This is a fascinating topic! I wonder though if Richard is right, whether the issue is not (just) common knowledge. It’s confusing, because the usual way of ensuring that something is common knowledge is for someone to state it publicly. However it can be argued that this does more than merely making it common knowledge, in that it is a provocative action which demands a response.
In particular, in situations where there is a known but unacknowledged fact, is that fact actually common knowledge, or not? Everyone knows the fact, and everyone knows that everyone else knows the fact, but is there some point in the recursion where knowledge peters out? Would it be false that everyone knows that everyone knows that everyone knows that everyone knows the fact? Is there a “doubt amplification” effect where even the smallest doubt that everyone else really does know the fact, gets amplified as we proceed down the recursive chain, until when we go deep enough, we really don’t know whether everyone else knows they all know it, to the nth degree?
Or OTOH would it be more correct to say that everyone knows that everyone knows… as far as you want to go, that the fact is truly common knowledge, yet it is still unacknowledged. And then as Richard quotes from Nagel, the problem is taking the next step and discussing it openly.
This is a fascinating topic! I wonder though if Richard is right, whether the issue is not (just) common knowledge. It’s confusing, because the usual way of ensuring that something is common knowledge is for someone to state it publicly. However it can be argued that this does more than merely making it common knowledge, in that it is a provocative action which demands a response.
In particular, in situations where there is a known but unacknowledged fact, is that fact actually common knowledge, or not? Everyone knows the fact, and everyone knows that everyone else knows the fact, but is there some point in the recursion where knowledge peters out? Would it be false that everyone knows that everyone knows that everyone knows that everyone knows the fact? Is there a “doubt amplification” effect where even the smallest doubt that everyone else really does know the fact, gets amplified as we proceed down the recursive chain, until when we go deep enough, we really don’t know whether everyone else knows they all know it, to the nth degree?
Or OTOH would it be more correct to say that everyone knows that everyone knows… as far as you want to go, that the fact is truly common knowledge, yet it is still unacknowledged. And then as Richard quotes from Nagel, the problem is taking the next step and discussing it openly.