Good reply, and good points. It's probably a better paradox than I thought at a glance.
But while one doesn't want to throw out too many babies with the bathwater, at least with fruit trees, it's often better to prune too much than too little. You might get less fruit this year, but you end up with a stronger tree and better root system.
In this case, I think the better solution would be to make a page about the paradox, and link to that. It's hard to know, but I think a more fully fleshed out blog post about the paradox might have produced better discussion.
So, don't read to much into Gödel, you also can't prove 1 + 1 = 2 except by making an equivalent assumption. Yet, that does not mean what you think it means.
PS: I don't think HN has jumped the shark, but I do try and keep it clean. IMO, it was fairly close to the acceptable line but to close to the HN equivalent of a funny cat photo, (hey look a paradox how cute), but a longer post taking about a well defined paradox and it's implications would have been acceptable and had a much cleaner discussion.
Paradoxes in the true mathematical sense are useful in mathematics, and I thought that many here on HN would find that they sufficiently provoke their intellectual curiosity to be regarded on topic.
However, clearly you disagree, so clearly we disagree. I found the submission interesting, the discussion less so, and wish the inappropriate comments had been flagged/killed to allow the interesting and contentful discussion to flow. That's not what happened.
People complain that HN has jumped the shark, and the submissions are of poor quality. Personally I think it's the inappropriate comments that are dragging HN down, the insistance by so many to add largely content-free and insight-free comments. And yes, I admit that I've done it too.
PG says that the greatest threat to HN isn't the poor quality of submission, but the poor quality of comment. Perhaps submissions should die less often, and comment be killed more often.
Perhaps not. I don't have solutions, but I do know that this submission was a paradox, and that some true paradoxes are of interest and use in formal mathematics. Others aren't - it would be interesting to know if this is the former, and that's what I'll be exploring with some of my colleagues over the next few days.