I think I would prefer to attempt to define it, than to simply assert that we don't have it (or some aspect of it).
It's demonstrably true that our species' intellectual capabilities extend to solving problems far beyond those faced by our evolutionarily-equivalent ancestors who out-competed the other hominids. They only needed to be somewhat better at tool making, communicating and forming co-operative groups, to win that scenario, but it turns out that we can also derive a lot of abstract mathematics, predict the existence of cosmological phenomena before we find them, build machines that can leave the planet, etc, etc.
We may not fully qualify as general intelligence if we define that to mean "can solve any solvable problem", and for sure we have specialisations, but to simply throw up an assertion that we are not general at all, seems odd?
My intelligence is apparently not general enough to comprehend this perspective. I would say that the goals our intelligence evolved to meet are narrow, but that life (especially social life) became so complex that our intelligence did in fact become what can reasonably be called general. And we went way off-script in terms of its applications. "Adaptation executors, not fitness maximizers."
Our intelligence isn't task specific, but that doesn't mean it can solve any problem. It's actually full of biases and very optimized for our survival (vs being a general problem solver). It's ok to talk about more or less narrow/general tasks/intelligence. But what threshold of generality is "general"?
And the problem is that once people assert this "absolute" level of generality, they assume it can do anything, including make itself more intelligent.
I don't think it's right to suggest that an absolute level of generality would be necessary for that kind of self-improvement.
If we assume a future where humans are able to create a human-level AI, then it would have at least two substantial advantages over us:
* It would probably have substantially more insight into how its "brain" works than we have of ours, because it would know how we created it. This suggests it could at least make small improvements.
* Unlike our relatively fixed brains, it would be able to remake itself over and over, either very quickly, or at least over comparatively vast timescales.
The obvious conclusion from those two factors is that it would likely be able to start at human-level, but rapidly accelerate up a curve and go far beyond our intellect in probably a lot less time than it took for evolution to come up with us.
Yet humans realized we are biased and devised ways to mitigate that. It still sounds like you’re referring more to our basic goals than to our faculties. I agree that the word general is fuzzy, but to say we do not do general problem solving seems incorrect.
Aside, but a long time ago, Yudkowsky wrote that an AGI should be able to derive general relativity from a millisecond video of an apple falling. Later, he took to calling them optimization processes. Say what you will about the fellow, he has a way with words and ideas.
People seem to forget that we have no full understanding of how the mind works in order to replicate it.
Anyone who studied ML knows what the current tech is able to, still far from topping us.
How such software would create AGI is just absurd.