Wolfgang Schwarz

Pragmatic intrusion, validity, and compositional pragmatics

Sometimes, implicatures appear to survive under embedding. Take

1) the column will fail and the bridge will collapse,

which in a suitable context implicates that (the speaker believes that) the bridge will collapse as a result of the column failing. This implicature is still present if (1) gets embedded in, say, a conditional:

2) if it rains, the column will fail and the bridge will collapse;

3) if the column will fail and the bridge will collapse, you'll be in trouble.

(2) is likely to convey that if it rains, the bridge will collapse as a result of the column failing, and (3) that if the bridge will collapse as a result of the column failing, then you'll be trouble.

This is annoying. On a Gricean account, implicatures are derived from acts of assertion, and you don't assert (1) by uttering (2) or (3). So the Gricean story cannot explain this phenomenon. (Or so it seems.)

Jeffrey King and Jason Stanley (PDF) argue that the phenomenon is an illusion. For example, they explain away (3) by a closest worlds account of the conditional: the epistemically closest worlds where the column fails and the bridge collapses are presumably worlds where the collapse is due to the failure. That's why in a suitable context, the antecedent in (3) is equivalent to the stronger claim involving a causal connection.

There's a lot to be said for this view. After all, many implicatures (even generalized ones) do not survive under embedding: an embedded disjunction "A or B" can usually not be replaced by "A or B and the speaker doesn't know which". Moreover, the best candidates for embedding are often doubtful candidates for implicature in the first place, like scalar implicatures involving numbers (see Jonathan Horn, "The said and the unsaid"). Nevertheless, there are too many plausible candidates left, and I'm afraid the King and Stanley strategy of individual patches will not always work.

(The implicatures that survive under embedding seem to be mostly generalized implicatures generated by something like the maxim of manner, where the implicature depends not only on the content of the utterance, but also on how it is expressed: (1) is of this kind, as are inferences from metaphors and irony, as are those from "there's a flying object in the backyard" to "there's a flying non-bird in the backyard", and from "some" to "not all". For example, replacing "some" by the semantically equivalent "some or all" destroys the some-to-not-all implicature. By contrast, as Grice notes, the non-manner inference from "he has been visiting NY a lot lately" to "he has a girlfriend there" does not survive under embedding: you can't deny the latter by denying the former. Manner implicatures are special anyway, as here what is implicated is not inferred from what is said together with the assumption that the speaker cooperates.)

Let's assume King and Stanley are wrong and the phenomenon exists. The most common approach then says that under embedding, the relevant implicatures become part of semantic content. (Francois Recanati (PDF) discusses various such moves in linguistics, Mitchell Green (PDF) mentions approval in philosophy.) This is also Grice's own conclusion, most explicit in his 1989 "Retrospective Epilogue", p.375:

The denial of a conditional needs to be treated as denying not the conventional import but the standard implicatum attaching to an isolated use of the embedded sentence. It certainly does not seem reasonable to subscribe to an absolute ban on the possibility that an embedding locution may govern the standard nonconventional implicatum rather than the conventional import of the embedded sentence.

I don't like this solution either. One problem is that even under embedding, the implicature still seems to be an implicature, just as it is outside the embedding. Thus one can cancel the implicature in (2) by saying

2') if it rains, the column will fail and the bridge will collapse; but it won't collapse because of the failing column: the column is actually redundant. It's just so that rain will destroy both the redundant column and the non-redundant arches.

Another problem is that on this view, lots of valid inference patterns would be invalid, including Double Negation Introduction (A |= ~~A), Disjunction Introduction (A |= A v B), Conjunction Introduction (A, B |= A & B), and Modus Ponens (A, A -> B |= B). As for Negation Introduction, consider

4) it's not true that it's not the case that the column will fail and the bridge collapse.

This is the double negation of (1), and an argument from (1) to (4) seems clearly valid. But it is invalid if (4) expresses the negation of the negation not of (1), but of (1) together with what is merely implicated by (1).

