I have in mind a scenario something like what Dennett describes in Consciousness Explained: we imagine that our awareness of our own thoughts is in some mysterious way infinitely recursive, because when we go looking for a bound on how many times we can repeat the step of becoming aware of the previous level of awareness, we don't find one; but the bound arrives exactly whenever we care to stop looking. There's no bound on how often we can reflect on the way we're deciding a particular question and decide if that, in turn, is rational, but there will have to come a point at which you have to stop recursing if you want to actually decide the base question.

There again, it may be a mistake to look for a sensible meaning in Annoyance's usual vague crap.