Content, Context and the First Dimension -- Second Try
This is a rewrite of last week's posting, which I now find rather obscure. Basically, I'm trying to introduce A-intensions in a way different from the possibilities discussed in David Chalmers' "Foundations". The "contextual" approaches he discusses look like non-starters to me, and I don't like his own "epistemic" account, partly because of worries about his use of ideal language and partly because I would very much like to explain a priori knowledge with knowledge of A-intensions rather than the converse. Most importantly, I think there is something wrong with the very question he asks. Or at least there's something wrong with where the question is asked.
One of the most important things I want from an interpretation of a language is that it assigns truth conditions to sentences. The truth conditions assigned to a sentence determine a certain class of possible situations, namely the class of situations at which the conditions obtain. In modal semantics, we take these classses as our (main) semantic value for sentences. Let's call them "A-intensions" and their members, the possible situations, "scenarios". For most applications it doesn't really matter what these scenarios are. They might be triples of a possible world, a time and an individual, or time-slices of world-bound individuals, or sentences in some neutral metalanguage.
At any rate, if interpretations assign these A-intensions to sentences, we get the immediate result that a sentence S is true under an interpretation I at a scenario W iff W belongs to the value that I assigns to S.
Hence I find it strange that in the literature on two-dimensional modal semantics, one ofen finds discussions of what makes it the case, for a given sentence S of a language L and a scenario W, that W belongs to the A-intension of S. Clearly, just looking at the string of symbols and the scenario won't help: Take the German string "Es regnet" and various scenarios. You can't find out whether the string is true at these scenarios, that is, whether the truth conditions of the string obtain there, unless you know what the truth conditions of the string are (in German). Hence it would be a sign of utter confusion to select those scenarios where by some coincidence that very string occurs -- maybe because it is uttered by a speaker or maybe because the waves of an ocean have arranged sticks and pebbles in the appropriate shape -- and investigate into the properties of these occurrences. Unless you know the semantic value of "Es regnet", this will tell you nothing at all about which scenarios belong to its A-intension. On the other hand, once the interpretation is taken into account, there is nothing left to ask, for the interpretations explicitly tells you which scenarios belong to the string's A-intension.
(Note by the way, that the same can be said about all kinds of context-dependence. If you want to find out at which actual times and places (in our world) "Es regnet" is true, it's no help to investigate into the properties of occurrences of that string at those times and places. Hence I think that the dependence of truth value on which world is actual exactly resembles the dependence on what time is present and what place is here. Since the latter dependences are customarily called "context-dependence" I would also call the former so. However this has little to do with the "contextual" approaches discussed by Dave Chalmers. These fail to account for time- and place-dependence just as they fail to account for world-dependence.)
So I think it makes little sense to ask what it is about a sentence S, an interpretation I and a scenario W that makes is the case that W belongs to the A-intension under I of S. The good question that remains is what it is about (a token of) S that makes it the case that I is its interpretation, and hence that W belongs to its A-intension.
But this is not the same question. Or, if it is, then the most obvious candidates for answering it are often ignored. For the question now is what makes a certain interpretation the correct interpretation for a given sentence, or more generally, for a given language. For a public language, an answer would probably have to involve conventions. But let's look at idiolects, where two-dimensionalism is better applicable.
There are many different approaches to how sentences in an idiolect get the meaning they have. Some appeal to inferential roles, some to causal connections, and some say one can't do semantics for idiolects at all. As a Lewis scholar without any own positions, I would appeal to the rules of (radical) interpretation: Somebody's sentence S has the semantic value V roughly iff this is what the rules of (radical) interpretation say. Many of these rules operate on what Somebody says in various situations, and to which sentences he assents in these situations. Thus if Somebody assents to "Es regnet" in precisely those situations in which it is raining this is a prima facie reason to take those scenarios as the A-intension. Luckily, if we want to find out whether in Somebody's idiolect "Es regnet" is also true when it snows, we don't have to wait until it snows. We can cheat, for we only need to make him believe that it snows, for example by replacing the windows with monitors showing a landscape in which it snows. Similarly, if we want to find out whether Somebody would assent to "water is H2O" even in situations where the watery stuff in his surroundings is not H2O, we don't need to replace the watery stuff (which is tricky in particular if "his surroundings" includes his past surroundings). We only have to make him believe that scientists made certain discoveries.
Even better, if Somebody is like most of us, he can make quite reliable statements about what he would say if certain conditions obtained, without actually believing that they do obtain. So we can simply ask him what he would say if scientists found out that the watery stuff is not H2O. Here a "neutral" vocabulary for describing possible conditions can be useful, though we don't need to describe a single scenario, so we don't need an artificial language with infinite sentences (that wouldn't help us anyway unless Somebody happens to understand that language). What is Somebody doing when he says what he would say if certain conditions obtained? Well, he pretends that these conditions really obtain. (He "considers those worlds as actual".) We all can do this, and I don't think it needs philosophical explanation. And how do we find out what we'd say under these conditions? Well, how do we do find out what's true under the actual conditions? Looking out of the window, I think it would be true to say "It's raining". I don't know how exactly I'm doing this, but I think I'm not trying to figure out whether some neutral infinite description of reality is a priori compatible with the negation of "It's raining". I'm willing to take our ability to evaluate our expressions under different possible conditions as given, and I'd say that this partly constitutes knowledge of language.
Returning to the big picture, it's important that Somebody's intuitions about what he would say under certain conditions are not the only facts relevant for the semantics of his idiolect. We also have his actual utterances. More importantly, there are other rules such as naturalness and systematicity. Maybe Somebody can't tell us whether some very complicated sentence of his idiolect is true, and whether it would be true under certain other conditions, simply because the sentence is too complicated for him to understand. It doesn't follow that the semantic value of this sentence is undefined. With the rules of naturalness and systematicity (including compositionality), semantic values can be determined for an entire idiolect on a comparatively tiny basis of actual behaviour and intuitions. This way, we also get truth conditions for evidence-transcending sentences, including sentences like "I do not exist" and "all evidence strongly suggests that the watery stuff is H2O whereas in fact it is XYZ", for which it is quite difficult to pretend that one has strong evidence to believe them. So we don't need to say that a scenario belongs to the semantic value of a sentence in Somebody's idiolect iff he intuits that under certain conditions that obtain at the scenario he would assent to the sentence. With other rules of interpretation at our hands, the biconditional fails in both directions.