Archbishop of Canterbury admits he has doubts about God

[Lek]

If something dealing with a supposedly factual matter can in principle only be arrived at by faith, then that is direct evidence that that thing is wrong to believe.

That's the way you view it. I see evidence in the scriptures, testimony from others as to their experience, and my own experience. But that isn't solid proof. I must take the leap of faith.

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Looking for evidence would seem to be a lack of faith.

The evidence is often what brings us to faith.