User blog comment:Wythagoras/All my stuff/@comment-7484840-20130715121715/@comment-5529393-20130715170211

I don't see how the time argument takes care of higher order functions. Type 0 definitions contain all definitions that don't refer to the totality of definitions, so it contains all definitions referred to by the iota function, now or as far into the future as you care to take it. So the iota function, at any time, cannot refer to a type 1 definition, as that would lead to circularity. It seems clear that ¥(googolplex) will be greater than iota(googolplex) at any time, since humanity will never be able to conceive of a googolplex long notation. And ¥ is a type 1 function, so we can surpass it with higher order functions.