Again this is descending into nitpicking at the extremes. PG is not saying everything we understand will be in common with aliens, or that our cognitive match with them will be 1 to 1, just that there is likely to be overlap. That given the universality of human cognition, there is likely to be thoughts we can mutually appreciate. I am not claiming that human brains are capable of all thought possible to aliens, only that there will be common ground. That’s all. It’s a very minimal claim.
Pointing out possible edge cases is a non sequitur. Of course there will be things we don’t have in common. Yes, we know that. The fact we’re explicitly looking at common ground from first principles implicitly acknowledges there will be ground not in common. That’s given.
You said that JackFr was provably incorrect. I'm not pointing out an edge case but pointing out the massive hole in your argument.
As a limited computing system, our brain has been optimized to process the world in specific ways using various heuristics and compression techniques. Alien brains would presumably be optimized in different ways. Given our limited capabilities, it seems quite possible that translating any concepts between the two systems would be unfeasible for either our brain or the alien one.
I would like to think that there would common ground but that isn't something that can be known a priori, and is thus not presently "proveable".
Edit: We do have some fairly "alien" brains here on earth but we haven't had much luck teaching any mollusks any of our mathematical truths.
Pointing out possible edge cases is a non sequitur. Of course there will be things we don’t have in common. Yes, we know that. The fact we’re explicitly looking at common ground from first principles implicitly acknowledges there will be ground not in common. That’s given.