Papal infallibility.
A lot of the Protestants I talk with on the Gamespot Christian Union forum seem to...well...they just don't understand the concept at all. And to be honest, that comes as no surprise. Many Catholics don't really understand the concept of infallibility, and in particular that it is such a limited thing.
That is to say: the Pope can't just look up at the sky and call it green, when clearly it is blue. The Pope is not being infallible there, he's being a dork. And we Catholics would probably call him a dork as well for doing so.
Infallibility is more limited than that. In fact, it is so limited, that it even takes on one of those characteristic Catholic "quirks" that crop up once in a while. Consider:
The Pope's words are infallible in only certain specific situations.The Bishop of Rome's words are not infallible, not ever.
And yet, they are the same person, the Pope and the Bishop of Rome.
But jest aside, it is perhaps best that we start looking at infallibility in the Papacy by looking at something entirely different to begin with. Mark Shea, with his typical incisiveness, chronicles his encounters, from his younger, non-believing days, with Christian moral principle, making the particular observation that "[w]hatever may be wrong with Christians (of whatever stripe) at any rate their insistence on revealed inviolable truth had landed even the least of them on their feet... They may believe in a goofy and harmless six day creationism, but by God they are not such fools as to prostitute themselves to the "Might Makes Right" philosophy which much of the academy, claiming to be wise, now fondly embraces. Fools that Christians were, they had not the "sophistication" (nor the permission of Almighty God) to define all relationships as power plays and call Good "whatever wins." Indeed, these glorious fools still say and think that Auschwitz was simply evil and cannot be "contextualized" out of the pit of Hell. They still believe in and practice love (that great 60s buzzword) as a thing in accord, not with "good vibes," but with God's eternal and unchanging will. Love--painful, sacrificing, ecstatic and wonderfully co-dependent--is still in fashion for them. For it is no fashion but a command.". And in the middle of this revelation, he found a paradox: "So I was confronted with the strange paradox of "dogmatic" Christian (and especially Catholic) theology salvaging my secular education's own best treasures while secularism went a-whoring after power. I wondered why.".
G.K. Chesterton, a man of unappreciated brilliance, once wrote (and Shea cites him on this), that "the modern world, with its modern movements, is living on its Catholic capital. It is using, and using up, the truths that remain to it out of the old treasury of Christendom.". That is to say, the fundamental progression of academic thought in the modern age from the enlightenment of the Rennaissance to the power-focused and censorous sanitization of fell-good relativism is reflective of the way in which much of the Protestant reformation was seen as a sanitization of Catholicism, a retention of what was thought to be "good" and a discarding of what was thought to be "bad". But no truth that came out of the Reformation was a "new" truth -- it had all been discovered years before, and can still be found to be confirmed and enriched in Catholic doctrine (much like many of the truths of academia can still be found in the old principles of the philosophers).
But wheras Protestantism had managed to hold onto those truths, of course, academia had lost its truths in pursuit of the abstract notion of Reason, in the illusion that this was somehow a thing apart from the old truths of faith. But, as Shea notes, "the Enlightened who held a childlike Catholic faith in the validity of Reason were not immortal. For without the safeguard of other Catholic dogmas to balance their faith in materialism they were eventually forced to conclude that reason itself is, at root, simply a function of molecular activity in brain tissue if materialism is the only truth. Thus truth itself became relativized till, by the time I got to high school and college, the shredding of the whole cloth of Catholic truth had resulted in a deeply rooted cultural assumption (180° opposed to the Reformers and their popish opponents) that no one can know truth about anything at all. Even the few old fashioned ideologues (such as Carl Sagan) with a 19th century faith in atheistic rationalism are starting to look rather antique, for they have largely been replaced in the academy by new-fashioned ideologues with an even stronger faith in atheistic irrationalism.
Yet trendy irrationalism is hopeless too. For "no truth" means, in real life, "no way of saying it's wrong to shoot someone for a pair of Nikes." There is no way to write coherent laws to punish unpleasant people like child pornographers (Next on Geraldo: "Kidpornos: Bottom Feeding Scum or Cutting Edge Artists?") There's no way you can speak with anyone about anything coherently. So when Rationalism is sacrificed on the altar of "Revolt Against Religious Dogma" by its usurping bastard Irrationalism there is only one option left: the worship of power which now grips the liberal academy (and will, I fear, soon grip our culture as a whole).
In contrast, to all this the Magisterium states there is such a thing as truth possessing a real shape and texture. The Church dares to say definitely "You cannot believe whatever you like and call it true since truth is from God, not created by humans. You cannot deny the Trinity and call it 'alternative Christianity.' You cannot practice witchcraft and declare it to be 'diversity in the Body of Christ.' You cannot write the Book of Mormon and reconcile it with Scripture. You cannot interpret the Bible privately. You cannot pass laws that declare black white by main force. You cannot run a nation--even a secular one--on terms which defy the will of God in Christ."
