The following remarks were written when I was wrestling with these problems over an extended period. They might act as a stimulus to someone.
1. What determines reference?
2. Not, in general, descriptive or conceptual content associated with the name. Although the usual counterexamples to descriptivism do not apply to a range of names - for example, names of mathematical objects.
3. Not, in general, a causal connection between the object and the name. Both because the kind of connection in question is unclear, and because there is clearly no such thing in many cases - e.g. mathematical objects. But there is no clear counterexample in a range of cases: names of spatiotemporal individuals which someone in the linguistic community at some time has been perceptually acquainted with, for example.
4. What determines reference? - What gives this question its power?
5. The question seems to be: given that someone is referring to a particular object, what determines which particular object that is?
6. This is to be distinguished from: What is it which characterizes all cases of representation of, or reference to, an object? I.e. what do they all have in common which distinguishes them from other phenomena, apart from 'involving representation of an object'? But it is close to: Given some particular object O, what characterizes all cases of representation of, or reference to, O?
7. The thing we just can't accept is that we have nothing definitive to say in answer to the question: what determines reference?
8. It is extremely remarkable and important that people have tried hard to say something definitive here. It not a matter of course that anyone is moved in this way by that question. (Many people innocent of philosophy would find the whole thing quite unnatural and meaningless.)
9. I would like to talk about the feeling that, when the investigation goes empirical and scientific, we have left the realm of essence, so to speak. Is that right, anyway? Could one not maintain that by increasing our knowledge of the contingent facts - how reference actually gets going - we may be better able to penetrate to the essence? I.e. to what it takes in principle for reference to get going?
10. Well, historical development itself cannot be part of the essence. It is clear enough that there is no logical impossibility in a whole lot of organisms being spontaneously generated out of nowhere and beginning to speak of things.
11. When we think of the representation of external, physical objects, some kind of correspondence or covariance theory seems attractive. One thinks of primitive representation (or proto-representation) which is of this kind.
12. However, the merest thought of arithmetic, and Wittgenstein's builders, at once makes all this look inessential.
13. There is no reason why one cannot erect a concept which applies, for example, only to the representation of physical phenomena. But if one is inclined to say that we refer also to abstracta, and to wonder how reference in general is possible, then an investigation of the first concept alone will never satisfy.
14. It is clear enough that the idea of referring, which is primitively connected with the ideas of looking-at and pointing - the picture of representation and represented - is widely useful, and widely used.
15. Now, it looks very much as though one might, having noticed this, ask for an explanation of why it is. I.e., what makes the picture of representation and represented apply in this wide range of cases. Or better: what is it about all these cases which makes the picture of representation and represented apply to them?
16. This traces the problem down quite deeply. At this point we see that none of the common 'theories of reference' is going to help us here.
17. No answer comes to this question. This seems to have something to do with the fact that, once you are talking about a potential object of reference, you have already prejudged, so to speak, that the picture of representation and represented applies. Wherever we think of an object, there already we have the material for a higher-order thought about our representation of that object.
18. 'The problem of the essence of the representation of things leads, in a certain sense, to the problem of the essence of things.' The problem of the essence of things is obviously no ordinary one!
19. To explain this tracing again: whenever we find ourselves in conditions where we can refer to an object, we thereby find ourselves in conditions where we can apply the picture of reference.
20. But, this is not the same as saying: wherever the conditions for objecthood are fulfilled, thereby are the conditions for a representation. For this is refuted by imagining a world in which there is just one object and nothing else. (This sort of distinction is important all through logical philosophy. It appears to be neglected, for instance, when people try to analyze existence and identity statements as designation and codesignation statements respectively.)
21. Two senses of truth conditions, two conceptions of what I will call fulfilment worlds for representations:
(1) All conditions/worlds in which what the representation actually represents to be the case is the case.
(2) The narrower set of all conditions/worlds in which the representation exists, represents what it actually represents, and where what it represents is the case.
22. What I was saying above now comes to: all the fulfilment worlds in the second sense for 'x exists' are automatically fulfilment worlds in the first sense for '"x" refers to x'. Or: once 'x exists' is fulfilled in the second sense, '"x" refers to x' is fulfilled in the first. (This holds not just for 'x exists' but for any proposition which contains 'x' in an extensional context.)
22. By dwelling on this we can start to see that reference is no ordinary relation.
23. As long as one is prepared to ignore the distinction between (1) and (2), or to openly switch from one to the other mid-analysis, then one can analyze existence and identity both in terms of reference. (Early Frege, Geach.)