Fallibilism as a philosophy was advanced by Kwame Anthony Appiah in his Commencement address at Swarthmore in May 2006. Perhaps it applies to Anglicans.
Appiah began his address:
Often I find myself seated next to a stranger on an airplane who asks me what I do. Sometimes I say I'm a philosopher. The commonest responses are:
(1) An expression that combines boredom and alarm, and the end of the conversation (which leaves you with the pretzels and the soda, and the really fascinating article from the Review of Metaphysics you've been meaning to get to for a couple of years) and
(2) "So, what's your philosophy?"
To that question, I usually reply: "Everything is much more complicated than you first thought." In philosophy at least, that really is my philosophy. So, I can tell the truth and we can both get back to those wonderfully inviting pretzels.
The truth, I said: I happen to be a great believer in objective truth. But one way in which things get more complicated than you thought is that I am also a great believer in what philosophers call fallibilism. Fallibilism is the idea that our knowledge is imperfect, provisional, subject to revision in the face of new evidence. Fallibilism says: Here's what I know to a moral certainty, know well enough to live by. But I could be wrong.
He continues on the subject of tolerance:
Yet tolerance, too, is more complicated than it looks. We can't suppose that mindless tolerance of cruelty and repression is a virtue. Yet how much evil is done by fanatics who can't countenance the possibility that their beliefs, sanctioned by ideological or religious authority, might conceivably be mistaken! Here, then, is one of the uncompleted tasks of our era: to spread fallibilism - not skepticism about the truth or indifference to it, but just the glimmering recognition that one may not be in full possession of it - from the empyrean of scientific fact to the hardpan of moral conviction: to make it as common as Coca-Cola. People say that common sense is the ability to see what's in front of your eyes. But even madmen and extremists can see what's in front of their eyes; so, again, I think it's more complicated than that. Common sense, I'd prefer to say, involves the ability to see what's in front of the other fellow's eyes. That's what makes it something we might have in common.
Read the address here.
Read more on Appiah here