According to an externalist position, one can claim without contradiction that two speakers could be in exactly the same brain state at the time of an utterance, and yet mean different things by that utterance -- that is, at the least, that their terms could pick out different referents.
The philosopher Hilary Putnam (1975/1985) proposed this position and summarized it with the statement "meanings just ain't in the head!"
His Twin Earth thought experiment, from the aforementioned paper, is widely cited to illustrate his argument for externalism to this day.
Externalism is generally thought to be a necessary consequence of any causal theory of reference; since the causal history of a term is not internal, the involvement of that history in determining the term's referent is enough to satisfy the externalist thesis.
Putnam presented a variety of arguments for the externalist position, the most famous being those that concerned Twin Earth.