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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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I’ll give the alternate view that reduction moves in the opposite direction of emergence, which seems obvious.

Starting with physics, we can say that all things are made of particles, perhaps strings, but that’s not confirmed. This is the foundation of all our understanding of the physical universe. From these particles phenomena emerge such as density, surface tension, pressure, and so on, which are governed by the fundamental forces. These forces can’t be broken down any further and there may be such a thing as their unification at very high energies unifying all the forces into one.

So we’ve got physics, next add emergent phenomena in chemistry which is dependent on physics. Chemical bonding is an emergent phenomena as the individual atoms or particles do not exhibit chemical bonding. There are many other examples. Chemistry gives rise to biology and DNA, cells, proteins, etc. These things are emergent as the individual molecules don’t exhibit these properties.

Next you can get neuroscience, psychology, sociology, political science, economics, and so on. All emerging from their lower domains.

Reductionism, is the opposite process. Let’s take consciousness as an example. We want to know about the emotion of anger. What we can in theory do is reduce anger or break down the experience of anger into the parts that make it up. This doesn’t work for reductionism because consciousness is strongly emergent. Ie there is no possible way you could predict that the experience of anger would emerge from just looking at the constituent parts of a person’s brain who is angry.

So let’s instead look at a weakly emergent phenomena: an enzyme. The enzyme is a protein which is made of amino acids. Looking at the amino acids one would not know that if you had a bunch of them together to make a protein/enzyme that it would become a chemical catalyst. The only way you would know is if you saw the mechanism of one. Looking at the parts individually would yield no knowledge. We therefore say that the enzyme is weakly emergent (unexpected properties of a higher domain from a lower domain but in principle this can be explained).

We could look at an enzyme, its individual parts and build it back together and see on a biochemical level what’s going on - chemical catalysis.

Reductionism would do much the same thing. It would break things down into simpler components to understand the phenomena in question. But reduction moves from high level to lower level moving down the chain from one emergent phenomena to the more basic emergent phenomena or fundamental phenomena, whereas emergence moves in the opposite direction moving from simple to complex.

There are plenty of other examples of emergent phenomena, in fact I believe they are ubiquitous. Chaotic systems, everyday objects, conscious experiences, etc.

Reference:

David Chalmer’s paper on emergence

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Emergence is a propensity of systems of matter and energy to interact in ways that lead to more-complicated systems or properties. Reductionism is a propensity of humans to try to analyse more-complex systems or properties in terms of simpler systems of matter and energy.

Emergence is a widespread natural process. Reductionism is a pattern of thinking developed by humans.

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