Authority Is An Ultrafilter

We define an ultrafilter U as a set of subsets of a set so that:

1) The empty set does not belong to U (it is "small" we do not want it, as it screws up the following.)
2) If sets X and Y are in U then so is their intersection. (they maintain some form of "largeness".)
3) If a set X in U is contained in a set Y the Y must be in U also. ("bigger" sets than X with the same elements are also members.)
4) For any subset X of the collection M, either X is in U or M\X is in U (a set is large, or it's complement is large.)

(1) The devil has no divine authority placed upon him to correct him, he is at fault in every respect - he is never forgiven or corrected to salvation. Likewise those that are never redeemed have no authority exercised over them to correction to predestination, they are lawless. (There is no authority applied that does not lead to correction.)

2) If X and Y both have been corrected with divine authority then they are or must be both predestinated. A person that is correct in respect to the faults redeemed that are common to both X and Y are themselves corrected with authority (if that redeemed fault common to both by the gospel be the sin under the law.) This intersection excludes every individual with faults that are in one or the other only, or are not redeemed - such a person may without fault be predestined under grace; C.f. children under the authority of both believing parents (a child's sole law.) Such authority always exists to correct..

3) if X is corrected to predestination and has redeemed faults properly contained in those of another Y, We deduce that the interval for the latter is shorter, because X yet has unredeemed faults redeemed in Y. Y may also have such faults, but there are less of them; Y is able to correct X and would not be a hypocrite, Y may use authority to do so. Compare with (2). (Here, Y is correct on a greater subset of the law by L(G), and is finer on that law - but if L(G) be present in X (X is corrected to predestination) then that correction by the gospel is present in Y also. Y is also corrected by divine authority.)

4) A person can be corrected or not; yet a person is predestined or not. Divine authority is present or not. Christ redeemed all, but an individual is saved or not. On the basis of (1) it does not follow that everyone is corrected unless done so by Christ. Christ therefore generates the ultrafilter. The salt lost its savour and Christ salted it again. Christ's interval is always zero. For us, we are redeemed and only those whom are saved are corrected by Christ by definition of "authority" here. Christ came "but for the lost sheep of the house of Israel." Authority is always successful to correct in the ultrafilter - those whom have no authority exercised on them are given over to a reprobate mind, so (4) holds.

Principal or non-principal? Clearly if Christ generates the ultrafilter then it is principal, yet the redeemed and corrected are forgiven: so we may substitute t2-t1 = 0 for any interval present. The arguments in the ultrafilter reduce to those that simply hold L(G) in all respects as before.

If however divine authority is present with us when we are not with the bridegroom, we must have a non-principal ultrafilter: There is then the realisation that the freche filter may be contained in the filter - that every cofinite set is in the filter if it be infinite. What this looks like may be very strange - the arguments would reduce to matters of redeemed fault only without predestination.

1) would be so, since law has been given, there is the condition where people are condemned for their unbelief only. (a cofinite set in all L(X) not L(G))

2) people at fault under the law would be able to correct each other on their opposite's faults that they do not share, they would be hypocrites with respect to those they share in their intersection - that would be a fault. L(X) and L(Y) result from each other in neither having L(G) after correction, yet they would be "finer" together.

3) Clearly, a greater set of faults in the latter imply that the ability to correct is found in the former over those that are not shared: X would be innocent of much of the faults of Y - this is only "relative" though. L(X) would be able to "salt" L(Y).

4) An individual may correct or not merely on the basis of that which they are innocent of. In that case they are innocent with a zero interval for those faults.

There is also another case of the law that has been given by God.

1) God has always given law - there has been no creation without it - there are virtues found in God and His creations, and sin was forbidden or excluded from His creation.

2) A person is under the law when it is broken, two such people under the law are under similar condemnation, whether they share the same faults or not. In regards to the sin, the indiviuals have both found fault with the law itself - this ensures that there is always an intersection in sin under that condemnation, for to find the law itself faulty is a fault - it is blasphemy. In doing so the whole law is broken and sinners are under the whole of the law.

3) If the law is broken, any individual requiring correction with a superset of the same faults as another requires correction also. They are both under the whole of the law and are as guilty as each other. Authority to correct is found in neither - they lost their salt. The superset has less virtue in its complement, but is just as guilty.

4) Any set of faults has its complement in virtue: (There are a set of virtues that do not private any positive properties.) given a fault - that fault entailed an exclusion of some virtue: A set of faults then excludes a set of virtues, and virtues do not exclude the law. The law is such that the man with virtue will have no trouble keeping it. Of course, virtues are defined by the morality of the maker, and as we are his creations that stands for God only. The law does not prevent virtue, it does not over constrain it. Faults are faults or they are justified by virtue in the place of the fault. There is no sin in such virtue. Breaking one commandment to do another whilst doing well is not sin. The judgement is given God, (C.f. the Son of man is Lord also of the sabbath.)

Of course the same argument has many forms, but we remember that the law was given only to those in the OT land of Israel, and hypocrites were to be forced out under penalty of death. Likewise, election is just as exclusionary in its severity; it is absolute and there are no greys in between the black and white. Truth however is the domain of God's judgement, and that is upon the gospel.

Authority then is found only when correction is needed, and that is at the house of God. If there is no interest in the virtues of God or His law - there is no impulse to ever repent. There is no calling to continually educate those that are obstinate and refusing to listen except to ridicule in return. Avoid them all.

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