Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Contra Common Knowledge, published by Abram Demski on January 4, 2023 on The AI Alignment Forum.

This post assumes some background knowledge about "common knowledge", a technical term in philosophy. See the tag page for an introduction and a list of LessWrong essays on the subject.

Epistemic effort: basically reading the SEP article on common knowledge and forming my own conclusions. I've also gained something by discussing these issues with Scott Garrabrant and Sahil Kulshrestha.

Consider a statement like "LessWrong curated posts help to establish common knowledge".

On the one hand, this seems obviously valid in practice. Curating a post boosts the number of people who see it, in a public way which also communicates the meta-knowledge (you know that lots of people will know about this post, and they'll also know that fact, etc).

On the other hand, this is a long way off from actually establishing common knowledge. People don't check LessWrong constantly. Lots of people will miss any given curated post.

In this post, I will argue that common knowledge never occurs in the real world.

But this leaves us with a paradoxical state of affairs. We use the concept to explain things in the real world all the time. Common knowledge is an important coordination tool, right? For example, social norms are supposed to require common knowledge in order to work.

I'll also offer some evidence that common knowledge is not as important as it is typically made out to be.

Can't Have It!

Several arguments about the impossibility of common knowledge have been made in the philosophical literature; see Common Knowledge Revisited and Uncommon Knowledge. Whether nontrivial common knowledge is realistically possible is still debated, according to SEP (Stanford Encyclopedia of Philosophy).

SEP makes a big deal about how we don't literally need to explicitly believe infinitely many levels of knowledge in order to have common knowledge, because we can have a single concept ("common knowledge" itself) which implies any level of recursive knowledge.

However, I don't find this particularly reassuring.

I will make the following argument: Common knowledge requires absolute certainty of common knowledge. If anyone has the slightest doubt that common knowledge has been established, it hasn't. But we are never 100% certain of such things in the real world! Therefore, common knowledge is impossible.

It is often stated that common knowledge requires a public event: some event which everyone observes, and which everyone knows that everyone observes. I have approximately two questions about this:

How did we physically arrange an event which we can be absolutely certain everyone observes, when quantum mechanics makes every phenomenon in our universe at least a little noisy? Any communication channels have some degree of unreliability. Even setting aside quantum mechanics, how about human psychology? How are you certain everyone was paying attention?

How did we establish common knowledge that we had done so? Does establishing new common knowledge always require some seed of pre-existing common knowledge? Doesn't this create an infinite regress?

Common Knowledge Revisited also shows that establishing common knowledge requires simultaneity. Suppose that there is a public event which everyone can see, and indeed does see, but there is some small uncertainty about when they'll see it. You might expect that common knowledge will be established anyway; but, this is not the case!!

To summarize, any uncertainty about message delivery, or even about the time of message delivery, blocks the formation of common knowledge. The real world seems too full of such uncertainty for common knowledge to be established in practice.

The Partition Assumption

I should also mention that the standard treatment of common knowledge makes ...