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.)

Comments

# on 12 July 2006, 18:08

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.

# on 12 July 2006, 21:35

Hi Robbie,

yes, using the invariance of aboutness to explain away intuitions against inscrutability is exactly what I'm trying to do in the main part of the post, before the final brackets. Have you worked that out somewhere?

Re your first point: I'd rather not talk about the semantic value, nor about the reference of "reference" (because paradox is lurking here), and just say that there are certain quasi-analytic constraints on the use of "refer" that rule out that "WWII" refers to a cherry.

I don't know much about what Putnam, Davidson and Field have said about all this, but I used to believe (half-heartedly) something that sounds similar: that our concept of reference is mostly exhausted by disquotation principles and hence that what we should demand of a semantics in this respect is only that it be compatible with those principles.

But I think I'd really prefer to have more than this, though it's a little hard to explain what. In a sense, I want to respect the intuition that "Berlin is broke" is about Berlin, and not just the intuition that "'Berlin is broke' is about Berlin" is true. And I'd like to have determinate intra-linguistic aboutness: "Millionen Russen starben im zweiten Weltkrieg" should be determinately about the Second World War, too. Maybe the crucial point is that Putnam, Davidson and Field would all accept that *in some sense*, it is indeterminate whether "Berlin is broke" (in English) is about Berlin. Whatever exactly that claim amounts to, I'd rather deny it.

I definitely wouldn't want to impose a further general constraint on semantics besides conventions of use. I suspect it is just an accident that there are workable semantics for all our languages that make use of reference (rightly-so-called). So I suspect the further constraint would render some possible languages un-interpretable (or un-interpretable by any reasonable semantics). I also believe it's important to keep different semantic roles separated: it's one thing to figure in the best systematic description of our linguistic practice, it's another thing to satisfy aboutness conditions. If we can find semantic values that do both, great. But that doesn't mean these very different roles always belonged together or constitute some especially important and unified semantic notion.

# on 13 July 2006, 10:47

That's really interesting. When you say that it's an accident that workable semantics make use of reference, is that because there might be languages with some totally "other" semantics (e.g. the Quine algebraic stuff). Or that there're languages where there's not sufficient complexity in use to lead us to detect singular term reference (Evans suggested something like that in "Identity and predication"). Or that there are languages that e.g. use quantifiers rather than singular terms, so aren't interpretable via singular-term reference? Or something else? I guess one response would be to maintain that the constraints are conditional in nature: if "t" is a singular term in sentences that are about O, then CP semantics should have assign O to "t". If there are no singular terms, then the constraint just lapses. But it does seem kinda ugly to me, especially in the first two cases.

What I was thinking of for Putnam and Davidson is really just the "just more theory" moves. One way of thinking of that argument is as making the point that you don't need determinate semantic value, to have sensible reference-talk (and, one might add, to fulfill at least some of the explanatory roles associated with reference). That seems to me the interesting core of the "just more theory" considerations, anyway.

I think that reading of the "just more theory" move is found in the Field article. And Field (at the time) was still wanting a reductive theory of truth-conditions in terms of a causal theory of reference (he wasn't yet into his deflationist phase). He wanted to (a) resist the idea that the "just more theory" considerations undermined what he was doing in "Tarski's theory of truth" (b) concede that there's no "deep" reason why we should talk about the reference-relation (i.e. the Fieldian causal relation) rather than some permuted variant, for the purpose of semantics: there's no explanatory job that could be done with the first that couldn't be done with the latter. It's a pretty delicate line to tread: did seem to me similiar in spirit to what you were proposing.

I see the point about the inter-linguistic usage of "reference". That does seem to be something gained over straight appeal to the disquotational notion.

p.s.
I haven't worked out this stuff anywhere: there's about a paragraph about Aboutness in this context in my thesis, and there's a paper I'm working on where I repeat that stuff. (It's page 6 of http://www.personal.leeds.ac.uk/~phljrgw/wip/thepriceofinscrutability.pdf)
Really, it's just an idea that intrigued me and that I want to think more about in the future. In particular, I wanted to make sure that I understood "aboutness": I think I picked up the characterization I use from Lewis's "Events". I wonder whether something more sophisticated is going on in "Statements..." and "Relevant Implication".

I was thinking of appealing to facts on a sentence-by-sentence basis: e.g. appealing to the fact that whatever goes on sub-sententially, "Socrates is wise" is about Socrates. One problem with that is that e.g. "water is H20" and "1+1=2" aren't distinctively about water or the number 2, on the formulation I had in mind (necessarily true statements turn out to be about everything). And I was also concerned with statements that contain names referring to people that don't exist in this possible world... So it all seemed a bit messy around the edges. One nice thing about your way of doing things (construed as explaining-away intuitions, rather than anything stronger) is that by dropping the sentence-by-sentence appeal, at least some of these problems go away: it's because of the fact that "water is wet" is about Water, that we relate "water is H20" to Water.

# on 15 July 2006, 12:58

What I had in mind as a semantics that makes no use of reference were 1) semantics for a language about things with very unclear temporal and modal boundaries, like feelings and weather conditions: think of a language that contains only sentences translating "it's raining", "it's snowing heavily", "yesterday, it rained all day", etc. It isn't obvious that a workable semantics here will inevitably involve referents; 2) semantics for a language whose sentences directly express possible distributions of fundamental properties in a world, without naming any hooks for these properties to attach to; 3) something in the direction of a semantics that interprets all singular terms as generalized quantifiers or as functions from various indices (world, time, place) to properties or the like.

I have sympathies with what you describe as Field's view (I still haven't looked up the article), but it's not what I'd like to promise now. Which is: First, even if semantic values of subsentential expressions are radically indeterminate, what the sentences are about is not; second, one should only speak of "reference" (as opposed to "semantic value") if, in normal cases, the terms in a sentence refer to objects the sentence is about. ("In normal cases" excludes, for instance, necessary truths.) It follows that while semantic values are underdetermined, reference is not.

I'm not sure "water is H20" and "1+1=2" are distinctively about water or the number 2. I think there's something right about the logical empiricists' claim that necessary/a priori truths aren't distinctively about anything. Nevertheless, if in virtue of its occurrence in other sentences, "water" *refers* to water, one could say that "water is H2O" is about water in another sense of aboutness, by containing a name that refers to water. One could also define aboutness in terms of A-intensions rather than C-intensions. Neither move will help for numbers, though.

# on 21 July 2006, 06:38

Weird coincidence. I just (about a 2 months ago) came across Goodman's paper "About" (Mind, Vol. 70) and Ryle's with the same title but placed in single quotes. Now that I do a search, I notice that there are probably tons of papers on the subject (e.g. Putnam & Ullian's, Thalheimer's, Rescher's, etc.). It just struck me as strange that there is an entire enterprise built around giving an analysis of 'about'.

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