CathInfo.com

You just summarized the problem in the new rites...(1) the prayers/form no longer adequately provides the Church’s intention, so such intention must be provided by the minister.  In the True Rite, the intention of the minister is irrelevant because the prayer/form perfectly says what the Church intends.  
.
(2) Because the new rite NEEDS the intention of the minister to be valid, such intention is NECESSARILY INTERNAL because the prayer/form is too ambiguous and general.  Thus, there is NO EXTERNAL SIGN THAT THE INTENTION IS INVALID (or valid), unless you can read minds.
.
So the new-sspx’s policy is neither grounded in reality nor logical.  It’s also not consistent because it contradicts +Tissier’s past doubts on consexrations/ordinations.  

BS. From Fr. Marie O. P
“

Solution of the difficulties: defect of intention
1) We have never seen anything to suggest that the new rite was made in view of ecuмenism with the Anglicans. The “ecuмenical” argument envisaged the Eastern Rites. Let us revisit Dom Botte’s memoirs:
If I was paying attention to this text it wasn’t because I had just finished a critical edition of it, but because my study of the oriental rites made me notice that the formula always survived under more evolved forms. Thus, in the Syrian Rite the prayer for the patriarch’s ordination was none other than the one in the Testamentum Domini, a reworking of the Apostolic Tradition. The same is true for the Coptic Rite where the prayer for the bishop’s ordination is close to that of the Apostolic Constitutions, another reworking of Hipploytus’ text. The essential ideas of the Apostolic Tradition can be found everywhere. Reusing the old text in the Roman Rite would affirm a unity of outlook between East and West on the episcopacy. This was an ecuмenical argument. It was decisive.[117]
The situation is quite different from that in which the new Mass was redacted, during which the reformers clearly manifested their desire for ecuмenism with the Protestants who participated in the elaboration of the new rite. Such a rapprochement and such collaboration with heretics was a danger to the orthodoxy of the faith, and in fact resulted in a new Mass favens haeresim(favoring heresy). In this case the rapprochement is with rites in usage in the East by Catholics as well as by schismatics. The fact of desiring to establish cordial relations with these Rites does not manifest a priori any intention dangerous to the faith. And in fact the new rite does not deserve to be characterized as “favens haeresim,” even if one might have other valid reasons for refusing it.[118]
If there are Anglicans who have adopted (ad libitum) a liturgy similar to Pope Paul VI’s rite, different explanations can be offered:

I consider that the ordination on the occasion of Bishop Hänggi’s consecration is a very beautiful fruit of the efforts of the Council in liturgical matters. As a Protestant, I can only say that I could have participated completely in this liturgy (a few passages excepted), and that this could also be an example for the investiture of the Protestant ministers of the Church.[119]
Consequently, nothing supports the allegation that conciliar Rome adopted the new rite because they share the ideas of the Anglicans concerning the episcopacy and their non-Catholic intention, even if the new rite is more easily acceptable to the Protestants than the old rite.
2) The most contestable point of doctrine issuing from Vatican II as regards the episcopacy is collegiality. We know that Pope Paul VI himself was obliged to insert a nota explicativa prævia (preliminary explanatory note) 120 to the Dogmatic Constitution on the Church in order to avoid a heterodox interpretation being given to the Conciliar text. Here is the passage of this note that especially concerns us:
A person becomes a member of the College by virtue of episcopal consecration and hierarchical communion with the head of the College and its members. Cf. Article 22, §1, at the end.
In consecration is given an ontological participation in sacred functions, as is clear beyond doubt from tradition, even liturgical. The word functions is deliberately employed, rather than powers , since this latter word could be understood as ready to go into action. But for such ready power to be had, it needs canonical or juridical determination by hierarchical authority. This determination of power can consist in the granting of a particular office, or in an assigning of subjects; and it is given according to norms approved by the highest authority. Such an ulterior norm is demanded by the nature of the case, since there is question of functions which must be exercised by several subjects working together by Christ’s will in a hierarchical manner. It is clear that this “communion” has been in the life of the Church according to circuмstances of the times, before it was, so to speak, codified in law”

You just summarized the problem in the new rites...(1) the prayers/form no longer adequately provides the Church’s intention, so such intention must be provided by the minister.  In the True Rite, the intention of the minister is irrelevant because the prayer/form perfectly says what the Church intends.  
.
(2) Because the new rite NEEDS the intention of the minister to be valid, such intention is NECESSARILY INTERNAL because the prayer/form is too ambiguous and general.  Thus, there is NO EXTERNAL SIGN THAT THE INTENTION IS INVALID (or valid), unless you can read minds.
.
So the new-sspx’s policy is neither grounded in reality nor logical.  It’s also not consistent because it contradicts +Tissier’s past doubts on consexrations/ordinations.  

I have to disagree.  This intention theology is faulty and has been invented and propagated precisely in order to back up this notion that "even though we don't think the Rite is doubtful, we think there still may be doubt".  That was so they could have their cake and eat it too.  While putting it out there for public consumption (including by the Vatican "authorities") that, oh, no, there really isn't a doubt, they could still resolve their secret doubts by justifying the practice of conditional ordination.  It was so as not to offend the Conciliar authorities.  "Oh, no, it's not your Rite that's doubtful, really ..."

It is not required for the minister to intend the Sacramental effect, merely for the minister to DO what the Church does.  That's why atheists can validly baptized.  All they have to intend is, "I'm doing this thing that Catholics do." (and even that vaguely).  They don't have to believe that it has any effect.

I had an SSPX priest who was conditionally ordained tell me that he himself had no doubts about his ordination, but he did it for "pastoral" reasons because a lot of the faithful at his chapel did have doubts.  So he wanted to put THEIR consciences at ease.

See, I think the doubt theology evolved.  Most early Traditionalists held the NO Rite to be doubtful in and of itself.  So the SSPX used to do conditional ordinations without any kind of investigation or any requirement to demonstrate any reason for positive doubt, since the positive doubt was in the Rite itself.  When this began to shift, to appease the Conciliarists, they came up with a new justification for continuing to do conditional ordinations (so the faithful wouldn't start leaving their chapels).  So they came up with this "intention of the minister" problem to justify them.  Well, as time went on, as LastTrad pointed out, fewer and fewer Traditional Catholics cared, so now they've stopped doing them altogether.  That "intention of the minister" doubt is merely a negative doubt and it would require some positive doubt to establish whether or not conditional ordination would be licit in any particular case.  Now they just don't bother anymore because they don't feel the need to.