But there is enough evidence, I believe, for moral certainty in the matter.
 
Pull up Sacramentum Ordinis in Latin in one window and in the official English translation in another window. Notice how the words "validitatem" and "valorum" are used precisely (in the Latin) to mean different things. But in the English translation both of those different Latin words are translated as the same word, "validity."

Also, look at the use of the words referring to "essence" and "substance." These are technical theological terms. In Aquinas, these words refer to very different cognitive and ontological topoi. Any "substance" consists of "matter" and "form" as the genetic components of that "substance." A "substance" cannot "exist" unless there is FIRST a coalescence of matter and form. So a Sacrament (as a particular instance of the Eucharist, for example) cannot "exist" without the presence of BOTH matter and form. The "substance" refers to a particular reality, the thing itself.

An "essence" is very different. The "essence" of a thing is a mental abstraction of properties from already existing things possessing that "essence." The essence is determined by empirical examination of already existing realities (that is, things already built up by the coalescence of matter and form). Another name for "essence" in Thomism is quiddity, or the "whatness" of the thing.  An "essence" is conceptual in nature, a construct of the mind, it is not "the thing itself."

So, only the "substance" of the Sacrament pertains to its "validity." This is Thomism. And it is the basis of the quote from Trent in paragraph 1 of SO, that the "substance of the Sacraments" cannot be changed. Note, however, that in SO paragraph 5, each quoted phrase mentioned is introduced as being "essentialia ideoque ad valorem requisita [essential and therefore required for value]." Nothing in the Latin text, in that section, refers to "substance" or "validity." What???? This should set off alarm bells.


So what is going on in paragraph 5? "Essences," using the precise Thomistic theological terminology, are not related to "validity," but instead, they can add "value" to help us understand the Sacrament better, in this case, the Sacrament of Orders. Why do they "add value?" Because they define the "whatness," or the quiddity, of the particular Order referenced. In other words, something "essential" is helpful to know, but it is not a constituent of "validity." Only the matter and form are constituents related to "validity" of a Sacrament, which is a "substance," an ontological reality. In the case of the Sacrament of Orders, the ontological reality is the indelible character imprinted on the soul of the recipient of the Sacrament.

So the "essential" words that are quoted in SO paragraph 5 are not required for "validity." They are simply the most important (highest value) words in the Preface. The ENTIRE PREFACE is required for "validity" because the ENTIRE PREFACE (and no less) is "the form." To apply the same idea to another Sacrament, would be like saying the following: "I baptize thee, in the name of the Father, and of the Son, and of the Holy Spirit is the form of baptism, of which the word 'baptize' is essential and therefore required for value." In other words, don't use a word like "wash" or "cleanse" or whatever instead of "baptize" because the specific word "baptize" reflects something "essential" in that Sacrament. That particular word helps us understand Baptism in a definitive way.

Bottomline: Pius XII stated that "the form" of each Order is the ENTIRE Preface (for each level of Order). It is reductionism leading to invalidity to restrict the required words of "the form" to only the quoted words that are "essential and therefore required for value."

Interesting, Angelus, but way above my pay grade!
I already pretend to be too much of a theologian as it is :-)
From my perspective, there are some serious minds on both sides of the debate, above all there is Fr Calderon in the SSPX who says there is a shadow of a doubt.
I think that makes it a little rash for non-theologians to make definitive judgments about certain validity or non. Only the Magisterium can do that, or so it appears to me.
But that should settle the matter for anyone in the SSPX, that is what is important. Then add to that the issue of defective intention.
As you say, and as Fr Calderon says, the sacraments are too important to our salvation to tolerate any doubt, which we are obviously obliged, before God, to remove, at the peril of our own damnation - if we are the ones who can remove that doubt and refuse to do so.
I would have thought that every priest in the SSPX has a role to play in removing this doubt with regard to the Huonder shenanigans.
However, they are becoming so subtly conciliarised that they now eat doubt for dinner without even knowing.
It is a grave matter.

