I’ve always seen it as a claim that systems with axioms are incomplete and thus systems with premises which undermines analytic philosophy but doesn’t really touch continental or eastern philosophy due to their resisting axiomatic simplifications.

It seems like the completeness theory would mean that one can deductively make some conclusions that are well grounded but deductive reasoning would require that one is operating within a certain environment. It would be more subjective because you would be making statements based on the observations at hand. . .

Or at least that’s the impression I get.