This is great for understanding why simpler logics (Boolean) are computable but too expressive ones (FO) are not. As soon as the logic is able to make statements about itself, things get 'weird'. A not formal(!) but imho still intuitive example:

"This sentence has five words."

This is a true statement. And we know that the conjunction of two true statements should also be true.

"This sentence has five words and this sentence has five words."

With eleven words each part of this statement is obviously false and here we can't rely on the "and", which we are used to from the simpler logics, anymore.