Page 25 - Geology and Geochemistry of Oil and Gas

4 SYSTEMS APPROACH IN SCIENCE

Thus, the rules of formal logic demand a deductive approach to development of C.
In geological sciences, C usually developed using an inductive approach. The total of
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all objects within a ‘‘species’’ creates a new ‘‘genus’’, with all properties and phe-
nomena pertinent to this ‘‘genus’’. In the process, some ‘‘species’’ may disappear and
some previously non-existing ‘‘species’’, appear. Some ‘‘species’’ (e.g., certain sec-
ondary minerals) may be selected that may exist, as objects, only on a level of a
‘‘genus’’ concept.
Kosygin (1978) noted that development of C comprises the following steps:
(1) Identification of some aggregate of objects (object domain) that is subject to the
taxonomic analysis.
(2) Identification of parameters of objects.
(3) Establishing the distribution of parameters among the objects.
(4) Grouping the objects into taxons according to this distribution.
(5) Determination of subordination of taxons (within the hierarchical C).
In the above process, the following formal conditions are implicit or explicit:
(1) The taxons must be discrete, i.e., any object may belong only to one single-rank
taxon.
(2) Parameters of objects may be represented as discrete parameters.
(3) Possibility (in principle) to arrive at an apodictic (categorical) and reliable
opinion about a parameter (P) belonging to an object (O).
(4) Possibility (in principle) to arrive at a similar opinion about correspondence of
the parameter P in the object O 1 to the same parameter P in the object O 2 .
If all five steps in developing C and four conditions above were fulfilled when
classifying natural objects, there would have been no problems with the classifica-
tion. In reality, not a single one of the stated four conditions is fulfilled. Moreover,
when developing a C, we are forced to neglect some formal rules of subdividing
the volume of concepts. The rule of consistency as a basis for subdivision is often
not applicable. The requirement for consistent and commensurate subdivision
(for classes not to overlap) may often be satisfied only by stretching. Striving to
comply with the discrete nature of classes leads to a progressive taxon fragmentation,
with the taxons having overlapping parameters. The requirement for classes not
to overlap is disrupted by hybrids. No formal rules can account for the common
(and apparently unavoidable) subdivision of rocks into sedimentary, volcanic, and
metamorphic. The parameters that are believed to have been observed, in reality are
often inferred by analogy. That is why, opinions that these parameters belong to a
given object have a probabilistic nature. ‘‘The actual or potential polymorphism of
the parameters results in our characterization of taxons not by the presence or
absence of a parameter, but by the frequency of its occurrence’’ (Kosygin 1978).
Thus, there is a disagreement between the way of developing C as recommended by
formal logic (deductive approach) and the way it is done in geologic sciences (in-
ductive approach). Any attempt to use formal logic for the evaluation of inductively

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Herein after the words ‘‘species’’, ‘‘genus’’, and ‘‘class’’ are used only in the narrow sense of subordinated
taxons.