User blog comment:Winrobee/A Hierarchy of Largest Number Principles/@comment-34422464-20191106135231/@comment-29832930-20191109204956

The point is that larger numbers can be made/described by not relying on exact definitions, but in the form of instructions. The critical factor is to make the numbers largest that they can be, in a procedure that comes to a stop in a finite number of steps. This way we can define processes to have to be invoked within the instructions that we cant define directly, and even whose logic is incomprehensible. Stipulating that the processes will come to an end enables definitions that are the maximally performing approximations of the original instructions to be reffered to, by the instructions, without having to directly provide googologically large definitions.