Wolfgang Schwarz

Lewis on Indeterminacy and Meaning Constraints

It is widely assumed that Lewis takes the objective naturalness of semantic values to be an important constraint on semantics, needed to prevent radical indeterminacy of meaning. On rereading some of his remarks today, I found them a little confusing, and now I think the situation is far more complicated.

Lewis discusses Putnam's model theoretic argument for radical indeterminacy extensively in "New work for a theory of universals" (NW) and "Putnam's paradox" (PP). In both papers, he says there is something wrong with posing the problem as a problem about language, because in fact the interpretation of language is settled by the assignment of content to propositional attitudes (NW 49, PP 58f.). But, he says, focussing on attitudes only relocates the problem without solving it, so that he might as well talk about language in the rest of PP, which he does. He points at NW for a discussion of the properly relocated problem.

The relocated problem is the problem of indeterminacy in the attribution of content to beliefs and desires. On Lewis's view, such attributions are largely governed by folk-psychological rationality constraints: the correct attribution of content is one that makes sense of the subject's behaviour. Many of these rationality constraints are causal, linking mental states to other mental states, or to external causes and effects: "If a state is to be interpreted as an intention to raise one's hand, it had better typically cause the hand to go up [...]. A state typically caused by round things before the eyes is a good candidate for interpretation as the visual experience of confronting something round" (NW 50, for more on this see e.g. "Veridical hallucination and prosthetic vision" and §2 of "Naming the colours"). However, in NW (51) Lewis argues that these constraints do not suffice to determine content. He shows that on a simplified model, quite different assignments of content are compatible with the same actual input (observations) and output (behaviour). So we need additional constraints, which he calls 'principles of charity'. Some of these involve naturalness: they say we should prefer attribution of objectively natural over less natural content: "The principles of charity impute a bias toward believing that things are green rather than grue" (NW 52). Not all principles of charity refer to objective naturalness, though: "They will impute other things as well, but it is the imputed eligibility that matters to us at present" (ibid). For instance, elsewhere he argues for a principle ruling out a basic desire for a saucer of mud (see e.g. "Radical interpretation" and On the plurality of worlds, 38f.).

If on Lewis's view this is the real problem of indeterminacy (and its solution), a couple of things deserve to be emphasized.

First, this problem has nothing to do with the assignment of semantic values to sentences or constituents of sentences. Lewis is not trying to give a semantics for the language of thought, for he believes it is an open empirical question whether there is a language of thought, whereas it is not an open empirical question whether we have beliefs and desires. Words and sentences don't enter into the picture at all. In particular, we aren't told that terms and predicates should be assigned fairly natural semantic values. We're only told that propositional attitudes should be assigned natural semantic values. Moreover, recall that Lewis doesn't even believe that agents with beliefs and desires necessarily have distinct states corresponding to distinct beliefs and desires ("Reduction of mind", 310f.). So the constraint is ultimately on the assignment of content to a subject's total belief state or total desire state.

Second, note the abundance of causal constraints on correct interpretations. One might have thought from Lewis's remarks on the non-relocated problem, e.g. in PP, that he generally rejects causal constraints to solve the indeterminacy problem, and that the only external constraint he endorses is objective naturalness. Not so for the relocated problem -- which is the genuine problem on Lewis's view. Here, naturalness is only one of many constraints, and a lot of the other constraints are causal. (Note also that the alternative to external causal constraints, causal descriptivism, is not even an option here: causal descriptivism is a thesis about the reference of terms, but we're currently not talking about terms at all.)

Third, is there really a problem of radical indeterminacy here? To repeat, Lewis's only argument is that on a simplified model of rationality constraints, different assignments of content equally rationalize the subject's actual behaviour. The difference between these assignments always concerns the credence (or value) assigned to somewhat remote possibilities. But if we remove the simplifications, and in particular (a 'simplification' Lewis doesn't mention) also take into account other actual and possible people who are in the same state, it isn't obvious that much indeterminacy remains. (See again "Reduction of mind" and "Mad pain and martian pain" for why counterfactual people must be taken into account). Surely in some possible individuals the difference between taking grass to be green and taking it to be grue shows up. Even if there remains some indeterminacy -- perhaps between intentions to add and intentions to quadd, where quaddition differs from addition only for very large numbers -- it is nothing like the radical indeterminacy Putnam argued for.

Let's return to language and the non-relocated problem. From PP, one gets the impression that Lewis's theory of language is something like Global Descriptivism together with a constraint on naturalness of semantic values. More precisely, let T be our total theory of the world, expressed in our language. The correct interpretation of T then is the one that does best on 1) making large chunks of T true and 2) assigning natural referents to the terms in T (PP 65f.). But I think that's not Lewis's theory of language at all. Besides, it seems to give the wrong results. Suppose our theory is completely wrong about many things, perhaps because we're brains in vats. Then couldn't it happen that there is some deviant interpretation of the terms in our theory that fares better on the two criteria than the correct interpretation? Indeed, mightn't we be brains in vats living in a world that contains natural elements (things and properties) such that if our words are reinterpreted so as to refer to those elements, our theory comes out entirely true? That would still be a misinterpretation, even though it does much better on both criteria than the correct one.

(Yes I know, some people claim that if it did turn out we are brains in vats, our opinions about the world would nevertheless be true. I find that quite incredible, and I think those people are either misguided by a false theory of reference or by a futile attempt to fend off skepticism. If I were to wake up tomorrow in a strange world and somehow discover that until now I've been a brain in a vat, I would conclude that virtually all my previous beliefs about me and the world had been wrong. Wouldn't you?)

