Rayo on Vague Representation

I found "Vague Representation" to be a little unsatisfying, and it is worthwhile to wonder why. Perhaps most theorists of vagueness are trying to do something impossible, like trying to find out why a physical constant has the value it has (Fine 1975). It is what it is; explanation should just end there. I am not sure if I would characterize someone who tries to go further as being "in the grip of" some misguided "picture" (probably, to the effect that semantic competence involves "rules"), but perhaps whether the description is accurate will emerge in time.

The goal of the paper is to give a theory of assertoric content for a vague language. Since theories of assertoric content situate themselves at the semantics-pragmatics border, the paper opens with some clearly correct observations about how vague language is felicitously used. (The question will be, of course, what import these observations have for vagueness conceived as a semantic puzzle, and whether they could possibly constitute a complete answer to that puzzle.) The observations are: first, the use of a vague utterance presupposes that it will be interpreted so as to impart some information. Hence, for example, we can expect a speaker to intend her utterance to be interpreted in a way that excludes some but not all open possibilities from the context set---this is just another way of saying that we expect the speaker to be informative relative to the context. Because of this, a borderline case can sometimes be excluded (relative to competitors) and sometimes included (relative to different competitors) on the basis of the same vague utterance (e.g., "Susan lives in a blue house."). Another observation to add to this is that the context relative to which the speaker seeks to be informative may not be the context of utterance---for example, Susan may say "I live in a blue house", intending only that her utterance be sufficiently informative to me a few hours from now, when I arrive on her street looking for her house. So it is not necessary (indeed, probably not even possible) for her utterance to uniquely pick out the color of her house relative to the entire color-wheel: it only needs to pick it out relative to the other houses on the block. This spectrum already excludes most possibilities; it features "gaps." Rayo describes several maxims of conversation qua their relationship to gappy contexts [gappy in the parameter of application]: utterances should make nontrivial partitions on gappy contexts. (This will be an utterance's "essential effect".)

These maxims, of course, are used not only to determine whether an utterance is felicitous but to calculate what was said (and what the words meant) in the first place.

The presentation of all this in the paper is semantically conservative, and close to supervaluationism, in the following way. The maxims are presented as doing their work--the work of informing a "semi-principled" [that is, semi-constrained] decision [deciding what to throw out of the context set] against a background spectrum of classical semantic theories. There is a spectrum for the same reason there's one in supervaluations: there is a range of classical theories compatible with the extension of "blue" as use determines it. [This is not explicitly explained, but there must be some reason for it!] What we must choose, on an occasion of utterance-processing, is not which classical theory to use but which partition to make; and we can often do the latter without having to do the former. We are aided by (i) certain features all the classical theories respect (the supervaluationist's supertruths); (ii) the maxims about gaps and informative partitions; and (iii) information about which classical theories are rendered most plausible in light of past uses of the term--which ones are admissible in the supervaluationist's sense.

It is (iii) that is likely to give rise to the most protest, in terms of whether "localism" about vagueness is the solution to the puzzles of vagueness. After all, a standard objection to supervaluations is that they do not account for higher-order vagueness. The observation here is that the same puzzle afflicts this account, although in a more indirect way, since an account has been given of the way in which admissibility, in the supervaluationist's sense, needs to do only part of the job [it is aided by maxims and contextual information] and it is clear that the job is not as big as it is often taken to be [it only needs to make a partition, for the nonce, in a gappy context].

In response to the complaint about higher-order vagueness, we get instrumentalism as a metaphilosophical response. The idea is that what we have is good enough. I think it might be good enough for a lot of purposes, but then again, for a lot of purposes, vagueness isn't a problem in the first place. Rayo seems to suggest, by way of saying that this is good enough, that it is as good as anything can be, once we take an instrumentalist picture of...is it language, or explanation?...It is explanations of language use:

"[Higher order vagueness] might well constitute a source for concern if one thinks of theories of assertoric content non-instrumentally. But here we are thinking of a theory of assertoric content as a tool for predicting the evolution of the context set [I guess this means we are still thinking of the context set non-instrumentally.] Accordingly, there is no sense to be made of the question whether a partition is really salient, over and above the question whether treating the partition as salient is a good way of making sense of our linguistic practice (and therefore no sense to be made of the question whether an assertion really has a particular local content, over and above the question whether ascribing that content to that assertion is a good way of making sense of linguistic practice)." (363)

The original suggestion, in contrasting localism with globalism, is that globalism flatfootedly plugs the semantic theory into the theory of assertoric content; the relationship between the two is a big fat "=". Localism is supposed to be less flatfooted, though I'm not sure exactly how this is supposed to help us with concerns about the semantics. It is good to point out that there could be something more complicated there than a big fat "=." But if that's where the suggestion ends, then I don't see how localism even inform any of the semantic puzzles about vagueness. Since we've denied to state any sort of equivalence between semantic and assertoric content, to be instrumentalist or anti-realist about (local) assertoric content doesn't determine that one is instrumentalist about semantic content.

[It should be noted that the picture ascribed to the globalist isn't really that semantic content = assertoric content, rather, it is, I suppose, that semantic content = a function from contexts to assertoric contents, i.e. a function from contexts to propositions. Rayo idealizes away from indexicality for the sake of simplifying the discussion. This seems like the right way to put the orthodox view: semantic content determines assertoric content.]

