Dear Paul:

No one, not even the Pope, can dissolve a valid Sacramental marriage.

There is nothing contradictory in Canon 1056. There is no language in the Canon that says "more firm". Rather it says that "in Christian marriage they acquire a distinctive firmness by reason of the sacrament."

The canon is saying that the essential properties of marriage are made firm and indissoluble by the Sacrament. Only a Sacramental marriage is indissoluble. Non-Sacramental marriages can be dissolved.

If two non-baptized persons marry, the marriage is not validly Sacramental. If a Catholic marries a non-believer (not Baptized), the marriage is not validly Sacramental.

By the way, a Catholic has to have a dispensation from the Bishop to marry a non-believer; and has to get permission from the Bishop to marry a baptized non-Catholic Chrisitan.

As for Pauline and Petrine privileges, those apply to non-Sacramental marriages.

The Pauline privilege is described in 1 Corinthians 7:10-15:

To the married I give charge, not I but the Lord, that the wife should not separate from her husband ... and that the husband should not divorce his wife. To the rest I say, not the Lord, ... But if the unbelieving partner desires to separate, let it be so; in such a case the brother or sister is not bound. For God has called us to peace.

If a Catholic marries a non-believer (not Baptized), the marriage is not Sacramental. The Catholic has to have a dispensation from the Bishop, by the way, to marry a non-believer.

Anytime two baptized persons (one man and one woman) are married, Protestant or Catholic, the marriage is presumed to Sacramental and valid, unless evidence is revealed to suggest otherwise.

The Pauline privilege says that in the case of two unbaptized persons marrying, then one of them converts and is baptized, the Christian may not leave the marriage. But, if the non-believing spouse leaves the marriage, the Christian spouse is free, by the Pauline Privilege, to marry again because the Christian's marriage was not Sacramental to begin with.

The Petrine Privilege, also called Privilege of Faith, is reserved to the Holy See. The Petrine Privilege is an extension of the Pauline Privilege and again deals with a non-sacramental marriage.

Borrowing the definition from the Archdiocese of Chicago:

"A Petrine Privilege or Privilege of the Faith is a dissolution of marriage in which at least one of the parties to a previous marriage was non-baptized throughout the entire duration of their married life. If the petitioner is the non-baptized party or was baptized in another Christian church, he or she must either wish to be baptized or received into the Catholic Church, or seek to marry a baptized, practicing Catholic. If the petitioner is a baptized Catholic who was married to a non-baptized person, he or she must either wish to enter into marriage with a baptized Christian, or promise to enter marriage with a baptized Christian in the future. Privilege of the Faith cases involve a special petition to the Holy Father and are decided in Rome."

What this means is that if non-believing person had a previous marriage and was non-believing all through the marriage (meaning that marriage was not sacramental), but now wishes to convert to Christianity, they may receive single status, which allows them to marry in the Church, due to the their new found Faith -- Privilege of Faith -- in which any future marriage they promise to be with a practicing Catholic.

The same goes for a baptized Catholic who had a previous marriage with a non-baptized spouse. The Privilege of Faith is granted when the Catholic promises to enter into any future marriage with a baptized Christian.

These cases of Pauline and Petrine Privilege deal with "natural marriage" and not Sacramental marriage (which is the only kind of marriage that is indissoluble).

I know this is rather complicated, but there are no contradictions here. It has to do with Sacramentality. Either a marriage is Sacramental before God and His Church or it is not. If it is Sacramental no one can dissolve it. If is is not Sacramental, then it can be dissolved.

God Bless,
Bro. Ignatius Mary