Hm well, the short answer is you might be right. Now for the long answer.
First I want to eleborate a bit on cognition or cognitive processes. In AI cognition is currently an IMHO bad buzzword. Emergence used to be a buzzword but it's now rather well established. It's now heavily leaking into popular science and is a buzzword there. The trouble with cognition is that nobody seems to know what it's really about. Sometimes it means everything that goes on in human (and maybe other) minds. Sometimes it refers to deliberate judgement (whatever that is). My boss thinks that cognition has to do with manipulable world models and I think that might prove to be a promising approach.
Anyway, I don't like using the notion and would rather refer to biological information processing or something alike. From what is currently known, biological information processing relies (beside other mechanisms) on neural networks. The renowned artificial neural networks are very special cases of neural networks, but it can be shown, that the basic architecture of even these special neural networks allows for turing complete systems.
That means arbitrary functions can be implemented with them. Or arbitrary streams of information can be mapped into different arbitrary streams of information.
If you could write down such a function you had a definition of the mental process. If you forget about Heisenberg it's theoreticly possible to achieve such a complete defenition of a given biological information processing system. If you insist: you get a concrete instance of cognition. It's a function.
You can then go and try to break that function down into logical subfunctions. You can e.g. say that some parts of such a function are representations of concrete things or abstract notions. You might e.g. find something in the function that is a representation of the notion "emergence". That is what you refer to when you say emergence is a cognitive process.
Philosophy has a long history of arguing the relations between ideas and the minds they are represented in. Platon was famous for (beside other things) stating that ideas have independent existence. That would mean abstractions can be part of a mental processes, but there is more to them then that. Now I'm certainly no philosopher. Thus if you were really serious about asking me as an expert, then you got the wrong man.
That said, I do in fact think ideas/abstractions/whatever are more than mental representations. Take e.g. the number pi. If there were no sentience in the universe would pi not be 3.14 (or the equivalent in arbitraryly based numeric systems)?
The fact that every sentient being that tried to determine the area of a circle from its radius would evetually discover pi, suggests - to me - that there is something more to pi than it being a mental representation in my particular mind.
As for what abstractions are if they are not (just) mental representations - I have no clue how to approach the problem.
I was just trying to remind that we cannot observe without interpreting, emergent properties are a way of observing/interpreting things.
Right, but it's not the only possible way of interpreting things. Our original animistic religions did probably not use the concept of emergence. Complex behaviours were interpreted as the actions of spirits. I don't know how old the concept of emergence is, but that's not that interesting anyway. The interesting question is: How useful is it. Is it just a way of hiding our ignorance as a couple of comments suggested? Or does it add to our understanding? I'd say it can do both.
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