Containing one self is problematic. This is the SRH.
As argued in this math stack exchange : containing ones boundary creates a new boundary and so contradicts the definition.
Specifically for any counting numbers you can always +1 to get a new element. This is the whole definition of countably infinite. So if you add Countably Infinite itself to the set you get an element that is the limit and so can't +1.
Not rigorous but it seems to me that Cantor's explosion of infinites comes from the SRH. Every time you create a set, you create a new boundary and so a new type of number via its cardinality. And this is recursive and so it explodes. I called this the +1 or Horatio Theorem before rather conservatively because any idea such a "I know everything" becomes a new item of information and so you can't. But actually from Cantor its not just +1 item of information but an explosion of new information because you need to adjust everything to incorporate the new boundary.
Knowledge does not approach an unobtainable limit of "everything" so that you are left with a trickle of +1s as you negotiate the limit. Knowledge actually expands exponentially and gets further and further away from any limit the more you learn.
SRH has interesting implications of ideas of Reality. If Reality is the moment when your knowledge matches what there is to know, so that there is nothing left to learn then mankind is getting further and further from Reality! Science is not a gradual approach to singular Truth, but an exponentially explosion away from a singularity of ignorance like the Big Bang. Which raises questions about what we are learning all this about?
The classic naive view of Reality is there is some actual stuff hidden out there and Science and Learning is an investigator uncovering it. We are simply revealing a fixed Reality.
SRH identifies the inevitable problem here that sooner or later we are going to stop looking "there" and start looking "here." Essentially the scientist starting to ask how the uncovering actually happens. And when we start to uncover ourselves we have a contradiction because weren't we supposed to be the collection of everything uncovered already? So it turns out that Science itself is a mystery that needs uncovering and then you are in real SRH trouble. Hegel smashes this when he says that you can't use a faulty telescope to look at itself to find the faults. If the telescope is faulty then your data is going to be faulty. One has to begin "where you are" and have no choice but to take that as the starting point. Quite how you get here is fundamentally an unsolvable mystery. This is the inspiration for Phenomenology. And it is EXACTLY what Present Moment in Buddhism is and what Meditation seeks to get clear.
So Reality is necessarily unlike anything we will ever think, its boundary is unfathomable, and the process of knowledge and discovery is explosive. All those people who are struggling for a Theory of Everything look out, your great^n grandchildren will still be searching.
As far as I can tell SRH is the closest you can get to a Theory of Everything. Its the recognition that "Everything" is a self contradictory idea because if you ever add that boundary to itself you smash up all the knowledge you already have and make the problem even worse.
Perhaps this is where Hubris comes from. All those civilisations who think they have mastered the universe actually end up smashing themselves because the struggle to grasp that shows them they have not.
It still remains to get a handle on SRH. Is there is a general formulation of it outside the informal ramblings of a blog. The more I look at it, it seems to have its own answer. If SRH was ever fully formulated it would explode itself. Very casually written, we did much better earlier in the year where we realised that the contradiction at the heart of "everything" may actually be helpful in giving the Theory of Everything an exception to really be Everything. Two -ve make a +ve kind of thing.
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