Is it true that it is impossible for a bishop who is in communion with the Pope to teach errors that would lead people away from salvation? If so then what about the Arian heresy?
That’s not really the way that infallibility works. The Pope exercises it in certain situations; the bishops, acting as a single body, and in conjunction with the Pope, exercise it in certain other situations. However, when you’re talking about a single bishop, you’re really only saying that, when he teaches in a way that’s in concert with the teachings of the Pope and/or the Pope with the bishops, then in that instance the single bishop shares in the infallibility that they exercise. It’s not, though, that by defining a bishop as “in communion with the Pope”, he automatically is declared as free from error in whatever he teaches.
Does that make sense? It’s not that you can make any forward-looking statement about the teachings of a single bishop; it’s only that, when looking at a particular teaching, you can look back at it and say, “yes, it’s infallible, by virtue of the fact that it’s in step with an infallible teaching of the Pope and/or College of Bishops”.
So, if Arius had said, “Jesus Christ is the Son of God”, we’d say, ‘yep, that’s in line with the teaching of the Pope and the College of Bishops, so it shares with the freedom from error with which they teach.’ But, when Arius said, “Jesus Christ was created by God the Father, so there was a time when Jesus didn’t exist”, we’d say 'hold on now! that’s not right!" … so we’d say that he wasn’t automatically free from error.
Does that help?
I wasn’t asking about infallibility. I was asking if it was true that Catholic bishops are protected from teaching errors so grievous that they would lead people away from salvation.
No, it is not true. Individual bishops are quite capable of serious heresy. As a whole, however, when considered altogether and not individually, the bishops of the world cannot err en masse.
Which is what the definition of ‘infallibility’ is all about.
But, as Katholish mentioned, the protection against error that is infallibility doesn’t extend to a single bishop, strictly speaking.