SRH - the final stages!! Self, Contradiction, God

In Godel and Tarski the basic issue is that once a method of self-reference has been established (by which statements in one domain can predicate statements in that same domain and therefore themselves) then it is a trivial matter to create a contradiction where a statement predicates something about itself that contradicts itself. The most famous example in common language is "This is a lie.". Godel's theorem has a function which predicates "theoremhood" i.e. does x in Pxy represent a proof of y, and Tarski has a function which determines "truth". The basic problem is any formula that tries to separate all formulii into one of two groups comes into problems when it tries to classify itself. That is the crux!

Godel's contradiction: ~(x)(y)(Pxy · Qfy) [ref]
Tarski's contradiction:

[ref]

general ref on diagonalisation
http://www.math.hawaii.edu/~dale/godel/godel.html#TarskiUndefinability


Basis of SRH: Self Predication enables contradiction.
(assuming excluded middle.)

So it seems that actually it is precisely because of self-reference that we can never have a comprehensive system. Once a system becomes powerful to entertain statements about itself it becomes powerful enough to create contradictions in the system which imply that there is a new meta layer.

So the SRH is not that self-reference is impossible, but actually contrarily it is the very existence of self-reference that ensures that a system will never be complete because a contradiction will always be possible. But rather than be negative the existence of contradiction points outside the system to the meta system - that is to God.

So the various aspects of the SRH come to this general point - that is more general than the particular proofs of Godel, Tarski, Caitin et al. which have been expressed purely in logic - that once we have a system which can refer to itself then immediately and necessarily we can create a contradiction which immediately and necessarily points outside the system. self is thus the window which ensures that there is always something greater than our philosophy (Horatio), that any system when it tries to establish completeness and self-knowledge will be too small, and that for any belief set large enough to try to explain itself we will find God (God being the principle that there is always something outside our beliefs).

Science has been immune from God because it absolutely refuses to examine itself and its own validity. Why for example is evidence so important? What evidence is there for this belief? Quickly the Aristotelian edifice starts to crack.

Religions and Philosophy have always been fascinated by the relationship between God and Self. They have also struggled joyfully with the absurdity and contradictions of faith and the irony of the world. It seems in this analysis that this is the very structure that arises when we seek completeness and totality. The Absolute is by necessity fractured and incomplete, and the contradictions become ever more powerful as we seek the Absolute. Gos is always beyond our grasp - that is his definition in any system small or large that we wish to frame the universe in.

At last a complete definition of the SRH. Will need to read back over the last 3 years of posts to make sure that this really fits the bill and think over my development since the days of A.I.M.E. in 97 and the insights as a child which led to this fascination with the SRH. Got my copy of Godel, Esher, Bach will read that again to see if SRH really does the trick.

Next up what to do with this? Is there a more general proof that Godel, Tarski et al, not that logic fails because of a few proofs but that these *types* of proof are necessary always.

Problem with the Godel and Tarski is that they are so formal and precise that it has been very difficult for people to draw general philosophical lessons and there is a lot of misunderstanding about them - I hope not including the above.

Need to add that this fits with the Hegelian dialectic perfectly that it is through the contradictions in the thesis that the antithesis is formed and then the aufhebung synthesis that follows. Altho here we are saying that it is the desire for totality that through self-reference creates the contradictions in the thesis and thus generates the antithesis which automatically is the leverage required to expand the perspective on the thesis.

When Archimedes stands beyond the world with his lever ... no time but will use this to illustrate the SRH.

Problem before was that I was hoping to find the SRH in logic, when actually the SRH governs logic like everything else. Self is a phenomenon that goes way outside formal systems and computability... ironically ;-) Precisely because Self lies inside systems of sufficient complexity it lies outside :-)