A Ciceronian Academic position, or, at a different level of subtlety, a strong late-Wittgenstein stance addresses your friend's position. The position is perfectly logical, but it makes all other stances entirely irrelevant at the cost of its own meaning, if one takes it quite literally. It is kind of a hard-line stance against stances.
Strong positions for skepticism ultimately contradict absolute nihilism. So writers like Cicero, Montaigne or an honest version of Wittgenstein take the route that your first comment suggests -- "reductio ad absurdum". By agreeing with him, you can deduce that it is absurd for him to still be alive.
After all, he is correct. We do not know what we are talking about. It seems obvious. Nobody does. But we are talking. So we must think we know. OK, so we do realize, at some level, that we really do not know, and that everyone else knows that, too. But even if we know that we do not know, we have decided to play this game of pretending we know. Is there any other choice? How would one find out? So there isn't.
We think we know what meanings are because our words have effects, or we realize that the game is what gives certain words effects. If this is the best you can manage, why bother disputing it? Simply follow the words' effects to learn the rules of the game, and ignore their supposed meaning. If you are trapped in an infinite puzzle your entire life, knowing it is infinite, why resist? Just play as well as you can comfortably manage, and attempt to discern why the other players are playing.
If you attempt to escape from all language-games entirely, that includes economics, child-rearing and romance, not just philosophy. You have no effect. You are isolated and lose traction on all social activity. You enter the realm of schizophrenia or monasticism. So then why take part in any argument? To remain in a situation where the impossible is necessary seems crazy. So accept the necessity and minimize the relevance of the impossibility.
If you insist on harping on the meaninglessness knowing that meaninglessness is essentially mandatory, you are either cheating, or you are just a bad player.
This argument does not criticize philosophical debate. It gave us science after all. What it criticizes is the notion that one can arbitrarily take a position outside a game and comment reasonably on that game by breaking its rules.
Things have meaning in context, and that meaning is always backed by something other than sheer logic. Most 'deep' philosophical questions arise when we try to inject maneuvers proper to a different context wherever we want and take the result too seriously.
This particular kind of skepticism is one of those 'deep' approaches. It takes the 'game' of learning language and tries to use its rules to evade full participation in the 'game' of deduction or transmission of knowledge. It is not a legitimate way to argue. It is not based on any particular false premise, but it is tone-deaf to what is useful and productive.
Fleshing that out, learning a language presumes someone knows it, but he is denying that anyone knows it, so asking definitions is just silliness. If he is truly skeptical of language, he should want sensory or other proof, not definitions.
But just agreeing on what that proof should be, would have to be negotiated in some terms. So he can evade alanf's arguments indefinitely as well, in the same way Lakatos's commentary on Kuhn imagines incompatible theories can avoid admitting one another's evidence indefinitely.
So there is no point in backing away from the argument to find middle ground. It is correct, and it proves he should just go die. If he can ignore it, so can you.
