Hi wavejumper. Thanks for reading the links. There’s a tremendous amount of information out there on emergence, so I’m glad to see someone is open to reading some of it.
There are various classifications of emergence and definitions as to what these classifications should be. Chalmers defines strong emergence the same way Anderson might:
Chalmers: We can say that a high-level phenomenon is strongly emergent with respect to a low-level domain when the high-level phenomenon arises from the low-level domain, but truths concerning that phenomenon are not deducible even in principal from truths in the low-level domain.
Anderson: For most systems of interest, however, the basic laws of physics, though not incorrect, are inadequate. The reason is emergence, which says that when a system becomes large and complex enough, its constituents self-organize into arrangements that one could never deduce a priori, even though the laws of physics are obeyed.
In another paper, “More is Different”, Anderson talks about the “constructionist” who might claim that things are in principal calculable from a lower level. Anderson states "The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity." Obviously, Anderson is not a constructionist, though there probably aren’t too many. I think he misses the mark here though because simply not being able to deduce something because of scale or complexity is not the hallmark of an emergent system.
Similarly, the article Laughlin writes uses the same basic definition of emergence. Laughlin states:
The existence or nonexistence of mesoscopic organizing principals has become an issue of deeply held belief, rarely discussed in public yet informing much of what we do.
So the real point trying to be made here is as Chalmers points out, that there are phenomena that are not deducible even in principal from the lower level domain. Further, there may be “organizing principals” which govern at various ‘levels’ of nature. See Chalmers, "Strong and Weak Emergence" available on the net.
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There’s another line of reasoning that basically says that inseparable phenomena are emergent. Compare/contrast this with the concept above where phenomena are emergent because they are not deducible even in principal.
Alwyn Scott for example wants to say that all nonlinear phenomena are inseparable in the sense that the whole is greater than the sum of its parts. Here, he lists various physical phenomena as being emergent such as tornadoes, lynch mobs, optical solitons, schools of fish, nerve impulses, rivers, etc… because they are “nonlinear”. See Alwyn Scott, “Reductionism Revisited”. Similarly, Robert Bishop wrote about Rayleigh-Benard convection, stating that is an example of a nonlinear system which is both emergent and “a model for downward causation in classical mechanics”. <yikes!> I disagree with this school of thought. I think the main problem is that these types of phenomena are all deducible from very low level facts as is commonly done throughout science and engineering for example when finite element and multi-physics software packages are employed to deduce the phenomena produced by these types of physical interactions.
In a similar vein that I WOULD agree with however, Frederick Kronz put an excellent paper out called “Emergence and Quantum Mechanics” which proposes that emergent phenomena can be found at the quantum level. He says, “Because the direct sum is used in classical mechanics to define the states of a composite system in terms of its components, rather than the tensor product operation as in quantum mechanics, there are no nonseparable states in classical mechanics. There are nonseparable Hamiltonians in classical mechanics – the Hamiltonian corresponds to the total energy of the system and is related to the time evolution of the system. This type of nonseparability is the result of nonlinear terms in the equations of motion. Perhaps a kind of emergence can be associated with it. Some measure of plausibility is given to this claim since a classical system can exhibit chaotic behavior only if its Hamitonian is nonseparable.” Kronz is certainly not alone in his claims, and I would agree that at the quantum level, there are emergent phenomena produced, however, there is still work to be done to better define why such things are emergent, if they are more than “weakly emergent” and what kind of physical properties are truly emerging. The debate is still open.
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There are various other ideas floating around about emergence. They don’t all fall under the catagories and definitions provided above. An interesting summary of at least some of these concepts was provided by http://pagesperso-orange.fr/michel.bitbol/EmergenceMB.pdf" in which he goes through the various philosophical debates, though his conclusion steps away from committing one way or the other.
