GEB Ch1 - The MU-Puzzle and Achilles with the Tortoise

This Chapter 1 of GEB introduces the MIU-system, a formal system defined by a simple alphabet (M, I, U), one axiom (MI), and four rules for transforming strings, posing the "MU-puzzle" which asks if the string "MU" can be derived. It discusses the concepts of theorems, axioms, rules of production, derivation, and the distinction between working within and thinking about the system, also touching upon the idea of a decision procedure. The second source, a dialogue by Lewis Carroll titled "Two-Part Invention," presents a paradox concerning logical inference where a Tortoise challenges Achilles to logically necessitate the conclusion of a simple syllogism, revealing an infinite regress of needing to accept the rule of inference itself as a premise