It's more God In The Gaps. Something is declared ineffable, beyond the grasp of the mind, science, tools, AI. Then we have an undeniable breakthrough, and they roll back that stance the very smallest amount to accommodate the new knowledge.
There's a strong historical pattern that the appearance of the limits of reason has always been due to a lack of imagination, often in the very people who just spent their lives expanding its borders. And these arguments so often rest on "je ne sais quois," it comes off as more ridiculous than parsimonious. If you think you found an illogical or indeterminate system, I'd bet that your body of kmowledge just needs reframing.
Though ever further we might see, surely dragons further be! c: