User blog comment:P進大好きbot/What does a computable large number mean?/@comment-4224897-20180610135217/@comment-35470197-20180610215947

Thank you for the comment!

I agree with that the computability makes sense not for natural numbers themselves, but for the names, i.e. the declarations of natural numbers together with the definitions.

And I would like to know to what extent googologists regard googolisms using the outputs of computable functions as computable large ones (e.g. (1)--(6)).

(By the way, as I wrote in my other blog post http://googology.wikia.com/wiki/User_blog:P%E9%80%B2%E5%A4%A7%E5%A5%BD%E3%81%8Dbot/Whether_Rayo%27s_number_is_well-defined_or_not, I think that uncomputable large numbers based on Rayo's method are not well-defined because of mathematically incorrect arguments such as an invalid reference from the meta theory to a Platonist universe of the coded theory or an invalid identification from a set model of the meta theory and a set model of the coded theory. Therefore they can never be bounds of computable large numbers.)