Human morphology can climb Mount Everest and do Olympic ice-skating even though it was evolved for running in the savanna. That still doesn't mean it is a general locomotion system -- it is hyperspecialized.
However, it *was* selected for strong adaptability. As a result, it works in a far wider range of environments than the one it comes from.
Human cognition is the same: it was selected, in part, for adaptability & strong generalization. As such, despite its specialization, it achieves a *degree* of generality. It can solve an incredible range of problems.
This is still finite, and it still always ties back to the original purpose of the human mind -- to generate embodied behavior. That's the lens through which we process even the most abstract of problems.
Importantly, you should note that humans as a collective, over time -- civilization -- implement a problem-solvimg system capable of a far greater level of generality than an individual brain.
This is still not general intelligence, though. It still ties back to the four Fs.
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