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From Re-Thinking God and Existence


Mathematical Theorems


Goedel’s Theorems of Incompleteness and Inconsistency


Goedel's famous Incompleteness Theorem states that in any system of axioms*, supposing that the system is consistent, there will always be at least one statement pertinent to that system of axioms that can neither be proved nor disproved. All axiomatic systems are inherently incomplete.  No axiomatic system is thereby capacity of determining the validity of all statements within its system of axioms. More simply, any theory, system, or interrelated set of ideas, that is, anything we can think of, is inherently incomplete. There will always be aspects of any system or theory that the system or theory cannot explain, account for, or made valid.


Goedel’s second strong conclusion proves the following: In any consistent axiom system it is impossible to prove that the axioms are consistent. Even more radically, the second strong statement proves that if we can show that there is no contradiction in our beliefs, then in fact there is a contradiction in our beliefs!


To briefly summarize Goedel’s Theorems of Incompleteness and Inconsistency:


  1. Incompleteness: There are always questions any set of axioms cannot answer.

  2. Inconsistency: There are always contradictions in any set or system of axioms


Any system of ideas, beliefs, or axioms, that offers a complete answer to existence, or a complete answer to all the questions of the universe, or for that matter, all the questions in any other system, is necessarily incomplete and inconsistent. Without a doubt, there are always flaws in the arguments presented by any set of axioms. Contradictions must exist even if they have yet to be found.


Kubacki-Blackmore Theorems of Totality and Boundary Conditions


1. Kubacki-Blackmore Theorem of Totality. This theorem proves that the incompleteness and insufficiency of any X is an infinite incompleteness or uncertainty. The totality of this infinity results in a definition of existence where everything known, imaginable, and unimaginable exists and is interconnected. The totality of everything imaginable and unimaginable is equated with the totality of existence or God. Finiteness and certainty are thereby shown to be untrue and illusionary.


2. Kubacki-Blackmore Theorem of Boundary Conditions. This theorem proves that any set of axioms, theories, physical systems, or any X, must have limits and boundaries in order to maintain coherence, structure, and order. Without boundaries and limitations nothing could be cogently analyzed, chaos would ensue, and separateness among objects would not be possible. These boundaries, however, are not constant nor fixed, but probabilistic and change in interaction with the rest of existence.


*Axioms are assumptions or statements that are presumed to be true.


Download the Mathematical Proofs

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