According to the axiom of virtue, the binding together of p&q-1 is such that the necessarily positive p entails only positive predicate Pos(s) (and all that positivity which is entailed of that "s" only) as from Pos(p)&Pos(q-1). However Pos(q) is true and so Pos(q-1) appears to always evaluate as false.

It becomes clear from the embedding of the octal, that on choosing that outcome Pos(s), there is always the principal element of rest present: in fact the conjunction of Pos(p)&Pos(q-1) will always entail Pos(p)&Pos(eq), without fail. (And eq is positive.)

Yet how, then, can the binding of p to q-1 provide the sense of linearity required to generate all Pos(s) from Pos(p&q-1)?

In truth, the virtue required to entail Pos(s) from that conjunct appears to be the same between any two disjunctions sharing
Pos(s) on that one side, independent of the other side of the disjunction in q or r. This independence at first glance appears fatally flawed. Is God then inconsistent?

For God, Ω is found complete in all positive predicates across every disjunction, so the conditions of the axiom of virtue maximise the sets in disjunction. I.e. N¬(Pos(r)=>Pos(s)) and N¬(Pos(s)=>Pos(r)).

Then the only constraint on Pos(s) need be the disjunction itself, as if between worlds or otherwise found in a "choice" made.

Every property r, s not in scope becomes as some u-1 or v-1, or else an excluded middle or its positive negation.

Omnipotence, then, is such that given each disjunction (as if considered to appear in a different "world"), each world sharing but one side of the disjunction has an independent or different "constraint" due nature, and locally by Leibniz' law as of indiscernables, each similar disjunction is found "locally" unique (and evaluated at the disjunction). The constraint of each "world" is dependent on the virtue acting.

That p&r-1=>s and p&s-1 =>r, indicates there is such a singular "p" for preserving the sets on both side of any disjunction: the axiom of virtue would indicate that Pos(p)&er=>Pos(s) is independent of "r", and by rearranging, Pos(p)&es=>Pos(r) is independent of "s". As these sets in complement are consequent of nature and occur by "happenstance", the only contingency is the act of virtue in p. For, then, there is liberty present in the form of ep.

There is no sense that Pos(p)&es=>Pos(r) is truly only Pos(r&ep)&es=>Pos(r&er) with the octal's valid er=ep&es. That independence either side ensures p, r, s remain as completely disjoint sets (else there is only one set found and no disjunction), and though it is true that q-1 is not positive, it yet logically remains on the side in Pos(s) though God then rests on the positive eq only. (Just as p-1 is required to close the ultrafilter in q and/or r.) There is a unique virtue not ep for every q-1 not eq on that one side in Pos(s).

Then life (liberty), the world (universe) and everything (Ω) agree in the octal, and the 42 possible and valid logical schemas with it.

Each disjunction is found to constrain virtue: ¬Pos(s-1)=>p-1&Pos(q)=>Pos(r) which will not allow the inclusion condition of the ultrafilter in all r to include p-1 which is necessarily negative, and so will not include ¬Pos(s-1) which entails it; which is also negative. Liberty, then (as p) is the restrictive condition on each side of the disjunction, and the real constraint on liberty remains that which is possible only, even for God in the old name/mystery, but not in the new name. (Each middle is found (re)workable, and God may alter the creation or disjunction to make a virtuous "paradise".)

God's hands are not tied.

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