Comment by gpm
Most facts about the world can't be deduced from logic. They're just facts, to memorize. The King's lefthanded. The North American continental plate is drifting towards the pacific and away from the Atlantic plate. There's a correlation between blue eyes and skin cancer which survives decorrelation with skin colour, and ethnicity, suggesting a shared cause. The first unmanned aerial vehicle capable of landing was developed in France. A general named Rogers led the British in the war of 1812.
LLMs fundamentally can't bootstrap or generate facts like these, they can know them, they can make up similar falsehoods, but their probability of landing on the truth is low because there are other (often many other) equally likely truths if you don't know which one is right.
(Please note: I made up all the "facts" in this post)
Then a very important first question is how do we (humans) discern facts in such cases?