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 proces

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.