Indeterminate Reference, Determinate Aboutness
Sentences aren't just about the things they name. You can write an entire book about the Second World War without ever mentioning the whole war by name.
Very roughly, a sentence is about something X iff the way X is matters for the truth value of the sentence. "It's raining" is about the weather because differences with respect to the weather affect the truth value of the sentence. By contrast, "it's raining" (or at least "it's raining in Berlin on July 11, 2006") is not about the Second World War because any way the Second World War might have been is compossible with (just about) any state of the current weather. (Arguably, the current weather counterfactually depends on details about the Second World War. But what counts is compossibility, not counterfactual dependence.)
As I said, this criterion of aboutness is rough, and rather uninformative. If ending 22345 days before it rains in Berlin is a relevant way the Second World War might have been, the truth value of "it's raining in Berlin on July 11, 2006" will not be compossible with any way the Second World War might have been. So I should say something to rule out such artificially extrinsic ways (or 'differences with respect to'). But let me move on to explain what I'd like to do with this notion of aboutness. Then we can worry afterwards whether the criterion can be made more precise for that job (ideally by adopting one of Lewis' many analyses of partial aboutness in "Statements partly about observation").
Consider a language just like English except that "the Second World War" denotes a certain cherry and the meaning of all predicates is suitably adjusted so that all sentences end up having exactly the same truth-conditions as in English. For instance, x and y satisfy "dies in" in this language iff either y is that cherry and x dies in the Second World War or y is not that cherry and x dies in y.
So here is another sentence (in that language) about the Second World War that doesn't mention it by name: "millions of Russians died in the Second World War".
What the sentence names is only a certain cherry (and perhaps, in an extended sense of "naming", also Russians and a certain strange relation). But since the sentence is true iff the like-worded English sentence is true, it is just as much about the Second World War as the English sentence: differences with respect to the Second World War do matter for the truth value of the sentence.
By contrast, despite the fact that the sentence names a certain cherry, it is not about that cherry: differences with respect to the cherry do not affect the truth value of the sentence (except artificially extrinsic differences).
So permutation of reference does not go with permutation of aboutness. Indeed, any assignment of referents that leaves the truth-conditions of English sentences unchanged will also preserve all aboutness facts.
That's nice. For many theories of meaning (including Davidson's and Lewis's) leave the assignment of semantic values to subsentential expressions underdetermined: any assignment that produces the right truth-conditions will do. So it is arguably indeterminate whether "the Second World War" denotes the Second World War or a certain cherry. But isn't "millions of Russians died in the Second World War" determinately about the Second World War, and not about that cherry? It is.
(In fact, if the cherry is assigned as semantic value to "the Second World War", I think we shouldn't call that semantic value the "referent" of the term. "Reference" is conceptually tied to aboutness: normally, "a" refers to x iff the truth value of sentences of the form "a is F" depends on the way x is. Any reasonable semantics for English will, I believe, involve semantic values that either satisfy this condition or somehow determine other values that satisfy it. So the non-semantic facts determine the truth-conditions, the truth-conditions determine the aboutness facts, and any reasonable semantics will somehow respect these facts in the assignment of subsentential values and hence involve claims about reference. I think this may well be how the description theory of reference is part of a two-dimensional semantics for English.)
Hi Wo,
I heartily approve of appealing to aboutness in this context (and I too would like a workable theory of that notion to be around). For what it is worth, the way I want to play a similar thought is to use the invariance of "aboutness" facts to explain away intuitions against inscrutability of reference (in the semantic-value sense).
I guess what your line turns on is what we say about our use of (seemingly) semantic vocabularly, e.g. "reference". You shouldn't insist that the semantic value of "reference" is a relation that pairs "WWII" to WWII, otherwise you'd be pulling determinacy of subsentential *semantic values* out of the air. Rather, your claim has to be that the reference of "reference" is a relation that pairs "WWII" to WWII.
Here's one question for you if what I've just said is right: what progress does the appeal to aboutness make? Putnam, Davidson and others noted that by reinterpreting "reference" (and "aboutness" and "causality" etc) in ways appropriate to a permutated interpretation of a language, we can make all the familiar disquotational principles come out true. ("reference" in this sense is penumbrally connected, in Fine's sense, to all the singular terms in the language)? Why do we need to say more than this? What exactly is the further thing as-yet-undone that requires we start talking about aboutness?
There's a really nice paper by Hartry Field, from back in the day (I think it's "Conventionalism and instrumentalism in semantics" Nous 1975). I'd be interested to know whether you think that the idea in that paper are strategically similar to the ones you're suggesting here.
There's an entirely different way of taking what you say (which I think that Brian Weatherson has suggested in the past)---and that's to say that aboutness-facts as constitutive of semantic facts in the same way as conventions of truthfulness for Lewis: that is, no semantic theory counts as successful unless it respects both facts about conventions of truthfulness and "conventions of aboutness". I took it that you weren't taking this direction since you were conceding that "semantic value" was radically inscrutable, even though "reference" turned out not to be.
Anyway, be interested in hearing whether'll you'd want to associate yourself with either of these approaches.