One of the most profound findings from Godel’s incompleteness theorem is that meaning can be mapped onto a system that was specifically designed to prevent it. Principia Mathematica, the system Godel was poking at, was designed—amongst other reasons—to solve the paradoxes of set theory and logic with a constrained set of rules. Godel abstracted over the symbolic logic (converting proofs into numbers) to show a self-referencing statement could not only be represented in PM but was also undecidable.
This proof shows that new meaning can be mapped onto existing things through analogy and abstractions are real.
From I Am a Strange Loop.