I apologise for the little delay, but work actually intruded this morning. The Congregation for the Doctrine of the Faith has issued another very important document restating and reaffirming one of the important truths of the faith. This document will be most helpful, in my opinion, to the ongoing efforts to reach a mutual understanding and reconciliation with the Society of St. Pius X. It is of a part with the recent documents coming from the Holy See.

From the Vatican website, the English version of the document (for space concerns, footnotes are omitted and can be read at the linked story):

CONGREGATION FOR THE DOCTRINE OF THE FAITH
RESPONSES TO SOME QUESTIONS REGARDING CERTAIN ASPECTS
OF THE DOCTRINE ON THE CHURCH
Introduction
The Second Vatican Council, with its Dogmatic Constitution Lumen gentium, and its Decrees on Ecumenism (Unitatis redintegratio) and the Oriental Churches (Orientalium Ecclesiarum), has contributed in a decisive way to the renewal of Catholic ecclesiolgy. The Supreme Pontiffs have also contributed to this renewal by offering their own insights and orientations for praxis: Paul VI in his Encyclical Letter Ecclesiam suam (1964) and John Paul II in his Encyclical Letter Ut unum sint (1995).
The consequent duty of theologians to expound with greater clarity the diverse aspects of ecclesiology has resulted in a flowering of writing in this field. In fact it has become evident that this theme is a most fruitful one which, however, has also at times required clarification by way of precise definition and correction, for instance in the declaration Mysterium Ecclesiae (1973), the Letter addressed to the Bishops of the Catholic Church Communionis notio (1992), and the declaration Dominus Iesus (2000), all published by the Congregation for the Doctrine of the Faith.
The vastness of the subject matter and the novelty of many of the themes involved continue to provoke theological reflection. Among the many new contributions to the field, some are not immune from erroneous interpretation which in turn give rise to confusion and doubt. A number of these interpretations have been referred to the attention of the Congregation for the Doctrine of the Faith. Given the universality of Catholic doctrine on the Church, the Congregation wishes to respond to these questions by clarifying the authentic meaning of some ecclesiological expressions used by the magisterium which are open to misunderstanding in the theological debate.
RESPONSES TO THE QUESTIONS
First Question: Did the Second Vatican Council change the Catholic doctrine on the Church?
Response: The Second Vatican Council neither changed nor intended to change this doctrine, rather it developed, deepened and more fully explained it.
This was exactly what John XXIII said at the beginning of the Council1. Paul VI affirmed it2 and commented in the act of promulgating the Constitution Lumen gentium: “There is no better comment to make than to say that this promulgation really changes nothing of the traditional doctrine. What Christ willed, we also will. What was, still is. What the Church has taught down through the centuries, we also teach. In simple terms that which was assumed, is now explicit; that which was uncertain, is now clarified; that which was meditated upon, discussed and sometimes argued over, is now put together in one clear formulation”3. The Bishops repeatedly expressed and fulfilled this intention4.
Second Question: What is the meaning of the affirmation that the Church of Christ subsists in the Catholic Church?
Response: Christ “established here on earth” only one Church and instituted it as a “visible and spiritual community”5, that from its beginning and throughout the centuries has always existed and will always exist, and in which alone are found all the elements that Christ himself instituted.6 “This one Church of Christ, which we confess in the Creed as one, holy, catholic and apostolic […]. This Church, constituted and organised in this world as a society, subsists in the Catholic Church, governed by the successor of Peter and the Bishops in communion with him”7.
In number 8 of the Dogmatic Constitution Lumen Gentium ‘subsistence’ means this perduring, historical continuity and the permanence of all the elements instituted by Christ in the Catholic Church8, in which the Church of Christ is concretely found on this earth.
It is possible, according to Catholic doctrine, to affirm correctly that the Church of Christ is present and operative in the churches and ecclesial Communities not yet fully in communion with the Catholic Church, on account of the elements of sanctification and truth that are present in them.9 Nevertheless, the word “subsists” can only be attributed to the Catholic Church alone precisely because it refers to the mark of unity that we profess in the symbols of the faith (I believe… in the “one” Church); and this “one” Church subsists in the Catholic Church.10
Third Question: Why was the expression “subsists in” adopted instead of the simple word “is”?
Response: The use of this expression, which indicates the full identity of the Church of Christ with the Catholic Church, does not change the doctrine on the Church. Rather, it comes from and brings out more clearly the fact that there are “numerous elements of sanctification and of truth” which are found outside her structure, but which “as gifts properly belonging to the Church of Christ, impel towards Catholic Unity”11.
