Dilettante: As for the entities being worshipped, don't they have to be supernatural entities to qualify as religion? I've known people who were obsessively devoted to the Beatles, yet few people would call that a religion.
Yes, we need the supernatural in there somewhere.
Also, can a mystical experience--which is always entirely subjective--be "shared" in any way, like BeHereNow wrote? Can they be accurately regarded as a source of knowledge, or rather, as a source of faith? Science and knowledge can be shared. Mystical experiences can't.
Well, we have some disagreement here.
Pentecost is an early example of a shared mystical experience. More recently, I attended a church committee decision making meeting one evening. The following day our leader remarked to the larger congregation that one could feel the spirit of the Holy Spirit move across the room that evening. I noticed many agreed with him. Shared experience.
I believe mystical experiences can lead not to knowledge, but to objective understanding, without the subjective bias. I believe this is the goal of mystical experiences, to unite being, with the Eternal, which holds all truth. This of course is not to say that all mystical experiences accomplish this. Also note that from a personal perspective, I accept “mystical” in the looser sense, which means simply beyond normal understanding, not necessarily supernatural. The more common usage would require the supernatural. I believe shared experiences are possible with the supernatural or without.
By way of analogy, my family experiences a Thanksgiving turkey dinner each year, a shared family tradition. We may each have our own subjective opinion of whether the turkey is too dry, or underdone, but this does not take away from the shared experience.
Historians have ways of discovering the truth or falsity of alleged events in the past.
Many times they do.
Many times they do not.