You should define what it means to be normal and abnormal. Suppose abnormal is defined as a set where its a member of itself. Otherwise it is normal. I'm going to go a bit mathy

So a bunch of geeks would be normal since a set of geeks is not a geek. Contrarily, a bunch of non-geeks would be abnormal since they each can be a member of their own set.

Consider a set of ALL things that are normal N and ask ourselves. Is the set of all things that are normal N actually normal?

Assume that it is abnormal. If it is, then it doesn't belong in the set N because it should contain all stuff that is normal. But then N does not contain itself so therefore its NORMAL even though we assumed that it was ABNORMAL. Contradiction.

Assume that N is normal. If it is, then it does belong in the set N. But then N would contain itself as a member. Which is the definition of something that is abnormal. Therefore its ABNORMAL when we assumed that it was NORMAL. Contradiction.

Russells Paradox.