Even John Paul II’s declaration that the Church cannot ordain women was quickly clarified as not being an exercise of ex cathedra infallibility, but merely a restatement of what the Church has always believed and taught (and therefore irreformable not by the Pope’s personal charism of infallibility, but by the infallibility of the ordinary magisterium).
Doctrinal *ex cathedra *definitions are not that “rare”, although this has been a common fallacy. Papal dogmas (such as on the Assumption) are “rare”.
Pastor Aeternus has the dogma of Vatican I on papal infallibility: ewtn.com/library/COUNCILS/V1.HTM#6
“On the infallible teaching authority of the Roman pontiff
….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.” [My emphasis].
So the Pope’s ‘ex cathedra’ definitions may be either of revealed dogma, to be believed with divine faith, or of other truths necessary for guarding and expounding revealed truth. Vatican Council II and the post-conciliar Magisterium have explicitly affirmed that both ecclesial and papal infallibility extend to the secondary doctrinal truths necessary for guarding and expounding revelation. Thus Humanae Vitae (Encyclical) and Ordinatio Sacerdotalis (Apostolic Epistle) contain infallible doctrinal definitions, to remove all doubt.
In fact, the 1983 revision of Canon Law had replaced in #749.3 “dogmatically declared or defined” with “infallibly defined”, thus NOT expressing a limitation of infallibility to dogmas. ATF better enables Canon Law to apply to the understanding of infallibility with the Profession of Faith covering the two categories of infallible doctrine.
The meaning of the word ‘define’ was explained to the Fathers of Vatican I, before they promulgated the dogma of papal infallibility, as follows: “the pope is said to ‘define’ a doctrine when he passes judgment directly and finally, ‘in such a way that each and every Catholic can be certain as to the mind of the Apostolic See and of the Roman Pontiff.’ ”
The Pope’s own words in Ordinatio Sacerdotalis: definitive tenendum, mean precisely “requiring to be held definitively.”
Closely following Bishop Gasser’s explanation, Vatican II shows that it considers the words “define” and “proclaim” to be equivalent by using the word “definition” when it states: “Therefore his definitions are rightly called irreformable, etc.” [Lumen Gentium, 25].
“In the final analysis, therefore, the reason the Church has always rejected female service in the sanctuary is that such service is very closely related, both symbolically and often causally, to the ministerial priesthood itself. And this can never possibly be conferred upon women, as John Paul II declared on the Feast of Pentecost last year in what is clearly an infallible, ex cathedra definition. 10
“10. It stops short, however, of being a solemn dogmatic definition on a par with those of the Immaculate Conception and Assumption, which are defined as truths of faith, binding on pain of heresy. Cf. the present writer’s article, “Cardinal Ratzinger on Ordinatio Sacerdotalis,” *The Priest *(Journal of the Australian Confraternity of Catholic Clergy), Spring 1994 / Summer 1995, pp. 5-6.”