[AleoMagus]

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My guess is that this paradox is resolved by the fact that most Catholics don't actually truly believe it.

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Maybe this goes back to all the discussion about beleif and certainty, etc... but I also think this is the case.

In fact, I suspect that a large number of religious people of many different faiths would fail 'beleif tests' on many issues central to their particular religious doctrine. (I say belief tests to avoid the tangential questions about polygraph accuracy, etc...)

Maybe this has something to do with what religious faith is. Accepting something as true, even if we know that we rationally shouldn't and cannot really bring ourselves to believe in it in the same way that we believe in our past experiences. In a way that would pass your hypothetical polygraph.

Of course I say this as a very non-religious person. I guess I just have too much confidence in people's inherent rationality to think that they truly accept such things. I think it's more about wanting to believe (understand?) what we actually don't believe or understand.

Another thought - Do you suppose most mathematicians would pass the same test if asked whether there are some infinities which are greater than others, along with all the other bizzare consequences of transfinite arithmetic?

Regards
Brad S