Do you have a dumb question that you're kind of embarrassed to ask in the main thread? Is there something you're just not sure about?
This is your opportunity to ask questions. No question too simple or too silly.
Culture war topics are accepted, and proposals for a better intro post are appreciated.
Jump in the discussion.
No email address required.
Notes -
My Grandpa used to chew tobacco in secret. Officially, this was not okay behavior. He wanted to do it, Grandma disapproved, so he "wasn't allowed to". Partly because it was bad for his health, partly because it's gross. So, not wanting to cause trouble, he pretended to quit, and then went off and did it in secret.
Obviously, Grandpa knows that grandpa chews tobacco. Let's call this level 1 knowledge. Knowledge of the object level fact itself.
He thought he was being sneaky about it, but he wasn't all that sneaky. Grandma found enough evidence to figure it out, so she has level 1 knowledge about him chewing. But since he obviously knows he chews, Grandma knows that he knows, so she has level 2 knowledge: knowledge that Grandpa has level 1 knowledge.
But she doesn't confront Grandpa. Because if she does they might have a fight, or he might decide that now the cat's out of the bag he might as well do it openly in front of people, which is gross. So she says nothing. Everyone knows that Grandpa chews, it is shared knowledge. But it's not common knowledge, because Grandpa doesn't know that she knows.
The lack of common knowledge is meaningful because it allows people to credibly pretend and act like they don't know even when they do.
Now, this didn't happen in real life (I think), but suppose that Grandpa is snooping around and happens to see a text (or more likely overhear a conversation, they're old after all), where Grandma was telling someone about this situation. He's like, "oh crap, I've been discovered. But Grandma chose not to confront me because she doesn't approve but also doesn't want to start a fight. If I want to I could just address this openly, admit what I've been doing, and then either stop or else have the fight and force my way to doing it openly. But I'm reasonably happy the way things have been going, and also I don't want to admit that I've been snooping, so I'll just keep chewing in secret and pretend I don't know that they know." Grandpa now has level 3 knowledge. Everyone knows that Grandpa chews, everyone knows that everyone knows, it's a bit of an "open secret", but not everyone knows that everyone knows that everyone knows, because nobody knows about Grandpa's snooping, so everyone else thinks that Grandpa is still oblivious to their knowledge, when he's not. This is meaningfully different from the previous scenario, where Grandpa actually thought he was being sneaky about the chewing, and is meaningfully different from common knowledge where it's all out in the open and nobody thinks they know more than someone else.
You can continue this pattern any finite number of steps upward, maybe Grandma planned for Grandpa to overhear her, and maybe Grandpa then discovers that it was a ruse, and so on and so on, but it becomes increasingly convoluted to understand or explain, and also there's little practical difference between level 19 knowledge and level 24 knowledge other than who happens to be on top at the moment, but they still differ from common knowledge, in that any large but finite number of steps creates an open secret that everyone knows but doesn't talk about, while the infinite recursion of common knowledge makes it just not a secret at all and it's harder for people to pretend it's a secret when it's obviously not.
The easier illustrative example of this is from poker. Poker pros talk about this all the time.
Level 1: I know what's in my hand.
Level 2: I know what's in my opponent's hand.
Level 3: I know what my opponent thinks is in my hand.
Level 4: I know what my opponent thinks I think is in his hand.
Level 5: I know what my opponent thinks I think he thinks is in my hand.
Etc.
Many poker players never advance beyond level 2. Even pros have trouble getting beyond 5.
Normally people cite this when it comes to these types of recursive logic.
More options
Context Copy link
More options
Context Copy link
More options
Context Copy link