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God At Rest - Godel's Incompleteness

That p&q-1 may simply entail Pos(q-1) without a positive property in "s" (excepting p) is a distinct possibility. Liberty must be positive and it is arguable in this case that there must be an equivalence to liberty found in a positive property not virtue.

It was argued that s was "in the filter" and v not so. Yet there is a different filter {p, u-1, v-1} that operates on the converse of this principle, stating that s is not in the filter as it may not be positively "rested upon" whereas v most certainly so.

Then the two statements compatible with both sides of the disjunction in either filter are respectively (r&s)-1 and u&v. It is no wonder then that {p, (r&s)-1, u&v} also form a filter. Then the octal is closed.

As the terms of {p, (r&s)-1, u&v} are necessarily true given either outcome of the previous two filters {p, r, s} and {p, u-1, v-1}, there is free exercise between the pair (r&s)-1 and u&v given the virtue in p.

So, I do not expect for there to be any properties that are positive and outside of the grasp of God: the exceptions being r&s etc. which are clearly not-positively exemplifiable. Does God "rest" on these? He can not logically perform these acts; so in some sense He must do so!

Comparing this to the situation corresponding to the statement that a God of all truth would never truthfully be able to answer the question as to the decidability of the statement "The God will always say this statement is false", i.e. whether it is true or false. (Cf. Godels completeness theorem on this site.) I may argue as I also do;

God is at liberty to state as r: "it is true" or as s: "it is false". In fact, the statement (r&s)-1 is true on both sides of the disjunction, r&s is our expected quandary present in the trap of the question, but (r&s)-1 is the ability to rest or skirt the question and freely state either r or s as any human would. God, is not trapped and may rest at will as do I when I am asked the same question. I can flip-flop and God is just as free to do so as I am. I operate on the same logic!

Considering this principle; it is natural now to state that if there is a decidability as to two acts; say u-1 and v-1 then Pos(u&v) is a given. - it is true no matter which side of the conjunction u-1 <=> ¬v-1 is carried by free exercise of virtue. I can likewise generate a suitable statement: "The God will never rest if the alternative is always to rest." Then God is free to perform (u&v) and logic is satisfied.

Likewise, "God will never act if the alternative is always to act" would leave us with r<=>¬s resulting in the statement (r&s)-1 being always positive.

Then the ultrafilter (and subgroup) {p, (r&s)-1, u&v} become an expression of the freedom found in the Holy Trinity; which for ourselves has given us a sense that God is inconsistent (I may skirt the existence of God by denying that r&s etc. are not positive! I find inconsistencies not in God, but in my own logical understanding of God.)

{p, (r&s)-1, u&v} then is a statement of liberty: Is God at liberty to rest or act? In truth He is free to do either; I should prepare a statement as before: "God is not free if the alternative is always freedom." Yet then, freedom for God indicates that He may rest!


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