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Proof Two

In the first proof, we saw that when we consider the irreducible information content of any partitioning of the Universe (defined as everything that exists), it is not possible for that entire Universe to be partitioned into two (or, obviously, more) non-empty irreducible sets and have one contain a necessary and perfect representation of the other. This was because entropy is an extensive quantity - all of the information carrying capacity of the ``God channel'' is being consumed by irreducibly specifying the God state and there is none left over for specifying the not-God state. The God channel can irreducibly encode the Universe only if it is the irreducibly encoded Universe. One is led to a contradiction whether or not one begins with the fully reduced Universe and attempts to partition it or one begins with it partitioned, fully reduces each partition, and then attempts to ``identify'' one part in the other, although this short work contents itself only with the simplest sufficient proof and doesn't examine all possible variants of partitioning on domains with various dimensionality and cardinality. The problem is in the partitioning itself - the moment the whole is broken up into two distinct parts, at least one bit of entropy is introduced that differentiates one part from the other even if the two sets are otherwise identical.

If God can perfectly visualize all non-God real existing things in Its real existing but distinct ``mind's eye'' (anthropomorphizing, of course, but what else can one do when thinking about knowledge), then it knows that its knowledge is of those things (in Its mind) and is not those things (outside of Its mind) - not to know this is to not know all things. The map, after all, is not the territory - God is as subject to this precept of General Semantics as any other informational system. God's knowledge is therefore not complete - it cannot know these things as they really are outside of Its mind, its abstract knowledge is not the same as the territory itself any more than your abstract knowledge is. Furthermore God cannot, as we saw above, be certain that its visualization is in fact correct, that its secret decoder ring is giving it the right values for the non-God part as the mapping it defines is certainly not unique, the space of possibilities it selects from is large, and recall, in this timeless view of things there is no such thing as looking. There is only an enormous DVD, broken into two pieces, where even if one piece contains a complete redundant copy of the data on the other there is no way of knowing that from possession of the one piece only - even if it is large and complex enough to contain a complete language and encoding system that self-consistently says that it does: it could simply be mistaken.

However, there is another way to prove the same conclusion in an entirely different context. This proof similarly relies on the axioms and definitions used in the first proof but in a very different way. To them we add the axioms that support Gödel's theorem, as they appear manifestly true for the Universe itself. Suppose then, as before, that the existential Universe has a self-encoded irreducible state that is capable of symbolically encoded self-reference. This is not a terrible stretch, since you are a part of the Universe and you are thinking about the Universe in symbolically encoded ways - it is therefore empirically self-evident that this is true to any mind thinking about itself and the Universe. The proof then follows as:

In order for God to possess complete abstract/symbolic knowledge of the Universe, that knowledge must include an expression of arithmetic, as the abstract expression of arithmetic manifestly exists in human knowledge if nowhere else; God's knowledge could hardly be complete if God cannot add two and two to get four. This body of knowledge is therefore subject to Gödel's first (completeness) theorem; since it is capable of the expression of arithmetic (and is in any event intrinsically both complex and self-referential, containing all human-known examples of Gödelian knots of unknowable propositions or set-theoretic paradoxes as a simple subset) it can be complete or consistent but not both.

God's knowledge of the Universe cannot therefore be symbolic (encoded in any way that has to be decoded by a deductive process) and inconsistent with the true state of the Universe and still be arguably correct knowledge. The Universe is real and hence cannot be inconsistent - it simply is what it is (timelessly). Neither can its symbolic knowledge be incomplete or God is not omniscient and hence is not God.

This is a contradiction. God's knowledge of the Universe must be both consistent and complete in order not to violate the definition of God given above, but if that knowledge is indirect and symbolic, capable of self-reference and encoded at a high level upon itself, Gödel's theorem tells us that it can't be both complete and consistent.

God's omniscient knowledge of the Universe cannot, therefore, be indirect and symbolic. Symbolic reduction and projection of the existential reality (all state information) of the Universe into a subset of the Universe as code that is necessarily self-referential and capable of expressing arithmetic renders it incomplete, inconsistent, or (most likely) both.

In order for God to be omniscient (and omnipresent and omnipotent), its knowledge can only be direct knowledge of the Universe itself as the Universe itself, complete and consistent by the existential property of the Universe.

Therefore: If God exists, God is the Universe itself.

Another amusing corrolary comes from considering Gödel's second (consistency) theorem:

If God can prove that its symbolic, encoded knowledge of the Universe is consistent, then it isn't consistent. God can therefore never be certain that any symbolic encoding of the knowledge of the Universe (including itself) is consistent and hence true.

Again, only existential, self-encoded information lacking any partitioning and the consequently necessary layer of projective abstraction is guaranteed to be complete and consistent when speaking of the Universe.

We conclude that God's knowledge of the Universe (including itself) cannot therefore be a symbolic map or encoding of any sort, which is a result that is entirely consistent with the information theoretic analysis above. In addition to the entropy problem, the self-referential symbolic representation suffices to trigger Gödel's theorems so that true omniscience is literally impossible. Again, let's try to illuminate the difficulty with a concrete example, this one familiar to all readers as they contemplate their own knowledge of the Universe.

next up previous contents
Next: Example: Human Knowledge Up: The Pandeist Theorem Previous: Example: Partitioning a Finite   Contents
Robert G. Brown 2014-02-06