What is Common Knowledge?

I wrote here about social knowledge. I suggest reading it first, as common knowledge is a special case of social knowledge.

A lot has been written about common knowledge. Consider the following:

• Wikipedia's entry, which is technical and focuses on logic.
• SEP's entry is quite detailed, with many philosophical motivating examples.
• Ben Pace's article is the closest to what I want to write here.

Here, I focus on a physicalist explanation of common knowledge, in the spirit of Information is Physical and Social Knowledge.

Social Knowledge

As explained in the page about social knowledge, social knowledge is knowledge about other people's knowledge, rather than knowledge about the world.

Social knowledge can be nested, i.e. it is possible to have social knowledge of other people's social knowledge.
For instance, let's say that I am planning a surprise party for Bob. I have simple social knowledge about it: I know that there is a surprise that Bob doesn't know about.
But if I tell Alice about it, now I have social knowledge of her social knowledge: I know that Alice knows that there is a surprise that Bob doesn't know about.

Common knowledge introduces another layer of complexity. Common knowledge is shared knowledge within a group, that is held to be true by the group.

Shared Knowledge ^[1]

By default, knowledge is not shared. Each person has their own knowledge: everyone knows different things.

But when it is beneficial for everyone in the team to know something, we pay the cost to ensure that the relevant knowledge is shared. That shared knowledge itself can be social or not.
For instance, in a team at work, we make it explicit who knows what. This is useful social knowledge to have: everyone knows who to ask for help when they need it.
There's also the more boring non-social knowledge of facts that everyone knows, such as the company's policies, or how to operate the tools.

Common Knowledge

Common knowledge is an advanced form of knowledge that is both social and shared.

Shared knowledge is just knowledge that is known by everyone in a group, whereas common knowledge is knowledge held to be true by the group itself.

It means that everyone in a group knows something, everyone knows that everyone else knows it, everyone thinks it is obvious to everyone, everyone could use it in group conversations without having to explain it, and so on.
Basically, it is knowledge that is better represented as being held by the group than by individuals. When something is common knowledge, it is not that everyone has a deep model of how everyone else thinks. It is that everyone has a strong feeling that the group as a whole has the relevant knowledge.

To make it concrete, let's investigate a situation where some knowledge is shared across a group, but is still not common knowledge.

Let's consider three friends: Alice, Bob, and Charlie. Charlie did something embarassing. She consumed some cringe content, and enjoyed it!!! She tells Alice, who laughs. Alice then tells Bob without telling Charlie.
Now, that Charlie did something embarassing is shared knowledge among the three friends. But it is not common knowledge. If all of them hanged out together, Alice would not talk about it: even though Bob knows about it, she doesn't want Charlie to know that she talked about it.

Now, if David came over, and told everyone about Charlie's cringeworthy action, that would become common knowledge. Everyone would know about it, Charlie would know that everyone knows about it, Alice could freely talk about it, and so on.

Common knowledge is much stronger than shared knowledge. Knowledge being shared is a precondition for it being common knowledge, but it is far from sufficient.

While shared knowledge can be social or not, common knowledge is always partly social. It is not merely knowledge of a fact, it is also knowledge that everyone in a group clearly knows that fact.

I initially planned to integrate to this page why common knowledge is necessary and how it can be created. But it got too long, so I moved those to separate pages: Why is Common Knowledge Necessary? and How to Create Common Knowledge? (missing).