It's not that religion exists outside science. It is that reality, Truth, is bigger than the box of science. And bigger than the box of philosopy/reason/logic.
What can be "known" by pure science alone are only those aspects of reality that have size, quantity, specific location and can be detected by the senses (or their extensions).
This scientific knowledge is very firm, it's the firmest knowledge we have, and is designed to be so. However, it excludes a great deal of reality that we know to exist.
The error is not when science says: "I know it exists scientifically," but when science says: "I cannot know it using science, therefore it does not exist." This is scientism and fails logically due to performance error: It's not supported by it's own logic.
Philosophy/reason/logic can be used for knowledge that transcends science - not contradicts but includes reality that does not have the limited requirements of scientific knowledge. Values (as in better than, worse than) are in this category. Science cannot "prove" that life is better than death or any other value of this type.
Logic/reason's limits (in this area of discussion) are reached when we look at the unconditional, absolute values. Logic has to start with axioms, "self-evident" assumptions. By definition these are not proved - else they would become conditional and the chain is merely moved back a link.
Religion deals with knowing these absolutes. For example: goodness, truth and beauty. These transcend logic/reason. Note again, they don't contradict logic, they include more of reality than logic can "see."
Faith, wonder, awe, love of God… none of these exist outside of science (the senses), they INCLUDE them. When we see the world anew, we are still seeing, but transcending our senses.
The errors of the past, and unfortunately the present, are when we deduce upward from science to philosophy or religion, or infer downwards from theology or philosophy. If you want to know how much a rock weighs, we use science. If we want to know the value of scientifically knowing how much a rock weighs, we can use philosophy; if we wish to know who we really are and our relationship to the universe, neither of these is going to take us where we wish to go.
I think we're agreeing on this basic point. Thank you for your reply...
Thanks again.