I know that he knows that I know that he knows


Not sure if this is the right place for this question but here goes...

Some time in the past I've stumbled upon some site/article/post/etc that discussed the issue of 2 parties having (or not) some information and being aware of the other party knowing it. Something like:

A: knows X

B: knows that A knows X

A: knows that B knows that A knows X

and so on...

Now in the source I've seen there was a statement that with enough of those "cycles" (like 4 or 5 maybe?) both parties have like a perfect knowledge of the situation - they know and they're aware that the other party knows and so on... So this doesn't (need to) go infinitely, at some point everyone is aware of everything. Apparently, it's a known problem and there's already been some work/reasoning devoted to it.

Unfortunately, I wasn't able to find anything on the internet that concerned this topic and I'm curious. So my question is: has anyone ever heard about something like this? Does this problem have an established name? Can you point me to any articles/sources of information? I'd appreciate it.


Posted 2020-04-19T13:54:36.683

Reputation: 101

1I don't understand what's being asked. You speak of a 'known problem', but what is the problem? This might be just me. – None – 2020-04-19T14:47:47.460

The huge problem with the term [know] is that the Tarski undefinability theorem "proved" that no criterion measure of truth can possibly exist therefore any [knowledge] can't possibly be more than presumption. – polcott – 2020-04-19T15:17:57.983


That sounds a bit like the traditional definition of 'common knowledge'. Maybe that's what you're looking for? See here: https://plato.stanford.edu/entries/common-knowledge/.

– Eliran – 2020-04-19T17:03:12.000

The key thing here is defining what [know] means. Before you do that the whole question is not anchored. In my not at all humble opinion none of philosophy has sufficiently addressed that issue at all. – polcott – 2020-04-19T19:29:41.520

Could you link or reference the source that you've seen, it is hard to tell what the problem is without context. They might have in mind some version of blue eyes exile puzzle.

– Conifold – 2020-04-20T06:53:24.530

@Eliran "Common knowledge" and "mutual knowledge" definitely belong to the area I'm interested in. It's not the exact problem/theorem/etc in that area that I had in mind but at least you pointed me in the right direction. – NPS – 2020-04-20T12:40:26.057

@PeterJ, Conifold I don't know the name of the problem and I don't have a link do the source I've seen and that's the point - if I did, I wouldn't have asked this question. I was hoping that someone here might be able to point me in the right direction. – NPS – 2020-04-20T12:42:20.640

@NPS - What I meant was that I don't see a problem, not that I don't know its name. You describe a situation, but where's the problem? – None – 2020-04-20T18:32:56.900

No answers