How other fields compare
Set theory
Foundational, but not self-reflective
Can’t form the set of all sets → paradoxes
Algebra
Powerful, but “algebras of algebras” are not coherent as a general notion
Analysis
Doesn’t scale to describing itself
Logic / Type theory
Some self-reflection (e.g., universe levels), but often needs a meta-system
Related to category theory via Curry–Howard–Lambek