So I’ve been spending time that I should be spending writing about disagreements about taste, fragmented belief, perception, and funny kinds of context dependence, thinking instead about a lyric from a Black Eyed Peas song (“Latin Girls”) that I was listening to while surfing the web writing about all of the very important topics that I ought to be writing about. Anyway, here’s the lyric:

“Girl, you know I know you know what I mean.”

And I started wondering (as one does):

(a) What’s the difference between the overall communicative effects of asserting,

(i) You know what I mean
and
(ii) You know I know you know what I mean

(b) Whatever the differences are, can you get an adding-to-common-knowledge view of assertion to predict them?

On (a): There do seem to be some, but I don’t feel like I’ve got my finger on what they are, exactly. They seem to be useful for either encouraging people not to engage in two different kinds of mock-ignorance, or else for giving people two different kinds of reasons for not engaging in the same kind of mock-ignorance. Or something like that.

On (b): Here’s the obvious reason to think not. On this sort of view, asserting either (i) or (ii) is going to add exactly the same stuff to common knowledge. You can’t make (i) common knowledge without making (ii) common knowledge, because as you iterate up the attitudes from (i), you’ll hit (ii), and then you keep going forever, just as you would if you’d started with (ii). And making (ii) common knowledge will also – given some pretty weak closure-under-dead-obvious-consequence conditions – make (i) common knowledge, on account of the factivity of knowledge. (Since you can’t know I know you know what I mean unless I know you know what I mean, and I can’t know you know what I mean unless you know what I mean. I’m sorry, that probably wasn’t the clearest way to say that, but it probably was the most fun way.)

A guess at what’s going on, due to Ben Blumson: The difference in effects is due to the fact that the upward iteration of attitudes probably does, in actual cases, stop after not too many steps.

Problem: Say just what the difference in effects of the two assertions is, and just which attitudes are bearing the load in explaining the effects in the two cases.