Varon said:
Ok. Let's be scientific as it's the name of the game. After reading at Wikipedia. It seems physics has its own meaning of Emergence that is different from mainstream. [...]
Firstly "mainstream" is relative, who's to say physicists aren't mainstream and professors of philosophy are?
Secondly you are focusing on the wrong aspects of both definitions you cite...(partly a function of the variability of definitions found on wikipedia).
In both definitions one critical aspect is a change of scale with increasing scale (most specifically in the size of the systems under consideration in terms of fundamental degrees of freedom.)
There is also typically a higher level of abstraction when considering the level at which the emergent property manifests. (e.g. an object with emergent properties is a collection of many pre-emergent objects.)
To my mind, the canonical example in science is the distinction between the subjects of chemistry and physics. A snooty particle physicist might say to the chemist, "you're just doing applied physics!" but the chemist would then challenge the physicist to build a reactor for the production of benzene and the physicist would be stumped (unless he also studied chemistry). What the chemist knows and the particle physicist doesn't is the emergent properties of aggregates of fundamental particles. In some ways they are simpler and in some ways more complex. (Try defining complexity as an exercise)
The property of "being carbon" is not simply a matter of counting electrons protons and neutrons as e.g. "three helium atoms" is not carbon. It is of course a function of their arrangement and interaction within a certain scale of energies.
A similar relationship exists between the chemist and biologist or between the biologist and the physician. "illness" and "health" are multi-level emergent properties well above the level of the quarks and leptons of with the referent organism is composed.
There is a simplification in the empirical determination of the emergent property, i.e. we can see if you're ill without having to check each atom, but rather checking your temperature, reflexes, heart rate and breathing sounds.
Let me also mention, to relate to the other thread, from my Copenhagen Interpretation perspective the states of
objective reality are emergent properties of the more fundamental underlying
quantum actuality.
Thus the quantum correspondence principle
IS the derivation of the behavior emergent properties from the more fundamental scale quantum theory.
Finally I would point you to the Standford Encyclopedia of Philosophy for your definitions wherein you'll find e.g. definitions of http://plato.stanford.edu/entries/properties-emergent/" along with some history and context of usage and most especially citation and reference of sources.