To Tread On Serpents
Now, as the dialectic is privated by a serpent transposition - it makes sense to once again backtrack to the original K4 form of the filter in {p, r_{0}, s_{0}} and examine how to counter such arguments - for in the form of the K4 filter the argument simplifies somewhat.
Whether there are two or three people present: (or more) there is one constant that remains in scope - the believer.
Assuming the believer is not in a 1-1 conversation but is actually being manoevred into compromise or exclusion, in order to remove the applied word of God from the discussion - there is then the dialectic process made present for the believer to overcome.
Assuming two opposing roles, (one of which could be the believer) when two or more gather against one: and there is made the dialectic or the excluded middle as an impossible burden to private readiness of virtue: i.e the logical disjunction of virtue N¬(p&¬(r_{0}&s_{0})): then, without any equivocation we shall state that the believer takes the place of the minister of virtue "p".
Then in order for virtue "p" to be privated there is either the middle found initially as r_{0}&s_{0} breaking closure or the middle is found in N¬(p&¬(r&v^{-1}&s_{0})) say, where v has traded sides to conjoin to r. (Properly that disjunction should become N¬(p&r_{0}^{-1}&¬(s&v^{-1})) which appears to be completely logical and indistinguishable from the correctly formed N¬(p&s_{0}^{-1}&¬(r&u^{-1 } )). After all, the only difference is N¬(p&v&¬(r_{0}&s)), it is near identical but for the placement of the closure of the sets in the octal. For from the mapping table in chapter 4 of the book it is clear that the correct inference to make is one of N¬(p&(r_{0}&s_{0})^{-1}&¬(u&v)^{-1}) and it becomes a consequence of (r&s) v (p&(r&s)^{-1}=>(u&v)^{-1}) that the initial conditions of both (u&v)^{-1} => u^{-1} or v^{-1} etc. hold quite separately, wholly permitting the appearance of this dialectic device.
So, if there appears to be the same logic, how would one tread? Carefully I hope.
Once the believer is engaged in the dialectic the believer is immediately forced to concede to the position that the earthly filter is possibly in effect and the logic subject now to it's irregularities. For it is not the middle that is dismissed, but the virtue: as it is impossible for the virtue to be found operating r&v^{-1} as well as s&u^{-1} in scope with that virtue in p. (They have presence in the octal, but together private virtue in that particular triple.)
Did you miss it? There is the requirement for virtue to be privated to a positive property (or directly to the empty set: one should then counter by not hurting the oil or wine) otherwise found from a different set in the octal. One may immediately counter with conjunctions of virtue as in the "lamb": for if x is a virtue and y not so: then in a setting where y becomes "as virtue" to partly private the worth of virtue in x; there is a positive property in x&y that is sufficiently indistinguishable from a virtue: and that virtue x&y is either able to be exemplified or is part of an excluded middle. In the former case we are done and the lamb won the argument: but in the latter we should possibly move to a closure in a different K4 group, whether of {p, u^{-1}, v^{-1}} or of (p, (r&s)^{-1}, u&v}.
So, since this occurrence to tread on serpents and scorpions occurs only at one point in the argument: having the "readiness of the gospel" is to have the right words to say at exactly the right time - and it is altogether an opportunity too easily missed. The result? The believer overstays their effectiveness and should withdraw swiftly, in order to avoid giving any validity to the appearance of any "godly compromise".
Treading then, is to ensure that the middle with virtue is not dismissed but overcome (virtue is never privated in the readiness to act positively by axiom of virtue) and so for any exemplifiable positive property bound with a virtue p&x^{-1}, if we instead found x^{-1} to be positive from the other side of a disjunction we would have p&x positive; yet the disjunction may be inverted so that instead of x v (p&x^{-1})=>y we would have x^{-1} v p&x => y^{-1}.
Then, by axiom of virtue - given any lack; for any possible positive property in the octal (the whole set of positive properties) there is a virtue permitting the free exercise of that possible positive property upon that lack. (note the "possible" in the disjunction).
So, given a virtue that cannot be privated "p", given any suggestion that there is a positive property that could certainly be exemplified in that settting: there is most certainly some virtue p&x that would entail that positivity required. (The lamb wins).
