This post, and indeed this Weblog assumes that the Church is serious when she says "the Church has no authority whatsoever to confer priestly ordination on women." (OS 4) And further, we believe the CDF response to this document when it says "it has been set forth infallibly by the ordinary and universal Magisterium." (Responsum ad Dubium) Therefore, we assume women can not receive the sacrament of Holy Orders, that this has been infallibly declared, and that it is to be held definitively by the faithful.
Now, we consider the case of the validity of Anglican Orders. As you may know, the Anglicans are a protestant denomination which is not in communion with Rome and the See of Peter. The Anglican church started during the reign of King Henry VIII. The details are unimportant, but as time went on, it happened that the various liturgical texts were changed, including the rites for ordination. In 1896, the Papal Bull Apostolicae Curae was issued by Pope Leo XIII, and it stated that Anglican Orders were "absolutely null and utterly void." The primary argument at hand was that the Anglican Rites of Ordination lacked proper form; that the words of ordination had changed in such a way as to no longer reflect the proper nature of the ordained priesthood. This papal bull was reaffirmed in 1998 by the CDF, when given as an example of a papal teaching that the faithful must affirm.
The story actually complicates from there. In 1931 (which is after the 1896 Bull), the Bonn Agreement between the Anglican Church and various schismatic groups established communion between the groups. Bishops, who, though schismatic, still retained valid ordination and apostolic succession, joined in ordinations in the Anglican church. At this point, it has been argued, some semblance of apostolic succession could have been reestablished, perhaps re-validating the ministerial priesthood and the sacraments within the Anglican Church.
Recalling our initial assumption, however, that women cannot be ordained, it has also been argued that the Anglicans, if they ever did reestablish valid succession, no longer retain it universally because the bishops (in general) no longer have a proper understanding of the Priesthood (or Episcopacy), and as such cannot form the proper intention to ordain to the priesthood. Essentially, they do not ordain because their intention is to ordain to a priesthood that doesn't exist. This deficiency may not be universal, we will permit the possibility that individuals or groups who do properly understand the ordained priesthood could retain valid orders.
We take an aside here to state that this is not a well-defined area. It is manifestly unclear if some or all or most or none of the Anglican orders are or were valid at any point in history. Each of the arguments put forward are just that, arguments. They are not declarations (with probably the exception of the Bull of Pius XIII), and as such aren't definitive.
An important question here, really the important question, is considering what constitutes a requisite intention for a valid ordination. We know that for a sacrament to be valid, we must have a valid minister, proper form and matter, and proper intentions of both the minister and the recipient of the sacrament. In the case of holy orders, we need a validly ordained Bishop (minister) and a man who has been baptized and confirmed (recipient). There seem to be required words. Laying on of hands is necessary. Finally, the Bishop must intend to confer the ministry of Christ's priesthood and the recipient must intend and be free to receive it.
So again, we must ask what is requisite in this intention. It has been pointed out to me that there is little if any belief required in Baptism. In fact, the catechism states "The faith required for Baptism is not a perfect and mature faith, but a beginning that is called to develop." (CCC 1253) And, "...anyone, even a nonbaptized person, with the required intention, can baptize. The intention required is to will to do what the church does when she baptizes." That said, there is no such statement I can find regarding Orders. Likewise, I was also reminded that an otherwise validly ordained priest who no longer believes in the Real Presence can validly consecrate. On the other hand, someone who does not believe in the real presence cannot receive the sacramental graces from the Eucharist without belief. The code of canon law requires that Bishops gather documentation of "the sound doctrine of the candidate" among other things (cf. CIC 1051).
This still doesn't answer our question. What is the (minimum necessary) required intention of the ordaining minister and the ordination candidate to remain valid? Let me be clear, my worry is that in this day and age when there are seminarians (at some of the less orthodox seminaries), priests, and sadly even Bishops (recall this post), who do not understand, or believe in the ministerial priesthood in the way that the Church does, there could be problems with regards to intention in receiving or giving orders. If it it possible (as I stated, it is not certain) that the Anglicans could have been deficient in their intention to ordain, in part, by believing that Women can be admitted into the Priesthood and Episcopate, then we must logically admit the possibility (again not certainty) that the same deficiency could exist in the Catholic Church.
Perhaps the answer to our question is "to confer (or receive) the ordination to the Church's priesthood" regardless of personal misunderstandings. If this were the case it would perhaps be harder to invalidate a priori the Anglican Orders as well, or at least those conferred on males. This is the reason we require so much of our bishops and seminarians. We don't want to be at the point where we question absolute minimums to be ordained.
Above all else, though, we can pray. Pray for our bishops, for all the seminarians, and those who educate them. Pray that the Spirit may help lead them along a path to holiness, and indeed obedience and orthodoxy. Perhaps all of these problems could be settled if more would pray for them. After all, the priesthood is the cornerstone of the sacramental life of the Church, and is a favorite target of the devil.
Ne nos inducas in tentationem, sed libera nos a malo.