One sort of consideration which may seem to augur for Millianism, and against both descriptivism and my view of names, comes from the idea that meanings must be public items, shared by communicators. If the subject matter of semantics is supposed to be the public meanings of linguistic expressions - where this might be conceived as the stuff we must have implicit knowledge of in order to be competent speakers - then it is hard to see what, in any given case, could be essential to using a name correctly, except for using it to denote the right bearer. On the other hand, there does seem to be a technique of using certain empty names like 'Santa Claus' which is more specific than: using it such that it has no bearer. But perhaps we want a minimal conception of semantics on which such specific techniques are regarded as extra-semantic.
Given such a minimal conception of semantics, it will be hard to avoid the conclusion that belief-contents, proposition-meanings and propositions and have more to their identity than their structures and the semantics of their components. (That is, unless we are prepared to bite bullets like: '”Hesperus is Hesperus” means the same as “Hesperus is Phosphorus”'.) And if we accept this, then we must deny that the identity of a proposition can always be reckoned as being determined by its structure plus the meanings of its parts, in the relevant minimal sense of 'meaning'.
We can reinstate compositionality either by moving to a very coarse-grained notion of belief-contents or propositions (and so biting the bullet on 'Hesperus is Hesperus' and 'Hesperus is Phosphorus'), or by moving to a finer-grained conception of the meanings of parts such as names, a conception which will include things beyond public meanings and minimal competence conditions. This latter is, in effect, what I advocate in my view of names as having uses, or being tied to individual concepts, which can differ even though the names do not differ as regards extension.
'Hesperus and Phosphorus' seems to be a different proposition – seems to mean something different from – 'Hesperus is Hesperus'. And, quite apart from any general thesis about meaning-determination, this difference seems like it has to be laid at the door of the names 'Hesperus' and 'Phosphorus'. And that is what my view of names enables us to do, while remaining invulnerable to Kripkean anti-descriptivist arguments.
Why can't we all go home, then? Well, this kind of solution seems to worry people. It seems like they can see what its virtues would be, but don't feel they can help themselves to it. I suspect that one of the major causes of this reluctance is some kind of conceptual intuition to the effect that meanings – anything worth calling 'a meaning' – have, by definition, to be public and shared by competent communicators. I suspect that another major cause, perhaps even more active, is that people have sensed that on this way of going, there won't be any general story to tell about how to count meanings – i.e. about how to determine whether to say that two expressions, or instances thereof, are synonymous or not.
We can appease the first worry to some degree, I think, by allowing that there is a natural conception, which it is not improper to use the word 'meaning' in connection with, according to which meanings, in order to be meanings, must be public and shared. But we can also have a richer, more idiolectic conception, and maintain that this is what we're talking about in connection with names, and the semantic difference between 'Hesperus and Hesperus' and 'Hesperus is Phosphorus'.
Furthermore, these two sorts of conceptions need not be seen as two utterly different things, but as continuous. Both deal with systematic use-patterns of signs, or roles of signs in systems. Taking the 'public and shared' conception as our starting point, we may yet ask: how public and how shared must these use-patterns or system-roles be to count as meanings? We could have a conception on which the patterns or roles must be shared by all who competently speak the language. But how do we individuate languages? Peter Ludlow's recent work on 'the dynamic lexicon' can help prepare the ground for what I am saying here, being consonant with it in important ways.
This appearance of continuity and fluidity is not some nasty imprecision in our philosophy, but a faithful capturing of the facts. People differ from each other – and from themselves over time – in their use of symbols and the way their understandings work, and in most cases, the question whether two symbol-instances align in meaning can be given different answers for different purposes. When we're talking about something we're both familiar with, and our ideas of that thing are similar enough, our talk can be said to align in meaning. But notice that, in speaking just then of ideas being similar enough, I have already hinted that there might be a finer granularity at which our ideas are not type-identical – a finer granularity at which it may be said that we don't mean exactly the same thing. This seems realistic.
Regarding the second worry, my answer is already implicit in the above; I think the most fruitful response is not to try to explain it away, but to embrace it. There is no single way of counting meanings, since we can individuate them and count them differently at different granularities. We are already pushed toward this by considering Kripke's puzzle, and its character as a solution there is only strengthened when we see it has further applications, such as here to this worry about the very idea that names have internal meanings, to questions about the individuation of facts, and elsewhere.