Pax, that's not right. Jurisdiction is the authority to teach, govern and sanctify. It was conferred upon the Apostles by Christ when he said: “Going therefore, teach ye all nations; baptizing them in the name of the Father, and of the Son, and of the Holy Ghost. Teaching them to observe all things whatsoever I have commanded you: and behold I am with you all days, even to the consummation of the world,” (Mt. 28 ) not when He consecrated them bishops on Holy Thursday (a few months earlier).
I'm not a canon lawyer, but I see jurisdiction as a Church invention, therefore its rules can be excepted (as canon law does make exceptions). On the contrary, a Bishop's charge to teach, govern, sanctify is of DIVINE invention, therefore this is of the essence of the office. I see jurisdiction as simply a necessary (and important) governmental matter, which gives to the Bishops the TERRITORY in which to teach, govern, sanctify. Jurisdiction is both a permission and a parameter in which to work. But the work itself (teach, govern, sanctify) is part of the sacrament/Divine charge.So too today, this three-fold authority does not come to a bishop by means of a valid consecration. They receive it by legitimate appointment by the pope, and only by appointment from the Pope (as Pius XII teaching in three encyclicals).
I wouldn't define these 3 powers as an "authority" but as part of the sacramental grace/character. The grace of the sacrament is different from jurisdiction/authority because an excommunicated priest/bishop has no jurisdiction but he can still provide confession (I.e. he has the validity and power to provide sacraments) in danger of death.
Any validly ordained bishop who has not been legitimately appointed by a Pope (directly or indirectly), has no authority to teach and govern, although in cases of necessity the Church does supply the authority needed to sanctify (e.g. supplied jurisdiction for confession).
Correct. But the Church only supplies the legal framework for the cleric to act; She provides the full office/validity/grace of the sacrament FOREVER, once the ordination/consecration is complete.
Now, the Church must possess a hierarchy of bishops with the authority to teach, govern and sanctify, since this is necessary for the Church to carry out her mission. Without a true hierarchy, the Church, as Christ founded it, does not exist. Similarly, without a true hierarchy (bishops who were appointed by a Pope), the Church lacks the mark of Apostolicity, which the true Church must always possess. That's what Xavier was getting at.
True, but if a priest/bishop is validly and legally ordained/consecrated then they have the authority to teach, govern, sanctify in potentia. The idea of jurisdiction is simply the "details" of where to carry out the 3-fold powers.
No traditional bishop today has ordinary jurisdiction, nor does any claim to have it. Therefore, they are not part of the hierarchy, or “lawful ministers of the word and of the sacraments.”
All Trad clerics are part of the hierarchy, in the sense that they are validly ordained and that canon law allows them to preach the Faith, provide sacraments, mass and doctrine, under the emergency canons. Everyone agrees they don't have proper jurisdiction, because the Church is in a state of persecution/confusion and the jurisdiction rules are in disarray. I do believe they are "lawful ministers" because canon law provides them to operate legally, therefore their activities are "lawful".
Council of Trent, Session XXIII, CANON VI. "If any one saith, that bishops … who have neither been rightly [legally] ordained, nor sent by ecclesiastical and canonical power, but come from elsewhere, are lawful ministers of the word and of the sacraments; let him be anathema."
I disagree with your interpretation above, and I say that "rightly" means "validly" because the second part of the sentence, which deals with "ecclesiastical and canonical power" deals with legality, not the first part.
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Now all Trad clerics have been rightly/validly ordained/consecrated so they have the 3-fold sacramental duty to carry out. The only question is, where to carry out this mission? In normal times, the Church would give them a diocese. Since we aren't in normal times, canon law allows them to provide the sacraments when the faithful asks them for assistance and in cases of death. Therefore, their providing such is lawful, which makes them "lawful ministers."
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This canon does not apply to any Trad cleric. It would apply to schismatics or to doubtfully ordained clerics.