1) Mermaids don't exist.
2) We have a shared concept of mermaids.
3) We have a shared notion of existence.
4) There is no entity that exists that corresponds to our shared concept of mermaids.
what's the big deal?
If mermaids do not exist, then how can we say of them that they don't exist? What is it we are saying don't exist? But I think that what you say is right. When we say that mermaids do not exist, we are not talking about mermaids at all; although it looks as if we are. In fact, we are talking about the concept
of mermaids, and we are not, of course saying about the concept
that it does not exist, but we are saying about the concept that it has no referent, as you indicate. Now, the question to you is how this solution (I agree with) would be a matter of "getting our terms straight"? Except in a very extended sense. It is deeper than that. It has to so with recognizing that when we say of X that it exists (or does not exist) that we are really not talking about X at all, but talking about the concept of X. Although when we say that elephants are not reptiles, we are talking about elephants, and not the concept of elephants. So, what comes out of this, is that to say of something that it exists (or does not exist) is not to say of it that it has a property
(as it appears on the surface)but rather to say something about its concept
, and to say about its concept
that it does not have an object to which it corresponds. That is why Wittgenstein describe philosophy as an investigation into the "workings of language". When we say that when we say of something that it exists or does not exist, it may look as if we are saying of it that it has a certain property or not, but, in fact, that is deceptive. In fact, we are saying of the concept, that it has a referent (object) or not. We are not talking about things, but about words or concepts. But this does not have to do with agreement about the meanings of words.