It seems that the most trad-friendly Prelates of the Church actually want the Traditional Mass to disappear. Thus, Cardinal Burke said in 2011:
It seems to me that is what he [Pope Benedict] has in mind is that this mutual enrichment would seem to naturally produce a new form of the Roman rite – the 'reform of the reform,' if we may – all of which I would welcome and look forward to its advent.
Cardinal Sarah has now said the same thing.
It is a priority that, with the help of the Holy Spirit, we can examine through prayer and study, how to return to a common reformed rite always with this goal of a reconciliation inside the Church,
Cardinal Sarah's concrete suggestions point to an intermediate state, in which the two 'Forms' have converged somewhat. I have addressed these suggestions in a post on the Catholic Herald blog (no longer available there, but reposted here). Notably, the Novus Ordo Lectionary cannot be simply be inserted into the Vetus Ordo Missal, because it reflects a liturgical vision which is completely different from that of the ancient Mass: which is why all the other changes were made at the same time. A compromise between these two two understandings of what the liturgy is for and how it should work will not produce a perfect synthesis, but a muddle.
I've made the argument about the Lectionary at length here, and about the 'Reform of the Reform' falling between two stools here.
Leaving open the question of how Cardinal Burke's thinking may have developed since 2011, why would he or Cardinals Sarah want to get rid of the ancient Mass?
One justification appears to be the idea that the existence of two Forms of the Roman Rite is, regardless of the merits or demerits of the forms themselves, itself a problem. I suppose this idea is related to a certain conservative yen for centralisation and uniformity, but I doubt either Cardinal would want to apply it to the Eastern Rites, even in the West, and I suspect they would not really want to stop the Dominicans, Norbertines, or Carthusians - or the former Anglicans - from celebrating their own rites and usages. So although talk of 'disunity' has a superficial force I don't think this is really driving their thinking here. They don't really want to contradict Vatican II's praise of liturgical diversity. (I have written about liturgical pluralism here.)
I think the more powerful consideration is that they are unhappy with the Ordinary Form. Cardinal Sarah, in particular, has taken up points hammered by Cardinal Ratzinger in The Spirit of the Liturgy, notably about how celebration 'facing the people' was a mistake, and how the reformed Mass should have more silence in it. This is the argument of the 'Reform of the Reform', and it is an argument which has no direct connection with the Extraordinary Form. But Sarah and others seem to think that the existence of the Extraordinary Form creates an extra reason to undertake the Reform of the Reform. 'Look!' he seems to be saying: 'Here are a whole lot of Catholics who refuse to go to the Novus Ordo because it lacks silence, and the priest usually faces the people. Let's make those changes and draw these people back in.'
In other words, his sympathy for some of the arguments about the merits of the Traditional Mass made by its adherents has given Cardinal Sarah the idea of making a purely tactical use of the movement to leverage his position on the future development of the Ordinary Form.
Perhaps things would be different if the EF looked about to take over the whole Church, but if that is going to happen, it would seem it would take at least a century.
I can't say I'm too worried by these proposals. They revive discussions on liturgical matters, which is positive, but opposition by progressive and - let's be honest - middle-of-the-road Novus Ordo priests and faithful to the Reform of the Reform makes the implementation of Cardinal Sarah's programme by fiat from Rome unimaginable, even if he were to become Pope tomorrow.
It should, all the same, stimulate supporters of the Church's ancient liturgical traditions to explain ever more forcefully the point of the ancient Lectionary, and any other threatened features of the Mass they love.
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