We should certainly try to understand the terms.

Pertinacity is one of the most incorrectly used terms.  Let's understand it by contrast.  Priest utters a heresy.  You point it out and he says it was a slip of the tongue.  Not petinacious.  You point it out, he looks it up, and he says, "oh, my bad ..." and retracts the view.  Not pertinacious.

Those are the types of things that pertinacity rules out, so someone doesn't lose membership for merely uttering a heresy.

Now, pertinacity does not require someone to consciously think, "I know that the Church teaches this and that it's heretical to deny it, and I deny it anyway."  That degree of conscious and deliberate rejection of dogma is not required, and there has been an attempt by R&R to turn pertinacity into some phenomenon that can only be discerned in the internal forum.

It suffices for petinacity that someone repeatedly make the assertion (so not a slip of the tongue or simple mistake) and appear to be very strongly in favor of it, i.e. for them to adhere to it.

Bergoglio, for instance, and actually all the other V2 papal claimants as well, teach the heresy that there can be salvation outside the Church, that the Old Covenant continues in force and is salvific for the Jews (the heresy Father Kramer points out) ... and they're certainly PERTINACIOUS about it.  They say it over and over again and teach it, and they're clearly adhering to it as something they strongly believe in.  That suffices for pertinacity.  Period.  There's no requirement to discern the internal forum, nor is that ordinarily possible.

We should certainly try to understand the terms.

Pertinacity is one of the most incorrectly used terms.  Let's understand it by contrast.  Priest utters a heresy.  You point it out and he says it was a slip of the tongue.  Not petinacious.  You point it out, he looks it up, and he says, "oh, my bad ..." and retracts the view.  Not pertinacious.

Those are the types of things that pertinacity rules out, so someone doesn't lose membership for merely uttering a heresy.

Now, pertinacity does not require someone to consciously think, "I know that the Church teaches this and that it's heretical to deny it, and I deny it anyway."  That degree of conscious and deliberate rejection of dogma is not required, and there has been an attempt by R&R to turn pertinacity into some phenomenon that can only be discerned in the internal forum.

It suffices for petinacity that someone repeatedly make the assertion (so not a slip of the tongue or simple mistake) and appear to be very strongly in favor of it, i.e. for them to adhere to it.

Bergoglio, for instance, and actually all the other V2 papal claimants as well, teach the heresy that there can be salvation outside the Church, that the Old Covenant continues in force and is salvific for the Jews (the heresy Father Kramer points out) ... and they're certainly PERTINACIOUS about it.  They say it over and over again and teach it, and they're clearly adhering to it as something they strongly believe in.  That suffices for pertinacity.  Period.  There's no requirement to discern the internal forum, nor is that ordinarily possible.

I think your definition of "pertinacity" is loosey-goosey.  Do you have a source?

How do penitent Catholics get absolved from their sins? They go to confession.
How do penitent non-Catholics get absolved from their sins? They can't.
   

A heretic must abjure his heresy to be absolved of his sins. There is no sacrament without absolution, right? So, is it possible that the abjuration of heresy is what causes the former member of the Church to re-enter the Church, allowing him to receive absolution (the Sacrament) which only Catholics can receive?

A heretic must abjure his heresy to be absolved of his sins. There is no sacrament without absolution, right? So, is it possible that the abjuration of heresy is what causes the former member of the Church to re-enter the Church, allowing him to receive absolution (the Sacrament) which only Catholics can receive?

No, I thought the same thing for a long time, but if you look it up in canon law, you will find under normal circuмstances, a public abjuration of heresy is only required for new converts prior to their baptism, or if the bishop or confessor makes it a requirement. Otherwise the penitent walks into the confession as a Catholic same as you and I do.

Obviously it depends on the authority, the heretic and the censure that is attached to the sin, and if it is reserved to the Holy See, or to the bishop, or whatever other penalties/requirements are part of that censure. But let's face it, nowadays nobody with the authority to do it is going to excommunicate anyone for heresy, schism or apostacy, which makes this whole conversation somewhat mute. But public abjuration is not always required in every case.

Fr. Wathen notes in Who Shall Ascend?:
"It may surprise lay readers to learn that in the traditional formula of absolution in the Sacrament of Penance there is a general absolution from the censures of the Church. This means, of course, that everyone who has received a censure, and everyone who is "under a censure," is a Catholic, since he goes to confession to seek its removal. [The priest first lifts the censure then forgives the sin].... "May our Lord Jesus Christ absolve you: and I, by His authority, absolve you from every bond of excommunication, suspension, and interdict, in so far as I am able and you are needful. Next, I absolve you from your sins, in the Name of the Father, and of the Son, and of the Holy Ghost. Amen."

