User blog comment:Wythagoras/All my stuff/@comment-7484840-20130716082643/@comment-7484840-20130716091148

If one plus the largest number definable in at most a googolplex characters makes no sense, then neither does 1+¥(googolplex), because they mean the same thing. If that statement does not define a number, then neither does the ¥ function.

The problem with self-reference is where to stop: using rayo's function as an example, if it can define rayos function, then it could just self refer once, and the second rayo function within the first, and if the second one does not go on to define rayos function, then that is a completely acceptable definition. However, why not have a third level and then stop it, as this would also be fine? Or a fifth, or a sixth or so on. It's a 'slippery slope' argument, and it leads to the function making no sense at all.