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Dear Plenus Venter, thanks for your response. I know the son of the Mr. Wilson to whom you refer. In my opinion, Plenus, we cannot go wrong by accepting the praxis of our Bishops and Superiors on this; it should be noted that, as you say, defect of intention and so on can crop in, Fr. Pierre Marie's study admits this, and thus a careful background investigation into the concerned candidate is generally carried out. The Bishops and Priests of the Society would discuss together what to do about it, and then go ahead, and imho, it's almost inconceivable that they in their collective wisdom could make a mistake on such a matter. If grave positive doubts were present, and especially if it was requested, there would be conditional consecration. But I think we as lay faithful Catholics would do well to accept their judgment.

Just passing through now and don't intend to answer Meg and others right away. I'll just post an excerpt from the new rite in the text of St. Hippolytus, which effectively depends on an eastern rite still in use, and thus we can assure ourselves, is in itself certainly valid.

"Let the bishop be ordained after he has been chosen by all the people. When he has been named and shall please all, let him, with the presbytery and such bishops as may be present, assemble with the people on a Sunday. While all give their consent, the bishops shall lay their hands upon him, and the presbytery shall stand by in silence. All indeed shall keep silent, praying in their heart for the descent of the Spirit. Then one of the bishops who are present shall, at the request of all, lay his hand on him who is [to be] ordained bishop, and shall pray as follows, saying:

‘God and Father of our Lord Jesus Christ, Father of mercies and God of all comfort, who dwellest on high yet hast respect to the lowly, who knowest all things before they come to pass. Thou hast appointed the borders of thy church by the word of thy grace, predestinating from the beginning the righteous race of Abraham. And making them princes and priests, and leaving not thy sanctuary without a ministry, thou hast from the beginning of the world been well pleased to be glorified among those whom thou hast chosen. Pour forth now that power, which is thine, of Thy Principal Spirit, which thou gavest to thy beloved Servant Jesus Christ, which he bestowed on his holy apostles, who established the church in every place, the church which thou hast sanctified unto unceasing glory and praise of thy name. Thou who knowest the hearts of all, grant to this thy servant, whom thou hast chosen to be bishop, [to feed thy holy flock] and to serve as thy high priest without blame, ministering night and day, to propitiate thy countenance without ceasing and to offer thee the gifts of thy holy church. And by the Spirit of high-priesthood to have authority to remit sins according to thy commandment, to assign the lots according to thy precept, to loose every bond according to the authority which thou gavest to thy apostles, and to please thee in meekness and purity of heart, offering to thee an odour of sweet savour. Through thy Servant Jesus Christ our Lord, through whom be to thee glory, might, honour, with [the] Holy Spirit in [the] holy church, both now and always and world without end. Amen'." (The Apostolic Tradition of St. Hyppolitus).

Mention is made of high Priests [summus sacerdos] and the Spirit of High Priesthood in the rite, which is just another term sacred Tradition, the Fathers and ancient liturgies use for the Episcopacy. By analogy with the three grades of order that existed in ancient Israel, the Deacons are Levites, simple Priests are Priests and Bishops are high Priests. This analogy is pointed out often by the Church Fathers. It is clear in the rite above that the specific grace of the Spirit of the High Priesthood or the Episcopal Authority given to the Apostles is being conferred. It is not doubtful that high Priesthood is univocal. Simple Priests are not High Priests. Moreover, is it doubtful that the Apostles were Bishops? No.

Part of the problems here are antiquarianism, and also a desire for ecuмenism with the East. That is sufficient to not use the rite. But it doesn't matter how much or how far the ecuмenists look in antiquity, or in the East, they won't be able to find an invalid rite, without minimal significations of the episcopacy at least.

Here's Fr. Pierre Marie's original study for those who wish to pursue their inquiry further: http://sspx.org/en/validity-new-rite-episcopal-consecrations

"Let us note in passing that these two rites are perfectly Catholic ... To assure ourselves of the validity of Pope Paul VI’s rite, it will suffice for us to place side by side the new consecratory prayer and the two Eastern rites in question. The validity of these two rites can in no wise be called into question, otherwise the Coptic Church (Catholic as well as Orthodox) and the Syrian Church (which includes the Maronites) would have neither bishops nor priests, nor would they ever have had them. We have prepared a four-column comparison (refer Table 3: Four-column comparison of 1968 edition with Hippolytus text, Coptic and Maronite Rites) with, in order from left to right, Pope Paul VI’s new consecratory prayer,[77] the Latin version of the Apostolic Tradition [i.e., “of Hippolytus”—Ed.],[78] the Coptic rite, and the Syrian rite. For the latter two texts we have used the Denzinger translation.[79] With the four prayers transcribed into the same language, the comparison is made easy." See Table 3 http://sspx.org/en/table-3-validity-new-episcopal-consecrations

To be fair, the FSSP has agreed to some things the SSPX has not.

One of the big ones, in my opinion, is the view on the new Mass. FSSP clergy sign a statement that includes, among other things, agreeing to the "valitudinem" (health, wellness) of the new Mass.

This is much much more than agreeing to the "validitatem" (validity) of the new Mass (according to the typical edition, in Latin, etc.) that the Archbishop seemed to agree to at least at one point.

By saying the new Mass is "healthy", the FSSP is in principle saying that there's nothing really wrong with the new Mass, though they may think the old Mass is "better". That's hardly a position from which to restore tradition.

Yes, you are right. Though I think that there may be many clergy in the FSSP who really can't stand the New Mass, but they have to keep quiet about it. At least the SSPX does, at times, still speak out against the New Mass. That's a good thing, of course. But they rarely speak out against Modernism.

On the other hand, at the local SSPX chapel here, the laity stand during the Agnus Dei and Sanctus at a High Mass (which appears to be in keeping with the practice in the New Mass). But....the local FSSP still kneel during the Angus Dei and Sanctus. What are we to make of that?

Well, Mr. Ladislaus, I don't have to justify my choice to anyone; but let me explain. I believe the SSPX is the best Fraternity for Catholic Tradition by far - doesn't mean I think the FSSP, the ICK and other Indult groups are bad or non-Catholic, I don't. The SSPX has a special role to play in Church Restoration. As of Spring 2017, beside others not mentioned, the Society had Priests : 612 Seminarians : 204 Pre-seminarians : 36 SSPX Brothers : 116 working around the world and around the clock for the salvation of souls worldwide. Why should I choose any other Fraternity? It's not a case of good or bad, but of the SSPX being better and the best.  

Really?  You prefer SSPX over FSSP due to the size of their organization?  I was asking specifically with a view to their respective theological positions.  Why is the theological position/status of the SSPX better than that of FSSP?  By answering this way, you're demonstrating that you have no other reason for your preference than personal taste.  Consequently, people like you are in fact schismatic for refusing full communion with the Church when you have no reasons in conscience to prevent you from going with FSSP.  Dear God, I would never break communion with the Church for reasons this superficial.  You're the kind of seminarian SSPX was trying to draw with their fancy new seminary.

So you cite alleged Eucharistic miracles and words purportedly uttered during some exorcism as theological proofs for your "positions" ... such as they are?

Lord, please deliver us from the priests who derive their "principles" from emotional considerations (feel-good pseudo-revelation and the coolness of the seminary).  We're in a world of trouble.