This post came out of a conversation I had with Andy Egan and Gillian Russell the other day, and then similar topics came up in Ryan Muldoon’s comments on Ed Epsen’s paper the next day at FEW. I don’t remember exactly how the topic came up, but we were trying to figure out whether silences can carry implicatures, or more ordinarily, whether you can say something without words. And of course the answer is yes:
Q: “What do you like about John?”
This one works almost exactly like Grice’s recommendation letter example in “Logic and Conversation”. (By the way, anyone who hasn’t read this paper really should. I think the notion of implicature is one of the most significant advances philosophy has made in our understanding of the world. The paper is widely reprinted, but unfortunately not available online – there’s a two-page excerpt here.) Based on the conversational context, A is expected to make a contribution to the conversation mentioning some positive fact about John. A’s silence violates the maxim of quantity (she hasn’t said as much as is expected), so Q can infer that some other conversational principle (one requiring politeness) must conflict with anything that A would be in a position to say. Therefore, Q comes to believe that there is nothing (or at least nothing relevant) about John that A likes.
But then I realized that we should think about this (and perhaps the original recommendation letter example) a bit more carefully. It seems that the story given above could work in at least two different ways. In one case, A is struggling for an answer, and the silence just comes about because she can’t think of anything she likes about John. In the second case, A knows there is nothing she likes about John and remains actively silent. I think the second case is an example of an implicature carried by a silence, but the first is not.
The explanation of the distinction comes from Grice’s earlier classic paper, “Meaning” in which he suggests that speaker A means y by utterance x iff “A intended the utterance of x to produce some effect [y] in an audience by means of recognition of this intention.” He comes to this recursive intention account of meaning by way of a bunch of examples, which I think parallel the situation here. If I don’t intend you to believe (or consider) something by means of my action, then I didn’t mean it, even if it’s true. Thus, my silence can reveal my dislike for John, just as an accidentally dropped photograph can reveal where I was the other day, but neither means it. But even just performing the action intentionally isn’t enough – Grice suggests that showing someone a photograph doesn’t constitute a meaning of what is depicted, because my intention plays only an unnecessary role in the observer’s coming to believe the truth of what is depicted.
However, showing someone a drawing can constitute a meaning, since the person has to recognize the intention of the person who made the drawing in order to come to believe in the truth of what is depicted (assuming that this was in fact the intent of the drawer). One reason for this distinction that Grice doesn’t discuss in that paper is that only a recursive intention like this can help the speaker and hearer achieve “common knowledge” of the content of the proposition. (That is, not only do you know p, but I know you know p, and you know I know you know p, and …) If the utterance succeeds, then the listener believes that p. But in addition, the listener believes that the utterer intended her to believe that p, so the listener can believe that the listener believes that the utterer now believes that p. But the listener believes that the utterer intended her to believe this, and the cycle can repeat, generating common knowledge. Common knowledge is important in a lot of acts of communication, and a simple, non-recursive, intention can’t generate it.
So for a silence to really implicate (in Grice’s “speaker meaning” sense) something, it has to be intentionally given, and its meaning must be intentional as well, and so on. This makes it much harder than I initially thought for a silence to mean something, but a slighty specification of the original example can fix it.
(Ed’s paper was on zero-knowledge signalling in games of imperfect information, and Ryan pointed out that in Ed’s particular example, one player comes to know that the other player knows some fact, but not because the other player intended her to come to know this. However, it seems that a slightly modified version of the example will put the Gricean condition back in. It was quite an interesting application of the zero-knowledge proof literature in computer science to game theory.)