In the twin Earth thought experiment Putnam determines that meanings are not in the head. Later interpretations, by himself and by others, take it to falsify functionalism.
It seems to me that the argument can't disprove functionalism, and even that it might even entail that functionalism is true:
(1) I take it that when I say "water" or "gold" I don't fully understand the term, and that it's determined by the physical and the social surrounding. Yet, part of it I do understand, and hence while I say "water" I am in a functional state of believing that I see water to the extent that my knowledge allows me. I am in some kind of a state - that can be (potentially) explained in computational terms - even though I don't grasp the full meaning of water. "Water" has meaning in my head, definitely, but it's not the most precise one. it's narrow (as Block calls it), while the full meaning is wide. In other words, when I think of "water" (H2O) and when my twin on twin earth thinks of "water" (XYZ) we are both in the same mental state, and this fact cannot say anything to falsify functionalism. What is wrong with that (very simple) answer to Putnam?
I can rewrite this question in terms that I believe are equivalent (though I might be wrong, and this might be my problem to understand). Putnam says that while talking about indexicals ("I", "That", "now") - intention doesn't determine extension. It seems right, because when I say "I" and when you say "I" - we both have the same intention (meaning), but the extension (what we refer to) is different. My "I" is me while your "I" is you. If we take this to other terms, like natural kinds, we have no problem. My "water" (H2O) and your "water" (XYZ) have different extensions, and yet the meaning of "water" for you and the meaning of "water" for me is the same. Hence - when we both say water, we are in the same state. Intention doesn't determine extension, I take it, but intention itself is only a concept, and therefore a mental state. functionalism still works. It seems like for some reason Putnam doesn't want to take the indexicals case onto the other terms case (I can't see why). If we follow him, I don't understand the picture we can derive.
(2) Assuming (1) is explained, and meanings are not in the head. Now, as I see it - the problem with functionalism is that we cannot see how a computer program creates real meaning. Algorithms can be interpreted in various ways. As long as the machine is concerned - it only manipulates symbols. We, being external to the machine, interpret it's result and give it a meaning. According to this, machines cannot create genuine meaning, while it feels like we, humans, can. In other words, machines have only derived meanings, while we have original meanings. But then comes Putnam and says that the meanings we humans have are not really in the head, but are meaningful only external to us. It seems like a good solution for the problem with functionalism just described. A machine cannot have a genuine meaning, but it's not a problem after Putnam, because also humans cannot. Meaning is always external (and hence always derived), and hence we can definitely be described computationally.
I assume that my understanding of Putnam isn't complete, but I can't see how my claims above won't hold.