05.4 Meta-Mathematical Abstraction
5.4 Meta-Mathematical Abstraction Meta-mathematical abstraction studies mathematics itself as an object. Instead of working inside one theory, it steps outside and examines the theory's language, axioms, proofs, models, and limits. At the concrete level, we compute. At the algebraic level, we manipulate symbols under rules. At the categorical level, we study objects through maps. At the meta-mathematical level, we study the systems that make those activities possible. A formal theory...