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DVB: Some in the Church see the conservatism personified by the new pope as the reason for the decline of membership in Europe and to a lesser extent the U.S. Others, however, feel that Church has not explicitly enough stated its guiding values strongly enough, and that a stronger sense of what the Church stands for would have avoided the decline in numbers. For the latter group, Benedict XVI's papacy offers a great deal of hope. But the more common analysis is that people in the West have left the Church because not only do they disagree with some of its teachings, they are not allowed to disagree out loud on questions such as the ordination of women. The closing down of dissent which the new Pope had an active part in during his previous job doesn't sit well with the norms of post-Enlightenment Western cultures.
By that analysis, the Church would continue to shrink in the West under Benedict XVI, unless he turns out to be extremely gifted pastorally. But that would not necessarily bother him that much. He has previously indicated that he would be comfortable with an extremely small Church, preferring a small church of true believers to a larger one whose numbers are swelled by people he would not see as good Catholics. Benedict XVI has previously argued that it is not unhealthy for church to be a counter culture rather than a dominant player in secular Western society. He's willing to see it play the role of an oppositional minority to a cultural drift he sees at odds with Church teachings.
TIME.com: John Paul II was celebrated for his outreach to other Christian sects, and to Jews and Muslims. Cardinal Ratzinger was clearly uncomfortable with some of these efforts and took a lead in restating the differences between the Church and these other groups. He's also on record, for example, of opposing Turkey's entry into the European Union for fear of diluting Europe's Christian identity. Can we expect a change in the Church's attitude to other Christians, and other faiths?
DVB: It may be expected that ecumenical efforts in relation to other churches are unlikely to advance during the new papacy. Benedict XVI has, for example, insisted that other Christian churches not be called "sister churches," but "daughter churches." And given that view of the relationship, I'm not sure ecumenism will be a major party of his legacy. The same might be true on interfaith efforts. After John Paul II had pulled together the remarkable convocation of religious leaders of every stripe at Assisi in 1986 where they prayed, in one another's presence, for peace, Cardinal Ratzinger was quoted as saying that this could not be the model.
On the other hand, Benedict XVI won't leave any doubt in the minds of other religious leaders where they stand with him. There's often a lot of cotton in interfaith conversation that allows everyone to participate in good faith, but prevents things getting down to brass tacks. Benedict XVI is all about brass tacks. So, while it may not move interfaith dialogue forward in the way that John Paul II did, his approach may define it more clearly.
TIME.com: It was notable both in his Easter homily and in the one he delivered before the Conclave began that Cardinal Ratzinger was inclined to paint the Church as in a state of considerable crisis. Over Easter, he spoke of "filth" inside the Church, and likened it to a boat shipping water from all sides. Yet this is an institution that John Paul II, and Ratzinger himself as the chief enforcer, have controlled for two decades. How does this square with his picture of a Church in crisis?
DVB: Benedict XVI feels that he and John Paul II were involved in a battle for the duration of the previous papacy, and the battle continues. They were on crisis footing when he came in, and they continue to be on crisis footing. He sees the society surrounding the church in the West, and elsewhere, has having become worse, in the sense of making it harder to be a good Catholic and a comfortable member of society at large. And in this ongoing crisis, he appears to be willing to make the Church a minority clearly defined by its strong values and identity a process that he would see as having only just begun under John Paul II. Of course, that Church would be very different fro the current Church, and the transformation would involve a tremendous amount of stress.