When I first encountered Bellarmine's view of the Felix/Liberius affair, it seemed totally at odds with the rest of his doctrine. I thought (at the time) that someone either is or isn't pope, and if one man is pope there really is nothing at all in the world that can make him not pope (aside from his own death or resignation/vacation of the office). Who people think is pope does not at all affect who actually is pope. The very idea smacks of relativism. Or so I thought.
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If, on the other hand, we view the papacy as a relation-- which we should!-- Bellarmine's account starts to make more sense. It is true that a man either is or isn't pope, but there is a special category of man who is pope and who cannot prove it to the satisfaction of his inferiors. In such an instance, the relational aspect of the papacy has basically dissolved. We know, axiomatically, that a doubtful superior is no superior at all. But we do not often consider how this axiom is more than practical guidance. In a certain sense, doubt about a superior can itself suffice to divest him of any office, precisely because the relationship between him and his subordinates has dissolved.
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Anyways, that seems to be what animates Bellarmine's account of the whole affair, even though he doesn't put it in those exact terms.
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It's an interesting idea, and believable. Whether or not one ultimately agrees. I first stumbled across this about three years ago, and I'm still not sure exactly what to make of it.