User blog:Vel!/Googology and well-defined-ness

There's been an ongoing argument about the problem of the ambiguity of BEAF and exactly how crippling it is. Is it reasonable to say that meameamealokkapoowa has size comparable to X? Can we argue that an array has this ordinal growth rate?

More generally this brings us to a debate over what we should do with ambiguous googology. Sbiis proposed the following "grading system" for googology:


 * Grade A definitions meet any reasonable standard of mathematical rigor. The definitions are one hundred percent precise, and their totality can only be disputed from a metamathematical standpoint.
 * Grade B may have a definition which isn't strictly formal, but it is cohesive enough that it makes sense. You can always figure out what to do next, but it isn't known to be total.
 * Grade C would be systems lacking a definition clear enough to say that it makes sense. It may be subject to multiple interpretations. It can still be gauged based on theories of what a "reasonable" interpretation is.
 * Grade D would be numbers of a definition so vague or strange that it's not even clear what order-type we are talking about, or whether it makes sense. None the less, Grade D still at least provides some semblance of an idea.
 * Grade F is crank land. Anything and everything goes. It could be complete nonsense and it would still be grade F.

The question is: Can we make claims about googology that isn't grade A?

(more to come)