As for Modus Ponens, consider

3) if the column will fail and the bridge will collapse, you'll be in trouble;
5) the column will fail and the bridge will collapse;
therefore, 6) you'll be in trouble.

This, too, looks like a valid argument, but it would be an equivocation if the antecedent of (3) expresses not just what (5) expresses, but in addition what (5) merely implicates.

(By the way, this shows that there is also something wrong with King and Stanley's account of (3). What is wrong depends on whether in the analysis of the conditional, the actual world always counts as closest, even if it is ruled out in the conversational context (or by the speaker's beliefs). Suppose it is always closest. Then on the King and Stanley account, given the mere truth of (5), (3) is not equivalent to "if the column will fail and the bridge will collapse as a result, you'll be in trouble" -- which leaves it unexplained why we naturally interpret it this way. On the other hand, if the actual world does not automatically count as closest, then the alleged pragmatic intrusion can be explained away, but Modus Ponens becomes invalid. Either consequence is pretty bad.)

It's interesting to see what happens when the implicature in (5) is canceled:

3) if the column will fail and the bridge will collapse, you'll be in trouble;
5) the column will fail and the bridge will collapse;
7) but the two events will be causally unrelated;
therefore, 6) you'll be in trouble.

This inference is intuitively less compelling than the previous one. But if validity means anything like "it's impossible for the premises to be true and the conclusion false" -- which I hereby stipulate --, then the validity of an argument cannot be destroyed by adding further premisses: if it's impossible that A, B, ~C are all true, then it can't be possible that A, B, D, ~C are all true. So if the second argument is invalid, then so is the first. This might be taken to undermine the validity of (the English counterpart of) Modus Ponens. I think this is clearly the wrong conclusion. The right thing to say is that the second argument is valid, like

8) I ate all the cake;
therefore, 9) I ate some of the cake,

which also might appear to be invalid because the conclusion, unlike the premise, implicates that I didn't eat all the cake.

So I don't like the standard semantic treatment of pragmatic intrusion. Here's a (rather obvious) alternative: the implicature of a complex sentence depends not only on the semantic content of the embedded sentences, but also on what they implicate. That is, there is a kind of compositional pragmatics alongside compositional semantics. The rules of compositional pragmatics are simple. Let the pragmatic content of a sentence (in a context) be what the sentence conveys in virtue of its semantic content and the kind of implicature that survives embedding (if it is present in the relevant context). Thus the pragmatic content of (1), "the column will fail and the bridge will collapse" is normally that the column will fail and the bridge will collapse as a result of the failing. Thinking of contents as sets of possibilities, the pragmatic content of expressions can be recursively defined as follows:

• the pragmatic content of an expression A that doesn't embed another sentence is the union of the semantic content of A and those implicatures of A that survive embedding;
• the pragmatic content of a conjunction A & B is the intersection of the pragmatic content of A and the pragmatic content of B;
• in general, whenever the semantic content of a complex sentence K(A,B,...) results from the semantic contents of A,B,... by a function f, then so does the pragmatic content of K(A,B,...) result from the pragmatic contents of A,B,.... by f.

Applications:

The pragmatic content of ~(1),

10) it is not the case that the column will fail and the bridge will collapse

rules out those possibilities in which the bridge collapses as a result of the columns failure. In this case, the pragmatic content is strictly weaker than the semantic content. To 'cancel' the difference, we have to add more information that rules out worlds where the column fails and the bridge collapses for some other reason. Since this canceling looks the same as simply saying more, such cases can't help distinguish between this approach and the standard one. The same holds for

3) if the column will fail and the bridge will collapse, you'll be in trouble.

The two accounts come apart for 'positive' embeddings, like

11) either the weather will be fine, or the column will fail and the bridge will collapse

and

2) if it rains, the column will fail and the bridge will collapse.