If the argument were simply "we want to perform r&v^{-1} given a virtue p and an antagonism "s", (v as in the mapping table), then the result is quite simple: in order for the dialectic practitioner to tread on the believer instead, they must insist the believer provide the impossible solution to resolve the problem of the logically obtained middle that is impossible to exemplify - so that the believer would show themselves ineffective and the gospel unable to show any worth, virtue privated: that result is for the believer to then be logically excluded from the discussion. That is to have ones "back broken". The result is to find nothing of value in extending from the K4 form to the octal whole: It, (as God) is denied, virtue privated as ineffective and the gospel is misrepresented by those that see no value in it. Then the dialectic is made to appear valid without virtue. The correction is actually to state that their choice of virtue in "p" is faulty and it should be inferred that another choice should be made axiomatic to the discusssion: for in real terms the burden should shift for v^{-1} to to be acted upon by the other party in dialogue: or for s&v^{-1} to be the conclusion: (Not always a possibility with the same virtue in p). The converse could hold also: that given p, r&u^{-1} may truly be exemplifiable but the believer saddled with the project to find and realise s&u^{-1} given that same p. The result is that the minister of virtue is given an **impossible** task were it not for reapplying virtue in p&x as above, and then stating clearly that p&x=>p and that there is no real difference beyond that extra step in virtue. The result should become that given p&s=>r^{-1} and the required p&s=>v^{-1}, the substituting of (s&v^{-1}) for s should be made and the mapping table is preserved in the same virtue with the proper closure yet with a subtle change in virtue: a minimal change by any account.
So, the subtlety of the serpent is to exclaim that in r v (s&u^{-1}) in a disjunction with virtue p, is resolved by the use of u&v => u or u&v => v (But these are not "logically exemplifiable" properties in that scope.)
The serpents fault is to exclaim that p&r^{-1} => (s&u^{-1}) or N¬(p&¬r&¬s&u) or N¬(p&u¬(r&s)) are valid : yet their validity is found in the K4 form as N¬(p&(u&v)&¬(r&s)) as the negation of the octal's schema and the inference that u&v=>u etc. But u and v are not in scope with u&v when p is axiomatically true.
The solution then is to find u&v properly whole and reform the disjunction in the same virtue p: but that which is perfect does not always come unless that which is in part has been done away with. Asking then, for the resolution in dialogue to be made by including the missing property of u&v (whole in this case) permits the disjunction to be made perfect by loosening the constraint upon r and s by ensuring the overconstrained virtue p, (due to the **lack** of rest upon one of u or v), is relieved from action, constraint in u^{-1} say, thus refined, and grace/virtue abound freely without hampering. There is then some sense in the "unjust steward" operating in the mammon of unrighteousness with the statement of "make it fifty" made to the ungodly instead. (For when they, as ministers of virtue, would otherwise fail; yet then come into habitations eternal.)
There is no "crossing the divide" to practise the dialectic other than preaching Christ crucified: and no reason to try to offer deceit to turn things back on such a failure.
To tread on a snake requires good timing and readiness to lay "down the law". That law should be the wholeness of the octal and it is readily reconstructed if there is the acknowledgement that all the sets in the octal are valid - that there is more than action and inaction on both sides of a disjunction - there is virtue and closure to resolve. In "making it fifty" - who could refuse the opportunity to get what they want by doing less than they are already? In that manner the believer exercises full control without disgracing the gospel, and also solves an otherwise difficult issue without the dialectic and without that earthly and fiat ultrafilter raising itself over the gospel of God.
So, to recap on that logic, the disjunction r_{0} v p&r_{0}^{-1}=>s_{0} is locally, N¬(p&r_{0}^{-1}&¬s_{0}) which is rearranged to the "faulty inference" N¬(p&¬(r_{0}&s_{0})) or N¬(p&(r_{0}&s_{0})^{-1}).
Now, to construct the octal I split those values r_{0}, s_{0} to: r_{0} = r&u^{-1} and s_{0} = s&v^{-1}.
So that faulty inference is reconciled with: N¬(p&¬(r&s)&(u&v)) or the disjunction (r&s)^{-1} v p&r&s=>u&v.
Yet the serpent spirits would switch r for s, or u for v, or even (r&s)^{-1} for u&v.
So; that inference is regrouped from N¬(p&(r^{-1}&u)&(s^{-1}&v)) to N¬(p&(r^{-1}&v)&(s^{-1}&u)).
The fault in the logic is clearly made to appear in that overconstrained virtue. (The closure of a K4 group in the octal is broken.)
The situation is made far worse when those serpents act on their liberty to infer u&v=>u etc reducing the above inference to:
N¬(p&(r^{-1}&u)&s^{-1}).Which could be rephrased for clarity to N¬(p&(r^{-1}&u)&(s_{0}^{-1})). Note that virtue is then overconstrained and a fallacy of equivocation raised. For "p" is not in scope, but some other set in the mapping table (forming the proper row of the filter table). Yet without raising the conjunction of p and whatever "would be" virtue has replaced it in scope to form a new octal, I continue as follows.
