Thats also an appropriate analogy, I think. The main point is, type theory is a tool for reasoning, while set theory is a thing reasoned about. At least in the

Thats also an appropriate analogy, I think. The main point is, type theory is a tool for reasoning, while set theory is a thing reasoned about. At least in the context of foundational questions. You can flip them, but then it becomes kind of silly, imo.