Philosophers of language sometimes like to speak of “reference” as the relation between language and the world. This is a fine enough name, but it runs into trouble when we try to say what the relation really consists of. (The problem is not so trivial: it seems almost impossible to say how language links up with the world in anything other than metaphorical terms, precisely because we have to say it. Whatever answer we give, we can ask what makes that answer so privileged as not to be subject to the same question, namely, what is the relation between that statement or set of statements and the real relation they are supposed to describe?)
It is easy to get into a tizzy about these things, and in order to avoid the sort of ‘infinite regress’ problem of saying what the language-world relation is, some philosophers have answered that ‘reference’ is a metaphysically primitive notion. We simply cannot define it; it is the notion that we require in order to make sense of all our other definitions. But this cannot be right.
For one thing, ‘reference’ seems an awfully complicated notion to be primitive. The statements “This spot on my carpet is blue” and “2 + 2 = 4” don’t seem to refer in the same way, because they don’t refer to the same sorts of objects. Someone will reply: “The objects may change, but the relation is the same: its domain is the set of all statements, and it ranges over all the objects, including mathematical and physical ones.” This reply is apt, but it only expresses the speaker’s commitment to reference as a primitive relation. Relations must be appropriate to a domain of some sort of object. You may artificially conjoin (or more probably, disjoin) two relations that range over two sorts of objects and insist that now you have a single relation whose domain is the whole set of both sorts of objects, but all you are doing is refusing to recognize that your relation has two smaller parts to it.
Complications are not a decisive reason to throw out a concept, however, because the world can be a very complicated place. A better objection to the idea that reference is a primitive relation, I think, will parallel the problem I raised above; it will ask, to what does the term “reference” refer? The immediate reply will be that this sort of question commits the logical fallacy of self-application. I do not think this is so, because we are not asking what the relation of reference refers to, but the word “reference.” Well, then, our philosophers will say, it’s just what we’ve been telling you: it refers to a primitive metaphysical relation between statements and objects in the world.
Now, then, we are entitled to ask what this means, and since we’ve already tried asking outright, and only heard that no definition can be given for primitive relations, we can take a different tack and ask what each of the words “primitive” “metaphysical” “relation” “between” “statements” “and” “the world” refer to. If they can give answers for all of these, without being logically circular, they are very good philosophers indeed, and now the task is easy: we just need to link up the references of these terms in the right way, and we’ll know what “reference” refers to. (Of course, I am supposing that the meaning of statements is somehow related to the meanings of the words in them, but this doesn’t seem to me to be a terribly controversial assumption.) Well, if that could be done, I imagine that we would have done it already, with the aid of a dictionary, maybe. Certainly these philosophers could have saved themselves a lot of trouble by giving that answer in the first place. It seems very unlikely, however, that it can be done properly, and even if it could, we would want to know why a relation that could be obtained by properly adjoining the references of some other terms should be considered “primitive.”
That, I suppose, goes some way toward disposing of the notion of ‘reference’ as a primitive relation. I do not, however, have a plausible alternative view, particularly not one that answers the ‘infinite regress’ problem I began with. I can say, though, where I would likely start such an account. The whole notion of ‘reference’ gets brought into play after we have conceived of language as being essentially divorced from the world, as somehow representing it (or its possible states) without being inside of it, and so we need some way to join them back up again in order to make sense of our experience of both. If we start instead by recognizing that language is a feature of the world, a view which has its own difficulties but which escapes the problem of trying to bridge an infinitely wide gap, we might have gotten something right.
I will close with an analogy. A mirror is a perfectly ordinary object. We know how it works, and we can describe the laws according to which it reflects the objects of the world using ordinary physics. If we were to imagine a mirror as being outside our universe, though, and then ask how it could possibly reflect the objects in our universe, we would scratch our heads for quite a long time. Language is often described as “reflecting” the world somehow, but we have trouble saying what it means to reflect it. If we start by remembering that language, like mirrors, only works when it’s in the world, we may have an easier time.