The Church says this because she still quite scandalously claims that she is, by direct apostolic succession from Christ Himself, the pillar and foundation of the truth (as Paul says in 1 Timothy 3:15) and that she is therefore competent to speak truth to the nations.".
So when someone asks how we Catholics can be sure that when the Pope speaks in a situation befitting infallibility (i.e. statements of doctrine made ex cathedra, but we are coming to explore that more in a moment), the first reason is that he is, as the head of the Church, speaking in direct apostolic succession from Christ, and as such is speaking as a pillar and foundation of truth, in keeping with the teachings of St. Paul.
But that is only where the reality begins. Where it ends is something totally different. For as Shea notes yet again, "unlike the rigid ideologies which are coming to dominate the culture, the supreme irony is that infallibility does not mean never having to say you're sorry. For the gift of infallibility necessarily implies that the Church receiving it needs it. It is because those Borgia Popes, pedophile priests, radical nuns (and worst of all, because people like me) fail in their individual lives to obey that which the Spirit infallibly reveals through the Church that the Church must be supported by Christ at every step or she is ruined. That's the point of all those Acts of Contrition. Not exactly prideful--especially in contrast to the arrogant noise from the academy that all is Race War, Class War and Gender War (accompanied by threats against chattel students who dare to differ). In comparison to these snarls from elitists in the Vanguard of History, the Church's claim of infallibility is refreshingly humble and hopeful. For it is just another way of expressing confidence in Christ's promise to guide us none-too-bright sheep into truth, freedom and love "even unto the end of the age.".
And so the second reason why we believe that the Pope is saying God's will in those infallible situations (however rare, I cannot stress enough), is that we need those statements to be from God, because we are a church of human beings (as all churches are), and we fail and fall into sin time and again. If Christ is not inspiring us at every stage, we have only our human selves...and we are lost.
But let's take a look for a moment at the actual doctrine surrounding infallibility. Within the Catechism of the Catholic Church, infallibility is definied as "the gift of the Holy Spirit to the Church whereby the pastors of the Church, the pope and the bishops in union with him can definitively proclaim a doctrine of faith or morals for the belief of the faithful. This gift is related to the inability of the whole body of the faithful to err in matters of faith and morals.
Two articles of the Catechism add to this definition:
889 In order to preserve the Church in the purity of the faith handed on by the apostles, Christ who is the Truth willed to confer on her a share in his own infallibility. By a "supernatural sense of faith" the People of God, under the guidance of the Church's living Magisterium, "unfailingly adheres to this faith."
890 The mission of the Magisterium is linked to the definitive nature of the covenant established by God with his people in Christ. It is this Magisterium's task to preserve God's people from deviations and defections and to guarantee them the objective possibility of professing the true faith without error. Thus, the pastoral duty of the Magisterium is aimed at seeing to it that the People of God abides in the truth that liberates. To fulfill this service, Christ endowed the Church's shepherds with the charism of infallibility in matters of faith and morals. the exercise of this charism takes several forms:
891 "The Roman Pontiff, head of the college of bishops, enjoys this infallibility in virtue of his office, when, as supreme pastor and teacher of all the faithful - who confirms his brethren in the faith he proclaims by a definitive act a doctrine pertaining to faith or morals.... the infallibility promised to the Church is also present in the body of bishops when, together with Peter's successor, they exercise the supreme Magisterium," above all in an Ecumenical Council. When the Church through its supreme Magisterium proposes a doctrine "for belief as being divinely revealed," and as the teaching of Christ, the definitions "must be adhered to with the obedience of faith." This infallibility extends as far as the deposit of divine Revelation itself.
Now, what we can draw from this are several observations. For one, the above passages confirm what Shea had observed earlier...that the Church, in apostolic succession from Christ, is given a share in Christ's own infallibility and grace, for the preservation and guidance of the Church through the workings of the Holy Spirit. As such, as was noted by St. Paul in the letter to Timothy, this gives the Church the ability to speak in capacity as a pillar of truth and revelation from God -- in essence, this is how the Church derives moral authority.
But we can also observe that infallibility is limited. It doesn't apply except when the Pope is making a statement on a definitive act of doctrine pertaining to faith or morals (such as the Assumption of Mary, or that procurement or administration of abortion is a sufficiently grave moral evil that any Catholic who engages in the act receives an automatic excommunication without need for official declaration). And what is more, it doesn't apply when the Pope is making a statement on his own -- infallibility is not the Pope's personal playground, for it applies also to the Magisterium (the teaching office of the Church, the bishops), and in fact it is the Magisterium's task to oversee those articles of doctrine that are ultimately put forth ex cathedra (i.e. from the Papal seat, which is the only place infallible statements can be delivered from).
So the final reason, and the most important reason, why Catholics believe that the Pope, in those rare times when he speaks with infallibility, is actually speaking God's true will, is because this is what the Spirit has bestowed on the Church, and through the office of the Magisterium and through all Catholics everywhere the Spirit watches over what is said, guides what is taught, and ensures that nothing is spoken as a binding article of faith that is contrary to God's plan for humanity, or contrary to God's truth.