The man who was transformed last week from Jorge Mario Bergoglio into the first Pope Francis faces a long list of challenges, each seemingly more daunting than the last. There's the immediate need to reform a Vatican bureaucracy whose dysfunction helped sabotage his predecessor's reign. There's the larger challenge of lifting the shadow of the sex abuse crisis from the Western church. And then comes the task of making Catholic Christianity seem vital and appealing in cultures where the new pope's church is widely regarded as archaic, irrelevant, or malign.

But in a sense all of these challenges have one solution, or at least one place where any solution has to start. Francis's reign will be a success if it begins to restore the moral credibility of the church's hierarchy and clergy, and it will be a failure if it does not.

Catholics believe that their church is designed to survive the lapses of its leaders. The Mass is the Mass even if the priest is a sinner. Bishops do not need to be holy to preserve the teachings of the faith. The litany of the saints includes countless figures - from Joan of Arc to the newly canonized Mary MacKillop, an Australian nun involved in the reporting of child abuse by a priest - who suffered injustices from church authorities in their lifetimes.

But it's one thing for Catholics in a Catholic culture, possessed of shared premises and shared moral ideals, to accept a certain amount of "do as I say, not as I do" from their pastors and preachers.

It's quite another to ask a culture that doesn't accept Catholic moral ideals to respect an institution whose leaders can't seem to live out the virtues that they urge on others.

In that culture - our culture - priestly sex abuse and corruption in the Vatican aren't just seen as evidence that all men are sinners. They're seen as evidence that the church has no authority to judge what is and isn't sin, that the renunciation Catholicism preaches mostly warps and rarely fulfills, and that the world's approach to sex (and money, and ambition) is the only sane approach there is.

Such worldliness should not be confused with atheism. Our age is still religious; it's just made its peace with human appetites and all the varied ways they intertwine. From the sermons of Joel Osteen to the epiphanies of "Eat, Pray, Love," our spiritual oracles still urge us to seek the supernatural, the numinous, the divine. They just dismiss the idea that the divine could possibly want anything for us except for what we already want for ourselves.

Religion without renunciation has obvious appeal. But its cultural consequences are not all self-evidently positive. Absent ideals of chastity, people are less likely to form families. Absent ideals of solidarity, more people live and age and die alone. The social landscape that we take for granted is one that many earlier generations would have regarded as dystopian: sex and reproduction have both been ruthlessly commodified, adult freedoms are enjoyed at the expense of children's interests, fewer children grow up with both a mother and a father, and fewer and fewer children are even born at all.

So there are shadows on our liberated society, doubts that creep in around the edges, moments when scolds and moralists and even popes almost seem to have a point. Which helps explain, perhaps, the strange, self-contradictory defensiveness that greets the Catholic Church's persistent refusal to simply bless every new development and call it progress. (Nobody cares what the pope thinks - and I demand that he think exactly as I do!)

It explains, too, why the appropriate moral outrage with which the secular press has covered scandals in the church has often included a subtext of vindication and relief. (They stand in judgment on the rest of us, but their own "ideals" just lead to repression and perversion. They claim to be above materialism, but they're obviously in it for the same things as everyone else ...)

If Catholicism has a future in the Western world as something more than a foil, an Other and a symbol of the Benighted Past We Have Safely Left Behind, it needs its leaders to set an example that proves these voices wrong. Before anything else, that requires a generation of priests and bishops who hold themselves to a higher standard - higher than their immediate predecessors, and higher than the world.

It also requires more from the new pope than an evocative name and a humble posture. Catholicism needs someone like Pius V, the 16th-century pontiff at whose tomb Francis prayed on the day after his elevation - a disciplinarian whose housecleaning helped further the Counter-Reformation. The Vatican needs purgation at the top, to enable real renewal from below. And the church as a whole needs to offer and embody proof - in Rome, the local parish and everywhere in between - that the alternative Catholicism preaches can actually be lived.