This is an extensive study of the conditions that allow or impede
reductionism. After an overview of the different anti-reductionist conditions
in approaches like holism, downward causation, emergence, supervenience, and
several forms of uncertainty and sensitive dependence, a more detailed analysis
of downward causation and holism is presented. For the latter, strong and numerous
arguments could be identified why the whole is more than the sum of its parts.
However, the examination of the case of official big bang theory, specifically
a finite universe based on ultimate particles, allows the formulation of a
potential reductionist theory in principle. The key notions for the further
argumentation are different forms of infinity: the infinitely small, the infinitely
big and the infinity of points in a continuous space-time, even if this is
finite in its extension. Several cases are presented in which systems are at
the same time holistic and reductionist if conditions of infinity are applied.
This is identified as a natural ontological property of such systems as soon as
infinity intervenes. The final conclusion, however, is that the certainties of
reductionism are methodologically only useful on very small objects. In the
macroscopic world the only way to influence things is by controlling or
directing the processes by downward causation, which is based on the
elimination or management of uncertainties at higher non-microscopic levels.
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