– An abstraction level of experiential cognition whose method of study is experience and experiment. From these, empirical concepts, judgments, and conclusions can be derived through individual abstraction.
– The abstraction level of logical cognition, at which logical concepts, judgments, conclusions, relations and internal relations can be generated from the results of experiential cognition as a starting data set with the help of logical operations. (These logical operations can be additional abstraction, conjunction, disjunction, analysis, synthesis, analogy, logical mapping, etc.).
– The abstraction level of systems theory cognition, at which system theory concepts, judgments, and relations, deepest-lying alternatives and relations, and the deepest-lying internal relations can be identified from the results of logical cognition as a starting data set. (Systems theory operations: deepest and final abstraction, structure and model creation, structure and model mapping, examination of deepest alternatives and correlations, structure analysis, etc.)
Our mathematical and scientific research takes place at these three levels of abstraction. The higher the level of abstraction operations, the more fundamental insights and conclusions we can reach. Of course, in the meantime, we cannot step off the ground of reality and objectivity. This is ensured by repeated experience, repeated logical operations based on experience, and system theory considerations based on repeated results of logic.
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