I'm not proposing solutions or saying that there are errors with these proofs. Rather, when I finally understood them years ago it induced an existential crisis that I don't see any pathways to resolve.
My hypothesis is that humans aren't capable of conceptualizing experiments or building tools that could approach the three most intractable problems in epistemilogy. Maybe we don't have the math to do it, or it's fundamentally intractable and it will never be resolved, I dunno. But those are much more interesting questions than "is there an amoeba on europa?"