In discussing the possibly of the Church's ordaining of women to the priesthood, I generally like to note that the Church's teaching is infallible, and that it cannot be changed. For me as a Catholic, this means that the teaching is decisive, authoritative, binding (both to my intellect and my will), and final. One tactic which I have noticed increasingly is the insistence that the teaching is not infallible--this even by some Catholics who presumably do accept that the Church can teaching infallibly on matters of doctrine and morality. Their argument hinges largely on an interpretation from Canon Law (itself fallible) which states that in order for a teaching to be infallible, there can be no speculation as to whether or not the doctrine has been taught infallibly.

Such speculation exists in the case of the teaching regarding priestly ordination. Therefore, it is concluded by some that the teaching against ordaining women to the priesthood is not infallible. This speculation is apparently not dispelled by Pope John Paull II's Ordinatio Sacerdotalis, which stated rather conclusively that

Priestly ordination, which hands on the office entrusted by Christ to his Apostles of teaching, sanctifying and governing the faithful, has in the Catholic Church from the beginning always been reserved to men alone. This tradition has also been faithfully maintained by the Oriental Churches....Although the teaching that priestly ordination is to be reserved to men alone has been preserved by the constant and universal Tradition of the Church and firmly taught by the Magisterium in its more recent documents, at the present time in some places it is nonetheless considered still open to debate, or the Church's judgment that women are not to be admitted to ordination is considered to have a merely disciplinary force.

Wherefore, in order that all doubt may be removed regarding a matter of great importance, a matter which pertains to the Church's divine constitution itself, in virtue of my ministry of confirming the brethren (cf. Lk 22:32) I declare that the Church has no authority whatsoever to confer priestly ordination on women and that this judgment is to be definitively held by all the Church's faithful.

As if this is not definitive enough, then Cardinal Ratzinger issued a statement on behalf of the Congregation for the Doctrine of the Faith, which says unequivocally that this is an infallible teaching. Still there are Catholics who maintain that this issue hasn't really been settled decisively--that is, there is still some speculation as to whether or not this teaching is infallible. Most cite the difference in language between John Paul II's letter and those which previously defined dogma ex cathedra (infallibly). The apostolic constitution Munificentissimus Deus by pope Pius XII, concludes by saying:

by our own authority, we pronounce, declare, and define it to be a divinely revealed dogma:

that the Immaculate Mother of God, the ever Virgin Mary, having completed the course of her earthly life, was assumed body and soul into heavenly glory.

45. Hence if anyone, which God forbid, should dare willfully to deny or to call into doubt that which we have defined, let him know that he has fallen away completely from the divine and Catholic Faith.

46. In order that this, our definition of the bodily Assumption of the Virgin Mary into heaven may be brought to the attention of the universal Church, we desire that this, our Apostolic Letter, should stand for perpetual remembrance, commanding that written copies of it, or even printed copies, signed by the hand of any public notary and bearing the seal of a person constituted in ecclesiastical dignity, should be accorded by all men the same reception they would give to this present letter, were it tendered or shown.

47. It is forbidden to any man to change this, our declaration, pronouncement, and definition or, by rash attempt, to oppose and counter it. If any man should presume to make such an attempt, let him know that he will incur the wrath of Almighty God and of the Blessed Apostles Peter and Paul.

The apostolic constitution Ineffabilis Deus issued by Pope Pius XI which infallibly define the Immaculate conception concludes with similar language (my emphasis added):

Wherefore, in humility and fasting, we unceasingly offered our private prayers as well as the public prayers of the Church to God the Father through his Son, that he would deign to direct and strengthen our mind by the power of the Holy Spirit. In like manner did we implore the help of the entire heavenly host as we ardently invoked the Paraclete. Accordingly, by the inspiration of the Holy Spirit, for the honor of the Holy and undivided Trinity, for the glory and adornment of the Virgin Mother of God, for the exaltation of the Catholic Faith, and for the furtherance of the Catholic religion, by the authority of Jesus Christ our Lord, of the Blessed Apostles Peter and Paul, and by our own: "We declare, pronounce, and define that the doctrine which holds that the most Blessed Virgin Mary, in the first instance of her conception, by a singular grace and privilege granted by Almighty God, in view of the merits of Jesus Christ, the Savior of the human race, was preserved free from all stain of original sin, is a doctrine revealed by God and therefore to be believed firmly and constantly by all the faithful."

