User blog comment:Wythagoras/My well-definedness-grades/@comment-1605058-20141007152447/@comment-1605058-20141007162418

A possible issue with Rayo function is purely philosophical/metamathematical, as it assumes the existence of "the" universe of sets in which "the" truth about every statement holds.

In reality, similar considerations can be made for other functions, for example BB function. There are some Turing machines which either halt or don't halt - depending on the choice of the model. And we cannot argue which model is more "true". Thus these machines can be falsely judged by some models to be Busy Beavers.