[ukj]

Heh, how did I know you are going to appeal to infinity-categories at some point?

"defining categories" and their respective categorisation rules is the process of classification. They don't account for the classifiers themselves.

You are super-close to a deeper realisation even.

If any notation is meaningful (even one that uses symbols like ∞), then it's Turing-recognisable.

Type-0 Chomsky grammar. In formal languages syntax is semantics.

In so far as understanding (comprehension?) goes, you could say that I subscribe to the axiom of unrestricted comprehension. It's rather un-Mathematical doing so.