Common knowledge

Language is based on common knowledge. This is true in a trivial sense: If I say

Cats are mammals.

Your ability to interpret that sentence relies on our common knowledge that the word cat refers to a furry domestic animal that meows. Likewise, I only believe that the sentence will be successful in communicating with you based on my belief that you know what a cat is. 

Common knowledge and inference

Language requires common knowledge in a much more subtle way as well. Suppose I say:

I am going to Paris tomorrow.

Your ability to interpret this sentence correctly depends on your being able to correctly assign meaning to tomorrow. Consider the fact that the sentence means different things spoken on different days. For us to successfully communicate about tomorrow, we must have interpreted it the same way and know that we have interpreted it the same way.

Notice that the word I and even the word Paris has the same problem.

It actually gets worse, since some communication requires the even more stringent concept mutual knowledge. Suppose I ask my wife if she has fed the cats today. Technically, she could response "yes" as long as she has fed at least two cats today. But of course, I am asking whether she fed our cats. I assume she will understand that's what I mean. 

Now suppose she just answers "yes." For me to interpret this as meaning she fed our cats, I have to assume she knows that I was referring to our cats. Of course, for her to be confident that I will correctly interpret her response, she has to assume I assume that she assumes that I originally asked about her feeding our cats.

And so on.

Certain knowledge?

In their highly influential book Relevance, Sperber and Wilson argue that common knowledge cannot exist (actually, they talk about "mutual knowledge," which is something slightly different, but the differences aren't important here):

"Mutual knowledge must be certain, or else it does not exist; and since it can never be certain it can never exist." (p. 20)

Why do they think mutual knowledge can never be certain? Because, in a philosophical sense, it is true. I can never be certain my wife knows I'm talking about our cats. And she can't be certain that I am referring to our cats. Probabilities get multiplied. So if confident is always 90%, my confidence that she knows that I know that she knows that I know that she knows I'm referring to our cats is only 53%. 

Sperber and Wilson use a much-expanded version of this argument to claim that mutual knowledge just doesn't exist and can't play a role in language, beyond perhaps giving the basic meaning of basic words like cat.

Are we certain philosophers?

A potential problem with their argument is that they assume people are only certain when certainty is justified. This is clearly not the case.

In recent talks, Steven Pinker has presented evidence that, at least in some circumstances, people really do act as if they believe in mutual knowledge. Pinker is interested indirect speech, so his study involved innuendo. Suppose John says to Mary, "Would you like to come up to my apartment for a nightcap."

How certain are you that John is proposing sex? Most people are fairly certain. 

How certain are you that Mary knows that John is proposing sex? Most people are a little less certain. 

How certain are you that John knows Mary knows John is proposing sex? Certainty drops again.

etc.

Now, change the scenario. What if John is particularly crass and says to Mary, "How would you like to go back to my apartment and have sex?"

How certain are you that John is proposing sex? That Mary knows John is proposing sex? That John knows that Mary knows that John is proposing sex? Most people remain certain no matter how far out the question is extended.

Notice that, at least in theory, Sperber & Wilson's argument should have applied. Nobody should be completely certain. Mary could have misheard. John might have a really odd idiolect. But people don't seem to be phased.

Does mutual knowledge exist?

Well, at least sometimes. But I'm not completely sure how this affects Sperber & Wilson's argument. They weren't talking just about indirect speech, but about a much broader range of phenomena. They were arguing against theories that invoke mutual knowledge right and left, so it still remains to be seen whether mutual knowledge is such a pervasive phenomenon.