An Ontological Proof
“The world is everything that is the case.
The world is the totality of facts, not of things.
The world is determined by the facts, and by those being all the facts.
For the totality of facts determines both what is the case, and also all that is not the case.
The facts in logical space are the world.
The world divides into facts” (page 25).¹
The totality of facts is the rearrangement of things and is defined by the relationship of things to one another.
Things are rearrangeable in a proximally closed space within a larger open topology.
Let any collection of things be defined as set (xₙ) at any time (tₙ) within the world, defined as set (W) within topological space (X), where x ∈ W.
Therefore any collection of sets xₙ exist in {W} within space X and the set of all sets {xₙ} is the closed set {W}.
{W} is the totality of space where γ:[xₙ,xₙ₊₁]->W
{W} in topology X has a complement, defined as {∁W}.
All elements x ∈ ∁W are outside of W.
∁W is the totality of space where γ:[xₙ,xₙ₊₁]->∁W
Therefore, the world is everything that is the case, but everything is the case within the world only if there is space outside of the world for things that are not the case to change.
Let us name set ∁W where γ:[xₙ,xₙ₊₁]->∁W “God”
The world plus God is the totality of facts at tₙ and of potential states of facts at tₙ₊ᵧ.
The world minus God is the totality of facts at tₙ and cannot move to tₙ₊ᵧ because the world minus God is an undefinable set.
Therefore, both the world and God exist. However, it is still undetermined whether “God” is a null set or non-null set.
All sets are non-null sets in nature since “state |0) such that ap |0) = 0 for all p is the ground state or vacuum, and has E = 0” still contains nonzero elements x (page 98).²
God, therefore, is a non-null set.
God exists and is something.