“It follows that these separated churches and Communities, though we believe they suffer from defects, are deprived neither of significance nor importance in the mystery of salvation. In fact the Spirit of Christ has not refrained from using them as instruments of salvation, whose value derives from that fullness of grace and of truth which has been entrusted to the Catholic Church”12.
Fourth Question: Why does the Second Vatican Council use the term “Church” in reference to the oriental Churches separated from full communion with the Catholic Church?
Response: The Council wanted to adopt the traditional use of the term. “Because these Churches, although separated, have true sacraments and above all – because of the apostolic succession – the priesthood and the Eucharist, by means of which they remain linked to us by very close bonds”13, they merit the title of “particular or local Churches”14, and are called sister Churches of the particular Catholic Churches15.
“It is through the celebration of the Eucharist of the Lord in each of these Churches that the Church of God is built up and grows in stature”16. However, since communion with the Catholic Church, the visible head of which is the Bishop of Rome and the Successor of Peter, is not some external complement to a particular Church but rather one of its internal constitutive principles, these venerable Christian communities lack something in their condition as particular churches17.
On the other hand, because of the division between Christians, the fullness of universality, which is proper to the Church governed by the Successor of Peter and the Bishops in communion with him, is not fully realised in history18.
Fifth Question: Why do the texts of the Council and those of the Magisterium since the Council not use the title of “Church” with regard to those Christian Communities born out of the Reformation of the sixteenth century?
Response: According to Catholic doctrine, these Communities do not enjoy apostolic succession in the sacrament of Orders, and are, therefore, deprived of a constitutive element of the Church. These ecclesial Communities which, specifically because of the absence of the sacramental priesthood, have not preserved the genuine and integral substance of the Eucharistic Mystery19 cannot, according to Catholic doctrine, be called “Churches” in the proper sense20.
The Supreme Pontiff Benedict XVI, at the Audience granted to the undersigned Cardinal Prefect of the Congregation for the Doctrine of the Faith, ratified and confirmed these Responses, adopted in the Plenary Session of the Congregation, and ordered their publication.
Rome, from the Offices of the Congregation for the Doctrine of the Faith, June 29, 2007, the Solemnity of the Holy Apostles Peter and Paul.
William Cardinal Levada
Prefect
+ Angelo Amato, S.D.B.Titular Archbishop of Sila
Secretary
______________
Wow. We start with a bang, don’t we? Confirming what every long suffering traditional Catholic has known, the Congregation, with the approval of the Holy Father, confirms that Vatican II, and Lumen Gentium specifically, neither changed traditional Catholic doctrine nor intended to change it. Citing Paul VI himself was a nice touch.
Next: “subsists in” is clarified, more or less. I say more or less because the word itself is a little nebulous, but the CDF states that 1) it doesn’t change the traditional Catholic understanding, 2) it indicates that the marks and identity of the visible Church Christ founded can only be found in completeness in the Catholic Church, and 3) the term “subsists in”, because it means the completeness of all these marks, can ONLY be applied to the Catholic Church. In other words, though some elements of truth might be found in one of the imperfectly constituted ecclesial communities, the Church of Christ does NOT subsist in any of them– only in the Catholic Church. The response would be fantastic if its final usage of “subsists in” were replaced with “is”.
The rest, though perhaps more likely to be fodder for the secular press or the protestant leaders (definition of groups as “churches” or not), is restating matters not as subject to recent confusion as the first two.
I am a small fish in this big pond, and I admit freely I have no inside information about the state of the relations behind the scenes between Rome and the SSPX. But I cannot help but observe that many, many of the issues identified by the Society as problems, and which the Holy Father has maintained have perfectly sound explanations consistent with Catholic Tradition, are being wonderfully addressed by the Pope to assure all Catholics of the proper interpretation of these matters.
Beginning with the Christmas address to the Curia in 2005, followed by certain elements of his encyclical and exhortation, then followed by elements of the letter to the Chinese, and finally the landmark Motu Proprio and this doctrinal clarification–they all point to a serious attempt to provide a basis for understanding with the Society. Of course, they are also a gift to all Catholics in maintaining a “hermeneutic of continuity” as the Holy Father rightly points out.
I wouldn’t be surprised if there were some formal agreement, or protocol of agreement with the SSPX in the reasonably near future. If you haven’t read the 1988 protocol that was signed by Cardinal Ratzinger and Abp. Lefebvre lately, you should.