the way i've come to grapple with godel is to come to terms with what we call "mathematics" itself being a model to understand this thing out there that should be called mathematics in greater generality. the maddening thing is that godel died as ever a platonist as he ever was to start, but i think that's what he must have really dismantled. and, i think the only thing that you can really do in response is to begin to embrace mathematics as a science, in contrast to this whole kantian thing that goes back to euclid, and is so embedded in even the way we teach basic geometry to children, still. now, he's right - that doesn't tell us anything about how the world is but it does present a different framework to try to understand it through.