Then rearranging to the abberation:
N¬(p&r^{-1}&(s_{0}^{-1}&u)) and this is the final error of the serpent spirit's deception. Virtue has been privated
N¬(p&r^{-1}&(s_{0}^{-1}&u)) rearranges to the disjunction: r v p&r_{}^{-1}=>s_{0}&u_{}^{-1}.
The closure of the virtue broken, that faulty disjunction has a solution in r&u_{}^{-1} v p&r_{}^{-1}&u=>s&v_{}^{-1}. It may be made clear that the inference of Pos(u&s_{0}^{-1})=>Pos(r_{}&p_{}^{-1})=>Pos(r) may be made and that u and r may not private each other. (They may only appear on the same side of the disjunction - and this undoes the transposition made, but the dialectic may still be "spun".)
Similarly, N¬(p&r^{-1}&(s_{0}^{-1}&u)) rearranges to N¬(p&u&¬(r&s_{0})) which overconstrains virtue. It is this final case in which the believer should offer not a compromise, but a lifting of that restraint to the terms of "make it fifty". Properly the division of r_{0} to r&u^{-1} results in N¬(p&(u&v)&¬(r&s)) and this has proper closure in sets of the octal as parenthesised. I.e. (u&v)^{-1} v p&u&v=>r&s
In fact, the division is made on the axiomatic falsehood of r&s within the K4 group. Instead of N¬(p&¬(r&s)) I instead began with N¬(p&r&s) or rather N¬Pos(p&r&s), as that inference from p to r&s is one that cannot be made positively. I.e. there is no inverting the disjunction in scope that would entail r&s or (r&s)^{-1}, that is, given r&s not positive, there is no disjunction (r&s)^{-1} v p&r&s => Pos(r&s).
Then we easily deduce the overconstraint on virtue in r and s are the sets of u and v respectively. To solve the disjunction; u&v should return to scope: each property of u^{-1} and v^{-1} should be relaxed: Pos(r&s) is overconstrained and there is required a solution in u&v instead of the empty set: for without them we only have from that binding (r&s)^{-1} v p&r&s => Pos(∅). p is privated as it can entail nothing else positive: and axiom of virtue leaves p arbitrary; the binding of predicates is made to fail. No virtue becomes with effect.
So, although sets have switched sides in the disjunction - the logical inference is the same in terms of N¬(p&r^{-1}&¬(s&u^{-1})) as equal to the correct N¬(p&(r^{-1}&u)&¬s).
Then correcting the appearance of the empty set in place of "v^{-1}" the result may be stated that either s is doing "too much" and should be refined to ease the constraint on p, or else the disjunction on one side is incomplete - that there is a real "v^{-1}" entailed along with s that belongs in a closure above that of the present or local octal and "Ω" - and so there is a lack of faith in the divine instead, and a solution offered in correct "faith". This last effort is fine within the setting of the believer's fellowship, but not so useful outside of it.
Note the error is in binding: for N¬(p&r^{-1}&¬(s&u^{-1})) is N¬(p&u&¬(r&s)) or N¬(p&¬(u^{-1}&r&s)). And so:
Note that u^{-1}&r&s permits (u^{-1}&r)&s as well as r&(u^{-1}&s). Then in order for the property u in the disjunction to switch sides, it does so only in the middle r&s. That illegality of closure is actually required, and it directly privates virtue by breaking it's closure. Then whilst preserving the middle:
(r&u^{-1})&s v p&(r^{-1}&u)&s^{-1}=>∅ so we actually find that the disjunction is overconstrained: In returning to the dialectic, one recovers v^{-1} so then the disjunction becomes: (r&u^{-1})&(s&v^{-1}) v p&(r^{-1}&u)&(s^{-1}&v)=>∅. And virtue again appears completely arbitrary across the earthy elements: but then this is also a fallacy because of binding, and the predicates should in truth split and properly index the sets in the octal as properly derived.
So, treading on serpents is to find that missing element in u or v upon which the loosening of constraint upon virtue may be made so that the logical inference of virtue with its consequent positive result may appear: and then to give a result in the disjunction (r&s)^{-1} v (u&v).
Then, this is to use the same "keys of hell and death", and the words given to counter such arguments are given by gift of God as much as from intellect. (Were it possible to find the intellect for that!)
Without those keys, the setting is wholly dialectic: virtue would have no part but to be privated: as either become arbitrary or empty. The dialectic operates not with virtue: but in the elements r, s, u^{-1} and v^{-1} in that setting instead.
Then, if you do "fail" and cannot operate in the gospel, the result is become the requirement to leave, and to do so swiftly - the relationship will not profit God in the dialectic.
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