User blog comment:LittlePeng9/FOOT is not as strong as I thought/@comment-12.144.5.2-20170912183523/@comment-5529393-20170912221333

I am sorry to hear that what you wrote got deleted. I would be surprised if a comment on a blog or user subpage got deleted; if it was posted as a main article, that would be different I suppose. If you accept the philosophical implications of nth order set theory (or nth order oodle theory, although as this article shows once we start going to higher predicates the oodles aren't all that powerful), meaning you believe all nth order statements have a truth value, then n-OST(m) = "the largest number definable in nth order set theory using m symbols or less" would be huge indeed! Once we accept that, we can stick whatever we want into n, like BIGG, or better yet BB(1000), or Rayo's number, or better yet we can define f(n) = n-OST(n) and start a hierarchy of fast-growing functions from that.

I believe (Wojowu or Emlightened, correct me if I am wrong) using (n+1)th order set theory on the set-theoretic universe V is the same as augmenting V by n additional classes, so we can talk instead of adding classes rather than going to higher predicates. In this case, we can contemplate adding a transfinite number of classes - first an ordinal number of classes for ordinals in V, then for "ordinals" outside of V. Perhaps this is the state of the art. (But again, it depends on where you stand philisophically.)