I asked him kindly to change his username and he kindly sent Matthew a PM.  I think it was just changed today.

The definition of indefectibility remains intact, or at least had remained intact for centuries, despite repeated interregna and periods of a lack of a successor of Peter on the papal throne. During such times when a successor to Peter was absent, the Church remained indefectible on the Church’s own terms of understanding indefectibility. Agreed.

We’re discussing indefectibility, not “perpetual successors to Peter.” Deal with the argument. Okay.

The argument is as follows: the “indefectibility” of the Church, on the Church’s own terms as she understands it, requires a hierarchy that has 3 components: a) it, as a composite body united under a certain teaching, teaches or provides to mankind the faith without error; (sounds like trad bishops) b) it provides mankind with the means of sanctification (i.e., sacraments); (sounds like all trad clergy; in fact, I'm fairly certain no one besides trad clergy meet this definition) c) it has the power of ruling and governing with regard to the faith, morality, Church discipline etc. (Yes, trad clergy do these things.)

"There are two types of power in the Church, power of orders and power of jurisdiction. With regard to the latter, we teach that it is not only power in the internal and sacramental forum, but also power in the external and public forum, power that is absolute and quite complete, that is, legislative, judicial, and coercive. The subject of this power are the shepherds and teachers given by Christ, and they exercise it freely and independently of all secular dominion. Therefore, with full authority they rule the Church of God by needed laws that oblige in conscience, by definitive judgements, and by salutary penalties for the guilty, even if they are unwilling; and they do this not only with regard to matters that concern faith and morals, worship and sanctification, but also with regard to matters concerning the external discipline and administration of the Church."

Okay, thanks.

You say above that this definitely ends the R&R position. Do you know how many times sedevacantists have made this same proclamation over the years regarding the end of R&R, using various arguments? And yet.....R&R is still going strong. And your definition of the Council and St Thomas seems only to back up R&R, by saying that the heretics will not prevail against the Church. That's something that we already know.

The Catholic Church is still in Rome, and visible, though she is occupied by modernist heretics. I can't see changing my view of this by reason of the quotes from the Council or St. Thomas and other Fathers, though others here may have a different view of the situation.

Pope Paul IV
cuм Ex Apostolatus Officio
Apostolic Constitution - 15 February 1559

6. In addition, [by this Our Constitution, which is to remain valid in perpetuity We enact, determine, decree and define:-] that if ever at any time it shall appear that any Bishop, even if he be acting as an Archbishop, Patriarch or Primate; or any Cardinal of the aforesaid Roman Church, or, as has already been mentioned, any legate, or even the Roman Pontiff, prior to his promotion or his elevation as Cardinal or Roman Pontiff, has deviated from the Catholic Faith or fallen into some heresy:

(i) the promotion or elevation, even if it shall have been uncontested and by the unanimous assent of all the Cardinals, shall be null, void and worthless;

(ii) it shall not be possible for it to acquire validity (nor for it to be said that it has thus acquired validity) through the acceptance of the office, of consecration, of subsequent authority, nor through possession of administration, nor through the putative enthronement of a Roman Pontiff, or Veneration, or obedience accorded to such by all, nor through the lapse of any period of time in the foregoing situation;

(iii) it shall not be held as partially legitimate in any way;

(iv) to any so promoted to be Bishops, or Archbishops, or Patriarchs, or Primates or elevated as Cardinals, or as Roman Pontiff, no authority shall have been granted, nor shall it be considered to have been so granted either in the spiritual or the temporal domain;So then,
just as he sent apostles, whom he chose out of the world [39] ,
even as he had been sent by the Father [40],
in like manner it was his will that in his church there should be shepherds and teachers until the end of time.
In order, then, that
the episcopal office should be one and undivided and that,
by the union of the clergy,
the whole multitude of believers should be held together in the unity of
faith and
communion,
he set blessed Peter over the rest of the apostles and
instituted in him the permanent principle of both unities and
their visible foundation.
Upon the strength of this foundation was to be built the eternal temple, and the church whose topmost part reaches heaven was to rise upon the firmness of this foundation [41] .
And since the gates of hell trying, if they can, to overthrow the church, make their assault with a hatred that increases day by day against its divinely laid foundation,
we judge it necessary,
with the approbation of the sacred council, and
for the protection, defence and growth of the catholic flock,
to propound the doctrine concerning the
institution,
permanence and
nature
of the sacred and apostolic primacy,
upon which the strength and coherence of the whole church depends.
This doctrine is to be believed and held by all the faithful in accordance with the ancient and unchanging faith of the whole church.
Furthermore, we shall proscribe and condemn the contrary errors which are so harmful to the Lord’s flock.

(v) each and all of their words, deeds, actions and enactments, howsoever made, and anything whatsoever to which these may give rise, shall be without force and shall grant no stability whatsoever nor any right to anyone;

(vi) those thus promoted or elevated shall be deprived automatically, and without need for any further declaration, of all dignity, position, honour, title, authority, office and power.

Vatican I, Session 4, Chapter 3

9.
So, then,
if anyone says that
the Roman pontiff has merely an office of supervision and guidance, and
not the full and supreme power of jurisdiction over the whole church, and this
not only in matters of
faith and morals, but also in those which concern the
discipline and government of the church dispersed throughout the whole world; or that
he has only the principal part, but not the absolute fullness, of this supreme power; or that
this power of his is not ordinary and immediate both over all and each of the churches and over all and each of the pastors and faithful:
let him be anathema.

SESSION 4 : 18 July 1870

3. So then,
just as he sent apostles, whom he chose out of the world [39] ,
even as he had been sent by the Father [40],
in like manner it was his will that in his church there should be shepherds and teachers until the end of time.
4. In order, then, that
the episcopal office should be one and undivided and that,
by the union of the clergy,
the whole multitude of believers should be held together in the unity of
faith and
communion,
he set blessed Peter over the rest of the apostles and
instituted in him the permanent principle of both unities and
their visible foundation.
5. Upon the strength of this foundation was to be built the eternal temple, and the church whose topmost part reaches heaven was to rise upon the firmness of this foundation [41] .
6. And since the gates of hell trying, if they can, to overthrow the church, make their assault with a hatred that increases day by day against its divinely laid foundation,
we judge it necessary,
with the approbation of the sacred council, and
for the protection, defence and growth of the catholic flock,
to propound the doctrine concerning the
institution,
permanence and
nature
of the sacred and apostolic primacy,
upon which the strength and coherence of the whole church depends.
7. This doctrine is to be believed and held by all the faithful in accordance with the ancient and unchanging faith of the whole church.
8. Furthermore, we shall proscribe and condemn the contrary errors which are so harmful to the Lord’s flock.

So, where does your position fit in?  What is your position? That the NO is the Catholic Church and those "bishops" are the Church hierarchy?

So the current Catholic Church is just acting badly/sinfully? Where do you go to mass?