I think it's important to actually focus better on tags having a much more concrete and understandable meaning, moreso than necessarily a singular meaning at all. Multiple meanings are fine, as long as it isn't ambiguous. In essence, it should be that the target expert audience of the site should be able to understand the tag fairly intuitively and not be confused as to its meaning.
For example, string is fairly universal in its meaning to programmers, even though it is both a common word and it has variances between programming languages. But in all scenarios, it has most of the same meaning, the context dependency doesn't hurt its ability to classify questions across the site.
When the individual word is insufficient to truly clarify what is being spoken of, it may mislead experts as to what the question is about, and may waste time. Even with dependency on other tags, users aren't necessarily going to know which one is the primary tag - is a user new to the site going to immediately know that a question tagged "float" is going to mean a floating point number if and only if it isn't accompanied by the "css" tag? It's important that tags aren't ambiguous in their meaning, because there's an expectation of simplicity.
However, there's a bit of a hitch I think, and it's that it is difficult and perhaps unwise to go through these at the speed that it seems to be running at. Between scope, float, and table, there are almost 6000 posts to handle, give or take a few for intersection. That's a lot, and disambiguation is a long job. Scope was brought up in early March, while both of the latter two came in just the previous week. I'm all for disambiguation (I do plan to restart language, once I get better time), but it is a big job and there are often much more pressing matters that have to be dealt with (such as really bad tags).
So in summary: I think it's important to make clear tags that have concrete and intuitive meanings, which may sometimes mean more singular meanings. Precision is important, and is of similar concern as dealing with bad tags. But I don't think it's an extremely pressing matter, especially when thinking of the colossus that is disambiguating some of the more ancient tags that we have.
faq-on-taggingwith the tag excerpt providing help?