Reductionism
[4][5][6] For the sciences, application of methodological reductionism attempts explanation of entire systems in terms of their individual, constituent parts and their interactions.
For example, what John Polkinghorne terms 'conceptual' or 'epistemological' reductionism[5] is the definition provided by Simon Blackburn[10] and by Jaegwon Kim:[11] that form of reductionism which concerns a program of replacing the facts or entities involved in one type of discourse with other facts or entities from another type, thereby providing a relationship between them.
[19] Anthropologists Edward Burnett Tylor and James George Frazer employed some religious reductionist arguments.
Furthermore, the reduction is considered beneficial because Newtonian mechanics is a more general theory—that is, it explains more events than Galileo's or Kepler's.
It has been argued that the generally accepted method of justifying mathematical axioms by their usefulness in common practice can potentially weaken Zermelo's reductionist claim.
[24][25] The incompleteness theorems of Kurt Gödel, published in 1931, caused doubt about the attainability of an axiomatic foundation for all of mathematics.
Reductionist thinking and methods form the basis for many of the well-developed topics of modern science, including much of physics, chemistry and molecular biology.
[27] The role of reduction in computer science can be thought as a precise and unambiguous mathematical formalization of the philosophical idea of "theory reductionism".
German philosophers introduced the concept of the "noumenal" realm that is not governed by the deterministic laws of "phenomenal" nature, where every event is completely determined by chains of causality.
[28] The most influential formulation was by Immanuel Kant, who distinguished between the causal deterministic framework the mind imposes on the world—the phenomenal realm—and the world as it exists for itself, the noumenal realm, which, as he believed, included free will.
To insulate theology from reductionism, 19th century post-Enlightenment German theologians, especially Friedrich Schleiermacher and Albrecht Ritschl, used the Romantic method of basing religion on the human spirit, so that it is a person's feeling or sensibility about spiritual matters that comprises religion.
For this theory, knowledge is seen as the construction of successful mental models of the exterior world, rather than the accumulation of independent "nuggets of truth".
In particular, ecologist Robert Ulanowicz says that science must develop techniques to study ways in which larger scales of organization influence smaller ones, and also ways in which feedback loops create structure at a given level, independently of details at a lower level of organization.
[34] The limits of the application of reductionism are claimed to be especially evident at levels of organization with greater complexity, including living cells,[35] neural networks (biology), ecosystems, society, and other systems formed from assemblies of large numbers of diverse components linked by multiple feedback loops.
