Technical Papers

The G Proof is a work in progress. It currently exists in two Versions. Version 1 is presented in the Nine Videos, which are targeted for people who are intelligent but need to be educated in formal mathematics.

Both Versions are presented in the Technical Papers, written in English, which are targeted for people who are already mathematically sophisticated. However, even for such people, Videos 6, 7 and 9 are highly recommended, because they include a lot of important discussion not included in the Version 1 Technical Paper.

The Technical Papers are pdf files that you may download for free — see the download links at the bottom of this page.

Comparing Versions 1 and 2 of G Theory

The distinction between Version 1 and Version 2 is in how "absolute phenomena" are treated, and in the corresponding way "omnipotence" is defined. A "relative phenomenon" is caused by a different phenomenon. An absolute phenomenon is a phenomenon that is not a relative phenomenon, which means it either causes itself or is uncaused.

In Version 1, absolute phenomena are assumed to be self-caused. Based on this assumption, omnipotence is defined to mean causation of all phenomena. This results in a substantial simplification of G Theory, and it is what is presented in the Nine Videos (although remarks are made about Version 2 in Videos 1, 6, 7, and 9).

In Version 2, the assumption is removed, which means absolute phenomena can be either self-caused or uncaused. If phenomena exist that are not caused by anything, then they cannot be caused by an omnipotent phenomenon. Consequently, the definition of omnipotence is weakened to mean causation of all relative phenomena. Version 2 of G Theory is more complex, but the results are more interesting, as shown in the following table.

  Version 1 Version 2
Purpose of the Version First level proof that God exists Second level, more advanced proof that God exists. Looks deeper into the nature of God.
Absolute phenomena Self-caused Can be either self-caused or un-caused
How is God absolute? God is self-caused. God is either self-caused or uncaused.
How is God omnipotent? God causes all phenomena. God causes all relative phenomena.
What are the parts of God? (Not covered) Absolute phenomena (other than God) are parts of God. Metaphorically, they are "cells" in the "body" of God.
What is not a part of God? (Not covered) Relative phenomena are not parts of God.
What is God a part of? (Not covered, other than h) (Not covered — topic of future research)

Abstract of Version 1 Technical Paper (30 pages)

Title: G Theory Version 1: Theory of Phenomena and Causation
Author: Mark Laurence Donald Emerson, B.A. Mathematics, UCLA

A formal mathematical Theory of Phenomena and Causation is presented based on First Order Predicate Logic, as expressed in the extraordinarily elegant notation of Donald Kalish (1919-2000) and Richard Montague (1930-1971), revised (and hopefully made even more elegant) by Mark Emerson, who was a student of Kalish.

We take the following three terms as undefined: (a) phenomenon, (b) "is a part of" and (c) "causes." Phenomena are the nouns of our theory, and every variable represents a sphenomenon. A phenomenon is understood, without definition, to mean anything that exists or happens. "Is a part of" is a two-place predicate that means a first phenomenon is a part of a second phenomenon. "Causes" is a two-place predicate that means a first phenomenon causes a second phenomenon.

We make several definitions, the most important of which is omnipotence — an omnipotent phenomenon causes all phenomena.

Five Axioms, A1-A5, are taken. A1 states that every phenomenon has a cause. A2 states that causation is transitive. A3 states that causation is not circular except for self-causation. A4 says that causation is complete, in that if a first phenomenon causes a second phenomenon, where the latter contains phenomena that are its parts, then the first phenomenon also causes all those parts. A5 states that there exists a phenomenon that includes, as its parts, all phenomena that cause anything. Each axiom is justified in the light of science as it is understood today. Axioms A1-A5 are shown to be consistent, because a simple model comprised of just two phenomena satisfies each Axiom.

We prove that there exists a unique, self-causing, omnipotent phenomenon. This can only be "God" as that word is commonly understood. God is formally defined by a proper description to be this unique phenomenon.

Lastly, crossing the bridge from pure mathematics into science, we theorize scientifically that science as a whole provides a vast, complex interpretation for the three undefined terms, albeit an incomplete and continually evolving interpretation, which satisfies all five Axioms. This means that, according to science, God exists as formally defined.

Abstract of Version 2 Technical Paper (52 pages)

Title: G Theory Version 2: Theory of Absolute Phenomena
Author: Jonathan Richard Emerson

Version 1 of G Theory is presented in Nine Videos. Using five axioms, A1 through A5, and First Order Predicate Logic, the existence of a unique, self-causing, omnipotent phenomenon is proven. However, skeptics may question whether some of axioms A1-A5 accurately depict reality. In the spirit of skepticism, Version 2 of G Theory is presented here, entitled the Theory of Absolute Phenomena (TAP). TAP excludes A1, includes A2 and A3, modifies A4 and A5, and justifies 5 additional axioms, A6 through A10. This new theory features a second G proof and a modified definition for God, giving a slightly different result or "flavor" of God. A variation of TAP, which revises A1 and excludes some of the other axioms, also proves the same result.

TAP is consistent with the theory presented in Version 1, i.e. they may both be true; and if you happen to accept all of the axioms of Version 1, then you will probably also accept the axioms of TAP. On the other hand, some may believe that there exist Absolute (either self-causing, or entirely causeless) phenomena other than God; while Version 1 prohibits this, TAP specifically addresses this possibility.

The Causal Equivalence Principle demonstrates that in TAP, the question of whether Absolute phenomena should be self-causing or causeless is irrelevant because it bears no substantive consequences either way.

In order to maintain the philosophical position of atheism, rejections of Version 1, TAP, and its variation are all required. The logical consequences of these rejections are categorized such that any atheist must believe in something bizarre or impossible from one of a small number of categories.

Origin of G Theory from Hatcher and Its Divergence from Hatcher

The original concept for G Theory is due to the astonishing, ingenious, groundbreaking work of the great mathematician William S. Hatcher (1935-2005), including two of the three undefined terms, the concept for the third undefined term, a portion of the axiomatization, and the essential idea of the Version 1 proof that God exists.

However, several modifications have been made to Hatcher's axiomatization so as to greatly improve the clarity and simplicity of the theory. For example, with enormous respect to Hatcher, his rather confusing distinctions of "element," "composite," "entity" and "part" are eliminated in favor of the single, undefined term "part." Also, we have omitted one of Hatcher's axioms (called "p.3" by him), which he used to prove that God is "indivisible."

In Version 2, the axiomatization is substantially different from Hatcher's, and it is expressly shown that all absolute phenomena other than God are parts of God, contrary to Hatcher's "indivisibility" of God. In Version 1, we do not prove "indivisibility," because doing so would be inconsistent with this result in Version 2.

The variable h and the constant H used in the Videos and in the Version 2 Technical Paper are in honor of Hatcher.

Free Download Links

Click here to download the Version 1 Techincal Paper in pdf format.

Click here to download the Version 2 Techincal Paper in pdf format.