Reference Magnetism
Suppose
1) the facts about use etc. underdetermine the semantic value of term x (to a certain degree).
But
2) the semantic value of x is not underdetermined (to that degree).
Let V1,V2,... be the semantic values between which x is underdetermined, and suppose V2 is in fact the value (or range of values) of x. What is it about V2 that makes it the semantic value? Not 'use etc'. But suppose all obvious candidates like causal facts are part of 'use etc.'. Then the relationship between x and V2 -- let's call it "reference" -- is inscrutable insofar as knowing all ordinary facts about use and causation and so on is not enough to find out that x refers to V2. There must be something over and above all this that privileges V2. Let's say (with Lewis) that V2 is a reference magnet (with respect to x).
The doctrine of reference magnetism comes in different degrees.
Weak magnetism holds that if conditions (1) and (2) obtain, the reference of x is the most magnetic candidate compatible with the facts about use etc.
Intermediate magnetism holds that the reference of x is the value that strikes the best balance between satisfying the facts about use etc. and being magnetic. That is, if V' is not among the original values V1,V2,... (determined by the facts about use etc.), it may still be the value of x, if it is more magnetic than any of the V1,V2,....
Strong magnetism holds that being magnetic always trumps use etc.: if V' is the most magnetic entity with respect to x, then x refers to V', no matter the facts about use etc. Only if several candidates are equally magnetic with respect to x do facts about use etc. enter into the picture, selecting among the most magnetic values the one that best fits those facts.
A classical form of magnetism is the epistemic theory of vagueness on which e.g. "bald" denotes some precise property even though facts about use etc. will not tell us what property that is. Essentialism can also be understood as a form of magnetism, on which the intension of, say, "Kripke" is not determined by facts about our use etc. of "Kripke", but by an intension-magnet called "Kripke's essence". (Look at it in terms of the lump theory: What fusion of counterparts "Kripke" denotes is determined by Kripke's essence.)
A less precise kind of magnetism is assumed by Kripke and Stalnaker when they say that reference is not analyzable in terms of use etc. Yet another kind of magnetism is suggested by Lewis when he argues that objective naturalness of semantic values can solve the indeterminay problem for Global Descriptivism. (Presumably some further kind of magnetism is accepted by Lewis, though it's hard to say from his writings just what this magnetism amounts to.)
Finally, Brian Weatherson and Ted Sider appeal to magnetism in order to show how people can mean the very same thing by x even if they differ in their use of x. Notice that weak magnetism is not enough here: being magnetic must be able to trump facts about use etc.
The main problem I have with magnetism is that it conflicts with what I think we do with language. Suppose the colour red is a very magnetic property, so that all colour predicates end up denoting redness. Then how can I use "that book is blue" to communicate that the book is blue? What sense does it make to say that I really communicate that the book is red if that isn't reflected by our usage, by the beliefs I express, by the beliefs you acquire, by your subsequent behaviour, by the conditions under which we criticise such utterances, and so on?
I also haven't yet seen a convincing argument that magnetism is really needed. The usual argument proceed via (1) and (2). But do (1) and (2) ever obtain if all relevant facts about use etc. are taken into account? What exactly is wrong about leaving semantic values indeterminate if those facts don't suffice to settle them? More importantly, even if (1) and (2) sometimes obtain, they only support weak magnetism. Some rather different argument is needed to support stronger versions, but I'm not aware of any such arguments.
Note that I do not reject objective naturalness or individual essences. Accepting them allows me to offer a nice replacement for magnetism for cases where it looks attractive. For instance, by using natural kind terms we mean to communicate information about more or less natural classes. This is reflected by our usage, by the beliefs we express and acquire, by our behaviour, etc. So the facts about use etc. determine that the referent of, say, "tiger" is a class of things satisfying (to a sufficient degree) conditions like: containing animals; containing things we've heard of under the name "tiger"; ...; and being objectively natural. Here naturalness is not needed as an additional constraint on reference, over and above facts about use etc. Similarly, one could say that facts about usage etc. determine that we mean "Kripke" to denote at every possible world an entity that shares Kripke's essence.
Do you think that Lewis wouldn't extend the 'objective naturalness of semantic values' strategy to his own convention-based account? I thought that in 'Meaning without use' he pretty much endorses exactly this strategy. And that article is explicitly about his own convention-based approach, not global descriptivism. There he says "use determines some meanings, those meanings determines the rules, and the rules determine the rest of the meanings." (p.149). The 'rules' he's talking about here have got to be the assignment of subsentential semantic values (a grammar, in his sense).
What underpins the extrapolation from a limited range of conventions to a grammar? He puts a footnote to New Work for a Theory of Universals.
The only good interpretation of the article that I can think of is to think that Lewis is again saying that what makes a grammar right (makes the extrapolation to it good) is a combination of eligibility + meeting constraints of fit. And this is exactly analogously to the Lewis suggestion in the case of global descriptivism.