Your use of "natural" is confusing. There is natural selection, which is without goals. Then there is selection with "non-human emergent goal-seeking behaviours" that, if successful, will be accepted as natural.
I thought I already mentioned that the word 'natural' is used differently in different contexts - if I didn't mention it, my bad. The issue with non-human goal-seeking behaviours is a problem of the 'no goals' meaning becoming ambiguous.
If other creatures show intentional goal-seeking behaviour and we still want to consider them part of the 'natural world', then we cannot justifiably distinguish human activities from the natural world. But considering human activities separately can be a useful viewpoint, particularly in environmental, ecological, and behavioural sciences. So there's a problem - the semantics of the traditional human/nature division have broken down.
I think the problem is twofold - firstly, science has outgrown the classical concept of 'nature'; secondly, there's a mixing of the language and concepts of different levels of emergence (conceptual & semantic emergence), which is always problematic. But I don't think it really matters - it's just semantics.
Common definitions of 'supernatural' typically define it as 'beyond the reach of science', or 'inexplicable to science', so if the phenomena do fall within the reach of science and con become explicable, it seems reasonable to suppose the 'supernatural' cap no longer fits - so I suggest that, at that point, they become 'non-supernatural', i.e. 'natural'. But, frankly, who cares what they're labeled?
You keep making this connection that success in science means something is "natural".
No, I don't. Success in science is supporting or falsifying a hypothesis or theory.
It feels as if there is a subtext of meaning you're tying to "natural" that you're not expressing. Why is successful science "natural"? Why isn't it just successful science?
Yeah, you're just reading things into my posts that I haven't said. Again.
Or another question: Does this mean psychology, since it is focused on people, can never be natural, and therefore can never be successful science? Because natural also apparently means "not people".
Please read what I said above about differing meanings and contexts. When someone starts talking about natural and unnatural psychology, that will be the time to ask what they mean.