I don't he means co-exist as in "Can they not kill each other?" Obviously, they can do that.
But co-exist in the sense of "Are they essentially in conflict with one another, or can they be reconciled with one another?"
There's 3 different views:
1 - They cannot co-exist and are in fundamental disagreement ("Conflicting Worlds" viewpoint)
2 - They can be reconciled both through religious belief and science, and do not need to be in conflict ("Same Worlds" viewpoint)
3 - They are in seperate realms, not related to one another, and do not need to be in conflict nor reconciled....like trying to compare botany and dentistry ("Differrent Worlds" viewpoint).
Type 1: Someone like Richard Dawkins would fall into this realm. Everything that there is to be known has the potential to be known, even if we will never reach that point. Religion, which naturally deals with that which is supernatural or paranormal, and not explainable, is in conflict with science because it doesn't make rational sense.
Type 2: Religious apologists and/or religious scientists would fall into this realm, attempting (and sometimes, but not always, succeeding) in showing how the two are not at odds with one another. Many Eastern schools of thought would agree with this, though proponents of type 1 would argue that if it is explainable through rational means, involving mystical explanations for it only obscures the truth. It should only be considered a philosophy, a set of guidelines for living life according to a set of principles. Because to mix religious belief with rational evidence is to obscure both.
Type 3: This basically stems from the idea that all religious thought is meant to be interpreted metaphorically as stories that can help humans through various stages of their lives and acheive happiness and harmony with themselves and the world around them. Once this is done, and religion is moved away from dogmatic belief, there is no conflict with science because the two aren't attempting to explain the same things two different ways. Botany/dentistry. Mythologist Joseph Campbell would be a proponent of this, and spent a lifetime explaining myths in this light.
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Or maybe that's not what this thread is about.