It has hit me (and no doubt I am not the first) that the Lord/liar/lunatic argument can be adapted to the Catholic Church. The Catholic Church claims immense dogmatic and practical authority over Christians. She claims infallibility. She is, thus, either infallible, or liar, or lunatic.
Is she a liar? Then we have the puzzle that she has done so well at preserving early Christian doctrines in the face of heresy after heresy. In our time this is particularly clear, I think, in the case of her teachings on sexuality and the protection of human life, her unyielding insistence on the infallibility of Scripture, and the central preaching of the doctrines of the Trinity and Incarnation.
Is she a lunatic? Then we have the puzzle that lunacy would be the domain of the Church of such men and women as Augustine, Anselm, Thomas Aquinas, Duns Scotus, Teresa of Avila, John of the Cross, Descartes, Pascal, Terese de Lisieux and John Paul II. The Church with the most intellectually seriously worked out intellectual tradition that the Christian world has known (and probably that the world has known) would then be a lunatic. That is not so plausible.
So the most plausible story is that she is infallible.
We may supplement this argument as follows. Paul talks about the Church as the pillar and bulwark of truth (1 Tim 3:15). Jesus talks of the Holy Spirit's guidance for the Church. All this at least suggests that there is a Church which is a reliable guide. But which Church has a plausible claim of being a reliable guide over the centuries? In the end, I think only the Catholic Church, though a case (I believe in the end somewhat weaker) can also be made for the Orthodox Church. But if the Catholic Church is a reliable guide, it is implausible that she is also a liar or a lunatic. And so she's infallible.
If I am right in this post, then earlier, less ecumenical Protestants, in their condemnations of papistry, may have been onto something important: one can't be ambivalent towards the Catholic Church, just as one can't be ambivalent towards Christ. For if the Catholic Church is not infallible as she claims, she is a liar or a lunatic.