Old Skool SRH is back!

Rethinking the SRH can now be reformulated with a better understanding.

SRH Definition

A system cannot refer to itself without using aspects of a meta-language that cannot be exressed within the system.

This is why the SRH makes the claim that self-reference is impossible, because actually within a system it is impossible. It is only by using aspects that the observer (outside the system) can see that we can interpret anything as self-reference. Thus to self-reference we by definition are not entirely ourself - that is what the SRH saw but seeks to prove.

Godel numbering maps the formulii of Principia Mathematica to the Natural Numbers. These are coded within PM (as I understand it) as repeated applications of the successor function on the symbol 0. So the number 5 is represented by sentence "0SSSSS".

Now I failed a few posts ago to find a contradiction with the conception of such a formula within PM. But then wondered what was gained by mapping expresions in PM onto the subset of expressions {"0","0S","oSS","oSSS", and so on} also in PM. It means that there are two names for any expression: itself and "0SS..S" the Godel number of times. Is this all that was required?...

Think some more...

The problem maybe is that while we know which mapping is being used, can PM?