Wednesday, 26 February 2014

Fine Tuning the Proof of God

Have been looking for a neat proof of the conditions under which the "Viscious Circle Principle" (previously the Self Reference Hypothesis - SRH, that some self-references were impossible) could be tightened to prove fatal for certain types of arguments that presuppose themselves. This is the basis of a proof of God.

BackGround
The observation is that when an argument becomes so general that it starts making statements about its own foundations then it becomes meaningless.

The classic example would be the search for the Unified Theory in physics. Were such a theory to become really comprehensive it would have to start making statements about the reasons why the theory was in the form it was. Why for example does it concern things like fields at all. All theories must be limited then, since any theory which could theorise about itself would cease to be meaningful.

Another example (and the first I noticed) is with consciousness. I believed it was the singularity created when a sensing system sensed itself. Like the neurologist examining a patients visual system using his own visual system: there are things he cannot conclude because those conclusions undermine his own vision: for example the idea that the patient sees only an image on their retina. Such a thought would imply that he wasn't seeing the patient but only an image himself. The Viscous Circle begins and ends defeating his aspiration of discovery.

This is related to the idea Fixed Points in mathematics and fractals. A fixed point is a point that remains unchanged when operated on by some function. Function here means any procedure that can be used to move from input to output reliably. A fractal is a complex fixed point generated by repeated application of a function or series of functions and the system tends to become "trapped" in a stable space attracted to but not arriving at a "Strange Attractor". Certainly meaning is created by self-reference, and self-referential systems have some very interesting forms. However "interesting" fractals require mapping to subsets of the space to create internal structure and hierarchy. It is that mapping structure that creates the form of the fractal and that mapping structure is not itself part of the fractal space. The viewer can work this out for simple fractals (like a tree) and very simply "compress" or understand the fractal. Godel's Theorem, Turing's Halting Problem and all the paradoxes of logic depend upon anti fixed points that contradict themselves when put through the system.

The observation is that no system can support itself. All systems must ultimately be grounded in the "outside" world, or the system in which they are embedded, or the context. This fits with almost all philosophy and religion that states that the Truth is beyond the grasp of Man and must be in principle also. It fits the Buddhist ideas of emptiness (sunyata) and non-self (anatta) also : that is that there are no fixed knowable entities that somehow underlie the world of impermanence, and that there is no such self that hides within us.

Conclusion
Russel's Paradox however puts an end to this search however. The goal is to create a method for generating the set of self-referential systems (SRSs) that defeat themselves (SRS0) (like the Unified Theory) and the SRSs that do not (SRS1).

However the union of these two sets is the set of all self-referential systems {SRS}. There is no issue with this set, but the complement of it is the set of all non-self-referential systems {¬SRS}. Now which set does {¬SRS} go in; it must be in one. If if it is in {¬SRS} then it does contain itself so is self-referential so contradicts its definition, and if it goes in {SRS} then it is not self-referential either.

It turns out the idea of the SRH (or VCP) it is an example of self-defeating self-reference. The theory is impossible due to the theory it itself is espousing! It is self-contradictory.

So the proof of God remains but it can't be accurately defined with the my current understanding of self-reference.

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