The Empty Essence Is Incompossible
By the model of GF(8) it is not possible for the empty essence φ to be found both sides of a disjunction (giving an empty world). I then state that it, φ, is incompossible. An empty essence simply cannot hold both sides and remain empty of essence.
So, here is a proof that the empty essence may only apply to one element of the octal - as otherwise there is a disjunction with φ found both sides. The operation of the octal and the symmetry of virtue allow the essence (to which φ is falsely applied) to be re-instantiated or regenerated by the necessary existence of the remaining elements, which are also N.E. That essence is completely recovered, excepting the case when φ is applied to the unity (or set of virtues). Then, there is a little more work to be done, which will follow on another page.
I merely state here that the axiom of virtue, when it is assumed to hold, affirms the existence of that unity and virtue without contradiction; no disjunction in virtue ever fails in privation with one or both sides negative: as the axiom holds firm and also leads to no inconsistency in Gödel's axioms, I may safely discard the empty essence. (For the axiom of virtue only depends on freely decided disjunctions; which are here found present in GF(8) whole. The empty essence appears to decide every disjunction necessarily, yet by symmetry the choice is always freely made.)
So, the empty essence φ cannot be the equivalent of any such Godlike individual in the partition of Ω (and again also if it is partitioned with the model in GF(8)). As no other predicates are found possible in Ω for such a Godlike being, the self-difference contains no essence or property in its scope. Then the portion of Ω remaining in the empty self-difference is also empty; it is no essence of that Godlike individual. It may not appear in any freely decidable disjunction with a Godlike essence; only similarly Godlike sets are so freely decided.
As the only possible sets that are compossible with the Godlike are also Godlike (closed to aspiration), assuming the empty self-difference is also an essence for the Godlike individual in GF(8) leads to a useful contradiction rather than simple antinomy overall, as there can be no empty self difference, only the empty predicate equalling itself, as also excluded from every ultrafilter by axiom. Then as the empty self difference leads to that simple contradiction of self-equality in the remainder; it is not an essence for God, it must be completely empty; then the axiom of virtue holds firm every axiom of Gödel's own; with that proposition of φ (or lemma) negated for the Godlike partitioning Ω. The empty essence is an essence, but not for the Godlike in GF(8).
Now, if the empty essence cannot be compossible across all of Ω, then it may yet be applied to every set in the partition separately, as if valid "for every individual". However, each such set in the angel's (the least's) circuit is of an octal maximised; and therefore each individual set is also not compossible with the empty essence. Thus; no set in the octal is compossible with the empty essence!
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