Does that make them not pope? That is where we differ. I say no, that means we resist them. We do not have the right to make that decision. The Church needs to hold them to account (a Council, St Robert Bellarmine would say). There lies the mystery, as God has so allowed His Church to be overshadowed by this crisis that for the time being God wills that we must patiently suffer this evil, but as St Robert says:

Not even a Council can depose a pope. But if it is a Council in union with a living pope denouncing a previous pope or declaring them to be antipopes, then yes that is possible.

Interesting, Angelus, but way above my pay grade!

Angelus has been badly discredit on several issues already, displaying gross ignorance of basic concepts; his run-on text was absolute gibberish, thus giving the impression that it was erudite, but it was in point of fact meaningless.

Nobody is makinga any definitive judgments about validity.  What's at issue is that there's clear positive doubt and for all intents and purposes we are required doubtful Sacraments invalid except in danger of death if we have no other option.

Agreed. Although some do make this definitive judgement, in line with "absolutely null and utterly void" and "still null and void"!

Not even a Council can depose a pope. But if it is a Council in union with a living pope denouncing a previous pope or declaring them to be antipopes, then yes that is possible.

Here is more from St Robert Bellarmine, Ch IX On the Utility or even the Necessity of Celebrating Councils:

d) The fourth reason is suspicion of heresy in the Roman Pontiff, if perhaps it might happen, or if he were an incorrigible tyrant; for then a general Council ought to be gathered either to depose the Pope if he should be found to be a heretic, or certainly to admonish him, if he seemed incorrigible in morals. As it is related in the 8th Council, act. ult. can. 21, general Councils ought to impose judgment on controversies arising in regard to the Roman Pontiff - albeit not rashly...

Yet a council CAN declare the fact of a pope’s heresy, and that consequently God has deposed him.

I'm not sure if that is feasible since a valid council requires the council to be in union with the Pope. The Pope has no superior on earth, not even a Council can judge or depose him, or else you fall into the error of the schismatic and heretical Greeks. The scenario you painted is possible with Conclavist councils which is another can of worms. Or like I said previously, a later Council in union with a later Pope can do so.

The author confuses defect of form and defect of intention. The SSPX have never claimed any of the New Rites are defective per se. Any conditional re-ordinations done in the past were due to defect of intention, which were done on a case by case basis and usually involved something the minister had said or done that may give a positive doubt regarding his intention.

Bp. Tissier de Mallerais no longer holds the episcopal consecration form is invalid. Indeed, implicit in his private letter (which was based on a rushed reading of Cosmaraswany's booklet), is that he would also have to conclude that the old Abyssinian/Coptic rites must be invalid since they used the same form – something the Church has never said even when dealing with Anglican Orders (Anglicans used this in their defense). Rather, the form doesn’t become invalid but indeterminate and the correct intention is provided ex adjunctis.

Another error Bp. TdM makes is in his claim that the power to confirm is supplied to a simple priest. Firstly, the Church has never defined what power is delegated by the pope; it could be one of order, or jurisdiction, or some order/jurisdiction hybrid, or some other unknown third power. But the supplementary principle will only supply jurisdiction. Secondly, if a delegated power of the pope can be supplied then why not the delegated power to ordain? There are at least three instances in medieval times where three different popes have delegated power to simple priests to ordain to the diaconate and priesthood. It is now generally accepted that a priest is the extraordinary minister of ordination.

If the common practice in the SSPX used to be to conditionally re-ordain novus ordo priests based on a defective intention of the ordaining bishop, then that begs the question of whether or not the SSPX has "realized" that doing conditional re-ordinations based on a defect of intention doesn't make any sense, and that it logically leads to accepting the new rite if ordination/episcopal consecration as valid per se.

Let us not forget that when the New Mass was foisted upon us in 1969 there was a great multitude of "theologians" with their pre-Vatican II diplomas...

The head 'theologian', of course, was the Freemason Annibale Bugnini who initially went to work starting in 1948.  The other 'theologians' include those six Protestants brought in as 'observers' who gave their humble 'opinions' on the matter.  New rite concocted with the help of the sworn enemies of the Church.  Doesn't smell legit.