The Debt Of Love
So, the disjunctions forming the octal have results which follow from the same virtue both sides; r&u^{-1} and also s&v^{-1} are consequences of the same virtue.
That the virtue splits into disjoint sets; to entail say r or s is found a constant in virtue but to alter one of u^{-1} or v^{-1} is to alter a virtue separate to that entailing r or s, and this is an astonishing result (see the book), but these sets must be also disjoint - which is an equivalent of the outcome of the reasoning to follow.
Now, when I hold equivalent r and p&s^{-1} as well as s and p&r^{-1}, r and s are outcomes of the same virtue p. However, I balance these accordingly with the reasoning that the charitable love (agape) that motivates someone to aid another as if "r" is the equivalent to that which is in action when the alternative (to r), is not rested upon, but when there is a functor of virtue (a "debt of love" ) in p.
Similarly, that same love is present when "s" is the result whenever that functor acts upon r^{-1}, when "r" is at rest. Yet how may this be?
I should reason along the following lines, that as "r" and "s" are wholly positive and p is a virtue, r^{-1} as well as s^{-1} are never positive but p is "bound" to either r^{-1} or s^{-1}so that p&r^{-1} or p&s^{-1} are **only** positive and Pos(r^{-1}) or Pos(s^{-1}) are a nonsense (for breaking the closure of p is impossible as virtue is closed).
Then I suggest (once in the know) to ignore p, and simply state r = p&s^{-1} with the equality.
So, if I do not complete a positive act "r", and I do "s" which is also found a wholly positive act instead, I act in the same love that is in "r" to do "s", because I was moved with compassion out of love, rather than moved directly with agape love itself as "r".
Is there any difference? In virtue there is no sense that "r" is less positive than "s", the love needed to choose "s" instead of or over "r", is no different than that in choosing to do "r" instead of "s", that one (as "r") was readily performed in agape love, and for the other, one was moved with compassion for the sake of its opposite not worked (as s^{-1}), I should note that virtue, bound as it is is ever-moving on inaction, and that the equality to "r" and "s" with virtue bound as it is entails that virtue is required for "r", as it is for "s" whether or not "r" or "s" are considered at rest; for there is no rest while agape love is acting in compassion.
If r^{-1} is considered a debt, then "s" is the same debt paid with the same love in "r", that of p; for r is p&s^{-1}.
Now, what of (r&s)^{-1}? This is also a consequence of the same love in p, acting as it does in p&(u&v)^{-1}. The argument is symmetry once again, yet here virtue has acted on that which it has already completed. (both of u&v conjoined are rested upon, and on the other side, r, s, are works already completed, as p&r&s is also u&v, then if p&(u&v)^{-1} is as positive as (r&s)^{-1} then there is only rest; a product of agape love already and most surely having acted.) Then u&v ∨ (r&s)^{-1} is merely indicative of the freedom found in virtue; and that virtue also has a residue.
If I choose to rest on (r&s)^{-1} then counter intuitively this requires me to have rested on both "u" and "v" conjoined; yet these works are positive when in action together as u&v. Those works must have already been done in order for the octal to rest on them as u^{-1}and v^{-1}separated.
Now, that love acts to one side or the other if the alternative is not worked is, I hope, now apparent; but also the very same motive to do either: which is to excel upon the alternative out of agape love. There is no debt for the perfect, but to act in compassion as on p&s^{-1} without the direct love of "r" is to love as with agape love, with no difference. Even if "r" and "s" are sets totally disjoint in positive properties.
As they are disjoint, I should note that the disjunction is always freely decided: to act one side or the other is positive, and each side is a choice of compassion or agape love (whether indirect or not). The love acting directly in r is the same love acting indirectly in p&s^{-1}, because agape love is compassion and pity and charity and to put the self aside to instead help another. There is no difference to motive, Paul truly had it right with his more excellent way.
Now, to rest on p&(u&v)^{-1} = (r&s)^{-1} in equality is **NEVER** equal to performing a "work of nothing" out of love. It is a sure reckoning on charity that God, will always act to the positive; for the works p&r&s as well as its equal u&v are freely decided also. If this is the case, then for the free decidability of virtuous choice (and agape love) it is impossible for the works in r&s not to have been completed already, as are also those works in u&v just as certainly worked.
Those works found completed r&s instead become works in u&v because virtue has acted. Virtue is never bound to the empty set, not ever. Instead there is is a dynamic at work in the octal, a life more abundant.
If God chooses p&(u&v)^{-1} = (r&s)^{-1} it is only ever to rest upon works already completed (here u&v), otherwise virtue is nothing as it is (in truth) never inactive when it is present. Those perverts that would sit idle and call it virtue have a reckoning coming indeed, and it will surely come as a thief in the night.
That there is a split of virtue is crucial for this separation; for the octal is just as positive in virtue when r and s are out of scope altogether and replaced with the sets' principal elements e_{r} and e_{s} alone instead. Though imperfect, the disjunction now found composed of e_{r}&u^{-1} and e_{s}&v^{-1} must remain positive; this is fine, and not imperfect unless out of some faulty rearrangement the freedom of virtue "r" is now some "u" and "s" is now become some "v".
Instead, a different set of virtue may be employed out of the ever-present liberty to rest on "r" and "s".
Then I could annotate the altered disjunction in that different virtue as e_{r}&(r&u)^{-1} ∨ e_{s}&(s&v)^{-1} which is now perfected. Therefore, I hope it is become more apparent that to rest on u^{-1} and v^{-1} is to rest only on works completed that accrue over time. For any set to move from "r" to "u"
requires a virtuous choice in the same disjunction as that of r&u^{-1} ∨ s&v^{-1}; then imperfection (perverse as it is) would apparently close the octal to an inactive (perverted) subset without either having good works completed in u and v, or is found lacking, without ever completing works yet (or once) to do in "r" and "s". Those practicing such deceit are truly perverting the good works and name of Jesus Christ.
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