NoR 4.2: Fixing Fit

This is one of a series of posts setting out my work on the Nature of Representation. You can view the whole series by following this link

Let us suppose that the base facts about whole-sentence-content (for those sentences which feature in actual patterns of use) have been established. The story about how we fix word-content was the following: that the correct compositional interpretation was whatever “best explains” the facts about whole-sentence content.

So what makes one compositional interpretation of a language better than another?  I will work with a familiar model: that betterness is determined by the tradeoff between virtues of fit, strength and simplicity. If the datapoints are facts about linguistic content (for a constrained range of sentences) then the contents assigned by the compositional theory should explain that data, which minimally requires being consistent with it. The theory should be strong, in that it should predict as much of this data as possible. But this is balanced by simplicity. As in an earlier post, the model for this is compactness of expression, when the interpretation is expressed in some canonical language.

“Fitting” the base facts about sentential content does not mean the the compositional interpretation should assign the same content to whole sentences that the base facts supply. It would be bold to bet that there is a unique content conventionally associated with each sentence, and an even bolder bet that that will turn out to be the semantic content that can be generated compositionally. No, “fit” is a looser, more interesting criterion that this. The constraint as I understand it is the following: given the content that the compositional interpretation assigns to the sentence, plus suitable auxiliarly hypotheses (general information about rational agents and conventions of cooperation, special purpose pragmatic principles) as much as possible of the range of contents that are conventionally associated with the sentence should be explicable. It’s easy to explain why there will be a regularity of truthfulness and trust connecting “Harry is a bachelor” to the content that Harry is male, on the basis of a compositional interpretation of it as having the content that Harry is a bachelor, since generally we believe the obvious logical consequences of what we believe. The reverse would not be easy. Again, general information about Gricean conventions of orderliness together with the standard compositional content will explain why “Harry had five drinks and drove home” is conventionally associated with the content, inter alia that the drinking preceded the driving. So even if these regularities of truthfulness and trust count as conventions, the standard interpretations fit them well.

If Fit and Strength were the only determinants of “best explanation” of the language in use, then the account would be subject to counterexample. It is well known that the same sentence-level truth-conditions can be generated by a variety of lexical interpretations, some of which are obviously crazy. I introduced two in an earlier post:

  • Permuted interpretations. Where the standard interpretation has “Tibbles” referring to Tibbles, and “is sleeping” picking out the property of sleeping, the permuted interpretation says that “Tibbles” refers to the image under the permutation p of Tibbles, and “is sleeping” picks out the property of being the image under p of something which is sleeping. Systematically implemented, the permuted interpretation can be shown to produce exactly the same truth-conditions at the level of whole sentences as does the standard interpretation. But, apparently, that means that they fit with and predicts the same sentence-level facts about conventions. So we can’t explain on this basis the obvious fact that the permuted interpretation is obviously and determinately incorrect.
  • Skolemite interpretations. Where the standard interpretation has the quantifier “everything” (in suitable contexts) ranging over absolutely everything, the skolemite interpretation takes it to be quantify restrictedly only over a countable domain (this domain may vary counterfactually, but relative to every counterfactual situation its domain is countable). And (with a few caveats) we can show that the skolemite interpretation and the original are truth-conditionally equivalent. But, apparently, that means that they fit with and predict the same sentence-level facts about conventions. So we can’t explain on this basis the obvious fact that the skolemite interpretation is obviously and determinately incorrect.

We met these kind of deviant interpretations in the context of the metaphysics of mental representation. Under the assumption that thought had a language-like structure that allows us to pose such puzzles, I argued that normative facts about the way in which we handle universal quantification in thought and inductively generalize would solve the problem.

Now Lewis denied the starting point of this earlier story. He stuck resolutely to theorizing thought content in a coarse-grained way (as a set of worlds, and later a set of centred worlds/individuals), ignoring issues of individual representational states and any compositional structure they might have. That only delayed the day of reckoning, since once he reached this point in the story—with public language and its compositional structure—he had to face the challenge head on. Further, nothing that Lewis did earlier on helps him here. Remember, the the raw materials for selecting interpretations are conventions of the form: utter S only if one believes p; and come to believe p if one hears someone utter S. And since for Lewis the “p” here picks up a coarse-grained truth condition. But the permuted and skolemite interpretations fit that sort of data perfectly. So underdetermination looms for him.

