User blog comment:Kyodaisuu/Pseudo Rayo's number/@comment-180.214.232.81-20141219180355/@comment-1605058-20141219184457

As for definition of "ill-defined" number, it's every number which isn't well-defined. And I take a number to be well-defined if it has a definition from which it's possible to infer that this number exists, that this number is unique.

Bowers' definition fails to satisfy the first part of this, because definition Bowers left is not enough to show that reduction leads to a single number. Even worse, he didn't leave us enough clues to always make a step of reduction.