User blog comment:Kyodaisuu/English description of Fish numbers/@comment-25418284-20131102173245/@comment-5529393-20131103232820

@LittlePeng9: It's true that you can define a self-interpreter within FOST, but I believe that you can also define a self-interpreter in a Turing-complete language like Python, but that doesn't change the fact that the Busy Beaver function for Python is well-defined. The reason is that there is no way to tell whether a computer program halts or not, so we can't program the Busy Beaver function in Python. Similarly, for FOST there is no way to define truth, by Tarski's Theorem. So we cannot define whether for a formula phi there is a unique number m such that phi(m) is true. So we cannot define Rayo's function.