(There is one way in which we might try to replay those earlier thoughts. Among the conventions of truthfulness and trust will be an association between, say, “everything is physical” and Jack being physical. That is obviously not going to be the semantic content, but we need to explain why there is a convention of truthfulness and trust there, given the semantic content we assign. Here is the suggestion: a restricted interpretation, even one that de facto includes Jack in the domain D of the quantifier, won’t afford such an explanation. That’s because the audience couldn’t rationally infer just from the information that everything in D is physical, to Jack being physical, except under the presupposition that Jack is in D (so what we should expect, under a restricted interpretation, is that we only get conventional association with: if Jack is in D, then he’s physical). This is a natural way to try to lever the earlier account I gave into the current setting. But unfortunately, I don’t think Lewis can appeal to it. For him, the contents that everything is physical and that everything in D is physical are identical—since they’re truth conditionally equivalent, denoting the same set of worlds. So it’s not an option for Lewis to say that believing one supports believing Jack is physical, while believing the other supports believing only the conditional—that’s a distinction we can only make if we presuppose a finer-grained individuation of the two contents.)

So Lewis needs something more than fit and strength in his account of better explanation. But so does everyone else. At first it might not seem this way. After all, if we’ve already solved these puzzles at the level of thought-content, then surely linguistic content should be able to inherit this determinate content? There are two problems with the proposal. First, it’s surprisingly tricky to get a workable story of how determinate content is inherited by language from thought. And second, there are further underdetermination challenges beyond the two just mentioned for which this strategy won’t help.

On the first point, let us assume, pace Lewis, that the structure of thought was itself language-like, and that we confronted and solved the problem of permuted and skolemite interpretations as it arose at this lower layer of representation in the way I described earlier. We will have already earned the right to ascribe to agents, for example, a truly universal belief that everything is physical (modelled perhaps by a structured proposition, rather than a Lewisian set of worlds).  The “inheritance” gambit then works as follows: there will be a regularity of uttering “everything is physical” only when the utterer believes that truly universal structured content. And to the extent that this regularity is entrenched in the beliefs and preferences of the community so that it counts as a convention (plausible enough), the constraint on linguistic interpretation will not simply be that we fit/predict data characterized by coarse-grained content, but that it fits and predicts fine-grained data. Ta-da!

But we have already seen that “fit” cannot simply be a matter of identity between the content of thought and language. And theorizing thought in a fine-grained way amplifies this. None of our assumptions entail that for each sentence in public language, there is a belief whose content exactly matches its structured content. Here’s a toy example: suppose we have no single concept “bachelor” in our language, but do have the concepts “unmarried” and “adult male”. Then the fine-grained belief content conventionally associated with “Harry is a bachelor” may be a conjunctive structured proposition: Harry is unmarried and Harry is an adult male. But we shouldn’t require a semantic theory to compositionally assign that particular proposition to the atomic sentence in question—it may be impossible to do that. What seems attractive is to say that the assignment of the stuctured proposition <Harry, being a bachelor> to the sentence explains the conventional data well enough: after all, at the level of truth-conditions, it is obviously equivalent to the conventionally associated content. But certainly the structured contents ascribed by the permuted interpretation are also obviously truth-conditionally equivalent to the structured contents conventionally associated with the sentence, so fit equally well. Maybe matters are less obvious in the case of the skolemite interpretation, but it’s still necessarily and a priori equivalent. Given the needed flexibility in how to measure “fit”, it’s far from obvious we are on solid ground in insisting that the fine-grain content of thought must be the semantic content of the sentences. (There are moves one can make, of course: arguing that something fits better the closer the content assigned is to conventional content. But this is not obviously independently motivated, and as we’re about to see, won’t do all the work).

But the real killer is the following challenge:

  • Compositionally twisted interpretations. O’Leary-Hawthorne once asked Lewis to say what fixed the compositional rules that must be part of any compositional interpretation. One version of this challenge is as follows: the standard compositional rules say, for example, that if the semantic value of “a” is x, and the semantic value of “F” is the function f (at each world, mapping an object to a truth value), then the semantic value of the sentence “Fa” is the function that maps a world w to the True iff at w, f maps o to the True (or, if one wants a fine-grained content, then it is the structured proposition <f,a>). But a twisted rule might take the following disjunctive form: if “Fa” is a sentence that is tokened in the community, the semantic value of the whole is determined just as previously. But if “Fa” is never tokened, then its semantic value is a function that maps a world w to the False iff at w, f maps o to the true (respectively for fine-grained content: it is the structured proposition <neg(f),a>, where neg(f).

Now, the trouble here is that the standard and the twisted interpretation agree on all the datapoints. They can even agree on the fine-grained structured content associated with each sentence ever used. So they’ll fit and predict the sentential data equally well (remember: the language in use which provides the data is restricted to those sentences where there are actually existing regularities). The “constraining content” we inherit from the work we did on pinning down determinate thoughts is already exhausted by this stage: that at most constrains how our interpretation relates to the datapoints, but the projection beyond this to unused sentences is in the purview of the metaphysics of linguistic content alone. This “Kripkensteinian” underdetermination challenge will remain, even if we battle to relocate some of the others to the level of thought.

Something more is required. And if what determines best explanation is fit, strength and simplicity, it looks like simplicity must do the job.



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