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Isn't a system, which emerged from simpler system also reducible to the simpler system? More general, is emergence the reverse term to reducitionism?

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Emergence and reductionism aren't generally considered to be opposite concepts, though they are related and sometimes conflict. There are quite a few academics which fall into one camp or another and they occasionally raise their voices to each other. However, philosophy and science is undergoing something of a technocratic revolution. In many journals, one finds that the employment of emergentism or reductionism hinges on the feasibility of their respective explanations.

Emergence, in philosophy, can be best described as the Gestalt property of a complex system. In a complex system, behaviors emerge which appear to adapt to conditions for which the system was not intended. In other words: "much arises from little." Reductionism takes a related approach to complex systems by saying that systems are no more than the sum of their parts.

Emergence relates closely to human psychology. While a system may appear to exhibit behavior not expected from the interaction of its parts, that appearance is a failure of comprehension, not magical properties of the system. A reductionist approach to emergence attempts to excise that human failure by examining the interaction of a system's components.

Especially in psychology and sociology, there is some opposition between reductionists and emergentists. It is understood that this opposition arises from the apparent impossibility of accounting for all the components of the human mind and human society. In short, reductionists do not reject that complex systems have emergent properties, while emergentists often question the ability of scientists to provide a reductionist explanation of the mind and society.

Emergence and Levels of Abstraction, Damper

Emergence in Psychology: Lessons from the History of Non-Reductionist Science, Sawyer

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I can't write a comment, due to the reputation system, but it is important to make a distinction between strong and weak emergence. Look at the following for details.

In short, there are two versions of emergence, the first (weak emergence) says that new properties can arise from systems due to the interactions of their parts and can be explained in principle by these parts.

Strong emergence says that the new properties are unique to the system and cannot be reduced to the parts of the system. This second emergence is incompatible with reductionism, and is mostly applied to things like consciousness and free-will and things of the sort.

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