> What are the philosophical implications of unsolvable mathematical problems? > Does this mean that mathematical reality, hence physical reality, is > ultimately unknowable?
It's not clear to me that the root "know" is terribly useful here; IMHO there is regularity and there is the random (whether it be absolute or effectively so - both are equivalent from the receiving end); the mere fact that we are having this discussion indicates some level of regularity in the interaction; but there is randomness as well; As Gellmann noted, the "perceived" proportion of each is always a function of a "judge" (sentient or otherwise) and that implies an inherent subjectivity. when and where there is agreement among "judges" upon the intersection of recognized patterns, it is labeled shared "reality". Where there is not intersection, "I" call it reality and "you" call me delusional... Cheers CMR <-- insert gratuitous quotation that implies my profundity here -->