This is a fascinating argument, but not because it tells us much about whether we are brains in vats. Instead, it tells us something deep and interesting about linguistic meaning, and the mysterious relationship between statements and propositions.

Putnam is not actually saying that we aren't brains in vats. Rather, he is saying that we cannot form accurate and meaningful statements to that effect if we are.

The argument, as I understand it, turns on a statement's ability to refer. Putnam's point, as you nicely summarized it, is that in order to accurately describe the world (I make a point here of not talking about whether the statement is true) a statement has to be causally related to the things it describes in the right way. This seems plausible.

But this is different (on must theories) from saying that the abstract proposition that might be represented by such a statement cannot be true. It could be! The puzzle is just whether you could form a linguistic statement to properly express that proposition due to the reference problems Putnam points out.

Putnam's own example demonstrates the point. A bunch of ants cannot draw an image that represents Winston Churchill in the grass, because they cannot know what Winston Churchill is or (probably) what he looks like. Any similarity between an ant-made image, and a real image of Winston Churchill has to be merely coincidental. Ants cannot close the causal link that we normally require in order to say that an image "represents" something. But this doesn't mean that there is no such thing as an image of Winston Churchill. Or that an ant-made imagine cannot resemble Winston Churchill. It just means that ants can't form a representation of him!

Likewise, our putative inability to form an accurate statement to the effect that we are brains in a vat does not mean that we aren't brains in a vat. An omniscient being (perhaps the one who put us in the vats!) might, for example, read our silly HN posts about brains in vats and say, "gee, its incredible that this series of symbols actually matches the symbols that you would use to form a true statement statement about the world, if only the speaker were in the necessary causal relation to my vats in order to truly say such a thing." Likewise, we say about the ants "gee, its amazing that they managed to make an imagine resembling Winston Churchill even though they don't know what he looks like and therefore can't truly be said to have 'represented' him."

(There is a parallel line of argument that you might run about our ability to know something, since knowledge, it is often said, has to be related to the external world in a certain way in order to be more than a mere belief.)

In any case, classic Putnam.