Detecting Emptiness
Thought experiments about reference often focus on cases where a term intuitively refers to something other than what a certain theory would predict. This way, we can find sufficient conditions for reference. I think it is just as interesting to consider cases where the term does not refer at all, which gives us necessary conditions.
For example, suppose "hydrogen" and "Aristotle" refer causally, that is, denote whatever stands in a certain causal relation to our use of these expressions. Then what would it take to find out that hydrogen does not exist? We would have to acquire etymological information about the causal-historical origin of the term "hydrogen": only if something went wrong in that causal path could we conclude that there is no hydrogen.
In my view, this clearly refutes purely causal theories. Of course physicists could find out that there is no hydrogen, and not by doing etymology. It also wasn't by doing etymology that chemists found out that there is no phlogiston. The information needed to conclude that there is no hydrogen is that nothing comes even close to satisfying our physical/chemical hydrogen theory. Thus we learn that a necessary condition for something to be the referent of "hydrogen" is that it comes at least close to satisfying our physical/chemical hydrogen theory.
To a lesser degree, this also applies to "Aristotle". We do find out from time to time that some allegedly historical characters, say, Moses or King Arthur or Robin Hood, never really existed. It is very unclear what exactly it takes to arrive at this conclusion. But again, etymology is not the only, or even the most relevant concern. If it turns out that nobody comes even close to satisfying the biblical Moses stories, most people would probably conclude that Moses didn't exist. Of course, Kripke says that
[...] in that case maybe no one would have done any of the things that the Bible relates of Moses. That doesn't in itself mean that in such a possible world Moses wouldn't have existed. [1972: 66-67]
But this is irrelevant, as we're not asking what could have happened in the sense of what happens at other possible world. This would also refute the causal accounts: of course different things could have stood in such-and-such a causal-historical relation to our names.
Consider this:
Thought experiments of the kind “what would X refer to if...” do not give us any clue as to what the true semantics of the term is. We do not have stable and interesting intuitions on reference, because “reference” is a technical term.
In the case on “aluminium” it is important to decide if this is a term in a scientific theory of some kind or not. If the term is used in scientific theories, the theory will determine what it means that the term is in fact empty.
“Aluminium” in ordinary natural language might be a completely different story. Reference and meaning are not the scientific ones (the same applies of course to “water”), so procedures should and would differ. What these procedures and the meaning of the term is, is far more difficult to determine. What can not be the case is a kind of descriptivism that makes it altogether very unlikely that there isn’t any aluminium at all – “phlogiston”-type examples show that this can not be the true.
With reference of names in counterfactual situation, Kripke seems to rely strongly on semantic intuitions: “what we would say, what scholars would say” (s. the example with “Columbus” in N&N, “Moses”, “Jonah”). Intuitions are not as clear cut as he takes them to be, compare for instance the (methodologically speaking weak but interesting) work by Stich & Machery, Semantics, Cross Cultural Style that investigates into differences between cultures on “semantic intuitions”.
You are of course right, “no reference”-cases as discussed e.g. in Perry, 2002 are one of the main problems for causal theories.
M.