[srcreigh]

You got it - the creative developments of a stronger theory. This allows the creation of tools which can categorize TMs, tools which wouldn’t exist otherwise.

It’s fascinating that the entire space of finite amounts of random gibberish contains every such stronger theory.

As a thought experiment it does well. Interestingly the Church-Turing thesis seems to exclude ingenuity. That is, it doesn’t try to say there aren’t functions on natural numbers which are uncomputable but can be calculated with ingenuity. Seems that a ton of people conflate those things.