Necessity - Good and Evil

First I think it good to begin with a logical "paradox" (though these examples are not so), entailed of properties that are of necessity false.

Given a property x that is necessarily impossible, I may also write N¬(x). I can also arbitrarily attach any other property y in conjunction and write: N¬(x&¬y). I.e. every such conjunction will entail an arbitrary y.

In this manner I have x => y for every property y.

Similarly, if I have N(z) I may write N¬(y&¬z) for all properties y. Then y => z.

So, does this throw a spanner in the works as regards God? What is virtue but a predicate necessary to Him?

The problem is resolved in that virtue is a predicate necessarily positive, not necessarily held, else all would be virtue!

The real struggle comes from the notion that N¬(Pos(¬p)) for some virtue p, and that consequently God will never act with ¬p. Does this force N(¬p)?

In truth, no it doesn't. That N¬(Pos(¬p)) makes no judgement on whether it renders ¬p possible also, is to be found correct. God, created both good and evil, His creations are free to withhold themselves from virtuous acts, just as much as God is free to rest on works that are already sufficient. A "virtue" cannot be inconsistent with virtue as exemplified by God already; given that virtues p&¬q=>v entailing such v are "suspended" to permit some other virtue p0&¬q=>¬v is enough to show that there is no "necessity" found in Pos(¬p). Liberty may make any "cut" without engendering such a "paradox".

God, will always leave Himself more freedom to work with virtue (comparing the Testaments for example; in particular, that of the law with all grace).

So given ¬Pos(s-1)=>p-1&Pos(q)=>Pos(q)=>Pos(r) is consistent, say, I state that s-1=>p-1&q=>r is truthfully (logically) correct, and that this also depends on the "manifold of virtue" (see chapters 3, 4 and 16 in the book) as also it does on the octal. So, the sets are wholly disjoint, not entailing one another; and in the manifold they have a solution in the octal. Alternatively, consider the manifold a freely resolved "binding on variables" rather than a mere logical "inference".

That every positive property in q is unable to stretch the ultrafilter on "perfections" to include the superset p-1&q with Pos(p-1), does not entail any N(p) or N(p-1) at all. Instead, it only entails ¬Pos(p-1). Every set is maintained disjoint, so out of liberty, there is no such logical "paradox".

Yet, again, there is a caveat. God, must necessarily possess the predicate of liberty in the set of virtue.

But again, can it be said that every individual has that same liberty? If that liberty is found in the right hand, the least or as the zero, the answer would appear to be no. If, however, liberty was a predicate in a singular model the answer could be "yes". Is this predicate only in the set of virtue? (Does it float as zero in the octal as well?)

Whilst human liberty is given to decide every disjunction freely, God has instead chosen to write every disjunction instead (preparing the world for judgement). Then God's minimal liberty "l" (always present) will break closure without rewriting every disjunction. (For that is Christ's pleasure alone.)

It cannot be said that the "least" is another's own free will: but God's rest with him as if upon the octal of the old name is His free choice.

Then liberty (making a cut for God in virtue) is not the liberty of all or any other, being only the conjunction of all the gx. So, by the identity of indiscernibles (Leibniz's law) there is only one such God, with the only essence which is found of the (unique) least "l".

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