Word Meaning and Sentence Meaning

Reading a draft chapter of Philip Ebert's PhD thesis today reminded me of a thought I've been batting about for a while concerning Frege's context principle.

Interpretations of the context principle usually seem to take it to be a claim to the effect that (certain) whole sentences in which a word occurs have some kind of semantic priority over the words themselves. But I've never been able to see exactly why a semantic priority claim is what's needed.

Suppose, for instance, that you think that what the context principle does is reveal that it suffices for epistemic access to the referents of mathematical singular terms if we have knowledge of (the propositions expressed by) the whole sentences in which these terms occur. Wouldn't it be enough to support that conclusion if we said that word meaning and sentence meaning are interdependent, so that understanding (certain) sentences in which a term occurs is always sufficient for understanding the term itself? With this principle in place we can argue that understanding the relevant sentences suffices for a grasp of the putative referent of a mathematical term, and that this together with knowledge that the sentences are true suffices for knowledge that the referent exists. (There are other assumptions at work here, of course, but only ones that are needed anyway.)

At most, we might feel pressured to say that our knowledge of the meaning of the sentences is prior to our grasp of the putative referent of the term (e.g. if we wanted an explanation of our grasp of the putative referent that was clearly naturalistically acceptable - didn't rely on intuition of abstract objects). But that's a matter of epistemological priority about semantics, not semantic priority. It doesn't imply that the fact that the term means what it does depends in any interesting (asymmetrical) way on the fact that the sentence means what it does.

In the background to all this is a lurking intuition that it is obvious that neither word nor sentence is semantically prior to the other - that word meaning and sentence meaning are clearly interdependent in such a way as to make claims of asymmetric semantic dependence implausible. I'd be interested, though, if anyone can set me straight as to why a full-on semantic priority claim will buy us more of what we want.