Perhaps in order to address these concerns, Rayo does return to the sorites paradox itself at the end of the paper. He concedes that the localist response to the conditional premise is quite a lot like the supervaluationist's. However, the localist declines to assign a special status ("supertruth") to sentences which are true in light of every semantic theory: he does not quantify over semantic theories in this way.

"the role of semantic theories in characterizing the notion of truth is not that of articulating possible completions of the language. Their role is to supply the information about past linguistic usage that is used to characterize salience [i.e. the salience of certain partitions of the context set]. " (366)

It does indeed seem like truth is being left out altogether here: Rayo does not characterize an assertion by saying that it is true or untrue, or even that it expresses a truth or an untruth. Instead of expressing anything of the kind, it enables the hearer to partition the context set, and that is that.

...Or is it? We still need truth in a derivative way, since truth is what makes the candidate semantic theories what they are. It seems like little more than an exercise in re-labeling to say that (i) Gricean reasoning demands a context-contingent partition of the context set; (ii) such a partition will be a proposition; (iii) which proposition will do the job is a question with a range of answers; (iv) for reasons listed above, there is a subset of the range of answers we can therefore decline to choose between. We recover the supervaluationist's jargon by saying e.g. that a certain partition---{house 1} out of {house 1, house 2}, for example---is recommended

because "~house 2" is supertrue with respect to context {house 1, house 2} by way of being recommended by every classical semantic theory compatible with the Gricean constraints on semantic theory choice. This seems like supervalutionism sensibly updated so as to take explicit account of conversational pragmatics in its accounting of "admissible valuations" and "what is left open by speaker usage." Perhaps this presentation of localism also gives us a way to explain what is pathological about a sorites series: it lacks gaps, and vague language is not felicitous in the absence of gaps.

Here, then, are old two worries raised anew. On a Stalnakerian picture, content interacts with context, and vice-versa. In the metaphysical order of things, semantic content determines assertoric content, by way being a function from contexts to propositions. We rely on our knowledge of context to determine assertoric content (sometimes because this is part of the compositional semantics and sometimes because it is part of the pragmatics); one way this is done is with our systematic knowledge of indexicals; another is via general Gricean mechanisms we employ to disambiguate between homophonic or ambiguous sentences; another may be by way of metalinguistic reinterpretation a la "Assertion"; and finally, there might be some particular forms that Gricean maxims take in vague cases, such as Rayo's "Principle of Clarity." But certainly the three items on this list rely on a classical picture of truth-conditional contents; why should we think that the last does not? And if it does, why don't the puzzles of vagueness simply reintroduce themselves? One reason, after all, for not being satisfied with pragmatics instead of semantics is that a sentence's felicity-at-a-context profile is not sufficient to determine the felicity of embedded occurrences. Put another way: knowing all this about vague language isn't enough to tell us what vague predicates mean. But this was what we wanted to know in the first place. Or, at least, this is one thing worth knowing.

The second worry is really a constellation: the regular objections to supervaluations. Let us remind ourselves what they are. The first is that supervaluationist logic, while it preserves classical validities, doesn't preserve classical inference patterns. Williamson identifies the root of the trouble as the Supervaluationist's identification of truth with supertruth: this identification conflicts with the role truth plays in the classical inference patterns, as well as the disquotational schema (T(`p') <->p, with `<->' in the object language). This family of objections is distinct from the objections from higher-order vagueness, and I do not see how instrumentalism provides any kind of relevant response. Supervaluationists like McL/McG have responded by acknowledging that there are two kinds of truth for the Supervaluationist, supertruth and pluth (that is, global truth and local truth), the former of which is truth on all admissible valuations and the latter of which is disquotational and classical-inference-preserving. Keefe goes further and argues that in fact the failure of classical inference patterns is appropriate for deductions involving vague terms: when we reason with vague terms, we actually do/should use definite truth rather than pluth.

What Rayo's considerations suggest to me is another way of thinking of truth vs. pluth. McG/McL argue that supertruth is the aim of assertion, because we aim to assert what we know. Another reason we might aim for supertruth is that we wish to restrict ourselves to assertions which our audience will accept; since we don't know exactly which classical theory, or set of classical theories, our audience accepts, we aim for truth on all of them. Perhaps iterated knowledge plays a role here: I assume that my audience has a range of classical theories because he cannot know what classical theory I use; he knows this, hence...etc.

****

We begin by contrasting "localism" and "globalism," which are both theories of assertoric content:

Globalism: "[It is] tempting to suppose that the various instances of local usage fall into patterns that are usefully described in terms of global contents: contents that determine a definite partition of the entire space of possibilities. Accordingly, it is tempting to think of the task of constructing a theory of assertoric content as the task of finding an assignment of global contents that fits local usage as neatly as possible...

[Two steps.] The first is to choose a context-insensitive semantic theory (I ignore indexicals to keep things simple.) The second step is to identify the global content of an assertion with the proposition assigned to the sentence asserted by one's preferred semantic theory. The task of constructing a theory of assertoric content therefore boils down to the task of finding an assignment of semantic values to basic lexical items which yields the result that actual instances of usage reliably correct." (348)

****

Finally, it should be noted that the tantalizing suggestion is raised (367, with a hat tip to "Assertion") that the right way of taking the conditional premise might be a metalinguistic one---thus the premise records a fact about admissible usage and not truth. Rayo isn't sure what to make of this and neither am I; but it is quite possible that this is the most interesting thing a classical approach to vagueness should take from the consideration of assertoric content.