Anyway, Lewis's own theory of language looks quite different: the correct interpretation of a language is part of the best systematic account of the linguistic conventions prevailing in the relevant community. These conventions (for assertions anyway) are conventions to utter a sentence only when it is true and to take other peoples's utterance as true. The basic task for semantics in this picture is to specify which sentences are true in which contexts, so that the conventions can be explained as conventions to utter sentences only in a matching context and to infer from an utterance that it took place in a matching context. (That's simplified in some respects, but it will do for present purposes.)

Conventions themselves are based on beliefs and desires in the community: A convention to utter S only in such-and-such situations requires that the members of the community believe that all of them are committed to uttering S only in such-and-such situations. That's how the attitudes of persons fix the semantic values of their sentences. And that's why Lewis said that the indeterminacy problem should be relocated to attitudes: once these are determined, the interpretation of public language is determined as well (PP 58f.).

But that's not entirely true. The linguistic conventions only settle the semantic values of sentences. They are silent on the values of smaller constituents (see e.g. "Languages and language", 177). If two languages agree on the truth conditions of all sentences while disagreeing on the reference of constituents, any convention of truthfulness and trust in the one will also be a convention of truthfulness and trust in the other.

So here we have second problem of indeterminacy: how to determine the semantic values of sentence constituents. This one is a genuinely linguistic problem. Moreover, it looks in many ways more like Putnam's original problem. Putnam too argues that many very different assignments of reference to constituents can give rise to exactly the same truth conditions for sentences. -- On the other hand, the main point of Putnam's argument is that reinterpretation can make almost any false theory true, where in this case the reinterpretation obviously changes the truth conditions of sentences. For Lewis, there is no problem of distinguishing between true and false sentences or theories: An utterance of a sentence is true if the context of utterance is contained in the conventionally established semantic value of the sentence. So we don't need to solve the indeterminacy problem in order to save anything that might reasonably be called realism.

We only need to solve the second indeterminacy problem because perhaps it seems obvious that the semantic values of our terms are not completely indeterminate. This time, objective naturalness seems to be an adequate solution: the correct grammar (in Lewis's sense of an interpreted grammar) is the most natural grammar among those that conform to the truth-conditions determined by convention. A grammar is natural insofar as the entities it assigns as semantic values to constituents are natural, and insofar as its compositional rules are straight and simple. Perhaps this is what Lewis tries to defend in "Meaning without use", though his emphasis there is on straight versus bent compositional rules.

This time it also makes sense to decide between external causal constraints and causal descriptivism. Invoking external causal constraints would mean to postulate that the correct grammar is one that assigns to all (?) terms things that stand in appropriate causal relations to tokens of the terms. On the other hand, a causal descriptivist would turn this requirement into "just more theory": the correct grammar ought to make the true sentences true, and as it happens some of these true sentences say that certain terms denote certain causal ancestors of their tokens.

(By the way, I've read complaints that Lewis's solution doesn't work because we can always find deviant interpretations that assign an equally natural referent to a given term as the correct interpretation. That's true but irrelevant. What must be shown is that the deviant interpretation is also at least as natural both in what it assigns to all other expressions and in its compositional rules. It's not clear that the examples I've seen show this.)

Two final remarks on the second problem. First, as far as I can see Lewis doesn't offer any good arguments for why the naturalness constraints used here can't be based on some psychological kind of naturalness. He says in "Meaning without use" (151) that it would be circular to define naturalness (or the difference between 'straight' and 'bent' rules) in terms of short expressibility in our language. "Likewise, mutatis mutandis," he continues, it would be circular "if we must rely on the bent-straight distinction still earlier to reach an analysis of the content of thought". I'm not sure what he means by that. In NW (54) he argues that we can't say that naturalness is somehow determined by the content of our mental states -- e.g. by what we are interested in --, as this would presuppose getting at that content without using naturalness. Perhaps that's what he alludes to in the quoted remark. If so, and if Lewis is right that objective naturalness is required to determine mental content, it still doesn't follow that eligible grammars are in any direct way related to objective naturalness, e.g. to the objective naturalness of their referents. Suppose the scale of naturalness relevant for grammars is determined by what we find natural, or what we are interested in. Then it can easily happen that a candidate referent is more eligible but less objectively natural than an alternative.

Finally, how bad is the second kind of indeterminacy? Is it a Moorean fact that there is one true grammar for our language? I doubt it. I think we ought to distinguish between a grammar and an analysis of our everyday semantic idiom. It is a sort of Moorean fact that "Kripke" denotes Kripke and not, say, a cat, or a certain function from worlds to individuals. But that doesn't really matter for semantics. If our best, systematic grammar assigns some cat or function as semantic value to "Kripke", it only follows that we shouldn't use "denotation", or "reference" when we mean that semantic value. I'm sure that "Kripke" denotes Kripke. But I'm not sure the semantic value of "Kripke" is Kripke. Rather, I'm inclined to say that there is no such thing as the semantic value of "Kripke". What semantic value you choose depends on your semantic project, and if several projects work equally well, I don't mind calling all their values for "Kripke" semantic values. In this case there isn't really any second problem of indeterminacy.

(In "Meaning without use", Lewis needs the constraints on grammars not to save the intuition that there is one true grammar but because he needs further constraints on truth conditions. For he argues that the truth conditions of very complicated sentences are not determined by convention. But to deal with this problem, we presumably only need constraints on compositional rules, not on basic semantic values -- which explains why Lewis focuses on rules in the paper.)