and
actually is considered in two ways, from two dialectically
opposite sides.
We treat the object in its concrete aspect, on the one
hand, as something "in itself", estranged from the other, taken
in itself, without any relation to the other, in its internal
unity, and on the other - as something "for the other",
contrasted with the other, in relation to the other, in its
external diversity – the principle of unity and diversity.
We also treat the object in its abstract aspect from two
dialectically opposite sides: as something separate single,
identical to any other object of a given genus and in total
commonalty with the other. A monad identity with the other, and
a coenosic commonalty with the other constitute inseparable,
dialectically symmetric sides of the object – the principle of a
separate and a common.
1. The principle of unity and diversity
Any object in its concrete definiteness is something
unified in itself and diverse for the other. "Once – Aristoteles
remarks – we speak of the object on taking it in itself, and
another time – in its relation to the other". Dialectically, any
concrete object must be regarded both "in itself" and "for the
other", in its unity and diversity. In conformity with the
triple law, this dependence can be modeled as follows:
Principle of unity and diversity
——————————–
OBJECT
——————————–
Unity | Diversity
——————————–
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2. The principle of a separate and a common
Any object in its abstract definiteness is something
separate – identical to the other and something common -
combined with the other: Man and society, the existent and the
world, etc. A separate does not exist differently than in this
relation which leads to a common. A common exists in a separate
and through a separate. As an individual man does not
exist differently than in that relation which forms a society.
Society exists in each individual man , through each
individual human being. In just the same way, an individual
existent does not exist differently than in this relation which
forms the world. The world exists in each individual existent,
through each individual existent.
A separate is an abstract deprived of individuality, one
identical to the other. This provides the basis for the initial
mathematical abstraction – the unit – the reference point.
A separate is a totality of objects of a given genus in
co-existence, a multitude taken in unity. A common as such has
its own peculiarities of being and development. Thus, the laws
of being and development of the eternal and infinite world – an
aggregate commonalty of all the existent, are different from the
laws of being and development of a finite and transient
individual existent. The laws of being and development of
society are different from the laws of being and development of
individual Man. Although one does not exist without the other.
In accordance with the triple law, this dependence can be
modeled as follows:
Principle of a separate and a common
————————————
OBJECT
————————————
Separate | Common
————————————
The principle of a separate and a common is the same
logical corollary of the triple law as is the principle of unity
and diversity. Both of them express, albeit in different aspects
– abstract and concrete, the regularities of dialectical
dichotomy – merging of opposites that define one and the same
object.
3. The law of double dichotomy
The abstract does not exist without the concrete, and the
concrete necessarily leads to the abstract. A dual character of
the approach to considering objects is a regularity immanently
inherent in dialectical dichotomy - analysis-synthesis - of
opposites that define the object in its multivalence. Therein
lies the specific character of predicative dichotomy, its
difference from genetic dichotomy. This difference is expressed
in terms of the notions: the law of double dichotomy, and the
law of dual division.
The law of dual division is representative of the specific
character of genetic dichotomy in the process of eternal
circulation of matter.
The law of double dichotomy represents the specific
character of a predicative definition of objects – their
single-separatedness and definiteness in themselves.
Constructively, the law of double dichotomy is modeled as
follows:
Law of double dichotomy
————————————–
The separate | The general
————————————–
OBJECT
————————————–
Unity | Diversity
————————————–
The law of doble dichotomy opens up the way for a
consistent definition of the object in all its multi-sidedness.
Not only do the principle of unity and diversity, the separate
and the common complement each other but also penetrate each
other. Each parameter of one principle can be considered in
relation to the other principle. This offers real scope for a
consistent, dialectical development of the entire aggregate of
definitions for any kind of objects into groups, series and
systems of contradictions.
The law of double dichotomy is an algorithm of dialectical
motion of definitions and forms an heuristic basis for a
categorial-dialectical modeling - a construction of systems of
categories that adequately represent objects of cognition. It
opens the door to a structural description of any object in its
single-separatedness. The law of double dichotomy is used to
construct a system of: ontological categories, natural,
gnosiological, teleological, astral, mineralogical, biological,
anthropological, ecological, existential, economic, gentile,
ethical, aesthetical, social, ideological, and others that
emerge from the genetic structure of the world.
This furnishes an apportunity to create a unified system of
knowledge of the real world and to do what thinkers had been
dreaming of for millenia. Only on this basis is it possible to
resolve the problem of reproduction of human life and to crack
the challenge of survival of the human genus. The proposed
system of knowledge, as a representation of the real picture of
the world, must serve as a basis for education, as the image of
the real world, out of which Man had come into existence and in
which he lives.
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A unified system of knowledge of the real world can provide
the basis for a categorial-system encyclopaedism which, unlike
an arbitrary-alphabetical one, is a consistent development of
categories of genera of the existent.
This does not come within the capabilities of an individual
man and an individual collective body. Since it is a
general-scientific problem, it requires pooling efforts of all
scientists. The unified world and the unity of knowledge thereof
must be opposed by the unity of scientists, both conceptually-
methodological and organizational. The unified world recognizes
no national borders, much as a unified knowledge thereof does
not recognize any national borders.
The task is a considerable challenge but it has to come
under the scrutiny of science; otherwise, we can never get out
of the pluro-relativistic abyss to provide the scientific basis
for rational reproduction of human life, and, as before, we will
continue beating our heads against the walls in our national
quarters, helplessly and carelessly anticipating a global
catastrophe. A practical problem of survival must initially be
solved theoretically.
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