Right, but what I am saying is the abjuration of heresy (public or privately in the confessional) takes place before the absolution of sins. The censure is lifted in the confessional prior to absolution of sins. The sacrament is not effected without absolution of sins, so I think there might be some distinction to be made between the heretic abjuring his heresies/the censures being lifted, and the absolution (the sacrament, which only Catholics can receive) being given only after those things occur

Well, yes, I would expect that the priest, at the very least, would ask something along the lines of: "So you agree to stop preaching that heresy from now on and you know it's heresy and no longer believe it?" then lift the censure and then absolve the sinner.  

But the whole point is that if it is a Catholic who commits the sin of manifest heresy, he is still a Catholic, he is still a member of the Church since he can still go to confession if he decides to repent.          

Well, yes, I would expect that the priest, at the very least, would ask something along the lines of: "So you agree to stop preaching that heresy from now on and you know it's heresy and no longer believe it?" then lift the censure and then absolve the sinner. 

But the whole point is that if it is a Catholic who commits the sin of manifest heresy, he is still a Catholic, he is still a member of the Church since he can still go to confession if he decides to repent.         

There is nothing stopping anybody at all from walking into a confessional and confessing their sins. Simply being in a confessional with a priest does not necessarily mean someone is Catholic. Hypothetically, a jew, Protestant, Hindu, etc. could do that. But they cannot receive absolution (the sacrament) because they are not Catholic. My point is, a heretic must abjure his heresy before being absolved of his sins. That is what allows a former heretic, someone who was outside of the Church, but is no longer, to receive absolution.

>Heretic enters confessional. *No sacrament at this point

>Heretic abjures his heresy and confesses other sins if necessary. It is evident he is no longer a heretic *No sacrament at this point

>Censure is lifted, former heretic is now a member of the Church again *Still no sacrament at this point

>Former heretic receives absolution *The Sacrament is effected, which only Catholics can receive

I really cannot agree with Fr. Wathen's "once a Catholic always a Catholic" and "heretics are still members of the Church" ideas. It seems incredibly novel to me and flies in the face of what the popes have taught:

[The Church] firmly believes, professes and preaches that all those who are outside the catholic church, not only pagans but also Jews or heretics and schismatics, cannot share in eternal life and will go into the everlasting fire which was prepared for the devil and his angels, unless they are joined to the catholic church before the end of their lives; that the unity of the ecclesiastical body is of such importance that only for those who abide in it do the church’s sacraments contribute to salvation and do fasts, almsgiving and other works of piety and practices of the Christian militia produce eternal rewards; and that nobody can be saved, no matter how much he has given away in alms and even if he has shed his blood in the name of Christ, unless he has persevered in the bosom and the unity of the catholic church.

Pope Eugene IV, Cantate Domino

The practice of the Church has always been the same, as is shown by the unanimous teaching of the Fathers, who were wont to hold as outside Catholic communion, and alien to the Church, whoever would recede in the least degree from any point of doctrine proposed by her authoritative Magisterium. Epiphanius, Augustine, Theodore :, drew up a long list of the heresies of their times. St. Augustine notes that other heresies may spring up, to a single one of which, should any one give his assent, he is by the very fact cut off from Catholic unity. “No one who merely disbelieves in all (these heresies) can for that reason regard himself as a Catholic or call himself one. For there may be or may arise some other heresies, which are not set out in this work of ours, and, if any one holds to one single one of these he is not a Catholic” (S. Augustinus, De Haeresibus, n. 88). 

Pope Leo XII, Satis Cognitum

Actually only those are to be included as members of the Church who have been baptized and profess the true faith, and who have not been so unfortunate as to separate themselves from the unity of the Body, or been excluded by legitimate authority for grave faults committed

...

For not every sin, however grave it may be, is such as of its own nature to sever a man from the Body of the Church, as does schism or heresy or apostasy


Pope Pius XII, Mystici Corporis

It’s not that simple.  Heresy is a MAJOR SIN.  A simple confession does NOT fix the grave harm done by heresy.

A Catholic who is guilty of  heresy commits a mortal sin. Heresy is the worst of all the sins, that is what heresy is, a sin. The only way a Catholic can be absolved of mortal sin is through confession.  

IF the censure attached to the sin requires an abjuration then so be it, once completed in what, 60 seconds? 2 minutes? 3 minutes? they then would walk right into the confessional to be absolved exactly the same as you and I and all Catholics have done all of our lives. 

Whereas as typically, the priest always presumes our contrition and firm purpose of amendment prior to absolution, the censure attached to the sin of heresy requires the heretic to profess as much with the abjuration, privately or publicly.  

Compare that to a heretic who was never Catholic and wanted to repent. Before they could go to confession they would first have to become a member of the Church through all the usual catechetical instructions etc.,

This is basic Catholicism, it is not complicated. It really is not the least bit complicated. 

I have a close family member that was denied absolution by a priest for schism (not SV because this individual is a NO).  That person was sent to the bishop for absolution.