The Fear of Common Knowledge

Fol­lowup to: Belief in Belief

One of those in­sights that made me sit up­right and say “Aha!” From The Un­cred­ible Hallq:

Minor acts of dishon­esty are in­te­gral to hu­man life, rang­ing from how we deal with ca­sual ac­quain­tances to writ­ing for­mal agree­ments be­tween na­tion states. Steven Pinker has an ex­cel­lent chap­ter on this in The Stuff of Thought, a ver­sion of which can be found at TIME mag­a­z­ine’s web­site. What didn’t make it into the TIME ver­sion is Pinker’s pro­posal that, while there are sev­eral rea­sons we do this, the most im­por­tant rea­son is to avoid mu­tual knowl­edge: “She prob­a­bly knows I just blew a pass at her, but does she know I know she knows? Does she know I know she knows I know she knows?” Etc. Mu­tual knowl­edge is that night­mare where, for all in­tents and pur­poses, the known-knows can be ex­tended out to in­finity. The ul­ti­mate ex­am­ple of this has to be the joke “No, it wasn’t awk­ward un­til you said, ‘well, this is awk­ward.’” A situ­a­tion might be a lit­tle awk­ward, but what’s re­ally awk­ward is mu­tual knowl­edge, cre­ated when some­one blurts out what’s go­ing on for all to hear...

The story of the Em­peror’s New Clothes is an­other ex­am­ple of the power of mu­tual knowl­edge...

The power of real de­cep­tion—out­right lies—is easy for even us nerds to un­der­stand.

The no­tion of a lie that the other per­son knows is a lie, seems very odd at first. Up un­til I read the Hallq’s ex­pla­na­tion of Pinker, I had thought in terms of peo­ple sup­press­ing un­com­fortable thoughts: “If it isn’t said out loud, I don’t have to deal with it.”

Like the friends of a ter­mi­nal pa­tient, whose dis­ease has pro­gressed to a stage that—if you look it up on­line—turns out to be nearly uni­ver­sally fatal. So the friends gather around, and wish the pa­tient best hopes for their med­i­cal treat­ment. No one says, “Well, we all know you’re go­ing to die; and now it’s too late for you to get life in­surance and sign up for cry­on­ics. I hope it isn’t too painful; let me know if you want me to smug­gle you a heroin over­dose.”

So even that is pos­si­ble for a nerd to un­der­stand—in terms of, as Vas­sar puts it, think­ing of non-nerds as defec­tive nerds...

But the no­tion of a lie that the other per­son knows is a lie, but they aren’t sure that you know they know it’s a lie, and so the so­cial situ­a­tion oc­cu­pies a differ­ent state from com­mon knowl­edge...

I think that’s the clos­est I’ve ever seen life get to imi­tat­ing a Ray­mond Smul­lyan logic puz­zle.

Added: Richard quotes Nagel on a fur­ther pur­pose of mu­tual hypocrisy: pre­vent­ing an is­sue from ris­ing to the level where it must be pub­li­cly ac­knowl­edged and dealt with, be­cause com­mon ground on that is­sue is not eas­ily available.