I went to the library with the intention of getting somewhere with this and realised that there are really 2 possible proofs of SRH:
(1) The Boundary proof
This proof aims to show that a system cannot contain its own boundary.
(2) The dialectic proof.
This proof aims to show that a system cannot define itself without reference to things which are not within the system.
I realise today that they are the same thing. The SRH is not really about self-reference this has been a red-herring: there are lots of examples of self-reference. The problem is to do with self-definition.
Now if something cannot define itself then it must be defined in terms of things that are not part of the system. This has two implications
(1) A system is never complete. No system can construct "All Things", so there is no system called "Totality"
(2) A system is really "not itself" since it is defined with elements that are not itself. The Yin-Yang.
It is easy to see that a circle boundary is not contained "in" a circle. But there is work tio do
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