Attempts by the head of the Roman Catholic Church to first convert them and second to have them work towards a world government sounds to me, and I daresay others, like an absolutely ridiculous proposal.
It would be most prudent for America to pull out of the UN, expel its headquarters and go about our quest for peace, freedom and love of God within our own nation which can never be achieved when our government is comprised mainly of liberal, godless pansies who rule and ruin our lives, mock our God and our religion.
The main problem with current papal writings is that they are, apparently by design, very difficult to understand their true intent.
It's bad enough when we have to wade through the verbosity of our so-called 'leaders' without the burden of doing the same wading through what the leader of our Church is saying.
and "world political authority" isn't necessarily synonymous with "world government," at least as the latter is popularly construed.
That said, any halfwit can see that sooner or later global government will be established. It's been attempted repeatedly throughout history. It has never been more imminent than now, the day when weapons of mass destruction, instaneous communication, near instantaneous travel, instantaneous capital formation, legacy stockpiles of weapons, highly trained militaries, and breakdown of social order in the West are manifest.
In fact, the high level of interaction in legal and commercial matters argues that in some senses, it already has. Would you have it not be so? If you think the market forces that push globalization, much less the unholy ambitions of men, can be tamed with legal structures you need to familiarize yourself with black markets. The Holy Father addresses this fact squarely, and argues for the very same thing he would argue for at any level of social development: truth in love for the human person.
Perhaps your disagreement with him is such you think he shouldn't address the realities of modern life, but he does, just like he's supposed to.
The problem is technology at the disposal of fallen human nature; the problem is not the Holy Father's diagnosis and prescription.