For (11), the compositional pragmatics account predicts that the semantic content rules out possibilities where the weather is bad and yet the column doesn't fail or the bridge doesn't collapse, but what is pragmatically conveyed (in a suitable context) also rules out worlds where the weather is bad and the bridge collapses for reasons other than the failed column. This seems right. Moreover, this implicature can be canceled, by saying something like

12) The column doesn't actually support the bridge; but if it rains, not only will the column dissolve, but also the arches will be washed away, bringing down the bridge.

The semantic content of (2) depends on the interpretation of the conditional. But in any case, the pragmatic account predicts that the sentence will typically convey the same as

13) if it rains, the column will fail and the bridge will collapse as a result of that,

and that again, the implicature can be canceled by uttering (12). This, too, seems right. Next, let's negate (11):

14) It's not true that either the weather will be fine, or the column will fail and the bridge will collapse.

Semantically, this is true iff the weather will be bad and the column either won't fail or the bridge won't collapse. But now some implicatures of "or" also become embedded, especially the exclusiveness. The complement of (A xor B) is ((A & B) v (~A & ~B)). This is why, intuitively, you don't commit yourself to the weather being bad by saying (14). Like with (10), the pragmatic content of (14) is weaker in this respect than its semantic content. (Compare Grice's "it's not the case that if God exists, human life is a product of chance", which is true on his account of conditionals only if God exists. But intuitively, you're not committed to God's existence by saying this. The present explanation covers this as well, given that "if" often implicates "iff".)

I've so far ignored the deeply embedded conjunction in (14). Suppose we 'cancel' the exclusive implicature of the "or", say, by adding "so neither of these is the case" after (14). Then the remaining implicature from the conjunction again weakens what is conveyed: what is conveyed is that the weather will be bad and the bridge will not collapse due to the column failing. This, too, can be 'canceled' by adding further information to the effect that it will not be the case that the bridge collapses and the column fails anyway.

Finally:

15) either it rains heavily and the bridge gets wet, or it's not true that the column will fail and the bridge will collapse.

Here the predicted pragmatic content is neither weaker nor stronger than the semantic content: the two contents only overlap. The semantic content contains all worlds where it rains heavily and the bridge gets wet (not necessarily due to the rain) and all worlds where the column doesn't fail and all worlds where the bridge doesn't collapse. For simplicity, ignore the implicatures that come with "or". Then the pragmatic content of (15) contains all worlds where it rains heavily and the bridge gets wet as a result and all worlds where the bridge doesn't collapse due to the column failing. So in a suitable context, only the pragmatic content rules out worlds where it rains heavily, the bridge gets wet for some other reason and collapses due to the column failing. (Imagine, if needed, that the column is especially sensitive to a lot of water coming from above.) And only the semantic content rules out worlds where it doesn't rain heavily, the column fails and the bridge collapses, but for a reason other than the failing column. Again, this weakening of pragmatic content can be 'canceled' by simply giving further information, whereas the strengthening of the pragmatic content with respect to the rain can be canceled by saying that the bridge will collapse anyway if it gets wet, no matter if it's due to rain.

So all in all, the compositional pragmatics account seems to fit the data reasonably well. Though admittedly, adding compositional pragmatics to compositional semantics is not very satisfactory.

Why do I call pragmatic content "pragmatic" and semantic content "semantic"? Isn't what I call pragmatic content just what the others call semantic content? In a sense, yes. But there are good reasons for having my semantic content as well, and for calling it semantic. One is that what pragmatic content adds to (or subtracts from, or both) semantic content can be canceled, just like implicatures of unembedded sentences. Another reason is that, again like implicatures, the pragmatic content only arises in suitable contexts. A third advantage is that the pragmatic account preserves the validity of classical, and intuitively valid, inference patterns.

Is what I call semantic content really what is intuitively said? Probably not. But intuitions about what is said are always distorted by pragmatics (see e.g. Gibbs & Moise, "Pragmatics in understanding what is said" (PDF)). So that's not a problem.