Shared reference without descriptive knowledge
In August, I posted an argument purportedly showing that if it is common knowledge within a linguistic community that everyone refers to the same thing by some name N, then the descriptions individuals associate with that name can only differ for very remote possibilities. The argument went like this:
If we know something, it holds in all possible situations that might, for all we know, be actual. So if we know that our terms corefer, they do corefer in all situations that might, for all we know, be actual. And if I know that you know that our terms corefer, they do also corefer in all situations that might, for all I know, be situations that might, for all you know, be actual. And if I know that you know that I know that our terms corefer, they do also corefer in situations I believe you might believe I might believe to be actual. And so on. In conclusion, our terms corefer in all situations that have some chance of being believed (or believed to be believed, etc.) to be actual in our community. So if we consider the corresponding functions from possible situations to extensions, our idiosyncratic functions will only differ for quite remote possibilities.
There must be something wrong with this argument, for its conclusion is false. Suppose the description you associate with "quicksand" is "a bed of loose sand mixed with water forming a soft shifting mass that yields easily to pressure and tends to engulf any object resting on its surface", whereas what I associate with the term is "what you call 'quicksand'". Suppose also it is common knowledge between us that that's the description I associate. So it is common knowledge between us that our descriptions pick out the same stuff. But clearly, I do not know what kind of phenomenon "quicksand" refers to. That's why I don't know how to behave when you tell me that there's quicksand nearby. For all I know, you could be telling me that there's watery stuff nearby (and mean watery stuff by "quicksand") or that there are houses nearby (and mean houses by "quicksand"), and so on.
The problem is that a situation (considered as actuual) in which our terms corefer need not be a situation in which the descriptions we actually associate with our terms also corefer. In the situation where you mean watery stuff by "quicksand" (and I mean "whatever you mean"), our terms do indeed corefer. But they do not corefer with the description you actually associate with "quicksand". I had overlooked this possibility because I thought rigidification wouldn't make a difference for situations considered as actual. In a sense, of course, that's right: it wouldn't make a difference if my description went "what you actually mean by 'quicksand'". Nevertheless, it makes a big difference whether what you mean in a counterfactual situation considered as actual is the same as what you actually mean.