The problem I see in this whole issue is that this 'intuitive knowledge,' as you call it, is indiscernable from what could just be a human desire to know that god exists or a psychological illusion. Intuition is not a very good basis for knowledge.
Even if the open windows of science at first make us shiver after the cozy indoor warmth of traditional humanizing myths, in the end the fresh air brings vigor, and the great spaces have a splendor of their own - Bertrand Russell