SRH - final expression & proof of God

The Self Reference Hypothesis is not that self-reference is impossible, quite the contrary. It is precisely because self-reference is possible that things can contradict themselves, and it is precisely because self-referential things must contradict themselves that the self is never enough.

The search for a problem with self-reference itself was misguided. Things cannot know themselves ironically because they can refer to themselves. It is the making statements about themselves which creates the contradictions that make things incomplete (in the normal sense of the word). And it is this incompleteness and which demands a larger system (a meta system) must exist.

The necessity of a recursive larger self brought about through self-reference is the proof of God that the SRH was seeking. God is not a thing Himself, but simply the awareness that there are more things in Heaven and Earth than are dreamt of in our philosophy (Hamlet to his friend Horatio in the eponymous play). If we look carefully at the teachings of religion this is a much more accurate description of God than is often offered by believers and non-believers alike (to believe and to not-believe both entail a belief about God).

Tarski's Undefinability Theorem is the formal expression of this idea. The recent turn about in SRH thinking was not that formal systems prove the principle but rather that the more general principle is expressed where ever there is self-reference, which includes formal systems.

Suppose, in some logical system, that there was a formula with one free (input) variable that was only ever true when that variable was bound to a true formula and only ever false when bound to a false statement, that is the formula True(x) is true when x is true and False when x is false. This is written:

True(x) ⇔ x

But then we can use the True formula to create a statement by negating this:

¬True(x) ⇔ x

This states that if x is True then ¬True(x) is true in other words True(x) is false, which means that the True formula doesn't work, and can't work.

This argument works for any attempt to create a formula to identify a predicate in a system.

AND INTERESTINGLY IT uses the weakest form of self-reference with the system only referring to statements in general... if doesn't need to deal with statements that refer to themselves!!! That changes a lot... stuff to rethink... SRH not over yet....

RECONSIDER...

Two aspects of systems cause of problem for self-reference. One is the existence of statements of the form where a self-reference is negated such as "It is not the case that I am truthful". By negating such statements a self-contradiction is created - essentially modelling the self and then saying not-me within the model which is isomorphic with something outside the model itself. This I wish to explore as a conclusion to the SRH myself. The other is the Halting problem. Systems which depend upon their own output form infinite loops and so never return a value. They cannot thus determine whether they are themselves an infinite loop, which implies "infinite loop" must be a term from a meta-level. So self-reference in statements is analogous to recursion, and contradictions analogous to infinite loops both which imply a meta-level.