Today I was trying to explaining the Gödel's theorem to a layman, I've drawn a figure similar to the one below and said that:
- A truth is a consequence of the axioms (with the axioms also being truth).
- The lines between the axioms and the theorems and the lines between theorems and theorems are the employed notions to show the truth of that theorem.
- And that there are theorems that are true (red diamonds) but unreachable by any arrangement of lines from the axioms to the theorems to them. The red lines are meant to show that there is no line that reaches there.
Is this visual analogy accurate? I know that perhaps I'm oversimplifying, but does it captures the big picture or is there something else I should add?