From the first episode of The Magicians, two students reason about being a brain in a vat:

Quentin: "Am I hallucinating?"

Elliot: "If you were, would asking me help?"

So, I either I don't understand Putnam's argument or it's plainly wrong.

I recognize that when we say "We are brains in the vat" it seems, at the surface, self-referentially false. Because if we are brains in a vat, we wouldn't have the experience of being brains in a vat--- we'd have the experience of walking around and being people. But I can make a statement like: "Despite my experiences, I think that I am a sentient being that is contained inside a vat."

His argument that the word "vat" refers to different things in "vat-English" and normal English doesn't matter. The concept held behind vat & brain are fundamental enough that they would be self-generating among a community of sentient beings. If we say: "I am a sentient meatcomputer inside a vase filled with liquid food" we may be saying something different, but we are still expressing the core idea.

Even though the simulated world might be vastly different than the host world, language allows abstractions such that we can make the statement.

Putnam goes on to entertain the idea of a twin earth where beeches and elmes are switched, or a world where water has a different chemical forumula than H2O. That is a better starting point, but it doesn't help. I can simply generalize my statement: "I am a sentient being experiencing a hallucination, and the brain which executes my thoughts are self-contained in an environment I cannot perceive, but which nurtures my brain while networking stimulus with it."

I'd like to add a thought experiment to this. Imagine you have two vastly different communities with vastly different chemistry, and possibly operating with more than 3space and 1time dimensions. What would happen if, by the act of an Angel, both communities were given the rules for chess?

The names of the pieces don't especially matter--- if one community never had a bishop, we can simply pick a different word. Or call it piece #4.

With enough games played and thought put into it, the communities would discover tactics. They would compare and contrast the Queen's Pawn vs King's pawn. They would figure out 3-move checkmate. They would understand why en passant was a good rule to be added. And despite have different words and names for all of these concepts, these concepts still refer to the same things. Even if one world played chess with stone pieces, and the other world used leashed rabbits with hats.

A great example of this is when I went to China and play Go (or Weiqi, as they call it). I spoke 10 words of mandarin, and they spoke zero english. I was able to play a couple of games without having any shared language about the game. In the second game, an older chinese guy would sometimes yell at me and move the stone I had just played--- essentially saying: "no, that's not the best move, HERE it is." I didn't always understand why it was the best move, but often it was plainly clear that I was incorrectly read the truth of the board.

So. The act of thought supersedes what we immediately refer to in language, by it's ability to abstract. boom!