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Super natural is a super set, not a subset.
True, but its effect is a subset.And that can be measured.So I suppose we could take beta decay as a example of an effect with no apparent cause, at least one that cannot be predicted.Is this the sort of event you would look for as evidemce of the supernatural?
The supernatural question is not HOW atoms hold together or the universe expand, but WHY?
But belief in a God does not answer the why.If a God actually existed and interacts with people on their level {physical} through thoughts or feelings then these are measureable since they are manifested on a physical level.The atoms are responding to what if not a physical agent.