Knowledge is not a lattice

by Redxaxder

When some fact is common knowledge, it’s implicitly common knowledge for a particular group. “Everyone knows” refers to different “everyones” when spoken by different people or in different situations.

These groups can overlap, but their overlap doesn’t make them fuse. Say I tell you a secret, and I also tell that secret to Alice, but I don’t tell both of you together. Now “we” (you and me) know it, and “we” (me and Alice) know it, but “you” (you and Alice) don’t, and “we” (the three of us together) don’t know it either. If you tell my secret to Alice, the state of knowledge changes. Now you two also know it together. But you still shouldn’t bring it up among the three of us!

That’s wild! It seems like introducing a fact to larger groups usually requires having a larger gathering to announce it.

But sometimes it doesn’t? Maybe? I think that when the state of knowledge gets large and complex enough that we lose track of it and collapse into treating a fact as if it is common knowledge in a bigger group even if it technically isn’t.

I think there are more ways this transition happens, too.