One way to see this is to point out that when Alice tells Bob that everybody knows X, either Bob is asserting X because people act as if they don’t know X, or Bob does not know X. That’s why Alice is telling Bob in the first place.
It could also be that everybody (suitable quantification might be limited to: every student in this course/everyone at this party/every thinker on this site/every co-conspirator of our coup/etc) does in fact know X, but not everybody knows that everybody knows X. Depending on the circumstance of this being pointed out this can be part of creating common knowledge of X. This is related, but not identical to the fourth mode (of self-fulfilling prophecies) you describe. Consider the three statements:
X: “the king is wicked and his servants corrupt”
X’: everybody in our conspiracy knows X
X″: it’s common knowledge in our conspiracy that X
It’s clear that saying X’ can’t make X true as long as our conspiracy doesn’t leak information to the king or his servants. It’s also clear that saying X’ at a meeting of our whole conspiracy makes X″ true, and that this can be a useful tool for collective action. In fact if X’ is not quite true (some people have doubts) saying it can make it true (if our co-conspirators are modal logicians using something like the T axiom).
From a more individualistic view-point such a statement of this form could still contain information if Bob does not know that he knows X (consider Zizek’s description of ideology as unknown knowns).
What does the claim that ‘everybody knows’ mean?
I think you point to a valid type of problem with conspiracies of savvy and complicity, but mistakenly paint these as weapons asymmetrically favoring the forces of darkness. Perhaps the Common Knowledge framing makes it clearer, but the modes you describe are degenerate cases of tools for Justice:
The first central mode is ‘this is obviously true because social proof, so I don’t have to actually provide that social proof.’
The first mode attempts to look as deferral to experts on a question of fact. This often isn’t as useful as discussing the object level, but might be more effective and legible if used as basis for a decision if the statement about expert opinion is not a lie.
The second central mode of ‘everyone knows’ is when it means ‘if you do not know this, or you question it, you are stupid, ignorant and blameworthy.’
We need to be able to punish defection in a legible way so it doesn’t degenerate into blame games. For this we need common knowledge about these things so that people don’t have excuses for saying or acting along the lines of not-X, but it really needs to be common knowledge so that people don’t have excuses for not punishing defection on this point.
A third central mode is ‘if you do not know this (and, often, also claim everyone knows this), you do not count as part of everyone, and therefore are no one. If you wish to be someone, or to avoid becoming no one, know this.’
Restricting the universe over which you quantify can be really useful. In particular if you want to coordinate around a concrete project (like building Justice or a spaceship) it’s necessary to restrict your notion of ‘somebody’ to a set that only includes people willing and able to accept certain facts/norms as given.
The fourth central mode is ‘we are establishing this as true, and ideally as unquestionable, so pass that information along as something everyone knows.’ It’s aspirational, a self-fulfilling prophecy. [...]
As mentioned above the self-fulfilling nature can be subtle, but it’s not necessarily an ominous prophecy. It could be more along the lines of: “We all band together in accomplishing our goal, so we accomplish it and everyone who took part is greatly rewarded.”
So they’ll cross their fingers rather than demand fair dice. So that they’ll stop trying to fight the war.
Is often not just false, but backwards.
The reason you say “everyone knows Bob is a liar” isn’t always to protect Bob and blame the victims for being fooled. Sometimes it’s to punish Bob, by taking things from the “trial” phase to the “sentencing” phase. So long as “Bob is a liar!” is a thing that needs to be said/argued, Bob is still on trial. Once “everyone knows” Bob is a liar, you can start actually treating him like a liar and trust that people will coordinate with you instead of against you for trying to punish someone whose guilt hasn’t been established.
Things often do get stuck at the stage where (pretty much) everyone knows but no one moves on to doing something about it because they feel they need to keep asserting the thing instead of declaring that it’s worth taking as granted and moving on to dealing with it.
I agree that these are (sometimes) legitimate things to do, and that people often use the ‘everybody knows’ framing to do them implicitly. But I think that using this framing, rather than saying the thing more explicitly, is useful for those trying to do other things, and counter-productive for those trying to do the exact things you are describing, unless they also want to do other things.
It could also be that everybody (suitable quantification might be limited to: every student in this course/everyone at this party/every thinker on this site/every co-conspirator of our coup/etc) does in fact know X, but not everybody knows that everybody knows X. Depending on the circumstance of this being pointed out this can be part of creating common knowledge of X. This is related, but not identical to the fourth mode (of self-fulfilling prophecies) you describe. Consider the three statements:
X: “the king is wicked and his servants corrupt”
X’: everybody in our conspiracy knows X
X″: it’s common knowledge in our conspiracy that X
It’s clear that saying X’ can’t make X true as long as our conspiracy doesn’t leak information to the king or his servants. It’s also clear that saying X’ at a meeting of our whole conspiracy makes X″ true, and that this can be a useful tool for collective action. In fact if X’ is not quite true (some people have doubts) saying it can make it true (if our co-conspirators are modal logicians using something like the T axiom).
From a more individualistic view-point such a statement of this form could still contain information if Bob does not know that he knows X (consider Zizek’s description of ideology as unknown knowns).
I think you point to a valid type of problem with conspiracies of savvy and complicity, but mistakenly paint these as weapons asymmetrically favoring the forces of darkness. Perhaps the Common Knowledge framing makes it clearer, but the modes you describe are degenerate cases of tools for Justice:
The first mode attempts to look as deferral to experts on a question of fact. This often isn’t as useful as discussing the object level, but might be more effective and legible if used as basis for a decision if the statement about expert opinion is not a lie.
We need to be able to punish defection in a legible way so it doesn’t degenerate into blame games. For this we need common knowledge about these things so that people don’t have excuses for saying or acting along the lines of not-X, but it really needs to be common knowledge so that people don’t have excuses for not punishing defection on this point.
Restricting the universe over which you quantify can be really useful. In particular if you want to coordinate around a concrete project (like building Justice or a spaceship) it’s necessary to restrict your notion of ‘somebody’ to a set that only includes people willing and able to accept certain facts/norms as given.
As mentioned above the self-fulfilling nature can be subtle, but it’s not necessarily an ominous prophecy. It could be more along the lines of: “We all band together in accomplishing our goal, so we accomplish it and everyone who took part is greatly rewarded.”
Similarly, this:
Is often not just false, but backwards.
The reason you say “everyone knows Bob is a liar” isn’t always to protect Bob and blame the victims for being fooled. Sometimes it’s to punish Bob, by taking things from the “trial” phase to the “sentencing” phase. So long as “Bob is a liar!” is a thing that needs to be said/argued, Bob is still on trial. Once “everyone knows” Bob is a liar, you can start actually treating him like a liar and trust that people will coordinate with you instead of against you for trying to punish someone whose guilt hasn’t been established.
Things often do get stuck at the stage where (pretty much) everyone knows but no one moves on to doing something about it because they feel they need to keep asserting the thing instead of declaring that it’s worth taking as granted and moving on to dealing with it.
I agree that these are (sometimes) legitimate things to do, and that people often use the ‘everybody knows’ framing to do them implicitly. But I think that using this framing, rather than saying the thing more explicitly, is useful for those trying to do other things, and counter-productive for those trying to do the exact things you are describing, unless they also want to do other things.