There is quite a deal of debate about whether externalism is true but not much about what it means. We know the thought experiments (Twin Earth etc.) but how should we formulate their conclusion? Putnam puts it by saying that meanings are not “in the head”—and by extension mental content is not “in the head”. But that is too crude: what if the brain was not in the head and yet content supervenes on brain states? The brain is in your chest instead, but it fully fixes everything you think and mean. Is that externalism? Obviously not. So should we say that externalism is the view that mental content is not in the brain? But that would be agreed to by a dualist for non-externalist reasons; and besides do we really want to commit the externalist to holding that there is anything mental that is literally in the brain? That sounds like a materialist speaking not an externalist: it isn’t that the externalist holds that some of the mind is in the brain and some isn’t—he or she may reject such spatial talk as a category mistake. Similarly, we don’t want to say that externalism holds that the mind is spatially external to the body and brain—as it might be, over there. Nothing in the intuitions surrounding the usual thought experiments implies that mental content is distributed over the spatially remote, still less that the mind extends over space. Space doesn’t come into it. We can accept externalism for mathematical thought without supposing that numbers exist at some distance from the thinker’s body. Likewise we can defend an externalist position for psychological concepts without supposing that minds are located in space: other people’s mental states may be said to fix my concepts for those states without assuming that the states in question occupy space. For example, there may be two types of mental illness on earth and twin earth that can’t be distinguished by the people there and yet the term for these two types has different reference (say, schizophrenia and twitzophrenia). We can stipulate this kind of case without assuming that states of mind are spatially located.
We might try saying that externalism is the view that causal relations to the environment enter into content determination: but this presupposes that all externalist content is caused by what it is about (what about thoughts concerning numbers?), and what is to be meant by the “environment”? Are platonic forms in the environment? What about other people’s mental states? Doesn’t the physical environment start just where the skin stops, i.e. well short of things like water? A better approach would be to advert to introspection: externalism says that introspection doesn’t reveal the full nature of one’s mental contents. That applies to natural kind cases like H2O and XYZ, but it also applies to any mental state whose nature is not given to introspection, like abilities and traits of character. Just because my psychology is not fully known to me by introspection doesn’t imply that my mind is fixed by something “external”. Nor will the concept of the physical help us, as in “Mental content is fixed by the physical world”. That is clearly not sufficient since brain states are physical if anything is, but it is also not necessary. Suppose you are an idealist a la Berkeley: you hold that everything is an idea in the mind of God. Then twin earth is an idea just like earth, so that what fixes the meaning of “water” in the two places is something mental, viz. God’s ideas of H2O and XYZ. Thus you can be an externalist about “water” while accepting that nothing physical is involved: idealism and externalism are logically compatible.
I think the best we can do is the following: externalism is the doctrine that the phenomenology of a mental state does not wholly fix the content of that state but that something not identical to the state must be invoked. Thus our phenomenology of water (and “water”) does not fix the meaning of that word but something not identical to what has that phenomenology does, viz. water. Here we make no reference to location, space, externality, causation, the environment, or the physical—we merely speak of phenomenology and identity. Something not identical to anything in the state that has a phenomenology enters the individuation of the state. Numbers, natural kinds, individual objects, and other minds are not identical to anything in the state of mind that has a certain phenomenology, yet they fix at least part of the content of that state (“wide content”). The essence of the doctrine, then, is that the mind is not individuated purely phenomenologically, even when dealing with states that have a phenomenology (and have it essentially). It is a form of anti-subjectivism in one sense of “subjective”. This says nothing about supervenience on brain states, or the causal impact of the physical environment, or spatial separation; it is purely a point about phenomenology and what it doesn’t fix. To cover the full range of cases we use the abstract topic-neutral concept of identity not relations like spatial separation or causation or non-supervenience on brain states. That is the real logical thrust of the doctrine labeled “externalism”: we could say that it invokes something extrinsic to phenomenology—“external” in that non-spatial sense. Instead of saying “meaning isn’t in the head” we can say, “meaning isn’t in the phenomenology”, where the “in” here is not spatial. Intuitively, what confers content is not identical to the mental state on which content is conferred—it could be a number, a natural kind, a type of mental phenomenon, or an individual object. It stands outside (careful!) the representational state and yet it fixes that state’s content. In particular, it is not identical to the phenomenological character of the state. The thesis is really about the relation between phenomenology and meaning with all the other formulations more or less misleading. This is why we focus on how it seems to the speakers on earth and twin earth—for the question is whether the identity of seeming implies identity of meaning. Whether their brains are in the same state is beside the point, as is the question of what kind of thing earth and twin earth are (whether material objects or ideas in the mind of God). We do better to formulate the thought experiment by specifying that speakers on earth and twin earth are phenomenological twins and leave it at that.
 After all, nobody really thinks that brain states alone can distinguish the two meanings of “water” independently of their impact on phenomenological state. That is, no one is a non-psychological internalist, holding that purely physical brain states on earth and twin earth can force a distinction of meaning. It was always about whether subjective facts are the sole determinant of semantic facts, not internal facts more generally.