Hence, if anyone shall dare -- which God forbid! -- to think otherwise than as has been defined by us, let him know and understand that he is condemned by his own judgment; that he has suffered shipwreck in the faith; that he has separated from the unity of the Church; and that, furthermore, by his own action he incurs the penalties established by law if he should are to express in words or writing or by any other outward means the errors he think in his heart.

Ok, so this is a bit of semantics on the part of some. I see two differences here: first, the two which are accepted as infallible are apostolic constitution, whereas John Paul II's statement is an apostolic letter; and both of the apostolic constitutions come with the harshest of warnings against those who seek to contradict or change the dogma, whereas the more pastoral John Paull II states only that he writes "in order that all doubt may be removed regarding a matter of great importance, a matter which pertains to the Church's divine constitution itself." However, neither of these differences rules out infallibility; in fact, the statement by John Paul that the matter pertains to the constitution of the Church, so the first difference is a matter of semantic, as best.

As to the second difference, it has been noted before that there is not official "linguistic formula" to infallibility. Indeed, the apostolic letter meets all of the objective criteria given by the First Dogmatic Constitution on the Church of Christ, which is the Vatican I statement defining papal infallibility. Said Dogmatic Constitution states that

Therefore, faithfully adhering to the tradition received from the beginning of the Christian faith, to the glory of God our savior, for the exaltation of the Catholic religion and for the salvation of the Christian people, with the approval of the Sacred Council, we teach and define as a divinely revealed dogma that when the Roman Pontiff speaks EX CATHEDRA, that is, when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his supreme apostolic authority, he defines a doctrine concerning faith or morals to be held by the whole Church, he possesses, by the divine assistance promised to him in blessed Peter, that infallibility which the divine Redeemer willed his Church to enjoy in defining doctrine concerning faith or morals. Therefore, such definitions of the Roman Pontiff are of themselves, and not by the consent of the Church, irreformable.

Thus, for our late pope's apostolic letter to have not been infallible, one of four criteria must be absent. These criteria may be stated as questions, all of which must be answered in the affirmative for a teaching to be infallible. 1) Was the pope intending to teach? The obvious answer here is, "yes." He references this doctrine as a teaching twice, and is writing to uphold and clarify said taching. 2) Was the pope teaching by virtue of his supreme apostolic authority (was he acting ex cathedra? Again, the answer is yes, as the pope himself notes that he is writing "in virtue of my ministry of confirming the brethren" (see Luke 22:32). 3) Is the subject in question a matter of faith or morals? Once again, yes--it is a matter of faith, hence the satement that the matte pertains to the Church's divine constitution itself. Finally, 4) Does the pope intend for this teaching to be binding for all the faithful? Even this last one is answered in the affirmative, as the pope wrote that "this judgment is to be definitively held by all the Church's faithful." If this is not meant to be binding and definitive, then no statement is.

It is to no avail to cite Canon Law as "evidence" (let alone proof) that the teaching is not infallible. Canon Law interprets practice, not dogma, and the dogma taught by the first Vatican council is clear: infallibility does not hinge on the presence or lack of speculation among the Faithful. That some bishops or other theologians wish to speculate as to whether or not John Paul's teaching is infalliblie does not change the fact of its infallibility. There will always be those within the Church who dissent to a dogmatic teaching, either openly or by equivocation; for some, the speculation as to the infalliblity of this teaching is merely a means of dissenting indirectly by equivocation. More revealing than this speculation would be their honest answer as to whether they would assent to its infalliblity if the teaching was re-presented in an apostolic constitution, complete with the language and warnings of anethema used by Popes Pius XI and XII. Equally revealing would be their honest answer to the question of whether or not they accept the teaching as binding and authoritative to both their intellect and their will, as even fallible exercises of the Ordinary Magisterium are to be received as such.